Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 5 x^{13} - 9 x^{12} + 76 x^{11} - 12 x^{10} - 414 x^{9} + 331 x^{8} + 959 x^{7} - 1067 x^{6} - 875 x^{5} + 1134 x^{4} + 301 x^{3} - 418 x^{2} - 42 x + 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(1.86702\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.86702 | 1.32018 | 0.660092 | − | 0.751185i | \(-0.270517\pi\) | ||||
0.660092 | + | 0.751185i | \(0.270517\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.48577 | 0.742885 | ||||||||
\(5\) | 4.06976 | 1.82005 | 0.910026 | − | 0.414550i | \(-0.136061\pi\) | ||||
0.910026 | + | 0.414550i | \(0.136061\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −0.960078 | −0.339439 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.59833 | 2.40280 | ||||||||
\(11\) | −0.0552813 | −0.0166679 | −0.00833397 | − | 0.999965i | \(-0.502653\pi\) | ||||
−0.00833397 | + | 0.999965i | \(0.502653\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.30564 | −1.47152 | −0.735760 | − | 0.677243i | \(-0.763175\pi\) | ||||
−0.735760 | + | 0.677243i | \(0.763175\pi\) | |||||||
\(14\) | −1.86702 | −0.498983 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.76403 | −1.19101 | ||||||||
\(17\) | 1.80614 | 0.438054 | 0.219027 | − | 0.975719i | \(-0.429712\pi\) | ||||
0.219027 | + | 0.975719i | \(0.429712\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.67845 | 1.76156 | 0.880779 | − | 0.473528i | \(-0.157020\pi\) | ||||
0.880779 | + | 0.473528i | \(0.157020\pi\) | |||||||
\(20\) | 6.04673 | 1.35209 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.103211 | −0.0220047 | ||||||||
\(23\) | 8.46285 | 1.76463 | 0.882313 | − | 0.470662i | \(-0.155985\pi\) | ||||
0.882313 | + | 0.470662i | \(0.155985\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.5630 | 2.31259 | ||||||||
\(26\) | −9.90574 | −1.94268 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.48577 | −0.280784 | ||||||||
\(29\) | 2.19120 | 0.406897 | 0.203448 | − | 0.979086i | \(-0.434785\pi\) | ||||
0.203448 | + | 0.979086i | \(0.434785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.83287 | 1.40683 | 0.703413 | − | 0.710782i | \(-0.251659\pi\) | ||||
0.703413 | + | 0.710782i | \(0.251659\pi\) | |||||||
\(32\) | −6.97439 | −1.23291 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.37211 | 0.578312 | ||||||||
\(35\) | −4.06976 | −0.687915 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.03734 | 0.334936 | 0.167468 | − | 0.985877i | \(-0.446441\pi\) | ||||
0.167468 | + | 0.985877i | \(0.446441\pi\) | |||||||
\(38\) | 14.3358 | 2.32558 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.90729 | −0.617796 | ||||||||
\(41\) | −2.50415 | −0.391082 | −0.195541 | − | 0.980695i | \(-0.562646\pi\) | ||||
−0.195541 | + | 0.980695i | \(0.562646\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.74934 | −1.48676 | −0.743380 | − | 0.668869i | \(-0.766779\pi\) | ||||
−0.743380 | + | 0.668869i | \(0.766779\pi\) | |||||||
\(44\) | −0.0821353 | −0.0123824 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15.8003 | 2.32963 | ||||||||
\(47\) | −5.74714 | −0.838307 | −0.419153 | − | 0.907915i | \(-0.637673\pi\) | ||||
−0.419153 | + | 0.907915i | \(0.637673\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 21.5883 | 3.05305 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.88296 | −1.09317 | ||||||||
\(53\) | −3.80018 | −0.521995 | −0.260998 | − | 0.965339i | \(-0.584051\pi\) | ||||
−0.260998 | + | 0.965339i | \(0.584051\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.224982 | −0.0303365 | ||||||||
\(56\) | 0.960078 | 0.128296 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.09103 | 0.537178 | ||||||||
\(59\) | −7.25461 | −0.944470 | −0.472235 | − | 0.881473i | \(-0.656553\pi\) | ||||
−0.472235 | + | 0.881473i | \(0.656553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.8375 | 1.64367 | 0.821834 | − | 0.569726i | \(-0.192951\pi\) | ||||
0.821834 | + | 0.569726i | \(0.192951\pi\) | |||||||
\(62\) | 14.6241 | 1.85727 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.49328 | −0.436660 | ||||||||
\(65\) | −21.5927 | −2.67824 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.02309 | 0.124991 | 0.0624954 | − | 0.998045i | \(-0.480094\pi\) | ||||
0.0624954 | + | 0.998045i | \(0.480094\pi\) | |||||||
\(68\) | 2.68352 | 0.325424 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.59833 | −0.908175 | ||||||||
\(71\) | 4.59524 | 0.545354 | 0.272677 | − | 0.962106i | \(-0.412091\pi\) | ||||
0.272677 | + | 0.962106i | \(0.412091\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.190964 | −0.0223506 | −0.0111753 | − | 0.999938i | \(-0.503557\pi\) | ||||
−0.0111753 | + | 0.999938i | \(0.503557\pi\) | |||||||
\(74\) | 3.80375 | 0.442177 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.4084 | 1.30864 | ||||||||
\(77\) | 0.0552813 | 0.00629989 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.89583 | 1.00086 | 0.500429 | − | 0.865777i | \(-0.333176\pi\) | ||||
0.500429 | + | 0.865777i | \(0.333176\pi\) | |||||||
\(80\) | −19.3885 | −2.16770 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.67530 | −0.516301 | ||||||||
\(83\) | −4.28568 | −0.470415 | −0.235207 | − | 0.971945i | \(-0.575577\pi\) | ||||
−0.235207 | + | 0.971945i | \(0.575577\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.35058 | 0.797282 | ||||||||
\(86\) | −18.2022 | −1.96280 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.0530743 | 0.00565774 | ||||||||
\(89\) | −8.76663 | −0.929261 | −0.464631 | − | 0.885505i | \(-0.653813\pi\) | ||||
−0.464631 | + | 0.885505i | \(0.653813\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.30564 | 0.556182 | ||||||||
\(92\) | 12.5739 | 1.31092 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.7300 | −1.10672 | ||||||||
\(95\) | 31.2495 | 3.20613 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2594 | 1.24475 | 0.622375 | − | 0.782719i | \(-0.286168\pi\) | ||||
0.622375 | + | 0.782719i | \(0.286168\pi\) | |||||||
\(98\) | 1.86702 | 0.188598 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 17.1799 | 1.71799 | ||||||||
\(101\) | 14.8833 | 1.48095 | 0.740473 | − | 0.672086i | \(-0.234601\pi\) | ||||
0.740473 | + | 0.672086i | \(0.234601\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.81265 | −0.966869 | −0.483434 | − | 0.875381i | \(-0.660611\pi\) | ||||
−0.483434 | + | 0.875381i | \(0.660611\pi\) | |||||||
\(104\) | 5.09382 | 0.499491 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.09502 | −0.689130 | ||||||||
\(107\) | 2.99814 | 0.289841 | 0.144921 | − | 0.989443i | \(-0.453707\pi\) | ||||
0.144921 | + | 0.989443i | \(0.453707\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9832 | 1.43513 | 0.717567 | − | 0.696489i | \(-0.245256\pi\) | ||||
