Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(76,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("525.76");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.h (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: | \(14.3052138789\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.12 | ||
Root | \(1.86875 + 3.23677i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.76 |
Dual form | 525.3.h.d.76.11 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.80460 | 1.90230 | 0.951150 | − | 0.308728i | \(-0.0999033\pi\) | ||||
0.951150 | + | 0.308728i | \(0.0999033\pi\) | |||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 10.4750 | 2.61875 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.58976i | 1.09829i | ||||||||
\(7\) | −2.44621 | − | 6.55866i | −0.349458 | − | 0.936952i | ||||
\(8\) | 24.6348 | 3.07935 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.4489 | 1.31354 | 0.656768 | − | 0.754092i | \(-0.271923\pi\) | ||||
0.656768 | + | 0.754092i | \(0.271923\pi\) | |||||||
\(12\) | 18.1432i | 1.51193i | ||||||||
\(13\) | 16.9427i | 1.30329i | 0.758526 | + | 0.651643i | \(0.225920\pi\) | ||||
−0.758526 | + | 0.651643i | \(0.774080\pi\) | |||||||
\(14\) | −9.30684 | − | 24.9531i | −0.664774 | − | 1.78236i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 51.8255 | 3.23909 | ||||||||
\(17\) | 13.0093i | 0.765251i | 0.923904 | + | 0.382625i | \(0.124980\pi\) | ||||
−0.923904 | + | 0.382625i | \(0.875020\pi\) | |||||||
\(18\) | −11.4138 | −0.634100 | ||||||||
\(19\) | − | 18.6908i | − | 0.983729i | −0.870672 | − | 0.491864i | \(-0.836316\pi\) | ||
0.870672 | − | 0.491864i | \(-0.163684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.3599 | − | 4.23695i | 0.540950 | − | 0.201760i | ||||
\(22\) | 54.9723 | 2.49874 | ||||||||
\(23\) | −10.3861 | −0.451570 | −0.225785 | − | 0.974177i | \(-0.572495\pi\) | ||||
−0.225785 | + | 0.974177i | \(0.572495\pi\) | |||||||
\(24\) | 42.6687i | 1.77786i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 64.4602i | 2.47924i | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −25.6240 | − | 68.7020i | −0.915142 | − | 2.45364i | ||||
\(29\) | −13.7269 | −0.473341 | −0.236671 | − | 0.971590i | \(-0.576056\pi\) | ||||
−0.236671 | + | 0.971590i | \(0.576056\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 42.4383i | − | 1.36898i | −0.729024 | − | 0.684488i | \(-0.760026\pi\) | ||
0.729024 | − | 0.684488i | \(-0.239974\pi\) | |||||||
\(32\) | 98.6363 | 3.08238 | ||||||||
\(33\) | 25.0262i | 0.758371i | ||||||||
\(34\) | 49.4951i | 1.45574i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −31.4250 | −0.872916 | ||||||||
\(37\) | −28.7434 | −0.776850 | −0.388425 | − | 0.921480i | \(-0.626981\pi\) | ||||
−0.388425 | + | 0.921480i | \(0.626981\pi\) | |||||||
\(38\) | − | 71.1112i | − | 1.87135i | ||||||
\(39\) | −29.3456 | −0.752452 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 28.8060i | 0.702585i | 0.936266 | + | 0.351293i | \(0.114258\pi\) | ||||
−0.936266 | + | 0.351293i | \(0.885742\pi\) | |||||||
\(42\) | 43.2200 | − | 16.1199i | 1.02905 | − | 0.383807i | ||||
\(43\) | 5.84593 | 0.135952 | 0.0679759 | − | 0.997687i | \(-0.478346\pi\) | ||||
0.0679759 | + | 0.997687i | \(0.478346\pi\) | |||||||
\(44\) | 151.352 | 3.43982 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −39.5151 | −0.859023 | ||||||||
\(47\) | 10.5013i | 0.223432i | 0.993740 | + | 0.111716i | \(0.0356347\pi\) | ||||
−0.993740 | + | 0.111716i | \(0.964365\pi\) | |||||||
\(48\) | 89.7644i | 1.87009i | ||||||||
\(49\) | −37.0322 | + | 32.0877i | −0.755758 | + | 0.654851i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −22.5327 | −0.441818 | ||||||||
\(52\) | 177.475i | 3.41298i | ||||||||
\(53\) | −81.9074 | −1.54542 | −0.772712 | − | 0.634757i | \(-0.781100\pi\) | ||||
−0.772712 | + | 0.634757i | \(0.781100\pi\) | |||||||
\(54\) | − | 19.7693i | − | 0.366098i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −60.2617 | − | 161.571i | −1.07610 | − | 2.88520i | ||||
\(57\) | 32.3735 | 0.567956 | ||||||||
\(58\) | −52.2254 | −0.900438 | ||||||||
\(59\) | − | 35.1680i | − | 0.596067i | −0.954555 | − | 0.298033i | \(-0.903669\pi\) | ||
0.954555 | − | 0.298033i | \(-0.0963307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 68.4826i | 1.12267i | 0.827590 | + | 0.561333i | \(0.189711\pi\) | ||||
−0.827590 | + | 0.561333i | \(0.810289\pi\) | |||||||
\(62\) | − | 161.461i | − | 2.60421i | ||||||
\(63\) | 7.33862 | + | 19.6760i | 0.116486 | + | 0.312317i | ||||
\(64\) | 167.970 | 2.62453 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 95.2149i | 1.44265i | ||||||||
\(67\) | −47.4637 | −0.708414 | −0.354207 | − | 0.935167i | \(-0.615249\pi\) | ||||
−0.354207 | + | 0.935167i | \(0.615249\pi\) | |||||||
\(68\) | 136.272i | 2.00400i | ||||||||
\(69\) | − | 17.9893i | − | 0.260714i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 47.6548 | 0.671194 | 0.335597 | − | 0.942006i | \(-0.391062\pi\) | ||||
0.335597 | + | 0.942006i | \(0.391062\pi\) | |||||||
\(72\) | −73.9043 | −1.02645 | ||||||||
\(73\) | − | 125.967i | − | 1.72557i | −0.505569 | − | 0.862786i | \(-0.668717\pi\) | ||
0.505569 | − | 0.862786i | \(-0.331283\pi\) | |||||||
\(74\) | −109.357 | −1.47780 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 195.786i | − | 2.57614i | ||||||
\(77\) | −35.3450 | − | 94.7655i | −0.459026 | − | 1.23072i | ||||
\(78\) | −111.648 | −1.43139 | ||||||||
\(79\) | −129.527 | −1.63958 | −0.819790 | − | 0.572665i | \(-0.805910\pi\) | ||||
−0.819790 | + | 0.572665i | \(0.805910\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 109.595i | 1.33653i | ||||||||
\(83\) | − | 42.6906i | − | 0.514345i | −0.966365 | − | 0.257173i | \(-0.917209\pi\) | ||
0.966365 | − | 0.257173i | \(-0.0827909\pi\) | |||||||
\(84\) | 118.995 | − | 44.3820i | 1.41661 | − | 0.528358i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 22.2414 | 0.258621 | ||||||||
\(87\) | − | 23.7757i | − | 0.273284i | ||||||
\(88\) | 355.945 | 4.04483 | ||||||||
\(89\) | − | 25.5329i | − | 0.286886i | −0.989659 | − | 0.143443i | \(-0.954183\pi\) | ||
0.989659 | − | 0.143443i | \(-0.0458174\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 111.122 | − | 41.4453i | 1.22112 | − | 0.455443i | ||||
\(92\) | −108.795 | −1.18255 | ||||||||
\(93\) | 73.5053 | 0.790379 | ||||||||
\(94\) | 39.9533i | 0.425035i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 170.843i | 1.77961i | ||||||||
\(97\) | 28.7310i | 0.296196i | 0.988973 | + | 0.148098i | \(0.0473151\pi\) | ||||
−0.988973 | + | 0.148098i | \(0.952685\pi\) | |||||||
\(98\) | −140.893 | + | 122.081i | −1.43768 | + | 1.24572i | ||||
\(99\) | −43.3467 | −0.437846 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.4609i | 0.123375i | 0.998096 | + | 0.0616875i | \(0.0196482\pi\) | ||||
−0.998096 | + | 0.0616875i | \(0.980352\pi\) | |||||||
\(102\) | −85.7280 | −0.840470 | ||||||||
\(103\) | − | 38.4795i | − | 0.373587i | −0.982399 | − | 0.186794i | \(-0.940190\pi\) | ||
0.982399 | − | 0.186794i | \(-0.0598096\pi\) | |||||||
\(104\) | 417.380i | 4.01326i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −311.625 | −2.93986 | ||||||||
\(107\) | 87.7985 | 0.820547 | 0.410273 | − | 0.911963i | \(-0.365433\pi\) | ||||
0.410273 | + | 0.911963i | \(0.365433\pi\) | |||||||
\(108\) | − | 54.4297i | − | 0.503978i | ||||||
\(109\) | 130.012 | 1.19277 | 0.596386 | − | 0.802698i | \(-0.296603\pi\) | ||||
0.596386 | + | 0.802698i | \(0.296603\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 49.7851i | − | 0.448515i | ||||||
\(112\) | −126.776 | − | 339.906i | −1.13193 | − | 3.03487i | ||||
