Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(274,525)]
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, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.274");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Root | \(1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.4.d.i.274.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.56155i | 1.96631i | 0.182785 | + | 0.983153i | \(0.441489\pi\) | ||||
−0.182785 | + | 0.983153i | \(0.558511\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | −22.9309 | −2.86636 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 16.6847 | 1.13525 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | − 83.0388i | − 3.66983i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −33.6155 | −0.921406 | −0.460703 | − | 0.887554i | \(-0.652403\pi\) | ||||
−0.460703 | + | 0.887554i | \(0.652403\pi\) | |||||||
\(12\) | 68.7926i | 1.65489i | ||||||||
\(13\) | − 38.3542i | − 0.818272i | −0.912474 | − | 0.409136i | \(-0.865830\pi\) | ||||
0.912474 | − | 0.409136i | \(-0.134170\pi\) | |||||||
\(14\) | −38.9309 | −0.743194 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 278.378 | 4.34965 | ||||||||
\(17\) | − 65.7235i | − 0.937664i | −0.883287 | − | 0.468832i | \(-0.844675\pi\) | ||||
0.883287 | − | 0.468832i | \(-0.155325\pi\) | |||||||
\(18\) | − 50.0540i | − 0.655435i | ||||||||
\(19\) | −33.3996 | −0.403284 | −0.201642 | − | 0.979459i | \(-0.564628\pi\) | ||||
−0.201642 | + | 0.979459i | \(0.564628\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | − 186.955i | − 1.81177i | ||||||||
\(23\) | 207.447i | 1.88068i | 0.340234 | + | 0.940341i | \(0.389494\pi\) | ||||
−0.340234 | + | 0.940341i | \(0.610506\pi\) | |||||||
\(24\) | −249.116 | −2.11878 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 213.309 | 1.60897 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | − 160.516i | − 1.08338i | ||||||||
\(29\) | 189.170 | 1.21131 | 0.605656 | − | 0.795726i | \(-0.292911\pi\) | ||||
0.605656 | + | 0.795726i | \(0.292911\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 202.108 | 1.17096 | 0.585478 | − | 0.810688i | \(-0.300907\pi\) | ||||
0.585478 | + | 0.810688i | \(0.300907\pi\) | |||||||
\(32\) | 883.902i | 4.88292i | ||||||||
\(33\) | 100.847i | 0.531974i | ||||||||
\(34\) | 365.525 | 1.84373 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 206.378 | 0.955453 | ||||||||
\(37\) | 16.5227i | 0.0734141i | 0.999326 | + | 0.0367070i | \(0.0116868\pi\) | ||||
−0.999326 | + | 0.0367070i | \(0.988313\pi\) | |||||||
\(38\) | − 185.754i | − 0.792980i | ||||||||
\(39\) | −115.062 | −0.472429 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 388.617 | 1.48029 | 0.740144 | − | 0.672448i | \(-0.234757\pi\) | ||||
0.740144 | + | 0.672448i | \(0.234757\pi\) | |||||||
\(42\) | 116.793i | 0.429083i | ||||||||
\(43\) | 41.8144i | 0.148294i | 0.997247 | + | 0.0741469i | \(0.0236234\pi\) | ||||
−0.997247 | + | 0.0741469i | \(0.976377\pi\) | |||||||
\(44\) | 770.833 | 2.64108 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1153.73 | −3.69800 | ||||||||
\(47\) | − 368.648i | − 1.14410i | −0.820218 | − | 0.572051i | \(-0.806148\pi\) | ||||
0.820218 | − | 0.572051i | \(-0.193852\pi\) | |||||||
\(48\) | − 835.133i | − 2.51127i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −197.170 | −0.541360 | ||||||||
\(52\) | 879.494i | 2.34546i | ||||||||
\(53\) | 458.172i | 1.18745i | 0.804668 | + | 0.593725i | \(0.202343\pi\) | ||||
−0.804668 | + | 0.593725i | \(0.797657\pi\) | |||||||
\(54\) | −150.162 | −0.378416 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 581.272 | 1.38707 | ||||||||
\(57\) | 100.199i | 0.232836i | ||||||||
\(58\) | 1052.08i | 2.38181i | ||||||||
\(59\) | −256.216 | −0.565364 | −0.282682 | − | 0.959214i | \(-0.591224\pi\) | ||||
−0.282682 | + | 0.959214i | \(0.591224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −123.511 | −0.259246 | −0.129623 | − | 0.991563i | \(-0.541377\pi\) | ||||
−0.129623 | + | 0.991563i | \(0.541377\pi\) | |||||||
\(62\) | 1124.03i | 2.30246i | ||||||||
\(63\) | − 63.0000i | − 0.125988i | ||||||||
\(64\) | −2688.85 | −5.25166 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −560.864 | −1.04602 | ||||||||
\(67\) | 336.277i | 0.613175i | 0.951843 | + | 0.306587i | \(0.0991872\pi\) | ||||
−0.951843 | + | 0.306587i | \(0.900813\pi\) | |||||||
\(68\) | 1507.10i | 2.68768i | ||||||||
\(69\) | 622.341 | 1.08581 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −453.312 | −0.757722 | −0.378861 | − | 0.925454i | \(-0.623684\pi\) | ||||
−0.378861 | + | 0.925454i | \(0.623684\pi\) | |||||||
\(72\) | 747.349i | 1.22328i | ||||||||
\(73\) | 22.0436i | 0.0353426i | 0.999844 | + | 0.0176713i | \(0.00562524\pi\) | ||||
−0.999844 | + | 0.0176713i | \(0.994375\pi\) | |||||||
\(74\) | −91.8920 | −0.144355 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 765.882 | 1.15596 | ||||||||
\(77\) | − 235.309i | − 0.348259i | ||||||||
\(78\) | − 639.926i | − 0.928941i | ||||||||
\(79\) | −385.417 | −0.548896 | −0.274448 | − | 0.961602i | \(-0.588495\pi\) | ||||
−0.274448 | + | 0.961602i | \(0.588495\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 2161.32i | 2.91070i | ||||||||
\(83\) | 23.7501i | 0.0314085i | 0.999877 | + | 0.0157043i | \(0.00499903\pi\) | ||||
−0.999877 | + | 0.0157043i | \(0.995001\pi\) | |||||||
\(84\) | −481.548 | −0.625491 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −232.553 | −0.291591 | ||||||||
\(87\) | − 567.511i | − 0.699352i | ||||||||
\(88\) | 2791.39i | 3.38140i | ||||||||
\(89\) | 1482.81 | 1.76604 | 0.883020 | − | 0.469335i | \(-0.155506\pi\) | ||||
0.883020 | + | 0.469335i | \(0.155506\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 268.479 | 0.309278 | ||||||||
\(92\) | − 4756.94i | − 5.39071i | ||||||||
\(93\) | − 606.324i | − 0.676052i | ||||||||
\(94\) | 2050.25 | 2.24965 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2651.71 | 2.81915 | ||||||||
\(97\) | − 51.9867i | − 0.0544170i | −0.999630 | − | 0.0272085i | \(-0.991338\pi\) | ||||
0.999630 | − | 0.0272085i | \(-0.00866181\pi\) | |||||||
\(98\) | − 272.516i | − 0.280901i | ||||||||
\(99\) | 302.540 | 0.307135 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1429.30 | 1.40812 | 0.704062 | − | 0.710138i | \(-0.251368\pi\) | ||||
0.704062 | + | 0.710138i | \(0.251368\pi\) | |||||||
\(102\) | − 1096.57i | − 1.06448i | ||||||||
\(103\) | 434.212i | 0.415381i | 0.978195 | + | 0.207690i | \(0.0665946\pi\) | ||||
−0.978195 | + | 0.207690i | \(0.933405\pi\) | |||||||
\(104\) | −3184.88 | −3.00292 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2548.15 | −2.33489 | ||||||||
\(107\) | − 666.307i | − 0.602003i | −0.953624 | − | 0.301001i | \(-0.902679\pi\) | ||||
0.953624 | − | 0.301001i | \(-0.0973209\pi\) | |||||||
\(108\) | − 619.133i | − 0.551631i | ||||||||
\(109\) | 1199.51 | 1.05406 | 0.527029 | − | 0.849847i | \(-0.323306\pi\) | ||||
0.527029 | + | 0.849847i | \(0.323306\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 49.5682 | 0.0423856 | ||||||||
\(112\) | 1948.64i | 1.64401i | ||||||||
