Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.28523 | −0.908797 | −0.454399 | − | 0.890798i | \(-0.650146\pi\) | ||||
−0.454399 | + | 0.890798i | \(0.650146\pi\) | |||||||
\(3\) | −0.829686 | −0.479019 | −0.239510 | − | 0.970894i | \(-0.576987\pi\) | ||||
−0.239510 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(4\) | −0.348175 | −0.174088 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.06634 | 0.435332 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.01795 | 1.06701 | ||||||||
\(9\) | −2.31162 | −0.770540 | ||||||||
\(10\) | 1.28523 | 0.406426 | ||||||||
\(11\) | −2.11972 | −0.639121 | −0.319560 | − | 0.947566i | \(-0.603535\pi\) | ||||
−0.319560 | + | 0.947566i | \(0.603535\pi\) | |||||||
\(12\) | 0.288876 | 0.0833913 | ||||||||
\(13\) | 3.07149 | 0.851879 | 0.425940 | − | 0.904752i | \(-0.359944\pi\) | ||||
0.425940 | + | 0.904752i | \(0.359944\pi\) | |||||||
\(14\) | 1.28523 | 0.343493 | ||||||||
\(15\) | 0.829686 | 0.214224 | ||||||||
\(16\) | −3.18242 | −0.795606 | ||||||||
\(17\) | −6.86780 | −1.66569 | −0.832843 | − | 0.553509i | \(-0.813288\pi\) | ||||
−0.832843 | + | 0.553509i | \(0.813288\pi\) | |||||||
\(18\) | 2.97097 | 0.700265 | ||||||||
\(19\) | −3.15147 | −0.722997 | −0.361499 | − | 0.932373i | \(-0.617735\pi\) | ||||
−0.361499 | + | 0.932373i | \(0.617735\pi\) | |||||||
\(20\) | 0.348175 | 0.0778543 | ||||||||
\(21\) | 0.829686 | 0.181052 | ||||||||
\(22\) | 2.72434 | 0.580831 | ||||||||
\(23\) | −0.512282 | −0.106818 | −0.0534091 | − | 0.998573i | \(-0.517009\pi\) | ||||
−0.0534091 | + | 0.998573i | \(0.517009\pi\) | |||||||
\(24\) | −2.50395 | −0.511117 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.94759 | −0.774186 | ||||||||
\(27\) | 4.40698 | 0.848123 | ||||||||
\(28\) | 0.348175 | 0.0657989 | ||||||||
\(29\) | 3.17302 | 0.589216 | 0.294608 | − | 0.955618i | \(-0.404811\pi\) | ||||
0.294608 | + | 0.955618i | \(0.404811\pi\) | |||||||
\(30\) | −1.06634 | −0.194686 | ||||||||
\(31\) | 3.72476 | 0.668987 | 0.334494 | − | 0.942398i | \(-0.391435\pi\) | ||||
0.334494 | + | 0.942398i | \(0.391435\pi\) | |||||||
\(32\) | −1.94575 | −0.343963 | ||||||||
\(33\) | 1.75871 | 0.306151 | ||||||||
\(34\) | 8.82673 | 1.51377 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0.804849 | 0.134141 | ||||||||
\(37\) | −5.59920 | −0.920503 | −0.460251 | − | 0.887789i | \(-0.652241\pi\) | ||||
−0.460251 | + | 0.887789i | \(0.652241\pi\) | |||||||
\(38\) | 4.05038 | 0.657058 | ||||||||
\(39\) | −2.54838 | −0.408067 | ||||||||
\(40\) | −3.01795 | −0.477180 | ||||||||
\(41\) | −7.64566 | −1.19405 | −0.597025 | − | 0.802222i | \(-0.703651\pi\) | ||||
−0.597025 | + | 0.802222i | \(0.703651\pi\) | |||||||
\(42\) | −1.06634 | −0.164540 | ||||||||
\(43\) | −5.76988 | −0.879898 | −0.439949 | − | 0.898023i | \(-0.645003\pi\) | ||||
−0.439949 | + | 0.898023i | \(0.645003\pi\) | |||||||
\(44\) | 0.738035 | 0.111263 | ||||||||
\(45\) | 2.31162 | 0.344596 | ||||||||
\(46\) | 0.658402 | 0.0970760 | ||||||||
\(47\) | −10.3490 | −1.50956 | −0.754779 | − | 0.655979i | \(-0.772256\pi\) | ||||
−0.754779 | + | 0.655979i | \(0.772256\pi\) | |||||||
\(48\) | 2.64041 | 0.381111 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.28523 | −0.181759 | ||||||||
\(51\) | 5.69812 | 0.797896 | ||||||||
\(52\) | −1.06942 | −0.148302 | ||||||||
\(53\) | 5.76232 | 0.791516 | 0.395758 | − | 0.918355i | \(-0.370482\pi\) | ||||
0.395758 | + | 0.918355i | \(0.370482\pi\) | |||||||
\(54\) | −5.66400 | −0.770772 | ||||||||
\(55\) | 2.11972 | 0.285824 | ||||||||
\(56\) | −3.01795 | −0.403291 | ||||||||
\(57\) | 2.61473 | 0.346330 | ||||||||
\(58\) | −4.07808 | −0.535478 | ||||||||
\(59\) | −0.788910 | −0.102707 | −0.0513537 | − | 0.998681i | \(-0.516354\pi\) | ||||
−0.0513537 | + | 0.998681i | \(0.516354\pi\) | |||||||
\(60\) | −0.288876 | −0.0372937 | ||||||||
\(61\) | 5.99308 | 0.767335 | 0.383668 | − | 0.923471i | \(-0.374661\pi\) | ||||
0.383668 | + | 0.923471i | \(0.374661\pi\) | |||||||
\(62\) | −4.78719 | −0.607974 | ||||||||
\(63\) | 2.31162 | 0.291237 | ||||||||
\(64\) | 8.86559 | 1.10820 | ||||||||
\(65\) | −3.07149 | −0.380972 | ||||||||
\(66\) | −2.26035 | −0.278230 | ||||||||
\(67\) | −11.9757 | −1.46306 | −0.731530 | − | 0.681810i | \(-0.761193\pi\) | ||||
−0.731530 | + | 0.681810i | \(0.761193\pi\) | |||||||
\(68\) | 2.39120 | 0.289975 | ||||||||
\(69\) | 0.425033 | 0.0511680 | ||||||||
\(70\) | −1.28523 | −0.153615 | ||||||||
\(71\) | −15.5425 | −1.84455 | −0.922276 | − | 0.386533i | \(-0.873673\pi\) | ||||
−0.922276 | + | 0.386533i | \(0.873673\pi\) | |||||||
\(72\) | −6.97636 | −0.822172 | ||||||||
\(73\) | 9.76873 | 1.14334 | 0.571672 | − | 0.820482i | \(-0.306295\pi\) | ||||
0.571672 | + | 0.820482i | \(0.306295\pi\) | |||||||
\(74\) | 7.19628 | 0.836550 | ||||||||
\(75\) | −0.829686 | −0.0958039 | ||||||||
\(76\) | 1.09726 | 0.125865 | ||||||||
\(77\) | 2.11972 | 0.241565 | ||||||||
\(78\) | 3.27526 | 0.370850 | ||||||||
\(79\) | −9.51566 | −1.07059 | −0.535297 | − | 0.844664i | \(-0.679800\pi\) | ||||
−0.535297 | + | 0.844664i | \(0.679800\pi\) | |||||||
\(80\) | 3.18242 | 0.355806 | ||||||||
\(81\) | 3.27846 | 0.364273 | ||||||||
\(82\) | 9.82645 | 1.08515 | ||||||||
\(83\) | −2.71309 | −0.297801 | −0.148900 | − | 0.988852i | \(-0.547573\pi\) | ||||
−0.148900 | + | 0.988852i | \(0.547573\pi\) | |||||||
\(84\) | −0.288876 | −0.0315190 | ||||||||
\(85\) | 6.86780 | 0.744918 | ||||||||
\(86\) | 7.41564 | 0.799649 | ||||||||
\(87\) | −2.63261 | −0.282246 | ||||||||
\(88\) | −6.39723 | −0.681947 | ||||||||
\(89\) | −16.0539 | −1.70171 | −0.850856 | − | 0.525399i | \(-0.823916\pi\) | ||||
−0.850856 | + | 0.525399i | \(0.823916\pi\) | |||||||
\(90\) | −2.97097 | −0.313168 | ||||||||
\(91\) | −3.07149 | −0.321980 | ||||||||
\(92\) | 0.178364 | 0.0185957 | ||||||||
\(93\) | −3.09038 | −0.320458 | ||||||||
\(94\) | 13.3009 | 1.37188 | ||||||||
\(95\) | 3.15147 | 0.323334 | ||||||||
\(96\) | 1.61436 | 0.164765 | ||||||||
\(97\) | −0.759265 | −0.0770917 | −0.0385458 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385458 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(98\) | −1.28523 | −0.129828 | ||||||||
\(99\) | 4.90000 | 0.492468 | ||||||||
\(100\) | −0.348175 | −0.0348175 | ||||||||
\(101\) | −4.01405 | −0.399413 | −0.199706 | − | 0.979856i | \(-0.563999\pi\) | ||||
−0.199706 | + | 0.979856i | \(0.563999\pi\) | |||||||
\(102\) | −7.32341 | −0.725126 | ||||||||
\(103\) | −17.0160 | −1.67664 | −0.838320 | − | 0.545178i | \(-0.816462\pi\) | ||||
−0.838320 | + | 0.545178i | \(0.816462\pi\) | |||||||
\(104\) | 9.26963 | 0.908962 | ||||||||
\(105\) | −0.829686 | −0.0809691 | ||||||||
\(106\) | −7.40593 | −0.719327 | ||||||||
\(107\) | 1.70018 | 0.164363 | 0.0821814 | − | 0.996617i | \(-0.473811\pi\) | ||||
0.0821814 | + | 0.996617i | \(0.473811\pi\) | |||||||
\(108\) | −1.53440 | −0.147648 | ||||||||
\(109\) | 11.6739 | 1.11816 | 0.559078 | − | 0.829115i | \(-0.311155\pi\) | ||||
0.559078 | + | 0.829115i | \(0.311155\pi\) | |||||||
\(110\) | −2.72434 | −0.259756 | ||||||||
\(111\) | 4.64558 | 0.440939 | ||||||||
\(112\) | 3.18242 | 0.300711 | ||||||||
