Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
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: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} + \cdots + 768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-0.782524\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.21809 | 1.88639 | 0.943193 | − | 0.332244i | \(-0.107806\pi\) | ||||
0.943193 | + | 0.332244i | \(0.107806\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −4.81342 | −1.81930 | −0.909651 | − | 0.415374i | \(-0.863651\pi\) | ||||
−0.909651 | + | 0.415374i | \(0.863651\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.21809 | −1.33388 | ||||||||
\(11\) | −4.29400 | −1.29469 | −0.647345 | − | 0.762197i | \(-0.724121\pi\) | ||||
−0.647345 | + | 0.762197i | \(0.724121\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 4.81342 | 1.28644 | ||||||||
\(15\) | 4.21809 | 1.08911 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.64843 | −0.642338 | −0.321169 | − | 0.947022i | \(-0.604076\pi\) | ||||
−0.321169 | + | 0.947022i | \(0.604076\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0.655968 | 0.150489 | 0.0752446 | − | 0.997165i | \(-0.476026\pi\) | ||||
0.0752446 | + | 0.997165i | \(0.476026\pi\) | |||||||
\(20\) | 4.21809 | 0.943193 | ||||||||
\(21\) | −4.81342 | −1.05037 | ||||||||
\(22\) | 4.29400 | 0.915485 | ||||||||
\(23\) | 1.52610 | 0.318215 | 0.159107 | − | 0.987261i | \(-0.449138\pi\) | ||||
0.159107 | + | 0.987261i | \(0.449138\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 12.7923 | 2.55846 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.81342 | −0.909651 | ||||||||
\(29\) | −0.992673 | −0.184335 | −0.0921674 | − | 0.995744i | \(-0.529379\pi\) | ||||
−0.0921674 | + | 0.995744i | \(0.529379\pi\) | |||||||
\(30\) | −4.21809 | −0.770114 | ||||||||
\(31\) | 1.93587 | 0.347692 | 0.173846 | − | 0.984773i | \(-0.444380\pi\) | ||||
0.173846 | + | 0.984773i | \(0.444380\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.29400 | −0.747490 | ||||||||
\(34\) | 2.64843 | 0.454202 | ||||||||
\(35\) | −20.3034 | −3.43191 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.13733 | −1.17337 | −0.586685 | − | 0.809815i | \(-0.699567\pi\) | ||||
−0.586685 | + | 0.809815i | \(0.699567\pi\) | |||||||
\(38\) | −0.655968 | −0.106412 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −4.21809 | −0.666938 | ||||||||
\(41\) | 7.02108 | 1.09651 | 0.548254 | − | 0.836312i | \(-0.315293\pi\) | ||||
0.548254 | + | 0.836312i | \(0.315293\pi\) | |||||||
\(42\) | 4.81342 | 0.742727 | ||||||||
\(43\) | −4.82571 | −0.735913 | −0.367957 | − | 0.929843i | \(-0.619943\pi\) | ||||
−0.367957 | + | 0.929843i | \(0.619943\pi\) | |||||||
\(44\) | −4.29400 | −0.647345 | ||||||||
\(45\) | 4.21809 | 0.628796 | ||||||||
\(46\) | −1.52610 | −0.225012 | ||||||||
\(47\) | 1.34179 | 0.195721 | 0.0978603 | − | 0.995200i | \(-0.468800\pi\) | ||||
0.0978603 | + | 0.995200i | \(0.468800\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 16.1690 | 2.30986 | ||||||||
\(50\) | −12.7923 | −1.80910 | ||||||||
\(51\) | −2.64843 | −0.370854 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −1.36163 | −0.187034 | −0.0935168 | − | 0.995618i | \(-0.529811\pi\) | ||||
−0.0935168 | + | 0.995618i | \(0.529811\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −18.1125 | −2.44229 | ||||||||
\(56\) | 4.81342 | 0.643220 | ||||||||
\(57\) | 0.655968 | 0.0868850 | ||||||||
\(58\) | 0.992673 | 0.130344 | ||||||||
\(59\) | −14.8662 | −1.93542 | −0.967710 | − | 0.252067i | \(-0.918890\pi\) | ||||
−0.967710 | + | 0.252067i | \(0.918890\pi\) | |||||||
\(60\) | 4.21809 | 0.544553 | ||||||||
\(61\) | −9.04935 | −1.15865 | −0.579325 | − | 0.815097i | \(-0.696684\pi\) | ||||
−0.579325 | + | 0.815097i | \(0.696684\pi\) | |||||||
\(62\) | −1.93587 | −0.245856 | ||||||||
\(63\) | −4.81342 | −0.606434 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.21809 | 0.523190 | ||||||||
\(66\) | 4.29400 | 0.528555 | ||||||||
\(67\) | 3.79388 | 0.463496 | 0.231748 | − | 0.972776i | \(-0.425556\pi\) | ||||
0.231748 | + | 0.972776i | \(0.425556\pi\) | |||||||
\(68\) | −2.64843 | −0.321169 | ||||||||
\(69\) | 1.52610 | 0.183721 | ||||||||
\(70\) | 20.3034 | 2.42672 | ||||||||
\(71\) | 4.83297 | 0.573568 | 0.286784 | − | 0.957995i | \(-0.407414\pi\) | ||||
0.286784 | + | 0.957995i | \(0.407414\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 1.21359 | 0.142040 | 0.0710199 | − | 0.997475i | \(-0.477375\pi\) | ||||
0.0710199 | + | 0.997475i | \(0.477375\pi\) | |||||||
\(74\) | 7.13733 | 0.829698 | ||||||||
\(75\) | 12.7923 | 1.47713 | ||||||||
\(76\) | 0.655968 | 0.0752446 | ||||||||
\(77\) | 20.6688 | 2.35543 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −14.6709 | −1.65061 | −0.825305 | − | 0.564688i | \(-0.808997\pi\) | ||||
−0.825305 | + | 0.564688i | \(0.808997\pi\) | |||||||
\(80\) | 4.21809 | 0.471597 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.02108 | −0.775348 | ||||||||
\(83\) | 8.38742 | 0.920639 | 0.460319 | − | 0.887753i | \(-0.347735\pi\) | ||||
0.460319 | + | 0.887753i | \(0.347735\pi\) | |||||||
\(84\) | −4.81342 | −0.525187 | ||||||||
\(85\) | −11.1713 | −1.21170 | ||||||||
\(86\) | 4.82571 | 0.520369 | ||||||||
\(87\) | −0.992673 | −0.106426 | ||||||||
\(88\) | 4.29400 | 0.457742 | ||||||||
\(89\) | 12.2086 | 1.29410 | 0.647052 | − | 0.762446i | \(-0.276002\pi\) | ||||
0.647052 | + | 0.762446i | \(0.276002\pi\) | |||||||
\(90\) | −4.21809 | −0.444626 | ||||||||
\(91\) | −4.81342 | −0.504584 | ||||||||
\(92\) | 1.52610 | 0.159107 | ||||||||
\(93\) | 1.93587 | 0.200740 | ||||||||
\(94\) | −1.34179 | −0.138395 | ||||||||
\(95\) | 2.76693 | 0.283881 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 2.87820 | 0.292237 | 0.146118 | − | 0.989267i | \(-0.453322\pi\) | ||||
0.146118 | + | 0.989267i | \(0.453322\pi\) | |||||||
\(98\) | −16.1690 | −1.63332 | ||||||||
\(99\) | −4.29400 | −0.431564 | ||||||||
\(100\) | 12.7923 | 1.27923 | ||||||||
\(101\) | −14.6408 | −1.45681 | −0.728405 | − | 0.685147i | \(-0.759738\pi\) | ||||
−0.728405 | + | 0.685147i | \(0.759738\pi\) | |||||||
\(102\) | 2.64843 | 0.262233 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −20.3034 | −1.98141 | ||||||||
\(106\) | 1.36163 | 0.132253 | ||||||||
\(107\) | −13.4887 | −1.30401 | −0.652003 | − | 0.758216i | \(-0.726071\pi\) | ||||
−0.652003 | + | 0.758216i | \(0.726071\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −2.10949 | −0.202052 | −0.101026 | − | 0.994884i | \(-0.532213\pi\) | ||||
−0.101026 | + | 0.994884i | \(0.532213\pi\) | |||||||
\(110\) | 18.1125 | 1.72696 | ||||||||
\(111\) | −7.13733 | −0.677446 | ||||||||
\(112\) | −4.81342 | −0.454825 | ||||||||
\(113\) | −3.48546 | −0.327884 | −0.163942 | − | 0.986470i | \(-0.552421\pi\) | ||||
−0.163942 | + | 0.986470i | \(0.552421\pi\) | |||||||
\(114\) | −0.655968 | −0.0614370 | ||||||||
\(115\) | 6.43724 | 0.600276 | ||||||||
\(116\) | −0.992673 | −0.0921674 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 14.8662 | 1.36855 | ||||||||
\(119\) | 12.7480 | 1.16861 | ||||||||
