Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(-2.42429\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.42429 | 1.71423 | 0.857117 | − | 0.515121i | \(-0.172253\pi\) | ||||
0.857117 | + | 0.515121i | \(0.172253\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.87720 | 1.93860 | ||||||||
\(5\) | 0.275174 | 0.123062 | 0.0615308 | − | 0.998105i | \(-0.480402\pi\) | ||||
0.0615308 | + | 0.998105i | \(0.480402\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.16310 | −1.95147 | −0.975735 | − | 0.218956i | \(-0.929735\pi\) | ||||
−0.975735 | + | 0.218956i | \(0.929735\pi\) | |||||||
\(8\) | 4.55089 | 1.60898 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.667103 | 0.210957 | ||||||||
\(11\) | 4.59700 | 1.38605 | 0.693024 | − | 0.720915i | \(-0.256278\pi\) | ||||
0.693024 | + | 0.720915i | \(0.256278\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.58445 | 0.716799 | 0.358399 | − | 0.933568i | \(-0.383323\pi\) | ||||
0.358399 | + | 0.933568i | \(0.383323\pi\) | |||||||
\(14\) | −12.5169 | −3.34528 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.27829 | 0.819573 | ||||||||
\(17\) | −6.77779 | −1.64386 | −0.821928 | − | 0.569591i | \(-0.807101\pi\) | ||||
−0.821928 | + | 0.569591i | \(0.807101\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.93422 | −1.82024 | −0.910118 | − | 0.414350i | \(-0.864009\pi\) | ||||
−0.910118 | + | 0.414350i | \(0.864009\pi\) | |||||||
\(20\) | 1.06691 | 0.238567 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.1445 | 2.37601 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92428 | −0.984856 | ||||||||
\(26\) | 6.26548 | 1.22876 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −20.0184 | −3.78312 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.54451 | −0.277402 | −0.138701 | − | 0.990334i | \(-0.544293\pi\) | ||||
−0.138701 | + | 0.990334i | \(0.544293\pi\) | |||||||
\(32\) | −1.15424 | −0.204043 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.4314 | −2.81796 | ||||||||
\(35\) | −1.42075 | −0.240151 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.24464 | −0.204617 | −0.102308 | − | 0.994753i | \(-0.532623\pi\) | ||||
−0.102308 | + | 0.994753i | \(0.532623\pi\) | |||||||
\(38\) | −19.2349 | −3.12031 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.25229 | 0.198004 | ||||||||
\(41\) | 1.39786 | 0.218308 | 0.109154 | − | 0.994025i | \(-0.465186\pi\) | ||||
0.109154 | + | 0.994025i | \(0.465186\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.777148 | −0.118514 | −0.0592570 | − | 0.998243i | \(-0.518873\pi\) | ||||
−0.0592570 | + | 0.998243i | \(0.518873\pi\) | |||||||
\(44\) | 17.8235 | 2.68699 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.42429 | −0.357443 | ||||||||
\(47\) | 5.57928 | 0.813822 | 0.406911 | − | 0.913468i | \(-0.366606\pi\) | ||||
0.406911 | + | 0.913468i | \(0.366606\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.6576 | 2.80823 | ||||||||
\(50\) | −11.9379 | −1.68827 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.0205 | 1.38959 | ||||||||
\(53\) | −11.5021 | −1.57994 | −0.789970 | − | 0.613145i | \(-0.789904\pi\) | ||||
−0.789970 | + | 0.613145i | \(0.789904\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.26498 | 0.170569 | ||||||||
\(56\) | −23.4967 | −3.13988 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.42429 | 0.318325 | ||||||||
\(59\) | −7.31928 | −0.952889 | −0.476444 | − | 0.879205i | \(-0.658075\pi\) | ||||
−0.476444 | + | 0.879205i | \(0.658075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.28650 | 0.164719 | 0.0823596 | − | 0.996603i | \(-0.473754\pi\) | ||||
0.0823596 | + | 0.996603i | \(0.473754\pi\) | |||||||
\(62\) | −3.74434 | −0.475532 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.35480 | −1.16935 | ||||||||
\(65\) | 0.711175 | 0.0882105 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.1934 | 1.24533 | 0.622663 | − | 0.782490i | \(-0.286051\pi\) | ||||
0.622663 | + | 0.782490i | \(0.286051\pi\) | |||||||
\(68\) | −26.2789 | −3.18678 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.44432 | −0.411675 | ||||||||
\(71\) | −4.16451 | −0.494236 | −0.247118 | − | 0.968985i | \(-0.579484\pi\) | ||||
−0.247118 | + | 0.968985i | \(0.579484\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2878 | −1.20409 | −0.602046 | − | 0.798462i | \(-0.705648\pi\) | ||||
−0.602046 | + | 0.798462i | \(0.705648\pi\) | |||||||
\(74\) | −3.01736 | −0.350761 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −30.7626 | −3.52871 | ||||||||
\(77\) | −23.7348 | −2.70483 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.19088 | −0.133985 | −0.0669923 | − | 0.997753i | \(-0.521340\pi\) | ||||
−0.0669923 | + | 0.997753i | \(0.521340\pi\) | |||||||
\(80\) | 0.902101 | 0.100858 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.38881 | 0.374232 | ||||||||
\(83\) | 5.53442 | 0.607482 | 0.303741 | − | 0.952755i | \(-0.401764\pi\) | ||||
0.303741 | + | 0.952755i | \(0.401764\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.86507 | −0.202296 | ||||||||
\(86\) | −1.88404 | −0.203161 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 20.9204 | 2.23013 | ||||||||
\(89\) | −13.4423 | −1.42488 | −0.712441 | − | 0.701732i | \(-0.752410\pi\) | ||||
−0.712441 | + | 0.701732i | \(0.752410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.3438 | −1.39881 | ||||||||
\(92\) | −3.87720 | −0.404226 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.5258 | 1.39508 | ||||||||
\(95\) | −2.18329 | −0.224001 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.41413 | 0.346652 | 0.173326 | − | 0.984865i | \(-0.444549\pi\) | ||||
0.173326 | + | 0.984865i | \(0.444549\pi\) | |||||||
\(98\) | 47.6559 | 4.81397 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −19.0924 | −1.90924 | ||||||||
\(101\) | 6.22013 | 0.618926 | 0.309463 | − | 0.950912i | \(-0.399851\pi\) | ||||
0.309463 | + | 0.950912i | \(0.399851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.78182 | −0.569699 | −0.284850 | − | 0.958572i | \(-0.591944\pi\) | ||||
−0.284850 | + | 0.958572i | \(0.591944\pi\) | |||||||
\(104\) | 11.7616 | 1.15332 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −27.8846 | −2.70839 | ||||||||
\(107\) | −18.4577 | −1.78437 | −0.892185 | − | 0.451670i | \(-0.850829\pi\) | ||||
−0.892185 | + | 0.451670i | \(0.850829\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.772038 | −0.0739478 | −0.0369739 | − | 0.999316i | \(-0.511772\pi\) | ||||
−0.0369739 | + | 0.999316i | \(0.511772\pi\) | |||||||
\(110\) | 3.06667 | 0.292396 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −16.9261 | −1.59937 | ||||||||