\(113\) | − 81.5171i | − 0.0678627i | −0.999424 | − | 0.0339314i | \(-0.989197\pi\) | ||||
0.999424 | − | 0.0339314i | \(-0.0108028\pi\) | |||||||
\(114\) | −557.261 | −0.457827 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4337.84 | −3.47206 | ||||||||
\(117\) | 345.187i | 0.272757i | ||||||||
\(118\) | − 1424.96i | − 1.11168i | ||||||||
\(119\) | 460.064 | 0.354404 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −200.996 | −0.151011 | ||||||||
\(122\) | − 686.915i | − 0.509757i | ||||||||
\(123\) | − 1165.85i | − 0.854645i | ||||||||
\(124\) | −4634.51 | −3.35638 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 350.378 | 0.247731 | ||||||||
\(127\) | 336.985i | 0.235453i | 0.993046 | + | 0.117727i | \(0.0375607\pi\) | ||||
−0.993046 | + | 0.117727i | \(0.962439\pi\) | |||||||
\(128\) | − 7882.95i | − 5.44344i | ||||||||
\(129\) | 125.443 | 0.0856175 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2931.15 | 1.95493 | 0.977465 | − | 0.211097i | \(-0.0677035\pi\) | ||||
0.977465 | + | 0.211097i | \(0.0677035\pi\) | |||||||
\(132\) | − 2312.50i | − 1.52483i | ||||||||
\(133\) | − 233.797i | − 0.152427i | ||||||||
\(134\) | −1870.22 | −1.20569 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5457.60 | −3.44107 | ||||||||
\(137\) | 1585.07i | 0.988477i | 0.869326 | + | 0.494238i | \(0.164553\pi\) | ||||
−0.869326 | + | 0.494238i | \(0.835447\pi\) | |||||||
\(138\) | 3461.18i | 2.13504i | ||||||||
\(139\) | 1298.85 | 0.792569 | 0.396284 | − | 0.918128i | \(-0.370299\pi\) | ||||
0.396284 | + | 0.918128i | \(0.370299\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1105.94 | −0.660548 | ||||||||
\(142\) | − 2521.12i | − 1.48991i | ||||||||
\(143\) | 1289.30i | 0.753960i | ||||||||
\(144\) | −2505.40 | −1.44988 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −122.597 | −0.0694943 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | − 378.881i | − 0.210431i | ||||||||
\(149\) | 2003.29 | 1.10145 | 0.550724 | − | 0.834687i | \(-0.314352\pi\) | ||||
0.550724 | + | 0.834687i | \(0.314352\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2740.96 | 1.47719 | 0.738596 | − | 0.674148i | \(-0.235489\pi\) | ||||
0.738596 | + | 0.674148i | \(0.235489\pi\) | |||||||
\(152\) | 2773.47i | 1.47999i | ||||||||
\(153\) | 591.511i | 0.312555i | ||||||||
\(154\) | 1308.68 | 0.684783 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2638.48 | 1.35415 | ||||||||
\(157\) | − 3644.22i | − 1.85249i | −0.376928 | − | 0.926243i | \(-0.623019\pi\) | ||||
0.376928 | − | 0.926243i | \(-0.376981\pi\) | |||||||
\(158\) | − 2143.52i | − 1.07930i | ||||||||
\(159\) | 1374.52 | 0.685574 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1452.13 | −0.710831 | ||||||||
\(162\) | 450.486i | 0.218478i | ||||||||
\(163\) | 2774.27i | 1.33311i | 0.745454 | + | 0.666557i | \(0.232233\pi\) | ||||
−0.745454 | + | 0.666557i | \(0.767767\pi\) | |||||||
\(164\) | −8911.33 | −4.24304 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −132.087 | −0.0617588 | ||||||||
\(167\) | − 1154.91i | − 0.535149i | −0.963537 | − | 0.267574i | \(-0.913778\pi\) | ||||
0.963537 | − | 0.267574i | \(-0.0862221\pi\) | |||||||
\(168\) | − 1743.82i | − 0.800823i | ||||||||
\(169\) | 725.958 | 0.330432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 300.597 | 0.134428 | ||||||||
\(172\) | − 958.841i | − 0.425064i | ||||||||
\(173\) | − 3387.46i | − 1.48869i | −0.667794 | − | 0.744346i | \(-0.732761\pi\) | ||||
0.667794 | − | 0.744346i | \(-0.267239\pi\) | |||||||
\(174\) | 3156.24 | 1.37514 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9357.82 | −4.00780 | ||||||||
\(177\) | 768.648i | 0.326413i | ||||||||
\(178\) | 8246.73i | 3.47258i | ||||||||
\(179\) | −1603.32 | −0.669486 | −0.334743 | − | 0.942309i | \(-0.608650\pi\) | ||||
−0.334743 | + | 0.942309i | \(0.608650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 544.220 | 0.223489 | 0.111745 | − | 0.993737i | \(-0.464356\pi\) | ||||
0.111745 | + | 0.993737i | \(0.464356\pi\) | |||||||
\(182\) | 1493.16i | 0.608134i | ||||||||
\(183\) | 370.534i | 0.149676i | ||||||||
\(184\) | 17226.2 | 6.90179 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3372.10 | 1.32933 | ||||||||
\(187\) | 2209.33i | 0.863969i | ||||||||
\(188\) | 8453.41i | 3.27941i | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2993.44 | 1.13402 | 0.567010 | − | 0.823711i | \(-0.308100\pi\) | ||||
0.567010 | + | 0.823711i | \(0.308100\pi\) | |||||||
\(192\) | 8066.54i | 3.03204i | ||||||||
\(193\) | 1309.32i | 0.488325i | 0.969734 | + | 0.244163i | \(0.0785131\pi\) | ||||
−0.969734 | + | 0.244163i | \(0.921487\pi\) | |||||||
\(194\) | 289.127 | 0.107001 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1123.61 | 0.409480 | ||||||||
\(197\) | 1141.38i | 0.412790i | 0.978469 | + | 0.206395i | \(0.0661733\pi\) | ||||
−0.978469 | + | 0.206395i | \(0.933827\pi\) | |||||||
\(198\) | 1682.59i | 0.603922i | ||||||||
\(199\) | −2370.23 | −0.844327 | −0.422164 | − | 0.906520i | \(-0.638729\pi\) | ||||
−0.422164 | + | 0.906520i | \(0.638729\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1008.83 | 0.354017 | ||||||||
\(202\) | 7949.12i | 2.76880i | ||||||||
\(203\) | 1324.19i | 0.457833i | ||||||||
\(204\) | 4521.29 | 1.55173 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2414.89 | −0.816765 | ||||||||
\(207\) | − 1867.02i | − 0.626894i | ||||||||
\(208\) | − 10676.9i | − 3.55920i | ||||||||
\(209\) | 1122.75 | 0.371588 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −687.159 | −0.224199 | −0.112099 | − | 0.993697i | \(-0.535758\pi\) | ||||
−0.112099 | + | 0.993697i | \(0.535758\pi\) | |||||||
\(212\) | − 10506.3i | − 3.40366i | ||||||||
\(213\) | 1359.94i | 0.437471i | ||||||||
\(214\) | 3705.70 | 1.18372 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2242.05 | 0.706260 | ||||||||
\(217\) | 1414.76i | 0.442580i | ||||||||
\(218\) | 6671.15i | 2.07260i | ||||||||
\(219\) | 66.1308 | 0.0204050 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2520.77 | −0.767264 | ||||||||
\(222\) | 275.676i | 0.0833431i | ||||||||
\(223\) | 990.496i | 0.297437i | 0.988880 | + | 0.148719i | \(0.0475149\pi\) | ||||
−0.988880 | + | 0.148719i | \(0.952485\pi\) | |||||||
\(224\) | −6187.32 | −1.84557 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 453.362 | 0.133439 | ||||||||
\(227\) | − 1479.25i | − 0.432517i | −0.976336 | − | 0.216258i | \(-0.930615\pi\) | ||||
0.976336 | − | 0.216258i | \(-0.0693853\pi\) | |||||||
\(228\) | − 2297.65i | − 0.667392i | ||||||||
\(229\) | −6704.47 | −1.93469 | −0.967345 | − | 0.253463i | \(-0.918430\pi\) | ||||
−0.967345 | + | 0.253463i | \(0.918430\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −705.926 | −0.201067 | ||||||||
\(232\) | − 15708.5i | − 4.44531i | ||||||||
\(233\) | − 1749.09i | − 0.491789i | −0.969297 | − | 0.245895i | \(-0.920918\pi\) | ||||
0.969297 | − | 0.245895i | \(-0.0790817\pi\) | |||||||
\(234\) | −1919.78 | −0.536324 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5875.25 | 1.62054 | ||||||||
\(237\) | 1156.25i | 0.316905i | ||||||||
\(238\) | 2558.67i | 0.696866i | ||||||||