\(120\) | −4.21809 | −0.385057 | ||||||||
\(121\) | 7.43847 | 0.676225 | ||||||||
\(122\) | 9.04935 | 0.819289 | ||||||||
\(123\) | 7.02108 | 0.633069 | ||||||||
\(124\) | 1.93587 | 0.173846 | ||||||||
\(125\) | 32.8685 | 2.93985 | ||||||||
\(126\) | 4.81342 | 0.428814 | ||||||||
\(127\) | −18.7851 | −1.66691 | −0.833456 | − | 0.552585i | \(-0.813641\pi\) | ||||
−0.833456 | + | 0.552585i | \(0.813641\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.82571 | −0.424880 | ||||||||
\(130\) | −4.21809 | −0.369951 | ||||||||
\(131\) | −2.17667 | −0.190176 | −0.0950881 | − | 0.995469i | \(-0.530313\pi\) | ||||
−0.0950881 | + | 0.995469i | \(0.530313\pi\) | |||||||
\(132\) | −4.29400 | −0.373745 | ||||||||
\(133\) | −3.15745 | −0.273785 | ||||||||
\(134\) | −3.79388 | −0.327741 | ||||||||
\(135\) | 4.21809 | 0.363035 | ||||||||
\(136\) | 2.64843 | 0.227101 | ||||||||
\(137\) | 10.6655 | 0.911213 | 0.455606 | − | 0.890181i | \(-0.349422\pi\) | ||||
0.455606 | + | 0.890181i | \(0.349422\pi\) | |||||||
\(138\) | −1.52610 | −0.129911 | ||||||||
\(139\) | −7.36838 | −0.624978 | −0.312489 | − | 0.949921i | \(-0.601163\pi\) | ||||
−0.312489 | + | 0.949921i | \(0.601163\pi\) | |||||||
\(140\) | −20.3034 | −1.71595 | ||||||||
\(141\) | 1.34179 | 0.112999 | ||||||||
\(142\) | −4.83297 | −0.405574 | ||||||||
\(143\) | −4.29400 | −0.359083 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.18718 | −0.347727 | ||||||||
\(146\) | −1.21359 | −0.100437 | ||||||||
\(147\) | 16.1690 | 1.33360 | ||||||||
\(148\) | −7.13733 | −0.586685 | ||||||||
\(149\) | −4.93093 | −0.403958 | −0.201979 | − | 0.979390i | \(-0.564737\pi\) | ||||
−0.201979 | + | 0.979390i | \(0.564737\pi\) | |||||||
\(150\) | −12.7923 | −1.04449 | ||||||||
\(151\) | −9.49514 | −0.772703 | −0.386352 | − | 0.922352i | \(-0.626265\pi\) | ||||
−0.386352 | + | 0.922352i | \(0.626265\pi\) | |||||||
\(152\) | −0.655968 | −0.0532060 | ||||||||
\(153\) | −2.64843 | −0.214113 | ||||||||
\(154\) | −20.6688 | −1.66554 | ||||||||
\(155\) | 8.16567 | 0.655882 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 12.2902 | 0.980861 | 0.490430 | − | 0.871480i | \(-0.336840\pi\) | ||||
0.490430 | + | 0.871480i | \(0.336840\pi\) | |||||||
\(158\) | 14.6709 | 1.16716 | ||||||||
\(159\) | −1.36163 | −0.107984 | ||||||||
\(160\) | −4.21809 | −0.333469 | ||||||||
\(161\) | −7.34578 | −0.578928 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 4.10109 | 0.321223 | 0.160611 | − | 0.987018i | \(-0.448653\pi\) | ||||
0.160611 | + | 0.987018i | \(0.448653\pi\) | |||||||
\(164\) | 7.02108 | 0.548254 | ||||||||
\(165\) | −18.1125 | −1.41006 | ||||||||
\(166\) | −8.38742 | −0.650990 | ||||||||
\(167\) | −7.18868 | −0.556277 | −0.278139 | − | 0.960541i | \(-0.589717\pi\) | ||||
−0.278139 | + | 0.960541i | \(0.589717\pi\) | |||||||
\(168\) | 4.81342 | 0.371363 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 11.1713 | 0.856800 | ||||||||
\(171\) | 0.655968 | 0.0501631 | ||||||||
\(172\) | −4.82571 | −0.367957 | ||||||||
\(173\) | −14.0660 | −1.06942 | −0.534709 | − | 0.845036i | \(-0.679579\pi\) | ||||
−0.534709 | + | 0.845036i | \(0.679579\pi\) | |||||||
\(174\) | 0.992673 | 0.0752543 | ||||||||
\(175\) | −61.5746 | −4.65460 | ||||||||
\(176\) | −4.29400 | −0.323673 | ||||||||
\(177\) | −14.8662 | −1.11742 | ||||||||
\(178\) | −12.2086 | −0.915070 | ||||||||
\(179\) | −21.1002 | −1.57710 | −0.788551 | − | 0.614969i | \(-0.789169\pi\) | ||||
−0.788551 | + | 0.614969i | \(0.789169\pi\) | |||||||
\(180\) | 4.21809 | 0.314398 | ||||||||
\(181\) | −18.8679 | −1.40244 | −0.701219 | − | 0.712946i | \(-0.747360\pi\) | ||||
−0.701219 | + | 0.712946i | \(0.747360\pi\) | |||||||
\(182\) | 4.81342 | 0.356794 | ||||||||
\(183\) | −9.04935 | −0.668947 | ||||||||
\(184\) | −1.52610 | −0.112506 | ||||||||
\(185\) | −30.1059 | −2.21343 | ||||||||
\(186\) | −1.93587 | −0.141945 | ||||||||
\(187\) | 11.3724 | 0.831629 | ||||||||
\(188\) | 1.34179 | 0.0978603 | ||||||||
\(189\) | −4.81342 | −0.350125 | ||||||||
\(190\) | −2.76693 | −0.200734 | ||||||||
\(191\) | −1.99582 | −0.144412 | −0.0722062 | − | 0.997390i | \(-0.523004\pi\) | ||||
−0.0722062 | + | 0.997390i | \(0.523004\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −14.0177 | −1.00902 | −0.504508 | − | 0.863407i | \(-0.668326\pi\) | ||||
−0.504508 | + | 0.863407i | \(0.668326\pi\) | |||||||
\(194\) | −2.87820 | −0.206643 | ||||||||
\(195\) | 4.21809 | 0.302064 | ||||||||
\(196\) | 16.1690 | 1.15493 | ||||||||
\(197\) | 0.236467 | 0.0168476 | 0.00842378 | − | 0.999965i | \(-0.497319\pi\) | ||||
0.00842378 | + | 0.999965i | \(0.497319\pi\) | |||||||
\(198\) | 4.29400 | 0.305162 | ||||||||
\(199\) | −21.3648 | −1.51451 | −0.757255 | − | 0.653119i | \(-0.773460\pi\) | ||||
−0.757255 | + | 0.653119i | \(0.773460\pi\) | |||||||
\(200\) | −12.7923 | −0.904551 | ||||||||
\(201\) | 3.79388 | 0.267599 | ||||||||
\(202\) | 14.6408 | 1.03012 | ||||||||
\(203\) | 4.77815 | 0.335361 | ||||||||
\(204\) | −2.64843 | −0.185427 | ||||||||
\(205\) | 29.6155 | 2.06844 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 1.52610 | 0.106072 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −2.81673 | −0.194837 | ||||||||
\(210\) | 20.3034 | 1.40107 | ||||||||
\(211\) | −8.26635 | −0.569079 | −0.284539 | − | 0.958664i | \(-0.591841\pi\) | ||||
−0.284539 | + | 0.958664i | \(0.591841\pi\) | |||||||
\(212\) | −1.36163 | −0.0935168 | ||||||||
\(213\) | 4.83297 | 0.331150 | ||||||||
\(214\) | 13.4887 | 0.922072 | ||||||||
\(215\) | −20.3553 | −1.38822 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −9.31815 | −0.632557 | ||||||||
\(218\) | 2.10949 | 0.142872 | ||||||||
\(219\) | 1.21359 | 0.0820067 | ||||||||
\(220\) | −18.1125 | −1.22114 | ||||||||
\(221\) | −2.64843 | −0.178153 | ||||||||
\(222\) | 7.13733 | 0.479026 | ||||||||
\(223\) | −2.67211 | −0.178938 | −0.0894689 | − | 0.995990i | \(-0.528517\pi\) | ||||
−0.0894689 | + | 0.995990i | \(0.528517\pi\) | |||||||
\(224\) | 4.81342 | 0.321610 | ||||||||
\(225\) | 12.7923 | 0.852819 | ||||||||
\(226\) | 3.48546 | 0.231849 | ||||||||
\(227\) | 12.4207 | 0.824392 | 0.412196 | − | 0.911095i | \(-0.364762\pi\) | ||||
0.412196 | + | 0.911095i | \(0.364762\pi\) | |||||||
\(228\) | 0.655968 | 0.0434425 | ||||||||
\(229\) | −24.6135 | −1.62651 | −0.813253 | − | 0.581911i | \(-0.802305\pi\) | ||||
−0.813253 | + | 0.581911i | \(0.802305\pi\) | |||||||
\(230\) | −6.43724 | −0.424459 | ||||||||
\(231\) | 20.6688 | 1.35991 | ||||||||
\(232\) | 0.992673 | 0.0651722 | ||||||||
\(233\) | 5.52696 | 0.362083 | 0.181042 | − | 0.983475i | \(-0.442053\pi\) | ||||
0.181042 | + | 0.983475i | \(0.442053\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 5.65980 | 0.369205 | ||||||||
\(236\) | −14.8662 | −0.967710 | ||||||||
\(237\) | −14.6709 | −0.952980 | ||||||||
\(238\) | −12.7480 | −0.826330 | ||||||||
\(239\) | 14.7857 | 0.956410 | 0.478205 | − | 0.878248i | \(-0.341288\pi\) | ||||
0.478205 | + | 0.878248i | \(0.341288\pi\) | |||||||
\(240\) | 4.21809 | 0.272276 | ||||||||