\(113\) | 158.597 | 1.40351 | 0.701757 | − | 0.712417i | \(-0.252399\pi\) | ||||
0.701757 | + | 0.712417i | \(0.252399\pi\) | |||||||
\(114\) | 123.168 | 1.08042 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −143.789 | −1.23956 | ||||||||
\(117\) | − | 50.8281i | − | 0.434428i | ||||||
\(118\) | − | 133.800i | − | 1.13390i | ||||||
\(119\) | 85.3234 | − | 31.8233i | 0.717003 | − | 0.267423i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 87.7709 | 0.725379 | ||||||||
\(122\) | 260.549i | 2.13565i | ||||||||
\(123\) | −49.8934 | −0.405638 | ||||||||
\(124\) | − | 444.541i | − | 3.58501i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 27.9205 | + | 74.8593i | 0.221591 | + | 0.594122i | ||||
\(127\) | −43.0643 | −0.339089 | −0.169545 | − | 0.985523i | \(-0.554230\pi\) | ||||
−0.169545 | + | 0.985523i | \(0.554230\pi\) | |||||||
\(128\) | 244.513 | 1.91026 | ||||||||
\(129\) | 10.1254i | 0.0784919i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.686731i | 0.00524222i | 0.999997 | + | 0.00262111i | \(0.000834326\pi\) | ||||
−0.999997 | + | 0.00262111i | \(0.999166\pi\) | |||||||
\(132\) | 262.150i | 1.98598i | ||||||||
\(133\) | −122.587 | + | 45.7216i | −0.921707 | + | 0.343772i | ||||
\(134\) | −180.581 | −1.34762 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 320.480i | 2.35647i | ||||||||
\(137\) | −76.2084 | −0.556266 | −0.278133 | − | 0.960543i | \(-0.589716\pi\) | ||||
−0.278133 | + | 0.960543i | \(0.589716\pi\) | |||||||
\(138\) | − | 68.4421i | − | 0.495957i | ||||||
\(139\) | 49.0445i | 0.352838i | 0.984315 | + | 0.176419i | \(0.0564514\pi\) | ||||
−0.984315 | + | 0.176419i | \(0.943549\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.1888 | −0.128998 | ||||||||
\(142\) | 181.307 | 1.27681 | ||||||||
\(143\) | 244.804i | 1.71191i | ||||||||
\(144\) | −155.476 | −1.07970 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 479.253i | − | 3.28256i | ||||||
\(147\) | −55.5775 | − | 64.1416i | −0.378078 | − | 0.436337i | ||||
\(148\) | −301.087 | −2.03437 | ||||||||
\(149\) | −242.344 | −1.62647 | −0.813236 | − | 0.581934i | \(-0.802296\pi\) | ||||
−0.813236 | + | 0.581934i | \(0.802296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 107.704 | 0.713271 | 0.356636 | − | 0.934244i | \(-0.383924\pi\) | ||||
0.356636 | + | 0.934244i | \(0.383924\pi\) | |||||||
\(152\) | − | 460.445i | − | 3.02924i | ||||||
\(153\) | − | 39.0278i | − | 0.255084i | ||||||
\(154\) | −134.474 | − | 360.545i | −0.873205 | − | 2.34120i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −307.395 | −1.97048 | ||||||||
\(157\) | 76.1684i | 0.485149i | 0.970133 | + | 0.242575i | \(0.0779919\pi\) | ||||
−0.970133 | + | 0.242575i | \(0.922008\pi\) | |||||||
\(158\) | −492.798 | −3.11897 | ||||||||
\(159\) | − | 141.868i | − | 0.892250i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.4066 | + | 68.1191i | 0.157805 | + | 0.423100i | ||||
\(162\) | 34.2414 | 0.211367 | ||||||||
\(163\) | −10.4287 | −0.0639800 | −0.0319900 | − | 0.999488i | \(-0.510184\pi\) | ||||
−0.0319900 | + | 0.999488i | \(0.510184\pi\) | |||||||
\(164\) | 301.743i | 1.83989i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 162.421i | − | 0.978439i | ||||||
\(167\) | 75.7598i | 0.453652i | 0.973935 | + | 0.226826i | \(0.0728348\pi\) | ||||
−0.973935 | + | 0.226826i | \(0.927165\pi\) | |||||||
\(168\) | 279.849 | − | 104.376i | 1.66577 | − | 0.621287i | ||||
\(169\) | −118.055 | −0.698552 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 56.0725i | 0.327910i | ||||||||
\(172\) | 61.2361 | 0.356024 | ||||||||
\(173\) | − | 325.843i | − | 1.88349i | −0.336333 | − | 0.941743i | \(-0.609187\pi\) | ||
0.336333 | − | 0.941743i | \(-0.390813\pi\) | |||||||
\(174\) | − | 90.4570i | − | 0.519868i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 748.822 | 4.25467 | ||||||||
\(177\) | 60.9127 | 0.344139 | ||||||||
\(178\) | − | 97.1424i | − | 0.545744i | ||||||
\(179\) | −30.9215 | −0.172746 | −0.0863728 | − | 0.996263i | \(-0.527528\pi\) | ||||
−0.0863728 | + | 0.996263i | \(0.527528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 211.403i | 1.16797i | 0.811764 | + | 0.583985i | \(0.198507\pi\) | ||||
−0.811764 | + | 0.583985i | \(0.801493\pi\) | |||||||
\(182\) | 422.773 | − | 157.683i | 2.32293 | − | 0.866390i | ||||
\(183\) | −118.615 | −0.648171 | ||||||||
\(184\) | −255.860 | −1.39054 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 279.658 | 1.50354 | ||||||||
\(187\) | 187.970i | 1.00519i | ||||||||
\(188\) | 110.001i | 0.585112i | ||||||||
\(189\) | −34.0798 | + | 12.7109i | −0.180317 | + | 0.0672532i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 112.093 | 0.586874 | 0.293437 | − | 0.955978i | \(-0.405201\pi\) | ||||
0.293437 | + | 0.955978i | \(0.405201\pi\) | |||||||
\(192\) | 290.932i | 1.51527i | ||||||||
\(193\) | 293.541 | 1.52094 | 0.760470 | − | 0.649373i | \(-0.224969\pi\) | ||||
0.760470 | + | 0.649373i | \(0.224969\pi\) | |||||||
\(194\) | 109.310i | 0.563453i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −387.912 | + | 336.118i | −1.97914 | + | 1.71489i | ||||
\(197\) | 90.7583 | 0.460702 | 0.230351 | − | 0.973108i | \(-0.426013\pi\) | ||||
0.230351 | + | 0.973108i | \(0.426013\pi\) | |||||||
\(198\) | −164.917 | −0.832914 | ||||||||
\(199\) | 389.421i | 1.95689i | 0.206505 | + | 0.978445i | \(0.433791\pi\) | ||||
−0.206505 | + | 0.978445i | \(0.566209\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 82.2096i | − | 0.409003i | ||||||
\(202\) | 47.4086i | 0.234696i | ||||||||
\(203\) | 33.5788 | + | 90.0301i | 0.165413 | + | 0.443498i | ||||
\(204\) | −236.030 | −1.15701 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 146.399i | − | 0.710676i | ||||||
\(207\) | 31.1584 | 0.150523 | ||||||||
\(208\) | 878.064i | 4.22146i | ||||||||
\(209\) | − | 270.062i | − | 1.29216i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.1049 | −0.100023 | −0.0500115 | − | 0.998749i | \(-0.515926\pi\) | ||||
−0.0500115 | + | 0.998749i | \(0.515926\pi\) | |||||||
\(212\) | −857.980 | −4.04707 | ||||||||
\(213\) | 82.5405i | 0.387514i | ||||||||
\(214\) | 334.038 | 1.56093 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 128.006i | − | 0.592620i | ||||||
\(217\) | −278.338 | + | 103.813i | −1.28267 | + | 0.478400i | ||||
\(218\) | 494.645 | 2.26901 | ||||||||
\(219\) | 218.181 | 0.996259 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −220.412 | −0.997340 | ||||||||
\(222\) | − | 189.413i | − | 0.853209i | ||||||
\(223\) | 293.039i | 1.31408i | 0.753857 | + | 0.657039i | \(0.228191\pi\) | ||||
−0.753857 | + | 0.657039i | \(0.771809\pi\) | |||||||
\(224\) | −241.285 | − | 646.922i | −1.07716 | − | 2.88805i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 603.398 | 2.66990 | ||||||||
\(227\) | 73.9333i | 0.325697i | 0.986651 | + | 0.162849i | \(0.0520682\pi\) | ||||
−0.986651 | + | 0.162849i | \(0.947932\pi\) | |||||||
\(228\) | 339.112 | 1.48733 | ||||||||
\(229\) | 233.516i | 1.01972i | 0.860257 | + | 0.509860i | \(0.170303\pi\) | ||||
−0.860257 | + | 0.509860i | \(0.829697\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 164.139 | − | 61.2193i | 0.710557 | − | 0.265019i | ||||
\(232\) | −338.159 | −1.45758 | ||||||||
\(233\) | 385.429 | 1.65420 | 0.827101 | − | 0.562054i | \(-0.189989\pi\) | ||||
0.827101 | + | 0.562054i | \(0.189989\pi\) | |||||||
\(234\) | − | 193.381i | − | 0.826413i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 368.384i | − | 1.56095i | ||||||
\(237\) | − | 224.347i | − | 0.946611i | ||||||
