Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,3,Mod(13,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([0, 19]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.k (of order \(20\), degree \(8\), 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: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 67.9 | ||
Character | \(\chi\) | \(=\) | 75.67 |
Dual form | 75.3.k.a.28.9 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{13}{20}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.51991 | − | 2.98300i | 0.759957 | − | 1.49150i | −0.107618 | − | 0.994192i | \(-0.534322\pi\) |
0.867575 | − | 0.497306i | \(-0.165678\pi\) | |||||||
\(3\) | −0.270952 | + | 1.71073i | −0.0903175 | + | 0.570242i | ||||
\(4\) | −4.23700 | − | 5.83172i | −1.05925 | − | 1.45793i | ||||
\(5\) | 3.83005 | − | 3.21415i | 0.766009 | − | 0.642829i | ||||
\(6\) | 4.69127 | + | 3.40841i | 0.781878 | + | 0.568068i | ||||
\(7\) | −3.58606 | − | 3.58606i | −0.512294 | − | 0.512294i | 0.402935 | − | 0.915229i | \(-0.367990\pi\) |
−0.915229 | + | 0.402935i | \(0.867990\pi\) | |||||||
\(8\) | −10.6092 | + | 1.68033i | −1.32615 | + | 0.210041i | ||||
\(9\) | −2.85317 | − | 0.927051i | −0.317019 | − | 0.103006i | ||||
\(10\) | −3.76645 | − | 16.3102i | −0.376645 | − | 1.63102i | ||||
\(11\) | 2.52268 | + | 7.76402i | 0.229335 | + | 0.705820i | 0.997823 | + | 0.0659554i | \(0.0210095\pi\) |
−0.768488 | + | 0.639864i | \(0.778990\pi\) | |||||||
\(12\) | 11.1245 | − | 5.66822i | 0.927043 | − | 0.472352i | ||||
\(13\) | 8.08027 | + | 15.8584i | 0.621559 | + | 1.21988i | 0.960292 | + | 0.278996i | \(0.0900017\pi\) |
−0.338733 | + | 0.940883i | \(0.609998\pi\) | |||||||
\(14\) | −16.1477 | + | 5.24671i | −1.15341 | + | 0.374765i | ||||
\(15\) | 4.46077 | + | 7.42304i | 0.297384 | + | 0.494870i | ||||
\(16\) | −2.20252 | + | 6.77867i | −0.137658 | + | 0.423667i | ||||
\(17\) | 4.14599 | + | 26.1767i | 0.243882 | + | 1.53981i | 0.740630 | + | 0.671913i | \(0.234527\pi\) |
−0.496748 | + | 0.867895i | \(0.665473\pi\) | |||||||
\(18\) | −7.10196 | + | 7.10196i | −0.394553 | + | 0.394553i | ||||
\(19\) | 7.05272 | − | 9.70724i | 0.371196 | − | 0.510907i | −0.582029 | − | 0.813168i | \(-0.697741\pi\) |
0.953225 | + | 0.302260i | \(0.0977412\pi\) | |||||||
\(20\) | −34.9719 | − | 8.71745i | −1.74860 | − | 0.435872i | ||||
\(21\) | 7.10642 | − | 5.16312i | 0.338401 | − | 0.245863i | ||||
\(22\) | 26.9943 | + | 4.27548i | 1.22701 | + | 0.194340i | ||||
\(23\) | −29.8372 | − | 15.2028i | −1.29727 | − | 0.660992i | −0.337380 | − | 0.941369i | \(-0.609541\pi\) |
−0.959890 | + | 0.280377i | \(0.909541\pi\) | |||||||
\(24\) | − | 18.6047i | − | 0.775195i | ||||||
\(25\) | 4.33852 | − | 24.6207i | 0.173541 | − | 0.984827i | ||||
\(26\) | 59.5869 | 2.29181 | ||||||||
\(27\) | 2.35900 | − | 4.62981i | 0.0873705 | − | 0.171474i | ||||
\(28\) | −5.71879 | + | 36.1070i | −0.204243 | + | 1.28954i | ||||
\(29\) | 23.3243 | + | 32.1031i | 0.804285 | + | 1.10700i | 0.992180 | + | 0.124814i | \(0.0398334\pi\) |
−0.187895 | + | 0.982189i | \(0.560167\pi\) | |||||||
\(30\) | 28.9229 | − | 2.02407i | 0.964096 | − | 0.0674691i | ||||
\(31\) | −9.95722 | − | 7.23434i | −0.321201 | − | 0.233366i | 0.415487 | − | 0.909599i | \(-0.363611\pi\) |
−0.736688 | + | 0.676233i | \(0.763611\pi\) | |||||||
\(32\) | −13.5082 | − | 13.5082i | −0.422131 | − | 0.422131i | ||||
\(33\) | −13.9656 | + | 2.21194i | −0.423201 | + | 0.0670285i | ||||
\(34\) | 84.3867 | + | 27.4189i | 2.48196 | + | 0.806438i | ||||
\(35\) | −25.2609 | − | 2.20865i | −0.721740 | − | 0.0631043i | ||||
\(36\) | 6.68256 | + | 20.5668i | 0.185627 | + | 0.571300i | ||||
\(37\) | −29.4467 | + | 15.0038i | −0.795857 | + | 0.405509i | −0.804128 | − | 0.594456i | \(-0.797367\pi\) |
0.00827090 | + | 0.999966i | \(0.497367\pi\) | |||||||
\(38\) | −18.2371 | − | 35.7924i | −0.479925 | − | 0.941906i | ||||
\(39\) | −29.3188 | + | 9.52625i | −0.751764 | + | 0.244263i | ||||
\(40\) | −35.2328 | + | 40.5352i | −0.880820 | + | 1.01338i | ||||
\(41\) | 6.99156 | − | 21.5178i | 0.170526 | − | 0.524824i | −0.828875 | − | 0.559434i | \(-0.811019\pi\) |
0.999401 | + | 0.0346093i | \(0.0110187\pi\) | |||||||
\(42\) | −4.60042 | − | 29.0459i | −0.109534 | − | 0.691569i | ||||
\(43\) | −8.95040 | + | 8.95040i | −0.208149 | + | 0.208149i | −0.803480 | − | 0.595331i | \(-0.797021\pi\) |
0.595331 | + | 0.803480i | \(0.297021\pi\) | |||||||
\(44\) | 34.5890 | − | 47.6077i | 0.786114 | − | 1.08199i | ||||
\(45\) | −13.9075 | + | 5.61986i | −0.309054 | + | 0.124886i | ||||
\(46\) | −90.6999 | + | 65.8973i | −1.97174 | + | 1.43255i | ||||
\(47\) | −46.2544 | − | 7.32597i | −0.984136 | − | 0.155872i | −0.356429 | − | 0.934322i | \(-0.616006\pi\) |
−0.627706 | + | 0.778450i | \(0.716006\pi\) | |||||||
\(48\) | −10.9997 | − | 5.60461i | −0.229160 | − | 0.116763i | ||||
\(49\) | − | 23.2804i | − | 0.475109i | ||||||
\(50\) | −66.8492 | − | 50.3631i | −1.33698 | − | 1.00726i | ||||
\(51\) | −45.9046 | −0.900090 | ||||||||
\(52\) | 58.2459 | − | 114.314i | 1.12011 | − | 2.19835i | ||||
\(53\) | −10.1740 | + | 64.2359i | −0.191962 | + | 1.21200i | 0.683951 | + | 0.729528i | \(0.260260\pi\) |
−0.875913 | + | 0.482470i | \(0.839740\pi\) | |||||||
\(54\) | −10.2252 | − | 14.0738i | −0.189356 | − | 0.260626i | ||||
\(55\) | 34.6167 | + | 21.6283i | 0.629394 | + | 0.393241i | ||||
\(56\) | 44.0709 | + | 32.0194i | 0.786980 | + | 0.571775i | ||||
\(57\) | 14.6955 | + | 14.6955i | 0.257815 | + | 0.257815i | ||||
\(58\) | 131.214 | − | 20.7823i | 2.26232 | − | 0.358316i | ||||
\(59\) | 82.9473 | + | 26.9512i | 1.40589 | + | 0.456800i | 0.911089 | − | 0.412209i | \(-0.135243\pi\) |
0.494796 | + | 0.869009i | \(0.335243\pi\) | |||||||
\(60\) | 24.3889 | − | 57.4654i | 0.406482 | − | 0.957756i | ||||
\(61\) | −24.5238 | − | 75.4766i | −0.402030 | − | 1.23732i | −0.923350 | − | 0.383960i | \(-0.874560\pi\) |
0.521319 | − | 0.853362i | \(-0.325440\pi\) | |||||||
\(62\) | −36.7141 | + | 18.7068i | −0.592163 | + | 0.301722i | ||||
\(63\) | 6.90718 | + | 13.5561i | 0.109638 | + | 0.215176i | ||||
\(64\) | −87.9409 | + | 28.5737i | −1.37408 | + | 0.446465i | ||||
\(65\) | 81.9191 | + | 34.7673i | 1.26029 | + | 0.534882i | ||||
\(66\) | −14.6283 | + | 45.0214i | −0.221642 | + | 0.682143i | ||||
\(67\) | −17.6154 | − | 111.219i | −0.262917 | − | 1.65999i | −0.666843 | − | 0.745199i | \(-0.732355\pi\) |
0.403926 | − | 0.914792i | \(-0.367645\pi\) | |||||||
\(68\) | 135.089 | − | 135.089i | 1.98660 | − | 1.98660i | ||||
\(69\) | 34.0923 | − | 46.9240i | 0.494092 | − | 0.680059i | ||||
\(70\) | −44.9828 | + | 71.9962i | −0.642611 | + | 1.02852i | ||||
\(71\) | −25.0631 | + | 18.2094i | −0.353002 | + | 0.256471i | −0.750127 | − | 0.661293i | \(-0.770008\pi\) |
0.397125 | + | 0.917764i | \(0.370008\pi\) | |||||||
\(72\) | 31.8275 | + | 5.04098i | 0.442049 | + | 0.0700137i | ||||
\(73\) | −63.6499 | − | 32.4313i | −0.871917 | − | 0.444264i | −0.0400230 | − | 0.999199i | \(-0.512743\pi\) |
−0.831894 | + | 0.554935i | \(0.812743\pi\) | |||||||
\(74\) | 110.644i | 1.49519i | ||||||||
\(75\) | 40.9437 | + | 14.0930i | 0.545916 | + | 0.187907i | ||||
\(76\) | −86.4923 | −1.13806 | ||||||||
\(77\) | 18.7957 | − | 36.8887i | 0.244101 | − | 0.479074i | ||||
\(78\) | −16.1452 | + | 101.937i | −0.206990 | + | 1.30688i | ||||
\(79\) | −4.19556 | − | 5.77470i | −0.0531084 | − | 0.0730975i | 0.781637 | − | 0.623734i | \(-0.214385\pi\) |
−0.834745 | + | 0.550636i | \(0.814385\pi\) | |||||||
\(80\) | 13.3519 | + | 33.0419i | 0.166899 | + | 0.413023i | ||||
\(81\) | 7.28115 | + | 5.29007i | 0.0898908 | + | 0.0653095i | ||||
\(82\) | −53.5610 | − | 53.5610i | −0.653183 | − | 0.653183i | ||||
\(83\) | −16.9166 | + | 2.67933i | −0.203815 | + | 0.0322811i | −0.257507 | − | 0.966276i | \(-0.582901\pi\) |
0.0536920 | + | 0.998558i | \(0.482901\pi\) | |||||||
\(84\) | −60.2197 | − | 19.5666i | −0.716902 | − | 0.232935i | ||||
\(85\) | 100.015 | + | 86.9323i | 1.17665 | + | 1.02273i | ||||
\(86\) | 13.0952 | + | 40.3029i | 0.152270 | + | 0.468638i | ||||
\(87\) | −61.2394 | + | 31.2030i | −0.703901 | + | 0.358655i | ||||
\(88\) | −39.8097 | − | 78.1309i | −0.452383 | − | 0.887851i | ||||
\(89\) | −1.13062 | + | 0.367359i | −0.0127035 | + | 0.00412763i | −0.315362 | − | 0.948971i | \(-0.602126\pi\) |
0.302658 | + | 0.953099i | \(0.402126\pi\) | |||||||
\(90\) | −4.37409 | + | 50.0276i | −0.0486010 | + | 0.555862i | ||||
\(91\) | 27.8929 | − | 85.8456i | 0.306516 | − | 0.943358i | ||||
\(92\) | 37.7615 | + | 238.417i | 0.410451 | + | 2.59148i | ||||
\(93\) | 15.0739 | − | 15.0739i | 0.162085 | − | 0.162085i | ||||
\(94\) | −92.1560 | + | 126.842i | −0.980383 | + | 1.34938i | ||||
\(95\) | −4.18824 | − | 59.8477i | −0.0440868 | − | 0.629976i | ||||
\(96\) | 26.7689 | − | 19.4488i | 0.278843 | − | 0.202591i | ||||
\(97\) | 82.1151 | + | 13.0058i | 0.846548 | + | 0.134080i | 0.564615 | − | 0.825354i | \(-0.309025\pi\) |
0.281932 | + | 0.959434i | \(0.409025\pi\) | |||||||
\(98\) | −69.4452 | − | 35.3841i | −0.708625 | − | 0.361062i | ||||
\(99\) | − | 24.4907i | − | 0.247381i | ||||||
\(100\) | −161.963 | + | 79.0166i | −1.61963 | + | 0.790166i | ||||
\(101\) | 20.1616 | 0.199620 | 0.0998099 | − | 0.995007i | \(-0.468177\pi\) | ||||
0.0998099 | + | 0.995007i | \(0.468177\pi\) | |||||||
\(102\) | −69.7710 | + | 136.933i | −0.684029 | + | 1.34248i | ||||
\(103\) | −16.6494 | + | 105.120i | −0.161644 | + | 1.02058i | 0.764832 | + | 0.644230i | \(0.222822\pi\) |
−0.926476 | + | 0.376353i | \(0.877178\pi\) | |||||||
\(104\) | −112.372 | − | 154.667i | −1.08050 | − | 1.48719i | ||||
\(105\) | 10.6229 | − | 42.6160i | 0.101170 | − | 0.405867i | ||||
\(106\) | 176.152 | + | 127.982i | 1.66181 | + | 1.20738i | ||||
\(107\) | 150.099 | + | 150.099i | 1.40279 | + | 1.40279i | 0.791075 | + | 0.611719i | \(0.209522\pi\) |
0.611719 | + | 0.791075i | \(0.290478\pi\) | |||||||
\(108\) | −36.9948 | + | 5.85941i | −0.342545 | + | 0.0542538i | ||||
\(109\) | 66.6825 | + | 21.6664i | 0.611766 | + | 0.198775i | 0.598481 | − | 0.801137i | \(-0.295771\pi\) |
0.0132847 | + | 0.999912i | \(0.495771\pi\) | |||||||
\(110\) | 117.131 | − | 70.3884i | 1.06483 | − | 0.639894i | ||||
\(111\) | −17.6888 | − | 54.4406i | −0.159359 | − | 0.490456i | ||||
\(112\) | 32.2071 | − | 16.4103i | 0.287563 | − | 0.146521i | ||||
\(113\) | −12.8863 | − | 25.2908i | −0.114038 | − | 0.223812i | 0.826932 | − | 0.562302i | \(-0.190084\pi\) |
