Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,4,Mod(19,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.19");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.b (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: | \(2.65508595026\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 21x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.4 | ||
Root | \(3.70156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.19 |
Dual form | 45.4.b.b.19.1 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.70156i | 1.66225i | 0.556083 | + | 0.831127i | \(0.312304\pi\) | ||||
−0.556083 | + | 0.831127i | \(0.687696\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −14.1047 | −1.76309 | ||||||||
\(5\) | −11.1047 | + | 1.29844i | −0.993233 | + | 0.116136i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.2094i | 0.875224i | 0.899164 | + | 0.437612i | \(0.144176\pi\) | ||||
−0.899164 | + | 0.437612i | \(0.855824\pi\) | |||||||
\(8\) | − | 28.7016i | − | 1.26844i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.10469 | − | 52.2094i | −0.193047 | − | 1.65101i | ||||
\(11\) | 40.2094 | 1.10214 | 0.551072 | − | 0.834458i | \(-0.314219\pi\) | ||||
0.551072 | + | 0.834458i | \(0.314219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.7906i | 0.422226i | 0.977462 | + | 0.211113i | \(0.0677087\pi\) | ||||
−0.977462 | + | 0.211113i | \(0.932291\pi\) | |||||||
\(14\) | −76.2094 | −1.45484 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 22.1047 | 0.345386 | ||||||||
\(17\) | 83.0156i | 1.18437i | 0.805803 | + | 0.592184i | \(0.201734\pi\) | ||||
−0.805803 | + | 0.592184i | \(0.798266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 48.8375 | 0.589689 | 0.294844 | − | 0.955545i | \(-0.404732\pi\) | ||||
0.294844 | + | 0.955545i | \(0.404732\pi\) | |||||||
\(20\) | 156.628 | − | 18.3141i | 1.75116 | − | 0.204757i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 189.047i | 1.83204i | ||||||||
\(23\) | − | 1.61250i | − | 0.0146186i | −0.999973 | − | 0.00730932i | \(-0.997673\pi\) | ||
0.999973 | − | 0.00730932i | \(-0.00232665\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 121.628 | − | 28.8375i | 0.973025 | − | 0.230700i | ||||
\(26\) | −93.0469 | −0.701846 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 228.628i | − | 1.54309i | ||||||
\(29\) | −24.5344 | −0.157101 | −0.0785504 | − | 0.996910i | \(-0.525029\pi\) | ||||
−0.0785504 | + | 0.996910i | \(0.525029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −12.4187 | −0.0719507 | −0.0359754 | − | 0.999353i | \(-0.511454\pi\) | ||||
−0.0359754 | + | 0.999353i | \(0.511454\pi\) | |||||||
\(32\) | − | 125.686i | − | 0.694323i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −390.303 | −1.96872 | ||||||||
\(35\) | −21.0469 | − | 180.000i | −0.101645 | − | 0.869302i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 325.884i | − | 1.44797i | −0.689813 | − | 0.723987i | \(-0.742307\pi\) | ||
0.689813 | − | 0.723987i | \(-0.257693\pi\) | |||||||
\(38\) | 229.612i | 0.980212i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 37.2672 | + | 318.722i | 0.147312 | + | 1.25986i | ||||
\(41\) | 242.419 | 0.923401 | 0.461701 | − | 0.887036i | \(-0.347239\pi\) | ||||
0.461701 | + | 0.887036i | \(0.347239\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 367.350i | 1.30280i | 0.758735 | + | 0.651399i | \(0.225818\pi\) | ||||
−0.758735 | + | 0.651399i | \(0.774182\pi\) | |||||||
\(44\) | −567.141 | −1.94317 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.58125 | 0.0242999 | ||||||||
\(47\) | − | 204.544i | − | 0.634804i | −0.948291 | − | 0.317402i | \(-0.897190\pi\) | ||
0.948291 | − | 0.317402i | \(-0.102810\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 80.2562 | 0.233983 | ||||||||
\(50\) | 135.581 | + | 571.842i | 0.383482 | + | 1.61741i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 279.141i | − | 0.744420i | ||||||
\(53\) | 61.5281i | 0.159463i | 0.996816 | + | 0.0797314i | \(0.0254063\pi\) | ||||
−0.996816 | + | 0.0797314i | \(0.974594\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −446.512 | + | 52.2094i | −1.09469 | + | 0.127998i | ||||
\(56\) | 465.234 | 1.11017 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 115.350i | − | 0.261141i | ||||||
\(59\) | −112.209 | −0.247600 | −0.123800 | − | 0.992307i | \(-0.539508\pi\) | ||||
−0.123800 | + | 0.992307i | \(0.539508\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 477.350 | 1.00194 | 0.500970 | − | 0.865464i | \(-0.332977\pi\) | ||||
0.500970 | + | 0.865464i | \(0.332977\pi\) | |||||||
\(62\) | − | 58.3875i | − | 0.119600i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 767.758 | 1.49953 | ||||||||
\(65\) | −25.6969 | − | 219.769i | −0.0490355 | − | 0.419369i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 558.094i | − | 1.01764i | −0.860872 | − | 0.508821i | \(-0.830082\pi\) | ||
0.860872 | − | 0.508821i | \(-0.169918\pi\) | |||||||
\(68\) | − | 1170.91i | − | 2.08814i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 846.281 | − | 98.9531i | 1.44500 | − | 0.168959i | ||||
\(71\) | −558.281 | −0.933180 | −0.466590 | − | 0.884474i | \(-0.654518\pi\) | ||||
−0.466590 | + | 0.884474i | \(0.654518\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1011.77i | 1.62217i | 0.584927 | + | 0.811086i | \(0.301123\pi\) | ||||
−0.584927 | + | 0.811086i | \(0.698877\pi\) | |||||||
\(74\) | 1532.17 | 2.40690 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −688.837 | −1.03967 | ||||||||
\(77\) | 651.769i | 0.964623i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1150.47 | −1.63845 | −0.819227 | − | 0.573470i | \(-0.805597\pi\) | ||||
−0.819227 | + | 0.573470i | \(0.805597\pi\) | |||||||
\(80\) | −245.466 | + | 28.7016i | −0.343049 | + | 0.0401117i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1139.75i | 1.53493i | ||||||||
\(83\) | 1157.92i | 1.53131i | 0.643251 | + | 0.765655i | \(0.277585\pi\) | ||||
−0.643251 | + | 0.765655i | \(0.722415\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −107.791 | − | 921.862i | −0.137547 | − | 1.17635i | ||||
\(86\) | −1727.12 | −2.16558 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1154.07i | − | 1.39801i | ||||||
\(89\) | 96.9751 | 0.115498 | 0.0577491 | − | 0.998331i | \(-0.481608\pi\) | ||||
0.0577491 | + | 0.998331i | \(0.481608\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −320.794 | −0.369542 | ||||||||
\(92\) | 22.7438i | 0.0257739i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 961.675 | 1.05520 | ||||||||
\(95\) | −542.325 | + | 63.4124i | −0.585699 | + | 0.0684840i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1152.37i | 1.20625i | 0.797648 | + | 0.603123i | \(0.206077\pi\) | ||||
−0.797648 | + | 0.603123i | \(0.793923\pi\) | |||||||
\(98\) | 377.330i | 0.388939i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1715.53 | + | 406.744i | −1.71553 | + | 0.406744i | ||||
\(101\) | 1156.49 | 1.13936 | 0.569679 | − | 0.821867i | \(-0.307068\pi\) | ||||
0.569679 | + | 0.821867i | \(0.307068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1333.70i | − | 1.27585i | −0.770096 | − | 0.637927i | \(-0.779792\pi\) | ||
0.770096 | − | 0.637927i | \(-0.220208\pi\) | |||||||
\(104\) | 568.022 | 0.535569 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −289.278 | −0.265068 | ||||||||
\(107\) | − | 798.263i | − | 0.721224i | −0.932716 | − | 0.360612i | \(-0.882568\pi\) | ||
0.932716 | − | 0.360612i | \(-0.117432\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 985.119 | 0.865663 | 0.432831 | − | 0.901475i | \(-0.357515\pi\) | ||||