0.717567 | + | 0.696489i | \(0.245256\pi\) | |||||||
\(110\) | −0.420046 | −0.0400498 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.76403 | 0.450158 | ||||||||
\(113\) | 9.11161 | 0.857149 | 0.428574 | − | 0.903507i | \(-0.359016\pi\) | ||||
0.428574 | + | 0.903507i | \(0.359016\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 34.4418 | 3.21171 | ||||||||
\(116\) | 3.25563 | 0.302277 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.5445 | −1.24687 | ||||||||
\(119\) | −1.80614 | −0.165569 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9969 | −0.999722 | ||||||||
\(122\) | 23.9678 | 2.16995 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.6379 | 1.04511 | ||||||||
\(125\) | 26.7097 | 2.38899 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 7.42675 | 0.656438 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −40.3140 | −3.53577 | ||||||||
\(131\) | 9.44110 | 0.824873 | 0.412436 | − | 0.910986i | \(-0.364678\pi\) | ||||
0.412436 | + | 0.910986i | \(0.364678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.67845 | −0.665806 | ||||||||
\(134\) | 1.91014 | 0.165011 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.73404 | −0.148693 | ||||||||
\(137\) | −12.2081 | −1.04301 | −0.521506 | − | 0.853248i | \(-0.674630\pi\) | ||||
−0.521506 | + | 0.853248i | \(0.674630\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.66264 | −0.734755 | −0.367378 | − | 0.930072i | \(-0.619744\pi\) | ||||
−0.367378 | + | 0.930072i | \(0.619744\pi\) | |||||||
\(140\) | −6.04673 | −0.511042 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.57941 | 0.719968 | ||||||||
\(143\) | 0.293303 | 0.0245272 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.91768 | 0.740573 | ||||||||
\(146\) | −0.356534 | −0.0295069 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.02702 | 0.248819 | ||||||||
\(149\) | 11.0129 | 0.902215 | 0.451108 | − | 0.892470i | \(-0.351029\pi\) | ||||
0.451108 | + | 0.892470i | \(0.351029\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.8494 | −1.69670 | −0.848348 | − | 0.529439i | \(-0.822403\pi\) | ||||
−0.848348 | + | 0.529439i | \(0.822403\pi\) | |||||||
\(152\) | −7.37191 | −0.597941 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.103211 | 0.00831701 | ||||||||
\(155\) | 31.8779 | 2.56050 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.2607 | 1.05832 | 0.529160 | − | 0.848522i | \(-0.322507\pi\) | ||||
0.529160 | + | 0.848522i | \(0.322507\pi\) | |||||||
\(158\) | 16.6087 | 1.32132 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −28.3841 | −2.24396 | ||||||||
\(161\) | −8.46285 | −0.666966 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.2204 | 0.957173 | 0.478587 | − | 0.878040i | \(-0.341149\pi\) | ||||
0.478587 | + | 0.878040i | \(0.341149\pi\) | |||||||
\(164\) | −3.72059 | −0.290529 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.00147 | −0.621034 | ||||||||
\(167\) | −9.53262 | −0.737656 | −0.368828 | − | 0.929498i | \(-0.620241\pi\) | ||||
−0.368828 | + | 0.929498i | \(0.620241\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.1498 | 1.16537 | ||||||||
\(170\) | 13.7237 | 1.05256 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.4853 | −1.10449 | ||||||||
\(173\) | −15.7093 | −1.19436 | −0.597179 | − | 0.802108i | \(-0.703712\pi\) | ||||
−0.597179 | + | 0.802108i | \(0.703712\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.5630 | −0.874078 | ||||||||
\(176\) | 0.263362 | 0.0198516 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.3675 | −1.22680 | ||||||||
\(179\) | 14.1899 | 1.06060 | 0.530302 | − | 0.847809i | \(-0.322078\pi\) | ||||
0.530302 | + | 0.847809i | \(0.322078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.68771 | −0.274105 | −0.137053 | − | 0.990564i | \(-0.543763\pi\) | ||||
−0.137053 | + | 0.990564i | \(0.543763\pi\) | |||||||
\(182\) | 9.90574 | 0.734263 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.12500 | −0.598983 | ||||||||
\(185\) | 8.29148 | 0.609602 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0998461 | −0.00730147 | ||||||||
\(188\) | −8.53894 | −0.622766 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 58.3434 | 4.23268 | ||||||||
\(191\) | 5.60888 | 0.405845 | 0.202922 | − | 0.979195i | \(-0.434956\pi\) | ||||
0.202922 | + | 0.979195i | \(0.434956\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.02831 | 0.577890 | 0.288945 | − | 0.957346i | \(-0.406695\pi\) | ||||
0.288945 | + | 0.957346i | \(0.406695\pi\) | |||||||
\(194\) | 22.8885 | 1.64330 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.48577 | 0.106126 | ||||||||
\(197\) | 25.1278 | 1.79028 | 0.895140 | − | 0.445785i | \(-0.147075\pi\) | ||||
0.895140 | + | 0.445785i | \(0.147075\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.16230 | 0.365946 | 0.182973 | − | 0.983118i | \(-0.441428\pi\) | ||||
0.182973 | + | 0.983118i | \(0.441428\pi\) | |||||||
\(200\) | −11.1013 | −0.784983 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 27.7875 | 1.95512 | ||||||||
\(203\) | −2.19120 | −0.153792 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.1913 | −0.711791 | ||||||||
\(206\) | −18.3204 | −1.27644 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 25.2762 | 1.75259 | ||||||||
\(209\) | −0.424475 | −0.0293615 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.6293 | 0.731750 | 0.365875 | − | 0.930664i | \(-0.380770\pi\) | ||||
0.365875 | + | 0.930664i | \(0.380770\pi\) | |||||||
\(212\) | −5.64620 | −0.387783 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.59760 | 0.382644 | ||||||||
\(215\) | −39.6775 | −2.70598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.83287 | −0.531730 | ||||||||
\(218\) | 27.9740 | 1.89464 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.334271 | −0.0225366 | ||||||||
\(221\) | −9.58275 | −0.644606 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.250705 | −0.0167884 | −0.00839421 | − | 0.999965i | \(-0.502672\pi\) | ||||
−0.00839421 | + | 0.999965i | \(0.502672\pi\) | |||||||
\(224\) | 6.97439 | 0.465996 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.0116 | 1.13159 | ||||||||
\(227\) | 20.9788 | 1.39241 | 0.696205 | − | 0.717843i | \(-0.254870\pi\) | ||||
0.696205 | + | 0.717843i | \(0.254870\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.3191 | −1.93746 | −0.968729 | − | 0.248122i | \(-0.920187\pi\) | ||||
−0.968729 | + | 0.248122i | \(0.920187\pi\) | |||||||
\(230\) | 64.3036 | 4.24005 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.10373 | −0.138116 | ||||||||
\(233\) | −0.354551 | −0.0232274 | −0.0116137 | − | 0.999933i | \(-0.503697\pi\) | ||||
