Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(376,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.376");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.bt (of order \(6\), degree \(2\), 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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(54\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 376.7 | ||
Character | \(\chi\) | \(=\) | 585.376 |
Dual form | 585.2.bt.b.571.7 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91643 | − | 1.10645i | −1.35512 | − | 0.782380i | −0.366161 | − | 0.930552i | \(-0.619328\pi\) |
−0.988962 | + | 0.148171i | \(0.952661\pi\) | |||||||
\(3\) | 1.62047 | + | 0.611626i | 0.935577 | + | 0.353122i | ||||
\(4\) | 1.44848 | + | 2.50883i | 0.724238 | + | 1.25442i | ||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | −2.42878 | − | 2.96511i | −0.991546 | − | 1.21050i | ||||
\(7\) | 0.916933 | + | 0.529392i | 0.346568 | + | 0.200091i | 0.663173 | − | 0.748466i | \(-0.269209\pi\) |
−0.316605 | + | 0.948558i | \(0.602543\pi\) | |||||||
\(8\) | − | 1.98487i | − | 0.701757i | ||||||
\(9\) | 2.25183 | + | 1.98224i | 0.750609 | + | 0.660746i | ||||
\(10\) | −2.21291 | −0.699782 | ||||||||
\(11\) | −1.05983 | − | 0.611891i | −0.319550 | − | 0.184492i | 0.331642 | − | 0.943405i | \(-0.392397\pi\) |
−0.651192 | + | 0.758913i | \(0.725731\pi\) | |||||||
\(12\) | 0.812740 | + | 4.95141i | 0.234618 | + | 1.42935i | ||||
\(13\) | 3.38513 | + | 1.24132i | 0.938867 | + | 0.344281i | ||||
\(14\) | −1.17149 | − | 2.02909i | −0.313095 | − | 0.542296i | ||||
\(15\) | 1.70918 | − | 0.280550i | 0.441308 | − | 0.0724377i | ||||
\(16\) | 0.700788 | − | 1.21380i | 0.175197 | − | 0.303450i | ||||
\(17\) | −1.24095 | −0.300975 | −0.150488 | − | 0.988612i | \(-0.548084\pi\) | ||||
−0.150488 | + | 0.988612i | \(0.548084\pi\) | |||||||
\(18\) | −2.12222 | − | 6.29037i | −0.500213 | − | 1.48265i | ||||
\(19\) | 4.23962i | 0.972635i | 0.873782 | + | 0.486317i | \(0.161660\pi\) | ||||
−0.873782 | + | 0.486317i | \(0.838340\pi\) | |||||||
\(20\) | 2.50883 | + | 1.44848i | 0.560992 | + | 0.323889i | ||||
\(21\) | 1.16207 | + | 1.41868i | 0.253585 | + | 0.309582i | ||||
\(22\) | 1.35406 | + | 2.34530i | 0.288686 | + | 0.500019i | ||||
\(23\) | −0.567930 | − | 0.983684i | −0.118422 | − | 0.205112i | 0.800721 | − | 0.599038i | \(-0.204450\pi\) |
−0.919142 | + | 0.393926i | \(0.871117\pi\) | |||||||
\(24\) | 1.21400 | − | 3.21641i | 0.247806 | − | 0.656548i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −5.11391 | − | 6.12440i | −1.00292 | − | 1.20109i | ||||
\(27\) | 2.43663 | + | 4.58943i | 0.468929 | + | 0.883236i | ||||
\(28\) | 3.06724i | 0.579655i | ||||||||
\(29\) | 1.73591 | − | 3.00669i | 0.322351 | − | 0.558328i | −0.658622 | − | 0.752474i | \(-0.728860\pi\) |
0.980973 | + | 0.194146i | \(0.0621936\pi\) | |||||||
\(30\) | −3.58594 | − | 1.35347i | −0.654700 | − | 0.247109i | ||||
\(31\) | 1.71755 | − | 0.991626i | 0.308481 | − | 0.178101i | −0.337766 | − | 0.941230i | \(-0.609671\pi\) |
0.646246 | + | 0.763129i | \(0.276338\pi\) | |||||||
\(32\) | −6.12392 | + | 3.53565i | −1.08257 | + | 0.625020i | ||||
\(33\) | −1.34317 | − | 1.63977i | −0.233815 | − | 0.285447i | ||||
\(34\) | 2.37820 | + | 1.37306i | 0.407858 | + | 0.235477i | ||||
\(35\) | 1.05878 | 0.178967 | ||||||||
\(36\) | −1.71139 | + | 8.52069i | −0.285232 | + | 1.42011i | ||||
\(37\) | 11.5907i | 1.90550i | 0.303750 | + | 0.952752i | \(0.401761\pi\) | ||||
−0.303750 | + | 0.952752i | \(0.598239\pi\) | |||||||
\(38\) | 4.69094 | − | 8.12494i | 0.760970 | − | 1.31804i | ||||
\(39\) | 4.72627 | + | 4.08196i | 0.756809 | + | 0.653636i | ||||
\(40\) | −0.992434 | − | 1.71895i | −0.156918 | − | 0.271789i | ||||
\(41\) | 3.01508 | − | 1.74076i | 0.470876 | − | 0.271860i | −0.245730 | − | 0.969338i | \(-0.579028\pi\) |
0.716606 | + | 0.697478i | \(0.245694\pi\) | |||||||
\(42\) | −0.657326 | − | 4.00458i | −0.101428 | − | 0.617921i | ||||
\(43\) | −2.57139 | + | 4.45377i | −0.392133 | + | 0.679194i | −0.992731 | − | 0.120357i | \(-0.961596\pi\) |
0.600598 | + | 0.799551i | \(0.294929\pi\) | |||||||
\(44\) | − | 3.54524i | − | 0.534465i | ||||||
\(45\) | 2.94126 | + | 0.590755i | 0.438457 | + | 0.0880646i | ||||
\(46\) | 2.51355i | 0.370603i | ||||||||
\(47\) | 4.19252 | + | 2.42055i | 0.611541 | + | 0.353074i | 0.773568 | − | 0.633713i | \(-0.218470\pi\) |
−0.162027 | + | 0.986786i | \(0.551803\pi\) | |||||||
\(48\) | 1.87800 | − | 1.53830i | 0.271065 | − | 0.222035i | ||||
\(49\) | −2.93949 | − | 5.09134i | −0.419927 | − | 0.727335i | ||||
\(50\) | −1.91643 | + | 1.10645i | −0.271024 | + | 0.156476i | ||||
\(51\) | −2.01092 | − | 0.758998i | −0.281586 | − | 0.106281i | ||||
\(52\) | 1.78901 | + | 10.2908i | 0.248091 | + | 1.42707i | ||||
\(53\) | 3.53594 | 0.485699 | 0.242849 | − | 0.970064i | \(-0.421918\pi\) | ||||
0.242849 | + | 0.970064i | \(0.421918\pi\) | |||||||
\(54\) | 0.408359 | − | 11.4913i | 0.0555707 | − | 1.56377i | ||||
\(55\) | −1.22378 | −0.165015 | ||||||||
\(56\) | 1.05077 | − | 1.81999i | 0.140415 | − | 0.243207i | ||||
\(57\) | −2.59306 | + | 6.87016i | −0.343459 | + | 0.909975i | ||||
\(58\) | −6.65352 | + | 3.84141i | −0.873650 | + | 0.504402i | ||||
\(59\) | −0.233139 | + | 0.134603i | −0.0303521 | + | 0.0175238i | −0.515099 | − | 0.857131i | \(-0.672245\pi\) |
0.484747 | + | 0.874654i | \(0.338912\pi\) | |||||||
\(60\) | 3.17956 | + | 3.88167i | 0.410479 | + | 0.501122i | ||||
\(61\) | 5.60990 | − | 9.71663i | 0.718274 | − | 1.24409i | −0.243409 | − | 0.969924i | \(-0.578266\pi\) |
0.961683 | − | 0.274164i | \(-0.0884010\pi\) | |||||||
\(62\) | −4.38875 | −0.557372 | ||||||||
\(63\) | 1.01540 | + | 3.00968i | 0.127928 | + | 0.379184i | ||||
\(64\) | 12.8450 | 1.60562 | ||||||||
\(65\) | 3.55227 | − | 0.617550i | 0.440605 | − | 0.0765977i | ||||
\(66\) | 0.759762 | + | 4.62865i | 0.0935203 | + | 0.569748i | ||||
\(67\) | 4.51431 | − | 2.60634i | 0.551511 | − | 0.318415i | −0.198220 | − | 0.980158i | \(-0.563516\pi\) |
0.749731 | + | 0.661742i | \(0.230183\pi\) | |||||||
\(68\) | −1.79749 | − | 3.11334i | −0.217978 | − | 0.377548i | ||||
\(69\) | −0.318666 | − | 1.94139i | −0.0383629 | − | 0.233716i | ||||
\(70\) | −2.02909 | − | 1.17149i | −0.242522 | − | 0.140020i | ||||
\(71\) | − | 5.36211i | − | 0.636365i | −0.948029 | − | 0.318183i | \(-0.896927\pi\) | ||
0.948029 | − | 0.318183i | \(-0.103073\pi\) | |||||||
\(72\) | 3.93448 | − | 4.46958i | 0.463683 | − | 0.526745i | ||||
\(73\) | − | 8.09939i | − | 0.947962i | −0.880535 | − | 0.473981i | \(-0.842817\pi\) | ||
0.880535 | − | 0.473981i | \(-0.157183\pi\) | |||||||
\(74\) | 12.8246 | − | 22.2128i | 1.49083 | − | 2.58219i | ||||
\(75\) | 1.33992 | − | 1.09755i | 0.154720 | − | 0.126734i | ||||
\(76\) | −10.6365 | + | 6.14098i | −1.22009 | + | 0.704419i | ||||
\(77\) | −0.647860 | − | 1.12213i | −0.0738306 | − | 0.127878i | ||||
\(78\) | −4.54109 | − | 13.0522i | −0.514177 | − | 1.47787i | ||||
\(79\) | 3.73605 | − | 6.47103i | 0.420339 | − | 0.728048i | −0.575634 | − | 0.817708i | \(-0.695245\pi\) |
0.995972 | + | 0.0896596i | \(0.0285779\pi\) | |||||||
\(80\) | − | 1.40158i | − | 0.156701i | ||||||
\(81\) | 1.14146 | + | 8.92732i | 0.126829 | + | 0.991925i | ||||
\(82\) | −7.70426 | −0.850793 | ||||||||
\(83\) | −1.26565 | − | 0.730723i | −0.138923 | − | 0.0802073i | 0.428928 | − | 0.903339i | \(-0.358892\pi\) |
−0.567851 | + | 0.823132i | \(0.692225\pi\) | |||||||
\(84\) | −1.87600 | + | 4.97037i | −0.204689 | + | 0.542312i | ||||
\(85\) | −1.07470 | + | 0.620476i | −0.116567 | + | 0.0673001i | ||||
\(86\) | 9.85578 | − | 5.69024i | 1.06278 | − | 0.613594i | ||||
\(87\) | 4.65196 | − | 3.81051i | 0.498742 | − | 0.408530i | ||||
\(88\) | −1.21452 | + | 2.10362i | −0.129469 | + | 0.224246i | ||||
\(89\) | − | 16.4481i | − | 1.74349i | −0.489955 | − | 0.871747i | \(-0.662987\pi\) | ||
0.489955 | − | 0.871747i | \(-0.337013\pi\) | |||||||
\(90\) | −4.98308 | − | 4.38651i | −0.525263 | − | 0.462378i | ||||
\(91\) | 2.44679 | + | 2.93027i | 0.256494 | + | 0.307176i | ||||
\(92\) | 1.64527 | − | 2.84968i | 0.171531 | − | 0.297100i | ||||
\(93\) | 3.38973 | − | 0.556402i | 0.351499 | − | 0.0576962i | ||||
\(94\) | −5.35645 | − | 9.27764i | −0.552476 | − | 0.956916i | ||||
\(95\) | 2.11981 | + | 3.67162i | 0.217488 | + | 0.376700i | ||||
\(96\) | −12.0861 | + | 1.98385i | −1.23353 | + | 0.202476i | ||||
\(97\) | 3.53755 | + | 2.04240i | 0.359183 | + | 0.207375i | 0.668723 | − | 0.743512i | \(-0.266841\pi\) |
−0.309539 | + | 0.950887i | \(0.600175\pi\) | |||||||
\(98\) | 13.0096i | 1.31417i | ||||||||
\(99\) | −1.17363 | − | 3.47870i | −0.117955 | − | 0.349623i | ||||
\(100\) | 2.89695 | 0.289695 | ||||||||
\(101\) | −6.61239 | + | 11.4530i | −0.657958 | + | 1.13962i | 0.323186 | + | 0.946336i | \(0.395246\pi\) |
−0.981143 | + | 0.193281i | \(0.938087\pi\) | |||||||
\(102\) | 3.01400 | + | 3.67956i | 0.298431 | + | 0.364331i | ||||
\(103\) | 1.09724 | + | 1.90048i | 0.108114 | + | 0.187259i | 0.915006 | − | 0.403439i | \(-0.132185\pi\) |
−0.806892 | + | 0.590699i | \(0.798852\pi\) | |||||||
\(104\) | 2.46386 | − | 6.71904i | 0.241601 | − | 0.658856i | ||||
\(105\) | 1.71572 | + | 0.647579i | 0.167437 | + | 0.0631972i | ||||
\(106\) | −6.77639 | − | 3.91235i | −0.658181 | − | 0.380001i | ||||
\(107\) | −14.1628 | −1.36917 | −0.684585 | − | 0.728933i | \(-0.740017\pi\) | ||||
−0.684585 | + | 0.728933i | \(0.740017\pi\) | |||||||
\(108\) | −7.98472 | + | 12.7608i | −0.768330 | + | 1.22790i | ||||
\(109\) | 0.673663i | 0.0645252i | 0.999479 | + | 0.0322626i | \(0.0102713\pi\) | ||||
−0.999479 | + | 0.0322626i | \(0.989729\pi\) | |||||||
\(110\) | 2.34530 | + | 1.35406i | 0.223615 | + | 0.129104i | ||||
\(111\) | −7.08919 | + | 18.7824i | −0.672876 | + | 1.78275i | ||||
\(112\) | 1.28515 | − | 0.741983i | 0.121435 | − | 0.0701108i | ||||
\(113\) | 8.22843 | + | 14.2521i | 0.774066 | + | 1.34072i | 0.935318 | + | 0.353808i | \(0.115113\pi\) |
