Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.96070 | −1.38643 | −0.693214 | − | 0.720732i | \(-0.743806\pi\) | ||||
−0.693214 | + | 0.720732i | \(0.743806\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.84436 | 0.922182 | ||||||||
\(5\) | −2.84151 | −1.27076 | −0.635381 | − | 0.772199i | \(-0.719157\pi\) | ||||
−0.635381 | + | 0.772199i | \(0.719157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.21458 | −0.837033 | −0.418517 | − | 0.908209i | \(-0.637450\pi\) | ||||
−0.418517 | + | 0.908209i | \(0.637450\pi\) | |||||||
\(8\) | 0.305158 | 0.107890 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.57136 | 1.76182 | ||||||||
\(11\) | 1.29670 | 0.390968 | 0.195484 | − | 0.980707i | \(-0.437372\pi\) | ||||
0.195484 | + | 0.980707i | \(0.437372\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.673949 | −0.186920 | −0.0934600 | − | 0.995623i | \(-0.529793\pi\) | ||||
−0.0934600 | + | 0.995623i | \(0.529793\pi\) | |||||||
\(14\) | 4.34214 | 1.16049 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.28705 | −1.07176 | ||||||||
\(17\) | 1.19266 | 0.289264 | 0.144632 | − | 0.989486i | \(-0.453800\pi\) | ||||
0.144632 | + | 0.989486i | \(0.453800\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.61616 | −1.28844 | −0.644218 | − | 0.764842i | \(-0.722817\pi\) | ||||
−0.644218 | + | 0.764842i | \(0.722817\pi\) | |||||||
\(20\) | −5.24077 | −1.17187 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.54244 | −0.542049 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.07417 | 0.614834 | ||||||||
\(26\) | 1.32142 | 0.259151 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.08449 | −0.771897 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.05642 | −0.728555 | −0.364277 | − | 0.931290i | \(-0.618684\pi\) | ||||
−0.364277 | + | 0.931290i | \(0.618684\pi\) | |||||||
\(32\) | 7.79533 | 1.37803 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.33846 | −0.401043 | ||||||||
\(35\) | 6.29275 | 1.06367 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.39113 | 0.557499 | 0.278749 | − | 0.960364i | \(-0.410080\pi\) | ||||
0.278749 | + | 0.960364i | \(0.410080\pi\) | |||||||
\(38\) | 11.0116 | 1.78632 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.867109 | −0.137102 | ||||||||
\(41\) | 9.19828 | 1.43653 | 0.718265 | − | 0.695770i | \(-0.244937\pi\) | ||||
0.718265 | + | 0.695770i | \(0.244937\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.58517 | 1.46172 | 0.730862 | − | 0.682525i | \(-0.239118\pi\) | ||||
0.730862 | + | 0.682525i | \(0.239118\pi\) | |||||||
\(44\) | 2.39158 | 0.360544 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.96070 | −0.289090 | ||||||||
\(47\) | −4.53489 | −0.661481 | −0.330741 | − | 0.943722i | \(-0.607299\pi\) | ||||
−0.330741 | + | 0.943722i | \(0.607299\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.09562 | −0.299375 | ||||||||
\(50\) | −6.02754 | −0.852423 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.24301 | −0.172374 | ||||||||
\(53\) | 3.31678 | 0.455595 | 0.227797 | − | 0.973709i | \(-0.426848\pi\) | ||||
0.227797 | + | 0.973709i | \(0.426848\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.68457 | −0.496828 | ||||||||
\(56\) | −0.675798 | −0.0903073 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.96070 | −0.257453 | ||||||||
\(59\) | 7.04726 | 0.917475 | 0.458738 | − | 0.888572i | \(-0.348302\pi\) | ||||
0.458738 | + | 0.888572i | \(0.348302\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.0676 | −1.67314 | −0.836568 | − | 0.547864i | \(-0.815441\pi\) | ||||
−0.836568 | + | 0.547864i | \(0.815441\pi\) | |||||||
\(62\) | 7.95344 | 1.01009 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.71023 | −0.838779 | ||||||||
\(65\) | 1.91503 | 0.237531 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.14971 | 0.506967 | 0.253484 | − | 0.967340i | \(-0.418424\pi\) | ||||
0.253484 | + | 0.967340i | \(0.418424\pi\) | |||||||
\(68\) | 2.19971 | 0.266753 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.3382 | −1.47470 | ||||||||
\(71\) | −4.40083 | −0.522282 | −0.261141 | − | 0.965301i | \(-0.584099\pi\) | ||||
−0.261141 | + | 0.965301i | \(0.584099\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.12240 | −0.716573 | −0.358287 | − | 0.933612i | \(-0.616639\pi\) | ||||
−0.358287 | + | 0.933612i | \(0.616639\pi\) | |||||||
\(74\) | −6.64901 | −0.772932 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.3582 | −1.18817 | ||||||||
\(77\) | −2.87164 | −0.327254 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.11103 | 0.125001 | 0.0625005 | − | 0.998045i | \(-0.480092\pi\) | ||||
0.0625005 | + | 0.998045i | \(0.480092\pi\) | |||||||
\(80\) | 12.1817 | 1.36195 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −18.0351 | −1.99164 | ||||||||
\(83\) | −2.93238 | −0.321871 | −0.160935 | − | 0.986965i | \(-0.551451\pi\) | ||||
−0.160935 | + | 0.986965i | \(0.551451\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.38897 | −0.367585 | ||||||||
\(86\) | −18.7937 | −2.02657 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.395697 | 0.0421815 | ||||||||
\(89\) | 13.3205 | 1.41197 | 0.705986 | − | 0.708225i | \(-0.250504\pi\) | ||||
0.705986 | + | 0.708225i | \(0.250504\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.49252 | 0.156458 | ||||||||
\(92\) | 1.84436 | 0.192288 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.89157 | 0.917096 | ||||||||
\(95\) | 15.9584 | 1.63730 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.608559 | 0.0617898 | 0.0308949 | − | 0.999523i | \(-0.490164\pi\) | ||||
0.0308949 | + | 0.999523i | \(0.490164\pi\) | |||||||
\(98\) | 4.10890 | 0.415062 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.66989 | 0.566989 | ||||||||
\(101\) | −0.680930 | −0.0677551 | −0.0338775 | − | 0.999426i | \(-0.510786\pi\) | ||||
−0.0338775 | + | 0.999426i | \(0.510786\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.78839 | −0.274748 | −0.137374 | − | 0.990519i | \(-0.543866\pi\) | ||||
−0.137374 | + | 0.990519i | \(0.543866\pi\) | |||||||
\(104\) | −0.205661 | −0.0201667 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.50322 | −0.631649 | ||||||||
\(107\) | −0.980463 | −0.0947849 | −0.0473924 | − | 0.998876i | \(-0.515091\pi\) | ||||
−0.0473924 | + | 0.998876i | \(0.515091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.2190 | 1.64928 | 0.824640 | − | 0.565658i | \(-0.191378\pi\) | ||||
0.824640 | + | 0.565658i | \(0.191378\pi\) | |||||||
\(110\) | 7.22436 | 0.688815 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.49403 | 0.897101 | ||||||||
\(113\) | −3.78339 | −0.355912 | −0.177956 | − | 0.984038i | \(-0.556948\pi\) | ||||
