Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(151,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.c (of order \(2\), degree \(1\), 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: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 42x^{12} + 677x^{10} + 5313x^{8} + 21125x^{6} + 40138x^{4} + 30565x^{2} + 3675 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.4 | ||
Root | \(-2.34822i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.151 |
Dual form | 475.3.c.h.151.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.34822i | − | 1.17411i | −0.809547 | − | 0.587055i | \(-0.800287\pi\) | ||
0.809547 | − | 0.587055i | \(-0.199713\pi\) | |||||||
\(3\) | − | 5.73703i | − | 1.91234i | −0.292809 | − | 0.956171i | \(-0.594590\pi\) | ||
0.292809 | − | 0.956171i | \(-0.405410\pi\) | |||||||
\(4\) | −1.51415 | −0.378537 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −13.4718 | −2.24530 | ||||||||
\(7\) | −9.56678 | −1.36668 | −0.683342 | − | 0.730099i | \(-0.739474\pi\) | ||||
−0.683342 | + | 0.730099i | \(0.739474\pi\) | |||||||
\(8\) | − | 5.83734i | − | 0.729667i | ||||||
\(9\) | −23.9135 | −2.65705 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.15630 | 0.377846 | 0.188923 | − | 0.981992i | \(-0.439500\pi\) | ||||
0.188923 | + | 0.981992i | \(0.439500\pi\) | |||||||
\(12\) | 8.68670i | 0.723891i | ||||||||
\(13\) | − | 4.55775i | − | 0.350596i | −0.984515 | − | 0.175298i | \(-0.943911\pi\) | ||
0.984515 | − | 0.175298i | \(-0.0560889\pi\) | |||||||
\(14\) | 22.4649i | 1.60464i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.7639 | −1.23525 | ||||||||
\(17\) | 27.9397 | 1.64351 | 0.821757 | − | 0.569838i | \(-0.192994\pi\) | ||||
0.821757 | + | 0.569838i | \(0.192994\pi\) | |||||||
\(18\) | 56.1541i | 3.11967i | ||||||||
\(19\) | 7.04287 | − | 17.6465i | 0.370677 | − | 0.928762i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 54.8849i | 2.61357i | ||||||||
\(22\) | − | 9.75992i | − | 0.443633i | ||||||
\(23\) | 13.9626 | 0.607069 | 0.303534 | − | 0.952820i | \(-0.401833\pi\) | ||||
0.303534 | + | 0.952820i | \(0.401833\pi\) | |||||||
\(24\) | −33.4890 | −1.39537 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −10.7026 | −0.411639 | ||||||||
\(27\) | 85.5590i | 3.16885i | ||||||||
\(28\) | 14.4855 | 0.517340 | ||||||||
\(29\) | − | 14.6141i | − | 0.503934i | −0.967736 | − | 0.251967i | \(-0.918923\pi\) | ||
0.967736 | − | 0.251967i | \(-0.0810775\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28.9385i | 0.933499i | 0.884389 | + | 0.466750i | \(0.154575\pi\) | ||||
−0.884389 | + | 0.466750i | \(0.845425\pi\) | |||||||
\(32\) | 23.0608i | 0.720650i | ||||||||
\(33\) | − | 23.8448i | − | 0.722570i | ||||||
\(34\) | − | 65.6087i | − | 1.92967i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.2085 | 1.00579 | ||||||||
\(37\) | − | 30.8172i | − | 0.832896i | −0.909160 | − | 0.416448i | \(-0.863275\pi\) | ||
0.909160 | − | 0.416448i | \(-0.136725\pi\) | |||||||
\(38\) | −41.4378 | − | 16.5382i | −1.09047 | − | 0.435216i | ||||
\(39\) | −26.1479 | −0.670460 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 44.2953i | 1.08037i | 0.841545 | + | 0.540187i | \(0.181646\pi\) | ||||
−0.841545 | + | 0.540187i | \(0.818354\pi\) | |||||||
\(42\) | 128.882 | 3.06862 | ||||||||
\(43\) | −69.2593 | −1.61068 | −0.805340 | − | 0.592813i | \(-0.798017\pi\) | ||||
−0.805340 | + | 0.592813i | \(0.798017\pi\) | |||||||
\(44\) | −6.29325 | −0.143028 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 32.7872i | − | 0.712766i | ||||||
\(47\) | −30.1880 | −0.642299 | −0.321149 | − | 0.947029i | \(-0.604069\pi\) | ||||
−0.321149 | + | 0.947029i | \(0.604069\pi\) | |||||||
\(48\) | 113.386i | 2.36221i | ||||||||
\(49\) | 42.5233 | 0.867823 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 160.291i | − | 3.14296i | ||||||
\(52\) | 6.90110i | 0.132714i | ||||||||
\(53\) | − | 54.3939i | − | 1.02630i | −0.858299 | − | 0.513150i | \(-0.828478\pi\) | ||
0.858299 | − | 0.513150i | \(-0.171522\pi\) | |||||||
\(54\) | 200.912 | 3.72058 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 55.8445i | 0.997224i | ||||||||
\(57\) | −101.238 | − | 40.4051i | −1.77611 | − | 0.708862i | ||||
\(58\) | −34.3171 | −0.591675 | ||||||||
\(59\) | 31.3331i | 0.531069i | 0.964101 | + | 0.265534i | \(0.0855484\pi\) | ||||
−0.964101 | + | 0.265534i | \(0.914452\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 99.9646 | 1.63876 | 0.819382 | − | 0.573248i | \(-0.194317\pi\) | ||||
0.819382 | + | 0.573248i | \(0.194317\pi\) | |||||||
\(62\) | 67.9540 | 1.09603 | ||||||||
\(63\) | 228.775 | 3.63135 | ||||||||
\(64\) | −24.9039 | −0.389124 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −55.9929 | −0.848378 | ||||||||
\(67\) | 3.05833i | 0.0456468i | 0.999740 | + | 0.0228234i | \(0.00726554\pi\) | ||||
−0.999740 | + | 0.0228234i | \(0.992734\pi\) | |||||||
\(68\) | −42.3049 | −0.622130 | ||||||||
\(69\) | − | 80.1037i | − | 1.16092i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 23.0099i | − | 0.324084i | −0.986784 | − | 0.162042i | \(-0.948192\pi\) | ||
0.986784 | − | 0.162042i | \(-0.0518079\pi\) | |||||||
\(72\) | 139.591i | 1.93876i | ||||||||
\(73\) | −21.1499 | −0.289724 | −0.144862 | − | 0.989452i | \(-0.546274\pi\) | ||||
−0.144862 | + | 0.989452i | \(0.546274\pi\) | |||||||
\(74\) | −72.3655 | −0.977912 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.6639 | + | 26.7193i | −0.140315 | + | 0.351570i | ||||
\(77\) | −39.7625 | −0.516395 | ||||||||
\(78\) | 61.4012i | 0.787195i | ||||||||
\(79\) | 77.7042i | 0.983597i | 0.870709 | + | 0.491799i | \(0.163660\pi\) | ||||
−0.870709 | + | 0.491799i | \(0.836340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 275.633 | 3.40288 | ||||||||
\(82\) | 104.015 | 1.26848 | ||||||||
\(83\) | −93.1651 | −1.12247 | −0.561236 | − | 0.827656i | \(-0.689674\pi\) | ||||
−0.561236 | + | 0.827656i | \(0.689674\pi\) | |||||||
\(84\) | − | 83.1038i | − | 0.989330i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 162.636i | 1.89112i | ||||||||
\(87\) | −83.8415 | −0.963695 | ||||||||
\(88\) | − | 24.2617i | − | 0.275702i | ||||||
\(89\) | − | 126.623i | − | 1.42273i | −0.702821 | − | 0.711366i | \(-0.748077\pi\) | ||
0.702821 | − | 0.711366i | \(-0.251923\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 43.6030i | 0.479154i | ||||||||
\(92\) | −21.1414 | −0.229798 | ||||||||
\(93\) | 166.021 | 1.78517 | ||||||||
\(94\) | 70.8882i | 0.754130i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 132.300 | 1.37813 | ||||||||
\(97\) | − | 77.2807i | − | 0.796708i | −0.917232 | − | 0.398354i | \(-0.869582\pi\) | ||
0.917232 | − | 0.398354i | \(-0.130418\pi\) | |||||||
\(98\) | − | 99.8542i | − | 1.01892i | ||||||
\(99\) | −99.3917 | −1.00396 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −145.782 | −1.44339 | −0.721693 | − | 0.692213i | \(-0.756636\pi\) | ||||
−0.721693 | + | 0.692213i | \(0.756636\pi\) | |||||||
\(102\) | −376.399 | −3.69019 | ||||||||
\(103\) | 7.27524i | 0.0706334i | 0.999376 | + | 0.0353167i | \(0.0112440\pi\) | ||||
−0.999376 | + | 0.0353167i | \(0.988756\pi\) | |||||||
\(104\) | −26.6051 | −0.255819 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −127.729 | −1.20499 | ||||||||
\(107\) | 128.949i | 1.20513i | 0.798068 | + | 0.602567i | \(0.205855\pi\) | ||||
−0.798068 | + | 0.602567i | \(0.794145\pi\) | |||||||