0.432831 | + | 0.901475i | \(0.357515\pi\) | |||||||
\(110\) | −245.466 | − | 2099.31i | −0.212766 | − | 1.81965i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 358.303i | 0.302290i | ||||||||
\(113\) | − | 1888.25i | − | 1.57196i | −0.618253 | − | 0.785979i | \(-0.712159\pi\) | ||
0.618253 | − | 0.785979i | \(-0.287841\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.09373 | + | 17.9063i | 0.00169775 | + | 0.0145197i | ||||
\(116\) | 346.050 | 0.276982 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 527.559i | − | 0.411574i | ||||||
\(119\) | −1345.63 | −1.03659 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 285.794 | 0.214721 | ||||||||
\(122\) | 2244.29i | 1.66548i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 175.163 | 0.126855 | ||||||||
\(125\) | −1313.20 | + | 478.158i | −0.939648 | + | 0.342142i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 620.859i | 0.433798i | 0.976194 | + | 0.216899i | \(0.0695943\pi\) | ||||
−0.976194 | + | 0.216899i | \(0.930406\pi\) | |||||||
\(128\) | 2604.17i | 1.79827i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1033.26 | − | 120.816i | 0.697097 | − | 0.0815094i | ||||
\(131\) | 2588.35 | 1.72630 | 0.863151 | − | 0.504947i | \(-0.168488\pi\) | ||||
0.863151 | + | 0.504947i | \(0.168488\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 791.625i | 0.516110i | ||||||||
\(134\) | 2623.91 | 1.69158 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2382.68 | 1.50230 | ||||||||
\(137\) | − | 1656.29i | − | 1.03289i | −0.856319 | − | 0.516447i | \(-0.827254\pi\) | ||
0.856319 | − | 0.516447i | \(-0.172746\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 153.256 | 0.0935182 | 0.0467591 | − | 0.998906i | \(-0.485111\pi\) | ||||
0.0467591 | + | 0.998906i | \(0.485111\pi\) | |||||||
\(140\) | 296.859 | + | 2538.84i | 0.179209 | + | 1.53265i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 2624.79i | − | 1.55118i | ||||||
\(143\) | 795.769i | 0.465353i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 272.447 | − | 31.8564i | 0.156038 | − | 0.0182450i | ||||
\(146\) | −4756.89 | −2.69646 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4596.50i | 2.55290i | ||||||||
\(149\) | 1483.38 | 0.815591 | 0.407795 | − | 0.913073i | \(-0.366298\pi\) | ||||
0.407795 | + | 0.913073i | \(0.366298\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −394.281 | −0.212491 | −0.106246 | − | 0.994340i | \(-0.533883\pi\) | ||||
−0.106246 | + | 0.994340i | \(0.533883\pi\) | |||||||
\(152\) | − | 1401.71i | − | 0.747986i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3064.33 | −1.60345 | ||||||||
\(155\) | 137.906 | − | 16.1250i | 0.0714639 | − | 0.00835606i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1727.05i | − | 0.877922i | −0.898506 | − | 0.438961i | \(-0.855347\pi\) | ||
0.898506 | − | 0.438961i | \(-0.144653\pi\) | |||||||
\(158\) | − | 5409.00i | − | 2.72352i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 163.195 | + | 1395.70i | 0.0806358 | + | 0.689625i | ||||
\(161\) | 26.1376 | 0.0127946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2034.28i | − | 0.977529i | −0.872416 | − | 0.488764i | \(-0.837448\pi\) | ||
0.872416 | − | 0.488764i | \(-0.162552\pi\) | |||||||
\(164\) | −3419.24 | −1.62804 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5444.06 | −2.54543 | ||||||||
\(167\) | 192.900i | 0.0893835i | 0.999001 | + | 0.0446918i | \(0.0142306\pi\) | ||||
−0.999001 | + | 0.0446918i | \(0.985769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1805.33 | 0.821726 | ||||||||
\(170\) | 4334.19 | − | 506.784i | 1.95540 | − | 0.228639i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 5181.36i | − | 2.29695i | ||||||
\(173\) | 1239.91i | 0.544905i | 0.962169 | + | 0.272452i | \(0.0878347\pi\) | ||||
−0.962169 | + | 0.272452i | \(0.912165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 467.438 | + | 1971.52i | 0.201914 | + | 0.851615i | ||||
\(176\) | 888.816 | 0.380665 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 455.934i | 0.191987i | ||||||||
\(179\) | −2636.86 | −1.10105 | −0.550525 | − | 0.834818i | \(-0.685573\pi\) | ||||
−0.550525 | + | 0.834818i | \(0.685573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3317.58 | 1.36240 | 0.681199 | − | 0.732099i | \(-0.261459\pi\) | ||||
0.681199 | + | 0.732099i | \(0.261459\pi\) | |||||||
\(182\) | − | 1508.23i | − | 0.614272i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −46.2812 | −0.0185429 | ||||||||
\(185\) | 423.141 | + | 3618.84i | 0.168162 | + | 1.43818i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3338.01i | 1.30534i | ||||||||
\(188\) | 2885.02i | 1.11921i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −298.138 | − | 2549.77i | −0.113838 | − | 0.973579i | ||||
\(191\) | 624.506 | 0.236585 | 0.118292 | − | 0.992979i | \(-0.462258\pi\) | ||||
0.118292 | + | 0.992979i | \(0.462258\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 436.144i | − | 0.162665i | −0.996687 | − | 0.0813324i | \(-0.974082\pi\) | ||
0.996687 | − | 0.0813324i | \(-0.0259175\pi\) | |||||||
\(194\) | −5417.96 | −2.00509 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1131.99 | −0.412532 | ||||||||
\(197\) | 3355.81i | 1.21366i | 0.794831 | + | 0.606831i | \(0.207560\pi\) | ||||
−0.794831 | + | 0.606831i | \(0.792440\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3799.77 | −1.35356 | −0.676780 | − | 0.736185i | \(-0.736625\pi\) | ||||
−0.676780 | + | 0.736185i | \(0.736625\pi\) | |||||||
\(200\) | −827.681 | − | 3490.92i | −0.292629 | − | 1.23423i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5437.31i | 1.89390i | ||||||||
\(203\) | − | 397.687i | − | 0.137498i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2691.98 | + | 314.766i | −0.917153 | + | 0.107240i | ||||
\(206\) | 6270.46 | 2.12079 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 437.466i | 0.145831i | ||||||||
\(209\) | 1963.72 | 0.649922 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2365.27 | 0.771715 | 0.385857 | − | 0.922558i | \(-0.373906\pi\) | ||||
0.385857 | + | 0.922558i | \(0.373906\pi\) | |||||||
\(212\) | − | 867.834i | − | 0.281147i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3753.08 | 1.19886 | ||||||||
\(215\) | −476.981 | − | 4079.31i | −0.151302 | − | 1.29398i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 201.300i | − | 0.0629730i | ||||||
\(218\) | 4631.60i | 1.43895i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6297.92 | − | 736.397i | 1.93003 | − | 0.225672i | ||||
\(221\) | −1642.93 | −0.500070 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3328.58i | − | 0.999545i | −0.866157 | − | 0.499772i | \(-0.833417\pi\) | ||
0.866157 | − | 0.499772i | \(-0.166583\pi\) | |||||||
\(224\) | 2037.29 | 0.607688 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8877.71 | 2.61299 | ||||||||
\(227\) | − | 527.100i | − | 0.154118i | −0.997027 | − | 0.0770592i | \(-0.975447\pi\) | ||
0.997027 | − | 0.0770592i | \(-0.0245530\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2566.06 | −0.740479 | −0.370240 | − | 0.928936i | \(-0.620724\pi\) | ||||
−0.370240 | + | 0.928936i | \(0.620724\pi\) | |||||||
\(230\) | −84.1875 | + | 9.84379i | −0.0241355 | + | 0.00282209i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 704.175i | 0.199273i | ||||||||
\(233\) | − | 5534.99i | − | 1.55626i | −0.628101 | − | 0.778132i | \(-0.716168\pi\) | ||
0.628101 | − | 0.778132i | \(-0.283832\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 265.587 | + | 2271.39i | 0.0737234 | + | 0.630508i | ||||
