Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [805,2,Mod(1,805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(805, 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("805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 805 = 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 805.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: | \(6.42795736271\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24698 | −1.58885 | −0.794427 | − | 0.607359i | \(-0.792229\pi\) | ||||
−0.794427 | + | 0.607359i | \(0.792229\pi\) | |||||||
\(3\) | 1.35690 | 0.783404 | 0.391702 | − | 0.920092i | \(-0.371886\pi\) | ||||
0.391702 | + | 0.920092i | \(0.371886\pi\) | |||||||
\(4\) | 3.04892 | 1.52446 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −3.04892 | −1.24472 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.35690 | −0.833289 | ||||||||
\(9\) | −1.15883 | −0.386278 | ||||||||
\(10\) | 2.24698 | 0.710557 | ||||||||
\(11\) | −0.753020 | −0.227044 | −0.113522 | − | 0.993535i | \(-0.536213\pi\) | ||||
−0.113522 | + | 0.993535i | \(0.536213\pi\) | |||||||
\(12\) | 4.13706 | 1.19427 | ||||||||
\(13\) | 3.58211 | 0.993497 | 0.496749 | − | 0.867894i | \(-0.334527\pi\) | ||||
0.496749 | + | 0.867894i | \(0.334527\pi\) | |||||||
\(14\) | 2.24698 | 0.600531 | ||||||||
\(15\) | −1.35690 | −0.350349 | ||||||||
\(16\) | −0.801938 | −0.200484 | ||||||||
\(17\) | −2.85086 | −0.691434 | −0.345717 | − | 0.938339i | \(-0.612364\pi\) | ||||
−0.345717 | + | 0.938339i | \(0.612364\pi\) | |||||||
\(18\) | 2.60388 | 0.613739 | ||||||||
\(19\) | 1.04892 | 0.240638 | 0.120319 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120319 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(20\) | −3.04892 | −0.681759 | ||||||||
\(21\) | −1.35690 | −0.296099 | ||||||||
\(22\) | 1.69202 | 0.360740 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −3.19806 | −0.652802 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −8.04892 | −1.57852 | ||||||||
\(27\) | −5.64310 | −1.08602 | ||||||||
\(28\) | −3.04892 | −0.576191 | ||||||||
\(29\) | −7.38404 | −1.37118 | −0.685591 | − | 0.727987i | \(-0.740456\pi\) | ||||
−0.685591 | + | 0.727987i | \(0.740456\pi\) | |||||||
\(30\) | 3.04892 | 0.556654 | ||||||||
\(31\) | −1.44504 | −0.259537 | −0.129769 | − | 0.991544i | \(-0.541423\pi\) | ||||
−0.129769 | + | 0.991544i | \(0.541423\pi\) | |||||||
\(32\) | 6.51573 | 1.15183 | ||||||||
\(33\) | −1.02177 | −0.177867 | ||||||||
\(34\) | 6.40581 | 1.09859 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −3.53319 | −0.588865 | ||||||||
\(37\) | −3.74094 | −0.615007 | −0.307503 | − | 0.951547i | \(-0.599494\pi\) | ||||
−0.307503 | + | 0.951547i | \(0.599494\pi\) | |||||||
\(38\) | −2.35690 | −0.382339 | ||||||||