−0.0116137 | + | 0.999933i | \(0.503697\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.3895 | −1.52576 | ||||||||
\(236\) | −10.7787 | −0.701633 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.37211 | −0.218582 | ||||||||
\(239\) | 15.3007 | 0.989717 | 0.494859 | − | 0.868974i | \(-0.335220\pi\) | ||||
0.494859 | + | 0.868974i | \(0.335220\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.37634 | 0.153073 | 0.0765367 | − | 0.997067i | \(-0.475614\pi\) | ||||
0.0765367 | + | 0.997067i | \(0.475614\pi\) | |||||||
\(242\) | −20.5315 | −1.31982 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 19.0735 | 1.22106 | ||||||||
\(245\) | 4.06976 | 0.260008 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −40.7391 | −2.59217 | ||||||||
\(248\) | −7.52017 | −0.477531 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 49.8676 | 3.15390 | ||||||||
\(251\) | 11.8899 | 0.750485 | 0.375243 | − | 0.926927i | \(-0.377559\pi\) | ||||
0.375243 | + | 0.926927i | \(0.377559\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.467838 | −0.0294127 | ||||||||
\(254\) | −1.86702 | −0.117147 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.8525 | 1.30328 | ||||||||
\(257\) | −15.7227 | −0.980757 | −0.490378 | − | 0.871510i | \(-0.663141\pi\) | ||||
−0.490378 | + | 0.871510i | \(0.663141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.03734 | −0.126594 | ||||||||
\(260\) | −32.0818 | −1.98963 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.6267 | 1.08898 | ||||||||
\(263\) | −19.8326 | −1.22293 | −0.611467 | − | 0.791270i | \(-0.709420\pi\) | ||||
−0.611467 | + | 0.791270i | \(0.709420\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.4658 | −0.950059 | ||||||||
\(266\) | −14.3358 | −0.878987 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.52008 | 0.0928538 | ||||||||
\(269\) | −1.39070 | −0.0847926 | −0.0423963 | − | 0.999101i | \(-0.513499\pi\) | ||||
−0.0423963 | + | 0.999101i | \(0.513499\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.6311 | 1.43549 | 0.717743 | − | 0.696308i | \(-0.245175\pi\) | ||||
0.717743 | + | 0.696308i | \(0.245175\pi\) | |||||||
\(272\) | −8.60452 | −0.521726 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.7929 | −1.37697 | ||||||||
\(275\) | −0.639216 | −0.0385462 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.4732 | −1.41037 | −0.705185 | − | 0.709023i | \(-0.749136\pi\) | ||||
−0.705185 | + | 0.709023i | \(0.749136\pi\) | |||||||
\(278\) | −16.1733 | −0.970012 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.90729 | 0.233505 | ||||||||
\(281\) | 19.5302 | 1.16507 | 0.582536 | − | 0.812805i | \(-0.302061\pi\) | ||||
0.582536 | + | 0.812805i | \(0.302061\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.65763 | −0.276867 | −0.138434 | − | 0.990372i | \(-0.544207\pi\) | ||||
−0.138434 | + | 0.990372i | \(0.544207\pi\) | |||||||
\(284\) | 6.82747 | 0.405136 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.547603 | 0.0323804 | ||||||||
\(287\) | 2.50415 | 0.147815 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.7378 | −0.808108 | ||||||||
\(290\) | 16.6495 | 0.977693 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.283728 | −0.0166040 | ||||||||
\(293\) | −11.0040 | −0.642863 | −0.321432 | − | 0.946933i | \(-0.604164\pi\) | ||||
−0.321432 | + | 0.946933i | \(0.604164\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.5245 | −1.71898 | ||||||||
\(296\) | −1.95600 | −0.113690 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.5614 | 1.19109 | ||||||||
\(299\) | −44.9008 | −2.59668 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.74934 | 0.561942 | ||||||||
\(302\) | −38.9262 | −2.23995 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −36.5804 | −2.09803 | ||||||||
\(305\) | 52.2454 | 2.99156 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.9605 | −0.682622 | −0.341311 | − | 0.939950i | \(-0.610871\pi\) | ||||
−0.341311 | + | 0.939950i | \(0.610871\pi\) | |||||||
\(308\) | 0.0821353 | 0.00468010 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 59.5168 | 3.38033 | ||||||||
\(311\) | −3.41715 | −0.193769 | −0.0968843 | − | 0.995296i | \(-0.530888\pi\) | ||||
−0.0968843 | + | 0.995296i | \(0.530888\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.8014 | −1.28881 | −0.644405 | − | 0.764685i | \(-0.722895\pi\) | ||||
−0.644405 | + | 0.764685i | \(0.722895\pi\) | |||||||
\(314\) | 24.7580 | 1.39718 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.2172 | 0.743523 | ||||||||
\(317\) | −30.8873 | −1.73480 | −0.867401 | − | 0.497610i | \(-0.834211\pi\) | ||||
−0.867401 | + | 0.497610i | \(0.834211\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.121133 | −0.00678213 | ||||||||
\(320\) | −14.2168 | −0.794744 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.8003 | −0.880518 | ||||||||
\(323\) | 13.8684 | 0.771658 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −61.3489 | −3.40302 | ||||||||
\(326\) | 22.8157 | 1.26364 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.40418 | 0.132748 | ||||||||
\(329\) | 5.74714 | 0.316850 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.37607 | 0.460391 | 0.230195 | − | 0.973144i | \(-0.426064\pi\) | ||||
0.230195 | + | 0.973144i | \(0.426064\pi\) | |||||||
\(332\) | −6.36754 | −0.349464 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.7976 | −0.973842 | ||||||||
\(335\) | 4.16375 | 0.227490 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.8021 | −1.35105 | −0.675527 | − | 0.737335i | \(-0.736084\pi\) | ||||
−0.675527 | + | 0.737335i | \(0.736084\pi\) | |||||||
\(338\) | 28.2850 | 1.53850 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.9213 | 0.592289 | ||||||||
\(341\) | −0.433012 | −0.0234489 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 9.36012 | 0.504664 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −29.3296 | −1.57677 | ||||||||
\(347\) | 0.992249 | 0.0532667 | 0.0266333 | − | 0.999645i | \(-0.491521\pi\) | ||||
0.0266333 | + | 0.999645i | \(0.491521\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.1236 | −1.45189 | −0.725947 | − | 0.687751i | \(-0.758598\pi\) | ||||
−0.725947 | + | 0.687751i | \(0.758598\pi\) | |||||||
\(350\) | −21.5883 | −1.15394 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.385553 | 0.0205501 | ||||||||
\(353\) | −18.5948 | −0.989700 | −0.494850 | − | 0.868979i | \(-0.664777\pi\) | ||||
−0.494850 | + | 0.868979i | \(0.664777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.7015 | 0.992574 | ||||||||
\(356\) | −13.0252 | −0.690334 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 26.4929 | 1.40019 | ||||||||
\(359\) | −5.21516 | −0.275246 | −0.137623 | − | 0.990485i | \(-0.543946\pi\) | ||||
