Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,3,Mod(11,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.j (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.04360198270\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 11.11 | ||
Character | \(\chi\) | \(=\) | 75.11 |
Dual form | 75.3.j.a.41.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.146095 | + | 0.201083i | 0.0730476 | + | 0.100541i | 0.843977 | − | 0.536379i | \(-0.180208\pi\) |
−0.770930 | + | 0.636920i | \(0.780208\pi\) | |||||||
\(3\) | 2.65119 | + | 1.40399i | 0.883729 | + | 0.467998i | ||||
\(4\) | 1.21698 | − | 3.74547i | 0.304244 | − | 0.936368i | ||||
\(5\) | 3.70242 | − | 3.36037i | 0.740485 | − | 0.672073i | ||||
\(6\) | 0.105007 | + | 0.738225i | 0.0175011 | + | 0.123038i | ||||
\(7\) | −11.1634 | −1.59478 | −0.797388 | − | 0.603467i | \(-0.793786\pi\) | ||||
−0.797388 | + | 0.603467i | \(0.793786\pi\) | |||||||
\(8\) | 1.87649 | − | 0.609710i | 0.234562 | − | 0.0762137i | ||||
\(9\) | 5.05760 | + | 7.44451i | 0.561955 | + | 0.827168i | ||||
\(10\) | 1.21662 | + | 0.253561i | 0.121662 | + | 0.0253561i | ||||
\(11\) | 9.01376 | + | 12.4064i | 0.819433 | + | 1.12785i | 0.989799 | + | 0.142471i | \(0.0455049\pi\) |
−0.170366 | + | 0.985381i | \(0.554495\pi\) | |||||||
\(12\) | 8.48506 | − | 8.22132i | 0.707088 | − | 0.685110i | ||||
\(13\) | −2.81877 | − | 2.04796i | −0.216828 | − | 0.157535i | 0.474069 | − | 0.880487i | \(-0.342785\pi\) |
−0.690898 | + | 0.722952i | \(0.742785\pi\) | |||||||
\(14\) | −1.63092 | − | 2.24477i | −0.116495 | − | 0.160341i | ||||
\(15\) | 14.5338 | − | 3.71078i | 0.968917 | − | 0.247385i | ||||
\(16\) | −12.3476 | − | 8.97106i | −0.771725 | − | 0.560691i | ||||
\(17\) | −19.9100 | + | 6.46915i | −1.17118 | + | 0.380538i | −0.829082 | − | 0.559128i | \(-0.811136\pi\) |
−0.342094 | + | 0.939666i | \(0.611136\pi\) | |||||||
\(18\) | −0.758072 | + | 2.10460i | −0.0421151 | + | 0.116922i | ||||
\(19\) | 6.71475 | + | 20.6659i | 0.353408 | + | 1.08768i | 0.956927 | + | 0.290329i | \(0.0937648\pi\) |
−0.603519 | + | 0.797349i | \(0.706235\pi\) | |||||||
\(20\) | −8.08039 | − | 17.9568i | −0.404019 | − | 0.897841i | ||||
\(21\) | −29.5964 | − | 15.6734i | −1.40935 | − | 0.746352i | ||||
\(22\) | −1.17784 | + | 3.62502i | −0.0535383 | + | 0.164774i | ||||
\(23\) | −1.07612 | − | 1.48115i | −0.0467878 | − | 0.0643979i | 0.784982 | − | 0.619519i | \(-0.212672\pi\) |
−0.831770 | + | 0.555121i | \(0.812672\pi\) | |||||||
\(24\) | 5.83097 | + | 1.01813i | 0.242957 | + | 0.0424221i | ||||
\(25\) | 2.41589 | − | 24.8830i | 0.0966355 | − | 0.995320i | ||||
\(26\) | − | 0.866003i | − | 0.0333078i | ||||||
\(27\) | 2.95660 | + | 26.8376i | 0.109504 | + | 0.993986i | ||||
\(28\) | −13.5856 | + | 41.8123i | −0.485202 | + | 1.49330i | ||||
\(29\) | −0.892770 | − | 0.290079i | −0.0307852 | − | 0.0100027i | 0.293584 | − | 0.955933i | \(-0.405152\pi\) |
−0.324369 | + | 0.945931i | \(0.605152\pi\) | |||||||
\(30\) | 2.86949 | + | 2.38036i | 0.0956496 | + | 0.0793454i | ||||
\(31\) | −10.8994 | − | 33.5448i | −0.351592 | − | 1.08209i | −0.957959 | − | 0.286904i | \(-0.907374\pi\) |
0.606367 | − | 0.795185i | \(-0.292626\pi\) | |||||||
\(32\) | − | 11.6858i | − | 0.365180i | ||||||
\(33\) | 6.47869 | + | 45.5469i | 0.196324 | + | 1.38021i | ||||
\(34\) | −4.20959 | − | 3.05844i | −0.123811 | − | 0.0899543i | ||||
\(35\) | −41.3318 | + | 37.5132i | −1.18091 | + | 1.07181i | ||||
\(36\) | 34.0382 | − | 9.88329i | 0.945505 | − | 0.274536i | ||||
\(37\) | −28.6827 | − | 20.8392i | −0.775208 | − | 0.563221i | 0.128329 | − | 0.991732i | \(-0.459039\pi\) |
−0.903537 | + | 0.428510i | \(0.859039\pi\) | |||||||
\(38\) | −3.17456 | + | 4.36941i | −0.0835411 | + | 0.114984i | ||||
\(39\) | −4.59777 | − | 9.38705i | −0.117892 | − | 0.240694i | ||||
\(40\) | 4.89873 | − | 8.56311i | 0.122468 | − | 0.214078i | ||||
\(41\) | 21.7900 | − | 29.9914i | 0.531464 | − | 0.731497i | −0.455889 | − | 0.890037i | \(-0.650679\pi\) |
0.987353 | + | 0.158539i | \(0.0506785\pi\) | |||||||
\(42\) | −1.17224 | − | 8.24113i | −0.0279104 | − | 0.196217i | ||||
\(43\) | 0.351471 | 0.00817375 | 0.00408688 | − | 0.999992i | \(-0.498699\pi\) | ||||
0.00408688 | + | 0.999992i | \(0.498699\pi\) | |||||||
\(44\) | 57.4373 | − | 18.6625i | 1.30539 | − | 0.424148i | ||||
\(45\) | 43.7416 | + | 10.5673i | 0.972036 | + | 0.234830i | ||||
\(46\) | 0.140618 | − | 0.432779i | 0.00305692 | − | 0.00940823i | ||||
\(47\) | 26.1739 | + | 8.50441i | 0.556891 | + | 0.180945i | 0.573922 | − | 0.818910i | \(-0.305421\pi\) |
−0.0170306 | + | 0.999855i | \(0.505421\pi\) | |||||||
\(48\) | −20.1405 | − | 41.1199i | −0.419594 | − | 0.856665i | ||||
\(49\) | 75.6222 | 1.54331 | ||||||||
\(50\) | 5.35649 | − | 3.14949i | 0.107130 | − | 0.0629899i | ||||
\(51\) | −61.8678 | − | 10.8026i | −1.21309 | − | 0.211815i | ||||
\(52\) | −11.1009 | + | 8.06530i | −0.213480 | + | 0.155102i | ||||
\(53\) | 45.7550 | + | 14.8667i | 0.863302 | + | 0.280504i | 0.707007 | − | 0.707207i | \(-0.250045\pi\) |
0.156295 | + | 0.987710i | \(0.450045\pi\) | |||||||
\(54\) | −4.96464 | + | 4.51537i | −0.0919378 | + | 0.0836180i | ||||
\(55\) | 75.0627 | + | 15.6441i | 1.36478 | + | 0.284439i | ||||
\(56\) | −20.9481 | + | 6.80645i | −0.374073 | + | 0.121544i | ||||
\(57\) | −11.2127 | + | 64.2166i | −0.196714 | + | 1.12661i | ||||
\(58\) | −0.0720996 | − | 0.221900i | −0.00124310 | − | 0.00382586i | ||||
\(59\) | −6.66036 | + | 9.16720i | −0.112887 | + | 0.155376i | −0.861722 | − | 0.507381i | \(-0.830614\pi\) |
0.748835 | + | 0.662757i | \(0.230614\pi\) | |||||||
\(60\) | 3.78864 | − | 58.9517i | 0.0631440 | − | 0.982529i | ||||
\(61\) | −31.8388 | + | 23.1322i | −0.521948 | + | 0.379217i | −0.817337 | − | 0.576160i | \(-0.804551\pi\) |
0.295389 | + | 0.955377i | \(0.404551\pi\) | |||||||
\(62\) | 5.15293 | − | 7.09240i | 0.0831118 | − | 0.114394i | ||||
\(63\) | −56.4602 | − | 83.1063i | −0.896193 | − | 1.31915i | ||||
\(64\) | −47.0406 | + | 34.1770i | −0.735010 | + | 0.534016i | ||||
\(65\) | −17.3182 | + | 1.88969i | −0.266433 | + | 0.0290722i | ||||
\(66\) | −8.21219 | + | 7.95694i | −0.124427 | + | 0.120560i | ||||
\(67\) | 12.3027 | + | 37.8637i | 0.183622 | + | 0.565130i | 0.999922 | − | 0.0124984i | \(-0.00397846\pi\) |
−0.816300 | + | 0.577628i | \(0.803978\pi\) | |||||||
\(68\) | 82.4451i | 1.21243i | ||||||||
\(69\) | −0.773468 | − | 5.43768i | −0.0112097 | − | 0.0788070i | ||||
\(70\) | −13.5816 | − | 2.83061i | −0.194023 | − | 0.0404372i | ||||
\(71\) | 59.9097 | + | 19.4658i | 0.843798 | + | 0.274167i | 0.698846 | − | 0.715272i | \(-0.253697\pi\) |
0.144952 | + | 0.989439i | \(0.453697\pi\) | |||||||
\(72\) | 14.0295 | + | 10.8859i | 0.194855 | + | 0.151193i | ||||
\(73\) | 43.3505 | − | 31.4960i | 0.593842 | − | 0.431451i | −0.249846 | − | 0.968286i | \(-0.580380\pi\) |
0.843688 | + | 0.536834i | \(0.180380\pi\) | |||||||
\(74\) | − | 8.81210i | − | 0.119082i | ||||||
\(75\) | 41.3406 | − | 62.5776i | 0.551207 | − | 0.834368i | ||||
\(76\) | 85.5752 | 1.12599 | ||||||||
\(77\) | −100.624 | − | 138.498i | −1.30681 | − | 1.79867i | ||||
\(78\) | 1.21586 | − | 2.29594i | 0.0155880 | − | 0.0294351i | ||||
\(79\) | 15.3080 | − | 47.1131i | 0.193772 | − | 0.596368i | −0.806217 | − | 0.591620i | \(-0.798489\pi\) |
0.999989 | − | 0.00474795i | \(-0.00151133\pi\) | |||||||
\(80\) | −75.8621 | + | 8.27780i | −0.948276 | + | 0.103472i | ||||
\(81\) | −29.8414 | + | 75.3027i | −0.368412 | + | 0.929663i | ||||
\(82\) | 9.21417 | 0.112368 | ||||||||
\(83\) | −35.1756 | + | 11.4292i | −0.423802 | + | 0.137702i | −0.513150 | − | 0.858299i | \(-0.671522\pi\) |
0.0893480 | + | 0.996000i | \(0.471522\pi\) | |||||||
\(84\) | −94.7224 | + | 91.7782i | −1.12765 | + | 1.09260i | ||||
\(85\) | −51.9765 | + | 90.8563i | −0.611488 | + | 1.06890i | ||||
\(86\) | 0.0513483 | + | 0.0706749i | 0.000597073 | + | 0.000821801i | ||||
\(87\) | −1.95963 | − | 2.02250i | −0.0225245 | − | 0.0232471i | ||||
\(88\) | 24.4785 | + | 17.7847i | 0.278165 | + | 0.202099i | ||||
\(89\) | −98.1080 | − | 135.034i | −1.10234 | − | 1.51724i | −0.832249 | − | 0.554402i | \(-0.812947\pi\) |
−0.270088 | − | 0.962836i | \(-0.587053\pi\) | |||||||
\(90\) | 4.26553 | + | 10.3395i | 0.0473948 | + | 0.114884i | ||||
\(91\) | 31.4671 | + | 22.8622i | 0.345793 | + | 0.251233i | ||||
\(92\) | −6.85723 | + | 2.22805i | −0.0745351 | + | 0.0242179i | ||||
\(93\) | 18.2004 | − | 104.236i | 0.195703 | − | 1.12082i | ||||
\(94\) | 2.11379 | + | 6.50557i | 0.0224871 | + | 0.0692082i | ||||
\(95\) | 94.3058 | + | 53.9498i | 0.992692 | + | 0.567893i | ||||
\(96\) | 16.4068 | − | 30.9812i | 0.170904 | − | 0.322721i | ||||
\(97\) | 28.3759 | − | 87.3321i | 0.292535 | − | 0.900331i | −0.691503 | − | 0.722374i | \(-0.743051\pi\) |
0.984038 | − | 0.177957i | \(-0.0569489\pi\) | |||||||
\(98\) | 11.0480 | + | 15.2063i | 0.112735 | + | 0.155167i | ||||
\(99\) | −46.7714 | + | 129.849i | −0.472438 | + | 1.31161i | ||||
\(100\) | −90.2585 | − | 39.3307i | −0.902585 | − | 0.393307i | ||||
\(101\) | 84.8899i | 0.840494i | 0.907410 | + | 0.420247i | \(0.138057\pi\) | ||||
−0.907410 | + | 0.420247i | \(0.861943\pi\) | |||||||
\(102\) | −6.86637 | − | 14.0188i | −0.0673174 | − | 0.137439i | ||||
\(103\) | 16.4641 | − | 50.6714i | 0.159846 | − | 0.491956i | −0.838774 | − | 0.544480i | \(-0.816727\pi\) |
0.998620 | + | 0.0525248i | \(0.0167269\pi\) | |||||||
\(104\) | −6.53806 | − | 2.12434i | −0.0628660 | − | 0.0204264i | ||||
\(105\) | −162.247 | + | 41.4250i | −1.54521 | + | 0.394524i | ||||
\(106\) | 3.69515 | + | 11.3725i | 0.0348599 | + | 0.107288i | ||||
\(107\) | 76.9750i | 0.719393i | 0.933069 | + | 0.359696i | \(0.117120\pi\) | ||||
−0.933069 | + | 0.359696i | \(0.882880\pi\) | |||||||
\(108\) | 104.118 | + | 21.5869i | 0.964053 | + | 0.199879i | ||||
\(109\) | −52.5097 | − | 38.1505i | −0.481740 | − | 0.350005i | 0.320259 | − | 0.947330i | \(-0.396230\pi\) |
−0.801999 | + | 0.597325i | \(0.796230\pi\) | |||||||
\(110\) | 7.82054 | + | 17.3794i | 0.0710958 | + | 0.157994i | ||||
\(111\) | −46.7851 | − | 95.5190i | −0.421487 | − | 0.860531i | ||||
\(112\) | 137.842 | + | 100.148i | 1.23073 | + | 0.894177i | ||||
\(113\) | −67.3204 | + | 92.6585i | −0.595756 | + | 0.819987i | −0.995311 | − | 0.0967217i | \(-0.969164\pi\) |
0.399556 | + | 0.916709i | \(0.369164\pi\) | |||||||
\(114\) | −14.5510 | + | 7.12706i | −0.127640 | + | 0.0625181i | ||||
\(115\) | −8.96147 | − | 1.86770i | −0.0779258 | − | 0.0162408i | ||||