\(236\) | 1582.68 | 0.436541 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 6326.57i | − | 1.72307i | ||||||
\(239\) | 1010.01 | 0.273355 | 0.136678 | − | 0.990616i | \(-0.456358\pi\) | ||||
0.136678 | + | 0.990616i | \(0.456358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4074.29 | −1.08900 | −0.544498 | − | 0.838762i | \(-0.683280\pi\) | ||||
−0.544498 | + | 0.838762i | \(0.683280\pi\) | |||||||
\(242\) | 1343.68i | 0.356921i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6732.87 | −1.76651 | ||||||||
\(245\) | −891.220 | + | 104.208i | −0.232400 | + | 0.0271738i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 966.525i | 0.248982i | ||||||||
\(248\) | 356.437i | 0.0912653i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2248.09 | − | 6174.08i | −0.568726 | − | 1.56193i | ||||
\(251\) | −1773.98 | −0.446107 | −0.223054 | − | 0.974806i | \(-0.571602\pi\) | ||||
−0.223054 | + | 0.974806i | \(0.571602\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 64.8375i | − | 0.0161119i | ||||||
\(254\) | −2919.01 | −0.721082 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6101.62 | −1.48965 | ||||||||
\(257\) | 662.784i | 0.160869i | 0.996760 | + | 0.0804345i | \(0.0256308\pi\) | ||||
−0.996760 | + | 0.0804345i | \(0.974369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5282.38 | 1.26730 | ||||||||
\(260\) | 362.447 | + | 3099.77i | 0.0864538 | + | 0.739383i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12169.3i | 2.86955i | ||||||||
\(263\) | − | 712.312i | − | 0.167008i | −0.996507 | − | 0.0835039i | \(-0.973389\pi\) | ||
0.996507 | − | 0.0835039i | \(-0.0266111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −79.8904 | − | 683.250i | −0.0185194 | − | 0.158384i | ||||
\(266\) | −3721.87 | −0.857905 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7871.74i | 1.79419i | ||||||||
\(269\) | −3136.41 | −0.710894 | −0.355447 | − | 0.934696i | \(-0.615671\pi\) | ||||
−0.355447 | + | 0.934696i | \(0.615671\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2275.69 | −0.510105 | −0.255053 | − | 0.966927i | \(-0.582093\pi\) | ||||
−0.255053 | + | 0.966927i | \(0.582093\pi\) | |||||||
\(272\) | 1835.03i | 0.409064i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7787.15 | 1.71693 | ||||||||
\(275\) | 4890.59 | − | 1159.54i | 1.07241 | − | 0.254264i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5171.00i | − | 1.12164i | −0.827937 | − | 0.560821i | \(-0.810485\pi\) | ||
0.827937 | − | 0.560821i | \(-0.189515\pi\) | |||||||
\(278\) | 720.544i | 0.155451i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5166.28 | + | 604.078i | −1.10266 | + | 0.128931i | ||||
\(281\) | −2240.14 | −0.475571 | −0.237785 | − | 0.971318i | \(-0.576422\pi\) | ||||
−0.237785 | + | 0.971318i | \(0.576422\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 225.244i | 0.0473123i | 0.999720 | + | 0.0236561i | \(0.00753068\pi\) | ||||
−0.999720 | + | 0.0236561i | \(0.992469\pi\) | |||||||
\(284\) | 7874.38 | 1.64528 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3741.36 | −0.773535 | ||||||||
\(287\) | 3929.46i | 0.808183i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1978.59 | −0.402726 | ||||||||
\(290\) | 149.775 | + | 1280.93i | 0.0303279 | + | 0.259374i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 14270.7i | − | 2.86003i | ||||||
\(293\) | − | 1139.86i | − | 0.227274i | −0.993522 | − | 0.113637i | \(-0.963750\pi\) | ||
0.993522 | − | 0.113637i | \(-0.0362501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1246.05 | − | 145.697i | 0.245925 | − | 0.0287553i | ||||
\(296\) | −9353.39 | −1.83667 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6974.19i | 1.35572i | ||||||||
\(299\) | 31.9123 | 0.00617237 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5954.51 | −1.14024 | ||||||||
\(302\) | − | 1853.74i | − | 0.353214i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1079.54 | 0.203670 | ||||||||
\(305\) | −5300.82 | + | 619.809i | −0.995161 | + | 0.116361i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5244.86i | − | 0.975049i | −0.873109 | − | 0.487525i | \(-0.837900\pi\) | ||
0.873109 | − | 0.487525i | \(-0.162100\pi\) | |||||||
\(308\) | − | 9192.99i | − | 1.70071i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 75.8125 | + | 648.375i | 0.0138899 | + | 0.118791i | ||||
\(311\) | 5188.26 | 0.945977 | 0.472989 | − | 0.881068i | \(-0.343175\pi\) | ||||
0.472989 | + | 0.881068i | \(0.343175\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 486.656i | 0.0878832i | 0.999034 | + | 0.0439416i | \(0.0139915\pi\) | ||||
−0.999034 | + | 0.0439416i | \(0.986008\pi\) | |||||||
\(314\) | 8119.85 | 1.45933 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16227.0 | 2.88873 | ||||||||
\(317\) | − | 4218.87i | − | 0.747493i | −0.927531 | − | 0.373747i | \(-0.878073\pi\) | ||
0.927531 | − | 0.373747i | \(-0.121927\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −986.512 | −0.173148 | ||||||||
\(320\) | −8525.71 | + | 996.886i | −1.48938 | + | 0.174149i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 122.887i | 0.0212678i | ||||||||
\(323\) | 4054.27i | 0.698408i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 570.712 | + | 2407.10i | 0.0974074 | + | 0.410836i | ||||
\(326\) | 9564.30 | 1.62490 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6957.80i | − | 1.17128i | ||||||
\(329\) | 3315.53 | 0.555595 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7439.94 | 1.23546 | 0.617728 | − | 0.786392i | \(-0.288053\pi\) | ||||
0.617728 | + | 0.786392i | \(0.288053\pi\) | |||||||
\(332\) | − | 16332.2i | − | 2.69983i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −906.931 | −0.148578 | ||||||||
\(335\) | 724.650 | + | 6197.46i | 0.118185 | + | 1.01076i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6555.39i | 1.05963i | 0.848113 | + | 0.529815i | \(0.177739\pi\) | ||||
−0.848113 | + | 0.529815i | \(0.822261\pi\) | |||||||
\(338\) | 8487.88i | 1.36592i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1520.35 | + | 13002.6i | 0.242508 | + | 2.07401i | ||||
\(341\) | −499.350 | −0.0793000 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6860.72i | 1.08001i | ||||||||
\(344\) | 10543.5 | 1.65252 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5829.51 | −0.905770 | ||||||||
\(347\) | 1950.56i | 0.301763i | 0.988552 | + | 0.150881i | \(0.0482112\pi\) | ||||
−0.988552 | + | 0.150881i | \(0.951789\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1426.74 | 0.218830 | 0.109415 | − | 0.993996i | \(-0.465102\pi\) | ||||
0.109415 | + | 0.993996i | \(0.465102\pi\) | |||||||
\(350\) | −9269.20 | + | 2197.69i | −1.41560 | + | 0.335632i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 5053.75i | − | 0.765244i | ||||||
\(353\) | 7078.96i | 1.06735i | 0.845689 | + | 0.533676i | \(0.179190\pi\) | ||||
−0.845689 | + | 0.533676i | \(0.820810\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6199.54 | − | 724.893i | 0.926866 | − | 0.108376i | ||||
\(356\) | −1367.80 | −0.203633 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 12397.4i | − | 1.83023i | ||||||
\(359\) | −5409.79 | −0.795314 | −0.397657 | − | 0.917534i | \(-0.630177\pi\) | ||||
−0.397657 | + | 0.917534i | \(0.630177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4473.90 | −0.652267 | ||||||||
\(362\) | 15597.8i | 2.26465i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4524.69 | 0.651534 | ||||||||