−0.940970 | + | 0.338490i | \(0.890084\pi\) | |||||||
\(114\) | 66.1724 | − | 21.5007i | 0.580460 | − | 0.188603i | ||||
\(115\) | −163.142 | + | 37.6737i | −1.41863 | + | 0.327597i | ||||
\(116\) | 88.3916 | − | 272.041i | 0.761996 | − | 2.34518i | ||||
\(117\) | −8.35281 | − | 52.7376i | −0.0713916 | − | 0.450749i | ||||
\(118\) | 206.468 | − | 206.468i | 1.74973 | − | 1.74973i | ||||
\(119\) | 79.0036 | − | 108.739i | 0.663896 | − | 0.913774i | ||||
\(120\) | −59.7982 | − | 71.2568i | −0.498318 | − | 0.593807i | ||||
\(121\) | 43.9750 | − | 31.9497i | 0.363430 | − | 0.264047i | ||||
\(122\) | −262.421 | − | 41.5634i | −2.15099 | − | 0.340683i | ||||
\(123\) | 34.9167 | + | 17.7909i | 0.283875 | + | 0.144642i | ||||
\(124\) | 88.7196i | 0.715481i | ||||||||
\(125\) | −62.5177 | − | 108.243i | −0.500142 | − | 0.865943i | ||||
\(126\) | 50.9361 | 0.404255 | ||||||||
\(127\) | −75.5353 | + | 148.246i | −0.594766 | + | 1.16729i | 0.375855 | + | 0.926679i | \(0.377349\pi\) |
−0.970621 | + | 0.240615i | \(0.922651\pi\) | |||||||
\(128\) | −36.4734 | + | 230.284i | −0.284948 | + | 1.79909i | ||||
\(129\) | −12.8866 | − | 17.7368i | −0.0998958 | − | 0.137495i | ||||
\(130\) | 228.221 | − | 191.521i | 1.75554 | − | 1.47324i | ||||
\(131\) | −97.4968 | − | 70.8356i | −0.744251 | − | 0.540730i | 0.149789 | − | 0.988718i | \(-0.452141\pi\) |
−0.894039 | + | 0.447988i | \(0.852141\pi\) | |||||||
\(132\) | 72.0718 | + | 72.0718i | 0.545998 | + | 0.545998i | ||||
\(133\) | −60.1022 | + | 9.51926i | −0.451896 | + | 0.0715734i | ||||
\(134\) | −358.541 | − | 116.497i | −2.67568 | − | 0.869381i | ||||
\(135\) | −5.84578 | − | 25.3146i | −0.0433021 | − | 0.187515i | ||||
\(136\) | −87.9710 | − | 270.747i | −0.646846 | − | 1.99079i | ||||
\(137\) | 197.518 | − | 100.641i | 1.44174 | − | 0.734603i | 0.454042 | − | 0.890980i | \(-0.349982\pi\) |
0.987697 | + | 0.156377i | \(0.0499816\pi\) | |||||||
\(138\) | −88.1569 | − | 173.018i | −0.638818 | − | 1.25375i | ||||
\(139\) | −6.03287 | + | 1.96020i | −0.0434019 | + | 0.0141021i | −0.330637 | − | 0.943758i | \(-0.607264\pi\) |
0.287236 | + | 0.957860i | \(0.407264\pi\) | |||||||
\(140\) | 94.1501 | + | 156.673i | 0.672501 | + | 1.11909i | ||||
\(141\) | 25.0655 | − | 77.1436i | 0.177769 | − | 0.547118i | ||||
\(142\) | 16.2249 | + | 102.440i | 0.114260 | + | 0.721409i | ||||
\(143\) | −102.741 | + | 102.741i | −0.718470 | + | 0.718470i | ||||
\(144\) | 12.5684 | − | 17.2989i | 0.0872802 | − | 0.120131i | ||||
\(145\) | 192.517 | + | 47.9887i | 1.32770 | + | 0.330957i | ||||
\(146\) | −193.485 | + | 140.575i | −1.32524 | + | 0.962841i | ||||
\(147\) | 39.8263 | + | 6.30787i | 0.270927 | + | 0.0429107i | ||||
\(148\) | 212.264 | + | 108.154i | 1.43422 | + | 0.730769i | ||||
\(149\) | 114.482i | 0.768336i | 0.923263 | + | 0.384168i | \(0.125512\pi\) | ||||
−0.923263 | + | 0.384168i | \(0.874488\pi\) | |||||||
\(150\) | 104.270 | − | 100.715i | 0.695136 | − | 0.671432i | ||||
\(151\) | −17.3173 | −0.114684 | −0.0573421 | − | 0.998355i | \(-0.518263\pi\) | ||||
−0.0573421 | + | 0.998355i | \(0.518263\pi\) | |||||||
\(152\) | −58.5122 | + | 114.837i | −0.384949 | + | 0.755505i | ||||
\(153\) | 12.4380 | − | 78.5302i | 0.0812939 | − | 0.513269i | ||||
\(154\) | −81.4711 | − | 112.135i | −0.529033 | − | 0.728151i | ||||
\(155\) | −61.3888 | + | 4.29609i | −0.396057 | + | 0.0277167i | ||||
\(156\) | 179.778 | + | 130.616i | 1.15242 | + | 0.837285i | ||||
\(157\) | −5.55440 | − | 5.55440i | −0.0353783 | − | 0.0353783i | 0.689196 | − | 0.724575i | \(-0.257964\pi\) |
−0.724575 | + | 0.689196i | \(0.757964\pi\) | |||||||
\(158\) | −23.6028 | + | 3.73832i | −0.149385 | + | 0.0236602i | ||||
\(159\) | −107.133 | − | 34.8097i | −0.673794 | − | 0.218929i | ||||
\(160\) | −95.1544 | − | 8.31969i | −0.594715 | − | 0.0519981i | ||||
\(161\) | 52.4798 | + | 161.516i | 0.325961 | + | 1.00321i | ||||
\(162\) | 26.8470 | − | 13.6792i | 0.165722 | − | 0.0844396i | ||||
\(163\) | 6.93150 | + | 13.6038i | 0.0425245 | + | 0.0834591i | 0.911291 | − | 0.411763i | \(-0.135087\pi\) |
−0.868767 | + | 0.495222i | \(0.835087\pi\) | |||||||
\(164\) | −155.109 | + | 50.3980i | −0.945787 | + | 0.307305i | ||||
\(165\) | −46.3795 | + | 53.3595i | −0.281088 | + | 0.323391i | ||||
\(166\) | −17.7194 | + | 54.5347i | −0.106743 | + | 0.328522i | ||||
\(167\) | −35.4877 | − | 224.061i | −0.212501 | − | 1.34168i | −0.831165 | − | 0.556025i | \(-0.812326\pi\) |
0.618664 | − | 0.785656i | \(-0.287674\pi\) | |||||||
\(168\) | −66.7175 | + | 66.7175i | −0.397128 | + | 0.397128i | ||||
\(169\) | −86.8631 | + | 119.557i | −0.513983 | + | 0.707437i | ||||
\(170\) | 411.333 | − | 166.216i | 2.41961 | − | 0.977738i | ||||
\(171\) | −29.1217 | + | 21.1582i | −0.170302 | + | 0.123732i | ||||
\(172\) | 90.1191 | + | 14.2735i | 0.523948 | + | 0.0829853i | ||||
\(173\) | −4.00151 | − | 2.03887i | −0.0231301 | − | 0.0117854i | 0.442387 | − | 0.896824i | \(-0.354132\pi\) |
−0.465517 | + | 0.885039i | \(0.654132\pi\) | |||||||
\(174\) | 230.103i | 1.32243i | ||||||||
\(175\) | −103.849 | + | 72.7330i | −0.593425 | + | 0.415617i | ||||
\(176\) | −58.1860 | −0.330602 | ||||||||
\(177\) | −68.5809 | + | 134.598i | −0.387463 | + | 0.760438i | ||||
\(178\) | −0.622605 | + | 3.93098i | −0.00349778 | + | 0.0220841i | ||||
\(179\) | −111.815 | − | 153.900i | −0.624664 | − | 0.859776i | 0.373018 | − | 0.927824i | \(-0.378323\pi\) |
−0.997682 | + | 0.0680483i | \(0.978323\pi\) | |||||||
\(180\) | 91.6993 | + | 57.2931i | 0.509440 | + | 0.318295i | ||||
\(181\) | −178.031 | − | 129.347i | −0.983596 | − | 0.714624i | −0.0250865 | − | 0.999685i | \(-0.507986\pi\) |
−0.958509 | + | 0.285061i | \(0.907986\pi\) | |||||||
\(182\) | −213.682 | − | 213.682i | −1.17408 | − | 1.17408i | ||||
\(183\) | 135.765 | − | 21.5030i | 0.741884 | − | 0.117503i | ||||
\(184\) | 342.094 | + | 111.153i | 1.85921 | + | 0.604092i | ||||
\(185\) | −64.5577 | + | 152.111i | −0.348960 | + | 0.822224i | ||||
\(186\) | −22.0544 | − | 67.8765i | −0.118572 | − | 0.364927i | ||||
\(187\) | −192.778 | + | 98.2251i | −1.03090 | + | 0.525268i | ||||
\(188\) | 153.257 | + | 300.783i | 0.815194 | + | 1.59991i | ||||
\(189\) | −25.0623 | + | 8.14323i | −0.132605 | + | 0.0430859i | ||||
\(190\) | −184.891 | − | 78.4698i | −0.973112 | − | 0.412999i | ||||
\(191\) | −36.4604 | + | 112.214i | −0.190892 | + | 0.587506i | −1.00000 | 0.000154600i | \(-0.999951\pi\) | |
0.809108 | + | 0.587660i | \(0.199951\pi\) | |||||||
\(192\) | −25.0540 | − | 158.185i | −0.130490 | − | 0.823880i | ||||
\(193\) | 63.8407 | − | 63.8407i | 0.330781 | − | 0.330781i | −0.522102 | − | 0.852883i | \(-0.674852\pi\) |
0.852883 | + | 0.522102i | \(0.174852\pi\) | |||||||
\(194\) | 163.604 | − | 225.182i | 0.843319 | − | 1.16073i | ||||
\(195\) | −81.6736 | + | 130.721i | −0.418839 | + | 0.670364i | ||||
\(196\) | −135.765 | + | 98.6388i | −0.692677 | + | 0.503259i | ||||
\(197\) | 84.0087 | + | 13.3057i | 0.426440 | + | 0.0675415i | 0.365966 | − | 0.930628i | \(-0.380739\pi\) |
0.0604744 | + | 0.998170i | \(0.480739\pi\) | |||||||
\(198\) | −73.0557 | − | 37.2238i | −0.368968 | − | 0.187999i | ||||
\(199\) | − | 112.218i | − | 0.563909i | −0.959428 | − | 0.281954i | \(-0.909017\pi\) | ||
0.959428 | − | 0.281954i | \(-0.0909827\pi\) | |||||||
\(200\) | −4.65726 | + | 268.495i | −0.0232863 | + | 1.34248i | ||||
\(201\) | 195.039 | 0.970342 | ||||||||
\(202\) | 30.6439 | − | 60.1420i | 0.151702 | − | 0.297733i | ||||
\(203\) | 31.4814 | − | 198.766i | 0.155081 | − | 0.979142i | ||||
\(204\) | 194.498 | + | 267.703i | 0.953419 | + | 1.31227i | ||||
\(205\) | −42.3834 | − | 104.886i | −0.206748 | − | 0.511639i | ||||
\(206\) | 288.267 | + | 209.438i | 1.39936 | + | 1.01669i | ||||
\(207\) | 71.0368 | + | 71.0368i | 0.343173 | + | 0.343173i | ||||
\(208\) | −125.296 | + | 19.8449i | −0.602385 | + | 0.0954084i | ||||
\(209\) | 93.1590 | + | 30.2692i | 0.445737 | + | 0.144829i | ||||
\(210\) | −110.978 | − | 96.4608i | −0.528465 | − | 0.459337i | ||||
\(211\) | 31.2858 | + | 96.2878i | 0.148274 | + | 0.456340i | 0.997417 | − | 0.0718220i | \(-0.0228813\pi\) |
−0.849144 | + | 0.528162i | \(0.822881\pi\) | |||||||
\(212\) | 417.713 | − | 212.835i | 1.97034 | − | 1.00394i | ||||
\(213\) | −24.3605 | − | 47.8101i | −0.114368 | − | 0.224460i | ||||
\(214\) | 675.882 | − | 219.607i | 3.15833 | − | 1.02620i | ||||
\(215\) | −5.51255 | + | 63.0484i | −0.0256398 | + | 0.293248i | ||||
\(216\) | −17.2475 | + | 53.0823i | −0.0798495 | + | 0.245751i | ||||
\(217\) | 9.76439 | + | 61.6499i | 0.0449972 | + | 0.284101i | ||||
\(218\) | 165.982 | − | 165.982i | 0.761388 | − | 0.761388i | ||||
\(219\) | 72.7271 | − | 100.100i | 0.332087 | − | 0.457079i | ||||
\(220\) | −20.5406 | − | 293.514i | −0.0933664 | − | 1.33415i | ||||
\(221\) | −381.621 | + | 277.264i | −1.72679 | + | 1.25459i | ||||
\(222\) | −189.282 | − | 29.9793i | −0.852620 | − | 0.135042i | ||||
\(223\) | 164.504 | + | 83.8191i | 0.737688 | + | 0.375871i | 0.782108 | − | 0.623142i | \(-0.214144\pi\) |
−0.0444209 | + | 0.999013i | \(0.514144\pi\) | |||||||
\(224\) | 96.8824i | 0.432511i | ||||||||
\(225\) | −35.2031 | + | 66.2249i | −0.156458 | + | 0.294333i | ||||
\(226\) | −95.0283 | −0.420479 | ||||||||
\(227\) | 98.2222 | − | 192.772i | 0.432697 | − | 0.849216i | −0.566978 | − | 0.823733i | \(-0.691888\pi\) |
0.999675 | − | 0.0254830i | \(-0.00811238\pi\) | |||||||
\(228\) | 23.4353 | − | 147.965i | 0.102786 | − | 0.648968i | ||||
\(229\) | −0.628163 | − | 0.864593i | −0.00274307 | − | 0.00377551i | 0.807643 | − | 0.589671i | \(-0.200743\pi\) |
−0.810386 | + | 0.585896i | \(0.800743\pi\) | |||||||
\(230\) | −135.581 | + | 543.913i | −0.589483 | + | 2.36484i | ||||
\(231\) | 58.0138 | + | 42.1495i | 0.251142 | + | 0.182465i | ||||
\(232\) | −301.395 | − | 301.395i | −1.29912 | − | 1.29912i | ||||
\(233\) | −412.482 | + | 65.3308i | −1.77031 | + | 0.280390i | −0.954561 | − | 0.298016i | \(-0.903675\pi\) |
−0.815750 | + | 0.578405i | \(0.803675\pi\) | |||||||
\(234\) | −170.012 | − | 55.2401i | −0.726545 | − | 0.236069i | ||||
\(235\) | −200.703 | + | 120.610i | −0.854056 | + | 0.513232i | ||||
\(236\) | −194.275 | − | 597.918i | −0.823200 | − | 2.53355i | ||||
\(237\) | 11.0157 | − | 5.61279i | 0.0464799 | − | 0.0236827i | ||||
\(238\) | −204.290 | − | 400.941i | −0.858361 | − | 1.68463i | ||||