\(108\) | − | 129.549i | − | 1.19953i | ||||||
\(109\) | − | 74.4133i | − | 0.682691i | −0.939938 | − | 0.341346i | \(-0.889117\pi\) | ||
0.939938 | − | 0.341346i | \(-0.110883\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −176.799 | −1.59278 | ||||||||
\(112\) | 189.077 | 1.68819 | ||||||||
\(113\) | − | 174.597i | − | 1.54511i | −0.634949 | − | 0.772554i | \(-0.718979\pi\) | ||
0.634949 | − | 0.772554i | \(-0.281021\pi\) | |||||||
\(114\) | −94.8802 | + | 237.730i | −0.832283 | + | 2.08535i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 22.1279i | 0.190758i | ||||||||
\(117\) | 108.992i | 0.931553i | ||||||||
\(118\) | 73.5770 | 0.623534 | ||||||||
\(119\) | −267.293 | −2.24616 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −103.725 | −0.857233 | ||||||||
\(122\) | − | 234.739i | − | 1.92409i | ||||||
\(123\) | 254.123 | 2.06604 | ||||||||
\(124\) | − | 43.8171i | − | 0.353364i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 537.215i | − | 4.26361i | ||||||
\(127\) | − | 81.1228i | − | 0.638762i | −0.947626 | − | 0.319381i | \(-0.896525\pi\) | ||
0.947626 | − | 0.319381i | \(-0.103475\pi\) | |||||||
\(128\) | 150.723i | 1.17752i | ||||||||
\(129\) | 397.342i | 3.08017i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −51.8609 | −0.395885 | −0.197942 | − | 0.980214i | \(-0.563426\pi\) | ||||
−0.197942 | + | 0.980214i | \(0.563426\pi\) | |||||||
\(132\) | 36.1046i | 0.273519i | ||||||||
\(133\) | −67.3776 | + | 168.820i | −0.506599 | + | 1.26932i | ||||
\(134\) | 7.18165 | 0.0535944 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 163.094i | − | 1.19922i | ||||||
\(137\) | −11.6713 | −0.0851920 | −0.0425960 | − | 0.999092i | \(-0.513563\pi\) | ||||
−0.0425960 | + | 0.999092i | \(0.513563\pi\) | |||||||
\(138\) | −188.101 | −1.36305 | ||||||||
\(139\) | 115.309 | 0.829564 | 0.414782 | − | 0.909921i | \(-0.363858\pi\) | ||||
0.414782 | + | 0.909921i | \(0.363858\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 173.190i | 1.22830i | ||||||||
\(142\) | −54.0324 | −0.380510 | ||||||||
\(143\) | − | 18.9434i | − | 0.132471i | ||||||
\(144\) | 472.625 | 3.28212 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 49.6645i | 0.340168i | ||||||||
\(147\) | − | 243.958i | − | 1.65957i | ||||||
\(148\) | 46.6617i | 0.315282i | ||||||||
\(149\) | 149.512 | 1.00343 | 0.501717 | − | 0.865032i | \(-0.332702\pi\) | ||||
0.501717 | + | 0.865032i | \(0.332702\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 262.436i | − | 1.73799i | −0.494823 | − | 0.868994i | \(-0.664767\pi\) | ||
0.494823 | − | 0.868994i | \(-0.335233\pi\) | |||||||
\(152\) | −103.008 | − | 41.1116i | −0.677687 | − | 0.270471i | ||||
\(153\) | −668.136 | −4.36690 | ||||||||
\(154\) | 93.3711i | 0.606306i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 39.5918 | 0.253794 | ||||||||
\(157\) | 106.277 | 0.676926 | 0.338463 | − | 0.940980i | \(-0.390093\pi\) | ||||
0.338463 | + | 0.940980i | \(0.390093\pi\) | |||||||
\(158\) | 182.467 | 1.15485 | ||||||||
\(159\) | −312.059 | −1.96264 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −133.577 | −0.829671 | ||||||||
\(162\) | − | 647.247i | − | 3.99535i | ||||||
\(163\) | −173.109 | −1.06202 | −0.531009 | − | 0.847366i | \(-0.678187\pi\) | ||||
−0.531009 | + | 0.847366i | \(0.678187\pi\) | |||||||
\(164\) | − | 67.0696i | − | 0.408961i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 218.772i | 1.31791i | ||||||||
\(167\) | − | 30.8456i | − | 0.184704i | −0.995726 | − | 0.0923522i | \(-0.970561\pi\) | ||
0.995726 | − | 0.0923522i | \(-0.0294386\pi\) | |||||||
\(168\) | 320.382 | 1.90703 | ||||||||
\(169\) | 148.227 | 0.877082 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −168.419 | + | 421.988i | −0.984909 | + | 2.46777i | ||||
\(172\) | 104.869 | 0.609702 | ||||||||
\(173\) | − | 14.7393i | − | 0.0851981i | −0.999092 | − | 0.0425990i | \(-0.986436\pi\) | ||
0.999092 | − | 0.0425990i | \(-0.0135638\pi\) | |||||||
\(174\) | 196.878i | 1.13148i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −82.1450 | −0.466733 | ||||||||
\(177\) | 179.759 | 1.01559 | ||||||||
\(178\) | −297.339 | −1.67045 | ||||||||
\(179\) | 166.782i | 0.931745i | 0.884852 | + | 0.465873i | \(0.154259\pi\) | ||||
−0.884852 | + | 0.465873i | \(0.845741\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 200.231i | 1.10625i | 0.833099 | + | 0.553124i | \(0.186564\pi\) | ||||
−0.833099 | + | 0.553124i | \(0.813436\pi\) | |||||||
\(182\) | 102.390 | 0.562580 | ||||||||
\(183\) | − | 573.499i | − | 3.13388i | ||||||
\(184\) | − | 81.5043i | − | 0.442958i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 389.854i | − | 2.09599i | ||||||
\(187\) | 116.126 | 0.620995 | ||||||||
\(188\) | 45.7091 | 0.243134 | ||||||||
\(189\) | − | 818.524i | − | 4.33082i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 264.646 | 1.38558 | 0.692792 | − | 0.721138i | \(-0.256381\pi\) | ||||
0.692792 | + | 0.721138i | \(0.256381\pi\) | |||||||
\(192\) | 142.875i | 0.744138i | ||||||||
\(193\) | 170.535i | 0.883600i | 0.897113 | + | 0.441800i | \(0.145660\pi\) | ||||
−0.897113 | + | 0.441800i | \(0.854340\pi\) | |||||||
\(194\) | −181.472 | −0.935423 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −64.3866 | −0.328503 | ||||||||
\(197\) | 193.450 | 0.981979 | 0.490989 | − | 0.871166i | \(-0.336635\pi\) | ||||
0.490989 | + | 0.871166i | \(0.336635\pi\) | |||||||
\(198\) | 233.394i | 1.17876i | ||||||||
\(199\) | 247.455 | 1.24349 | 0.621747 | − | 0.783218i | \(-0.286423\pi\) | ||||
0.621747 | + | 0.783218i | \(0.286423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.5457 | 0.0872923 | ||||||||
\(202\) | 342.329i | 1.69470i | ||||||||
\(203\) | 139.810i | 0.688719i | ||||||||
\(204\) | 242.704i | 1.18973i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.0839 | 0.0829315 | ||||||||
\(207\) | −333.894 | −1.61301 | ||||||||
\(208\) | 90.0792i | 0.433073i | ||||||||
\(209\) | 29.2723 | − | 73.3441i | 0.140059 | − | 0.350929i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 103.882i | 0.492331i | 0.969228 | + | 0.246166i | \(0.0791707\pi\) | ||||
−0.969228 | + | 0.246166i | \(0.920829\pi\) | |||||||
\(212\) | 82.3604i | 0.388492i | ||||||||
\(213\) | −132.009 | −0.619759 | ||||||||
\(214\) | 302.802 | 1.41496 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 499.437 | 2.31221 | ||||||||
\(217\) | − | 276.848i | − | 1.27580i | ||||||
\(218\) | −174.739 | −0.801555 | ||||||||
\(219\) | 121.337i | 0.554051i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 127.342i | − | 0.576210i | ||||||
\(222\) | 415.163i | 1.87010i | ||||||||
\(223\) | − | 68.3811i | − | 0.306642i | −0.988176 | − | 0.153321i | \(-0.951003\pi\) | ||
0.988176 | − | 0.153321i | \(-0.0489968\pi\) | |||||||
\(224\) | − | 220.618i | − | 0.984900i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −409.993 | −1.81413 | ||||||||
\(227\) | − | 199.560i | − | 0.879121i | −0.898213 | − | 0.439560i | \(-0.855134\pi\) | ||
0.898213 | − | 0.439560i | \(-0.144866\pi\) | |||||||
\(228\) | 153.290 | + | 61.1793i | 0.672323 | + | 0.268330i | ||||
\(229\) | −75.3592 | −0.329079 | −0.164540 | − | 0.986370i | \(-0.552614\pi\) | ||||
−0.164540 | + | 0.986370i | \(0.552614\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 228.118i | 0.987525i | ||||||||
\(232\) | −85.3074 | −0.367704 | ||||||||
