Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(401,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.l (of order \(4\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1201.6 | ||
Root | \(0.618969 + 1.27156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1201 |
Dual form | 1600.2.l.g.401.6 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 2.16859 | − | 2.16859i | 1.25203 | − | 1.25203i | 0.297227 | − | 0.954807i | \(-0.403938\pi\) |
0.954807 | − | 0.297227i | \(-0.0960617\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.30519i | − | 1.24924i | −0.780927 | − | 0.624622i | \(-0.785253\pi\) | ||
0.780927 | − | 0.624622i | \(-0.214747\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 6.40553i | − | 2.13518i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.01163 | − | 2.01163i | −0.606530 | − | 0.606530i | 0.335507 | − | 0.942038i | \(-0.391092\pi\) |
−0.942038 | + | 0.335507i | \(0.891092\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.794042 | + | 0.794042i | −0.220228 | + | 0.220228i | −0.808594 | − | 0.588367i | \(-0.799771\pi\) |
0.588367 | + | 0.808594i | \(0.299771\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.61575 | −1.11948 | −0.559741 | − | 0.828667i | \(-0.689100\pi\) | ||||
−0.559741 | + | 0.828667i | \(0.689100\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.48786 | − | 3.48786i | 0.800169 | − | 0.800169i | −0.182953 | − | 0.983122i | \(-0.558566\pi\) |
0.983122 | + | 0.182953i | \(0.0585655\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.16759 | − | 7.16759i | −1.56410 | − | 1.56410i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.99801i | 1.66770i | 0.551991 | + | 0.833850i | \(0.313868\pi\) | ||||
−0.551991 | + | 0.833850i | \(0.686132\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.38518 | − | 7.38518i | −1.42128 | − | 1.42128i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.95065 | + | 1.95065i | −0.362227 | + | 0.362227i | −0.864632 | − | 0.502406i | \(-0.832448\pi\) |
0.502406 | + | 0.864632i | \(0.332448\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.12695 | 0.920828 | 0.460414 | − | 0.887704i | \(-0.347701\pi\) | ||||
0.460414 | + | 0.887704i | \(0.347701\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.72480 | −1.51879 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.448156 | − | 0.448156i | −0.0736764 | − | 0.0736764i | 0.669308 | − | 0.742985i | \(-0.266591\pi\) |
−0.742985 | + | 0.669308i | \(0.766591\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.44390i | 0.551465i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.02230i | − | 0.628177i | −0.949394 | − | 0.314089i | \(-0.898301\pi\) | ||
0.949394 | − | 0.314089i | \(-0.101699\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.97000 | + | 4.97000i | 0.757918 | + | 0.757918i | 0.975943 | − | 0.218025i | \(-0.0699615\pi\) |
−0.218025 | + | 0.975943i | \(0.569961\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.49112 | −0.800962 | −0.400481 | − | 0.916305i | \(-0.631157\pi\) | ||||
−0.400481 | + | 0.916305i | \(0.631157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.92429 | −0.560612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.0096 | + | 10.0096i | −1.40163 | + | 1.40163i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.35125 | + | 3.35125i | 0.460330 | + | 0.460330i | 0.898763 | − | 0.438434i | \(-0.144467\pi\) |
−0.438434 | + | 0.898763i | \(0.644467\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 15.1274i | − | 2.00368i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.07673 | − | 2.07673i | −0.270367 | − | 0.270367i | 0.558881 | − | 0.829248i | \(-0.311231\pi\) |
−0.829248 | + | 0.558881i | \(0.811231\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.557208 | + | 0.557208i | −0.0713432 | + | 0.0713432i | −0.741878 | − | 0.670535i | \(-0.766065\pi\) |
0.670535 | + | 0.741878i | \(0.266065\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −21.1715 | −2.66736 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.636094 | + | 0.636094i | −0.0777112 | + | 0.0777112i | −0.744894 | − | 0.667183i | \(-0.767500\pi\) |
0.667183 | + | 0.744894i | \(0.267500\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.3444 | + | 17.3444i | 2.08802 | + | 2.08802i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.85258i | − | 0.813252i | −0.913595 | − | 0.406626i | \(-0.866705\pi\) | ||
0.913595 | − | 0.406626i | \(-0.133295\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.5177i | − | 1.23101i | −0.788134 | − | 0.615504i | \(-0.788953\pi\) | ||
0.788134 | − | 0.615504i | \(-0.211047\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.64883 | + | 6.64883i | −0.757705 | + | 0.757705i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.3005 | 1.94646 | 0.973230 | − | 0.229833i | \(-0.0738179\pi\) | ||||
0.973230 | + | 0.229833i | \(0.0738179\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −12.8142 | −1.42380 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.48015 | − | 9.48015i | 1.04058 | − | 1.04058i | 0.0414412 | − | 0.999141i | \(-0.486805\pi\) |
0.999141 | − | 0.0414412i | \(-0.0131949\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.46030i | 0.907040i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.62073i | − | 0.807796i | −0.914804 | − | 0.403898i | \(-0.867655\pi\) | ||
0.914804 | − | 0.403898i | \(-0.132345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.62446 | + | 2.62446i | 0.275118 | + | 0.275118i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.1182 | − | 11.1182i | 1.15291 | − | 1.15291i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.709082 | −0.0719964 | −0.0359982 | − | 0.999352i | \(-0.511461\pi\) | ||||
−0.0359982 | + | 0.999352i | \(0.511461\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.8856 | + | 12.8856i | −1.29505 | + | 1.29505i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.16223 | + | 6.16223i | 0.613164 | + | 0.613164i | 0.943769 | − | 0.330605i | \(-0.107253\pi\) |
−0.330605 | + | 0.943769i | \(0.607253\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.9410i | − | 1.57072i | −0.619040 | − | 0.785359i | \(-0.712478\pi\) | ||
0.619040 | − | 0.785359i | \(-0.287522\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.38717 | − | 3.38717i | −0.327450 | − | 0.327450i | 0.524166 | − | 0.851616i | \(-0.324377\pi\) |
−0.851616 | + | 0.524166i | \(0.824377\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.43964 | + | 2.43964i | −0.233675 | + | 0.233675i | −0.814225 | − | 0.580550i | \(-0.802838\pi\) |