−0.137623 | + | 0.990485i | \(0.543946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.9586 | 2.10309 | ||||||||
\(362\) | −6.88504 | −0.361870 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.88296 | 0.413179 | ||||||||
\(365\) | −0.777177 | −0.0406793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.94418 | 0.205885 | 0.102942 | − | 0.994687i | \(-0.467174\pi\) | ||||
0.102942 | + | 0.994687i | \(0.467174\pi\) | |||||||
\(368\) | −40.3173 | −2.10168 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 15.4804 | 0.804786 | ||||||||
\(371\) | 3.80018 | 0.197296 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.5188 | −0.699978 | −0.349989 | − | 0.936754i | \(-0.613815\pi\) | ||||
−0.349989 | + | 0.936754i | \(0.613815\pi\) | |||||||
\(374\) | −0.186415 | −0.00963928 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.51770 | 0.284554 | ||||||||
\(377\) | −11.6257 | −0.598756 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.4645 | −0.845727 | −0.422863 | − | 0.906193i | \(-0.638975\pi\) | ||||
−0.422863 | + | 0.906193i | \(0.638975\pi\) | |||||||
\(380\) | 46.4295 | 2.38179 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.4719 | 0.535789 | ||||||||
\(383\) | 2.34362 | 0.119754 | 0.0598768 | − | 0.998206i | \(-0.480929\pi\) | ||||
0.0598768 | + | 0.998206i | \(0.480929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.224982 | 0.0114661 | ||||||||
\(386\) | 14.9890 | 0.762922 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.2146 | 0.924707 | ||||||||
\(389\) | −24.2313 | −1.22858 | −0.614289 | − | 0.789081i | \(-0.710557\pi\) | ||||
−0.614289 | + | 0.789081i | \(0.710557\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.2851 | 0.773003 | ||||||||
\(392\) | −0.960078 | −0.0484912 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 46.9141 | 2.36350 | ||||||||
\(395\) | 36.2039 | 1.82162 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.9611 | −1.35314 | −0.676570 | − | 0.736378i | \(-0.736534\pi\) | ||||
−0.676570 | + | 0.736378i | \(0.736534\pi\) | |||||||
\(398\) | 9.63813 | 0.483116 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −55.0863 | −2.75431 | ||||||||
\(401\) | −4.82431 | −0.240915 | −0.120457 | − | 0.992718i | \(-0.538436\pi\) | ||||
−0.120457 | + | 0.992718i | \(0.538436\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.5584 | −2.07017 | ||||||||
\(404\) | 22.1132 | 1.10017 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.09103 | −0.203034 | ||||||||
\(407\) | −0.112627 | −0.00558270 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.0183 | 1.03929 | 0.519645 | − | 0.854382i | \(-0.326064\pi\) | ||||
0.519645 | + | 0.854382i | \(0.326064\pi\) | |||||||
\(410\) | −19.0274 | −0.939694 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.5793 | −0.718273 | ||||||||
\(413\) | 7.25461 | 0.356976 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.4417 | −0.856180 | ||||||||
\(416\) | 37.0036 | 1.81425 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.792504 | −0.0387626 | ||||||||
\(419\) | −16.2607 | −0.794386 | −0.397193 | − | 0.917735i | \(-0.630016\pi\) | ||||
−0.397193 | + | 0.917735i | \(0.630016\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5008 | −0.511779 | −0.255889 | − | 0.966706i | \(-0.582368\pi\) | ||||
−0.255889 | + | 0.966706i | \(0.582368\pi\) | |||||||
\(422\) | 19.8451 | 0.966045 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.64847 | 0.177185 | ||||||||
\(425\) | 20.8844 | 1.01304 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.8375 | −0.621248 | ||||||||
\(428\) | 4.45455 | 0.215319 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −74.0787 | −3.57239 | ||||||||
\(431\) | −25.0340 | −1.20585 | −0.602923 | − | 0.797799i | \(-0.705997\pi\) | ||||
−0.602923 | + | 0.797799i | \(0.705997\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.3517 | 1.07415 | 0.537077 | − | 0.843533i | \(-0.319529\pi\) | ||||
0.537077 | + | 0.843533i | \(0.319529\pi\) | |||||||
\(434\) | −14.6241 | −0.701981 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.2617 | 1.06614 | ||||||||
\(437\) | 64.9816 | 3.10849 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.586878 | −0.0280102 | −0.0140051 | − | 0.999902i | \(-0.504458\pi\) | ||||
−0.0140051 | + | 0.999902i | \(0.504458\pi\) | |||||||
\(440\) | 0.216000 | 0.0102974 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.8912 | −0.850998 | ||||||||
\(443\) | 33.8683 | 1.60913 | 0.804565 | − | 0.593865i | \(-0.202399\pi\) | ||||
0.804565 | + | 0.593865i | \(0.202399\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −35.6781 | −1.69130 | ||||||||
\(446\) | −0.468071 | −0.0221638 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.49328 | 0.165042 | ||||||||
\(449\) | −28.6096 | −1.35017 | −0.675085 | − | 0.737740i | \(-0.735893\pi\) | ||||
−0.675085 | + | 0.737740i | \(0.735893\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.138433 | 0.00651854 | ||||||||
\(452\) | 13.5378 | 0.636763 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 39.1678 | 1.83824 | ||||||||
\(455\) | 21.5927 | 1.01228 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.0367 | −1.03084 | −0.515418 | − | 0.856939i | \(-0.672363\pi\) | ||||
−0.515418 | + | 0.856939i | \(0.672363\pi\) | |||||||
\(458\) | −54.7393 | −2.55780 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 51.1726 | 2.38594 | ||||||||
\(461\) | 9.68071 | 0.450876 | 0.225438 | − | 0.974258i | \(-0.427619\pi\) | ||||
0.225438 | + | 0.974258i | \(0.427619\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.8056 | −1.94287 | −0.971436 | − | 0.237301i | \(-0.923737\pi\) | ||||
−0.971436 | + | 0.237301i | \(0.923737\pi\) | |||||||
\(464\) | −10.4390 | −0.484617 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.661955 | −0.0306645 | ||||||||
\(467\) | 25.8390 | 1.19569 | 0.597843 | − | 0.801613i | \(-0.296025\pi\) | ||||
0.597843 | + | 0.801613i | \(0.296025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.02309 | −0.0472421 | ||||||||
\(470\) | −43.6687 | −2.01429 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.96499 | 0.320590 | ||||||||
\(473\) | 0.538956 | 0.0247812 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 88.7856 | 4.07376 | ||||||||
\(476\) | −2.68352 | −0.122999 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 28.5667 | 1.30661 | ||||||||
\(479\) | 35.4921 | 1.62167 | 0.810837 | − | 0.585272i | \(-0.199012\pi\) | ||||
0.810837 | + | 0.585272i | \(0.199012\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.8094 | −0.492865 | ||||||||
\(482\) | 4.43667 | 0.202085 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.3389 | −0.742679 | ||||||||
