Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1040,2,Mod(289,1040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1040.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1040 = 2^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1040.dh (of order \(6\), degree \(2\), not 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: | \(8.30444181021\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.513226913958144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6x^{10} + 28x^{8} - 46x^{6} + 58x^{4} - 8x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 529.4 | ||
Root | \(1.75675 - 1.01426i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1040.529 |
Dual form | 1040.2.dh.c.289.4 |
$q$-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 \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(417\) | \(561\) | \(911\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.201864 | + | 0.116546i | 0.116546 | + | 0.0672881i | 0.557140 | − | 0.830419i | \(-0.311899\pi\) |
−0.440594 | + | 0.897707i | \(0.645232\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.11491 | + | 0.726062i | −0.945815 | + | 0.324705i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.71537 | − | 2.14507i | 1.40428 | − | 0.810760i | 0.409450 | − | 0.912333i | \(-0.365721\pi\) |
0.994828 | + | 0.101573i | \(0.0323874\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.47283 | − | 2.55102i | −0.490945 | − | 0.850341i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.51351 | − | 0.809492i | −0.974471 | − | 0.224513i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.511544 | − | 0.0999188i | −0.132080 | − | 0.0257989i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.31164 | + | 1.91198i | −0.803191 | + | 0.463723i | −0.844586 | − | 0.535420i | \(-0.820153\pi\) |
0.0413947 | + | 0.999143i | \(0.486820\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.14207 | − | 1.97813i | −0.262010 | − | 0.453814i | 0.704766 | − | 0.709440i | \(-0.251052\pi\) |
−0.966776 | + | 0.255626i | \(0.917719\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.97295 | − | 2.87113i | −1.03693 | − | 0.598672i | −0.117968 | − | 0.993017i | \(-0.537638\pi\) |
−0.918962 | + | 0.394345i | \(0.870972\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.94567 | − | 3.07111i | 0.789134 | − | 0.614222i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.38589i | − | 0.266715i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.14207 | + | 1.97813i | −0.212078 | + | 0.367329i | −0.952365 | − | 0.304962i | \(-0.901356\pi\) |
0.740287 | + | 0.672291i | \(0.234690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.22982 | 1.11891 | 0.559454 | − | 0.828861i | \(-0.311011\pi\) | ||||
0.559454 | + | 0.828861i | \(0.311011\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.201864 | + | 0.116546i | −0.0351400 | + | 0.0202881i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.30021 | + | 7.23421i | −1.06493 | + | 1.22281i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.82679 | − | 3.36410i | −0.957919 | − | 0.553055i | −0.0623871 | − | 0.998052i | \(-0.519871\pi\) |
−0.895532 | + | 0.444997i | \(0.853205\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.614908 | − | 0.572894i | −0.0984640 | − | 0.0917364i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.33076 | + | 2.30494i | −0.207830 | + | 0.359972i | −0.951031 | − | 0.309097i | \(-0.899973\pi\) |
0.743201 | + | 0.669068i | \(0.233307\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.97130 | + | 3.44753i | −0.910615 | + | 0.525744i | −0.880629 | − | 0.473807i | \(-0.842880\pi\) |
−0.0299858 | + | 0.999550i | \(0.509546\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.96711 | + | 4.32581i | 0.740453 | + | 0.644854i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.60840i | − | 0.963934i | −0.876189 | − | 0.481967i | \(-0.839922\pi\) | ||
0.876189 | − | 0.481967i | \(-0.160078\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.70265 | − | 9.87728i | 0.814664 | − | 1.41104i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.891336 | −0.124812 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.04299i | − | 0.692707i | −0.938104 | − | 0.346354i | \(-0.887420\pi\) | ||
0.938104 | − | 0.346354i | \(-0.112580\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.428666 | − | 2.19459i | 0.0578013 | − | 0.295919i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.532418i | − | 0.0705205i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.56058 | − | 9.63120i | −0.723925 | − | 1.25388i | −0.959415 | − | 0.281998i | \(-0.909003\pi\) |
0.235490 | − | 0.971877i | \(-0.424331\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.08774 | − | 3.61607i | −0.267308 | − | 0.462991i | 0.700858 | − | 0.713301i | \(-0.252801\pi\) |
−0.968166 | + | 0.250310i | \(0.919467\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.9442 | − | 6.31866i | −1.37885 | − | 0.796077i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.01848 | − | 0.839022i | 0.994570 | − | 0.104068i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.76176 | + | 2.17185i | 0.459572 | + | 0.265334i | 0.711864 | − | 0.702317i | \(-0.247851\pi\) |
−0.252292 | + | 0.967651i | \(0.581184\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.669240 | − | 1.15916i | −0.0805670 | − | 0.139546i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.37189 | − | 5.84028i | −0.400170 | − | 0.693114i | 0.593577 | − | 0.804778i | \(-0.297715\pi\) |
−0.993746 | + | 0.111664i | \(0.964382\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.5697i | − | 1.58821i | −0.607779 | − | 0.794106i | \(-0.707939\pi\) | ||
0.607779 | − | 0.794106i | \(-0.292061\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.15442 | − | 0.160094i | 0.133300 | − | 0.0184860i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.29014i | 0.488907i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4053 | 1.28320 | 0.641598 | − | 0.767041i | \(-0.278272\pi\) | ||||
0.641598 | + | 0.767041i | \(0.278272\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.25698 | + | 7.37331i | −0.472998 | + | 0.819256i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0324i | 1.10120i | 0.834769 | + | 0.550600i | \(0.185601\pi\) | ||||
−0.834769 | + | 0.550600i | \(0.814399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.61560 | − | 6.44811i | 0.609098 | − | 0.699396i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.461087 | + | 0.266209i | −0.0494338 | + | 0.0285406i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.56058 | + | 9.63120i | −0.589420 | + | 1.02091i | 0.404889 | + | 0.914366i | \(0.367310\pi\) |
−0.994309 | + | 0.106539i | \(0.966023\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.7904 | + | 4.52915i | −1.55045 | + | 0.474784i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.25758 | + | 0.726062i | 0.130405 | + | 0.0752891i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.85162 | + | 3.35434i | 0.395168 | + | 0.344149i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.8538 | + | 7.42115i | −1.30511 | + | 0.753503i | −0.981275 | − | 0.192611i | \(-0.938304\pi\) |
−0.323831 | + | 0.946115i | \(0.604971\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.94567 | 0.296051 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.48680 | − | 16.4316i | 0.943972 | − | 1.63501i | 0.186174 | − | 0.982517i | \(-0.440391\pi\) |
0.757797 | − | 0.652490i | \(-0.226275\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 17.9796i | − | 1.77159i | −0.464080 | − | 0.885793i | \(-0.653615\pi\) | ||
0.464080 | − | 0.885793i | \(-0.346385\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.11491 | + | 0.726062i | −0.206394 | + | 0.0708564i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.97459 | + | 2.29473i | 0.384238 | + | 0.221840i | 0.679661 | − | 0.733527i | \(-0.262127\pi\) |
−0.295422 | + | 0.955367i | \(0.595460\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.147558 | 0.0141335 | 0.00706676 | − | 0.999975i | \(-0.497751\pi\) | ||||