−0.161252 | + | 0.986913i | \(0.551553\pi\) | |||||||
\(114\) | 12.5709 | − | 10.2971i | 1.17738 | − | 0.964412i | ||||
\(115\) | −0.983684 | − | 0.567930i | −0.0917290 | − | 0.0529598i | ||||
\(116\) | 10.0577 | 0.933834 | ||||||||
\(117\) | 5.16214 | + | 9.50538i | 0.477240 | + | 0.878773i | ||||
\(118\) | 0.595727 | 0.0548411 | ||||||||
\(119\) | −1.13787 | − | 0.656950i | −0.104308 | − | 0.0602225i | ||||
\(120\) | −0.556855 | − | 3.39249i | −0.0508337 | − | 0.309691i | ||||
\(121\) | −4.75118 | − | 8.22928i | −0.431925 | − | 0.748116i | ||||
\(122\) | −21.5020 | + | 12.4142i | −1.94670 | + | 1.12393i | ||||
\(123\) | 5.95053 | − | 0.976739i | 0.536541 | − | 0.0880696i | ||||
\(124\) | 4.97565 | + | 2.87269i | 0.446826 | + | 0.257975i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 1.38413 | − | 6.89133i | 0.123308 | − | 0.613929i | ||||
\(127\) | −18.7156 | −1.66074 | −0.830371 | − | 0.557211i | \(-0.811871\pi\) | ||||
−0.830371 | + | 0.557211i | \(0.811871\pi\) | |||||||
\(128\) | −12.3686 | − | 7.14104i | −1.09324 | − | 0.631185i | ||||
\(129\) | −6.89089 | + | 5.64447i | −0.606709 | + | 0.496968i | ||||
\(130\) | −7.49098 | − | 2.74693i | −0.657002 | − | 0.240921i | ||||
\(131\) | 7.24460 | + | 12.5480i | 0.632963 | + | 1.09632i | 0.986943 | + | 0.161071i | \(0.0514950\pi\) |
−0.353979 | + | 0.935253i | \(0.615172\pi\) | |||||||
\(132\) | 2.16836 | − | 5.74494i | 0.188731 | − | 0.500033i | ||||
\(133\) | −2.24442 | + | 3.88744i | −0.194616 | + | 0.337084i | ||||
\(134\) | −11.5352 | −0.996487 | ||||||||
\(135\) | 4.40489 | + | 2.75625i | 0.379113 | + | 0.237220i | ||||
\(136\) | 2.46313i | 0.211211i | ||||||||
\(137\) | −1.03496 | − | 0.597533i | −0.0884225 | − | 0.0510507i | 0.455137 | − | 0.890422i | \(-0.349590\pi\) |
−0.543559 | + | 0.839371i | \(0.682924\pi\) | |||||||
\(138\) | −1.53735 | + | 4.07313i | −0.130868 | + | 0.346728i | ||||
\(139\) | 3.18816 | + | 5.52206i | 0.270416 | + | 0.468375i | 0.968968 | − | 0.247184i | \(-0.0795053\pi\) |
−0.698552 | + | 0.715559i | \(0.746172\pi\) | |||||||
\(140\) | 1.53362 | + | 2.65631i | 0.129615 | + | 0.224499i | ||||
\(141\) | 5.31336 | + | 6.48667i | 0.447466 | + | 0.546276i | ||||
\(142\) | −5.93292 | + | 10.2761i | −0.497880 | + | 0.862353i | ||||
\(143\) | −2.82810 | − | 3.38692i | −0.236498 | − | 0.283228i | ||||
\(144\) | 3.98410 | − | 1.34414i | 0.332008 | − | 0.112012i | ||||
\(145\) | − | 3.47182i | − | 0.288319i | ||||||
\(146\) | −8.96159 | + | 15.5219i | −0.741667 | + | 1.28460i | ||||
\(147\) | −1.64935 | − | 10.0482i | −0.136036 | − | 0.828764i | ||||
\(148\) | −29.0792 | + | 16.7889i | −2.39030 | + | 1.38004i | ||||
\(149\) | −14.4733 | + | 8.35614i | −1.18570 | + | 0.684561i | −0.957325 | − | 0.289013i | \(-0.906673\pi\) |
−0.228370 | + | 0.973574i | \(0.573340\pi\) | |||||||
\(150\) | −3.78225 | + | 0.620831i | −0.308819 | + | 0.0506906i | ||||
\(151\) | −6.42988 | − | 3.71229i | −0.523256 | − | 0.302102i | 0.215010 | − | 0.976612i | \(-0.431022\pi\) |
−0.738266 | + | 0.674510i | \(0.764355\pi\) | |||||||
\(152\) | 8.41508 | 0.682553 | ||||||||
\(153\) | −2.79441 | − | 2.45986i | −0.225915 | − | 0.198868i | ||||
\(154\) | 2.86731i | 0.231054i | ||||||||
\(155\) | 0.991626 | − | 1.71755i | 0.0796493 | − | 0.137957i | ||||
\(156\) | −3.39506 | + | 17.7700i | −0.271822 | + | 1.42274i | ||||
\(157\) | −6.65410 | − | 11.5252i | −0.531055 | − | 0.919814i | −0.999343 | − | 0.0362382i | \(-0.988463\pi\) |
0.468288 | − | 0.883576i | \(-0.344871\pi\) | |||||||
\(158\) | −14.3198 | + | 8.26753i | −1.13922 | + | 0.657729i | ||||
\(159\) | 5.72987 | + | 2.16267i | 0.454409 | + | 0.171511i | ||||
\(160\) | −3.53565 | + | 6.12392i | −0.279517 | + | 0.484138i | ||||
\(161\) | − | 1.20263i | − | 0.0947805i | ||||||
\(162\) | 7.69013 | − | 18.3716i | 0.604194 | − | 1.44341i | ||||
\(163\) | − | 17.2668i | − | 1.35244i | −0.736699 | − | 0.676221i | \(-0.763616\pi\) | ||
0.736699 | − | 0.676221i | \(-0.236384\pi\) | |||||||
\(164\) | 8.73453 | + | 5.04288i | 0.682052 | + | 0.393783i | ||||
\(165\) | −1.98310 | − | 0.748497i | −0.154384 | − | 0.0582704i | ||||
\(166\) | 1.61702 | + | 2.80076i | 0.125505 | + | 0.217381i | ||||
\(167\) | −17.1671 | + | 9.91143i | −1.32843 | + | 0.766969i | −0.985057 | − | 0.172230i | \(-0.944903\pi\) |
−0.343373 | + | 0.939199i | \(0.611570\pi\) | |||||||
\(168\) | 2.81590 | − | 2.30656i | 0.217251 | − | 0.177955i | ||||
\(169\) | 9.91824 | + | 8.40408i | 0.762942 | + | 0.646467i | ||||
\(170\) | 2.74611 | 0.210617 | ||||||||
\(171\) | −8.40393 | + | 9.54689i | −0.642665 | + | 0.730069i | ||||
\(172\) | −14.8984 | −1.13599 | ||||||||
\(173\) | −3.56636 | + | 6.17711i | −0.271145 | + | 0.469637i | −0.969155 | − | 0.246451i | \(-0.920736\pi\) |
0.698010 | + | 0.716088i | \(0.254069\pi\) | |||||||
\(174\) | −13.1313 | + | 2.15542i | −0.995482 | + | 0.163402i | ||||
\(175\) | 0.916933 | − | 0.529392i | 0.0693136 | − | 0.0400182i | ||||
\(176\) | −1.48543 | + | 0.857613i | −0.111968 | + | 0.0646450i | ||||
\(177\) | −0.460121 | + | 0.0755258i | −0.0345848 | + | 0.00567686i | ||||
\(178\) | −18.1990 | + | 31.5217i | −1.36408 | + | 2.36265i | ||||
\(179\) | −9.02185 | −0.674325 | −0.337162 | − | 0.941447i | \(-0.609467\pi\) | ||||
−0.337162 | + | 0.941447i | \(0.609467\pi\) | |||||||
\(180\) | 2.77824 | + | 8.23482i | 0.207078 | + | 0.613788i | ||||
\(181\) | 3.08861 | 0.229575 | 0.114787 | − | 0.993390i | \(-0.463381\pi\) | ||||
0.114787 | + | 0.993390i | \(0.463381\pi\) | |||||||
\(182\) | −1.44691 | − | 8.32293i | −0.107252 | − | 0.616936i | ||||
\(183\) | 15.0336 | − | 12.3143i | 1.11132 | − | 0.910301i | ||||
\(184\) | −1.95248 | + | 1.12727i | −0.143939 | + | 0.0831032i | ||||
\(185\) | 5.79536 | + | 10.0379i | 0.426084 | + | 0.737998i | ||||
\(186\) | −7.11183 | − | 2.68427i | −0.521464 | − | 0.196820i | ||||
\(187\) | 1.31520 | + | 0.759328i | 0.0961766 | + | 0.0555276i | ||||
\(188\) | 14.0244i | 1.02284i | ||||||||
\(189\) | −0.195383 | + | 5.49813i | −0.0142120 | + | 0.399930i | ||||
\(190\) | − | 9.38187i | − | 0.680632i | ||||||
\(191\) | 10.2536 | − | 17.7598i | 0.741927 | − | 1.28506i | −0.209690 | − | 0.977768i | \(-0.567245\pi\) |
0.951617 | − | 0.307287i | \(-0.0994212\pi\) | |||||||
\(192\) | 20.8148 | + | 7.85630i | 1.50218 | + | 0.566980i | ||||
\(193\) | −4.73010 | + | 2.73093i | −0.340480 | + | 0.196576i | −0.660484 | − | 0.750840i | \(-0.729649\pi\) |
0.320004 | + | 0.947416i | \(0.396316\pi\) | |||||||
\(194\) | −4.51965 | − | 7.82826i | −0.324492 | − | 0.562036i | ||||
\(195\) | 6.13405 | + | 1.17194i | 0.439268 | + | 0.0839244i | ||||
\(196\) | 8.51556 | − | 14.7494i | 0.608254 | − | 1.05353i | ||||
\(197\) | − | 10.3771i | − | 0.739340i | −0.929163 | − | 0.369670i | \(-0.879471\pi\) | ||
0.929163 | − | 0.369670i | \(-0.120529\pi\) | |||||||
\(198\) | −1.59983 | + | 7.96527i | −0.113695 | + | 0.566067i | ||||
\(199\) | −25.1188 | −1.78062 | −0.890311 | − | 0.455354i | \(-0.849513\pi\) | ||||
−0.890311 | + | 0.455354i | \(0.849513\pi\) | |||||||
\(200\) | −1.71895 | − | 0.992434i | −0.121548 | − | 0.0701757i | ||||
\(201\) | 8.90940 | − | 1.46242i | 0.628421 | − | 0.103151i | ||||
\(202\) | 25.3444 | − | 14.6326i | 1.78323 | − | 1.02955i | ||||
\(203\) | 3.18343 | − | 1.83795i | 0.223433 | − | 0.128999i | ||||
\(204\) | −1.00857 | − | 6.14446i | −0.0706142 | − | 0.430198i | ||||
\(205\) | 1.74076 | − | 3.01508i | 0.121580 | − | 0.210582i | ||||
\(206\) | − | 4.85618i | − | 0.338346i | ||||||
\(207\) | 0.671015 | − | 3.34086i | 0.0466388 | − | 0.232206i | ||||
\(208\) | 3.87898 | − | 3.23897i | 0.268959 | − | 0.224582i | ||||
\(209\) | 2.59418 | − | 4.49326i | 0.179444 | − | 0.310805i | ||||
\(210\) | −2.57155 | − | 3.13941i | −0.177454 | − | 0.216640i | ||||
\(211\) | −5.56068 | − | 9.63138i | −0.382813 | − | 0.663052i | 0.608650 | − | 0.793439i | \(-0.291711\pi\) |
−0.991463 | + | 0.130387i | \(0.958378\pi\) | |||||||
\(212\) | 5.12172 | + | 8.87108i | 0.351761 | + | 0.609268i | ||||
\(213\) | 3.27960 | − | 8.68912i | 0.224715 | − | 0.595369i | ||||
\(214\) | 27.1421 | + | 15.6705i | 1.85539 | + | 1.07121i | ||||
\(215\) | 5.14277i | 0.350734i | ||||||||
\(216\) | 9.10941 | − | 4.83638i | 0.619817 | − | 0.329074i | ||||
\(217\) | 2.09983 | 0.142546 | ||||||||
\(218\) | 0.745376 | − | 1.29103i | 0.0504832 | − | 0.0874395i | ||||
\(219\) | 4.95380 | − | 13.1248i | 0.334747 | − | 0.886892i | ||||
\(220\) | −1.77262 | − | 3.07027i | −0.119510 | − | 0.206997i | ||||
\(221\) | −4.20079 | − | 1.54042i | −0.282576 | − | 0.103620i | ||||
\(222\) | 34.3678 | − | 28.1513i | 2.30661 | − | 1.88939i | ||||
\(223\) | 11.0073 | + | 6.35506i | 0.737102 | + | 0.425566i | 0.821015 | − | 0.570907i | \(-0.193408\pi\) |
−0.0839124 | + | 0.996473i | \(0.526742\pi\) | |||||||
\(224\) | −7.48697 | −0.500244 | ||||||||
\(225\) | 2.84258 | − | 0.959021i | 0.189506 | − | 0.0639347i | ||||
\(226\) | − | 36.4175i | − | 2.42246i | ||||||
\(227\) | −12.8509 | − | 7.41948i | −0.852945 | − | 0.492448i | 0.00869815 | − | 0.999962i | \(-0.497231\pi\) |
−0.861644 | + | 0.507514i | \(0.830565\pi\) | |||||||
\(228\) | −20.9921 | + | 3.44571i | −1.39023 | + | 0.228197i | ||||
\(229\) | 8.61681 | − | 4.97492i | 0.569415 | − | 0.328752i | −0.187501 | − | 0.982264i | \(-0.560039\pi\) |
0.756916 | + | 0.653513i | \(0.226705\pi\) | |||||||
\(230\) | 1.25678 | + | 2.17680i | 0.0828693 | + | 0.143534i | ||||
\(231\) | −0.363515 | − | 2.21462i | −0.0239175 | − | 0.145711i | ||||
\(232\) | −5.96788 | − | 3.44556i | −0.391810 | − | 0.226212i | ||||
\(233\) | 14.2054 | 0.930628 | 0.465314 | − | 0.885146i | \(-0.345941\pi\) | ||||
0.465314 | + | 0.885146i | \(0.345941\pi\) | |||||||
\(234\) | 0.624367 | − | 23.9281i | 0.0408161 | − | 1.56423i | ||||
\(235\) | 4.84110 | 0.315799 | ||||||||
\(236\) | −0.675393 | − | 0.389938i | −0.0439643 | − | 0.0253828i | ||||
\(237\) | 10.0120 | − | 8.20103i | 0.650349 | − | 0.532714i | ||||
\(238\) | 1.45377 | + | 2.51800i | 0.0942338 | + | 0.163218i | ||||