\(241\) | −15.9625 | −1.02823 | −0.514117 | − | 0.857720i | \(-0.671880\pi\) | ||||
−0.514117 | + | 0.857720i | \(0.671880\pi\) | |||||||
\(242\) | −7.43847 | −0.478163 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −9.04935 | −0.579325 | ||||||||
\(245\) | 68.2023 | 4.35729 | ||||||||
\(246\) | −7.02108 | −0.447647 | ||||||||
\(247\) | 0.655968 | 0.0417382 | ||||||||
\(248\) | −1.93587 | −0.122928 | ||||||||
\(249\) | 8.38742 | 0.531531 | ||||||||
\(250\) | −32.8685 | −2.07879 | ||||||||
\(251\) | −7.52069 | −0.474702 | −0.237351 | − | 0.971424i | \(-0.576279\pi\) | ||||
−0.237351 | + | 0.971424i | \(0.576279\pi\) | |||||||
\(252\) | −4.81342 | −0.303217 | ||||||||
\(253\) | −6.55309 | −0.411990 | ||||||||
\(254\) | 18.7851 | 1.17869 | ||||||||
\(255\) | −11.1713 | −0.699574 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.5314 | −1.71736 | −0.858681 | − | 0.512511i | \(-0.828715\pi\) | ||||
−0.858681 | + | 0.512511i | \(0.828715\pi\) | |||||||
\(258\) | 4.82571 | 0.300435 | ||||||||
\(259\) | 34.3550 | 2.13471 | ||||||||
\(260\) | 4.21809 | 0.261595 | ||||||||
\(261\) | −0.992673 | −0.0614449 | ||||||||
\(262\) | 2.17667 | 0.134475 | ||||||||
\(263\) | −4.79598 | −0.295733 | −0.147866 | − | 0.989007i | \(-0.547241\pi\) | ||||
−0.147866 | + | 0.989007i | \(0.547241\pi\) | |||||||
\(264\) | 4.29400 | 0.264278 | ||||||||
\(265\) | −5.74346 | −0.352818 | ||||||||
\(266\) | 3.15745 | 0.193596 | ||||||||
\(267\) | 12.2086 | 0.747151 | ||||||||
\(268\) | 3.79388 | 0.231748 | ||||||||
\(269\) | −18.4173 | −1.12292 | −0.561462 | − | 0.827503i | \(-0.689761\pi\) | ||||
−0.561462 | + | 0.827503i | \(0.689761\pi\) | |||||||
\(270\) | −4.21809 | −0.256705 | ||||||||
\(271\) | 27.1420 | 1.64876 | 0.824380 | − | 0.566037i | \(-0.191524\pi\) | ||||
0.824380 | + | 0.566037i | \(0.191524\pi\) | |||||||
\(272\) | −2.64843 | −0.160585 | ||||||||
\(273\) | −4.81342 | −0.291321 | ||||||||
\(274\) | −10.6655 | −0.644325 | ||||||||
\(275\) | −54.9301 | −3.31241 | ||||||||
\(276\) | 1.52610 | 0.0918606 | ||||||||
\(277\) | 30.3796 | 1.82533 | 0.912667 | − | 0.408704i | \(-0.134019\pi\) | ||||
0.912667 | + | 0.408704i | \(0.134019\pi\) | |||||||
\(278\) | 7.36838 | 0.441926 | ||||||||
\(279\) | 1.93587 | 0.115897 | ||||||||
\(280\) | 20.3034 | 1.21336 | ||||||||
\(281\) | −22.8883 | −1.36540 | −0.682700 | − | 0.730698i | \(-0.739195\pi\) | ||||
−0.682700 | + | 0.730698i | \(0.739195\pi\) | |||||||
\(282\) | −1.34179 | −0.0799026 | ||||||||
\(283\) | 17.8384 | 1.06038 | 0.530192 | − | 0.847877i | \(-0.322120\pi\) | ||||
0.530192 | + | 0.847877i | \(0.322120\pi\) | |||||||
\(284\) | 4.83297 | 0.286784 | ||||||||
\(285\) | 2.76693 | 0.163899 | ||||||||
\(286\) | 4.29400 | 0.253910 | ||||||||
\(287\) | −33.7954 | −1.99488 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −9.98583 | −0.587402 | ||||||||
\(290\) | 4.18718 | 0.245880 | ||||||||
\(291\) | 2.87820 | 0.168723 | ||||||||
\(292\) | 1.21359 | 0.0710199 | ||||||||
\(293\) | −15.8528 | −0.926131 | −0.463065 | − | 0.886324i | \(-0.653251\pi\) | ||||
−0.463065 | + | 0.886324i | \(0.653251\pi\) | |||||||
\(294\) | −16.1690 | −0.942996 | ||||||||
\(295\) | −62.7071 | −3.65095 | ||||||||
\(296\) | 7.13733 | 0.414849 | ||||||||
\(297\) | −4.29400 | −0.249163 | ||||||||
\(298\) | 4.93093 | 0.285641 | ||||||||
\(299\) | 1.52610 | 0.0882568 | ||||||||
\(300\) | 12.7923 | 0.738563 | ||||||||
\(301\) | 23.2282 | 1.33885 | ||||||||
\(302\) | 9.49514 | 0.546384 | ||||||||
\(303\) | −14.6408 | −0.841089 | ||||||||
\(304\) | 0.655968 | 0.0376223 | ||||||||
\(305\) | −38.1710 | −2.18566 | ||||||||
\(306\) | 2.64843 | 0.151401 | ||||||||
\(307\) | 28.0252 | 1.59948 | 0.799742 | − | 0.600343i | \(-0.204969\pi\) | ||||
0.799742 | + | 0.600343i | \(0.204969\pi\) | |||||||
\(308\) | 20.6688 | 1.17772 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −8.16567 | −0.463779 | ||||||||
\(311\) | −10.6744 | −0.605288 | −0.302644 | − | 0.953104i | \(-0.597869\pi\) | ||||
−0.302644 | + | 0.953104i | \(0.597869\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 15.8503 | 0.895912 | 0.447956 | − | 0.894056i | \(-0.352152\pi\) | ||||
0.447956 | + | 0.894056i | \(0.352152\pi\) | |||||||
\(314\) | −12.2902 | −0.693573 | ||||||||
\(315\) | −20.3034 | −1.14397 | ||||||||
\(316\) | −14.6709 | −0.825305 | ||||||||
\(317\) | 22.0671 | 1.23941 | 0.619705 | − | 0.784835i | \(-0.287252\pi\) | ||||
0.619705 | + | 0.784835i | \(0.287252\pi\) | |||||||
\(318\) | 1.36163 | 0.0763561 | ||||||||
\(319\) | 4.26254 | 0.238657 | ||||||||
\(320\) | 4.21809 | 0.235798 | ||||||||
\(321\) | −13.4887 | −0.752868 | ||||||||
\(322\) | 7.34578 | 0.409364 | ||||||||
\(323\) | −1.73728 | −0.0966650 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 12.7923 | 0.709588 | ||||||||
\(326\) | −4.10109 | −0.227139 | ||||||||
\(327\) | −2.10949 | −0.116655 | ||||||||
\(328\) | −7.02108 | −0.387674 | ||||||||
\(329\) | −6.45861 | −0.356075 | ||||||||
\(330\) | 18.1125 | 0.997060 | ||||||||
\(331\) | −5.84180 | −0.321095 | −0.160547 | − | 0.987028i | \(-0.551326\pi\) | ||||
−0.160547 | + | 0.987028i | \(0.551326\pi\) | |||||||
\(332\) | 8.38742 | 0.460319 | ||||||||
\(333\) | −7.13733 | −0.391123 | ||||||||
\(334\) | 7.18868 | 0.393347 | ||||||||
\(335\) | 16.0029 | 0.874332 | ||||||||
\(336\) | −4.81342 | −0.262594 | ||||||||
\(337\) | 6.31009 | 0.343732 | 0.171866 | − | 0.985120i | \(-0.445020\pi\) | ||||
0.171866 | + | 0.985120i | \(0.445020\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −3.48546 | −0.189304 | ||||||||
\(340\) | −11.1713 | −0.605849 | ||||||||
\(341\) | −8.31263 | −0.450154 | ||||||||
\(342\) | −0.655968 | −0.0354707 | ||||||||
\(343\) | −44.1343 | −2.38303 | ||||||||
\(344\) | 4.82571 | 0.260185 | ||||||||
\(345\) | 6.43724 | 0.346569 | ||||||||
\(346\) | 14.0660 | 0.756193 | ||||||||
\(347\) | 11.8496 | 0.636122 | 0.318061 | − | 0.948070i | \(-0.396968\pi\) | ||||
0.318061 | + | 0.948070i | \(0.396968\pi\) | |||||||
\(348\) | −0.992673 | −0.0532129 | ||||||||
\(349\) | 2.98569 | 0.159820 | 0.0799102 | − | 0.996802i | \(-0.474537\pi\) | ||||
0.0799102 | + | 0.996802i | \(0.474537\pi\) | |||||||
\(350\) | 61.5746 | 3.29130 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 4.29400 | 0.228871 | ||||||||
\(353\) | −33.7345 | −1.79550 | −0.897752 | − | 0.440501i | \(-0.854801\pi\) | ||||
−0.897752 | + | 0.440501i | \(0.854801\pi\) | |||||||
\(354\) | 14.8662 | 0.790132 | ||||||||
\(355\) | 20.3859 | 1.08197 | ||||||||
\(356\) | 12.2086 | 0.647052 | ||||||||
\(357\) | 12.7480 | 0.674696 | ||||||||
\(358\) | 21.1002 | 1.11518 | ||||||||
\(359\) | −6.51521 | −0.343860 | −0.171930 | − | 0.985109i | \(-0.555000\pi\) | ||||
−0.171930 | + | 0.985109i | \(0.555000\pi\) | |||||||
\(360\) | −4.21809 | −0.222313 | ||||||||
\(361\) | −18.5697 | −0.977353 | ||||||||
\(362\) | 18.8679 | 0.991673 | ||||||||
\(363\) | 7.43847 | 0.390418 | ||||||||
\(364\) | −4.81342 | −0.252292 | ||||||||
\(365\) | 5.11902 | 0.267942 | ||||||||
\(366\) | 9.04935 | 0.473017 | ||||||||