0.00706676 | + | 0.999975i | \(0.497751\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.784147 | − | 1.35818i | −0.0744280 | − | 0.128913i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.9503 | + | 8.05419i | −1.31233 | + | 0.757675i | −0.982482 | − | 0.186359i | \(-0.940331\pi\) |
−0.329849 | + | 0.944034i | \(0.606998\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.6019 | + | 2.46151i | 1.17514 | + | 0.229537i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.10978 | + | 10.1553i | 0.287499 | + | 0.938856i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.20265 | + | 14.2074i | −0.751936 | + | 1.30239i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.537266 | + | 0.310190i | −0.0484436 | + | 0.0279689i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.11491 | + | 9.35991i | −0.546934 | + | 0.837176i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.98829 | + | 5.18939i | 0.797582 | + | 0.460484i | 0.842625 | − | 0.538501i | \(-0.181009\pi\) |
−0.0450429 | + | 0.998985i | \(0.514342\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.60719 | −0.141505 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.6351 | 1.54079 | 0.770393 | − | 0.637569i | \(-0.220060\pi\) | ||||
0.770393 | + | 0.637569i | \(0.220060\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.48645 | − | 4.89966i | −0.735869 | − | 0.424854i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00624 | + | 2.93103i | 0.0866036 | + | 0.252263i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.56757 | − | 3.21444i | 0.475670 | − | 0.274628i | −0.242940 | − | 0.970041i | \(-0.578112\pi\) |
0.718610 | + | 0.695413i | \(0.244779\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.48680 | + | 12.9675i | 0.635022 | + | 1.09989i | 0.986511 | + | 0.163698i | \(0.0523422\pi\) |
−0.351489 | + | 0.936192i | \(0.614324\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.770185 | − | 1.33400i | 0.0648613 | − | 0.112343i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.45779 | − | 2.63804i | 0.205531 | − | 0.220604i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.979135 | − | 5.01278i | 0.0813128 | − | 0.416289i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.30232 | − | 1.32925i | 0.189892 | − | 0.109634i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.84472 | + | 13.5875i | 0.642665 | + | 1.11313i | 0.984836 | + | 0.173490i | \(0.0555045\pi\) |
−0.342171 | + | 0.939638i | \(0.611162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.17548 | 0.0956594 | 0.0478297 | − | 0.998856i | \(-0.484770\pi\) | ||||
0.0478297 | + | 0.998856i | \(0.484770\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.75500 | + | 5.63205i | 0.788645 | + | 0.455324i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.1755 | + | 4.52323i | −1.05828 | + | 0.363315i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.45560i | − | 0.435405i | −0.976015 | − | 0.217702i | \(-0.930144\pi\) | ||
0.976015 | − | 0.217702i | \(-0.0698562\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.587741 | − | 1.01800i | 0.0466109 | − | 0.0807325i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.6351 | −1.94152 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.02098 | − | 2.32152i | 0.314948 | − | 0.181835i | −0.334191 | − | 0.942506i | \(-0.608463\pi\) |
0.649138 | + | 0.760670i | \(0.275130\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.342304 | − | 0.393051i | 0.0266483 | − | 0.0305989i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.76341 | − | 1.59545i | −0.213839 | − | 0.123460i | 0.389255 | − | 0.921130i | \(-0.372732\pi\) |
−0.603094 | + | 0.797670i | \(0.706066\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6894 | + | 5.68831i | 0.899188 | + | 0.437562i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.36417 | + | 5.82691i | −0.257264 | + | 0.445595i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.00603 | + | 1.73553i | −0.228544 | + | 0.131950i | −0.609900 | − | 0.792478i | \(-0.708790\pi\) |
0.381356 | + | 0.924428i | \(0.375457\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.07187 | − | 19.8740i | 0.610176 | − | 1.50234i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.59226i | − | 0.194846i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.56058 | + | 4.43505i | −0.191386 | + | 0.331491i | −0.945710 | − | 0.325012i | \(-0.894632\pi\) |
0.754324 | + | 0.656503i | \(0.227965\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.14756 | −0.308286 | −0.154143 | − | 0.988049i | \(-0.549262\pi\) | ||||
−0.154143 | + | 0.988049i | \(0.549262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.973274i | − | 0.0719465i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.7657 | + | 2.88415i | 1.08559 | + | 0.212047i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.82395i | − | 0.279635i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.97283 | − | 5.14910i | −0.216242 | − | 0.374542i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.404539 | − | 0.700683i | −0.0292714 | − | 0.0506996i | 0.851019 | − | 0.525136i | \(-0.175985\pi\) |
−0.880290 | + | 0.474436i | \(0.842652\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.34195 | − | 4.81623i | −0.600466 | − | 0.346679i | 0.168759 | − | 0.985657i | \(-0.446024\pi\) |
−0.769225 | + | 0.638978i | \(0.779358\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.71643 | + | 0.765156i | 0.122916 | + | 0.0547940i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.0650 | + | 8.12043i | 1.00209 | + | 0.578556i | 0.908866 | − | 0.417089i | \(-0.136950\pi\) |
0.0932234 | + | 0.995645i | \(0.470283\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.06829 | − | 3.58239i | −0.146618 | − | 0.253949i | 0.783358 | − | 0.621571i | \(-0.213505\pi\) |
−0.929975 | + | 0.367622i | \(0.880172\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.506243 | + | 0.876839i | 0.0357076 | + | 0.0618474i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.79931i | 0.687777i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.14090 | − | 5.84096i | 0.0796841 | − | 0.407950i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.9148i | 1.17566i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.28415 | 0.157998 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.80359 | − | 8.32007i | 0.330693 | − | 0.572777i | −0.651955 | − | 0.758258i | \(-0.726051\pi\) |
0.982648 | + | 0.185481i | \(0.0593842\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.57192i | − | 0.107707i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.1256 | − | 11.6267i | 0.690562 | − | 0.792937i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.1461 | − | 13.3634i | 1.57126 | − | 0.907166i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.58150 | − | 2.73924i | 0.106868 | − | 0.185100i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.1832 | − | 4.03700i | 0.886798 | − | 0.271558i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.0447 | − | 7.53136i | −0.873538 | − | 0.504337i | −0.00501557 | − | 0.999987i | \(-0.501597\pi\) |
−0.868522 | + | 0.495650i | \(0.834930\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.6458 | − | 5.54226i | −0.909719 | − | 0.369484i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.4174 | + | 10.0559i | −1.15603 | + | 0.667436i | −0.950350 | − | 0.311183i | \(-0.899275\pi\) |
−0.205683 | + | 0.978619i | \(0.565941\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5683 | −0.830536 | −0.415268 | − | 0.909699i | \(-0.636312\pi\) | ||||
−0.415268 | + | 0.909699i | \(0.636312\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.500000 | + | 0.866025i | −0.0328976 | + | 0.0569803i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.3712i | − | 0.744954i | −0.928041 | − | 0.372477i | \(-0.878508\pi\) | ||
0.928041 | − | 0.372477i | \(-0.121492\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.79811 | + | 13.9762i | 0.312994 | + | 0.911704i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.30232 | + | 1.32925i | 0.149552 | + | 0.0863438i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3510 | 1.18703 | 0.593513 | − | 0.804825i | \(-0.297741\pi\) | ||||
0.593513 | + | 0.804825i | \(0.297741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.688687 | + | 1.19284i | 0.0443622 | + | 0.0768376i | 0.887354 | − | 0.461089i | \(-0.152541\pi\) |