\(365\) | −1313.72 | − | 11235.4i | −0.188392 | − | 1.61120i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4940.09i | − | 0.702645i | −0.936255 | − | 0.351322i | \(-0.885732\pi\) | ||
0.936255 | − | 0.351322i | \(-0.114268\pi\) | |||||||
\(368\) | − | 35.6437i | − | 0.00504907i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −17014.2 | + | 1989.42i | −2.39061 | + | 0.279527i | ||||
\(371\) | −997.332 | −0.139566 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12891.9i | 1.78959i | 0.446473 | + | 0.894797i | \(0.352680\pi\) | ||||
−0.446473 | + | 0.894797i | \(0.647320\pi\) | |||||||
\(374\) | −15693.8 | −2.16981 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5870.72 | −0.805211 | ||||||||
\(377\) | − | 485.551i | − | 0.0663320i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9475.15 | 1.28418 | 0.642092 | − | 0.766627i | \(-0.278067\pi\) | ||||
0.642092 | + | 0.766627i | \(0.278067\pi\) | |||||||
\(380\) | 7649.32 | − | 894.413i | 1.03264 | − | 0.120743i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2936.16i | 0.393264i | ||||||||
\(383\) | 5800.97i | 0.773931i | 0.922094 | + | 0.386966i | \(0.126477\pi\) | ||||
−0.922094 | + | 0.386966i | \(0.873523\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −846.281 | − | 7237.69i | −0.112027 | − | 0.958095i | ||||
\(386\) | 2050.56 | 0.270390 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 16253.9i | − | 2.12672i | ||||||
\(389\) | 13779.7 | 1.79603 | 0.898016 | − | 0.439962i | \(-0.145008\pi\) | ||||
0.898016 | + | 0.439962i | \(0.145008\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 133.862 | 0.0173138 | ||||||||
\(392\) | − | 2303.48i | − | 0.296794i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15777.5 | −2.01741 | ||||||||
\(395\) | 12775.6 | − | 1493.81i | 1.62737 | − | 0.190283i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2816.46i | 0.356056i | 0.984025 | + | 0.178028i | \(0.0569718\pi\) | ||||
−0.984025 | + | 0.178028i | \(0.943028\pi\) | |||||||
\(398\) | − | 17864.8i | − | 2.24996i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2688.55 | − | 637.444i | 0.336069 | − | 0.0796805i | ||||
\(401\) | −11986.4 | −1.49270 | −0.746352 | − | 0.665551i | \(-0.768196\pi\) | ||||
−0.746352 | + | 0.665551i | \(0.768196\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 245.775i | − | 0.0303794i | ||||||
\(404\) | −16311.9 | −2.00879 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1869.75 | 0.228557 | ||||||||
\(407\) | − | 13103.6i | − | 1.59588i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3339.07 | 0.403683 | 0.201841 | − | 0.979418i | \(-0.435307\pi\) | ||||
0.201841 | + | 0.979418i | \(0.435307\pi\) | |||||||
\(410\) | −1479.89 | − | 12656.5i | −0.178260 | − | 1.52454i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18811.4i | 2.24944i | ||||||||
\(413\) | − | 1818.84i | − | 0.216706i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1503.49 | − | 12858.4i | −0.177840 | − | 1.52095i | ||||
\(416\) | 2487.40 | 0.293161 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9232.57i | 1.08033i | ||||||||
\(419\) | 1688.52 | 0.196873 | 0.0984363 | − | 0.995143i | \(-0.468616\pi\) | ||||
0.0984363 | + | 0.995143i | \(0.468616\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2664.27 | −0.308429 | −0.154214 | − | 0.988037i | \(-0.549285\pi\) | ||||
−0.154214 | + | 0.988037i | \(0.549285\pi\) | |||||||
\(422\) | 11120.5i | 1.28279i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1765.95 | 0.202269 | ||||||||
\(425\) | 2393.96 | + | 10097.0i | 0.273233 | + | 1.15242i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7737.54i | 0.876923i | ||||||||
\(428\) | 11259.2i | 1.27158i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19179.1 | − | 2242.56i | 2.15093 | − | 0.251502i | ||||
\(431\) | −12266.0 | −1.37084 | −0.685420 | − | 0.728148i | \(-0.740381\pi\) | ||||
−0.685420 | + | 0.728148i | \(0.740381\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15647.3i | − | 1.73664i | −0.496008 | − | 0.868318i | \(-0.665201\pi\) | ||
0.496008 | − | 0.868318i | \(-0.334799\pi\) | |||||||
\(434\) | 946.425 | 0.104677 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13894.8 | −1.52624 | ||||||||
\(437\) | − | 78.7503i | − | 0.00862045i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16131.0 | −1.75373 | −0.876867 | − | 0.480733i | \(-0.840371\pi\) | ||||
−0.876867 | + | 0.480733i | \(0.840371\pi\) | |||||||
\(440\) | 1498.49 | + | 12815.6i | 0.162358 | + | 1.38855i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 7724.34i | − | 0.831243i | ||||||
\(443\) | − | 10053.7i | − | 1.07825i | −0.842225 | − | 0.539127i | \(-0.818754\pi\) | ||
0.842225 | − | 0.539127i | \(-0.181246\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1076.88 | + | 125.916i | −0.114717 | + | 0.0134135i | ||||
\(446\) | 15649.5 | 1.66150 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12444.9i | 1.31242i | ||||||||
\(449\) | 7477.71 | 0.785957 | 0.392979 | − | 0.919548i | \(-0.371445\pi\) | ||||
0.392979 | + | 0.919548i | \(0.371445\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9747.51 | 1.01772 | ||||||||
\(452\) | 26633.1i | 2.77150i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2478.19 | 0.256184 | ||||||||
\(455\) | 3562.31 | − | 416.531i | 0.367041 | − | 0.0429170i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1363.46i | − | 0.139562i | −0.997562 | − | 0.0697812i | \(-0.977770\pi\) | ||
0.997562 | − | 0.0697812i | \(-0.0222301\pi\) | |||||||
\(458\) | − | 12064.5i | − | 1.23086i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −29.5314 | − | 252.562i | −0.00299328 | − | 0.0255995i | ||||
\(461\) | −5276.77 | −0.533109 | −0.266555 | − | 0.963820i | \(-0.585885\pi\) | ||||
−0.266555 | + | 0.963820i | \(0.585885\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5740.02i | 0.576159i | 0.957607 | + | 0.288079i | \(0.0930167\pi\) | ||||
−0.957607 | + | 0.288079i | \(0.906983\pi\) | |||||||
\(464\) | −542.325 | −0.0542604 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26023.1 | 2.58690 | ||||||||
\(467\) | 6233.36i | 0.617657i | 0.951118 | + | 0.308828i | \(0.0999368\pi\) | ||||
−0.951118 | + | 0.308828i | \(0.900063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9046.35 | 0.890664 | ||||||||
\(470\) | −10679.1 | + | 1248.68i | −1.04806 | + | 0.122547i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3220.58i | 0.314067i | ||||||||
\(473\) | 14770.9i | 1.43587i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5940.01 | − | 1408.35i | 0.573782 | − | 0.136041i | ||||
\(476\) | 18979.7 | 1.82759 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4748.61i | 0.454385i | ||||||||
\(479\) | −19688.2 | −1.87803 | −0.939013 | − | 0.343881i | \(-0.888258\pi\) | ||||
−0.939013 | + | 0.343881i | \(0.888258\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6449.46 | 0.611372 | ||||||||
\(482\) | − | 19155.5i | − | 1.81019i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4031.03 | −0.378572 | ||||||||
\(485\) | −1496.29 | − | 12796.8i | −0.140088 | − | 1.19808i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3955.08i | 0.368012i | 0.982925 | + | 0.184006i | \(0.0589065\pi\) | ||||
−0.982925 | + | 0.184006i | \(0.941093\pi\) | |||||||
\(488\) | − | 13700.7i | − | 1.27090i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −489.939 | − | 4190.13i | −0.0451698 | − | 0.386308i | ||||
\(491\) | 13893.5 | 1.27699 | 0.638497 | − | 0.769624i | \(-0.279557\pi\) | ||||
0.638497 | + | 0.769624i | \(0.279557\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2036.74i | − | 0.186065i | ||||||