−0.177956 | + | 0.984038i | \(0.556948\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.84151 | −0.264972 | ||||||||
\(116\) | 1.84436 | 0.171245 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.8176 | −1.27201 | ||||||||
\(119\) | −2.64125 | −0.242123 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.31858 | −0.847144 | ||||||||
\(122\) | 25.6217 | 2.31968 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.48151 | −0.671860 | ||||||||
\(125\) | 5.47226 | 0.489454 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1839 | 1.34736 | 0.673679 | − | 0.739024i | \(-0.264713\pi\) | ||||
0.673679 | + | 0.739024i | \(0.264713\pi\) | |||||||
\(128\) | −2.43387 | −0.215126 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.75481 | −0.329319 | ||||||||
\(131\) | 8.78208 | 0.767294 | 0.383647 | − | 0.923480i | \(-0.374668\pi\) | ||||
0.383647 | + | 0.923480i | \(0.374668\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.4375 | 1.07846 | ||||||||
\(134\) | −8.13635 | −0.702874 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.363951 | 0.0312086 | ||||||||
\(137\) | 6.22749 | 0.532050 | 0.266025 | − | 0.963966i | \(-0.414290\pi\) | ||||
0.266025 | + | 0.963966i | \(0.414290\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.443368 | 0.0376060 | 0.0188030 | − | 0.999823i | \(-0.494014\pi\) | ||||
0.0188030 | + | 0.999823i | \(0.494014\pi\) | |||||||
\(140\) | 11.6061 | 0.980897 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.62873 | 0.724107 | ||||||||
\(143\) | −0.873907 | −0.0730798 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.84151 | −0.235974 | ||||||||
\(146\) | 12.0042 | 0.993477 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.25448 | 0.514115 | ||||||||
\(149\) | −1.36917 | −0.112166 | −0.0560832 | − | 0.998426i | \(-0.517861\pi\) | ||||
−0.0560832 | + | 0.998426i | \(0.517861\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8135 | 1.04274 | 0.521372 | − | 0.853329i | \(-0.325420\pi\) | ||||
0.521372 | + | 0.853329i | \(0.325420\pi\) | |||||||
\(152\) | −1.71382 | −0.139009 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.63044 | 0.453714 | ||||||||
\(155\) | 11.5264 | 0.925819 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.07935 | 0.564993 | 0.282497 | − | 0.959268i | \(-0.408837\pi\) | ||||
0.282497 | + | 0.959268i | \(0.408837\pi\) | |||||||
\(158\) | −2.17841 | −0.173305 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −22.1505 | −1.75115 | ||||||||
\(161\) | −2.21458 | −0.174534 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.3823 | 1.43982 | 0.719908 | − | 0.694069i | \(-0.244184\pi\) | ||||
0.719908 | + | 0.694069i | \(0.244184\pi\) | |||||||
\(164\) | 16.9650 | 1.32474 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.74953 | 0.446250 | ||||||||
\(167\) | −16.1543 | −1.25006 | −0.625030 | − | 0.780601i | \(-0.714913\pi\) | ||||
−0.625030 | + | 0.780601i | \(0.714913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5458 | −0.965061 | ||||||||
\(170\) | 6.64476 | 0.509630 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.6785 | 1.34797 | ||||||||
\(173\) | −4.63833 | −0.352646 | −0.176323 | − | 0.984332i | \(-0.556420\pi\) | ||||
−0.176323 | + | 0.984332i | \(0.556420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.80800 | −0.514637 | ||||||||
\(176\) | −5.55900 | −0.419025 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −26.1176 | −1.95760 | ||||||||
\(179\) | 22.3814 | 1.67287 | 0.836434 | − | 0.548068i | \(-0.184637\pi\) | ||||
0.836434 | + | 0.548068i | \(0.184637\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0727 | −1.12034 | −0.560171 | − | 0.828377i | \(-0.689265\pi\) | ||||
−0.560171 | + | 0.828377i | \(0.689265\pi\) | |||||||
\(182\) | −2.92638 | −0.216918 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.305158 | 0.0224966 | ||||||||
\(185\) | −9.63594 | −0.708448 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.54652 | 0.113093 | ||||||||
\(188\) | −8.36398 | −0.610006 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −31.2897 | −2.26999 | ||||||||
\(191\) | 12.0277 | 0.870291 | 0.435146 | − | 0.900360i | \(-0.356697\pi\) | ||||
0.435146 | + | 0.900360i | \(0.356697\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0358 | −0.722392 | −0.361196 | − | 0.932490i | \(-0.617632\pi\) | ||||
−0.361196 | + | 0.932490i | \(0.617632\pi\) | |||||||
\(194\) | −1.19320 | −0.0856671 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.86509 | −0.276078 | ||||||||
\(197\) | 15.2492 | 1.08646 | 0.543229 | − | 0.839584i | \(-0.317201\pi\) | ||||
0.543229 | + | 0.839584i | \(0.317201\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.5103 | −1.02861 | −0.514304 | − | 0.857608i | \(-0.671950\pi\) | ||||
−0.514304 | + | 0.857608i | \(0.671950\pi\) | |||||||
\(200\) | 0.938108 | 0.0663343 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.33510 | 0.0939375 | ||||||||
\(203\) | −2.21458 | −0.155433 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.1370 | −1.82549 | ||||||||
\(206\) | 5.46721 | 0.380919 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.88926 | 0.200334 | ||||||||
\(209\) | −7.28246 | −0.503738 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.6728 | 1.76739 | 0.883694 | − | 0.468065i | \(-0.155049\pi\) | ||||
0.883694 | + | 0.468065i | \(0.155049\pi\) | |||||||
\(212\) | 6.11734 | 0.420141 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.92240 | 0.131412 | ||||||||
\(215\) | −27.2363 | −1.85750 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.98328 | 0.609825 | ||||||||
\(218\) | −33.7614 | −2.28661 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.79569 | −0.458165 | ||||||||
\(221\) | −0.803795 | −0.0540691 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1664 | −0.814724 | −0.407362 | − | 0.913267i | \(-0.633551\pi\) | ||||
−0.407362 | + | 0.913267i | \(0.633551\pi\) | |||||||
\(224\) | −17.2634 | −1.15346 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.41811 | 0.493446 | ||||||||
\(227\) | −0.928537 | −0.0616292 | −0.0308146 | − | 0.999525i | \(-0.509810\pi\) | ||||
−0.0308146 | + | 0.999525i | \(0.509810\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.3364 | 1.27779 | 0.638894 | − | 0.769295i | \(-0.279392\pi\) | ||||
0.638894 | + | 0.769295i | \(0.279392\pi\) | |||||||
\(230\) | 5.57136 | 0.367365 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.305158 | 0.0200346 | ||||||||
\(233\) | −1.34224 | −0.0879334 | −0.0439667 | − | 0.999033i | \(-0.514000\pi\) | ||||
−0.0439667 | + | 0.999033i | \(0.514000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8859 | 0.840585 | ||||||||