0.580550 | + | 0.814225i | \(0.302838\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.94373 | −0.184491 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.09801 | −0.103292 | −0.0516461 | − | 0.998665i | \(-0.516447\pi\) | ||||
−0.0516461 | + | 0.998665i | \(0.516447\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.08626 | + | 5.08626i | 0.470225 | + | 0.470225i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.2559i | 1.39851i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.90666i | − | 0.264242i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.72270 | − | 8.72270i | −0.786499 | − | 0.786499i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.51159 | −0.134131 | −0.0670657 | − | 0.997749i | \(-0.521364\pi\) | ||||
−0.0670657 | + | 0.997749i | \(0.521364\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21.5557 | 1.89788 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.21660 | − | 9.21660i | 0.805258 | − | 0.805258i | −0.178654 | − | 0.983912i | \(-0.557174\pi\) |
0.983912 | + | 0.178654i | \(0.0571743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.5280 | − | 11.5280i | −0.999607 | − | 0.999607i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.38639i | 0.289318i | 0.989482 | + | 0.144659i | \(0.0462086\pi\) | ||||
−0.989482 | + | 0.144659i | \(0.953791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.09626 | + | 2.09626i | 0.177802 | + | 0.177802i | 0.790397 | − | 0.612595i | \(-0.209874\pi\) |
−0.612595 | + | 0.790397i | \(0.709874\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.9080 | + | 11.9080i | −1.00283 | + | 1.00283i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.19464 | 0.267149 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.51015 | + | 8.51015i | −0.701906 | + | 0.701906i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.45247 | − | 2.45247i | −0.200915 | − | 0.200915i | 0.599477 | − | 0.800392i | \(-0.295375\pi\) |
−0.800392 | + | 0.599477i | \(0.795375\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.11727i | − | 0.0909222i | −0.998966 | − | 0.0454611i | \(-0.985524\pi\) | ||
0.998966 | − | 0.0454611i | \(-0.0144757\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.5663i | 2.39029i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8377 | + | 15.8377i | −1.26398 | + | 1.26398i | −0.314839 | + | 0.949145i | \(0.601950\pi\) |
−0.949145 | + | 0.314839i | \(0.898050\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.5349 | 1.15270 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 26.4349 | 2.08337 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.22102 | + | 7.22102i | −0.565594 | + | 0.565594i | −0.930891 | − | 0.365297i | \(-0.880967\pi\) |
0.365297 | + | 0.930891i | \(0.380967\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 13.2304i | − | 1.02380i | −0.859044 | − | 0.511901i | \(-0.828941\pi\) | ||
0.859044 | − | 0.511901i | \(-0.171059\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7390i | 0.903000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22.3416 | − | 22.3416i | −1.70850 | − | 1.70850i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.7503 | + | 11.7503i | −0.893355 | + | 0.893355i | −0.994837 | − | 0.101482i | \(-0.967641\pi\) |
0.101482 | + | 0.994837i | \(0.467641\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.00712 | −0.677017 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.84732 | + | 4.84732i | −0.362306 | + | 0.362306i | −0.864661 | − | 0.502355i | \(-0.832467\pi\) |
0.502355 | + | 0.864661i | \(0.332467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5742 | + | 10.5742i | 0.785976 | + | 0.785976i | 0.980832 | − | 0.194856i | \(-0.0624240\pi\) |
−0.194856 | + | 0.980832i | \(0.562424\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.41671i | 0.178648i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.28519 | + | 9.28519i | 0.679000 | + | 0.679000i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −24.4094 | + | 24.4094i | −1.77553 | + | 1.77553i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.94268 | −0.574712 | −0.287356 | − | 0.957824i | \(-0.592776\pi\) | ||||
−0.287356 | + | 0.957824i | \(0.592776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.8617 | 1.50166 | 0.750829 | − | 0.660496i | \(-0.229654\pi\) | ||||
0.750829 | + | 0.660496i | \(0.229654\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.07707 | − | 2.07707i | −0.147985 | − | 0.147985i | 0.629232 | − | 0.777217i | \(-0.283369\pi\) |
−0.777217 | + | 0.629232i | \(0.783369\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 23.2807i | − | 1.65033i | −0.564893 | − | 0.825164i | \(-0.691083\pi\) | ||
0.564893 | − | 0.825164i | \(-0.308917\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.75885i | 0.194594i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.44727 | + | 6.44727i | 0.452510 | + | 0.452510i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 51.2315 | 3.56083 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.0326 | −0.970653 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.51586 | − | 2.51586i | 0.173199 | − | 0.173199i | −0.615184 | − | 0.788383i | \(-0.710918\pi\) |
0.788383 | + | 0.615184i | \(0.210918\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.8604 | − | 14.8604i | −1.01822 | − | 1.01822i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.9456i | − | 1.15034i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −22.8086 | − | 22.8086i | −1.54126 | − | 1.54126i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.66510 | − | 3.66510i | 0.246541 | − | 0.246541i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9088 | 0.730507 | 0.365253 | − | 0.930908i | \(-0.380982\pi\) | ||||
0.365253 | + | 0.930908i | \(0.380982\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.6347 | + | 11.6347i | −0.772220 | + | 0.772220i | −0.978494 | − | 0.206275i | \(-0.933866\pi\) |
0.206275 | + | 0.978494i | \(0.433866\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.60760 | − | 1.60760i | −0.106233 | − | 0.106233i | 0.651992 | − | 0.758226i | \(-0.273933\pi\) |
−0.758226 | + | 0.651992i | \(0.773933\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 28.8371i | 1.89734i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.8100i | 1.55985i | 0.625875 | + | 0.779924i | \(0.284742\pi\) | ||||