\(116\) | −2.17296 | + | 2.99083i | −0.0187324 | + | 0.0257830i | ||||
\(117\) | 0.989818 | − | 31.3421i | 0.00845998 | − | 0.267881i | ||||
\(118\) | −2.81641 | −0.0238679 | ||||||||
\(119\) | 222.264 | − | 72.2179i | 1.86776 | − | 0.606873i | ||||
\(120\) | 25.0100 | − | 15.8246i | 0.208417 | − | 0.131872i | ||||
\(121\) | −35.2792 | + | 108.578i | −0.291564 | + | 0.897341i | ||||
\(122\) | −9.30300 | − | 3.02273i | −0.0762541 | − | 0.0247765i | ||||
\(123\) | 99.8772 | − | 48.9198i | 0.812010 | − | 0.397722i | ||||
\(124\) | −138.905 | −1.12020 | ||||||||
\(125\) | −74.6713 | − | 100.246i | −0.597371 | − | 0.801965i | ||||
\(126\) | 8.46268 | − | 23.4946i | 0.0671641 | − | 0.186465i | ||||
\(127\) | 83.0386 | − | 60.3310i | 0.653847 | − | 0.475048i | −0.210733 | − | 0.977544i | \(-0.567585\pi\) |
0.864579 | + | 0.502496i | \(0.167585\pi\) | |||||||
\(128\) | −58.2001 | − | 18.9104i | −0.454688 | − | 0.147737i | ||||
\(129\) | 0.931817 | + | 0.493464i | 0.00722339 | + | 0.00382530i | ||||
\(130\) | −2.91009 | − | 3.20631i | −0.0223853 | − | 0.0246639i | ||||
\(131\) | 187.251 | − | 60.8414i | 1.42939 | − | 0.464438i | 0.510820 | − | 0.859688i | \(-0.329342\pi\) |
0.918574 | + | 0.395250i | \(0.129342\pi\) | |||||||
\(132\) | 178.479 | + | 31.1638i | 1.35211 | + | 0.236089i | ||||
\(133\) | −74.9597 | − | 230.702i | −0.563607 | − | 1.73460i | ||||
\(134\) | −5.81638 | + | 8.00556i | −0.0434058 | + | 0.0597430i | ||||
\(135\) | 101.131 | + | 89.4290i | 0.749117 | + | 0.662437i | ||||
\(136\) | −33.4166 | + | 24.2786i | −0.245711 | + | 0.178519i | ||||
\(137\) | 119.320 | − | 164.231i | 0.870952 | − | 1.19876i | −0.107893 | − | 0.994162i | \(-0.534410\pi\) |
0.978846 | − | 0.204601i | \(-0.0655896\pi\) | |||||||
\(138\) | 0.980425 | − | 0.949951i | 0.00710453 | − | 0.00688370i | ||||
\(139\) | −34.9778 | + | 25.4129i | −0.251639 | + | 0.182826i | −0.706453 | − | 0.707760i | \(-0.749706\pi\) |
0.454814 | + | 0.890586i | \(0.349706\pi\) | |||||||
\(140\) | 90.2048 | + | 200.460i | 0.644320 | + | 1.43185i | ||||
\(141\) | 57.4518 | + | 59.2948i | 0.407459 | + | 0.420530i | ||||
\(142\) | 4.83827 | + | 14.8907i | 0.0340724 | + | 0.104864i | ||||
\(143\) | − | 53.4305i | − | 0.373640i | ||||||
\(144\) | 4.33589 | − | 137.294i | 0.0301104 | − | 0.953430i | ||||
\(145\) | −4.28018 | + | 1.92604i | −0.0295185 | + | 0.0132830i | ||||
\(146\) | 12.6666 | + | 4.11563i | 0.0867575 | + | 0.0281892i | ||||
\(147\) | 200.489 | + | 106.173i | 1.36387 | + | 0.722266i | ||||
\(148\) | −112.959 | + | 82.0694i | −0.763235 | + | 0.554523i | ||||
\(149\) | 120.868i | 0.811197i | 0.914051 | + | 0.405599i | \(0.132937\pi\) | ||||
−0.914051 | + | 0.405599i | \(0.867063\pi\) | |||||||
\(150\) | 18.6229 | − | 0.829414i | 0.124153 | − | 0.00552943i | ||||
\(151\) | −23.1445 | −0.153275 | −0.0766375 | − | 0.997059i | \(-0.524418\pi\) | ||||
−0.0766375 | + | 0.997059i | \(0.524418\pi\) | |||||||
\(152\) | 25.2004 | + | 34.6853i | 0.165792 | + | 0.228193i | ||||
\(153\) | −148.856 | − | 115.502i | −0.972917 | − | 0.754913i | ||||
\(154\) | 13.1488 | − | 40.4677i | 0.0853815 | − | 0.262777i | ||||
\(155\) | −153.077 | − | 87.5711i | −0.987592 | − | 0.564975i | ||||
\(156\) | −40.7543 | + | 5.79698i | −0.261246 | + | 0.0371601i | ||||
\(157\) | −103.680 | −0.660379 | −0.330190 | − | 0.943915i | \(-0.607113\pi\) | ||||
−0.330190 | + | 0.943915i | \(0.607113\pi\) | |||||||
\(158\) | 11.7100 | − | 3.80482i | 0.0741142 | − | 0.0240812i | ||||
\(159\) | 100.432 | + | 103.654i | 0.631650 | + | 0.651913i | ||||
\(160\) | −39.2684 | − | 43.2657i | −0.245428 | − | 0.270410i | ||||
\(161\) | 12.0132 | + | 16.5347i | 0.0746161 | + | 0.102700i | ||||
\(162\) | −19.5018 | + | 5.00077i | −0.120381 | + | 0.0308690i | ||||
\(163\) | 96.5088 | + | 70.1177i | 0.592079 | + | 0.430170i | 0.843058 | − | 0.537822i | \(-0.180753\pi\) |
−0.250980 | + | 0.967992i | \(0.580753\pi\) | |||||||
\(164\) | −85.8139 | − | 118.113i | −0.523256 | − | 0.720200i | ||||
\(165\) | 177.041 | + | 146.863i | 1.07298 | + | 0.890080i | ||||
\(166\) | −7.43721 | − | 5.40345i | −0.0448025 | − | 0.0325509i | ||||
\(167\) | −261.133 | + | 84.8473i | −1.56367 | + | 0.508068i | −0.957786 | − | 0.287484i | \(-0.907181\pi\) |
−0.605886 | + | 0.795551i | \(0.707181\pi\) | |||||||
\(168\) | −65.0936 | − | 11.3658i | −0.387462 | − | 0.0676538i | ||||
\(169\) | −48.4725 | − | 149.183i | −0.286820 | − | 0.882740i | ||||
\(170\) | −25.8632 | + | 2.82210i | −0.152136 | + | 0.0166006i | ||||
\(171\) | −119.887 | + | 154.508i | −0.701092 | + | 0.903554i | ||||
\(172\) | 0.427733 | − | 1.31643i | 0.00248682 | − | 0.00765364i | ||||
\(173\) | 94.5358 | + | 130.117i | 0.546450 | + | 0.752123i | 0.989525 | − | 0.144361i | \(-0.0461127\pi\) |
−0.443076 | + | 0.896484i | \(0.646113\pi\) | |||||||
\(174\) | 0.120396 | − | 0.689526i | 0.000691934 | − | 0.00396279i | ||||
\(175\) | −26.9696 | + | 277.780i | −0.154112 | + | 1.58731i | ||||
\(176\) | − | 234.052i | − | 1.32984i | ||||||
\(177\) | −30.5286 | + | 14.9529i | −0.172478 | + | 0.0844795i | ||||
\(178\) | 12.8199 | − | 39.4557i | 0.0720221 | − | 0.221661i | ||||
\(179\) | 109.860 | + | 35.6956i | 0.613742 | + | 0.199417i | 0.599360 | − | 0.800480i | \(-0.295422\pi\) |
0.0143820 | + | 0.999897i | \(0.495422\pi\) | |||||||
\(180\) | 92.8123 | − | 150.973i | 0.515624 | − | 0.838738i | ||||
\(181\) | 32.9018 | + | 101.261i | 0.181778 | + | 0.559455i | 0.999878 | − | 0.0156211i | \(-0.00497255\pi\) |
−0.818100 | + | 0.575076i | \(0.804973\pi\) | |||||||
\(182\) | 9.66756i | 0.0531185i | ||||||||
\(183\) | −116.888 | + | 16.6264i | −0.638733 | + | 0.0908548i | ||||
\(184\) | −2.92241 | − | 2.12325i | −0.0158826 | − | 0.0115394i | ||||
\(185\) | −176.223 | + | 19.2288i | −0.952556 | + | 0.103939i | ||||
\(186\) | 23.6191 | − | 11.5686i | 0.126984 | − | 0.0621968i | ||||
\(187\) | −259.722 | − | 188.699i | −1.38889 | − | 1.00909i | ||||
\(188\) | 63.7061 | − | 87.6839i | 0.338862 | − | 0.466404i | ||||
\(189\) | −33.0058 | − | 299.600i | −0.174634 | − | 1.58519i | ||||
\(190\) | 2.92924 | + | 26.8451i | 0.0154170 | + | 0.141290i | ||||
\(191\) | −146.771 | + | 202.013i | −0.768434 | + | 1.05766i | 0.228031 | + | 0.973654i | \(0.426771\pi\) |
−0.996465 | + | 0.0840054i | \(0.973229\pi\) | |||||||
\(192\) | −172.698 | + | 24.5649i | −0.899468 | + | 0.127942i | ||||
\(193\) | 92.3075 | 0.478277 | 0.239139 | − | 0.970985i | \(-0.423135\pi\) | ||||
0.239139 | + | 0.970985i | \(0.423135\pi\) | |||||||
\(194\) | 21.7066 | − | 7.05290i | 0.111890 | − | 0.0363551i | ||||
\(195\) | −48.5668 | − | 19.3047i | −0.249061 | − | 0.0989983i | ||||
\(196\) | 92.0305 | − | 283.241i | 0.469543 | − | 1.44511i | ||||
\(197\) | −37.3697 | − | 12.1421i | −0.189694 | − | 0.0616352i | 0.212630 | − | 0.977133i | \(-0.431797\pi\) |
−0.402323 | + | 0.915498i | \(0.631797\pi\) | |||||||
\(198\) | −32.9436 | + | 9.56547i | −0.166382 | + | 0.0483104i | ||||
\(199\) | 203.017 | 1.02019 | 0.510094 | − | 0.860119i | \(-0.329611\pi\) | ||||
0.510094 | + | 0.860119i | \(0.329611\pi\) | |||||||
\(200\) | −10.6380 | − | 48.1658i | −0.0531900 | − | 0.240829i | ||||
\(201\) | −20.5437 | + | 117.657i | −0.102208 | + | 0.585356i | ||||
\(202\) | −17.0699 | + | 12.4020i | −0.0845045 | + | 0.0613961i | ||||
\(203\) | 9.96638 | + | 3.23827i | 0.0490954 | + | 0.0159521i | ||||
\(204\) | −115.752 | + | 218.577i | −0.567414 | + | 1.07146i | ||||
\(205\) | −20.1061 | − | 184.263i | −0.0980787 | − | 0.898845i | ||||
\(206\) | 12.5945 | − | 4.09220i | 0.0611383 | − | 0.0198650i | ||||
\(207\) | 5.58387 | − | 15.5023i | 0.0269752 | − | 0.0748902i | ||||
\(208\) | 16.4327 | + | 50.5747i | 0.0790034 | + | 0.243148i | ||||
\(209\) | −195.864 | + | 269.583i | −0.937146 | + | 1.28987i | ||||
\(210\) | −32.0333 | − | 26.5730i | −0.152540 | − | 0.126538i | ||||
\(211\) | 13.7196 | − | 9.96790i | 0.0650220 | − | 0.0472412i | −0.554799 | − | 0.831984i | \(-0.687205\pi\) |
0.619821 | + | 0.784743i | \(0.287205\pi\) | |||||||
\(212\) | 111.366 | − | 153.282i | 0.525309 | − | 0.723026i | ||||
\(213\) | 131.502 | + | 135.720i | 0.617380 | + | 0.637185i | ||||
\(214\) | −15.4784 | + | 11.2457i | −0.0723288 | + | 0.0525499i | ||||
\(215\) | 1.30130 | − | 1.18107i | 0.00605254 | − | 0.00549336i | ||||
\(216\) | 21.9112 | + | 48.5580i | 0.101441 | + | 0.224805i | ||||
\(217\) | 121.674 | + | 374.475i | 0.560711 | + | 1.72569i | ||||
\(218\) | − | 16.1324i | − | 0.0740018i | ||||||
\(219\) | 159.150 | − | 22.6379i | 0.726714 | − | 0.103369i | ||||
\(220\) | 149.944 | − | 262.107i | 0.681565 | − | 1.19139i | ||||
\(221\) | 69.3702 | + | 22.5397i | 0.313892 | + | 0.101990i | ||||
\(222\) | 12.3721 | − | 23.3625i | 0.0557304 | − | 0.105237i | ||||
\(223\) | −274.804 | + | 199.657i | −1.23230 | + | 0.895321i | −0.997061 | − | 0.0766160i | \(-0.975588\pi\) |
−0.235242 | + | 0.971937i | \(0.575588\pi\) | |||||||
\(224\) | 130.453i | 0.582381i | ||||||||
\(225\) | 197.460 | − | 107.863i | 0.877601 | − | 0.479392i | ||||
\(226\) | −28.4672 | −0.125961 | ||||||||
\(227\) | −45.4592 | − | 62.5693i | −0.200261 | − | 0.275636i | 0.697061 | − | 0.717012i | \(-0.254491\pi\) |
−0.897322 | + | 0.441376i | \(0.854491\pi\) | |||||||
\(228\) | 226.876 | + | 120.147i | 0.995070 | + | 0.526961i | ||||
\(229\) | −77.3633 | + | 238.100i | −0.337831 | + | 1.03974i | 0.627479 | + | 0.778633i | \(0.284087\pi\) |
−0.965311 | + | 0.261104i | \(0.915913\pi\) | |||||||
\(230\) | −0.933666 | − | 2.07486i | −0.00405942 | − | 0.00902113i | ||||
\(231\) | −72.3244 | − | 508.460i | −0.313093 | − | 2.20112i | ||||
\(232\) | −1.85214 | −0.00798336 | ||||||||
\(233\) | 204.093 | − | 66.3140i | 0.875938 | − | 0.284609i | 0.163668 | − | 0.986515i | \(-0.447667\pi\) |
0.712269 | + | 0.701906i | \(0.247667\pi\) | |||||||
\(234\) | 6.44696 | − | 4.37989i | 0.0275511 | − | 0.0187175i | ||||
\(235\) | 125.485 | − | 56.4669i | 0.533978 | − | 0.240285i | ||||
\(236\) | 26.2300 | + | 36.1025i | 0.111144 | + | 0.152977i | ||||
\(237\) | 106.731 | − | 103.413i | 0.450341 | − | 0.436343i | ||||
\(238\) | 46.9934 | + | 34.1427i | 0.197451 | + | 0.143457i | ||||
\(239\) | −111.594 | − | 153.596i | −0.466919 | − | 0.642659i | 0.509006 | − | 0.860763i | \(-0.330013\pi\) |
−0.975926 | + | 0.218104i | \(0.930013\pi\) | |||||||
\(240\) | −212.747 | − | 84.5640i | −0.886445 | − | 0.352350i | ||||
\(241\) | −220.380 | − | 160.115i | −0.914438 | − | 0.664378i | 0.0276955 | − | 0.999616i | \(-0.491183\pi\) |