\(236\) | 12.9977 | 0.846079 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.17872 | 0.335686 | ||||||||
\(239\) | −14.6847 | −0.949874 | −0.474937 | − | 0.880020i | \(-0.657529\pi\) | ||||
−0.474937 | + | 0.880020i | \(0.657529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.98783 | −0.578957 | −0.289478 | − | 0.957185i | \(-0.593482\pi\) | ||||
−0.289478 | + | 0.957185i | \(0.593482\pi\) | |||||||
\(242\) | 18.2710 | 1.17450 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −24.1014 | −1.54293 | ||||||||
\(245\) | 5.95474 | 0.380434 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.78501 | 0.240834 | ||||||||
\(248\) | −1.23785 | −0.0786035 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.7295 | −0.678592 | ||||||||
\(251\) | −18.5933 | −1.17360 | −0.586800 | − | 0.809732i | \(-0.699613\pi\) | ||||
−0.586800 | + | 0.809732i | \(0.699613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.29670 | 0.0815226 | ||||||||
\(254\) | −29.7712 | −1.86801 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.1926 | 1.13704 | ||||||||
\(257\) | 7.89783 | 0.492653 | 0.246327 | − | 0.969187i | \(-0.420776\pi\) | ||||
0.246327 | + | 0.969187i | \(0.420776\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.50995 | −0.466645 | ||||||||
\(260\) | 3.53202 | 0.219046 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.2191 | −1.06380 | ||||||||
\(263\) | −17.9046 | −1.10405 | −0.552023 | − | 0.833829i | \(-0.686144\pi\) | ||||
−0.552023 | + | 0.833829i | \(0.686144\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.42465 | −0.578952 | ||||||||
\(266\) | −24.3862 | −1.49521 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.65357 | 0.467516 | ||||||||
\(269\) | −17.5255 | −1.06855 | −0.534275 | − | 0.845311i | \(-0.679415\pi\) | ||||
−0.534275 | + | 0.845311i | \(0.679415\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.0244 | 1.15565 | 0.577824 | − | 0.816161i | \(-0.303902\pi\) | ||||
0.577824 | + | 0.816161i | \(0.303902\pi\) | |||||||
\(272\) | −5.11301 | −0.310022 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.2103 | −0.737649 | ||||||||
\(275\) | 3.98626 | 0.240381 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0189 | −0.601975 | −0.300987 | − | 0.953628i | \(-0.597316\pi\) | ||||
−0.300987 | + | 0.953628i | \(0.597316\pi\) | |||||||
\(278\) | −0.869314 | −0.0521380 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.92029 | 0.114759 | ||||||||
\(281\) | −6.16169 | −0.367575 | −0.183788 | − | 0.982966i | \(-0.558836\pi\) | ||||
−0.183788 | + | 0.982966i | \(0.558836\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.23812 | −0.489705 | −0.244853 | − | 0.969560i | \(-0.578740\pi\) | ||||
−0.244853 | + | 0.969560i | \(0.578740\pi\) | |||||||
\(284\) | −8.11673 | −0.481639 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.71347 | 0.101320 | ||||||||
\(287\) | −20.3703 | −1.20242 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5776 | −0.916327 | ||||||||
\(290\) | 5.57136 | 0.327161 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.2919 | −0.660811 | ||||||||
\(293\) | 11.1979 | 0.654190 | 0.327095 | − | 0.944991i | \(-0.393930\pi\) | ||||
0.327095 | + | 0.944991i | \(0.393930\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.0249 | −1.16589 | ||||||||
\(296\) | 1.03483 | 0.0601484 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.68453 | 0.155511 | ||||||||
\(299\) | −0.673949 | −0.0389755 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.2271 | −1.22351 | ||||||||
\(302\) | −25.1234 | −1.44569 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 24.0768 | 1.38090 | ||||||||
\(305\) | 37.1317 | 2.12616 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.4442 | −0.995596 | −0.497798 | − | 0.867293i | \(-0.665858\pi\) | ||||
−0.497798 | + | 0.867293i | \(0.665858\pi\) | |||||||
\(308\) | −5.29635 | −0.301787 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −22.5998 | −1.28358 | ||||||||
\(311\) | 33.3243 | 1.88965 | 0.944823 | − | 0.327581i | \(-0.106233\pi\) | ||||
0.944823 | + | 0.327581i | \(0.106233\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.59645 | −0.203283 | −0.101642 | − | 0.994821i | \(-0.532409\pi\) | ||||
−0.101642 | + | 0.994821i | \(0.532409\pi\) | |||||||
\(314\) | −13.8805 | −0.783322 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.04915 | 0.115274 | ||||||||
\(317\) | −22.9986 | −1.29173 | −0.645865 | − | 0.763452i | \(-0.723503\pi\) | ||||
−0.645865 | + | 0.763452i | \(0.723503\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.29670 | 0.0726010 | ||||||||
\(320\) | 19.0672 | 1.06589 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.34214 | 0.241978 | ||||||||
\(323\) | −6.69820 | −0.372698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.07184 | −0.114925 | ||||||||
\(326\) | −36.0424 | −1.99620 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.80693 | 0.154987 | ||||||||
\(329\) | 10.0429 | 0.553682 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.5418 | −1.18405 | −0.592023 | − | 0.805921i | \(-0.701671\pi\) | ||||
−0.592023 | + | 0.805921i | \(0.701671\pi\) | |||||||
\(332\) | −5.40838 | −0.296823 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 31.6739 | 1.73312 | ||||||||
\(335\) | −11.7914 | −0.644235 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.44117 | 0.241926 | 0.120963 | − | 0.992657i | \(-0.461402\pi\) | ||||
0.120963 | + | 0.992657i | \(0.461402\pi\) | |||||||
\(338\) | 24.5986 | 1.33799 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.25048 | −0.338980 | ||||||||
\(341\) | −5.25994 | −0.284842 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1430 | 1.08762 | ||||||||
\(344\) | 2.92499 | 0.157705 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.09439 | 0.488918 | ||||||||
\(347\) | −32.7661 | −1.75898 | −0.879488 | − | 0.475922i | \(-0.842114\pi\) | ||||
−0.879488 | + | 0.475922i | \(0.842114\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.88733 | −0.422199 | −0.211099 | − | 0.977465i | \(-0.567704\pi\) | ||||
−0.211099 | + | 0.977465i | \(0.567704\pi\) | |||||||
\(350\) | 13.3485 | 0.713507 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.1082 | 0.538767 | ||||||||
\(353\) | 1.42984 | 0.0761027 | 0.0380514 | − | 0.999276i | \(-0.487885\pi\) | ||||
0.0380514 | + | 0.999276i | \(0.487885\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.5050 | 0.663696 | ||||||||
\(356\) | 24.5679 | 1.30210 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −43.8834 | −2.31931 | ||||||||
\(359\) | 19.6228 | 1.03565 | 0.517827 | − | 0.855486i | \(-0.326741\pi\) | ||||
0.517827 | + | 0.855486i | \(0.326741\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.5413 | 0.660069 | ||||||||