\(239\) | 6320.89 | 1.71073 | 0.855365 | − | 0.518027i | \(-0.173333\pi\) | ||||
0.855365 | + | 0.518027i | \(0.173333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3359.62 | 0.897975 | 0.448988 | − | 0.893538i | \(-0.351785\pi\) | ||||
0.448988 | + | 0.893538i | \(0.351785\pi\) | |||||||
\(242\) | − 1117.85i | − 0.296935i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 2832.22 | 0.743092 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6483.95 | 1.68049 | ||||||||
\(247\) | 1281.01i | 0.329996i | ||||||||
\(248\) | − 16782.8i | − 4.29721i | ||||||||
\(249\) | 71.2502 | 0.0181337 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1330.50 | −0.334582 | −0.167291 | − | 0.985908i | \(-0.553502\pi\) | ||||
−0.167291 | + | 0.985908i | \(0.553502\pi\) | |||||||
\(252\) | 1444.64i | 0.361127i | ||||||||
\(253\) | − 6973.44i | − 1.73287i | ||||||||
\(254\) | −1874.16 | −0.462973 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 22330.6 | 5.45182 | ||||||||
\(257\) | 2476.95i | 0.601197i | 0.953751 | + | 0.300599i | \(0.0971865\pi\) | ||||
−0.953751 | + | 0.300599i | \(0.902814\pi\) | |||||||
\(258\) | 697.659i | 0.168350i | ||||||||
\(259\) | −115.659 | −0.0277479 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1702.53 | −0.403771 | ||||||||
\(262\) | 16301.8i | 3.84399i | ||||||||
\(263\) | − 5152.56i | − 1.20806i | −0.796960 | − | 0.604032i | \(-0.793560\pi\) | ||||
0.796960 | − | 0.604032i | \(-0.206440\pi\) | |||||||
\(264\) | 8374.18 | 1.95225 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1300.28 | 0.299718 | ||||||||
\(267\) | − 4448.43i | − 1.01962i | ||||||||
\(268\) | − 7711.11i | − 1.75758i | ||||||||
\(269\) | 1150.97 | 0.260876 | 0.130438 | − | 0.991456i | \(-0.458362\pi\) | ||||
0.130438 | + | 0.991456i | \(0.458362\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1838.32 | 0.412067 | 0.206034 | − | 0.978545i | \(-0.433944\pi\) | ||||
0.206034 | + | 0.978545i | \(0.433944\pi\) | |||||||
\(272\) | − 18296.0i | − 4.07851i | ||||||||
\(273\) | − 805.437i | − 0.178561i | ||||||||
\(274\) | −8815.43 | −1.94365 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14270.8 | −3.11233 | ||||||||
\(277\) | − 568.447i | − 0.123302i | −0.998098 | − | 0.0616510i | \(-0.980363\pi\) | ||||
0.998098 | − | 0.0616510i | \(-0.0196366\pi\) | |||||||
\(278\) | 7223.62i | 1.55843i | ||||||||
\(279\) | −1818.97 | −0.390319 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6015.00 | 1.27696 | 0.638479 | − | 0.769640i | \(-0.279564\pi\) | ||||
0.638479 | + | 0.769640i | \(0.279564\pi\) | |||||||
\(282\) | − 6150.76i | − 1.29884i | ||||||||
\(283\) | 3985.75i | 0.837202i | 0.908170 | + | 0.418601i | \(0.137479\pi\) | ||||
−0.908170 | + | 0.418601i | \(0.862521\pi\) | |||||||
\(284\) | 10394.8 | 2.17190 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7170.48 | −1.48252 | ||||||||
\(287\) | 2720.32i | 0.559497i | ||||||||
\(288\) | − 7955.12i | − 1.62764i | ||||||||
\(289\) | 593.424 | 0.120787 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −155.960 | −0.0314177 | ||||||||
\(292\) | − 505.479i | − 0.101305i | ||||||||
\(293\) | − 2490.01i | − 0.496478i | −0.968699 | − | 0.248239i | \(-0.920148\pi\) | ||||
0.968699 | − | 0.248239i | \(-0.0798518\pi\) | |||||||
\(294\) | −817.548 | −0.162178 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1372.03 | 0.269417 | ||||||||
\(297\) | − 907.619i | − 0.177325i | ||||||||
\(298\) | 11141.4i | 2.16578i | ||||||||
\(299\) | 7956.45 | 1.53891 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −292.701 | −0.0560498 | ||||||||
\(302\) | 15244.0i | 2.90461i | ||||||||
\(303\) | − 4287.90i | − 0.812981i | ||||||||
\(304\) | −9297.72 | −1.75415 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3289.72 | −0.614578 | ||||||||
\(307\) | 141.853i | 0.0263712i | 0.999913 | + | 0.0131856i | \(0.00419723\pi\) | ||||
−0.999913 | + | 0.0131856i | \(0.995803\pi\) | |||||||
\(308\) | 5395.83i | 0.998234i | ||||||||
\(309\) | 1302.64 | 0.239820 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2091.92 | 0.381420 | 0.190710 | − | 0.981646i | \(-0.438921\pi\) | ||||
0.190710 | + | 0.981646i | \(0.438921\pi\) | |||||||
\(312\) | 9554.65i | 1.73374i | ||||||||
\(313\) | 5521.44i | 0.997094i | 0.866863 | + | 0.498547i | \(0.166133\pi\) | ||||
−0.866863 | + | 0.498547i | \(0.833867\pi\) | |||||||
\(314\) | 20267.5 | 3.64255 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8837.94 | 1.57333 | ||||||||
\(317\) | − 5351.63i | − 0.948195i | −0.880472 | − | 0.474097i | \(-0.842774\pi\) | ||||
0.880472 | − | 0.474097i | \(-0.157226\pi\) | |||||||
\(318\) | 7644.45i | 1.34805i | ||||||||
\(319\) | −6359.06 | −1.11611 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1998.92 | −0.347567 | ||||||||
\(322\) | − 8076.09i | − 1.39771i | ||||||||
\(323\) | 2195.14i | 0.378145i | ||||||||
\(324\) | −1857.40 | −0.318484 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15429.2 | −2.62131 | ||||||||
\(327\) | − 3598.53i | − 0.608561i | ||||||||
\(328\) | − 32270.3i | − 5.43241i | ||||||||
\(329\) | 2580.53 | 0.432430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4383.52 | −0.727916 | −0.363958 | − | 0.931415i | \(-0.618575\pi\) | ||||
−0.363958 | + | 0.931415i | \(0.618575\pi\) | |||||||
\(332\) | − 544.609i | − 0.0900281i | ||||||||
\(333\) | − 148.705i | − 0.0244714i | ||||||||
\(334\) | 6423.11 | 1.05227 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5845.93 | 0.949172 | ||||||||
\(337\) | 7124.57i | 1.15163i | 0.817579 | + | 0.575817i | \(0.195316\pi\) | ||||
−0.817579 | + | 0.575817i | \(0.804684\pi\) | |||||||
\(338\) | 4037.46i | 0.649730i | ||||||||
\(339\) | −244.551 | −0.0391806 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6793.97 | −1.07893 | ||||||||
\(342\) | 1671.78i | 0.264327i | ||||||||
\(343\) | − 343.000i | − 0.0539949i | ||||||||
\(344\) | 3472.22 | 0.544214 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18839.5 | 2.92722 | ||||||||
\(347\) | − 507.743i | − 0.0785506i | −0.999228 | − | 0.0392753i | \(-0.987495\pi\) | ||||
0.999228 | − | 0.0392753i | \(-0.0125049\pi\) | |||||||
\(348\) | 13013.5i | 2.00459i | ||||||||
\(349\) | −6155.14 | −0.944060 | −0.472030 | − | 0.881582i | \(-0.656479\pi\) | ||||
−0.472030 | + | 0.881582i | \(0.656479\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1035.56 | 0.157476 | ||||||||
\(352\) | − 29712.8i | − 4.49915i | ||||||||
\(353\) | − 6429.56i | − 0.969437i | −0.874670 | − | 0.484718i | \(-0.838922\pi\) | ||||
0.874670 | − | 0.484718i | \(-0.161078\pi\) | |||||||
\(354\) | −4274.87 | −0.641828 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −34002.1 | −5.06211 | ||||||||
\(357\) | − 1380.19i | − 0.204615i | ||||||||
\(358\) | − 8916.97i | − 1.31641i | ||||||||
\(359\) | −10075.4 | −1.48123 | −0.740614 | − | 0.671931i | \(-0.765465\pi\) | ||||
−0.740614 | + | 0.671931i | \(0.765465\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5743.46 | −0.837362 | ||||||||
\(362\) | 3026.71i | 0.439448i | ||||||||
\(363\) | 602.989i | 0.0871865i | ||||||||
\(364\) | −6156.46 | −0.886501 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2060.74 | −0.294308 | ||||||||