−0.842992 | + | 0.537927i | \(0.819208\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.31932 | + | 3.07111i | −0.341234 | + | 0.197012i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.88906 | + | 25.0300i | −0.312351 | + | 1.59911i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.41140 | + | 7.87467i | 0.153434 | + | 0.501053i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.16924 | + | 2.02518i | −0.0740976 | + | 0.128341i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.6149 | − | 21.8497i | −0.796246 | − | 1.37914i | −0.922045 | − | 0.387083i | \(-0.873483\pi\) |
0.125799 | − | 0.992056i | \(-0.459851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.97295 | − | 2.87113i | 0.312646 | − | 0.180507i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.88509 | − | 0.647165i | 0.118049 | − | 0.0405270i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.3596 | + | 15.2187i | 1.64427 | + | 0.949318i | 0.979292 | + | 0.202451i | \(0.0648907\pi\) |
0.664974 | + | 0.746866i | \(0.268443\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.8649 | −1.79358 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.72834 | 0.416474 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.80980 | + | 1.62224i | 0.173260 | + | 0.100032i | 0.584122 | − | 0.811666i | \(-0.301439\pi\) |
−0.410862 | + | 0.911697i | \(0.634772\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.66152 | + | 10.6654i | 0.224925 | + | 0.655173i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.24496 | + | 1.29613i | −0.137389 | + | 0.0793218i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.554332 | − | 0.960132i | −0.0337982 | − | 0.0585403i | 0.848632 | − | 0.528984i | \(-0.177427\pi\) |
−0.882430 | + | 0.470444i | \(0.844094\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0877 | + | 26.1327i | −0.916515 | + | 1.58745i | −0.111847 | + | 0.993725i | \(0.535677\pi\) |
−0.804668 | + | 0.593725i | \(0.797657\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.51351 | − | 0.809492i | −0.212647 | − | 0.0489927i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.686824 | + | 4.95260i | 0.0414170 | + | 0.298653i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.4941 | − | 12.9870i | 1.35154 | − | 0.780311i | 0.363073 | − | 0.931761i | \(-0.381727\pi\) |
0.988465 | + | 0.151449i | \(0.0483941\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.17548 | − | 15.8924i | −0.549322 | − | 0.951453i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.7827 | 1.06083 | 0.530413 | − | 0.847740i | \(-0.322037\pi\) | ||||
0.530413 | + | 0.847740i | \(0.322037\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.37503 | − | 3.68062i | −0.378956 | − | 0.218790i | 0.298408 | − | 0.954438i | \(-0.403544\pi\) |
−0.677364 | + | 0.735648i | \(0.736878\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.386568 | + | 1.12601i | 0.0228983 | + | 0.0666994i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.4183i | 0.674001i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.18869 | + | 2.05887i | −0.0699227 | + | 0.121110i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.45963 | −0.202807 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.5449 | + | 8.39750i | −0.849722 | + | 0.490587i | −0.860557 | − | 0.509354i | \(-0.829884\pi\) |
0.0108351 | + | 0.999941i | \(0.496551\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.7530 | + | 16.3318i | 1.09184 | + | 0.950873i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.20022 | + | 0.692946i | 0.0696437 | + | 0.0402088i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.1483 | + | 14.1133i | 0.876050 | + | 0.816193i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.7904 | + | 25.6177i | −0.852504 | + | 1.47658i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.83009 | − | 2.21130i | 0.220033 | − | 0.127036i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.04087 | + | 6.13183i | 0.403159 | + | 0.351108i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.12468i | 0.178335i | 0.996017 | + | 0.0891674i | \(0.0284206\pi\) | ||||
−0.996017 | + | 0.0891674i | \(0.971579\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.09546 | − | 3.62944i | 0.119207 | − | 0.206472i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.6072 | 1.05512 | 0.527558 | − | 0.849519i | \(-0.323108\pi\) | ||||
0.527558 | + | 0.849519i | \(0.323108\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.5732i | 0.993295i | 0.867952 | + | 0.496647i | \(0.165436\pi\) | ||||
−0.867952 | + | 0.496647i | \(0.834564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 27.7338 | + | 5.41719i | 1.56262 | + | 0.305224i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 22.2633i | − | 1.25043i | −0.780453 | − | 0.625215i | \(-0.785011\pi\) | ||
0.780453 | − | 0.625215i | \(-0.214989\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.14207 | − | 1.97813i | −0.0639438 | − | 0.110754i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.534885 | + | 0.926448i | 0.0298544 | + | 0.0517093i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.56428 | + | 4.36724i | 0.420888 | + | 0.243000i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.3492 | + | 7.59637i | −0.906888 | + | 0.421371i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0297867 | + | 0.0171974i | 0.00164721 | + | 0.000951017i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.1755 | − | 24.5527i | −0.781520 | − | 1.35363i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.2026 | + | 24.5997i | 0.780648 | + | 1.35212i | 0.931565 | + | 0.363576i | \(0.118444\pi\) |
−0.150916 | + | 0.988547i | \(0.548222\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.8190i | 1.08608i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.53268 | − | 1.86200i | −0.520826 | − | 0.101732i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.87960i | 0.483703i | 0.970313 | + | 0.241851i | \(0.0777547\pi\) | ||||
−0.970313 | + | 0.241851i | \(0.922245\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.75475 | −0.203930 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.11491 | + | 5.39518i | −0.168682 | + | 0.292165i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.8993i | − | 1.02047i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.25700 | + | 1.96560i | 0.121513 | + | 0.105824i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.9652 | − | 8.64018i | 0.803376 | − | 0.463829i | −0.0412745 | − | 0.999148i | \(-0.513142\pi\) |
0.844650 | + | 0.535319i | \(0.179808\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.37189 | + | 9.30438i | −0.287551 | + | 0.498052i | −0.973225 | − | 0.229857i | \(-0.926174\pi\) |
0.685674 | + | 0.727909i | \(0.259508\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.12187 | + | 4.86934i | −0.0598809 | + | 0.259906i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.8598 | − | 16.0849i | −1.48283 | − | 0.856111i | −0.483017 | − | 0.875611i | \(-0.660459\pi\) |
−0.999810 | + | 0.0195003i | \(0.993792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.3716 | + | 9.90346i | 0.603544 | + | 0.525621i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.31164 | + | 1.91198i | −0.175271 | + | 0.101193i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.8913 | −0.733157 | −0.366578 | − | 0.930387i | \(-0.619471\pi\) | ||||
−0.366578 | + | 0.930387i | \(0.619471\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.89134 | − | 11.9361i | 0.362702 | − | 0.628218i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.33093i | 0.122342i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.85244 | + | 28.6987i | 0.515700 | + | 1.50216i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.6282 | − | 9.02293i | −0.815784 | − | 0.470993i | 0.0331762 | − | 0.999450i | \(-0.489438\pi\) |
−0.848961 | + | 0.528456i | \(0.822771\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.83996 | 0.408132 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.8176 | − | 18.7366i | −0.561620 | − | 0.972754i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.1267 | − | 10.4655i | 0.938566 | − | 0.541882i | 0.0490558 | − | 0.998796i | \(-0.484379\pi\) |