\(39\) | 4.86054 | 0.778310 | ||||||||
\(40\) | 2.35690 | 0.372658 | ||||||||
\(41\) | −8.70171 | −1.35898 | −0.679489 | − | 0.733685i | \(-0.737799\pi\) | ||||
−0.679489 | + | 0.733685i | \(0.737799\pi\) | |||||||
\(42\) | 3.04892 | 0.470458 | ||||||||
\(43\) | 2.24698 | 0.342661 | 0.171331 | − | 0.985214i | \(-0.445193\pi\) | ||||
0.171331 | + | 0.985214i | \(0.445193\pi\) | |||||||
\(44\) | −2.29590 | −0.346119 | ||||||||
\(45\) | 1.15883 | 0.172749 | ||||||||
\(46\) | 2.24698 | 0.331299 | ||||||||
\(47\) | −1.76271 | −0.257118 | −0.128559 | − | 0.991702i | \(-0.541035\pi\) | ||||
−0.128559 | + | 0.991702i | \(0.541035\pi\) | |||||||
\(48\) | −1.08815 | −0.157060 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.24698 | −0.317771 | ||||||||
\(51\) | −3.86831 | −0.541672 | ||||||||
\(52\) | 10.9215 | 1.51455 | ||||||||
\(53\) | 12.2446 | 1.68192 | 0.840962 | − | 0.541095i | \(-0.181990\pi\) | ||||
0.840962 | + | 0.541095i | \(0.181990\pi\) | |||||||
\(54\) | 12.6799 | 1.72552 | ||||||||
\(55\) | 0.753020 | 0.101537 | ||||||||
\(56\) | 2.35690 | 0.314953 | ||||||||
\(57\) | 1.42327 | 0.188517 | ||||||||
\(58\) | 16.5918 | 2.17861 | ||||||||
\(59\) | −2.59419 | −0.337734 | −0.168867 | − | 0.985639i | \(-0.554011\pi\) | ||||
−0.168867 | + | 0.985639i | \(0.554011\pi\) | |||||||
\(60\) | −4.13706 | −0.534093 | ||||||||
\(61\) | −8.76271 | −1.12195 | −0.560975 | − | 0.827833i | \(-0.689574\pi\) | ||||
−0.560975 | + | 0.827833i | \(0.689574\pi\) | |||||||
\(62\) | 3.24698 | 0.412367 | ||||||||
\(63\) | 1.15883 | 0.145999 | ||||||||
\(64\) | −13.0368 | −1.62960 | ||||||||
\(65\) | −3.58211 | −0.444305 | ||||||||
\(66\) | 2.29590 | 0.282605 | ||||||||
\(67\) | 6.47219 | 0.790704 | 0.395352 | − | 0.918530i | \(-0.370623\pi\) | ||||
0.395352 | + | 0.918530i | \(0.370623\pi\) | |||||||
\(68\) | −8.69202 | −1.05406 | ||||||||
\(69\) | −1.35690 | −0.163351 | ||||||||
\(70\) | −2.24698 | −0.268565 | ||||||||
\(71\) | −14.9269 | −1.77150 | −0.885750 | − | 0.464163i | \(-0.846355\pi\) | ||||
−0.885750 | + | 0.464163i | \(0.846355\pi\) | |||||||
\(72\) | 2.73125 | 0.321881 | ||||||||
\(73\) | 2.76271 | 0.323351 | 0.161675 | − | 0.986844i | \(-0.448310\pi\) | ||||
0.161675 | + | 0.986844i | \(0.448310\pi\) | |||||||
\(74\) | 8.40581 | 0.977156 | ||||||||
\(75\) | 1.35690 | 0.156681 | ||||||||
\(76\) | 3.19806 | 0.366843 | ||||||||
\(77\) | 0.753020 | 0.0858146 | ||||||||
\(78\) | −10.9215 | −1.23662 | ||||||||
\(79\) | −11.0761 | −1.24615 | −0.623077 | − | 0.782160i | \(-0.714118\pi\) | ||||
−0.623077 | + | 0.782160i | \(0.714118\pi\) | |||||||
\(80\) | 0.801938 | 0.0896594 | ||||||||
\(81\) | −4.18060 | −0.464512 | ||||||||
\(82\) | 19.5526 | 2.15922 | ||||||||
\(83\) | −13.6256 | −1.49561 | −0.747804 | − | 0.663919i | \(-0.768892\pi\) | ||||