\(113\) | 4.59727 | 0.432475 | 0.216237 | − | 0.976341i | \(-0.430622\pi\) | ||||
0.216237 | + | 0.976341i | \(0.430622\pi\) | |||||||
\(114\) | −3.36054 | −0.314744 | ||||||||
\(115\) | 0.512282 | 0.0477705 | ||||||||
\(116\) | −1.10477 | −0.102575 | ||||||||
\(117\) | −7.10013 | −0.656407 | ||||||||
\(118\) | 1.01393 | 0.0933402 | ||||||||
\(119\) | 6.86780 | 0.629570 | ||||||||
\(120\) | 2.50395 | 0.228579 | ||||||||
\(121\) | −6.50677 | −0.591524 | ||||||||
\(122\) | −7.70250 | −0.697352 | ||||||||
\(123\) | 6.34349 | 0.571974 | ||||||||
\(124\) | −1.29687 | −0.116462 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.97097 | −0.264675 | ||||||||
\(127\) | 20.5253 | 1.82132 | 0.910662 | − | 0.413152i | \(-0.135572\pi\) | ||||
0.910662 | + | 0.413152i | \(0.135572\pi\) | |||||||
\(128\) | −7.50285 | −0.663165 | ||||||||
\(129\) | 4.78719 | 0.421488 | ||||||||
\(130\) | 3.94759 | 0.346226 | ||||||||
\(131\) | 13.3057 | 1.16252 | 0.581262 | − | 0.813717i | \(-0.302559\pi\) | ||||
0.581262 | + | 0.813717i | \(0.302559\pi\) | |||||||
\(132\) | −0.612337 | −0.0532971 | ||||||||
\(133\) | 3.15147 | 0.273267 | ||||||||
\(134\) | 15.3915 | 1.32962 | ||||||||
\(135\) | −4.40698 | −0.379292 | ||||||||
\(136\) | −20.7267 | −1.77730 | ||||||||
\(137\) | −11.9618 | −1.02197 | −0.510983 | − | 0.859591i | \(-0.670719\pi\) | ||||
−0.510983 | + | 0.859591i | \(0.670719\pi\) | |||||||
\(138\) | −0.546267 | −0.0465013 | ||||||||
\(139\) | −2.77551 | −0.235416 | −0.117708 | − | 0.993048i | \(-0.537555\pi\) | ||||
−0.117708 | + | 0.993048i | \(0.537555\pi\) | |||||||
\(140\) | −0.348175 | −0.0294262 | ||||||||
\(141\) | 8.58643 | 0.723107 | ||||||||
\(142\) | 19.9757 | 1.67632 | ||||||||
\(143\) | −6.51072 | −0.544454 | ||||||||
\(144\) | 7.35656 | 0.613047 | ||||||||
\(145\) | −3.17302 | −0.263505 | ||||||||
\(146\) | −12.5551 | −1.03907 | ||||||||
\(147\) | −0.829686 | −0.0684313 | ||||||||
\(148\) | 1.94950 | 0.160248 | ||||||||
\(149\) | −11.2506 | −0.921682 | −0.460841 | − | 0.887483i | \(-0.652452\pi\) | ||||
−0.460841 | + | 0.887483i | \(0.652452\pi\) | |||||||
\(150\) | 1.06634 | 0.0870663 | ||||||||
\(151\) | 11.2784 | 0.917821 | 0.458911 | − | 0.888482i | \(-0.348240\pi\) | ||||
0.458911 | + | 0.888482i | \(0.348240\pi\) | |||||||
\(152\) | −9.51099 | −0.771444 | ||||||||
\(153\) | 15.8758 | 1.28348 | ||||||||
\(154\) | −2.72434 | −0.219534 | ||||||||
\(155\) | −3.72476 | −0.299180 | ||||||||
\(156\) | 0.887281 | 0.0710393 | ||||||||
\(157\) | −16.1105 | −1.28576 | −0.642880 | − | 0.765967i | \(-0.722261\pi\) | ||||
−0.642880 | + | 0.765967i | \(0.722261\pi\) | |||||||
\(158\) | 12.2298 | 0.972954 | ||||||||
\(159\) | −4.78092 | −0.379151 | ||||||||
\(160\) | 1.94575 | 0.153825 | ||||||||
\(161\) | 0.512282 | 0.0403735 | ||||||||
\(162\) | −4.21358 | −0.331050 | ||||||||
\(163\) | −23.8170 | −1.86549 | −0.932744 | − | 0.360539i | \(-0.882593\pi\) | ||||
−0.932744 | + | 0.360539i | \(0.882593\pi\) | |||||||
\(164\) | 2.66203 | 0.207869 | ||||||||
\(165\) | −1.75871 | −0.136915 | ||||||||
\(166\) | 3.48696 | 0.270641 | ||||||||
\(167\) | −0.127154 | −0.00983946 | −0.00491973 | − | 0.999988i | \(-0.501566\pi\) | ||||
−0.00491973 | + | 0.999988i | \(0.501566\pi\) | |||||||
\(168\) | 2.50395 | 0.193184 | ||||||||
\(169\) | −3.56592 | −0.274302 | ||||||||
\(170\) | −8.82673 | −0.676979 | ||||||||
\(171\) | 7.28501 | 0.557099 | ||||||||
\(172\) | 2.00893 | 0.153179 | ||||||||
\(173\) | 4.69164 | 0.356699 | 0.178349 | − | 0.983967i | \(-0.442924\pi\) | ||||
0.178349 | + | 0.983967i | \(0.442924\pi\) | |||||||
\(174\) | 3.38352 | 0.256504 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 6.74586 | 0.508488 | ||||||||
\(177\) | 0.654548 | 0.0491988 | ||||||||
\(178\) | 20.6330 | 1.54651 | ||||||||
\(179\) | 4.51041 | 0.337124 | 0.168562 | − | 0.985691i | \(-0.446088\pi\) | ||||
0.168562 | + | 0.985691i | \(0.446088\pi\) | |||||||
\(180\) | −0.804849 | −0.0599899 | ||||||||
\(181\) | −11.0214 | −0.819214 | −0.409607 | − | 0.912262i | \(-0.634334\pi\) | ||||
−0.409607 | + | 0.912262i | \(0.634334\pi\) | |||||||
\(182\) | 3.94759 | 0.292615 | ||||||||
\(183\) | −4.97237 | −0.367568 | ||||||||
\(184\) | −1.54604 | −0.113976 | ||||||||
\(185\) | 5.59920 | 0.411661 | ||||||||
\(186\) | 3.97187 | 0.291231 | ||||||||
\(187\) | 14.5578 | 1.06458 | ||||||||
\(188\) | 3.60327 | 0.262795 | ||||||||
\(189\) | −4.40698 | −0.320560 | ||||||||
\(190\) | −4.05038 | −0.293845 | ||||||||
\(191\) | −15.9321 | −1.15280 | −0.576402 | − | 0.817166i | \(-0.695544\pi\) | ||||
−0.576402 | + | 0.817166i | \(0.695544\pi\) | |||||||
\(192\) | −7.35566 | −0.530849 | ||||||||
\(193\) | 12.7166 | 0.915363 | 0.457681 | − | 0.889116i | \(-0.348680\pi\) | ||||
0.457681 | + | 0.889116i | \(0.348680\pi\) | |||||||
\(194\) | 0.975833 | 0.0700607 | ||||||||
\(195\) | 2.54838 | 0.182493 | ||||||||
\(196\) | −0.348175 | −0.0248696 | ||||||||
\(197\) | −23.1318 | −1.64807 | −0.824037 | − | 0.566536i | \(-0.808283\pi\) | ||||
−0.824037 | + | 0.566536i | \(0.808283\pi\) | |||||||
\(198\) | −6.29764 | −0.447554 | ||||||||
\(199\) | −16.3500 | −1.15902 | −0.579509 | − | 0.814966i | \(-0.696756\pi\) | ||||
−0.579509 | + | 0.814966i | \(0.696756\pi\) | |||||||
\(200\) | 3.01795 | 0.213402 | ||||||||
\(201\) | 9.93603 | 0.700834 | ||||||||
\(202\) | 5.15899 | 0.362985 | ||||||||
\(203\) | −3.17302 | −0.222703 | ||||||||
\(204\) | −1.98394 | −0.138904 | ||||||||
\(205\) | 7.64566 | 0.533996 | ||||||||
\(206\) | 21.8696 | 1.52373 | ||||||||
\(207\) | 1.18420 | 0.0823077 | ||||||||
\(208\) | −9.77480 | −0.677760 | ||||||||
\(209\) | 6.68025 | 0.462083 | ||||||||
\(210\) | 1.06634 | 0.0735845 | ||||||||
\(211\) | −1.13399 | −0.0780671 | −0.0390335 | − | 0.999238i | \(-0.512428\pi\) | ||||
−0.0390335 | + | 0.999238i | \(0.512428\pi\) | |||||||
\(212\) | −2.00630 | −0.137793 | ||||||||
\(213\) | 12.8954 | 0.883576 | ||||||||
\(214\) | −2.18513 | −0.149372 | ||||||||
\(215\) | 5.76988 | 0.393502 | ||||||||
\(216\) | 13.3001 | 0.904954 | ||||||||
\(217\) | −3.72476 | −0.252853 | ||||||||
\(218\) | −15.0037 | −1.01618 | ||||||||
\(219\) | −8.10498 | −0.547684 | ||||||||
\(220\) | −0.738035 | −0.0497583 | ||||||||
\(221\) | −21.0944 | −1.41896 | ||||||||
\(222\) | −5.97065 | −0.400724 | ||||||||
\(223\) | 0.407893 | 0.0273145 | 0.0136573 | − | 0.999907i | \(-0.495653\pi\) | ||||
0.0136573 | + | 0.999907i | \(0.495653\pi\) | |||||||
\(224\) | 1.94575 | 0.130006 | ||||||||
\(225\) | −2.31162 | −0.154108 | ||||||||
\(226\) | −5.90856 | −0.393032 | ||||||||
\(227\) | 16.7163 | 1.10950 | 0.554751 | − | 0.832016i | \(-0.312813\pi\) | ||||
0.554751 | + | 0.832016i | \(0.312813\pi\) | |||||||
\(228\) | −0.910385 | −0.0602917 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −0.658402 | −0.0434137 | ||||||||
\(231\) | −1.75871 | −0.115714 | ||||||||
\(232\) | 9.57603 | 0.628697 | ||||||||
\(233\) | −25.0566 | −1.64151 | −0.820757 | − | 0.571278i | \(-0.806448\pi\) | ||||
−0.820757 | + | 0.571278i | \(0.806448\pi\) | |||||||
\(234\) | 9.12533 | 0.596541 | ||||||||
\(235\) | 10.3490 | 0.675095 | ||||||||
\(236\) | 0.274679 | 0.0178801 | ||||||||
\(237\) | 7.89501 | 0.512836 | ||||||||