\(239\) | 70.0752 | − | 22.7688i | 0.293202 | − | 0.0952670i | −0.158723 | − | 0.987323i | \(-0.550738\pi\) |
0.451925 | + | 0.892056i | \(0.350738\pi\) | |||||||
\(240\) | −60.1433 | + | 13.8886i | −0.250597 | + | 0.0578693i | ||||
\(241\) | 14.6723 | − | 45.1568i | 0.0608811 | − | 0.187373i | −0.915990 | − | 0.401200i | \(-0.868593\pi\) |
0.976871 | + | 0.213828i | \(0.0685931\pi\) | |||||||
\(242\) | −28.4677 | − | 179.738i | −0.117635 | − | 0.742719i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | −336.252 | + | 462.811i | −1.37808 | + | 1.89676i | ||||
\(245\) | −74.8265 | − | 89.1648i | −0.305414 | − | 0.363938i | ||||
\(246\) | 106.141 | − | 77.1157i | 0.431466 | − | 0.313478i | ||||
\(247\) | 210.929 | + | 33.4079i | 0.853965 | + | 0.135255i | ||||
\(248\) | 117.794 | + | 60.0190i | 0.474975 | + | 0.242012i | ||||
\(249\) | − | 29.6657i | − | 0.119139i | ||||||
\(250\) | −417.910 | + | 21.9704i | −1.67164 | + | 0.0878816i | ||||
\(251\) | 94.4412 | 0.376260 | 0.188130 | − | 0.982144i | \(-0.439757\pi\) | ||||
0.188130 | + | 0.982144i | \(0.439757\pi\) | |||||||
\(252\) | 49.7897 | − | 97.7179i | 0.197578 | − | 0.387769i | ||||
\(253\) | 42.7651 | − | 270.008i | 0.169032 | − | 1.06723i | ||||
\(254\) | 327.411 | + | 450.643i | 1.28902 | + | 1.77419i | ||||
\(255\) | −175.817 | + | 147.544i | −0.689477 | + | 0.578604i | ||||
\(256\) | 332.272 | + | 241.410i | 1.29794 | + | 0.943007i | ||||
\(257\) | 232.079 | + | 232.079i | 0.903031 | + | 0.903031i | 0.995697 | − | 0.0926660i | \(-0.0295389\pi\) |
−0.0926660 | + | 0.995697i | \(0.529539\pi\) | |||||||
\(258\) | −72.4954 | + | 11.4821i | −0.280990 | + | 0.0445044i | ||||
\(259\) | 159.402 | + | 51.7930i | 0.615453 | + | 0.199973i | ||||
\(260\) | −144.338 | − | 625.039i | −0.555144 | − | 2.40400i | ||||
\(261\) | −36.7869 | − | 113.218i | −0.140946 | − | 0.433787i | ||||
\(262\) | −359.489 | + | 183.169i | −1.37210 | + | 0.699118i | ||||
\(263\) | −20.4201 | − | 40.0768i | −0.0776431 | − | 0.152383i | 0.848921 | − | 0.528519i | \(-0.177253\pi\) |
−0.926564 | + | 0.376136i | \(0.877253\pi\) | |||||||
\(264\) | 144.447 | − | 46.9337i | 0.547148 | − | 0.177779i | ||||
\(265\) | 167.497 | + | 278.727i | 0.632063 | + | 1.05180i | ||||
\(266\) | −62.9542 | + | 193.753i | −0.236670 | + | 0.728396i | ||||
\(267\) | −0.322108 | − | 2.03371i | −0.00120640 | − | 0.00761689i | ||||
\(268\) | −573.964 | + | 573.964i | −2.14166 | + | 2.14166i | ||||
\(269\) | −59.8116 | + | 82.3236i | −0.222348 | + | 0.306036i | −0.905588 | − | 0.424158i | \(-0.860570\pi\) |
0.683240 | + | 0.730194i | \(0.260570\pi\) | |||||||
\(270\) | −84.3983 | − | 21.0380i | −0.312586 | − | 0.0779184i | ||||
\(271\) | 238.788 | − | 173.490i | 0.881137 | − | 0.640183i | −0.0524153 | − | 0.998625i | \(-0.516692\pi\) |
0.933552 | + | 0.358442i | \(0.116692\pi\) | |||||||
\(272\) | −186.575 | − | 29.5506i | −0.685938 | − | 0.108642i | ||||
\(273\) | 139.301 | + | 70.9772i | 0.510259 | + | 0.259990i | ||||
\(274\) | − | 742.161i | − | 2.70862i | ||||||
\(275\) | 202.100 | − | 28.4258i | 0.734909 | − | 0.103367i | ||||
\(276\) | −418.097 | −1.51484 | ||||||||
\(277\) | 228.565 | − | 448.584i | 0.825145 | − | 1.61944i | 0.0407548 | − | 0.999169i | \(-0.487024\pi\) |
0.784390 | − | 0.620268i | \(-0.212976\pi\) | |||||||
\(278\) | −3.32217 | + | 20.9754i | −0.0119502 | + | 0.0754509i | ||||
\(279\) | 21.7030 | + | 29.8716i | 0.0777886 | + | 0.107067i | ||||
\(280\) | 271.709 | − | 19.0146i | 0.970388 | − | 0.0679094i | ||||
\(281\) | −8.79106 | − | 6.38708i | −0.0312849 | − | 0.0227298i | 0.572033 | − | 0.820231i | \(-0.306155\pi\) |
−0.603318 | + | 0.797501i | \(0.706155\pi\) | |||||||
\(282\) | −192.022 | − | 192.022i | −0.680928 | − | 0.680928i | ||||
\(283\) | −155.546 | + | 24.6361i | −0.549632 | + | 0.0870532i | −0.425073 | − | 0.905159i | \(-0.639752\pi\) |
−0.124559 | + | 0.992212i | \(0.539752\pi\) | |||||||
\(284\) | 212.385 | + | 69.0080i | 0.747834 | + | 0.242986i | ||||
\(285\) | 103.518 | + | 9.05094i | 0.363220 | + | 0.0317577i | ||||
\(286\) | 150.319 | + | 462.634i | 0.525591 | + | 1.61760i | ||||
\(287\) | −102.236 | + | 52.0920i | −0.356224 | + | 0.181505i | ||||
\(288\) | 26.0184 | + | 51.0640i | 0.0903417 | + | 0.177305i | ||||
\(289\) | −393.177 | + | 127.751i | −1.36047 | + | 0.442045i | ||||
\(290\) | 435.759 | − | 501.339i | 1.50262 | − | 1.72876i | ||||
\(291\) | −44.4986 | + | 136.953i | −0.152916 | + | 0.470627i | ||||
\(292\) | 80.5543 | + | 508.600i | 0.275871 | + | 1.74178i | ||||
\(293\) | 170.980 | − | 170.980i | 0.583549 | − | 0.583549i | −0.352328 | − | 0.935877i | \(-0.614610\pi\) |
0.935877 | + | 0.352328i | \(0.114610\pi\) | |||||||
\(294\) | 79.3489 | − | 109.214i | 0.269894 | − | 0.371477i | ||||
\(295\) | 404.317 | − | 163.380i | 1.37057 | − | 0.553832i | ||||
\(296\) | 287.194 | − | 208.659i | 0.970249 | − | 0.704927i | ||||
\(297\) | 41.8969 | + | 6.63582i | 0.141067 | + | 0.0223428i | ||||
\(298\) | 341.500 | + | 174.003i | 1.14597 | + | 0.583902i | ||||
\(299\) | − | 596.014i | − | 1.99336i | ||||||
\(300\) | −91.2915 | − | 298.485i | −0.304305 | − | 0.994948i | ||||
\(301\) | 64.1934 | 0.213267 | ||||||||
\(302\) | −26.3208 | + | 51.6575i | −0.0871551 | + | 0.171051i | ||||
\(303\) | −5.46283 | + | 34.4910i | −0.0180292 | + | 0.113832i | ||||
\(304\) | 50.2684 | + | 69.1885i | 0.165357 | + | 0.227594i | ||||
\(305\) | −336.521 | − | 210.256i | −1.10335 | − | 0.689363i | ||||
\(306\) | −215.351 | − | 156.461i | −0.703761 | − | 0.511312i | ||||
\(307\) | −15.9029 | − | 15.9029i | −0.0518008 | − | 0.0518008i | 0.680732 | − | 0.732533i | \(-0.261662\pi\) |
−0.732533 | + | 0.680732i | \(0.761662\pi\) | |||||||
\(308\) | −294.762 | + | 46.6858i | −0.957021 | + | 0.151577i | ||||
\(309\) | −175.320 | − | 56.9651i | −0.567380 | − | 0.184353i | ||||
\(310\) | −80.4905 | + | 189.652i | −0.259647 | + | 0.611782i | ||||
\(311\) | 83.1955 | + | 256.049i | 0.267510 | + | 0.823310i | 0.991105 | + | 0.133085i | \(0.0424883\pi\) |
−0.723595 | + | 0.690225i | \(0.757512\pi\) | |||||||
\(312\) | 295.041 | − | 150.331i | 0.945644 | − | 0.481830i | ||||
\(313\) | 45.8839 | + | 90.0523i | 0.146594 | + | 0.287707i | 0.952614 | − | 0.304181i | \(-0.0983828\pi\) |
−0.806020 | + | 0.591888i | \(0.798383\pi\) | |||||||
\(314\) | −25.0109 | + | 8.12655i | −0.0796527 | + | 0.0258807i | ||||
\(315\) | 70.0261 | + | 29.7198i | 0.222305 | + | 0.0943486i | ||||
\(316\) | −15.8999 | + | 48.9348i | −0.0503160 | + | 0.154857i | ||||
\(317\) | −20.1030 | − | 126.926i | −0.0634165 | − | 0.400396i | −0.998894 | − | 0.0470107i | \(-0.985030\pi\) |
0.935478 | − | 0.353385i | \(-0.114970\pi\) | |||||||
\(318\) | −266.671 | + | 266.671i | −0.838587 | + | 0.838587i | ||||
\(319\) | −190.409 | + | 262.076i | −0.596894 | + | 0.821555i | ||||
\(320\) | −244.978 | + | 392.094i | −0.765555 | + | 1.22529i | ||||
\(321\) | −297.448 | + | 216.109i | −0.926629 | + | 0.673235i | ||||
\(322\) | 561.567 | + | 88.9435i | 1.74400 | + | 0.276222i | ||||
\(323\) | 283.344 | + | 144.371i | 0.877227 | + | 0.446970i | ||||
\(324\) | − | 64.8757i | − | 0.200234i | ||||||
\(325\) | 425.501 | − | 130.140i | 1.30923 | − | 0.400430i | ||||
\(326\) | 51.1155 | 0.156796 | ||||||||
\(327\) | −55.1331 | + | 108.205i | −0.168603 | + | 0.330902i | ||||
\(328\) | −38.0177 | + | 240.034i | −0.115908 | + | 0.731811i | ||||
\(329\) | 139.600 | + | 192.142i | 0.424315 | + | 0.584019i | ||||
\(330\) | 88.6782 | + | 219.452i | 0.268722 | + | 0.665005i | ||||
\(331\) | 315.837 | + | 229.469i | 0.954191 | + | 0.693260i | 0.951794 | − | 0.306737i | \(-0.0992372\pi\) |
0.00239645 | + | 0.999997i | \(0.499237\pi\) | |||||||
\(332\) | 87.3009 | + | 87.3009i | 0.262955 | + | 0.262955i | ||||
\(333\) | 97.9258 | − | 15.5099i | 0.294071 | − | 0.0465763i | ||||
\(334\) | −722.311 | − | 234.693i | −2.16261 | − | 0.702674i | ||||
\(335\) | −424.943 | − | 369.357i | −1.26849 | − | 1.10256i | ||||
\(336\) | 19.3470 | + | 59.5440i | 0.0575804 | + | 0.177214i | ||||
\(337\) | −242.809 | + | 123.717i | −0.720501 | + | 0.367114i | −0.775478 | − | 0.631374i | \(-0.782491\pi\) |
0.0549775 | + | 0.998488i | \(0.482491\pi\) | |||||||
\(338\) | 224.613 | + | 440.828i | 0.664536 | + | 1.30423i | ||||
\(339\) | 46.7571 | − | 15.1923i | 0.137927 | − | 0.0448151i | ||||
\(340\) | 83.2012 | − | 951.593i | 0.244709 | − | 2.79880i | ||||
\(341\) | 31.0487 | − | 95.5580i | 0.0910518 | − | 0.280229i | ||||
\(342\) | 18.8523 | + | 119.029i | 0.0551236 | + | 0.348037i | ||||
\(343\) | −259.202 | + | 259.202i | −0.755690 | + | 0.755690i | ||||
\(344\) | 79.9168 | − | 109.996i | 0.232316 | − | 0.319756i | ||||
\(345\) | −20.2456 | − | 289.299i | −0.0586830 | − | 0.838548i | ||||
\(346\) | −12.1639 | + | 8.83759i | −0.0351558 | + | 0.0255422i | ||||
\(347\) | 162.867 | + | 25.7956i | 0.469357 | + | 0.0743389i | 0.386633 | − | 0.922234i | \(-0.373638\pi\) |
0.0827242 | + | 0.996572i | \(0.473638\pi\) | |||||||
\(348\) | 441.438 | + | 224.924i | 1.26850 | + | 0.646334i | ||||
\(349\) | − | 504.026i | − | 1.44420i | −0.691789 | − | 0.722100i | \(-0.743177\pi\) | ||
0.691789 | − | 0.722100i | \(-0.256823\pi\) | |||||||
\(350\) | 59.1204 | + | 420.330i | 0.168915 | + | 1.20094i | ||||
\(351\) | 92.4828 | 0.263484 | ||||||||
\(352\) | 70.8010 | − | 138.955i | 0.201139 | − | 0.394758i | ||||
\(353\) | 2.03030 | − | 12.8188i | 0.00575157 | − | 0.0363140i | −0.984646 | − | 0.174565i | \(-0.944148\pi\) |
0.990397 | + | 0.138251i | \(0.0441481\pi\) | |||||||
\(354\) | 297.267 | + | 409.153i | 0.839738 | + | 1.15580i | ||||
\(355\) | −37.4652 | + | 150.300i | −0.105536 | + | 0.423379i | ||||
\(356\) | 6.93275 | + | 5.03694i | 0.0194740 | + | 0.0141487i | ||||
\(357\) | 164.617 | + | 164.617i | 0.461111 | + | 0.461111i | ||||
\(358\) | −629.032 | + | 99.6288i | −1.75707 | + | 0.278293i | ||||
\(359\) | 43.0843 | + | 13.9989i | 0.120012 | + | 0.0389942i | 0.368407 | − | 0.929664i | \(-0.379903\pi\) |
−0.248395 | + | 0.968659i | \(0.579903\pi\) | |||||||
\(360\) | 138.103 | − | 82.9911i | 0.383620 | − | 0.230531i | ||||
\(361\) | 67.0655 | + | 206.406i | 0.185777 | + | 0.571763i | ||||
\(362\) | −656.433 | + | 334.469i | −1.81335 | + | 0.923949i | ||||
\(363\) | 42.7421 | + | 83.8860i | 0.117747 | + | 0.231091i | ||||
\(364\) | −618.810 | + | 201.064i | −1.70003 | + | 0.552372i | ||||
\(365\) | −348.021 | + | 80.3670i | −0.953482 | + | 0.220184i | ||||
\(366\) | 142.207 | − | 437.668i | 0.388544 | − | 1.19582i | ||||