−0.747804 | + | 0.663919i | \(0.768892\pi\) | |||||||
\(84\) | −4.13706 | −0.451391 | ||||||||
\(85\) | 2.85086 | 0.309219 | ||||||||
\(86\) | −5.04892 | −0.544439 | ||||||||
\(87\) | −10.0194 | −1.07419 | ||||||||
\(88\) | 1.77479 | 0.189193 | ||||||||
\(89\) | 3.46681 | 0.367481 | 0.183741 | − | 0.982975i | \(-0.441179\pi\) | ||||
0.183741 | + | 0.982975i | \(0.441179\pi\) | |||||||
\(90\) | −2.60388 | −0.274473 | ||||||||
\(91\) | −3.58211 | −0.375507 | ||||||||
\(92\) | −3.04892 | −0.317872 | ||||||||
\(93\) | −1.96077 | −0.203323 | ||||||||
\(94\) | 3.96077 | 0.408522 | ||||||||
\(95\) | −1.04892 | −0.107617 | ||||||||
\(96\) | 8.84117 | 0.902348 | ||||||||
\(97\) | −0.560335 | −0.0568934 | −0.0284467 | − | 0.999595i | \(-0.509056\pi\) | ||||
−0.0284467 | + | 0.999595i | \(0.509056\pi\) | |||||||
\(98\) | −2.24698 | −0.226979 | ||||||||
\(99\) | 0.872625 | 0.0877021 | ||||||||
\(100\) | 3.04892 | 0.304892 | ||||||||
\(101\) | −4.25667 | −0.423554 | −0.211777 | − | 0.977318i | \(-0.567925\pi\) | ||||
−0.211777 | + | 0.977318i | \(0.567925\pi\) | |||||||
\(102\) | 8.69202 | 0.860638 | ||||||||
\(103\) | −5.81163 | −0.572637 | −0.286318 | − | 0.958135i | \(-0.592431\pi\) | ||||
−0.286318 | + | 0.958135i | \(0.592431\pi\) | |||||||
\(104\) | −8.44265 | −0.827870 | ||||||||
\(105\) | 1.35690 | 0.132419 | ||||||||
\(106\) | −27.5133 | −2.67233 | ||||||||
\(107\) | −13.7681 | −1.33101 | −0.665506 | − | 0.746393i | \(-0.731784\pi\) | ||||
−0.665506 | + | 0.746393i | \(0.731784\pi\) | |||||||
\(108\) | −17.2054 | −1.65559 | ||||||||
\(109\) | 3.65279 | 0.349874 | 0.174937 | − | 0.984580i | \(-0.444028\pi\) | ||||
0.174937 | + | 0.984580i | \(0.444028\pi\) | |||||||
\(110\) | −1.69202 | −0.161328 | ||||||||
\(111\) | −5.07606 | −0.481799 | ||||||||
\(112\) | 0.801938 | 0.0757760 | ||||||||
\(113\) | −18.2687 | −1.71858 | −0.859290 | − | 0.511489i | \(-0.829094\pi\) | ||||
−0.859290 | + | 0.511489i | \(0.829094\pi\) | |||||||
\(114\) | −3.19806 | −0.299526 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | −22.5133 | −2.09031 | ||||||||
\(117\) | −4.15106 | −0.383766 | ||||||||
\(118\) | 5.82908 | 0.536611 | ||||||||
\(119\) | 2.85086 | 0.261337 | ||||||||
\(120\) | 3.19806 | 0.291942 | ||||||||
\(121\) | −10.4330 | −0.948451 | ||||||||
\(122\) | 19.6896 | 1.78262 | ||||||||
\(123\) | −11.8073 | −1.06463 | ||||||||
\(124\) | −4.40581 | −0.395654 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.60388 | −0.231972 | ||||||||
\(127\) | 19.4209 | 1.72332 | 0.861662 | − | 0.507482i | \(-0.169424\pi\) | ||||
0.861662 | + | 0.507482i | \(0.169424\pi\) | |||||||
\(128\) | 16.2620 | 1.43738 | ||||||||
\(129\) | 3.04892 | 0.268442 | ||||||||
\(130\) | 8.04892 | 0.705937 | ||||||||