\(238\) | −8.82673 | −0.572152 | ||||||||
\(239\) | −9.02309 | −0.583655 | −0.291828 | − | 0.956471i | \(-0.594263\pi\) | ||||
−0.291828 | + | 0.956471i | \(0.594263\pi\) | |||||||
\(240\) | −2.64041 | −0.170438 | ||||||||
\(241\) | 2.89667 | 0.186591 | 0.0932955 | − | 0.995638i | \(-0.470260\pi\) | ||||
0.0932955 | + | 0.995638i | \(0.470260\pi\) | |||||||
\(242\) | 8.36272 | 0.537576 | ||||||||
\(243\) | −15.9410 | −1.02262 | ||||||||
\(244\) | −2.08664 | −0.133583 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −8.15287 | −0.519808 | ||||||||
\(247\) | −9.67973 | −0.615906 | ||||||||
\(248\) | 11.2412 | 0.713815 | ||||||||
\(249\) | 2.25102 | 0.142652 | ||||||||
\(250\) | 1.28523 | 0.0812853 | ||||||||
\(251\) | −23.8655 | −1.50638 | −0.753188 | − | 0.657805i | \(-0.771485\pi\) | ||||
−0.753188 | + | 0.657805i | \(0.771485\pi\) | |||||||
\(252\) | −0.804849 | −0.0507007 | ||||||||
\(253\) | 1.08590 | 0.0682697 | ||||||||
\(254\) | −26.3798 | −1.65521 | ||||||||
\(255\) | −5.69812 | −0.356830 | ||||||||
\(256\) | −8.08826 | −0.505516 | ||||||||
\(257\) | −5.23631 | −0.326632 | −0.163316 | − | 0.986574i | \(-0.552219\pi\) | ||||
−0.163316 | + | 0.986574i | \(0.552219\pi\) | |||||||
\(258\) | −6.15265 | −0.383047 | ||||||||
\(259\) | 5.59920 | 0.347917 | ||||||||
\(260\) | 1.06942 | 0.0663225 | ||||||||
\(261\) | −7.33483 | −0.454014 | ||||||||
\(262\) | −17.1009 | −1.05650 | ||||||||
\(263\) | 2.68393 | 0.165498 | 0.0827491 | − | 0.996570i | \(-0.473630\pi\) | ||||
0.0827491 | + | 0.996570i | \(0.473630\pi\) | |||||||
\(264\) | 5.30769 | 0.326666 | ||||||||
\(265\) | −5.76232 | −0.353977 | ||||||||
\(266\) | −4.05038 | −0.248345 | ||||||||
\(267\) | 13.3197 | 0.815153 | ||||||||
\(268\) | 4.16963 | 0.254700 | ||||||||
\(269\) | 13.5689 | 0.827312 | 0.413656 | − | 0.910433i | \(-0.364252\pi\) | ||||
0.413656 | + | 0.910433i | \(0.364252\pi\) | |||||||
\(270\) | 5.66400 | 0.344700 | ||||||||
\(271\) | −12.0364 | −0.731159 | −0.365579 | − | 0.930780i | \(-0.619129\pi\) | ||||
−0.365579 | + | 0.930780i | \(0.619129\pi\) | |||||||
\(272\) | 21.8563 | 1.32523 | ||||||||
\(273\) | 2.54838 | 0.154235 | ||||||||
\(274\) | 15.3737 | 0.928760 | ||||||||
\(275\) | −2.11972 | −0.127824 | ||||||||
\(276\) | −0.147986 | −0.00890771 | ||||||||
\(277\) | 5.00271 | 0.300584 | 0.150292 | − | 0.988642i | \(-0.451979\pi\) | ||||
0.150292 | + | 0.988642i | \(0.451979\pi\) | |||||||
\(278\) | 3.56718 | 0.213945 | ||||||||
\(279\) | −8.61024 | −0.515482 | ||||||||
\(280\) | 3.01795 | 0.180357 | ||||||||
\(281\) | −0.978797 | −0.0583901 | −0.0291951 | − | 0.999574i | \(-0.509294\pi\) | ||||
−0.0291951 | + | 0.999574i | \(0.509294\pi\) | |||||||
\(282\) | −11.0356 | −0.657158 | ||||||||
\(283\) | −20.8717 | −1.24069 | −0.620347 | − | 0.784327i | \(-0.713008\pi\) | ||||
−0.620347 | + | 0.784327i | \(0.713008\pi\) | |||||||
\(284\) | 5.41150 | 0.321113 | ||||||||
\(285\) | −2.61473 | −0.154883 | ||||||||
\(286\) | 8.36780 | 0.494798 | ||||||||
\(287\) | 7.64566 | 0.451309 | ||||||||
\(288\) | 4.49783 | 0.265037 | ||||||||
\(289\) | 30.1667 | 1.77451 | ||||||||
\(290\) | 4.07808 | 0.239473 | ||||||||
\(291\) | 0.629952 | 0.0369284 | ||||||||
\(292\) | −3.40123 | −0.199042 | ||||||||
\(293\) | 27.8956 | 1.62968 | 0.814840 | − | 0.579686i | \(-0.196825\pi\) | ||||
0.814840 | + | 0.579686i | \(0.196825\pi\) | |||||||
\(294\) | 1.06634 | 0.0621902 | ||||||||
\(295\) | 0.788910 | 0.0459321 | ||||||||
\(296\) | −16.8981 | −0.982183 | ||||||||
\(297\) | −9.34158 | −0.542053 | ||||||||
\(298\) | 14.4596 | 0.837622 | ||||||||
\(299\) | −1.57347 | −0.0909962 | ||||||||
\(300\) | 0.288876 | 0.0166783 | ||||||||
\(301\) | 5.76988 | 0.332570 | ||||||||
\(302\) | −14.4953 | −0.834113 | ||||||||
\(303\) | 3.33040 | 0.191326 | ||||||||
\(304\) | 10.0293 | 0.575221 | ||||||||
\(305\) | −5.99308 | −0.343163 | ||||||||
\(306\) | −20.4041 | −1.16642 | ||||||||
\(307\) | 24.8123 | 1.41611 | 0.708055 | − | 0.706157i | \(-0.249573\pi\) | ||||
0.708055 | + | 0.706157i | \(0.249573\pi\) | |||||||
\(308\) | −0.738035 | −0.0420535 | ||||||||
\(309\) | 14.1180 | 0.803143 | ||||||||
\(310\) | 4.78719 | 0.271894 | ||||||||
\(311\) | −8.78571 | −0.498192 | −0.249096 | − | 0.968479i | \(-0.580133\pi\) | ||||
−0.249096 | + | 0.968479i | \(0.580133\pi\) | |||||||
\(312\) | −7.69088 | −0.435410 | ||||||||
\(313\) | −7.29795 | −0.412505 | −0.206252 | − | 0.978499i | \(-0.566127\pi\) | ||||
−0.206252 | + | 0.978499i | \(0.566127\pi\) | |||||||
\(314\) | 20.7058 | 1.16850 | ||||||||
\(315\) | −2.31162 | −0.130245 | ||||||||
\(316\) | 3.31311 | 0.186377 | ||||||||
\(317\) | −12.0895 | −0.679012 | −0.339506 | − | 0.940604i | \(-0.610260\pi\) | ||||
−0.339506 | + | 0.940604i | \(0.610260\pi\) | |||||||
\(318\) | 6.14459 | 0.344572 | ||||||||
\(319\) | −6.72593 | −0.376580 | ||||||||
\(320\) | −8.86559 | −0.495601 | ||||||||
\(321\) | −1.41062 | −0.0787330 | ||||||||
\(322\) | −0.658402 | −0.0366913 | ||||||||
\(323\) | 21.6437 | 1.20429 | ||||||||
\(324\) | −1.14148 | −0.0634154 | ||||||||
\(325\) | 3.07149 | 0.170376 | ||||||||
\(326\) | 30.6104 | 1.69535 | ||||||||
\(327\) | −9.68567 | −0.535619 | ||||||||
\(328\) | −23.0742 | −1.27406 | ||||||||
\(329\) | 10.3490 | 0.570559 | ||||||||
\(330\) | 2.26035 | 0.124428 | ||||||||
\(331\) | −13.5342 | −0.743907 | −0.371953 | − | 0.928251i | \(-0.621312\pi\) | ||||
−0.371953 | + | 0.928251i | \(0.621312\pi\) | |||||||
\(332\) | 0.944632 | 0.0518434 | ||||||||
\(333\) | 12.9432 | 0.709285 | ||||||||
\(334\) | 0.163422 | 0.00894208 | ||||||||
\(335\) | 11.9757 | 0.654300 | ||||||||
\(336\) | −2.64041 | −0.144046 | ||||||||
\(337\) | −14.4378 | −0.786476 | −0.393238 | − | 0.919437i | \(-0.628645\pi\) | ||||
−0.393238 | + | 0.919437i | \(0.628645\pi\) | |||||||
\(338\) | 4.58304 | 0.249285 | ||||||||
\(339\) | −3.81429 | −0.207164 | ||||||||
\(340\) | −2.39120 | −0.129681 | ||||||||
\(341\) | −7.89547 | −0.427564 | ||||||||
\(342\) | −9.36294 | −0.506290 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −17.4132 | −0.938858 | ||||||||
\(345\) | −0.425033 | −0.0228830 | ||||||||
\(346\) | −6.02985 | −0.324167 | ||||||||
\(347\) | 10.6126 | 0.569716 | 0.284858 | − | 0.958570i | \(-0.408054\pi\) | ||||
0.284858 | + | 0.958570i | \(0.408054\pi\) | |||||||
\(348\) | 0.916610 | 0.0491355 | ||||||||
\(349\) | 8.40627 | 0.449977 | 0.224989 | − | 0.974361i | \(-0.427765\pi\) | ||||
0.224989 | + | 0.974361i | \(0.427765\pi\) | |||||||
\(350\) | 1.28523 | 0.0686986 | ||||||||
\(351\) | 13.5360 | 0.722499 | ||||||||
\(352\) | 4.12445 | 0.219834 | ||||||||
\(353\) | −2.25429 | −0.119984 | −0.0599920 | − | 0.998199i | \(-0.519108\pi\) | ||||
−0.0599920 | + | 0.998199i | \(0.519108\pi\) | |||||||
\(354\) | −0.841247 | −0.0447118 | ||||||||
\(355\) | 15.5425 | 0.824908 | ||||||||
\(356\) | 5.58957 | 0.296247 | ||||||||
\(357\) | −5.69812 | −0.301576 | ||||||||
\(358\) | −5.79693 | −0.306377 | ||||||||
\(359\) | 31.0720 | 1.63992 | 0.819958 | − | 0.572424i | \(-0.193997\pi\) | ||||
0.819958 | + | 0.572424i | \(0.193997\pi\) | |||||||
\(360\) | 6.97636 | 0.367687 | ||||||||
\(361\) | −9.06822 | −0.477275 | ||||||||
