Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2667,2,Mod(1,2667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2667, 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("2667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2667 = 3 \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2667.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: | \(21.2961022191\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 10 x^{11} + 53 x^{10} + 19 x^{9} - 242 x^{8} + 61 x^{7} + 467 x^{6} - 211 x^{5} + \cdots - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.423652\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2667.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.423652 | −0.299567 | −0.149784 | − | 0.988719i | \(-0.547858\pi\) | ||||
−0.149784 | + | 0.988719i | \(0.547858\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.82052 | −0.910259 | ||||||||
\(5\) | 2.66196 | 1.19046 | 0.595232 | − | 0.803554i | \(-0.297060\pi\) | ||||
0.595232 | + | 0.803554i | \(0.297060\pi\) | |||||||
\(6\) | 0.423652 | 0.172955 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.61857 | 0.572251 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.12774 | −0.356624 | ||||||||
\(11\) | 3.97552 | 1.19866 | 0.599332 | − | 0.800500i | \(-0.295433\pi\) | ||||
0.599332 | + | 0.800500i | \(0.295433\pi\) | |||||||
\(12\) | 1.82052 | 0.525539 | ||||||||
\(13\) | 4.95058 | 1.37304 | 0.686522 | − | 0.727109i | \(-0.259136\pi\) | ||||
0.686522 | + | 0.727109i | \(0.259136\pi\) | |||||||
\(14\) | −0.423652 | −0.113226 | ||||||||
\(15\) | −2.66196 | −0.687315 | ||||||||
\(16\) | 2.95533 | 0.738832 | ||||||||
\(17\) | 5.63178 | 1.36591 | 0.682954 | − | 0.730462i | \(-0.260695\pi\) | ||||
0.682954 | + | 0.730462i | \(0.260695\pi\) | |||||||
\(18\) | −0.423652 | −0.0998558 | ||||||||
\(19\) | 3.72073 | 0.853595 | 0.426797 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426797 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(20\) | −4.84615 | −1.08363 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −1.68424 | −0.359081 | ||||||||
\(23\) | −4.13626 | −0.862469 | −0.431235 | − | 0.902240i | \(-0.641922\pi\) | ||||
−0.431235 | + | 0.902240i | \(0.641922\pi\) | |||||||
\(24\) | −1.61857 | −0.330389 | ||||||||
\(25\) | 2.08603 | 0.417205 | ||||||||
\(26\) | −2.09732 | −0.411319 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.82052 | −0.344046 | ||||||||
\(29\) | 7.04468 | 1.30816 | 0.654082 | − | 0.756423i | \(-0.273055\pi\) | ||||
0.654082 | + | 0.756423i | \(0.273055\pi\) | |||||||
\(30\) | 1.12774 | 0.205897 | ||||||||
\(31\) | −2.57265 | −0.462062 | −0.231031 | − | 0.972946i | \(-0.574210\pi\) | ||||
−0.231031 | + | 0.972946i | \(0.574210\pi\) | |||||||
\(32\) | −4.48917 | −0.793581 | ||||||||
\(33\) | −3.97552 | −0.692049 | ||||||||
\(34\) | −2.38592 | −0.409181 | ||||||||
\(35\) | 2.66196 | 0.449953 | ||||||||
\(36\) | −1.82052 | −0.303420 | ||||||||
\(37\) | 2.65212 | 0.436006 | 0.218003 | − | 0.975948i | \(-0.430046\pi\) | ||||
0.218003 | + | 0.975948i | \(0.430046\pi\) | |||||||
\(38\) | −1.57630 | −0.255709 | ||||||||
\(39\) | −4.95058 | −0.792728 | ||||||||
\(40\) | 4.30857 | 0.681245 | ||||||||
\(41\) | 2.05217 | 0.320494 | 0.160247 | − | 0.987077i | \(-0.448771\pi\) | ||||
0.160247 | + | 0.987077i | \(0.448771\pi\) | |||||||
\(42\) | 0.423652 | 0.0653709 | ||||||||
\(43\) | 4.03075 | 0.614683 | 0.307342 | − | 0.951599i | \(-0.400561\pi\) | ||||
0.307342 | + | 0.951599i | \(0.400561\pi\) | |||||||
\(44\) | −7.23751 | −1.09110 | ||||||||
\(45\) | 2.66196 | 0.396821 | ||||||||
\(46\) | 1.75233 | 0.258368 | ||||||||
\(47\) | −7.52083 | −1.09703 | −0.548513 | − | 0.836142i | \(-0.684806\pi\) | ||||
−0.548513 | + | 0.836142i | \(0.684806\pi\) | |||||||
\(48\) | −2.95533 | −0.426565 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.883750 | −0.124981 | ||||||||
\(51\) | −5.63178 | −0.788607 | ||||||||
\(52\) | −9.01263 | −1.24983 | ||||||||
\(53\) | 0.214398 | 0.0294499 | 0.0147249 | − | 0.999892i | \(-0.495313\pi\) | ||||
0.0147249 | + | 0.999892i | \(0.495313\pi\) | |||||||
\(54\) | 0.423652 | 0.0576517 | ||||||||
\(55\) | 10.5827 | 1.42697 | ||||||||
\(56\) | 1.61857 | 0.216291 | ||||||||
\(57\) | −3.72073 | −0.492823 | ||||||||
\(58\) | −2.98449 | −0.391883 | ||||||||
\(59\) | −12.5754 | −1.63718 | −0.818591 | − | 0.574376i | \(-0.805245\pi\) | ||||
−0.818591 | + | 0.574376i | \(0.805245\pi\) | |||||||
\(60\) | 4.84615 | 0.625635 | ||||||||
\(61\) | −2.37431 | −0.303999 | −0.151999 | − | 0.988381i | \(-0.548571\pi\) | ||||
−0.151999 | + | 0.988381i | \(0.548571\pi\) | |||||||
\(62\) | 1.08991 | 0.138419 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −4.00881 | −0.501101 | ||||||||
\(65\) | 13.1783 | 1.63456 | ||||||||
\(66\) | 1.68424 | 0.207315 | ||||||||
\(67\) | 4.26602 | 0.521177 | 0.260588 | − | 0.965450i | \(-0.416083\pi\) | ||||
0.260588 | + | 0.965450i | \(0.416083\pi\) | |||||||
\(68\) | −10.2528 | −1.24333 | ||||||||
\(69\) | 4.13626 | 0.497947 | ||||||||
\(70\) | −1.12774 | −0.134791 | ||||||||
\(71\) | −13.7119 | −1.62731 | −0.813653 | − | 0.581351i | \(-0.802524\pi\) | ||||
−0.813653 | + | 0.581351i | \(0.802524\pi\) | |||||||
\(72\) | 1.61857 | 0.190750 | ||||||||
\(73\) | −10.8892 | −1.27449 | −0.637244 | − | 0.770662i | \(-0.719926\pi\) | ||||
−0.637244 | + | 0.770662i | \(0.719926\pi\) | |||||||
\(74\) | −1.12358 | −0.130613 | ||||||||
\(75\) | −2.08603 | −0.240874 | ||||||||
\(76\) | −6.77367 | −0.776993 | ||||||||
\(77\) | 3.97552 | 0.453053 | ||||||||
\(78\) | 2.09732 | 0.237475 | ||||||||
\(79\) | 2.69299 | 0.302985 | 0.151492 | − | 0.988458i | \(-0.451592\pi\) | ||||
0.151492 | + | 0.988458i | \(0.451592\pi\) | |||||||
\(80\) | 7.86696 | 0.879553 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.869404 | −0.0960096 | ||||||||
\(83\) | 4.22143 | 0.463362 | 0.231681 | − | 0.972792i | \(-0.425577\pi\) | ||||
0.231681 | + | 0.972792i | \(0.425577\pi\) | |||||||
\(84\) | 1.82052 | 0.198635 | ||||||||
\(85\) | 14.9916 | 1.62606 | ||||||||
\(86\) | −1.70763 | −0.184139 | ||||||||
\(87\) | −7.04468 | −0.755269 | ||||||||
\(88\) | 6.43466 | 0.685937 | ||||||||
\(89\) | 4.08362 | 0.432863 | 0.216431 | − | 0.976298i | \(-0.430558\pi\) | ||||
0.216431 | + | 0.976298i | \(0.430558\pi\) | |||||||
\(90\) | −1.12774 | −0.118875 | ||||||||
\(91\) | 4.95058 | 0.518962 | ||||||||
\(92\) | 7.53014 | 0.785071 | ||||||||
\(93\) | 2.57265 | 0.266772 | ||||||||
\(94\) | 3.18621 | 0.328633 | ||||||||
\(95\) | 9.90444 | 1.01617 | ||||||||
\(96\) | 4.48917 | 0.458174 | ||||||||
\(97\) | 0.135110 | 0.0137183 | 0.00685917 | − | 0.999976i | \(-0.497817\pi\) | ||||
0.00685917 | + | 0.999976i | \(0.497817\pi\) | |||||||
\(98\) | −0.423652 | −0.0427953 | ||||||||
\(99\) | 3.97552 | 0.399555 | ||||||||
\(100\) | −3.79765 | −0.379765 | ||||||||
\(101\) | 0.725428 | 0.0721828 | 0.0360914 | − | 0.999348i | \(-0.488509\pi\) | ||||
0.0360914 | + | 0.999348i | \(0.488509\pi\) | |||||||
\(102\) | 2.38592 | 0.236241 | ||||||||
\(103\) | 14.2476 | 1.40386 | 0.701930 | − | 0.712245i | \(-0.252322\pi\) | ||||
0.701930 | + | 0.712245i | \(0.252322\pi\) | |||||||
\(104\) | 8.01287 | 0.785726 | ||||||||
\(105\) | −2.66196 | −0.259781 | ||||||||