\(131\) | 14.4940 | 1.26634 | 0.633172 | − | 0.774011i | \(-0.281753\pi\) | ||||
0.633172 | + | 0.774011i | \(0.281753\pi\) | |||||||
\(132\) | −3.11529 | −0.271151 | ||||||||
\(133\) | −1.04892 | −0.0909527 | ||||||||
\(134\) | −14.5429 | −1.25631 | ||||||||
\(135\) | 5.64310 | 0.485681 | ||||||||
\(136\) | 6.71917 | 0.576164 | ||||||||
\(137\) | −5.04354 | −0.430899 | −0.215449 | − | 0.976515i | \(-0.569122\pi\) | ||||
−0.215449 | + | 0.976515i | \(0.569122\pi\) | |||||||
\(138\) | 3.04892 | 0.259541 | ||||||||
\(139\) | 7.21313 | 0.611810 | 0.305905 | − | 0.952062i | \(-0.401041\pi\) | ||||
0.305905 | + | 0.952062i | \(0.401041\pi\) | |||||||
\(140\) | 3.04892 | 0.257681 | ||||||||
\(141\) | −2.39181 | −0.201427 | ||||||||
\(142\) | 33.5405 | 2.81465 | ||||||||
\(143\) | −2.69740 | −0.225568 | ||||||||
\(144\) | 0.929312 | 0.0774427 | ||||||||
\(145\) | 7.38404 | 0.613211 | ||||||||
\(146\) | −6.20775 | −0.513757 | ||||||||
\(147\) | 1.35690 | 0.111915 | ||||||||
\(148\) | −11.4058 | −0.937552 | ||||||||
\(149\) | −6.03923 | −0.494753 | −0.247376 | − | 0.968919i | \(-0.579568\pi\) | ||||
−0.247376 | + | 0.968919i | \(0.579568\pi\) | |||||||
\(150\) | −3.04892 | −0.248943 | ||||||||
\(151\) | 9.67025 | 0.786954 | 0.393477 | − | 0.919334i | \(-0.371272\pi\) | ||||
0.393477 | + | 0.919334i | \(0.371272\pi\) | |||||||
\(152\) | −2.47219 | −0.200521 | ||||||||
\(153\) | 3.30367 | 0.267086 | ||||||||
\(154\) | −1.69202 | −0.136347 | ||||||||
\(155\) | 1.44504 | 0.116069 | ||||||||
\(156\) | 14.8194 | 1.18650 | ||||||||
\(157\) | −7.59419 | −0.606082 | −0.303041 | − | 0.952978i | \(-0.598002\pi\) | ||||
−0.303041 | + | 0.952978i | \(0.598002\pi\) | |||||||
\(158\) | 24.8877 | 1.97996 | ||||||||
\(159\) | 16.6146 | 1.31763 | ||||||||
\(160\) | −6.51573 | −0.515114 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 9.39373 | 0.738041 | ||||||||
\(163\) | 5.15346 | 0.403650 | 0.201825 | − | 0.979422i | \(-0.435313\pi\) | ||||
0.201825 | + | 0.979422i | \(0.435313\pi\) | |||||||
\(164\) | −26.5308 | −2.07171 | ||||||||
\(165\) | 1.02177 | 0.0795447 | ||||||||
\(166\) | 30.6165 | 2.37630 | ||||||||
\(167\) | 17.8552 | 1.38167 | 0.690837 | − | 0.723010i | \(-0.257242\pi\) | ||||
0.690837 | + | 0.723010i | \(0.257242\pi\) | |||||||
\(168\) | 3.19806 | 0.246736 | ||||||||
\(169\) | −0.168522 | −0.0129633 | ||||||||
\(170\) | −6.40581 | −0.491303 | ||||||||
\(171\) | −1.21552 | −0.0929532 | ||||||||
\(172\) | 6.85086 | 0.522373 | ||||||||
\(173\) | 2.18060 | 0.165788 | 0.0828941 | − | 0.996558i | \(-0.473584\pi\) | ||||
0.0828941 | + | 0.996558i | \(0.473584\pi\) | |||||||
\(174\) | 22.5133 | 1.70673 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0.603875 | 0.0455188 | ||||||||
\(177\) | −3.52004 | −0.264583 | ||||||||