−0.942133 | + | 0.335238i | \(0.891183\pi\) | |||||||
\(242\) | −26.9874 | + | 8.76872i | −0.111518 | + | 0.0362344i | ||||
\(243\) | −184.840 | + | 157.744i | −0.760657 | + | 0.649154i | ||||
\(244\) | 47.8941 | + | 147.403i | 0.196287 | + | 0.604110i | ||||
\(245\) | 279.985 | − | 254.118i | 1.14280 | − | 1.03722i | ||||
\(246\) | 24.4285 | + | 12.9366i | 0.0993029 | + | 0.0525880i | ||||
\(247\) | 23.3955 | − | 72.0039i | 0.0947185 | − | 0.291514i | ||||
\(248\) | −40.9051 | − | 56.3011i | −0.164940 | − | 0.227020i | ||||
\(249\) | −109.304 | − | 19.0853i | −0.438971 | − | 0.0766476i | ||||
\(250\) | 9.24856 | − | 29.6605i | 0.0369942 | − | 0.118642i | ||||
\(251\) | 79.8846i | 0.318265i | 0.987257 | + | 0.159133i | \(0.0508697\pi\) | ||||
−0.987257 | + | 0.159133i | \(0.949130\pi\) | |||||||
\(252\) | −379.983 | + | 110.331i | −1.50787 | + | 0.437823i | ||||
\(253\) | 8.67585 | − | 26.7015i | 0.0342919 | − | 0.105540i | ||||
\(254\) | 24.2631 | + | 7.88355i | 0.0955239 | + | 0.0310376i | ||||
\(255\) | −265.361 | + | 167.903i | −1.04063 | + | 0.658441i | ||||
\(256\) | 67.1714 | + | 206.732i | 0.262388 | + | 0.807549i | ||||
\(257\) | 248.577i | 0.967227i | 0.875282 | + | 0.483614i | \(0.160676\pi\) | ||||
−0.875282 | + | 0.483614i | \(0.839324\pi\) | |||||||
\(258\) | 0.0369069 | + | 0.259465i | 0.000143050 | + | 0.00100568i | ||||
\(259\) | 320.197 | + | 232.637i | 1.23628 | + | 0.898212i | ||||
\(260\) | −13.9980 | + | 67.1644i | −0.0538385 | + | 0.258325i | ||||
\(261\) | −2.35578 | − | 8.11333i | −0.00902598 | − | 0.0310856i | ||||
\(262\) | 39.5906 | + | 28.7642i | 0.151109 | + | 0.109787i | ||||
\(263\) | 85.3573 | − | 117.484i | 0.324552 | − | 0.446708i | −0.615298 | − | 0.788295i | \(-0.710964\pi\) |
0.939850 | + | 0.341587i | \(0.110964\pi\) | |||||||
\(264\) | 39.9276 | + | 81.5183i | 0.151241 | + | 0.308782i | ||||
\(265\) | 219.362 | − | 98.7107i | 0.827781 | − | 0.372493i | ||||
\(266\) | 35.4390 | − | 48.7776i | 0.133229 | − | 0.183374i | ||||
\(267\) | −70.5157 | − | 495.744i | −0.264104 | − | 1.85672i | ||||
\(268\) | 156.789 | 0.585035 | ||||||||
\(269\) | 111.258 | − | 36.1500i | 0.413599 | − | 0.134387i | −0.0948235 | − | 0.995494i | \(-0.530229\pi\) |
0.508423 | + | 0.861107i | \(0.330229\pi\) | |||||||
\(270\) | −3.20791 | + | 33.4008i | −0.0118812 | + | 0.123707i | ||||
\(271\) | 92.3309 | − | 284.165i | 0.340704 | − | 1.04858i | −0.623139 | − | 0.782111i | \(-0.714143\pi\) |
0.963844 | − | 0.266469i | \(-0.0858570\pi\) | |||||||
\(272\) | 303.876 | + | 98.7352i | 1.11719 | + | 0.362997i | ||||
\(273\) | 51.3269 | + | 104.792i | 0.188011 | + | 0.383852i | ||||
\(274\) | 50.4561 | 0.184146 | ||||||||
\(275\) | 330.484 | − | 194.317i | 1.20176 | − | 0.706607i | ||||
\(276\) | −21.3080 | − | 3.72054i | −0.0772028 | − | 0.0134802i | ||||
\(277\) | 44.3143 | − | 32.1963i | 0.159980 | − | 0.116232i | −0.504915 | − | 0.863169i | \(-0.668476\pi\) |
0.664895 | + | 0.746937i | \(0.268476\pi\) | |||||||
\(278\) | −10.2202 | − | 3.32074i | −0.0367632 | − | 0.0119451i | ||||
\(279\) | 194.600 | − | 250.796i | 0.697490 | − | 0.898912i | ||||
\(280\) | −54.6866 | + | 95.5936i | −0.195309 | + | 0.341406i | ||||
\(281\) | −302.422 | + | 98.2628i | −1.07623 | + | 0.349690i | −0.792913 | − | 0.609335i | \(-0.791436\pi\) |
−0.283322 | + | 0.959025i | \(0.591436\pi\) | |||||||
\(282\) | −3.52974 | + | 20.2153i | −0.0125168 | + | 0.0716853i | ||||
\(283\) | 125.667 | + | 386.765i | 0.444054 | + | 1.36666i | 0.883517 | + | 0.468398i | \(0.155169\pi\) |
−0.439463 | + | 0.898261i | \(0.644831\pi\) | |||||||
\(284\) | 145.817 | − | 200.701i | 0.513442 | − | 0.706692i | ||||
\(285\) | 174.277 | + | 275.436i | 0.611499 | + | 0.966442i | ||||
\(286\) | 10.7440 | − | 7.80594i | 0.0375663 | − | 0.0272935i | ||||
\(287\) | −243.251 | + | 334.807i | −0.847566 | + | 1.16657i | ||||
\(288\) | 86.9948 | − | 59.1019i | 0.302065 | − | 0.205215i | ||||
\(289\) | 120.752 | − | 87.7312i | 0.417826 | − | 0.303568i | ||||
\(290\) | −1.01261 | − | 0.579286i | −0.00349175 | − | 0.00199754i | ||||
\(291\) | 197.844 | − | 191.694i | 0.679875 | − | 0.658743i | ||||
\(292\) | −65.2107 | − | 200.698i | −0.223324 | − | 0.687321i | ||||
\(293\) | 18.0217i | 0.0615076i | 0.999527 | + | 0.0307538i | \(0.00979078\pi\) | ||||
−0.999527 | + | 0.0307538i | \(0.990209\pi\) | |||||||
\(294\) | 7.94084 | + | 55.8262i | 0.0270097 | + | 0.189885i | ||||
\(295\) | 6.14566 | + | 56.3221i | 0.0208328 | + | 0.190922i | ||||
\(296\) | −66.5287 | − | 21.6165i | −0.224759 | − | 0.0730287i | ||||
\(297\) | −306.308 | + | 278.589i | −1.03134 | + | 0.938009i | ||||
\(298\) | −24.3046 | + | 17.6583i | −0.0815589 | + | 0.0592560i | ||||
\(299\) | 6.37888i | 0.0213340i | ||||||||
\(300\) | −184.072 | − | 230.995i | −0.613574 | − | 0.769985i | ||||
\(301\) | −3.92363 | −0.0130353 | ||||||||
\(302\) | −3.38131 | − | 4.65397i | −0.0111964 | − | 0.0154105i | ||||
\(303\) | −119.185 | + | 225.059i | −0.393350 | + | 0.742770i | ||||
\(304\) | 102.484 | − | 315.413i | 0.337118 | − | 1.03754i | ||||
\(305\) | −40.1480 | + | 192.635i | −0.131633 | + | 0.631592i | ||||
\(306\) | 1.47821 | − | 46.8067i | 0.00483074 | − | 0.152963i | ||||
\(307\) | −541.607 | −1.76419 | −0.882096 | − | 0.471070i | \(-0.843868\pi\) | ||||
−0.882096 | + | 0.471070i | \(0.843868\pi\) | |||||||
\(308\) | −641.197 | + | 208.338i | −2.08181 | + | 0.676421i | ||||
\(309\) | 114.792 | − | 111.224i | 0.371495 | − | 0.359948i | ||||
\(310\) | −4.75473 | − | 43.5748i | −0.0153378 | − | 0.140564i | ||||
\(311\) | −145.822 | − | 200.707i | −0.468882 | − | 0.645360i | 0.507439 | − | 0.861688i | \(-0.330592\pi\) |
−0.976321 | + | 0.216327i | \(0.930592\pi\) | |||||||
\(312\) | −14.3511 | − | 14.8114i | −0.0459970 | − | 0.0474725i | ||||
\(313\) | −124.283 | − | 90.2972i | −0.397072 | − | 0.288489i | 0.371276 | − | 0.928523i | \(-0.378921\pi\) |
−0.768347 | + | 0.640033i | \(0.778921\pi\) | |||||||
\(314\) | −15.1471 | − | 20.8482i | −0.0482391 | − | 0.0663954i | ||||
\(315\) | −488.307 | − | 117.968i | −1.55018 | − | 0.374501i | ||||
\(316\) | −157.831 | − | 114.671i | −0.499466 | − | 0.362883i | ||||
\(317\) | 374.496 | − | 121.681i | 1.18137 | − | 0.383852i | 0.348497 | − | 0.937310i | \(-0.386692\pi\) |
0.832877 | + | 0.553458i | \(0.186692\pi\) | |||||||
\(318\) | −6.17039 | + | 35.3386i | −0.0194037 | + | 0.111128i | ||||
\(319\) | −4.44839 | − | 13.6907i | −0.0139448 | − | 0.0429177i | ||||
\(320\) | −59.3171 | + | 284.611i | −0.185366 | + | 0.889411i | ||||
\(321\) | −108.073 | + | 204.075i | −0.336675 | + | 0.635749i | ||||
\(322\) | −1.56978 | + | 4.83130i | −0.00487510 | + | 0.0150040i | ||||
\(323\) | −267.381 | − | 368.019i | −0.827806 | − | 1.13938i | ||||
\(324\) | 245.728 | + | 203.412i | 0.758419 | + | 0.627814i | ||||
\(325\) | −57.7691 | + | 65.1918i | −0.177751 | + | 0.200590i | ||||
\(326\) | 29.6501i | 0.0909513i | ||||||||
\(327\) | −85.6499 | − | 174.867i | −0.261926 | − | 0.534763i | ||||
\(328\) | 22.6028 | − | 69.5642i | 0.0689109 | − | 0.212086i | ||||
\(329\) | −292.190 | − | 94.9384i | −0.888117 | − | 0.288567i | ||||
\(330\) | −3.66680 | + | 57.0559i | −0.0111115 | + | 0.172897i | ||||
\(331\) | 71.0336 | + | 218.619i | 0.214603 | + | 0.660480i | 0.999182 | + | 0.0404507i | \(0.0128794\pi\) |
−0.784578 | + | 0.620030i | \(0.787121\pi\) | |||||||
\(332\) | 145.658i | 0.438730i | ||||||||
\(333\) | 10.0720 | − | 318.925i | 0.0302462 | − | 0.957732i | ||||
\(334\) | −55.2117 | − | 40.1136i | −0.165304 | − | 0.120101i | ||||
\(335\) | 172.785 | + | 98.8460i | 0.515777 | + | 0.295063i | ||||
\(336\) | 224.837 | + | 459.040i | 0.669158 | + | 1.36619i | ||||
\(337\) | 87.9776 | + | 63.9195i | 0.261061 | + | 0.189672i | 0.710615 | − | 0.703581i | \(-0.248417\pi\) |
−0.449554 | + | 0.893253i | \(0.648417\pi\) | |||||||
\(338\) | 22.9166 | − | 31.5419i | 0.0678005 | − | 0.0933193i | ||||
\(339\) | −308.571 | + | 151.138i | −0.910239 | + | 0.445834i | ||||
\(340\) | 277.046 | + | 305.247i | 0.814840 | + | 0.897784i | ||||
\(341\) | 317.925 | − | 437.586i | 0.932331 | − | 1.28324i | ||||
\(342\) | −48.5838 | − | 1.53433i | −0.142058 | − | 0.00448634i | ||||
\(343\) | −297.195 | −0.866458 | ||||||||
\(344\) | 0.659534 | − | 0.214295i | 0.00191725 | − | 0.000622952i | ||||
\(345\) | −21.1363 | − | 17.5335i | −0.0612647 | − | 0.0508217i | ||||
\(346\) | −12.3531 | + | 38.0190i | −0.0357027 | + | 0.109882i | ||||
\(347\) | 283.414 | + | 92.0867i | 0.816754 | + | 0.265380i | 0.687456 | − | 0.726226i | \(-0.258728\pi\) |
0.129298 | + | 0.991606i | \(0.458728\pi\) | |||||||
\(348\) | −9.96003 | + | 4.87841i | −0.0286208 | + | 0.0140184i | ||||
\(349\) | −332.066 | −0.951477 | −0.475739 | − | 0.879587i | \(-0.657819\pi\) | ||||
−0.475739 | + | 0.879587i | \(0.657819\pi\) | |||||||
\(350\) | −59.7968 | + | 35.1592i | −0.170848 | + | 0.100455i | ||||
\(351\) | 46.6283 | − | 81.7041i | 0.132844 | − | 0.232775i | ||||
\(352\) | 144.978 | − | 105.333i | 0.411869 | − | 0.299241i | ||||
\(353\) | −2.63525 | − | 0.856246i | −0.00746531 | − | 0.00242563i | 0.305282 | − | 0.952262i | \(-0.401249\pi\) |
−0.312747 | + | 0.949836i | \(0.601249\pi\) | |||||||
\(354\) | −7.46684 | − | 3.95423i | −0.0210928 | − | 0.0111701i | ||||
\(355\) | 287.223 | − | 129.248i | 0.809080 | − | 0.364078i | ||||
\(356\) | −625.162 | + | 203.127i | −1.75607 | + | 0.570582i | ||||
\(357\) | 690.657 | + | 120.594i | 1.93461 | + | 0.337798i | ||||
\(358\) | 8.87222 | + | 27.3059i | 0.0247827 | + | 0.0762734i | ||||
\(359\) | −252.013 | + | 346.866i | −0.701986 | + | 0.966201i | 0.297946 | + | 0.954583i | \(0.403698\pi\) |
−0.999933 | + | 0.0116187i | \(0.996302\pi\) | |||||||
\(360\) | 88.5239 | − | 6.84015i | 0.245900 | − | 0.0190004i | ||||
\(361\) | −89.9357 | + | 65.3421i | −0.249129 | + | 0.181003i | ||||
\(362\) | −15.5551 | + | 21.4098i | −0.0429699 | + | 0.0591430i | ||||
\(363\) | −245.975 | + | 238.330i | −0.677618 | + | 0.656555i | ||||
\(364\) | 123.925 | − | 90.0365i | 0.340452 | − | 0.247353i | ||||
\(365\) | 54.6639 | − | 262.285i | 0.149764 | − | 0.718588i | ||||
\(366\) | −20.4201 | − | 21.0752i | −0.0557926 | − | 0.0575824i | ||||
\(367\) | 165.528 | + | 509.443i | 0.451030 | + | 1.38813i | 0.875733 | + | 0.482795i | \(0.160378\pi\) |
−0.424703 | + | 0.905333i | \(0.639622\pi\) | |||||||
\(368\) | 27.9426i | 0.0759311i | ||||||||
\(369\) | 333.476 | + | 10.5315i | 0.903730 | + | 0.0285408i | ||||
\(370\) | −29.6119 | − | 32.6261i | −0.0800321 | − | 0.0881788i | ||||