\(362\) | 29.5530 | 1.55327 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.75274 | 0.144283 | ||||||||
\(365\) | 17.3969 | 0.910594 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.79683 | −0.250392 | −0.125196 | − | 0.992132i | \(-0.539956\pi\) | ||||
−0.125196 | + | 0.992132i | \(0.539956\pi\) | |||||||
\(368\) | −4.28705 | −0.223478 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.8932 | 0.982212 | ||||||||
\(371\) | −7.34528 | −0.381348 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.4532 | −1.00725 | −0.503624 | − | 0.863923i | \(-0.668000\pi\) | ||||
−0.503624 | + | 0.863923i | \(0.668000\pi\) | |||||||
\(374\) | −3.03227 | −0.156795 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.38386 | −0.0713670 | ||||||||
\(377\) | −0.673949 | −0.0347102 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.96263 | 0.203547 | 0.101773 | − | 0.994808i | \(-0.467548\pi\) | ||||
0.101773 | + | 0.994808i | \(0.467548\pi\) | |||||||
\(380\) | 29.4330 | 1.50988 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −23.5827 | −1.20660 | ||||||||
\(383\) | −21.5143 | −1.09933 | −0.549665 | − | 0.835385i | \(-0.685244\pi\) | ||||
−0.549665 | + | 0.835385i | \(0.685244\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.15979 | 0.415861 | ||||||||
\(386\) | 19.6772 | 1.00154 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.12240 | 0.0569814 | ||||||||
\(389\) | 9.42136 | 0.477682 | 0.238841 | − | 0.971059i | \(-0.423233\pi\) | ||||
0.238841 | + | 0.971059i | \(0.423233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.19266 | 0.0603156 | ||||||||
\(392\) | −0.639497 | −0.0322995 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −29.8991 | −1.50630 | ||||||||
\(395\) | −3.15701 | −0.158847 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.73525 | −0.287844 | −0.143922 | − | 0.989589i | \(-0.545971\pi\) | ||||
−0.143922 | + | 0.989589i | \(0.545971\pi\) | |||||||
\(398\) | 28.4504 | 1.42609 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.1791 | −0.658956 | ||||||||
\(401\) | 15.1016 | 0.754138 | 0.377069 | − | 0.926185i | \(-0.376932\pi\) | ||||
0.377069 | + | 0.926185i | \(0.376932\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.73382 | 0.136181 | ||||||||
\(404\) | −1.25588 | −0.0624825 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.34214 | 0.215497 | ||||||||
\(407\) | 4.39727 | 0.217965 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.2492 | −0.655132 | −0.327566 | − | 0.944828i | \(-0.606228\pi\) | ||||
−0.327566 | + | 0.944828i | \(0.606228\pi\) | |||||||
\(410\) | 51.2469 | 2.53090 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.14281 | −0.253368 | ||||||||
\(413\) | −15.6067 | −0.767958 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.33239 | 0.409021 | ||||||||
\(416\) | −5.25365 | −0.257582 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.2787 | 0.698396 | ||||||||
\(419\) | −1.15337 | −0.0563456 | −0.0281728 | − | 0.999603i | \(-0.508969\pi\) | ||||
−0.0281728 | + | 0.999603i | \(0.508969\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.5973 | −1.73491 | −0.867453 | − | 0.497519i | \(-0.834245\pi\) | ||||
−0.867453 | + | 0.497519i | \(0.834245\pi\) | |||||||
\(422\) | −50.3368 | −2.45035 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.01214 | 0.0491540 | ||||||||
\(425\) | 3.66645 | 0.177849 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.9393 | 1.40047 | ||||||||
\(428\) | −1.80833 | −0.0874089 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 53.4024 | 2.57529 | ||||||||
\(431\) | −7.03642 | −0.338932 | −0.169466 | − | 0.985536i | \(-0.554204\pi\) | ||||
−0.169466 | + | 0.985536i | \(0.554204\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.3154 | 0.495726 | 0.247863 | − | 0.968795i | \(-0.420272\pi\) | ||||
0.247863 | + | 0.968795i | \(0.420272\pi\) | |||||||
\(434\) | −17.6136 | −0.845478 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 31.7581 | 1.52094 | ||||||||
\(437\) | −5.61616 | −0.268658 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.8585 | −1.32962 | −0.664808 | − | 0.747015i | \(-0.731486\pi\) | ||||
−0.664808 | + | 0.747015i | \(0.731486\pi\) | |||||||
\(440\) | −1.12438 | −0.0536026 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.57601 | 0.0749629 | ||||||||
\(443\) | −26.6762 | −1.26742 | −0.633712 | − | 0.773569i | \(-0.718470\pi\) | ||||
−0.633712 | + | 0.773569i | \(0.718470\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.8504 | −1.79428 | ||||||||
\(446\) | 23.8548 | 1.12956 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14.8604 | 0.702086 | ||||||||
\(449\) | 16.4948 | 0.778437 | 0.389219 | − | 0.921145i | \(-0.372745\pi\) | ||||
0.389219 | + | 0.921145i | \(0.372745\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.9274 | 0.561638 | ||||||||
\(452\) | −6.97795 | −0.328215 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.82059 | 0.0854444 | ||||||||
\(455\) | −4.24100 | −0.198821 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.6252 | −1.52614 | −0.763070 | − | 0.646316i | \(-0.776309\pi\) | ||||
−0.763070 | + | 0.646316i | \(0.776309\pi\) | |||||||
\(458\) | −37.9131 | −1.77156 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.24077 | −0.244352 | ||||||||
\(461\) | −39.2060 | −1.82600 | −0.913002 | − | 0.407956i | \(-0.866242\pi\) | ||||
−0.913002 | + | 0.407956i | \(0.866242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.6448 | 0.680600 | 0.340300 | − | 0.940317i | \(-0.389471\pi\) | ||||
0.340300 | + | 0.940317i | \(0.389471\pi\) | |||||||
\(464\) | −4.28705 | −0.199021 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.63175 | 0.121913 | ||||||||
\(467\) | −12.7214 | −0.588677 | −0.294339 | − | 0.955701i | \(-0.595099\pi\) | ||||
−0.294339 | + | 0.955701i | \(0.595099\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.18987 | −0.424349 | ||||||||
\(470\) | −25.2655 | −1.16541 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.15053 | 0.0989861 | ||||||||
\(473\) | 12.4290 | 0.571488 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.2650 | −0.792175 | ||||||||
\(476\) | −4.87143 | −0.223282 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 28.7923 | 1.31693 | ||||||||
\(479\) | 32.0057 | 1.46238 | 0.731190 | − | 0.682174i | \(-0.238965\pi\) | ||||
0.731190 | + | 0.682174i | \(0.238965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.28545 | −0.104208 | ||||||||
\(482\) | 17.6225 | 0.802682 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.1868 | −0.781220 | ||||||||
\(485\) | −1.72923 | −0.0785201 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.0321749 | 0.00145798 | 0.000728991 | − | 1.00000i | \(-0.499768\pi\) | ||||