\(178\) | −7.78986 | −0.583874 | ||||||||
\(179\) | −3.36898 | −0.251809 | −0.125905 | − | 0.992042i | \(-0.540183\pi\) | ||||
−0.125905 | + | 0.992042i | \(0.540183\pi\) | |||||||
\(180\) | 3.53319 | 0.263348 | ||||||||
\(181\) | 1.61596 | 0.120113 | 0.0600566 | − | 0.998195i | \(-0.480872\pi\) | ||||
0.0600566 | + | 0.998195i | \(0.480872\pi\) | |||||||
\(182\) | 8.04892 | 0.596625 | ||||||||
\(183\) | −11.8901 | −0.878940 | ||||||||
\(184\) | 2.35690 | 0.173753 | ||||||||
\(185\) | 3.74094 | 0.275039 | ||||||||
\(186\) | 4.40581 | 0.323050 | ||||||||
\(187\) | 2.14675 | 0.156986 | ||||||||
\(188\) | −5.37435 | −0.391965 | ||||||||
\(189\) | 5.64310 | 0.410475 | ||||||||
\(190\) | 2.35690 | 0.170987 | ||||||||
\(191\) | 0.833397 | 0.0603025 | 0.0301512 | − | 0.999545i | \(-0.490401\pi\) | ||||
0.0301512 | + | 0.999545i | \(0.490401\pi\) | |||||||
\(192\) | −17.6896 | −1.27664 | ||||||||
\(193\) | 12.0218 | 0.865346 | 0.432673 | − | 0.901551i | \(-0.357570\pi\) | ||||
0.432673 | + | 0.901551i | \(0.357570\pi\) | |||||||
\(194\) | 1.25906 | 0.0903953 | ||||||||
\(195\) | −4.86054 | −0.348071 | ||||||||
\(196\) | 3.04892 | 0.217780 | ||||||||
\(197\) | 23.9584 | 1.70696 | 0.853482 | − | 0.521122i | \(-0.174487\pi\) | ||||
0.853482 | + | 0.521122i | \(0.174487\pi\) | |||||||
\(198\) | −1.96077 | −0.139346 | ||||||||
\(199\) | −21.4590 | −1.52119 | −0.760596 | − | 0.649226i | \(-0.775093\pi\) | ||||
−0.760596 | + | 0.649226i | \(0.775093\pi\) | |||||||
\(200\) | −2.35690 | −0.166658 | ||||||||
\(201\) | 8.78209 | 0.619441 | ||||||||
\(202\) | 9.56465 | 0.672966 | ||||||||
\(203\) | 7.38404 | 0.518258 | ||||||||
\(204\) | −11.7942 | −0.825757 | ||||||||
\(205\) | 8.70171 | 0.607754 | ||||||||
\(206\) | 13.0586 | 0.909836 | ||||||||
\(207\) | 1.15883 | 0.0805445 | ||||||||
\(208\) | −2.87263 | −0.199181 | ||||||||
\(209\) | −0.789856 | −0.0546355 | ||||||||
\(210\) | −3.04892 | −0.210395 | ||||||||
\(211\) | 13.7778 | 0.948501 | 0.474251 | − | 0.880390i | \(-0.342719\pi\) | ||||
0.474251 | + | 0.880390i | \(0.342719\pi\) | |||||||
\(212\) | 37.3327 | 2.56402 | ||||||||
\(213\) | −20.2543 | −1.38780 | ||||||||
\(214\) | 30.9366 | 2.11478 | ||||||||
\(215\) | −2.24698 | −0.153243 | ||||||||
\(216\) | 13.3002 | 0.904965 | ||||||||
\(217\) | 1.44504 | 0.0980958 | ||||||||
\(218\) | −8.20775 | −0.555899 | ||||||||
\(219\) | 3.74871 | 0.253314 | ||||||||
\(220\) | 2.29590 | 0.154789 | ||||||||
\(221\) | −10.2121 | −0.686938 | ||||||||
\(222\) | 11.4058 | 0.765508 | ||||||||
\(223\) | 3.94139 | 0.263935 | 0.131968 | − | 0.991254i | \(-0.457871\pi\) | ||||
0.131968 | + | 0.991254i | \(0.457871\pi\) | |||||||
\(224\) | −6.51573 | −0.435350 | ||||||||
\(225\) | −1.15883 | −0.0772556 | ||||||||
\(226\) | 41.0495 | 2.73057 | ||||||||