\(113\) | 12.7996 | 1.20408 | 0.602041 | − | 0.798465i | \(-0.294354\pi\) | ||||
0.602041 | + | 0.798465i | \(0.294354\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.275174 | −0.0256601 | ||||||||
\(116\) | 3.87720 | 0.359989 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.7441 | −1.63347 | ||||||||
\(119\) | 34.9944 | 3.20793 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1324 | 0.921127 | ||||||||
\(122\) | 3.11885 | 0.282367 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.98837 | −0.537772 | ||||||||
\(125\) | −2.73091 | −0.244260 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1484 | 1.34420 | 0.672102 | − | 0.740458i | \(-0.265392\pi\) | ||||
0.672102 | + | 0.740458i | \(0.265392\pi\) | |||||||
\(128\) | −20.3703 | −1.80050 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.72410 | 0.151213 | ||||||||
\(131\) | 3.96670 | 0.346572 | 0.173286 | − | 0.984872i | \(-0.444562\pi\) | ||||
0.173286 | + | 0.984872i | \(0.444562\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 40.9652 | 3.55213 | ||||||||
\(134\) | 24.7119 | 2.13478 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −30.8450 | −2.64494 | ||||||||
\(137\) | −8.86496 | −0.757385 | −0.378692 | − | 0.925523i | \(-0.623626\pi\) | ||||
−0.378692 | + | 0.925523i | \(0.623626\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.1764 | 1.45689 | 0.728443 | − | 0.685106i | \(-0.240244\pi\) | ||||
0.728443 | + | 0.685106i | \(0.240244\pi\) | |||||||
\(140\) | −5.50855 | −0.465557 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.0960 | −0.847237 | ||||||||
\(143\) | 11.8807 | 0.993517 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.275174 | 0.0228520 | ||||||||
\(146\) | −24.9406 | −2.06410 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.82570 | −0.396670 | ||||||||
\(149\) | 19.2755 | 1.57911 | 0.789557 | − | 0.613677i | \(-0.210310\pi\) | ||||
0.789557 | + | 0.613677i | \(0.210310\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.14403 | 0.418615 | 0.209307 | − | 0.977850i | \(-0.432879\pi\) | ||||
0.209307 | + | 0.977850i | \(0.432879\pi\) | |||||||
\(152\) | −36.1078 | −2.92873 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −57.5401 | −4.63671 | ||||||||
\(155\) | −0.425009 | −0.0341376 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.4758 | −1.39472 | −0.697360 | − | 0.716721i | \(-0.745642\pi\) | ||||
−0.697360 | + | 0.716721i | \(0.745642\pi\) | |||||||
\(158\) | −2.88704 | −0.229681 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.317617 | −0.0251098 | ||||||||
\(161\) | 5.16310 | 0.406909 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.5511 | −0.904750 | −0.452375 | − | 0.891828i | \(-0.649423\pi\) | ||||
−0.452375 | + | 0.891828i | \(0.649423\pi\) | |||||||
\(164\) | 5.41977 | 0.423213 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.4171 | 1.04137 | ||||||||
\(167\) | −16.8806 | −1.30626 | −0.653128 | − | 0.757247i | \(-0.726544\pi\) | ||||
−0.653128 | + | 0.757247i | \(0.726544\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.32059 | −0.486200 | ||||||||
\(170\) | −4.52149 | −0.346782 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.01316 | −0.229751 | ||||||||
\(173\) | 2.08494 | 0.158515 | 0.0792574 | − | 0.996854i | \(-0.474745\pi\) | ||||
0.0792574 | + | 0.996854i | \(0.474745\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 25.4246 | 1.92192 | ||||||||
\(176\) | 15.0703 | 1.13597 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −32.5881 | −2.44258 | ||||||||
\(179\) | −8.87412 | −0.663283 | −0.331641 | − | 0.943406i | \(-0.607602\pi\) | ||||
−0.331641 | + | 0.943406i | \(0.607602\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.0114 | −1.56176 | −0.780881 | − | 0.624680i | \(-0.785229\pi\) | ||||
−0.780881 | + | 0.624680i | \(0.785229\pi\) | |||||||
\(182\) | −32.3493 | −2.39789 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.55089 | −0.335496 | ||||||||
\(185\) | −0.342492 | −0.0251805 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −31.1575 | −2.27846 | ||||||||
\(188\) | 21.6320 | 1.57768 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.29295 | −0.383991 | ||||||||
\(191\) | 9.11834 | 0.659780 | 0.329890 | − | 0.944019i | \(-0.392988\pi\) | ||||
0.329890 | + | 0.944019i | \(0.392988\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.41977 | −0.102197 | −0.0510987 | − | 0.998694i | \(-0.516272\pi\) | ||||
−0.0510987 | + | 0.998694i | \(0.516272\pi\) | |||||||
\(194\) | 8.27684 | 0.594243 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 76.2166 | 5.44404 | ||||||||
\(197\) | 2.98927 | 0.212977 | 0.106488 | − | 0.994314i | \(-0.466039\pi\) | ||||
0.106488 | + | 0.994314i | \(0.466039\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.2526 | 1.01034 | 0.505170 | − | 0.863020i | \(-0.331430\pi\) | ||||
0.505170 | + | 0.863020i | \(0.331430\pi\) | |||||||
\(200\) | −22.4098 | −1.58462 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.0794 | 1.06098 | ||||||||
\(203\) | −5.16310 | −0.362379 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.384654 | 0.0268654 | ||||||||
\(206\) | −14.0168 | −0.976598 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.47259 | 0.587469 | ||||||||
\(209\) | −36.4736 | −2.52293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.99505 | −0.343874 | −0.171937 | − | 0.985108i | \(-0.555002\pi\) | ||||
−0.171937 | + | 0.985108i | \(0.555002\pi\) | |||||||
\(212\) | −44.5961 | −3.06287 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −44.7468 | −3.05883 | ||||||||
\(215\) | −0.213851 | −0.0145845 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.97446 | 0.541341 | ||||||||
\(218\) | −1.87165 | −0.126764 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.90457 | 0.330666 | ||||||||
\(221\) | −17.5169 | −1.17831 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.0823 | 1.14391 | 0.571956 | − | 0.820284i | \(-0.306185\pi\) | ||||
0.571956 | + | 0.820284i | \(0.306185\pi\) | |||||||
\(224\) | 5.95945 | 0.398183 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 31.0299 | 2.06408 | ||||||||
\(227\) | 5.65703 | 0.375471 | 0.187735 | − | 0.982220i | \(-0.439885\pi\) | ||||
0.187735 | + | 0.982220i | \(0.439885\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.6271 | −0.900503 | −0.450251 | − | 0.892902i | \(-0.648666\pi\) | ||||
−0.450251 | + | 0.892902i | \(0.648666\pi\) | |||||||
\(230\) | −0.667103 | −0.0439875 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.55089 | 0.298781 | ||||||||
\(233\) | 8.31854 | 0.544965 | 0.272483 | − | 0.962161i | \(-0.412155\pi\) | ||||
0.272483 | + | 0.962161i | \(0.412155\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.53527 | 0.100150 | ||||||||