\(233\) | −10.3384 | −0.0443709 | −0.0221854 | − | 0.999754i | \(-0.507062\pi\) | ||||
−0.0221854 | + | 0.999754i | \(0.507062\pi\) | |||||||
\(234\) | 255.937 | 1.09375 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 47.4428i | − | 0.201029i | ||||||
\(237\) | 445.791 | 1.88097 | ||||||||
\(238\) | 627.664i | 2.63724i | ||||||||
\(239\) | −360.813 | −1.50968 | −0.754840 | − | 0.655909i | \(-0.772285\pi\) | ||||
−0.754840 | + | 0.655909i | \(0.772285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 446.555i | − | 1.85293i | −0.376384 | − | 0.926464i | \(-0.622833\pi\) | ||
0.376384 | − | 0.926464i | \(-0.377167\pi\) | |||||||
\(242\) | 243.570i | 1.00649i | ||||||||
\(243\) | − | 811.283i | − | 3.33861i | ||||||
\(244\) | −151.361 | −0.620332 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 596.738i | − | 2.42577i | ||||||
\(247\) | −80.4282 | − | 32.0997i | −0.325620 | − | 0.129958i | ||||
\(248\) | 168.924 | 0.681144 | ||||||||
\(249\) | 534.491i | 2.14655i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −295.147 | −1.17588 | −0.587942 | − | 0.808903i | \(-0.700062\pi\) | ||||
−0.587942 | + | 0.808903i | \(0.700062\pi\) | |||||||
\(252\) | −346.399 | −1.37460 | ||||||||
\(253\) | 58.0327 | 0.229378 | ||||||||
\(254\) | −190.494 | −0.749978 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 254.316 | 0.993420 | ||||||||
\(257\) | − | 96.9364i | − | 0.377185i | −0.982055 | − | 0.188592i | \(-0.939608\pi\) | ||
0.982055 | − | 0.188592i | \(-0.0603925\pi\) | |||||||
\(258\) | 933.048 | 3.61646 | ||||||||
\(259\) | 294.821i | 1.13831i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 349.474i | 1.33898i | ||||||||
\(262\) | 121.781i | 0.464812i | ||||||||
\(263\) | −288.418 | −1.09665 | −0.548323 | − | 0.836267i | \(-0.684733\pi\) | ||||
−0.548323 | + | 0.836267i | \(0.684733\pi\) | |||||||
\(264\) | −139.190 | −0.527236 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 396.427 | + | 158.218i | 1.49033 | + | 0.594803i | ||||
\(267\) | −726.441 | −2.72075 | ||||||||
\(268\) | − | 4.63077i | − | 0.0172790i | ||||||
\(269\) | − | 174.475i | − | 0.648607i | −0.945953 | − | 0.324304i | \(-0.894870\pi\) | ||
0.945953 | − | 0.324304i | \(-0.105130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 127.454 | 0.470311 | 0.235155 | − | 0.971958i | \(-0.424440\pi\) | ||||
0.235155 | + | 0.971958i | \(0.424440\pi\) | |||||||
\(272\) | −552.199 | −2.03015 | ||||||||
\(273\) | 250.152 | 0.916307 | ||||||||
\(274\) | 27.4068i | 0.100025i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 121.289i | 0.439452i | ||||||||
\(277\) | 424.528 | 1.53259 | 0.766295 | − | 0.642488i | \(-0.222098\pi\) | ||||
0.766295 | + | 0.642488i | \(0.222098\pi\) | |||||||
\(278\) | − | 270.772i | − | 0.974001i | ||||||
\(279\) | − | 692.020i | − | 2.48036i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 166.293i | − | 0.591791i | −0.955220 | − | 0.295895i | \(-0.904382\pi\) | ||
0.955220 | − | 0.295895i | \(-0.0956180\pi\) | |||||||
\(282\) | 406.688 | 1.44215 | ||||||||
\(283\) | −221.482 | −0.782621 | −0.391310 | − | 0.920259i | \(-0.627978\pi\) | ||||
−0.391310 | + | 0.920259i | \(0.627978\pi\) | |||||||
\(284\) | 34.8404i | 0.122677i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −44.4833 | −0.155536 | ||||||||
\(287\) | − | 423.764i | − | 1.47653i | ||||||
\(288\) | − | 551.464i | − | 1.91480i | ||||||
\(289\) | 491.629 | 1.70114 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −443.361 | −1.52358 | ||||||||
\(292\) | 32.0240 | 0.109671 | ||||||||
\(293\) | 38.0208i | 0.129764i | 0.997893 | + | 0.0648819i | \(0.0206671\pi\) | ||||
−0.997893 | + | 0.0648819i | \(0.979333\pi\) | |||||||
\(294\) | −572.866 | −1.94853 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −179.890 | −0.607737 | ||||||||
\(297\) | 355.609i | 1.19734i | ||||||||
\(298\) | − | 351.087i | − | 1.17814i | ||||||
\(299\) | − | 63.6380i | − | 0.212836i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 662.588 | 2.20129 | ||||||||
\(302\) | −616.258 | −2.04059 | ||||||||
\(303\) | 836.355i | 2.76025i | ||||||||
\(304\) | −139.195 | + | 348.764i | −0.457878 | + | 1.14725i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1568.93i | 5.12723i | ||||||||
\(307\) | 285.495i | 0.929950i | 0.885324 | + | 0.464975i | \(0.153937\pi\) | ||||
−0.885324 | + | 0.464975i | \(0.846063\pi\) | |||||||
\(308\) | 60.2062 | 0.195475 | ||||||||
\(309\) | 41.7382 | 0.135075 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.55195 | −0.0146365 | −0.00731825 | − | 0.999973i | \(-0.502329\pi\) | ||||
−0.00731825 | + | 0.999973i | \(0.502329\pi\) | |||||||
\(312\) | 152.634i | 0.489213i | ||||||||
\(313\) | 298.019 | 0.952136 | 0.476068 | − | 0.879408i | \(-0.342062\pi\) | ||||
0.476068 | + | 0.879408i | \(0.342062\pi\) | |||||||
\(314\) | − | 249.563i | − | 0.794786i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 117.655i | − | 0.372327i | ||||||
\(317\) | 179.077i | 0.564910i | 0.959280 | + | 0.282455i | \(0.0911489\pi\) | ||||
−0.959280 | + | 0.282455i | \(0.908851\pi\) | |||||||
\(318\) | 732.785i | 2.30435i | ||||||||
\(319\) | − | 60.7406i | − | 0.190409i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 739.786 | 2.30463 | ||||||||
\(322\) | 313.668i | 0.974126i | ||||||||
\(323\) | 196.776 | − | 493.038i | 0.609213 | − | 1.52643i | ||||
\(324\) | −417.349 | −1.28811 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 406.499i | 1.24693i | ||||||||
\(327\) | −426.911 | −1.30554 | ||||||||
\(328\) | 258.567 | 0.788313 | ||||||||
\(329\) | 288.802 | 0.877819 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 330.043i | − | 0.997109i | −0.866858 | − | 0.498554i | \(-0.833864\pi\) | ||
0.866858 | − | 0.498554i | \(-0.166136\pi\) | |||||||
\(332\) | 141.066 | 0.424896 | ||||||||
\(333\) | 736.945i | 2.21305i | ||||||||
\(334\) | −72.4324 | −0.216863 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 1084.74i | − | 3.22840i | ||||||
\(337\) | − | 7.17182i | − | 0.0212814i | −0.999943 | − | 0.0106407i | \(-0.996613\pi\) | ||
0.999943 | − | 0.0106407i | \(-0.00338710\pi\) | |||||||
\(338\) | − | 348.070i | − | 1.02979i | ||||||
\(339\) | −1001.67 | −2.95477 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 120.277i | 0.352719i | ||||||||
\(342\) | 990.923 | + | 395.486i | 2.89743 | + | 1.15639i | ||||
\(343\) | 61.9608 | 0.180644 | ||||||||
\(344\) | 404.290i | 1.17526i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −34.6111 | −0.100032 | ||||||||
\(347\) | 38.9167 | 0.112152 | 0.0560759 | − | 0.998427i | \(-0.482141\pi\) | ||||
0.0560759 | + | 0.998427i | \(0.482141\pi\) | |||||||
\(348\) | 126.948 | 0.364794 | ||||||||
\(349\) | 342.266 | 0.980704 | 0.490352 | − | 0.871525i | \(-0.336868\pi\) | ||||
0.490352 | + | 0.871525i | \(0.336868\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 389.957 | 1.11099 | ||||||||
\(352\) | 95.8476i | 0.272294i | ||||||||
\(353\) | 17.5325 | 0.0496671 | 0.0248335 | − | 0.999692i | \(-0.492094\pi\) | ||||
0.0248335 | + | 0.999692i | \(0.492094\pi\) | |||||||
\(354\) | − | 422.113i | − | 1.19241i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 191.726i | 0.538556i | ||||||||
\(357\) | 1533.47i | 4.29543i | ||||||||
\(358\) | 391.642 | 1.09397 | ||||||||
\(359\) | 452.975 | 1.26177 | 0.630885 | − | 0.775876i | \(-0.282692\pi\) | ||||