\(227\) | −17.2567 | −1.14537 | −0.572683 | − | 0.819777i | \(-0.694097\pi\) | ||||
−0.572683 | + | 0.819777i | \(0.694097\pi\) | |||||||
\(228\) | 4.33944 | 0.287386 | ||||||||
\(229\) | 12.4862 | 0.825111 | 0.412555 | − | 0.910933i | \(-0.364636\pi\) | ||||
0.412555 | + | 0.910933i | \(0.364636\pi\) | |||||||
\(230\) | −2.24698 | −0.148161 | ||||||||
\(231\) | 1.02177 | 0.0672275 | ||||||||
\(232\) | 17.4034 | 1.14259 | ||||||||
\(233\) | 14.2838 | 0.935764 | 0.467882 | − | 0.883791i | \(-0.345017\pi\) | ||||
0.467882 | + | 0.883791i | \(0.345017\pi\) | |||||||
\(234\) | 9.32736 | 0.609748 | ||||||||
\(235\) | 1.76271 | 0.114986 | ||||||||
\(236\) | −7.90946 | −0.514862 | ||||||||
\(237\) | −15.0291 | −0.976243 | ||||||||
\(238\) | −6.40581 | −0.415227 | ||||||||
\(239\) | 7.99761 | 0.517322 | 0.258661 | − | 0.965968i | \(-0.416719\pi\) | ||||
0.258661 | + | 0.965968i | \(0.416719\pi\) | |||||||
\(240\) | 1.08815 | 0.0702395 | ||||||||
\(241\) | 8.43727 | 0.543492 | 0.271746 | − | 0.962369i | \(-0.412399\pi\) | ||||
0.271746 | + | 0.962369i | \(0.412399\pi\) | |||||||
\(242\) | 23.4426 | 1.50695 | ||||||||
\(243\) | 11.2567 | 0.722116 | ||||||||
\(244\) | −26.7168 | −1.71037 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 26.5308 | 1.69154 | ||||||||
\(247\) | 3.75733 | 0.239073 | ||||||||
\(248\) | 3.40581 | 0.216269 | ||||||||
\(249\) | −18.4886 | −1.17167 | ||||||||
\(250\) | 2.24698 | 0.142111 | ||||||||
\(251\) | 3.54048 | 0.223473 | 0.111737 | − | 0.993738i | \(-0.464359\pi\) | ||||
0.111737 | + | 0.993738i | \(0.464359\pi\) | |||||||
\(252\) | 3.53319 | 0.222570 | ||||||||
\(253\) | 0.753020 | 0.0473420 | ||||||||
\(254\) | −43.6383 | −2.73811 | ||||||||
\(255\) | 3.86831 | 0.242243 | ||||||||
\(256\) | −10.4668 | −0.654176 | ||||||||
\(257\) | −4.62671 | −0.288606 | −0.144303 | − | 0.989534i | \(-0.546094\pi\) | ||||
−0.144303 | + | 0.989534i | \(0.546094\pi\) | |||||||
\(258\) | −6.85086 | −0.426516 | ||||||||
\(259\) | 3.74094 | 0.232451 | ||||||||
\(260\) | −10.9215 | −0.677325 | ||||||||
\(261\) | 8.55688 | 0.529657 | ||||||||
\(262\) | −32.5676 | −2.01203 | ||||||||
\(263\) | −11.9812 | −0.738793 | −0.369397 | − | 0.929272i | \(-0.620436\pi\) | ||||
−0.369397 | + | 0.929272i | \(0.620436\pi\) | |||||||
\(264\) | 2.40821 | 0.148215 | ||||||||
\(265\) | −12.2446 | −0.752179 | ||||||||
\(266\) | 2.35690 | 0.144511 | ||||||||
\(267\) | 4.70410 | 0.287886 | ||||||||
\(268\) | 19.7332 | 1.20540 | ||||||||
\(269\) | 24.2610 | 1.47922 | 0.739609 | − | 0.673037i | \(-0.235010\pi\) | ||||
0.739609 | + | 0.673037i | \(0.235010\pi\) | |||||||
\(270\) | −12.6799 | −0.771677 | ||||||||
\(271\) | −12.0422 | −0.731512 | −0.365756 | − | 0.930711i | \(-0.619190\pi\) | ||||
−0.365756 | + | 0.930711i | \(0.619190\pi\) | |||||||