\(106\) | −0.0908303 | −0.00882222 | ||||||||
\(107\) | −18.0628 | −1.74620 | −0.873098 | − | 0.487544i | \(-0.837893\pi\) | ||||
−0.873098 | + | 0.487544i | \(0.837893\pi\) | |||||||
\(108\) | 1.82052 | 0.175180 | ||||||||
\(109\) | −7.40505 | −0.709276 | −0.354638 | − | 0.935004i | \(-0.615396\pi\) | ||||
−0.354638 | + | 0.935004i | \(0.615396\pi\) | |||||||
\(110\) | −4.48337 | −0.427473 | ||||||||
\(111\) | −2.65212 | −0.251728 | ||||||||
\(112\) | 2.95533 | 0.279252 | ||||||||
\(113\) | 18.6046 | 1.75017 | 0.875087 | − | 0.483966i | \(-0.160804\pi\) | ||||
0.875087 | + | 0.483966i | \(0.160804\pi\) | |||||||
\(114\) | 1.57630 | 0.147634 | ||||||||
\(115\) | −11.0105 | −1.02674 | ||||||||
\(116\) | −12.8250 | −1.19077 | ||||||||
\(117\) | 4.95058 | 0.457682 | ||||||||
\(118\) | 5.32761 | 0.490446 | ||||||||
\(119\) | 5.63178 | 0.516264 | ||||||||
\(120\) | −4.30857 | −0.393317 | ||||||||
\(121\) | 4.80477 | 0.436797 | ||||||||
\(122\) | 1.00588 | 0.0910681 | ||||||||
\(123\) | −2.05217 | −0.185038 | ||||||||
\(124\) | 4.68357 | 0.420597 | ||||||||
\(125\) | −7.75688 | −0.693796 | ||||||||
\(126\) | −0.423652 | −0.0377419 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 10.6767 | 0.943694 | ||||||||
\(129\) | −4.03075 | −0.354888 | ||||||||
\(130\) | −5.58299 | −0.489661 | ||||||||
\(131\) | 11.7101 | 1.02312 | 0.511559 | − | 0.859248i | \(-0.329068\pi\) | ||||
0.511559 | + | 0.859248i | \(0.329068\pi\) | |||||||
\(132\) | 7.23751 | 0.629945 | ||||||||
\(133\) | 3.72073 | 0.322629 | ||||||||
\(134\) | −1.80731 | −0.156127 | ||||||||
\(135\) | −2.66196 | −0.229105 | ||||||||
\(136\) | 9.11543 | 0.781642 | ||||||||
\(137\) | 2.39147 | 0.204317 | 0.102159 | − | 0.994768i | \(-0.467425\pi\) | ||||
0.102159 | + | 0.994768i | \(0.467425\pi\) | |||||||
\(138\) | −1.75233 | −0.149169 | ||||||||
\(139\) | −2.14800 | −0.182191 | −0.0910953 | − | 0.995842i | \(-0.529037\pi\) | ||||
−0.0910953 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(140\) | −4.84615 | −0.409574 | ||||||||
\(141\) | 7.52083 | 0.633368 | ||||||||
\(142\) | 5.80909 | 0.487488 | ||||||||
\(143\) | 19.6811 | 1.64582 | ||||||||
\(144\) | 2.95533 | 0.246277 | ||||||||
\(145\) | 18.7527 | 1.55732 | ||||||||
\(146\) | 4.61324 | 0.381795 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −4.82823 | −0.396878 | ||||||||
\(149\) | −2.05953 | −0.168723 | −0.0843615 | − | 0.996435i | \(-0.526885\pi\) | ||||
−0.0843615 | + | 0.996435i | \(0.526885\pi\) | |||||||
\(150\) | 0.883750 | 0.0721579 | ||||||||
\(151\) | 12.3000 | 1.00096 | 0.500478 | − | 0.865749i | \(-0.333157\pi\) | ||||
0.500478 | + | 0.865749i | \(0.333157\pi\) | |||||||
\(152\) | 6.02227 | 0.488471 | ||||||||
\(153\) | 5.63178 | 0.455302 | ||||||||
\(154\) | −1.68424 | −0.135720 | ||||||||
\(155\) | −6.84830 | −0.550069 | ||||||||
\(156\) | 9.01263 | 0.721588 | ||||||||
\(157\) | −19.3425 | −1.54370 | −0.771850 | − | 0.635804i | \(-0.780669\pi\) | ||||
−0.771850 | + | 0.635804i | \(0.780669\pi\) | |||||||
\(158\) | −1.14089 | −0.0907643 | ||||||||
\(159\) | −0.214398 | −0.0170029 | ||||||||
\(160\) | −11.9500 | −0.944730 | ||||||||
\(161\) | −4.13626 | −0.325983 | ||||||||
\(162\) | −0.423652 | −0.0332853 | ||||||||
\(163\) | −12.4805 | −0.977551 | −0.488775 | − | 0.872410i | \(-0.662556\pi\) | ||||
−0.488775 | + | 0.872410i | \(0.662556\pi\) | |||||||
\(164\) | −3.73601 | −0.291733 | ||||||||
\(165\) | −10.5827 | −0.823860 | ||||||||
\(166\) | −1.78842 | −0.138808 | ||||||||
\(167\) | 2.16315 | 0.167390 | 0.0836949 | − | 0.996491i | \(-0.473328\pi\) | ||||
0.0836949 | + | 0.996491i | \(0.473328\pi\) | |||||||
\(168\) | −1.61857 | −0.124875 | ||||||||
\(169\) | 11.5083 | 0.885252 | ||||||||
\(170\) | −6.35121 | −0.487115 | ||||||||
\(171\) | 3.72073 | 0.284532 | ||||||||
\(172\) | −7.33805 | −0.559521 | ||||||||
\(173\) | −15.5879 | −1.18513 | −0.592563 | − | 0.805524i | \(-0.701884\pi\) | ||||
−0.592563 | + | 0.805524i | \(0.701884\pi\) | |||||||
\(174\) | 2.98449 | 0.226254 | ||||||||
\(175\) | 2.08603 | 0.157689 | ||||||||
\(176\) | 11.7490 | 0.885612 | ||||||||
\(177\) | 12.5754 | 0.945228 | ||||||||
\(178\) | −1.73003 | −0.129671 | ||||||||
\(179\) | −11.1995 | −0.837090 | −0.418545 | − | 0.908196i | \(-0.637460\pi\) | ||||
−0.418545 | + | 0.908196i | \(0.637460\pi\) | |||||||
\(180\) | −4.84615 | −0.361210 | ||||||||
\(181\) | −6.72881 | −0.500148 | −0.250074 | − | 0.968227i | \(-0.580455\pi\) | ||||
−0.250074 | + | 0.968227i | \(0.580455\pi\) | |||||||
\(182\) | −2.09732 | −0.155464 | ||||||||
\(183\) | 2.37431 | 0.175514 | ||||||||
\(184\) | −6.69483 | −0.493549 | ||||||||
\(185\) | 7.05983 | 0.519049 | ||||||||
\(186\) | −1.08991 | −0.0799161 | ||||||||
\(187\) | 22.3893 | 1.63726 | ||||||||
\(188\) | 13.6918 | 0.998578 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −4.19604 | −0.304413 | ||||||||
\(191\) | 23.3444 | 1.68914 | 0.844570 | − | 0.535446i | \(-0.179856\pi\) | ||||
0.844570 | + | 0.535446i | \(0.179856\pi\) | |||||||
\(192\) | 4.00881 | 0.289311 | ||||||||
\(193\) | 2.13924 | 0.153986 | 0.0769928 | − | 0.997032i | \(-0.475468\pi\) | ||||
0.0769928 | + | 0.997032i | \(0.475468\pi\) | |||||||
\(194\) | −0.0572397 | −0.00410957 | ||||||||
\(195\) | −13.1783 | −0.943714 | ||||||||
\(196\) | −1.82052 | −0.130037 | ||||||||
\(197\) | 7.01767 | 0.499988 | 0.249994 | − | 0.968247i | \(-0.419571\pi\) | ||||
0.249994 | + | 0.968247i | \(0.419571\pi\) | |||||||
\(198\) | −1.68424 | −0.119694 | ||||||||
\(199\) | −18.7133 | −1.32655 | −0.663277 | − | 0.748374i | \(-0.730835\pi\) | ||||
−0.663277 | + | 0.748374i | \(0.730835\pi\) | |||||||
\(200\) | 3.37638 | 0.238746 | ||||||||
\(201\) | −4.26602 | −0.300902 | ||||||||
\(202\) | −0.307329 | −0.0216236 | ||||||||
\(203\) | 7.04468 | 0.494440 | ||||||||
\(204\) | 10.2528 | 0.717837 | ||||||||
\(205\) | 5.46278 | 0.381537 | ||||||||
\(206\) | −6.03604 | −0.420551 | ||||||||
\(207\) | −4.13626 | −0.287490 | ||||||||
\(208\) | 14.6306 | 1.01445 | ||||||||
\(209\) | 14.7919 | 1.02317 | ||||||||
\(210\) | 1.12774 | 0.0778218 | ||||||||
\(211\) | −11.4113 | −0.785585 | −0.392792 | − | 0.919627i | \(-0.628491\pi\) | ||||
−0.392792 | + | 0.919627i | \(0.628491\pi\) | |||||||
\(212\) | −0.390316 | −0.0268070 | ||||||||
\(213\) | 13.7119 | 0.939526 | ||||||||
\(214\) | 7.65234 | 0.523103 | ||||||||
\(215\) | 10.7297 | 0.731759 | ||||||||
\(216\) | −1.61857 | −0.110130 | ||||||||
\(217\) | −2.57265 | −0.174643 | ||||||||
\(218\) | 3.13717 | 0.212476 | ||||||||
\(219\) | 10.8892 | 0.735826 | ||||||||
\(220\) | −19.2660 | −1.29891 | ||||||||
\(221\) | 27.8806 | 1.87545 | ||||||||
\(222\) | 1.12358 | 0.0754095 | ||||||||
\(223\) | 12.7903 | 0.856505 | 0.428252 | − | 0.903659i | \(-0.359129\pi\) | ||||
0.428252 | + | 0.903659i | \(0.359129\pi\) | |||||||
\(224\) | −4.48917 | −0.299945 | ||||||||
\(225\) | 2.08603 | 0.139068 | ||||||||
\(226\) | −7.88188 | −0.524295 | ||||||||
\(227\) | −23.6675 | −1.57087 | −0.785434 | − | 0.618945i | \(-0.787560\pi\) | ||||
−0.785434 | + | 0.618945i | \(0.787560\pi\) | |||||||
\(228\) | 6.77367 | 0.448597 | ||||||||
\(229\) | −16.7152 | −1.10457 | −0.552287 | − | 0.833654i | \(-0.686245\pi\) | ||||
−0.552287 | + | 0.833654i | \(0.686245\pi\) | |||||||