\(367\) | −54.4774 | − | 343.957i | −0.148440 | − | 0.937212i | −0.943666 | − | 0.330899i | \(-0.892648\pi\) |
0.795226 | − | 0.606313i | \(-0.207352\pi\) | |||||||
\(368\) | 168.772 | − | 168.772i | 0.458620 | − | 0.458620i | ||||
\(369\) | −39.8962 | + | 54.9124i | −0.108120 | + | 0.148814i | ||||
\(370\) | 355.626 | + | 423.772i | 0.961151 | + | 1.14533i | ||||
\(371\) | 266.838 | − | 193.869i | 0.719240 | − | 0.522558i | ||||
\(372\) | −151.775 | − | 24.0388i | −0.407997 | − | 0.0646204i | ||||
\(373\) | −535.377 | − | 272.788i | −1.43533 | − | 0.731336i | −0.448602 | − | 0.893732i | \(-0.648078\pi\) |
−0.986726 | + | 0.162396i | \(0.948078\pi\) | |||||||
\(374\) | 724.349i | 1.93676i | ||||||||
\(375\) | 202.113 | − | 77.6221i | 0.538969 | − | 0.206992i | ||||
\(376\) | 503.031 | 1.33785 | ||||||||
\(377\) | −320.638 | + | 629.288i | −0.850499 | + | 1.66920i | ||||
\(378\) | −13.8013 | + | 87.1377i | −0.0365113 | + | 0.230523i | ||||
\(379\) | −126.752 | − | 174.459i | −0.334437 | − | 0.460313i | 0.608369 | − | 0.793654i | \(-0.291824\pi\) |
−0.942806 | + | 0.333341i | \(0.891824\pi\) | |||||||
\(380\) | −331.270 | + | 277.999i | −0.871762 | + | 0.731576i | ||||
\(381\) | −233.142 | − | 169.388i | −0.611922 | − | 0.444588i | ||||
\(382\) | 279.316 | + | 279.316i | 0.731194 | + | 0.731194i | ||||
\(383\) | 68.3267 | − | 10.8219i | 0.178399 | − | 0.0282556i | −0.0665959 | − | 0.997780i | \(-0.521214\pi\) |
0.244995 | + | 0.969524i | \(0.421214\pi\) | |||||||
\(384\) | −384.070 | − | 124.792i | −1.00018 | − | 0.324979i | ||||
\(385\) | −46.5772 | − | 201.698i | −0.120980 | − | 0.523890i | ||||
\(386\) | −93.4043 | − | 287.469i | −0.241980 | − | 0.744738i | ||||
\(387\) | 33.8345 | − | 17.2395i | 0.0874277 | − | 0.0445466i | ||||
\(388\) | −272.075 | − | 533.978i | −0.701225 | − | 1.37623i | ||||
\(389\) | −199.223 | + | 64.7314i | −0.512140 | + | 0.166405i | −0.553675 | − | 0.832733i | \(-0.686775\pi\) |
0.0415350 | + | 0.999137i | \(0.486775\pi\) | |||||||
\(390\) | 265.803 | + | 442.316i | 0.681547 | + | 1.13414i | ||||
\(391\) | 274.255 | − | 844.071i | 0.701420 | − | 2.15875i | ||||
\(392\) | 39.1186 | + | 246.985i | 0.0997924 | + | 0.630065i | ||||
\(393\) | 147.597 | − | 147.597i | 0.375566 | − | 0.375566i | ||||
\(394\) | 167.377 | − | 230.374i | 0.424814 | − | 0.584707i | ||||
\(395\) | −34.6299 | − | 8.63220i | −0.0876707 | − | 0.0218537i | ||||
\(396\) | −142.823 | + | 103.767i | −0.360664 | + | 0.262038i | ||||
\(397\) | −328.529 | − | 52.0338i | −0.827528 | − | 0.131068i | −0.271718 | − | 0.962377i | \(-0.587592\pi\) |
−0.555810 | + | 0.831309i | \(0.687592\pi\) | |||||||
\(398\) | −334.746 | − | 170.561i | −0.841069 | − | 0.428546i | ||||
\(399\) | − | 105.398i | − | 0.264155i | ||||||
\(400\) | 157.340 | + | 83.6370i | 0.393349 | + | 0.209092i | ||||
\(401\) | −143.082 | −0.356813 | −0.178406 | − | 0.983957i | \(-0.557094\pi\) | ||||
−0.178406 | + | 0.983957i | \(0.557094\pi\) | |||||||
\(402\) | 296.442 | − | 581.800i | 0.737418 | − | 1.44726i | ||||
\(403\) | 34.2682 | − | 216.361i | 0.0850329 | − | 0.536876i | ||||
\(404\) | −85.4246 | − | 117.577i | −0.211447 | − | 0.291032i | ||||
\(405\) | 44.8902 | − | 3.14149i | 0.110840 | − | 0.00775677i | ||||
\(406\) | −545.069 | − | 396.016i | −1.34253 | − | 0.975408i | ||||
\(407\) | −190.775 | − | 190.775i | −0.468734 | − | 0.468734i | ||||
\(408\) | 487.010 | − | 77.1348i | 1.19365 | − | 0.189056i | ||||
\(409\) | 711.765 | + | 231.266i | 1.74026 | + | 0.565444i | 0.994868 | − | 0.101186i | \(-0.0322637\pi\) |
0.745389 | + | 0.666630i | \(0.232264\pi\) | |||||||
\(410\) | −377.294 | − | 32.9882i | −0.920229 | − | 0.0804590i | ||||
\(411\) | 118.650 | + | 365.169i | 0.288687 | + | 0.888488i | ||||
\(412\) | 683.574 | − | 348.299i | 1.65916 | − | 0.845385i | ||||
\(413\) | −200.805 | − | 394.102i | −0.486211 | − | 0.954243i | ||||
\(414\) | 319.872 | − | 103.933i | 0.772639 | − | 0.251045i | ||||
\(415\) | −56.1798 | + | 64.6346i | −0.135373 | + | 0.155746i | ||||
\(416\) | 105.069 | − | 323.369i | 0.252569 | − | 0.777329i | ||||
\(417\) | −1.71874 | − | 10.8517i | −0.00412168 | − | 0.0260233i | ||||
\(418\) | 231.886 | − | 231.886i | 0.554752 | − | 0.554752i | ||||
\(419\) | −91.4003 | + | 125.802i | −0.218139 | + | 0.300243i | −0.904036 | − | 0.427456i | \(-0.859410\pi\) |
0.685897 | + | 0.727699i | \(0.259410\pi\) | |||||||
\(420\) | −293.534 | + | 118.614i | −0.698891 | + | 0.282415i | ||||
\(421\) | −440.152 | + | 319.789i | −1.04549 | + | 0.759595i | −0.971350 | − | 0.237653i | \(-0.923622\pi\) |
−0.0741422 | + | 0.997248i | \(0.523622\pi\) | |||||||
\(422\) | 334.778 | + | 53.0236i | 0.793312 | + | 0.125648i | ||||
\(423\) | 125.180 | + | 63.7824i | 0.295934 | + | 0.150786i | ||||
\(424\) | − | 698.585i | − | 1.64761i | ||||||
\(425\) | 662.476 | + | 11.4912i | 1.55877 | + | 0.0270381i | ||||
\(426\) | −179.643 | −0.421697 | ||||||||
\(427\) | −182.720 | + | 358.608i | −0.427915 | + | 0.839831i | ||||
\(428\) | 239.367 | − | 1511.30i | 0.559269 | − | 3.53109i | ||||
\(429\) | −147.924 | − | 203.600i | −0.344811 | − | 0.474592i | ||||
\(430\) | 179.695 | + | 112.272i | 0.417894 | + | 0.261098i | ||||
\(431\) | 100.126 | + | 72.7461i | 0.232312 | + | 0.168784i | 0.697851 | − | 0.716243i | \(-0.254140\pi\) |
−0.465539 | + | 0.885027i | \(0.654140\pi\) | |||||||
\(432\) | 26.1882 | + | 26.1882i | 0.0606208 | + | 0.0606208i | ||||
\(433\) | 702.066 | − | 111.196i | 1.62140 | − | 0.256804i | 0.721343 | − | 0.692578i | \(-0.243525\pi\) |
0.900056 | + | 0.435774i | \(0.143525\pi\) | |||||||
\(434\) | 198.743 | + | 64.5754i | 0.457932 | + | 0.148791i | ||||
\(435\) | −134.259 | + | 316.341i | −0.308640 | + | 0.727222i | ||||
\(436\) | −156.181 | − | 480.674i | −0.358212 | − | 1.10246i | ||||
\(437\) | −358.011 | + | 182.416i | −0.819247 | + | 0.417427i | ||||
\(438\) | −188.060 | − | 369.088i | −0.429361 | − | 0.842668i | ||||
\(439\) | 315.182 | − | 102.409i | 0.717955 | − | 0.233278i | 0.0728185 | − | 0.997345i | \(-0.476801\pi\) |
0.645136 | + | 0.764068i | \(0.276801\pi\) | |||||||
\(440\) | −403.597 | − | 171.291i | −0.917266 | − | 0.389297i | ||||
\(441\) | −21.5821 | + | 66.4228i | −0.0489389 | + | 0.150619i | ||||
\(442\) | 247.047 | + | 1559.79i | 0.558929 | + | 3.52894i | ||||
\(443\) | 374.913 | − | 374.913i | 0.846305 | − | 0.846305i | −0.143365 | − | 0.989670i | \(-0.545792\pi\) |
0.989670 | + | 0.143365i | \(0.0457922\pi\) | |||||||
\(444\) | −242.535 | + | 333.821i | −0.546250 | + | 0.751849i | ||||
\(445\) | −3.14956 | + | 5.04097i | −0.00707767 | + | 0.0113280i | ||||
\(446\) | 500.065 | − | 363.318i | 1.12122 | − | 0.814615i | ||||
\(447\) | −195.847 | − | 31.0192i | −0.438138 | − | 0.0693942i | ||||
\(448\) | 417.828 | + | 212.894i | 0.932653 | + | 0.475210i | ||||
\(449\) | 841.171i | 1.87343i | 0.350089 | + | 0.936716i | \(0.386151\pi\) | ||||
−0.350089 | + | 0.936716i | \(0.613849\pi\) | |||||||
\(450\) | 144.043 | + | 205.667i | 0.320096 | + | 0.457038i | ||||
\(451\) | 184.702 | 0.409539 | ||||||||
\(452\) | −92.8896 | + | 182.306i | −0.205508 | + | 0.403332i | ||||
\(453\) | 4.69217 | − | 29.6252i | 0.0103580 | − | 0.0653978i | ||||
\(454\) | −425.749 | − | 585.993i | −0.937773 | − | 1.29073i | ||||
\(455\) | −169.089 | − | 418.445i | −0.371625 | − | 0.919658i | ||||
\(456\) | −180.600 | − | 131.214i | −0.396053 | − | 0.287749i | ||||
\(457\) | −275.400 | − | 275.400i | −0.602626 | − | 0.602626i | 0.338383 | − | 0.941009i | \(-0.390120\pi\) |
−0.941009 | + | 0.338383i | \(0.890120\pi\) | |||||||
\(458\) | −3.53383 | + | 0.559704i | −0.00771579 | + | 0.00122206i | ||||
\(459\) | 130.974 | + | 42.5559i | 0.285345 | + | 0.0927144i | ||||
\(460\) | 910.934 | + | 791.776i | 1.98029 | + | 1.72125i | ||||
\(461\) | −54.8017 | − | 168.662i | −0.118876 | − | 0.365862i | 0.873860 | − | 0.486178i | \(-0.161609\pi\) |
−0.992736 | + | 0.120316i | \(0.961609\pi\) | |||||||
\(462\) | 213.908 | − | 108.991i | 0.463004 | − | 0.235912i | ||||
\(463\) | 341.485 | + | 670.202i | 0.737548 | + | 1.44752i | 0.888451 | + | 0.458971i | \(0.151782\pi\) |
−0.150903 | + | 0.988549i | \(0.548218\pi\) | |||||||
\(464\) | −268.989 | + | 87.3997i | −0.579717 | + | 0.188361i | ||||
\(465\) | 9.28401 | − | 106.184i | 0.0199656 | − | 0.228352i | ||||
\(466\) | −432.056 | + | 1329.73i | −0.927158 | + | 2.85350i | ||||
\(467\) | −114.260 | − | 721.406i | −0.244667 | − | 1.54477i | −0.737924 | − | 0.674883i | \(-0.764194\pi\) |
0.493257 | − | 0.869883i | \(-0.335806\pi\) | |||||||
\(468\) | −272.160 | + | 272.160i | −0.581539 | + | 0.581539i | ||||
\(469\) | −335.669 | + | 462.009i | −0.715713 | + | 0.985094i | ||||
\(470\) | 54.7266 | + | 782.013i | 0.116440 | + | 1.66386i | ||||
\(471\) | 11.0070 | − | 7.99707i | 0.0233695 | − | 0.0169789i | ||||
\(472\) | −925.289 | − | 146.551i | −1.96036 | − | 0.310490i | ||||
\(473\) | −92.0701 | − | 46.9121i | −0.194651 | − | 0.0991799i | ||||
\(474\) | − | 41.3908i | − | 0.0873225i | ||||||
\(475\) | −208.400 | − | 215.758i | −0.438738 | − | 0.454227i | ||||
\(476\) | −968.874 | −2.03545 | ||||||||
\(477\) | 88.5780 | − | 173.844i | 0.185698 | − | 0.364453i | ||||
\(478\) | 38.5889 | − | 243.641i | 0.0807299 | − | 0.509709i | ||||
\(479\) | 237.475 | + | 326.857i | 0.495773 | + | 0.682373i | 0.981440 | − | 0.191771i | \(-0.0614231\pi\) |
−0.485667 | + | 0.874144i | \(0.661423\pi\) | |||||||
\(480\) | 40.0150 | − | 160.529i | 0.0833647 | − | 0.334435i | ||||
\(481\) | −475.875 | − | 345.743i | −0.989344 | − | 0.718801i | ||||
\(482\) | −112.402 | − | 112.402i | −0.233199 | − | 0.233199i | ||||
\(483\) | −290.530 | + | 46.0154i | −0.601510 | + | 0.0952699i | ||||
\(484\) | −372.644 | − | 121.079i | −0.769925 | − | 0.250164i | ||||
\(485\) | 356.307 | − | 214.117i | 0.734654 | − | 0.441479i | ||||
\(486\) | 16.1271 | + | 49.6342i | 0.0331834 | + | 0.102128i | ||||
\(487\) | −167.213 | + | 85.1992i | −0.343353 | + | 0.174947i | −0.617160 | − | 0.786838i | \(-0.711717\pi\) |
0.273807 | + | 0.961785i | \(0.411717\pi\) | |||||||
\(488\) | 387.003 | + | 759.537i | 0.793040 | + | 1.55643i | ||||
\(489\) | −25.1505 | + | 8.17191i | −0.0514326 | + | 0.0167115i | ||||
\(490\) | −379.708 | + | 87.6844i | −0.774915 | + | 0.178948i | ||||
\(491\) | −145.170 | + | 446.788i | −0.295662 | + | 0.909955i | 0.687336 | + | 0.726340i | \(0.258780\pi\) |
−0.982998 | + | 0.183615i | \(0.941220\pi\) | |||||||