\(494\) | −4544.18 | −0.413871 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −274.512 | −0.0248508 | ||||||||
\(497\) | − | 9049.39i | − | 0.816741i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13523.7 | −1.21324 | −0.606618 | − | 0.794993i | \(-0.707474\pi\) | ||||
−0.606618 | + | 0.794993i | \(0.707474\pi\) | |||||||
\(500\) | 18522.3 | − | 6744.27i | 1.65668 | − | 0.603226i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 8340.50i | − | 0.741543i | ||||||
\(503\) | − | 13135.4i | − | 1.16437i | −0.813057 | − | 0.582184i | \(-0.802198\pi\) | ||
0.813057 | − | 0.582184i | \(-0.197802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12842.5 | + | 1501.63i | −1.13165 | + | 0.132320i | ||||
\(506\) | 304.837 | 0.0267820 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 8757.03i | − | 0.764823i | ||||||
\(509\) | −2222.71 | −0.193556 | −0.0967778 | − | 0.995306i | \(-0.530854\pi\) | ||||
−0.0967778 | + | 0.995306i | \(0.530854\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16400.1 | −1.41976 | ||||||||
\(512\) | − | 7853.76i | − | 0.677911i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3116.12 | −0.267405 | ||||||||
\(515\) | 1731.72 | + | 14810.3i | 0.148172 | + | 1.26722i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8224.57i | − | 0.699645i | ||||||
\(518\) | 24835.4i | 2.10658i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6307.71 | + | 737.541i | −0.531945 | + | 0.0621987i | ||||
\(521\) | 4916.42 | 0.413421 | 0.206710 | − | 0.978402i | \(-0.433724\pi\) | ||||
0.206710 | + | 0.978402i | \(0.433724\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17743.4i | 1.48349i | 0.670681 | + | 0.741746i | \(0.266002\pi\) | ||||
−0.670681 | + | 0.741746i | \(0.733998\pi\) | |||||||
\(524\) | −36507.9 | −3.04362 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3348.98 | 0.277609 | ||||||||
\(527\) | − | 1030.95i | − | 0.0852161i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12164.4 | 0.999786 | ||||||||
\(530\) | 3212.34 | − | 375.610i | 0.263274 | − | 0.0307839i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 11165.6i | − | 0.909946i | ||||||
\(533\) | 4797.62i | 0.389884i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1036.49 | + | 8864.46i | 0.0837599 | + | 0.716344i | ||||
\(536\) | −16018.2 | −1.29082 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 14746.0i | − | 1.18169i | ||||||
\(539\) | 3227.05 | 0.257883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12671.3 | −1.00699 | −0.503495 | − | 0.863998i | \(-0.667953\pi\) | ||||
−0.503495 | + | 0.863998i | \(0.667953\pi\) | |||||||
\(542\) | − | 10699.3i | − | 0.847924i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10433.9 | 0.822334 | ||||||||
\(545\) | −10939.4 | + | 1279.12i | −0.859805 | + | 0.100534i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5250.90i | − | 0.410443i | −0.978716 | − | 0.205221i | \(-0.934209\pi\) | ||
0.978716 | − | 0.205221i | \(-0.0657915\pi\) | |||||||
\(548\) | 23361.5i | 1.82108i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5451.64 | + | 22993.4i | 0.422652 | + | 1.78262i | ||||
\(551\) | −1198.20 | −0.0926406 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 18648.4i | − | 1.43401i | ||||||
\(554\) | 24311.8 | 1.86445 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2161.63 | −0.164881 | ||||||||
\(557\) | 25830.2i | 1.96492i | 0.186465 | + | 0.982462i | \(0.440297\pi\) | ||||
−0.186465 | + | 0.982462i | \(0.559703\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7270.09 | −0.550075 | ||||||||
\(560\) | −465.234 | − | 3978.84i | −0.0351067 | − | 0.300244i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 10532.1i | − | 0.790519i | ||||||
\(563\) | − | 2021.14i | − | 0.151298i | −0.997135 | − | 0.0756490i | \(-0.975897\pi\) | ||
0.997135 | − | 0.0756490i | \(-0.0241029\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2451.77 | + | 20968.4i | 0.182561 | + | 1.56132i | ||||
\(566\) | −1059.00 | −0.0786450 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16023.5i | 1.18368i | ||||||||
\(569\) | 8706.51 | 0.641469 | 0.320734 | − | 0.947169i | \(-0.396070\pi\) | ||||
0.320734 | + | 0.947169i | \(0.396070\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12194.5 | −0.893740 | −0.446870 | − | 0.894599i | \(-0.647461\pi\) | ||||
−0.446870 | + | 0.894599i | \(0.647461\pi\) | |||||||
\(572\) | − | 11224.1i | − | 0.820458i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18474.6 | −1.34340 | ||||||||
\(575\) | −46.5004 | − | 196.125i | −0.00337252 | − | 0.0142243i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15264.0i | 1.10130i | 0.834737 | + | 0.550649i | \(0.185620\pi\) | ||||
−0.834737 | + | 0.550649i | \(0.814380\pi\) | |||||||
\(578\) | − | 9302.48i | − | 0.669433i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3842.78 | + | 449.324i | −0.275108 | + | 0.0321675i | ||||
\(581\) | −18769.2 | −1.34024 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2474.01i | 0.175751i | ||||||||
\(584\) | 29039.3 | 2.05763 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5359.12 | 0.377787 | ||||||||
\(587\) | − | 8456.89i | − | 0.594639i | −0.954778 | − | 0.297319i | \(-0.903907\pi\) | ||
0.954778 | − | 0.297319i | \(-0.0960926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −606.500 | −0.0424285 | ||||||||
\(590\) | 685.003 | + | 5858.38i | 0.0477985 | + | 0.408789i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 7203.57i | − | 0.500110i | ||||||
\(593\) | 1225.23i | 0.0848467i | 0.999100 | + | 0.0424234i | \(0.0135078\pi\) | ||||
−0.999100 | + | 0.0424234i | \(0.986492\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14942.8 | − | 1747.22i | 1.02957 | − | 0.120385i | ||||
\(596\) | −20922.6 | −1.43796 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 150.038i | 0.0102600i | ||||||||
\(599\) | −16060.0 | −1.09548 | −0.547741 | − | 0.836648i | \(-0.684512\pi\) | ||||
−0.547741 | + | 0.836648i | \(0.684512\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9699.93 | 0.658350 | 0.329175 | − | 0.944269i | \(-0.393229\pi\) | ||||
0.329175 | + | 0.944269i | \(0.393229\pi\) | |||||||
\(602\) | − | 27995.5i | − | 1.89537i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5561.21 | 0.374640 | ||||||||
\(605\) | −3173.65 | + | 371.085i | −0.213268 | + | 0.0249368i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 23661.2i | − | 1.58217i | −0.611703 | − | 0.791087i | \(-0.709515\pi\) | ||
0.611703 | − | 0.791087i | \(-0.290485\pi\) | |||||||
\(608\) | − | 6138.19i | − | 0.409435i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2914.07 | − | 24922.1i | −0.193422 | − | 1.65421i | ||||
\(611\) | 4048.05 | 0.268030 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8085.63i | − | 0.532749i | −0.963870 | − | 0.266375i | \(-0.914174\pi\) | ||
0.963870 | − | 0.266375i | \(-0.0858258\pi\) | |||||||
\(614\) | 24659.0 | 1.62078 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18706.8 | 1.22357 | ||||||||
\(617\) | − | 11035.1i | − | 0.720029i | −0.932947 | − | 0.360014i | \(-0.882772\pi\) | ||
0.932947 | − | 0.360014i | \(-0.117228\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16826.3 | 1.09258 | 0.546290 | − | 0.837596i | \(-0.316040\pi\) | ||||
0.546290 | + | 0.837596i | \(0.316040\pi\) | |||||||
\(620\) | −1945.12 | + | 227.438i | −0.125997 | + | 0.0147324i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24392.9i | 1.57245i | ||||||||
\(623\) | 1571.90i | 0.101087i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13961.8 | − | 7014.90i | 0.893555 | − | 0.448954i | ||||