0.630885 | + | 0.775876i | \(0.282692\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −261.796 | − | 248.564i | −0.725197 | − | 0.688542i | ||||
\(362\) | 470.186 | 1.29886 | ||||||||
\(363\) | 595.074i | 1.63932i | ||||||||
\(364\) | − | 66.0214i | − | 0.181377i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1346.70 | −3.67952 | ||||||||
\(367\) | 290.156 | 0.790615 | 0.395308 | − | 0.918549i | \(-0.370638\pi\) | ||||
0.395308 | + | 0.918549i | \(0.370638\pi\) | |||||||
\(368\) | −275.956 | −0.749880 | ||||||||
\(369\) | − | 1059.26i | − | 2.87061i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 520.375i | 1.40263i | ||||||||
\(372\) | −251.380 | −0.675752 | ||||||||
\(373\) | 555.723i | 1.48987i | 0.667136 | + | 0.744936i | \(0.267520\pi\) | ||||
−0.667136 | + | 0.744936i | \(0.732480\pi\) | |||||||
\(374\) | − | 272.690i | − | 0.729117i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 176.218i | 0.468664i | ||||||||
\(377\) | −66.6074 | −0.176678 | ||||||||
\(378\) | −1922.08 | −5.08486 | ||||||||
\(379\) | − | 4.05619i | − | 0.0107023i | −0.999986 | − | 0.00535117i | \(-0.998297\pi\) | ||
0.999986 | − | 0.00535117i | \(-0.00170334\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −465.404 | −1.22153 | ||||||||
\(382\) | − | 621.449i | − | 1.62683i | ||||||
\(383\) | − | 392.529i | − | 1.02488i | −0.858723 | − | 0.512439i | \(-0.828742\pi\) | ||
0.858723 | − | 0.512439i | \(-0.171258\pi\) | |||||||
\(384\) | 864.703 | 2.25183 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 400.454 | 1.03744 | ||||||||
\(387\) | 1656.23 | 4.27966 | ||||||||
\(388\) | 117.014i | 0.301583i | ||||||||
\(389\) | 0.819385 | 0.00210639 | 0.00105319 | − | 0.999999i | \(-0.499665\pi\) | ||||
0.00105319 | + | 0.999999i | \(0.499665\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 390.111 | 0.997726 | ||||||||
\(392\) | − | 248.223i | − | 0.633222i | ||||||
\(393\) | 297.527i | 0.757067i | ||||||||
\(394\) | − | 454.263i | − | 1.15295i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 150.494 | 0.380034 | ||||||||
\(397\) | −132.366 | −0.333414 | −0.166707 | − | 0.986006i | \(-0.553313\pi\) | ||||
−0.166707 | + | 0.986006i | \(0.553313\pi\) | |||||||
\(398\) | − | 581.080i | − | 1.46000i | ||||||
\(399\) | 968.525 | + | 386.547i | 2.42738 | + | 0.968790i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 50.7026i | 0.126440i | 0.998000 | + | 0.0632202i | \(0.0201370\pi\) | ||||
−0.998000 | + | 0.0632202i | \(0.979863\pi\) | |||||||
\(402\) | − | 41.2013i | − | 0.102491i | ||||||
\(403\) | 131.894 | 0.327281 | ||||||||
\(404\) | 220.735 | 0.546375 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 328.305 | 0.808632 | ||||||||
\(407\) | − | 128.085i | − | 0.314706i | ||||||
\(408\) | −935.673 | −2.29332 | ||||||||
\(409\) | − | 67.8086i | − | 0.165791i | −0.996558 | − | 0.0828956i | \(-0.973583\pi\) | ||
0.996558 | − | 0.0828956i | \(-0.0264168\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 66.9586i | 0.162916i | ||||||||
\(412\) | − | 11.0158i | − | 0.0267373i | ||||||
\(413\) | − | 299.757i | − | 0.725803i | ||||||
\(414\) | 784.057i | 1.89386i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 105.105 | 0.252657 | ||||||||
\(417\) | − | 661.533i | − | 1.58641i | ||||||
\(418\) | −172.228 | − | 68.7379i | −0.412029 | − | 0.164445i | ||||
\(419\) | −222.546 | −0.531135 | −0.265568 | − | 0.964092i | \(-0.585559\pi\) | ||||
−0.265568 | + | 0.964092i | \(0.585559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 205.736i | − | 0.488684i | −0.969689 | − | 0.244342i | \(-0.921428\pi\) | ||
0.969689 | − | 0.244342i | \(-0.0785719\pi\) | |||||||
\(422\) | 243.938 | 0.578051 | ||||||||
\(423\) | 721.901 | 1.70662 | ||||||||
\(424\) | −317.516 | −0.748858 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 309.985i | 0.727665i | ||||||||
\(427\) | −956.339 | −2.23967 | ||||||||
\(428\) | − | 195.248i | − | 0.456187i | ||||||
\(429\) | −108.679 | −0.253331 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 479.116i | − | 1.11164i | −0.831303 | − | 0.555819i | \(-0.812405\pi\) | ||
0.831303 | − | 0.555819i | \(-0.187595\pi\) | |||||||
\(432\) | − | 1690.98i | − | 3.91431i | ||||||
\(433\) | − | 566.880i | − | 1.30919i | −0.755979 | − | 0.654596i | \(-0.772839\pi\) | ||
0.755979 | − | 0.654596i | \(-0.227161\pi\) | |||||||
\(434\) | −650.101 | −1.49793 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 112.673i | 0.258424i | ||||||||
\(437\) | 98.3367 | − | 246.390i | 0.225027 | − | 0.563822i | ||||
\(438\) | 284.927 | 0.650518 | ||||||||
\(439\) | − | 684.577i | − | 1.55940i | −0.626152 | − | 0.779701i | \(-0.715371\pi\) | ||
0.626152 | − | 0.779701i | \(-0.284629\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1016.88 | −2.30585 | ||||||||
\(442\) | −299.028 | −0.676534 | ||||||||
\(443\) | −473.575 | −1.06902 | −0.534509 | − | 0.845163i | \(-0.679504\pi\) | ||||
−0.534509 | + | 0.845163i | \(0.679504\pi\) | |||||||
\(444\) | 267.699 | 0.602926 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −160.574 | −0.360031 | ||||||||
\(447\) | − | 857.752i | − | 1.91891i | ||||||
\(448\) | 238.251 | 0.531809 | ||||||||
\(449\) | − | 315.053i | − | 0.701677i | −0.936436 | − | 0.350839i | \(-0.885897\pi\) | ||
0.936436 | − | 0.350839i | \(-0.114103\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 184.105i | 0.408215i | ||||||||
\(452\) | 264.366i | 0.584880i | ||||||||
\(453\) | −1505.60 | −3.32363 | ||||||||
\(454\) | −468.612 | −1.03219 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −235.858 | + | 590.962i | −0.517233 | + | 1.29597i | ||||
\(457\) | −259.302 | −0.567401 | −0.283700 | − | 0.958913i | \(-0.591562\pi\) | ||||
−0.283700 | + | 0.958913i | \(0.591562\pi\) | |||||||
\(458\) | 176.960i | 0.386376i | ||||||||
\(459\) | 2390.50i | 5.20805i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 681.783 | 1.47892 | 0.739461 | − | 0.673200i | \(-0.235081\pi\) | ||||
0.739461 | + | 0.673200i | \(0.235081\pi\) | |||||||
\(462\) | 535.672 | 1.15946 | ||||||||
\(463\) | 640.879 | 1.38419 | 0.692094 | − | 0.721808i | \(-0.256689\pi\) | ||||
0.692094 | + | 0.721808i | \(0.256689\pi\) | |||||||
\(464\) | 288.832i | 0.622483i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.2769i | 0.0520963i | ||||||||
\(467\) | 142.309 | 0.304730 | 0.152365 | − | 0.988324i | \(-0.451311\pi\) | ||||
0.152365 | + | 0.988324i | \(0.451311\pi\) | |||||||
\(468\) | − | 165.029i | − | 0.352627i | ||||||
\(469\) | − | 29.2584i | − | 0.0623847i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 609.716i | − | 1.29451i | ||||||
\(472\) | 182.902 | 0.387503 | ||||||||
\(473\) | −287.863 | −0.608589 | ||||||||
\(474\) | − | 1046.82i | − | 2.20847i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 404.721 | 0.850255 | ||||||||
\(477\) | 1300.75i | 2.72693i | ||||||||
\(478\) | 847.270i | 1.77253i | ||||||||
\(479\) | 303.821 | 0.634283 | 0.317141 | − | 0.948378i | \(-0.397277\pi\) | ||||
0.317141 | + | 0.948378i | \(0.397277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −140.457 | −0.292010 | ||||||||
\(482\) | −1048.61 | −2.17554 | ||||||||
\(483\) | 766.335i | 1.58661i | ||||||||
\(484\) | 157.055 | 0.324494 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1905.07 | −3.91990 | ||||||||
\(487\) | − | 0.541296i | − | 0.00111149i | −1.00000 | 0.000555746i | \(-0.999823\pi\) | |||