\(230\) | 4.66464 | 0.307577 | ||||||||
\(231\) | −3.97552 | −0.261570 | ||||||||
\(232\) | 11.4023 | 0.748599 | ||||||||
\(233\) | 27.5835 | 1.80706 | 0.903528 | − | 0.428529i | \(-0.140968\pi\) | ||||
0.903528 | + | 0.428529i | \(0.140968\pi\) | |||||||
\(234\) | −2.09732 | −0.137106 | ||||||||
\(235\) | −20.0201 | −1.30597 | ||||||||
\(236\) | 22.8938 | 1.49026 | ||||||||
\(237\) | −2.69299 | −0.174928 | ||||||||
\(238\) | −2.38592 | −0.154656 | ||||||||
\(239\) | −6.10076 | −0.394625 | −0.197313 | − | 0.980341i | \(-0.563221\pi\) | ||||
−0.197313 | + | 0.980341i | \(0.563221\pi\) | |||||||
\(240\) | −7.86696 | −0.507810 | ||||||||
\(241\) | −16.4442 | −1.05926 | −0.529632 | − | 0.848228i | \(-0.677670\pi\) | ||||
−0.529632 | + | 0.848228i | \(0.677670\pi\) | |||||||
\(242\) | −2.03555 | −0.130850 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.32247 | 0.276718 | ||||||||
\(245\) | 2.66196 | 0.170066 | ||||||||
\(246\) | 0.869404 | 0.0554312 | ||||||||
\(247\) | 18.4198 | 1.17202 | ||||||||
\(248\) | −4.16402 | −0.264416 | ||||||||
\(249\) | −4.22143 | −0.267522 | ||||||||
\(250\) | 3.28622 | 0.207839 | ||||||||
\(251\) | 31.2771 | 1.97420 | 0.987098 | − | 0.160118i | \(-0.0511875\pi\) | ||||
0.987098 | + | 0.160118i | \(0.0511875\pi\) | |||||||
\(252\) | −1.82052 | −0.114682 | ||||||||
\(253\) | −16.4438 | −1.03381 | ||||||||
\(254\) | 0.423652 | 0.0265823 | ||||||||
\(255\) | −14.9916 | −0.938808 | ||||||||
\(256\) | 3.49442 | 0.218401 | ||||||||
\(257\) | 15.4673 | 0.964824 | 0.482412 | − | 0.875944i | \(-0.339761\pi\) | ||||
0.482412 | + | 0.875944i | \(0.339761\pi\) | |||||||
\(258\) | 1.70763 | 0.106313 | ||||||||
\(259\) | 2.65212 | 0.164795 | ||||||||
\(260\) | −23.9913 | −1.48787 | ||||||||
\(261\) | 7.04468 | 0.436055 | ||||||||
\(262\) | −4.96102 | −0.306493 | ||||||||
\(263\) | −5.45766 | −0.336534 | −0.168267 | − | 0.985741i | \(-0.553817\pi\) | ||||
−0.168267 | + | 0.985741i | \(0.553817\pi\) | |||||||
\(264\) | −6.43466 | −0.396026 | ||||||||
\(265\) | 0.570720 | 0.0350590 | ||||||||
\(266\) | −1.57630 | −0.0966489 | ||||||||
\(267\) | −4.08362 | −0.249913 | ||||||||
\(268\) | −7.76636 | −0.474406 | ||||||||
\(269\) | 24.3057 | 1.48194 | 0.740971 | − | 0.671536i | \(-0.234365\pi\) | ||||
0.740971 | + | 0.671536i | \(0.234365\pi\) | |||||||
\(270\) | 1.12774 | 0.0686323 | ||||||||
\(271\) | 26.4187 | 1.60482 | 0.802410 | − | 0.596774i | \(-0.203551\pi\) | ||||
0.802410 | + | 0.596774i | \(0.203551\pi\) | |||||||
\(272\) | 16.6438 | 1.00918 | ||||||||
\(273\) | −4.95058 | −0.299623 | ||||||||
\(274\) | −1.01315 | −0.0612068 | ||||||||
\(275\) | 8.29304 | 0.500089 | ||||||||
\(276\) | −7.53014 | −0.453261 | ||||||||
\(277\) | −13.7390 | −0.825494 | −0.412747 | − | 0.910846i | \(-0.635431\pi\) | ||||
−0.412747 | + | 0.910846i | \(0.635431\pi\) | |||||||
\(278\) | 0.910003 | 0.0545784 | ||||||||
\(279\) | −2.57265 | −0.154021 | ||||||||
\(280\) | 4.30857 | 0.257486 | ||||||||
\(281\) | −5.06765 | −0.302311 | −0.151155 | − | 0.988510i | \(-0.548299\pi\) | ||||
−0.151155 | + | 0.988510i | \(0.548299\pi\) | |||||||
\(282\) | −3.18621 | −0.189736 | ||||||||
\(283\) | −27.6362 | −1.64280 | −0.821400 | − | 0.570353i | \(-0.806806\pi\) | ||||
−0.821400 | + | 0.570353i | \(0.806806\pi\) | |||||||
\(284\) | 24.9628 | 1.48127 | ||||||||
\(285\) | −9.90444 | −0.586688 | ||||||||
\(286\) | −8.33796 | −0.493034 | ||||||||
\(287\) | 2.05217 | 0.121135 | ||||||||
\(288\) | −4.48917 | −0.264527 | ||||||||
\(289\) | 14.7169 | 0.865702 | ||||||||
\(290\) | −7.94460 | −0.466523 | ||||||||
\(291\) | −0.135110 | −0.00792029 | ||||||||
\(292\) | 19.8240 | 1.16011 | ||||||||
\(293\) | 26.9116 | 1.57219 | 0.786097 | − | 0.618104i | \(-0.212099\pi\) | ||||
0.786097 | + | 0.618104i | \(0.212099\pi\) | |||||||
\(294\) | 0.423652 | 0.0247079 | ||||||||
\(295\) | −33.4753 | −1.94901 | ||||||||
\(296\) | 4.29264 | 0.249505 | ||||||||
\(297\) | −3.97552 | −0.230683 | ||||||||
\(298\) | 0.872522 | 0.0505439 | ||||||||
\(299\) | −20.4769 | −1.18421 | ||||||||
\(300\) | 3.79765 | 0.219258 | ||||||||
\(301\) | 4.03075 | 0.232328 | ||||||||
\(302\) | −5.21091 | −0.299854 | ||||||||
\(303\) | −0.725428 | −0.0416747 | ||||||||
\(304\) | 10.9960 | 0.630663 | ||||||||
\(305\) | −6.32031 | −0.361900 | ||||||||
\(306\) | −2.38592 | −0.136394 | ||||||||
\(307\) | −10.2148 | −0.582989 | −0.291494 | − | 0.956573i | \(-0.594152\pi\) | ||||
−0.291494 | + | 0.956573i | \(0.594152\pi\) | |||||||
\(308\) | −7.23751 | −0.412395 | ||||||||
\(309\) | −14.2476 | −0.810519 | ||||||||
\(310\) | 2.90130 | 0.164783 | ||||||||
\(311\) | 9.69180 | 0.549572 | 0.274786 | − | 0.961505i | \(-0.411393\pi\) | ||||
0.274786 | + | 0.961505i | \(0.411393\pi\) | |||||||
\(312\) | −8.01287 | −0.453639 | ||||||||
\(313\) | 13.6848 | 0.773509 | 0.386755 | − | 0.922183i | \(-0.373596\pi\) | ||||
0.386755 | + | 0.922183i | \(0.373596\pi\) | |||||||
\(314\) | 8.19450 | 0.462442 | ||||||||
\(315\) | 2.66196 | 0.149984 | ||||||||
\(316\) | −4.90263 | −0.275795 | ||||||||
\(317\) | 14.1092 | 0.792451 | 0.396226 | − | 0.918153i | \(-0.370320\pi\) | ||||
0.396226 | + | 0.918153i | \(0.370320\pi\) | |||||||
\(318\) | 0.0908303 | 0.00509351 | ||||||||
\(319\) | 28.0063 | 1.56805 | ||||||||
\(320\) | −10.6713 | −0.596543 | ||||||||
\(321\) | 18.0628 | 1.00817 | ||||||||
\(322\) | 1.75233 | 0.0976538 | ||||||||
\(323\) | 20.9544 | 1.16593 | ||||||||
\(324\) | −1.82052 | −0.101140 | ||||||||
\(325\) | 10.3271 | 0.572842 | ||||||||
\(326\) | 5.28740 | 0.292842 | ||||||||
\(327\) | 7.40505 | 0.409500 | ||||||||
\(328\) | 3.32157 | 0.183403 | ||||||||
\(329\) | −7.52083 | −0.414637 | ||||||||
\(330\) | 4.48337 | 0.246802 | ||||||||
\(331\) | 1.11891 | 0.0615011 | 0.0307505 | − | 0.999527i | \(-0.490210\pi\) | ||||
0.0307505 | + | 0.999527i | \(0.490210\pi\) | |||||||
\(332\) | −7.68520 | −0.421780 | ||||||||
\(333\) | 2.65212 | 0.145335 | ||||||||
\(334\) | −0.916424 | −0.0501445 | ||||||||
\(335\) | 11.3560 | 0.620442 | ||||||||
\(336\) | −2.95533 | −0.161226 | ||||||||
\(337\) | −23.4974 | −1.27999 | −0.639993 | − | 0.768381i | \(-0.721063\pi\) | ||||
−0.639993 | + | 0.768381i | \(0.721063\pi\) | |||||||
\(338\) | −4.87550 | −0.265192 | ||||||||
\(339\) | −18.6046 | −1.01046 | ||||||||
\(340\) | −27.2924 | −1.48014 | ||||||||
\(341\) | −10.2276 | −0.553858 | ||||||||
\(342\) | −1.57630 | −0.0852364 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 6.52405 | 0.351753 | ||||||||
\(345\) | 11.0105 | 0.592788 | ||||||||
\(346\) | 6.60384 | 0.355025 | ||||||||
\(347\) | 6.87719 | 0.369187 | 0.184593 | − | 0.982815i | \(-0.440903\pi\) | ||||
0.184593 | + | 0.982815i | \(0.440903\pi\) | |||||||
\(348\) | 12.8250 | 0.687491 | ||||||||
\(349\) | −3.13512 | −0.167819 | −0.0839094 | − | 0.996473i | \(-0.526741\pi\) | ||||
−0.0839094 | + | 0.996473i | \(0.526741\pi\) | |||||||
\(350\) | −0.883750 | −0.0472384 | ||||||||
\(351\) | −4.95058 | −0.264243 | ||||||||
\(352\) | −17.8468 | −0.951238 | ||||||||
\(353\) | −29.3356 | −1.56138 | −0.780689 | − | 0.624920i | \(-0.785131\pi\) | ||||
−0.780689 | + | 0.624920i | \(0.785131\pi\) | |||||||
\(354\) | −5.32761 | −0.283159 | ||||||||
\(355\) | −36.5006 | −1.93725 | ||||||||
\(356\) | −7.43430 | −0.394017 | ||||||||