\(239\) | −7.62843 | + | 4.40428i | −0.493442 | + | 0.284889i | −0.726001 | − | 0.687693i | \(-0.758623\pi\) |
0.232559 | + | 0.972582i | \(0.425290\pi\) | |||||||
\(240\) | 0.857240 | − | 2.27121i | 0.0553346 | − | 0.146606i | ||||
\(241\) | −20.2820 | − | 11.7098i | −1.30648 | − | 0.754296i | −0.324972 | − | 0.945724i | \(-0.605355\pi\) |
−0.981507 | + | 0.191427i | \(0.938688\pi\) | |||||||
\(242\) | 21.0278i | 1.35172i | ||||||||
\(243\) | −3.61048 | + | 15.1646i | −0.231613 | + | 0.972808i | ||||
\(244\) | 32.5032 | 2.08081 | ||||||||
\(245\) | −5.09134 | − | 2.93949i | −0.325274 | − | 0.187797i | ||||
\(246\) | −12.4845 | − | 4.71212i | −0.795982 | − | 0.300434i | ||||
\(247\) | −5.26273 | + | 14.3517i | −0.334859 | + | 0.913174i | ||||
\(248\) | −1.96825 | − | 3.40910i | −0.124984 | − | 0.216478i | ||||
\(249\) | −1.60401 | − | 1.95822i | −0.101650 | − | 0.124097i | ||||
\(250\) | −1.10645 | + | 1.91643i | −0.0699782 | + | 0.121206i | ||||
\(251\) | 7.47522 | 0.471832 | 0.235916 | − | 0.971774i | \(-0.424191\pi\) | ||||
0.235916 | + | 0.971774i | \(0.424191\pi\) | |||||||
\(252\) | −6.08001 | + | 6.90690i | −0.383005 | + | 0.435094i | ||||
\(253\) | 1.39005i | 0.0873915i | ||||||||
\(254\) | 35.8672 | + | 20.7079i | 2.25051 | + | 1.29933i | ||||
\(255\) | −2.12101 | + | 0.348149i | −0.132823 | + | 0.0218020i | ||||
\(256\) | 2.95749 | + | 5.12253i | 0.184843 | + | 0.320158i | ||||
\(257\) | 1.35692 | + | 2.35025i | 0.0846420 | + | 0.146604i | 0.905239 | − | 0.424904i | \(-0.139692\pi\) |
−0.820597 | + | 0.571508i | \(0.806359\pi\) | |||||||
\(258\) | 19.4513 | − | 3.19279i | 1.21098 | − | 0.198775i | ||||
\(259\) | −6.13603 | + | 10.6279i | −0.381275 | + | 0.660387i | ||||
\(260\) | 6.69471 | + | 8.01755i | 0.415188 | + | 0.497227i | ||||
\(261\) | 9.86895 | − | 3.32955i | 0.610873 | − | 0.206094i | ||||
\(262\) | − | 32.0632i | − | 1.98087i | ||||||
\(263\) | −11.3253 | + | 19.6160i | −0.698347 | + | 1.20957i | 0.270692 | + | 0.962666i | \(0.412747\pi\) |
−0.969039 | + | 0.246907i | \(0.920586\pi\) | |||||||
\(264\) | −3.25472 | + | 2.66601i | −0.200314 | + | 0.164081i | ||||
\(265\) | 3.06221 | − | 1.76797i | 0.188110 | − | 0.108606i | ||||
\(266\) | 8.60255 | − | 4.96668i | 0.527456 | − | 0.304527i | ||||
\(267\) | 10.0601 | − | 26.6536i | 0.615667 | − | 1.63117i | ||||
\(268\) | 13.0777 | + | 7.55044i | 0.798850 | + | 0.461216i | ||||
\(269\) | −21.8510 | −1.33228 | −0.666139 | − | 0.745827i | \(-0.732054\pi\) | ||||
−0.666139 | + | 0.745827i | \(0.732054\pi\) | |||||||
\(270\) | −5.39202 | − | 10.1560i | −0.328148 | − | 0.618073i | ||||
\(271\) | 13.5318i | 0.821999i | 0.911636 | + | 0.411000i | \(0.134820\pi\) | ||||
−0.911636 | + | 0.411000i | \(0.865180\pi\) | |||||||
\(272\) | −0.869645 | + | 1.50627i | −0.0527300 | + | 0.0913310i | ||||
\(273\) | 2.17272 | + | 6.24493i | 0.131499 | + | 0.377960i | ||||
\(274\) | 1.32229 | + | 2.29026i | 0.0798822 | + | 0.138360i | ||||
\(275\) | −1.05983 | + | 0.611891i | −0.0639100 | + | 0.0368984i | ||||
\(276\) | 4.40904 | − | 3.61153i | 0.265393 | − | 0.217389i | ||||
\(277\) | −0.0155003 | + | 0.0268472i | −0.000931320 | + | 0.00161309i | −0.866491 | − | 0.499193i | \(-0.833630\pi\) |
0.865559 | + | 0.500806i | \(0.166963\pi\) | |||||||
\(278\) | − | 14.1102i | − | 0.846274i | ||||||
\(279\) | 5.83326 | + | 1.17162i | 0.349228 | + | 0.0701429i | ||||
\(280\) | − | 2.10155i | − | 0.125591i | ||||||
\(281\) | 9.91681 | + | 5.72548i | 0.591588 | + | 0.341553i | 0.765725 | − | 0.643168i | \(-0.222380\pi\) |
−0.174137 | + | 0.984721i | \(0.555714\pi\) | |||||||
\(282\) | −3.00551 | − | 18.3103i | −0.178975 | − | 1.09036i | ||||
\(283\) | −15.9080 | − | 27.5534i | −0.945631 | − | 1.63788i | −0.754484 | − | 0.656319i | \(-0.772113\pi\) |
−0.191147 | − | 0.981561i | \(-0.561221\pi\) | |||||||
\(284\) | 13.4526 | − | 7.76688i | 0.798267 | − | 0.460880i | ||||
\(285\) | 1.18943 | + | 7.24626i | 0.0704555 | + | 0.429231i | ||||
\(286\) | 1.67240 | + | 9.61996i | 0.0988909 | + | 0.568840i | ||||
\(287\) | 3.68617 | 0.217588 | ||||||||
\(288\) | −20.7985 | − | 4.17740i | −1.22556 | − | 0.246156i | ||||
\(289\) | −15.4600 | −0.909414 | ||||||||
\(290\) | −3.84141 | + | 6.65352i | −0.225575 | + | 0.390708i | ||||
\(291\) | 4.48329 | + | 5.47330i | 0.262815 | + | 0.320851i | ||||
\(292\) | 20.3200 | − | 11.7318i | 1.18914 | − | 0.686550i | ||||
\(293\) | 24.7599 | − | 14.2951i | 1.44649 | − | 0.835131i | 0.448219 | − | 0.893924i | \(-0.352059\pi\) |
0.998270 | + | 0.0587932i | \(0.0187252\pi\) | |||||||
\(294\) | −7.95702 | + | 21.0817i | −0.464063 | + | 1.22951i | ||||
\(295\) | −0.134603 | + | 0.233139i | −0.00783689 | + | 0.0135739i | ||||
\(296\) | 23.0061 | 1.33720 | ||||||||
\(297\) | 0.225831 | − | 6.35495i | 0.0131041 | − | 0.368752i | ||||
\(298\) | 36.9827 | 2.14235 | ||||||||
\(299\) | −0.701451 | − | 4.03488i | −0.0405659 | − | 0.233343i | ||||
\(300\) | 4.69441 | + | 1.77185i | 0.271032 | + | 0.102298i | ||||
\(301\) | −4.71558 | + | 2.72254i | −0.271801 | + | 0.156925i | ||||
\(302\) | 8.21495 | + | 14.2287i | 0.472717 | + | 0.818770i | ||||
\(303\) | −17.7201 | + | 14.5149i | −1.01799 | + | 0.833860i | ||||
\(304\) | 5.14605 | + | 2.97107i | 0.295146 | + | 0.170403i | ||||
\(305\) | − | 11.2198i | − | 0.642444i | ||||||
\(306\) | 2.63358 | + | 7.80605i | 0.150552 | + | 0.446242i | ||||
\(307\) | − | 4.95115i | − | 0.282577i | −0.989968 | − | 0.141289i | \(-0.954875\pi\) | ||
0.989968 | − | 0.141289i | \(-0.0451245\pi\) | |||||||
\(308\) | 1.87682 | − | 3.25075i | 0.106942 | − | 0.185229i | ||||
\(309\) | 0.615662 | + | 3.75076i | 0.0350238 | + | 0.213373i | ||||
\(310\) | −3.80077 | + | 2.19437i | −0.215869 | + | 0.124632i | ||||
\(311\) | −0.638413 | − | 1.10576i | −0.0362011 | − | 0.0627021i | 0.847357 | − | 0.531023i | \(-0.178192\pi\) |
−0.883558 | + | 0.468321i | \(0.844859\pi\) | |||||||
\(312\) | 8.10214 | − | 9.38103i | 0.458694 | − | 0.531096i | ||||
\(313\) | 7.67494 | − | 13.2934i | 0.433813 | − | 0.751387i | −0.563385 | − | 0.826195i | \(-0.690501\pi\) |
0.997198 | + | 0.0748080i | \(0.0238344\pi\) | |||||||
\(314\) | 29.4498i | 1.66195i | ||||||||
\(315\) | 2.38420 | + | 2.09876i | 0.134334 | + | 0.118252i | ||||
\(316\) | 21.6463 | 1.21770 | ||||||||
\(317\) | 1.90330 | + | 1.09887i | 0.106900 | + | 0.0617186i | 0.552497 | − | 0.833515i | \(-0.313675\pi\) |
−0.445597 | + | 0.895234i | \(0.647009\pi\) | |||||||
\(318\) | −8.58802 | − | 10.4844i | −0.481592 | − | 0.587939i | ||||
\(319\) | −3.67953 | + | 2.12438i | −0.206014 | + | 0.118942i | ||||
\(320\) | 11.1241 | − | 6.42248i | 0.621853 | − | 0.359027i | ||||
\(321\) | −22.9504 | − | 8.66234i | −1.28096 | − | 0.483485i | ||||
\(322\) | −1.33065 | + | 2.30476i | −0.0741544 | + | 0.128439i | ||||
\(323\) | − | 5.26116i | − | 0.292739i | ||||||
\(324\) | −20.7438 | + | 15.7947i | −1.15243 | + | 0.877485i | ||||
\(325\) | 2.76758 | − | 2.31095i | 0.153518 | − | 0.128188i | ||||
\(326\) | −19.1049 | + | 33.0907i | −1.05812 | + | 1.83273i | ||||
\(327\) | −0.412029 | + | 1.09165i | −0.0227853 | + | 0.0603683i | ||||
\(328\) | −3.45517 | − | 5.98453i | −0.190780 | − | 0.330440i | ||||
\(329\) | 2.56284 | + | 4.43897i | 0.141294 | + | 0.244728i | ||||
\(330\) | 2.97230 | + | 3.62865i | 0.163620 | + | 0.199751i | ||||
\(331\) | 11.9839 | + | 6.91890i | 0.658694 | + | 0.380297i | 0.791779 | − | 0.610807i | \(-0.209155\pi\) |
−0.133085 | + | 0.991105i | \(0.542488\pi\) | |||||||
\(332\) | − | 4.23374i | − | 0.232357i | ||||||
\(333\) | −22.9756 | + | 26.1003i | −1.25905 | + | 1.43029i | ||||
\(334\) | 43.8661 | 2.40025 | ||||||||
\(335\) | 2.60634 | − | 4.51431i | 0.142400 | − | 0.246643i | ||||
\(336\) | 2.53636 | − | 0.416327i | 0.138370 | − | 0.0227125i | ||||
\(337\) | 6.57730 | + | 11.3922i | 0.358289 | + | 0.620574i | 0.987675 | − | 0.156518i | \(-0.0500271\pi\) |
−0.629386 | + | 0.777092i | \(0.716694\pi\) | |||||||
\(338\) | −9.70893 | − | 27.0799i | −0.528096 | − | 1.47295i | ||||
\(339\) | 4.61698 | + | 28.1277i | 0.250760 | + | 1.52769i | ||||
\(340\) | −3.11334 | − | 1.79749i | −0.168845 | − | 0.0974825i | ||||
\(341\) | −2.42707 | −0.131433 | ||||||||
\(342\) | 26.6687 | − | 8.99741i | 1.44208 | − | 0.486524i | ||||
\(343\) | − | 13.6360i | − | 0.736277i | ||||||
\(344\) | 8.84015 | + | 5.10386i | 0.476629 | + | 0.275182i | ||||
\(345\) | −1.24667 | − | 1.52196i | −0.0671183 | − | 0.0819395i | ||||
\(346\) | 13.6694 | − | 7.89201i | 0.734870 | − | 0.424277i | ||||
\(347\) | −0.354154 | − | 0.613413i | −0.0190120 | − | 0.0329297i | 0.856363 | − | 0.516374i | \(-0.172719\pi\) |
−0.875375 | + | 0.483445i | \(0.839385\pi\) | |||||||
\(348\) | 16.2982 | + | 6.15155i | 0.873674 | + | 0.329758i | ||||
\(349\) | −21.1121 | − | 12.1891i | −1.13010 | − | 0.652466i | −0.186143 | − | 0.982523i | \(-0.559599\pi\) |
−0.943961 | + | 0.330057i | \(0.892932\pi\) | |||||||
\(350\) | −2.34299 | −0.125238 | ||||||||
\(351\) | 2.55134 | + | 18.5605i | 0.136180 | + | 0.990684i | ||||
\(352\) | 8.65373 | 0.461245 | ||||||||
\(353\) | −19.1694 | − | 11.0675i | −1.02029 | − | 0.589063i | −0.106100 | − | 0.994356i | \(-0.533836\pi\) |
−0.914187 | + | 0.405293i | \(0.867170\pi\) | |||||||
\(354\) | 0.965356 | + | 0.364362i | 0.0513081 | + | 0.0193656i | ||||
\(355\) | −2.68105 | − | 4.64372i | −0.142296 | − | 0.246463i | ||||
\(356\) | 41.2655 | − | 23.8247i | 2.18707 | − | 1.26270i | ||||
\(357\) | −1.44207 | − | 1.76052i | −0.0763227 | − | 0.0931764i | ||||
\(358\) | 17.2898 | + | 9.98225i | 0.913793 | + | 0.527578i | ||||
\(359\) | − | 2.42368i | − | 0.127917i | −0.997953 | − | 0.0639586i | \(-0.979627\pi\) | ||
0.997953 | − | 0.0639586i | \(-0.0203725\pi\) | |||||||
\(360\) | 1.17257 | − | 5.83801i | 0.0617999 | − | 0.307690i | ||||
\(361\) | 1.02566 | 0.0539819 | ||||||||
\(362\) | −5.91911 | − | 3.41740i | −0.311102 | − | 0.179615i | ||||
\(363\) | −2.66589 | − | 16.2412i | −0.139923 | − | 0.852443i | ||||
\(364\) | −3.80744 | + | 10.3830i | −0.199564 | + | 0.544218i | ||||