1.00000 | 0.000555746i | \(-0.000176899\pi\) | ||||||||
\(488\) | − | 583.527i | − | 1.19575i | ||||||
\(489\) | 993.131i | 2.03094i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 463.173 | 0.943326 | 0.471663 | − | 0.881779i | \(-0.343654\pi\) | ||||
0.471663 | + | 0.881779i | \(0.343654\pi\) | |||||||
\(492\) | −384.780 | −0.782073 | ||||||||
\(493\) | − | 408.314i | − | 0.828223i | ||||||
\(494\) | −75.3771 | + | 188.863i | −0.152585 | + | 0.382315i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 571.939i | − | 1.15310i | ||||||
\(497\) | 220.131i | 0.442920i | ||||||||
\(498\) | 1255.10 | 2.52029 | ||||||||
\(499\) | 174.865 | 0.350431 | 0.175215 | − | 0.984530i | \(-0.443938\pi\) | ||||
0.175215 | + | 0.984530i | \(0.443938\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −176.962 | −0.353218 | ||||||||
\(502\) | 693.070i | 1.38062i | ||||||||
\(503\) | −503.015 | −1.00003 | −0.500015 | − | 0.866017i | \(-0.666672\pi\) | ||||
−0.500015 | + | 0.866017i | \(0.666672\pi\) | |||||||
\(504\) | − | 1335.44i | − | 2.64968i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 136.274i | − | 0.269316i | ||||||
\(507\) | − | 850.382i | − | 1.67728i | ||||||
\(508\) | 122.832i | 0.241795i | ||||||||
\(509\) | 358.496i | 0.704315i | 0.935941 | + | 0.352157i | \(0.114552\pi\) | ||||
−0.935941 | + | 0.352157i | \(0.885448\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 202.336 | 0.395961 | ||||||||
\(512\) | 5.70303i | 0.0111387i | ||||||||
\(513\) | 1509.81 | + | 602.581i | 2.94311 | + | 1.17462i | ||||
\(514\) | −227.628 | −0.442857 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 601.634i | − | 1.16596i | ||||||
\(517\) | −125.471 | −0.242690 | ||||||||
\(518\) | 692.305 | 1.33650 | ||||||||
\(519\) | −84.5596 | −0.162928 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 882.596i | 1.69404i | 0.531559 | + | 0.847022i | \(0.321607\pi\) | ||||
−0.531559 | + | 0.847022i | \(0.678393\pi\) | |||||||
\(522\) | 820.642 | 1.57211 | ||||||||
\(523\) | − | 2.57808i | − | 0.00492941i | −0.999997 | − | 0.00246471i | \(-0.999215\pi\) | ||
0.999997 | − | 0.00246471i | \(-0.000784541\pi\) | |||||||
\(524\) | 78.5250 | 0.149857 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 677.269i | 1.28758i | ||||||||
\(527\) | 808.534i | 1.53422i | ||||||||
\(528\) | 471.268i | 0.892553i | ||||||||
\(529\) | −334.046 | −0.631467 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 749.282i | − | 1.41108i | ||||||
\(532\) | 102.020 | − | 255.618i | 0.191766 | − | 0.480485i | ||||
\(533\) | 201.887 | 0.378775 | ||||||||
\(534\) | 1705.84i | 3.19446i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 17.8525 | 0.0333070 | ||||||||
\(537\) | 956.835 | 1.78182 | ||||||||
\(538\) | −409.707 | −0.761537 | ||||||||
\(539\) | 176.740 | 0.327903 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 382.112 | 0.706307 | 0.353154 | − | 0.935565i | \(-0.385109\pi\) | ||||
0.353154 | + | 0.935565i | \(0.385109\pi\) | |||||||
\(542\) | − | 299.291i | − | 0.552197i | ||||||
\(543\) | 1148.73 | 2.11552 | ||||||||
\(544\) | 644.312i | 1.18440i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 587.412i | − | 1.07585i | ||||||
\(547\) | − | 93.8141i | − | 0.171506i | −0.996316 | − | 0.0857532i | \(-0.972670\pi\) | ||
0.996316 | − | 0.0857532i | \(-0.0273297\pi\) | |||||||
\(548\) | 17.6721 | 0.0322483 | ||||||||
\(549\) | −2390.50 | −4.35428 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −257.887 | − | 102.925i | −0.468035 | − | 0.186797i | ||||
\(552\) | −467.592 | −0.847088 | ||||||||
\(553\) | − | 743.379i | − | 1.34427i | ||||||
\(554\) | − | 996.885i | − | 1.79943i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −174.595 | −0.314020 | ||||||||
\(557\) | −799.561 | −1.43548 | −0.717739 | − | 0.696313i | \(-0.754823\pi\) | ||||
−0.717739 | + | 0.696313i | \(0.754823\pi\) | |||||||
\(558\) | −1625.02 | −2.91221 | ||||||||
\(559\) | 315.667i | 0.564699i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 666.218i | − | 1.18755i | ||||||
\(562\) | −390.493 | −0.694828 | ||||||||
\(563\) | − | 676.517i | − | 1.20163i | −0.799389 | − | 0.600814i | \(-0.794843\pi\) | ||
0.799389 | − | 0.600814i | \(-0.205157\pi\) | |||||||
\(564\) | − | 262.234i | − | 0.464955i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 520.088i | 0.918884i | ||||||||
\(567\) | −2636.92 | −4.65065 | ||||||||
\(568\) | −134.317 | −0.236473 | ||||||||
\(569\) | − | 710.658i | − | 1.24896i | −0.781041 | − | 0.624480i | \(-0.785311\pi\) | ||
0.781041 | − | 0.624480i | \(-0.214689\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −812.896 | −1.42363 | −0.711817 | − | 0.702364i | \(-0.752128\pi\) | ||||
−0.711817 | + | 0.702364i | \(0.752128\pi\) | |||||||
\(572\) | 28.6831i | 0.0501452i | ||||||||
\(573\) | − | 1518.28i | − | 2.64971i | ||||||
\(574\) | −995.091 | −1.73361 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 595.540 | 1.03392 | ||||||||
\(577\) | −812.174 | −1.40758 | −0.703790 | − | 0.710408i | \(-0.748510\pi\) | ||||
−0.703790 | + | 0.710408i | \(0.748510\pi\) | |||||||
\(578\) | − | 1154.45i | − | 1.99733i | ||||||
\(579\) | 978.363 | 1.68975 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 891.291 | 1.53406 | ||||||||
\(582\) | 1041.11i | 1.78885i | ||||||||
\(583\) | − | 226.078i | − | 0.387783i | ||||||
\(584\) | 123.459i | 0.211402i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 89.2812 | 0.152357 | ||||||||
\(587\) | 332.138 | 0.565823 | 0.282912 | − | 0.959146i | \(-0.408700\pi\) | ||||
0.282912 | + | 0.959146i | \(0.408700\pi\) | |||||||
\(588\) | 369.387i | 0.628210i | ||||||||
\(589\) | 510.662 | + | 203.810i | 0.866998 | + | 0.346027i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 1109.83i | − | 1.87788i | ||||||
\(592\) | 609.069i | 1.02883i | ||||||||
\(593\) | −381.895 | −0.644005 | −0.322003 | − | 0.946739i | \(-0.604356\pi\) | ||||
−0.322003 | + | 0.946739i | \(0.604356\pi\) | |||||||
\(594\) | 835.049 | 1.40581 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −226.383 | −0.379837 | ||||||||
\(597\) | − | 1419.66i | − | 2.37798i | ||||||
\(598\) | −149.436 | −0.249893 | ||||||||
\(599\) | − | 391.286i | − | 0.653232i | −0.945157 | − | 0.326616i | \(-0.894092\pi\) | ||
0.945157 | − | 0.326616i | \(-0.105908\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 708.847i | − | 1.17945i | −0.807606 | − | 0.589723i | \(-0.799237\pi\) | ||
0.807606 | − | 0.589723i | \(-0.200763\pi\) | |||||||
\(602\) | − | 1555.90i | − | 2.58456i | ||||||
\(603\) | − | 73.1354i | − | 0.121286i | ||||||
\(604\) | 397.367i | 0.657892i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1963.95 | 3.24084 | ||||||||
\(607\) | − | 256.683i | − | 0.422872i | −0.977392 | − | 0.211436i | \(-0.932186\pi\) | ||
0.977392 | − | 0.211436i | \(-0.0678140\pi\) | |||||||
\(608\) | 406.942 | + | 162.414i | 0.669312 | + | 0.267129i | ||||
\(609\) | 802.093 | 1.31707 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 137.590i | 0.225188i | ||||||||
\(612\) | 1011.66 | 1.65303 | ||||||||
\(613\) | 730.296 | 1.19135 | 0.595674 | − | 0.803226i | \(-0.296885\pi\) | ||||
0.595674 | + | 0.803226i | \(0.296885\pi\) | |||||||
\(614\) | 670.405 | 1.09186 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 232.107i | 0.376797i | ||||||||
\(617\) | −91.8108 | −0.148802 | −0.0744009 | − | 0.997228i | \(-0.523704\pi\) | ||||