\(485\) | 49.8927 | 2.26551 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.33739 | 0.0606030 | 0.0303015 | − | 0.999541i | \(-0.490353\pi\) | ||||
0.0303015 | + | 0.999541i | \(0.490353\pi\) | |||||||
\(488\) | −12.3250 | −0.557925 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.59833 | 0.343258 | ||||||||
\(491\) | −23.5590 | −1.06320 | −0.531602 | − | 0.846994i | \(-0.678410\pi\) | ||||
−0.531602 | + | 0.846994i | \(0.678410\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.95763 | 0.178243 | ||||||||
\(494\) | −76.0608 | −3.42214 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −37.3160 | −1.67554 | ||||||||
\(497\) | −4.59524 | −0.206125 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.1256 | −1.25907 | −0.629537 | − | 0.776971i | \(-0.716755\pi\) | ||||
−0.629537 | + | 0.776971i | \(0.716755\pi\) | |||||||
\(500\) | 39.6845 | 1.77474 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.1987 | 0.990778 | ||||||||
\(503\) | −42.3200 | −1.88696 | −0.943478 | − | 0.331436i | \(-0.892467\pi\) | ||||
−0.943478 | + | 0.331436i | \(0.892467\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 60.5716 | 2.69540 | ||||||||
\(506\) | −0.873463 | −0.0388302 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.48577 | −0.0659204 | ||||||||
\(509\) | −6.94247 | −0.307720 | −0.153860 | − | 0.988093i | \(-0.549170\pi\) | ||||
−0.153860 | + | 0.988093i | \(0.549170\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.190964 | 0.00844774 | ||||||||
\(512\) | 24.0785 | 1.06413 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −29.3547 | −1.29478 | ||||||||
\(515\) | −39.9351 | −1.75975 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.317710 | 0.0139729 | ||||||||
\(518\) | −3.80375 | −0.167127 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 20.7307 | 0.909099 | ||||||||
\(521\) | −5.25810 | −0.230361 | −0.115181 | − | 0.993345i | \(-0.536745\pi\) | ||||
−0.115181 | + | 0.993345i | \(0.536745\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.3487 | 1.06469 | 0.532346 | − | 0.846527i | \(-0.321310\pi\) | ||||
0.532346 | + | 0.846527i | \(0.321310\pi\) | |||||||
\(524\) | 14.0273 | 0.612786 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −37.0280 | −1.61450 | ||||||||
\(527\) | 14.1473 | 0.616266 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.6199 | 2.11391 | ||||||||
\(530\) | −28.8751 | −1.25425 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.4084 | −0.494618 | ||||||||
\(533\) | 13.2861 | 0.575485 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.2017 | 0.527527 | ||||||||
\(536\) | −0.982249 | −0.0424267 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.59647 | −0.111942 | ||||||||
\(539\) | −0.0552813 | −0.00238113 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.0769 | −1.33610 | −0.668049 | − | 0.744117i | \(-0.732871\pi\) | ||||
−0.668049 | + | 0.744117i | \(0.732871\pi\) | |||||||
\(542\) | 44.1197 | 1.89511 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.5968 | −0.540081 | ||||||||
\(545\) | 60.9782 | 2.61202 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.8650 | 1.40520 | 0.702602 | − | 0.711583i | \(-0.252021\pi\) | ||||
0.702602 | + | 0.711583i | \(0.252021\pi\) | |||||||
\(548\) | −18.1385 | −0.774838 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.19343 | −0.0508880 | ||||||||
\(551\) | 16.8251 | 0.716772 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.89583 | −0.378289 | ||||||||
\(554\) | −43.8251 | −1.86195 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.8707 | −0.545839 | ||||||||
\(557\) | 29.1692 | 1.23594 | 0.617970 | − | 0.786202i | \(-0.287955\pi\) | ||||
0.617970 | + | 0.786202i | \(0.287955\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.7265 | 2.18780 | ||||||||
\(560\) | 19.3885 | 0.819312 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 36.4632 | 1.53811 | ||||||||
\(563\) | −12.0125 | −0.506266 | −0.253133 | − | 0.967431i | \(-0.581461\pi\) | ||||
−0.253133 | + | 0.967431i | \(0.581461\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.0821 | 1.56006 | ||||||||
\(566\) | −8.69590 | −0.365516 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.41179 | −0.185114 | ||||||||
\(569\) | 5.47747 | 0.229628 | 0.114814 | − | 0.993387i | \(-0.463373\pi\) | ||||
0.114814 | + | 0.993387i | \(0.463373\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0828 | 0.631195 | 0.315597 | − | 0.948893i | \(-0.397795\pi\) | ||||
0.315597 | + | 0.948893i | \(0.397795\pi\) | |||||||
\(572\) | 0.435780 | 0.0182209 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.67530 | 0.195143 | ||||||||
\(575\) | 97.8556 | 4.08086 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.1085 | 1.54485 | 0.772424 | − | 0.635107i | \(-0.219044\pi\) | ||||
0.772424 | + | 0.635107i | \(0.219044\pi\) | |||||||
\(578\) | −25.6488 | −1.06685 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.2496 | 0.550161 | ||||||||
\(581\) | 4.28568 | 0.177800 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.210079 | 0.00870059 | ||||||||
\(584\) | 0.183340 | 0.00758667 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.5448 | −0.848697 | ||||||||
\(587\) | −0.589414 | −0.0243277 | −0.0121639 | − | 0.999926i | \(-0.503872\pi\) | ||||
−0.0121639 | + | 0.999926i | \(0.503872\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 60.1443 | 2.47820 | ||||||||
\(590\) | −55.1229 | −2.26938 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.70593 | −0.398911 | ||||||||
\(593\) | −29.6443 | −1.21735 | −0.608673 | − | 0.793421i | \(-0.708298\pi\) | ||||
−0.608673 | + | 0.793421i | \(0.708298\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.35058 | −0.301344 | ||||||||
\(596\) | 16.3627 | 0.670243 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −83.8309 | −3.42810 | ||||||||
\(599\) | −34.5199 | −1.41044 | −0.705222 | − | 0.708987i | \(-0.749153\pi\) | ||||
−0.705222 | + | 0.708987i | \(0.749153\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.3294 | 1.35953 | 0.679767 | − | 0.733428i | \(-0.262081\pi\) | ||||
0.679767 | + | 0.733428i | \(0.262081\pi\) | |||||||
\(602\) | 18.2022 | 0.741867 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −30.9774 | −1.26045 | ||||||||
\(605\) | −44.7549 | −1.81955 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.90428 | 0.199059 | 0.0995294 | − | 0.995035i | \(-0.468266\pi\) | ||||
0.0995294 | + | 0.995035i | \(0.468266\pi\) | |||||||
\(608\) | −53.5525 | −2.17184 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 97.5433 | 3.94941 | ||||||||
\(611\) | 30.4923 | 1.23359 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.5427 | −1.39517 | −0.697584 | − | 0.716503i | \(-0.745741\pi\) | ||||
−0.697584 | + | 0.716503i | \(0.745741\pi\) | |||||||