−0.625875 | + | 0.779924i | \(0.715258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.5177 | − | 37.5177i | 2.43703 | − | 2.43703i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.199630 | 0.0129130 | 0.00645649 | − | 0.999979i | \(-0.497945\pi\) | ||||
0.00645649 | + | 0.999979i | \(0.497945\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.8755 | −1.08705 | −0.543525 | − | 0.839393i | \(-0.682911\pi\) | ||||
−0.543525 | + | 0.839393i | \(0.682911\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.63317 | + | 5.63317i | −0.361368 | + | 0.361368i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.53901i | 0.352439i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 41.1171i | − | 2.60569i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.10023 | + | 6.10023i | 0.385043 | + | 0.385043i | 0.872915 | − | 0.487872i | \(-0.162227\pi\) |
−0.487872 | + | 0.872915i | \(0.662227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0891 | − | 16.0891i | 1.01151 | − | 1.01151i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.8360 | 1.23733 | 0.618667 | − | 0.785653i | \(-0.287673\pi\) | ||||
0.618667 | + | 0.785653i | \(0.287673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.48124 | + | 1.48124i | −0.0920399 | + | 0.0920399i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.4949 | + | 12.4949i | 0.773418 | + | 0.773418i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 7.14438i | − | 0.440542i | −0.975439 | − | 0.220271i | \(-0.929306\pi\) | ||
0.975439 | − | 0.220271i | \(-0.0706941\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.5262 | − | 16.5262i | −1.01139 | − | 1.01139i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.7716 | − | 21.7716i | 1.32744 | − | 1.32744i | 0.419844 | − | 0.907596i | \(-0.362085\pi\) |
0.907596 | − | 0.419844i | \(-0.137915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.71328 | 0.286312 | 0.143156 | − | 0.989700i | \(-0.454275\pi\) | ||||
0.143156 | + | 0.989700i | \(0.454275\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.3827 | 0.688915 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.4588 | − | 20.4588i | −1.22925 | − | 1.22925i | −0.964247 | − | 0.265006i | \(-0.914626\pi\) |
−0.265006 | − | 0.964247i | \(-0.585374\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 32.8409i | − | 1.96613i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.6481i | − | 1.05280i | −0.850239 | − | 0.526398i | \(-0.823542\pi\) | ||
0.850239 | − | 0.526398i | \(-0.176458\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.1525 | + | 18.1525i | 1.07906 | + | 1.07906i | 0.996594 | + | 0.0824607i | \(0.0262779\pi\) |
0.0824607 | + | 0.996594i | \(0.473722\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.2945 | −0.784747 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.30511 | 0.253242 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.53771 | + | 1.53771i | −0.0901419 | + | 0.0901419i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.638480 | + | 0.638480i | 0.0373004 | + | 0.0373004i | 0.725511 | − | 0.688211i | \(-0.241603\pi\) |
−0.688211 | + | 0.725511i | \(0.741603\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 29.7126i | 1.72410i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.35076 | − | 6.35076i | −0.367274 | − | 0.367274i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.4268 | − | 16.4268i | 0.946825 | − | 0.946825i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 26.7266 | 1.53540 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.52224 | − | 4.52224i | 0.258098 | − | 0.258098i | −0.566182 | − | 0.824280i | \(-0.691580\pi\) |
0.824280 | + | 0.566182i | \(0.191580\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.5695 | − | 34.5695i | −1.96659 | − | 1.96659i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 14.1014i | − | 0.799620i | −0.916598 | − | 0.399810i | \(-0.869076\pi\) | ||
0.916598 | − | 0.399810i | \(-0.130924\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9204i | 0.673779i | 0.941544 | + | 0.336889i | \(0.109375\pi\) | ||||
−0.941544 | + | 0.336889i | \(0.890625\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.6516 | + | 17.6516i | −0.991410 | + | 0.991410i | −0.999963 | − | 0.00855359i | \(-0.997277\pi\) |
0.00855359 | + | 0.999963i | \(0.497277\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.84798 | 0.439403 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.6907 | −0.819958 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0991 | + | 16.0991i | −0.895775 | + | 0.895775i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.5811i | 0.585138i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.1492i | 1.00060i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.9785 | + | 24.9785i | 1.37294 | + | 1.37294i | 0.856053 | + | 0.516888i | \(0.172910\pi\) |
0.516888 | + | 0.856053i | \(0.327090\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.87068 | + | 2.87068i | −0.157312 | + | 0.157312i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.3167 | 1.32462 | 0.662308 | − | 0.749231i | \(-0.269577\pi\) | ||||
0.662308 | + | 0.749231i | \(0.269577\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.38113 | + | 2.38113i | −0.129325 | + | 0.129325i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.3136 | − | 10.3136i | −0.558510 | − | 0.558510i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 10.1658i | − | 0.548903i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.3818 | + | 17.3818i | 0.933106 | + | 0.933106i | 0.997899 | − | 0.0647931i | \(-0.0206387\pi\) |
−0.0647931 | + | 0.997899i | \(0.520639\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.773103 | + | 0.773103i | −0.0413832 | + | 0.0413832i | −0.727496 | − | 0.686112i | \(-0.759316\pi\) |
0.686112 | + | 0.727496i | \(0.259316\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.7283 | 0.626010 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.3720 | −0.711720 | −0.355860 | − | 0.934539i | \(-0.615812\pi\) | ||||
−0.355860 | + | 0.934539i | \(0.615812\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 33.0838 | + | 33.0838i | 1.75098 | + | 1.75098i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.5413i | 1.50635i | 0.657818 | + | 0.753177i | \(0.271480\pi\) | ||||
−0.657818 | + | 0.753177i | \(0.728520\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 5.33027i | − | 0.280541i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.30335 | − | 6.30335i | −0.330840 | − | 0.330840i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.909186 | −0.0474591 | −0.0237296 | − | 0.999718i | \(-0.507554\pi\) | ||||