\(626\) | −2288.04 | −0.146084 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24359.5i | 1.54785i | ||||||||
\(629\) | 27053.5 | 1.71493 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3705.91 | −0.233803 | −0.116902 | − | 0.993144i | \(-0.537296\pi\) | ||||
−0.116902 | + | 0.993144i | \(0.537296\pi\) | |||||||
\(632\) | 33020.2i | 2.07828i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19835.3 | 1.24252 | ||||||||
\(635\) | −806.147 | − | 6894.45i | −0.0503795 | − | 0.430863i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1588.32i | 0.0987937i | ||||||||
\(638\) | − | 4638.15i | − | 0.287815i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3381.36 | − | 28918.5i | −0.208844 | − | 1.78610i | ||||
\(641\) | 24597.4 | 1.51566 | 0.757829 | − | 0.652453i | \(-0.226260\pi\) | ||||
0.757829 | + | 0.652453i | \(0.226260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 21479.5i | − | 1.31737i | −0.752419 | − | 0.658685i | \(-0.771113\pi\) | ||
0.752419 | − | 0.658685i | \(-0.228887\pi\) | |||||||
\(644\) | −368.662 | −0.0225580 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19061.4 | −1.16093 | ||||||||
\(647\) | 27119.7i | 1.64789i | 0.566668 | + | 0.823946i | \(0.308232\pi\) | ||||
−0.566668 | + | 0.823946i | \(0.691768\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4511.87 | −0.272891 | ||||||||
\(650\) | −11317.1 | + | 2683.24i | −0.682913 | + | 0.161916i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 28692.9i | 1.72347i | ||||||||
\(653\) | − | 18476.4i | − | 1.10725i | −0.832765 | − | 0.553627i | \(-0.813243\pi\) | ||
0.832765 | − | 0.553627i | \(-0.186757\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28742.8 | + | 3360.82i | −1.71462 | + | 0.200485i | ||||
\(656\) | 5358.59 | 0.318930 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15588.1i | 0.923540i | ||||||||
\(659\) | −19273.5 | −1.13928 | −0.569641 | − | 0.821894i | \(-0.692918\pi\) | ||||
−0.569641 | + | 0.821894i | \(0.692918\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25605.3 | 1.50670 | 0.753352 | − | 0.657618i | \(-0.228436\pi\) | ||||
0.753352 | + | 0.657618i | \(0.228436\pi\) | |||||||
\(662\) | 34979.3i | 2.05364i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 33234.3 | 1.94238 | ||||||||
\(665\) | −1027.88 | − | 8790.75i | −0.0599388 | − | 0.512617i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.5616i | 0.00229660i | ||||||||
\(668\) | − | 2720.79i | − | 0.157591i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −29137.7 | + | 3406.99i | −1.68013 | + | 0.196453i | ||||
\(671\) | 19193.9 | 1.10428 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7855.52i | 0.449938i | 0.974366 | + | 0.224969i | \(0.0722280\pi\) | ||||
−0.974366 | + | 0.224969i | \(0.927772\pi\) | |||||||
\(674\) | −30820.6 | −1.76137 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25463.6 | −1.44877 | ||||||||
\(677\) | − | 6763.09i | − | 0.383939i | −0.981401 | − | 0.191970i | \(-0.938512\pi\) | ||
0.981401 | − | 0.191970i | \(-0.0614875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18679.3 | −1.05574 | ||||||||
\(680\) | −26458.9 | + | 3093.76i | −1.49214 | + | 0.174471i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 2347.72i | − | 0.131817i | ||||||
\(683\) | − | 15608.6i | − | 0.874447i | −0.899353 | − | 0.437224i | \(-0.855962\pi\) | ||
0.899353 | − | 0.437224i | \(-0.144038\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2150.59 | + | 18392.6i | 0.119956 | + | 1.02590i | ||||
\(686\) | −32256.1 | −1.79525 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8120.16i | 0.449968i | ||||||||
\(689\) | −1217.68 | −0.0673293 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6203.15 | 0.341504 | 0.170752 | − | 0.985314i | \(-0.445380\pi\) | ||||
0.170752 | + | 0.985314i | \(0.445380\pi\) | |||||||
\(692\) | − | 17488.5i | − | 0.960714i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9170.69 | −0.501606 | ||||||||
\(695\) | −1701.86 | + | 198.994i | −0.0928854 | + | 0.0108608i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20124.5i | 1.09365i | ||||||||
\(698\) | 6707.90i | 0.363750i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6593.06 | − | 27807.6i | −0.355992 | − | 1.50147i | ||||
\(701\) | 16507.9 | 0.889435 | 0.444718 | − | 0.895671i | \(-0.353304\pi\) | ||||
0.444718 | + | 0.895671i | \(0.353304\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 15915.4i | − | 0.853854i | ||||||
\(704\) | 30871.1 | 1.65269 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33282.2 | −1.77421 | ||||||||
\(707\) | 18746.0i | 0.997193i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25539.6 | 1.35283 | 0.676416 | − | 0.736520i | \(-0.263532\pi\) | ||||
0.676416 | + | 0.736520i | \(0.263532\pi\) | |||||||
\(710\) | 3408.13 | + | 29147.5i | 0.180148 | + | 1.54069i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 2783.34i | − | 0.146503i | ||||||
\(713\) | 20.0252i | 0.00105182i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1033.26 | − | 8836.76i | −0.0540442 | − | 0.462204i | ||||
\(716\) | 37192.1 | 1.94125 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 25434.4i | − | 1.32201i | ||||||
\(719\) | −7353.45 | −0.381415 | −0.190708 | − | 0.981647i | \(-0.561078\pi\) | ||||
−0.190708 | + | 0.981647i | \(0.561078\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21618.4 | 1.11666 | ||||||||
\(722\) | − | 21034.3i | − | 1.08423i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −46793.4 | −2.40202 | ||||||||
\(725\) | −2984.07 | + | 707.510i | −0.152863 | + | 0.0362431i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21696.5i | 1.10685i | 0.832900 | + | 0.553424i | \(0.186679\pi\) | ||||
−0.832900 | + | 0.553424i | \(0.813321\pi\) | |||||||
\(728\) | 9207.28i | 0.468742i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 52823.8 | − | 6176.53i | 2.67821 | − | 0.313156i | ||||
\(731\) | −30495.8 | −1.54299 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 90.2714i | 0.00454877i | 0.999997 | + | 0.00227439i | \(0.000723960\pi\) | ||||
−0.999997 | + | 0.00227439i | \(0.999276\pi\) | |||||||
\(734\) | 23226.1 | 1.16797 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −202.668 | −0.0101501 | ||||||||
\(737\) | − | 22440.6i | − | 1.12159i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14273.1 | −0.710479 | −0.355239 | − | 0.934775i | \(-0.615601\pi\) | ||||
−0.355239 | + | 0.934775i | \(0.615601\pi\) | |||||||
\(740\) | −5968.27 | − | 51042.7i | −0.296484 | − | 2.53563i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 4689.02i | − | 0.231994i | ||||||
\(743\) | − | 15866.6i | − | 0.783429i | −0.920087 | − | 0.391715i | \(-0.871882\pi\) | ||
0.920087 | − | 0.391715i | \(-0.128118\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16472.4 | + | 1926.07i | −0.810072 | + | 0.0947193i | ||||
\(746\) | −60612.2 | −2.97476 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 47081.5i | − | 2.30143i | ||||||
\(749\) | 12939.3 | 0.631232 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26776.9 | 1.30107 | 0.650534 | − | 0.759477i | \(-0.274545\pi\) | ||||
0.650534 | + | 0.759477i | \(0.274545\pi\) | |||||||
\(752\) | − | 4521.37i | − | 0.219252i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2282.85 | 0.110261 | ||||||||
\(755\) | 4378.37 | − | 511.950i | 0.211053 | − | 0.0246778i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 30478.0i | − | 1.46333i | −0.681663 | − | 0.731666i | \(-0.738743\pi\) | ||
0.681663 | − | 0.731666i | \(-0.261257\pi\) | |||||||