\(362\) | 14.1651 | 0.744500 | ||||||||
\(363\) | 5.39858 | 0.283352 | ||||||||
\(364\) | 1.06942 | 0.0560527 | ||||||||
\(365\) | −9.76873 | −0.511319 | ||||||||
\(366\) | 6.39066 | 0.334045 | ||||||||
\(367\) | 3.23848 | 0.169047 | 0.0845237 | − | 0.996421i | \(-0.473063\pi\) | ||||
0.0845237 | + | 0.996421i | \(0.473063\pi\) | |||||||
\(368\) | 1.63030 | 0.0849852 | ||||||||
\(369\) | 17.6739 | 0.920064 | ||||||||
\(370\) | −7.19628 | −0.374117 | ||||||||
\(371\) | −5.76232 | −0.299165 | ||||||||
\(372\) | 1.07599 | 0.0557877 | ||||||||
\(373\) | 29.2902 | 1.51659 | 0.758294 | − | 0.651913i | \(-0.226033\pi\) | ||||
0.758294 | + | 0.651913i | \(0.226033\pi\) | |||||||
\(374\) | −18.7102 | −0.967483 | ||||||||
\(375\) | 0.829686 | 0.0428448 | ||||||||
\(376\) | −31.2328 | −1.61071 | ||||||||
\(377\) | 9.74592 | 0.501941 | ||||||||
\(378\) | 5.66400 | 0.291324 | ||||||||
\(379\) | 7.33776 | 0.376916 | 0.188458 | − | 0.982081i | \(-0.439651\pi\) | ||||
0.188458 | + | 0.982081i | \(0.439651\pi\) | |||||||
\(380\) | −1.09726 | −0.0562885 | ||||||||
\(381\) | −17.0295 | −0.872449 | ||||||||
\(382\) | 20.4764 | 1.04766 | ||||||||
\(383\) | 34.1527 | 1.74512 | 0.872560 | − | 0.488506i | \(-0.162458\pi\) | ||||
0.872560 | + | 0.488506i | \(0.162458\pi\) | |||||||
\(384\) | 6.22501 | 0.317669 | ||||||||
\(385\) | −2.11972 | −0.108031 | ||||||||
\(386\) | −16.3438 | −0.831879 | ||||||||
\(387\) | 13.3378 | 0.677997 | ||||||||
\(388\) | 0.264357 | 0.0134207 | ||||||||
\(389\) | −8.03852 | −0.407569 | −0.203785 | − | 0.979016i | \(-0.565324\pi\) | ||||
−0.203785 | + | 0.979016i | \(0.565324\pi\) | |||||||
\(390\) | −3.27526 | −0.165849 | ||||||||
\(391\) | 3.51825 | 0.177926 | ||||||||
\(392\) | 3.01795 | 0.152430 | ||||||||
\(393\) | −11.0395 | −0.556871 | ||||||||
\(394\) | 29.7298 | 1.49777 | ||||||||
\(395\) | 9.51566 | 0.478785 | ||||||||
\(396\) | −1.70606 | −0.0857326 | ||||||||
\(397\) | 15.9574 | 0.800879 | 0.400440 | − | 0.916323i | \(-0.368857\pi\) | ||||
0.400440 | + | 0.916323i | \(0.368857\pi\) | |||||||
\(398\) | 21.0135 | 1.05331 | ||||||||
\(399\) | −2.61473 | −0.130900 | ||||||||
\(400\) | −3.18242 | −0.159121 | ||||||||
\(401\) | −7.11257 | −0.355185 | −0.177592 | − | 0.984104i | \(-0.556831\pi\) | ||||
−0.177592 | + | 0.984104i | \(0.556831\pi\) | |||||||
\(402\) | −12.7701 | −0.636916 | ||||||||
\(403\) | 11.4406 | 0.569897 | ||||||||
\(404\) | 1.39759 | 0.0695328 | ||||||||
\(405\) | −3.27846 | −0.162908 | ||||||||
\(406\) | 4.07808 | 0.202391 | ||||||||
\(407\) | 11.8688 | 0.588313 | ||||||||
\(408\) | 17.1967 | 0.851361 | ||||||||
\(409\) | −25.6282 | −1.26723 | −0.633615 | − | 0.773648i | \(-0.718430\pi\) | ||||
−0.633615 | + | 0.773648i | \(0.718430\pi\) | |||||||
\(410\) | −9.82645 | −0.485294 | ||||||||
\(411\) | 9.92454 | 0.489542 | ||||||||
\(412\) | 5.92456 | 0.291882 | ||||||||
\(413\) | 0.788910 | 0.0388197 | ||||||||
\(414\) | −1.52198 | −0.0748010 | ||||||||
\(415\) | 2.71309 | 0.133181 | ||||||||
\(416\) | −5.97636 | −0.293015 | ||||||||
\(417\) | 2.30280 | 0.112769 | ||||||||
\(418\) | −8.58568 | −0.419939 | ||||||||
\(419\) | −14.6556 | −0.715975 | −0.357987 | − | 0.933726i | \(-0.616537\pi\) | ||||
−0.357987 | + | 0.933726i | \(0.616537\pi\) | |||||||
\(420\) | 0.288876 | 0.0140957 | ||||||||
\(421\) | 33.3142 | 1.62363 | 0.811816 | − | 0.583913i | \(-0.198479\pi\) | ||||
0.811816 | + | 0.583913i | \(0.198479\pi\) | |||||||
\(422\) | 1.45744 | 0.0709471 | ||||||||
\(423\) | 23.9230 | 1.16318 | ||||||||
\(424\) | 17.3904 | 0.844553 | ||||||||
\(425\) | −6.86780 | −0.333137 | ||||||||
\(426\) | −16.5736 | −0.802991 | ||||||||
\(427\) | −5.99308 | −0.290025 | ||||||||
\(428\) | −0.591961 | −0.0286135 | ||||||||
\(429\) | 5.40185 | 0.260804 | ||||||||
\(430\) | −7.41564 | −0.357614 | ||||||||
\(431\) | −0.525063 | −0.0252914 | −0.0126457 | − | 0.999920i | \(-0.504025\pi\) | ||||
−0.0126457 | + | 0.999920i | \(0.504025\pi\) | |||||||
\(432\) | −14.0249 | −0.674772 | ||||||||
\(433\) | −17.1908 | −0.826136 | −0.413068 | − | 0.910700i | \(-0.635543\pi\) | ||||
−0.413068 | + | 0.910700i | \(0.635543\pi\) | |||||||
\(434\) | 4.78719 | 0.229793 | ||||||||
\(435\) | 2.63261 | 0.126224 | ||||||||
\(436\) | −4.06456 | −0.194657 | ||||||||
\(437\) | 1.61444 | 0.0772292 | ||||||||
\(438\) | 10.4168 | 0.497734 | ||||||||
\(439\) | 37.5515 | 1.79224 | 0.896118 | − | 0.443816i | \(-0.146376\pi\) | ||||
0.896118 | + | 0.443816i | \(0.146376\pi\) | |||||||
\(440\) | 6.39723 | 0.304976 | ||||||||
\(441\) | −2.31162 | −0.110077 | ||||||||
\(442\) | 27.1112 | 1.28955 | ||||||||
\(443\) | 23.0067 | 1.09308 | 0.546541 | − | 0.837432i | \(-0.315944\pi\) | ||||
0.546541 | + | 0.837432i | \(0.315944\pi\) | |||||||
\(444\) | −1.61747 | −0.0767619 | ||||||||
\(445\) | 16.0539 | 0.761028 | ||||||||
\(446\) | −0.524238 | −0.0248234 | ||||||||
\(447\) | 9.33443 | 0.441504 | ||||||||
\(448\) | −8.86559 | −0.418860 | ||||||||
\(449\) | −9.83944 | −0.464352 | −0.232176 | − | 0.972674i | \(-0.574585\pi\) | ||||
−0.232176 | + | 0.972674i | \(0.574585\pi\) | |||||||
\(450\) | 2.97097 | 0.140053 | ||||||||
\(451\) | 16.2067 | 0.763143 | ||||||||
\(452\) | −1.60065 | −0.0752884 | ||||||||
\(453\) | −9.35751 | −0.439654 | ||||||||
\(454\) | −21.4844 | −1.00831 | ||||||||
\(455\) | 3.07149 | 0.143994 | ||||||||
\(456\) | 7.89114 | 0.369536 | ||||||||
\(457\) | 2.68226 | 0.125471 | 0.0627354 | − | 0.998030i | \(-0.480018\pi\) | ||||
0.0627354 | + | 0.998030i | \(0.480018\pi\) | |||||||
\(458\) | −1.28523 | −0.0600550 | ||||||||
\(459\) | −30.2662 | −1.41271 | ||||||||
\(460\) | −0.178364 | −0.00831625 | ||||||||
\(461\) | 5.15966 | 0.240309 | 0.120155 | − | 0.992755i | \(-0.461661\pi\) | ||||
0.120155 | + | 0.992755i | \(0.461661\pi\) | |||||||
\(462\) | 2.26035 | 0.105161 | ||||||||
\(463\) | 22.1578 | 1.02976 | 0.514879 | − | 0.857263i | \(-0.327837\pi\) | ||||
0.514879 | + | 0.857263i | \(0.327837\pi\) | |||||||
\(464\) | −10.0979 | −0.468783 | ||||||||
\(465\) | 3.09038 | 0.143313 | ||||||||
\(466\) | 32.2036 | 1.49180 | ||||||||
\(467\) | 12.0699 | 0.558530 | 0.279265 | − | 0.960214i | \(-0.409909\pi\) | ||||
0.279265 | + | 0.960214i | \(0.409909\pi\) | |||||||
\(468\) | 2.47209 | 0.114272 | ||||||||
\(469\) | 11.9757 | 0.552984 | ||||||||
\(470\) | −13.3009 | −0.613524 | ||||||||
\(471\) | 13.3667 | 0.615904 | ||||||||
\(472\) | −2.38089 | −0.109590 | ||||||||
\(473\) | 12.2305 | 0.562361 | ||||||||
\(474\) | −10.1469 | −0.466064 | ||||||||
\(475\) | −3.15147 | −0.144599 | ||||||||
\(476\) | −2.39120 | −0.109600 | ||||||||
\(477\) | −13.3203 | −0.609895 | ||||||||
\(478\) | 11.5968 | 0.530425 | ||||||||
\(479\) | 1.77670 | 0.0811794 | 0.0405897 | − | 0.999176i | \(-0.487076\pi\) | ||||
0.0405897 | + | 0.999176i | \(0.487076\pi\) | |||||||
\(480\) | −1.61436 | −0.0736851 | ||||||||
\(481\) | −17.1979 | −0.784157 | ||||||||
\(482\) | −3.72290 | −0.169573 | ||||||||
\(483\) | −0.425033 | −0.0193397 | ||||||||
\(484\) | 2.26549 | 0.102977 | ||||||||
\(485\) | 0.759265 | 0.0344765 | ||||||||
\(486\) | 20.4879 | 0.929352 | ||||||||
\(487\) | 14.6185 | 0.662427 | 0.331214 | − | 0.943556i | \(-0.392542\pi\) | ||||