−0.0237296 | + | 0.999718i | \(0.507554\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25.7649 | −1.34127 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.0765 | − | 11.0765i | 0.575064 | − | 0.575064i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.5010 | + | 26.5010i | 1.37217 | + | 1.37217i | 0.857223 | + | 0.514946i | \(0.172188\pi\) |
0.514946 | + | 0.857223i | \(0.327812\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.09780i | − | 0.159545i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.23724 | − | 1.23724i | −0.0635529 | − | 0.0635529i | 0.674616 | − | 0.738169i | \(-0.264309\pi\) |
−0.738169 | + | 0.674616i | \(0.764309\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.27800 | + | 3.27800i | −0.167937 | + | 0.167937i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.7161 | −0.803057 | −0.401529 | − | 0.915846i | \(-0.631521\pi\) | ||||
−0.401529 | + | 0.915846i | \(0.631521\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 31.8355 | − | 31.8355i | 1.61829 | − | 1.61829i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.2799 | + | 16.2799i | 0.825423 | + | 0.825423i | 0.986880 | − | 0.161457i | \(-0.0516193\pi\) |
−0.161457 | + | 0.986880i | \(0.551619\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 36.9168i | − | 1.86696i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 39.9740i | − | 2.01642i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.8944 | + | 22.8944i | −1.14903 | + | 1.14903i | −0.162292 | + | 0.986743i | \(0.551889\pi\) |
−0.986743 | + | 0.162292i | \(0.948111\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −49.9990 | −2.50308 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.8553 | 0.791778 | 0.395889 | − | 0.918298i | \(-0.370437\pi\) | ||||
0.395889 | + | 0.918298i | \(0.370437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.07102 | + | 4.07102i | −0.202792 | + | 0.202792i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.80305i | 0.0893740i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.0220i | − | 0.495557i | −0.968817 | − | 0.247779i | \(-0.920299\pi\) | ||
0.968817 | − | 0.247779i | \(-0.0797006\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.34367 | + | 7.34367i | 0.362236 | + | 0.362236i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.86398 | + | 6.86398i | −0.337754 | + | 0.337754i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.09182 | 0.445228 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.4998 | + | 14.4998i | −0.708362 | + | 0.708362i | −0.966191 | − | 0.257829i | \(-0.916993\pi\) |
0.257829 | + | 0.966191i | \(0.416993\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.9983 | + | 12.9983i | 0.633498 | + | 0.633498i | 0.948944 | − | 0.315446i | \(-0.102154\pi\) |
−0.315446 | + | 0.948944i | \(0.602154\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 35.1735i | 1.71020i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.84168 | + | 1.84168i | 0.0891251 | + | 0.0891251i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.92786 | − | 6.92786i | 0.334480 | − | 0.334480i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.4404 | 1.65894 | 0.829469 | − | 0.558553i | \(-0.188643\pi\) | ||||
0.829469 | + | 0.558553i | \(0.188643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.5895 | 0.701128 | 0.350564 | − | 0.936539i | \(-0.385990\pi\) | ||||
0.350564 | + | 0.936539i | \(0.385990\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.8959 | + | 27.8959i | 1.33444 | + | 1.33444i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 5.70179i | − | 0.272131i | −0.990700 | − | 0.136066i | \(-0.956554\pi\) | ||
0.990700 | − | 0.136066i | \(-0.0434458\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 25.1371i | 1.19701i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.03375 | + | 5.03375i | 0.239161 | + | 0.239161i | 0.816503 | − | 0.577342i | \(-0.195910\pi\) |
−0.577342 | + | 0.816503i | \(0.695910\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.6368 | −0.503104 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.2502 | 1.05005 | 0.525025 | − | 0.851087i | \(-0.324056\pi\) | ||||
0.525025 | + | 0.851087i | \(0.324056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.09139 | + | 8.09139i | −0.381009 | + | 0.381009i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.42290 | − | 2.42290i | −0.113838 | − | 0.113838i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.92927i | 0.417694i | 0.977948 | + | 0.208847i | \(0.0669710\pi\) | ||||
−0.977948 | + | 0.208847i | \(0.933029\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 34.0881 | + | 34.0881i | 1.59110 | + | 1.59110i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.14776 | + | 8.14776i | −0.379479 | + | 0.379479i | −0.870914 | − | 0.491435i | \(-0.836472\pi\) |
0.491435 | + | 0.870914i | \(0.336472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.7058 | −1.47349 | −0.736747 | − | 0.676168i | \(-0.763639\pi\) | ||||
−0.736747 | + | 0.676168i | \(0.763639\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.7683 | + | 17.7683i | −0.822219 | + | 0.822219i | −0.986426 | − | 0.164207i | \(-0.947494\pi\) |
0.164207 | + | 0.986426i | \(0.447494\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.10241 | + | 2.10241i | 0.0970803 | + | 0.0970803i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 68.6907i | 3.16510i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 19.9956i | − | 0.919401i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.4665 | − | 21.4665i | 0.982885 | − | 0.982885i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.80806 | 0.356759 | 0.178380 | − | 0.983962i | \(-0.442914\pi\) | ||||
0.178380 | + | 0.983962i | \(0.442914\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.711710 | 0.0324512 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 57.3264 | − | 57.3264i | 2.60844 | − | 2.60844i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 27.6753i | − | 1.25409i | −0.778984 | − | 0.627044i | \(-0.784265\pi\) | ||
0.778984 | − | 0.627044i | \(-0.215735\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.3188i | 1.41629i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.7995 | + | 11.7995i | 0.532505 | + | 0.532505i | 0.921317 | − | 0.388812i | \(-0.127114\pi\) |