\(236\) | −28.3783 | −1.84727 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 84.8368 | 5.49915 | ||||||||
\(239\) | −10.6654 | −0.689886 | −0.344943 | − | 0.938624i | \(-0.612102\pi\) | ||||
−0.344943 | + | 0.938624i | \(0.612102\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.2982 | −1.24311 | −0.621554 | − | 0.783371i | \(-0.713498\pi\) | ||||
−0.621554 | + | 0.783371i | \(0.713498\pi\) | |||||||
\(242\) | 24.5639 | 1.57903 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.98801 | 0.319325 | ||||||||
\(245\) | 5.40927 | 0.345586 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.5056 | −1.30474 | ||||||||
\(248\) | −7.02889 | −0.446335 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.62052 | −0.418718 | ||||||||
\(251\) | −7.91467 | −0.499570 | −0.249785 | − | 0.968301i | \(-0.580360\pi\) | ||||
−0.249785 | + | 0.968301i | \(0.580360\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.59700 | −0.289011 | ||||||||
\(254\) | 36.7242 | 2.30428 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30.6740 | −1.91712 | ||||||||
\(257\) | −5.60389 | −0.349561 | −0.174781 | − | 0.984607i | \(-0.555922\pi\) | ||||
−0.174781 | + | 0.984607i | \(0.555922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.42618 | 0.399304 | ||||||||
\(260\) | 2.75737 | 0.171005 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.61644 | 0.594106 | ||||||||
\(263\) | 18.0911 | 1.11555 | 0.557774 | − | 0.829993i | \(-0.311656\pi\) | ||||
0.557774 | + | 0.829993i | \(0.311656\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.16509 | −0.194430 | ||||||||
\(266\) | 99.3117 | 6.08919 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 39.5220 | 2.41419 | ||||||||
\(269\) | −8.37348 | −0.510540 | −0.255270 | − | 0.966870i | \(-0.582164\pi\) | ||||
−0.255270 | + | 0.966870i | \(0.582164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.69125 | 0.163482 | 0.0817408 | − | 0.996654i | \(-0.473952\pi\) | ||||
0.0817408 | + | 0.996654i | \(0.473952\pi\) | |||||||
\(272\) | −22.2196 | −1.34726 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.4913 | −1.29834 | ||||||||
\(275\) | −22.6369 | −1.36506 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.6291 | 1.96049 | 0.980247 | − | 0.197776i | \(-0.0633718\pi\) | ||||
0.980247 | + | 0.197776i | \(0.0633718\pi\) | |||||||
\(278\) | 41.6408 | 2.49745 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.46569 | −0.386399 | ||||||||
\(281\) | 21.2594 | 1.26823 | 0.634114 | − | 0.773239i | \(-0.281365\pi\) | ||||
0.634114 | + | 0.773239i | \(0.281365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.43670 | −0.382622 | −0.191311 | − | 0.981529i | \(-0.561274\pi\) | ||||
−0.191311 | + | 0.981529i | \(0.561274\pi\) | |||||||
\(284\) | −16.1466 | −0.958127 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 28.8024 | 1.70312 | ||||||||
\(287\) | −7.21727 | −0.426022 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.9385 | 1.70226 | ||||||||
\(290\) | 0.667103 | 0.0391737 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −39.8877 | −2.33425 | ||||||||
\(293\) | 7.42249 | 0.433627 | 0.216813 | − | 0.976213i | \(-0.430434\pi\) | ||||
0.216813 | + | 0.976213i | \(0.430434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.01408 | −0.117264 | ||||||||
\(296\) | −5.66420 | −0.329225 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 46.7296 | 2.70697 | ||||||||
\(299\) | −2.58445 | −0.149463 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.01250 | 0.231276 | ||||||||
\(302\) | 12.4706 | 0.717604 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −26.0107 | −1.49181 | ||||||||
\(305\) | 0.354011 | 0.0202706 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.106672 | 0.00608808 | 0.00304404 | − | 0.999995i | \(-0.499031\pi\) | ||||
0.00304404 | + | 0.999995i | \(0.499031\pi\) | |||||||
\(308\) | −92.0245 | −5.24358 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.03035 | −0.0585198 | ||||||||
\(311\) | 16.3006 | 0.924324 | 0.462162 | − | 0.886796i | \(-0.347074\pi\) | ||||
0.462162 | + | 0.886796i | \(0.347074\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.55399 | 0.0878366 | 0.0439183 | − | 0.999035i | \(-0.486016\pi\) | ||||
0.0439183 | + | 0.999035i | \(0.486016\pi\) | |||||||
\(314\) | −42.3664 | −2.39088 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.61728 | −0.259743 | ||||||||
\(317\) | −32.8913 | −1.84736 | −0.923679 | − | 0.383166i | \(-0.874834\pi\) | ||||
−0.923679 | + | 0.383166i | \(0.874834\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.59700 | 0.257383 | ||||||||
\(320\) | −2.57420 | −0.143902 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.5169 | 0.697538 | ||||||||
\(323\) | 53.7765 | 2.99220 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.7266 | −0.705943 | ||||||||
\(326\) | −28.0032 | −1.55095 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.36149 | 0.351254 | ||||||||
\(329\) | −28.8064 | −1.58815 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5227 | 1.18299 | 0.591496 | − | 0.806308i | \(-0.298537\pi\) | ||||
0.591496 | + | 0.806308i | \(0.298537\pi\) | |||||||
\(332\) | 21.4581 | 1.17766 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −40.9234 | −2.23923 | ||||||||
\(335\) | 2.80497 | 0.153252 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.3271 | −1.65202 | −0.826012 | − | 0.563653i | \(-0.809396\pi\) | ||||
−0.826012 | + | 0.563653i | \(0.809396\pi\) | |||||||
\(338\) | −15.3230 | −0.833460 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.23127 | −0.392171 | ||||||||
\(341\) | −7.10011 | −0.384492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −65.3526 | −3.52871 | ||||||||
\(344\) | −3.53672 | −0.190687 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.05450 | 0.271732 | ||||||||
\(347\) | −1.44730 | −0.0776953 | −0.0388476 | − | 0.999245i | \(-0.512369\pi\) | ||||
−0.0388476 | + | 0.999245i | \(0.512369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.963889 | −0.0515958 | −0.0257979 | − | 0.999667i | \(-0.508213\pi\) | ||||
−0.0257979 | + | 0.999667i | \(0.508213\pi\) | |||||||
\(350\) | 61.6366 | 3.29462 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.30604 | −0.282813 | ||||||||
\(353\) | −19.4579 | −1.03564 | −0.517821 | − | 0.855489i | \(-0.673257\pi\) | ||||
−0.517821 | + | 0.855489i | \(0.673257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.14597 | −0.0608215 | ||||||||
\(356\) | −52.1186 | −2.76228 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.5135 | −1.13702 | ||||||||
\(359\) | 22.4871 | 1.18682 | 0.593411 | − | 0.804900i | \(-0.297781\pi\) | ||||