\(371\) | −510.783 | − | 165.963i | −1.37677 | − | 0.447341i | ||||
\(372\) | −368.264 | − | 195.022i | −0.989957 | − | 0.524253i | ||||
\(373\) | 512.750 | − | 372.535i | 1.37467 | − | 0.998753i | 0.377309 | − | 0.926088i | \(-0.376850\pi\) |
0.997356 | − | 0.0726651i | \(-0.0231504\pi\) | |||||||
\(374\) | − | 79.7938i | − | 0.213352i | ||||||
\(375\) | −57.2234 | − | 370.608i | −0.152596 | − | 0.988289i | ||||
\(376\) | 54.3003 | 0.144416 | ||||||||
\(377\) | 1.92244 | + | 2.64602i | 0.00509932 | + | 0.00701861i | ||||
\(378\) | 55.4224 | − | 50.4070i | 0.146620 | − | 0.133352i | ||||
\(379\) | −113.881 | + | 350.489i | −0.300477 | + | 0.924774i | 0.680849 | + | 0.732424i | \(0.261611\pi\) |
−0.981326 | + | 0.192350i | \(0.938389\pi\) | |||||||
\(380\) | 316.836 | − | 287.564i | 0.833778 | − | 0.756747i | ||||
\(381\) | 304.855 | − | 43.3633i | 0.800145 | − | 0.113814i | ||||
\(382\) | −62.0639 | −0.162471 | ||||||||
\(383\) | 627.010 | − | 203.728i | 1.63710 | − | 0.531927i | 0.661215 | − | 0.750197i | \(-0.270041\pi\) |
0.975888 | + | 0.218270i | \(0.0700413\pi\) | |||||||
\(384\) | −127.749 | − | 131.848i | −0.332681 | − | 0.343353i | ||||
\(385\) | −837.957 | − | 174.642i | −2.17651 | − | 0.453616i | ||||
\(386\) | 13.4857 | + | 18.5615i | 0.0349370 | + | 0.0480867i | ||||
\(387\) | 1.77760 | + | 2.61653i | 0.00459328 | + | 0.00676106i | ||||
\(388\) | −292.567 | − | 212.562i | −0.754039 | − | 0.547841i | ||||
\(389\) | 310.806 | + | 427.788i | 0.798987 | + | 1.09971i | 0.992930 | + | 0.118699i | \(0.0378723\pi\) |
−0.193943 | + | 0.981013i | \(0.562128\pi\) | |||||||
\(390\) | −3.21354 | − | 12.5863i | −0.00823986 | − | 0.0322725i | ||||
\(391\) | 31.0073 | + | 22.5281i | 0.0793026 | + | 0.0576167i | ||||
\(392\) | 141.905 | − | 46.1076i | 0.362001 | − | 0.117621i | ||||
\(393\) | 581.857 | + | 101.597i | 1.48055 | + | 0.258516i | ||||
\(394\) | −3.01795 | − | 9.28831i | −0.00765978 | − | 0.0235744i | ||||
\(395\) | −101.641 | − | 225.873i | −0.257318 | − | 0.571830i | ||||
\(396\) | 429.428 | + | 333.205i | 1.08441 | + | 0.841426i | ||||
\(397\) | 133.827 | − | 411.876i | 0.337095 | − | 1.03747i | −0.628587 | − | 0.777740i | \(-0.716366\pi\) |
0.965681 | − | 0.259731i | \(-0.0836338\pi\) | |||||||
\(398\) | 29.6599 | + | 40.8233i | 0.0745223 | + | 0.102571i | ||||
\(399\) | 125.172 | − | 716.878i | 0.313715 | − | 1.79669i | ||||
\(400\) | −253.057 | + | 285.572i | −0.632643 | + | 0.713931i | ||||
\(401\) | 542.686i | 1.35333i | 0.736290 | + | 0.676666i | \(0.236576\pi\) | ||||
−0.736290 | + | 0.676666i | \(0.763424\pi\) | |||||||
\(402\) | −26.6601 | + | 13.0581i | −0.0663186 | + | 0.0324828i | ||||
\(403\) | −37.9754 | + | 116.876i | −0.0942318 | + | 0.290016i | ||||
\(404\) | 317.953 | + | 103.309i | 0.787012 | + | 0.255716i | ||||
\(405\) | 142.559 | + | 379.080i | 0.351998 | + | 0.936001i | ||||
\(406\) | 0.804879 | + | 2.47716i | 0.00198246 | + | 0.00610139i | ||||
\(407\) | − | 543.688i | − | 1.33584i | ||||||
\(408\) | −122.681 | + | 17.4504i | −0.300688 | + | 0.0427706i | ||||
\(409\) | −599.208 | − | 435.350i | −1.46506 | − | 1.06443i | −0.982009 | − | 0.188832i | \(-0.939530\pi\) |
−0.483048 | − | 0.875594i | \(-0.660470\pi\) | |||||||
\(410\) | 34.1148 | − | 30.9630i | 0.0832068 | − | 0.0755195i | ||||
\(411\) | 546.920 | − | 267.881i | 1.33071 | − | 0.651778i | ||||
\(412\) | −169.752 | − | 123.332i | −0.412019 | − | 0.299349i | ||||
\(413\) | 74.3525 | − | 102.337i | 0.180030 | − | 0.247790i | ||||
\(414\) | 3.93302 | − | 1.14199i | 0.00950004 | − | 0.00275842i | ||||
\(415\) | −91.8285 | + | 160.519i | −0.221274 | + | 0.386792i | ||||
\(416\) | −23.9319 | + | 32.9395i | −0.0575287 | + | 0.0791814i | ||||
\(417\) | −128.412 | + | 18.2656i | −0.307943 | + | 0.0438025i | ||||
\(418\) | −82.8232 | −0.198142 | ||||||||
\(419\) | −707.190 | + | 229.780i | −1.68781 | + | 0.548401i | −0.986400 | − | 0.164362i | \(-0.947444\pi\) |
−0.701405 | + | 0.712763i | \(0.747444\pi\) | |||||||
\(420\) | −42.2942 | + | 658.103i | −0.100701 | + | 1.56691i | ||||
\(421\) | −8.91584 | + | 27.4401i | −0.0211778 | + | 0.0651784i | −0.961087 | − | 0.276246i | \(-0.910909\pi\) |
0.939909 | + | 0.341425i | \(0.110909\pi\) | |||||||
\(422\) | 4.00875 | + | 1.30252i | 0.00949940 | + | 0.00308654i | ||||
\(423\) | 69.0659 | + | 237.864i | 0.163276 | + | 0.562325i | ||||
\(424\) | 94.9233 | 0.223876 | ||||||||
\(425\) | 112.871 | + | 511.049i | 0.265580 | + | 1.20247i | ||||
\(426\) | −8.07925 | + | 46.2709i | −0.0189654 | + | 0.108617i | ||||
\(427\) | 355.430 | − | 258.235i | 0.832390 | − | 0.604766i | ||||
\(428\) | 288.308 | + | 93.6769i | 0.673616 | + | 0.218871i | ||||
\(429\) | 75.0161 | − | 141.654i | 0.174863 | − | 0.330196i | ||||
\(430\) | 0.427607 | + | 0.0891193i | 0.000994434 | + | 0.000207254i | ||||
\(431\) | 755.842 | − | 245.588i | 1.75369 | − | 0.569810i | 0.757177 | − | 0.653209i | \(-0.226578\pi\) |
0.996516 | + | 0.0833999i | \(0.0265779\pi\) | |||||||
\(432\) | 204.255 | − | 357.904i | 0.472813 | − | 0.828482i | ||||
\(433\) | 14.0932 | + | 43.3745i | 0.0325479 | + | 0.100172i | 0.966011 | − | 0.258502i | \(-0.0832289\pi\) |
−0.933463 | + | 0.358674i | \(0.883229\pi\) | |||||||
\(434\) | −57.5244 | + | 79.1756i | −0.132545 | + | 0.182432i | ||||
\(435\) | −14.0517 | − | 0.903059i | −0.0323028 | − | 0.00207600i | ||||
\(436\) | −206.795 | + | 150.245i | −0.474300 | + | 0.344599i | ||||
\(437\) | 23.3834 | − | 32.1846i | 0.0535090 | − | 0.0736489i | ||||
\(438\) | 27.8032 | + | 28.6951i | 0.0634776 | + | 0.0655140i | ||||
\(439\) | −338.183 | + | 245.705i | −0.770349 | + | 0.559691i | −0.902067 | − | 0.431596i | \(-0.857951\pi\) |
0.131718 | + | 0.991287i | \(0.457951\pi\) | |||||||
\(440\) | 150.393 | − | 16.4103i | 0.341802 | − | 0.0372962i | ||||
\(441\) | 382.467 | + | 562.970i | 0.867272 | + | 1.27658i | ||||
\(442\) | 5.60230 | + | 17.2421i | 0.0126749 | + | 0.0390093i | ||||
\(443\) | − | 382.973i | − | 0.864500i | −0.901754 | − | 0.432250i | \(-0.857720\pi\) | ||
0.901754 | − | 0.432250i | \(-0.142280\pi\) | |||||||
\(444\) | −414.700 | + | 58.9878i | −0.934009 | + | 0.132855i | ||||
\(445\) | −817.002 | − | 170.275i | −1.83596 | − | 0.382640i | ||||
\(446\) | −80.2950 | − | 26.0894i | −0.180034 | − | 0.0584965i | ||||
\(447\) | −169.699 | + | 320.445i | −0.379639 | + | 0.716879i | ||||
\(448\) | 525.135 | − | 381.533i | 1.17218 | − | 0.851635i | ||||
\(449\) | 495.237i | 1.10298i | 0.834183 | + | 0.551488i | \(0.185940\pi\) | ||||
−0.834183 | + | 0.551488i | \(0.814060\pi\) | |||||||
\(450\) | 50.5374 | + | 23.9476i | 0.112305 | + | 0.0532168i | ||||
\(451\) | 568.494 | 1.26052 | ||||||||
\(452\) | 265.123 | + | 364.910i | 0.586554 | + | 0.807323i | ||||
\(453\) | −61.3605 | − | 32.4948i | −0.135454 | − | 0.0717325i | ||||
\(454\) | 5.94023 | − | 18.2821i | 0.0130842 | − | 0.0402690i | ||||
\(455\) | 193.330 | − | 21.0955i | 0.424901 | − | 0.0463637i | ||||
\(456\) | 18.1129 | + | 127.339i | 0.0397213 | + | 0.279251i | ||||
\(457\) | 412.834 | 0.903357 | 0.451678 | − | 0.892181i | \(-0.350825\pi\) | ||||
0.451678 | + | 0.892181i | \(0.350825\pi\) | |||||||
\(458\) | −59.1802 | + | 19.2288i | −0.129214 | + | 0.0419843i | ||||
\(459\) | −232.482 | − | 515.210i | −0.506498 | − | 1.12246i | ||||
\(460\) | −17.9013 | + | 31.2920i | −0.0389159 | + | 0.0680261i | ||||
\(461\) | −63.6196 | − | 87.5649i | −0.138004 | − | 0.189946i | 0.734421 | − | 0.678694i | \(-0.237454\pi\) |
−0.872425 | + | 0.488748i | \(0.837454\pi\) | |||||||
\(462\) | 91.6763 | − | 88.8267i | 0.198433 | − | 0.192266i | ||||
\(463\) | −372.354 | − | 270.531i | −0.804220 | − | 0.584300i | 0.107929 | − | 0.994159i | \(-0.465578\pi\) |
−0.912149 | + | 0.409858i | \(0.865578\pi\) | |||||||
\(464\) | 8.42126 | + | 11.5909i | 0.0181493 | + | 0.0249803i | ||||
\(465\) | −282.886 | − | 447.086i | −0.608357 | − | 0.961476i | ||||
\(466\) | 43.1517 | + | 31.3515i | 0.0926002 | + | 0.0672780i | ||||
\(467\) | −412.064 | + | 133.888i | −0.882363 | + | 0.286697i | −0.714938 | − | 0.699188i | \(-0.753545\pi\) |
−0.167425 | + | 0.985885i | \(0.553545\pi\) | |||||||
\(468\) | −116.186 | − | 41.8499i | −0.248261 | − | 0.0894230i | ||||
\(469\) | −137.340 | − | 422.689i | −0.292836 | − | 0.901255i | ||||
\(470\) | 29.6873 | + | 16.9833i | 0.0631644 | + | 0.0361347i | ||||
\(471\) | −274.874 | − | 145.565i | −0.583596 | − | 0.309056i | ||||
\(472\) | −6.90879 | + | 21.2631i | −0.0146373 | + | 0.0450489i | ||||
\(473\) | 3.16808 | + | 4.36049i | 0.00669784 | + | 0.00921878i | ||||
\(474\) | 36.3875 | + | 6.35353i | 0.0767669 | + | 0.0134041i | ||||
\(475\) | 530.451 | − | 117.157i | 1.11674 | − | 0.246646i | ||||
\(476\) | − | 920.370i | − | 1.93355i | ||||||
\(477\) | 120.735 | + | 415.813i | 0.253113 | + | 0.871726i | ||||
\(478\) | 14.5821 | − | 44.8792i | 0.0305065 | − | 0.0938895i | ||||
\(479\) | −500.908 | − | 162.755i | −1.04574 | − | 0.339781i | −0.264743 | − | 0.964319i | \(-0.585287\pi\) |
−0.780994 | + | 0.624539i | \(0.785287\pi\) | |||||||
\(480\) | −43.3633 | − | 169.838i | −0.0903402 | − | 0.353829i | ||||
\(481\) | 38.1721 | + | 117.482i | 0.0793600 | + | 0.244245i | ||||
\(482\) | − | 67.7066i | − | 0.140470i | ||||||
\(483\) | 8.63455 | + | 60.7032i | 0.0178769 | + | 0.125679i | ||||
\(484\) | 363.743 | + | 264.275i | 0.751535 | + | 0.546022i | ||||
\(485\) | −188.408 | − | 418.694i | −0.388470 | − | 0.863287i | ||||
\(486\) | −58.7239 | − | 14.1224i | −0.120831 | − | 0.0290584i | ||||
\(487\) | 419.182 | + | 304.553i | 0.860743 | + | 0.625366i | 0.928087 | − | 0.372364i | \(-0.121453\pi\) |
−0.0673443 | + | 0.997730i | \(0.521453\pi\) | |||||||
\(488\) | −45.6413 | + | 62.8199i | −0.0935274 | + | 0.128729i | ||||
\(489\) | 157.418 | + | 321.393i | 0.321918 | + | 0.657246i | ||||
\(490\) | 92.0034 | + | 19.1748i | 0.187762 | + | 0.0391323i | ||||
\(491\) | −559.293 | + | 769.801i | −1.13909 | + | 1.56782i | −0.369567 | + | 0.929204i | \(0.620494\pi\) |
−0.769523 | + | 0.638619i | \(0.779506\pi\) | |||||||
\(492\) | −61.6793 | − | 433.621i | −0.125364 | − | 0.881344i | ||||
\(493\) | 19.6516 | 0.0398612 | ||||||||
\(494\) | 17.8967 | − | 5.81499i | 0.0362282 | − | 0.0117712i | ||||
\(495\) | 263.174 | + | 637.927i | 0.531665 | + | 1.28874i | ||||
\(496\) | −166.351 | + | 511.976i | −0.335385 | + | 1.03221i | ||||
\(497\) | −668.798 | − | 217.306i | −1.34567 | − | 0.437234i | ||||
\(498\) | −12.1310 | − | 24.7674i | −0.0243595 | − | 0.0497337i | ||||