\(357\) | −5.63178 | −0.298065 | ||||||||
\(358\) | 4.74469 | 0.250765 | ||||||||
\(359\) | −6.92912 | −0.365705 | −0.182852 | − | 0.983140i | \(-0.558533\pi\) | ||||
−0.182852 | + | 0.983140i | \(0.558533\pi\) | |||||||
\(360\) | 4.30857 | 0.227082 | ||||||||
\(361\) | −5.15614 | −0.271376 | ||||||||
\(362\) | 2.85067 | 0.149828 | ||||||||
\(363\) | −4.80477 | −0.252185 | ||||||||
\(364\) | −9.01263 | −0.472390 | ||||||||
\(365\) | −28.9867 | −1.51723 | ||||||||
\(366\) | −1.00588 | −0.0525782 | ||||||||
\(367\) | 20.4454 | 1.06724 | 0.533621 | − | 0.845724i | \(-0.320831\pi\) | ||||
0.533621 | + | 0.845724i | \(0.320831\pi\) | |||||||
\(368\) | −12.2240 | −0.637220 | ||||||||
\(369\) | 2.05217 | 0.106831 | ||||||||
\(370\) | −2.99091 | −0.155490 | ||||||||
\(371\) | 0.214398 | 0.0111310 | ||||||||
\(372\) | −4.68357 | −0.242832 | ||||||||
\(373\) | −1.24610 | −0.0645209 | −0.0322604 | − | 0.999479i | \(-0.510271\pi\) | ||||
−0.0322604 | + | 0.999479i | \(0.510271\pi\) | |||||||
\(374\) | −9.48526 | −0.490471 | ||||||||
\(375\) | 7.75688 | 0.400563 | ||||||||
\(376\) | −12.1730 | −0.627774 | ||||||||
\(377\) | 34.8753 | 1.79617 | ||||||||
\(378\) | 0.423652 | 0.0217903 | ||||||||
\(379\) | −11.8870 | −0.610592 | −0.305296 | − | 0.952258i | \(-0.598755\pi\) | ||||
−0.305296 | + | 0.952258i | \(0.598755\pi\) | |||||||
\(380\) | −18.0312 | −0.924982 | ||||||||
\(381\) | 1.00000 | 0.0512316 | ||||||||
\(382\) | −9.88989 | −0.506011 | ||||||||
\(383\) | −14.6285 | −0.747481 | −0.373741 | − | 0.927533i | \(-0.621925\pi\) | ||||
−0.373741 | + | 0.927533i | \(0.621925\pi\) | |||||||
\(384\) | −10.6767 | −0.544842 | ||||||||
\(385\) | 10.5827 | 0.539343 | ||||||||
\(386\) | −0.906292 | −0.0461290 | ||||||||
\(387\) | 4.03075 | 0.204894 | ||||||||
\(388\) | −0.245970 | −0.0124873 | ||||||||
\(389\) | −21.5646 | −1.09337 | −0.546685 | − | 0.837338i | \(-0.684110\pi\) | ||||
−0.546685 | + | 0.837338i | \(0.684110\pi\) | |||||||
\(390\) | 5.58299 | 0.282706 | ||||||||
\(391\) | −23.2945 | −1.17805 | ||||||||
\(392\) | 1.61857 | 0.0817502 | ||||||||
\(393\) | −11.7101 | −0.590698 | ||||||||
\(394\) | −2.97305 | −0.149780 | ||||||||
\(395\) | 7.16862 | 0.360693 | ||||||||
\(396\) | −7.23751 | −0.363699 | ||||||||
\(397\) | 8.65271 | 0.434267 | 0.217133 | − | 0.976142i | \(-0.430329\pi\) | ||||
0.217133 | + | 0.976142i | \(0.430329\pi\) | |||||||
\(398\) | 7.92794 | 0.397392 | ||||||||
\(399\) | −3.72073 | −0.186270 | ||||||||
\(400\) | 6.16489 | 0.308245 | ||||||||
\(401\) | −25.4873 | −1.27277 | −0.636387 | − | 0.771370i | \(-0.719572\pi\) | ||||
−0.636387 | + | 0.771370i | \(0.719572\pi\) | |||||||
\(402\) | 1.80731 | 0.0901402 | ||||||||
\(403\) | −12.7361 | −0.634432 | ||||||||
\(404\) | −1.32065 | −0.0657050 | ||||||||
\(405\) | 2.66196 | 0.132274 | ||||||||
\(406\) | −2.98449 | −0.148118 | ||||||||
\(407\) | 10.5436 | 0.522625 | ||||||||
\(408\) | −9.11543 | −0.451281 | ||||||||
\(409\) | 38.0003 | 1.87900 | 0.939498 | − | 0.342555i | \(-0.111292\pi\) | ||||
0.939498 | + | 0.342555i | \(0.111292\pi\) | |||||||
\(410\) | −2.31432 | −0.114296 | ||||||||
\(411\) | −2.39147 | −0.117963 | ||||||||
\(412\) | −25.9381 | −1.27788 | ||||||||
\(413\) | −12.5754 | −0.618797 | ||||||||
\(414\) | 1.75233 | 0.0861225 | ||||||||
\(415\) | 11.2373 | 0.551616 | ||||||||
\(416\) | −22.2240 | −1.08962 | ||||||||
\(417\) | 2.14800 | 0.105188 | ||||||||
\(418\) | −6.26660 | −0.306509 | ||||||||
\(419\) | −4.34686 | −0.212358 | −0.106179 | − | 0.994347i | \(-0.533862\pi\) | ||||
−0.106179 | + | 0.994347i | \(0.533862\pi\) | |||||||
\(420\) | 4.84615 | 0.236468 | ||||||||
\(421\) | 29.4508 | 1.43535 | 0.717673 | − | 0.696380i | \(-0.245207\pi\) | ||||
0.717673 | + | 0.696380i | \(0.245207\pi\) | |||||||
\(422\) | 4.83441 | 0.235335 | ||||||||
\(423\) | −7.52083 | −0.365675 | ||||||||
\(424\) | 0.347019 | 0.0168527 | ||||||||
\(425\) | 11.7480 | 0.569864 | ||||||||
\(426\) | −5.80909 | −0.281451 | ||||||||
\(427\) | −2.37431 | −0.114901 | ||||||||
\(428\) | 32.8837 | 1.58949 | ||||||||
\(429\) | −19.6811 | −0.950215 | ||||||||
\(430\) | −4.54565 | −0.219211 | ||||||||
\(431\) | 29.6562 | 1.42849 | 0.714245 | − | 0.699895i | \(-0.246770\pi\) | ||||
0.714245 | + | 0.699895i | \(0.246770\pi\) | |||||||
\(432\) | −2.95533 | −0.142188 | ||||||||
\(433\) | −9.59705 | −0.461205 | −0.230602 | − | 0.973048i | \(-0.574070\pi\) | ||||
−0.230602 | + | 0.973048i | \(0.574070\pi\) | |||||||
\(434\) | 1.08991 | 0.0523174 | ||||||||
\(435\) | −18.7527 | −0.899121 | ||||||||
\(436\) | 13.4810 | 0.645625 | ||||||||
\(437\) | −15.3899 | −0.736199 | ||||||||
\(438\) | −4.61324 | −0.220429 | ||||||||
\(439\) | −29.8729 | −1.42576 | −0.712878 | − | 0.701288i | \(-0.752609\pi\) | ||||
−0.712878 | + | 0.701288i | \(0.752609\pi\) | |||||||
\(440\) | 17.1288 | 0.816584 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −11.8117 | −0.561824 | ||||||||
\(443\) | 1.94573 | 0.0924444 | 0.0462222 | − | 0.998931i | \(-0.485282\pi\) | ||||
0.0462222 | + | 0.998931i | \(0.485282\pi\) | |||||||
\(444\) | 4.82823 | 0.229138 | ||||||||
\(445\) | 10.8704 | 0.515308 | ||||||||
\(446\) | −5.41865 | −0.256581 | ||||||||
\(447\) | 2.05953 | 0.0974122 | ||||||||
\(448\) | −4.00881 | −0.189398 | ||||||||
\(449\) | −17.6859 | −0.834650 | −0.417325 | − | 0.908757i | \(-0.637032\pi\) | ||||
−0.417325 | + | 0.908757i | \(0.637032\pi\) | |||||||
\(450\) | −0.883750 | −0.0416604 | ||||||||
\(451\) | 8.15843 | 0.384165 | ||||||||
\(452\) | −33.8700 | −1.59311 | ||||||||
\(453\) | −12.3000 | −0.577903 | ||||||||
\(454\) | 10.0268 | 0.470581 | ||||||||
\(455\) | 13.1783 | 0.617806 | ||||||||
\(456\) | −6.02227 | −0.282019 | ||||||||
\(457\) | −38.7242 | −1.81144 | −0.905721 | − | 0.423874i | \(-0.860670\pi\) | ||||
−0.905721 | + | 0.423874i | \(0.860670\pi\) | |||||||
\(458\) | 7.08144 | 0.330894 | ||||||||
\(459\) | −5.63178 | −0.262869 | ||||||||
\(460\) | 20.0449 | 0.934599 | ||||||||
\(461\) | 2.11009 | 0.0982766 | 0.0491383 | − | 0.998792i | \(-0.484352\pi\) | ||||
0.0491383 | + | 0.998792i | \(0.484352\pi\) | |||||||
\(462\) | 1.68424 | 0.0783578 | ||||||||
\(463\) | −16.3478 | −0.759747 | −0.379873 | − | 0.925038i | \(-0.624032\pi\) | ||||
−0.379873 | + | 0.925038i | \(0.624032\pi\) | |||||||
\(464\) | 20.8193 | 0.966514 | ||||||||
\(465\) | 6.84830 | 0.317582 | ||||||||
\(466\) | −11.6858 | −0.541335 | ||||||||
\(467\) | 15.8333 | 0.732679 | 0.366340 | − | 0.930481i | \(-0.380611\pi\) | ||||
0.366340 | + | 0.930481i | \(0.380611\pi\) | |||||||
\(468\) | −9.01263 | −0.416609 | ||||||||
\(469\) | 4.26602 | 0.196986 | ||||||||
\(470\) | 8.48157 | 0.391226 | ||||||||
\(471\) | 19.3425 | 0.891256 | ||||||||
\(472\) | −20.3542 | −0.936880 | ||||||||
\(473\) | 16.0243 | 0.736799 | ||||||||
\(474\) | 1.14089 | 0.0524028 | ||||||||
\(475\) | 7.76155 | 0.356124 | ||||||||
\(476\) | −10.2528 | −0.469935 | ||||||||
\(477\) | 0.214398 | 0.00981663 | ||||||||
\(478\) | 2.58460 | 0.118217 | ||||||||
\(479\) | −22.1361 | −1.01142 | −0.505712 | − | 0.862702i | \(-0.668770\pi\) | ||||
−0.505712 | + | 0.862702i | \(0.668770\pi\) | |||||||
\(480\) | 11.9500 | 0.545440 | ||||||||
\(481\) | 13.1295 | 0.598655 | ||||||||
\(482\) | 6.96661 | 0.317321 | ||||||||