\(238\) | 324.621 | − | 121.075i | 1.36396 | − | 0.508719i | ||||
\(239\) | 407.373 | 1.70449 | 0.852244 | − | 0.523144i | \(-0.175241\pi\) | ||||
0.852244 | + | 0.523144i | \(0.175241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 271.816i | 1.12787i | 0.825820 | + | 0.563934i | \(0.190713\pi\) | ||||
−0.825820 | + | 0.563934i | \(0.809287\pi\) | |||||||
\(242\) | 333.933 | 1.37989 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 717.355i | 2.93998i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −189.825 | −0.771645 | ||||||||
\(247\) | 316.673 | 1.28208 | ||||||||
\(248\) | − | 1045.46i | − | 4.21555i | ||||||
\(249\) | 73.9424 | 0.296957 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 442.250i | 1.76195i | 0.473162 | + | 0.880976i | \(0.343113\pi\) | ||||
−0.473162 | + | 0.880976i | \(0.656887\pi\) | |||||||
\(252\) | 76.8719 | + | 206.106i | 0.305047 | + | 0.817880i | ||||
\(253\) | −150.068 | −0.593154 | ||||||||
\(254\) | −163.843 | −0.645049 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 258.395 | 1.00935 | ||||||||
\(257\) | − | 390.436i | − | 1.51921i | −0.650386 | − | 0.759604i | \(-0.725393\pi\) | ||
0.650386 | − | 0.759604i | \(-0.274607\pi\) | |||||||
\(258\) | 38.5233i | 0.149315i | ||||||||
\(259\) | 70.3124 | + | 188.519i | 0.271476 | + | 0.727871i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 41.1807 | 0.157780 | ||||||||
\(262\) | 2.61274i | 0.00997228i | ||||||||
\(263\) | 1.63279 | 0.00620832 | 0.00310416 | − | 0.999995i | \(-0.499012\pi\) | ||||
0.00310416 | + | 0.999995i | \(0.499012\pi\) | |||||||
\(264\) | 616.515i | 2.33529i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −466.395 | + | 173.953i | −1.75336 | + | 0.653957i | ||||
\(267\) | 44.2242 | 0.165634 | ||||||||
\(268\) | −497.182 | −1.85516 | ||||||||
\(269\) | − | 410.340i | − | 1.52543i | −0.646737 | − | 0.762713i | \(-0.723867\pi\) | ||
0.646737 | − | 0.762713i | \(-0.276133\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 470.030i | − | 1.73443i | −0.497937 | − | 0.867213i | \(-0.665909\pi\) | ||
0.497937 | − | 0.867213i | \(-0.334091\pi\) | |||||||
\(272\) | 674.211i | 2.47872i | ||||||||
\(273\) | 71.7854 | + | 192.468i | 0.262950 | + | 0.705011i | ||||
\(274\) | −289.943 | −1.05818 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 188.438i | − | 0.682745i | ||||||
\(277\) | −366.582 | −1.32340 | −0.661701 | − | 0.749768i | \(-0.730165\pi\) | ||||
−0.661701 | + | 0.749768i | \(0.730165\pi\) | |||||||
\(278\) | 186.595i | 0.671204i | ||||||||
\(279\) | 127.315i | 0.456326i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1164 | 0.0360015 | 0.0180008 | − | 0.999838i | \(-0.494270\pi\) | ||||
0.0180008 | + | 0.999838i | \(0.494270\pi\) | |||||||
\(282\) | −69.2011 | −0.245394 | ||||||||
\(283\) | − | 121.896i | − | 0.430729i | −0.976534 | − | 0.215364i | \(-0.930906\pi\) | ||
0.976534 | − | 0.215364i | \(-0.0690939\pi\) | |||||||
\(284\) | 499.183 | 1.75769 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 931.380i | 3.25657i | ||||||||
\(287\) | 188.929 | − | 70.4654i | 0.658289 | − | 0.245524i | ||||
\(288\) | −295.909 | −1.02746 | ||||||||
\(289\) | 119.759 | 0.414391 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −49.7635 | −0.171009 | ||||||||
\(292\) | − | 1319.50i | − | 4.51884i | ||||||
\(293\) | 292.803i | 0.999327i | 0.866220 | + | 0.499663i | \(0.166543\pi\) | ||||
−0.866220 | + | 0.499663i | \(0.833457\pi\) | |||||||
\(294\) | −211.450 | − | 244.033i | −0.719218 | − | 0.830045i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −708.088 | −2.39219 | ||||||||
\(297\) | − | 75.0787i | − | 0.252790i | ||||||
\(298\) | −922.023 | −3.09404 | ||||||||
\(299\) | − | 175.969i | − | 0.588525i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.3003 | − | 38.3415i | −0.0475095 | − | 0.127380i | ||||
\(302\) | 409.771 | 1.35686 | ||||||||
\(303\) | −21.5829 | −0.0712306 | ||||||||
\(304\) | − | 968.662i | − | 3.18639i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 148.485i | − | 0.485246i | ||||||
\(307\) | 167.855i | 0.546758i | 0.961906 | + | 0.273379i | \(0.0881412\pi\) | ||||
−0.961906 | + | 0.273379i | \(0.911859\pi\) | |||||||
\(308\) | −370.238 | − | 992.668i | −1.20207 | − | 3.22295i | ||||
\(309\) | 66.6485 | 0.215691 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 303.739i | − | 0.976652i | −0.872661 | − | 0.488326i | \(-0.837608\pi\) | ||
0.872661 | − | 0.488326i | \(-0.162392\pi\) | |||||||
\(312\) | −722.923 | −2.31706 | ||||||||
\(313\) | 17.2151i | 0.0550004i | 0.999622 | + | 0.0275002i | \(0.00875470\pi\) | ||||
−0.999622 | + | 0.0275002i | \(0.991245\pi\) | |||||||
\(314\) | 289.790i | 0.922899i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1356.79 | −4.29364 | ||||||||
\(317\) | −82.8657 | −0.261406 | −0.130703 | − | 0.991422i | \(-0.541723\pi\) | ||||
−0.130703 | + | 0.991422i | \(0.541723\pi\) | |||||||
\(318\) | − | 539.750i | − | 1.69733i | ||||||
\(319\) | −198.339 | −0.621751 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 152.071i | 0.473743i | ||||||||
\(322\) | 96.6619 | + | 259.166i | 0.300192 | + | 0.804863i | ||||
\(323\) | 243.154 | 0.752799 | ||||||||
\(324\) | 94.2749 | 0.290972 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −39.6772 | −0.121709 | ||||||||
\(327\) | 225.188i | 0.688647i | ||||||||
\(328\) | 709.629i | 2.16350i | ||||||||
\(329\) | 68.8745 | − | 25.6883i | 0.209345 | − | 0.0780800i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −451.490 | −1.36402 | −0.682009 | − | 0.731343i | \(-0.738894\pi\) | ||||
−0.682009 | + | 0.731343i | \(0.738894\pi\) | |||||||
\(332\) | − | 447.184i | − | 1.34694i | ||||||
\(333\) | 86.2303 | 0.258950 | ||||||||
\(334\) | 288.236i | 0.862982i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 588.734 | − | 219.582i | 1.75219 | − | 0.653518i | ||||
\(337\) | −204.157 | −0.605808 | −0.302904 | − | 0.953021i | \(-0.597956\pi\) | ||||
−0.302904 | + | 0.953021i | \(0.597956\pi\) | |||||||
\(338\) | −449.153 | −1.32886 | ||||||||
\(339\) | 274.698i | 0.810319i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 613.187i | − | 1.79820i | ||||||
\(342\) | 213.334i | 0.623783i | ||||||||
\(343\) | 301.041 | + | 164.388i | 0.877669 | + | 0.479267i | ||||
\(344\) | 144.013 | 0.418643 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 1239.70i | − | 3.58296i | ||||||
\(347\) | −146.593 | −0.422458 | −0.211229 | − | 0.977437i | \(-0.567747\pi\) | ||||
−0.211229 | + | 0.977437i | \(0.567747\pi\) | |||||||
\(348\) | − | 249.050i | − | 0.715661i | ||||||
\(349\) | 11.4454i | 0.0327947i | 0.999866 | + | 0.0163974i | \(0.00521968\pi\) | ||||
−0.999866 | + | 0.0163974i | \(0.994780\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 88.0369 | 0.250817 | ||||||||
\(352\) | 1425.19 | 4.04882 | ||||||||
\(353\) | − | 177.817i | − | 0.503730i | −0.967762 | − | 0.251865i | \(-0.918956\pi\) | ||
0.967762 | − | 0.251865i | \(-0.0810439\pi\) | |||||||
\(354\) | 231.748 | 0.654657 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 267.457i | − | 0.751283i | ||||||
\(357\) | 55.1196 | + | 147.784i | 0.154397 | + | 0.413962i | ||||
\(358\) | −117.644 | −0.328614 | ||||||||
\(359\) | 653.079 | 1.81916 | 0.909581 | − | 0.415526i | \(-0.136402\pi\) | ||||
0.909581 | + | 0.415526i | \(0.136402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.6523 | 0.0322780 | ||||||||
\(362\) | 804.303i | 2.22183i | ||||||||
\(363\) | 152.024i | 0.418798i | ||||||||
\(364\) | 1164.00 | − | 434.140i | 3.19779 | − | 1.19269i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −451.284 | −1.23302 | ||||||||