\(499\) | −49.9179 | −0.100036 | −0.0500179 | − | 0.998748i | \(-0.515928\pi\) | ||||
−0.0500179 | + | 0.998748i | \(0.515928\pi\) | |||||||
\(500\) | −466.341 | + | 157.683i | −0.932681 | + | 0.315365i | ||||
\(501\) | −811.438 | − | 141.683i | −1.61964 | − | 0.282801i | ||||
\(502\) | −16.0634 | + | 11.6708i | −0.0319988 | + | 0.0232485i | ||||
\(503\) | −432.389 | − | 140.492i | −0.859620 | − | 0.279308i | −0.154150 | − | 0.988047i | \(-0.549264\pi\) |
−0.705470 | + | 0.708740i | \(0.749264\pi\) | |||||||
\(504\) | −156.618 | − | 121.524i | −0.310750 | − | 0.241119i | ||||
\(505\) | 285.261 | + | 314.298i | 0.564874 | + | 0.622373i | ||||
\(506\) | 6.63672 | − | 2.15640i | 0.0131160 | − | 0.00426166i | ||||
\(507\) | 80.9425 | − | 463.568i | 0.159650 | − | 0.914335i | ||||
\(508\) | −124.912 | − | 384.440i | −0.245890 | − | 0.756772i | ||||
\(509\) | 449.507 | − | 618.693i | 0.883117 | − | 1.21551i | −0.0924302 | − | 0.995719i | \(-0.529464\pi\) |
0.975548 | − | 0.219788i | \(-0.0705365\pi\) | |||||||
\(510\) | −72.5303 | − | 28.8298i | −0.142216 | − | 0.0565291i | ||||
\(511\) | −483.940 | + | 351.603i | −0.947045 | + | 0.688068i | ||||
\(512\) | −175.636 | + | 241.742i | −0.343038 | + | 0.472151i | ||||
\(513\) | −534.771 | + | 241.309i | −1.04244 | + | 0.470388i | ||||
\(514\) | −49.9846 | + | 36.3160i | −0.0972464 | + | 0.0706536i | ||||
\(515\) | −109.317 | − | 242.933i | −0.212267 | − | 0.471714i | ||||
\(516\) | 2.98225 | − | 2.88956i | 0.00577956 | − | 0.00559992i | ||||
\(517\) | 130.416 | + | 401.380i | 0.252256 | + | 0.776363i | ||||
\(518\) | 98.3733i | 0.189910i | ||||||||
\(519\) | 67.9481 | + | 477.693i | 0.130921 | + | 0.920411i | ||||
\(520\) | −31.3452 | + | 14.1050i | −0.0602793 | + | 0.0271251i | ||||
\(521\) | 647.821 | + | 210.490i | 1.24342 | + | 0.404011i | 0.855558 | − | 0.517707i | \(-0.173214\pi\) |
0.387861 | + | 0.921718i | \(0.373214\pi\) | |||||||
\(522\) | 1.28728 | − | 1.65903i | 0.00246606 | − | 0.00317821i | ||||
\(523\) | 155.910 | − | 113.275i | 0.298108 | − | 0.216588i | −0.428669 | − | 0.903461i | \(-0.641017\pi\) |
0.726777 | + | 0.686874i | \(0.241017\pi\) | |||||||
\(524\) | − | 775.384i | − | 1.47974i | ||||||
\(525\) | −461.503 | + | 698.581i | −0.879052 | + | 1.33063i | ||||
\(526\) | 36.0944 | 0.0686204 | ||||||||
\(527\) | 434.012 | + | 597.366i | 0.823552 | + | 1.13352i | ||||
\(528\) | 328.608 | − | 620.516i | 0.622363 | − | 1.17522i | ||||
\(529\) | 162.434 | − | 499.921i | 0.307059 | − | 0.945030i | ||||
\(530\) | 51.8967 | + | 29.6888i | 0.0979184 | + | 0.0560165i | ||||
\(531\) | −101.931 | − | 3.21908i | −0.191960 | − | 0.00606231i | ||||
\(532\) | −955.313 | −1.79570 | ||||||||
\(533\) | −122.842 | + | 39.9138i | −0.230473 | + | 0.0748852i | ||||
\(534\) | 89.3836 | − | 86.6053i | 0.167385 | − | 0.162182i | ||||
\(535\) | 258.664 | + | 284.994i | 0.483485 | + | 0.532699i | ||||
\(536\) | 46.1717 | + | 63.5499i | 0.0861412 | + | 0.118563i | ||||
\(537\) | 241.143 | + | 248.878i | 0.449055 | + | 0.463461i | ||||
\(538\) | 23.5234 | + | 17.0908i | 0.0437239 | + | 0.0317673i | ||||
\(539\) | 681.640 | + | 938.197i | 1.26464 | + | 1.74063i | ||||
\(540\) | 458.028 | − | 269.950i | 0.848200 | − | 0.499907i | ||||
\(541\) | 17.1958 | + | 12.4934i | 0.0317851 | + | 0.0230932i | 0.603564 | − | 0.797314i | \(-0.293747\pi\) |
−0.571779 | + | 0.820408i | \(0.693747\pi\) | |||||||
\(542\) | 70.6298 | − | 22.9490i | 0.130313 | − | 0.0423414i | ||||
\(543\) | −54.9415 | + | 314.657i | −0.101181 | + | 0.579478i | ||||
\(544\) | 75.5969 | + | 232.663i | 0.138965 | + | 0.427690i | ||||
\(545\) | −322.613 | + | 35.2023i | −0.591950 | + | 0.0645914i | ||||
\(546\) | −13.5732 | + | 25.6305i | −0.0248593 | + | 0.0469424i | ||||
\(547\) | 108.425 | − | 333.697i | 0.198217 | − | 0.610050i | −0.801707 | − | 0.597718i | \(-0.796074\pi\) |
0.999924 | − | 0.0123323i | \(-0.00392560\pi\) | |||||||
\(548\) | −469.911 | − | 646.776i | −0.857501 | − | 1.18025i | ||||
\(549\) | −333.236 | − | 120.031i | −0.606987 | − | 0.218635i | ||||
\(550\) | 87.3559 | + | 38.0659i | 0.158829 | + | 0.0692107i | ||||
\(551\) | − | 20.3977i | − | 0.0370194i | ||||||
\(552\) | −4.76681 | − | 9.73218i | −0.00863553 | − | 0.0176308i | ||||
\(553\) | −170.889 | + | 525.943i | −0.309022 | + | 0.951073i | ||||
\(554\) | 12.9482 | + | 4.20713i | 0.0233723 | + | 0.00759411i | ||||
\(555\) | −494.197 | − | 196.437i | −0.890445 | − | 0.353940i | ||||
\(556\) | 52.6159 | + | 161.935i | 0.0946330 | + | 0.291250i | ||||
\(557\) | 258.372i | 0.463864i | 0.972732 | + | 0.231932i | \(0.0745047\pi\) | ||||
−0.972732 | + | 0.231932i | \(0.925495\pi\) | |||||||
\(558\) | 78.8609 | + | 2.49051i | 0.141328 | + | 0.00446329i | ||||
\(559\) | −0.990717 | − | 0.719798i | −0.00177230 | − | 0.00128765i | ||||
\(560\) | 846.881 | − | 92.4086i | 1.51229 | − | 0.165015i | ||||
\(561\) | −423.640 | − | 864.926i | −0.755152 | − | 1.54176i | ||||
\(562\) | −63.9414 | − | 46.4561i | −0.113775 | − | 0.0826621i | ||||
\(563\) | −236.842 | + | 325.985i | −0.420678 | + | 0.579013i | −0.965782 | − | 0.259355i | \(-0.916490\pi\) |
0.545104 | + | 0.838368i | \(0.316490\pi\) | |||||||
\(564\) | 292.004 | − | 143.024i | 0.517738 | − | 0.253588i | ||||
\(565\) | 62.1180 | + | 569.282i | 0.109943 | + | 1.00758i | ||||
\(566\) | −59.4123 | + | 81.7740i | −0.104969 | + | 0.144477i | ||||
\(567\) | 333.132 | − | 840.636i | 0.587535 | − | 1.48260i | ||||
\(568\) | 124.289 | 0.218818 | ||||||||
\(569\) | −611.993 | + | 198.849i | −1.07556 | + | 0.349470i | −0.792650 | − | 0.609676i | \(-0.791299\pi\) |
−0.282909 | + | 0.959147i | \(0.591299\pi\) | |||||||
\(570\) | −29.9244 | + | 75.2840i | −0.0524989 | + | 0.132077i | ||||
\(571\) | 329.891 | − | 1015.30i | 0.577743 | − | 1.77811i | −0.0488991 | − | 0.998804i | \(-0.515571\pi\) |
0.626642 | − | 0.779307i | \(-0.284429\pi\) | |||||||
\(572\) | −200.122 | − | 65.0237i | −0.349864 | − | 0.113678i | ||||
\(573\) | −672.743 | + | 329.509i | −1.17407 | + | 0.575059i | ||||
\(574\) | −102.862 | −0.179202 | ||||||||
\(575\) | −39.4553 | + | 23.1988i | −0.0686179 | + | 0.0403457i | ||||
\(576\) | −492.344 | − | 177.341i | −0.854763 | − | 0.307883i | ||||
\(577\) | 448.369 | − | 325.759i | 0.777069 | − | 0.564573i | −0.127029 | − | 0.991899i | \(-0.540544\pi\) |
0.904098 | + | 0.427326i | \(0.140544\pi\) | |||||||
\(578\) | 35.2825 | + | 11.4640i | 0.0610424 | + | 0.0198339i | ||||
\(579\) | 244.725 | + | 129.599i | 0.422668 | + | 0.223833i | ||||
\(580\) | 2.00504 | + | 18.3752i | 0.00345697 | + | 0.0316815i | ||||
\(581\) | 392.680 | − | 127.590i | 0.675870 | − | 0.219603i | ||||
\(582\) | 67.4505 | + | 11.7774i | 0.115894 | + | 0.0202360i | ||||
\(583\) | 227.983 | + | 701.658i | 0.391051 | + | 1.20353i | ||||
\(584\) | 62.1435 | − | 85.5331i | 0.106410 | − | 0.146461i | ||||
\(585\) | −101.656 | − | 119.368i | −0.173771 | − | 0.204048i | ||||
\(586\) | −3.62386 | + | 2.63289i | −0.00618406 | + | 0.00449298i | ||||
\(587\) | 66.4863 | − | 91.5106i | 0.113265 | − | 0.155895i | −0.748621 | − | 0.662998i | \(-0.769284\pi\) |
0.861885 | + | 0.507103i | \(0.169284\pi\) | |||||||
\(588\) | 641.659 | − | 621.714i | 1.09126 | − | 1.05734i | ||||
\(589\) | 620.046 | − | 450.490i | 1.05271 | − | 0.764838i | ||||
\(590\) | −10.4276 | + | 9.46418i | −0.0176738 | + | 0.0160410i | ||||
\(591\) | −82.0265 | − | 84.6579i | −0.138793 | − | 0.143245i | ||||
\(592\) | 167.213 | + | 514.628i | 0.282454 | + | 0.869304i | ||||
\(593\) | − | 691.979i | − | 1.16691i | −0.812144 | − | 0.583456i | \(-0.801700\pi\) | ||
0.812144 | − | 0.583456i | \(-0.198300\pi\) | |||||||
\(594\) | −100.769 | − | 20.8927i | −0.169646 | − | 0.0351730i | ||||
\(595\) | 580.236 | − | 1014.27i | 0.975187 | − | 1.70465i | ||||
\(596\) | 452.709 | + | 147.094i | 0.759579 | + | 0.246802i | ||||
\(597\) | 538.237 | + | 285.035i | 0.901570 | + | 0.477446i | ||||
\(598\) | −1.28268 | + | 0.931923i | −0.00214495 | + | 0.00155840i | ||||
\(599\) | − | 466.680i | − | 0.779099i | −0.921006 | − | 0.389550i | \(-0.872631\pi\) | ||
0.921006 | − | 0.389550i | \(-0.127369\pi\) | |||||||
\(600\) | 39.4211 | − | 142.632i | 0.0657018 | − | 0.237720i | ||||
\(601\) | 1116.63 | 1.85796 | 0.928980 | − | 0.370131i | \(-0.120687\pi\) | ||||
0.928980 | + | 0.370131i | \(0.120687\pi\) | |||||||
\(602\) | −0.573223 | − | 0.788974i | −0.000952198 | − | 0.00131059i | ||||
\(603\) | −219.655 | + | 283.087i | −0.364270 | + | 0.469464i | ||||
\(604\) | −28.1664 | + | 86.6872i | −0.0466331 | + | 0.143522i | ||||
\(605\) | 234.244 | + | 520.554i | 0.387180 | + | 0.860420i | ||||
\(606\) | −62.6679 | + | 8.91402i | −0.103412 | + | 0.0147096i | ||||
\(607\) | −846.949 | −1.39530 | −0.697651 | − | 0.716438i | \(-0.745771\pi\) | ||||
−0.697651 | + | 0.716438i | \(0.745771\pi\) | |||||||
\(608\) | 241.497 | − | 78.4670i | 0.397198 | − | 0.129058i | ||||
\(609\) | 21.8762 | + | 22.5780i | 0.0359215 | + | 0.0370739i | ||||
\(610\) | −44.6011 | + | 20.0701i | −0.0731166 | + | 0.0329017i | ||||
\(611\) | −56.3615 | − | 77.5749i | −0.0922447 | − | 0.126964i | ||||
\(612\) | −613.763 | + | 416.974i | −1.00288 | + | 0.681330i | ||||
\(613\) | 827.328 | + | 601.089i | 1.34964 | + | 0.980569i | 0.999029 | + | 0.0440468i | \(0.0140251\pi\) |
0.350608 | + | 0.936522i | \(0.385975\pi\) | |||||||
\(614\) | −79.1262 | − | 108.908i | −0.128870 | − | 0.177374i | ||||
\(615\) | 205.399 | − | 516.746i | 0.333983 | − | 0.840237i | ||||
\(616\) | −273.264 | − | 198.538i | −0.443611 | − | 0.322302i | ||||
\(617\) | 752.392 | − | 244.467i | 1.21944 | − | 0.396219i | 0.372560 | − | 0.928008i | \(-0.378480\pi\) |
0.846877 | + | 0.531789i | \(0.178480\pi\) | |||||||
\(618\) | 39.1358 | + | 6.83341i | 0.0633265 | + | 0.0110573i | ||||
\(619\) | 236.920 | + | 729.166i | 0.382747 | + | 1.17797i | 0.938102 | + | 0.346360i | \(0.112582\pi\) |
−0.555355 | + | 0.831614i | \(0.687418\pi\) | |||||||
\(620\) | −514.286 | + | 466.772i | −0.829494 | + | 0.752859i | ||||
\(621\) | 36.5690 | − | 33.2597i | 0.0588872 | − | 0.0535583i | ||||
\(622\) | 19.0548 | − | 58.6447i | 0.0306348 | − | 0.0942841i | ||||
\(623\) | 1095.22 | + | 1507.44i | 1.75798 | + | 2.41965i | ||||
\(624\) | −27.4404 | + | 157.154i | −0.0439750 | + | 0.251850i | ||||
\(625\) | −613.327 | − | 120.229i | −0.981323 | − | 0.192366i | ||||
\(626\) | − | 38.1832i | − | 0.0609956i | ||||||
\(627\) | −897.764 | + | 439.724i | −1.43184 | + | 0.701314i | ||||