\(483\) | 4.13626 | 0.188206 | ||||||||
\(484\) | −8.74717 | −0.397599 | ||||||||
\(485\) | 0.359657 | 0.0163312 | ||||||||
\(486\) | 0.423652 | 0.0192172 | ||||||||
\(487\) | −0.348140 | −0.0157757 | −0.00788787 | − | 0.999969i | \(-0.502511\pi\) | ||||
−0.00788787 | + | 0.999969i | \(0.502511\pi\) | |||||||
\(488\) | −3.84298 | −0.173964 | ||||||||
\(489\) | 12.4805 | 0.564389 | ||||||||
\(490\) | −1.12774 | −0.0509463 | ||||||||
\(491\) | −7.28753 | −0.328882 | −0.164441 | − | 0.986387i | \(-0.552582\pi\) | ||||
−0.164441 | + | 0.986387i | \(0.552582\pi\) | |||||||
\(492\) | 3.73601 | 0.168432 | ||||||||
\(493\) | 39.6741 | 1.78683 | ||||||||
\(494\) | −7.80359 | −0.351100 | ||||||||
\(495\) | 10.5827 | 0.475656 | ||||||||
\(496\) | −7.60304 | −0.341386 | ||||||||
\(497\) | −13.7119 | −0.615064 | ||||||||
\(498\) | 1.78842 | 0.0801410 | ||||||||
\(499\) | −16.5620 | −0.741416 | −0.370708 | − | 0.928749i | \(-0.620885\pi\) | ||||
−0.370708 | + | 0.928749i | \(0.620885\pi\) | |||||||
\(500\) | 14.1215 | 0.631535 | ||||||||
\(501\) | −2.16315 | −0.0966425 | ||||||||
\(502\) | −13.2506 | −0.591404 | ||||||||
\(503\) | −19.6862 | −0.877766 | −0.438883 | − | 0.898544i | \(-0.644626\pi\) | ||||
−0.438883 | + | 0.898544i | \(0.644626\pi\) | |||||||
\(504\) | 1.61857 | 0.0720969 | ||||||||
\(505\) | 1.93106 | 0.0859310 | ||||||||
\(506\) | 6.96644 | 0.309696 | ||||||||
\(507\) | −11.5083 | −0.511100 | ||||||||
\(508\) | 1.82052 | 0.0807725 | ||||||||
\(509\) | 0.855626 | 0.0379249 | 0.0189625 | − | 0.999820i | \(-0.493964\pi\) | ||||
0.0189625 | + | 0.999820i | \(0.493964\pi\) | |||||||
\(510\) | 6.35121 | 0.281236 | ||||||||
\(511\) | −10.8892 | −0.481711 | ||||||||
\(512\) | −22.8338 | −1.00912 | ||||||||
\(513\) | −3.72073 | −0.164274 | ||||||||
\(514\) | −6.55276 | −0.289030 | ||||||||
\(515\) | 37.9266 | 1.67125 | ||||||||
\(516\) | 7.33805 | 0.323040 | ||||||||
\(517\) | −29.8992 | −1.31497 | ||||||||
\(518\) | −1.12358 | −0.0493671 | ||||||||
\(519\) | 15.5879 | 0.684233 | ||||||||
\(520\) | 21.3299 | 0.935379 | ||||||||
\(521\) | −19.7053 | −0.863303 | −0.431652 | − | 0.902040i | \(-0.642069\pi\) | ||||
−0.431652 | + | 0.902040i | \(0.642069\pi\) | |||||||
\(522\) | −2.98449 | −0.130628 | ||||||||
\(523\) | −45.5771 | −1.99295 | −0.996473 | − | 0.0839120i | \(-0.973259\pi\) | ||||
−0.996473 | + | 0.0839120i | \(0.973259\pi\) | |||||||
\(524\) | −21.3185 | −0.931303 | ||||||||
\(525\) | −2.08603 | −0.0910417 | ||||||||
\(526\) | 2.31215 | 0.100814 | ||||||||
\(527\) | −14.4886 | −0.631134 | ||||||||
\(528\) | −11.7490 | −0.511308 | ||||||||
\(529\) | −5.89137 | −0.256147 | ||||||||
\(530\) | −0.241787 | −0.0105025 | ||||||||
\(531\) | −12.5754 | −0.545728 | ||||||||
\(532\) | −6.77367 | −0.293676 | ||||||||
\(533\) | 10.1594 | 0.440053 | ||||||||
\(534\) | 1.73003 | 0.0748659 | ||||||||
\(535\) | −48.0824 | −2.07878 | ||||||||
\(536\) | 6.90485 | 0.298244 | ||||||||
\(537\) | 11.1995 | 0.483294 | ||||||||
\(538\) | −10.2971 | −0.443942 | ||||||||
\(539\) | 3.97552 | 0.171238 | ||||||||
\(540\) | 4.84615 | 0.208545 | ||||||||
\(541\) | 26.4890 | 1.13885 | 0.569426 | − | 0.822043i | \(-0.307166\pi\) | ||||
0.569426 | + | 0.822043i | \(0.307166\pi\) | |||||||
\(542\) | −11.1923 | −0.480751 | ||||||||
\(543\) | 6.72881 | 0.288761 | ||||||||
\(544\) | −25.2820 | −1.08396 | ||||||||
\(545\) | −19.7120 | −0.844367 | ||||||||
\(546\) | 2.09732 | 0.0897572 | ||||||||
\(547\) | −31.6604 | −1.35370 | −0.676850 | − | 0.736121i | \(-0.736655\pi\) | ||||
−0.676850 | + | 0.736121i | \(0.736655\pi\) | |||||||
\(548\) | −4.35372 | −0.185982 | ||||||||
\(549\) | −2.37431 | −0.101333 | ||||||||
\(550\) | −3.51337 | −0.149810 | ||||||||
\(551\) | 26.2114 | 1.11664 | ||||||||
\(552\) | 6.69483 | 0.284951 | ||||||||
\(553\) | 2.69299 | 0.114517 | ||||||||
\(554\) | 5.82054 | 0.247291 | ||||||||
\(555\) | −7.05983 | −0.299673 | ||||||||
\(556\) | 3.91047 | 0.165841 | ||||||||
\(557\) | 9.95634 | 0.421864 | 0.210932 | − | 0.977501i | \(-0.432350\pi\) | ||||
0.210932 | + | 0.977501i | \(0.432350\pi\) | |||||||
\(558\) | 1.08991 | 0.0461396 | ||||||||
\(559\) | 19.9546 | 0.843988 | ||||||||
\(560\) | 7.86696 | 0.332440 | ||||||||
\(561\) | −22.3893 | −0.945275 | ||||||||
\(562\) | 2.14692 | 0.0905624 | ||||||||
\(563\) | 13.7616 | 0.579983 | 0.289992 | − | 0.957029i | \(-0.406347\pi\) | ||||
0.289992 | + | 0.957029i | \(0.406347\pi\) | |||||||
\(564\) | −13.6918 | −0.576529 | ||||||||
\(565\) | 49.5247 | 2.08352 | ||||||||
\(566\) | 11.7081 | 0.492129 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −22.1937 | −0.931228 | ||||||||
\(569\) | −7.58374 | −0.317927 | −0.158963 | − | 0.987284i | \(-0.550815\pi\) | ||||
−0.158963 | + | 0.987284i | \(0.550815\pi\) | |||||||
\(570\) | 4.19604 | 0.175753 | ||||||||
\(571\) | 0.400150 | 0.0167458 | 0.00837288 | − | 0.999965i | \(-0.497335\pi\) | ||||
0.00837288 | + | 0.999965i | \(0.497335\pi\) | |||||||
\(572\) | −35.8299 | −1.49812 | ||||||||
\(573\) | −23.3444 | −0.975225 | ||||||||
\(574\) | −0.869404 | −0.0362882 | ||||||||
\(575\) | −8.62835 | −0.359827 | ||||||||
\(576\) | −4.00881 | −0.167034 | ||||||||
\(577\) | −18.6822 | −0.777748 | −0.388874 | − | 0.921291i | \(-0.627136\pi\) | ||||
−0.388874 | + | 0.921291i | \(0.627136\pi\) | |||||||
\(578\) | −6.23486 | −0.259336 | ||||||||
\(579\) | −2.13924 | −0.0889036 | ||||||||
\(580\) | −34.1396 | −1.41757 | ||||||||
\(581\) | 4.22143 | 0.175135 | ||||||||
\(582\) | 0.0572397 | 0.00237266 | ||||||||
\(583\) | 0.852345 | 0.0353005 | ||||||||
\(584\) | −17.6250 | −0.729327 | ||||||||
\(585\) | 13.1783 | 0.544854 | ||||||||
\(586\) | −11.4012 | −0.470978 | ||||||||
\(587\) | 35.7593 | 1.47595 | 0.737973 | − | 0.674830i | \(-0.235783\pi\) | ||||
0.737973 | + | 0.674830i | \(0.235783\pi\) | |||||||
\(588\) | 1.82052 | 0.0750769 | ||||||||
\(589\) | −9.57216 | −0.394414 | ||||||||
\(590\) | 14.1819 | 0.583859 | ||||||||
\(591\) | −7.01767 | −0.288668 | ||||||||
\(592\) | 7.83788 | 0.322135 | ||||||||
\(593\) | 27.4101 | 1.12560 | 0.562799 | − | 0.826594i | \(-0.309724\pi\) | ||||
0.562799 | + | 0.826594i | \(0.309724\pi\) | |||||||
\(594\) | 1.68424 | 0.0691051 | ||||||||
\(595\) | 14.9916 | 0.614594 | ||||||||
\(596\) | 3.74941 | 0.153582 | ||||||||
\(597\) | 18.7133 | 0.765886 | ||||||||
\(598\) | 8.67508 | 0.354750 | ||||||||
\(599\) | −13.9434 | −0.569711 | −0.284856 | − | 0.958570i | \(-0.591946\pi\) | ||||
−0.284856 | + | 0.958570i | \(0.591946\pi\) | |||||||
\(600\) | −3.37638 | −0.137840 | ||||||||
\(601\) | −26.8951 | −1.09708 | −0.548538 | − | 0.836126i | \(-0.684815\pi\) | ||||
−0.548538 | + | 0.836126i | \(0.684815\pi\) | |||||||
\(602\) | −1.70763 | −0.0695980 | ||||||||
\(603\) | 4.26602 | 0.173726 | ||||||||
\(604\) | −22.3923 | −0.911131 | ||||||||
\(605\) | 12.7901 | 0.519991 | ||||||||
\(606\) | 0.307329 | 0.0124844 | ||||||||
\(607\) | 18.7939 | 0.762819 | 0.381410 | − | 0.924406i | \(-0.375439\pi\) | ||||
0.381410 | + | 0.924406i | \(0.375439\pi\) | |||||||
\(608\) | −16.7030 | −0.677397 | ||||||||
\(609\) | −7.04468 | −0.285465 | ||||||||
\(610\) | 2.67761 | 0.108413 | ||||||||
\(611\) | −37.2325 | −1.50627 | ||||||||
\(612\) | −10.2528 | −0.414443 | ||||||||