\(272\) | 2.28621 | 0.138622 | ||||||||
\(273\) | −4.86054 | −0.294173 | ||||||||
\(274\) | 11.3327 | 0.684635 | ||||||||
\(275\) | −0.753020 | −0.0454088 | ||||||||
\(276\) | −4.13706 | −0.249022 | ||||||||
\(277\) | −10.8237 | −0.650334 | −0.325167 | − | 0.945657i | \(-0.605420\pi\) | ||||
−0.325167 | + | 0.945657i | \(0.605420\pi\) | |||||||
\(278\) | −16.2078 | −0.972076 | ||||||||
\(279\) | 1.67456 | 0.100253 | ||||||||
\(280\) | −2.35690 | −0.140851 | ||||||||
\(281\) | 14.7778 | 0.881568 | 0.440784 | − | 0.897613i | \(-0.354700\pi\) | ||||
0.440784 | + | 0.897613i | \(0.354700\pi\) | |||||||
\(282\) | 5.37435 | 0.320038 | ||||||||
\(283\) | 12.6635 | 0.752770 | 0.376385 | − | 0.926463i | \(-0.377167\pi\) | ||||
0.376385 | + | 0.926463i | \(0.377167\pi\) | |||||||
\(284\) | −45.5109 | −2.70058 | ||||||||
\(285\) | −1.42327 | −0.0843073 | ||||||||
\(286\) | 6.06100 | 0.358394 | ||||||||
\(287\) | 8.70171 | 0.513646 | ||||||||
\(288\) | −7.55065 | −0.444926 | ||||||||
\(289\) | −8.87263 | −0.521919 | ||||||||
\(290\) | −16.5918 | −0.974304 | ||||||||
\(291\) | −0.760316 | −0.0445705 | ||||||||
\(292\) | 8.42327 | 0.492935 | ||||||||
\(293\) | 28.5894 | 1.67021 | 0.835105 | − | 0.550090i | \(-0.185407\pi\) | ||||
0.835105 | + | 0.550090i | \(0.185407\pi\) | |||||||
\(294\) | −3.04892 | −0.177816 | ||||||||
\(295\) | 2.59419 | 0.151039 | ||||||||
\(296\) | 8.81700 | 0.512478 | ||||||||
\(297\) | 4.24937 | 0.246574 | ||||||||
\(298\) | 13.5700 | 0.786090 | ||||||||
\(299\) | −3.58211 | −0.207158 | ||||||||
\(300\) | 4.13706 | 0.238853 | ||||||||
\(301\) | −2.24698 | −0.129514 | ||||||||
\(302\) | −21.7289 | −1.25036 | ||||||||
\(303\) | −5.77586 | −0.331814 | ||||||||
\(304\) | −0.841166 | −0.0482442 | ||||||||
\(305\) | 8.76271 | 0.501751 | ||||||||
\(306\) | −7.42327 | −0.424360 | ||||||||
\(307\) | −9.38703 | −0.535746 | −0.267873 | − | 0.963454i | \(-0.586321\pi\) | ||||
−0.267873 | + | 0.963454i | \(0.586321\pi\) | |||||||
\(308\) | 2.29590 | 0.130821 | ||||||||
\(309\) | −7.88577 | −0.448606 | ||||||||
\(310\) | −3.24698 | −0.184416 | ||||||||
\(311\) | 1.70171 | 0.0964951 | 0.0482476 | − | 0.998835i | \(-0.484636\pi\) | ||||
0.0482476 | + | 0.998835i | \(0.484636\pi\) | |||||||
\(312\) | −11.4558 | −0.648557 | ||||||||
\(313\) | −31.7415 | −1.79414 | −0.897069 | − | 0.441891i | \(-0.854308\pi\) | ||||
−0.897069 | + | 0.441891i | \(0.854308\pi\) | |||||||
\(314\) | 17.0640 | 0.962976 | ||||||||
\(315\) | −1.15883 | −0.0652929 | ||||||||
\(316\) | −33.7700 | −1.89971 | ||||||||
\(317\) | 20.6950 | 1.16235 | 0.581174 | − | 0.813780i | \(-0.302594\pi\) | ||||
0.581174 | + | 0.813780i | \(0.302594\pi\) | |||||||
\(318\) | −37.3327 | −2.09352 | ||||||||
\(319\) | 5.56033 | 0.311319 | ||||||||