0.000728991 | 1.00000i | \(0.499768\pi\) | ||||||||
\(488\) | −3.98769 | −0.180514 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.6755 | −0.527444 | ||||||||
\(491\) | 5.05865 | 0.228294 | 0.114147 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114147 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.19266 | 0.0537149 | ||||||||
\(494\) | −7.42129 | −0.333900 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.3901 | 0.780838 | ||||||||
\(497\) | 9.74600 | 0.437168 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.2451 | 1.53302 | 0.766511 | − | 0.642231i | \(-0.221991\pi\) | ||||
0.766511 | + | 0.642231i | \(0.221991\pi\) | |||||||
\(500\) | 10.0928 | 0.451365 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 36.4560 | 1.62711 | ||||||||
\(503\) | −18.8257 | −0.839398 | −0.419699 | − | 0.907663i | \(-0.637864\pi\) | ||||
−0.419699 | + | 0.907663i | \(0.637864\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.93487 | 0.0861005 | ||||||||
\(506\) | −2.54244 | −0.113025 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 28.0047 | 1.24251 | ||||||||
\(509\) | −30.0086 | −1.33011 | −0.665054 | − | 0.746795i | \(-0.731592\pi\) | ||||
−0.665054 | + | 0.746795i | \(0.731592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.5586 | 0.599796 | ||||||||
\(512\) | −30.8025 | −1.36129 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.4853 | −0.683028 | ||||||||
\(515\) | 7.92324 | 0.349140 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.88037 | −0.258618 | ||||||||
\(518\) | 14.7248 | 0.646970 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.584388 | 0.0256271 | ||||||||
\(521\) | 12.9951 | 0.569328 | 0.284664 | − | 0.958627i | \(-0.408118\pi\) | ||||
0.284664 | + | 0.958627i | \(0.408118\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.9002 | −0.651540 | −0.325770 | − | 0.945449i | \(-0.605623\pi\) | ||||
−0.325770 | + | 0.945449i | \(0.605623\pi\) | |||||||
\(524\) | 16.1973 | 0.707584 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.1056 | 1.53068 | ||||||||
\(527\) | −4.83795 | −0.210744 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 18.4790 | 0.802675 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 22.9392 | 0.994540 | ||||||||
\(533\) | −6.19917 | −0.268516 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.78599 | 0.120449 | ||||||||
\(536\) | 1.26632 | 0.0546966 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.3624 | 1.48147 | ||||||||
\(539\) | −2.71739 | −0.117046 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.58232 | 0.368983 | 0.184491 | − | 0.982834i | \(-0.440936\pi\) | ||||
0.184491 | + | 0.982834i | \(0.440936\pi\) | |||||||
\(542\) | −37.3012 | −1.60222 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.29720 | 0.398614 | ||||||||
\(545\) | −48.9279 | −2.09584 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7984 | −0.675489 | −0.337744 | − | 0.941238i | \(-0.609664\pi\) | ||||
−0.337744 | + | 0.941238i | \(0.609664\pi\) | |||||||
\(548\) | 11.4858 | 0.490647 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.81589 | −0.333271 | ||||||||
\(551\) | −5.61616 | −0.239257 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.46048 | −0.104630 | ||||||||
\(554\) | 19.6440 | 0.834594 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.817732 | 0.0346795 | ||||||||
\(557\) | 1.23748 | 0.0524337 | 0.0262169 | − | 0.999656i | \(-0.491654\pi\) | ||||
0.0262169 | + | 0.999656i | \(0.491654\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.45992 | −0.273225 | ||||||||
\(560\) | −26.9774 | −1.14000 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.0812 | 0.509617 | ||||||||
\(563\) | −28.8167 | −1.21448 | −0.607239 | − | 0.794519i | \(-0.707723\pi\) | ||||
−0.607239 | + | 0.794519i | \(0.707723\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.7505 | 0.452279 | ||||||||
\(566\) | 16.1525 | 0.678941 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.34295 | −0.0563489 | ||||||||
\(569\) | 1.98271 | 0.0831195 | 0.0415597 | − | 0.999136i | \(-0.486767\pi\) | ||||
0.0415597 | + | 0.999136i | \(0.486767\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.8248 | 0.453004 | 0.226502 | − | 0.974011i | \(-0.427271\pi\) | ||||
0.226502 | + | 0.974011i | \(0.427271\pi\) | |||||||
\(572\) | −1.61180 | −0.0673928 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 39.9402 | 1.66707 | ||||||||
\(575\) | 3.07417 | 0.128202 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.9111 | 1.74478 | 0.872391 | − | 0.488809i | \(-0.162569\pi\) | ||||
0.872391 | + | 0.488809i | \(0.162569\pi\) | |||||||
\(578\) | 30.5430 | 1.27042 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.24077 | −0.217611 | ||||||||
\(581\) | 6.49400 | 0.269417 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.30085 | 0.178123 | ||||||||
\(584\) | −1.86830 | −0.0773109 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.9558 | −0.906988 | ||||||||
\(587\) | 22.4769 | 0.927721 | 0.463860 | − | 0.885908i | \(-0.346464\pi\) | ||||
0.463860 | + | 0.885908i | \(0.346464\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.7815 | 0.938697 | ||||||||
\(590\) | 39.2628 | 1.61642 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.5380 | −0.597507 | ||||||||
\(593\) | 26.6551 | 1.09459 | 0.547297 | − | 0.836938i | \(-0.315657\pi\) | ||||
0.547297 | + | 0.836938i | \(0.315657\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.50514 | 0.307681 | ||||||||
\(596\) | −2.52524 | −0.103438 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.32142 | 0.0540367 | ||||||||
\(599\) | −36.8292 | −1.50480 | −0.752400 | − | 0.658707i | \(-0.771104\pi\) | ||||
−0.752400 | + | 0.658707i | \(0.771104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.888255 | −0.0362327 | −0.0181163 | − | 0.999836i | \(-0.505767\pi\) | ||||
−0.0181163 | + | 0.999836i | \(0.505767\pi\) | |||||||
\(602\) | 41.6202 | 1.69631 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.6327 | 0.961599 | ||||||||
\(605\) | 26.4788 | 1.07652 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.3048 | −0.905322 | −0.452661 | − | 0.891683i | \(-0.649525\pi\) | ||||
−0.452661 | + | 0.891683i | \(0.649525\pi\) | |||||||
\(608\) | −43.7798 | −1.77551 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −72.8043 | −2.94776 | ||||||||
\(611\) | 3.05628 | 0.123644 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.2562 | −1.22204 | −0.611018 | − | 0.791617i | \(-0.709240\pi\) | ||||
−0.611018 | + | 0.791617i | \(0.709240\pi\) | |||||||
\(614\) | 34.2030 | 1.38032 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.876304 | −0.0353073 | ||||||||