0.889511 | + | 0.456914i | \(0.151045\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.32524 | + | 1.17676i | −0.120075 | + | 0.0607676i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.61396 | − | 6.02567i | 0.289134 | − | 0.310338i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.2089 | − | 21.1464i | 0.627129 | − | 1.08622i | −0.360996 | − | 0.932567i | \(-0.617563\pi\) |
0.988125 | − | 0.153652i | \(-0.0491033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.20961 | + | 2.09511i | 0.0619702 | + | 0.107335i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.9612 | − | 14.9887i | 1.32656 | − | 0.765887i | 0.341790 | − | 0.939776i | \(-0.388967\pi\) |
0.984765 | + | 0.173889i | \(0.0556335\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.11491 | − | 9.07325i | −0.158750 | − | 0.462416i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.5895 | + | 10.1553i | 0.894123 | + | 0.516222i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.80908 | 0.193128 | 0.0965640 | − | 0.995327i | \(-0.469215\pi\) | ||||
0.0965640 | + | 0.995327i | \(0.469215\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.9582 | 1.11047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.55990 | + | 2.05531i | 0.179573 | + | 0.103677i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.1212 | + | 8.28095i | −1.21367 | + | 0.416660i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.0330 | + | 5.79258i | −0.503544 | + | 0.290721i | −0.730176 | − | 0.683259i | \(-0.760562\pi\) |
0.226632 | + | 0.973980i | \(0.427229\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.14207 | − | 1.97813i | −0.0571752 | − | 0.0990303i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.74302 | − | 16.8754i | 0.486543 | − | 0.842717i | −0.513337 | − | 0.858187i | \(-0.671591\pi\) |
0.999880 | + | 0.0154696i | \(0.00492431\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.8885 | − | 5.04299i | −1.09034 | − | 0.251209i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.64964 | − | 18.6847i | 0.181352 | − | 0.928450i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.82679 | − | 3.36410i | 0.288823 | − | 0.166752i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.29811 | − | 3.98044i | −0.113634 | − | 0.196820i | 0.803599 | − | 0.595171i | \(-0.202916\pi\) |
−0.917233 | + | 0.398351i | \(0.869583\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.49852 | 0.0739167 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −41.3192 | − | 23.8556i | −2.03318 | − | 1.17386i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.28415 | − | 21.2176i | −0.357565 | − | 1.04153i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.49023i | 0.170918i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.38509 | + | 5.86315i | −0.165373 | + | 0.286434i | −0.936788 | − | 0.349899i | \(-0.886216\pi\) |
0.771415 | + | 0.636332i | \(0.219549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.1087 | −0.785088 | −0.392544 | − | 0.919733i | \(-0.628405\pi\) | ||||
−0.392544 | + | 0.919733i | \(0.628405\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.8582 | + | 9.73308i | −0.819673 | + | 0.473238i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.19475 | + | 17.7144i | −0.348997 | + | 0.859276i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.5135 | − | 8.95670i | −0.750749 | − | 0.433445i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.803594 | − | 0.246079i | 0.0387979 | − | 0.0118808i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.12887 | + | 1.95526i | −0.0543757 | + | 0.0941816i | −0.891932 | − | 0.452169i | \(-0.850650\pi\) |
0.837556 | + | 0.546351i | \(0.183984\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.03633 | + | 4.63978i | −0.386201 | + | 0.222974i | −0.680513 | − | 0.732736i | \(-0.738243\pi\) |
0.294312 | + | 0.955710i | \(0.404910\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.781873 | − | 0.897785i | 0.0374879 | − | 0.0430455i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.1162i | 0.627432i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.9659 | − | 22.4576i | 0.618827 | − | 1.07184i | −0.370873 | − | 0.928684i | \(-0.620941\pi\) |
0.989700 | − | 0.143157i | \(-0.0457253\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −33.5962 | −1.59982 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.4318i | 0.923231i | 0.887080 | + | 0.461615i | \(0.152730\pi\) | ||||
−0.887080 | + | 0.461615i | \(0.847270\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.76725 | − | 24.4064i | 0.225990 | − | 1.15698i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.65709i | 0.172975i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.7361 | − | 22.0595i | −0.601052 | − | 1.04105i | −0.992662 | − | 0.120921i | \(-0.961415\pi\) |
0.391610 | − | 0.920131i | \(-0.371918\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.33076 | − | 2.30494i | −0.0626631 | − | 0.108536i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.237288 | + | 0.136998i | 0.0111488 | + | 0.00643674i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.9919 | − | 20.3175i | 1.31228 | − | 0.952498i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.9321 | − | 9.77578i | −0.792053 | − | 0.457292i | 0.0486321 | − | 0.998817i | \(-0.484514\pi\) |
−0.840685 | + | 0.541525i | \(0.817847\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.64979 | + | 4.58958i | 0.123682 | + | 0.214223i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.1678 | − | 28.0034i | −0.753008 | − | 1.30425i | −0.946359 | − | 0.323118i | \(-0.895269\pi\) |
0.193351 | − | 0.981130i | \(-0.438064\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.8119i | − | 1.33900i | −0.742810 | − | 0.669502i | \(-0.766507\pi\) | ||
0.742810 | − | 0.669502i | \(-0.233493\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.18682 | − | 0.622476i | −0.147785 | − | 0.0288666i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 24.8085i | − | 1.14800i | −0.818856 | − | 0.573999i | \(-0.805391\pi\) | ||
0.818856 | − | 0.573999i | \(-0.194609\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.6351 | 0.860490 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.635830 | − | 1.10129i | 0.0292975 | − | 0.0507448i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.89506i | − | 0.317035i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.5813 | − | 4.29761i | −0.485503 | − | 0.197188i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.8648 | + | 7.42748i | −0.589038 | + | 0.340081i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.18945 | + | 5.52428i | −0.145729 | + | 0.252411i | −0.929645 | − | 0.368457i | \(-0.879886\pi\) |
0.783915 | + | 0.620868i | \(0.213220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.7493 | + | 16.5365i | 0.809297 | + | 0.754001i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.97295 | − | 2.87113i | −0.226277 | − | 0.130641i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.7964 | − | 25.0277i | 0.989723 | − | 1.13645i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.8874 | + | 9.17260i | −0.719927 | + | 0.415650i | −0.814726 | − | 0.579846i | \(-0.803113\pi\) |
0.0947988 | + | 0.995496i | \(0.469779\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.08226 | 0.0489413 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.95963 | − | 3.39418i | 0.0884369 | − | 0.153177i | −0.818414 | − | 0.574629i | \(-0.805146\pi\) |
0.906851 | + | 0.421452i | \(0.138480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.73447i | − | 0.393381i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.22982 | + | 2.13874i | −0.280009 | + | 0.0961291i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.0556 | − | 14.4659i | −1.12390 | − | 0.648883i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.6087 | −1.05687 | −0.528435 | − | 0.848974i | \(-0.677221\pi\) | ||||
−0.528435 | + | 0.848974i | \(0.677221\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.371889 | − | 0.644130i | −0.0166148 | − | 0.0287776i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.9636 | + | 9.21658i | −0.711781 | + | 0.410947i | −0.811720 | − | 0.584047i | \(-0.801469\pi\) |