\(367\) | 466.632i | 1.27148i | 0.771905 | + | 0.635738i | \(0.219304\pi\) | ||||
−0.771905 | + | 0.635738i | \(0.780696\pi\) | |||||||
\(368\) | −538.266 | −1.46268 | ||||||||
\(369\) | − | 86.4180i | − | 0.234195i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 200.362 | + | 537.203i | 0.540060 | + | 1.44799i | ||||
\(372\) | 769.967 | 2.06980 | ||||||||
\(373\) | 452.082 | 1.21202 | 0.606008 | − | 0.795459i | \(-0.292770\pi\) | ||||
0.606008 | + | 0.795459i | \(0.292770\pi\) | |||||||
\(374\) | 715.149i | 1.91216i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 258.697i | 0.688024i | ||||||||
\(377\) | − | 232.571i | − | 0.616899i | ||||||
\(378\) | −129.660 | + | 48.3597i | −0.343016 | + | 0.127936i | ||||
\(379\) | 326.478 | 0.861420 | 0.430710 | − | 0.902490i | \(-0.358263\pi\) | ||||
0.430710 | + | 0.902490i | \(0.358263\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 74.5896i | − | 0.195773i | ||||||
\(382\) | 426.469 | 1.11641 | ||||||||
\(383\) | − | 381.262i | − | 0.995462i | −0.867331 | − | 0.497731i | \(-0.834167\pi\) | ||
0.867331 | − | 0.497731i | \(-0.165833\pi\) | |||||||
\(384\) | 423.509i | 1.10289i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1116.81 | 2.89329 | ||||||||
\(387\) | −17.5378 | −0.0453173 | ||||||||
\(388\) | 300.957i | 0.775662i | ||||||||
\(389\) | −68.8443 | −0.176978 | −0.0884888 | − | 0.996077i | \(-0.528204\pi\) | ||||
−0.0884888 | + | 0.996077i | \(0.528204\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 135.116i | − | 0.345565i | ||||||
\(392\) | −912.278 | + | 790.472i | −2.32724 | + | 2.01651i | ||||
\(393\) | −1.18945 | −0.00302660 | ||||||||
\(394\) | 345.299 | 0.876394 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −454.056 | −1.14661 | ||||||||
\(397\) | 370.531i | 0.933328i | 0.884435 | + | 0.466664i | \(0.154544\pi\) | ||||
−0.884435 | + | 0.466664i | \(0.845456\pi\) | |||||||
\(398\) | 1481.59i | 3.72259i | ||||||||
\(399\) | −79.1922 | − | 212.327i | −0.198477 | − | 0.532148i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.95073 | 0.0223210 | 0.0111605 | − | 0.999938i | \(-0.496447\pi\) | ||||
0.0111605 | + | 0.999938i | \(0.496447\pi\) | |||||||
\(402\) | − | 312.775i | − | 0.778047i | ||||||
\(403\) | 719.019 | 1.78417 | ||||||||
\(404\) | 130.528i | 0.323088i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 127.754 | + | 342.529i | 0.314665 | + | 0.843667i | ||||
\(407\) | −415.311 | −1.02042 | ||||||||
\(408\) | −555.088 | −1.36051 | ||||||||
\(409\) | 63.1330i | 0.154359i | 0.997017 | + | 0.0771797i | \(0.0245915\pi\) | ||||
−0.997017 | + | 0.0771797i | \(0.975408\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 131.997i | − | 0.321160i | ||||||
\(412\) | − | 403.072i | − | 0.978331i | ||||||
\(413\) | −230.655 | + | 86.0280i | −0.558486 | + | 0.208300i | ||||
\(414\) | 118.545 | 0.286341 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1671.17i | 4.01722i | ||||||||
\(417\) | −84.9475 | −0.203711 | ||||||||
\(418\) | − | 1027.48i | − | 2.45808i | ||||||
\(419\) | 3.58774i | 0.00856263i | 0.999991 | + | 0.00428131i | \(0.00136279\pi\) | ||||
−0.999991 | + | 0.00428131i | \(0.998637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 119.594 | 0.284071 | 0.142035 | − | 0.989862i | \(-0.454635\pi\) | ||||
0.142035 | + | 0.989862i | \(0.454635\pi\) | |||||||
\(422\) | −80.2956 | −0.190274 | ||||||||
\(423\) | − | 31.5039i | − | 0.0744773i | ||||||
\(424\) | −2017.77 | −4.75889 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 314.034i | 0.737168i | ||||||||
\(427\) | 449.154 | − | 167.523i | 1.05188 | − | 0.392324i | ||||
\(428\) | 919.689 | 2.14881 | ||||||||
\(429\) | −424.012 | −0.988373 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −404.488 | −0.938488 | −0.469244 | − | 0.883069i | \(-0.655473\pi\) | ||||
−0.469244 | + | 0.883069i | \(0.655473\pi\) | |||||||
\(432\) | − | 269.293i | − | 0.623364i | ||||||
\(433\) | − | 116.085i | − | 0.268094i | −0.990975 | − | 0.134047i | \(-0.957203\pi\) | ||
0.990975 | − | 0.134047i | \(-0.0427974\pi\) | |||||||
\(434\) | −1058.97 | + | 394.966i | −2.44002 | + | 0.910060i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1361.88 | 3.12357 | ||||||||
\(437\) | 194.125i | 0.444223i | ||||||||
\(438\) | 830.091 | 1.89519 | ||||||||
\(439\) | 58.4183i | 0.133071i | 0.997784 | + | 0.0665357i | \(0.0211946\pi\) | ||||
−0.997784 | + | 0.0665357i | \(0.978805\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 111.096 | − | 96.2630i | 0.251919 | − | 0.218284i | ||||
\(442\) | −838.580 | −1.89724 | ||||||||
\(443\) | −267.301 | −0.603388 | −0.301694 | − | 0.953405i | \(-0.597552\pi\) | ||||
−0.301694 | + | 0.953405i | \(0.597552\pi\) | |||||||
\(444\) | − | 521.499i | − | 1.17455i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1114.90i | 2.49977i | ||||||||
\(447\) | − | 419.753i | − | 0.939044i | ||||||
\(448\) | −410.888 | − | 1101.66i | −0.917162 | − | 2.45906i | ||||
\(449\) | 296.478 | 0.660307 | 0.330154 | − | 0.943927i | \(-0.392899\pi\) | ||||
0.330154 | + | 0.943927i | \(0.392899\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 416.215i | 0.922872i | ||||||||
\(452\) | 1661.30 | 3.67545 | ||||||||
\(453\) | 186.549i | 0.411807i | ||||||||
\(454\) | 281.287i | 0.619574i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 797.513 | 1.74893 | ||||||||
\(457\) | −12.1251 | −0.0265320 | −0.0132660 | − | 0.999912i | \(-0.504223\pi\) | ||||
−0.0132660 | + | 0.999912i | \(0.504223\pi\) | |||||||
\(458\) | 888.435i | 1.93981i | ||||||||
\(459\) | 67.5981 | 0.147273 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 103.948i | − | 0.225483i | −0.993624 | − | 0.112741i | \(-0.964037\pi\) | ||
0.993624 | − | 0.112741i | \(-0.0359632\pi\) | |||||||
\(462\) | 624.482 | − | 232.915i | 1.35169 | − | 0.504145i | ||||
\(463\) | −498.831 | −1.07739 | −0.538694 | − | 0.842501i | \(-0.681082\pi\) | ||||
−0.538694 | + | 0.842501i | \(0.681082\pi\) | |||||||
\(464\) | −711.403 | −1.53320 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1466.40 | 3.14679 | ||||||||
\(467\) | − | 597.683i | − | 1.27983i | −0.768444 | − | 0.639917i | \(-0.778969\pi\) | ||
0.768444 | − | 0.639917i | \(-0.221031\pi\) | |||||||
\(468\) | − | 532.424i | − | 1.13766i | ||||||
\(469\) | 116.106 | + | 311.299i | 0.247561 | + | 0.663750i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −131.928 | −0.280101 | ||||||||
\(472\) | − | 866.354i | − | 1.83550i | ||||||
\(473\) | 84.4673 | 0.178578 | ||||||||
\(474\) | − | 853.551i | − | 1.80074i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 893.762 | − | 333.349i | 1.87765 | − | 0.700313i | ||||
\(477\) | 245.722 | 0.515141 | ||||||||
\(478\) | 1549.89 | 3.24245 | ||||||||
\(479\) | − | 276.703i | − | 0.577669i | −0.957379 | − | 0.288834i | \(-0.906732\pi\) | ||
0.957379 | − | 0.288834i | \(-0.0932677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 486.992i | − | 1.01246i | ||||||
\(482\) | 1034.15i | 2.14554i | ||||||||
\(483\) | −117.986 | + | 44.0055i | −0.244277 | + | 0.0911087i | ||||
\(484\) | 919.399 | 1.89958 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 59.3079i | 0.122033i | ||||||||
\(487\) | 542.653 | 1.11428 | 0.557138 | − | 0.830420i | \(-0.311899\pi\) | ||||
0.557138 | + | 0.830420i | \(0.311899\pi\) | |||||||
\(488\) | 1687.05i | 3.45708i | ||||||||
\(489\) | − | 18.0631i | − | 0.0369389i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 574.817 | 1.17071 | 0.585353 | − | 0.810778i | \(-0.300956\pi\) | ||||
0.585353 | + | 0.810778i | \(0.300956\pi\) | |||||||
\(492\) | −522.633 | −1.06226 | ||||||||