\(628\) | −126.176 | + | 388.329i | −0.200917 | + | 0.618358i | ||||
\(629\) | 705.884 | + | 229.356i | 1.12223 | + | 0.364635i | ||||
\(630\) | −47.6180 | − | 115.425i | −0.0755841 | − | 0.183214i | ||||
\(631\) | −312.146 | − | 960.687i | −0.494685 | − | 1.52248i | −0.817447 | − | 0.576004i | \(-0.804611\pi\) |
0.322762 | − | 0.946480i | \(-0.395389\pi\) | |||||||
\(632\) | − | 97.7407i | − | 0.154653i | ||||||
\(633\) | 50.3682 | − | 7.16448i | 0.0795706 | − | 0.0113183i | ||||
\(634\) | 79.1800 | + | 57.5276i | 0.124890 | + | 0.0907376i | ||||
\(635\) | 104.710 | − | 502.411i | 0.164897 | − | 0.791198i | ||||
\(636\) | 510.458 | − | 250.022i | 0.802606 | − | 0.393116i | ||||
\(637\) | −213.162 | − | 154.871i | −0.334634 | − | 0.243125i | ||||
\(638\) | 2.10308 | − | 2.89465i | 0.00329637 | − | 0.00453706i | ||||
\(639\) | 158.086 | + | 544.448i | 0.247395 | + | 0.852032i | ||||
\(640\) | −279.027 | + | 125.559i | −0.435980 | + | 0.196187i | ||||
\(641\) | 42.4466 | − | 58.4227i | 0.0662193 | − | 0.0911430i | −0.774623 | − | 0.632424i | \(-0.782060\pi\) |
0.840842 | + | 0.541280i | \(0.182060\pi\) | |||||||
\(642\) | −56.8249 | + | 8.08290i | −0.0885123 | + | 0.0125902i | ||||
\(643\) | −799.535 | −1.24344 | −0.621722 | − | 0.783238i | \(-0.713567\pi\) | ||||
−0.621722 | + | 0.783238i | \(0.713567\pi\) | |||||||
\(644\) | 76.5502 | − | 24.8727i | 0.118867 | − | 0.0386222i | ||||
\(645\) | 5.10820 | − | 1.30423i | 0.00791969 | − | 0.00202207i | ||||
\(646\) | 34.9391 | − | 107.532i | 0.0540853 | − | 0.166458i | ||||
\(647\) | −714.668 | − | 232.210i | −1.10459 | − | 0.358902i | −0.300721 | − | 0.953712i | \(-0.597227\pi\) |
−0.803866 | + | 0.594810i | \(0.797227\pi\) | |||||||
\(648\) | −10.0844 | + | 159.500i | −0.0155623 | + | 0.246141i | ||||
\(649\) | −173.767 | −0.267745 | ||||||||
\(650\) | −21.5487 | − | 2.09216i | −0.0331519 | − | 0.00321871i | ||||
\(651\) | −203.179 | + | 1163.63i | −0.312103 | + | 1.78745i | ||||
\(652\) | 380.073 | − | 276.139i | 0.582934 | − | 0.423526i | ||||
\(653\) | −210.330 | − | 68.3405i | −0.322098 | − | 0.104656i | 0.143505 | − | 0.989650i | \(-0.454163\pi\) |
−0.465603 | + | 0.884993i | \(0.654163\pi\) | |||||||
\(654\) | 22.6498 | − | 42.7700i | 0.0346327 | − | 0.0653976i | ||||
\(655\) | 488.832 | − | 854.491i | 0.746308 | − | 1.30457i | ||||
\(656\) | −538.109 | + | 174.842i | −0.820288 | + | 0.266528i | ||||
\(657\) | 453.721 | + | 163.429i | 0.690595 | + | 0.248750i | ||||
\(658\) | −23.5971 | − | 72.6245i | −0.0358619 | − | 0.110372i | ||||
\(659\) | 523.311 | − | 720.276i | 0.794099 | − | 1.09298i | −0.199487 | − | 0.979901i | \(-0.563927\pi\) |
0.993586 | − | 0.113083i | \(-0.0360726\pi\) | |||||||
\(660\) | 765.527 | − | 484.373i | 1.15989 | − | 0.733899i | ||||
\(661\) | −223.240 | + | 162.194i | −0.337731 | + | 0.245376i | −0.743704 | − | 0.668509i | \(-0.766933\pi\) |
0.405973 | + | 0.913885i | \(0.366933\pi\) | |||||||
\(662\) | −33.5829 | + | 46.2228i | −0.0507294 | + | 0.0698230i | ||||
\(663\) | 152.268 | + | 157.152i | 0.229665 | + | 0.237032i | ||||
\(664\) | −59.0382 | + | 42.8938i | −0.0889130 | + | 0.0645991i | ||||
\(665\) | −1052.78 | − | 602.265i | −1.58312 | − | 0.905662i | ||||
\(666\) | 65.6018 | − | 44.5681i | 0.0985012 | − | 0.0669191i | ||||
\(667\) | 0.531077 | + | 1.63449i | 0.000796218 | + | 0.00245051i | ||||
\(668\) | 1081.32i | 1.61875i | ||||||||
\(669\) | −1008.87 | + | 143.504i | −1.50803 | + | 0.214506i | ||||
\(670\) | 5.36690 | + | 49.1851i | 0.00801030 | + | 0.0734106i | ||||
\(671\) | −573.975 | − | 186.496i | −0.855402 | − | 0.277937i | ||||
\(672\) | −183.156 | + | 345.856i | −0.272553 | + | 0.514667i | ||||
\(673\) | −429.479 | + | 312.035i | −0.638156 | + | 0.463648i | −0.859216 | − | 0.511613i | \(-0.829048\pi\) |
0.221060 | + | 0.975260i | \(0.429048\pi\) | |||||||
\(674\) | 27.0291i | 0.0401026i | ||||||||
\(675\) | 674.944 | − | 8.73237i | 0.999916 | − | 0.0129368i | ||||
\(676\) | −617.751 | −0.913833 | ||||||||
\(677\) | −508.648 | − | 700.094i | −0.751326 | − | 1.03411i | −0.997886 | − | 0.0649846i | \(-0.979300\pi\) |
0.246560 | − | 0.969128i | \(-0.420700\pi\) | |||||||
\(678\) | −75.4720 | − | 39.9678i | −0.111316 | − | 0.0589496i | ||||
\(679\) | −316.773 | + | 974.926i | −0.466528 | + | 1.43583i | ||||
\(680\) | −42.1376 | + | 202.182i | −0.0619670 | + | 0.297326i | ||||
\(681\) | −32.6741 | − | 229.707i | −0.0479796 | − | 0.337309i | ||||
\(682\) | 134.438 | 0.197124 | ||||||||
\(683\) | 201.648 | − | 65.5196i | 0.295239 | − | 0.0959291i | −0.157652 | − | 0.987495i | \(-0.550392\pi\) |
0.452892 | + | 0.891566i | \(0.350392\pi\) | |||||||
\(684\) | 432.805 | + | 637.065i | 0.632756 | + | 0.931382i | ||||
\(685\) | −110.100 | − | 1009.01i | −0.160729 | − | 1.47301i | ||||
\(686\) | −43.4188 | − | 59.7609i | −0.0632927 | − | 0.0871150i | ||||
\(687\) | −539.396 | + | 522.630i | −0.785147 | + | 0.760742i | ||||
\(688\) | −4.33983 | − | 3.15307i | −0.00630789 | − | 0.00458295i | ||||
\(689\) | −98.5264 | − | 135.610i | −0.142999 | − | 0.196821i | ||||
\(690\) | 0.437767 | − | 6.81171i | 0.000634444 | − | 0.00987204i | ||||
\(691\) | −543.042 | − | 394.543i | −0.785878 | − | 0.570974i | 0.120860 | − | 0.992670i | \(-0.461435\pi\) |
−0.906737 | + | 0.421696i | \(0.861435\pi\) | |||||||
\(692\) | 602.399 | − | 195.731i | 0.870518 | − | 0.282849i | ||||
\(693\) | 522.129 | − | 1449.57i | 0.753433 | − | 2.09173i | ||||
\(694\) | 22.8883 | + | 70.4431i | 0.0329803 | + | 0.101503i | ||||
\(695\) | −44.1061 | + | 211.627i | −0.0634621 | + | 0.304500i | ||||
\(696\) | −4.91037 | − | 2.60039i | −0.00705513 | − | 0.00373620i | ||||
\(697\) | −239.820 | + | 738.091i | −0.344075 | + | 1.05895i | ||||
\(698\) | −48.5132 | − | 66.7727i | −0.0695032 | − | 0.0956629i | ||||
\(699\) | 634.195 | + | 110.735i | 0.907288 | + | 0.158419i | ||||
\(700\) | 1007.59 | + | 439.065i | 1.43942 | + | 0.627236i | ||||
\(701\) | 921.489i | 1.31454i | 0.753657 | + | 0.657268i | \(0.228288\pi\) | ||||
−0.753657 | + | 0.657268i | \(0.771712\pi\) | |||||||
\(702\) | 23.2415 | − | 2.56042i | 0.0331075 | − | 0.00364733i | ||||
\(703\) | 238.063 | − | 732.683i | 0.338639 | − | 1.04222i | ||||
\(704\) | −848.025 | − | 275.540i | −1.20458 | − | 0.391392i | ||||
\(705\) | 411.963 | + | 26.4756i | 0.584345 | + | 0.0375540i | ||||
\(706\) | −0.212822 | − | 0.654998i | −0.000301447 | − | 0.000927759i | ||||
\(707\) | − | 947.663i | − | 1.34040i | ||||||
\(708\) | 18.8529 | + | 132.541i | 0.0266285 | + | 0.187205i | ||||
\(709\) | 860.522 | + | 625.206i | 1.21371 | + | 0.881813i | 0.995563 | − | 0.0941023i | \(-0.0299981\pi\) |
0.218149 | + | 0.975915i | \(0.429998\pi\) | |||||||
\(710\) | 67.9515 | + | 38.8732i | 0.0957063 | + | 0.0547510i | ||||
\(711\) | 428.155 | − | 124.319i | 0.602187 | − | 0.174851i | ||||
\(712\) | −266.431 | − | 193.573i | −0.374200 | − | 0.271872i | ||||
\(713\) | −37.9559 | + | 52.2418i | −0.0532341 | + | 0.0732704i | ||||
\(714\) | 76.6523 | + | 156.497i | 0.107356 | + | 0.219184i | ||||
\(715\) | −179.546 | − | 197.822i | −0.251113 | − | 0.276675i | ||||
\(716\) | 267.394 | − | 368.036i | 0.373455 | − | 0.514017i | ||||
\(717\) | −80.2086 | − | 563.888i | −0.111867 | − | 0.786454i | ||||
\(718\) | −106.567 | −0.148422 | ||||||||
\(719\) | −699.629 | + | 227.323i | −0.973058 | + | 0.316166i | −0.752050 | − | 0.659106i | \(-0.770935\pi\) |
−0.221008 | + | 0.975272i | \(0.570935\pi\) | |||||||
\(720\) | −445.304 | − | 522.890i | −0.618478 | − | 0.726236i | ||||
\(721\) | −183.796 | + | 565.667i | −0.254919 | + | 0.784559i | ||||
\(722\) | −26.2783 | − | 8.53835i | −0.0363966 | − | 0.0118260i | ||||
\(723\) | −359.467 | − | 733.907i | −0.497188 | − | 1.01509i | ||||
\(724\) | 419.312 | 0.579160 | ||||||||
\(725\) | −9.37485 | + | 21.5140i | −0.0129308 | + | 0.0296745i | ||||
\(726\) | −83.8598 | − | 14.6426i | −0.115509 | − | 0.0201688i | ||||
\(727\) | −779.304 | + | 566.198i | −1.07195 | + | 0.778814i | −0.976261 | − | 0.216598i | \(-0.930504\pi\) |
−0.0956842 | + | 0.995412i | \(0.530504\pi\) | |||||||
\(728\) | 72.9872 | + | 23.7150i | 0.100257 | + | 0.0325755i | ||||
\(729\) | −711.517 | + | 158.696i | −0.976018 | + | 0.217690i | ||||
\(730\) | 60.7271 | − | 27.3266i | 0.0831878 | − | 0.0374337i | ||||
\(731\) | −6.99779 | + | 2.27372i | −0.00957290 | + | 0.00311042i | ||||
\(732\) | −79.9765 | + | 458.036i | −0.109258 | + | 0.625732i | ||||
\(733\) | −278.484 | − | 857.085i | −0.379924 | − | 1.16928i | −0.940096 | − | 0.340909i | \(-0.889265\pi\) |
0.560173 | − | 0.828376i | \(-0.310735\pi\) | |||||||
\(734\) | −78.2574 | + | 107.712i | −0.106618 | + | 0.146747i | ||||
\(735\) | 1099.07 | − | 280.617i | 1.49534 | − | 0.381792i | ||||
\(736\) | −17.3084 | + | 12.5753i | −0.0235169 | + | 0.0170860i | ||||
\(737\) | −358.858 | + | 493.925i | −0.486917 | + | 0.670184i | ||||
\(738\) | 46.6016 | + | 68.5950i | 0.0631458 | + | 0.0929471i | ||||
\(739\) | 608.566 | − | 442.149i | 0.823500 | − | 0.598308i | −0.0942130 | − | 0.995552i | \(-0.530033\pi\) |
0.917713 | + | 0.397244i | \(0.130033\pi\) | |||||||
\(740\) | −142.438 | + | 683.438i | −0.192484 | + | 0.923565i | ||||
\(741\) | 163.119 | − | 158.049i | 0.220133 | − | 0.213291i | ||||
\(742\) | −41.2505 | − | 126.956i | −0.0555937 | − | 0.171100i | ||||
\(743\) | 551.392i | 0.742116i | 0.928610 | + | 0.371058i | \(0.121005\pi\) | ||||
−0.928610 | + | 0.371058i | \(0.878995\pi\) | |||||||
\(744\) | −29.4008 | − | 206.695i | −0.0395172 | − | 0.277816i | ||||
\(745\) | 406.162 | + | 447.506i | 0.545184 | + | 0.600679i | ||||
\(746\) | 149.821 | + | 48.6797i | 0.200832 | + | 0.0652543i | ||||
\(747\) | −262.989 | − | 204.060i | −0.352060 | − | 0.273173i | ||||
\(748\) | −1022.84 | + | 743.140i | −1.36744 | + | 0.993503i | ||||
\(749\) | − | 859.306i | − | 1.14727i | ||||||
\(750\) | 66.1629 | − | 65.6507i | 0.0882172 | − | 0.0875343i | ||||
\(751\) | 3.56399 | 0.00474566 | 0.00237283 | − | 0.999997i | \(-0.499245\pi\) | ||||
0.00237283 | + | 0.999997i | \(0.499245\pi\) | |||||||
\(752\) | −246.891 | − | 339.817i | −0.328313 | − | 0.451884i | ||||
\(753\) | −112.157 | + | 211.789i | −0.148948 | + | 0.281260i | ||||
\(754\) | −0.251209 | + | 0.773141i | −0.000333168 | + | 0.00102539i | ||||
\(755\) | −85.6909 | + | 77.7741i | −0.113498 | + | 0.103012i | ||||
\(756\) | −1162.31 | − | 240.984i | −1.53745 | − | 0.318762i | ||||
\(757\) | −742.827 | −0.981277 | −0.490639 | − | 0.871363i | \(-0.663236\pi\) | ||||