−0.388812 | + | 0.921317i | \(0.627114\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00370 | − | 9.00370i | 0.405506 | − | 0.405506i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.6491 | −1.01595 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.0477 | − | 25.0477i | 1.12129 | − | 1.12129i | 0.129743 | − | 0.991548i | \(-0.458585\pi\) |
0.991548 | − | 0.129743i | \(-0.0414153\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.6914 | − | 28.6914i | −1.28184 | − | 1.28184i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.8644i | 1.01947i | 0.860331 | + | 0.509736i | \(0.170257\pi\) | ||||
−0.860331 | + | 0.509736i | \(0.829743\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.4570 | + | 25.4570i | 1.13059 | + | 1.13059i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.1633 | + | 17.1633i | −0.760748 | + | 0.760748i | −0.976458 | − | 0.215710i | \(-0.930794\pi\) |
0.215710 | + | 0.976458i | \(0.430794\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.7631 | −1.53783 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −51.5169 | −2.27453 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.0461 | + | 11.0461i | 0.485808 | + | 0.485808i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 50.9629i | 2.23702i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.5206i | 0.504726i | 0.967633 | + | 0.252363i | \(0.0812077\pi\) | ||||
−0.967633 | + | 0.252363i | \(0.918792\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.4249 | − | 25.4249i | −1.11175 | − | 1.11175i | −0.992913 | − | 0.118841i | \(-0.962082\pi\) |
−0.118841 | − | 0.992913i | \(-0.537918\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.6647 | −1.03085 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −40.9681 | −1.78122 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.3025 | + | 13.3025i | −0.577281 | + | 0.577281i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.19387 | + | 3.19387i | 0.138342 | + | 0.138342i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.0237i | 0.907239i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.89423 | + | 7.89423i | 0.340028 | + | 0.340028i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.7997 | + | 29.7997i | −1.28119 | + | 1.28119i | −0.341196 | + | 0.939992i | \(0.610832\pi\) |
−0.939992 | + | 0.341196i | \(0.889168\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.8622 | 1.96814 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.3699 | − | 28.3699i | 1.21301 | − | 1.21301i | 0.242979 | − | 0.970032i | \(-0.421875\pi\) |
0.970032 | − | 0.242979i | \(-0.0781246\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.56921 | + | 3.56921i | 0.152330 | + | 0.152330i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.6072i | 0.579685i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 57.1815i | − | 2.43161i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.7769 | − | 21.7769i | 0.922718 | − | 0.922718i | −0.0745028 | − | 0.997221i | \(-0.523737\pi\) |
0.997221 | + | 0.0745028i | \(0.0237370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.89278 | −0.333829 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.2715 | 1.70026 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.9022 | + | 10.9022i | −0.459473 | + | 0.459473i | −0.898482 | − | 0.439010i | \(-0.855329\pi\) |
0.439010 | + | 0.898482i | \(0.355329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 42.3534i | 1.77868i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.1881i | 1.30747i | 0.756723 | + | 0.653736i | \(0.226799\pi\) | ||||
−0.756723 | + | 0.653736i | \(0.773201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.20354 | + | 2.20354i | 0.0922153 | + | 0.0922153i | 0.751710 | − | 0.659494i | \(-0.229230\pi\) |
−0.659494 | + | 0.751710i | \(0.729230\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.2244 | + | 17.2244i | −0.719559 | + | 0.719559i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.42524 | 0.350747 | 0.175374 | − | 0.984502i | \(-0.443887\pi\) | ||||
0.175374 | + | 0.984502i | \(0.443887\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 45.2404 | − | 45.2404i | 1.88013 | − | 1.88013i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.3337 | − | 31.3337i | −1.29994 | − | 1.29994i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 13.4830i | − | 0.558408i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.3370 | + | 19.3370i | 0.798125 | + | 0.798125i | 0.982800 | − | 0.184675i | \(-0.0591231\pi\) |
−0.184675 | + | 0.982800i | \(0.559123\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8821 | − | 17.8821i | 0.736818 | − | 0.736818i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.00862 | −0.370565 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.1804 | 0.746580 | 0.373290 | − | 0.927715i | \(-0.378230\pi\) | ||||
0.373290 | + | 0.927715i | \(0.378230\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −50.4863 | − | 50.4863i | −2.06627 | − | 2.06627i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.64695i | 0.0672927i | 0.999434 | + | 0.0336463i | \(0.0107120\pi\) | ||||
−0.999434 | + | 0.0336463i | \(0.989288\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7485i | 0.520021i | 0.965606 | + | 0.260011i | \(0.0837261\pi\) | ||||
−0.965606 | + | 0.260011i | \(0.916274\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.07452 | + | 4.07452i | 0.165927 | + | 0.165927i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.6773 | −0.636322 | −0.318161 | − | 0.948037i | \(-0.603065\pi\) | ||||
−0.318161 | + | 0.948037i | \(0.603065\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.9629 | 1.13311 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.36018 | − | 4.36018i | 0.176394 | − | 0.176394i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.29399 | + | 8.29399i | 0.334991 | + | 0.334991i | 0.854478 | − | 0.519487i | \(-0.173877\pi\) |
−0.519487 | + | 0.854478i | \(0.673877\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 20.3330i | − | 0.818575i | −0.912406 | − | 0.409287i | \(-0.865777\pi\) | ||
0.912406 | − | 0.409287i | \(-0.134223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.5878 | − | 12.5878i | −0.505946 | − | 0.505946i | 0.407333 | − | 0.913280i | \(-0.366459\pi\) |
−0.913280 | + | 0.407333i | \(0.866459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 59.0667 | − | 59.0667i | 2.37027 | − | 2.37027i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.1880 | −1.00914 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30.4308 | + | 30.4308i | −1.21529 | + | 1.21529i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.06858 | + | 2.06858i | 0.0824795 | + | 0.0824795i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 21.4887i | − | 0.855453i | −0.903908 | − | 0.427726i | \(-0.859315\pi\) | ||