\(492\) | −44.1900 | − | 279.005i | −0.0898171 | − | 0.567083i | ||||
\(493\) | −743.652 | + | 743.652i | −1.50842 | + | 1.50842i | ||||
\(494\) | 420.250 | − | 578.425i | 0.850709 | − | 1.17090i | ||||
\(495\) | −78.7168 | − | 93.8006i | −0.159024 | − | 0.189496i | ||||
\(496\) | 70.9702 | − | 51.5629i | 0.143085 | − | 0.103957i | ||||
\(497\) | 155.178 | + | 24.5778i | 0.312230 | + | 0.0494523i | ||||
\(498\) | −88.4928 | − | 45.0893i | −0.177696 | − | 0.0905408i | ||||
\(499\) | 808.726i | 1.62069i | 0.585951 | + | 0.810347i | \(0.300721\pi\) | ||||
−0.585951 | + | 0.810347i | \(0.699279\pi\) | |||||||
\(500\) | −366.356 | + | 823.211i | −0.732711 | + | 1.64642i | ||||
\(501\) | 392.922 | 0.784276 | ||||||||
\(502\) | 143.542 | − | 281.718i | 0.285941 | − | 0.561191i | ||||
\(503\) | −65.3761 | + | 412.768i | −0.129972 | + | 0.820613i | 0.833444 | + | 0.552604i | \(0.186366\pi\) |
−0.963416 | + | 0.268009i | \(0.913634\pi\) | |||||||
\(504\) | −96.0581 | − | 132.213i | −0.190592 | − | 0.262327i | ||||
\(505\) | 77.2198 | − | 64.8023i | 0.152911 | − | 0.128321i | ||||
\(506\) | −740.435 | − | 537.958i | −1.46331 | − | 1.06316i | ||||
\(507\) | −180.993 | − | 180.993i | −0.356989 | − | 0.356989i | ||||
\(508\) | 1184.57 | − | 187.618i | 2.33184 | − | 0.369327i | ||||
\(509\) | −518.069 | − | 168.331i | −1.01782 | − | 0.330709i | −0.247855 | − | 0.968797i | \(-0.579726\pi\) |
−0.769963 | + | 0.638088i | \(0.779726\pi\) | |||||||
\(510\) | 172.898 | + | 748.715i | 0.339015 | + | 1.46807i | ||||
\(511\) | 111.952 | + | 344.553i | 0.219084 | + | 0.674272i | ||||
\(512\) | 394.180 | − | 200.845i | 0.769884 | − | 0.392275i | ||||
\(513\) | −28.3052 | − | 55.5522i | −0.0551759 | − | 0.108289i | ||||
\(514\) | 1045.03 | − | 339.551i | 2.03313 | − | 0.660605i | ||||
\(515\) | 274.103 | + | 456.128i | 0.532239 | + | 0.885686i | ||||
\(516\) | −48.8360 | + | 150.302i | −0.0946434 | + | 0.291282i | ||||
\(517\) | −59.8061 | − | 377.601i | −0.115679 | − | 0.730369i | ||||
\(518\) | 396.776 | − | 396.776i | 0.765977 | − | 0.765977i | ||||
\(519\) | 4.57217 | − | 6.29306i | 0.00880958 | − | 0.0121253i | ||||
\(520\) | −927.515 | − | 231.202i | −1.78368 | − | 0.444618i | ||||
\(521\) | 93.2392 | − | 67.7422i | 0.178962 | − | 0.130023i | −0.494698 | − | 0.869065i | \(-0.664721\pi\) |
0.673660 | + | 0.739042i | \(0.264721\pi\) | |||||||
\(522\) | −393.643 | − | 62.3469i | −0.754105 | − | 0.119439i | ||||
\(523\) | 444.646 | + | 226.559i | 0.850184 | + | 0.433190i | 0.824083 | − | 0.566469i | \(-0.191691\pi\) |
0.0261007 | + | 0.999659i | \(0.491691\pi\) | |||||||
\(524\) | 868.705i | 1.65783i | ||||||||
\(525\) | −96.2880 | − | 197.365i | −0.183406 | − | 0.375933i | ||||
\(526\) | −150.586 | −0.286285 | ||||||||
\(527\) | 148.089 | − | 290.641i | 0.281004 | − | 0.551501i | ||||
\(528\) | 15.7656 | − | 99.5404i | 0.0298592 | − | 0.188523i | ||||
\(529\) | 348.195 | + | 479.249i | 0.658213 | + | 0.905952i | ||||
\(530\) | 1086.02 | − | 76.0017i | 2.04910 | − | 0.143399i | ||||
\(531\) | −211.677 | − | 153.793i | −0.398639 | − | 0.289628i | ||||
\(532\) | 310.167 | + | 310.167i | 0.583020 | + | 0.583020i | ||||
\(533\) | 397.732 | − | 62.9946i | 0.746214 | − | 0.118189i | ||||
\(534\) | −6.55613 | − | 2.13022i | −0.0122774 | − | 0.00398917i | ||||
\(535\) | 1057.33 | + | 92.4459i | 1.97631 | + | 0.172796i | ||||
\(536\) | 373.770 | + | 1150.35i | 0.697332 | + | 2.14617i | ||||
\(537\) | 293.577 | − | 149.585i | 0.546698 | − | 0.278557i | ||||
\(538\) | 154.663 | + | 303.542i | 0.287477 | + | 0.564205i | ||||
\(539\) | 180.749 | − | 58.7289i | 0.335342 | − | 0.108959i | ||||
\(540\) | −122.859 | + | 141.349i | −0.227517 | + | 0.261757i | ||||
\(541\) | 105.130 | − | 323.556i | 0.194325 | − | 0.598070i | −0.805659 | − | 0.592379i | \(-0.798189\pi\) |
0.999984 | − | 0.00569041i | \(-0.00181132\pi\) | |||||||
\(542\) | −154.582 | − | 975.993i | −0.285207 | − | 1.80073i | ||||
\(543\) | 269.515 | − | 269.515i | 0.496345 | − | 0.496345i | ||||
\(544\) | 297.596 | − | 409.605i | 0.547051 | − | 0.752951i | ||||
\(545\) | 325.036 | − | 131.344i | 0.596396 | − | 0.240998i | ||||
\(546\) | 423.450 | − | 307.654i | 0.775549 | − | 0.563469i | ||||
\(547\) | −791.804 | − | 125.409i | −1.44754 | − | 0.229268i | −0.617323 | − | 0.786710i | \(-0.711783\pi\) |
−0.830216 | + | 0.557442i | \(0.811783\pi\) | |||||||
\(548\) | −1423.79 | − | 725.459i | −2.59816 | − | 1.32383i | ||||
\(549\) | 238.083i | 0.433666i | ||||||||
\(550\) | 222.380 | − | 646.069i | 0.404328 | − | 1.17467i | ||||
\(551\) | 476.132 | 0.864123 | ||||||||
\(552\) | −282.843 | + | 555.112i | −0.512398 | + | 1.00564i | ||||
\(553\) | −5.66287 | + | 35.7540i | −0.0102403 | + | 0.0646545i | ||||
\(554\) | −990.726 | − | 1363.62i | −1.78831 | − | 2.46140i | ||||
\(555\) | −242.729 | − | 151.656i | −0.437350 | − | 0.273253i | ||||
\(556\) | 36.9926 | + | 26.8767i | 0.0665334 | + | 0.0483393i | ||||
\(557\) | 570.324 | + | 570.324i | 1.02392 | + | 1.02392i | 0.999707 | + | 0.0242138i | \(0.00770824\pi\) |
0.0242138 | + | 0.999707i | \(0.492292\pi\) | |||||||
\(558\) | 122.094 | − | 19.3377i | 0.218806 | − | 0.0346555i | ||||
\(559\) | −214.261 | − | 69.6176i | −0.383293 | − | 0.124540i | ||||
\(560\) | 70.6095 | − | 166.371i | 0.126088 | − | 0.297091i | ||||
\(561\) | −115.803 | − | 356.404i | −0.206422 | − | 0.635301i | ||||
\(562\) | −32.4143 | + | 16.5159i | −0.0576767 | + | 0.0293877i | ||||
\(563\) | 334.231 | + | 655.966i | 0.593662 | + | 1.16513i | 0.971006 | + | 0.239054i | \(0.0768371\pi\) |
−0.377345 | + | 0.926073i | \(0.623163\pi\) | |||||||
\(564\) | −556.082 | + | 180.682i | −0.985962 | + | 0.320358i | ||||
\(565\) | −130.643 | − | 55.4464i | −0.231227 | − | 0.0981352i | ||||
\(566\) | −162.927 | + | 501.438i | −0.287857 | + | 0.885932i | ||||
\(567\) | −7.14015 | − | 45.0811i | −0.0125929 | − | 0.0795082i | ||||
\(568\) | 235.301 | − | 235.301i | 0.414263 | − | 0.414263i | ||||
\(569\) | 59.8729 | − | 82.4080i | 0.105225 | − | 0.144829i | −0.753157 | − | 0.657841i | \(-0.771470\pi\) |
0.858382 | + | 0.513011i | \(0.171470\pi\) | |||||||
\(570\) | 184.337 | − | 295.037i | 0.323398 | − | 0.517608i | ||||
\(571\) | 71.2359 | − | 51.7559i | 0.124756 | − | 0.0906408i | −0.523657 | − | 0.851929i | \(-0.675433\pi\) |
0.648414 | + | 0.761288i | \(0.275433\pi\) | |||||||
\(572\) | 1034.47 | + | 163.844i | 1.80852 | + | 0.286441i | ||||
\(573\) | −182.088 | − | 92.7783i | −0.317780 | − | 0.161917i | ||||
\(574\) | 384.146i | 0.669243i | ||||||||
\(575\) | −503.753 | + | 668.654i | −0.876091 | + | 1.16288i | ||||
\(576\) | 277.400 | 0.481597 | ||||||||
\(577\) | −310.098 | + | 608.602i | −0.537432 | + | 1.05477i | 0.449447 | + | 0.893307i | \(0.351621\pi\) |
−0.986879 | + | 0.161463i | \(0.948379\pi\) | |||||||
\(578\) | −216.514 | + | 1367.02i | −0.374592 | + | 2.36508i | ||||
\(579\) | 91.9162 | + | 126.512i | 0.158750 | + | 0.218500i | ||||
\(580\) | −535.837 | − | 1326.03i | −0.923857 | − | 2.28627i | ||||
\(581\) | 70.2724 | + | 51.0559i | 0.120951 | + | 0.0878758i | ||||
\(582\) | 340.895 | + | 340.895i | 0.585730 | + | 0.585730i | ||||
\(583\) | −524.394 | + | 83.0559i | −0.899475 | + | 0.142463i | ||||
\(584\) | 729.768 | + | 237.116i | 1.24960 | + | 0.406021i | ||||
\(585\) | −201.498 | − | 175.140i | −0.344441 | − | 0.299385i | ||||
\(586\) | −250.158 | − | 769.907i | −0.426891 | − | 1.31383i | ||||
\(587\) | −767.583 | + | 391.103i | −1.30764 | + | 0.666274i | −0.962245 | − | 0.272185i | \(-0.912254\pi\) |
−0.345391 | + | 0.938459i | \(0.612254\pi\) | |||||||
\(588\) | −131.958 | − | 258.983i | −0.224419 | − | 0.440446i | ||||
\(589\) | −140.451 | + | 45.6353i | −0.238457 | + | 0.0774793i | ||||
\(590\) | 127.164 | − | 1454.40i | 0.215531 | − | 2.46509i | ||||
\(591\) | −45.5248 | + | 140.111i | −0.0770300 | + | 0.237074i | ||||
\(592\) | −36.8491 | − | 232.656i | −0.0622451 | − | 0.393000i | ||||
\(593\) | 319.789 | − | 319.789i | 0.539274 | − | 0.539274i | −0.384042 | − | 0.923316i | \(-0.625468\pi\) |
0.923316 | + | 0.384042i | \(0.125468\pi\) | |||||||
\(594\) | 83.4743 | − | 114.893i | 0.140529 | − | 0.193422i | ||||
\(595\) | −46.9161 | − | 670.405i | −0.0788505 | − | 1.12673i | ||||
\(596\) | 667.628 | − | 485.060i | 1.12018 | − | 0.813859i | ||||
\(597\) | 191.974 | + | 30.4057i | 0.321565 | + | 0.0509308i | ||||
\(598\) | −1777.91 | − | 905.889i | −2.97309 | − | 1.51486i | ||||
\(599\) | − | 901.516i | − | 1.50503i | −0.658572 | − | 0.752517i | \(-0.728839\pi\) | ||
0.658572 | − | 0.752517i | \(-0.271161\pi\) | |||||||
\(600\) | −458.060 | − | 80.7167i | −0.763433 | − | 0.134528i | ||||
\(601\) | −149.364 | −0.248525 | −0.124263 | − | 0.992249i | \(-0.539657\pi\) | ||||
−0.124263 | + | 0.992249i | \(0.539657\pi\) | |||||||
\(602\) | 97.5683 | − | 191.489i | 0.162074 | − | 0.318087i | ||||
\(603\) | −52.8462 | + | 333.658i | −0.0876389 | + | 0.553330i | ||||
\(604\) | 73.3734 | + | 100.990i | 0.121479 | + | 0.167202i | ||||
\(605\) | 65.7352 | − | 263.711i | 0.108653 | − | 0.435886i | ||||
\(606\) | 94.5834 | + | 68.7189i | 0.156078 | + | 0.113398i | ||||
\(607\) | 337.242 | + | 337.242i | 0.555588 | + | 0.555588i | 0.928048 | − | 0.372460i | \(-0.121486\pi\) |
−0.372460 | + | 0.928048i | \(0.621486\pi\) | |||||||
\(608\) | −226.397 | + | 35.8578i | −0.372363 | + | 0.0589766i | ||||
\(609\) | 331.504 | + | 107.712i | 0.544341 | + | 0.176867i | ||||
\(610\) | −1138.67 | + | 684.269i | −1.86668 | + | 1.12175i | ||||
\(611\) | −257.569 | − | 792.717i | −0.421554 | − | 1.29741i | ||||
\(612\) | −510.666 | + | 260.197i | −0.834422 | + | 0.425159i | ||||
\(613\) | −303.580 | − | 595.809i | −0.495236 | − | 0.971955i | −0.994423 | − | 0.105461i | \(-0.966368\pi\) |
0.499188 | − | 0.866494i | \(-0.333632\pi\) | |||||||
\(614\) | −71.6091 | + | 23.2672i | −0.116627 | + | 0.0378945i | ||||
\(615\) | 190.915 | − | 44.0872i | 0.310431 | − | 0.0716866i | ||||
\(616\) | −137.422 | + | 422.942i | −0.223088 | + | 0.686594i | ||||
\(617\) | 26.8370 | + | 169.442i | 0.0434959 | + | 0.274623i | 0.999845 | − | 0.0176041i | \(-0.00560385\pi\) |
−0.956349 | + | 0.292227i | \(0.905604\pi\) | |||||||
\(618\) | −436.398 | + | 436.398i | −0.706146 | + | 0.706146i | ||||
\(619\) | −89.3476 | + | 122.976i | −0.144342 | + | 0.198669i | −0.875066 | − | 0.484003i | \(-0.839182\pi\) |
0.730725 | + | 0.682672i | \(0.239182\pi\) | |||||||
\(620\) | 285.158 | + | 339.800i | 0.459932 | + | 0.548065i | ||||