\(493\) | − | 178.577i | − | 0.362225i | ||||||
\(494\) | 1204.82 | 2.43890 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2199.38i | − | 4.43424i | ||||||
\(497\) | −116.573 | − | 312.552i | −0.234554 | − | 0.628877i | ||||
\(498\) | 281.321 | 0.564902 | ||||||||
\(499\) | −549.967 | −1.10214 | −0.551070 | − | 0.834459i | \(-0.685780\pi\) | ||||
−0.551070 | + | 0.834459i | \(0.685780\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −131.220 | −0.261916 | ||||||||
\(502\) | 1682.58i | 3.35176i | ||||||||
\(503\) | − | 397.053i | − | 0.789369i | −0.918817 | − | 0.394685i | \(-0.870854\pi\) | ||
0.918817 | − | 0.394685i | \(-0.129146\pi\) | |||||||
\(504\) | 180.785 | + | 484.713i | 0.358701 | + | 0.961733i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −570.949 | −1.12836 | ||||||||
\(507\) | − | 204.478i | − | 0.403309i | ||||||
\(508\) | −451.098 | −0.887989 | ||||||||
\(509\) | 557.813i | 1.09590i | 0.836511 | + | 0.547950i | \(0.184592\pi\) | ||||
−0.836511 | + | 0.547950i | \(0.815408\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −826.174 | + | 308.141i | −1.61678 | + | 0.603015i | ||||
\(512\) | 5.03806 | 0.00983995 | ||||||||
\(513\) | −97.1205 | −0.189319 | ||||||||
\(514\) | − | 1485.45i | − | 2.88999i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 106.064i | 0.205550i | ||||||||
\(517\) | 151.732i | 0.293486i | ||||||||
\(518\) | 267.511 | + | 717.238i | 0.516430 | + | 1.38463i | ||||
\(519\) | 564.377 | 1.08743 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 287.300i | − | 0.551439i | −0.961238 | − | 0.275719i | \(-0.911084\pi\) | ||
0.961238 | − | 0.275719i | \(-0.0889161\pi\) | |||||||
\(522\) | 156.676 | 0.300146 | ||||||||
\(523\) | − | 1012.28i | − | 1.93553i | −0.251853 | − | 0.967766i | \(-0.581040\pi\) | ||
0.251853 | − | 0.967766i | \(-0.418960\pi\) | |||||||
\(524\) | 7.19350i | 0.0137281i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.21211 | 0.0118101 | ||||||||
\(527\) | 552.091 | 1.04761 | ||||||||
\(528\) | 1297.00i | 2.45643i | ||||||||
\(529\) | −421.128 | −0.796084 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 105.504i | 0.198689i | ||||||||
\(532\) | −1284.10 | + | 478.934i | −2.41372 | + | 0.900252i | ||||
\(533\) | −488.051 | −0.915669 | ||||||||
\(534\) | 168.256 | 0.315085 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1169.26 | −2.18145 | ||||||||
\(537\) | − | 53.5575i | − | 0.0997347i | ||||||
\(538\) | − | 1561.18i | − | 2.90182i | ||||||
\(539\) | −535.074 | + | 463.632i | −0.992716 | + | 0.860170i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 526.853 | 0.973851 | 0.486925 | − | 0.873444i | \(-0.338118\pi\) | ||||
0.486925 | + | 0.873444i | \(0.338118\pi\) | |||||||
\(542\) | − | 1788.28i | − | 3.29940i | ||||||
\(543\) | −366.160 | −0.674328 | ||||||||
\(544\) | 1283.19i | 2.35880i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 273.115 | + | 732.265i | 0.500211 | + | 1.34114i | ||||
\(547\) | 250.549 | 0.458042 | 0.229021 | − | 0.973421i | \(-0.426447\pi\) | ||||
0.229021 | + | 0.973421i | \(0.426447\pi\) | |||||||
\(548\) | −798.282 | −1.45672 | ||||||||
\(549\) | − | 205.448i | − | 0.374222i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 256.567i | 0.465640i | ||||||||
\(552\) | − | 443.162i | − | 0.802829i | ||||||
\(553\) | 316.849 | + | 849.522i | 0.572964 | + | 1.53621i | ||||
\(554\) | −1394.70 | −2.51751 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 513.741i | 0.923994i | ||||||||
\(557\) | 64.1496 | 0.115170 | 0.0575849 | − | 0.998341i | \(-0.481660\pi\) | ||||
0.0575849 | + | 0.998341i | \(0.481660\pi\) | |||||||
\(558\) | 484.382i | 0.868069i | ||||||||
\(559\) | 99.0459i | 0.177184i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −325.573 | −0.580344 | ||||||||
\(562\) | 38.4890 | 0.0684857 | ||||||||
\(563\) | 17.3869i | 0.0308826i | 0.999881 | + | 0.0154413i | \(0.00491531\pi\) | ||||
−0.999881 | + | 0.0154413i | \(0.995085\pi\) | |||||||
\(564\) | −190.527 | −0.337814 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 463.767i | − | 0.819376i | ||||||
\(567\) | −22.0158 | − | 59.0280i | −0.0388287 | − | 0.104106i | ||||
\(568\) | 1173.96 | 2.06684 | ||||||||
\(569\) | 174.914 | 0.307405 | 0.153703 | − | 0.988117i | \(-0.450880\pi\) | ||||
0.153703 | + | 0.988117i | \(0.450880\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −376.637 | −0.659609 | −0.329805 | − | 0.944049i | \(-0.606983\pi\) | ||||
−0.329805 | + | 0.944049i | \(0.606983\pi\) | |||||||
\(572\) | 2564.32i | 4.48307i | ||||||||
\(573\) | 194.151i | 0.338832i | ||||||||
\(574\) | 718.799 | − | 268.093i | 1.25226 | − | 0.467060i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −503.909 | −0.874842 | ||||||||
\(577\) | − | 448.775i | − | 0.777773i | −0.921286 | − | 0.388886i | \(-0.872860\pi\) | ||
0.921286 | − | 0.388886i | \(-0.127140\pi\) | |||||||
\(578\) | 455.636 | 0.788297 | ||||||||
\(579\) | 508.429i | 0.878115i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −279.994 | + | 104.430i | −0.481917 | + | 0.179742i | ||||
\(582\) | −189.330 | −0.325310 | ||||||||
\(583\) | −1183.47 | −2.02997 | ||||||||
\(584\) | − | 3103.16i | − | 5.31363i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1114.00i | 1.90102i | ||||||||
\(587\) | − | 275.916i | − | 0.470044i | −0.971990 | − | 0.235022i | \(-0.924484\pi\) | ||
0.971990 | − | 0.235022i | \(-0.0755162\pi\) | |||||||
\(588\) | −582.174 | − | 671.883i | −0.990091 | − | 1.14266i | ||||
\(589\) | −793.207 | −1.34670 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 157.198i | 0.265986i | ||||||||
\(592\) | −1489.64 | −2.51629 | ||||||||
\(593\) | − | 893.938i | − | 1.50748i | −0.657171 | − | 0.753742i | \(-0.728247\pi\) | ||
0.657171 | − | 0.753742i | \(-0.271753\pi\) | |||||||
\(594\) | − | 285.645i | − | 0.480883i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2538.55 | −4.25932 | ||||||||
\(597\) | −674.497 | −1.12981 | ||||||||
\(598\) | − | 669.492i | − | 1.11955i | ||||||
\(599\) | −122.407 | −0.204352 | −0.102176 | − | 0.994766i | \(-0.532581\pi\) | ||||
−0.102176 | + | 0.994766i | \(0.532581\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 594.921i | − | 0.989885i | −0.868926 | − | 0.494943i | \(-0.835189\pi\) | ||
0.868926 | − | 0.494943i | \(-0.164811\pi\) | |||||||
\(602\) | −54.4071 | − | 145.874i | −0.0903773 | − | 0.242316i | ||||
\(603\) | 142.391 | 0.236138 | ||||||||
\(604\) | 1128.20 | 1.86788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −82.1142 | −0.135502 | ||||||||
\(607\) | 539.772i | 0.889246i | 0.895718 | + | 0.444623i | \(0.146662\pi\) | ||||
−0.895718 | + | 0.444623i | \(0.853338\pi\) | |||||||
\(608\) | − | 1843.60i | − | 3.03223i | ||||||
\(609\) | −155.937 | + | 58.1602i | −0.256054 | + | 0.0955012i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −177.920 | −0.291195 | ||||||||
\(612\) | − | 408.816i | − | 0.668000i | ||||||
\(613\) | −1180.07 | −1.92508 | −0.962540 | − | 0.271140i | \(-0.912599\pi\) | ||||
−0.962540 | + | 0.271140i | \(0.912599\pi\) | |||||||
\(614\) | 638.620i | 1.04010i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −870.715 | − | 2334.53i | −1.41350 | − | 3.78982i | ||||
\(617\) | 777.688 | 1.26043 | 0.630217 | − | 0.776419i | \(-0.282966\pi\) | ||||
0.630217 | + | 0.776419i | \(0.282966\pi\) | |||||||
\(618\) | 253.571 | 0.410309 | ||||||||
\(619\) | 285.107i | 0.460592i | 0.973121 | + | 0.230296i | \(0.0739695\pi\) | ||||
−0.973121 | + | 0.230296i | \(0.926030\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 53.9679i | 0.0869048i | ||||||||
\(622\) | − | 1155.60i | − | 1.85789i | ||||||