\(614\) | −22.3305 | −0.901187 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0530743 | −0.00213843 | ||||||||
\(617\) | −35.8258 | −1.44229 | −0.721147 | − | 0.692782i | \(-0.756385\pi\) | ||||
−0.721147 | + | 0.692782i | \(0.756385\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.37973 | 0.0956495 | 0.0478248 | − | 0.998856i | \(-0.484771\pi\) | ||||
0.0478248 | + | 0.998856i | \(0.484771\pi\) | |||||||
\(620\) | 47.3633 | 1.90216 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.37989 | −0.255810 | ||||||||
\(623\) | 8.76663 | 0.351228 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 50.8872 | 2.03549 | ||||||||
\(626\) | −42.5706 | −1.70147 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.7024 | 0.786210 | ||||||||
\(629\) | 3.67973 | 0.146720 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.370334 | 0.0147428 | 0.00737138 | − | 0.999973i | \(-0.497654\pi\) | ||||
0.00737138 | + | 0.999973i | \(0.497654\pi\) | |||||||
\(632\) | −8.54068 | −0.339730 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −57.6672 | −2.29026 | ||||||||
\(635\) | −4.06976 | −0.161504 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.30564 | −0.210217 | ||||||||
\(638\) | −0.226157 | −0.00895366 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 30.2251 | 1.19475 | ||||||||
\(641\) | 6.08684 | 0.240416 | 0.120208 | − | 0.992749i | \(-0.461644\pi\) | ||||
0.120208 | + | 0.992749i | \(0.461644\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.2301 | −0.403434 | −0.201717 | − | 0.979444i | \(-0.564652\pi\) | ||||
−0.201717 | + | 0.979444i | \(0.564652\pi\) | |||||||
\(644\) | −12.5739 | −0.495479 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.8926 | 1.01873 | ||||||||
\(647\) | 8.43033 | 0.331431 | 0.165715 | − | 0.986174i | \(-0.447007\pi\) | ||||
0.165715 | + | 0.986174i | \(0.447007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.401044 | 0.0157424 | ||||||||
\(650\) | −114.540 | −4.49262 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.1567 | 0.711070 | ||||||||
\(653\) | −28.7265 | −1.12415 | −0.562077 | − | 0.827085i | \(-0.689998\pi\) | ||||
−0.562077 | + | 0.827085i | \(0.689998\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.4230 | 1.50131 | ||||||||
\(656\) | 11.9298 | 0.465782 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.7300 | 0.418301 | ||||||||
\(659\) | 16.3064 | 0.635208 | 0.317604 | − | 0.948223i | \(-0.397122\pi\) | ||||
0.317604 | + | 0.948223i | \(0.397122\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.9195 | −1.78606 | −0.893030 | − | 0.449997i | \(-0.851425\pi\) | ||||
−0.893030 | + | 0.449997i | \(0.851425\pi\) | |||||||
\(662\) | 15.6383 | 0.607800 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.11459 | 0.159677 | ||||||||
\(665\) | −31.2495 | −1.21180 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.5438 | 0.718021 | ||||||||
\(668\) | −14.1633 | −0.547994 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.77380 | 0.300328 | ||||||||
\(671\) | −0.709672 | −0.0273966 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.4208 | 1.28828 | 0.644138 | − | 0.764909i | \(-0.277216\pi\) | ||||
0.644138 | + | 0.764909i | \(0.277216\pi\) | |||||||
\(674\) | −46.3060 | −1.78364 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.5091 | 0.865736 | ||||||||
\(677\) | 18.6310 | 0.716049 | 0.358024 | − | 0.933712i | \(-0.383450\pi\) | ||||
0.358024 | + | 0.933712i | \(0.383450\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.2594 | −0.470471 | ||||||||
\(680\) | −7.05713 | −0.270628 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.808442 | −0.0309568 | ||||||||
\(683\) | −46.4334 | −1.77672 | −0.888362 | − | 0.459144i | \(-0.848156\pi\) | ||||
−0.888362 | + | 0.459144i | \(0.848156\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −49.6842 | −1.89834 | ||||||||
\(686\) | −1.86702 | −0.0712832 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 46.4461 | 1.77074 | ||||||||
\(689\) | 20.1624 | 0.768126 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1069 | 0.460569 | 0.230284 | − | 0.973123i | \(-0.426034\pi\) | ||||
0.230284 | + | 0.973123i | \(0.426034\pi\) | |||||||
\(692\) | −23.3404 | −0.887271 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.85255 | 0.0703218 | ||||||||
\(695\) | −35.2549 | −1.33729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.52286 | −0.171315 | ||||||||
\(698\) | −50.6404 | −1.91677 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −17.1799 | −0.649339 | ||||||||
\(701\) | 21.1179 | 0.797610 | 0.398805 | − | 0.917036i | \(-0.369425\pi\) | ||||
0.398805 | + | 0.917036i | \(0.369425\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.6436 | 0.590010 | ||||||||
\(704\) | 0.193113 | 0.00727822 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34.7168 | −1.30659 | ||||||||
\(707\) | −14.8833 | −0.559745 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.36394 | −0.126335 | −0.0631676 | − | 0.998003i | \(-0.520120\pi\) | ||||
−0.0631676 | + | 0.998003i | \(0.520120\pi\) | |||||||
\(710\) | 34.9162 | 1.31038 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.41665 | 0.315427 | ||||||||
\(713\) | 66.2885 | 2.48252 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.19367 | 0.0446408 | ||||||||
\(716\) | 21.0830 | 0.787908 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.73682 | −0.363375 | ||||||||
\(719\) | −19.7953 | −0.738239 | −0.369120 | − | 0.929382i | \(-0.620341\pi\) | ||||
−0.369120 | + | 0.929382i | \(0.620341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.81265 | 0.365442 | ||||||||
\(722\) | 74.6036 | 2.77646 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.47909 | −0.203629 | ||||||||
\(725\) | 25.3368 | 0.940986 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.79554 | −0.363297 | −0.181648 | − | 0.983364i | \(-0.558143\pi\) | ||||
−0.181648 | + | 0.983364i | \(0.558143\pi\) | |||||||
\(728\) | −5.09382 | −0.188790 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.45101 | −0.0537042 | ||||||||
\(731\) | −17.6087 | −0.651282 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.06258 | −0.186991 | −0.0934953 | − | 0.995620i | \(-0.529804\pi\) | ||||
−0.0934953 | + | 0.995620i | \(0.529804\pi\) | |||||||
\(734\) | 7.36387 | 0.271805 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −59.0232 | −2.17562 | ||||||||
\(737\) | −0.0565579 | −0.00208334 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.5209 | 1.15952 | 0.579758 | − | 0.814789i | \(-0.303147\pi\) | ||||
0.579758 | + | 0.814789i | \(0.303147\pi\) | |||||||
\(740\) | 12.3192 | 0.452864 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.09502 | 0.260467 | ||||||||