0.593411 | + | 0.804900i | \(0.297781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 43.9519 | 2.31326 | ||||||||
\(362\) | −50.9377 | −2.67723 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −51.7366 | −2.71174 | ||||||||
\(365\) | −2.83093 | −0.148178 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.9126 | −1.19603 | −0.598014 | − | 0.801486i | \(-0.704043\pi\) | ||||
−0.598014 | + | 0.801486i | \(0.704043\pi\) | |||||||
\(368\) | −3.27829 | −0.170893 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.830301 | −0.0431653 | ||||||||
\(371\) | 59.3867 | 3.08321 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.09309 | 0.160154 | 0.0800770 | − | 0.996789i | \(-0.474483\pi\) | ||||
0.0800770 | + | 0.996789i | \(0.474483\pi\) | |||||||
\(374\) | −75.5349 | −3.90582 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 25.3907 | 1.30942 | ||||||||
\(377\) | 2.58445 | 0.133106 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.6064 | 1.62351 | 0.811756 | − | 0.583996i | \(-0.198512\pi\) | ||||
0.811756 | + | 0.583996i | \(0.198512\pi\) | |||||||
\(380\) | −8.46507 | −0.434249 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.1055 | 1.13102 | ||||||||
\(383\) | −14.6954 | −0.750898 | −0.375449 | − | 0.926843i | \(-0.622511\pi\) | ||||
−0.375449 | + | 0.926843i | \(0.622511\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.53120 | −0.332861 | ||||||||
\(386\) | −3.44195 | −0.175191 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.2373 | 0.672020 | ||||||||
\(389\) | −20.4520 | −1.03696 | −0.518478 | − | 0.855091i | \(-0.673501\pi\) | ||||
−0.518478 | + | 0.855091i | \(0.673501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.77779 | 0.342768 | ||||||||
\(392\) | 89.4597 | 4.51840 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.24687 | 0.365092 | ||||||||
\(395\) | −0.327700 | −0.0164884 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.93448 | 0.0970887 | 0.0485443 | − | 0.998821i | \(-0.484542\pi\) | ||||
0.0485443 | + | 0.998821i | \(0.484542\pi\) | |||||||
\(398\) | 34.5525 | 1.73196 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.1432 | −0.807161 | ||||||||
\(401\) | 4.44527 | 0.221986 | 0.110993 | − | 0.993821i | \(-0.464597\pi\) | ||||
0.110993 | + | 0.993821i | \(0.464597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.99171 | −0.198841 | ||||||||
\(404\) | 24.1167 | 1.19985 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.5169 | −0.621202 | ||||||||
\(407\) | −5.72159 | −0.283609 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.40105 | 0.365958 | 0.182979 | − | 0.983117i | \(-0.441426\pi\) | ||||
0.182979 | + | 0.983117i | \(0.441426\pi\) | |||||||
\(410\) | 0.932514 | 0.0460536 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −22.4173 | −1.10442 | ||||||||
\(413\) | 37.7902 | 1.85953 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.52293 | 0.0747577 | ||||||||
\(416\) | −2.98308 | −0.146257 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −88.4228 | −4.32490 | ||||||||
\(419\) | 39.3381 | 1.92179 | 0.960896 | − | 0.276910i | \(-0.0893103\pi\) | ||||
0.960896 | + | 0.276910i | \(0.0893103\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.1384 | 1.66380 | 0.831901 | − | 0.554924i | \(-0.187253\pi\) | ||||
0.831901 | + | 0.554924i | \(0.187253\pi\) | |||||||
\(422\) | −12.1095 | −0.589480 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −52.3450 | −2.54210 | ||||||||
\(425\) | 33.3757 | 1.61896 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.64232 | −0.321444 | ||||||||
\(428\) | −71.5641 | −3.45918 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.518438 | −0.0250013 | ||||||||
\(431\) | −19.7955 | −0.953518 | −0.476759 | − | 0.879034i | \(-0.658189\pi\) | ||||
−0.476759 | + | 0.879034i | \(0.658189\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.2150 | 1.64427 | 0.822134 | − | 0.569294i | \(-0.192783\pi\) | ||||
0.822134 | + | 0.569294i | \(0.192783\pi\) | |||||||
\(434\) | 19.3324 | 0.927986 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.99335 | −0.143355 | ||||||||
\(437\) | 7.93422 | 0.379545 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.25190 | −0.441569 | −0.220784 | − | 0.975323i | \(-0.570862\pi\) | ||||
−0.220784 | + | 0.975323i | \(0.570862\pi\) | |||||||
\(440\) | 5.75676 | 0.274443 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −42.4661 | −2.01991 | ||||||||
\(443\) | 6.68002 | 0.317377 | 0.158689 | − | 0.987329i | \(-0.449273\pi\) | ||||
0.158689 | + | 0.987329i | \(0.449273\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.69898 | −0.175348 | ||||||||
\(446\) | 41.4124 | 1.96093 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 48.2998 | 2.28195 | ||||||||
\(449\) | 5.68296 | 0.268195 | 0.134098 | − | 0.990968i | \(-0.457186\pi\) | ||||
0.134098 | + | 0.990968i | \(0.457186\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.42594 | 0.302586 | ||||||||
\(452\) | 49.6265 | 2.33424 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.7143 | 0.643645 | ||||||||
\(455\) | −3.67187 | −0.172140 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.4227 | −0.861776 | −0.430888 | − | 0.902405i | \(-0.641800\pi\) | ||||
−0.430888 | + | 0.902405i | \(0.641800\pi\) | |||||||
\(458\) | −33.0361 | −1.54367 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.06691 | −0.0497448 | ||||||||
\(461\) | −29.4473 | −1.37150 | −0.685749 | − | 0.727838i | \(-0.740525\pi\) | ||||
−0.685749 | + | 0.727838i | \(0.740525\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.0658 | 1.49022 | 0.745111 | − | 0.666941i | \(-0.232397\pi\) | ||||
0.745111 | + | 0.666941i | \(0.232397\pi\) | |||||||
\(464\) | 3.27829 | 0.152191 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.1666 | 0.934199 | ||||||||
\(467\) | −14.1343 | −0.654059 | −0.327029 | − | 0.945014i | \(-0.606048\pi\) | ||||
−0.327029 | + | 0.945014i | \(0.606048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −52.6298 | −2.43022 | ||||||||
\(470\) | 3.72196 | 0.171681 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −33.3092 | −1.53318 | ||||||||
\(473\) | −3.57255 | −0.164266 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 39.0703 | 1.79267 | ||||||||
\(476\) | 135.680 | 6.21890 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −25.8560 | −1.18263 | ||||||||
\(479\) | −8.84879 | −0.404312 | −0.202156 | − | 0.979353i | \(-0.564795\pi\) | ||||
−0.202156 | + | 0.979353i | \(0.564795\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.21670 | −0.146669 | ||||||||
\(482\) | −46.7846 | −2.13098 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 39.2854 | 1.78570 | ||||||||