\(621\) | −140.772 | + | 102.277i | −0.226686 | + | 0.164697i | ||||
\(622\) | 890.244 | + | 141.001i | 1.43126 | + | 0.226689i | ||||
\(623\) | 5.37183 | + | 2.73708i | 0.00862251 | + | 0.00439339i | ||||
\(624\) | − | 219.724i | − | 0.352122i | ||||||
\(625\) | −587.355 | − | 213.634i | −0.939767 | − | 0.341815i | ||||
\(626\) | 338.365 | 0.540520 | ||||||||
\(627\) | −77.0240 | + | 151.168i | −0.122845 | + | 0.241097i | ||||
\(628\) | −8.85776 | + | 55.9257i | −0.0141047 | + | 0.0890536i | ||||
\(629\) | −514.837 | − | 708.613i | −0.818501 | − | 1.12657i | ||||
\(630\) | 195.088 | − | 163.716i | 0.309663 | − | 0.259867i | ||||
\(631\) | 18.5290 | + | 13.4621i | 0.0293644 | + | 0.0213345i | 0.602371 | − | 0.798216i | \(-0.294223\pi\) |
−0.573006 | + | 0.819551i | \(0.694223\pi\) | |||||||
\(632\) | 54.2149 | + | 54.2149i | 0.0857830 | + | 0.0857830i | ||||
\(633\) | −173.199 | + | 27.4320i | −0.273616 | + | 0.0433365i | ||||
\(634\) | −409.173 | − | 132.948i | −0.645384 | − | 0.209698i | ||||
\(635\) | 187.182 | + | 810.572i | 0.294775 | + | 1.27649i | ||||
\(636\) | 250.923 | + | 772.261i | 0.394533 | + | 1.21425i | ||||
\(637\) | 369.190 | − | 188.112i | 0.579576 | − | 0.295309i | ||||
\(638\) | 492.366 | + | 966.323i | 0.771734 | + | 1.51461i | ||||
\(639\) | 88.3905 | − | 28.7198i | 0.138326 | − | 0.0449449i | ||||
\(640\) | 600.472 | + | 999.229i | 0.938237 | + | 1.56130i | ||||
\(641\) | −130.156 | + | 400.579i | −0.203052 | + | 0.624929i | 0.796736 | + | 0.604327i | \(0.206558\pi\) |
−0.999788 | + | 0.0206013i | \(0.993442\pi\) | |||||||
\(642\) | 192.556 | + | 1215.75i | 0.299932 | + | 1.89370i | ||||
\(643\) | −153.151 | + | 153.151i | −0.238182 | + | 0.238182i | −0.816097 | − | 0.577915i | \(-0.803867\pi\) |
0.577915 | + | 0.816097i | \(0.303867\pi\) | |||||||
\(644\) | 719.561 | − | 990.391i | 1.11733 | − | 1.53787i | ||||
\(645\) | −106.365 | − | 26.5136i | −0.164907 | − | 0.0411063i | ||||
\(646\) | 861.318 | − | 625.784i | 1.33331 | − | 0.968706i | ||||
\(647\) | −1003.06 | − | 158.869i | −1.55032 | − | 0.245546i | −0.678214 | − | 0.734864i | \(-0.737246\pi\) |
−0.872105 | + | 0.489318i | \(0.837246\pi\) | |||||||
\(648\) | −86.1361 | − | 43.8885i | −0.132926 | − | 0.0677292i | ||||
\(649\) | 711.993i | 1.09706i | ||||||||
\(650\) | 258.519 | − | 1467.07i | 0.397721 | − | 2.25703i | ||||
\(651\) | −108.112 | −0.166070 | ||||||||
\(652\) | 49.9651 | − | 98.0620i | 0.0766336 | − | 0.150402i | ||||
\(653\) | −104.253 | + | 658.227i | −0.159652 | + | 1.00800i | 0.769592 | + | 0.638537i | \(0.220460\pi\) |
−0.929244 | + | 0.369467i | \(0.879540\pi\) | |||||||
\(654\) | 238.977 | + | 328.924i | 0.365409 | + | 0.502942i | ||||
\(655\) | −601.094 | + | 42.0655i | −0.917700 | + | 0.0642222i | ||||
\(656\) | 130.463 | + | 94.7869i | 0.198877 | + | 0.144492i | ||||
\(657\) | 151.539 | + | 151.539i | 0.230652 | + | 0.230652i | ||||
\(658\) | 785.339 | − | 124.386i | 1.19352 | − | 0.189036i | ||||
\(659\) | 838.448 | + | 272.428i | 1.27230 | + | 0.413396i | 0.865863 | − | 0.500281i | \(-0.166770\pi\) |
0.406440 | + | 0.913678i | \(0.366770\pi\) | |||||||
\(660\) | 507.688 | + | 44.3890i | 0.769224 | + | 0.0672560i | ||||
\(661\) | 304.897 | + | 938.378i | 0.461267 | + | 1.41963i | 0.863617 | + | 0.504148i | \(0.168193\pi\) |
−0.402350 | + | 0.915486i | \(0.631807\pi\) | |||||||
\(662\) | 1164.55 | − | 593.368i | 1.75914 | − | 0.896327i | ||||
\(663\) | −370.921 | − | 727.974i | −0.559459 | − | 1.09800i | ||||
\(664\) | 174.969 | − | 56.8510i | 0.263508 | − | 0.0856190i | ||||
\(665\) | −199.598 | + | 229.637i | −0.300147 | + | 0.345318i | ||||
\(666\) | 102.573 | − | 315.686i | 0.154013 | − | 0.474003i | ||||
\(667\) | −207.873 | − | 1312.46i | −0.311654 | − | 1.96771i | ||||
\(668\) | −1156.30 | + | 1156.30i | −1.73099 | + | 1.73099i | ||||
\(669\) | −187.964 | + | 258.711i | −0.280963 | + | 0.386713i | ||||
\(670\) | −1747.67 | + | 706.214i | −2.60846 | + | 1.05405i | ||||
\(671\) | 524.136 | − | 380.807i | 0.781127 | − | 0.567522i | ||||
\(672\) | −165.739 | − | 26.2505i | −0.246636 | − | 0.0390633i | ||||
\(673\) | −864.100 | − | 440.281i | −1.28395 | − | 0.654207i | −0.327158 | − | 0.944970i | \(-0.606091\pi\) |
−0.956795 | + | 0.290763i | \(0.906091\pi\) | |||||||
\(674\) | 912.338i | 1.35362i | ||||||||
\(675\) | −103.754 | − | 78.1667i | −0.153710 | − | 0.115803i | ||||
\(676\) | 1065.26 | 1.57583 | ||||||||
\(677\) | −37.6719 | + | 73.9352i | −0.0556453 | + | 0.109210i | −0.917154 | − | 0.398532i | \(-0.869520\pi\) |
0.861509 | + | 0.507742i | \(0.169520\pi\) | |||||||
\(678\) | 25.7482 | − | 162.567i | 0.0379766 | − | 0.239775i | ||||
\(679\) | −247.830 | − | 341.109i | −0.364993 | − | 0.502370i | ||||
\(680\) | −1207.15 | − | 754.221i | −1.77523 | − | 1.10915i | ||||
\(681\) | 303.167 | + | 220.263i | 0.445179 | + | 0.323441i | ||||
\(682\) | −237.858 | − | 237.858i | −0.348765 | − | 0.348765i | ||||
\(683\) | 468.040 | − | 74.1303i | 0.685272 | − | 0.108536i | 0.195916 | − | 0.980621i | \(-0.437232\pi\) |
0.489356 | + | 0.872084i | \(0.337232\pi\) | |||||||
\(684\) | 246.777 | + | 80.1828i | 0.360785 | + | 0.117226i | ||||
\(685\) | 433.031 | − | 1020.31i | 0.632161 | − | 1.48951i | ||||
\(686\) | 379.234 | + | 1167.16i | 0.552819 | + | 1.70140i | ||||
\(687\) | 1.64928 | − | 0.840352i | 0.00240070 | − | 0.00122322i | ||||
\(688\) | −40.9584 | − | 80.3853i | −0.0595325 | − | 0.116839i | ||||
\(689\) | −1100.89 | + | 357.700i | −1.59781 | + | 0.519158i | ||||
\(690\) | −893.750 | − | 379.317i | −1.29529 | − | 0.549734i | ||||
\(691\) | 159.311 | − | 490.310i | 0.230552 | − | 0.709566i | −0.767128 | − | 0.641494i | \(-0.778315\pi\) |
0.997680 | − | 0.0680726i | \(-0.0216850\pi\) | |||||||
\(692\) | 5.06425 | + | 31.9744i | 0.00731828 | + | 0.0462058i | ||||
\(693\) | −87.8252 | + | 87.8252i | −0.126732 | + | 0.126732i | ||||
\(694\) | 324.492 | − | 446.625i | 0.467568 | − | 0.643552i | ||||
\(695\) | −16.8058 | + | 26.8982i | −0.0241810 | + | 0.0387024i | ||||
\(696\) | 597.268 | − | 433.940i | 0.858143 | − | 0.623478i | ||||
\(697\) | 592.252 | + | 93.8036i | 0.849717 | + | 0.134582i | ||||
\(698\) | −1503.51 | − | 766.075i | −2.15402 | − | 1.09753i | ||||
\(699\) | − | 723.346i | − | 1.03483i | ||||||
\(700\) | 864.168 | + | 297.451i | 1.23453 | + | 0.424931i | ||||
\(701\) | −503.480 | −0.718232 | −0.359116 | − | 0.933293i | \(-0.616922\pi\) | ||||
−0.359116 | + | 0.933293i | \(0.616922\pi\) | |||||||
\(702\) | 140.566 | − | 275.876i | 0.200236 | − | 0.392986i | ||||
\(703\) | −62.0335 | + | 391.664i | −0.0882411 | + | 0.557133i | ||||
\(704\) | −443.694 | − | 610.692i | −0.630247 | − | 0.867461i | ||||
\(705\) | −151.949 | − | 376.028i | −0.215530 | − | 0.533373i | ||||
\(706\) | −35.1526 | − | 25.5399i | −0.0497913 | − | 0.0361755i | ||||
\(707\) | −72.3007 | − | 72.3007i | −0.102264 | − | 0.102264i | ||||
\(708\) | 1075.51 | − | 170.345i | 1.51909 | − | 0.240600i | ||||
\(709\) | 514.565 | + | 167.192i | 0.725762 | + | 0.235814i | 0.648519 | − | 0.761198i | \(-0.275389\pi\) |
0.0772422 | + | 0.997012i | \(0.475389\pi\) | |||||||
\(710\) | 391.400 | + | 340.201i | 0.551267 | + | 0.479156i | ||||
\(711\) | 6.61722 | + | 20.3657i | 0.00930691 | + | 0.0286437i | ||||
\(712\) | 11.3776 | − | 5.79718i | 0.0159798 | − | 0.00814211i | ||||
\(713\) | 187.113 | + | 367.230i | 0.262431 | + | 0.515049i | ||||
\(714\) | 741.254 | − | 240.848i | 1.03817 | − | 0.337322i | ||||
\(715\) | −63.2782 | + | 723.729i | −0.0885010 | + | 1.01221i | ||||
\(716\) | −423.743 | + | 1304.15i | −0.591819 | + | 1.82143i | ||||
\(717\) | 19.9642 | + | 126.049i | 0.0278440 | + | 0.175800i | ||||
\(718\) | 107.243 | − | 107.243i | 0.149364 | − | 0.149364i | ||||
\(719\) | −129.983 | + | 178.907i | −0.180784 | + | 0.248827i | −0.889785 | − | 0.456380i | \(-0.849146\pi\) |
0.709002 | + | 0.705207i | \(0.249146\pi\) | |||||||
\(720\) | −7.46368 | − | 106.652i | −0.0103662 | − | 0.148128i | ||||
\(721\) | 436.672 | − | 317.261i | 0.605648 | − | 0.440029i | ||||
\(722\) | 717.644 | + | 113.664i | 0.993966 | + | 0.157429i | ||||
\(723\) | 73.2754 | + | 37.3357i | 0.101349 | + | 0.0516400i | ||||
\(724\) | 1586.27i | 2.19098i | ||||||||
\(725\) | 891.592 | − | 434.979i | 1.22978 | − | 0.599971i | ||||
\(726\) | 315.196 | 0.434154 | ||||||||
\(727\) | 323.090 | − | 634.099i | 0.444415 | − | 0.872213i | −0.554776 | − | 0.832000i | \(-0.687196\pi\) |
0.999191 | − | 0.0402135i | \(-0.0128038\pi\) | |||||||
\(728\) | −151.672 | + | 957.620i | −0.208341 | + | 1.31541i | ||||
\(729\) | −15.8702 | − | 21.8435i | −0.0217698 | − | 0.0299636i | ||||
\(730\) | −289.227 | + | 1160.30i | −0.396202 | + | 1.58945i | ||||
\(731\) | −271.401 | − | 197.184i | −0.371273 | − | 0.269746i | ||||
\(732\) | −700.634 | − | 700.634i | −0.957150 | − | 0.957150i | ||||
\(733\) | 822.224 | − | 130.227i | 1.12172 | − | 0.177664i | 0.432096 | − | 0.901828i | \(-0.357774\pi\) |
0.689628 | + | 0.724164i | \(0.257774\pi\) | |||||||
\(734\) | −1108.82 | − | 360.278i | −1.51066 | − | 0.490843i | ||||
\(735\) | 172.811 | − | 103.848i | 0.235117 | − | 0.141290i | ||||
\(736\) | 197.684 | + | 608.410i | 0.268593 | + | 0.826643i | ||||
\(737\) | 819.071 | − | 417.338i | 1.11136 | − | 0.566265i | ||||
\(738\) | 103.165 | + | 202.472i | 0.139790 | + | 0.274353i | ||||
\(739\) | −823.615 | + | 267.609i | −1.11450 | + | 0.362123i | −0.807666 | − | 0.589640i | \(-0.799270\pi\) |
−0.306834 | + | 0.951763i | \(0.599270\pi\) | |||||||
\(740\) | 1160.60 | − | 268.013i | 1.56838 | − | 0.362180i | ||||
\(741\) | −114.304 | + | 351.791i | −0.154256 | + | 0.474751i | ||||
\(742\) | −172.741 | − | 1090.64i | −0.232804 | − | 1.46987i | ||||
\(743\) | −82.9751 | + | 82.9751i | −0.111676 | + | 0.111676i | −0.760737 | − | 0.649061i | \(-0.775162\pi\) |
0.649061 | + | 0.760737i | \(0.275162\pi\) | |||||||
\(744\) | −134.593 | + | 185.251i | −0.180904 | + | 0.248993i | ||||
\(745\) | 367.962 | + | 438.472i | 0.493909 | + | 0.588553i | ||||
\(746\) | −1627.45 | + | 1182.41i | −2.18157 | + | 1.58501i | ||||
\(747\) | 50.7499 | + | 8.03800i | 0.0679383 | + | 0.0107604i | ||||
\(748\) | 1389.62 | + | 708.047i | 1.85778 | + | 0.946587i | ||||
\(749\) | − | 1076.53i | − | 1.43729i | ||||||
\(750\) | 75.6484 | − | 720.882i | 0.100865 | − | 0.961177i | ||||
\(751\) | −707.803 | −0.942481 | −0.471241 | − | 0.882005i | \(-0.656194\pi\) | ||||
−0.471241 | + | 0.882005i | \(0.656194\pi\) | |||||||