−0.490639 | + | 0.871363i | \(0.663236\pi\) | |||||||
\(758\) | −87.1148 | + | 28.3053i | −0.114927 | + | 0.0373421i | ||||
\(759\) | 60.4901 | − | 58.6099i | 0.0796971 | − | 0.0772199i | ||||
\(760\) | 209.858 | + | 43.7374i | 0.276129 | + | 0.0575492i | ||||
\(761\) | 166.103 | + | 228.622i | 0.218270 | + | 0.300423i | 0.904085 | − | 0.427353i | \(-0.140554\pi\) |
−0.685815 | + | 0.727776i | \(0.740554\pi\) | |||||||
\(762\) | 53.2575 | + | 54.9660i | 0.0698918 | + | 0.0721339i | ||||
\(763\) | 586.188 | + | 425.891i | 0.768268 | + | 0.558179i | ||||
\(764\) | 578.017 | + | 795.572i | 0.756566 | + | 1.04132i | ||||
\(765\) | −939.257 | + | 72.5755i | −1.22779 | + | 0.0948699i | ||||
\(766\) | 132.569 | + | 96.3174i | 0.173067 | + | 0.125741i | ||||
\(767\) | 37.5480 | − | 12.2001i | 0.0489544 | − | 0.0159063i | ||||
\(768\) | −112.167 | + | 642.395i | −0.146051 | + | 0.836452i | ||||
\(769\) | −389.989 | − | 1200.26i | −0.507138 | − | 1.56081i | −0.797147 | − | 0.603786i | \(-0.793658\pi\) |
0.290009 | − | 0.957024i | \(-0.406342\pi\) | |||||||
\(770\) | −87.3040 | − | 194.013i | −0.113382 | − | 0.251965i | ||||
\(771\) | −349.001 | + | 659.025i | −0.452660 | + | 0.854767i | ||||
\(772\) | 112.336 | − | 345.735i | 0.145513 | − | 0.447843i | ||||
\(773\) | 146.633 | + | 201.823i | 0.189694 | + | 0.261091i | 0.893262 | − | 0.449537i | \(-0.148411\pi\) |
−0.703568 | + | 0.710628i | \(0.748411\pi\) | |||||||
\(774\) | −0.266440 | + | 0.739708i | −0.000344238 | + | 0.000955695i | ||||
\(775\) | −861.026 | + | 190.168i | −1.11100 | + | 0.245378i | ||||
\(776\) | − | 181.179i | − | 0.233478i | ||||||
\(777\) | 522.282 | + | 1066.32i | 0.672178 | + | 1.37235i | ||||
\(778\) | −40.6135 | + | 124.996i | −0.0522025 | + | 0.160663i | ||||
\(779\) | 766.113 | + | 248.925i | 0.983457 | + | 0.319545i | ||||
\(780\) | −131.410 | + | 158.412i | −0.168474 | + | 0.203093i | ||||
\(781\) | 298.511 | + | 918.722i | 0.382216 | + | 1.17634i | ||||
\(782\) | 9.52630i | 0.0121820i | ||||||||
\(783\) | 5.14546 | − | 24.8175i | 0.00657147 | − | 0.0316954i | ||||
\(784\) | −933.753 | − | 678.411i | −1.19101 | − | 0.865321i | ||||
\(785\) | −383.865 | + | 348.401i | −0.489001 | + | 0.443823i | ||||
\(786\) | 64.5772 | + | 131.844i | 0.0821593 | + | 0.167741i | ||||
\(787\) | −149.815 | − | 108.847i | −0.190362 | − | 0.138306i | 0.488522 | − | 0.872552i | \(-0.337536\pi\) |
−0.678884 | + | 0.734245i | \(0.737536\pi\) | |||||||
\(788\) | −90.9561 | + | 125.190i | −0.115426 | + | 0.158871i | ||||
\(789\) | 391.245 | − | 191.632i | 0.495875 | − | 0.242879i | ||||
\(790\) | 30.5700 | − | 53.4371i | 0.0386961 | − | 0.0676419i | ||||
\(791\) | 751.526 | − | 1034.39i | 0.950097 | − | 1.30770i | ||||
\(792\) | −8.59570 | + | 272.179i | −0.0108532 | + | 0.343660i | ||||
\(793\) | 137.120 | 0.172913 | ||||||||
\(794\) | 102.373 | − | 33.2629i | 0.128933 | − | 0.0418928i | ||||
\(795\) | 720.159 | + | 46.2823i | 0.905860 | + | 0.0582168i | ||||
\(796\) | 247.068 | − | 760.396i | 0.310386 | − | 0.955271i | ||||
\(797\) | −139.284 | − | 45.2560i | −0.174760 | − | 0.0567829i | 0.220330 | − | 0.975425i | \(-0.429287\pi\) |
−0.395090 | + | 0.918642i | \(0.629287\pi\) | |||||||
\(798\) | 162.439 | − | 79.5624i | 0.203558 | − | 0.0997023i | ||||
\(799\) | −576.138 | −0.721074 | ||||||||
\(800\) | −290.777 | − | 28.2315i | −0.363471 | − | 0.0352894i | ||||
\(801\) | 509.071 | − | 1413.31i | 0.635545 | − | 1.76444i | ||||
\(802\) | −109.125 | + | 79.2839i | −0.136066 | + | 0.0988577i | ||||
\(803\) | 781.501 | + | 253.925i | 0.973227 | + | 0.316221i | ||||
\(804\) | 415.678 | + | 220.131i | 0.517013 | + | 0.273795i | ||||
\(805\) | 100.041 | + | 20.8499i | 0.124274 | + | 0.0259005i | ||||
\(806\) | −29.0499 | + | 9.43887i | −0.0360420 | + | 0.0117108i | ||||
\(807\) | 345.721 | + | 60.3655i | 0.428403 | + | 0.0748024i | ||||
\(808\) | 51.7582 | + | 159.295i | 0.0640572 | + | 0.197148i | ||||
\(809\) | 779.001 | − | 1072.20i | 0.962919 | − | 1.32534i | 0.0173747 | − | 0.999849i | \(-0.494469\pi\) |
0.945544 | − | 0.325495i | \(-0.105531\pi\) | |||||||
\(810\) | −55.3994 | + | 84.0480i | −0.0683943 | + | 0.103763i | ||||
\(811\) | 390.246 | − | 283.531i | 0.481192 | − | 0.349606i | −0.320595 | − | 0.947216i | \(-0.603883\pi\) |
0.801787 | + | 0.597610i | \(0.203883\pi\) | |||||||
\(812\) | 24.2577 | − | 33.3879i | 0.0298740 | − | 0.0411181i | ||||
\(813\) | 643.753 | − | 623.743i | 0.791824 | − | 0.767212i | ||||
\(814\) | 109.326 | − | 79.4302i | 0.134307 | − | 0.0975801i | ||||
\(815\) | 592.938 | − | 64.6992i | 0.727531 | − | 0.0793855i | ||||
\(816\) | 667.008 | + | 688.405i | 0.817412 | + | 0.843634i | ||||
\(817\) | 2.36004 | + | 7.26347i | 0.00288867 | + | 0.00889041i | ||||
\(818\) | − | 184.093i | − | 0.225053i | ||||||
\(819\) | −11.0498 | + | 349.885i | −0.0134918 | + | 0.427210i | ||||
\(820\) | −714.622 | − | 148.937i | −0.871490 | − | 0.181631i | ||||
\(821\) | −587.331 | − | 190.835i | −0.715385 | − | 0.232443i | −0.0713637 | − | 0.997450i | \(-0.522735\pi\) |
−0.644021 | + | 0.765008i | \(0.722735\pi\) | |||||||
\(822\) | 133.769 | + | 70.8401i | 0.162736 | + | 0.0861802i | ||||
\(823\) | −244.057 | + | 177.318i | −0.296546 | + | 0.215453i | −0.726102 | − | 0.687587i | \(-0.758670\pi\) |
0.429556 | + | 0.903040i | \(0.358670\pi\) | |||||||
\(824\) | − | 105.123i | − | 0.127576i | ||||||
\(825\) | 1149.00 | − | 51.1731i | 1.39272 | − | 0.0620279i | ||||
\(826\) | 31.4408 | 0.0380640 | ||||||||
\(827\) | 718.320 | + | 988.682i | 0.868585 | + | 1.19550i | 0.979454 | + | 0.201670i | \(0.0646367\pi\) |
−0.110869 | + | 0.993835i | \(0.535363\pi\) | |||||||
\(828\) | −51.2678 | − | 39.7801i | −0.0619177 | − | 0.0480436i | ||||
\(829\) | 53.9605 | − | 166.073i | 0.0650911 | − | 0.200330i | −0.913222 | − | 0.407463i | \(-0.866413\pi\) |
0.978313 | + | 0.207133i | \(0.0664134\pi\) | |||||||
\(830\) | −45.6933 | + | 4.98588i | −0.0550521 | + | 0.00600709i | ||||
\(831\) | 162.689 | − | 23.1412i | 0.195775 | − | 0.0278475i | ||||
\(832\) | 202.590 | 0.243497 | ||||||||
\(833\) | −1505.64 | + | 489.211i | −1.80749 | + | 0.587288i | ||||
\(834\) | −22.4333 | − | 23.1530i | −0.0268985 | − | 0.0277614i | ||||
\(835\) | −681.708 | + | 1191.64i | −0.816416 | + | 1.42712i | ||||
\(836\) | 771.354 | + | 1061.68i | 0.922672 | + | 1.26995i | ||||
\(837\) | 868.037 | − | 391.691i | 1.03708 | − | 0.467971i | ||||
\(838\) | −149.522 | − | 108.634i | −0.178427 | − | 0.129635i | ||||
\(839\) | −575.264 | − | 791.782i | −0.685654 | − | 0.943722i | 0.314330 | − | 0.949314i | \(-0.398220\pi\) |
−0.999984 | + | 0.00559200i | \(0.998220\pi\) | |||||||
\(840\) | −279.197 | + | 176.657i | −0.332378 | + | 0.210306i | ||||
\(841\) | −679.670 | − | 493.809i | −0.808169 | − | 0.587169i | ||||
\(842\) | −6.82030 | + | 2.21605i | −0.00810012 | + | 0.00263189i | ||||
\(843\) | −939.738 | − | 164.085i | −1.11475 | − | 0.194645i | ||||
\(844\) | −20.6380 | − | 63.5172i | −0.0244526 | − | 0.0752574i | ||||
\(845\) | −680.776 | − | 389.454i | −0.805652 | − | 0.460892i | ||||
\(846\) | −37.7401 | + | 48.6387i | −0.0446100 | + | 0.0574926i | ||||
\(847\) | 393.837 | − | 1212.11i | 0.464979 | − | 1.43106i | ||||
\(848\) | −431.594 | − | 594.039i | −0.508956 | − | 0.700517i | ||||
\(849\) | −209.847 | + | 1201.82i | −0.247170 | + | 1.41557i | ||||
\(850\) | −86.2732 | + | 97.3583i | −0.101498 | + | 0.114539i | ||||
\(851\) | 64.9089i | 0.0762737i | ||||||||
\(852\) | 668.372 | − | 327.368i | 0.784474 | − | 0.384235i | ||||
\(853\) | 373.540 | − | 1149.64i | 0.437914 | − | 1.34776i | −0.452157 | − | 0.891938i | \(-0.649345\pi\) |
0.890071 | − | 0.455822i | \(-0.150655\pi\) | |||||||
\(854\) | 103.853 | + | 33.7440i | 0.121608 | + | 0.0395129i | ||||
\(855\) | 75.3308 | + | 974.917i | 0.0881062 | + | 1.14025i | ||||
\(856\) | 46.9324 | + | 144.443i | 0.0548276 | + | 0.168742i | ||||
\(857\) | − | 431.301i | − | 0.503268i | −0.967822 | − | 0.251634i | \(-0.919032\pi\) | ||
0.967822 | − | 0.251634i | \(-0.0809680\pi\) | |||||||
\(858\) | 39.4437 | − | 5.61056i | 0.0459717 | − | 0.00653912i | ||||
\(859\) | −177.730 | − | 129.128i | −0.206903 | − | 0.150324i | 0.479508 | − | 0.877537i | \(-0.340815\pi\) |
−0.686412 | + | 0.727213i | \(0.740815\pi\) | |||||||
\(860\) | −2.84002 | − | 6.31131i | −0.00330235 | − | 0.00733873i | ||||
\(861\) | −1114.97 | + | 546.112i | −1.29497 | + | 0.634277i | ||||
\(862\) | 159.808 | + | 116.108i | 0.185393 | + | 0.134696i | ||||
\(863\) | 420.114 | − | 578.238i | 0.486807 | − | 0.670032i | −0.492988 | − | 0.870036i | \(-0.664095\pi\) |
0.979795 | + | 0.200004i | \(0.0640954\pi\) | |||||||
\(864\) | 313.618 | − | 34.5501i | 0.362984 | − | 0.0399886i | ||||
\(865\) | 787.253 | + | 164.075i | 0.910119 | + | 0.189682i | ||||
\(866\) | −6.66292 | + | 9.17072i | −0.00769390 | + | 0.0105897i | ||||
\(867\) | 443.310 | − | 63.0573i | 0.511314 | − | 0.0727305i | ||||
\(868\) | 1550.66 | 1.78647 | ||||||||
\(869\) | 722.484 | − | 234.749i | 0.831397 | − | 0.270137i | ||||
\(870\) | −1.87130 | − | 2.95749i | −0.00215092 | − | 0.00339942i | ||||
\(871\) | 42.8648 | − | 131.924i | 0.0492133 | − | 0.151463i | ||||
\(872\) | −121.795 | − | 39.5735i | −0.139673 | − | 0.0453825i | ||||
\(873\) | 793.659 | − | 230.446i | 0.909116 | − | 0.263970i | ||||
\(874\) | 9.88797 | 0.0113135 | ||||||||
\(875\) | 833.588 | + | 1119.09i | 0.952672 | + | 1.27896i | ||||
\(876\) | 108.893 | − | 623.643i | 0.124307 | − | 0.711921i | ||||
\(877\) | 835.864 | − | 607.290i | 0.953094 | − | 0.692463i | 0.00155752 | − | 0.999999i | \(-0.499504\pi\) |
0.951537 | + | 0.307535i | \(0.0995042\pi\) | |||||||
\(878\) | −98.8139 | − | 32.1066i | −0.112544 | − | 0.0365679i | ||||
\(879\) | −25.3024 | + | 47.7790i | −0.0287854 | + | 0.0543561i | ||||
\(880\) | −786.500 | − | 866.560i | −0.893750 | − | 0.984727i | ||||
\(881\) | 1492.03 | − | 484.789i | 1.69356 | − | 0.550271i | 0.706095 | − | 0.708117i | \(-0.250455\pi\) |
0.987464 | + | 0.157846i | \(0.0504549\pi\) | |||||||
\(882\) | −57.3271 | + | 159.155i | −0.0649967 | + | 0.180448i | ||||
\(883\) | −23.5866 | − | 72.5920i | −0.0267119 | − | 0.0822106i | 0.936812 | − | 0.349834i | \(-0.113762\pi\) |
−0.963524 | + | 0.267623i | \(0.913762\pi\) | |||||||
\(884\) | 168.844 | − | 232.394i | 0.191000 | − | 0.262889i | ||||
\(885\) | −62.7826 | + | 157.949i | −0.0709408 | + | 0.178473i | ||||
\(886\) | 77.0094 | − | 55.9506i | 0.0869180 | − | 0.0631496i | ||||
\(887\) | −14.4250 | + | 19.8543i | −0.0162627 | + | 0.0223837i | −0.817071 | − | 0.576537i | \(-0.804404\pi\) |