\(617\) | −3.71829 | −0.149693 | −0.0748464 | − | 0.997195i | \(-0.523847\pi\) | ||||
−0.0748464 | + | 0.997195i | \(0.523847\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.8048 | 0.876409 | 0.438205 | − | 0.898875i | \(-0.355615\pi\) | ||||
0.438205 | + | 0.898875i | \(0.355615\pi\) | |||||||
\(620\) | 21.2588 | 0.853773 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −65.3391 | −2.61986 | ||||||||
\(623\) | −29.4994 | −1.18187 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9203 | −1.23681 | ||||||||
\(626\) | 7.05157 | 0.281837 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.0569 | 0.521026 | ||||||||
\(629\) | 4.04448 | 0.161264 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.62402 | 0.184079 | 0.0920396 | − | 0.995755i | \(-0.470661\pi\) | ||||
0.0920396 | + | 0.995755i | \(0.470661\pi\) | |||||||
\(632\) | 0.339041 | 0.0134863 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 45.0934 | 1.79089 | ||||||||
\(635\) | −43.1453 | −1.71217 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.41234 | 0.0559591 | ||||||||
\(638\) | −2.54244 | −0.100656 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.91587 | 0.273374 | ||||||||
\(641\) | 29.0724 | 1.14829 | 0.574145 | − | 0.818754i | \(-0.305335\pi\) | ||||
0.574145 | + | 0.818754i | \(0.305335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.8775 | −1.05994 | −0.529972 | − | 0.848015i | \(-0.677797\pi\) | ||||
−0.529972 | + | 0.848015i | \(0.677797\pi\) | |||||||
\(644\) | −4.08449 | −0.160952 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.1332 | 0.516718 | ||||||||
\(647\) | −4.89089 | −0.192281 | −0.0961404 | − | 0.995368i | \(-0.530650\pi\) | ||||
−0.0961404 | + | 0.995368i | \(0.530650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.13815 | 0.358704 | ||||||||
\(650\) | 4.06226 | 0.159335 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 33.9037 | 1.32777 | ||||||||
\(653\) | −26.8174 | −1.04945 | −0.524723 | − | 0.851273i | \(-0.675831\pi\) | ||||
−0.524723 | + | 0.851273i | \(0.675831\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.9544 | −0.975047 | ||||||||
\(656\) | −39.4335 | −1.53962 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.6911 | −0.767640 | ||||||||
\(659\) | 36.0236 | 1.40328 | 0.701641 | − | 0.712531i | \(-0.252451\pi\) | ||||
0.701641 | + | 0.712531i | \(0.252451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.4082 | −1.10495 | −0.552476 | − | 0.833529i | \(-0.686317\pi\) | ||||
−0.552476 | + | 0.833529i | \(0.686317\pi\) | |||||||
\(662\) | 42.2372 | 1.64159 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.894840 | −0.0347265 | ||||||||
\(665\) | −35.3411 | −1.37047 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −29.7944 | −1.15278 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.1195 | 0.893185 | ||||||||
\(671\) | −16.9447 | −0.654143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.35661 | 0.360671 | 0.180335 | − | 0.983605i | \(-0.442282\pi\) | ||||
0.180335 | + | 0.983605i | \(0.442282\pi\) | |||||||
\(674\) | −8.70782 | −0.335413 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23.1390 | −0.889961 | ||||||||
\(677\) | −44.4912 | −1.70994 | −0.854968 | − | 0.518681i | \(-0.826423\pi\) | ||||
−0.854968 | + | 0.518681i | \(0.826423\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.34770 | −0.0517201 | ||||||||
\(680\) | −1.03417 | −0.0396586 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.3132 | 0.394913 | ||||||||
\(683\) | −15.2249 | −0.582563 | −0.291281 | − | 0.956637i | \(-0.594082\pi\) | ||||
−0.291281 | + | 0.956637i | \(0.594082\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.6955 | −0.676109 | ||||||||
\(686\) | −39.4945 | −1.50791 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −41.0921 | −1.56662 | ||||||||
\(689\) | −2.23534 | −0.0851597 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.8543 | −1.47809 | −0.739044 | − | 0.673657i | \(-0.764722\pi\) | ||||
−0.739044 | + | 0.673657i | \(0.764722\pi\) | |||||||
\(692\) | −8.55476 | −0.325203 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 64.2446 | 2.43869 | ||||||||
\(695\) | −1.25983 | −0.0477882 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.9705 | 0.415536 | ||||||||
\(698\) | 15.4647 | 0.585348 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.5564 | −0.474589 | ||||||||
\(701\) | −8.97613 | −0.339024 | −0.169512 | − | 0.985528i | \(-0.554219\pi\) | ||||
−0.169512 | + | 0.985528i | \(0.554219\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.0452 | −0.718302 | ||||||||
\(704\) | −8.70112 | −0.327936 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.80350 | −0.105511 | ||||||||
\(707\) | 1.50798 | 0.0567133 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.6591 | 0.850979 | 0.425489 | − | 0.904963i | \(-0.360102\pi\) | ||||
0.425489 | + | 0.904963i | \(0.360102\pi\) | |||||||
\(710\) | −24.5186 | −0.920167 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.06487 | 0.152337 | ||||||||
\(713\) | −4.05642 | −0.151914 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.48321 | 0.0928670 | ||||||||
\(716\) | 41.2795 | 1.54269 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −38.4746 | −1.43586 | ||||||||
\(719\) | −2.58167 | −0.0962802 | −0.0481401 | − | 0.998841i | \(-0.515329\pi\) | ||||
−0.0481401 | + | 0.998841i | \(0.515329\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.17512 | 0.229974 | ||||||||
\(722\) | −24.5898 | −0.915137 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27.7995 | −1.03316 | ||||||||
\(725\) | 3.07417 | 0.114172 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.2473 | −0.565490 | −0.282745 | − | 0.959195i | \(-0.591245\pi\) | ||||
−0.282745 | + | 0.959195i | \(0.591245\pi\) | |||||||
\(728\) | 0.455453 | 0.0168802 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −34.1101 | −1.26247 | ||||||||
\(731\) | 11.4319 | 0.422823 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.5375 | −1.31261 | −0.656303 | − | 0.754497i | \(-0.727881\pi\) | ||||
−0.656303 | + | 0.754497i | \(0.727881\pi\) | |||||||
\(734\) | 9.40516 | 0.347151 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.79533 | 0.287339 | ||||||||
\(737\) | 5.38091 | 0.198208 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.2272 | −1.36942 | −0.684712 | − | 0.728814i | \(-0.740072\pi\) | ||||
−0.684712 | + | 0.728814i | \(0.740072\pi\) | |||||||
\(740\) | −17.7722 | −0.653318 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.4019 | 0.528711 | ||||||||
\(743\) | 7.10823 | 0.260776 | 0.130388 | − | 0.991463i | \(-0.458378\pi\) | ||||