\(365\) | −4.04970 | − | 7.01428i | −0.211971 | − | 0.367144i | ||||
\(366\) | −42.4361 | + | 6.96560i | −2.21817 | + | 0.364098i | ||||
\(367\) | −0.0405583 | + | 0.0702491i | −0.00211713 | + | 0.00366697i | −0.867082 | − | 0.498165i | \(-0.834007\pi\) |
0.864965 | + | 0.501832i | \(0.167341\pi\) | |||||||
\(368\) | −1.59199 | −0.0829885 | ||||||||
\(369\) | 10.2400 | + | 2.05672i | 0.533075 | + | 0.107069i | ||||
\(370\) | − | 25.6492i | − | 1.33344i | ||||||
\(371\) | 3.24222 | + | 1.87190i | 0.168328 | + | 0.0971840i | ||||
\(372\) | 6.30586 | + | 7.69834i | 0.326944 | + | 0.399140i | ||||
\(373\) | 4.12234 | + | 7.14011i | 0.213447 | + | 0.369701i | 0.952791 | − | 0.303627i | \(-0.0981977\pi\) |
−0.739344 | + | 0.673328i | \(0.764864\pi\) | |||||||
\(374\) | −1.68032 | − | 2.91040i | −0.0868874 | − | 0.150493i | ||||
\(375\) | 0.611626 | − | 1.62047i | 0.0315842 | − | 0.0836806i | ||||
\(376\) | 4.80447 | − | 8.32159i | 0.247772 | − | 0.429153i | ||||
\(377\) | 9.60856 | − | 8.02321i | 0.494866 | − | 0.413216i | ||||
\(378\) | 6.45786 | − | 10.3206i | 0.332156 | − | 0.530835i | ||||
\(379\) | 28.1019i | 1.44350i | 0.692154 | + | 0.721749i | \(0.256662\pi\) | ||||
−0.692154 | + | 0.721749i | \(0.743338\pi\) | |||||||
\(380\) | −6.14098 | + | 10.6365i | −0.315026 | + | 0.545640i | ||||
\(381\) | −30.3280 | − | 11.4469i | −1.55375 | − | 0.586445i | ||||
\(382\) | −39.3008 | + | 22.6903i | −2.01080 | + | 1.16094i | ||||
\(383\) | 6.71744 | − | 3.87831i | 0.343245 | − | 0.198173i | −0.318461 | − | 0.947936i | \(-0.603166\pi\) |
0.661706 | + | 0.749763i | \(0.269833\pi\) | |||||||
\(384\) | −15.6753 | − | 19.1368i | −0.799929 | − | 0.976571i | ||||
\(385\) | −1.12213 | − | 0.647860i | −0.0571889 | − | 0.0330180i | ||||
\(386\) | 12.0866 | 0.615190 | ||||||||
\(387\) | −14.6188 | + | 4.93203i | −0.743113 | + | 0.250709i | ||||
\(388\) | 11.8335i | 0.600754i | ||||||||
\(389\) | 14.9645 | − | 25.9193i | 0.758732 | − | 1.31416i | −0.184765 | − | 0.982783i | \(-0.559152\pi\) |
0.943497 | − | 0.331380i | \(-0.107514\pi\) | |||||||
\(390\) | −10.4588 | − | 9.03298i | −0.529602 | − | 0.457403i | ||||
\(391\) | 0.704774 | + | 1.22070i | 0.0356420 | + | 0.0617337i | ||||
\(392\) | −10.1056 | + | 5.83450i | −0.510412 | + | 0.294687i | ||||
\(393\) | 4.06495 | + | 24.7646i | 0.205049 | + | 1.24921i | ||||
\(394\) | −11.4818 | + | 19.8871i | −0.578445 | + | 1.00190i | ||||
\(395\) | − | 7.47210i | − | 0.375962i | ||||||
\(396\) | 7.02751 | − | 7.98327i | 0.353146 | − | 0.401174i | ||||
\(397\) | − | 36.7191i | − | 1.84288i | −0.388524 | − | 0.921439i | \(-0.627015\pi\) | ||
0.388524 | − | 0.921439i | \(-0.372985\pi\) | |||||||
\(398\) | 48.1384 | + | 27.7927i | 2.41296 | + | 1.39312i | ||||
\(399\) | −6.01467 | + | 4.92673i | −0.301110 | + | 0.246645i | ||||
\(400\) | −0.700788 | − | 1.21380i | −0.0350394 | − | 0.0606900i | ||||
\(401\) | 18.1252 | − | 10.4646i | 0.905127 | − | 0.522576i | 0.0262672 | − | 0.999655i | \(-0.491638\pi\) |
0.878860 | + | 0.477079i | \(0.158305\pi\) | |||||||
\(402\) | −18.6924 | − | 7.05521i | −0.932290 | − | 0.351882i | ||||
\(403\) | 7.04505 | − | 1.22476i | 0.350939 | − | 0.0610095i | ||||
\(404\) | −38.3116 | −1.90607 | ||||||||
\(405\) | 5.45219 | + | 7.16056i | 0.270922 | + | 0.355811i | ||||
\(406\) | −8.13444 | −0.403705 | ||||||||
\(407\) | 7.09227 | − | 12.2842i | 0.351551 | − | 0.608904i | ||||
\(408\) | −1.50651 | + | 3.99142i | −0.0745835 | + | 0.197605i | ||||
\(409\) | −17.5031 | + | 10.1054i | −0.865471 | + | 0.499680i | −0.865840 | − | 0.500320i | \(-0.833216\pi\) |
0.000369696 | 1.00000i | \(0.499882\pi\) | ||||||||
\(410\) | −6.67208 | + | 3.85213i | −0.329511 | + | 0.190243i | ||||
\(411\) | −1.31165 | − | 1.60129i | −0.0646989 | − | 0.0789858i | ||||
\(412\) | −3.17865 | + | 5.50559i | −0.156601 | + | 0.271241i | ||||
\(413\) | −0.285031 | −0.0140254 | ||||||||
\(414\) | −4.98246 | + | 5.66009i | −0.244875 | + | 0.278178i | ||||
\(415\) | −1.46145 | −0.0717396 | ||||||||
\(416\) | −25.1192 | + | 4.36688i | −1.23157 | + | 0.214104i | ||||
\(417\) | 1.78888 | + | 10.8983i | 0.0876018 | + | 0.533691i | ||||
\(418\) | −9.94316 | + | 5.74069i | −0.486336 | + | 0.280786i | ||||
\(419\) | 14.1445 | + | 24.4990i | 0.691004 | + | 1.19685i | 0.971509 | + | 0.237002i | \(0.0761647\pi\) |
−0.280505 | + | 0.959852i | \(0.590502\pi\) | |||||||
\(420\) | 0.860516 | + | 5.24247i | 0.0419889 | + | 0.255806i | ||||
\(421\) | −18.6160 | − | 10.7480i | −0.907289 | − | 0.523824i | −0.0277313 | − | 0.999615i | \(-0.508828\pi\) |
−0.879558 | + | 0.475792i | \(0.842162\pi\) | |||||||
\(422\) | 24.6105i | 1.19802i | ||||||||
\(423\) | 4.64272 | + | 13.7612i | 0.225737 | + | 0.669094i | ||||
\(424\) | − | 7.01837i | − | 0.340842i | ||||||
\(425\) | −0.620476 | + | 1.07470i | −0.0300975 | + | 0.0521304i | ||||
\(426\) | −15.8992 | + | 13.0234i | −0.770321 | + | 0.630985i | ||||
\(427\) | 10.2878 | − | 5.93967i | 0.497862 | − | 0.287441i | ||||
\(428\) | −20.5145 | − | 35.5321i | −0.991605 | − | 1.71751i | ||||
\(429\) | −2.51132 | − | 7.21813i | −0.121248 | − | 0.348495i | ||||
\(430\) | 5.69024 | − | 9.85578i | 0.274408 | − | 0.475288i | ||||
\(431\) | 34.6370i | 1.66841i | 0.551457 | + | 0.834204i | \(0.314072\pi\) | ||||
−0.551457 | + | 0.834204i | \(0.685928\pi\) | |||||||
\(432\) | 7.27821 | + | 0.258640i | 0.350173 | + | 0.0124438i | ||||
\(433\) | 36.2199 | 1.74062 | 0.870308 | − | 0.492508i | \(-0.163920\pi\) | ||||
0.870308 | + | 0.492508i | \(0.163920\pi\) | |||||||
\(434\) | −4.02419 | − | 2.32337i | −0.193167 | − | 0.111525i | ||||
\(435\) | 2.12346 | − | 5.62598i | 0.101812 | − | 0.269745i | ||||
\(436\) | −1.69011 | + | 0.975784i | −0.0809415 | + | 0.0467316i | ||||
\(437\) | 4.17044 | − | 2.40781i | 0.199499 | − | 0.115181i | ||||
\(438\) | −24.0156 | + | 19.6716i | −1.14751 | + | 0.939948i | ||||
\(439\) | 3.62173 | − | 6.27302i | 0.172856 | − | 0.299395i | −0.766561 | − | 0.642171i | \(-0.778034\pi\) |
0.939417 | + | 0.342776i | \(0.111367\pi\) | |||||||
\(440\) | 2.42905i | 0.115800i | ||||||||
\(441\) | 3.47304 | − | 17.2916i | 0.165383 | − | 0.823410i | ||||
\(442\) | 6.34612 | + | 7.60009i | 0.301854 | + | 0.361499i | ||||
\(443\) | −13.9973 | + | 24.2440i | −0.665031 | + | 1.15187i | 0.314246 | + | 0.949341i | \(0.398248\pi\) |
−0.979277 | + | 0.202525i | \(0.935085\pi\) | |||||||
\(444\) | −57.3904 | + | 9.42025i | −2.72363 | + | 0.447065i | ||||
\(445\) | −8.22405 | − | 14.2445i | −0.389857 | − | 0.675253i | ||||
\(446\) | −14.0631 | − | 24.3581i | −0.665909 | − | 1.15339i | ||||
\(447\) | −28.5643 | + | 4.68863i | −1.35104 | + | 0.221765i | ||||
\(448\) | 11.7780 | + | 6.80001i | 0.556456 | + | 0.321270i | ||||
\(449\) | − | 32.0442i | − | 1.51226i | −0.654421 | − | 0.756130i | \(-0.727088\pi\) | ||
0.654421 | − | 0.756130i | \(-0.272912\pi\) | |||||||
\(450\) | −6.50873 | − | 1.30729i | −0.306824 | − | 0.0616260i | ||||
\(451\) | −4.26061 | −0.200625 | ||||||||
\(452\) | −23.8374 | + | 41.2875i | −1.12122 | + | 1.94200i | ||||
\(453\) | −8.14887 | − | 9.94832i | −0.382867 | − | 0.467413i | ||||
\(454\) | 16.4186 | + | 28.4379i | 0.770564 | + | 1.33466i | ||||
\(455\) | 3.58412 | + | 1.31429i | 0.168026 | + | 0.0616149i | ||||
\(456\) | 13.6364 | + | 5.14688i | 0.638581 | + | 0.241025i | ||||
\(457\) | −22.0113 | − | 12.7083i | −1.02965 | − | 0.594467i | −0.112763 | − | 0.993622i | \(-0.535970\pi\) |
−0.916883 | + | 0.399155i | \(0.869304\pi\) | |||||||
\(458\) | −22.0180 | −1.02884 | ||||||||
\(459\) | −3.02374 | − | 5.69526i | −0.141136 | − | 0.265832i | ||||
\(460\) | − | 3.29053i | − | 0.153422i | ||||||
\(461\) | 7.27198 | + | 4.19848i | 0.338690 | + | 0.195543i | 0.659692 | − | 0.751536i | \(-0.270687\pi\) |
−0.321003 | + | 0.947078i | \(0.604020\pi\) | |||||||
\(462\) | −1.75372 | + | 4.64638i | −0.0815904 | + | 0.216169i | ||||
\(463\) | 13.3439 | − | 7.70412i | 0.620145 | − | 0.358041i | −0.156780 | − | 0.987634i | \(-0.550111\pi\) |
0.776926 | + | 0.629592i | \(0.216778\pi\) | |||||||
\(464\) | −2.43301 | − | 4.21410i | −0.112950 | − | 0.195635i | ||||
\(465\) | 2.65739 | − | 2.17672i | 0.123234 | − | 0.100943i | ||||
\(466\) | −27.2237 | − | 15.7176i | −1.26112 | − | 0.728105i | ||||
\(467\) | 30.0028 | 1.38836 | 0.694182 | − | 0.719800i | \(-0.255766\pi\) | ||||
0.694182 | + | 0.719800i | \(0.255766\pi\) | |||||||
\(468\) | −16.3702 | + | 26.7193i | −0.756712 | + | 1.23510i | ||||
\(469\) | 5.51910 | 0.254848 | ||||||||
\(470\) | −9.27764 | − | 5.35645i | −0.427946 | − | 0.247075i | ||||
\(471\) | −3.73362 | − | 22.7461i | −0.172036 | − | 1.04808i | ||||
\(472\) | 0.267169 | + | 0.462750i | 0.0122975 | + | 0.0212998i | ||||
\(473\) | 5.45045 | − | 3.14682i | 0.250612 | − | 0.144691i | ||||
\(474\) | −28.2614 | + | 4.63891i | −1.29809 | + | 0.213072i | ||||
\(475\) | 3.67162 | + | 2.11981i | 0.168465 | + | 0.0972635i | ||||
\(476\) | − | 3.80630i | − | 0.174462i | ||||||
\(477\) | 7.96233 | + | 7.00908i | 0.364570 | + | 0.320924i | ||||
\(478\) | 19.4925 | 0.891566 | ||||||||
\(479\) | −0.742880 | − | 0.428902i | −0.0339431 | − | 0.0195970i | 0.482932 | − | 0.875658i | \(-0.339572\pi\) |
−0.516876 | + | 0.856061i | \(0.672905\pi\) | |||||||
\(480\) | −9.47495 | + | 7.76112i | −0.432470 | + | 0.354245i | ||||
\(481\) | −14.3878 | + | 39.2361i | −0.656028 | + | 1.78901i | ||||
\(482\) | 25.9127 | + | 44.8822i | 1.18029 | + | 2.04433i | ||||
\(483\) | 0.735559 | − | 1.94882i | 0.0334691 | − | 0.0886745i | ||||
\(484\) | 13.7639 | − | 23.8398i | 0.625633 | − | 1.08363i | ||||
\(485\) | 4.08481 | 0.185482 | ||||||||
\(486\) | 23.6981 | − | 25.0671i | 1.07497 | − | 1.13706i | ||||
\(487\) | 19.2888i | 0.874058i | 0.899448 | + | 0.437029i | \(0.143969\pi\) | ||||
−0.899448 | + | 0.437029i | \(0.856031\pi\) | |||||||
\(488\) | −19.2862 | − | 11.1349i | −0.873047 | − | 0.504054i | ||||
\(489\) | 10.5608 | − | 27.9803i | 0.477578 | − | 1.26531i | ||||
\(490\) | 6.50481 | + | 11.2667i | 0.293857 | + | 0.508976i | ||||