\(752\) | 151.537 | − | 297.408i | 0.201512 | − | 0.395489i | ||||
\(753\) | −25.5891 | + | 161.563i | −0.0339828 | + | 0.214559i | ||||
\(754\) | 1389.82 | + | 1912.92i | 1.84326 | + | 2.53704i | ||||
\(755\) | −66.3262 | + | 55.6604i | −0.0878492 | + | 0.0737224i | ||||
\(756\) | 153.678 | + | 111.654i | 0.203278 | + | 0.147690i | ||||
\(757\) | 149.107 | + | 149.107i | 0.196971 | + | 0.196971i | 0.798700 | − | 0.601729i | \(-0.205521\pi\) |
−0.601729 | + | 0.798700i | \(0.705521\pi\) | |||||||
\(758\) | −713.061 | + | 112.938i | −0.940714 | + | 0.148994i | ||||
\(759\) | 450.323 | + | 146.319i | 0.593311 | + | 0.192779i | ||||
\(760\) | 144.998 | + | 627.897i | 0.190786 | + | 0.826180i | ||||
\(761\) | −208.495 | − | 641.681i | −0.273975 | − | 0.843208i | −0.989489 | − | 0.144610i | \(-0.953807\pi\) |
0.715514 | − | 0.698598i | \(-0.246193\pi\) | |||||||
\(762\) | −859.640 | + | 438.008i | −1.12814 | + | 0.574814i | ||||
\(763\) | −161.430 | − | 316.824i | −0.211573 | − | 0.415235i | ||||
\(764\) | 808.881 | − | 262.821i | 1.05875 | − | 0.344007i | ||||
\(765\) | −204.770 | − | 340.752i | −0.267673 | − | 0.445427i | ||||
\(766\) | 71.5690 | − | 220.267i | 0.0934321 | − | 0.287554i | ||||
\(767\) | 242.833 | + | 1533.19i | 0.316601 | + | 1.99894i | ||||
\(768\) | −503.016 | + | 503.016i | −0.654969 | + | 0.654969i | ||||
\(769\) | 595.027 | − | 818.985i | 0.773768 | − | 1.06500i | −0.222175 | − | 0.975007i | \(-0.571315\pi\) |
0.995942 | − | 0.0899931i | \(-0.0286845\pi\) | |||||||
\(770\) | −672.457 | − | 167.623i | −0.873321 | − | 0.217693i | ||||
\(771\) | −459.906 | + | 334.141i | −0.596506 | + | 0.433387i | ||||
\(772\) | −642.794 | − | 101.809i | −0.832635 | − | 0.131876i | ||||
\(773\) | 896.098 | + | 456.585i | 1.15925 | + | 0.590666i | 0.924422 | − | 0.381371i | \(-0.124548\pi\) |
0.234826 | + | 0.972037i | \(0.424548\pi\) | |||||||
\(774\) | − | 127.131i | − | 0.164252i | ||||||
\(775\) | −221.314 | + | 213.767i | −0.285566 | + | 0.275828i | ||||
\(776\) | −893.027 | −1.15081 | ||||||||
\(777\) | −131.794 | + | 258.660i | −0.169619 | + | 0.332896i | ||||
\(778\) | −109.708 | + | 692.667i | −0.141012 | + | 0.890317i | ||||
\(779\) | −159.569 | − | 219.628i | −0.204838 | − | 0.281936i | ||||
\(780\) | 1108.38 | − | 77.5662i | 1.42100 | − | 0.0994439i | ||||
\(781\) | −204.605 | − | 148.654i | −0.261978 | − | 0.190338i | ||||
\(782\) | −2101.02 | − | 2101.02i | −2.68672 | − | 2.68672i | ||||
\(783\) | 203.653 | − | 32.2555i | 0.260093 | − | 0.0411947i | ||||
\(784\) | 157.810 | + | 51.2755i | 0.201288 | + | 0.0654025i | ||||
\(785\) | −39.1262 | − | 3.42095i | −0.0498423 | − | 0.00435790i | ||||
\(786\) | −215.947 | − | 664.618i | −0.274742 | − | 0.845569i | ||||
\(787\) | 1024.64 | − | 522.079i | 1.30195 | − | 0.663379i | 0.340994 | − | 0.940065i | \(-0.389236\pi\) |
0.960960 | + | 0.276686i | \(0.0892363\pi\) | |||||||
\(788\) | −278.350 | − | 546.292i | −0.353236 | − | 0.693264i | ||||
\(789\) | 74.0933 | − | 24.0744i | 0.0939079 | − | 0.0305125i | ||||
\(790\) | −78.3843 | + | 90.1808i | −0.0992207 | + | 0.114153i | ||||
\(791\) | −44.4832 | + | 136.905i | −0.0562366 | + | 0.173079i | ||||
\(792\) | 41.1524 | + | 259.826i | 0.0519602 | + | 0.328063i | ||||
\(793\) | 998.781 | − | 998.781i | 1.25950 | − | 1.25950i | ||||
\(794\) | −654.552 | + | 900.913i | −0.824372 | + | 1.13465i | ||||
\(795\) | −522.209 | + | 211.019i | −0.656867 | + | 0.265433i | ||||
\(796\) | −654.424 | + | 475.467i | −0.822141 | + | 0.597320i | ||||
\(797\) | 58.1783 | + | 9.21454i | 0.0729966 | + | 0.0115615i | 0.192826 | − | 0.981233i | \(-0.438235\pi\) |
−0.119829 | + | 0.992795i | \(0.538235\pi\) | |||||||
\(798\) | −314.401 | − | 160.195i | −0.393986 | − | 0.200746i | ||||
\(799\) | − | 1241.16i | − | 1.55339i | ||||||
\(800\) | −391.186 | + | 273.975i | −0.488983 | + | 0.342469i | ||||
\(801\) | 3.56640 | 0.00445243 | ||||||||
\(802\) | −217.472 | + | 426.813i | −0.271162 | + | 0.532186i | ||||
\(803\) | 91.2283 | − | 575.993i | 0.113609 | − | 0.717301i | ||||
\(804\) | −826.379 | − | 1137.41i | −1.02783 | − | 1.41469i | ||||
\(805\) | 720.137 | + | 449.937i | 0.894580 | + | 0.558928i | ||||
\(806\) | −593.320 | − | 431.072i | −0.736129 | − | 0.534829i | ||||
\(807\) | −124.627 | − | 124.627i | −0.154432 | − | 0.154432i | ||||
\(808\) | −213.898 | + | 33.8781i | −0.264725 | + | 0.0419283i | ||||
\(809\) | 890.150 | + | 289.227i | 1.10031 | + | 0.357512i | 0.802222 | − | 0.597026i | \(-0.203651\pi\) |
0.298088 | + | 0.954538i | \(0.403651\pi\) | |||||||
\(810\) | 58.8582 | − | 138.682i | 0.0726644 | − | 0.171213i | ||||
\(811\) | 354.720 | + | 1091.71i | 0.437385 | + | 1.34613i | 0.890622 | + | 0.454744i | \(0.150269\pi\) |
−0.453237 | + | 0.891390i | \(0.649731\pi\) | |||||||
\(812\) | −1292.53 | + | 658.579i | −1.59179 | + | 0.811058i | ||||
\(813\) | 232.093 | + | 455.508i | 0.285477 | + | 0.560281i | ||||
\(814\) | −859.042 | + | 279.120i | −1.05533 | + | 0.342899i | ||||
\(815\) | 70.2727 | + | 29.8245i | 0.0862242 | + | 0.0365944i | ||||
\(816\) | 101.106 | − | 311.172i | 0.123904 | − | 0.381338i | ||||
\(817\) | 23.7590 | + | 150.008i | 0.0290808 | + | 0.183609i | ||||
\(818\) | 1771.69 | − | 1771.69i | 2.16588 | − | 2.16588i | ||||
\(819\) | −159.166 | + | 219.074i | −0.194342 | + | 0.267489i | ||||
\(820\) | −432.088 | + | 691.570i | −0.526937 | + | 0.843378i | ||||
\(821\) | −598.631 | + | 434.931i | −0.729149 | + | 0.529758i | −0.889294 | − | 0.457336i | \(-0.848804\pi\) |
0.160145 | + | 0.987093i | \(0.448804\pi\) | |||||||
\(822\) | 1269.64 | + | 201.090i | 1.54457 | + | 0.244636i | ||||
\(823\) | −645.845 | − | 329.074i | −0.784744 | − | 0.399847i | 0.0152280 | − | 0.999884i | \(-0.495153\pi\) |
−0.799972 | + | 0.600037i | \(0.795153\pi\) | |||||||
\(824\) | − | 1143.21i | − | 1.38739i | ||||||
\(825\) | −6.13070 | + | 353.440i | −0.00743115 | + | 0.428412i | ||||
\(826\) | −1480.81 | −1.79275 | ||||||||
\(827\) | 240.680 | − | 472.361i | 0.291028 | − | 0.571175i | −0.698484 | − | 0.715626i | \(-0.746142\pi\) |
0.989512 | + | 0.144451i | \(0.0461417\pi\) | |||||||
\(828\) | 113.284 | − | 715.250i | 0.136817 | − | 0.863828i | ||||
\(829\) | 718.610 | + | 989.082i | 0.866840 | + | 1.19310i | 0.979895 | + | 0.199514i | \(0.0639363\pi\) |
−0.113055 | + | 0.993589i | \(0.536064\pi\) | |||||||
\(830\) | 107.416 | + | 265.823i | 0.129417 | + | 0.320269i | ||||
\(831\) | 705.475 | + | 512.557i | 0.848946 | + | 0.616796i | ||||
\(832\) | −1163.72 | − | 1163.72i | −1.39870 | − | 1.39870i | ||||
\(833\) | 609.404 | − | 96.5200i | 0.731577 | − | 0.115870i | ||||
\(834\) | −34.9829 | − | 11.3666i | −0.0419460 | − | 0.0136291i | ||||
\(835\) | −856.084 | − | 744.100i | −1.02525 | − | 0.891138i | ||||
\(836\) | −218.193 | − | 671.528i | −0.260996 | − | 0.803263i | ||||
\(837\) | −56.9827 | + | 29.0341i | −0.0680797 | + | 0.0346883i | ||||
\(838\) | 236.346 | + | 463.855i | 0.282036 | + | 0.553526i | ||||
\(839\) | −1186.02 | + | 385.361i | −1.41361 | + | 0.459310i | −0.913566 | − | 0.406691i | \(-0.866683\pi\) |
−0.500043 | + | 0.866000i | \(0.666683\pi\) | |||||||
\(840\) | −41.0913 | + | 469.971i | −0.0489182 | + | 0.559489i | ||||
\(841\) | −226.704 | + | 697.723i | −0.269565 | + | 0.829635i | ||||
\(842\) | 284.938 | + | 1799.03i | 0.338406 | + | 2.13661i | ||||
\(843\) | 13.3085 | − | 13.3085i | 0.0157871 | − | 0.0157871i | ||||
\(844\) | 428.966 | − | 590.421i | 0.508254 | − | 0.699551i | ||||
\(845\) | 51.5834 | + | 737.099i | 0.0610455 | + | 0.872307i | ||||
\(846\) | 380.525 | − | 276.468i | 0.449794 | − | 0.326794i | ||||
\(847\) | −272.270 | − | 43.1234i | −0.321453 | − | 0.0509131i | ||||
\(848\) | −413.025 | − | 210.447i | −0.487058 | − | 0.248169i | ||||
\(849\) | − | 272.772i | − | 0.321286i | ||||||
\(850\) | 1041.18 | − | 1958.70i | 1.22492 | − | 2.30435i | ||||
\(851\) | 1106.71 | 1.30048 | ||||||||
\(852\) | −175.600 | + | 344.635i | −0.206103 | + | 0.404501i | ||||
\(853\) | 203.770 | − | 1286.55i | 0.238887 | − | 1.50827i | −0.518372 | − | 0.855155i | \(-0.673462\pi\) |
0.757258 | − | 0.653115i | \(-0.226538\pi\) | |||||||
\(854\) | 792.008 | + | 1090.11i | 0.927410 | + | 1.27647i | ||||
\(855\) | −43.5321 | + | 174.638i | −0.0509147 | + | 0.204255i | ||||
\(856\) | −1844.64 | − | 1340.21i | −2.15496 | − | 1.56567i | ||||
\(857\) | −230.040 | − | 230.040i | −0.268424 | − | 0.268424i | 0.560041 | − | 0.828465i | \(-0.310785\pi\) |
−0.828465 | + | 0.560041i | \(0.810785\pi\) | |||||||
\(858\) | −832.170 | + | 131.803i | −0.969895 | + | 0.153616i | ||||
\(859\) | −200.365 | − | 65.1026i | −0.233254 | − | 0.0757889i | 0.190058 | − | 0.981773i | \(-0.439133\pi\) |
−0.423312 | + | 0.905984i | \(0.639133\pi\) | |||||||
\(860\) | 391.037 | − | 234.988i | 0.454695 | − | 0.273242i | ||||
\(861\) | −61.4139 | − | 189.013i | −0.0713286 | − | 0.219527i | ||||
\(862\) | 369.185 | − | 188.109i | 0.428289 | − | 0.218224i | ||||
\(863\) | −404.297 | − | 793.477i | −0.468478 | − | 0.919440i | −0.997489 | − | 0.0708248i | \(-0.977437\pi\) |
0.529011 | − | 0.848615i | \(-0.322563\pi\) | |||||||
\(864\) | −94.4062 | + | 30.6744i | −0.109266 | + | 0.0355028i | ||||
\(865\) | −21.8792 | + | 5.05247i | −0.0252939 | + | 0.00584101i | ||||
\(866\) | 735.381 | − | 2263.27i | 0.849169 | − | 2.61347i | ||||
\(867\) | −112.015 | − | 707.232i | −0.129198 | − | 0.815723i | ||||
\(868\) | 318.154 | − | 318.154i | 0.366537 | − | 0.366537i | ||||
\(869\) | 34.2508 | − | 47.1422i | 0.0394140 | − | 0.0542488i | ||||
\(870\) | 739.584 | + | 881.304i | 0.850097 | + | 1.01299i | ||||
\(871\) | 1621.43 | − | 1178.04i | 1.86157 | − | 1.35251i | ||||
\(872\) | −743.853 | − | 117.815i | −0.853042 | − | 0.135109i | ||||
\(873\) | −222.231 | − | 113.233i | −0.254561 | − | 0.129705i | ||||
\(874\) | 1345.20i | 1.53913i | ||||||||
\(875\) | −163.973 | + | 612.358i | −0.187398 | + | 0.699838i | ||||
\(876\) | −891.902 | −1.01815 | ||||||||
\(877\) | −355.726 | + | 698.152i | −0.405617 | + | 0.796068i | −0.999967 | − | 0.00813824i | \(-0.997409\pi\) |
0.594350 | + | 0.804207i | \(0.297409\pi\) | |||||||
\(878\) | 173.564 | − | 1095.84i | 0.197681 | − | 1.24811i | ||||
\(879\) | 246.172 | + | 338.827i | 0.280059 | + | 0.385469i | ||||
\(880\) | −222.855 | + | 187.018i | −0.253244 | + | 0.212521i | ||||
\(881\) | 1064.05 | + | 773.077i | 1.20777 | + | 0.877499i | 0.995027 | − | 0.0996082i | \(-0.0317589\pi\) |