\(485\) | 0.939479 | 0.0426596 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.30353 | 0.285640 | 0.142820 | − | 0.989749i | \(-0.454383\pi\) | ||||
0.142820 | + | 0.989749i | \(0.454383\pi\) | |||||||
\(488\) | 5.85471 | 0.265030 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.1137 | 0.592415 | ||||||||
\(491\) | 22.2801 | 1.00549 | 0.502743 | − | 0.864436i | \(-0.332324\pi\) | ||||
0.502743 | + | 0.864436i | \(0.332324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.77779 | −0.305256 | ||||||||
\(494\) | −49.7117 | −2.23663 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.06335 | −0.227351 | ||||||||
\(497\) | 21.5018 | 0.964487 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.66457 | −0.253581 | −0.126791 | − | 0.991930i | \(-0.540468\pi\) | ||||
−0.126791 | + | 0.991930i | \(0.540468\pi\) | |||||||
\(500\) | −10.5883 | −0.473522 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.1875 | −0.856380 | ||||||||
\(503\) | −25.2240 | −1.12468 | −0.562340 | − | 0.826906i | \(-0.690099\pi\) | ||||
−0.562340 | + | 0.826906i | \(0.690099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.71162 | 0.0761660 | ||||||||
\(506\) | −11.1445 | −0.495432 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 58.7335 | 2.60588 | ||||||||
\(509\) | −1.51350 | −0.0670847 | −0.0335423 | − | 0.999437i | \(-0.510679\pi\) | ||||
−0.0335423 | + | 0.999437i | \(0.510679\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 53.1168 | 2.34975 | ||||||||
\(512\) | −33.6222 | −1.48591 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.5855 | −0.599230 | ||||||||
\(515\) | −1.59101 | −0.0701081 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.6479 | 1.12800 | ||||||||
\(518\) | 15.5790 | 0.684500 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.23648 | 0.141929 | ||||||||
\(521\) | −3.07057 | −0.134524 | −0.0672621 | − | 0.997735i | \(-0.521426\pi\) | ||||
−0.0672621 | + | 0.997735i | \(0.521426\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.05915 | −0.352402 | −0.176201 | − | 0.984354i | \(-0.556381\pi\) | ||||
−0.176201 | + | 0.984354i | \(0.556381\pi\) | |||||||
\(524\) | 15.3797 | 0.671865 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 43.8583 | 1.91231 | ||||||||
\(527\) | 10.4684 | 0.456009 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −7.67312 | −0.333299 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 158.830 | 6.88617 | ||||||||
\(533\) | 3.61269 | 0.156483 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.07908 | −0.219588 | ||||||||
\(536\) | 46.3892 | 2.00371 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.2998 | −0.875186 | ||||||||
\(539\) | 90.3661 | 3.89234 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.7791 | 1.88221 | 0.941106 | − | 0.338112i | \(-0.109788\pi\) | ||||
0.941106 | + | 0.338112i | \(0.109788\pi\) | |||||||
\(542\) | 6.52437 | 0.280246 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.82319 | 0.335417 | ||||||||
\(545\) | −0.212445 | −0.00910014 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.38785 | −0.0593402 | −0.0296701 | − | 0.999560i | \(-0.509446\pi\) | ||||
−0.0296701 | + | 0.999560i | \(0.509446\pi\) | |||||||
\(548\) | −34.3713 | −1.46827 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −54.8785 | −2.34003 | ||||||||
\(551\) | −7.93422 | −0.338009 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.14864 | 0.261467 | ||||||||
\(554\) | 79.1026 | 3.36075 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 66.5965 | 2.82432 | ||||||||
\(557\) | −22.8042 | −0.966246 | −0.483123 | − | 0.875552i | \(-0.660498\pi\) | ||||
−0.483123 | + | 0.875552i | \(0.660498\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00850 | −0.0849507 | ||||||||
\(560\) | −4.65764 | −0.196821 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 51.5390 | 2.17404 | ||||||||
\(563\) | 7.80360 | 0.328883 | 0.164441 | − | 0.986387i | \(-0.447418\pi\) | ||||
0.164441 | + | 0.986387i | \(0.447418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.52211 | 0.148176 | ||||||||
\(566\) | −15.6045 | −0.655904 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.9522 | −0.795217 | ||||||||
\(569\) | 37.1514 | 1.55747 | 0.778733 | − | 0.627356i | \(-0.215863\pi\) | ||||
0.778733 | + | 0.627356i | \(0.215863\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.6811 | −0.949174 | −0.474587 | − | 0.880209i | \(-0.657403\pi\) | ||||
−0.474587 | + | 0.880209i | \(0.657403\pi\) | |||||||
\(572\) | 46.0640 | 1.92603 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −17.4968 | −0.730302 | ||||||||
\(575\) | 4.92428 | 0.205357 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.6189 | −0.816747 | −0.408374 | − | 0.912815i | \(-0.633904\pi\) | ||||
−0.408374 | + | 0.912815i | \(0.633904\pi\) | |||||||
\(578\) | 70.1553 | 2.91808 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.06691 | 0.0443009 | ||||||||
\(581\) | −28.5748 | −1.18548 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −52.8753 | −2.18987 | ||||||||
\(584\) | −46.8185 | −1.93736 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.9943 | 0.743338 | ||||||||
\(587\) | −15.7582 | −0.650411 | −0.325206 | − | 0.945643i | \(-0.605434\pi\) | ||||
−0.325206 | + | 0.945643i | \(0.605434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.2545 | 0.504937 | ||||||||
\(590\) | −4.88271 | −0.201018 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.08028 | −0.167698 | ||||||||
\(593\) | 7.35744 | 0.302134 | 0.151067 | − | 0.988524i | \(-0.451729\pi\) | ||||
0.151067 | + | 0.988524i | \(0.451729\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.62957 | 0.394774 | ||||||||
\(596\) | 74.7352 | 3.06127 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.26548 | −0.256214 | ||||||||
\(599\) | −27.0050 | −1.10340 | −0.551698 | − | 0.834044i | \(-0.686020\pi\) | ||||
−0.551698 | + | 0.834044i | \(0.686020\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.4245 | −0.955504 | −0.477752 | − | 0.878495i | \(-0.658548\pi\) | ||||
−0.477752 | + | 0.878495i | \(0.658548\pi\) | |||||||
\(602\) | 9.72747 | 0.396462 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.9444 | 0.811527 | ||||||||
\(605\) | 2.78818 | 0.113355 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.8139 | 0.804222 | 0.402111 | − | 0.915591i | \(-0.368277\pi\) | ||||
0.402111 | + | 0.915591i | \(0.368277\pi\) | |||||||
\(608\) | 9.15799 | 0.371405 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.858227 | 0.0347486 | ||||||||
\(611\) | 14.4194 | 0.583346 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.88252 | 0.318372 | 0.159186 | − | 0.987249i | \(-0.449113\pi\) | ||||
0.159186 | + | 0.987249i | \(0.449113\pi\) | |||||||