\(367\) | 25.6512 | 1.33898 | 0.669490 | − | 0.742821i | \(-0.266513\pi\) | ||||
0.669490 | + | 0.742821i | \(0.266513\pi\) | |||||||
\(368\) | 1.52610 | 0.0795536 | ||||||||
\(369\) | 7.02108 | 0.365503 | ||||||||
\(370\) | 30.1059 | 1.56513 | ||||||||
\(371\) | 6.55407 | 0.340271 | ||||||||
\(372\) | 1.93587 | 0.100370 | ||||||||
\(373\) | −14.8679 | −0.769830 | −0.384915 | − | 0.922952i | \(-0.625769\pi\) | ||||
−0.384915 | + | 0.922952i | \(0.625769\pi\) | |||||||
\(374\) | −11.3724 | −0.588051 | ||||||||
\(375\) | 32.8685 | 1.69732 | ||||||||
\(376\) | −1.34179 | −0.0691977 | ||||||||
\(377\) | −0.992673 | −0.0511253 | ||||||||
\(378\) | 4.81342 | 0.247576 | ||||||||
\(379\) | −8.72164 | −0.448001 | −0.224000 | − | 0.974589i | \(-0.571912\pi\) | ||||
−0.224000 | + | 0.974589i | \(0.571912\pi\) | |||||||
\(380\) | 2.76693 | 0.141940 | ||||||||
\(381\) | −18.7851 | −0.962392 | ||||||||
\(382\) | 1.99582 | 0.102115 | ||||||||
\(383\) | −4.66833 | −0.238541 | −0.119270 | − | 0.992862i | \(-0.538055\pi\) | ||||
−0.119270 | + | 0.992862i | \(0.538055\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 87.1830 | 4.44326 | ||||||||
\(386\) | 14.0177 | 0.713481 | ||||||||
\(387\) | −4.82571 | −0.245304 | ||||||||
\(388\) | 2.87820 | 0.146118 | ||||||||
\(389\) | −19.0163 | −0.964166 | −0.482083 | − | 0.876126i | \(-0.660120\pi\) | ||||
−0.482083 | + | 0.876126i | \(0.660120\pi\) | |||||||
\(390\) | −4.21809 | −0.213591 | ||||||||
\(391\) | −4.04178 | −0.204401 | ||||||||
\(392\) | −16.1690 | −0.816658 | ||||||||
\(393\) | −2.17667 | −0.109798 | ||||||||
\(394\) | −0.236467 | −0.0119130 | ||||||||
\(395\) | −61.8833 | −3.11369 | ||||||||
\(396\) | −4.29400 | −0.215782 | ||||||||
\(397\) | 12.2106 | 0.612833 | 0.306416 | − | 0.951898i | \(-0.400870\pi\) | ||||
0.306416 | + | 0.951898i | \(0.400870\pi\) | |||||||
\(398\) | 21.3648 | 1.07092 | ||||||||
\(399\) | −3.15745 | −0.158070 | ||||||||
\(400\) | 12.7923 | 0.639614 | ||||||||
\(401\) | 25.4544 | 1.27113 | 0.635567 | − | 0.772046i | \(-0.280767\pi\) | ||||
0.635567 | + | 0.772046i | \(0.280767\pi\) | |||||||
\(402\) | −3.79388 | −0.189221 | ||||||||
\(403\) | 1.93587 | 0.0964325 | ||||||||
\(404\) | −14.6408 | −0.728405 | ||||||||
\(405\) | 4.21809 | 0.209599 | ||||||||
\(406\) | −4.77815 | −0.237136 | ||||||||
\(407\) | 30.6477 | 1.51915 | ||||||||
\(408\) | 2.64843 | 0.131117 | ||||||||
\(409\) | −17.5734 | −0.868951 | −0.434475 | − | 0.900684i | \(-0.643066\pi\) | ||||
−0.434475 | + | 0.900684i | \(0.643066\pi\) | |||||||
\(410\) | −29.6155 | −1.46261 | ||||||||
\(411\) | 10.6655 | 0.526089 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 71.5575 | 3.52111 | ||||||||
\(414\) | −1.52610 | −0.0750039 | ||||||||
\(415\) | 35.3789 | 1.73668 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −7.36838 | −0.360831 | ||||||||
\(418\) | 2.81673 | 0.137771 | ||||||||
\(419\) | 25.0377 | 1.22317 | 0.611585 | − | 0.791179i | \(-0.290532\pi\) | ||||
0.611585 | + | 0.791179i | \(0.290532\pi\) | |||||||
\(420\) | −20.3034 | −0.990706 | ||||||||
\(421\) | 37.5028 | 1.82778 | 0.913888 | − | 0.405966i | \(-0.133065\pi\) | ||||
0.913888 | + | 0.405966i | \(0.133065\pi\) | |||||||
\(422\) | 8.26635 | 0.402400 | ||||||||
\(423\) | 1.34179 | 0.0652402 | ||||||||
\(424\) | 1.36163 | 0.0661264 | ||||||||
\(425\) | −33.8794 | −1.64339 | ||||||||
\(426\) | −4.83297 | −0.234158 | ||||||||
\(427\) | 43.5583 | 2.10793 | ||||||||
\(428\) | −13.4887 | −0.652003 | ||||||||
\(429\) | −4.29400 | −0.207316 | ||||||||
\(430\) | 20.3553 | 0.981618 | ||||||||
\(431\) | −9.35222 | −0.450480 | −0.225240 | − | 0.974303i | \(-0.572317\pi\) | ||||
−0.225240 | + | 0.974303i | \(0.572317\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −1.48956 | −0.0715835 | −0.0357917 | − | 0.999359i | \(-0.511395\pi\) | ||||
−0.0357917 | + | 0.999359i | \(0.511395\pi\) | |||||||
\(434\) | 9.31815 | 0.447285 | ||||||||
\(435\) | −4.18718 | −0.200760 | ||||||||
\(436\) | −2.10949 | −0.101026 | ||||||||
\(437\) | 1.00107 | 0.0478879 | ||||||||
\(438\) | −1.21359 | −0.0579875 | ||||||||
\(439\) | 35.5882 | 1.69853 | 0.849265 | − | 0.527967i | \(-0.177045\pi\) | ||||
0.849265 | + | 0.527967i | \(0.177045\pi\) | |||||||
\(440\) | 18.1125 | 0.863479 | ||||||||
\(441\) | 16.1690 | 0.769953 | ||||||||
\(442\) | 2.64843 | 0.125973 | ||||||||
\(443\) | −3.05759 | −0.145270 | −0.0726352 | − | 0.997359i | \(-0.523141\pi\) | ||||
−0.0726352 | + | 0.997359i | \(0.523141\pi\) | |||||||
\(444\) | −7.13733 | −0.338723 | ||||||||
\(445\) | 51.4968 | 2.44118 | ||||||||
\(446\) | 2.67211 | 0.126528 | ||||||||
\(447\) | −4.93093 | −0.233225 | ||||||||
\(448\) | −4.81342 | −0.227413 | ||||||||
\(449\) | −5.76893 | −0.272253 | −0.136126 | − | 0.990691i | \(-0.543465\pi\) | ||||
−0.136126 | + | 0.990691i | \(0.543465\pi\) | |||||||
\(450\) | −12.7923 | −0.603034 | ||||||||
\(451\) | −30.1485 | −1.41964 | ||||||||
\(452\) | −3.48546 | −0.163942 | ||||||||
\(453\) | −9.49514 | −0.446120 | ||||||||
\(454\) | −12.4207 | −0.582933 | ||||||||
\(455\) | −20.3034 | −0.951840 | ||||||||
\(456\) | −0.655968 | −0.0307185 | ||||||||
\(457\) | 28.6429 | 1.33986 | 0.669929 | − | 0.742425i | \(-0.266324\pi\) | ||||
0.669929 | + | 0.742425i | \(0.266324\pi\) | |||||||
\(458\) | 24.6135 | 1.15011 | ||||||||
\(459\) | −2.64843 | −0.123618 | ||||||||
\(460\) | 6.43724 | 0.300138 | ||||||||
\(461\) | 8.15612 | 0.379868 | 0.189934 | − | 0.981797i | \(-0.439173\pi\) | ||||
0.189934 | + | 0.981797i | \(0.439173\pi\) | |||||||
\(462\) | −20.6688 | −0.961602 | ||||||||
\(463\) | −10.4360 | −0.485001 | −0.242501 | − | 0.970151i | \(-0.577968\pi\) | ||||
−0.242501 | + | 0.970151i | \(0.577968\pi\) | |||||||
\(464\) | −0.992673 | −0.0460837 | ||||||||
\(465\) | 8.16567 | 0.378674 | ||||||||
\(466\) | −5.52696 | −0.256031 | ||||||||
\(467\) | −29.0299 | −1.34334 | −0.671671 | − | 0.740850i | \(-0.734423\pi\) | ||||
−0.671671 | + | 0.740850i | \(0.734423\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −18.2615 | −0.843239 | ||||||||
\(470\) | −5.65980 | −0.261067 | ||||||||
\(471\) | 12.2902 | 0.566300 | ||||||||
\(472\) | 14.8662 | 0.684274 | ||||||||
\(473\) | 20.7216 | 0.952780 | ||||||||
\(474\) | 14.6709 | 0.673858 | ||||||||
\(475\) | 8.39132 | 0.385020 | ||||||||
\(476\) | 12.7480 | 0.584303 | ||||||||
\(477\) | −1.36163 | −0.0623445 | ||||||||
\(478\) | −14.7857 | −0.676284 | ||||||||
\(479\) | 12.8742 | 0.588238 | 0.294119 | − | 0.955769i | \(-0.404974\pi\) | ||||
0.294119 | + | 0.955769i | \(0.404974\pi\) | |||||||
\(480\) | −4.21809 | −0.192529 | ||||||||
\(481\) | −7.13733 | −0.325434 | ||||||||
\(482\) | 15.9625 | 0.727071 | ||||||||
\(483\) | −7.34578 | −0.334244 | ||||||||
\(484\) | 7.43847 | 0.338112 | ||||||||
\(485\) | 12.1405 | 0.551272 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 1.48082 | 0.0671023 | 0.0335511 | − | 0.999437i | \(-0.489318\pi\) | ||||
0.0335511 | + | 0.999437i | \(0.489318\pi\) | |||||||
\(488\) | 9.04935 | 0.409645 | ||||||||
\(489\) | 4.10109 | 0.185458 | ||||||||
\(490\) | −68.2023 | −3.08107 | ||||||||