\(758\) | 44548.0i | 2.13464i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1820.04 | + | 15565.6i | 0.0868680 | + | 0.742925i | ||||
\(761\) | −29104.7 | −1.38639 | −0.693195 | − | 0.720750i | \(-0.743798\pi\) | ||||
−0.693195 | + | 0.720750i | \(0.743798\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15968.2i | 0.757649i | ||||||||
\(764\) | −8808.47 | −0.417119 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27273.6 | −1.28647 | ||||||||
\(767\) | − | 2220.69i | − | 0.104543i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4170.65 | −0.195575 | −0.0977876 | − | 0.995207i | \(-0.531177\pi\) | ||||
−0.0977876 | + | 0.995207i | \(0.531177\pi\) | |||||||
\(770\) | 34028.4 | − | 3978.84i | 1.59260 | − | 0.186218i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6151.67i | 0.286792i | ||||||||
\(773\) | 17738.5i | 0.825367i | 0.910874 | + | 0.412684i | \(0.135409\pi\) | ||||
−0.910874 | + | 0.412684i | \(0.864591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1510.47 | + | 358.125i | −0.0700099 | + | 0.0165990i | ||||
\(776\) | 33075.0 | 1.53005 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 64786.0i | 2.98546i | ||||||||
\(779\) | 11839.1 | 0.544519 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22448.1 | −1.02850 | ||||||||
\(782\) | 629.363i | 0.0287800i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1774.04 | 0.0808145 | ||||||||
\(785\) | 2242.47 | + | 19178.4i | 0.101958 | + | 0.871982i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3807.92i | 0.172475i | 0.996275 | + | 0.0862374i | \(0.0274844\pi\) | ||||
−0.996275 | + | 0.0862374i | \(0.972516\pi\) | |||||||
\(788\) | − | 47332.6i | − | 2.13979i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7023.25 | + | 60065.2i | 0.316299 | + | 2.70510i | ||||
\(791\) | 30607.3 | 1.37582 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9447.06i | 0.423045i | ||||||||
\(794\) | −13241.8 | −0.591856 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 53594.5 | 2.38644 | ||||||||
\(797\) | 23840.3i | 1.05956i | 0.848136 | + | 0.529779i | \(0.177725\pi\) | ||||
−0.848136 | + | 0.529779i | \(0.822275\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16980.3 | 0.751841 | ||||||||
\(800\) | −3624.47 | − | 15286.9i | −0.160180 | − | 0.675594i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 56355.0i | − | 2.48125i | ||||||
\(803\) | 40682.6i | 1.78787i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −290.249 | + | 33.9380i | −0.0127080 | + | 0.00148591i | ||||
\(806\) | 1155.53 | 0.0504983 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 33193.1i | − | 1.44521i | ||||||
\(809\) | −1984.22 | −0.0862316 | −0.0431158 | − | 0.999070i | \(-0.513728\pi\) | ||||
−0.0431158 | + | 0.999070i | \(0.513728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9713.78 | −0.420588 | −0.210294 | − | 0.977638i | \(-0.567442\pi\) | ||||
−0.210294 | + | 0.977638i | \(0.567442\pi\) | |||||||
\(812\) | 5609.25i | 0.242421i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 61607.4 | 2.65275 | ||||||||
\(815\) | 2641.39 | + | 22590.1i | 0.113526 | + | 0.970914i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17940.5i | 0.768246i | ||||||||
\(818\) | 15698.8i | 0.671023i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 37969.6 | − | 4439.67i | 1.61702 | − | 0.189073i | ||||
\(821\) | 19235.4 | 0.817686 | 0.408843 | − | 0.912605i | \(-0.365932\pi\) | ||||
0.408843 | + | 0.912605i | \(0.365932\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 12717.6i | − | 0.538650i | −0.963049 | − | 0.269325i | \(-0.913199\pi\) | ||
0.963049 | − | 0.269325i | \(-0.0868005\pi\) | |||||||
\(824\) | −38279.2 | −1.61835 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8551.41 | 0.360220 | ||||||||
\(827\) | − | 6744.75i | − | 0.283601i | −0.989895 | − | 0.141800i | \(-0.954711\pi\) | ||
0.989895 | − | 0.141800i | \(-0.0452891\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3404.22 | −0.142622 | −0.0713108 | − | 0.997454i | \(-0.522718\pi\) | ||||
−0.0713108 | + | 0.997454i | \(0.522718\pi\) | |||||||
\(830\) | 60454.5 | − | 7068.77i | 2.52820 | − | 0.295615i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15194.4i | 0.633139i | ||||||||
\(833\) | 6662.52i | 0.277122i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −250.469 | − | 2142.09i | −0.0103806 | − | 0.0887787i | ||||
\(836\) | −27697.7 | −1.14587 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7938.69i | 0.327252i | ||||||||
\(839\) | −21361.9 | −0.879015 | −0.439508 | − | 0.898239i | \(-0.644847\pi\) | ||||
−0.439508 | + | 0.898239i | \(0.644847\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23787.1 | −0.975319 | ||||||||
\(842\) | − | 12526.2i | − | 0.512687i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −33361.4 | −1.36060 | ||||||||
\(845\) | −20047.6 | + | 2344.11i | −0.816165 | + | 0.0954318i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4632.54i | 0.187929i | ||||||||
\(848\) | 1360.06i | 0.0550762i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −47471.8 | + | 11255.4i | −1.91561 | + | 0.454183i | ||||
\(851\) | −525.488 | −0.0211674 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10728.9i | − | 0.430657i | −0.976542 | − | 0.215328i | \(-0.930918\pi\) | ||
0.976542 | − | 0.215328i | \(-0.0690822\pi\) | |||||||
\(854\) | −36378.5 | −1.45767 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22911.4 | −0.914830 | ||||||||
\(857\) | − | 42895.2i | − | 1.70977i | −0.518817 | − | 0.854885i | \(-0.673627\pi\) | ||
0.518817 | − | 0.854885i | \(-0.326373\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35530.5 | −1.41127 | −0.705637 | − | 0.708574i | \(-0.749339\pi\) | ||||
−0.705637 | + | 0.708574i | \(0.749339\pi\) | |||||||
\(860\) | 6727.67 | + | 57537.3i | 0.266758 | + | 2.28140i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 57669.3i | − | 2.27868i | ||||||
\(863\) | − | 5704.35i | − | 0.225004i | −0.993652 | − | 0.112502i | \(-0.964114\pi\) | ||
0.993652 | − | 0.112502i | \(-0.0358865\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1609.94 | − | 13768.8i | −0.0632830 | − | 0.541218i | ||||
\(866\) | 73567.0 | 2.88673 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2839.27i | 0.111027i | ||||||||
\(869\) | −46259.6 | −1.80581 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11045.0 | 0.429674 | ||||||||
\(872\) | − | 28274.4i | − | 1.09804i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 370.249 | 0.0143294 | ||||||||
\(875\) | −7750.64 | − | 21286.1i | −0.299451 | − | 0.822403i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 50249.0i | − | 1.93476i | −0.253324 | − | 0.967382i | \(-0.581524\pi\) | ||
0.253324 | − | 0.967382i | \(-0.418476\pi\) | |||||||
\(878\) | − | 75840.7i | − | 2.91515i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9870.02 | + | 1154.07i | −0.378089 | + | 0.0442088i | ||||
\(881\) | 26864.5 | 1.02734 | 0.513672 | − | 0.857987i | \(-0.328285\pi\) | ||||
0.513672 | + | 0.857987i | \(0.328285\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18942.1i | 0.721918i | 0.932582 | + | 0.360959i | \(0.117551\pi\) | ||||
−0.932582 | + | 0.360959i | \(0.882449\pi\) | |||||||
\(884\) | 23173.0 | 0.881667 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 47268.2 | 1.79233 | ||||||||
\(887\) | − | 25344.8i | − | 0.959409i | −0.877430 | − | 0.479705i | \(-0.840744\pi\) | ||
0.877430 | − | 0.479705i | \(-0.159256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10063.7 | −0.379670 | ||||||||
\(890\) | −592.002 | − | 5063.01i | −0.0222966 | − | 0.190688i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 46948.6i | 1.76228i | ||||||||