\(614\) | 0.258604 | 0.0104364 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −108.014 | −4.35202 | ||||||||
\(617\) | 37.4119 | 1.50615 | 0.753073 | − | 0.657937i | \(-0.228571\pi\) | ||||
0.753073 | + | 0.657937i | \(0.228571\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.5529 | −0.584931 | −0.292465 | − | 0.956276i | \(-0.594476\pi\) | ||||
−0.292465 | + | 0.956276i | \(0.594476\pi\) | |||||||
\(620\) | −1.64785 | −0.0661791 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 39.5175 | 1.58451 | ||||||||
\(623\) | 69.4040 | 2.78061 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.8699 | 0.954797 | ||||||||
\(626\) | 3.76733 | 0.150573 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −67.7571 | −2.70380 | ||||||||
\(629\) | 8.43588 | 0.336361 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.1886 | −0.843504 | −0.421752 | − | 0.906711i | \(-0.638585\pi\) | ||||
−0.421752 | + | 0.906711i | \(0.638585\pi\) | |||||||
\(632\) | −5.41956 | −0.215579 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −79.7382 | −3.16681 | ||||||||
\(635\) | 4.16845 | 0.165420 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 50.8042 | 2.01294 | ||||||||
\(638\) | 11.1445 | 0.441214 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.60538 | −0.221572 | ||||||||
\(641\) | −25.4677 | −1.00591 | −0.502957 | − | 0.864312i | \(-0.667755\pi\) | ||||
−0.502957 | + | 0.864312i | \(0.667755\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.2517 | 1.42963 | 0.714814 | − | 0.699314i | \(-0.246511\pi\) | ||||
0.714814 | + | 0.699314i | \(0.246511\pi\) | |||||||
\(644\) | 20.0184 | 0.788835 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 130.370 | 5.12934 | ||||||||
\(647\) | −40.3128 | −1.58486 | −0.792430 | − | 0.609963i | \(-0.791184\pi\) | ||||
−0.792430 | + | 0.609963i | \(0.791184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.6467 | −1.32075 | ||||||||
\(650\) | −30.8530 | −1.21015 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −44.7858 | −1.75395 | ||||||||
\(653\) | −28.4754 | −1.11433 | −0.557164 | − | 0.830402i | \(-0.688111\pi\) | ||||
−0.557164 | + | 0.830402i | \(0.688111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.09153 | 0.0426497 | ||||||||
\(656\) | 4.58258 | 0.178920 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −69.8352 | −2.72246 | ||||||||
\(659\) | 4.69239 | 0.182790 | 0.0913948 | − | 0.995815i | \(-0.470867\pi\) | ||||
0.0913948 | + | 0.995815i | \(0.470867\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.8296 | 0.732386 | 0.366193 | − | 0.930539i | \(-0.380661\pi\) | ||||
0.366193 | + | 0.930539i | \(0.380661\pi\) | |||||||
\(662\) | 52.1773 | 2.02793 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 25.1865 | 0.977427 | ||||||||
\(665\) | 11.2726 | 0.437132 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −65.4493 | −2.53231 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.80008 | 0.262710 | ||||||||
\(671\) | 5.91403 | 0.228309 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.9078 | −0.613201 | −0.306600 | − | 0.951838i | \(-0.599192\pi\) | ||||
−0.306600 | + | 0.951838i | \(0.599192\pi\) | |||||||
\(674\) | −73.5219 | −2.83196 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.5062 | −0.942547 | ||||||||
\(677\) | −30.7038 | −1.18004 | −0.590022 | − | 0.807387i | \(-0.700881\pi\) | ||||
−0.590022 | + | 0.807387i | \(0.700881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.6275 | −0.676481 | ||||||||
\(680\) | −8.48775 | −0.325490 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17.2127 | −0.659110 | ||||||||
\(683\) | 12.1098 | 0.463369 | 0.231685 | − | 0.972791i | \(-0.425576\pi\) | ||||
0.231685 | + | 0.972791i | \(0.425576\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.43941 | −0.0932051 | ||||||||
\(686\) | −158.434 | −6.04904 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.54772 | −0.0971308 | ||||||||
\(689\) | −29.7268 | −1.13250 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.0959 | 1.41119 | 0.705597 | − | 0.708613i | \(-0.250679\pi\) | ||||
0.705597 | + | 0.708613i | \(0.250679\pi\) | |||||||
\(692\) | 8.08372 | 0.307297 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.50869 | −0.133188 | ||||||||
\(695\) | 4.72652 | 0.179287 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.47438 | −0.358868 | ||||||||
\(698\) | −2.33675 | −0.0884473 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 98.5761 | 3.72583 | ||||||||
\(701\) | −10.9045 | −0.411858 | −0.205929 | − | 0.978567i | \(-0.566022\pi\) | ||||
−0.205929 | + | 0.978567i | \(0.566022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.87522 | 0.372451 | ||||||||
\(704\) | −43.0040 | −1.62077 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −47.1718 | −1.77533 | ||||||||
\(707\) | −32.1151 | −1.20781 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.3176 | 0.462598 | 0.231299 | − | 0.972883i | \(-0.425702\pi\) | ||||
0.231299 | + | 0.972883i | \(0.425702\pi\) | |||||||
\(710\) | −2.77816 | −0.104262 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −61.1745 | −2.29261 | ||||||||
\(713\) | 1.54451 | 0.0578423 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.26927 | 0.122264 | ||||||||
\(716\) | −34.4067 | −1.28584 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 54.5152 | 2.03449 | ||||||||
\(719\) | −0.321584 | −0.0119931 | −0.00599654 | − | 0.999982i | \(-0.501909\pi\) | ||||
−0.00599654 | + | 0.999982i | \(0.501909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.8521 | 1.11175 | ||||||||
\(722\) | 106.552 | 3.96547 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −81.4653 | −3.02763 | ||||||||
\(725\) | −4.92428 | −0.182883 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.3701 | 0.644223 | 0.322111 | − | 0.946702i | \(-0.395607\pi\) | ||||
0.322111 | + | 0.946702i | \(0.395607\pi\) | |||||||
\(728\) | −60.7262 | −2.25066 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.86300 | −0.254011 | ||||||||
\(731\) | 5.26735 | 0.194820 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0450 | 0.444894 | 0.222447 | − | 0.974945i | \(-0.428596\pi\) | ||||
0.222447 | + | 0.974945i | \(0.428596\pi\) | |||||||
\(734\) | −55.5469 | −2.05027 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.15424 | 0.0425458 | ||||||||
\(737\) | 46.8592 | 1.72608 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.8201 | −0.618737 | −0.309368 | − | 0.950942i | \(-0.600118\pi\) | ||||
−0.309368 | + | 0.950942i | \(0.600118\pi\) | |||||||
\(740\) | −1.32791 | −0.0488149 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 143.971 | 5.28534 | ||||||||
\(743\) | 17.4044 | 0.638505 | 0.319253 | − | 0.947670i | \(-0.396568\pi\) | ||||