0.800808 | + | 0.598921i | \(0.204404\pi\) | |||||||
\(888\) | −146.031 | − | 150.715i | −0.164449 | − | 0.169724i | ||||
\(889\) | −926.995 | + | 673.501i | −1.04274 | + | 0.757594i | ||||
\(890\) | −85.1207 | − | 189.161i | −0.0956413 | − | 0.212541i | ||||
\(891\) | −1203.22 | + | 308.537i | −1.35041 | + | 0.346281i | ||||
\(892\) | 413.378 | + | 1272.25i | 0.463428 | + | 1.42629i | ||||
\(893\) | 598.012i | 0.669666i | ||||||||
\(894\) | −89.2281 | + | 12.6920i | −0.0998078 | + | 0.0141969i | ||||
\(895\) | 526.698 | − | 237.009i | 0.588489 | − | 0.264814i | ||||
\(896\) | 649.713 | + | 211.105i | 0.725126 | + | 0.235608i | ||||
\(897\) | −8.95591 | + | 16.9116i | −0.00998429 | + | 0.0188535i | ||||
\(898\) | −99.5836 | + | 72.3517i | −0.110895 | + | 0.0805698i | ||||
\(899\) | 33.1094i | 0.0368292i | ||||||||
\(900\) | −163.694 | − | 870.849i | −0.181882 | − | 0.967610i | ||||
\(901\) | −1007.16 | −1.11782 | ||||||||
\(902\) | 83.0543 | + | 114.314i | 0.0920780 | + | 0.126734i | ||||
\(903\) | −10.4023 | − | 5.50875i | −0.0115197 | − | 0.00610050i | ||||
\(904\) | −69.8314 | + | 214.919i | −0.0772471 | + | 0.237742i | ||||
\(905\) | 462.091 | + | 264.350i | 0.510598 | + | 0.292100i | ||||
\(906\) | −2.43033 | − | 17.0859i | −0.00268249 | − | 0.0188586i | ||||
\(907\) | 796.609 | 0.878290 | 0.439145 | − | 0.898416i | \(-0.355281\pi\) | ||||
0.439145 | + | 0.898416i | \(0.355281\pi\) | |||||||
\(908\) | −289.674 | + | 94.1209i | −0.319025 | + | 0.103657i | ||||
\(909\) | −631.964 | + | 429.339i | −0.695230 | + | 0.472320i | ||||
\(910\) | 32.4865 | + | 35.7934i | 0.0356995 | + | 0.0393334i | ||||
\(911\) | 12.6986 | + | 17.4781i | 0.0139392 | + | 0.0191856i | 0.815930 | − | 0.578151i | \(-0.196226\pi\) |
−0.801991 | + | 0.597337i | \(0.796226\pi\) | |||||||
\(912\) | 714.541 | − | 692.332i | 0.783488 | − | 0.759135i | ||||
\(913\) | −458.860 | − | 333.381i | −0.502585 | − | 0.365149i | ||||
\(914\) | 60.3131 | + | 83.0139i | 0.0659881 | + | 0.0908248i | ||||
\(915\) | −376.899 | + | 454.345i | −0.411911 | + | 0.496552i | ||||
\(916\) | 797.647 | + | 579.524i | 0.870793 | + | 0.632669i | ||||
\(917\) | −2090.36 | + | 679.199i | −2.27956 | + | 0.740675i | ||||
\(918\) | 69.6354 | − | 122.018i | 0.0758555 | − | 0.132917i | ||||
\(919\) | 355.874 | + | 1095.27i | 0.387240 | + | 1.19180i | 0.934842 | + | 0.355064i | \(0.115541\pi\) |
−0.547602 | + | 0.836739i | \(0.684459\pi\) | |||||||
\(920\) | −17.9549 | + | 1.95917i | −0.0195162 | + | 0.00212953i | ||||
\(921\) | −1435.90 | − | 760.413i | −1.55907 | − | 0.825639i | ||||
\(922\) | 8.31328 | − | 25.5856i | 0.00901657 | − | 0.0277502i | ||||
\(923\) | −129.006 | − | 177.562i | −0.139769 | − | 0.192375i | ||||
\(924\) | −1992.44 | − | 347.895i | −2.15632 | − | 0.376510i | ||||
\(925\) | −587.836 | + | 663.366i | −0.635498 | + | 0.717153i | ||||
\(926\) | − | 114.397i | − | 0.123539i | ||||||
\(927\) | 460.493 | − | 133.708i | 0.496756 | − | 0.144238i | ||||
\(928\) | −3.38979 | + | 10.4327i | −0.00365279 | + | 0.0112421i | ||||
\(929\) | −484.091 | − | 157.291i | −0.521088 | − | 0.169312i | 0.0366509 | − | 0.999328i | \(-0.488331\pi\) |
−0.557739 | + | 0.830016i | \(0.688331\pi\) | |||||||
\(930\) | 48.5731 | − | 122.201i | 0.0522292 | − | 0.131399i | ||||
\(931\) | 507.784 | + | 1562.80i | 0.545418 | + | 1.67862i | ||||
\(932\) | − | 845.129i | − | 0.906791i | ||||||
\(933\) | −104.811 | − | 736.846i | −0.112337 | − | 0.789760i | ||||
\(934\) | −87.1230 | − | 63.2986i | −0.0932795 | − | 0.0677715i | ||||
\(935\) | −1595.70 | + | 174.117i | −1.70663 | + | 0.186222i | ||||
\(936\) | −17.2522 | − | 59.4167i | −0.0184318 | − | 0.0634794i | ||||
\(937\) | 1380.66 | + | 1003.11i | 1.47349 | + | 1.07055i | 0.979583 | + | 0.201041i | \(0.0644323\pi\) |
0.493909 | + | 0.869514i | \(0.335568\pi\) | |||||||
\(938\) | 64.9307 | − | 89.3695i | 0.0692225 | − | 0.0952766i | ||||
\(939\) | −202.722 | − | 413.888i | −0.215891 | − | 0.440775i | ||||
\(940\) | −58.7830 | − | 538.719i | −0.0625351 | − | 0.573105i | ||||
\(941\) | −249.468 | + | 343.363i | −0.265109 | + | 0.364892i | −0.920731 | − | 0.390198i | \(-0.872407\pi\) |
0.655622 | + | 0.755090i | \(0.272407\pi\) | |||||||
\(942\) | −10.8871 | − | 76.5388i | −0.0115574 | − | 0.0812514i | ||||
\(943\) | −67.8705 | −0.0719730 | ||||||||
\(944\) | 164.479 | − | 53.4425i | 0.174236 | − | 0.0566128i | ||||
\(945\) | −1128.97 | − | 998.335i | −1.19467 | − | 1.05644i | ||||
\(946\) | −0.413978 | + | 1.27409i | −0.000437609 | + | 0.00134682i | ||||
\(947\) | 311.919 | + | 101.349i | 0.329376 | + | 0.107021i | 0.469037 | − | 0.883179i | \(-0.344601\pi\) |
−0.139661 | + | 0.990199i | \(0.544601\pi\) | |||||||
\(948\) | −257.443 | − | 525.609i | −0.271564 | − | 0.554439i | ||||
\(949\) | −186.697 | −0.196731 | ||||||||
\(950\) | 101.055 | + | 89.5486i | 0.106373 | + | 0.0942617i | ||||
\(951\) | 1163.70 | + | 203.191i | 1.22366 | + | 0.213660i | ||||
\(952\) | 373.044 | − | 271.033i | 0.391853 | − | 0.284698i | ||||
\(953\) | −344.909 | − | 112.068i | −0.361919 | − | 0.117595i | 0.122412 | − | 0.992479i | \(-0.460937\pi\) |
−0.484331 | + | 0.874885i | \(0.660937\pi\) | |||||||
\(954\) | −65.9741 | + | 85.0261i | −0.0691552 | + | 0.0891259i | ||||
\(955\) | 135.429 | + | 1241.14i | 0.141810 | + | 1.29962i | ||||
\(956\) | −711.095 | + | 231.049i | −0.743823 | + | 0.241683i | ||||
\(957\) | 7.42820 | − | 42.5422i | 0.00776196 | − | 0.0444537i | ||||
\(958\) | −40.4531 | − | 124.502i | −0.0422266 | − | 0.129960i | ||||
\(959\) | −1332.03 | + | 1833.38i | −1.38897 | + | 1.91176i | ||||
\(960\) | −556.854 | + | 671.278i | −0.580056 | + | 0.699248i | ||||
\(961\) | −228.990 | + | 166.371i | −0.238283 | + | 0.173123i | ||||
\(962\) | −18.0468 | + | 24.8393i | −0.0187597 | + | 0.0258205i | ||||
\(963\) | −573.041 | + | 389.309i | −0.595058 | + | 0.404267i | ||||
\(964\) | −867.903 | + | 630.569i | −0.900315 | + | 0.654117i | ||||
\(965\) | 341.761 | − | 310.187i | 0.354157 | − | 0.321437i | ||||
\(966\) | −10.9449 | + | 10.6047i | −0.0113301 | + | 0.0109780i | ||||
\(967\) | −354.097 | − | 1089.80i | −0.366181 | − | 1.12699i | −0.949238 | − | 0.314559i | \(-0.898143\pi\) |
0.583056 | − | 0.812432i | \(-0.301857\pi\) | |||||||
\(968\) | 225.256i | 0.232703i | ||||||||
\(969\) | −192.182 | − | 1351.09i | −0.198330 | − | 1.39431i | ||||
\(970\) | 56.6667 | − | 99.0548i | 0.0584192 | − | 0.102118i | ||||
\(971\) | 428.755 | + | 139.311i | 0.441560 | + | 0.143471i | 0.521355 | − | 0.853340i | \(-0.325427\pi\) |
−0.0797953 | + | 0.996811i | \(0.525427\pi\) | |||||||
\(972\) | 365.881 | + | 884.283i | 0.376421 | + | 0.909756i | ||||
\(973\) | 390.472 | − | 283.695i | 0.401308 | − | 0.291567i | ||||
\(974\) | 128.784i | 0.132222i | ||||||||
\(975\) | −244.686 | + | 91.7282i | −0.250960 | + | 0.0940802i | ||||
\(976\) | 600.654 | 0.615424 | ||||||||
\(977\) | −816.852 | − | 1124.30i | −0.836082 | − | 1.15077i | −0.986760 | − | 0.162185i | \(-0.948146\pi\) |
0.150679 | − | 0.988583i | \(-0.451854\pi\) | |||||||
\(978\) | −41.6286 | + | 78.6081i | −0.0425651 | + | 0.0803764i | ||||
\(979\) | 790.962 | − | 2434.33i | 0.807928 | − | 2.48655i | ||||
\(980\) | −611.057 | − | 1357.93i | −0.623527 | − | 1.38565i | ||||
\(981\) | 18.4389 | − | 583.859i | 0.0187960 | − | 0.595167i | ||||
\(982\) | −236.504 | −0.240839 | ||||||||
\(983\) | 1554.49 | − | 505.086i | 1.58138 | − | 0.513821i | 0.618966 | − | 0.785418i | \(-0.287552\pi\) |
0.962411 | + | 0.271597i | \(0.0875518\pi\) | |||||||
\(984\) | 157.592 | − | 152.694i | 0.160154 | − | 0.155176i | ||||
\(985\) | −179.160 | + | 80.6204i | −0.181889 | + | 0.0818481i | ||||
\(986\) | 2.87100 | + | 3.95160i | 0.00291177 | + | 0.00400771i | ||||
\(987\) | −641.359 | − | 661.933i | −0.649806 | − | 0.670652i | ||||
\(988\) | −241.217 | − | 175.254i | −0.244146 | − | 0.177383i | ||||
\(989\) | −0.378226 | − | 0.520583i | −0.000382432 | − | 0.000526373i | ||||
\(990\) | −89.8276 | + | 146.118i | −0.0907350 | + | 0.147594i | ||||
\(991\) | 1136.80 | + | 825.936i | 1.14713 | + | 0.833437i | 0.988096 | − | 0.153836i | \(-0.0491628\pi\) |
0.159032 | + | 0.987273i | \(0.449163\pi\) | |||||||
\(992\) | −391.996 | + | 127.367i | −0.395158 | + | 0.128394i | ||||
\(993\) | −118.616 | + | 679.331i | −0.119453 | + | 0.684120i | ||||
\(994\) | −54.0117 | − | 166.231i | −0.0543378 | − | 0.167234i | ||||
\(995\) | 751.657 | − | 682.213i | 0.755434 | − | 0.685641i | ||||
\(996\) | −204.503 | + | 386.168i | −0.205325 | + | 0.387718i | ||||
\(997\) | −309.456 | + | 952.408i | −0.310387 | + | 0.955274i | 0.667224 | + | 0.744857i | \(0.267482\pi\) |
−0.977612 | + | 0.210417i | \(0.932518\pi\) | |||||||
\(998\) | −7.29276 | − | 10.0376i | −0.00730738 | − | 0.0100577i | ||||
\(999\) | 474.471 | − | 831.389i | 0.474946 | − | 0.832221i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 75.3.j.a.11.11 | yes | 72 | |
3.2 | odd | 2 | inner | 75.3.j.a.11.8 | ✓ | 72 | |
5.2 | odd | 4 | 375.3.h.b.74.16 | 144 | |||
5.3 | odd | 4 | 375.3.h.b.74.21 | 144 | |||
5.4 | even | 2 | 375.3.j.a.176.8 | 72 | |||
15.2 | even | 4 | 375.3.h.b.74.22 | 144 | |||
15.8 | even | 4 | 375.3.h.b.74.15 | 144 | |||
15.14 | odd | 2 | 375.3.j.a.176.11 | 72 | |||
25.9 | even | 10 | 375.3.j.a.326.11 | 72 | |||
25.12 | odd | 20 | 375.3.h.b.299.15 | 144 | |||
25.13 | odd | 20 | 375.3.h.b.299.22 | 144 | |||
25.16 | even | 5 | inner | 75.3.j.a.41.8 | yes | 72 | |
75.38 | even | 20 | 375.3.h.b.299.16 | 144 | |||
75.41 | odd | 10 | inner | 75.3.j.a.41.11 | yes | 72 | |
75.59 | odd | 10 | 375.3.j.a.326.8 | 72 | |||
75.62 | even | 20 | 375.3.h.b.299.21 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.j.a.11.8 | ✓ | 72 | 3.2 | odd | 2 | inner | |
75.3.j.a.11.11 | yes | 72 | 1.1 | even | 1 | trivial | |
75.3.j.a.41.8 | yes | 72 | 25.16 | even | 5 | inner | |
75.3.j.a.41.11 | yes | 72 | 75.41 | odd | 10 | inner | |
375.3.h.b.74.15 | 144 | 15.8 | even | 4 | |||
375.3.h.b.74.16 | 144 | 5.2 | odd | 4 | |||
375.3.h.b.74.21 | 144 | 5.3 | odd | 4 | |||
375.3.h.b.74.22 | 144 | 15.2 | even | 4 | |||
375.3.h.b.299.15 | 144 | 25.12 | odd | 20 | |||
375.3.h.b.299.16 | 144 | 75.38 | even | 20 | |||
375.3.h.b.299.21 | 144 | 75.62 | even | 20 | |||
375.3.h.b.299.22 | 144 | 25.13 | odd | 20 | |||
375.3.j.a.176.8 | 72 | 5.4 | even | 2 | |||
375.3.j.a.176.11 | 72 | 15.14 | odd | 2 | |||
375.3.j.a.326.8 | 72 | 75.59 | odd | 10 | |||
375.3.j.a.326.11 | 72 | 25.9 | even | 10 |