\(367\) | − 816.898i | − 0.116190i | −0.998311 | − | 0.0580950i | \(-0.981497\pi\) | ||||
0.998311 | − | 0.0580950i | \(-0.0185026\pi\) | |||||||
\(368\) | 57748.6i | 8.18031i | ||||||||
\(369\) | −3497.56 | −0.493430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3207.21 | −0.448814 | ||||||||
\(372\) | 13903.5i | 1.93781i | ||||||||
\(373\) | − 3737.85i | − 0.518870i | −0.965761 | − | 0.259435i | \(-0.916464\pi\) | ||||
0.965761 | − | 0.259435i | \(-0.0835364\pi\) | |||||||
\(374\) | −12287.3 | −1.69883 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −30612.1 | −4.19866 | ||||||||
\(377\) | − 7255.47i | − 0.991183i | ||||||||
\(378\) | − 1051.13i | − 0.143028i | ||||||||
\(379\) | −1950.47 | −0.264351 | −0.132176 | − | 0.991226i | \(-0.542196\pi\) | ||||
−0.132176 | + | 0.991226i | \(0.542196\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1010.95 | 0.135939 | ||||||||
\(382\) | 16648.2i | 2.22983i | ||||||||
\(383\) | 6762.06i | 0.902155i | 0.892485 | + | 0.451077i | \(0.148960\pi\) | ||||
−0.892485 | + | 0.451077i | \(0.851040\pi\) | |||||||
\(384\) | −23648.8 | −3.14277 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7281.84 | −0.960197 | ||||||||
\(387\) | − 376.330i | − 0.0494313i | ||||||||
\(388\) | 1192.10i | 0.155979i | ||||||||
\(389\) | 2551.98 | 0.332624 | 0.166312 | − | 0.986073i | \(-0.446814\pi\) | ||||
0.166312 | + | 0.986073i | \(0.446814\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13634.1 | 1.76345 | ||||||||
\(392\) | 4068.90i | 0.524262i | ||||||||
\(393\) | − 8793.45i | − 1.12868i | ||||||||
\(394\) | −6347.83 | −0.811672 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6937.50 | −0.880360 | ||||||||
\(397\) | 4097.93i | 0.518058i | 0.965869 | + | 0.259029i | \(0.0834026\pi\) | ||||
−0.965869 | + | 0.259029i | \(0.916597\pi\) | |||||||
\(398\) | − 13182.2i | − 1.66021i | ||||||||
\(399\) | −701.392 | −0.0880038 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1046.81 | −0.130362 | −0.0651811 | − | 0.997873i | \(-0.520762\pi\) | ||||
−0.0651811 | + | 0.997873i | \(0.520762\pi\) | |||||||
\(402\) | 5610.66i | 0.696105i | ||||||||
\(403\) | − 7751.68i | − 0.958161i | ||||||||
\(404\) | −32775.1 | −4.03619 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7364.57 | −0.900240 | ||||||||
\(407\) | − 555.420i | − 0.0676441i | ||||||||
\(408\) | 16372.8i | 1.98670i | ||||||||
\(409\) | −6516.92 | −0.787876 | −0.393938 | − | 0.919137i | \(-0.628887\pi\) | ||||
−0.393938 | + | 0.919137i | \(0.628887\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4755.20 | 0.570697 | ||||||||
\(412\) | − 9956.86i | − 1.19063i | ||||||||
\(413\) | − 1793.51i | − 0.213687i | ||||||||
\(414\) | 10383.5 | 1.23267 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 33901.3 | 3.99555 | ||||||||
\(417\) | − 3896.55i | − 0.457590i | ||||||||
\(418\) | 6244.21i | 0.730656i | ||||||||
\(419\) | −12279.1 | −1.43168 | −0.715838 | − | 0.698267i | \(-0.753955\pi\) | ||||
−0.715838 | + | 0.698267i | \(0.753955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10146.9 | 1.17465 | 0.587325 | − | 0.809351i | \(-0.300181\pi\) | ||||
0.587325 | + | 0.809351i | \(0.300181\pi\) | |||||||
\(422\) | − 3821.67i | − 0.440844i | ||||||||
\(423\) | 3317.83i | 0.381367i | ||||||||
\(424\) | 38046.1 | 4.35774 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7563.36 | −0.860202 | ||||||||
\(427\) | − 864.579i | − 0.0979858i | ||||||||
\(428\) | 15279.0i | 1.72556i | ||||||||
\(429\) | 3867.89 | 0.435299 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7059.04 | 0.788914 | 0.394457 | − | 0.918914i | \(-0.370933\pi\) | ||||
0.394457 | + | 0.918914i | \(0.370933\pi\) | |||||||
\(432\) | 7516.20i | 0.837091i | ||||||||
\(433\) | 6468.98i | 0.717966i | 0.933344 | + | 0.358983i | \(0.116876\pi\) | ||||
−0.933344 | + | 0.358983i | \(0.883124\pi\) | |||||||
\(434\) | −7868.24 | −0.870248 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27505.8 | −3.02131 | ||||||||
\(437\) | − 6928.65i | − 0.758449i | ||||||||
\(438\) | 367.790i | 0.0401226i | ||||||||
\(439\) | −4767.13 | −0.518275 | −0.259137 | − | 0.965840i | \(-0.583438\pi\) | ||||
−0.259137 | + | 0.965840i | \(0.583438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | − 14019.4i | − 1.50868i | ||||||||
\(443\) | 2366.55i | 0.253810i | 0.991915 | + | 0.126905i | \(0.0405044\pi\) | ||||
−0.991915 | + | 0.126905i | \(0.959496\pi\) | |||||||
\(444\) | −1136.64 | −0.121492 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5508.70 | −0.584853 | ||||||||
\(447\) | − 6009.86i | − 0.635921i | ||||||||
\(448\) | − 18821.9i | − 1.98494i | ||||||||
\(449\) | −1814.17 | −0.190681 | −0.0953406 | − | 0.995445i | \(-0.530394\pi\) | ||||
−0.0953406 | + | 0.995445i | \(0.530394\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13063.6 | −1.36395 | ||||||||
\(452\) | 1869.26i | 0.194519i | ||||||||
\(453\) | − 8222.87i | − 0.852857i | ||||||||
\(454\) | 8226.93 | 0.850460 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8320.40 | 0.854470 | ||||||||
\(457\) | − 8284.13i | − 0.847955i | −0.905673 | − | 0.423977i | \(-0.860634\pi\) | ||||
0.905673 | − | 0.423977i | \(-0.139366\pi\) | |||||||
\(458\) | − 37287.3i | − 3.80419i | ||||||||
\(459\) | 1774.53 | 0.180453 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1384.62 | 0.139888 | 0.0699439 | − | 0.997551i | \(-0.477718\pi\) | ||||
0.0699439 | + | 0.997551i | \(0.477718\pi\) | |||||||
\(462\) | − 3926.05i | − 0.395360i | ||||||||
\(463\) | − 13210.3i | − 1.32599i | −0.748624 | − | 0.662994i | \(-0.769285\pi\) | ||||
0.748624 | − | 0.662994i | \(-0.230715\pi\) | |||||||
\(464\) | 52660.9 | 5.26879 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9727.67 | 0.967008 | ||||||||
\(467\) | 4574.24i | 0.453256i | 0.973981 | + | 0.226628i | \(0.0727701\pi\) | ||||
−0.973981 | + | 0.226628i | \(0.927230\pi\) | |||||||
\(468\) | − 7915.45i | − 0.781820i | ||||||||
\(469\) | −2353.94 | −0.231758 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10932.7 | −1.06953 | ||||||||
\(472\) | 21275.9i | 2.07479i | ||||||||
\(473\) | − 1405.61i | − 0.136639i | ||||||||
\(474\) | −6430.55 | −0.623132 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10549.7 | −1.01585 | ||||||||
\(477\) | − 4123.55i | − 0.395816i | ||||||||
\(478\) | 35154.0i | 3.36382i | ||||||||
\(479\) | 11031.8 | 1.05231 | 0.526154 | − | 0.850389i | \(-0.323634\pi\) | ||||
0.526154 | + | 0.850389i | \(0.323634\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 633.716 | 0.0600726 | ||||||||
\(482\) | 18684.7i | 1.76569i | ||||||||
\(483\) | 4356.39i | 0.410398i | ||||||||
\(484\) | 4609.02 | 0.432853 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1351.46 | 0.126139 | ||||||||
\(487\) | 5194.06i | 0.483296i | 0.970364 | + | 0.241648i | \(0.0776880\pi\) | ||||
−0.970364 | + | 0.241648i | \(0.922312\pi\) | |||||||
\(488\) | 10256.2i | 0.951389i | ||||||||
\(489\) | 8322.81 | 0.769673 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11954.7 | 1.09880 | 0.549398 | − | 0.835561i | \(-0.314857\pi\) | ||||