\(491\) | 11.9383 | 0.538769 | 0.269384 | − | 0.963033i | \(-0.413180\pi\) | ||||
0.269384 | + | 0.963033i | \(0.413180\pi\) | |||||||
\(492\) | 7.02108 | 0.316535 | ||||||||
\(493\) | 2.62902 | 0.118405 | ||||||||
\(494\) | −0.655968 | −0.0295134 | ||||||||
\(495\) | −18.1125 | −0.814096 | ||||||||
\(496\) | 1.93587 | 0.0869231 | ||||||||
\(497\) | −23.2631 | −1.04349 | ||||||||
\(498\) | −8.38742 | −0.375849 | ||||||||
\(499\) | −41.2431 | −1.84629 | −0.923147 | − | 0.384447i | \(-0.874392\pi\) | ||||
−0.923147 | + | 0.384447i | \(0.874392\pi\) | |||||||
\(500\) | 32.8685 | 1.46993 | ||||||||
\(501\) | −7.18868 | −0.321167 | ||||||||
\(502\) | 7.52069 | 0.335665 | ||||||||
\(503\) | −13.4839 | −0.601217 | −0.300608 | − | 0.953748i | \(-0.597190\pi\) | ||||
−0.300608 | + | 0.953748i | \(0.597190\pi\) | |||||||
\(504\) | 4.81342 | 0.214407 | ||||||||
\(505\) | −61.7560 | −2.74811 | ||||||||
\(506\) | 6.55309 | 0.291321 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −18.7851 | −0.833456 | ||||||||
\(509\) | 16.7375 | 0.741877 | 0.370939 | − | 0.928657i | \(-0.379036\pi\) | ||||
0.370939 | + | 0.928657i | \(0.379036\pi\) | |||||||
\(510\) | 11.1713 | 0.494674 | ||||||||
\(511\) | −5.84151 | −0.258413 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.655968 | 0.0289617 | ||||||||
\(514\) | 27.5314 | 1.21436 | ||||||||
\(515\) | −4.21809 | −0.185871 | ||||||||
\(516\) | −4.82571 | −0.212440 | ||||||||
\(517\) | −5.76166 | −0.253398 | ||||||||
\(518\) | −34.3550 | −1.50947 | ||||||||
\(519\) | −14.0660 | −0.617429 | ||||||||
\(520\) | −4.21809 | −0.184975 | ||||||||
\(521\) | 30.8017 | 1.34945 | 0.674723 | − | 0.738071i | \(-0.264263\pi\) | ||||
0.674723 | + | 0.738071i | \(0.264263\pi\) | |||||||
\(522\) | 0.992673 | 0.0434481 | ||||||||
\(523\) | 7.33470 | 0.320724 | 0.160362 | − | 0.987058i | \(-0.448734\pi\) | ||||
0.160362 | + | 0.987058i | \(0.448734\pi\) | |||||||
\(524\) | −2.17667 | −0.0950881 | ||||||||
\(525\) | −61.5746 | −2.68734 | ||||||||
\(526\) | 4.79598 | 0.209115 | ||||||||
\(527\) | −5.12701 | −0.223336 | ||||||||
\(528\) | −4.29400 | −0.186873 | ||||||||
\(529\) | −20.6710 | −0.898739 | ||||||||
\(530\) | 5.74346 | 0.249480 | ||||||||
\(531\) | −14.8662 | −0.645140 | ||||||||
\(532\) | −3.15745 | −0.136893 | ||||||||
\(533\) | 7.02108 | 0.304117 | ||||||||
\(534\) | −12.2086 | −0.528316 | ||||||||
\(535\) | −56.8967 | −2.45986 | ||||||||
\(536\) | −3.79388 | −0.163870 | ||||||||
\(537\) | −21.1002 | −0.910541 | ||||||||
\(538\) | 18.4173 | 0.794026 | ||||||||
\(539\) | −69.4298 | −2.99055 | ||||||||
\(540\) | 4.21809 | 0.181518 | ||||||||
\(541\) | 15.0975 | 0.649091 | 0.324545 | − | 0.945870i | \(-0.394789\pi\) | ||||
0.324545 | + | 0.945870i | \(0.394789\pi\) | |||||||
\(542\) | −27.1420 | −1.16585 | ||||||||
\(543\) | −18.8679 | −0.809698 | ||||||||
\(544\) | 2.64843 | 0.113550 | ||||||||
\(545\) | −8.89800 | −0.381149 | ||||||||
\(546\) | 4.81342 | 0.205995 | ||||||||
\(547\) | −9.07339 | −0.387950 | −0.193975 | − | 0.981006i | \(-0.562138\pi\) | ||||
−0.193975 | + | 0.981006i | \(0.562138\pi\) | |||||||
\(548\) | 10.6655 | 0.455606 | ||||||||
\(549\) | −9.04935 | −0.386217 | ||||||||
\(550\) | 54.9301 | 2.34223 | ||||||||
\(551\) | −0.651161 | −0.0277404 | ||||||||
\(552\) | −1.52610 | −0.0649553 | ||||||||
\(553\) | 70.6174 | 3.00296 | ||||||||
\(554\) | −30.3796 | −1.29071 | ||||||||
\(555\) | −30.1059 | −1.27792 | ||||||||
\(556\) | −7.36838 | −0.312489 | ||||||||
\(557\) | 25.0527 | 1.06152 | 0.530758 | − | 0.847523i | \(-0.321907\pi\) | ||||
0.530758 | + | 0.847523i | \(0.321907\pi\) | |||||||
\(558\) | −1.93587 | −0.0819518 | ||||||||
\(559\) | −4.82571 | −0.204106 | ||||||||
\(560\) | −20.3034 | −0.857977 | ||||||||
\(561\) | 11.3724 | 0.480141 | ||||||||
\(562\) | 22.8883 | 0.965484 | ||||||||
\(563\) | 27.3887 | 1.15430 | 0.577149 | − | 0.816639i | \(-0.304165\pi\) | ||||
0.577149 | + | 0.816639i | \(0.304165\pi\) | |||||||
\(564\) | 1.34179 | 0.0564997 | ||||||||
\(565\) | −14.7020 | −0.618516 | ||||||||
\(566\) | −17.8384 | −0.749805 | ||||||||
\(567\) | −4.81342 | −0.202145 | ||||||||
\(568\) | −4.83297 | −0.202787 | ||||||||
\(569\) | 7.91850 | 0.331961 | 0.165980 | − | 0.986129i | \(-0.446921\pi\) | ||||
0.165980 | + | 0.986129i | \(0.446921\pi\) | |||||||
\(570\) | −2.76693 | −0.115894 | ||||||||
\(571\) | 19.1442 | 0.801161 | 0.400581 | − | 0.916262i | \(-0.368808\pi\) | ||||
0.400581 | + | 0.916262i | \(0.368808\pi\) | |||||||
\(572\) | −4.29400 | −0.179541 | ||||||||
\(573\) | −1.99582 | −0.0833766 | ||||||||
\(574\) | 33.7954 | 1.41059 | ||||||||
\(575\) | 19.5223 | 0.814138 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 35.7241 | 1.48721 | 0.743607 | − | 0.668617i | \(-0.233113\pi\) | ||||
0.743607 | + | 0.668617i | \(0.233113\pi\) | |||||||
\(578\) | 9.98583 | 0.415356 | ||||||||
\(579\) | −14.0177 | −0.582555 | ||||||||
\(580\) | −4.18718 | −0.173863 | ||||||||
\(581\) | −40.3722 | −1.67492 | ||||||||
\(582\) | −2.87820 | −0.119305 | ||||||||
\(583\) | 5.84682 | 0.242151 | ||||||||
\(584\) | −1.21359 | −0.0502186 | ||||||||
\(585\) | 4.21809 | 0.174397 | ||||||||
\(586\) | 15.8528 | 0.654873 | ||||||||
\(587\) | −29.4458 | −1.21536 | −0.607680 | − | 0.794182i | \(-0.707900\pi\) | ||||
−0.607680 | + | 0.794182i | \(0.707900\pi\) | |||||||
\(588\) | 16.1690 | 0.666799 | ||||||||
\(589\) | 1.26987 | 0.0523239 | ||||||||
\(590\) | 62.7071 | 2.58161 | ||||||||
\(591\) | 0.236467 | 0.00972694 | ||||||||
\(592\) | −7.13733 | −0.293343 | ||||||||
\(593\) | −43.7704 | −1.79743 | −0.898717 | − | 0.438528i | \(-0.855500\pi\) | ||||
−0.898717 | + | 0.438528i | \(0.855500\pi\) | |||||||
\(594\) | 4.29400 | 0.176185 | ||||||||
\(595\) | 53.7722 | 2.20444 | ||||||||
\(596\) | −4.93093 | −0.201979 | ||||||||
\(597\) | −21.3648 | −0.874403 | ||||||||
\(598\) | −1.52610 | −0.0624070 | ||||||||
\(599\) | −37.2570 | −1.52228 | −0.761140 | − | 0.648588i | \(-0.775360\pi\) | ||||
−0.761140 | + | 0.648588i | \(0.775360\pi\) | |||||||
\(600\) | −12.7923 | −0.522243 | ||||||||
\(601\) | 27.2474 | 1.11145 | 0.555723 | − | 0.831368i | \(-0.312442\pi\) | ||||
0.555723 | + | 0.831368i | \(0.312442\pi\) | |||||||
\(602\) | −23.2282 | −0.946709 | ||||||||
\(603\) | 3.79388 | 0.154499 | ||||||||
\(604\) | −9.49514 | −0.386352 | ||||||||
\(605\) | 31.3761 | 1.27562 | ||||||||
\(606\) | 14.6408 | 0.594740 | ||||||||
\(607\) | 5.08465 | 0.206380 | 0.103190 | − | 0.994662i | \(-0.467095\pi\) | ||||
0.103190 | + | 0.994662i | \(0.467095\pi\) | |||||||
\(608\) | −0.655968 | −0.0266030 | ||||||||
\(609\) | 4.77815 | 0.193620 | ||||||||
\(610\) | 38.1710 | 1.54550 | ||||||||
\(611\) | 1.34179 | 0.0542831 | ||||||||
\(612\) | −2.64843 | −0.107056 | ||||||||
\(613\) | 38.3291 | 1.54810 | 0.774048 | − | 0.633127i | \(-0.218229\pi\) | ||||
0.774048 | + | 0.633127i | \(0.218229\pi\) | |||||||
\(614\) | −28.0252 | −1.13101 | ||||||||
\(615\) | 29.6155 | 1.19421 | ||||||||
\(616\) | −20.6688 | −0.832772 | ||||||||
\(617\) | 13.7858 | 0.554996 | 0.277498 | − | 0.960726i | \(-0.410495\pi\) | ||||