0.0999391 | + | 0.994994i | \(0.468135\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.13333 | + | 41.6393i | −0.361928 | + | 1.85293i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.69673 | + | 2.51063i | 0.0753544 | + | 0.111501i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.83848 | − | 11.8446i | 0.303110 | − | 0.525002i | −0.673729 | − | 0.738979i | \(-0.735308\pi\) |
0.976839 | + | 0.213977i | \(0.0686416\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.1079 | − | 50.4164i | −1.28766 | − | 2.23029i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.74147 | + | 1.58279i | −0.121039 | + | 0.0698819i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.0543 | + | 38.0253i | 0.575243 | + | 1.67559i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.72304 | + | 3.30420i | 0.251699 | + | 0.145319i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.809079 | −0.0355146 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.9472 | 1.13677 | 0.568383 | − | 0.822764i | \(-0.307569\pi\) | ||||
0.568383 | + | 0.822764i | \(0.307569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.4246 | − | 16.4110i | −1.24292 | − | 0.717601i | −0.273234 | − | 0.961948i | \(-0.588093\pi\) |
−0.969688 | + | 0.244346i | \(0.921427\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.94567 | − | 3.07111i | 0.172203 | − | 0.134034i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.6309 | + | 11.9113i | −0.898697 | + | 0.518863i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.98680 | + | 8.63738i | 0.216817 | + | 0.375538i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.3796 | + | 28.3703i | −0.710814 | + | 1.23117i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.54147 | − | 7.02120i | 0.283342 | − | 0.304122i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.0720 | − | 1.96735i | −0.435451 | − | 0.0850558i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.03378 | + | 0.596851i | −0.0446108 | + | 0.0257560i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.70265 | + | 9.87728i | 0.245630 | + | 0.425444i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.8370 | 0.981839 | 0.490920 | − | 0.871205i | \(-0.336661\pi\) | ||||
0.490920 | + | 0.871205i | \(0.336661\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.837243 | − | 0.483383i | −0.0359296 | − | 0.0207439i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.312072 | + | 0.107136i | −0.0133677 | + | 0.00458922i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 31.4513i | − | 1.34476i | −0.740207 | − | 0.672379i | \(-0.765272\pi\) | ||
0.740207 | − | 0.672379i | \(-0.234728\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.14979 | + | 10.6518i | −0.262467 | + | 0.454606i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.21733 | 0.222266 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.3749 | − | 24.4652i | 1.80196 | − | 1.04036i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.64452 | + | 2.30309i | 0.112254 | + | 0.0977608i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.9636 | − | 9.21658i | −0.676399 | − | 0.390519i | 0.122098 | − | 0.992518i | \(-0.461038\pi\) |
−0.798497 | + | 0.601999i | \(0.794371\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.7709 | − | 7.27920i | 1.00540 | − | 0.307877i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.445668 | − | 0.771919i | 0.0188161 | − | 0.0325905i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.51624 | − | 4.91685i | 0.358917 | − | 0.207221i | −0.309689 | − | 0.950838i | \(-0.600225\pi\) |
0.668605 | + | 0.743617i | \(0.266892\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.6557 | − | 27.1626i | 0.995202 | − | 1.14274i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.5261i | 1.53395i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.6017 | + | 37.4152i | −0.905591 | + | 1.56853i | −0.0854680 | + | 0.996341i | \(0.527239\pi\) |
−0.820123 | + | 0.572188i | \(0.806095\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.3106 | 0.724424 | 0.362212 | − | 0.932096i | \(-0.382022\pi\) | ||||
0.362212 | + | 0.932096i | \(0.382022\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 0.188590i | − | 0.00787847i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.4392 | + | 3.94392i | −1.18599 | + | 0.164473i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.245757i | 0.0102310i | 0.999987 | + | 0.00511550i | \(0.00162832\pi\) | ||||
−0.999987 | + | 0.00511550i | \(0.998372\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.12263 | − | 1.94445i | −0.0466548 | − | 0.0808084i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.5202 | + | 37.2741i | 0.892809 | + | 1.54639i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.36735 | + | 2.52149i | 0.180877 | + | 0.104430i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.9503 | − | 19.2196i | −0.576772 | − | 0.794632i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.9006 | − | 9.18021i | −0.656287 | − | 0.378908i | 0.134573 | − | 0.990904i | \(-0.457034\pi\) |
−0.790861 | + | 0.611996i | \(0.790367\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.11491 | − | 12.3234i | −0.293165 | − | 0.507776i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.89281 | + | 3.27845i | 0.0778599 | + | 0.134857i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.7514i | 0.852159i | 0.904686 | + | 0.426079i | \(0.140106\pi\) | ||||
−0.904686 | + | 0.426079i | \(0.859894\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.03239 | − | 36.0030i | 0.288300 | − | 1.47598i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 0.964208i | − | 0.0394624i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.80908 | 0.0739170 | 0.0369585 | − | 0.999317i | \(-0.488233\pi\) | ||||
0.0369585 | + | 0.999317i | \(0.488233\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.88585 | − | 13.6587i | 0.321671 | − | 0.557150i | −0.659162 | − | 0.752001i | \(-0.729089\pi\) |
0.980833 | + | 0.194851i | \(0.0624223\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12.7951i | − | 0.521058i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.8624 | − | 14.6853i | −0.685555 | − | 0.597043i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.3330 | − | 12.8939i | 0.906467 | − | 0.523349i | 0.0271746 | − | 0.999631i | \(-0.491349\pi\) |
0.879293 | + | 0.476281i | \(0.158016\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.14207 | + | 1.97813i | −0.0462792 | + | 0.0801579i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.34945 | + | 23.2187i | −0.216416 | + | 0.939326i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.10085 | + | 2.94498i | 0.206021 | + | 0.118946i | 0.599461 | − | 0.800404i | \(-0.295382\pi\) |
−0.393440 | + | 0.919350i | \(0.628715\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.911050 | − | 1.04611i | 0.0367371 | − | 0.0421833i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.07106 | + | 2.92778i | −0.204153 | + | 0.117868i | −0.598591 | − | 0.801055i | \(-0.704273\pi\) |
0.394438 | + | 0.918923i | \(0.370939\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.6740 | 1.19270 | 0.596350 | − | 0.802725i | \(-0.296617\pi\) | ||||
0.596350 | + | 0.802725i | \(0.296617\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.97908 | + | 6.89196i | −0.159675 | + | 0.276565i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 47.7113i | 1.91151i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.13659 | − | 24.2351i | 0.245464 | − | 0.969406i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.461087 | + | 0.266209i | 0.0184141 | + | 0.0106314i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.7283 | 1.02586 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.1483 | + | 26.2377i | 0.603045 | + | 1.04450i | 0.992357 | + | 0.123399i | \(0.0393794\pi\) |
−0.389312 | + | 0.921106i | \(0.627287\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.93935 | − | 1.11968i | 0.0770821 | − | 0.0445034i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.7772 | − | 4.44903i | −0.903887 | − | 0.176554i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.0319 | + | 30.0876i | −1.11066 | + | 1.19212i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.93246 | + | 17.2035i | −0.392922 | + | 0.680561i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.98604 | + | 15.5643i | 0.354927 | + | 0.614752i | 0.987105 | − | 0.160071i | \(-0.0511723\pi\) |