0.549398 | + | 0.835561i | \(0.314857\pi\) | |||||||
\(492\) | 26734.0i | 2.44972i | ||||||||
\(493\) | − 12432.9i | − 1.13580i | ||||||||
\(494\) | −7124.43 | −0.648873 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 56262.4 | 5.09326 | ||||||||
\(497\) | − 3173.19i | − 0.286392i | ||||||||
\(498\) | 396.262i | 0.0356564i | ||||||||
\(499\) | −2566.05 | −0.230205 | −0.115102 | − | 0.993354i | \(-0.536720\pi\) | ||||
−0.115102 | + | 0.993354i | \(0.536720\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3464.74 | −0.308968 | ||||||||
\(502\) | − 7399.62i | − 0.657891i | ||||||||
\(503\) | 21103.5i | 1.87069i | 0.353731 | + | 0.935347i | \(0.384913\pi\) | ||||
−0.353731 | + | 0.935347i | \(0.615087\pi\) | |||||||
\(504\) | −5231.45 | −0.462355 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 38783.1 | 3.40735 | ||||||||
\(507\) | − 2177.87i | − 0.190775i | ||||||||
\(508\) | − 7727.36i | − 0.674894i | ||||||||
\(509\) | 781.732 | 0.0680740 | 0.0340370 | − | 0.999421i | \(-0.489164\pi\) | ||||
0.0340370 | + | 0.999421i | \(0.489164\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −154.305 | −0.0133582 | ||||||||
\(512\) | 61129.5i | 5.27650i | ||||||||
\(513\) | − 901.790i | − 0.0776121i | ||||||||
\(514\) | −13775.7 | −1.18214 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2876.52 | −0.245411 | ||||||||
\(517\) | 12392.3i | 1.05418i | ||||||||
\(518\) | − 643.244i | − 0.0545609i | ||||||||
\(519\) | −10162.4 | −0.859497 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14013.0 | 1.17835 | 0.589176 | − | 0.808005i | \(-0.299453\pi\) | ||||
0.589176 | + | 0.808005i | \(0.299453\pi\) | |||||||
\(522\) | − 9468.73i | − 0.793937i | ||||||||
\(523\) | − 10310.7i | − 0.862052i | −0.902339 | − | 0.431026i | \(-0.858152\pi\) | ||||
0.902339 | − | 0.431026i | \(-0.141848\pi\) | |||||||
\(524\) | −67213.8 | −5.60353 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28656.3 | 2.37542 | ||||||||
\(527\) | − 13283.2i | − 1.09796i | ||||||||
\(528\) | 28073.5i | 2.31390i | ||||||||
\(529\) | −30867.2 | −2.53696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2305.94 | 0.188455 | ||||||||
\(532\) | 5361.18i | 0.436911i | ||||||||
\(533\) | − 14905.1i | − 1.21128i | ||||||||
\(534\) | 24740.2 | 2.00489 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 27924.0 | 2.25025 | ||||||||
\(537\) | 4809.97i | 0.386528i | ||||||||
\(538\) | 6401.16i | 0.512962i | ||||||||
\(539\) | 1647.16 | 0.131629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17562.9 | −1.39572 | −0.697862 | − | 0.716232i | \(-0.745865\pi\) | ||||
−0.697862 | + | 0.716232i | \(0.745865\pi\) | |||||||
\(542\) | 10223.9i | 0.810250i | ||||||||
\(543\) | − 1632.66i | − 0.129031i | ||||||||
\(544\) | 58093.1 | 4.57853 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4479.48 | 0.351107 | ||||||||
\(547\) | 19889.6i | 1.55469i | 0.629072 | + | 0.777347i | \(0.283435\pi\) | ||||
−0.629072 | + | 0.777347i | \(0.716565\pi\) | |||||||
\(548\) | − 36346.9i | − 2.83333i | ||||||||
\(549\) | 1111.60 | 0.0864153 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6318.22 | −0.488503 | ||||||||
\(552\) | − 51678.5i | − 3.98475i | ||||||||
\(553\) | − 2697.92i | − 0.207463i | ||||||||
\(554\) | 3161.45 | 0.242450 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −29783.8 | −2.27179 | ||||||||
\(557\) | − 5579.54i | − 0.424439i | −0.977222 | − | 0.212219i | \(-0.931931\pi\) | ||||
0.977222 | − | 0.212219i | \(-0.0680692\pi\) | |||||||
\(558\) | − 10116.3i | − 0.767486i | ||||||||
\(559\) | 1603.76 | 0.121345 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6627.99 | 0.498813 | ||||||||
\(562\) | 33452.8i | 2.51089i | ||||||||
\(563\) | − 24463.2i | − 1.83126i | −0.402022 | − | 0.915630i | \(-0.631693\pi\) | ||||
0.402022 | − | 0.915630i | \(-0.368307\pi\) | |||||||
\(564\) | 25360.2 | 1.89337 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −22167.0 | −1.64620 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | 37642.5i | 2.78071i | ||||||||
\(569\) | 8582.14 | 0.632306 | 0.316153 | − | 0.948708i | \(-0.397609\pi\) | ||||
0.316153 | + | 0.948708i | \(0.397609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17580.8 | 1.28850 | 0.644248 | − | 0.764816i | \(-0.277170\pi\) | ||||
0.644248 | + | 0.764816i | \(0.277170\pi\) | |||||||
\(572\) | − 29564.7i | − 2.16112i | ||||||||
\(573\) | − 8980.32i | − 0.654727i | ||||||||
\(574\) | −15129.2 | −1.10014 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24199.6 | 1.75055 | ||||||||
\(577\) | 8692.57i | 0.627169i | 0.949560 | + | 0.313585i | \(0.101530\pi\) | ||||
−0.949560 | + | 0.313585i | \(0.898470\pi\) | |||||||
\(578\) | 3300.36i | 0.237503i | ||||||||
\(579\) | 3927.95 | 0.281935 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −166.250 | −0.0118713 | ||||||||
\(582\) | − 867.381i | − 0.0617768i | ||||||||
\(583\) | − 15401.7i | − 1.09412i | ||||||||
\(584\) | 1830.47 | 0.129701 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13848.3 | 0.976227 | ||||||||
\(587\) | − 3584.61i | − 0.252049i | −0.992027 | − | 0.126024i | \(-0.959778\pi\) | ||||
0.992027 | − | 0.126024i | \(-0.0402217\pi\) | |||||||
\(588\) | − 3370.84i | − 0.236413i | ||||||||
\(589\) | −6750.33 | −0.472228 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3424.13 | 0.238325 | ||||||||
\(592\) | 4599.56i | 0.319326i | ||||||||
\(593\) | − 21853.6i | − 1.51335i | −0.653790 | − | 0.756676i | \(-0.726822\pi\) | ||||
0.653790 | − | 0.756676i | \(-0.273178\pi\) | |||||||
\(594\) | 5047.77 | 0.348674 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −45937.1 | −3.15714 | ||||||||
\(597\) | 7110.69i | 0.487472i | ||||||||
\(598\) | 44250.2i | 3.02596i | ||||||||
\(599\) | −9090.48 | −0.620078 | −0.310039 | − | 0.950724i | \(-0.600342\pi\) | ||||
−0.310039 | + | 0.950724i | \(0.600342\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19546.1 | −1.32663 | −0.663314 | − | 0.748341i | \(-0.730851\pi\) | ||||
−0.663314 | + | 0.748341i | \(0.730851\pi\) | |||||||
\(602\) | − 1627.87i | − 0.110211i | ||||||||
\(603\) | − 3026.49i | − 0.204392i | ||||||||
\(604\) | −62852.6 | −4.23416 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 23847.4 | 1.59857 | ||||||||
\(607\) | 15726.0i | 1.05157i | 0.850619 | + | 0.525783i | \(0.176227\pi\) | ||||
−0.850619 | + | 0.525783i | \(0.823773\pi\) | |||||||
\(608\) | − 29522.0i | − 1.96920i | ||||||||
\(609\) | 3972.58 | 0.264330 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14139.2 | −0.936186 | ||||||||
\(612\) | − 13563.9i | − 0.895894i | ||||||||
\(613\) | − 13572.5i | − 0.894269i | −0.894467 | − | 0.447135i | \(-0.852444\pi\) | ||||
0.894467 | − | 0.447135i | \(-0.147556\pi\) | |||||||
\(614\) | −788.921 | −0.0518538 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −19539.8 | −1.27805 | ||||||||
\(617\) | − 17378.5i | − 1.13393i | −0.823743 | − | 0.566964i | \(-0.808118\pi\) | ||||
0.823743 | − | 0.566964i | \(-0.191882\pi\) | |||||||
\(618\) | 7244.68i | 0.471560i | ||||||||
\(619\) | 25113.3 | 1.63068 | 0.815338 | − | 0.578985i | \(-0.196551\pi\) | ||||