0.277498 | + | 0.960726i | \(0.410495\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 35.3882 | 1.42237 | 0.711187 | − | 0.703003i | \(-0.248158\pi\) | ||||
0.711187 | + | 0.703003i | \(0.248158\pi\) | |||||||
\(620\) | 8.16567 | 0.327941 | ||||||||
\(621\) | 1.52610 | 0.0612404 | ||||||||
\(622\) | 10.6744 | 0.428004 | ||||||||
\(623\) | −58.7649 | −2.35437 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 74.6810 | 2.98724 | ||||||||
\(626\) | −15.8503 | −0.633505 | ||||||||
\(627\) | −2.81673 | −0.112489 | ||||||||
\(628\) | 12.2902 | 0.490430 | ||||||||
\(629\) | 18.9027 | 0.753701 | ||||||||
\(630\) | 20.3034 | 0.808908 | ||||||||
\(631\) | 13.8617 | 0.551827 | 0.275914 | − | 0.961182i | \(-0.411020\pi\) | ||||
0.275914 | + | 0.961182i | \(0.411020\pi\) | |||||||
\(632\) | 14.6709 | 0.583578 | ||||||||
\(633\) | −8.26635 | −0.328558 | ||||||||
\(634\) | −22.0671 | −0.876395 | ||||||||
\(635\) | −79.2374 | −3.14444 | ||||||||
\(636\) | −1.36163 | −0.0539919 | ||||||||
\(637\) | 16.1690 | 0.640640 | ||||||||
\(638\) | −4.26254 | −0.168756 | ||||||||
\(639\) | 4.83297 | 0.191189 | ||||||||
\(640\) | −4.21809 | −0.166735 | ||||||||
\(641\) | 39.4048 | 1.55640 | 0.778198 | − | 0.628019i | \(-0.216134\pi\) | ||||
0.778198 | + | 0.628019i | \(0.216134\pi\) | |||||||
\(642\) | 13.4887 | 0.532358 | ||||||||
\(643\) | 15.6956 | 0.618975 | 0.309488 | − | 0.950903i | \(-0.399842\pi\) | ||||
0.309488 | + | 0.950903i | \(0.399842\pi\) | |||||||
\(644\) | −7.34578 | −0.289464 | ||||||||
\(645\) | −20.3553 | −0.801488 | ||||||||
\(646\) | 1.73728 | 0.0683525 | ||||||||
\(647\) | 4.10390 | 0.161341 | 0.0806705 | − | 0.996741i | \(-0.474294\pi\) | ||||
0.0806705 | + | 0.996741i | \(0.474294\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 63.8357 | 2.50577 | ||||||||
\(650\) | −12.7923 | −0.501754 | ||||||||
\(651\) | −9.31815 | −0.365207 | ||||||||
\(652\) | 4.10109 | 0.160611 | ||||||||
\(653\) | 34.4890 | 1.34966 | 0.674830 | − | 0.737973i | \(-0.264217\pi\) | ||||
0.674830 | + | 0.737973i | \(0.264217\pi\) | |||||||
\(654\) | 2.10949 | 0.0824875 | ||||||||
\(655\) | −9.18137 | −0.358746 | ||||||||
\(656\) | 7.02108 | 0.274127 | ||||||||
\(657\) | 1.21359 | 0.0473466 | ||||||||
\(658\) | 6.45861 | 0.251783 | ||||||||
\(659\) | 3.43753 | 0.133907 | 0.0669535 | − | 0.997756i | \(-0.478672\pi\) | ||||
0.0669535 | + | 0.997756i | \(0.478672\pi\) | |||||||
\(660\) | −18.1125 | −0.705028 | ||||||||
\(661\) | −21.8422 | −0.849565 | −0.424782 | − | 0.905296i | \(-0.639649\pi\) | ||||
−0.424782 | + | 0.905296i | \(0.639649\pi\) | |||||||
\(662\) | 5.84180 | 0.227048 | ||||||||
\(663\) | −2.64843 | −0.102856 | ||||||||
\(664\) | −8.38742 | −0.325495 | ||||||||
\(665\) | −13.3184 | −0.516465 | ||||||||
\(666\) | 7.13733 | 0.276566 | ||||||||
\(667\) | −1.51492 | −0.0586580 | ||||||||
\(668\) | −7.18868 | −0.278139 | ||||||||
\(669\) | −2.67211 | −0.103310 | ||||||||
\(670\) | −16.0029 | −0.618246 | ||||||||
\(671\) | 38.8579 | 1.50009 | ||||||||
\(672\) | 4.81342 | 0.185682 | ||||||||
\(673\) | −29.9645 | −1.15505 | −0.577523 | − | 0.816374i | \(-0.695981\pi\) | ||||
−0.577523 | + | 0.816374i | \(0.695981\pi\) | |||||||
\(674\) | −6.31009 | −0.243055 | ||||||||
\(675\) | 12.7923 | 0.492375 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −32.0957 | −1.23354 | −0.616770 | − | 0.787144i | \(-0.711559\pi\) | ||||
−0.616770 | + | 0.787144i | \(0.711559\pi\) | |||||||
\(678\) | 3.48546 | 0.133858 | ||||||||
\(679\) | −13.8540 | −0.531667 | ||||||||
\(680\) | 11.1713 | 0.428400 | ||||||||
\(681\) | 12.4207 | 0.475963 | ||||||||
\(682\) | 8.31263 | 0.318307 | ||||||||
\(683\) | −48.1248 | −1.84144 | −0.920722 | − | 0.390218i | \(-0.872400\pi\) | ||||
−0.920722 | + | 0.390218i | \(0.872400\pi\) | |||||||
\(684\) | 0.655968 | 0.0250815 | ||||||||
\(685\) | 44.9879 | 1.71890 | ||||||||
\(686\) | 44.1343 | 1.68506 | ||||||||
\(687\) | −24.6135 | −0.939063 | ||||||||
\(688\) | −4.82571 | −0.183978 | ||||||||
\(689\) | −1.36163 | −0.0518738 | ||||||||
\(690\) | −6.43724 | −0.245062 | ||||||||
\(691\) | 35.3486 | 1.34472 | 0.672362 | − | 0.740222i | \(-0.265280\pi\) | ||||
0.672362 | + | 0.740222i | \(0.265280\pi\) | |||||||
\(692\) | −14.0660 | −0.534709 | ||||||||
\(693\) | 20.6688 | 0.785145 | ||||||||
\(694\) | −11.8496 | −0.449806 | ||||||||
\(695\) | −31.0805 | −1.17895 | ||||||||
\(696\) | 0.992673 | 0.0376272 | ||||||||
\(697\) | −18.5948 | −0.704329 | ||||||||
\(698\) | −2.98569 | −0.113010 | ||||||||
\(699\) | 5.52696 | 0.209049 | ||||||||
\(700\) | −61.5746 | −2.32730 | ||||||||
\(701\) | −14.7957 | −0.558826 | −0.279413 | − | 0.960171i | \(-0.590140\pi\) | ||||
−0.279413 | + | 0.960171i | \(0.590140\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −4.68186 | −0.176580 | ||||||||
\(704\) | −4.29400 | −0.161836 | ||||||||
\(705\) | 5.65980 | 0.213160 | ||||||||
\(706\) | 33.7345 | 1.26961 | ||||||||
\(707\) | 70.4721 | 2.65038 | ||||||||
\(708\) | −14.8662 | −0.558708 | ||||||||
\(709\) | 28.9327 | 1.08659 | 0.543296 | − | 0.839541i | \(-0.317176\pi\) | ||||
0.543296 | + | 0.839541i | \(0.317176\pi\) | |||||||
\(710\) | −20.3859 | −0.765070 | ||||||||
\(711\) | −14.6709 | −0.550203 | ||||||||
\(712\) | −12.2086 | −0.457535 | ||||||||
\(713\) | 2.95434 | 0.110641 | ||||||||
\(714\) | −12.7480 | −0.477082 | ||||||||
\(715\) | −18.1125 | −0.677369 | ||||||||
\(716\) | −21.1002 | −0.788551 | ||||||||
\(717\) | 14.7857 | 0.552184 | ||||||||
\(718\) | 6.51521 | 0.243146 | ||||||||
\(719\) | −38.8020 | −1.44707 | −0.723534 | − | 0.690288i | \(-0.757484\pi\) | ||||
−0.723534 | + | 0.690288i | \(0.757484\pi\) | |||||||
\(720\) | 4.21809 | 0.157199 | ||||||||
\(721\) | 4.81342 | 0.179261 | ||||||||
\(722\) | 18.5697 | 0.691093 | ||||||||
\(723\) | −15.9625 | −0.593651 | ||||||||
\(724\) | −18.8679 | −0.701219 | ||||||||
\(725\) | −12.6985 | −0.471612 | ||||||||
\(726\) | −7.43847 | −0.276068 | ||||||||
\(727\) | 16.6426 | 0.617238 | 0.308619 | − | 0.951186i | \(-0.400133\pi\) | ||||
0.308619 | + | 0.951186i | \(0.400133\pi\) | |||||||
\(728\) | 4.81342 | 0.178397 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.11902 | −0.189464 | ||||||||
\(731\) | 12.7805 | 0.472705 | ||||||||
\(732\) | −9.04935 | −0.334473 | ||||||||
\(733\) | −40.2474 | −1.48657 | −0.743285 | − | 0.668975i | \(-0.766733\pi\) | ||||
−0.743285 | + | 0.668975i | \(0.766733\pi\) | |||||||
\(734\) | −25.6512 | −0.946802 | ||||||||
\(735\) | 68.2023 | 2.51568 | ||||||||
\(736\) | −1.52610 | −0.0562529 | ||||||||
\(737\) | −16.2909 | −0.600084 | ||||||||
\(738\) | −7.02108 | −0.258449 | ||||||||
\(739\) | −40.9021 | −1.50461 | −0.752305 | − | 0.658815i | \(-0.771058\pi\) | ||||
−0.752305 | + | 0.658815i | \(0.771058\pi\) | |||||||
\(740\) | −30.1059 | −1.10672 | ||||||||
\(741\) | 0.655968 | 0.0240976 | ||||||||
\(742\) | −6.55407 | −0.240608 | ||||||||
\(743\) | −10.1196 | −0.371253 | −0.185627 | − | 0.982620i | \(-0.559432\pi\) | ||||
−0.185627 | + | 0.982620i | \(0.559432\pi\) | |||||||