−0.632178 | + | 0.774823i | \(0.717839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.1517 | + | 13.3666i | −0.913014 | + | 0.527129i | −0.881400 | − | 0.472371i | \(-0.843398\pi\) |
−0.0316144 | + | 0.999500i | \(0.510065\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.39905 | − | 1.16692i | 0.133838 | − | 0.0459474i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.8974 | + | 11.4878i | 0.782248 | + | 0.451631i | 0.837227 | − | 0.546856i | \(-0.184176\pi\) |
−0.0549781 | + | 0.998488i | \(0.517509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.1212 | 0.436543 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.22982 | 0.244166 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.4153 | + | 8.90006i | 0.603249 | + | 0.348286i | 0.770319 | − | 0.637659i | \(-0.220097\pi\) |
−0.167070 | + | 0.985945i | \(0.553430\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37.2966 | + | 12.8042i | −1.45730 | + | 0.500301i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −34.6166 | + | 19.9859i | −1.35052 | + | 0.779725i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.3587 | − | 28.3341i | −0.637244 | − | 1.10374i | −0.986035 | − | 0.166538i | \(-0.946741\pi\) |
0.348791 | − | 0.937200i | \(-0.386592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.10095 | − | 7.10305i | 0.159508 | − | 0.276276i | −0.775183 | − | 0.631737i | \(-0.782342\pi\) |
0.934691 | + | 0.355460i | \(0.115676\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.13171 | + | 0.721529i | 0.121626 | + | 0.0280219i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.5055 | + | 4.20063i | 0.833948 | + | 0.162893i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.3589 | − | 6.55809i | 0.439820 | − | 0.253930i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.75551 | − | 3.04062i | −0.0678718 | − | 0.117557i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.17548 | 0.161193 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.36805 | + | 4.25395i | 0.284017 | + | 0.163978i | 0.635241 | − | 0.772314i | \(-0.280901\pi\) |
−0.351223 | + | 0.936292i | \(0.614234\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.25622 | − | 5.46827i | −0.163822 | − | 0.210474i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 12.9710i | − | 0.498518i | −0.968437 | − | 0.249259i | \(-0.919813\pi\) | ||
0.968437 | − | 0.249259i | \(-0.0801870\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.8378 | + | 55.1446i | −1.22182 | + | 2.11626i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.68793 | −0.179642 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.3910 | − | 14.6595i | 0.971561 | − | 0.560931i | 0.0718490 | − | 0.997416i | \(-0.477110\pi\) |
0.899712 | + | 0.436485i | \(0.143777\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.44102 | + | 10.8406i | −0.360723 | + | 0.414200i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.53709 | − | 1.46479i | −0.0967959 | − | 0.0558852i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.08226 | + | 17.7186i | −0.155522 | + | 0.675023i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.6079 | − | 32.2299i | 0.707880 | − | 1.22608i | −0.257763 | − | 0.966208i | \(-0.582985\pi\) |
0.965642 | − | 0.259875i | \(-0.0836814\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.9442 | − | 6.31866i | 0.415738 | − | 0.240026i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.2491 | − | 21.9892i | −0.957753 | − | 0.834098i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.1775i | − | 0.385502i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.32528 | − | 2.29544i | 0.0501265 | − | 0.0868217i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.9472 | −1.88648 | −0.943240 | − | 0.332113i | \(-0.892238\pi\) | ||||
−0.943240 | + | 0.332113i | \(0.892238\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.3682i | 0.579623i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.660304 | + | 3.38049i | −0.0248685 | + | 0.127317i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 81.3994i | − | 3.06134i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.2438 | − | 26.4030i | −0.572492 | − | 0.991585i | −0.996309 | − | 0.0858376i | \(-0.972643\pi\) |
0.423817 | − | 0.905748i | \(-0.360690\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.7981 | − | 29.0952i | −0.629978 | − | 1.09115i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.9805 | − | 17.8866i | −1.16023 | − | 0.669859i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.28263 | + | 7.36372i | −0.122763 | + | 0.275387i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.70440 | + | 2.13874i | 0.138343 | + | 0.0798726i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.816798 | + | 1.41474i | 0.0304614 | + | 0.0527607i | 0.880854 | − | 0.473388i | \(-0.156969\pi\) |
−0.850393 | + | 0.526148i | \(0.823636\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.5676 | − | 66.8010i | −1.43633 | − | 2.48780i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.321056i | 0.0119402i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.56881 | + | 11.3125i | 0.0582640 | + | 0.420135i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.7936i | 0.659928i | 0.943993 | + | 0.329964i | \(0.107037\pi\) | ||||
−0.943993 | + | 0.329964i | \(0.892963\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.1102 | 0.892970 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.1832 | − | 22.8340i | 0.487598 | − | 0.844545i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.1438i | 0.817901i | 0.912557 | + | 0.408950i | \(0.134105\pi\) | ||||
−0.912557 | + | 0.408950i | \(0.865895\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.90408 | + | 4.48286i | −0.144004 | + | 0.165353i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.76176 | + | 2.17185i | −0.138566 | + | 0.0800013i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.99228 | − | 15.5751i | 0.330786 | − | 0.572939i | −0.651880 | − | 0.758322i | \(-0.726019\pi\) |
0.982666 | + | 0.185383i | \(0.0593527\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.430988 | + | 1.87065i | −0.0158327 | + | 0.0687202i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.2873 | + | 7.67144i | 0.487465 | + | 0.281438i | 0.723522 | − | 0.690301i | \(-0.242522\pi\) |
−0.236057 | + | 0.971739i | \(0.575855\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.4562 | − | 23.0405i | −0.969280 | − | 0.844137i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.5929 | − | 14.7761i | 0.936395 | − | 0.540628i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.6894 | 0.719437 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.1762 | − | 33.2142i | 0.699751 | − | 1.21200i | −0.268802 | − | 0.963196i | \(-0.586628\pi\) |
0.968553 | − | 0.248809i | \(-0.0800391\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 5.88088i | − | 0.214311i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.48604 | + | 0.853474i | −0.0904762 | + | 0.0310611i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.29135 | − | 1.32291i | −0.0832806 | − | 0.0480821i | 0.457781 | − | 0.889065i | \(-0.348644\pi\) |
−0.541062 | + | 0.840983i | \(0.681978\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.33848 | 0.0485837 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.3176 | − | 21.3346i | −0.446511 | − | 0.773380i | 0.551645 | − | 0.834079i | \(-0.314000\pi\) |
−0.998156 | + | 0.0606991i | \(0.980667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.548233 | − | 0.316523i | 0.0198474 | − | 0.0114589i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −24.7201 | − | 4.82853i | −0.893758 | − | 0.174576i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.7407 | + | 38.3405i | 0.423933 | + | 1.38440i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.05509 | + | 12.2198i | −0.254413 | + | 0.440656i | −0.964736 | − | 0.263220i | \(-0.915216\pi\) |