−0.0744009 | + | 0.997228i | \(0.523704\pi\) | |||||||
\(618\) | − | 98.0107i | − | 0.158593i | ||||||
\(619\) | 28.4153 | 0.0459052 | 0.0229526 | − | 0.999737i | \(-0.492693\pi\) | ||||
0.0229526 | + | 0.999737i | \(0.492693\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1194.62i | 1.92371i | ||||||||
\(622\) | 10.6890i | 0.0171849i | ||||||||
\(623\) | 1211.38i | 1.94442i | ||||||||
\(624\) | 516.787 | 0.828184 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 699.814i | − | 1.11791i | ||||||
\(627\) | −420.777 | − | 167.936i | −0.671096 | − | 0.267840i | ||||
\(628\) | −160.919 | −0.256241 | ||||||||
\(629\) | − | 861.023i | − | 1.36888i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 430.427 | 0.682134 | 0.341067 | − | 0.940039i | \(-0.389212\pi\) | ||||
0.341067 | + | 0.940039i | \(0.389212\pi\) | |||||||
\(632\) | 453.585 | 0.717698 | ||||||||
\(633\) | 595.973 | 0.941506 | ||||||||
\(634\) | 420.512 | 0.663268 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 472.504 | 0.742930 | ||||||||
\(637\) | − | 193.811i | − | 0.304256i | ||||||
\(638\) | −142.632 | −0.223562 | ||||||||
\(639\) | 550.247i | 0.861107i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 340.928i | 0.531868i | 0.963991 | + | 0.265934i | \(0.0856804\pi\) | ||||
−0.963991 | + | 0.265934i | \(0.914320\pi\) | |||||||
\(642\) | − | 1737.18i | − | 2.70589i | ||||||
\(643\) | −245.635 | −0.382014 | −0.191007 | − | 0.981589i | \(-0.561175\pi\) | ||||
−0.191007 | + | 0.981589i | \(0.561175\pi\) | |||||||
\(644\) | 202.255 | 0.314061 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1157.76 | − | 462.074i | −1.79220 | − | 0.715284i | ||||
\(647\) | 728.400 | 1.12581 | 0.562906 | − | 0.826521i | \(-0.309683\pi\) | ||||
0.562906 | + | 0.826521i | \(0.309683\pi\) | |||||||
\(648\) | − | 1608.96i | − | 2.48297i | ||||||
\(649\) | 130.230i | 0.200662i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1588.29 | −2.43976 | ||||||||
\(652\) | 262.112 | 0.402013 | ||||||||
\(653\) | −394.958 | −0.604836 | −0.302418 | − | 0.953175i | \(-0.597794\pi\) | ||||
−0.302418 | + | 0.953175i | \(0.597794\pi\) | |||||||
\(654\) | 1002.48i | 1.53285i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 875.450i | − | 1.33453i | ||||||
\(657\) | 505.766 | 0.769812 | ||||||||
\(658\) | − | 678.172i | − | 1.03066i | ||||||
\(659\) | − | 115.919i | − | 0.175901i | −0.996125 | − | 0.0879504i | \(-0.971968\pi\) | ||
0.996125 | − | 0.0879504i | \(-0.0280317\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1088.21i | 1.64631i | 0.567818 | + | 0.823154i | \(0.307788\pi\) | ||||
−0.567818 | + | 0.823154i | \(0.692212\pi\) | |||||||
\(662\) | −775.014 | −1.17072 | ||||||||
\(663\) | −730.567 | −1.10191 | ||||||||
\(664\) | 543.836i | 0.819030i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1730.51 | 2.59836 | ||||||||
\(667\) | − | 204.051i | − | 0.305923i | ||||||
\(668\) | 46.7048i | 0.0699174i | ||||||||
\(669\) | −392.304 | −0.586404 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 415.483 | 0.619200 | ||||||||
\(672\) | −1265.69 | −1.88347 | ||||||||
\(673\) | 1183.83i | 1.75903i | 0.475868 | + | 0.879517i | \(0.342134\pi\) | ||||
−0.475868 | + | 0.879517i | \(0.657866\pi\) | |||||||
\(674\) | −16.8410 | −0.0249867 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −224.437 | −0.332008 | ||||||||
\(677\) | − | 833.194i | − | 1.23071i | −0.788248 | − | 0.615357i | \(-0.789012\pi\) | ||
0.788248 | − | 0.615357i | \(-0.210988\pi\) | |||||||
\(678\) | 2352.14i | 3.46923i | ||||||||
\(679\) | 739.327i | 1.08885i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1144.88 | −1.68118 | ||||||||
\(682\) | 282.437 | 0.414131 | ||||||||
\(683\) | 979.686i | 1.43439i | 0.696874 | + | 0.717193i | \(0.254573\pi\) | ||||
−0.696874 | + | 0.717193i | \(0.745427\pi\) | |||||||
\(684\) | 255.012 | − | 638.952i | 0.372824 | − | 0.934141i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 145.498i | − | 0.212096i | ||||||
\(687\) | 432.338i | 0.629312i | ||||||||
\(688\) | 1368.84 | 1.98959 | ||||||||
\(689\) | −247.914 | −0.359817 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 268.944 | 0.389211 | 0.194605 | − | 0.980882i | \(-0.437657\pi\) | ||||
0.194605 | + | 0.980882i | \(0.437657\pi\) | |||||||
\(692\) | 22.3174i | 0.0322506i | ||||||||
\(693\) | 950.858 | 1.37209 | ||||||||
\(694\) | − | 91.3850i | − | 0.131679i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 489.411i | 0.703176i | ||||||||
\(697\) | 1237.60i | 1.77561i | ||||||||
\(698\) | − | 803.715i | − | 1.15145i | ||||||
\(699\) | 59.3118i | 0.0848523i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 555.168 | 0.791966 | 0.395983 | − | 0.918258i | \(-0.370404\pi\) | ||||
0.395983 | + | 0.918258i | \(0.370404\pi\) | |||||||
\(702\) | − | 915.705i | − | 1.30442i | ||||||
\(703\) | −543.814 | − | 217.041i | −0.773562 | − | 0.308736i | ||||
\(704\) | −103.508 | −0.147029 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 41.1702i | − | 0.0583147i | ||||||
\(707\) | 1394.66 | 1.97265 | ||||||||
\(708\) | −272.181 | −0.384436 | ||||||||
\(709\) | −409.398 | −0.577430 | −0.288715 | − | 0.957415i | \(-0.593228\pi\) | ||||
−0.288715 | + | 0.957415i | \(0.593228\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1858.18i | − | 2.61347i | ||||||
\(712\) | −739.142 | −1.03812 | ||||||||
\(713\) | 404.056i | 0.566698i | ||||||||
\(714\) | 3600.93 | 5.04331 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 252.533i | − | 0.352700i | ||||||
\(717\) | 2070.00i | 2.88702i | ||||||||
\(718\) | − | 1063.69i | − | 1.48146i | ||||||
\(719\) | 530.021 | 0.737164 | 0.368582 | − | 0.929595i | \(-0.379843\pi\) | ||||
0.368582 | + | 0.929595i | \(0.379843\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 69.6006i | − | 0.0965335i | ||||||
\(722\) | −583.683 | + | 614.755i | −0.808425 | + | 0.851461i | ||||
\(723\) | −2561.90 | −3.54343 | ||||||||
\(724\) | − | 303.179i | − | 0.418755i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1397.37 | 1.92475 | ||||||||
\(727\) | −60.1205 | −0.0826967 | −0.0413483 | − | 0.999145i | \(-0.513165\pi\) | ||||
−0.0413483 | + | 0.999145i | \(0.513165\pi\) | |||||||
\(728\) | 254.526 | 0.349623 | ||||||||
\(729\) | −2173.65 | −2.98169 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1935.09 | −2.64718 | ||||||||
\(732\) | 868.362i | 1.18629i | ||||||||
\(733\) | 625.418 | 0.853231 | 0.426616 | − | 0.904433i | \(-0.359706\pi\) | ||||
0.426616 | + | 0.904433i | \(0.359706\pi\) | |||||||
\(734\) | − | 681.350i | − | 0.928270i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 321.988i | 0.437484i | ||||||||
\(737\) | 12.7114i | 0.0172474i | ||||||||
\(738\) | −2487.37 | −3.37042 | ||||||||
\(739\) | −110.100 | −0.148985 | −0.0744923 | − | 0.997222i | \(-0.523734\pi\) | ||||
−0.0744923 | + | 0.997222i | \(0.523734\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −184.157 | + | 461.419i | −0.248524 | + | 0.622698i | ||||
\(742\) | 1221.96 | 1.64684 | ||||||||
\(743\) | 194.296i | 0.261503i | 0.991415 | + | 0.130751i | \(0.0417389\pi\) | ||||
−0.991415 | + | 0.130751i | \(0.958261\pi\) | |||||||
\(744\) | − | 969.119i | − | 1.30258i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1304.96 | 1.74928 | ||||||||
\(747\) | 2227.90 | 2.98247 | ||||||||
\(748\) | −175.832 | −0.235069 | ||||||||