\(491\) | −8.18301 | − | 14.1734i | −0.369294 | − | 0.639636i | 0.620161 | − | 0.784474i | \(-0.287067\pi\) |
−0.989455 | + | 0.144838i | \(0.953734\pi\) | |||||||
\(492\) | 11.0697 | + | 13.5141i | 0.499059 | + | 0.609262i | ||||
\(493\) | −2.15418 | + | 3.73116i | −0.0970196 | + | 0.168043i | ||||
\(494\) | 25.9651 | − | 21.6810i | 1.16822 | − | 0.975476i | ||||
\(495\) | −2.75575 | − | 2.42583i | −0.123862 | − | 0.109033i | ||||
\(496\) | − | 2.77968i | − | 0.124811i | ||||||
\(497\) | 2.83866 | − | 4.91670i | 0.127331 | − | 0.220544i | ||||
\(498\) | 0.907311 | + | 5.52756i | 0.0406576 | + | 0.247696i | ||||
\(499\) | −23.1110 | + | 13.3432i | −1.03459 | + | 0.597322i | −0.918297 | − | 0.395892i | \(-0.870435\pi\) |
−0.116296 | + | 0.993215i | \(0.537102\pi\) | |||||||
\(500\) | 2.50883 | − | 1.44848i | 0.112198 | − | 0.0647778i | ||||
\(501\) | −33.8808 | + | 5.56131i | −1.51368 | + | 0.248461i | ||||
\(502\) | −14.3258 | − | 8.27098i | −0.639390 | − | 0.369152i | ||||
\(503\) | −29.6619 | −1.32256 | −0.661280 | − | 0.750139i | \(-0.729987\pi\) | ||||
−0.661280 | + | 0.750139i | \(0.729987\pi\) | |||||||
\(504\) | 5.97382 | − | 2.01543i | 0.266095 | − | 0.0897742i | ||||
\(505\) | 13.2248i | 0.588495i | ||||||||
\(506\) | 1.53802 | − | 2.66393i | 0.0683734 | − | 0.118426i | ||||
\(507\) | 10.9320 | + | 19.6848i | 0.485509 | + | 0.874232i | ||||
\(508\) | −27.1091 | − | 46.9543i | −1.20277 | − | 2.08326i | ||||
\(509\) | −4.38296 | + | 2.53051i | −0.194271 | + | 0.112163i | −0.593981 | − | 0.804479i | \(-0.702444\pi\) |
0.399709 | + | 0.916642i | \(0.369111\pi\) | |||||||
\(510\) | 4.44998 | + | 1.67959i | 0.197049 | + | 0.0743736i | ||||
\(511\) | 4.28775 | − | 7.42660i | 0.189679 | − | 0.328533i | ||||
\(512\) | 15.4748i | 0.683898i | ||||||||
\(513\) | −19.4574 | + | 10.3304i | −0.859066 | + | 0.456096i | ||||
\(514\) | − | 6.00545i | − | 0.264889i | ||||||
\(515\) | 1.90048 | + | 1.09724i | 0.0837450 | + | 0.0483502i | ||||
\(516\) | −24.1423 | − | 9.11222i | −1.06281 | − | 0.401143i | ||||
\(517\) | −2.96223 | − | 5.13073i | −0.130279 | − | 0.225649i | ||||
\(518\) | 23.5186 | − | 13.5785i | 1.03335 | − | 0.596603i | ||||
\(519\) | −9.55725 | + | 7.82853i | −0.419517 | + | 0.343634i | ||||
\(520\) | −1.22576 | − | 7.05079i | −0.0537529 | − | 0.309198i | ||||
\(521\) | 14.4458 | 0.632881 | 0.316441 | − | 0.948612i | \(-0.397512\pi\) | ||||
0.316441 | + | 0.948612i | \(0.397512\pi\) | |||||||
\(522\) | −22.5972 | − | 4.53867i | −0.989051 | − | 0.198652i | ||||
\(523\) | 29.4092 | 1.28597 | 0.642987 | − | 0.765877i | \(-0.277695\pi\) | ||||
0.642987 | + | 0.765877i | \(0.277695\pi\) | |||||||
\(524\) | −20.9872 | + | 36.3510i | −0.916832 | + | 1.58800i | ||||
\(525\) | 1.80965 | − | 0.297042i | 0.0789796 | − | 0.0129640i | ||||
\(526\) | 43.4083 | − | 25.0618i | 1.89269 | − | 1.09275i | ||||
\(527\) | −2.13139 | + | 1.23056i | −0.0928450 | + | 0.0536041i | ||||
\(528\) | −2.93163 | + | 0.481207i | −0.127583 | + | 0.0209418i | ||||
\(529\) | 10.8549 | − | 18.8013i | 0.471953 | − | 0.817446i | ||||
\(530\) | −7.82470 | −0.339883 | ||||||||
\(531\) | −0.791804 | − | 0.159035i | −0.0343614 | − | 0.00690152i | ||||
\(532\) | −13.0039 | −0.563792 | ||||||||
\(533\) | 12.3673 | − | 2.15001i | 0.535686 | − | 0.0931272i | ||||
\(534\) | −48.7704 | + | 39.9488i | −2.11050 | + | 1.72875i | ||||
\(535\) | −12.2654 | + | 7.08140i | −0.530277 | + | 0.306156i | ||||
\(536\) | −5.17324 | − | 8.96032i | −0.223450 | − | 0.387027i | ||||
\(537\) | −14.6196 | − | 5.51800i | −0.630883 | − | 0.238119i | ||||
\(538\) | 41.8759 | + | 24.1771i | 1.80540 | + | 1.04235i | ||||
\(539\) | 7.19459i | 0.309893i | ||||||||
\(540\) | −0.534590 | + | 15.0435i | −0.0230051 | + | 0.647369i | ||||
\(541\) | 27.4422i | 1.17983i | 0.807465 | + | 0.589915i | \(0.200839\pi\) | ||||
−0.807465 | + | 0.589915i | \(0.799161\pi\) | |||||||
\(542\) | 14.9723 | − | 25.9328i | 0.643116 | − | 1.11391i | ||||
\(543\) | 5.00499 | + | 1.88907i | 0.214785 | + | 0.0810679i | ||||
\(544\) | 7.59949 | − | 4.38757i | 0.325826 | − | 0.188115i | ||||
\(545\) | 0.336831 | + | 0.583409i | 0.0144283 | + | 0.0249905i | ||||
\(546\) | 2.74584 | − | 14.3720i | 0.117511 | − | 0.615065i | ||||
\(547\) | −10.0951 | + | 17.4852i | −0.431635 | + | 0.747614i | −0.997014 | − | 0.0772173i | \(-0.975396\pi\) |
0.565379 | + | 0.824831i | \(0.308730\pi\) | |||||||
\(548\) | − | 3.46205i | − | 0.147891i | ||||||
\(549\) | 31.8932 | − | 10.7600i | 1.36117 | − | 0.459227i | ||||
\(550\) | 2.70812 | 0.115474 | ||||||||
\(551\) | 12.7472 | + | 7.35960i | 0.543049 | + | 0.313530i | ||||
\(552\) | −3.85340 | + | 0.632510i | −0.164012 | + | 0.0269214i | ||||
\(553\) | 6.85142 | − | 3.95567i | 0.291352 | − | 0.168212i | ||||
\(554\) | 0.0594104 | − | 0.0343006i | 0.00252411 | − | 0.00145729i | ||||
\(555\) | 3.25178 | + | 19.8106i | 0.138030 | + | 0.840914i | ||||
\(556\) | −9.23595 | + | 15.9971i | −0.391692 | + | 0.678430i | ||||
\(557\) | − | 4.02815i | − | 0.170678i | −0.996352 | − | 0.0853391i | \(-0.972803\pi\) | ||
0.996352 | − | 0.0853391i | \(-0.0271974\pi\) | |||||||
\(558\) | −9.88271 | − | 8.69955i | −0.418368 | − | 0.368281i | ||||
\(559\) | −14.2330 | + | 11.8847i | −0.601994 | + | 0.502669i | ||||
\(560\) | 0.741983 | − | 1.28515i | 0.0313545 | − | 0.0543076i | ||||
\(561\) | 1.66681 | + | 2.03487i | 0.0703726 | + | 0.0859124i | ||||
\(562\) | −12.6699 | − | 21.9450i | −0.534449 | − | 0.925693i | ||||
\(563\) | −18.1141 | − | 31.3746i | −0.763419 | − | 1.32228i | −0.941078 | − | 0.338188i | \(-0.890186\pi\) |
0.177659 | − | 0.984092i | \(-0.443147\pi\) | |||||||
\(564\) | −8.57770 | + | 22.7261i | −0.361186 | + | 0.956943i | ||||
\(565\) | 14.2521 | + | 8.22843i | 0.599589 | + | 0.346173i | ||||
\(566\) | 70.4057i | 2.95937i | ||||||||
\(567\) | −3.67941 | + | 8.79004i | −0.154521 | + | 0.369147i | ||||
\(568\) | −10.6431 | −0.446574 | ||||||||
\(569\) | 4.33283 | − | 7.50468i | 0.181642 | − | 0.314613i | −0.760798 | − | 0.648989i | \(-0.775192\pi\) |
0.942440 | + | 0.334376i | \(0.108526\pi\) | |||||||
\(570\) | 5.73819 | − | 15.2030i | 0.240346 | − | 0.636784i | ||||
\(571\) | 19.0500 | + | 32.9956i | 0.797219 | + | 1.38082i | 0.921421 | + | 0.388567i | \(0.127030\pi\) |
−0.124202 | + | 0.992257i | \(0.539637\pi\) | |||||||
\(572\) | 4.40078 | − | 12.0011i | 0.184006 | − | 0.501791i | ||||
\(573\) | 27.4780 | − | 22.5078i | 1.14791 | − | 0.940277i | ||||
\(574\) | −7.06429 | − | 4.07857i | −0.294858 | − | 0.170236i | ||||
\(575\) | −1.13586 | −0.0473686 | ||||||||
\(576\) | 28.9246 | + | 25.4618i | 1.20519 | + | 1.06091i | ||||
\(577\) | − | 4.98879i | − | 0.207686i | −0.994594 | − | 0.103843i | \(-0.966886\pi\) | ||
0.994594 | − | 0.103843i | \(-0.0331140\pi\) | |||||||
\(578\) | 29.6281 | + | 17.1058i | 1.23237 | + | 0.711508i | ||||
\(579\) | −9.33528 | + | 1.53232i | −0.387961 | + | 0.0636812i | ||||
\(580\) | 8.71023 | − | 5.02885i | 0.361673 | − | 0.208812i | ||||
\(581\) | −0.773678 | − | 1.34005i | −0.0320976 | − | 0.0555946i | ||||
\(582\) | −2.53598 | − | 15.4498i | −0.105120 | − | 0.640413i | ||||
\(583\) | −3.74748 | − | 2.16361i | −0.155205 | − | 0.0896076i | ||||
\(584\) | −16.0762 | −0.665239 | ||||||||
\(585\) | 9.22324 | + | 5.65083i | 0.381334 | + | 0.233633i | ||||
\(586\) | −63.2676 | −2.61356 | ||||||||
\(587\) | 30.8788 | + | 17.8279i | 1.27450 | + | 0.735835i | 0.975832 | − | 0.218521i | \(-0.0701232\pi\) |
0.298671 | + | 0.954356i | \(0.403457\pi\) | |||||||
\(588\) | 22.8203 | − | 18.6925i | 0.941092 | − | 0.770868i | ||||
\(589\) | 4.20411 | + | 7.28174i | 0.173228 | + | 0.300039i | ||||
\(590\) | 0.515915 | − | 0.297864i | 0.0212399 | − | 0.0122628i | ||||
\(591\) | 6.34692 | − | 16.8158i | 0.261078 | − | 0.691710i | ||||
\(592\) | 14.0688 | + | 8.12264i | 0.578225 | + | 0.333839i | ||||
\(593\) | 4.39457i | 0.180463i | 0.995921 | + | 0.0902317i | \(0.0287608\pi\) | ||||
−0.995921 | + | 0.0902317i | \(0.971239\pi\) | |||||||
\(594\) | −7.46424 | + | 11.9290i | −0.306262 | + | 0.489451i | ||||
\(595\) | −1.31390 | −0.0538646 | ||||||||
\(596\) | −41.9283 | − | 24.2073i | −1.71745 | − | 0.991571i | ||||
\(597\) | −40.7041 | − | 15.3633i | −1.66591 | − | 0.628777i | ||||
\(598\) | −3.12013 | + | 8.50870i | −0.127591 | + | 0.347947i | ||||
\(599\) | −19.6062 | − | 33.9589i | −0.801088 | − | 1.38752i | −0.918901 | − | 0.394489i | \(-0.870922\pi\) |
0.117813 | − | 0.993036i | \(-0.462412\pi\) | |||||||
\(600\) | −2.17850 | − | 2.65956i | −0.0889368 | − | 0.108576i | ||||
\(601\) | 17.9811 | − | 31.1443i | 0.733466 | − | 1.27040i | −0.221927 | − | 0.975063i | \(-0.571235\pi\) |
0.955393 | − | 0.295338i | \(-0.0954321\pi\) | |||||||
\(602\) | 12.0495 | 0.491099 | ||||||||
\(603\) | 15.3318 | + | 3.07942i | 0.624361 | + | 0.125404i | ||||
\(604\) | − | 21.5087i | − | 0.875175i | ||||||
\(605\) | −8.22928 | − | 4.75118i | −0.334568 | − | 0.193163i | ||||
\(606\) | 50.0195 | − | 8.21036i | 2.03190 | − | 0.333523i | ||||
\(607\) | −6.31059 | − | 10.9303i | −0.256139 | − | 0.443645i | 0.709065 | − | 0.705143i | \(-0.249117\pi\) |
−0.965204 | + | 0.261497i | \(0.915784\pi\) | |||||||
\(608\) | −14.9898 | − | 25.9631i | −0.607916 | − | 1.05294i | ||||
\(609\) | 6.28279 | − | 1.03128i | 0.254591 | − | 0.0417895i | ||||
\(610\) | −12.4142 | + | 21.5020i | −0.502635 | + | 0.870590i | ||||
\(611\) | 11.1875 | + | 13.3981i | 0.452599 | + | 0.542031i | ||||
\(612\) | 2.12375 | − | 10.5738i | 0.0858476 | − | 0.427419i | ||||
\(613\) | 13.6583i | 0.551652i | 0.961208 | + | 0.275826i | \(0.0889513\pi\) | ||||
−0.961208 | + | 0.275826i | \(0.911049\pi\) | |||||||
\(614\) | −5.47821 | + | 9.48854i | −0.221083 | + | 0.382926i | ||||
\(615\) | 4.66494 | − | 3.82114i | 0.188108 | − | 0.154083i | ||||
\(616\) | −2.22727 | + | 1.28592i | −0.0897395 | + | 0.0518111i | ||||
\(617\) | −10.1696 | + | 5.87142i | −0.409413 | + | 0.236375i | −0.690537 | − | 0.723297i | \(-0.742626\pi\) |
0.281125 | + | 0.959671i | \(0.409293\pi\) | |||||||