0.710323 | + | 0.703876i | \(0.248549\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.54737 | + | 6.14423i | 0.127755 | + | 0.221279i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.1130 | − | 7.57081i | 0.471643 | − | 0.272303i | −0.245284 | − | 0.969451i | \(-0.578881\pi\) |
0.716927 | + | 0.697148i | \(0.245548\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.5808 | − | 19.1324i | 0.882968 | − | 0.687257i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.82679 | − | 3.36410i | −0.209035 | − | 0.120686i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.07930 | 0.217814 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.74378 | 0.241311 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.74147 | + | 1.58279i | 0.0979722 | + | 0.0565643i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.96111 | + | 11.5381i | 0.141378 | + | 0.411812i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.7617 | − | 16.0282i | 0.989597 | − | 0.571344i | 0.0844431 | − | 0.996428i | \(-0.473089\pi\) |
0.905154 | + | 0.425084i | \(0.139756\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.378132 | + | 0.654944i | 0.0134619 | + | 0.0233166i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.5536 | + | 59.8486i | −1.22859 | + | 2.12797i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.40811 | + | 14.3951i | 0.156537 | + | 0.511185i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.503889 | + | 2.57971i | −0.0178711 | + | 0.0914928i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.4537 | + | 21.6239i | −1.32668 | + | 0.765957i | −0.984784 | − | 0.173781i | \(-0.944401\pi\) |
−0.341893 | + | 0.939739i | \(0.611068\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.6351 | + | 21.8847i | 0.446998 | + | 0.774224i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.7592 | 1.15749 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.7517 | + | 6.78485i | 0.414709 | + | 0.239432i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 52.1010 | − | 17.8866i | 1.83632 | − | 0.630421i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 0.258422i | − | 0.00909687i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.87737 | + | 10.1799i | −0.206637 | + | 0.357907i | −0.950653 | − | 0.310256i | \(-0.899585\pi\) |
0.744016 | + | 0.668162i | \(0.232919\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.4068 | −1.13796 | −0.568979 | − | 0.822352i | \(-0.692661\pi\) | ||||
−0.568979 | + | 0.822352i | \(0.692661\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.09135 | + | 3.51684i | −0.213633 | + | 0.123341i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.81845 | + | 7.82928i | −0.238840 | + | 0.274248i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.6393 | + | 7.87467i | 0.477180 | + | 0.275500i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 33.3378 | + | 31.0599i | 1.16492 | + | 1.08532i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.0877 | + | 27.8648i | −0.561466 | + | 0.972488i | 0.435903 | + | 0.899994i | \(0.356429\pi\) |
−0.997369 | + | 0.0724940i | \(0.976904\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.9608 | − | 13.2564i | 0.800363 | − | 0.462090i | −0.0432348 | − | 0.999065i | \(-0.513766\pi\) |
0.843598 | + | 0.536975i | \(0.180433\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.438563 | + | 1.07980i | −0.0152688 | + | 0.0375938i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 50.5431i | − | 1.75756i | −0.477229 | − | 0.878779i | \(-0.658359\pi\) | ||
0.477229 | − | 0.878779i | \(-0.341641\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.44567 | − | 5.96807i | 0.119673 | − | 0.207280i | −0.799965 | − | 0.600047i | \(-0.795149\pi\) |
0.919638 | + | 0.392767i | \(0.128482\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.05433 | 0.210022 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 43.6133i | 1.51111i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.00275 | + | 1.36783i | 0.242340 | + | 0.0473358i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 8.63385i | − | 0.298429i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.1134 | − | 40.0336i | −0.797964 | − | 1.38211i | −0.920940 | − | 0.389705i | \(-0.872577\pi\) |
0.122975 | − | 0.992410i | \(-0.460756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.8913 | + | 20.5964i | 0.410046 | + | 0.710221i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.58968 | + | 2.07250i | 0.123635 | + | 0.0713809i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.8522 | − | 3.54299i | −0.992545 | − | 0.121882i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.1537 | + | 21.4507i | 1.27662 | + | 0.737055i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.857926 | − | 1.48597i | −0.0294440 | − | 0.0509984i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.3176 | + | 33.4590i | 0.662197 | + | 1.14696i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 17.3274i | − | 0.593280i | −0.954989 | − | 0.296640i | \(-0.904134\pi\) | ||
0.954989 | − | 0.296640i | \(-0.0958661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.88421 | − | 14.7660i | 0.0986378 | − | 0.504986i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 0.186033i | − | 0.00635478i | −0.999995 | − | 0.00317739i | \(-0.998989\pi\) | ||
0.999995 | − | 0.00317739i | \(-0.00101140\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0947 | 0.753863 | 0.376931 | − | 0.926241i | \(-0.376979\pi\) | ||||
0.376931 | + | 0.926241i | \(0.376979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.33076 | + | 2.30494i | −0.0453522 | + | 0.0785523i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.5388i | 0.597027i | 0.954405 | + | 0.298514i | \(0.0964908\pi\) | ||||
−0.954405 | + | 0.298514i | \(0.903509\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.09737 | − | 5.85305i | 0.173316 | − | 0.199010i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.479906 | + | 0.277074i | −0.0162985 | + | 0.00940993i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.70265 | + | 9.87728i | −0.193449 | + | 0.335064i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.4589 | − | 10.6759i | −0.388269 | − | 0.361740i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 37.8630 | + | 21.8602i | 1.28147 | + | 0.739857i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.64148 | + | 47.8924i | −0.0892985 | + | 1.61906i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.7590 | − | 6.21170i | 0.363305 | − | 0.209754i | −0.307224 | − | 0.951637i | \(-0.599400\pi\) |
0.670530 | + | 0.741883i | \(0.266067\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.91479 | −0.132043 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.93171 | − | 6.80991i | 0.132463 | − | 0.229432i | −0.792163 | − | 0.610310i | \(-0.791045\pi\) |
0.924625 | + | 0.380878i | \(0.124378\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 18.9717i | − | 0.638450i | −0.947679 | − | 0.319225i | \(-0.896577\pi\) | ||
0.947679 | − | 0.319225i | \(-0.103423\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.88214 | + | 5.48239i | 0.0632675 | + | 0.184288i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.2459 | + | 5.91546i | 0.344023 | + | 0.198622i | 0.662049 | − | 0.749460i | \(-0.269687\pi\) |
−0.318027 | + | 0.948082i | \(0.603020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.5264 | 1.49337 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.25698 | − | 7.37331i | −0.142614 | − | 0.247015i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.0723 | + | 7.54728i | −0.437447 | + | 0.252560i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.19526 | − | 11.2389i | 0.0733795 | − | 0.375673i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.41305 | + | 4.61445i | 0.0471803 | + | 0.154072i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.11491 | + | 12.3234i | −0.237295 | + | 0.411008i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.64207 | + | 16.7006i | 0.321224 | + | 0.556376i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.97130 | + | 3.44753i | −0.198712 | + | 0.114727i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.77170 | − | 3.01138i | 0.291581 | − | 0.100102i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.16917 | − | 2.98442i | −0.171640 | − | 0.0990962i | 0.411719 | − | 0.911311i | \(-0.364928\pi\) |