\(613\) | 6.13877 | 0.247943 | 0.123971 | − | 0.992286i | \(-0.460437\pi\) | ||||
0.123971 | + | 0.992286i | \(0.460437\pi\) | |||||||
\(614\) | 4.32752 | 0.174644 | ||||||||
\(615\) | −5.46278 | −0.220281 | ||||||||
\(616\) | 6.43466 | 0.259260 | ||||||||
\(617\) | −16.3314 | −0.657477 | −0.328739 | − | 0.944421i | \(-0.606624\pi\) | ||||
−0.328739 | + | 0.944421i | \(0.606624\pi\) | |||||||
\(618\) | 6.03604 | 0.242805 | ||||||||
\(619\) | 18.1738 | 0.730465 | 0.365233 | − | 0.930916i | \(-0.380989\pi\) | ||||
0.365233 | + | 0.930916i | \(0.380989\pi\) | |||||||
\(620\) | 12.4675 | 0.500705 | ||||||||
\(621\) | 4.13626 | 0.165982 | ||||||||
\(622\) | −4.10595 | −0.164634 | ||||||||
\(623\) | 4.08362 | 0.163607 | ||||||||
\(624\) | −14.6306 | −0.585692 | ||||||||
\(625\) | −31.0786 | −1.24315 | ||||||||
\(626\) | −5.79759 | −0.231718 | ||||||||
\(627\) | −14.7919 | −0.590730 | ||||||||
\(628\) | 35.2134 | 1.40517 | ||||||||
\(629\) | 14.9362 | 0.595543 | ||||||||
\(630\) | −1.12774 | −0.0449304 | ||||||||
\(631\) | −22.8576 | −0.909945 | −0.454972 | − | 0.890506i | \(-0.650351\pi\) | ||||
−0.454972 | + | 0.890506i | \(0.650351\pi\) | |||||||
\(632\) | 4.35879 | 0.173383 | ||||||||
\(633\) | 11.4113 | 0.453558 | ||||||||
\(634\) | −5.97739 | −0.237393 | ||||||||
\(635\) | −2.66196 | −0.105637 | ||||||||
\(636\) | 0.390316 | 0.0154770 | ||||||||
\(637\) | 4.95058 | 0.196149 | ||||||||
\(638\) | −11.8649 | −0.469737 | ||||||||
\(639\) | −13.7119 | −0.542435 | ||||||||
\(640\) | 28.4209 | 1.12343 | ||||||||
\(641\) | 34.5503 | 1.36465 | 0.682327 | − | 0.731047i | \(-0.260968\pi\) | ||||
0.682327 | + | 0.731047i | \(0.260968\pi\) | |||||||
\(642\) | −7.65234 | −0.302014 | ||||||||
\(643\) | 4.29860 | 0.169520 | 0.0847601 | − | 0.996401i | \(-0.472988\pi\) | ||||
0.0847601 | + | 0.996401i | \(0.472988\pi\) | |||||||
\(644\) | 7.53014 | 0.296729 | ||||||||
\(645\) | −10.7297 | −0.422481 | ||||||||
\(646\) | −8.87735 | −0.349275 | ||||||||
\(647\) | −17.3258 | −0.681147 | −0.340573 | − | 0.940218i | \(-0.610621\pi\) | ||||
−0.340573 | + | 0.940218i | \(0.610621\pi\) | |||||||
\(648\) | 1.61857 | 0.0635835 | ||||||||
\(649\) | −49.9939 | −1.96243 | ||||||||
\(650\) | −4.37508 | −0.171605 | ||||||||
\(651\) | 2.57265 | 0.100830 | ||||||||
\(652\) | 22.7210 | 0.889825 | ||||||||
\(653\) | 29.1488 | 1.14068 | 0.570341 | − | 0.821408i | \(-0.306811\pi\) | ||||
0.570341 | + | 0.821408i | \(0.306811\pi\) | |||||||
\(654\) | −3.13717 | −0.122673 | ||||||||
\(655\) | 31.1719 | 1.21799 | ||||||||
\(656\) | 6.06482 | 0.236791 | ||||||||
\(657\) | −10.8892 | −0.424829 | ||||||||
\(658\) | 3.18621 | 0.124212 | ||||||||
\(659\) | −35.0106 | −1.36382 | −0.681910 | − | 0.731436i | \(-0.738850\pi\) | ||||
−0.681910 | + | 0.731436i | \(0.738850\pi\) | |||||||
\(660\) | 19.2660 | 0.749926 | ||||||||
\(661\) | 41.6401 | 1.61961 | 0.809806 | − | 0.586697i | \(-0.199572\pi\) | ||||
0.809806 | + | 0.586697i | \(0.199572\pi\) | |||||||
\(662\) | −0.474030 | −0.0184237 | ||||||||
\(663\) | −27.8806 | −1.08279 | ||||||||
\(664\) | 6.83269 | 0.265160 | ||||||||
\(665\) | 9.90444 | 0.384078 | ||||||||
\(666\) | −1.12358 | −0.0435377 | ||||||||
\(667\) | −29.1386 | −1.12825 | ||||||||
\(668\) | −3.93806 | −0.152368 | ||||||||
\(669\) | −12.7903 | −0.494503 | ||||||||
\(670\) | −4.81098 | −0.185864 | ||||||||
\(671\) | −9.43910 | −0.364393 | ||||||||
\(672\) | 4.48917 | 0.173174 | ||||||||
\(673\) | 6.26678 | 0.241567 | 0.120783 | − | 0.992679i | \(-0.461459\pi\) | ||||
0.120783 | + | 0.992679i | \(0.461459\pi\) | |||||||
\(674\) | 9.95473 | 0.383442 | ||||||||
\(675\) | −2.08603 | −0.0802912 | ||||||||
\(676\) | −20.9510 | −0.805809 | ||||||||
\(677\) | −35.5065 | −1.36463 | −0.682313 | − | 0.731060i | \(-0.739026\pi\) | ||||
−0.682313 | + | 0.731060i | \(0.739026\pi\) | |||||||
\(678\) | 7.88188 | 0.302702 | ||||||||
\(679\) | 0.135110 | 0.00518505 | ||||||||
\(680\) | 24.2649 | 0.930517 | ||||||||
\(681\) | 23.6675 | 0.906941 | ||||||||
\(682\) | 4.33296 | 0.165918 | ||||||||
\(683\) | 30.5511 | 1.16900 | 0.584502 | − | 0.811392i | \(-0.301290\pi\) | ||||
0.584502 | + | 0.811392i | \(0.301290\pi\) | |||||||
\(684\) | −6.77367 | −0.258998 | ||||||||
\(685\) | 6.36601 | 0.243233 | ||||||||
\(686\) | −0.423652 | −0.0161751 | ||||||||
\(687\) | 16.7152 | 0.637726 | ||||||||
\(688\) | 11.9122 | 0.454148 | ||||||||
\(689\) | 1.06140 | 0.0404360 | ||||||||
\(690\) | −4.66464 | −0.177580 | ||||||||
\(691\) | 21.9818 | 0.836229 | 0.418114 | − | 0.908394i | \(-0.362691\pi\) | ||||
0.418114 | + | 0.908394i | \(0.362691\pi\) | |||||||
\(692\) | 28.3781 | 1.07877 | ||||||||
\(693\) | 3.97552 | 0.151018 | ||||||||
\(694\) | −2.91354 | −0.110596 | ||||||||
\(695\) | −5.71788 | −0.216892 | ||||||||
\(696\) | −11.4023 | −0.432204 | ||||||||
\(697\) | 11.5573 | 0.437766 | ||||||||
\(698\) | 1.32820 | 0.0502730 | ||||||||
\(699\) | −27.5835 | −1.04330 | ||||||||
\(700\) | −3.79765 | −0.143538 | ||||||||
\(701\) | −5.79388 | −0.218832 | −0.109416 | − | 0.993996i | \(-0.534898\pi\) | ||||
−0.109416 | + | 0.993996i | \(0.534898\pi\) | |||||||
\(702\) | 2.09732 | 0.0791584 | ||||||||
\(703\) | 9.86783 | 0.372172 | ||||||||
\(704\) | −15.9371 | −0.600652 | ||||||||
\(705\) | 20.0201 | 0.754002 | ||||||||
\(706\) | 12.4281 | 0.467737 | ||||||||
\(707\) | 0.725428 | 0.0272825 | ||||||||
\(708\) | −22.8938 | −0.860403 | ||||||||
\(709\) | −12.2837 | −0.461324 | −0.230662 | − | 0.973034i | \(-0.574089\pi\) | ||||
−0.230662 | + | 0.973034i | \(0.574089\pi\) | |||||||
\(710\) | 15.4636 | 0.580337 | ||||||||
\(711\) | 2.69299 | 0.100995 | ||||||||
\(712\) | 6.60962 | 0.247706 | ||||||||
\(713\) | 10.6412 | 0.398515 | ||||||||
\(714\) | 2.38592 | 0.0892906 | ||||||||
\(715\) | 52.3904 | 1.95929 | ||||||||
\(716\) | 20.3889 | 0.761969 | ||||||||
\(717\) | 6.10076 | 0.227837 | ||||||||
\(718\) | 2.93554 | 0.109553 | ||||||||
\(719\) | −25.6425 | −0.956302 | −0.478151 | − | 0.878278i | \(-0.658693\pi\) | ||||
−0.478151 | + | 0.878278i | \(0.658693\pi\) | |||||||
\(720\) | 7.86696 | 0.293184 | ||||||||
\(721\) | 14.2476 | 0.530610 | ||||||||
\(722\) | 2.18441 | 0.0812953 | ||||||||
\(723\) | 16.4442 | 0.611566 | ||||||||
\(724\) | 12.2499 | 0.455265 | ||||||||
\(725\) | 14.6954 | 0.545774 | ||||||||
\(726\) | 2.03555 | 0.0755463 | ||||||||
\(727\) | 41.3287 | 1.53280 | 0.766399 | − | 0.642365i | \(-0.222047\pi\) | ||||
0.766399 | + | 0.642365i | \(0.222047\pi\) | |||||||
\(728\) | 8.01287 | 0.296977 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.2803 | 0.454513 | ||||||||
\(731\) | 22.7003 | 0.839600 | ||||||||
\(732\) | −4.32247 | −0.159763 | ||||||||
\(733\) | 27.6156 | 1.02001 | 0.510004 | − | 0.860172i | \(-0.329644\pi\) | ||||
0.510004 | + | 0.860172i | \(0.329644\pi\) | |||||||
\(734\) | −8.66174 | −0.319711 | ||||||||
\(735\) | −2.66196 | −0.0981878 | ||||||||
\(736\) | 18.5684 | 0.684439 | ||||||||
\(737\) | 16.9596 | 0.624716 | ||||||||
\(738\) | −0.869404 | −0.0320032 | ||||||||
\(739\) | −30.8185 | −1.13368 | −0.566839 | − | 0.823828i | \(-0.691834\pi\) | ||||
−0.566839 | + | 0.823828i | \(0.691834\pi\) | |||||||
\(740\) | −12.8526 | −0.472470 | ||||||||
\(741\) | −18.4198 | −0.676668 | ||||||||