\(893\) | − | 9989.40i | − | 0.374337i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29281.5 | − | 3423.80i | 1.09360 | − | 0.127871i | ||||
\(896\) | −42212.0 | −1.57389 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 35156.9i | 1.30646i | ||||||||
\(899\) | 304.686 | 0.0113035 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5107.79 | −0.188863 | ||||||||
\(902\) | 45828.5i | 1.69171i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −54195.6 | −1.99394 | ||||||||
\(905\) | −36840.7 | + | 4307.67i | −1.35318 | + | 0.158223i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 4800.11i | − | 0.175728i | −0.996132 | − | 0.0878639i | \(-0.971996\pi\) | ||
0.996132 | − | 0.0878639i | \(-0.0280041\pi\) | |||||||
\(908\) | 7434.58i | 0.271724i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1958.34 | + | 16748.4i | 0.0713390 | + | 0.610116i | ||||
\(911\) | 25731.7 | 0.935819 | 0.467909 | − | 0.883776i | \(-0.345007\pi\) | ||||
0.467909 | + | 0.883776i | \(0.345007\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46559.4i | 1.68772i | ||||||||
\(914\) | 6410.40 | 0.231988 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36193.4 | 1.30553 | ||||||||
\(917\) | 41955.6i | 1.51090i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12751.9 | 0.457722 | 0.228861 | − | 0.973459i | \(-0.426500\pi\) | ||||
0.228861 | + | 0.973459i | \(0.426500\pi\) | |||||||
\(920\) | 513.938 | − | 60.0932i | 0.0184174 | − | 0.00215350i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 24809.0i | − | 0.886163i | ||||||
\(923\) | − | 11048.7i | − | 0.394012i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9397.69 | − | 39636.7i | −0.334048 | − | 1.40892i | ||||
\(926\) | −26987.1 | −0.957722 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3083.63i | 0.109079i | ||||||||
\(929\) | 15557.8 | 0.549444 | 0.274722 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274722 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3919.51 | 0.137977 | ||||||||
\(932\) | 78069.3i | 2.74383i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −29306.5 | −1.02670 | ||||||||
\(935\) | −4334.19 | − | 37067.5i | −0.151597 | − | 1.29651i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23858.0i | 0.831811i | 0.909408 | + | 0.415905i | \(0.136535\pi\) | ||||
−0.909408 | + | 0.415905i | \(0.863465\pi\) | |||||||
\(938\) | 42532.0i | 1.48051i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3746.03 | − | 32037.3i | −0.129981 | − | 1.11164i | ||||
\(941\) | −9748.00 | −0.337700 | −0.168850 | − | 0.985642i | \(-0.554005\pi\) | ||||
−0.168850 | + | 0.985642i | \(0.554005\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 390.899i | − | 0.0134989i | ||||||
\(944\) | −2480.35 | −0.0855176 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −69446.4 | −2.38678 | ||||||||
\(947\) | − | 51537.0i | − | 1.76845i | −0.467057 | − | 0.884227i | \(-0.654686\pi\) | ||
0.467057 | − | 0.884227i | \(-0.345314\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20023.5 | −0.684923 | ||||||||
\(950\) | 6621.45 | + | 27927.3i | 0.226135 | + | 0.953771i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 38621.7i | 1.31485i | ||||||||
\(953\) | 5631.36i | 0.191414i | 0.995410 | + | 0.0957071i | \(0.0305112\pi\) | ||||
−0.995410 | + | 0.0957071i | \(0.969489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6934.95 | + | 810.883i | −0.234984 | + | 0.0274760i | ||||
\(956\) | −14245.8 | −0.481948 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 92565.1i | − | 3.12176i | ||||||
\(959\) | 26847.4 | 0.904013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29636.8 | −0.994823 | ||||||||
\(962\) | 30322.5i | 1.01625i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 57466.5 | 1.91999 | ||||||||
\(965\) | 566.305 | + | 4843.24i | 0.0188912 | + | 0.161564i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43360.9i | 1.44198i | 0.692946 | + | 0.720989i | \(0.256312\pi\) | ||||
−0.692946 | + | 0.720989i | \(0.743688\pi\) | |||||||
\(968\) | − | 8202.72i | − | 0.272361i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 60164.8 | − | 7034.89i | 1.99152 | − | 0.232862i | ||||
\(971\) | −12920.0 | −0.427007 | −0.213503 | − | 0.976942i | \(-0.568487\pi\) | ||||
−0.213503 | + | 0.976942i | \(0.568487\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2484.19i | 0.0818493i | ||||||||
\(974\) | −18595.0 | −0.611728 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10551.7 | 0.346056 | ||||||||
\(977\) | − | 10650.4i | − | 0.348759i | −0.984679 | − | 0.174379i | \(-0.944208\pi\) | ||
0.984679 | − | 0.174379i | \(-0.0557919\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3899.31 | 0.127296 | ||||||||
\(980\) | 12570.4 | − | 1469.82i | 0.409741 | − | 0.0479098i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 65321.0i | 2.12269i | ||||||||
\(983\) | 49450.3i | 1.60450i | 0.596991 | + | 0.802248i | \(0.296363\pi\) | ||||
−0.596991 | + | 0.802248i | \(0.703637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4357.31 | − | 37265.2i | −0.140950 | − | 1.20545i | ||||
\(986\) | 9575.85 | 0.309287 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 13632.5i | − | 0.438976i | ||||||
\(989\) | 592.351 | 0.0190452 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9410.47 | 0.301648 | 0.150824 | − | 0.988561i | \(-0.451807\pi\) | ||||
0.150824 | + | 0.988561i | \(0.451807\pi\) | |||||||
\(992\) | 1560.86i | 0.0499571i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 42546.3 | 1.35763 | ||||||||
\(995\) | 42195.2 | − | 4933.76i | 1.34440 | − | 0.157197i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 532.117i | − | 0.0169030i | −0.999964 | − | 0.00845151i | \(-0.997310\pi\) | ||
0.999964 | − | 0.00845151i | \(-0.00269023\pi\) | |||||||
\(998\) | − | 63582.6i | − | 2.01671i | ||||||
\(999\) | 0 | 0 |
(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 | 45.4.b.b.19.4 | 4 | ||
3.2 | odd | 2 | 15.4.b.a.4.1 | ✓ | 4 | ||
4.3 | odd | 2 | 720.4.f.j.289.2 | 4 | |||
5.2 | odd | 4 | 225.4.a.i.1.1 | 2 | |||
5.3 | odd | 4 | 225.4.a.o.1.2 | 2 | |||
5.4 | even | 2 | inner | 45.4.b.b.19.1 | 4 | ||
12.11 | even | 2 | 240.4.f.f.49.2 | 4 | |||
15.2 | even | 4 | 75.4.a.f.1.2 | 2 | |||
15.8 | even | 4 | 75.4.a.c.1.1 | 2 | |||
15.14 | odd | 2 | 15.4.b.a.4.4 | yes | 4 | ||
20.19 | odd | 2 | 720.4.f.j.289.1 | 4 | |||
24.5 | odd | 2 | 960.4.f.q.769.1 | 4 | |||
24.11 | even | 2 | 960.4.f.p.769.3 | 4 | |||
60.23 | odd | 4 | 1200.4.a.bt.1.1 | 2 | |||
60.47 | odd | 4 | 1200.4.a.bn.1.2 | 2 | |||
60.59 | even | 2 | 240.4.f.f.49.4 | 4 | |||
120.29 | odd | 2 | 960.4.f.q.769.3 | 4 | |||
120.59 | even | 2 | 960.4.f.p.769.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.b.a.4.1 | ✓ | 4 | 3.2 | odd | 2 | ||
15.4.b.a.4.4 | yes | 4 | 15.14 | odd | 2 | ||
45.4.b.b.19.1 | 4 | 5.4 | even | 2 | inner | ||
45.4.b.b.19.4 | 4 | 1.1 | even | 1 | trivial | ||
75.4.a.c.1.1 | 2 | 15.8 | even | 4 | |||
75.4.a.f.1.2 | 2 | 15.2 | even | 4 | |||
225.4.a.i.1.1 | 2 | 5.2 | odd | 4 | |||
225.4.a.o.1.2 | 2 | 5.3 | odd | 4 | |||
240.4.f.f.49.2 | 4 | 12.11 | even | 2 | |||
240.4.f.f.49.4 | 4 | 60.59 | even | 2 | |||
720.4.f.j.289.1 | 4 | 20.19 | odd | 2 | |||
720.4.f.j.289.2 | 4 | 4.3 | odd | 2 | |||
960.4.f.p.769.1 | 4 | 120.59 | even | 2 | |||
960.4.f.p.769.3 | 4 | 24.11 | even | 2 | |||
960.4.f.q.769.1 | 4 | 24.5 | odd | 2 | |||
960.4.f.q.769.3 | 4 | 120.29 | odd | 2 | |||
1200.4.a.bn.1.2 | 2 | 60.47 | odd | 4 | |||
1200.4.a.bt.1.1 | 2 | 60.23 | odd | 4 |