0.815338 | + | 0.578985i | \(0.196551\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5601.07 | −0.361937 | ||||||||
\(622\) | 11634.3i | 0.749989i | ||||||||
\(623\) | 10379.7i | 0.667501i | ||||||||
\(624\) | −32030.8 | −2.05490 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −30707.8 | −1.96059 | ||||||||
\(627\) | − 3368.24i | − 0.214537i | ||||||||
\(628\) | 83565.1i | 5.30989i | ||||||||
\(629\) | 1085.93 | 0.0688377 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10814.4 | −0.682276 | −0.341138 | − | 0.940013i | \(-0.610812\pi\) | ||||
−0.341138 | + | 0.940013i | \(0.610812\pi\) | |||||||
\(632\) | 32004.5i | 2.01436i | ||||||||
\(633\) | 2061.48i | 0.129441i | ||||||||
\(634\) | 29763.4 | 1.86444 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −31518.9 | −1.96510 | ||||||||
\(637\) | 1879.35i | 0.116896i | ||||||||
\(638\) | − 35366.3i | − 2.19461i | ||||||||
\(639\) | 4079.81 | 0.252574 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16359.0 | −1.00802 | −0.504010 | − | 0.863698i | \(-0.668143\pi\) | ||||
−0.504010 | + | 0.863698i | \(0.668143\pi\) | |||||||
\(642\) | − 11117.1i | − 0.683422i | ||||||||
\(643\) | 8819.47i | 0.540911i | 0.962732 | + | 0.270456i | \(0.0871744\pi\) | ||||
−0.962732 | + | 0.270456i | \(0.912826\pi\) | |||||||
\(644\) | 33298.6 | 2.03750 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12208.4 | −0.743549 | ||||||||
\(647\) | 13828.8i | 0.840290i | 0.907457 | + | 0.420145i | \(0.138021\pi\) | ||||
−0.907457 | + | 0.420145i | \(0.861979\pi\) | |||||||
\(648\) | − 6726.14i | − 0.407759i | ||||||||
\(649\) | 8612.83 | 0.520930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4244.27 | 0.255524 | ||||||||
\(652\) | − 63616.4i | − 3.82118i | ||||||||
\(653\) | 23988.7i | 1.43760i | 0.695219 | + | 0.718798i | \(0.255307\pi\) | ||||
−0.695219 | + | 0.718798i | \(0.744693\pi\) | |||||||
\(654\) | 20013.4 | 1.19662 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 108182. | 6.43874 | ||||||||
\(657\) | − 198.392i | − 0.0117809i | ||||||||
\(658\) | 14351.8i | 0.850289i | ||||||||
\(659\) | −3109.28 | −0.183794 | −0.0918972 | − | 0.995769i | \(-0.529293\pi\) | ||||
−0.0918972 | + | 0.995769i | \(0.529293\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22695.0 | 1.33545 | 0.667726 | − | 0.744407i | \(-0.267268\pi\) | ||||
0.667726 | + | 0.744407i | \(0.267268\pi\) | |||||||
\(662\) | − 24379.2i | − 1.43131i | ||||||||
\(663\) | 7562.31i | 0.442980i | ||||||||
\(664\) | 1972.18 | 0.115264 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 827.028 | 0.0481182 | ||||||||
\(667\) | 39242.8i | 2.27809i | ||||||||
\(668\) | 26483.2i | 1.53393i | ||||||||
\(669\) | 2971.49 | 0.171726 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4151.90 | 0.238871 | ||||||||
\(672\) | 18562.0i | 1.06554i | ||||||||
\(673\) | 22073.4i | 1.26429i | 0.774850 | + | 0.632145i | \(0.217825\pi\) | ||||
−0.774850 | + | 0.632145i | \(0.782175\pi\) | |||||||
\(674\) | −39623.7 | −2.26446 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16646.9 | −0.947136 | ||||||||
\(677\) | 2489.50i | 0.141328i | 0.997500 | + | 0.0706642i | \(0.0225119\pi\) | ||||
−0.997500 | + | 0.0706642i | \(0.977488\pi\) | |||||||
\(678\) | − 1360.09i | − 0.0770410i | ||||||||
\(679\) | 363.907 | 0.0205677 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4437.75 | −0.249714 | ||||||||
\(682\) | − 37785.0i | − 2.12150i | ||||||||
\(683\) | 7970.98i | 0.446561i | 0.974754 | + | 0.223280i | \(0.0716765\pi\) | ||||
−0.974754 | + | 0.223280i | \(0.928323\pi\) | |||||||
\(684\) | −6892.94 | −0.385319 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1907.61 | 0.106171 | ||||||||
\(687\) | 20113.4i | 1.11699i | ||||||||
\(688\) | 11640.2i | 0.645027i | ||||||||
\(689\) | 17572.8 | 0.971656 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23892.7 | −1.31537 | −0.657687 | − | 0.753292i | \(-0.728465\pi\) | ||||
−0.657687 | + | 0.753292i | \(0.728465\pi\) | |||||||
\(692\) | 77677.4i | 4.26712i | ||||||||
\(693\) | 2117.78i | 0.116086i | ||||||||
\(694\) | 2823.84 | 0.154454 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −47125.5 | −2.56650 | ||||||||
\(697\) | − 25541.3i | − 1.38801i | ||||||||
\(698\) | − 34232.1i | − 1.85631i | ||||||||
\(699\) | −5247.28 | −0.283935 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12197.0 | 0.657170 | 0.328585 | − | 0.944474i | \(-0.393428\pi\) | ||||
0.328585 | + | 0.944474i | \(0.393428\pi\) | |||||||
\(702\) | 5759.33i | 0.309647i | ||||||||
\(703\) | − 551.853i | − 0.0296067i | ||||||||
\(704\) | 90387.0 | 4.83891 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35758.4 | 1.90621 | ||||||||
\(707\) | 10005.1i | 0.532221i | ||||||||
\(708\) | − 17625.8i | − 0.935617i | ||||||||
\(709\) | 8982.28 | 0.475792 | 0.237896 | − | 0.971291i | \(-0.423542\pi\) | ||||
0.237896 | + | 0.971291i | \(0.423542\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3468.75 | 0.182965 | ||||||||
\(712\) | − 123131.i | − 6.48107i | ||||||||
\(713\) | 41926.7i | 2.20220i | ||||||||
\(714\) | 7676.02 | 0.402336 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 36765.6 | 1.91899 | ||||||||
\(717\) | − 18962.7i | − 0.987690i | ||||||||
\(718\) | − 56035.0i | − 2.91255i | ||||||||
\(719\) | 6501.61 | 0.337231 | 0.168616 | − | 0.985682i | \(-0.446070\pi\) | ||||
0.168616 | + | 0.985682i | \(0.446070\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3039.49 | −0.156999 | ||||||||
\(722\) | − 31942.6i | − 1.64651i | ||||||||
\(723\) | − 10078.9i | − 0.518446i | ||||||||
\(724\) | −12479.4 | −0.640600 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3353.55 | −0.171435 | ||||||||
\(727\) | 24228.7i | 1.23603i | 0.786168 | + | 0.618013i | \(0.212062\pi\) | ||||
−0.786168 | + | 0.618013i | \(0.787938\pi\) | |||||||
\(728\) | − 22294.2i | − 1.13500i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2748.19 | 0.139050 | ||||||||
\(732\) | − 8496.67i | − 0.429024i | ||||||||
\(733\) | 36719.1i | 1.85027i | 0.379636 | + | 0.925136i | \(0.376049\pi\) | ||||
−0.379636 | + | 0.925136i | \(0.623951\pi\) | |||||||
\(734\) | 4543.22 | 0.228465 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −183363. | −9.18321 | ||||||||
\(737\) | − 11304.1i | − 0.564983i | ||||||||
\(738\) | − 19451.8i | − 0.970234i | ||||||||
\(739\) | −23304.5 | −1.16004 | −0.580021 | − | 0.814602i | \(-0.696956\pi\) | ||||
−0.580021 | + | 0.814602i | \(0.696956\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3843.04 | 0.190523 | ||||||||
\(742\) | − 17837.0i | − 0.882505i | ||||||||
\(743\) | 6875.35i | 0.339478i | 0.985489 | + | 0.169739i | \(0.0542924\pi\) | ||||
−0.985489 | + | 0.169739i | \(0.945708\pi\) | |||||||
\(744\) | −50348.4 | −2.48100 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20788.3 | 1.02026 | ||||||||
\(747\) | − 213.751i | − 0.0104695i | ||||||||
\(748\) | − 50661.8i | − 2.47644i | ||||||||
\(749\) | 4664.15 | 0.227536 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1182.65 | 0.0574640 | 0.0287320 | − | 0.999587i | \(-0.490853\pi\) | ||||
0.0287320 | + | 0.999587i | \(0.490853\pi\) | |||||||
\(752\) | − 102623.i | − 4.97645i | ||||||||