0.331214 | + | 0.943556i | \(0.392542\pi\) | |||||||
\(488\) | 18.0868 | 0.818752 | ||||||||
\(489\) | 19.7606 | 0.893605 | ||||||||
\(490\) | 1.28523 | 0.0580609 | ||||||||
\(491\) | 4.77155 | 0.215337 | 0.107668 | − | 0.994187i | \(-0.465662\pi\) | ||||
0.107668 | + | 0.994187i | \(0.465662\pi\) | |||||||
\(492\) | −2.20865 | −0.0995735 | ||||||||
\(493\) | −21.7917 | −0.981448 | ||||||||
\(494\) | 12.4407 | 0.559734 | ||||||||
\(495\) | −4.90000 | −0.220239 | ||||||||
\(496\) | −11.8538 | −0.532250 | ||||||||
\(497\) | 15.5425 | 0.697175 | ||||||||
\(498\) | −2.89308 | −0.129642 | ||||||||
\(499\) | −0.0416221 | −0.00186326 | −0.000931630 | − | 1.00000i | \(-0.500297\pi\) | ||||
−0.000931630 | 1.00000i | \(0.500297\pi\) | ||||||||
\(500\) | 0.348175 | 0.0155709 | ||||||||
\(501\) | 0.105498 | 0.00471329 | ||||||||
\(502\) | 30.6727 | 1.36899 | ||||||||
\(503\) | 7.28459 | 0.324804 | 0.162402 | − | 0.986725i | \(-0.448076\pi\) | ||||
0.162402 | + | 0.986725i | \(0.448076\pi\) | |||||||
\(504\) | 6.97636 | 0.310752 | ||||||||
\(505\) | 4.01405 | 0.178623 | ||||||||
\(506\) | −1.39563 | −0.0620433 | ||||||||
\(507\) | 2.95860 | 0.131396 | ||||||||
\(508\) | −7.14639 | −0.317070 | ||||||||
\(509\) | −24.6010 | −1.09042 | −0.545211 | − | 0.838299i | \(-0.683550\pi\) | ||||
−0.545211 | + | 0.838299i | \(0.683550\pi\) | |||||||
\(510\) | 7.32341 | 0.324286 | ||||||||
\(511\) | −9.76873 | −0.432143 | ||||||||
\(512\) | 25.4010 | 1.12258 | ||||||||
\(513\) | −13.8885 | −0.613191 | ||||||||
\(514\) | 6.72988 | 0.296842 | ||||||||
\(515\) | 17.0160 | 0.749816 | ||||||||
\(516\) | −1.66678 | −0.0733758 | ||||||||
\(517\) | 21.9370 | 0.964790 | ||||||||
\(518\) | −7.19628 | −0.316186 | ||||||||
\(519\) | −3.89259 | −0.170866 | ||||||||
\(520\) | −9.26963 | −0.406500 | ||||||||
\(521\) | −20.4969 | −0.897987 | −0.448993 | − | 0.893535i | \(-0.648217\pi\) | ||||
−0.448993 | + | 0.893535i | \(0.648217\pi\) | |||||||
\(522\) | 9.42696 | 0.412607 | ||||||||
\(523\) | 16.0003 | 0.699643 | 0.349822 | − | 0.936816i | \(-0.386242\pi\) | ||||
0.349822 | + | 0.936816i | \(0.386242\pi\) | |||||||
\(524\) | −4.63271 | −0.202381 | ||||||||
\(525\) | 0.829686 | 0.0362105 | ||||||||
\(526\) | −3.44948 | −0.150404 | ||||||||
\(527\) | −25.5809 | −1.11432 | ||||||||
\(528\) | −5.59695 | −0.243576 | ||||||||
\(529\) | −22.7376 | −0.988590 | ||||||||
\(530\) | 7.40593 | 0.321693 | ||||||||
\(531\) | 1.82366 | 0.0791402 | ||||||||
\(532\) | −1.09726 | −0.0475724 | ||||||||
\(533\) | −23.4836 | −1.01719 | ||||||||
\(534\) | −17.1189 | −0.740809 | ||||||||
\(535\) | −1.70018 | −0.0735053 | ||||||||
\(536\) | −36.1420 | −1.56110 | ||||||||
\(537\) | −3.74223 | −0.161489 | ||||||||
\(538\) | −17.4392 | −0.751858 | ||||||||
\(539\) | −2.11972 | −0.0913030 | ||||||||
\(540\) | 1.53440 | 0.0660301 | ||||||||
\(541\) | 34.3532 | 1.47696 | 0.738481 | − | 0.674275i | \(-0.235544\pi\) | ||||
0.738481 | + | 0.674275i | \(0.235544\pi\) | |||||||
\(542\) | 15.4696 | 0.664475 | ||||||||
\(543\) | 9.14430 | 0.392420 | ||||||||
\(544\) | 13.3630 | 0.572935 | ||||||||
\(545\) | −11.6739 | −0.500055 | ||||||||
\(546\) | −3.27526 | −0.140168 | ||||||||
\(547\) | 2.07177 | 0.0885826 | 0.0442913 | − | 0.999019i | \(-0.485897\pi\) | ||||
0.0442913 | + | 0.999019i | \(0.485897\pi\) | |||||||
\(548\) | 4.16480 | 0.177912 | ||||||||
\(549\) | −13.8537 | −0.591263 | ||||||||
\(550\) | 2.72434 | 0.116166 | ||||||||
\(551\) | −9.99969 | −0.426001 | ||||||||
\(552\) | 1.28273 | 0.0545966 | ||||||||
\(553\) | 9.51566 | 0.404647 | ||||||||
\(554\) | −6.42965 | −0.273170 | ||||||||
\(555\) | −4.64558 | −0.197194 | ||||||||
\(556\) | 0.966364 | 0.0409829 | ||||||||
\(557\) | 44.3290 | 1.87828 | 0.939139 | − | 0.343537i | \(-0.111625\pi\) | ||||
0.939139 | + | 0.343537i | \(0.111625\pi\) | |||||||
\(558\) | 11.0662 | 0.468468 | ||||||||
\(559\) | −17.7221 | −0.749567 | ||||||||
\(560\) | −3.18242 | −0.134482 | ||||||||
\(561\) | −12.0784 | −0.509952 | ||||||||
\(562\) | 1.25798 | 0.0530648 | ||||||||
\(563\) | −0.434764 | −0.0183231 | −0.00916157 | − | 0.999958i | \(-0.502916\pi\) | ||||
−0.00916157 | + | 0.999958i | \(0.502916\pi\) | |||||||
\(564\) | −2.98958 | −0.125884 | ||||||||
\(565\) | −4.59727 | −0.193409 | ||||||||
\(566\) | 26.8250 | 1.12754 | ||||||||
\(567\) | −3.27846 | −0.137682 | ||||||||
\(568\) | −46.9064 | −1.96815 | ||||||||
\(569\) | −32.2191 | −1.35069 | −0.675347 | − | 0.737500i | \(-0.736006\pi\) | ||||
−0.675347 | + | 0.737500i | \(0.736006\pi\) | |||||||
\(570\) | 3.36054 | 0.140758 | ||||||||
\(571\) | −30.2732 | −1.26689 | −0.633446 | − | 0.773787i | \(-0.718360\pi\) | ||||
−0.633446 | + | 0.773787i | \(0.718360\pi\) | |||||||
\(572\) | 2.26687 | 0.0947826 | ||||||||
\(573\) | 13.2186 | 0.552215 | ||||||||
\(574\) | −9.82645 | −0.410148 | ||||||||
\(575\) | −0.512282 | −0.0213636 | ||||||||
\(576\) | −20.4939 | −0.853912 | ||||||||
\(577\) | −27.7311 | −1.15446 | −0.577231 | − | 0.816581i | \(-0.695867\pi\) | ||||
−0.577231 | + | 0.816581i | \(0.695867\pi\) | |||||||
\(578\) | −38.7713 | −1.61267 | ||||||||
\(579\) | −10.5508 | −0.438477 | ||||||||
\(580\) | 1.10477 | 0.0458730 | ||||||||
\(581\) | 2.71309 | 0.112558 | ||||||||
\(582\) | −0.809635 | −0.0335604 | ||||||||
\(583\) | −12.2145 | −0.505874 | ||||||||
\(584\) | 29.4816 | 1.21996 | ||||||||
\(585\) | 7.10013 | 0.293554 | ||||||||
\(586\) | −35.8524 | −1.48105 | ||||||||
\(587\) | 43.0865 | 1.77837 | 0.889184 | − | 0.457549i | \(-0.151273\pi\) | ||||
0.889184 | + | 0.457549i | \(0.151273\pi\) | |||||||
\(588\) | 0.288876 | 0.0119130 | ||||||||
\(589\) | −11.7385 | −0.483676 | ||||||||
\(590\) | −1.01393 | −0.0417430 | ||||||||
\(591\) | 19.1921 | 0.789459 | ||||||||
\(592\) | 17.8190 | 0.732358 | ||||||||
\(593\) | −12.9793 | −0.532997 | −0.266499 | − | 0.963835i | \(-0.585867\pi\) | ||||
−0.266499 | + | 0.963835i | \(0.585867\pi\) | |||||||
\(594\) | 12.0061 | 0.492617 | ||||||||
\(595\) | −6.86780 | −0.281552 | ||||||||
\(596\) | 3.91717 | 0.160453 | ||||||||
\(597\) | 13.5653 | 0.555192 | ||||||||
\(598\) | 2.02228 | 0.0826971 | ||||||||
\(599\) | −21.6877 | −0.886136 | −0.443068 | − | 0.896488i | \(-0.646110\pi\) | ||||
−0.443068 | + | 0.896488i | \(0.646110\pi\) | |||||||
\(600\) | −2.50395 | −0.102223 | ||||||||
\(601\) | 28.1572 | 1.14856 | 0.574278 | − | 0.818660i | \(-0.305283\pi\) | ||||
0.574278 | + | 0.818660i | \(0.305283\pi\) | |||||||
\(602\) | −7.41564 | −0.302239 | ||||||||
\(603\) | 27.6832 | 1.12735 | ||||||||
\(604\) | −3.92685 | −0.159781 | ||||||||
\(605\) | 6.50677 | 0.264538 | ||||||||
\(606\) | −4.28034 | −0.173877 | ||||||||
\(607\) | 39.8634 | 1.61801 | 0.809003 | − | 0.587804i | \(-0.200007\pi\) | ||||
0.809003 | + | 0.587804i | \(0.200007\pi\) | |||||||
\(608\) | 6.13197 | 0.248684 | ||||||||
\(609\) | 2.63261 | 0.106679 | ||||||||
\(610\) | 7.70250 | 0.311865 | ||||||||
\(611\) | −31.7869 | −1.28596 | ||||||||
\(612\) | −5.52754 | −0.223438 | ||||||||
\(613\) | 34.6287 | 1.39864 | 0.699319 | − | 0.714810i | \(-0.253487\pi\) | ||||
0.699319 | + | 0.714810i | \(0.253487\pi\) | |||||||
\(614\) | −31.8896 | −1.28696 | ||||||||