\(623\) | −167.462 | + | 62.4586i | −0.268799 | + | 0.100255i | ||||
\(624\) | −1520.85 | −2.43726 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 65.4967i | 0.104627i | ||||||||
\(627\) | 467.762 | 0.746031 | ||||||||
\(628\) | 797.863i | 1.27048i | ||||||||
\(629\) | − | 373.931i | − | 0.594485i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 506.946 | 0.803401 | 0.401700 | − | 0.915771i | \(-0.368419\pi\) | ||||
0.401700 | + | 0.915771i | \(0.368419\pi\) | |||||||
\(632\) | −3190.86 | −5.04883 | ||||||||
\(633\) | − | 36.5547i | − | 0.0577483i | ||||||
\(634\) | −315.271 | −0.497273 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 1486.06i | − | 2.33658i | ||||||
\(637\) | −543.652 | − | 627.425i | −0.853457 | − | 0.984969i | ||||
\(638\) | −754.600 | −1.18276 | ||||||||
\(639\) | −142.964 | −0.223731 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 537.896 | 0.839152 | 0.419576 | − | 0.907720i | \(-0.362179\pi\) | ||||
0.419576 | + | 0.907720i | \(0.362179\pi\) | |||||||
\(642\) | 578.571i | 0.901202i | ||||||||
\(643\) | 673.330i | 1.04717i | 0.851973 | + | 0.523585i | \(0.175406\pi\) | ||||
−0.851973 | + | 0.523585i | \(0.824594\pi\) | |||||||
\(644\) | 266.134 | + | 713.547i | 0.413251 | + | 1.10799i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 925.104 | 1.43205 | ||||||||
\(647\) | 1082.21i | 1.67266i | 0.548224 | + | 0.836332i | \(0.315304\pi\) | ||||
−0.548224 | + | 0.836332i | \(0.684696\pi\) | |||||||
\(648\) | 221.713 | 0.342149 | ||||||||
\(649\) | − | 508.138i | − | 0.782956i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −179.809 | − | 482.096i | −0.276204 | − | 0.740547i | ||||
\(652\) | −109.241 | −0.167547 | ||||||||
\(653\) | 491.429 | 0.752571 | 0.376285 | − | 0.926504i | \(-0.377201\pi\) | ||||
0.376285 | + | 0.926504i | \(0.377201\pi\) | |||||||
\(654\) | 856.749i | 1.31001i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1492.88i | 2.27574i | ||||||||
\(657\) | 377.900i | 0.575191i | ||||||||
\(658\) | 262.040 | − | 97.7339i | 0.398237 | − | 0.148532i | ||||
\(659\) | 248.373 | 0.376893 | 0.188447 | − | 0.982083i | \(-0.439655\pi\) | ||||
0.188447 | + | 0.982083i | \(0.439655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 681.545i | 1.03108i | 0.856865 | + | 0.515541i | \(0.172409\pi\) | ||||
−0.856865 | + | 0.515541i | \(0.827591\pi\) | |||||||
\(662\) | −1717.74 | −2.59477 | ||||||||
\(663\) | − | 381.765i | − | 0.575814i | ||||||
\(664\) | − | 1051.67i | − | 1.58385i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 328.072 | 0.492601 | ||||||||
\(667\) | 142.569 | 0.213747 | ||||||||
\(668\) | 793.584i | 1.18800i | ||||||||
\(669\) | −507.559 | −0.758683 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 989.499i | 1.47466i | ||||||||
\(672\) | 1120.50 | − | 417.917i | 1.66741 | − | 0.621900i | ||||
\(673\) | −86.1498 | −0.128009 | −0.0640043 | − | 0.997950i | \(-0.520387\pi\) | ||||
−0.0640043 | + | 0.997950i | \(0.520387\pi\) | |||||||
\(674\) | −776.737 | −1.15243 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1236.63 | −1.82933 | ||||||||
\(677\) | 793.846i | 1.17259i | 0.810096 | + | 0.586297i | \(0.199415\pi\) | ||||
−0.810096 | + | 0.586297i | \(0.800585\pi\) | |||||||
\(678\) | 1045.12i | 1.54147i | ||||||||
\(679\) | 188.437 | − | 70.2819i | 0.277521 | − | 0.103508i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −128.056 | −0.188041 | ||||||||
\(682\) | − | 2332.93i | − | 3.42072i | ||||||
\(683\) | 186.736 | 0.273406 | 0.136703 | − | 0.990612i | \(-0.456349\pi\) | ||||
0.136703 | + | 0.990612i | \(0.456349\pi\) | |||||||
\(684\) | 587.359i | 0.858712i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1145.34 | + | 625.433i | 1.66959 | + | 0.911709i | ||||
\(687\) | −404.461 | −0.588736 | ||||||||
\(688\) | 302.968 | 0.440361 | ||||||||
\(689\) | − | 1387.73i | − | 2.01413i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1030.46i | − | 1.49126i | −0.666361 | − | 0.745630i | \(-0.732149\pi\) | ||
0.666361 | − | 0.745630i | \(-0.267851\pi\) | |||||||
\(692\) | − | 3413.20i | − | 4.93238i | ||||||
\(693\) | 106.035 | + | 284.297i | 0.153009 | + | 0.410240i | ||||
\(694\) | −557.727 | −0.803642 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 585.709i | − | 0.841535i | ||||||
\(697\) | −374.745 | −0.537654 | ||||||||
\(698\) | 43.5450i | 0.0623854i | ||||||||
\(699\) | 667.582i | 0.955054i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1143.88 | −1.63179 | −0.815893 | − | 0.578203i | \(-0.803754\pi\) | ||||
−0.815893 | + | 0.578203i | \(0.803754\pi\) | |||||||
\(702\) | 334.945 | 0.477130 | ||||||||
\(703\) | 537.239i | 0.764210i | ||||||||
\(704\) | 2426.98 | 3.44741 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 676.521i | − | 0.958246i | ||||||
\(707\) | 81.7267 | − | 30.4818i | 0.115596 | − | 0.0431143i | ||||
\(708\) | 638.060 | 0.901214 | ||||||||
\(709\) | −316.757 | −0.446766 | −0.223383 | − | 0.974731i | \(-0.571710\pi\) | ||||
−0.223383 | + | 0.974731i | \(0.571710\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 388.580 | 0.546526 | ||||||||
\(712\) | − | 628.996i | − | 0.883422i | ||||||
\(713\) | 440.769i | 0.618190i | ||||||||
\(714\) | 209.708 | + | 562.261i | 0.293709 | + | 0.787480i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −323.902 | −0.452377 | ||||||||
\(717\) | 705.590i | 0.984087i | ||||||||
\(718\) | 2484.71 | 3.46059 | ||||||||
\(719\) | − | 1145.95i | − | 1.59381i | −0.604104 | − | 0.796906i | \(-0.706469\pi\) | ||
0.604104 | − | 0.796906i | \(-0.293531\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −252.374 | + | 94.1288i | −0.350034 | + | 0.130553i | ||||
\(722\) | 44.3325 | 0.0614024 | ||||||||
\(723\) | −470.799 | −0.651174 | ||||||||
\(724\) | 2214.44i | 3.05862i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 578.389i | 0.796679i | ||||||||
\(727\) | 149.829i | 0.206093i | 0.994677 | + | 0.103046i | \(0.0328590\pi\) | ||||
−0.994677 | + | 0.103046i | \(0.967141\pi\) | |||||||
\(728\) | 2737.45 | − | 1021.00i | 3.76024 | − | 1.40247i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 76.0512i | 0.104037i | ||||||||
\(732\) | −1242.49 | −1.69740 | ||||||||
\(733\) | 70.3231i | 0.0959388i | 0.998849 | + | 0.0479694i | \(0.0152750\pi\) | ||||
−0.998849 | + | 0.0479694i | \(0.984725\pi\) | |||||||
\(734\) | 1775.35i | 2.41873i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1024.45 | −1.39191 | ||||||||
\(737\) | −685.799 | −0.930528 | ||||||||
\(738\) | − | 328.786i | − | 0.445509i | ||||||
\(739\) | 774.145 | 1.04756 | 0.523779 | − | 0.851854i | \(-0.324522\pi\) | ||||
0.523779 | + | 0.851854i | \(0.324522\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 548.495i | 0.740209i | ||||||||
\(742\) | 762.299 | + | 2043.84i | 1.02736 | + | 2.75451i | ||||
\(743\) | −1071.79 | −1.44252 | −0.721260 | − | 0.692665i | \(-0.756437\pi\) | ||||
−0.721260 | + | 0.692665i | \(0.756437\pi\) | |||||||
\(744\) | 1810.78 | 2.43385 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1719.99 | 2.30562 | ||||||||
\(747\) | 128.072i | 0.171448i | ||||||||
\(748\) | 1968.98i | 2.63233i | ||||||||
\(749\) | −214.773 | − | 575.841i | −0.286747 | − | 0.768813i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 361.789 | 0.481742 | 0.240871 | − | 0.970557i | \(-0.422567\pi\) | ||||
0.240871 | + | 0.970557i | \(0.422567\pi\) | |||||||
\(752\) | 544.235i | 0.723717i | ||||||||
\(753\) | −765.999 | −1.01726 | ||||||||
\(754\) | − | 884.839i | − | 1.17353i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −356.986 | + | 133.146i | −0.472203 | + | 0.176119i | ||||