\(749\) | − | 1233.63i | − | 1.64704i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 62.7172i | 0.0835115i | 0.999128 | + | 0.0417558i | \(0.0132951\pi\) | ||||
−0.999128 | + | 0.0417558i | \(0.986705\pi\) | |||||||
\(752\) | 596.635 | 0.793397 | ||||||||
\(753\) | 1693.27i | 2.24869i | ||||||||
\(754\) | 156.409i | 0.207439i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1239.37i | 1.63937i | ||||||||
\(757\) | 580.530 | 0.766882 | 0.383441 | − | 0.923565i | \(-0.374739\pi\) | ||||
0.383441 | + | 0.923565i | \(0.374739\pi\) | |||||||
\(758\) | −9.52483 | −0.0125657 | ||||||||
\(759\) | − | 332.935i | − | 0.438650i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 599.456 | 0.787721 | 0.393861 | − | 0.919170i | \(-0.371139\pi\) | ||||
0.393861 | + | 0.919170i | \(0.371139\pi\) | |||||||
\(762\) | 1092.87i | 1.43421i | ||||||||
\(763\) | 711.896i | 0.933023i | ||||||||
\(764\) | −400.713 | −0.524494 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −921.744 | −1.20332 | ||||||||
\(767\) | 142.808 | 0.186191 | ||||||||
\(768\) | − | 1459.02i | − | 1.89976i | ||||||
\(769\) | −227.963 | −0.296441 | −0.148220 | − | 0.988954i | \(-0.547354\pi\) | ||||
−0.148220 | + | 0.988954i | \(0.547354\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −556.127 | −0.721306 | ||||||||
\(772\) | − | 258.215i | − | 0.334475i | ||||||
\(773\) | 984.904i | 1.27413i | 0.770809 | + | 0.637066i | \(0.219852\pi\) | ||||
−0.770809 | + | 0.637066i | \(0.780148\pi\) | |||||||
\(774\) | − | 3889.19i | − | 5.02480i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −451.113 | −0.581331 | ||||||||
\(777\) | 1691.40 | 2.17683 | ||||||||
\(778\) | − | 1.92410i | − | 0.00247313i | ||||||
\(779\) | 781.656 | + | 311.966i | 1.00341 | + | 0.400470i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 95.6363i | − | 0.122454i | ||||||
\(782\) | − | 916.067i | − | 1.17144i | ||||||
\(783\) | 1250.37 | 1.59689 | ||||||||
\(784\) | −840.429 | −1.07198 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 698.660 | 0.888880 | ||||||||
\(787\) | − | 567.593i | − | 0.721211i | −0.932718 | − | 0.360605i | \(-0.882570\pi\) | ||
0.932718 | − | 0.360605i | \(-0.117430\pi\) | |||||||
\(788\) | −292.911 | −0.371715 | ||||||||
\(789\) | 1654.66i | 2.09716i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1670.33i | 2.11167i | ||||||||
\(792\) | 580.183i | 0.732554i | ||||||||
\(793\) | − | 455.614i | − | 0.574544i | ||||||
\(794\) | 310.824i | 0.391466i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −374.683 | −0.470708 | ||||||||
\(797\) | 1174.98i | 1.47425i | 0.675757 | + | 0.737124i | \(0.263817\pi\) | ||||
−0.675757 | + | 0.737124i | \(0.736183\pi\) | |||||||
\(798\) | 907.698 | − | 2274.31i | 1.13747 | − | 2.85001i | ||||
\(799\) | −843.446 | −1.05563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3028.00i | 3.78028i | ||||||||
\(802\) | 119.061 | 0.148455 | ||||||||
\(803\) | −87.9052 | −0.109471 | ||||||||
\(804\) | −26.5668 | −0.0330433 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 309.717i | − | 0.384265i | ||||||
\(807\) | −1000.97 | −1.24036 | ||||||||
\(808\) | 850.979i | 1.05319i | ||||||||
\(809\) | −944.954 | −1.16805 | −0.584026 | − | 0.811735i | \(-0.698523\pi\) | ||||
−0.584026 | + | 0.811735i | \(0.698523\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 502.942i | − | 0.620151i | −0.950712 | − | 0.310075i | \(-0.899646\pi\) | ||
0.950712 | − | 0.310075i | \(-0.100354\pi\) | |||||||
\(812\) | − | 211.693i | − | 0.260705i | ||||||
\(813\) | − | 731.208i | − | 0.899395i | ||||||
\(814\) | −300.773 | −0.369500 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3167.98i | 3.88233i | ||||||||
\(817\) | −487.784 | + | 1222.18i | −0.597043 | + | 1.49594i | ||||
\(818\) | −159.230 | −0.194657 | ||||||||
\(819\) | − | 1042.70i | − | 1.27314i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1622.74 | −1.97654 | −0.988268 | − | 0.152732i | \(-0.951193\pi\) | ||||
−0.988268 | + | 0.152732i | \(0.951193\pi\) | |||||||
\(822\) | 157.234 | 0.191282 | ||||||||
\(823\) | 525.320 | 0.638299 | 0.319150 | − | 0.947704i | \(-0.396603\pi\) | ||||
0.319150 | + | 0.947704i | \(0.396603\pi\) | |||||||
\(824\) | 42.4680 | 0.0515389 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −703.895 | −0.852173 | ||||||||
\(827\) | 1529.88i | 1.84991i | 0.380075 | + | 0.924956i | \(0.375898\pi\) | ||||
−0.380075 | + | 0.924956i | \(0.624102\pi\) | |||||||
\(828\) | 505.564 | 0.610585 | ||||||||
\(829\) | 940.737i | 1.13479i | 0.823447 | + | 0.567393i | \(0.192048\pi\) | ||||
−0.823447 | + | 0.567393i | \(0.807952\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 2435.53i | − | 2.93084i | ||||||
\(832\) | 113.506i | 0.136425i | ||||||||
\(833\) | 1188.09 | 1.42628 | ||||||||
\(834\) | −1553.43 | −1.86262 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −44.3226 | + | 111.054i | −0.0530174 | + | 0.132839i | ||||
\(837\) | −2475.95 | −2.95812 | ||||||||
\(838\) | 522.586i | 0.623611i | ||||||||
\(839\) | 584.666i | 0.696861i | 0.937335 | + | 0.348430i | \(0.113285\pi\) | ||||
−0.937335 | + | 0.348430i | \(0.886715\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 627.428 | 0.746050 | ||||||||
\(842\) | −483.113 | −0.573769 | ||||||||
\(843\) | −954.029 | −1.13171 | ||||||||
\(844\) | − | 157.292i | − | 0.186365i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 1695.18i | − | 2.00376i | ||||||
\(847\) | 992.316 | 1.17157 | ||||||||
\(848\) | 1075.04i | 1.26773i | ||||||||
\(849\) | 1270.65i | 1.49664i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 430.287i | − | 0.505625i | ||||||
\(852\) | 199.880 | 0.234601 | ||||||||
\(853\) | 1035.83 | 1.21433 | 0.607167 | − | 0.794574i | \(-0.292306\pi\) | ||||
0.607167 | + | 0.794574i | \(0.292306\pi\) | |||||||
\(854\) | 2245.70i | 2.62962i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 752.721 | 0.879347 | ||||||||
\(857\) | − | 488.572i | − | 0.570096i | −0.958513 | − | 0.285048i | \(-0.907990\pi\) | ||
0.958513 | − | 0.285048i | \(-0.0920096\pi\) | |||||||
\(858\) | 255.202i | 0.297438i | ||||||||
\(859\) | 55.9552 | 0.0651399 | 0.0325699 | − | 0.999469i | \(-0.489631\pi\) | ||||
0.0325699 | + | 0.999469i | \(0.489631\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2431.14 | −2.82363 | ||||||||
\(862\) | −1125.07 | −1.30519 | ||||||||
\(863\) | 740.616i | 0.858188i | 0.903260 | + | 0.429094i | \(0.141167\pi\) | ||||
−0.903260 | + | 0.429094i | \(0.858833\pi\) | |||||||
\(864\) | −1973.06 | −2.28363 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1331.16 | −1.53714 | ||||||||
\(867\) | − | 2820.49i | − | 3.25316i | ||||||
\(868\) | 419.189i | 0.482936i | ||||||||
\(869\) | 322.962i | 0.371648i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.9391 | 0.0160036 | ||||||||
\(872\) | −434.376 | −0.498137 | ||||||||
\(873\) | 1848.05i | 2.11689i | ||||||||
\(874\) | −578.579 | − | 230.916i | −0.661990 | − | 0.264206i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 183.722i | − | 0.209729i | ||||||
\(877\) | − | 1241.85i | − | 1.41602i | −0.706204 | − | 0.708009i | \(-0.749594\pi\) | ||
0.706204 | − | 0.708009i | \(-0.250406\pi\) | |||||||
\(878\) | −1607.54 | −1.83091 | ||||||||
\(879\) | 218.126 | 0.248153 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −812.952 | −0.922761 | −0.461380 | − | 0.887202i | \(-0.652646\pi\) | ||||