0.903908 | − | 0.427726i | \(-0.140685\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 10.9117i | − | 0.433702i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.11605 | − | 3.11605i | 0.123462 | − | 0.123462i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −43.8944 | −1.73644 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.1687 | 1.03360 | 0.516800 | − | 0.856106i | \(-0.327123\pi\) | ||||
0.516800 | + | 0.856106i | \(0.327123\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.6501 | − | 14.6501i | 0.577743 | − | 0.577743i | −0.356538 | − | 0.934281i | \(-0.616043\pi\) |
0.934281 | + | 0.356538i | \(0.116043\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.2623i | 0.639337i | 0.947530 | + | 0.319668i | \(0.103571\pi\) | ||||
−0.947530 | + | 0.319668i | \(0.896429\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.35522i | 0.327971i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.7479 | − | 36.7479i | −1.44026 | − | 1.44026i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.0639 | + | 32.0639i | −1.25476 | + | 1.25476i | −0.301194 | + | 0.953563i | \(0.597385\pi\) |
−0.953563 | + | 0.301194i | \(0.902615\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −67.3717 | −2.62842 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.04696 | − | 7.04696i | 0.274511 | − | 0.274511i | −0.556402 | − | 0.830913i | \(-0.687819\pi\) |
0.830913 | + | 0.556402i | \(0.187819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.78655 | + | 5.78655i | 0.225071 | + | 0.225071i | 0.810630 | − | 0.585559i | \(-0.199125\pi\) |
−0.585559 | + | 0.810630i | \(0.699125\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 15.8962i | − | 0.617355i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.6013 | − | 15.6013i | −0.604085 | − | 0.604085i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.6567 | − | 23.6567i | 0.914619 | − | 0.914619i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.24180 | 0.0865436 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.3380 | −1.36218 | −0.681090 | − | 0.732200i | \(-0.738494\pi\) | ||||
−0.681090 | + | 0.732200i | \(0.738494\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.72259 | − | 7.72259i | −0.296803 | − | 0.296803i | 0.542957 | − | 0.839760i | \(-0.317305\pi\) |
−0.839760 | + | 0.542957i | \(0.817305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.34365i | 0.0899411i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 50.4615i | 1.93369i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.6011 | − | 15.6011i | −0.596958 | − | 0.596958i | 0.342544 | − | 0.939502i | \(-0.388711\pi\) |
−0.939502 | + | 0.342544i | \(0.888711\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.97246 | −0.266016 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.32207 | −0.202755 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.0975 | + | 30.0975i | −1.14496 | + | 1.14496i | −0.157433 | + | 0.987530i | \(0.550322\pi\) |
−0.987530 | + | 0.157433i | \(0.949678\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 42.5893 | + | 42.5893i | 1.61783 | + | 1.61783i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.5659i | 0.703234i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 51.6341 | + | 51.6341i | 1.95298 | + | 1.95298i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8151 | − | 14.8151i | 0.559559 | − | 0.559559i | −0.369623 | − | 0.929182i | \(-0.620513\pi\) |
0.929182 | + | 0.369623i | \(0.120513\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.12621 | −0.117907 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.3673 | − | 20.3673i | 0.765992 | − | 0.765992i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.26566 | + | 9.26566i | 0.347979 | + | 0.347979i | 0.859356 | − | 0.511377i | \(-0.170864\pi\) |
−0.511377 | + | 0.859356i | \(0.670864\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 110.819i | − | 4.15604i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 41.0054i | 1.53567i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.432914 | − | 0.432914i | 0.0161675 | − | 0.0161675i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.8143 | −1.52212 | −0.761058 | − | 0.648684i | \(-0.775320\pi\) | ||||
−0.761058 | + | 0.648684i | \(0.775320\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.6882 | −1.96221 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36.5961 | + | 36.5961i | −1.36102 | + | 1.36102i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.20944i | 0.193208i | 0.995323 | + | 0.0966038i | \(0.0307980\pi\) | ||||
−0.995323 | + | 0.0966038i | \(0.969202\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 14.0106i | − | 0.518911i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.9403 | − | 22.9403i | −0.848476 | − | 0.848476i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7039 | − | 14.7039i | 0.543099 | − | 0.543099i | −0.381337 | − | 0.924436i | \(-0.624536\pi\) |
0.924436 | + | 0.381337i | \(0.124536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.55917 | 0.0942684 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.68017 | + | 7.68017i | −0.282520 | + | 0.282520i | −0.834113 | − | 0.551594i | \(-0.814020\pi\) |
0.551594 | + | 0.834113i | \(0.314020\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0118 | + | 12.0118i | 0.441265 | + | 0.441265i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.9882i | 1.28359i | 0.766876 | + | 0.641796i | \(0.221810\pi\) | ||||
−0.766876 | + | 0.641796i | \(0.778190\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −60.7254 | − | 60.7254i | −2.22183 | − | 2.22183i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.1953 | + | 11.1953i | −0.409066 | + | 0.409066i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.1447 | 1.20947 | 0.604733 | − | 0.796428i | \(-0.293280\pi\) | ||||
0.604733 | + | 0.796428i | \(0.293280\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.4577 | 0.964174 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.1553 | − | 22.1553i | −0.805248 | − | 0.805248i | 0.178663 | − | 0.983910i | \(-0.442823\pi\) |
−0.983910 | + | 0.178663i | \(0.942823\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 69.7810i | − | 2.53289i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 48.1426i | − | 1.74517i | −0.488466 | − | 0.872583i | \(-0.662443\pi\) | ||