\(753\) | 3991.49i | 0.193171i | ||||||||
\(754\) | 40351.7 | 1.94897 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4333.93 | 0.208497 | ||||||||
\(757\) | − 25226.8i | − 1.21121i | −0.795766 | − | 0.605604i | \(-0.792932\pi\) | ||||
0.795766 | − | 0.605604i | \(-0.207068\pi\) | |||||||
\(758\) | − 10847.7i | − 0.519795i | ||||||||
\(759\) | −20920.3 | −1.00047 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10909.2 | −0.519655 | −0.259827 | − | 0.965655i | \(-0.583666\pi\) | ||||
−0.259827 | + | 0.965655i | \(0.583666\pi\) | |||||||
\(762\) | 5622.48i | 0.267298i | ||||||||
\(763\) | 8396.58i | 0.398397i | ||||||||
\(764\) | −68642.2 | −3.25051 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37607.6 | −1.77391 | ||||||||
\(767\) | 9826.95i | 0.462621i | ||||||||
\(768\) | − 66991.9i | − 3.14761i | ||||||||
\(769\) | 12771.6 | 0.598903 | 0.299451 | − | 0.954112i | \(-0.403196\pi\) | ||||
0.299451 | + | 0.954112i | \(0.403196\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7430.84 | 0.347101 | ||||||||
\(772\) | − 30023.8i | − 1.39972i | ||||||||
\(773\) | 2199.06i | 0.102322i | 0.998690 | + | 0.0511610i | \(0.0162922\pi\) | ||||
−0.998690 | + | 0.0511610i | \(0.983708\pi\) | |||||||
\(774\) | 2092.98 | 0.0971971 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4316.92 | −0.199701 | ||||||||
\(777\) | 346.977i | 0.0160203i | ||||||||
\(778\) | 14193.0i | 0.654041i | ||||||||
\(779\) | −12979.7 | −0.596977 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15238.3 | 0.698170 | ||||||||
\(782\) | 75827.0i | 3.46748i | ||||||||
\(783\) | 5107.60i | 0.233117i | ||||||||
\(784\) | −13640.5 | −0.621379 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 48905.3 | 2.21933 | ||||||||
\(787\) | 19587.7i | 0.887201i | 0.896225 | + | 0.443601i | \(0.146299\pi\) | ||||
−0.896225 | + | 0.443601i | \(0.853701\pi\) | |||||||
\(788\) | − 26172.8i | − 1.18321i | ||||||||
\(789\) | −15457.7 | −0.697476 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 570.620 | 0.0256497 | ||||||||
\(792\) | − 25122.5i | − 1.12713i | ||||||||
\(793\) | 4737.17i | 0.212134i | ||||||||
\(794\) | −22790.9 | −1.01866 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 54351.4 | 2.42014 | ||||||||
\(797\) | − 21699.3i | − 0.964401i | −0.876061 | − | 0.482200i | \(-0.839838\pi\) | ||||
0.876061 | − | 0.482200i | \(-0.160162\pi\) | |||||||
\(798\) | − 3900.83i | − 0.173042i | ||||||||
\(799\) | −24228.8 | −1.07278 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13345.3 | −0.588680 | ||||||||
\(802\) | − 5821.89i | − 0.256332i | ||||||||
\(803\) | − 741.007i | − 0.0325649i | ||||||||
\(804\) | −23133.3 | −1.01474 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 43111.4 | 1.88404 | ||||||||
\(807\) | − 3452.90i | − 0.150617i | ||||||||
\(808\) | − 118687.i | − 5.16758i | ||||||||
\(809\) | 15649.4 | 0.680103 | 0.340051 | − | 0.940407i | \(-0.389556\pi\) | ||||
0.340051 | + | 0.940407i | \(0.389556\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33267.3 | −1.44041 | −0.720206 | − | 0.693760i | \(-0.755953\pi\) | ||||
−0.720206 | + | 0.693760i | \(0.755953\pi\) | |||||||
\(812\) | − 30364.9i | − 1.31231i | ||||||||
\(813\) | − 5514.97i | − 0.237907i | ||||||||
\(814\) | 3089.00 | 0.133009 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −54887.9 | −2.35473 | ||||||||
\(817\) | − 1396.59i | − 0.0598046i | ||||||||
\(818\) | − 36244.2i | − 1.54920i | ||||||||
\(819\) | −2416.31 | −0.103093 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5158.58 | 0.219288 | 0.109644 | − | 0.993971i | \(-0.465029\pi\) | ||||
0.109644 | + | 0.993971i | \(0.465029\pi\) | |||||||
\(822\) | 26446.3i | 1.12217i | ||||||||
\(823\) | 26333.6i | 1.11535i | 0.830060 | + | 0.557674i | \(0.188306\pi\) | ||||
−0.830060 | + | 0.557674i | \(0.811694\pi\) | |||||||
\(824\) | 36056.5 | 1.52438 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9974.71 | 0.420175 | ||||||||
\(827\) | − 19572.7i | − 0.822988i | −0.911413 | − | 0.411494i | \(-0.865007\pi\) | ||||
0.911413 | − | 0.411494i | \(-0.134993\pi\) | |||||||
\(828\) | 42812.5i | 1.79690i | ||||||||
\(829\) | −9642.26 | −0.403968 | −0.201984 | − | 0.979389i | \(-0.564739\pi\) | ||||
−0.201984 | + | 0.979389i | \(0.564739\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1705.34 | −0.0711885 | ||||||||
\(832\) | 103128.i | 4.29728i | ||||||||
\(833\) | 3220.45i | 0.133952i | ||||||||
\(834\) | 21670.9 | 0.899761 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −25745.5 | −1.06511 | ||||||||
\(837\) | 5456.91i | 0.225351i | ||||||||
\(838\) | − 68290.7i | − 2.81511i | ||||||||
\(839\) | 31081.1 | 1.27895 | 0.639475 | − | 0.768812i | \(-0.279152\pi\) | ||||
0.639475 | + | 0.768812i | \(0.279152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11396.5 | 0.467278 | ||||||||
\(842\) | 56432.3i | 2.30972i | ||||||||
\(843\) | − 18045.0i | − 0.737252i | ||||||||
\(844\) | 15757.1 | 0.642634 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18452.3 | −0.749885 | ||||||||
\(847\) | − 1406.97i | − 0.0570770i | ||||||||
\(848\) | 127545.i | 5.16499i | ||||||||
\(849\) | 11957.2 | 0.483359 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3427.59 | −0.138068 | ||||||||
\(852\) | − 31184.5i | − 1.25395i | ||||||||
\(853\) | 25780.9i | 1.03484i | 0.855731 | + | 0.517421i | \(0.173108\pi\) | ||||
−0.855731 | + | 0.517421i | \(0.826892\pi\) | |||||||
\(854\) | 4808.40 | 0.192670 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −55329.3 | −2.20925 | ||||||||
\(857\) | − 14452.6i | − 0.576069i | −0.957620 | − | 0.288035i | \(-0.906998\pi\) | ||||
0.957620 | − | 0.288035i | \(-0.0930018\pi\) | |||||||
\(858\) | 21511.5i | 0.855931i | ||||||||
\(859\) | −889.366 | −0.0353257 | −0.0176628 | − | 0.999844i | \(-0.505623\pi\) | ||||
−0.0176628 | + | 0.999844i | \(0.505623\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8160.97 | 0.323025 | ||||||||
\(862\) | 39259.2i | 1.55125i | ||||||||
\(863\) | 41460.3i | 1.63537i | 0.575665 | + | 0.817685i | \(0.304743\pi\) | ||||
−0.575665 | + | 0.817685i | \(0.695257\pi\) | |||||||
\(864\) | −23865.4 | −0.939718 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −35977.6 | −1.41174 | ||||||||
\(867\) | − 1780.27i | − 0.0697361i | ||||||||
\(868\) | − 32441.6i | − 1.26859i | ||||||||
\(869\) | 12956.0 | 0.505756 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12897.6 | 0.501744 | ||||||||
\(872\) | − 99606.0i | − 3.86822i | ||||||||
\(873\) | 467.880i | 0.0181390i | ||||||||
\(874\) | 38534.1 | 1.49134 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1516.44 | −0.0584882 | ||||||||
\(877\) | − 21173.0i | − 0.815236i | −0.913153 | − | 0.407618i | \(-0.866360\pi\) | ||||
0.913153 | − | 0.407618i | \(-0.133640\pi\) | |||||||
\(878\) | − 26512.6i | − 1.01909i | ||||||||
\(879\) | −7470.03 | −0.286642 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9883.39 | 0.377957 | 0.188978 | − | 0.981981i | \(-0.439482\pi\) | ||||
0.188978 | + | 0.981981i | \(0.439482\pi\) | |||||||
\(882\) | 2452.64i | 0.0936336i | ||||||||