\(618\) | 2.97016 | − | 7.86928i | 0.119478 | − | 0.316549i | ||||
\(619\) | 15.4901 | + | 8.94321i | 0.622600 | + | 0.359458i | 0.777880 | − | 0.628412i | \(-0.216295\pi\) |
−0.155281 | + | 0.987870i | \(0.549628\pi\) | |||||||
\(620\) | 5.74538 | 0.230740 | ||||||||
\(621\) | 3.13071 | − | 5.00334i | 0.125631 | − | 0.200777i | ||||
\(622\) | 2.82550i | 0.113292i | ||||||||
\(623\) | 8.70749 | − | 15.0818i | 0.348858 | − | 0.604240i | ||||
\(624\) | 8.26680 | − | 2.87617i | 0.330937 | − | 0.115139i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −29.4170 | + | 16.9839i | −1.17574 | + | 0.678814i | ||||
\(627\) | 6.95199 | − | 5.69451i | 0.277636 | − | 0.227417i | ||||
\(628\) | 19.2766 | − | 33.3880i | 0.769220 | − | 1.33233i | ||||
\(629\) | − | 14.3835i | − | 0.573509i | ||||||
\(630\) | −2.24697 | − | 6.66014i | −0.0895216 | − | 0.265346i | ||||
\(631\) | 40.4209i | 1.60913i | 0.593864 | + | 0.804565i | \(0.297602\pi\) | ||||
−0.593864 | + | 0.804565i | \(0.702398\pi\) | |||||||
\(632\) | −12.8441 | − | 7.41557i | −0.510913 | − | 0.294976i | ||||
\(633\) | −3.12010 | − | 19.0084i | −0.124013 | − | 0.755516i | ||||
\(634\) | −2.43169 | − | 4.21181i | −0.0965748 | − | 0.167272i | ||||
\(635\) | −16.2082 | + | 9.35780i | −0.643202 | + | 0.371353i | ||||
\(636\) | 2.87380 | + | 17.5079i | 0.113954 | + | 0.694232i | ||||
\(637\) | −3.63056 | − | 20.8837i | −0.143848 | − | 0.827443i | ||||
\(638\) | 9.40210 | 0.372233 | ||||||||
\(639\) | 10.6290 | − | 12.0745i | 0.420476 | − | 0.477662i | ||||
\(640\) | −14.2821 | −0.564549 | ||||||||
\(641\) | 17.7262 | − | 30.7027i | 0.700143 | − | 1.21268i | −0.268273 | − | 0.963343i | \(-0.586453\pi\) |
0.968416 | − | 0.249340i | \(-0.0802137\pi\) | |||||||
\(642\) | 34.3984 | + | 41.9943i | 1.35759 | + | 1.65738i | ||||
\(643\) | 28.5026 | − | 16.4560i | 1.12403 | − | 0.648961i | 0.181606 | − | 0.983371i | \(-0.441870\pi\) |
0.942428 | + | 0.334410i | \(0.108537\pi\) | |||||||
\(644\) | 3.01720 | − | 1.74198i | 0.118894 | − | 0.0686436i | ||||
\(645\) | −3.14545 | + | 8.33370i | −0.123852 | + | 0.328139i | ||||
\(646\) | −5.82123 | + | 10.0827i | −0.229033 | + | 0.396697i | ||||
\(647\) | −37.7889 | −1.48564 | −0.742818 | − | 0.669494i | \(-0.766511\pi\) | ||||
−0.742818 | + | 0.669494i | \(0.766511\pi\) | |||||||
\(648\) | 17.7196 | − | 2.26564i | 0.696090 | − | 0.0890029i | ||||
\(649\) | 0.329450 | 0.0129320 | ||||||||
\(650\) | −7.86084 | + | 1.36658i | −0.308328 | + | 0.0536017i | ||||
\(651\) | 3.40271 | + | 1.28431i | 0.133363 | + | 0.0503362i | ||||
\(652\) | 43.3196 | − | 25.0106i | 1.69653 | − | 0.979490i | ||||
\(653\) | 11.3362 | + | 19.6348i | 0.443618 | + | 0.768369i | 0.997955 | − | 0.0639234i | \(-0.0203613\pi\) |
−0.554337 | + | 0.832292i | \(0.687028\pi\) | |||||||
\(654\) | 1.99748 | − | 1.63618i | 0.0781078 | − | 0.0639797i | ||||
\(655\) | 12.5480 | + | 7.24460i | 0.490291 | + | 0.283070i | ||||
\(656\) | − | 4.87960i | − | 0.190517i | ||||||
\(657\) | 16.0549 | − | 18.2384i | 0.626362 | − | 0.711549i | ||||
\(658\) | − | 11.3426i | − | 0.442182i | ||||||
\(659\) | 24.4766 | − | 42.3947i | 0.953472 | − | 1.65146i | 0.215646 | − | 0.976472i | \(-0.430814\pi\) |
0.737827 | − | 0.674990i | \(-0.235852\pi\) | |||||||
\(660\) | −0.994618 | − | 6.05945i | −0.0387154 | − | 0.235864i | ||||
\(661\) | 30.9756 | − | 17.8838i | 1.20481 | − | 0.695597i | 0.243189 | − | 0.969979i | \(-0.421806\pi\) |
0.961621 | + | 0.274381i | \(0.0884731\pi\) | |||||||
\(662\) | −15.3109 | − | 26.5192i | −0.595074 | − | 1.03070i | ||||
\(663\) | −5.86508 | − | 5.06551i | −0.227781 | − | 0.196728i | ||||
\(664\) | −1.45039 | + | 2.51215i | −0.0562860 | + | 0.0974903i | ||||
\(665\) | 4.48883i | 0.174070i | ||||||||
\(666\) | 72.9099 | − | 24.5981i | 2.82520 | − | 0.953157i | ||||
\(667\) | −3.94351 | −0.152693 | ||||||||
\(668\) | −49.7322 | − | 28.7129i | −1.92420 | − | 1.11094i | ||||
\(669\) | 13.9500 | + | 17.0305i | 0.539339 | + | 0.658437i | ||||
\(670\) | −9.98975 | + | 5.76758i | −0.385938 | + | 0.222821i | ||||
\(671\) | −11.8910 | + | 6.86530i | −0.459049 | + | 0.265032i | ||||
\(672\) | −12.1324 | − | 4.57922i | −0.468017 | − | 0.176647i | ||||
\(673\) | 15.0753 | − | 26.1112i | 0.581111 | − | 1.00651i | −0.414237 | − | 0.910169i | \(-0.635952\pi\) |
0.995348 | − | 0.0963447i | \(-0.0307151\pi\) | |||||||
\(674\) | − | 29.1099i | − | 1.12127i | ||||||
\(675\) | 5.19287 | + | 0.184535i | 0.199874 | + | 0.00710277i | ||||
\(676\) | −6.71810 | + | 37.0563i | −0.258388 | + | 1.42524i | ||||
\(677\) | −8.73261 | + | 15.1253i | −0.335621 | + | 0.581313i | −0.983604 | − | 0.180342i | \(-0.942280\pi\) |
0.647983 | + | 0.761655i | \(0.275613\pi\) | |||||||
\(678\) | 22.2739 | − | 59.0133i | 0.855423 | − | 2.26639i | ||||
\(679\) | 2.16246 | + | 3.74550i | 0.0829877 | + | 0.143739i | ||||
\(680\) | 1.23156 | + | 2.13313i | 0.0472283 | + | 0.0818018i | ||||
\(681\) | −16.2865 | − | 19.8830i | −0.624102 | − | 0.761917i | ||||
\(682\) | 4.65132 | + | 2.68544i | 0.178108 | + | 0.102831i | ||||
\(683\) | − | 20.0805i | − | 0.768360i | −0.923258 | − | 0.384180i | \(-0.874484\pi\) | ||
0.923258 | − | 0.384180i | \(-0.125516\pi\) | |||||||
\(684\) | −36.1244 | − | 7.25563i | −1.38125 | − | 0.277426i | ||||
\(685\) | −1.19507 | −0.0456612 | ||||||||
\(686\) | −15.0876 | + | 26.1326i | −0.576049 | + | 0.997746i | ||||
\(687\) | 17.0060 | − | 2.79143i | 0.648821 | − | 0.106500i | ||||
\(688\) | 3.60399 | + | 6.24230i | 0.137401 | + | 0.237986i | ||||
\(689\) | 11.9696 | + | 4.38924i | 0.456006 | + | 0.167217i | ||||
\(690\) | 0.705177 | + | 4.29611i | 0.0268456 | + | 0.163550i | ||||
\(691\) | −15.6067 | − | 9.01055i | −0.593708 | − | 0.342778i | 0.172854 | − | 0.984947i | \(-0.444701\pi\) |
−0.766562 | + | 0.642170i | \(0.778034\pi\) | |||||||
\(692\) | −20.6631 | −0.785494 | ||||||||
\(693\) | 0.765454 | − | 3.81105i | 0.0290772 | − | 0.144770i | ||||
\(694\) | 1.56742i | 0.0594984i | ||||||||
\(695\) | 5.52206 | + | 3.18816i | 0.209464 | + | 0.120934i | ||||
\(696\) | −7.56336 | − | 9.23352i | −0.286688 | − | 0.349996i | ||||
\(697\) | −3.74157 | + | 2.16020i | −0.141722 | + | 0.0818232i | ||||
\(698\) | 26.9733 | + | 46.7191i | 1.02095 | + | 1.76834i | ||||
\(699\) | 23.0194 | + | 8.68840i | 0.870675 | + | 0.328626i | ||||
\(700\) | 2.65631 | + | 1.53362i | 0.100399 | + | 0.0579655i | ||||
\(701\) | 23.9457 | 0.904417 | 0.452209 | − | 0.891912i | \(-0.350636\pi\) | ||||
0.452209 | + | 0.891912i | \(0.350636\pi\) | |||||||
\(702\) | 15.6468 | − | 38.3928i | 0.590550 | − | 1.44904i | ||||
\(703\) | −49.1402 | −1.85336 | ||||||||
\(704\) | −13.6134 | − | 7.85972i | −0.513075 | − | 0.296224i | ||||
\(705\) | 7.84484 | + | 2.96094i | 0.295454 | + | 0.111516i | ||||
\(706\) | 24.4913 | + | 42.4202i | 0.921742 | + | 1.59650i | ||||
\(707\) | −12.1262 | + | 7.00109i | −0.456054 | + | 0.263303i | ||||
\(708\) | −0.855955 | − | 1.04497i | −0.0321688 | − | 0.0392724i | ||||
\(709\) | −38.8600 | − | 22.4358i | −1.45942 | − | 0.842595i | −0.460434 | − | 0.887694i | \(-0.652306\pi\) |
−0.998983 | + | 0.0450989i | \(0.985640\pi\) | |||||||
\(710\) | 11.8658i | 0.445317i | ||||||||
\(711\) | 21.2401 | − | 7.16590i | 0.796565 | − | 0.268742i | ||||
\(712\) | −32.6473 | −1.22351 | ||||||||
\(713\) | −1.95089 | − | 1.12635i | −0.0730615 | − | 0.0421821i | ||||
\(714\) | 0.815710 | + | 4.96950i | 0.0305272 | + | 0.185979i | ||||
\(715\) | −4.14267 | − | 1.51911i | −0.154927 | − | 0.0568114i | ||||
\(716\) | −13.0679 | − | 22.6343i | −0.488371 | − | 0.845884i | ||||
\(717\) | −15.0554 | + | 2.47124i | −0.562254 | + | 0.0922902i | ||||
\(718\) | −2.68169 | + | 4.64483i | −0.100080 | + | 0.173343i | ||||
\(719\) | 4.04721 | 0.150935 | 0.0754677 | − | 0.997148i | \(-0.475955\pi\) | ||||
0.0754677 | + | 0.997148i | \(0.475955\pi\) | |||||||
\(720\) | 2.77826 | − | 3.15611i | 0.103540 | − | 0.117621i | ||||
\(721\) | 2.32348i | 0.0865309i | ||||||||
\(722\) | −1.96560 | − | 1.13484i | −0.0731521 | − | 0.0422344i | ||||
\(723\) | −25.7043 | − | 31.3804i | −0.955953 | − | 1.16705i | ||||
\(724\) | 4.47378 | + | 7.74881i | 0.166267 | + | 0.287982i | ||||
\(725\) | −1.73591 | − | 3.00669i | −0.0644702 | − | 0.111666i | ||||
\(726\) | −12.8612 | + | 34.0749i | −0.477322 | + | 1.26464i | ||||
\(727\) | −17.0401 | + | 29.5143i | −0.631981 | + | 1.09462i | 0.355165 | + | 0.934804i | \(0.384425\pi\) |
−0.987146 | + | 0.159820i | \(0.948909\pi\) | |||||||
\(728\) | 5.81620 | − | 4.85657i | 0.215563 | − | 0.179996i | ||||
\(729\) | −15.1257 | + | 22.3654i | −0.560212 | + | 0.828349i | ||||
\(730\) | 17.9232i | 0.663367i | ||||||||
\(731\) | 3.19097 | − | 5.52692i | 0.118022 | − | 0.204421i | ||||
\(732\) | 52.6704 | + | 19.8798i | 1.94675 | + | 0.734779i | ||||
\(733\) | −16.5146 | + | 9.53474i | −0.609982 | + | 0.352174i | −0.772959 | − | 0.634456i | \(-0.781224\pi\) |
0.162976 | + | 0.986630i | \(0.447891\pi\) | |||||||
\(734\) | 0.155455 | − | 0.0897518i | 0.00573794 | − | 0.00331280i | ||||
\(735\) | −6.45249 | − | 7.87734i | −0.238004 | − | 0.290560i | ||||
\(736\) | 6.95592 | + | 4.01600i | 0.256398 | + | 0.148032i | ||||
\(737\) | −6.37919 | −0.234980 | ||||||||
\(738\) | −17.3487 | − | 15.2717i | −0.638613 | − | 0.562158i | ||||
\(739\) | 46.8060i | 1.72179i | 0.508786 | + | 0.860893i | \(0.330094\pi\) | ||||
−0.508786 | + | 0.860893i | \(0.669906\pi\) | |||||||
\(740\) | −16.7889 | + | 29.0792i | −0.617172 | + | 1.06897i | ||||
\(741\) | −17.3059 | + | 20.0376i | −0.635749 | + | 0.736099i | ||||
\(742\) | −4.14233 | − | 7.17473i | −0.152070 | − | 0.263393i | ||||
\(743\) | −16.5257 | + | 9.54111i | −0.606269 | + | 0.350029i | −0.771504 | − | 0.636225i | \(-0.780495\pi\) |
0.165235 | + | 0.986254i | \(0.447162\pi\) | |||||||
\(744\) | −1.10438 | − | 6.72817i | −0.0404887 | − | 0.246667i | ||||
\(745\) | −8.35614 | + | 14.4733i | −0.306145 | + | 0.530259i | ||||
\(746\) | − | 18.2447i | − | 0.667986i | ||||||
\(747\) | −1.40156 | − | 4.15428i | −0.0512803 | − | 0.151997i | ||||