0.212747 | + | 0.977107i | \(0.431759\pi\) | |||||||
\(882\) | 165.336 | + | 165.336i | 0.187456 | + | 0.187456i | ||||
\(883\) | −306.337 | + | 48.5191i | −0.346928 | + | 0.0549480i | −0.327467 | − | 0.944863i | \(-0.606195\pi\) |
−0.0194609 | + | 0.999811i | \(0.506195\pi\) | |||||||
\(884\) | 3233.85 | + | 1050.74i | 3.65821 | + | 1.18862i | ||||
\(885\) | 169.948 | + | 735.944i | 0.192032 | + | 0.831575i | ||||
\(886\) | −548.530 | − | 1688.20i | −0.619108 | − | 1.90542i | ||||
\(887\) | −57.9184 | + | 29.5109i | −0.0652970 | + | 0.0332705i | −0.486334 | − | 0.873773i | \(-0.661666\pi\) |
0.421037 | + | 0.907043i | \(0.361666\pi\) | |||||||
\(888\) | 279.142 | + | 547.847i | 0.314349 | + | 0.616944i | ||||
\(889\) | 802.494 | − | 260.746i | 0.902693 | − | 0.293303i | ||||
\(890\) | 10.2501 | + | 17.0570i | 0.0115170 | + | 0.0191651i | ||||
\(891\) | −22.7041 | + | 69.8762i | −0.0254816 | + | 0.0784244i | ||||
\(892\) | −208.194 | − | 1314.49i | −0.233401 | − | 1.47364i | ||||
\(893\) | −397.334 | + | 397.334i | −0.444943 | + | 0.444943i | ||||
\(894\) | −390.201 | + | 537.066i | −0.436467 | + | 0.600745i | ||||
\(895\) | −922.913 | − | 230.054i | −1.03119 | − | 0.257044i | ||||
\(896\) | 956.608 | − | 695.016i | 1.06764 | − | 0.775688i | ||||
\(897\) | 1019.62 | + | 161.491i | 1.13670 | + | 0.180035i | ||||
\(898\) | 2509.21 | + | 1278.51i | 2.79422 | + | 1.42373i | ||||
\(899\) | − | 488.393i | − | 0.543263i | ||||||
\(900\) | 535.361 | − | 75.2997i | 0.594846 | − | 0.0836664i | ||||
\(901\) | −1723.67 | −1.91306 | ||||||||
\(902\) | 280.731 | − | 550.966i | 0.311232 | − | 0.610827i | ||||
\(903\) | −17.3933 | + | 109.817i | −0.0192617 | + | 0.121614i | ||||
\(904\) | 179.210 | + | 246.661i | 0.198241 | + | 0.272855i | ||||
\(905\) | −1097.61 | + | 76.8124i | −1.21283 | + | 0.0848755i | ||||
\(906\) | −81.2402 | − | 59.0245i | −0.0896691 | − | 0.0651484i | ||||
\(907\) | 867.106 | + | 867.106i | 0.956016 | + | 0.956016i | 0.999073 | − | 0.0430568i | \(-0.0137096\pi\) |
−0.0430568 | + | 0.999073i | \(0.513710\pi\) | |||||||
\(908\) | −1540.36 | + | 243.969i | −1.69643 | + | 0.268688i | ||||
\(909\) | −57.5244 | − | 18.6908i | −0.0632832 | − | 0.0205620i | ||||
\(910\) | −1505.22 | − | 131.607i | −1.65409 | − | 0.144623i | ||||
\(911\) | −59.9615 | − | 184.542i | −0.0658194 | − | 0.202571i | 0.912738 | − | 0.408545i | \(-0.133964\pi\) |
−0.978557 | + | 0.205974i | \(0.933964\pi\) | |||||||
\(912\) | −131.983 | + | 67.2487i | −0.144718 | + | 0.0737376i | ||||
\(913\) | −63.4777 | − | 124.582i | −0.0695265 | − | 0.136454i | ||||
\(914\) | −1240.10 | + | 402.933i | −1.35678 | + | 0.440846i | ||||
\(915\) | 450.871 | − | 518.725i | 0.492755 | − | 0.566913i | ||||
\(916\) | −2.38054 | + | 7.32655i | −0.00259884 | + | 0.00799842i | ||||
\(917\) | 95.6088 | + | 603.650i | 0.104263 | + | 0.658288i | ||||
\(918\) | 326.013 | − | 326.013i | 0.355134 | − | 0.355134i | ||||
\(919\) | 318.962 | − | 439.013i | 0.347075 | − | 0.477707i | −0.599416 | − | 0.800437i | \(-0.704601\pi\) |
0.946491 | + | 0.322730i | \(0.104601\pi\) | |||||||
\(920\) | 1667.50 | − | 673.818i | 1.81250 | − | 0.732411i | ||||
\(921\) | 31.5144 | − | 22.8965i | 0.0342175 | − | 0.0248605i | ||||
\(922\) | −586.413 | − | 92.8788i | −0.636023 | − | 0.100736i | ||||
\(923\) | −491.290 | − | 250.325i | −0.532275 | − | 0.271208i | ||||
\(924\) | − | 516.907i | − | 0.559424i | ||||||
\(925\) | 241.650 | + | 790.092i | 0.261243 | + | 0.854153i | ||||
\(926\) | 2518.24 | 2.71948 | ||||||||
\(927\) | 144.955 | − | 284.490i | 0.156370 | − | 0.306894i | ||||
\(928\) | 118.586 | − | 748.724i | 0.127787 | − | 0.806814i | ||||
\(929\) | 6.29997 | + | 8.67117i | 0.00678145 | + | 0.00933387i | 0.812394 | − | 0.583109i | \(-0.198164\pi\) |
−0.805613 | + | 0.592442i | \(0.798164\pi\) | |||||||
\(930\) | −302.634 | − | 189.084i | −0.325413 | − | 0.203316i | ||||
\(931\) | −225.988 | − | 164.190i | −0.242737 | − | 0.176359i | ||||
\(932\) | 2128.68 | + | 2128.68i | 2.28399 | + | 2.28399i | ||||
\(933\) | −460.572 | + | 72.9475i | −0.493647 | + | 0.0781859i | ||||
\(934\) | −2325.62 | − | 755.639i | −2.48995 | − | 0.809035i | ||||
\(935\) | −422.637 | + | 995.822i | −0.452019 | + | 1.06505i | ||||
\(936\) | 177.233 | + | 545.467i | 0.189351 | + | 0.582764i | ||||
\(937\) | −240.296 | + | 122.437i | −0.256453 | + | 0.130669i | −0.577491 | − | 0.816397i | \(-0.695968\pi\) |
0.321038 | + | 0.947066i | \(0.395968\pi\) | |||||||
\(938\) | 867.984 | + | 1703.51i | 0.925356 | + | 1.81611i | ||||
\(939\) | −166.487 | + | 54.0950i | −0.177303 | + | 0.0576091i | ||||
\(940\) | 1553.74 | + | 659.423i | 1.65292 | + | 0.701514i | ||||
\(941\) | 247.068 | − | 760.397i | 0.262559 | − | 0.808073i | −0.729687 | − | 0.683781i | \(-0.760334\pi\) |
0.992246 | − | 0.124292i | \(-0.0396658\pi\) | |||||||
\(942\) | −7.12553 | − | 44.9888i | −0.00756425 | − | 0.0477588i | ||||
\(943\) | −535.739 | + | 535.739i | −0.568122 | + | 0.568122i | ||||
\(944\) | −365.387 | + | 502.912i | −0.387062 | + | 0.532745i | ||||
\(945\) | −69.8162 | + | 111.743i | −0.0738796 | + | 0.118246i | ||||
\(946\) | −279.877 | + | 203.343i | −0.295853 | + | 0.214950i | ||||
\(947\) | −1164.88 | − | 184.500i | −1.23008 | − | 0.194825i | −0.492636 | − | 0.870235i | \(-0.663967\pi\) |
−0.737443 | + | 0.675410i | \(0.763967\pi\) | |||||||
\(948\) | −79.4059 | − | 40.4593i | −0.0837615 | − | 0.0426786i | ||||
\(949\) | − | 1271.44i | − | 1.33977i | ||||||
\(950\) | −960.355 | + | 293.725i | −1.01090 | + | 0.309184i | ||||
\(951\) | 222.582 | 0.234050 | ||||||||
\(952\) | −655.445 | + | 1286.38i | −0.688493 | + | 1.35124i | ||||
\(953\) | 181.717 | − | 1147.31i | 0.190679 | − | 1.20390i | −0.687723 | − | 0.725973i | \(-0.741390\pi\) |
0.878401 | − | 0.477924i | \(-0.158610\pi\) | |||||||
\(954\) | −383.945 | − | 528.456i | −0.402459 | − | 0.553937i | ||||
\(955\) | 221.026 | + | 546.972i | 0.231441 | + | 0.572746i | ||||
\(956\) | −429.690 | − | 312.188i | −0.449466 | − | 0.326556i | ||||
\(957\) | −396.748 | − | 396.748i | −0.414575 | − | 0.414575i | ||||
\(958\) | 1335.95 | − | 211.594i | 1.39452 | − | 0.220871i | ||||
\(959\) | −1069.22 | − | 347.409i | −1.11493 | − | 0.362262i | ||||
\(960\) | −604.388 | − | 525.328i | −0.629571 | − | 0.547217i | ||||
\(961\) | −250.155 | − | 769.898i | −0.260307 | − | 0.801142i | ||||
\(962\) | −1754.64 | + | 894.033i | −1.82395 | + | 0.929349i | ||||
\(963\) | −289.108 | − | 567.407i | −0.300216 | − | 0.589208i | ||||
\(964\) | −325.509 | + | 105.764i | −0.337665 | + | 0.109714i | ||||
\(965\) | 39.3194 | − | 449.706i | 0.0407455 | − | 0.466017i | ||||
\(966\) | −304.316 | + | 936.588i | −0.315027 | + | 0.969553i | ||||
\(967\) | 175.279 | + | 1106.67i | 0.181261 | + | 1.14444i | 0.895674 | + | 0.444711i | \(0.146694\pi\) |
−0.714413 | + | 0.699724i | \(0.753306\pi\) | |||||||
\(968\) | −412.852 | + | 412.852i | −0.426500 | + | 0.426500i | ||||
\(969\) | −323.752 | + | 445.607i | −0.334110 | + | 0.459863i | ||||
\(970\) | −97.1558 | − | 1388.30i | −0.100161 | − | 1.43124i | ||||
\(971\) | −806.422 | + | 585.900i | −0.830507 | + | 0.603399i | −0.919703 | − | 0.392615i | \(-0.871570\pi\) |
0.0891956 | + | 0.996014i | \(0.471570\pi\) | |||||||
\(972\) | 110.985 | + | 17.5782i | 0.114182 | + | 0.0180846i | ||||
\(973\) | 28.6636 | + | 14.6048i | 0.0294590 | + | 0.0150101i | ||||
\(974\) | 628.291i | 0.645063i | ||||||||
\(975\) | 107.343 | + | 763.178i | 0.110095 | + | 0.782747i | ||||
\(976\) | 565.646 | 0.579555 | ||||||||
\(977\) | 9.63744 | − | 18.9145i | 0.00986432 | − | 0.0193598i | −0.886022 | − | 0.463644i | \(-0.846542\pi\) |
0.895886 | + | 0.444284i | \(0.146542\pi\) | |||||||
\(978\) | −13.8499 | + | 87.4446i | −0.0141614 | + | 0.0894117i | ||||
\(979\) | −5.70437 | − | 7.85139i | −0.00582673 | − | 0.00801980i | ||||
\(980\) | −202.945 | + | 814.159i | −0.207087 | + | 0.830774i | ||||
\(981\) | −170.170 | − | 123.636i | −0.173466 | − | 0.126031i | ||||
\(982\) | 1112.12 | + | 1112.12i | 1.13251 | + | 1.13251i | ||||
\(983\) | −836.347 | + | 132.464i | −0.850810 | + | 0.134755i | −0.566586 | − | 0.824003i | \(-0.691736\pi\) |
−0.284224 | + | 0.958758i | \(0.591736\pi\) | |||||||
\(984\) | −400.332 | − | 130.076i | −0.406841 | − | 0.132191i | ||||
\(985\) | 364.524 | − | 219.055i | 0.370075 | − | 0.222391i | ||||
\(986\) | 1088.03 | + | 3348.60i | 1.10347 | + | 3.39614i | ||||
\(987\) | −366.528 | + | 186.755i | −0.371355 | + | 0.189215i | ||||
\(988\) | −698.881 | − | 1371.63i | −0.707370 | − | 1.38829i | ||||
\(989\) | 403.126 | − | 130.984i | 0.407610 | − | 0.132441i | ||||
\(990\) | −399.450 | + | 92.2432i | −0.403484 | + | 0.0931749i | ||||
\(991\) | −359.275 | + | 1105.74i | −0.362538 | + | 1.11578i | 0.588970 | + | 0.808155i | \(0.299534\pi\) |
−0.951508 | + | 0.307623i | \(0.900466\pi\) | |||||||
\(992\) | 36.7811 | + | 232.227i | 0.0370778 | + | 0.234100i | ||||
\(993\) | −478.136 | + | 478.136i | −0.481506 | + | 0.481506i | ||||
\(994\) | 309.173 | − | 425.540i | 0.311039 | − | 0.428108i | ||||
\(995\) | −360.685 | − | 429.800i | −0.362497 | − | 0.431960i | ||||
\(996\) | −173.002 | + | 125.694i | −0.173697 | + | 0.126198i | ||||
\(997\) | 496.275 | + | 78.6022i | 0.497768 | + | 0.0788387i | 0.400270 | − | 0.916397i | \(-0.368916\pi\) |
0.0974975 | + | 0.995236i | \(0.468916\pi\) | |||||||
\(998\) | 2412.43 | + | 1229.19i | 2.41726 | + | 1.23166i | ||||
\(999\) | 171.727i | 0.171899i |
(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.k.a.67.9 | yes | 80 | |
3.2 | odd | 2 | 225.3.r.b.217.2 | 80 | |||
5.2 | odd | 4 | 375.3.k.b.268.9 | 80 | |||
5.3 | odd | 4 | 375.3.k.c.268.2 | 80 | |||
5.4 | even | 2 | 375.3.k.a.232.2 | 80 | |||
25.3 | odd | 20 | inner | 75.3.k.a.28.9 | ✓ | 80 | |
25.4 | even | 10 | 375.3.k.b.7.9 | 80 | |||
25.21 | even | 5 | 375.3.k.c.7.2 | 80 | |||
25.22 | odd | 20 | 375.3.k.a.118.2 | 80 | |||
75.53 | even | 20 | 225.3.r.b.28.2 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.k.a.28.9 | ✓ | 80 | 25.3 | odd | 20 | inner | |
75.3.k.a.67.9 | yes | 80 | 1.1 | even | 1 | trivial | |
225.3.r.b.28.2 | 80 | 75.53 | even | 20 | |||
225.3.r.b.217.2 | 80 | 3.2 | odd | 2 | |||
375.3.k.a.118.2 | 80 | 25.22 | odd | 20 | |||
375.3.k.a.232.2 | 80 | 5.4 | even | 2 | |||
375.3.k.b.7.9 | 80 | 25.4 | even | 10 | |||
375.3.k.b.268.9 | 80 | 5.2 | odd | 4 | |||
375.3.k.c.7.2 | 80 | 25.21 | even | 5 | |||
375.3.k.c.268.2 | 80 | 5.3 | odd | 4 |