\(744\) | −1.93587 | −0.0709724 | ||||||||
\(745\) | −20.7991 | −0.762020 | ||||||||
\(746\) | 14.8679 | 0.544352 | ||||||||
\(747\) | 8.38742 | 0.306880 | ||||||||
\(748\) | 11.3724 | 0.415815 | ||||||||
\(749\) | 64.9270 | 2.37238 | ||||||||
\(750\) | −32.8685 | −1.20019 | ||||||||
\(751\) | 2.57695 | 0.0940342 | 0.0470171 | − | 0.998894i | \(-0.485028\pi\) | ||||
0.0470171 | + | 0.998894i | \(0.485028\pi\) | |||||||
\(752\) | 1.34179 | 0.0489302 | ||||||||
\(753\) | −7.52069 | −0.274069 | ||||||||
\(754\) | 0.992673 | 0.0361510 | ||||||||
\(755\) | −40.0513 | −1.45762 | ||||||||
\(756\) | −4.81342 | −0.175062 | ||||||||
\(757\) | 39.8064 | 1.44679 | 0.723394 | − | 0.690435i | \(-0.242581\pi\) | ||||
0.723394 | + | 0.690435i | \(0.242581\pi\) | |||||||
\(758\) | 8.72164 | 0.316784 | ||||||||
\(759\) | −6.55309 | −0.237862 | ||||||||
\(760\) | −2.76693 | −0.100367 | ||||||||
\(761\) | 43.5365 | 1.57820 | 0.789098 | − | 0.614267i | \(-0.210548\pi\) | ||||
0.789098 | + | 0.614267i | \(0.210548\pi\) | |||||||
\(762\) | 18.7851 | 0.680514 | ||||||||
\(763\) | 10.1538 | 0.367594 | ||||||||
\(764\) | −1.99582 | −0.0722062 | ||||||||
\(765\) | −11.1713 | −0.403899 | ||||||||
\(766\) | 4.66833 | 0.168674 | ||||||||
\(767\) | −14.8662 | −0.536789 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 3.22205 | 0.116190 | 0.0580950 | − | 0.998311i | \(-0.481497\pi\) | ||||
0.0580950 | + | 0.998311i | \(0.481497\pi\) | |||||||
\(770\) | −87.1830 | −3.14186 | ||||||||
\(771\) | −27.5314 | −0.991519 | ||||||||
\(772\) | −14.0177 | −0.504508 | ||||||||
\(773\) | 31.7493 | 1.14194 | 0.570971 | − | 0.820970i | \(-0.306567\pi\) | ||||
0.570971 | + | 0.820970i | \(0.306567\pi\) | |||||||
\(774\) | 4.82571 | 0.173456 | ||||||||
\(775\) | 24.7642 | 0.889555 | ||||||||
\(776\) | −2.87820 | −0.103321 | ||||||||
\(777\) | 34.3550 | 1.23248 | ||||||||
\(778\) | 19.0163 | 0.681768 | ||||||||
\(779\) | 4.60560 | 0.165013 | ||||||||
\(780\) | 4.21809 | 0.151032 | ||||||||
\(781\) | −20.7528 | −0.742594 | ||||||||
\(782\) | 4.04178 | 0.144534 | ||||||||
\(783\) | −0.992673 | −0.0354752 | ||||||||
\(784\) | 16.1690 | 0.577465 | ||||||||
\(785\) | 51.8410 | 1.85028 | ||||||||
\(786\) | 2.17667 | 0.0776391 | ||||||||
\(787\) | −20.9982 | −0.748504 | −0.374252 | − | 0.927327i | \(-0.622101\pi\) | ||||
−0.374252 | + | 0.927327i | \(0.622101\pi\) | |||||||
\(788\) | 0.236467 | 0.00842378 | ||||||||
\(789\) | −4.79598 | −0.170741 | ||||||||
\(790\) | 61.8833 | 2.20171 | ||||||||
\(791\) | 16.7770 | 0.596520 | ||||||||
\(792\) | 4.29400 | 0.152581 | ||||||||
\(793\) | −9.04935 | −0.321352 | ||||||||
\(794\) | −12.2106 | −0.433338 | ||||||||
\(795\) | −5.74346 | −0.203699 | ||||||||
\(796\) | −21.3648 | −0.757255 | ||||||||
\(797\) | 31.6900 | 1.12252 | 0.561258 | − | 0.827641i | \(-0.310318\pi\) | ||||
0.561258 | + | 0.827641i | \(0.310318\pi\) | |||||||
\(798\) | 3.15745 | 0.111772 | ||||||||
\(799\) | −3.55364 | −0.125719 | ||||||||
\(800\) | −12.7923 | −0.452275 | ||||||||
\(801\) | 12.2086 | 0.431368 | ||||||||
\(802\) | −25.4544 | −0.898827 | ||||||||
\(803\) | −5.21115 | −0.183898 | ||||||||
\(804\) | 3.79388 | 0.133800 | ||||||||
\(805\) | −30.9851 | −1.09208 | ||||||||
\(806\) | −1.93587 | −0.0681881 | ||||||||
\(807\) | −18.4173 | −0.648320 | ||||||||
\(808\) | 14.6408 | 0.515060 | ||||||||
\(809\) | −15.3005 | −0.537937 | −0.268969 | − | 0.963149i | \(-0.586683\pi\) | ||||
−0.268969 | + | 0.963149i | \(0.586683\pi\) | |||||||
\(810\) | −4.21809 | −0.148209 | ||||||||
\(811\) | 35.3356 | 1.24080 | 0.620400 | − | 0.784286i | \(-0.286970\pi\) | ||||
0.620400 | + | 0.784286i | \(0.286970\pi\) | |||||||
\(812\) | 4.77815 | 0.167680 | ||||||||
\(813\) | 27.1420 | 0.951912 | ||||||||
\(814\) | −30.6477 | −1.07420 | ||||||||
\(815\) | 17.2988 | 0.605950 | ||||||||
\(816\) | −2.64843 | −0.0927135 | ||||||||
\(817\) | −3.16551 | −0.110747 | ||||||||
\(818\) | 17.5734 | 0.614441 | ||||||||
\(819\) | −4.81342 | −0.168195 | ||||||||
\(820\) | 29.6155 | 1.03422 | ||||||||
\(821\) | −47.5746 | −1.66037 | −0.830183 | − | 0.557491i | \(-0.811764\pi\) | ||||
−0.830183 | + | 0.557491i | \(0.811764\pi\) | |||||||
\(822\) | −10.6655 | −0.372001 | ||||||||
\(823\) | −33.6003 | −1.17123 | −0.585616 | − | 0.810589i | \(-0.699147\pi\) | ||||
−0.585616 | + | 0.810589i | \(0.699147\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −54.9301 | −1.91242 | ||||||||
\(826\) | −71.5575 | −2.48980 | ||||||||
\(827\) | 45.2481 | 1.57343 | 0.786715 | − | 0.617316i | \(-0.211780\pi\) | ||||
0.786715 | + | 0.617316i | \(0.211780\pi\) | |||||||
\(828\) | 1.52610 | 0.0530358 | ||||||||
\(829\) | 2.31906 | 0.0805443 | 0.0402721 | − | 0.999189i | \(-0.487178\pi\) | ||||
0.0402721 | + | 0.999189i | \(0.487178\pi\) | |||||||
\(830\) | −35.3789 | −1.22802 | ||||||||
\(831\) | 30.3796 | 1.05386 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −42.8225 | −1.48371 | ||||||||
\(834\) | 7.36838 | 0.255146 | ||||||||
\(835\) | −30.3225 | −1.04935 | ||||||||
\(836\) | −2.81673 | −0.0974185 | ||||||||
\(837\) | 1.93587 | 0.0669134 | ||||||||
\(838\) | −25.0377 | −0.864911 | ||||||||
\(839\) | −15.1801 | −0.524076 | −0.262038 | − | 0.965058i | \(-0.584395\pi\) | ||||
−0.262038 | + | 0.965058i | \(0.584395\pi\) | |||||||
\(840\) | 20.3034 | 0.700535 | ||||||||
\(841\) | −28.0146 | −0.966021 | ||||||||
\(842\) | −37.5028 | −1.29243 | ||||||||
\(843\) | −22.8883 | −0.788315 | ||||||||
\(844\) | −8.26635 | −0.284539 | ||||||||
\(845\) | 4.21809 | 0.145107 | ||||||||
\(846\) | −1.34179 | −0.0461318 | ||||||||
\(847\) | −35.8045 | −1.23026 | ||||||||
\(848\) | −1.36163 | −0.0467584 | ||||||||
\(849\) | 17.8384 | 0.612213 | ||||||||
\(850\) | 33.8794 | 1.16205 | ||||||||
\(851\) | −10.8923 | −0.373384 | ||||||||
\(852\) | 4.83297 | 0.165575 | ||||||||
\(853\) | 7.81605 | 0.267617 | 0.133808 | − | 0.991007i | \(-0.457279\pi\) | ||||
0.133808 | + | 0.991007i | \(0.457279\pi\) | |||||||
\(854\) | −43.5583 | −1.49053 | ||||||||
\(855\) | 2.76693 | 0.0946270 | ||||||||
\(856\) | 13.4887 | 0.461036 | ||||||||
\(857\) | −49.9702 | −1.70695 | −0.853475 | − | 0.521134i | \(-0.825509\pi\) | ||||
−0.853475 | + | 0.521134i | \(0.825509\pi\) | |||||||
\(858\) | 4.29400 | 0.146595 | ||||||||
\(859\) | −28.9793 | −0.988761 | −0.494380 | − | 0.869246i | \(-0.664605\pi\) | ||||
−0.494380 | + | 0.869246i | \(0.664605\pi\) | |||||||
\(860\) | −20.3553 | −0.694109 | ||||||||
\(861\) | −33.7954 | −1.15174 | ||||||||
\(862\) | 9.35222 | 0.318538 | ||||||||
\(863\) | −40.7436 | −1.38693 | −0.693463 | − | 0.720492i | \(-0.743916\pi\) | ||||
−0.693463 | + | 0.720492i | \(0.743916\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −59.3317 | −2.01734 | ||||||||
\(866\) | 1.48956 | 0.0506172 | ||||||||
\(867\) | −9.98583 | −0.339137 | ||||||||
\(868\) | −9.31815 | −0.316279 | ||||||||
\(869\) | 62.9971 | 2.13703 | ||||||||
\(870\) | 4.18718 | 0.141959 | ||||||||
\(871\) | 3.79388 | 0.128551 | ||||||||
\(872\) | 2.10949 | 0.0714362 | ||||||||
\(873\) | 2.87820 | 0.0974123 | ||||||||