\(748\) | 4.39947i | 0.160861i | ||||||||
\(749\) | −12.9863 | − | 7.49767i | −0.474511 | − | 0.273959i | ||||
\(750\) | −2.96511 | + | 2.42878i | −0.108271 | + | 0.0886865i | ||||
\(751\) | 14.0126 | + | 24.2705i | 0.511326 | + | 0.885643i | 0.999914 | + | 0.0131283i | \(0.00417899\pi\) |
−0.488587 | + | 0.872515i | \(0.662488\pi\) | |||||||
\(752\) | 5.87613 | − | 3.39259i | 0.214280 | − | 0.123715i | ||||
\(753\) | 12.1133 | + | 4.57204i | 0.441435 | + | 0.166614i | ||||
\(754\) | −27.2915 | + | 4.74453i | −0.993896 | + | 0.172785i | ||||
\(755\) | −7.42458 | −0.270208 | ||||||||
\(756\) | −14.0769 | + | 7.47372i | −0.511972 | + | 0.271817i | ||||
\(757\) | −2.77014 | −0.100682 | −0.0503412 | − | 0.998732i | \(-0.516031\pi\) | ||||
−0.0503412 | + | 0.998732i | \(0.516031\pi\) | |||||||
\(758\) | 31.0935 | − | 53.8554i | 1.12937 | − | 1.95612i | ||||
\(759\) | −0.850188 | + | 2.25252i | −0.0308599 | + | 0.0817615i | ||||
\(760\) | 7.28767 | − | 4.20754i | 0.264352 | − | 0.152624i | ||||
\(761\) | −24.7126 | + | 14.2678i | −0.895831 | + | 0.517208i | −0.875845 | − | 0.482592i | \(-0.839695\pi\) |
−0.0199856 | + | 0.999800i | \(0.506362\pi\) | |||||||
\(762\) | 45.4561 | + | 55.4938i | 1.64670 | + | 2.01033i | ||||
\(763\) | −0.356631 | + | 0.617704i | −0.0129109 | + | 0.0223624i | ||||
\(764\) | 59.4086 | 2.14933 | ||||||||
\(765\) | −3.64996 | − | 0.733099i | −0.131965 | − | 0.0265053i | ||||
\(766\) | −17.1647 | −0.620185 | ||||||||
\(767\) | −0.956292 | + | 0.166248i | −0.0345297 | + | 0.00600287i | ||||
\(768\) | 1.65945 | + | 10.1098i | 0.0598803 | + | 0.364805i | ||||
\(769\) | 43.3223 | − | 25.0121i | 1.56224 | − | 0.901961i | 0.565212 | − | 0.824946i | \(-0.308794\pi\) |
0.997030 | − | 0.0770150i | \(-0.0245389\pi\) | |||||||
\(770\) | 1.43365 | + | 2.48316i | 0.0516653 | + | 0.0894869i | ||||
\(771\) | 0.761366 | + | 4.63842i | 0.0274199 | + | 0.167049i | ||||
\(772\) | −13.7029 | − | 7.91136i | −0.493177 | − | 0.284736i | ||||
\(773\) | 51.3118i | 1.84556i | 0.385332 | + | 0.922778i | \(0.374087\pi\) | ||||
−0.385332 | + | 0.922778i | \(0.625913\pi\) | |||||||
\(774\) | 33.4729 | + | 6.72307i | 1.20316 | + | 0.241656i | ||||
\(775\) | − | 1.98325i | − | 0.0712405i | ||||||
\(776\) | 4.05390 | − | 7.02156i | 0.145527 | − | 0.252059i | ||||
\(777\) | −16.4436 | + | 13.4692i | −0.589909 | + | 0.483206i | ||||
\(778\) | −57.3571 | + | 33.1151i | −2.05635 | + | 1.18723i | ||||
\(779\) | 7.38014 | + | 12.7828i | 0.264421 | + | 0.457990i | ||||
\(780\) | 5.94482 | + | 17.0868i | 0.212859 | + | 0.611807i | ||||
\(781\) | −3.28103 | + | 5.68291i | −0.117404 | + | 0.203350i | ||||
\(782\) | − | 3.11920i | − | 0.111542i | ||||||
\(783\) | 18.0287 | + | 0.640674i | 0.644295 | + | 0.0228958i | ||||
\(784\) | −8.23984 | −0.294280 | ||||||||
\(785\) | −11.5252 | − | 6.65410i | −0.411353 | − | 0.237495i | ||||
\(786\) | 19.6107 | − | 51.9574i | 0.699490 | − | 1.85326i | ||||
\(787\) | −2.53351 | + | 1.46272i | −0.0903098 | + | 0.0521404i | −0.544475 | − | 0.838777i | \(-0.683271\pi\) |
0.454165 | + | 0.890918i | \(0.349938\pi\) | |||||||
\(788\) | 26.0345 | − | 15.0310i | 0.927441 | − | 0.535458i | ||||
\(789\) | −30.3499 | + | 24.8602i | −1.08048 | + | 0.885046i | ||||
\(790\) | −8.26753 | + | 14.3198i | −0.294146 | + | 0.509475i | ||||
\(791\) | 17.4243i | 0.619535i | ||||||||
\(792\) | −6.90477 | + | 2.32951i | −0.245350 | + | 0.0827754i | ||||
\(793\) | 31.0517 | − | 25.9284i | 1.10268 | − | 0.920744i | ||||
\(794\) | −40.6279 | + | 70.3696i | −1.44183 | + | 2.49732i | ||||
\(795\) | 6.04355 | − | 0.992009i | 0.214343 | − | 0.0351829i | ||||
\(796\) | −36.3839 | − | 63.0188i | −1.28959 | − | 2.23364i | ||||
\(797\) | 0.0823808 | + | 0.142688i | 0.00291808 | + | 0.00505426i | 0.867481 | − | 0.497471i | \(-0.165738\pi\) |
−0.864563 | + | 0.502525i | \(0.832404\pi\) | |||||||
\(798\) | 16.9779 | − | 2.78681i | 0.601011 | − | 0.0986519i | ||||
\(799\) | −5.20271 | − | 3.00379i | −0.184059 | − | 0.106266i | ||||
\(800\) | 7.07129i | 0.250008i | ||||||||
\(801\) | 32.6041 | − | 37.0383i | 1.15201 | − | 1.30868i | ||||
\(802\) | −46.3142 | −1.63541 | ||||||||
\(803\) | −4.95595 | + | 8.58395i | −0.174892 | + | 0.302921i | ||||
\(804\) | 16.5740 | + | 20.2339i | 0.584520 | + | 0.713595i | ||||
\(805\) | −0.601315 | − | 1.04151i | −0.0211936 | − | 0.0367083i | ||||
\(806\) | −14.8565 | − | 5.44785i | −0.523298 | − | 0.191892i | ||||
\(807\) | −35.4088 | − | 13.3646i | −1.24645 | − | 0.470457i | ||||
\(808\) | 22.7327 | + | 13.1247i | 0.799734 | + | 0.461726i | ||||
\(809\) | 32.2178 | 1.13272 | 0.566360 | − | 0.824158i | \(-0.308351\pi\) | ||||
0.566360 | + | 0.824158i | \(0.308351\pi\) | |||||||
\(810\) | −2.52594 | − | 19.7553i | −0.0887524 | − | 0.694131i | ||||
\(811\) | − | 25.5331i | − | 0.896587i | −0.893886 | − | 0.448294i | \(-0.852032\pi\) | ||
0.893886 | − | 0.448294i | \(-0.147968\pi\) | |||||||
\(812\) | 9.22224 | + | 5.32446i | 0.323637 | + | 0.186852i | ||||
\(813\) | −8.27641 | + | 21.9279i | −0.290266 | + | 0.769044i | ||||
\(814\) | −27.1837 | + | 15.6945i | −0.952788 | + | 0.550093i | ||||
\(815\) | −8.63342 | − | 14.9535i | −0.302415 | − | 0.523799i | ||||
\(816\) | −2.33050 | + | 1.90896i | −0.0815840 | + | 0.0668271i | ||||
\(817\) | −18.8823 | − | 10.9017i | −0.660608 | − | 0.381402i | ||||
\(818\) | 44.7246 | 1.56376 | ||||||||
\(819\) | −0.298734 | + | 11.4486i | −0.0104386 | + | 0.400046i | ||||
\(820\) | 10.0858 | 0.352210 | ||||||||
\(821\) | 21.3774 | + | 12.3422i | 0.746076 | + | 0.430747i | 0.824274 | − | 0.566190i | \(-0.191583\pi\) |
−0.0781981 | + | 0.996938i | \(0.524917\pi\) | |||||||
\(822\) | 0.741935 | + | 4.52004i | 0.0258779 | + | 0.157655i | ||||
\(823\) | −0.855265 | − | 1.48136i | −0.0298127 | − | 0.0516371i | 0.850734 | − | 0.525596i | \(-0.176158\pi\) |
−0.880547 | + | 0.473959i | \(0.842824\pi\) | |||||||
\(824\) | 3.77219 | − | 2.17788i | 0.131411 | − | 0.0758700i | ||||
\(825\) | −2.09166 | + | 0.343333i | −0.0728224 | + | 0.0119533i | ||||
\(826\) | 0.546242 | + | 0.315373i | 0.0190062 | + | 0.0109732i | ||||
\(827\) | − | 18.3595i | − | 0.638423i | −0.947683 | − | 0.319212i | \(-0.896582\pi\) | ||
0.947683 | − | 0.319212i | \(-0.103418\pi\) | |||||||
\(828\) | 9.35361 | − | 3.15569i | 0.325060 | − | 0.109668i | ||||
\(829\) | −29.8986 | −1.03842 | −0.519211 | − | 0.854646i | \(-0.673774\pi\) | ||||
−0.519211 | + | 0.854646i | \(0.673774\pi\) | |||||||
\(830\) | 2.80076 | + | 1.61702i | 0.0972159 | + | 0.0561276i | ||||
\(831\) | −0.0415381 | + | 0.0340247i | −0.00144094 | + | 0.00118030i | ||||
\(832\) | 43.4819 | + | 15.9447i | 1.50746 | + | 0.552784i | ||||
\(833\) | 3.64777 | + | 6.31812i | 0.126388 | + | 0.218910i | ||||
\(834\) | 8.63016 | − | 22.8651i | 0.298838 | − | 0.791754i | ||||
\(835\) | −9.91143 | + | 17.1671i | −0.342999 | + | 0.594092i | ||||
\(836\) | 15.0305 | 0.519839 | ||||||||
\(837\) | 8.73602 | + | 5.46634i | 0.301961 | + | 0.188944i | ||||
\(838\) | − | 62.6009i | − | 2.16251i | ||||||
\(839\) | −19.7284 | − | 11.3902i | −0.681101 | − | 0.393234i | 0.119169 | − | 0.992874i | \(-0.461977\pi\) |
−0.800270 | + | 0.599640i | \(0.795310\pi\) | |||||||
\(840\) | 1.28536 | − | 3.40549i | 0.0443491 | − | 0.117500i | ||||
\(841\) | 8.47322 | + | 14.6760i | 0.292180 | + | 0.506071i | ||||
\(842\) | 23.7842 | + | 41.1955i | 0.819659 | + | 1.41969i | ||||
\(843\) | 12.5680 | + | 15.3433i | 0.432866 | + | 0.528452i | ||||
\(844\) | 16.1090 | − | 27.9016i | 0.554495 | − | 0.960414i | ||||
\(845\) | 12.7915 | + | 2.31902i | 0.440041 | + | 0.0797768i | ||||
\(846\) | 6.32870 | − | 31.5094i | 0.217585 | − | 1.08332i | ||||
\(847\) | − | 10.0609i | − | 0.345698i | ||||||
\(848\) | 2.47794 | − | 4.29193i | 0.0850930 | − | 0.147385i | ||||
\(849\) | −8.92597 | − | 54.3791i | −0.306338 | − | 1.86629i | ||||
\(850\) | 2.37820 | − | 1.37306i | 0.0815716 | − | 0.0470954i | ||||
\(851\) | 11.4016 | − | 6.58272i | 0.390842 | − | 0.225653i | ||||
\(852\) | 26.5500 | − | 4.35800i | 0.909587 | − | 0.149303i | ||||
\(853\) | −41.1579 | − | 23.7625i | −1.40922 | − | 0.813614i | −0.413908 | − | 0.910319i | \(-0.635836\pi\) |
−0.995313 | + | 0.0967050i | \(0.969170\pi\) | |||||||
\(854\) | −26.2879 | −0.899552 | ||||||||
\(855\) | −2.50458 | + | 12.4698i | −0.0856547 | + | 0.426459i | ||||
\(856\) | 28.1113i | 0.960825i | ||||||||
\(857\) | −1.21310 | + | 2.10115i | −0.0414387 | + | 0.0717739i | −0.886001 | − | 0.463684i | \(-0.846527\pi\) |
0.844562 | + | 0.535457i | \(0.179861\pi\) | |||||||
\(858\) | −3.17375 | + | 16.6117i | −0.108350 | + | 0.567115i | ||||
\(859\) | 6.75571 | + | 11.7012i | 0.230502 | + | 0.399241i | 0.957956 | − | 0.286915i | \(-0.0926299\pi\) |
−0.727454 | + | 0.686156i | \(0.759297\pi\) | |||||||
\(860\) | −12.9024 | + | 7.44918i | −0.439967 | + | 0.254015i | ||||
\(861\) | 5.97331 | + | 2.25455i | 0.203570 | + | 0.0768350i | ||||
\(862\) | 38.3242 | − | 66.3795i | 1.30533 | − | 2.26090i | ||||
\(863\) | − | 11.2875i | − | 0.384230i | −0.981372 | − | 0.192115i | \(-0.938465\pi\) | ||
0.981372 | − | 0.192115i | \(-0.0615346\pi\) | |||||||
\(864\) | −31.1483 | − | 19.4902i | −1.05969 | − | 0.663072i | ||||
\(865\) | 7.13271i | 0.242520i | ||||||||
\(866\) | −69.4129 | − | 40.0756i | −2.35875 | − | 1.36182i | ||||
\(867\) | −25.0525 | − | 9.45576i | −0.850827 | − | 0.321134i | ||||
\(868\) | 3.04156 | + | 5.26813i | 0.103237 | + | 0.178812i | ||||
\(869\) | −7.91914 | + | 4.57212i | −0.268638 | + | 0.155098i | ||||
\(870\) | −10.2943 | + | 8.43230i | −0.349011 | + | 0.285882i | ||||
\(871\) | 18.5169 | − | 3.21909i | 0.627420 | − | 0.109075i | ||||
\(872\) | 1.33713 | 0.0452810 | ||||||||
\(873\) | 3.91742 | + | 11.6114i | 0.132584 | + | 0.392987i | ||||
\(874\) | −10.6565 | −0.360461 | ||||||||
\(875\) | 0.529392 | − | 0.916933i | 0.0178967 | − | 0.0309980i | ||||
\(876\) | 40.1034 | − | 6.58270i | 1.35497 | − | 0.222409i | ||||
\(877\) | −23.2929 | + | 13.4482i | −0.786546 | + | 0.454112i | −0.838745 | − | 0.544524i | \(-0.816710\pi\) |