0.130388 | + | 0.991463i | \(0.458378\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.89049 | 0.142537 | ||||||||
\(746\) | 38.1419 | 1.39648 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.85235 | 0.104292 | ||||||||
\(749\) | 2.17132 | 0.0793381 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.55783 | 0.202808 | 0.101404 | − | 0.994845i | \(-0.467667\pi\) | ||||
0.101404 | + | 0.994845i | \(0.467667\pi\) | |||||||
\(752\) | 19.4413 | 0.708951 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.32142 | 0.0481231 | ||||||||
\(755\) | −36.4095 | −1.32508 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0525 | −0.365365 | −0.182683 | − | 0.983172i | \(-0.558478\pi\) | ||||
−0.182683 | + | 0.983172i | \(0.558478\pi\) | |||||||
\(758\) | −7.76955 | −0.282203 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.86983 | 0.176647 | ||||||||
\(761\) | −31.3006 | −1.13465 | −0.567324 | − | 0.823495i | \(-0.692021\pi\) | ||||
−0.567324 | + | 0.823495i | \(0.692021\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.1329 | −1.38050 | ||||||||
\(764\) | 22.1834 | 0.802567 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 42.1832 | 1.52414 | ||||||||
\(767\) | −4.74950 | −0.171494 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.2084 | 1.70238 | 0.851190 | − | 0.524858i | \(-0.175881\pi\) | ||||
0.851190 | + | 0.524858i | \(0.175881\pi\) | |||||||
\(770\) | −15.9989 | −0.576562 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.5096 | −0.666177 | ||||||||
\(773\) | −0.309737 | −0.0111405 | −0.00557023 | − | 0.999984i | \(-0.501773\pi\) | ||||
−0.00557023 | + | 0.999984i | \(0.501773\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.4701 | −0.447940 | ||||||||
\(776\) | 0.185707 | 0.00666648 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.4725 | −0.662272 | ||||||||
\(779\) | −51.6590 | −1.85088 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.70654 | −0.204196 | ||||||||
\(782\) | −2.33846 | −0.0836232 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.98405 | 0.320859 | ||||||||
\(785\) | −20.1160 | −0.717972 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.1845 | −0.434330 | −0.217165 | − | 0.976135i | \(-0.569681\pi\) | ||||
−0.217165 | + | 0.976135i | \(0.569681\pi\) | |||||||
\(788\) | 28.1250 | 1.00191 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.18997 | 0.220229 | ||||||||
\(791\) | 8.37863 | 0.297910 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.80690 | 0.312742 | ||||||||
\(794\) | 11.2451 | 0.399074 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.7623 | −0.948563 | ||||||||
\(797\) | −1.87618 | −0.0664576 | −0.0332288 | − | 0.999448i | \(-0.510579\pi\) | ||||
−0.0332288 | + | 0.999448i | \(0.510579\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.40860 | −0.191342 | ||||||||
\(800\) | 23.9642 | 0.847261 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −29.6098 | −1.04556 | ||||||||
\(803\) | −7.93890 | −0.280158 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.29275 | 0.221790 | ||||||||
\(806\) | −5.36022 | −0.188806 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.207791 | −0.00731007 | ||||||||
\(809\) | −2.02618 | −0.0712369 | −0.0356184 | − | 0.999365i | \(-0.511340\pi\) | ||||
−0.0356184 | + | 0.999365i | \(0.511340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.11691 | 0.0392201 | 0.0196101 | − | 0.999808i | \(-0.493758\pi\) | ||||
0.0196101 | + | 0.999808i | \(0.493758\pi\) | |||||||
\(812\) | −4.08449 | −0.143338 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.62175 | −0.302192 | ||||||||
\(815\) | −52.2336 | −1.82966 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −53.8319 | −1.88334 | ||||||||
\(818\) | 25.9778 | 0.908293 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −48.2061 | −1.68343 | ||||||||
\(821\) | −3.23186 | −0.112793 | −0.0563964 | − | 0.998408i | \(-0.517961\pi\) | ||||
−0.0563964 | + | 0.998408i | \(0.517961\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.69183 | −0.337836 | −0.168918 | − | 0.985630i | \(-0.554027\pi\) | ||||
−0.168918 | + | 0.985630i | \(0.554027\pi\) | |||||||
\(824\) | −0.850900 | −0.0296425 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.6002 | 1.06472 | ||||||||
\(827\) | 40.6735 | 1.41436 | 0.707178 | − | 0.707036i | \(-0.249968\pi\) | ||||
0.707178 | + | 0.707036i | \(0.249968\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.7723 | −0.617257 | −0.308629 | − | 0.951183i | \(-0.599870\pi\) | ||||
−0.308629 | + | 0.951183i | \(0.599870\pi\) | |||||||
\(830\) | −16.3373 | −0.567078 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.52235 | 0.156784 | ||||||||
\(833\) | −2.49938 | −0.0865983 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.9027 | 1.58853 | ||||||||
\(836\) | −13.4315 | −0.464538 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.26141 | 0.0781191 | ||||||||
\(839\) | 1.41911 | 0.0489932 | 0.0244966 | − | 0.999700i | \(-0.492202\pi\) | ||||
0.0244966 | + | 0.999700i | \(0.492202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 69.7958 | 2.40532 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 47.3499 | 1.62985 | ||||||||
\(845\) | 35.6490 | 1.22636 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.6368 | 0.709088 | ||||||||
\(848\) | −14.2192 | −0.488289 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.18883 | −0.246575 | ||||||||
\(851\) | 3.39113 | 0.116247 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.9878 | −0.787086 | −0.393543 | − | 0.919306i | \(-0.628751\pi\) | ||||
−0.393543 | + | 0.919306i | \(0.628751\pi\) | |||||||
\(854\) | −56.7414 | −1.94165 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.299196 | −0.0102263 | ||||||||
\(857\) | −9.16185 | −0.312963 | −0.156481 | − | 0.987681i | \(-0.550015\pi\) | ||||
−0.156481 | + | 0.987681i | \(0.550015\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.1195 | −1.50534 | −0.752670 | − | 0.658398i | \(-0.771234\pi\) | ||||
−0.752670 | + | 0.658398i | \(0.771234\pi\) | |||||||
\(860\) | −50.2337 | −1.71295 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.7963 | 0.469905 | ||||||||
\(863\) | −25.6405 | −0.872813 | −0.436406 | − | 0.899750i | \(-0.643749\pi\) | ||||
−0.436406 | + | 0.899750i | \(0.643749\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.1799 | 0.448128 | ||||||||
\(866\) | −20.2254 | −0.687288 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.5684 | 0.562369 | ||||||||
\(869\) | 1.44067 | 0.0488715 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.79669 | −0.0947623 | ||||||||
\(872\) | 5.25451 | 0.177940 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.0116 | 0.372474 | ||||||||