0.319253 | + | 0.947670i | \(0.396568\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.30413 | 0.194328 | ||||||||
\(746\) | 7.49856 | 0.274542 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −120.804 | −4.41703 | ||||||||
\(749\) | 95.2988 | 3.48214 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.100736 | −0.00367590 | −0.00183795 | − | 0.999998i | \(-0.500585\pi\) | ||||
−0.00183795 | + | 0.999998i | \(0.500585\pi\) | |||||||
\(752\) | 18.2905 | 0.666986 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.26548 | 0.228175 | ||||||||
\(755\) | 1.41550 | 0.0515155 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.1198 | 1.24010 | 0.620052 | − | 0.784561i | \(-0.287111\pi\) | ||||
0.620052 | + | 0.784561i | \(0.287111\pi\) | |||||||
\(758\) | 76.6232 | 2.78308 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.93593 | −0.360414 | ||||||||
\(761\) | −23.5537 | −0.853822 | −0.426911 | − | 0.904294i | \(-0.640398\pi\) | ||||
−0.426911 | + | 0.904294i | \(0.640398\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.98611 | 0.144307 | ||||||||
\(764\) | 35.3536 | 1.27905 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −35.6259 | −1.28722 | ||||||||
\(767\) | −18.9163 | −0.683029 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.02730 | 0.325533 | 0.162766 | − | 0.986665i | \(-0.447958\pi\) | ||||
0.162766 | + | 0.986665i | \(0.447958\pi\) | |||||||
\(770\) | −15.8335 | −0.570602 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.50475 | −0.198120 | ||||||||
\(773\) | −53.4367 | −1.92198 | −0.960992 | − | 0.276577i | \(-0.910800\pi\) | ||||
−0.960992 | + | 0.276577i | \(0.910800\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.60559 | 0.273201 | ||||||||
\(776\) | 15.5373 | 0.557757 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −49.5816 | −1.77759 | ||||||||
\(779\) | −11.0909 | −0.397373 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.1442 | −0.685035 | ||||||||
\(782\) | 16.4314 | 0.587584 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 64.4434 | 2.30155 | ||||||||
\(785\) | −4.80889 | −0.171636 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.7500 | 1.70210 | 0.851052 | − | 0.525081i | \(-0.175965\pi\) | ||||
0.851052 | + | 0.525081i | \(0.175965\pi\) | |||||||
\(788\) | 11.5900 | 0.412877 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.794440 | −0.0282649 | ||||||||
\(791\) | −66.0855 | −2.34973 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.32489 | 0.118070 | ||||||||
\(794\) | 4.68974 | 0.166433 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 55.2602 | 1.95865 | ||||||||
\(797\) | −6.00759 | −0.212800 | −0.106400 | − | 0.994323i | \(-0.533932\pi\) | ||||
−0.106400 | + | 0.994323i | \(0.533932\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.8152 | −1.33781 | ||||||||
\(800\) | 5.68380 | 0.200953 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.7767 | 0.380537 | ||||||||
\(803\) | −47.2928 | −1.66893 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.42075 | 0.0500750 | ||||||||
\(806\) | −9.67709 | −0.340861 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 28.3071 | 0.995840 | ||||||||
\(809\) | −33.4712 | −1.17678 | −0.588392 | − | 0.808576i | \(-0.700239\pi\) | ||||
−0.588392 | + | 0.808576i | \(0.700239\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.2370 | 0.429700 | 0.214850 | − | 0.976647i | \(-0.431074\pi\) | ||||
0.214850 | + | 0.976647i | \(0.431074\pi\) | |||||||
\(812\) | −20.0184 | −0.702508 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.8708 | −0.486172 | ||||||||
\(815\) | −3.17856 | −0.111340 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.16607 | 0.215723 | ||||||||
\(818\) | 17.9423 | 0.627339 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.49138 | 0.0520813 | ||||||||
\(821\) | 13.9476 | 0.486774 | 0.243387 | − | 0.969929i | \(-0.421742\pi\) | ||||
0.243387 | + | 0.969929i | \(0.421742\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.34522 | 0.0817493 | 0.0408746 | − | 0.999164i | \(-0.486986\pi\) | ||||
0.0408746 | + | 0.999164i | \(0.486986\pi\) | |||||||
\(824\) | −26.3124 | −0.916636 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 91.6145 | 3.18768 | ||||||||
\(827\) | −14.5485 | −0.505901 | −0.252950 | − | 0.967479i | \(-0.581401\pi\) | ||||
−0.252950 | + | 0.967479i | \(0.581401\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.6227 | −0.507866 | −0.253933 | − | 0.967222i | \(-0.581724\pi\) | ||||
−0.253933 | + | 0.967222i | \(0.581724\pi\) | |||||||
\(830\) | 3.69203 | 0.128152 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −24.1770 | −0.838188 | ||||||||
\(833\) | −133.235 | −4.61633 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.64510 | −0.160750 | ||||||||
\(836\) | −141.416 | −4.89096 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 95.3671 | 3.29440 | ||||||||
\(839\) | −7.29576 | −0.251878 | −0.125939 | − | 0.992038i | \(-0.540194\pi\) | ||||
−0.125939 | + | 0.992038i | \(0.540194\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 82.7615 | 2.85215 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19.3668 | −0.666634 | ||||||||
\(845\) | −1.73926 | −0.0598325 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −52.3146 | −1.79755 | ||||||||
\(848\) | −37.7074 | −1.29488 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 80.9126 | 2.77528 | ||||||||
\(851\) | 1.24464 | 0.0426656 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.430558 | 0.0147420 | 0.00737101 | − | 0.999973i | \(-0.497654\pi\) | ||||
0.00737101 | + | 0.999973i | \(0.497654\pi\) | |||||||
\(854\) | −16.1029 | −0.551031 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −83.9988 | −2.87102 | ||||||||
\(857\) | −14.3303 | −0.489513 | −0.244756 | − | 0.969585i | \(-0.578708\pi\) | ||||
−0.244756 | + | 0.969585i | \(0.578708\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.5387 | −0.973730 | −0.486865 | − | 0.873477i | \(-0.661860\pi\) | ||||
−0.486865 | + | 0.873477i | \(0.661860\pi\) | |||||||
\(860\) | −0.829144 | −0.0282736 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −47.9902 | −1.63455 | ||||||||
\(863\) | −3.69031 | −0.125620 | −0.0628098 | − | 0.998026i | \(-0.520006\pi\) | ||||
−0.0628098 | + | 0.998026i | \(0.520006\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.573721 | 0.0195071 | ||||||||
\(866\) | 82.9472 | 2.81866 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 30.9186 | 1.04945 | ||||||||
\(869\) | −5.47448 | −0.185709 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.3445 | 0.892649 | ||||||||
\(872\) | −3.51346 | −0.118981 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.2349 | 0.650630 | ||||||||