0.0521995 | + | 0.998637i | \(0.483377\pi\) | |||||||
\(878\) | −13.8816 | + | 8.01455i | −0.468481 | + | 0.270478i | ||||
\(879\) | 48.8659 | − | 8.02101i | 1.64821 | − | 0.270542i | ||||
\(880\) | −0.857613 | + | 1.48543i | −0.0289101 | + | 0.0500738i | ||||
\(881\) | 19.3845 | 0.653082 | 0.326541 | − | 0.945183i | \(-0.394117\pi\) | ||||
0.326541 | + | 0.945183i | \(0.394117\pi\) | |||||||
\(882\) | −25.7882 | + | 29.2954i | −0.868333 | + | 0.986429i | ||||
\(883\) | −41.9619 | −1.41213 | −0.706065 | − | 0.708147i | \(-0.749531\pi\) | ||||
−0.706065 | + | 0.708147i | \(0.749531\pi\) | |||||||
\(884\) | −2.22008 | − | 12.7703i | −0.0746693 | − | 0.429513i | ||||
\(885\) | −0.360714 | + | 0.295468i | −0.0121253 | + | 0.00993204i | ||||
\(886\) | 53.6497 | − | 30.9747i | 1.80240 | − | 1.04061i | ||||
\(887\) | 25.0333 | + | 43.3589i | 0.840536 | + | 1.45585i | 0.889443 | + | 0.457047i | \(0.151093\pi\) |
−0.0489071 | + | 0.998803i | \(0.515574\pi\) | |||||||
\(888\) | 37.2806 | + | 14.0711i | 1.25105 | + | 0.472195i | ||||
\(889\) | −17.1610 | − | 9.90789i | −0.575560 | − | 0.332300i | ||||
\(890\) | 36.3981i | 1.22007i | ||||||||
\(891\) | 4.25280 | − | 10.1599i | 0.142474 | − | 0.340368i | ||||
\(892\) | 36.8206i | 1.23284i | ||||||||
\(893\) | −10.2622 | + | 17.7747i | −0.343412 | + | 0.594806i | ||||
\(894\) | 59.9292 | + | 22.6196i | 2.00433 | + | 0.756511i | ||||
\(895\) | −7.81315 | + | 4.51093i | −0.261165 | + | 0.150784i | ||||
\(896\) | −7.56081 | − | 13.0957i | −0.252589 | − | 0.437497i | ||||
\(897\) | 1.33116 | − | 6.96742i | 0.0444462 | − | 0.232635i | ||||
\(898\) | −35.4554 | + | 61.4106i | −1.18316 | + | 2.04930i | ||||
\(899\) | − | 6.88550i | − | 0.229644i | ||||||
\(900\) | 6.52344 | + | 5.74245i | 0.217448 | + | 0.191415i | ||||
\(901\) | −4.38793 | −0.146183 | ||||||||
\(902\) | 8.16518 | + | 4.71417i | 0.271871 | + | 0.156965i | ||||
\(903\) | −9.30662 | + | 1.52762i | −0.309705 | + | 0.0508360i | ||||
\(904\) | 28.2885 | − | 16.3324i | 0.940860 | − | 0.543206i | ||||
\(905\) | 2.67481 | − | 1.54430i | 0.0889138 | − | 0.0513344i | ||||
\(906\) | 4.60941 | + | 28.0816i | 0.153137 | + | 0.932950i | ||||
\(907\) | −5.69329 | + | 9.86106i | −0.189043 | + | 0.327431i | −0.944931 | − | 0.327269i | \(-0.893872\pi\) |
0.755889 | + | 0.654700i | \(0.227205\pi\) | |||||||
\(908\) | − | 42.9877i | − | 1.42660i | ||||||
\(909\) | −37.5926 | + | 12.6828i | −1.24687 | + | 0.420663i | ||||
\(910\) | −5.41453 | − | 6.48441i | −0.179490 | − | 0.214956i | ||||
\(911\) | −9.28246 | + | 16.0777i | −0.307542 | + | 0.532678i | −0.977824 | − | 0.209428i | \(-0.932840\pi\) |
0.670282 | + | 0.742106i | \(0.266173\pi\) | |||||||
\(912\) | 6.52182 | + | 7.96198i | 0.215959 | + | 0.263648i | ||||
\(913\) | 0.894247 | + | 1.54888i | 0.0295952 | + | 0.0512605i | ||||
\(914\) | 28.1222 | + | 48.7090i | 0.930198 | + | 1.61115i | ||||
\(915\) | 6.86232 | − | 18.1813i | 0.226861 | − | 0.601056i | ||||
\(916\) | 24.9625 | + | 14.4121i | 0.824783 | + | 0.476189i | ||||
\(917\) | 15.3409i | 0.506602i | ||||||||
\(918\) | −0.506754 | + | 14.2602i | −0.0167254 | + | 0.470657i | ||||
\(919\) | 35.4777 | 1.17030 | 0.585151 | − | 0.810925i | \(-0.301035\pi\) | ||||
0.585151 | + | 0.810925i | \(0.301035\pi\) | |||||||
\(920\) | −1.12727 | + | 1.95248i | −0.0371649 | + | 0.0643714i | ||||
\(921\) | 3.02825 | − | 8.02318i | 0.0997842 | − | 0.264373i | ||||
\(922\) | −9.29083 | − | 16.0922i | −0.305977 | − | 0.529968i | ||||
\(923\) | 6.65610 | − | 18.1514i | 0.219088 | − | 0.597462i | ||||
\(924\) | 5.02957 | − | 4.11982i | 0.165461 | − | 0.135532i | ||||
\(925\) | 10.0379 | + | 5.79536i | 0.330043 | + | 0.190550i | ||||
\(926\) | −34.0970 | −1.12050 | ||||||||
\(927\) | −1.29640 | + | 6.45454i | −0.0425794 | + | 0.211995i | ||||
\(928\) | 24.5503i | 0.805903i | ||||||||
\(929\) | 20.4710 | + | 11.8189i | 0.671632 | + | 0.387767i | 0.796695 | − | 0.604382i | \(-0.206580\pi\) |
−0.125063 | + | 0.992149i | \(0.539913\pi\) | |||||||
\(930\) | −7.50116 | + | 1.23126i | −0.245973 | + | 0.0403748i | ||||
\(931\) | 21.5853 | − | 12.4623i | 0.707431 | − | 0.408436i | ||||
\(932\) | 20.5762 | + | 35.6390i | 0.673996 | + | 1.16740i | ||||
\(933\) | −0.358214 | − | 2.18232i | −0.0117274 | − | 0.0714461i | ||||
\(934\) | −57.4983 | − | 33.1967i | −1.88140 | − | 1.08623i | ||||
\(935\) | 1.51866 | 0.0496654 | ||||||||
\(936\) | 18.8669 | − | 10.2462i | 0.616685 | − | 0.334906i | ||||
\(937\) | −15.7766 | −0.515398 | −0.257699 | − | 0.966225i | \(-0.582964\pi\) | ||||
−0.257699 | + | 0.966225i | \(0.582964\pi\) | |||||||
\(938\) | −10.5770 | − | 6.10662i | −0.345351 | − | 0.199388i | ||||
\(939\) | 20.5676 | − | 16.8473i | 0.671197 | − | 0.549791i | ||||
\(940\) | 7.01222 | + | 12.1455i | 0.228713 | + | 0.396143i | ||||
\(941\) | 39.4024 | − | 22.7490i | 1.28448 | − | 0.741595i | 0.306816 | − | 0.951769i | \(-0.400736\pi\) |
0.977664 | + | 0.210174i | \(0.0674031\pi\) | |||||||
\(942\) | −18.0122 | + | 47.7224i | −0.586871 | + | 1.55488i | ||||
\(943\) | −3.42471 | − | 1.97726i | −0.111524 | − | 0.0643883i | ||||
\(944\) | 0.377313i | 0.0122805i | ||||||||
\(945\) | 2.57986 | + | 4.85921i | 0.0839228 | + | 0.158070i | ||||
\(946\) | −13.9272 | −0.452813 | ||||||||
\(947\) | 23.1767 | + | 13.3811i | 0.753142 | + | 0.434827i | 0.826828 | − | 0.562455i | \(-0.190143\pi\) |
−0.0736859 | + | 0.997281i | \(0.523476\pi\) | |||||||
\(948\) | 35.0772 | + | 13.2394i | 1.13925 | + | 0.429997i | ||||
\(949\) | 10.0539 | − | 27.4175i | 0.326365 | − | 0.890010i | ||||
\(950\) | −4.69094 | − | 8.12494i | −0.152194 | − | 0.263608i | ||||
\(951\) | 2.41213 | + | 2.94478i | 0.0782187 | + | 0.0954912i | ||||
\(952\) | −1.30396 | + | 2.25852i | −0.0422616 | + | 0.0731992i | ||||
\(953\) | 1.14387 | 0.0370536 | 0.0185268 | − | 0.999828i | \(-0.494102\pi\) | ||||
0.0185268 | + | 0.999828i | \(0.494102\pi\) | |||||||
\(954\) | −7.50405 | − | 22.2424i | −0.242953 | − | 0.720123i | ||||
\(955\) | − | 20.5073i | − | 0.663600i | ||||||
\(956\) | −22.0992 | − | 12.7590i | −0.714739 | − | 0.412655i | ||||
\(957\) | −7.26189 | + | 1.19199i | −0.234744 | + | 0.0385316i | ||||
\(958\) | 0.949120 | + | 1.64392i | 0.0306647 | + | 0.0531128i | ||||
\(959\) | −0.632658 | − | 1.09580i | −0.0204296 | − | 0.0353851i | ||||
\(960\) | 21.9543 | − | 3.60365i | 0.708572 | − | 0.116307i | ||||
\(961\) | −13.5334 | + | 23.4405i | −0.436560 | + | 0.756144i | ||||
\(962\) | 70.9862 | − | 59.2740i | 2.28869 | − | 1.91107i | ||||
\(963\) | −31.8922 | − | 28.0741i | −1.02771 | − | 0.904674i | ||||
\(964\) | − | 67.8456i | − | 2.18516i | ||||||
\(965\) | −2.73093 | + | 4.73010i | −0.0879116 | + | 0.152267i | ||||
\(966\) | −3.56593 | + | 2.92092i | −0.114732 | + | 0.0939792i | ||||
\(967\) | −36.6240 | + | 21.1449i | −1.17775 | + | 0.679974i | −0.955493 | − | 0.295014i | \(-0.904676\pi\) |
−0.222257 | + | 0.974988i | \(0.571342\pi\) | |||||||
\(968\) | −16.3340 | + | 9.43046i | −0.524996 | + | 0.303107i | ||||
\(969\) | 3.21786 | − | 8.52554i | 0.103373 | − | 0.273880i | ||||
\(970\) | −7.82826 | − | 4.51965i | −0.251350 | − | 0.145117i | ||||
\(971\) | −48.9893 | −1.57214 | −0.786071 | − | 0.618136i | \(-0.787888\pi\) | ||||
−0.786071 | + | 0.618136i | \(0.787888\pi\) | |||||||
\(972\) | −43.2751 | + | 12.9074i | −1.38805 | + | 0.414006i | ||||
\(973\) | 6.75115i | 0.216432i | ||||||||
\(974\) | 21.3421 | − | 36.9656i | 0.683845 | − | 1.18446i | ||||
\(975\) | 5.89821 | − | 2.05209i | 0.188894 | − | 0.0657196i | ||||
\(976\) | −7.86270 | − | 13.6186i | −0.251679 | − | 0.435921i | ||||
\(977\) | 36.9860 | − | 21.3539i | 1.18329 | − | 0.683172i | 0.226515 | − | 0.974008i | \(-0.427267\pi\) |
0.956773 | + | 0.290836i | \(0.0939334\pi\) | |||||||
\(978\) | −51.1980 | + | 41.9373i | −1.63713 | + | 1.34101i | ||||
\(979\) | −10.0645 | + | 17.4321i | −0.321661 | + | 0.557134i | ||||
\(980\) | − | 17.0311i | − | 0.544039i | ||||||
\(981\) | −1.33536 | + | 1.51697i | −0.0426348 | + | 0.0484332i | ||||
\(982\) | 36.2165i | 1.15571i | ||||||||
\(983\) | −14.1606 | − | 8.17563i | −0.451653 | − | 0.260762i | 0.256875 | − | 0.966445i | \(-0.417307\pi\) |
−0.708528 | + | 0.705683i | \(0.750640\pi\) | |||||||
\(984\) | −1.93870 | − | 11.8110i | −0.0618034 | − | 0.376521i | ||||
\(985\) | −5.18857 | − | 8.98686i | −0.165322 | − | 0.286345i | ||||
\(986\) | 8.25670 | − | 4.76701i | 0.262947 | − | 0.151812i | ||||
\(987\) | 1.43801 | + | 8.76070i | 0.0457723 | + | 0.278856i | ||||
\(988\) | −43.6289 | + | 7.58473i | −1.38802 | + | 0.241302i | ||||
\(989\) | 5.84147 | 0.185748 | ||||||||
\(990\) | 2.59714 | + | 7.69805i | 0.0825425 | + | 0.244660i | ||||
\(991\) | 14.5897 | 0.463458 | 0.231729 | − | 0.972780i | \(-0.425562\pi\) | ||||
0.231729 | + | 0.972780i | \(0.425562\pi\) | |||||||
\(992\) | −7.01208 | + | 12.1453i | −0.222634 | + | 0.385613i | ||||
\(993\) | 15.1877 | + | 18.5415i | 0.481968 | + | 0.588397i | ||||
\(994\) | −10.8802 | + | 6.28168i | −0.345098 | + | 0.199243i | ||||
\(995\) | −21.7535 | + | 12.5594i | −0.689632 | + | 0.398159i | ||||
\(996\) | 2.58946 | − | 6.86064i | 0.0820503 | − | 0.217388i | ||||
\(997\) | 16.2063 | − | 28.0701i | 0.513259 | − | 0.888991i | −0.486623 | − | 0.873612i | \(-0.661771\pi\) |
0.999882 | − | 0.0153784i | \(-0.00489528\pi\) | |||||||
\(998\) | 59.0543 | 1.86933 | ||||||||
\(999\) | −53.1948 | + | 28.2423i | −1.68301 | + | 0.893545i |
(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 | 585.2.bt.b.376.7 | ✓ | 108 | |
9.4 | even | 3 | inner | 585.2.bt.b.571.48 | yes | 108 | |
13.12 | even | 2 | inner | 585.2.bt.b.376.48 | yes | 108 | |
117.103 | even | 6 | inner | 585.2.bt.b.571.7 | yes | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.bt.b.376.7 | ✓ | 108 | 1.1 | even | 1 | trivial | |
585.2.bt.b.376.48 | yes | 108 | 13.12 | even | 2 | inner | |
585.2.bt.b.571.7 | yes | 108 | 117.103 | even | 6 | inner | |
585.2.bt.b.571.48 | yes | 108 | 9.4 | even | 3 | inner |