0.488466 | − | 0.872583i | \(-0.337557\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.06347 | + | 8.06347i | 0.291917 | + | 0.291917i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.29802 | 0.119084 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.1054 | −1.48230 | −0.741150 | − | 0.671339i | \(-0.765719\pi\) | ||||
−0.741150 | + | 0.671339i | \(0.765719\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43.0160 | − | 43.0160i | 1.54918 | − | 1.54918i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.8044 | − | 10.8044i | −0.388607 | − | 0.388607i | 0.485583 | − | 0.874190i | \(-0.338607\pi\) |
−0.874190 | + | 0.485583i | \(0.838607\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.42440i | 0.230474i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.0292 | − | 14.0292i | −0.502648 | − | 0.502648i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.7849 | + | 13.7849i | −0.493262 | + | 0.493262i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28.8118 | 1.02965 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.7496 | − | 11.7496i | 0.418826 | − | 0.418826i | −0.465973 | − | 0.884799i | \(-0.654296\pi\) |
0.884799 | + | 0.465973i | \(0.154296\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.4932 | − | 15.4932i | −0.551573 | − | 0.551573i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.62914i | 0.129037i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.884894i | − | 0.0314235i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.9126 | + | 15.9126i | −0.563652 | + | 0.563652i | −0.930343 | − | 0.366691i | \(-0.880491\pi\) |
0.366691 | + | 0.930343i | \(0.380491\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.3456 | 0.896663 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −48.8148 | −1.72479 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.1578 | + | 21.1578i | −0.746643 | + | 0.746643i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 94.4274i | − | 3.32400i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.06814i | 0.318819i | 0.987213 | + | 0.159409i | \(0.0509590\pi\) | ||||
−0.987213 | + | 0.159409i | \(0.949041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.0825 | + | 17.0825i | 0.599849 | + | 0.599849i | 0.940272 | − | 0.340424i | \(-0.110570\pi\) |
−0.340424 | + | 0.940272i | \(0.610570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.2212 | − | 10.2212i | 0.358472 | − | 0.358472i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.6693 | 1.21293 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.8111 | − | 16.8111i | 0.587426 | − | 0.587426i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0531 | + | 18.0531i | 0.630057 | + | 0.630057i | 0.948082 | − | 0.318026i | \(-0.103020\pi\) |
−0.318026 | + | 0.948082i | \(0.603020\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25.3535i | − | 0.883767i | −0.897072 | − | 0.441884i | \(-0.854310\pi\) | ||
0.897072 | − | 0.441884i | \(-0.145690\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.3396 | + | 15.3396i | 0.533410 | + | 0.533410i | 0.921585 | − | 0.388176i | \(-0.126895\pi\) |
−0.388176 | + | 0.921585i | \(0.626895\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.2546 | − | 37.2546i | 1.29391 | − | 1.29391i | 0.361555 | − | 0.932351i | \(-0.382246\pi\) |
0.932351 | − | 0.361555i | \(-0.117754\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −88.7335 | −3.07813 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.1135 | 0.627596 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −37.8635 | − | 37.8635i | −1.30875 | − | 1.30875i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 17.9621i | − | 0.620120i | −0.950717 | − | 0.310060i | \(-0.899651\pi\) | ||
0.950717 | − | 0.310060i | \(-0.100349\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.3899i | 0.737584i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −38.2713 | − | 38.2713i | −1.31813 | − | 1.31813i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.60708 | −0.330103 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 78.7306 | 2.70203 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.58436 | − | 3.58436i | 0.122870 | − | 0.122870i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.29007 | + | 9.29007i | 0.318086 | + | 0.318086i | 0.848032 | − | 0.529946i | \(-0.177788\pi\) |
−0.529946 | + | 0.848032i | \(0.677788\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 10.3997i | − | 0.355246i | −0.984099 | − | 0.177623i | \(-0.943159\pi\) | ||
0.984099 | − | 0.177623i | \(-0.0568407\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.3452 | − | 15.3452i | −0.523571 | − | 0.523571i | 0.395077 | − | 0.918648i | \(-0.370718\pi\) |
−0.918648 | + | 0.395077i | \(0.870718\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.8302 | + | 28.8302i | −0.982530 | + | 0.982530i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.81329 | 0.300008 | 0.150004 | − | 0.988685i | \(-0.452071\pi\) | ||||
0.150004 | + | 0.988685i | \(0.452071\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.33601 | − | 9.33601i | 0.317067 | − | 0.317067i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34.8023 | − | 34.8023i | −1.18059 | − | 1.18059i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.01017i | − | 0.0342283i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.54205i | 0.153725i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.68862 | − | 5.68862i | 0.192091 | − | 0.192091i | −0.604508 | − | 0.796599i | \(-0.706630\pi\) |
0.796599 | + | 0.604508i | \(0.206630\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.76920 | 0.0934028 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.3573 | −0.685856 | −0.342928 | − | 0.939362i | \(-0.611419\pi\) | ||||
−0.342928 | + | 0.939362i | \(0.611419\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.3524 | + | 19.3524i | −0.651262 | + | 0.651262i | −0.953297 | − | 0.302035i | \(-0.902334\pi\) |
0.302035 | + | 0.953297i | \(0.402334\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 12.7863i | − | 0.429323i | −0.976689 | − | 0.214661i | \(-0.931135\pi\) | ||