\(883\) | − 45273.9i | − 1.72547i | −0.505658 | − | 0.862734i | \(-0.668750\pi\) | ||||
0.505658 | − | 0.862734i | \(-0.331250\pi\) | |||||||
\(884\) | 57803.4 | 2.19925 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13161.7 | −0.499069 | ||||||||
\(887\) | − 644.388i | − 0.0243928i | −0.999926 | − | 0.0121964i | \(-0.996118\pi\) | ||||
0.999926 | − | 0.0121964i | \(-0.00388233\pi\) | |||||||
\(888\) | − 4116.08i | − 0.155548i | ||||||||
\(889\) | −2358.89 | −0.0889930 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2722.86 | −0.102378 | ||||||||
\(892\) | − 22712.9i | − 0.852562i | ||||||||
\(893\) | 12312.7i | 0.461398i | ||||||||
\(894\) | 33424.2 | 1.25042 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 55180.6 | 2.05743 | ||||||||
\(897\) | − 23869.4i | − 0.888489i | ||||||||
\(898\) | − 10089.6i | − 0.374937i | ||||||||
\(899\) | 38232.8 | 1.41839 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30112.7 | 1.11343 | ||||||||
\(902\) | − 72653.8i | − 2.68194i | ||||||||
\(903\) | 878.103i | 0.0323604i | ||||||||
\(904\) | −6769.09 | −0.249045 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 45732.0 | 1.67698 | ||||||||
\(907\) | 15065.2i | 0.551522i | 0.961226 | + | 0.275761i | \(0.0889299\pi\) | ||||
−0.961226 | + | 0.275761i | \(0.911070\pi\) | |||||||
\(908\) | 33920.5i | 1.23975i | ||||||||
\(909\) | −12863.7 | −0.469375 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28789.9 | 1.04704 | 0.523520 | − | 0.852014i | \(-0.324619\pi\) | ||||
0.523520 | + | 0.852014i | \(0.324619\pi\) | |||||||
\(912\) | 27893.1i | 1.01276i | ||||||||
\(913\) | − 798.371i | − 0.0289400i | ||||||||
\(914\) | 46072.6 | 1.66734 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 153739. | 5.54552 | ||||||||
\(917\) | 20518.1i | 0.738894i | ||||||||
\(918\) | 9869.16i | 0.354827i | ||||||||
\(919\) | 24163.8 | 0.867345 | 0.433673 | − | 0.901070i | \(-0.357217\pi\) | ||||
0.433673 | + | 0.901070i | \(0.357217\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 425.558 | 0.0152254 | ||||||||
\(922\) | 7700.65i | 0.275062i | ||||||||
\(923\) | 17386.4i | 0.620023i | ||||||||
\(924\) | 16187.5 | 0.576331 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 73469.5 | 2.60730 | ||||||||
\(927\) | − 3907.91i | − 0.138460i | ||||||||
\(928\) | 167208.i | 5.91474i | ||||||||
\(929\) | 35115.4 | 1.24015 | 0.620075 | − | 0.784542i | \(-0.287102\pi\) | ||||
0.620075 | + | 0.784542i | \(0.287102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1636.58 | 0.0576120 | ||||||||
\(932\) | 40108.2i | 1.40964i | ||||||||
\(933\) | − 6275.75i | − 0.220213i | ||||||||
\(934\) | −25439.9 | −0.891239 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 28664.0 | 1.00097 | ||||||||
\(937\) | 15512.6i | 0.540849i | 0.962741 | + | 0.270424i | \(0.0871640\pi\) | ||||
−0.962741 | + | 0.270424i | \(0.912836\pi\) | |||||||
\(938\) | − 13091.5i | − 0.455708i | ||||||||
\(939\) | 16564.3 | 0.575672 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53283.8 | −1.84591 | −0.922956 | − | 0.384905i | \(-0.874234\pi\) | ||||
−0.922956 | + | 0.384905i | \(0.874234\pi\) | |||||||
\(942\) | − 60802.5i | − 2.10303i | ||||||||
\(943\) | 80617.5i | 2.78395i | ||||||||
\(944\) | −71324.8 | −2.45914 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7817.39 | 0.268674 | ||||||||
\(947\) | 55509.7i | 1.90478i | 0.304890 | + | 0.952388i | \(0.401380\pi\) | ||||
−0.304890 | + | 0.952388i | \(0.598620\pi\) | |||||||
\(948\) | − 26513.8i | − 0.908364i | ||||||||
\(949\) | 845.464 | 0.0289198 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16054.9 | −0.547441 | ||||||||
\(952\) | − 38203.2i | − 1.30060i | ||||||||
\(953\) | − 28080.6i | − 0.954480i | −0.878773 | − | 0.477240i | \(-0.841637\pi\) | ||||
0.878773 | − | 0.477240i | \(-0.158363\pi\) | |||||||
\(954\) | 22933.3 | 0.778296 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −144943. | −4.90356 | ||||||||
\(957\) | 19077.2i | 0.644387i | ||||||||
\(958\) | 61353.9i | 2.06916i | ||||||||
\(959\) | −11095.5 | −0.373609 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11056.6 | 0.371140 | ||||||||
\(962\) | 3524.44i | 0.118121i | ||||||||
\(963\) | 5996.76i | 0.200668i | ||||||||
\(964\) | −77039.0 | −2.57392 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −24228.3 | −0.806969 | ||||||||
\(967\) | − 56609.3i | − 1.88256i | −0.337634 | − | 0.941278i | \(-0.609626\pi\) | ||||
0.337634 | − | 0.941278i | \(-0.390374\pi\) | |||||||
\(968\) | 16690.5i | 0.554187i | ||||||||
\(969\) | 6585.42 | 0.218322 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6782.17 | −0.224151 | −0.112075 | − | 0.993700i | \(-0.535750\pi\) | ||||
−0.112075 | + | 0.993700i | \(0.535750\pi\) | |||||||
\(972\) | 5572.20i | 0.183877i | ||||||||
\(973\) | 9091.95i | 0.299563i | ||||||||
\(974\) | −28887.0 | −0.950309 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34382.8 | −1.12763 | ||||||||
\(977\) | 45655.0i | 1.49502i | 0.664252 | + | 0.747509i | \(0.268750\pi\) | ||||
−0.664252 | + | 0.747509i | \(0.731250\pi\) | |||||||
\(978\) | 46287.7i | 1.51341i | ||||||||
\(979\) | −49845.5 | −1.62724 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10795.6 | −0.351353 | ||||||||
\(982\) | 66486.8i | 2.16057i | ||||||||
\(983\) | − 10102.3i | − 0.327785i | −0.986478 | − | 0.163893i | \(-0.947595\pi\) | ||||
0.986478 | − | 0.163893i | \(-0.0524050\pi\) | |||||||
\(984\) | −96811.0 | −3.13640 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 69146.4 | 2.23334 | ||||||||
\(987\) | − 7741.60i | − 0.249664i | ||||||||
\(988\) | − 29374.8i | − 0.945887i | ||||||||
\(989\) | −8674.27 | −0.278894 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25416.2 | 0.814705 | 0.407353 | − | 0.913271i | \(-0.366452\pi\) | ||||
0.407353 | + | 0.913271i | \(0.366452\pi\) | |||||||
\(992\) | 178644.i | 5.71768i | ||||||||
\(993\) | 13150.6i | 0.420262i | ||||||||
\(994\) | 17647.8 | 0.563135 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1633.83 | −0.0519777 | ||||||||
\(997\) | − 48152.5i | − 1.52959i | −0.644271 | − | 0.764797i | \(-0.722839\pi\) | ||||
0.644271 | − | 0.764797i | \(-0.277161\pi\) | |||||||
\(998\) | − 14271.2i | − 0.452653i | ||||||||
\(999\) | −446.114 | −0.0141285 |
(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 | 525.4.d.i.274.4 | 4 | ||
5.2 | odd | 4 | 105.4.a.c.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 525.4.a.p.1.2 | 2 | |||
5.4 | even | 2 | inner | 525.4.d.i.274.1 | 4 | ||
15.2 | even | 4 | 315.4.a.m.1.2 | 2 | |||
15.8 | even | 4 | 1575.4.a.m.1.1 | 2 | |||
20.7 | even | 4 | 1680.4.a.bk.1.2 | 2 | |||
35.27 | even | 4 | 735.4.a.k.1.1 | 2 | |||
105.62 | odd | 4 | 2205.4.a.bh.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.c.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
315.4.a.m.1.2 | 2 | 15.2 | even | 4 | |||
525.4.a.p.1.2 | 2 | 5.3 | odd | 4 | |||
525.4.d.i.274.1 | 4 | 5.4 | even | 2 | inner | ||
525.4.d.i.274.4 | 4 | 1.1 | even | 1 | trivial | ||
735.4.a.k.1.1 | 2 | 35.27 | even | 4 | |||
1575.4.a.m.1.1 | 2 | 15.8 | even | 4 | |||
1680.4.a.bk.1.2 | 2 | 20.7 | even | 4 | |||
2205.4.a.bh.1.2 | 2 | 105.62 | odd | 4 |