\(743\) | −27.1607 | −0.996430 | −0.498215 | − | 0.867053i | \(-0.666011\pi\) | ||||
−0.498215 | + | 0.867053i | \(0.666011\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.8201 | 1.64208 | ||||||||
\(746\) | −25.2399 | −0.924100 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.148348 | −0.00542415 | ||||||||
\(749\) | −2.99814 | −0.109550 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.8959 | −0.798992 | −0.399496 | − | 0.916735i | \(-0.630815\pi\) | ||||
−0.399496 | + | 0.916735i | \(0.630815\pi\) | |||||||
\(752\) | 27.3795 | 0.998429 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −21.7055 | −0.790468 | ||||||||
\(755\) | −84.8519 | −3.08808 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.6416 | −1.65887 | −0.829437 | − | 0.558600i | \(-0.811339\pi\) | ||||
−0.829437 | + | 0.558600i | \(0.811339\pi\) | |||||||
\(758\) | −30.7397 | −1.11651 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −30.0019 | −1.08828 | ||||||||
\(761\) | 7.09246 | 0.257101 | 0.128551 | − | 0.991703i | \(-0.458967\pi\) | ||||
0.128551 | + | 0.991703i | \(0.458967\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.9832 | −0.542430 | ||||||||
\(764\) | 8.33351 | 0.301496 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.37560 | 0.158097 | ||||||||
\(767\) | 38.4903 | 1.38981 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.6365 | −0.780232 | −0.390116 | − | 0.920766i | \(-0.627565\pi\) | ||||
−0.390116 | + | 0.920766i | \(0.627565\pi\) | |||||||
\(770\) | 0.420046 | 0.0151374 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.9282 | 0.429306 | ||||||||
\(773\) | 23.7001 | 0.852434 | 0.426217 | − | 0.904621i | \(-0.359846\pi\) | ||||
0.426217 | + | 0.904621i | \(0.359846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 90.5712 | 3.25341 | ||||||||
\(776\) | −11.7699 | −0.422516 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −45.2404 | −1.62195 | ||||||||
\(779\) | −19.2280 | −0.688914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.254031 | −0.00908994 | ||||||||
\(782\) | 28.5377 | 1.02051 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.76403 | −0.170144 | ||||||||
\(785\) | 53.9679 | 1.92620 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.9099 | 0.994880 | 0.497440 | − | 0.867498i | \(-0.334274\pi\) | ||||
0.497440 | + | 0.867498i | \(0.334274\pi\) | |||||||
\(788\) | 37.3341 | 1.32997 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 67.5935 | 2.40487 | ||||||||
\(791\) | −9.11161 | −0.323972 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −68.1109 | −2.41869 | ||||||||
\(794\) | −50.3370 | −1.78639 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.66999 | 0.271856 | ||||||||
\(797\) | −10.7267 | −0.379959 | −0.189979 | − | 0.981788i | \(-0.560842\pi\) | ||||
−0.189979 | + | 0.981788i | \(0.560842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.3802 | −0.367224 | ||||||||
\(800\) | −80.6446 | −2.85122 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.00710 | −0.318052 | ||||||||
\(803\) | 0.0105567 | 0.000372539 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34.4418 | −1.21391 | ||||||||
\(806\) | −77.5904 | −2.73301 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14.2892 | −0.502691 | ||||||||
\(809\) | 3.45583 | 0.121500 | 0.0607502 | − | 0.998153i | \(-0.480651\pi\) | ||||
0.0607502 | + | 0.998153i | \(0.480651\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.65266 | −0.268721 | −0.134361 | − | 0.990932i | \(-0.542898\pi\) | ||||
−0.134361 | + | 0.990932i | \(0.542898\pi\) | |||||||
\(812\) | −3.25563 | −0.114250 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.210277 | −0.00737019 | ||||||||
\(815\) | 49.7340 | 1.74211 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −74.8598 | −2.61901 | ||||||||
\(818\) | 39.2417 | 1.37205 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.1419 | −0.528779 | ||||||||
\(821\) | −40.9623 | −1.42959 | −0.714797 | − | 0.699332i | \(-0.753481\pi\) | ||||
−0.714797 | + | 0.699332i | \(0.753481\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.5752 | −0.786923 | −0.393462 | − | 0.919341i | \(-0.628723\pi\) | ||||
−0.393462 | + | 0.919341i | \(0.628723\pi\) | |||||||
\(824\) | 9.42090 | 0.328193 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.5445 | 0.471274 | ||||||||
\(827\) | −21.4059 | −0.744356 | −0.372178 | − | 0.928161i | \(-0.621389\pi\) | ||||
−0.372178 | + | 0.928161i | \(0.621389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −49.8305 | −1.73069 | −0.865343 | − | 0.501180i | \(-0.832899\pi\) | ||||
−0.865343 | + | 0.501180i | \(0.832899\pi\) | |||||||
\(830\) | −32.5641 | −1.13032 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 18.5341 | 0.642554 | ||||||||
\(833\) | 1.80614 | 0.0625792 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38.7955 | −1.34257 | ||||||||
\(836\) | −0.630672 | −0.0218123 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −30.3590 | −1.04874 | ||||||||
\(839\) | 27.9367 | 0.964481 | 0.482241 | − | 0.876039i | \(-0.339823\pi\) | ||||
0.482241 | + | 0.876039i | \(0.339823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.1986 | −0.834435 | ||||||||
\(842\) | −19.6053 | −0.675642 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.7927 | 0.543607 | ||||||||
\(845\) | 61.6561 | 2.12103 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9969 | 0.377859 | ||||||||
\(848\) | 18.1042 | 0.621700 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 38.9916 | 1.33740 | ||||||||
\(851\) | 17.2417 | 0.591038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.3478 | −0.696696 | −0.348348 | − | 0.937365i | \(-0.613257\pi\) | ||||
−0.348348 | + | 0.937365i | \(0.613257\pi\) | |||||||
\(854\) | −23.9678 | −0.820162 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.87845 | −0.0983834 | ||||||||
\(857\) | −4.57410 | −0.156248 | −0.0781241 | − | 0.996944i | \(-0.524893\pi\) | ||||
−0.0781241 | + | 0.996944i | \(0.524893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.7050 | −0.569968 | −0.284984 | − | 0.958532i | \(-0.591988\pi\) | ||||
−0.284984 | + | 0.958532i | \(0.591988\pi\) | |||||||
\(860\) | −58.9516 | −2.01023 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −46.7390 | −1.59194 | ||||||||
\(863\) | 49.1110 | 1.67176 | 0.835879 | − | 0.548913i | \(-0.184958\pi\) | ||||
0.835879 | + | 0.548913i | \(0.184958\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −63.9332 | −2.17379 | ||||||||
\(866\) | 41.7311 | 1.41808 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.6379 | −0.395014 | ||||||||
\(869\) | −0.491773 | −0.0166823 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.42816 | −0.183926 | ||||||||