\(742\) | −0.0908303 | −0.00333449 | ||||||||
\(743\) | 24.3137 | 0.891983 | 0.445991 | − | 0.895037i | \(-0.352851\pi\) | ||||
0.445991 | + | 0.895037i | \(0.352851\pi\) | |||||||
\(744\) | 4.16402 | 0.152661 | ||||||||
\(745\) | −5.48237 | −0.200859 | ||||||||
\(746\) | 0.527915 | 0.0193283 | ||||||||
\(747\) | 4.22143 | 0.154454 | ||||||||
\(748\) | −40.7601 | −1.49034 | ||||||||
\(749\) | −18.0628 | −0.660000 | ||||||||
\(750\) | −3.28622 | −0.119996 | ||||||||
\(751\) | 13.6195 | 0.496984 | 0.248492 | − | 0.968634i | \(-0.420065\pi\) | ||||
0.248492 | + | 0.968634i | \(0.420065\pi\) | |||||||
\(752\) | −22.2265 | −0.810517 | ||||||||
\(753\) | −31.2771 | −1.13980 | ||||||||
\(754\) | −14.7750 | −0.538073 | ||||||||
\(755\) | 32.7420 | 1.19160 | ||||||||
\(756\) | 1.82052 | 0.0662116 | ||||||||
\(757\) | 33.4512 | 1.21580 | 0.607902 | − | 0.794012i | \(-0.292011\pi\) | ||||
0.607902 | + | 0.794012i | \(0.292011\pi\) | |||||||
\(758\) | 5.03593 | 0.182913 | ||||||||
\(759\) | 16.4438 | 0.596871 | ||||||||
\(760\) | 16.0310 | 0.581507 | ||||||||
\(761\) | 18.4399 | 0.668446 | 0.334223 | − | 0.942494i | \(-0.391526\pi\) | ||||
0.334223 | + | 0.942494i | \(0.391526\pi\) | |||||||
\(762\) | −0.423652 | −0.0153473 | ||||||||
\(763\) | −7.40505 | −0.268081 | ||||||||
\(764\) | −42.4989 | −1.53755 | ||||||||
\(765\) | 14.9916 | 0.542021 | ||||||||
\(766\) | 6.19739 | 0.223921 | ||||||||
\(767\) | −62.2558 | −2.24793 | ||||||||
\(768\) | −3.49442 | −0.126094 | ||||||||
\(769\) | 42.6719 | 1.53879 | 0.769394 | − | 0.638774i | \(-0.220558\pi\) | ||||
0.769394 | + | 0.638774i | \(0.220558\pi\) | |||||||
\(770\) | −4.48337 | −0.161570 | ||||||||
\(771\) | −15.4673 | −0.557041 | ||||||||
\(772\) | −3.89452 | −0.140167 | ||||||||
\(773\) | 17.6637 | 0.635319 | 0.317659 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317659 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(774\) | −1.70763 | −0.0613797 | ||||||||
\(775\) | −5.36663 | −0.192775 | ||||||||
\(776\) | 0.218685 | 0.00785034 | ||||||||
\(777\) | −2.65212 | −0.0951443 | ||||||||
\(778\) | 9.13590 | 0.327538 | ||||||||
\(779\) | 7.63556 | 0.273572 | ||||||||
\(780\) | 23.9913 | 0.859025 | ||||||||
\(781\) | −54.5121 | −1.95059 | ||||||||
\(782\) | 9.86876 | 0.352906 | ||||||||
\(783\) | −7.04468 | −0.251756 | ||||||||
\(784\) | 2.95533 | 0.105547 | ||||||||
\(785\) | −51.4890 | −1.83772 | ||||||||
\(786\) | 4.96102 | 0.176954 | ||||||||
\(787\) | 34.4904 | 1.22945 | 0.614724 | − | 0.788742i | \(-0.289267\pi\) | ||||
0.614724 | + | 0.788742i | \(0.289267\pi\) | |||||||
\(788\) | −12.7758 | −0.455119 | ||||||||
\(789\) | 5.45766 | 0.194298 | ||||||||
\(790\) | −3.03700 | −0.108052 | ||||||||
\(791\) | 18.6046 | 0.661503 | ||||||||
\(792\) | 6.43466 | 0.228646 | ||||||||
\(793\) | −11.7542 | −0.417404 | ||||||||
\(794\) | −3.66574 | −0.130092 | ||||||||
\(795\) | −0.570720 | −0.0202413 | ||||||||
\(796\) | 34.0680 | 1.20751 | ||||||||
\(797\) | −11.8100 | −0.418333 | −0.209166 | − | 0.977880i | \(-0.567075\pi\) | ||||
−0.209166 | + | 0.977880i | \(0.567075\pi\) | |||||||
\(798\) | 1.57630 | 0.0558003 | ||||||||
\(799\) | −42.3556 | −1.49844 | ||||||||
\(800\) | −9.36453 | −0.331086 | ||||||||
\(801\) | 4.08362 | 0.144288 | ||||||||
\(802\) | 10.7977 | 0.381282 | ||||||||
\(803\) | −43.2904 | −1.52768 | ||||||||
\(804\) | 7.76636 | 0.273898 | ||||||||
\(805\) | −11.0105 | −0.388071 | ||||||||
\(806\) | 5.39569 | 0.190055 | ||||||||
\(807\) | −24.3057 | −0.855600 | ||||||||
\(808\) | 1.17416 | 0.0413067 | ||||||||
\(809\) | 6.66413 | 0.234298 | 0.117149 | − | 0.993114i | \(-0.462624\pi\) | ||||
0.117149 | + | 0.993114i | \(0.462624\pi\) | |||||||
\(810\) | −1.12774 | −0.0396249 | ||||||||
\(811\) | −1.22927 | −0.0431654 | −0.0215827 | − | 0.999767i | \(-0.506871\pi\) | ||||
−0.0215827 | + | 0.999767i | \(0.506871\pi\) | |||||||
\(812\) | −12.8250 | −0.450069 | ||||||||
\(813\) | −26.4187 | −0.926543 | ||||||||
\(814\) | −4.46680 | −0.156561 | ||||||||
\(815\) | −33.2227 | −1.16374 | ||||||||
\(816\) | −16.6438 | −0.582648 | ||||||||
\(817\) | 14.9973 | 0.524691 | ||||||||
\(818\) | −16.0989 | −0.562885 | ||||||||
\(819\) | 4.95058 | 0.172987 | ||||||||
\(820\) | −9.94510 | −0.347298 | ||||||||
\(821\) | 28.1827 | 0.983582 | 0.491791 | − | 0.870713i | \(-0.336342\pi\) | ||||
0.491791 | + | 0.870713i | \(0.336342\pi\) | |||||||
\(822\) | 1.01315 | 0.0353378 | ||||||||
\(823\) | −24.6122 | −0.857926 | −0.428963 | − | 0.903322i | \(-0.641121\pi\) | ||||
−0.428963 | + | 0.903322i | \(0.641121\pi\) | |||||||
\(824\) | 23.0608 | 0.803361 | ||||||||
\(825\) | −8.29304 | −0.288727 | ||||||||
\(826\) | 5.32761 | 0.185371 | ||||||||
\(827\) | −1.75039 | −0.0608670 | −0.0304335 | − | 0.999537i | \(-0.509689\pi\) | ||||
−0.0304335 | + | 0.999537i | \(0.509689\pi\) | |||||||
\(828\) | 7.53014 | 0.261690 | ||||||||
\(829\) | −34.2634 | −1.19002 | −0.595009 | − | 0.803719i | \(-0.702851\pi\) | ||||
−0.595009 | + | 0.803719i | \(0.702851\pi\) | |||||||
\(830\) | −4.76070 | −0.165246 | ||||||||
\(831\) | 13.7390 | 0.476599 | ||||||||
\(832\) | −19.8459 | −0.688034 | ||||||||
\(833\) | 5.63178 | 0.195130 | ||||||||
\(834\) | −0.910003 | −0.0315108 | ||||||||
\(835\) | 5.75822 | 0.199271 | ||||||||
\(836\) | −26.9289 | −0.931354 | ||||||||
\(837\) | 2.57265 | 0.0889240 | ||||||||
\(838\) | 1.84156 | 0.0636155 | ||||||||
\(839\) | 35.2195 | 1.21591 | 0.607955 | − | 0.793971i | \(-0.291990\pi\) | ||||
0.607955 | + | 0.793971i | \(0.291990\pi\) | |||||||
\(840\) | −4.30857 | −0.148660 | ||||||||
\(841\) | 20.6276 | 0.711296 | ||||||||
\(842\) | −12.4769 | −0.429983 | ||||||||
\(843\) | 5.06765 | 0.174539 | ||||||||
\(844\) | 20.7744 | 0.715086 | ||||||||
\(845\) | 30.6346 | 1.05386 | ||||||||
\(846\) | 3.18621 | 0.109544 | ||||||||
\(847\) | 4.80477 | 0.165094 | ||||||||
\(848\) | 0.633617 | 0.0217585 | ||||||||
\(849\) | 27.6362 | 0.948471 | ||||||||
\(850\) | −4.97708 | −0.170713 | ||||||||
\(851\) | −10.9699 | −0.376042 | ||||||||
\(852\) | −24.9628 | −0.855212 | ||||||||
\(853\) | −0.785201 | −0.0268848 | −0.0134424 | − | 0.999910i | \(-0.504279\pi\) | ||||
−0.0134424 | + | 0.999910i | \(0.504279\pi\) | |||||||
\(854\) | 1.00588 | 0.0344205 | ||||||||
\(855\) | 9.90444 | 0.338725 | ||||||||
\(856\) | −29.2359 | −0.999263 | ||||||||
\(857\) | 33.4829 | 1.14375 | 0.571876 | − | 0.820340i | \(-0.306216\pi\) | ||||
0.571876 | + | 0.820340i | \(0.306216\pi\) | |||||||
\(858\) | 8.33796 | 0.284653 | ||||||||
\(859\) | −8.16211 | −0.278488 | −0.139244 | − | 0.990258i | \(-0.544467\pi\) | ||||
−0.139244 | + | 0.990258i | \(0.544467\pi\) | |||||||
\(860\) | −19.5336 | −0.666090 | ||||||||
\(861\) | −2.05217 | −0.0699376 | ||||||||
\(862\) | −12.5639 | −0.427929 | ||||||||
\(863\) | −5.62343 | −0.191424 | −0.0957119 | − | 0.995409i | \(-0.530513\pi\) | ||||
−0.0957119 | + | 0.995409i | \(0.530513\pi\) | |||||||
\(864\) | 4.48917 | 0.152725 | ||||||||
\(865\) | −41.4943 | −1.41085 | ||||||||
\(866\) | 4.06581 | 0.138162 | ||||||||
\(867\) | −14.7169 | −0.499814 | ||||||||
\(868\) | 4.68357 | 0.158971 | ||||||||
\(869\) | 10.7060 | 0.363177 | ||||||||
\(870\) | 7.94460 | 0.269347 | ||||||||
\(871\) | 21.1193 | 0.715599 | ||||||||
\(872\) | −11.9856 | −0.405884 | ||||||||