−0.461380 | + | 0.887202i | \(0.652646\pi\) | |||||||
\(882\) | 2387.86i | 2.70733i | ||||||||
\(883\) | −512.623 | −0.580547 | −0.290274 | − | 0.956944i | \(-0.593746\pi\) | ||||
−0.290274 | + | 0.956944i | \(0.593746\pi\) | |||||||
\(884\) | 192.815i | 0.218117i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1112.06i | 1.25515i | ||||||||
\(887\) | 600.453i | 0.676948i | 0.940976 | + | 0.338474i | \(0.109911\pi\) | ||||
−0.940976 | + | 0.338474i | \(0.890089\pi\) | |||||||
\(888\) | 1032.03i | 1.16220i | ||||||||
\(889\) | 776.085i | 0.872986i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1145.61 | 1.28576 | ||||||||
\(892\) | 103.539i | 0.116075i | ||||||||
\(893\) | −212.610 | + | 532.713i | −0.238086 | + | 0.596543i | ||||
\(894\) | −2014.19 | −2.25301 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1441.94i | − | 1.60930i | ||||||
\(897\) | −365.093 | −0.407015 | ||||||||
\(898\) | −739.815 | −0.823847 | ||||||||
\(899\) | 422.910 | 0.470422 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1519.75i | − | 1.68674i | ||||||
\(902\) | 432.319 | 0.479289 | ||||||||
\(903\) | − | 3801.29i | − | 4.20962i | ||||||
\(904\) | −1019.18 | −1.12741 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3535.49i | 3.90231i | ||||||||
\(907\) | 139.480i | 0.153782i | 0.997040 | + | 0.0768910i | \(0.0244993\pi\) | ||||
−0.997040 | + | 0.0768910i | \(0.975501\pi\) | |||||||
\(908\) | 302.164i | 0.332779i | ||||||||
\(909\) | 3486.15 | 3.83515 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 897.235i | 0.984890i | 0.870344 | + | 0.492445i | \(0.163897\pi\) | ||||
−0.870344 | + | 0.492445i | \(0.836103\pi\) | |||||||
\(912\) | 2000.87 | + | 798.565i | 2.19393 | + | 0.875619i | ||||
\(913\) | −387.223 | −0.424121 | ||||||||
\(914\) | 608.899i | 0.666191i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 114.105 | 0.124569 | ||||||||
\(917\) | 496.142 | 0.541049 | ||||||||
\(918\) | 5613.42 | 6.11483 | ||||||||
\(919\) | −79.2393 | −0.0862234 | −0.0431117 | − | 0.999070i | \(-0.513727\pi\) | ||||
−0.0431117 | + | 0.999070i | \(0.513727\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1637.89 | 1.77838 | ||||||||
\(922\) | − | 1600.98i | − | 1.73642i | ||||||
\(923\) | −104.874 | −0.113623 | ||||||||
\(924\) | − | 345.404i | − | 0.373814i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1504.93i | − | 1.62519i | ||||||
\(927\) | − | 173.976i | − | 0.187677i | ||||||
\(928\) | 337.013 | 0.363160 | ||||||||
\(929\) | −535.116 | −0.576013 | −0.288007 | − | 0.957628i | \(-0.592993\pi\) | ||||
−0.288007 | + | 0.957628i | \(0.592993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 299.486 | − | 750.387i | 0.321682 | − | 0.806001i | ||||
\(932\) | 15.6539 | 0.0167960 | ||||||||
\(933\) | 26.1147i | 0.0279900i | ||||||||
\(934\) | − | 334.173i | − | 0.357787i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 636.221 | 0.679723 | ||||||||
\(937\) | −1523.13 | −1.62554 | −0.812768 | − | 0.582587i | \(-0.802041\pi\) | ||||
−0.812768 | + | 0.582587i | \(0.802041\pi\) | |||||||
\(938\) | −68.7053 | −0.0732466 | ||||||||
\(939\) | − | 1709.74i | − | 1.82081i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 283.647i | − | 0.301432i | −0.988577 | − | 0.150716i | \(-0.951842\pi\) | ||
0.988577 | − | 0.150716i | \(-0.0481578\pi\) | |||||||
\(942\) | −1431.75 | −1.51990 | ||||||||
\(943\) | 618.477i | 0.655861i | ||||||||
\(944\) | − | 619.265i | − | 0.656001i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 675.965i | 0.714551i | ||||||||
\(947\) | 1604.67 | 1.69448 | 0.847239 | − | 0.531211i | \(-0.178263\pi\) | ||||
0.847239 | + | 0.531211i | \(0.178263\pi\) | |||||||
\(948\) | −674.993 | −0.712018 | ||||||||
\(949\) | 96.3958i | 0.101576i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1027.37 | 1.08030 | ||||||||
\(952\) | 1560.28i | 1.63895i | ||||||||
\(953\) | 490.181i | 0.514356i | 0.966364 | + | 0.257178i | \(0.0827927\pi\) | ||||
−0.966364 | + | 0.257178i | \(0.917207\pi\) | |||||||
\(954\) | 3054.44 | 3.20172 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 546.324 | 0.571469 | ||||||||
\(957\) | −348.471 | −0.364128 | ||||||||
\(958\) | − | 713.440i | − | 0.744718i | ||||||
\(959\) | 111.657 | 0.116431 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 123.564 | 0.128579 | ||||||||
\(962\) | 329.824i | 0.342853i | ||||||||
\(963\) | − | 3083.63i | − | 3.20211i | ||||||
\(964\) | 676.150i | 0.701401i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1799.52 | 1.86286 | ||||||||
\(967\) | −969.777 | −1.00287 | −0.501436 | − | 0.865195i | \(-0.667195\pi\) | ||||
−0.501436 | + | 0.865195i | \(0.667195\pi\) | |||||||
\(968\) | 605.479i | 0.625494i | ||||||||
\(969\) | −2828.57 | − | 1128.91i | −2.91906 | − | 1.16502i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 521.725i | 0.537307i | 0.963237 | + | 0.268653i | \(0.0865786\pi\) | ||||
−0.963237 | + | 0.268653i | \(0.913421\pi\) | |||||||
\(972\) | 1228.40i | 1.26379i | ||||||||
\(973\) | −1103.14 | −1.13375 | ||||||||
\(974\) | −1.27108 | −0.00130501 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1975.69 | −2.02428 | ||||||||
\(977\) | 631.913i | 0.646790i | 0.946264 | + | 0.323395i | \(0.104824\pi\) | ||||
−0.946264 | + | 0.323395i | \(0.895176\pi\) | |||||||
\(978\) | 2332.09 | 2.38455 | ||||||||
\(979\) | − | 526.284i | − | 0.537573i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1779.48i | 1.81395i | ||||||||
\(982\) | − | 1087.63i | − | 1.10757i | ||||||
\(983\) | − | 903.596i | − | 0.919223i | −0.888120 | − | 0.459611i | \(-0.847989\pi\) | ||
0.888120 | − | 0.459611i | \(-0.152011\pi\) | |||||||
\(984\) | − | 1483.40i | − | 1.50752i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −958.812 | −0.972426 | ||||||||
\(987\) | − | 1656.87i | − | 1.67869i | ||||||
\(988\) | 121.780 | + | 48.6036i | 0.123259 | + | 0.0491939i | ||||
\(989\) | −967.038 | −0.977794 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 691.185i | 0.697462i | 0.937223 | + | 0.348731i | \(0.113387\pi\) | ||||
−0.937223 | + | 0.348731i | \(0.886613\pi\) | |||||||
\(992\) | −667.344 | −0.672726 | ||||||||
\(993\) | −1893.47 | −1.90681 | ||||||||
\(994\) | 516.917 | 0.520037 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 809.297i | − | 0.812547i | ||||||
\(997\) | −285.575 | −0.286435 | −0.143217 | − | 0.989691i | \(-0.545745\pi\) | ||||
−0.143217 | + | 0.989691i | \(0.545745\pi\) | |||||||
\(998\) | − | 410.622i | − | 0.411445i | ||||||
\(999\) | 2636.69 | 2.63932 |
(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 | 475.3.c.h.151.4 | ✓ | 14 | |
5.2 | odd | 4 | 475.3.d.d.474.22 | 28 | |||
5.3 | odd | 4 | 475.3.d.d.474.7 | 28 | |||
5.4 | even | 2 | 475.3.c.i.151.11 | yes | 14 | ||
19.18 | odd | 2 | inner | 475.3.c.h.151.11 | yes | 14 | |
95.18 | even | 4 | 475.3.d.d.474.21 | 28 | |||
95.37 | even | 4 | 475.3.d.d.474.8 | 28 | |||
95.94 | odd | 2 | 475.3.c.i.151.4 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.3.c.h.151.4 | ✓ | 14 | 1.1 | even | 1 | trivial | |
475.3.c.h.151.11 | yes | 14 | 19.18 | odd | 2 | inner | |
475.3.c.i.151.4 | yes | 14 | 95.94 | odd | 2 | ||
475.3.c.i.151.11 | yes | 14 | 5.4 | even | 2 | ||
475.3.d.d.474.7 | 28 | 5.3 | odd | 4 | |||
475.3.d.d.474.8 | 28 | 95.37 | even | 4 | |||
475.3.d.d.474.21 | 28 | 95.18 | even | 4 | |||
475.3.d.d.474.22 | 28 | 5.2 | odd | 4 |