\(757\) | −812.552 | −1.07338 | −0.536692 | − | 0.843778i | \(-0.680326\pi\) | ||||
−0.536692 | + | 0.843778i | \(0.680326\pi\) | |||||||
\(758\) | 1242.12 | 1.63868 | ||||||||
\(759\) | − | 259.926i | − | 0.342458i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 728.812i | − | 0.957703i | −0.877896 | − | 0.478851i | \(-0.841053\pi\) | ||
0.877896 | − | 0.478851i | \(-0.158947\pi\) | |||||||
\(762\) | − | 283.784i | − | 0.372419i | ||||||
\(763\) | −318.036 | − | 852.706i | −0.416824 | − | 1.11757i | ||||
\(764\) | 1174.17 | 1.53688 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 1450.55i | − | 1.89367i | ||||||
\(767\) | 595.840 | 0.776845 | ||||||||
\(768\) | 447.553i | 0.582751i | ||||||||
\(769\) | − | 624.378i | − | 0.811935i | −0.913888 | − | 0.405967i | \(-0.866935\pi\) | ||
0.913888 | − | 0.405967i | \(-0.133065\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 676.255 | 0.877115 | ||||||||
\(772\) | 3074.84 | 3.98296 | ||||||||
\(773\) | − | 34.6106i | − | 0.0447744i | −0.999749 | − | 0.0223872i | \(-0.992873\pi\) | ||
0.999749 | − | 0.0223872i | \(-0.00712666\pi\) | |||||||
\(774\) | −66.7243 | −0.0862071 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 707.781i | 0.912089i | ||||||||
\(777\) | −326.524 | + | 121.785i | −0.420237 | + | 0.156737i | ||||
\(778\) | −261.925 | −0.336665 | ||||||||
\(779\) | 538.408 | 0.691153 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 688.559 | 0.881638 | ||||||||
\(782\) | − | 514.062i | − | 0.657368i | ||||||
\(783\) | 71.3271i | 0.0910946i | ||||||||
\(784\) | −1919.21 | + | 1662.96i | −2.44797 | + | 2.12112i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.52539 | −0.00575750 | ||||||||
\(787\) | − | 563.953i | − | 0.716586i | −0.933609 | − | 0.358293i | \(-0.883359\pi\) | ||
0.933609 | − | 0.358293i | \(-0.116641\pi\) | |||||||
\(788\) | 950.692 | 1.20646 | ||||||||
\(789\) | 2.82807i | 0.00358437i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −387.961 | − | 1040.18i | −0.490469 | − | 1.31502i | ||||
\(792\) | −1067.84 | −1.34828 | ||||||||
\(793\) | −1160.28 | −1.46315 | ||||||||
\(794\) | 1409.72i | 1.77547i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4079.18i | 5.12460i | ||||||||
\(797\) | − | 887.777i | − | 1.11390i | −0.830546 | − | 0.556949i | \(-0.811972\pi\) | ||
0.830546 | − | 0.556949i | \(-0.188028\pi\) | |||||||
\(798\) | −301.295 | − | 807.819i | −0.377562 | − | 1.01230i | ||||
\(799\) | −136.614 | −0.170981 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 76.5986i | 0.0956287i | ||||||||
\(802\) | 34.0540 | 0.0424613 | ||||||||
\(803\) | − | 1820.08i | − | 2.26660i | ||||||
\(804\) | − | 861.145i | − | 1.07108i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2735.58 | 3.39402 | ||||||||
\(807\) | 710.729 | 0.880706 | ||||||||
\(808\) | 306.971i | 0.379914i | ||||||||
\(809\) | −1338.15 | −1.65408 | −0.827041 | − | 0.562142i | \(-0.809977\pi\) | ||||
−0.827041 | + | 0.562142i | \(0.809977\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1002.03i | 1.23555i | 0.786353 | + | 0.617777i | \(0.211967\pi\) | ||||
−0.786353 | + | 0.617777i | \(0.788033\pi\) | |||||||
\(812\) | 351.738 | + | 943.065i | 0.433175 | + | 1.16141i | ||||
\(813\) | 814.115 | 1.00137 | ||||||||
\(814\) | −1580.09 | −1.94115 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1167.77 | −1.43109 | ||||||||
\(817\) | − | 109.265i | − | 0.133740i | ||||||
\(818\) | 240.196i | 0.293638i | ||||||||
\(819\) | −333.365 | + | 124.336i | −0.407039 | + | 0.151814i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −519.980 | −0.633349 | −0.316675 | − | 0.948534i | \(-0.602566\pi\) | ||||
−0.316675 | + | 0.948534i | \(0.602566\pi\) | |||||||
\(822\) | − | 502.195i | − | 0.610943i | ||||||
\(823\) | 35.2676 | 0.0428524 | 0.0214262 | − | 0.999770i | \(-0.493179\pi\) | ||||
0.0214262 | + | 0.999770i | \(0.493179\pi\) | |||||||
\(824\) | − | 947.933i | − | 1.15040i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −877.550 | + | 327.302i | −1.06241 | + | 0.396250i | ||||
\(827\) | 1047.83 | 1.26703 | 0.633514 | − | 0.773731i | \(-0.281612\pi\) | ||||
0.633514 | + | 0.773731i | \(0.281612\pi\) | |||||||
\(828\) | 326.384 | 0.394183 | ||||||||
\(829\) | − | 125.947i | − | 0.151926i | −0.997111 | − | 0.0759632i | \(-0.975797\pi\) | ||
0.997111 | − | 0.0759632i | \(-0.0242031\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 634.939i | − | 0.764067i | ||||||
\(832\) | 2845.86i | 3.42051i | ||||||||
\(833\) | −417.437 | − | 481.761i | −0.501125 | − | 0.578345i | ||||
\(834\) | −323.192 | −0.387520 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 2828.90i | − | 3.38385i | ||||||
\(837\) | −220.516 | −0.263460 | ||||||||
\(838\) | 13.6499i | 0.0162887i | ||||||||
\(839\) | − | 456.709i | − | 0.544349i | −0.962248 | − | 0.272174i | \(-0.912257\pi\) | ||
0.962248 | − | 0.272174i | \(-0.0877427\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −652.572 | −0.775948 | ||||||||
\(842\) | 455.007 | 0.540388 | ||||||||
\(843\) | 17.5222i | 0.0207855i | ||||||||
\(844\) | −221.073 | −0.261935 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 119.860i | − | 0.141678i | ||||||
\(847\) | −214.706 | − | 575.660i | −0.253489 | − | 0.679645i | ||||
\(848\) | −4244.89 | −5.00577 | ||||||||
\(849\) | 211.131 | 0.248681 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 298.533 | 0.350802 | ||||||||
\(852\) | 864.611i | 1.01480i | ||||||||
\(853\) | 815.418i | 0.955941i | 0.878376 | + | 0.477971i | \(0.158627\pi\) | ||||
−0.878376 | + | 0.477971i | \(0.841373\pi\) | |||||||
\(854\) | 1708.85 | − | 637.356i | 2.00100 | − | 0.746319i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2162.90 | 2.52675 | ||||||||
\(857\) | 609.807i | 0.711560i | 0.934570 | + | 0.355780i | \(0.115785\pi\) | ||||
−0.934570 | + | 0.355780i | \(0.884215\pi\) | |||||||
\(858\) | −1613.20 | −1.88018 | ||||||||
\(859\) | 136.971i | 0.159454i | 0.996817 | + | 0.0797272i | \(0.0254049\pi\) | ||||
−0.996817 | + | 0.0797272i | \(0.974595\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 122.050 | + | 327.234i | 0.141753 | + | 0.380063i | ||||
\(862\) | −1538.92 | −1.78529 | ||||||||
\(863\) | −305.240 | −0.353696 | −0.176848 | − | 0.984238i | \(-0.556590\pi\) | ||||
−0.176848 | + | 0.984238i | \(0.556590\pi\) | |||||||
\(864\) | − | 512.529i | − | 0.593205i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 441.657i | − | 0.509996i | ||||||
\(867\) | 207.429i | 0.239249i | ||||||||
\(868\) | −2915.59 | + | 1087.44i | −3.35898 | + | 1.25281i | ||||
\(869\) | −1871.52 | −2.15365 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 804.164i | − | 0.923266i | ||||||
\(872\) | 3202.82 | 3.67296 | ||||||||
\(873\) | − | 86.1929i | − | 0.0987319i | ||||||
\(874\) | 738.570i | 0.845045i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2285.44 | 2.60895 | ||||||||
\(877\) | −621.320 | −0.708461 | −0.354231 | − | 0.935158i | \(-0.615257\pi\) | ||||
−0.354231 | + | 0.935158i | \(0.615257\pi\) | |||||||
\(878\) | 222.258i | 0.253142i | ||||||||
\(879\) | −507.149 | −0.576962 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 739.549i | 0.839443i | 0.907653 | + | 0.419721i | \(0.137872\pi\) | ||||
−0.907653 | + | 0.419721i | \(0.862128\pi\) | |||||||
\(882\) | 422.678 | − | 366.242i | 0.479227 | − | 0.415241i | ||||
\(883\) | −643.821 | −0.729129 | −0.364564 | − | 0.931178i | \(-0.618782\pi\) | ||||
−0.364564 | + | 0.931178i | \(0.618782\pi\) | |||||||
\(884\) | −2308.82 | −2.61178 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1016.97 | −1.14782 | ||||||||