\(873\) | 0.135110 | 0.00457278 | ||||||||
\(874\) | 6.51997 | 0.220541 | ||||||||
\(875\) | −7.75688 | −0.262230 | ||||||||
\(876\) | −19.8240 | −0.669793 | ||||||||
\(877\) | 2.77495 | 0.0937033 | 0.0468516 | − | 0.998902i | \(-0.485081\pi\) | ||||
0.0468516 | + | 0.998902i | \(0.485081\pi\) | |||||||
\(878\) | 12.6557 | 0.427110 | ||||||||
\(879\) | −26.9116 | −0.907706 | ||||||||
\(880\) | 31.2753 | 1.05429 | ||||||||
\(881\) | −36.0262 | −1.21375 | −0.606876 | − | 0.794797i | \(-0.707578\pi\) | ||||
−0.606876 | + | 0.794797i | \(0.707578\pi\) | |||||||
\(882\) | −0.423652 | −0.0142651 | ||||||||
\(883\) | 9.10055 | 0.306258 | 0.153129 | − | 0.988206i | \(-0.451065\pi\) | ||||
0.153129 | + | 0.988206i | \(0.451065\pi\) | |||||||
\(884\) | −50.7571 | −1.70715 | ||||||||
\(885\) | 33.4753 | 1.12526 | ||||||||
\(886\) | −0.824312 | −0.0276933 | ||||||||
\(887\) | 46.7522 | 1.56979 | 0.784893 | − | 0.619632i | \(-0.212718\pi\) | ||||
0.784893 | + | 0.619632i | \(0.212718\pi\) | |||||||
\(888\) | −4.29264 | −0.144052 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −4.60528 | −0.154369 | ||||||||
\(891\) | 3.97552 | 0.133185 | ||||||||
\(892\) | −23.2851 | −0.779641 | ||||||||
\(893\) | −27.9830 | −0.936415 | ||||||||
\(894\) | −0.872522 | −0.0291815 | ||||||||
\(895\) | −29.8126 | −0.996526 | ||||||||
\(896\) | 10.6767 | 0.356683 | ||||||||
\(897\) | 20.4769 | 0.683703 | ||||||||
\(898\) | 7.49268 | 0.250034 | ||||||||
\(899\) | −18.1235 | −0.604454 | ||||||||
\(900\) | −3.79765 | −0.126588 | ||||||||
\(901\) | 1.20744 | 0.0402258 | ||||||||
\(902\) | −3.45633 | −0.115083 | ||||||||
\(903\) | −4.03075 | −0.134135 | ||||||||
\(904\) | 30.1129 | 1.00154 | ||||||||
\(905\) | −17.9118 | −0.595409 | ||||||||
\(906\) | 5.21091 | 0.173121 | ||||||||
\(907\) | 50.9022 | 1.69018 | 0.845090 | − | 0.534623i | \(-0.179547\pi\) | ||||
0.845090 | + | 0.534623i | \(0.179547\pi\) | |||||||
\(908\) | 43.0872 | 1.42990 | ||||||||
\(909\) | 0.725428 | 0.0240609 | ||||||||
\(910\) | −5.58299 | −0.185074 | ||||||||
\(911\) | −29.0201 | −0.961480 | −0.480740 | − | 0.876863i | \(-0.659632\pi\) | ||||
−0.480740 | + | 0.876863i | \(0.659632\pi\) | |||||||
\(912\) | −10.9960 | −0.364113 | ||||||||
\(913\) | 16.7824 | 0.555416 | ||||||||
\(914\) | 16.4056 | 0.542649 | ||||||||
\(915\) | 6.32031 | 0.208943 | ||||||||
\(916\) | 30.4304 | 1.00545 | ||||||||
\(917\) | 11.7101 | 0.386702 | ||||||||
\(918\) | 2.38592 | 0.0787469 | ||||||||
\(919\) | −34.4150 | −1.13525 | −0.567623 | − | 0.823288i | \(-0.692137\pi\) | ||||
−0.567623 | + | 0.823288i | \(0.692137\pi\) | |||||||
\(920\) | −17.8214 | −0.587553 | ||||||||
\(921\) | 10.2148 | 0.336589 | ||||||||
\(922\) | −0.893943 | −0.0294405 | ||||||||
\(923\) | −67.8820 | −2.23436 | ||||||||
\(924\) | 7.23751 | 0.238097 | ||||||||
\(925\) | 5.53239 | 0.181904 | ||||||||
\(926\) | 6.92578 | 0.227595 | ||||||||
\(927\) | 14.2476 | 0.467954 | ||||||||
\(928\) | −31.6248 | −1.03813 | ||||||||
\(929\) | 41.0030 | 1.34526 | 0.672632 | − | 0.739977i | \(-0.265164\pi\) | ||||
0.672632 | + | 0.739977i | \(0.265164\pi\) | |||||||
\(930\) | −2.90130 | −0.0951373 | ||||||||
\(931\) | 3.72073 | 0.121942 | ||||||||
\(932\) | −50.2163 | −1.64489 | ||||||||
\(933\) | −9.69180 | −0.317295 | ||||||||
\(934\) | −6.70782 | −0.219487 | ||||||||
\(935\) | 59.5993 | 1.94911 | ||||||||
\(936\) | 8.01287 | 0.261909 | ||||||||
\(937\) | 45.4052 | 1.48332 | 0.741662 | − | 0.670774i | \(-0.234038\pi\) | ||||
0.741662 | + | 0.670774i | \(0.234038\pi\) | |||||||
\(938\) | −1.80731 | −0.0590106 | ||||||||
\(939\) | −13.6848 | −0.446586 | ||||||||
\(940\) | 36.4470 | 1.18877 | ||||||||
\(941\) | 6.54913 | 0.213496 | 0.106748 | − | 0.994286i | \(-0.465956\pi\) | ||||
0.106748 | + | 0.994286i | \(0.465956\pi\) | |||||||
\(942\) | −8.19450 | −0.266991 | ||||||||
\(943\) | −8.48828 | −0.276417 | ||||||||
\(944\) | −37.1645 | −1.20960 | ||||||||
\(945\) | −2.66196 | −0.0865935 | ||||||||
\(946\) | −6.78874 | −0.220721 | ||||||||
\(947\) | −30.9829 | −1.00681 | −0.503405 | − | 0.864051i | \(-0.667919\pi\) | ||||
−0.503405 | + | 0.864051i | \(0.667919\pi\) | |||||||
\(948\) | 4.90263 | 0.159230 | ||||||||
\(949\) | −53.9080 | −1.74993 | ||||||||
\(950\) | −3.28820 | −0.106683 | ||||||||
\(951\) | −14.1092 | −0.457522 | ||||||||
\(952\) | 9.11543 | 0.295433 | ||||||||
\(953\) | 51.1779 | 1.65782 | 0.828908 | − | 0.559385i | \(-0.188963\pi\) | ||||
0.828908 | + | 0.559385i | \(0.188963\pi\) | |||||||
\(954\) | −0.0908303 | −0.00294074 | ||||||||
\(955\) | 62.1418 | 2.01086 | ||||||||
\(956\) | 11.1065 | 0.359211 | ||||||||
\(957\) | −28.0063 | −0.905315 | ||||||||
\(958\) | 9.37801 | 0.302990 | ||||||||
\(959\) | 2.39147 | 0.0772247 | ||||||||
\(960\) | 10.6713 | 0.344414 | ||||||||
\(961\) | −24.3814 | −0.786498 | ||||||||
\(962\) | −5.56236 | −0.179338 | ||||||||
\(963\) | −18.0628 | −0.582066 | ||||||||
\(964\) | 29.9370 | 0.964204 | ||||||||
\(965\) | 5.69456 | 0.183314 | ||||||||
\(966\) | −1.75233 | −0.0563804 | ||||||||
\(967\) | −38.9551 | −1.25271 | −0.626356 | − | 0.779538i | \(-0.715454\pi\) | ||||
−0.626356 | + | 0.779538i | \(0.715454\pi\) | |||||||
\(968\) | 7.77686 | 0.249958 | ||||||||
\(969\) | −20.9544 | −0.673151 | ||||||||
\(970\) | −0.152370 | −0.00489229 | ||||||||
\(971\) | 42.6229 | 1.36783 | 0.683917 | − | 0.729559i | \(-0.260275\pi\) | ||||
0.683917 | + | 0.729559i | \(0.260275\pi\) | |||||||
\(972\) | 1.82052 | 0.0583932 | ||||||||
\(973\) | −2.14800 | −0.0688616 | ||||||||
\(974\) | 0.147490 | 0.00472589 | ||||||||
\(975\) | −10.3271 | −0.330730 | ||||||||
\(976\) | −7.01685 | −0.224604 | ||||||||
\(977\) | 49.7039 | 1.59017 | 0.795084 | − | 0.606500i | \(-0.207427\pi\) | ||||
0.795084 | + | 0.606500i | \(0.207427\pi\) | |||||||
\(978\) | −5.28740 | −0.169073 | ||||||||
\(979\) | 16.2345 | 0.518857 | ||||||||
\(980\) | −4.84615 | −0.154804 | ||||||||
\(981\) | −7.40505 | −0.236425 | ||||||||
\(982\) | 3.08738 | 0.0985222 | ||||||||
\(983\) | −20.5978 | −0.656968 | −0.328484 | − | 0.944510i | \(-0.606538\pi\) | ||||
−0.328484 | + | 0.944510i | \(0.606538\pi\) | |||||||
\(984\) | −3.32157 | −0.105888 | ||||||||
\(985\) | 18.6808 | 0.595218 | ||||||||
\(986\) | −16.8080 | −0.535276 | ||||||||
\(987\) | 7.52083 | 0.239391 | ||||||||
\(988\) | −33.5336 | −1.06685 | ||||||||
\(989\) | −16.6722 | −0.530146 | ||||||||
\(990\) | −4.48337 | −0.142491 | ||||||||
\(991\) | −40.6235 | −1.29045 | −0.645224 | − | 0.763994i | \(-0.723236\pi\) | ||||
−0.645224 | + | 0.763994i | \(0.723236\pi\) | |||||||
\(992\) | 11.5491 | 0.366684 | ||||||||
\(993\) | −1.11891 | −0.0355077 | ||||||||
\(994\) | 5.80909 | 0.184253 | ||||||||
\(995\) | −49.8141 | −1.57921 | ||||||||
\(996\) | 7.68520 | 0.243515 | ||||||||
\(997\) | −34.6749 | −1.09817 | −0.549083 | − | 0.835768i | \(-0.685023\pi\) | ||||
−0.549083 | + | 0.835768i | \(0.685023\pi\) | |||||||
\(998\) | 7.01652 | 0.222104 | ||||||||
\(999\) | −2.65212 | −0.0839094 |
(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 | 2667.2.a.l.1.5 | ✓ | 13 | |
3.2 | odd | 2 | 8001.2.a.o.1.9 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.l.1.5 | ✓ | 13 | 1.1 | even | 1 | trivial | |
8001.2.a.o.1.9 | 13 | 3.2 | odd | 2 |