\(875\) | −12.1188 | −0.409689 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.5935 | −0.594091 | −0.297045 | − | 0.954863i | \(-0.596001\pi\) | ||||
−0.297045 | + | 0.954863i | \(0.596001\pi\) | |||||||
\(878\) | 54.6224 | 1.84342 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 15.7959 | 0.532481 | ||||||||
\(881\) | −33.7623 | −1.13748 | −0.568741 | − | 0.822517i | \(-0.692569\pi\) | ||||
−0.568741 | + | 0.822517i | \(0.692569\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.69578 | 0.326289 | 0.163145 | − | 0.986602i | \(-0.447836\pi\) | ||||
0.163145 | + | 0.986602i | \(0.447836\pi\) | |||||||
\(884\) | −1.48249 | −0.0498615 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 52.3041 | 1.75719 | ||||||||
\(887\) | 28.1087 | 0.943796 | 0.471898 | − | 0.881653i | \(-0.343569\pi\) | ||||
0.471898 | + | 0.881653i | \(0.343569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.6261 | −1.12778 | ||||||||
\(890\) | 74.2134 | 2.48764 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −22.4393 | −0.751324 | ||||||||
\(893\) | 25.4687 | 0.852276 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −63.5970 | −2.12581 | ||||||||
\(896\) | 5.39001 | 0.180068 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −32.3414 | −1.07925 | ||||||||
\(899\) | −4.05642 | −0.135289 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.95580 | 0.131787 | ||||||||
\(902\) | −23.3860 | −0.778670 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.15453 | −0.0383992 | ||||||||
\(905\) | 42.8291 | 1.42369 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5584 | 0.350585 | 0.175292 | − | 0.984516i | \(-0.443913\pi\) | ||||
0.175292 | + | 0.984516i | \(0.443913\pi\) | |||||||
\(908\) | −1.71256 | −0.0568333 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.31534 | 0.275651 | ||||||||
\(911\) | −36.6663 | −1.21481 | −0.607405 | − | 0.794393i | \(-0.707789\pi\) | ||||
−0.607405 | + | 0.794393i | \(0.707789\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.80241 | −0.125841 | ||||||||
\(914\) | 63.9683 | 2.11588 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 35.6634 | 1.17835 | ||||||||
\(917\) | −19.4486 | −0.642251 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.8602 | −1.44681 | −0.723407 | − | 0.690422i | \(-0.757425\pi\) | ||||
−0.723407 | + | 0.690422i | \(0.757425\pi\) | |||||||
\(920\) | −0.867109 | −0.0285878 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 76.8713 | 2.53162 | ||||||||
\(923\) | 2.96594 | 0.0976250 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.4249 | 0.342769 | ||||||||
\(926\) | −28.7141 | −0.943602 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.79533 | 0.255894 | ||||||||
\(929\) | 31.9067 | 1.04683 | 0.523413 | − | 0.852079i | \(-0.324658\pi\) | ||||
0.523413 | + | 0.852079i | \(0.324658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.7694 | 0.385726 | ||||||||
\(932\) | −2.47559 | −0.0810905 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24.9429 | 0.816158 | ||||||||
\(935\) | −4.39446 | −0.143714 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.0133 | 1.37251 | 0.686257 | − | 0.727359i | \(-0.259252\pi\) | ||||
0.686257 | + | 0.727359i | \(0.259252\pi\) | |||||||
\(938\) | 18.0186 | 0.588329 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 23.7663 | 0.775172 | ||||||||
\(941\) | 30.3371 | 0.988963 | 0.494481 | − | 0.869188i | \(-0.335358\pi\) | ||||
0.494481 | + | 0.869188i | \(0.335358\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.19828 | 0.299537 | ||||||||
\(944\) | −30.2120 | −0.983316 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.3697 | −0.792327 | ||||||||
\(947\) | 15.9902 | 0.519610 | 0.259805 | − | 0.965661i | \(-0.416342\pi\) | ||||
0.259805 | + | 0.965661i | \(0.416342\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.12619 | 0.133942 | ||||||||
\(950\) | 33.8517 | 1.09829 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.806000 | −0.0261226 | ||||||||
\(953\) | −27.9450 | −0.905228 | −0.452614 | − | 0.891707i | \(-0.649508\pi\) | ||||
−0.452614 | + | 0.891707i | \(0.649508\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.1767 | −1.10593 | ||||||||
\(956\) | −27.0839 | −0.875956 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −62.7538 | −2.02748 | ||||||||
\(959\) | −13.7913 | −0.445344 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.5454 | −0.469208 | ||||||||
\(962\) | 4.48110 | 0.144476 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.5768 | −0.533903 | ||||||||
\(965\) | 28.5168 | 0.917988 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.3686 | −0.783642 | −0.391821 | − | 0.920041i | \(-0.628155\pi\) | ||||
−0.391821 | + | 0.920041i | \(0.628155\pi\) | |||||||
\(968\) | −2.84364 | −0.0913981 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.39050 | 0.108862 | ||||||||
\(971\) | 11.2336 | 0.360503 | 0.180251 | − | 0.983621i | \(-0.442309\pi\) | ||||
0.180251 | + | 0.983621i | \(0.442309\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.981875 | −0.0314775 | ||||||||
\(974\) | −0.0630854 | −0.00202139 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 56.0215 | 1.79320 | ||||||||
\(977\) | 7.55369 | 0.241664 | 0.120832 | − | 0.992673i | \(-0.461444\pi\) | ||||
0.120832 | + | 0.992673i | \(0.461444\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.2727 | 0.552037 | ||||||||
\(980\) | 10.9827 | 0.350829 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.91852 | −0.316513 | ||||||||
\(983\) | −11.8587 | −0.378233 | −0.189116 | − | 0.981955i | \(-0.560562\pi\) | ||||
−0.189116 | + | 0.981955i | \(0.560562\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −43.3307 | −1.38063 | ||||||||
\(986\) | −2.33846 | −0.0744718 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.98093 | 0.222093 | ||||||||
\(989\) | 9.58517 | 0.304791 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.70198 | 0.244662 | 0.122331 | − | 0.992489i | \(-0.460963\pi\) | ||||
0.122331 | + | 0.992489i | \(0.460963\pi\) | |||||||
\(992\) | −31.6211 | −1.00397 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −19.1090 | −0.606101 | ||||||||
\(995\) | 41.2311 | 1.30711 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.9155 | 1.32748 | 0.663738 | − | 0.747965i | \(-0.268969\pi\) | ||||
0.663738 | + | 0.747965i | \(0.268969\pi\) | |||||||
\(998\) | −67.1445 | −2.12542 | ||||||||
\(999\) | 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 | 6003.2.a.t.1.5 | ✓ | 22 | |
3.2 | odd | 2 | 6003.2.a.u.1.18 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.5 | ✓ | 22 | 1.1 | even | 1 | trivial | |
6003.2.a.u.1.18 | yes | 22 | 3.2 | odd | 2 |