−0.583359 | + | 0.812215i | \(0.698262\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −55.8899 | −1.85375 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.7952 | −0.987158 | −0.493579 | − | 0.869701i | \(-0.664312\pi\) | ||||
−0.493579 | + | 0.869701i | \(0.664312\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.68832 | − | 5.01620i | −0.287541 | − | 0.166012i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.706658 | + | 2.05839i | 0.0233614 | + | 0.0680481i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 65.5210 | − | 37.8285i | 2.16369 | − | 1.24921i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.0070 | + | 20.7967i | 0.396074 | + | 0.686021i | 0.993238 | − | 0.116099i | \(-0.0370389\pi\) |
−0.597163 | + | 0.802120i | \(0.703706\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.364170 | + | 0.630760i | −0.0119998 | + | 0.0207843i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.11949 | + | 23.2494i | 0.234341 | + | 0.765263i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33.3221 | + | 4.62109i | −1.09562 | + | 0.151940i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45.8665 | + | 26.4810i | −1.50645 | + | 0.869751i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.350207 | + | 0.606577i | 0.0114899 | + | 0.0199011i | 0.871713 | − | 0.490016i | \(-0.163009\pi\) |
−0.860223 | + | 0.509918i | \(0.829676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0514 | −0.853800 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.75612 | + | 2.16860i | 0.122970 | + | 0.0709968i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.77643 | + | 8.08731i | 0.0907989 | + | 0.264483i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.65849i | − | 0.0868491i | −0.999057 | − | 0.0434246i | \(-0.986173\pi\) | ||
0.999057 | − | 0.0434246i | \(-0.0138268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.04809 | + | 3.54739i | −0.0668369 | + | 0.115765i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.8370 | −0.874861 | −0.437431 | − | 0.899252i | \(-0.644111\pi\) | ||||
−0.437431 | + | 0.899252i | \(0.644111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.2356 | − | 7.64158i | 0.431010 | − | 0.248844i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.0258 | + | 8.73141i | 0.326140 | + | 0.284033i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.0871459 | − | 0.0503137i | −0.00283186 | − | 0.00163498i | 0.498583 | − | 0.866842i | \(-0.333854\pi\) |
−0.501415 | + | 0.865207i | \(0.667187\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.9846 | + | 47.6772i | −0.356574 | + | 1.54767i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.59470 | − | 4.49416i | 0.0841390 | − | 0.145733i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.4924 | − | 27.4197i | 1.53843 | − | 0.888212i | 0.539497 | − | 0.841987i | \(-0.318614\pi\) |
0.998931 | − | 0.0462245i | \(-0.0147190\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.36430 | + | 1.18816i | 0.0441478 | + | 0.0384479i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.532418i | − | 0.0172106i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.7904 | − | 23.8857i | 0.445315 | − | 0.771308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.81060 | 0.251955 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 13.5190i | − | 0.435645i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.1393 | + | 4.12910i | 0.680499 | + | 0.132920i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.0788i | 1.83553i | 0.397123 | + | 0.917765i | \(0.370009\pi\) | ||||
−0.397123 | + | 0.917765i | \(0.629991\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.01797 | + | 1.76318i | 0.0327019 | + | 0.0566414i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.46735 | − | 4.27357i | −0.0791810 | − | 0.137146i | 0.823716 | − | 0.567003i | \(-0.191897\pi\) |
−0.902897 | + | 0.429857i | \(0.858564\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 55.6324 | + | 32.1194i | 1.78349 | + | 1.02970i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.18564 | − | 0.372000i | −0.134048 | − | 0.0119135i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.99957 | + | 5.19590i | 0.287922 | + | 0.166232i | 0.637004 | − | 0.770860i | \(-0.280173\pi\) |
−0.349083 | + | 0.937092i | \(0.613507\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.56058 | − | 9.63120i | −0.177717 | − | 0.307814i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.217329 | − | 0.376424i | −0.00693877 | − | 0.0120183i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.8531i | 1.46249i | 0.682117 | + | 0.731243i | \(0.261059\pi\) | ||||
−0.682117 | + | 0.731243i | \(0.738941\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.6421 | − | 6.96189i | −1.13565 | − | 0.221824i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 6.60840i | − | 0.210348i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39.5933 | 1.25899 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.0070 | + | 24.2608i | −0.444947 | + | 0.770671i | −0.998049 | − | 0.0624430i | \(-0.980111\pi\) |
0.553101 | + | 0.833114i | \(0.313444\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.62107i | 0.210113i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.97529 | + | 6.07472i | 0.221132 | + | 0.192581i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.4998 | + | 6.06204i | −0.332531 | + | 0.191987i | −0.656964 | − | 0.753922i | \(-0.728160\pi\) |
0.324433 | + | 0.945909i | \(0.394826\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.66228 | + | 8.07530i | −0.147508 | + | 0.255491i |
(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 | 1040.2.dh.c.529.4 | 12 | ||
4.3 | odd | 2 | 260.2.ba.a.9.3 | ✓ | 12 | ||
5.4 | even | 2 | inner | 1040.2.dh.c.529.3 | 12 | ||
12.11 | even | 2 | 2340.2.de.a.2089.5 | 12 | |||
13.3 | even | 3 | inner | 1040.2.dh.c.289.3 | 12 | ||
20.3 | even | 4 | 1300.2.i.i.1101.4 | 12 | |||
20.7 | even | 4 | 1300.2.i.i.1101.3 | 12 | |||
20.19 | odd | 2 | 260.2.ba.a.9.4 | yes | 12 | ||
52.3 | odd | 6 | 260.2.ba.a.29.4 | yes | 12 | ||
52.7 | even | 12 | 3380.2.d.c.1689.7 | 12 | |||
52.19 | even | 12 | 3380.2.d.c.1689.8 | 12 | |||
52.35 | odd | 6 | 3380.2.c.a.2029.4 | 6 | |||
52.43 | odd | 6 | 3380.2.c.b.2029.4 | 6 | |||
60.59 | even | 2 | 2340.2.de.a.2089.6 | 12 | |||
65.29 | even | 6 | inner | 1040.2.dh.c.289.4 | 12 | ||
156.107 | even | 6 | 2340.2.de.a.289.5 | 12 | |||
260.3 | even | 12 | 1300.2.i.i.601.4 | 12 | |||
260.19 | even | 12 | 3380.2.d.c.1689.5 | 12 | |||
260.59 | even | 12 | 3380.2.d.c.1689.6 | 12 | |||
260.107 | even | 12 | 1300.2.i.i.601.3 | 12 | |||
260.139 | odd | 6 | 3380.2.c.a.2029.3 | 6 | |||
260.159 | odd | 6 | 260.2.ba.a.29.3 | yes | 12 | ||
260.199 | odd | 6 | 3380.2.c.b.2029.3 | 6 | |||
780.419 | even | 6 | 2340.2.de.a.289.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.ba.a.9.3 | ✓ | 12 | 4.3 | odd | 2 | ||
260.2.ba.a.9.4 | yes | 12 | 20.19 | odd | 2 | ||
260.2.ba.a.29.3 | yes | 12 | 260.159 | odd | 6 | ||
260.2.ba.a.29.4 | yes | 12 | 52.3 | odd | 6 | ||
1040.2.dh.c.289.3 | 12 | 13.3 | even | 3 | inner | ||
1040.2.dh.c.289.4 | 12 | 65.29 | even | 6 | inner | ||
1040.2.dh.c.529.3 | 12 | 5.4 | even | 2 | inner | ||
1040.2.dh.c.529.4 | 12 | 1.1 | even | 1 | trivial | ||
1300.2.i.i.601.3 | 12 | 260.107 | even | 12 | |||
1300.2.i.i.601.4 | 12 | 260.3 | even | 12 | |||
1300.2.i.i.1101.3 | 12 | 20.7 | even | 4 | |||
1300.2.i.i.1101.4 | 12 | 20.3 | even | 4 | |||
2340.2.de.a.289.5 | 12 | 156.107 | even | 6 | |||
2340.2.de.a.289.6 | 12 | 780.419 | even | 6 | |||
2340.2.de.a.2089.5 | 12 | 12.11 | even | 2 | |||
2340.2.de.a.2089.6 | 12 | 60.59 | even | 2 | |||
3380.2.c.a.2029.3 | 6 | 260.139 | odd | 6 | |||
3380.2.c.a.2029.4 | 6 | 52.35 | odd | 6 | |||
3380.2.c.b.2029.3 | 6 | 260.199 | odd | 6 | |||
3380.2.c.b.2029.4 | 6 | 52.43 | odd | 6 | |||
3380.2.d.c.1689.5 | 12 | 260.19 | even | 12 | |||
3380.2.d.c.1689.6 | 12 | 260.59 | even | 12 | |||
3380.2.d.c.1689.7 | 12 | 52.7 | even | 12 | |||
3380.2.d.c.1689.8 | 12 | 52.19 | even | 12 |