\(872\) | −14.3851 | −0.487140 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 121.322 | 4.10378 | ||||||||
\(875\) | −26.7097 | −0.902952 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.8961 | 0.604309 | 0.302155 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302155 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(878\) | −1.09571 | −0.0369786 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.07182 | 0.0361310 | ||||||||
\(881\) | 35.6129 | 1.19983 | 0.599915 | − | 0.800064i | \(-0.295201\pi\) | ||||
0.599915 | + | 0.800064i | \(0.295201\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.4740 | 1.63128 | 0.815641 | − | 0.578559i | \(-0.196385\pi\) | ||||
0.815641 | + | 0.578559i | \(0.196385\pi\) | |||||||
\(884\) | −14.2378 | −0.478868 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 63.2328 | 2.12435 | ||||||||
\(887\) | 39.7389 | 1.33430 | 0.667151 | − | 0.744922i | \(-0.267513\pi\) | ||||
0.667151 | + | 0.744922i | \(0.267513\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −66.6118 | −2.23283 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.372489 | −0.0124719 | ||||||||
\(893\) | −44.1292 | −1.47673 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 57.7496 | 1.93036 | ||||||||
\(896\) | −7.42675 | −0.248110 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −53.4147 | −1.78247 | ||||||||
\(899\) | 17.1634 | 0.572432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.86368 | −0.228662 | ||||||||
\(902\) | 0.258457 | 0.00860567 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.74786 | −0.290949 | ||||||||
\(905\) | −15.0081 | −0.498886 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.3855 | −0.975731 | −0.487865 | − | 0.872919i | \(-0.662224\pi\) | ||||
−0.487865 | + | 0.872919i | \(0.662224\pi\) | |||||||
\(908\) | 31.1696 | 1.03440 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 40.3140 | 1.33640 | ||||||||
\(911\) | −50.3431 | −1.66794 | −0.833971 | − | 0.551808i | \(-0.813938\pi\) | ||||
−0.833971 | + | 0.551808i | \(0.813938\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.236918 | 0.00784085 | ||||||||
\(914\) | −41.1431 | −1.36089 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −43.5614 | −1.43931 | ||||||||
\(917\) | −9.44110 | −0.311773 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.03780 | 0.265143 | 0.132571 | − | 0.991173i | \(-0.457677\pi\) | ||||
0.132571 | + | 0.991173i | \(0.457677\pi\) | |||||||
\(920\) | −33.0668 | −1.09018 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.0741 | 0.595239 | ||||||||
\(923\) | −24.3807 | −0.802500 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.5577 | 0.774571 | ||||||||
\(926\) | −78.0520 | −2.56495 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.2823 | −0.501666 | ||||||||
\(929\) | 9.67839 | 0.317538 | 0.158769 | − | 0.987316i | \(-0.449248\pi\) | ||||
0.158769 | + | 0.987316i | \(0.449248\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.67845 | 0.251651 | ||||||||
\(932\) | −0.526782 | −0.0172553 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 48.2420 | 1.57853 | ||||||||
\(935\) | −0.406350 | −0.0132891 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.14789 | −0.102837 | −0.0514185 | − | 0.998677i | \(-0.516374\pi\) | ||||
−0.0514185 | + | 0.998677i | \(0.516374\pi\) | |||||||
\(938\) | −1.91014 | −0.0623682 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −34.7514 | −1.13347 | ||||||||
\(941\) | 38.8319 | 1.26589 | 0.632943 | − | 0.774199i | \(-0.281847\pi\) | ||||
0.632943 | + | 0.774199i | \(0.281847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.1922 | −0.690115 | ||||||||
\(944\) | 34.5612 | 1.12487 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.00624 | 0.0327158 | ||||||||
\(947\) | 1.96494 | 0.0638521 | 0.0319260 | − | 0.999490i | \(-0.489836\pi\) | ||||
0.0319260 | + | 0.999490i | \(0.489836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.01319 | 0.0328894 | ||||||||
\(950\) | 165.765 | 5.37812 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.73404 | 0.0562005 | ||||||||
\(953\) | −48.9601 | −1.58597 | −0.792986 | − | 0.609240i | \(-0.791475\pi\) | ||||
−0.792986 | + | 0.609240i | \(0.791475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.8268 | 0.738659 | ||||||||
\(956\) | 22.7333 | 0.735246 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 66.2645 | 2.14091 | ||||||||
\(959\) | 12.2081 | 0.394222 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.3539 | 0.979158 | ||||||||
\(962\) | −20.1813 | −0.650673 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.53069 | 0.113716 | ||||||||
\(965\) | 32.6733 | 1.05179 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.40139 | 0.141539 | 0.0707695 | − | 0.997493i | \(-0.477455\pi\) | ||||
0.0707695 | + | 0.997493i | \(0.477455\pi\) | |||||||
\(968\) | 10.5579 | 0.339344 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 93.1508 | 2.99089 | ||||||||
\(971\) | −41.7382 | −1.33944 | −0.669720 | − | 0.742613i | \(-0.733586\pi\) | ||||
−0.669720 | + | 0.742613i | \(0.733586\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.66264 | 0.277711 | ||||||||
\(974\) | 2.49694 | 0.0800071 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −61.1580 | −1.95762 | ||||||||
\(977\) | 0.788999 | 0.0252423 | 0.0126212 | − | 0.999920i | \(-0.495982\pi\) | ||||
0.0126212 | + | 0.999920i | \(0.495982\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.484631 | 0.0154889 | ||||||||
\(980\) | 6.04673 | 0.193156 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −43.9852 | −1.40362 | ||||||||
\(983\) | 17.9857 | 0.573656 | 0.286828 | − | 0.957982i | \(-0.407399\pi\) | ||||
0.286828 | + | 0.957982i | \(0.407399\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 102.264 | 3.25840 | ||||||||
\(986\) | 7.38899 | 0.235313 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −60.5289 | −1.92568 | ||||||||
\(989\) | −82.5072 | −2.62358 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.9431 | −1.84062 | −0.920311 | − | 0.391188i | \(-0.872064\pi\) | ||||
−0.920311 | + | 0.391188i | \(0.872064\pi\) | |||||||
\(992\) | −54.6295 | −1.73449 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.57941 | −0.272122 | ||||||||
\(995\) | 21.0093 | 0.666041 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.4955 | −1.66255 | −0.831274 | − | 0.555862i | \(-0.812388\pi\) | ||||
−0.831274 | + | 0.555862i | \(0.812388\pi\) | |||||||
\(998\) | −52.5111 | −1.66221 | ||||||||
\(999\) | 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 | 8001.2.a.p.1.11 | 14 | ||
3.2 | odd | 2 | 2667.2.a.m.1.4 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.m.1.4 | ✓ | 14 | 3.2 | odd | 2 | ||
8001.2.a.p.1.11 | 14 | 1.1 | even | 1 | trivial |