\(875\) | 14.0999 | 0.476665 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.6342 | −0.527928 | −0.263964 | − | 0.964532i | \(-0.585030\pi\) | ||||
−0.263964 | + | 0.964532i | \(0.585030\pi\) | |||||||
\(878\) | −22.4293 | −0.756953 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.14696 | 0.139794 | ||||||||
\(881\) | −39.8258 | −1.34176 | −0.670882 | − | 0.741564i | \(-0.734084\pi\) | ||||
−0.670882 | + | 0.741564i | \(0.734084\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.23215 | 0.209729 | 0.104864 | − | 0.994487i | \(-0.466559\pi\) | ||||
0.104864 | + | 0.994487i | \(0.466559\pi\) | |||||||
\(884\) | −67.9165 | −2.28428 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.1943 | 0.544059 | ||||||||
\(887\) | −1.08225 | −0.0363383 | −0.0181691 | − | 0.999835i | \(-0.505784\pi\) | ||||
−0.0181691 | + | 0.999835i | \(0.505784\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −78.2128 | −2.62317 | ||||||||
\(890\) | −8.96741 | −0.300588 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 66.2313 | 2.21759 | ||||||||
\(893\) | −44.2672 | −1.48135 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.44193 | −0.0816247 | ||||||||
\(896\) | 105.174 | 3.51361 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.7772 | 0.459750 | ||||||||
\(899\) | −1.54451 | −0.0515123 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 77.9591 | 2.59720 | ||||||||
\(902\) | 15.5784 | 0.518703 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 58.2494 | 1.93735 | ||||||||
\(905\) | −5.78179 | −0.192193 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.9237 | 0.927192 | 0.463596 | − | 0.886047i | \(-0.346559\pi\) | ||||
0.463596 | + | 0.886047i | \(0.346559\pi\) | |||||||
\(908\) | 21.9335 | 0.727888 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.90170 | −0.295088 | ||||||||
\(911\) | 6.32742 | 0.209637 | 0.104818 | − | 0.994491i | \(-0.466574\pi\) | ||||
0.104818 | + | 0.994491i | \(0.466574\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.4417 | 0.841998 | ||||||||
\(914\) | −44.6620 | −1.47729 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −52.8349 | −1.74572 | ||||||||
\(917\) | −20.4805 | −0.676324 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.729760 | −0.0240726 | −0.0120363 | − | 0.999928i | \(-0.503831\pi\) | ||||
−0.0120363 | + | 0.999928i | \(0.503831\pi\) | |||||||
\(920\) | −1.25229 | −0.0412867 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −71.3889 | −2.35107 | ||||||||
\(923\) | −10.7630 | −0.354268 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.12893 | 0.201518 | ||||||||
\(926\) | 77.7368 | 2.55459 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.15424 | −0.0378898 | ||||||||
\(929\) | 16.4689 | 0.540327 | 0.270164 | − | 0.962814i | \(-0.412922\pi\) | ||||
0.270164 | + | 0.962814i | \(0.412922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −155.968 | −5.11164 | ||||||||
\(932\) | 32.2526 | 1.05647 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.2658 | −1.12121 | ||||||||
\(935\) | −8.57374 | −0.280391 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.5792 | −0.476283 | −0.238142 | − | 0.971230i | \(-0.576538\pi\) | ||||
−0.238142 | + | 0.971230i | \(0.576538\pi\) | |||||||
\(938\) | −127.590 | −4.16596 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.95257 | 0.194151 | ||||||||
\(941\) | 48.4759 | 1.58027 | 0.790134 | − | 0.612934i | \(-0.210011\pi\) | ||||
0.790134 | + | 0.612934i | \(0.210011\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.39786 | −0.0455204 | ||||||||
\(944\) | −23.9947 | −0.780961 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.66091 | −0.281591 | ||||||||
\(947\) | 18.1893 | 0.591074 | 0.295537 | − | 0.955331i | \(-0.404501\pi\) | ||||
0.295537 | + | 0.955331i | \(0.404501\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.5883 | −0.863091 | ||||||||
\(950\) | 94.7180 | 3.07306 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 159.256 | 5.16151 | ||||||||
\(953\) | 18.1827 | 0.588995 | 0.294497 | − | 0.955652i | \(-0.404848\pi\) | ||||
0.294497 | + | 0.955652i | \(0.404848\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.50913 | 0.0811936 | ||||||||
\(956\) | −41.3518 | −1.33741 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.4521 | −0.693085 | ||||||||
\(959\) | 45.7707 | 1.47801 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6145 | −0.923048 | ||||||||
\(962\) | −7.79824 | −0.251425 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −74.8231 | −2.40989 | ||||||||
\(965\) | −0.390685 | −0.0125766 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.0895 | −0.613876 | −0.306938 | − | 0.951729i | \(-0.599304\pi\) | ||||
−0.306938 | + | 0.951729i | \(0.599304\pi\) | |||||||
\(968\) | 46.1114 | 1.48208 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.27757 | 0.0731285 | ||||||||
\(971\) | −30.5549 | −0.980554 | −0.490277 | − | 0.871567i | \(-0.663104\pi\) | ||||
−0.490277 | + | 0.871567i | \(0.663104\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −88.6837 | −2.84307 | ||||||||
\(974\) | 15.2816 | 0.489655 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.21751 | 0.134999 | ||||||||
\(977\) | −33.4036 | −1.06868 | −0.534338 | − | 0.845271i | \(-0.679439\pi\) | ||||
−0.534338 | + | 0.845271i | \(0.679439\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −61.7943 | −1.97495 | ||||||||
\(980\) | 20.9728 | 0.669953 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 54.0135 | 1.72364 | ||||||||
\(983\) | −17.9500 | −0.572517 | −0.286259 | − | 0.958152i | \(-0.592412\pi\) | ||||
−0.286259 | + | 0.958152i | \(0.592412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.822570 | 0.0262093 | ||||||||
\(986\) | −16.4314 | −0.523281 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −79.5045 | −2.52937 | ||||||||
\(989\) | 0.777148 | 0.0247119 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.9973 | −1.36586 | −0.682928 | − | 0.730486i | \(-0.739294\pi\) | ||||
−0.682928 | + | 0.730486i | \(0.739294\pi\) | |||||||
\(992\) | 1.78273 | 0.0566018 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 52.1266 | 1.65336 | ||||||||
\(995\) | 3.92195 | 0.124334 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.34146 | −0.232506 | −0.116253 | − | 0.993220i | \(-0.537088\pi\) | ||||
−0.116253 | + | 0.993220i | \(0.537088\pi\) | |||||||
\(998\) | −13.7326 | −0.434698 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.q.1.15 | 16 | ||
3.2 | odd | 2 | 667.2.a.d.1.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.d.1.2 | ✓ | 16 | 3.2 | odd | 2 | ||
6003.2.a.q.1.15 | 16 | 1.1 | even | 1 | trivial |