0.976689 | − | 0.214661i | \(-0.0688648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.99608i | 0.167563i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25.7775 | + | 25.7775i | 0.863579 | + | 0.863579i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.1522 | + | 19.1522i | −0.640905 | + | 0.640905i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.5443 | −0.919678 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.0009 | + | 10.0009i | −0.333548 | + | 0.333548i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.4685 | − | 15.4685i | −0.515331 | − | 0.515331i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 71.2459i | − | 2.37091i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.88449 | − | 2.88449i | −0.0957780 | − | 0.0957780i | 0.657594 | − | 0.753372i | \(-0.271574\pi\) |
−0.753372 | + | 0.657594i | \(0.771574\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 39.4723 | − | 39.4723i | 1.30921 | − | 1.30921i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −59.0271 | −1.95565 | −0.977827 | − | 0.209412i | \(-0.932845\pi\) | ||||
−0.977827 | + | 0.209412i | \(0.932845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.1412 | −1.26229 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.4626 | − | 30.4626i | −1.00596 | − | 1.00596i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0062i | 0.791893i | 0.918274 | + | 0.395946i | \(0.129583\pi\) | ||||
−0.918274 | + | 0.395946i | \(0.870417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 19.6137i | − | 0.646294i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.44124 | + | 5.44124i | 0.179100 | + | 0.179100i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −102.111 | −3.35376 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.1568 | 0.497279 | 0.248639 | − | 0.968596i | \(-0.420017\pi\) | ||||
0.248639 | + | 0.968596i | \(0.420017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.6873 | + | 13.6873i | −0.448585 | + | 0.448585i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.5802 | − | 30.5802i | −1.00115 | − | 1.00115i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 39.9323i | − | 1.30453i | −0.757991 | − | 0.652266i | \(-0.773819\pi\) | ||
0.757991 | − | 0.652266i | \(-0.226181\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.8503 | + | 25.8503i | 0.843594 | + | 0.843594i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.6002 | + | 21.6002i | −0.704145 | + | 0.704145i | −0.965298 | − | 0.261153i | \(-0.915897\pi\) |
0.261153 | + | 0.965298i | \(0.415897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.1704 | 1.04761 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.2944 | + | 16.2944i | −0.529498 | + | 0.529498i | −0.920423 | − | 0.390925i | \(-0.872155\pi\) |
0.390925 | + | 0.920423i | \(0.372155\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.35152 | + | 8.35152i | 0.271102 | + | 0.271102i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 76.5578i | 2.48256i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.0232i | 0.389468i | 0.980856 | + | 0.194734i | \(0.0623844\pi\) | ||||
−0.980856 | + | 0.194734i | \(0.937616\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.0190 | − | 17.0190i | 0.550147 | − | 0.550147i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.1927 | 0.361430 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.71434 | −0.152076 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.6966 | + | 21.6966i | −0.699164 | + | 0.699164i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.8237i | 1.40927i | 0.709568 | + | 0.704637i | \(0.248890\pi\) | ||||
−0.709568 | + | 0.704637i | \(0.751110\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 69.8244i | 2.24308i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.9986 | − | 35.9986i | −1.15525 | − | 1.15525i | −0.985484 | − | 0.169766i | \(-0.945699\pi\) |
−0.169766 | − | 0.985484i | \(-0.554301\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.92852 | − | 6.92852i | 0.222118 | − | 0.222118i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.204913 | −0.00655576 | −0.00327788 | − | 0.999995i | \(-0.501043\pi\) | ||||
−0.00327788 | + | 0.999995i | \(0.501043\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.3301 | + | 15.3301i | −0.489953 | + | 0.489953i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.6272 | + | 15.6272i | 0.498937 | + | 0.498937i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.0060i | 1.08462i | 0.840177 | + | 0.542312i | \(0.182451\pi\) | ||||
−0.840177 | + | 0.542312i | \(0.817549\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 39.3581 | + | 39.3581i | 1.25278 | + | 1.25278i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.7501 | + | 39.7501i | −1.26398 | + | 1.26398i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.8223 | −0.439079 | −0.219539 | − | 0.975604i | \(-0.570455\pi\) | ||||
−0.219539 | + | 0.975604i | \(0.570455\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 108.336 | 3.43794 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.37875 | + | 6.37875i | 0.202017 | + | 0.202017i | 0.800864 | − | 0.598847i | \(-0.204374\pi\) |
−0.598847 | + | 0.800864i | \(0.704374\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.61943i | 0.209429i |
(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 | 1600.2.l.g.1201.6 | 12 | ||
4.3 | odd | 2 | 400.2.l.f.101.4 | ✓ | 12 | ||
5.2 | odd | 4 | 1600.2.q.e.49.1 | 12 | |||
5.3 | odd | 4 | 1600.2.q.f.49.6 | 12 | |||
5.4 | even | 2 | 1600.2.l.f.1201.1 | 12 | |||
16.3 | odd | 4 | 400.2.l.f.301.4 | yes | 12 | ||
16.13 | even | 4 | inner | 1600.2.l.g.401.6 | 12 | ||
20.3 | even | 4 | 400.2.q.f.149.1 | 12 | |||
20.7 | even | 4 | 400.2.q.e.149.6 | 12 | |||
20.19 | odd | 2 | 400.2.l.g.101.3 | yes | 12 | ||
80.3 | even | 4 | 400.2.q.e.349.6 | 12 | |||
80.13 | odd | 4 | 1600.2.q.e.849.1 | 12 | |||
80.19 | odd | 4 | 400.2.l.g.301.3 | yes | 12 | ||
80.29 | even | 4 | 1600.2.l.f.401.1 | 12 | |||
80.67 | even | 4 | 400.2.q.f.349.1 | 12 | |||
80.77 | odd | 4 | 1600.2.q.f.849.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.4 | ✓ | 12 | 4.3 | odd | 2 | ||
400.2.l.f.301.4 | yes | 12 | 16.3 | odd | 4 | ||
400.2.l.g.101.3 | yes | 12 | 20.19 | odd | 2 | ||
400.2.l.g.301.3 | yes | 12 | 80.19 | odd | 4 | ||
400.2.q.e.149.6 | 12 | 20.7 | even | 4 | |||
400.2.q.e.349.6 | 12 | 80.3 | even | 4 | |||
400.2.q.f.149.1 | 12 | 20.3 | even | 4 | |||
400.2.q.f.349.1 | 12 | 80.67 | even | 4 | |||
1600.2.l.f.401.1 | 12 | 80.29 | even | 4 | |||
1600.2.l.f.1201.1 | 12 | 5.4 | even | 2 | |||
1600.2.l.g.401.6 | 12 | 16.13 | even | 4 | inner | ||
1600.2.l.g.1201.6 | 12 | 1.1 | even | 1 | trivial | ||
1600.2.q.e.49.1 | 12 | 5.2 | odd | 4 | |||
1600.2.q.e.849.1 | 12 | 80.13 | odd | 4 | |||
1600.2.q.f.49.6 | 12 | 5.3 | odd | 4 | |||
1600.2.q.f.849.6 | 12 | 80.77 | odd | 4 |