\(615\) | −6.34349 | −0.255794 | ||||||||
\(616\) | 6.39723 | 0.257752 | ||||||||
\(617\) | 10.7919 | 0.434465 | 0.217233 | − | 0.976120i | \(-0.430297\pi\) | ||||
0.217233 | + | 0.976120i | \(0.430297\pi\) | |||||||
\(618\) | −18.1449 | −0.729895 | ||||||||
\(619\) | −7.55894 | −0.303819 | −0.151910 | − | 0.988394i | \(-0.548542\pi\) | ||||
−0.151910 | + | 0.988394i | \(0.548542\pi\) | |||||||
\(620\) | 1.29687 | 0.0520836 | ||||||||
\(621\) | −2.25761 | −0.0905949 | ||||||||
\(622\) | 11.2917 | 0.452755 | ||||||||
\(623\) | 16.0539 | 0.643186 | ||||||||
\(624\) | 8.11001 | 0.324660 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.37957 | 0.374883 | ||||||||
\(627\) | −5.54251 | −0.221347 | ||||||||
\(628\) | 5.60929 | 0.223835 | ||||||||
\(629\) | 38.4542 | 1.53327 | ||||||||
\(630\) | 2.97097 | 0.118366 | ||||||||
\(631\) | −36.1018 | −1.43719 | −0.718595 | − | 0.695429i | \(-0.755214\pi\) | ||||
−0.718595 | + | 0.695429i | \(0.755214\pi\) | |||||||
\(632\) | −28.7178 | −1.14233 | ||||||||
\(633\) | 0.940855 | 0.0373956 | ||||||||
\(634\) | 15.5378 | 0.617084 | ||||||||
\(635\) | −20.5253 | −0.814521 | ||||||||
\(636\) | 1.66460 | 0.0660055 | ||||||||
\(637\) | 3.07149 | 0.121697 | ||||||||
\(638\) | 8.64440 | 0.342235 | ||||||||
\(639\) | 35.9283 | 1.42130 | ||||||||
\(640\) | 7.50285 | 0.296576 | ||||||||
\(641\) | −18.3572 | −0.725067 | −0.362534 | − | 0.931971i | \(-0.618088\pi\) | ||||
−0.362534 | + | 0.931971i | \(0.618088\pi\) | |||||||
\(642\) | 1.81297 | 0.0715523 | ||||||||
\(643\) | 15.1575 | 0.597753 | 0.298876 | − | 0.954292i | \(-0.403388\pi\) | ||||
0.298876 | + | 0.954292i | \(0.403388\pi\) | |||||||
\(644\) | −0.178364 | −0.00702852 | ||||||||
\(645\) | −4.78719 | −0.188495 | ||||||||
\(646\) | −27.8172 | −1.09445 | ||||||||
\(647\) | −16.4182 | −0.645467 | −0.322733 | − | 0.946490i | \(-0.604602\pi\) | ||||
−0.322733 | + | 0.946490i | \(0.604602\pi\) | |||||||
\(648\) | 9.89422 | 0.388682 | ||||||||
\(649\) | 1.67227 | 0.0656424 | ||||||||
\(650\) | −3.94759 | −0.154837 | ||||||||
\(651\) | 3.09038 | 0.121122 | ||||||||
\(652\) | 8.29247 | 0.324758 | ||||||||
\(653\) | 39.9952 | 1.56513 | 0.782567 | − | 0.622566i | \(-0.213910\pi\) | ||||
0.782567 | + | 0.622566i | \(0.213910\pi\) | |||||||
\(654\) | 12.4483 | 0.486769 | ||||||||
\(655\) | −13.3057 | −0.519896 | ||||||||
\(656\) | 24.3317 | 0.949994 | ||||||||
\(657\) | −22.5816 | −0.880993 | ||||||||
\(658\) | −13.3009 | −0.518523 | ||||||||
\(659\) | −46.2910 | −1.80324 | −0.901621 | − | 0.432527i | \(-0.857622\pi\) | ||||
−0.901621 | + | 0.432527i | \(0.857622\pi\) | |||||||
\(660\) | 0.612337 | 0.0238352 | ||||||||
\(661\) | 1.10700 | 0.0430572 | 0.0215286 | − | 0.999768i | \(-0.493147\pi\) | ||||
0.0215286 | + | 0.999768i | \(0.493147\pi\) | |||||||
\(662\) | 17.3946 | 0.676060 | ||||||||
\(663\) | 17.5017 | 0.679711 | ||||||||
\(664\) | −8.18799 | −0.317756 | ||||||||
\(665\) | −3.15147 | −0.122209 | ||||||||
\(666\) | −16.6351 | −0.644596 | ||||||||
\(667\) | −1.62548 | −0.0629389 | ||||||||
\(668\) | 0.0442718 | 0.00171293 | ||||||||
\(669\) | −0.338423 | −0.0130842 | ||||||||
\(670\) | −15.3915 | −0.594626 | ||||||||
\(671\) | −12.7037 | −0.490420 | ||||||||
\(672\) | −1.61436 | −0.0622753 | ||||||||
\(673\) | 20.3284 | 0.783601 | 0.391801 | − | 0.920050i | \(-0.371852\pi\) | ||||
0.391801 | + | 0.920050i | \(0.371852\pi\) | |||||||
\(674\) | 18.5559 | 0.714747 | ||||||||
\(675\) | 4.40698 | 0.169625 | ||||||||
\(676\) | 1.24156 | 0.0477525 | ||||||||
\(677\) | 39.2118 | 1.50703 | 0.753516 | − | 0.657429i | \(-0.228356\pi\) | ||||
0.753516 | + | 0.657429i | \(0.228356\pi\) | |||||||
\(678\) | 4.90225 | 0.188270 | ||||||||
\(679\) | 0.759265 | 0.0291379 | ||||||||
\(680\) | 20.7267 | 0.794833 | ||||||||
\(681\) | −13.8693 | −0.531473 | ||||||||
\(682\) | 10.1475 | 0.388569 | ||||||||
\(683\) | −4.94760 | −0.189315 | −0.0946573 | − | 0.995510i | \(-0.530176\pi\) | ||||
−0.0946573 | + | 0.995510i | \(0.530176\pi\) | |||||||
\(684\) | −2.53646 | −0.0969839 | ||||||||
\(685\) | 11.9618 | 0.457037 | ||||||||
\(686\) | 1.28523 | 0.0490704 | ||||||||
\(687\) | −0.829686 | −0.0316545 | ||||||||
\(688\) | 18.3622 | 0.700052 | ||||||||
\(689\) | 17.6989 | 0.674276 | ||||||||
\(690\) | 0.546267 | 0.0207960 | ||||||||
\(691\) | −1.07221 | −0.0407888 | −0.0203944 | − | 0.999792i | \(-0.506492\pi\) | ||||
−0.0203944 | + | 0.999792i | \(0.506492\pi\) | |||||||
\(692\) | −1.63351 | −0.0620968 | ||||||||
\(693\) | −4.90000 | −0.186136 | ||||||||
\(694\) | −13.6397 | −0.517757 | ||||||||
\(695\) | 2.77551 | 0.105281 | ||||||||
\(696\) | −7.94510 | −0.301158 | ||||||||
\(697\) | 52.5089 | 1.98891 | ||||||||
\(698\) | −10.8040 | −0.408938 | ||||||||
\(699\) | 20.7891 | 0.786317 | ||||||||
\(700\) | 0.348175 | 0.0131598 | ||||||||
\(701\) | 6.44084 | 0.243267 | 0.121634 | − | 0.992575i | \(-0.461187\pi\) | ||||
0.121634 | + | 0.992575i | \(0.461187\pi\) | |||||||
\(702\) | −17.3969 | −0.656605 | ||||||||
\(703\) | 17.6457 | 0.665521 | ||||||||
\(704\) | −18.7926 | −0.708273 | ||||||||
\(705\) | −8.58643 | −0.323383 | ||||||||
\(706\) | 2.89729 | 0.109041 | ||||||||
\(707\) | 4.01405 | 0.150964 | ||||||||
\(708\) | −0.227897 | −0.00856490 | ||||||||
\(709\) | 17.9478 | 0.674045 | 0.337023 | − | 0.941497i | \(-0.390580\pi\) | ||||
0.337023 | + | 0.941497i | \(0.390580\pi\) | |||||||
\(710\) | −19.9757 | −0.749675 | ||||||||
\(711\) | 21.9966 | 0.824937 | ||||||||
\(712\) | −48.4500 | −1.81574 | ||||||||
\(713\) | −1.90813 | −0.0714600 | ||||||||
\(714\) | 7.32341 | 0.274072 | ||||||||
\(715\) | 6.51072 | 0.243487 | ||||||||
\(716\) | −1.57041 | −0.0586891 | ||||||||
\(717\) | 7.48634 | 0.279582 | ||||||||
\(718\) | −39.9347 | −1.49035 | ||||||||
\(719\) | 20.0385 | 0.747311 | 0.373656 | − | 0.927568i | \(-0.378104\pi\) | ||||
0.373656 | + | 0.927568i | \(0.378104\pi\) | |||||||
\(720\) | −7.35656 | −0.274163 | ||||||||
\(721\) | 17.0160 | 0.633711 | ||||||||
\(722\) | 11.6548 | 0.433746 | ||||||||
\(723\) | −2.40333 | −0.0893807 | ||||||||
\(724\) | 3.83738 | 0.142615 | ||||||||
\(725\) | 3.17302 | 0.117843 | ||||||||
\(726\) | −6.93843 | −0.257509 | ||||||||
\(727\) | −11.3970 | −0.422692 | −0.211346 | − | 0.977411i | \(-0.567785\pi\) | ||||
−0.211346 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(728\) | −9.26963 | −0.343555 | ||||||||
\(729\) | 3.39068 | 0.125581 | ||||||||
\(730\) | 12.5551 | 0.464685 | ||||||||
\(731\) | 39.6264 | 1.46563 | ||||||||
\(732\) | 1.73126 | 0.0639891 | ||||||||
\(733\) | −26.2293 | −0.968800 | −0.484400 | − | 0.874847i | \(-0.660962\pi\) | ||||
−0.484400 | + | 0.874847i | \(0.660962\pi\) | |||||||
\(734\) | −4.16220 | −0.153630 | ||||||||
\(735\) | 0.829686 | 0.0306034 | ||||||||
\(736\) | 0.996772 | 0.0367415 | ||||||||
\(737\) | 25.3851 | 0.935072 | ||||||||
\(738\) | −22.7150 | −0.836152 | ||||||||
\(739\) | 11.3041 | 0.415829 | 0.207914 | − | 0.978147i | \(-0.433332\pi\) | ||||
0.207914 | + | 0.978147i | \(0.433332\pi\) | |||||||
\(740\) | −1.94950 | −0.0716651 | ||||||||
\(741\) | 8.03114 | 0.295031 | ||||||||
\(742\) | 7.40593 | 0.271880 | ||||||||
\(743\) | −17.7554 | −0.651381 | −0.325690 | − | 0.945476i | \(-0.605597\pi\) | ||||