\(887\) | 926.753i | 1.04482i | 0.852695 | + | 0.522409i | \(0.174966\pi\) | ||||
−0.852695 | + | 0.522409i | \(0.825034\pi\) | |||||||
\(888\) | − | 1226.44i | − | 1.38113i | ||||||
\(889\) | 105.344 | + | 282.444i | 0.118497 | + | 0.317710i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 130.040 | 0.145949 | ||||||||
\(892\) | 3069.58i | 3.44124i | ||||||||
\(893\) | 196.278 | 0.219796 | ||||||||
\(894\) | − | 1596.99i | − | 1.78634i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −598.128 | − | 1603.68i | −0.667554 | − | 1.78982i | ||||
\(897\) | 304.787 | 0.339785 | ||||||||
\(898\) | 1127.98 | 1.25610 | ||||||||
\(899\) | 582.546i | 0.647994i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1065.56i | − | 1.18264i | ||||||
\(902\) | 1583.53i | 1.75558i | ||||||||
\(903\) | 66.4094 | − | 24.7689i | 0.0735431 | − | 0.0274296i | ||||
\(904\) | 3907.00 | 4.32190 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 709.744i | 0.783382i | ||||||||
\(907\) | 1540.97 | 1.69898 | 0.849489 | − | 0.527607i | \(-0.176910\pi\) | ||||
0.849489 | + | 0.527607i | \(0.176910\pi\) | |||||||
\(908\) | 774.450i | 0.852919i | ||||||||
\(909\) | − | 37.3826i | − | 0.0411250i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1187.49 | −1.30350 | −0.651748 | − | 0.758435i | \(-0.725964\pi\) | ||||
−0.651748 | + | 0.758435i | \(0.725964\pi\) | |||||||
\(912\) | 1677.77 | 1.83966 | ||||||||
\(913\) | − | 616.833i | − | 0.675611i | ||||||
\(914\) | −46.1312 | −0.0504718 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2446.08i | 2.67039i | ||||||||
\(917\) | 4.50404 | − | 1.67988i | 0.00491171 | − | 0.00183194i | ||||
\(918\) | 257.184 | 0.280157 | ||||||||
\(919\) | 223.009 | 0.242665 | 0.121333 | − | 0.992612i | \(-0.461283\pi\) | ||||
0.121333 | + | 0.992612i | \(0.461283\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −290.733 | −0.315671 | ||||||||
\(922\) | − | 395.479i | − | 0.428936i | ||||||
\(923\) | 807.401i | 0.874757i | ||||||||
\(924\) | 1719.35 | − | 641.272i | 1.86077 | − | 0.694017i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1897.85 | −2.04952 | ||||||||
\(927\) | 115.439i | 0.124529i | ||||||||
\(928\) | −1353.97 | −1.45902 | ||||||||
\(929\) | 1482.17i | 1.59545i | 0.603024 | + | 0.797723i | \(0.293962\pi\) | ||||
−0.603024 | + | 0.797723i | \(0.706038\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 599.746 | + | 692.162i | 0.644195 | + | 0.743461i | ||||
\(932\) | 4037.36 | 4.33194 | ||||||||
\(933\) | 526.091 | 0.563870 | ||||||||
\(934\) | − | 2273.95i | − | 2.43463i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 1252.14i | − | 1.33775i | ||||||
\(937\) | − | 836.508i | − | 0.892751i | −0.894846 | − | 0.446376i | \(-0.852715\pi\) | ||
0.894846 | − | 0.446376i | \(-0.147285\pi\) | |||||||
\(938\) | 441.737 | + | 1184.37i | 0.470935 | + | 1.26265i | ||||
\(939\) | −29.8175 | −0.0317545 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1637.85i | 1.74055i | 0.492569 | + | 0.870273i | \(0.336058\pi\) | ||||
−0.492569 | + | 0.870273i | \(0.663942\pi\) | |||||||
\(942\) | −501.932 | −0.532836 | ||||||||
\(943\) | − | 299.183i | − | 0.317267i | ||||||
\(944\) | − | 1822.60i | − | 1.93072i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 321.364 | 0.339709 | ||||||||
\(947\) | −748.381 | −0.790265 | −0.395133 | − | 0.918624i | \(-0.629301\pi\) | ||||
−0.395133 | + | 0.918624i | \(0.629301\pi\) | |||||||
\(948\) | − | 2350.03i | − | 2.47894i | ||||||
\(949\) | 2134.22 | 2.24891 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 143.528i | − | 0.150923i | ||||||
\(952\) | 2101.92 | − | 783.960i | 2.20790 | − | 0.823487i | ||||
\(953\) | 942.124 | 0.988588 | 0.494294 | − | 0.869295i | \(-0.335427\pi\) | ||||
0.494294 | + | 0.869295i | \(0.335427\pi\) | |||||||
\(954\) | 934.875 | 0.979953 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4267.23 | 4.46362 | ||||||||
\(957\) | − | 343.533i | − | 0.358968i | ||||||
\(958\) | − | 1052.75i | − | 1.09890i | ||||||
\(959\) | 186.421 | + | 499.825i | 0.194391 | + | 0.521194i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −840.008 | −0.874098 | ||||||||
\(962\) | − | 1852.81i | − | 1.92600i | ||||||
\(963\) | −263.396 | −0.273516 | ||||||||
\(964\) | 2847.27i | 2.95360i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −448.889 | + | 167.423i | −0.464688 | + | 0.173316i | ||||
\(967\) | 1654.90 | 1.71138 | 0.855690 | − | 0.517489i | \(-0.173133\pi\) | ||||
0.855690 | + | 0.517489i | \(0.173133\pi\) | |||||||
\(968\) | 2162.21 | 2.23369 | ||||||||
\(969\) | 421.155i | 0.434629i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 354.436i | − | 0.365022i | −0.983204 | − | 0.182511i | \(-0.941578\pi\) | ||
0.983204 | − | 0.182511i | \(-0.0584224\pi\) | |||||||
\(972\) | 163.289i | 0.167993i | ||||||||
\(973\) | 321.666 | − | 119.973i | 0.330592 | − | 0.123302i | ||||
\(974\) | 2064.58 | 2.11969 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3549.14i | 3.63642i | ||||||||
\(977\) | −1726.63 | −1.76727 | −0.883637 | − | 0.468173i | \(-0.844912\pi\) | ||||
−0.883637 | + | 0.468173i | \(0.844912\pi\) | |||||||
\(978\) | − | 68.7229i | − | 0.0702688i | ||||||
\(979\) | − | 368.922i | − | 0.376836i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −390.037 | −0.397591 | ||||||||
\(982\) | 2186.95 | 2.22704 | ||||||||
\(983\) | − | 1635.34i | − | 1.66362i | −0.555062 | − | 0.831809i | \(-0.687306\pi\) | ||
0.555062 | − | 0.831809i | \(-0.312694\pi\) | |||||||
\(984\) | −1229.11 | −1.24910 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 679.414i | − | 0.689061i | ||||||
\(987\) | 44.4935 | + | 119.294i | 0.0450795 | + | 0.120865i | ||||
\(988\) | 3317.15 | 3.35744 | ||||||||
\(989\) | −60.7165 | −0.0613919 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −313.579 | −0.316427 | −0.158213 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158213 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(992\) | − | 4185.95i | − | 4.21971i | ||||||
\(993\) | − | 782.004i | − | 0.787517i | ||||||
\(994\) | −443.515 | − | 1189.13i | −0.446192 | − | 1.19631i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 774.546 | 0.777656 | ||||||||
\(997\) | − | 17.3708i | − | 0.0174231i | −0.999962 | − | 0.00871155i | \(-0.997227\pi\) | ||
0.999962 | − | 0.00871155i | \(-0.00277301\pi\) | |||||||
\(998\) | −2092.41 | −2.09660 | ||||||||
\(999\) | 149.355i | 0.149505i |
(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 | 525.3.h.d.76.12 | 12 | ||
5.2 | odd | 4 | 525.3.e.c.349.4 | 24 | |||
5.3 | odd | 4 | 525.3.e.c.349.11 | 24 | |||
5.4 | even | 2 | 105.3.h.a.76.1 | ✓ | 12 | ||
7.6 | odd | 2 | inner | 525.3.h.d.76.11 | 12 | ||
15.14 | odd | 2 | 315.3.h.d.181.12 | 12 | |||
20.19 | odd | 2 | 1680.3.s.c.1441.8 | 12 | |||
35.13 | even | 4 | 525.3.e.c.349.3 | 24 | |||
35.27 | even | 4 | 525.3.e.c.349.12 | 24 | |||
35.34 | odd | 2 | 105.3.h.a.76.2 | yes | 12 | ||
105.104 | even | 2 | 315.3.h.d.181.11 | 12 | |||
140.139 | even | 2 | 1680.3.s.c.1441.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.h.a.76.1 | ✓ | 12 | 5.4 | even | 2 | ||
105.3.h.a.76.2 | yes | 12 | 35.34 | odd | 2 | ||
315.3.h.d.181.11 | 12 | 105.104 | even | 2 | |||
315.3.h.d.181.12 | 12 | 15.14 | odd | 2 | |||
525.3.e.c.349.3 | 24 | 35.13 | even | 4 | |||
525.3.e.c.349.4 | 24 | 5.2 | odd | 4 | |||
525.3.e.c.349.11 | 24 | 5.3 | odd | 4 | |||
525.3.e.c.349.12 | 24 | 35.27 | even | 4 | |||
525.3.h.d.76.11 | 12 | 7.6 | odd | 2 | inner | ||
525.3.h.d.76.12 | 12 | 1.1 | even | 1 | trivial | ||
1680.3.s.c.1441.5 | 12 | 140.139 | even | 2 | |||
1680.3.s.c.1441.8 | 12 | 20.19 | odd | 2 |