\(874\) | −1.00107 | −0.0338618 | ||||||||
\(875\) | −158.210 | −5.34847 | ||||||||
\(876\) | 1.21359 | 0.0410034 | ||||||||
\(877\) | −42.0415 | −1.41964 | −0.709820 | − | 0.704384i | \(-0.751224\pi\) | ||||
−0.709820 | + | 0.704384i | \(0.751224\pi\) | |||||||
\(878\) | −35.5882 | −1.20104 | ||||||||
\(879\) | −15.8528 | −0.534702 | ||||||||
\(880\) | −18.1125 | −0.610572 | ||||||||
\(881\) | −24.3898 | −0.821714 | −0.410857 | − | 0.911700i | \(-0.634770\pi\) | ||||
−0.410857 | + | 0.911700i | \(0.634770\pi\) | |||||||
\(882\) | −16.1690 | −0.544439 | ||||||||
\(883\) | 12.4278 | 0.418230 | 0.209115 | − | 0.977891i | \(-0.432942\pi\) | ||||
0.209115 | + | 0.977891i | \(0.432942\pi\) | |||||||
\(884\) | −2.64843 | −0.0890763 | ||||||||
\(885\) | −62.7071 | −2.10788 | ||||||||
\(886\) | 3.05759 | 0.102722 | ||||||||
\(887\) | 2.20287 | 0.0739651 | 0.0369826 | − | 0.999316i | \(-0.488225\pi\) | ||||
0.0369826 | + | 0.999316i | \(0.488225\pi\) | |||||||
\(888\) | 7.13733 | 0.239513 | ||||||||
\(889\) | 90.4208 | 3.03262 | ||||||||
\(890\) | −51.4968 | −1.72618 | ||||||||
\(891\) | −4.29400 | −0.143855 | ||||||||
\(892\) | −2.67211 | −0.0894689 | ||||||||
\(893\) | 0.880173 | 0.0294539 | ||||||||
\(894\) | 4.93093 | 0.164915 | ||||||||
\(895\) | −89.0025 | −2.97503 | ||||||||
\(896\) | 4.81342 | 0.160805 | ||||||||
\(897\) | 1.52610 | 0.0509551 | ||||||||
\(898\) | 5.76893 | 0.192512 | ||||||||
\(899\) | −1.92168 | −0.0640918 | ||||||||
\(900\) | 12.7923 | 0.426409 | ||||||||
\(901\) | 3.60617 | 0.120139 | ||||||||
\(902\) | 30.1485 | 1.00384 | ||||||||
\(903\) | 23.2282 | 0.772984 | ||||||||
\(904\) | 3.48546 | 0.115925 | ||||||||
\(905\) | −79.5864 | −2.64554 | ||||||||
\(906\) | 9.49514 | 0.315455 | ||||||||
\(907\) | 18.8620 | 0.626303 | 0.313152 | − | 0.949703i | \(-0.398615\pi\) | ||||
0.313152 | + | 0.949703i | \(0.398615\pi\) | |||||||
\(908\) | 12.4207 | 0.412196 | ||||||||
\(909\) | −14.6408 | −0.485603 | ||||||||
\(910\) | 20.3034 | 0.673052 | ||||||||
\(911\) | 7.57458 | 0.250957 | 0.125479 | − | 0.992096i | \(-0.459953\pi\) | ||||
0.125479 | + | 0.992096i | \(0.459953\pi\) | |||||||
\(912\) | 0.655968 | 0.0217213 | ||||||||
\(913\) | −36.0156 | −1.19194 | ||||||||
\(914\) | −28.6429 | −0.947423 | ||||||||
\(915\) | −38.1710 | −1.26189 | ||||||||
\(916\) | −24.6135 | −0.813253 | ||||||||
\(917\) | 10.4772 | 0.345988 | ||||||||
\(918\) | 2.64843 | 0.0874111 | ||||||||
\(919\) | −35.9284 | −1.18517 | −0.592584 | − | 0.805508i | \(-0.701892\pi\) | ||||
−0.592584 | + | 0.805508i | \(0.701892\pi\) | |||||||
\(920\) | −6.43724 | −0.212230 | ||||||||
\(921\) | 28.0252 | 0.923463 | ||||||||
\(922\) | −8.15612 | −0.268607 | ||||||||
\(923\) | 4.83297 | 0.159079 | ||||||||
\(924\) | 20.6688 | 0.679955 | ||||||||
\(925\) | −91.3028 | −3.00202 | ||||||||
\(926\) | 10.4360 | 0.342948 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 0.992673 | 0.0325861 | ||||||||
\(929\) | −16.4262 | −0.538927 | −0.269464 | − | 0.963011i | \(-0.586846\pi\) | ||||
−0.269464 | + | 0.963011i | \(0.586846\pi\) | |||||||
\(930\) | −8.16567 | −0.267763 | ||||||||
\(931\) | 10.6063 | 0.347609 | ||||||||
\(932\) | 5.52696 | 0.181042 | ||||||||
\(933\) | −10.6744 | −0.349463 | ||||||||
\(934\) | 29.0299 | 0.949886 | ||||||||
\(935\) | 47.9696 | 1.56877 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 51.2234 | 1.67340 | 0.836698 | − | 0.547665i | \(-0.184483\pi\) | ||||
0.836698 | + | 0.547665i | \(0.184483\pi\) | |||||||
\(938\) | 18.2615 | 0.596260 | ||||||||
\(939\) | 15.8503 | 0.517255 | ||||||||
\(940\) | 5.65980 | 0.184602 | ||||||||
\(941\) | 22.0325 | 0.718238 | 0.359119 | − | 0.933292i | \(-0.383077\pi\) | ||||
0.359119 | + | 0.933292i | \(0.383077\pi\) | |||||||
\(942\) | −12.2902 | −0.400435 | ||||||||
\(943\) | 10.7149 | 0.348925 | ||||||||
\(944\) | −14.8662 | −0.483855 | ||||||||
\(945\) | −20.3034 | −0.660471 | ||||||||
\(946\) | −20.7216 | −0.673717 | ||||||||
\(947\) | −36.1189 | −1.17371 | −0.586854 | − | 0.809693i | \(-0.699634\pi\) | ||||
−0.586854 | + | 0.809693i | \(0.699634\pi\) | |||||||
\(948\) | −14.6709 | −0.476490 | ||||||||
\(949\) | 1.21359 | 0.0393947 | ||||||||
\(950\) | −8.39132 | −0.272250 | ||||||||
\(951\) | 22.0671 | 0.715574 | ||||||||
\(952\) | −12.7480 | −0.413165 | ||||||||
\(953\) | −25.1622 | −0.815083 | −0.407541 | − | 0.913187i | \(-0.633614\pi\) | ||||
−0.407541 | + | 0.913187i | \(0.633614\pi\) | |||||||
\(954\) | 1.36163 | 0.0440842 | ||||||||
\(955\) | −8.41855 | −0.272418 | ||||||||
\(956\) | 14.7857 | 0.478205 | ||||||||
\(957\) | 4.26254 | 0.137788 | ||||||||
\(958\) | −12.8742 | −0.415947 | ||||||||
\(959\) | −51.3374 | −1.65777 | ||||||||
\(960\) | 4.21809 | 0.136138 | ||||||||
\(961\) | −27.2524 | −0.879110 | ||||||||
\(962\) | 7.13733 | 0.230117 | ||||||||
\(963\) | −13.4887 | −0.434669 | ||||||||
\(964\) | −15.9625 | −0.514117 | ||||||||
\(965\) | −59.1279 | −1.90339 | ||||||||
\(966\) | 7.34578 | 0.236347 | ||||||||
\(967\) | −1.46713 | −0.0471797 | −0.0235898 | − | 0.999722i | \(-0.507510\pi\) | ||||
−0.0235898 | + | 0.999722i | \(0.507510\pi\) | |||||||
\(968\) | −7.43847 | −0.239082 | ||||||||
\(969\) | −1.73728 | −0.0558096 | ||||||||
\(970\) | −12.1405 | −0.389808 | ||||||||
\(971\) | 40.7250 | 1.30693 | 0.653464 | − | 0.756957i | \(-0.273315\pi\) | ||||
0.653464 | + | 0.756957i | \(0.273315\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 35.4671 | 1.13702 | ||||||||
\(974\) | −1.48082 | −0.0474485 | ||||||||
\(975\) | 12.7923 | 0.409681 | ||||||||
\(976\) | −9.04935 | −0.289663 | ||||||||
\(977\) | −15.3214 | −0.490176 | −0.245088 | − | 0.969501i | \(-0.578817\pi\) | ||||
−0.245088 | + | 0.969501i | \(0.578817\pi\) | |||||||
\(978\) | −4.10109 | −0.131139 | ||||||||
\(979\) | −52.4236 | −1.67547 | ||||||||
\(980\) | 68.2023 | 2.17864 | ||||||||
\(981\) | −2.10949 | −0.0673507 | ||||||||
\(982\) | −11.9383 | −0.380967 | ||||||||
\(983\) | 15.3087 | 0.488272 | 0.244136 | − | 0.969741i | \(-0.421496\pi\) | ||||
0.244136 | + | 0.969741i | \(0.421496\pi\) | |||||||
\(984\) | −7.02108 | −0.223824 | ||||||||
\(985\) | 0.997438 | 0.0317810 | ||||||||
\(986\) | −2.62902 | −0.0837251 | ||||||||
\(987\) | −6.45861 | −0.205580 | ||||||||
\(988\) | 0.655968 | 0.0208691 | ||||||||
\(989\) | −7.36453 | −0.234178 | ||||||||
\(990\) | 18.1125 | 0.575653 | ||||||||
\(991\) | 56.9074 | 1.80772 | 0.903862 | − | 0.427825i | \(-0.140720\pi\) | ||||
0.903862 | + | 0.427825i | \(0.140720\pi\) | |||||||
\(992\) | −1.93587 | −0.0614639 | ||||||||
\(993\) | −5.84180 | −0.185384 | ||||||||
\(994\) | 23.2631 | 0.737862 | ||||||||
\(995\) | −90.1186 | −2.85695 | ||||||||
\(996\) | 8.38742 | 0.265766 | ||||||||
\(997\) | 58.7078 | 1.85930 | 0.929648 | − | 0.368449i | \(-0.120111\pi\) | ||||
0.929648 | + | 0.368449i | \(0.120111\pi\) | |||||||
\(998\) | 41.2431 | 1.30553 | ||||||||
\(999\) | −7.13733 | −0.225815 |
(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 | 8034.2.a.w.1.12 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.w.1.12 | ✓ | 12 | 1.1 | even | 1 | trivial |