−0.325690 | + | 0.945476i | \(0.605597\pi\) | |||||||
\(744\) | −9.32664 | −0.341931 | ||||||||
\(745\) | 11.2506 | 0.412189 | ||||||||
\(746\) | −37.6447 | −1.37827 | ||||||||
\(747\) | 6.27165 | 0.229468 | ||||||||
\(748\) | −5.06868 | −0.185329 | ||||||||
\(749\) | −1.70018 | −0.0621233 | ||||||||
\(750\) | −1.06634 | −0.0389372 | ||||||||
\(751\) | 49.1304 | 1.79279 | 0.896397 | − | 0.443251i | \(-0.146175\pi\) | ||||
0.896397 | + | 0.443251i | \(0.146175\pi\) | |||||||
\(752\) | 32.9349 | 1.20101 | ||||||||
\(753\) | 19.8009 | 0.721583 | ||||||||
\(754\) | −12.5258 | −0.456162 | ||||||||
\(755\) | −11.2784 | −0.410462 | ||||||||
\(756\) | 1.53440 | 0.0558056 | ||||||||
\(757\) | 32.2813 | 1.17328 | 0.586642 | − | 0.809846i | \(-0.300450\pi\) | ||||
0.586642 | + | 0.809846i | \(0.300450\pi\) | |||||||
\(758\) | −9.43074 | −0.342540 | ||||||||
\(759\) | −0.900953 | −0.0327025 | ||||||||
\(760\) | 9.51099 | 0.345000 | ||||||||
\(761\) | 3.15537 | 0.114382 | 0.0571910 | − | 0.998363i | \(-0.481786\pi\) | ||||
0.0571910 | + | 0.998363i | \(0.481786\pi\) | |||||||
\(762\) | 21.8869 | 0.792880 | ||||||||
\(763\) | −11.6739 | −0.422624 | ||||||||
\(764\) | 5.54715 | 0.200689 | ||||||||
\(765\) | −15.8758 | −0.573989 | ||||||||
\(766\) | −43.8942 | −1.58596 | ||||||||
\(767\) | −2.42313 | −0.0874943 | ||||||||
\(768\) | 6.71072 | 0.242152 | ||||||||
\(769\) | 14.3547 | 0.517644 | 0.258822 | − | 0.965925i | \(-0.416666\pi\) | ||||
0.258822 | + | 0.965925i | \(0.416666\pi\) | |||||||
\(770\) | 2.72434 | 0.0981784 | ||||||||
\(771\) | 4.34450 | 0.156463 | ||||||||
\(772\) | −4.42761 | −0.159353 | ||||||||
\(773\) | 9.99331 | 0.359435 | 0.179717 | − | 0.983718i | \(-0.442482\pi\) | ||||
0.179717 | + | 0.983718i | \(0.442482\pi\) | |||||||
\(774\) | −17.1421 | −0.616162 | ||||||||
\(775\) | 3.72476 | 0.133797 | ||||||||
\(776\) | −2.29143 | −0.0822574 | ||||||||
\(777\) | −4.64558 | −0.166659 | ||||||||
\(778\) | 10.3314 | 0.370398 | ||||||||
\(779\) | 24.0951 | 0.863296 | ||||||||
\(780\) | −0.887281 | −0.0317698 | ||||||||
\(781\) | 32.9457 | 1.17889 | ||||||||
\(782\) | −4.52177 | −0.161698 | ||||||||
\(783\) | 13.9834 | 0.499727 | ||||||||
\(784\) | −3.18242 | −0.113658 | ||||||||
\(785\) | 16.1105 | 0.575010 | ||||||||
\(786\) | 14.1884 | 0.506083 | ||||||||
\(787\) | −13.4187 | −0.478327 | −0.239163 | − | 0.970979i | \(-0.576873\pi\) | ||||
−0.239163 | + | 0.970979i | \(0.576873\pi\) | |||||||
\(788\) | 8.05392 | 0.286909 | ||||||||
\(789\) | −2.22682 | −0.0792769 | ||||||||
\(790\) | −12.2298 | −0.435118 | ||||||||
\(791\) | −4.59727 | −0.163460 | ||||||||
\(792\) | 14.7880 | 0.525468 | ||||||||
\(793\) | 18.4077 | 0.653677 | ||||||||
\(794\) | −20.5090 | −0.727837 | ||||||||
\(795\) | 4.78092 | 0.169562 | ||||||||
\(796\) | 5.69265 | 0.201771 | ||||||||
\(797\) | −3.57274 | −0.126553 | −0.0632765 | − | 0.997996i | \(-0.520155\pi\) | ||||
−0.0632765 | + | 0.997996i | \(0.520155\pi\) | |||||||
\(798\) | 3.36054 | 0.118962 | ||||||||
\(799\) | 71.0749 | 2.51445 | ||||||||
\(800\) | −1.94575 | −0.0687926 | ||||||||
\(801\) | 37.1106 | 1.31124 | ||||||||
\(802\) | 9.14131 | 0.322791 | ||||||||
\(803\) | −20.7070 | −0.730735 | ||||||||
\(804\) | −3.45948 | −0.122006 | ||||||||
\(805\) | −0.512282 | −0.0180556 | ||||||||
\(806\) | −14.7038 | −0.517920 | ||||||||
\(807\) | −11.2579 | −0.396298 | ||||||||
\(808\) | −12.1142 | −0.426176 | ||||||||
\(809\) | −27.7845 | −0.976851 | −0.488425 | − | 0.872606i | \(-0.662429\pi\) | ||||
−0.488425 | + | 0.872606i | \(0.662429\pi\) | |||||||
\(810\) | 4.21358 | 0.148050 | ||||||||
\(811\) | −0.586590 | −0.0205980 | −0.0102990 | − | 0.999947i | \(-0.503278\pi\) | ||||
−0.0102990 | + | 0.999947i | \(0.503278\pi\) | |||||||
\(812\) | 1.10477 | 0.0387697 | ||||||||
\(813\) | 9.98643 | 0.350239 | ||||||||
\(814\) | −15.2541 | −0.534657 | ||||||||
\(815\) | 23.8170 | 0.834272 | ||||||||
\(816\) | −18.1338 | −0.634811 | ||||||||
\(817\) | 18.1836 | 0.636164 | ||||||||
\(818\) | 32.9382 | 1.15166 | ||||||||
\(819\) | 7.10013 | 0.248099 | ||||||||
\(820\) | −2.66203 | −0.0929620 | ||||||||
\(821\) | 27.8267 | 0.971158 | 0.485579 | − | 0.874193i | \(-0.338609\pi\) | ||||
0.485579 | + | 0.874193i | \(0.338609\pi\) | |||||||
\(822\) | −12.7554 | −0.444894 | ||||||||
\(823\) | −49.6784 | −1.73168 | −0.865840 | − | 0.500321i | \(-0.833215\pi\) | ||||
−0.865840 | + | 0.500321i | \(0.833215\pi\) | |||||||
\(824\) | −51.3536 | −1.78899 | ||||||||
\(825\) | 1.75871 | 0.0612303 | ||||||||
\(826\) | −1.01393 | −0.0352793 | ||||||||
\(827\) | −11.1529 | −0.387823 | −0.193912 | − | 0.981019i | \(-0.562118\pi\) | ||||
−0.193912 | + | 0.981019i | \(0.562118\pi\) | |||||||
\(828\) | −0.412309 | −0.0143287 | ||||||||
\(829\) | 23.5046 | 0.816349 | 0.408174 | − | 0.912904i | \(-0.366166\pi\) | ||||
0.408174 | + | 0.912904i | \(0.366166\pi\) | |||||||
\(830\) | −3.48696 | −0.121034 | ||||||||
\(831\) | −4.15068 | −0.143985 | ||||||||
\(832\) | 27.2306 | 0.944051 | ||||||||
\(833\) | −6.86780 | −0.237955 | ||||||||
\(834\) | −2.95964 | −0.102484 | ||||||||
\(835\) | 0.127154 | 0.00440034 | ||||||||
\(836\) | −2.32590 | −0.0804428 | ||||||||
\(837\) | 16.4150 | 0.567384 | ||||||||
\(838\) | 18.8359 | 0.650676 | ||||||||
\(839\) | −9.87033 | −0.340761 | −0.170381 | − | 0.985378i | \(-0.554500\pi\) | ||||
−0.170381 | + | 0.985378i | \(0.554500\pi\) | |||||||
\(840\) | −2.50395 | −0.0863946 | ||||||||
\(841\) | −18.9319 | −0.652825 | ||||||||
\(842\) | −42.8165 | −1.47555 | ||||||||
\(843\) | 0.812094 | 0.0279700 | ||||||||
\(844\) | 0.394827 | 0.0135905 | ||||||||
\(845\) | 3.56592 | 0.122671 | ||||||||
\(846\) | −30.7466 | −1.05709 | ||||||||
\(847\) | 6.50677 | 0.223575 | ||||||||
\(848\) | −18.3381 | −0.629735 | ||||||||
\(849\) | 17.3170 | 0.594317 | ||||||||
\(850\) | 8.82673 | 0.302754 | ||||||||
\(851\) | 2.86837 | 0.0983264 | ||||||||
\(852\) | −4.48985 | −0.153820 | ||||||||
\(853\) | 5.39797 | 0.184823 | 0.0924115 | − | 0.995721i | \(-0.470542\pi\) | ||||
0.0924115 | + | 0.995721i | \(0.470542\pi\) | |||||||
\(854\) | 7.70250 | 0.263574 | ||||||||
\(855\) | −7.28501 | −0.249142 | ||||||||
\(856\) | 5.13107 | 0.175376 | ||||||||
\(857\) | −32.0359 | −1.09433 | −0.547163 | − | 0.837026i | \(-0.684292\pi\) | ||||
−0.547163 | + | 0.837026i | \(0.684292\pi\) | |||||||
\(858\) | −6.94264 | −0.237018 | ||||||||
\(859\) | 9.28563 | 0.316822 | 0.158411 | − | 0.987373i | \(-0.449363\pi\) | ||||
0.158411 | + | 0.987373i | \(0.449363\pi\) | |||||||
\(860\) | −2.00893 | −0.0685039 | ||||||||
\(861\) | −6.34349 | −0.216186 | ||||||||
\(862\) | 0.674829 | 0.0229848 | ||||||||
\(863\) | 19.6009 | 0.667222 | 0.333611 | − | 0.942711i | \(-0.391733\pi\) | ||||
0.333611 | + | 0.942711i | \(0.391733\pi\) | |||||||
\(864\) | −8.57487 | −0.291723 | ||||||||
\(865\) | −4.69164 | −0.159521 | ||||||||
\(866\) | 22.0941 | 0.750790 | ||||||||
\(867\) | −25.0289 | −0.850026 | ||||||||
\(868\) | 1.29687 | 0.0440186 | ||||||||
\(869\) | 20.1706 | 0.684240 | ||||||||
\(870\) | −3.38352 | −0.114712 | ||||||||
\(871\) | −36.7832 | −1.24635 | ||||||||
\(872\) | 35.2313 | 1.19308 | ||||||||
\(873\) | 1.75513 | 0.0594023 | ||||||||
\(874\) | −2.07493 | −0.0701857 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 2.82195 | 0.0953450 | ||||||||
\(877\) | 41.2933 | 1.39438 | 0.697188 | − | 0.716888i | \(-0.254434\pi\) | ||||
0.697188 | + | 0.716888i | \(0.254434\pi\) | |||||||
\(878\) | −48.2625 | −1.62878 | ||||||||
\(879\) | −23.1446 | −0.780649 | ||||||||
\(880\) | −6.74586 | −0.227403 | ||||||||
\(881\) | 31.7879 | 1.07096 | 0.535481 | − | 0.844547i | \(-0.320130\pi\) | ||||
0.535481 | + | 0.844547i | \(0.320130\pi\) | |||||||
\(882\) | 2.97097 | 0.100038 | ||||||||
\(883\) | 2.44560 | 0.0823009 | 0.0411504 | − | 0.999153i | \(-0.486898\pi\) | ||||
0.0411504 | + | 0.999153i | \(0.486898\pi\) | |||||||
\(884\) | 7.34455 | 0.247024 | ||||||||
\(885\) | −0.654548 | −0.0220024 | ||||||||
\(886\) | −29.5690 | −0.993390 | ||||||||
\(887\) | −7.18207 | −0.241150 | −0.120575 | − | 0.992704i | \(-0.538474\pi\) | ||||
−0.120575 | + | 0.992704i | \(0.538474\pi\) | |||||||
\(888\) | 14.0201 | 0.470485 | ||||||||
\(889\) | −20.5253 | −0.688396 | ||||||||
\(890\) | −20.6330 | −0.691621 | ||||||||
\(891\) | −6.94942 | −0.232814 | ||||||||
\(892\) | −0.142018 | −0.00475512 | ||||||||
\(893\) | 32.6146 | 1.09141 | ||||||||
\(894\) | −11.9969 | −0.401237 | ||||||||
\(895\) | −4.51041 | −0.150766 | ||||||||
\(896\) | 7.50285 | 0.250653 | ||||||||
\(897\) | 1.30549 | 0.0435889 | ||||||||
\(898\) | 12.6460 | 0.422002 | ||||||||
\(899\) | 11.8188 | 0.394178 | ||||||||
\(900\) | 0.804849 | 0.0268283 | ||||||||
\(901\) | −39.5745 | −1.31842 | ||||||||
\(902\) | −20.8294 | −0.693542 | ||||||||
\(903\) | −4.78719 | −0.159308 | ||||||||
\(904\) | 13.8743 | 0.461454 | ||||||||
\(905\) | 11.0214 | 0.366364 | ||||||||
\(906\) | 12.0266 | 0.399556 | ||||||||
\(907\) | −16.9745 | −0.563629 | −0.281814 | − | 0.959469i | \(-0.590936\pi\) | ||||
−0.281814 | + | 0.959469i | \(0.590936\pi\) | |||||||
\(908\) | −5.82022 | −0.193151 | ||||||||
\(909\) | 9.27896 | 0.307764 | ||||||||
\(910\) | −3.94759 | −0.130861 | ||||||||
\(911\) | −15.6286 | −0.517800 | −0.258900 | − | 0.965904i | \(-0.583360\pi\) | ||||
−0.258900 | + | 0.965904i | \(0.583360\pi\) | |||||||
\(912\) | −8.32119 | −0.275542 | ||||||||
\(913\) | 5.75101 | 0.190331 | ||||||||
\(914\) | −3.44733 | −0.114027 | ||||||||
\(915\) | 4.97237 | 0.164382 | ||||||||
\(916\) | −0.348175 | −0.0115040 | ||||||||
\(917\) | −13.3057 | −0.439393 | ||||||||
\(918\) | 38.8992 | 1.28386 | ||||||||
\(919\) | −42.8669 | −1.41405 | −0.707023 | − | 0.707190i | \(-0.749962\pi\) | ||||
−0.707023 | + | 0.707190i | \(0.749962\pi\) | |||||||
\(920\) | 1.54604 | 0.0509715 | ||||||||
\(921\) | −20.5864 | −0.678345 | ||||||||
\(922\) | −6.63136 | −0.218392 | ||||||||
\(923\) | −47.7386 | −1.57134 | ||||||||
\(924\) | 0.612337 | 0.0201444 | ||||||||
\(925\) | −5.59920 | −0.184101 | ||||||||
\(926\) | −28.4779 | −0.935842 | ||||||||
\(927\) | 39.3346 | 1.29192 | ||||||||
\(928\) | −6.17390 | −0.202668 | ||||||||
\(929\) | −4.58841 | −0.150541 | −0.0752704 | − | 0.997163i | \(-0.523982\pi\) | ||||
−0.0752704 | + | 0.997163i | \(0.523982\pi\) | |||||||
\(930\) | −3.97187 | −0.130243 | ||||||||
\(931\) | −3.15147 | −0.103285 | ||||||||
\(932\) | 8.72409 | 0.285767 | ||||||||
\(933\) | 7.28938 | 0.238644 | ||||||||
\(934\) | −15.5127 | −0.507590 | ||||||||
\(935\) | −14.5578 | −0.476092 | ||||||||
\(936\) | −21.4279 | −0.700392 | ||||||||
\(937\) | 36.5381 | 1.19365 | 0.596825 | − | 0.802372i | \(-0.296429\pi\) | ||||
0.596825 | + | 0.802372i | \(0.296429\pi\) | |||||||
\(938\) | −15.3915 | −0.502551 | ||||||||
\(939\) | 6.05501 | 0.197598 | ||||||||
\(940\) | −3.60327 | −0.117526 | ||||||||
\(941\) | −40.5683 | −1.32249 | −0.661244 | − | 0.750171i | \(-0.729971\pi\) | ||||
−0.661244 | + | 0.750171i | \(0.729971\pi\) | |||||||
\(942\) | −17.1793 | −0.559732 | ||||||||
\(943\) | 3.91673 | 0.127546 | ||||||||
\(944\) | 2.51065 | 0.0817146 | ||||||||
\(945\) | 4.40698 | 0.143359 | ||||||||
\(946\) | −15.7191 | −0.511072 | ||||||||
\(947\) | −21.5637 | −0.700725 | −0.350363 | − | 0.936614i | \(-0.613942\pi\) | ||||
−0.350363 | + | 0.936614i | \(0.613942\pi\) | |||||||
\(948\) | −2.74884 | −0.0892783 | ||||||||
\(949\) | 30.0046 | 0.973991 | ||||||||
\(950\) | 4.05038 | 0.131412 | ||||||||
\(951\) | 10.0305 | 0.325260 | ||||||||
\(952\) | 20.7267 | 0.671756 | ||||||||
\(953\) | 27.6494 | 0.895653 | 0.447826 | − | 0.894121i | \(-0.352198\pi\) | ||||
0.447826 | + | 0.894121i | \(0.352198\pi\) | |||||||
\(954\) | 17.1197 | 0.554271 | ||||||||
\(955\) | 15.9321 | 0.515549 | ||||||||
\(956\) | 3.14162 | 0.101607 | ||||||||
\(957\) | 5.58041 | 0.180389 | ||||||||
\(958\) | −2.28347 | −0.0737756 | ||||||||
\(959\) | 11.9618 | 0.386267 | ||||||||
\(960\) | 7.35566 | 0.237403 | ||||||||
\(961\) | −17.1261 | −0.552456 | ||||||||
\(962\) | 22.1033 | 0.712640 | ||||||||
\(963\) | −3.93018 | −0.126648 | ||||||||
\(964\) | −1.00855 | −0.0324832 | ||||||||
\(965\) | −12.7166 | −0.409363 | ||||||||
\(966\) | 0.546267 | 0.0175758 | ||||||||
\(967\) | 31.2170 | 1.00387 | 0.501936 | − | 0.864905i | \(-0.332621\pi\) | ||||
0.501936 | + | 0.864905i | \(0.332621\pi\) | |||||||
\(968\) | −19.6371 | −0.631161 | ||||||||
\(969\) | −17.9575 | −0.576877 | ||||||||
\(970\) | −0.975833 | −0.0313321 | ||||||||
\(971\) | 44.8773 | 1.44018 | 0.720090 | − | 0.693881i | \(-0.244100\pi\) | ||||
0.720090 | + | 0.693881i | \(0.244100\pi\) | |||||||
\(972\) | 5.55027 | 0.178025 | ||||||||
\(973\) | 2.77551 | 0.0889788 | ||||||||
\(974\) | −18.7882 | −0.602012 | ||||||||
\(975\) | −2.54838 | −0.0816134 | ||||||||
\(976\) | −19.0725 | −0.610496 | ||||||||
\(977\) | 49.4673 | 1.58260 | 0.791299 | − | 0.611429i | \(-0.209405\pi\) | ||||
0.791299 | + | 0.611429i | \(0.209405\pi\) | |||||||
\(978\) | −25.3970 | −0.812106 | ||||||||
\(979\) | 34.0299 | 1.08760 | ||||||||
\(980\) | 0.348175 | 0.0111220 | ||||||||
\(981\) | −26.9856 | −0.861585 | ||||||||
\(982\) | −6.13255 | −0.195698 | ||||||||
\(983\) | 15.3198 | 0.488626 | 0.244313 | − | 0.969696i | \(-0.421438\pi\) | ||||
0.244313 | + | 0.969696i | \(0.421438\pi\) | |||||||
\(984\) | 19.1444 | 0.610300 | ||||||||
\(985\) | 23.1318 | 0.737041 | ||||||||
\(986\) | 28.0074 | 0.891938 | ||||||||
\(987\) | −8.58643 | −0.273309 | ||||||||
\(988\) | 3.37024 | 0.107222 | ||||||||
\(989\) | 2.95580 | 0.0939891 | ||||||||
\(990\) | 6.29764 | 0.200152 | ||||||||
\(991\) | −20.4127 | −0.648431 | −0.324215 | − | 0.945983i | \(-0.605100\pi\) | ||||
−0.324215 | + | 0.945983i | \(0.605100\pi\) | |||||||
\(992\) | −7.24745 | −0.230107 | ||||||||
\(993\) | 11.2291 | 0.356346 | ||||||||
\(994\) | −19.9757 | −0.633591 | ||||||||
\(995\) | 16.3500 | 0.518329 | ||||||||
\(996\) | −0.783748 | −0.0248340 | ||||||||
\(997\) | −33.0932 | −1.04807 | −0.524036 | − | 0.851696i | \(-0.675574\pi\) | ||||
−0.524036 | + | 0.851696i | \(0.675574\pi\) | |||||||
\(998\) | 0.0534941 | 0.00169333 | ||||||||
\(999\) | −24.6755 | −0.780700 |
(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 | 8015.2.a.l.1.19 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.19 | ✓ | 62 | 1.1 | even | 1 | trivial |