\(320\) | 13.0368 | 0.728781 | ||||||||
\(321\) | −18.6819 | −1.04272 | ||||||||
\(322\) | −2.24698 | −0.125219 | ||||||||
\(323\) | −2.99031 | −0.166385 | ||||||||
\(324\) | −12.7463 | −0.708129 | ||||||||
\(325\) | 3.58211 | 0.198699 | ||||||||
\(326\) | −11.5797 | −0.641341 | ||||||||
\(327\) | 4.95646 | 0.274093 | ||||||||
\(328\) | 20.5090 | 1.13242 | ||||||||
\(329\) | 1.76271 | 0.0971813 | ||||||||
\(330\) | −2.29590 | −0.126385 | ||||||||
\(331\) | −0.109916 | −0.00604154 | −0.00302077 | − | 0.999995i | \(-0.500962\pi\) | ||||
−0.00302077 | + | 0.999995i | \(0.500962\pi\) | |||||||
\(332\) | −41.5435 | −2.27999 | ||||||||
\(333\) | 4.33513 | 0.237563 | ||||||||
\(334\) | −40.1202 | −2.19528 | ||||||||
\(335\) | −6.47219 | −0.353613 | ||||||||
\(336\) | 1.08815 | 0.0593632 | ||||||||
\(337\) | −19.0683 | −1.03872 | −0.519358 | − | 0.854557i | \(-0.673829\pi\) | ||||
−0.519358 | + | 0.854557i | \(0.673829\pi\) | |||||||
\(338\) | 0.378666 | 0.0205967 | ||||||||
\(339\) | −24.7888 | −1.34634 | ||||||||
\(340\) | 8.69202 | 0.471391 | ||||||||
\(341\) | 1.08815 | 0.0589264 | ||||||||
\(342\) | 2.73125 | 0.147689 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −5.29590 | −0.285536 | ||||||||
\(345\) | 1.35690 | 0.0730528 | ||||||||
\(346\) | −4.89977 | −0.263413 | ||||||||
\(347\) | −28.0489 | −1.50574 | −0.752872 | − | 0.658167i | \(-0.771332\pi\) | ||||
−0.752872 | + | 0.658167i | \(0.771332\pi\) | |||||||
\(348\) | −30.5483 | −1.63756 | ||||||||
\(349\) | 28.9691 | 1.55068 | 0.775341 | − | 0.631543i | \(-0.217578\pi\) | ||||
0.775341 | + | 0.631543i | \(0.217578\pi\) | |||||||
\(350\) | 2.24698 | 0.120106 | ||||||||
\(351\) | −20.2142 | −1.07895 | ||||||||
\(352\) | −4.90648 | −0.261516 | ||||||||
\(353\) | 16.5579 | 0.881290 | 0.440645 | − | 0.897681i | \(-0.354750\pi\) | ||||
0.440645 | + | 0.897681i | \(0.354750\pi\) | |||||||
\(354\) | 7.90946 | 0.420383 | ||||||||
\(355\) | 14.9269 | 0.792239 | ||||||||
\(356\) | 10.5700 | 0.560210 | ||||||||
\(357\) | 3.86831 | 0.204733 | ||||||||
\(358\) | 7.57002 | 0.400088 | ||||||||
\(359\) | −15.0043 | −0.791897 | −0.395949 | − | 0.918273i | \(-0.629584\pi\) | ||||
−0.395949 | + | 0.918273i | \(0.629584\pi\) | |||||||
\(360\) | −2.73125 | −0.143950 | ||||||||
\(361\) | −17.8998 | −0.942093 | ||||||||
\(362\) | −3.63102 | −0.190842 | ||||||||
\(363\) | −14.1564 | −0.743020 | ||||||||
\(364\) | −10.9215 | −0.572444 | ||||||||
\(365\) | −2.76271 | −0.144607 | ||||||||
\(366\) | 26.7168 | 1.39651 | ||||||||
\(367\) | 3.05131 | 0.159277 | 0.0796385 | − | 0.996824i | \(-0.474623\pi\) | ||||
0.0796385 | + | 0.996824i | \(0.474623\pi\) | |||||||
\(368\) | 0.801938 | 0.0418039 | ||||||||
\(369\) | 10.0838 | 0.524943 | ||||||||
\(370\) | −8.40581 | −0.436997 | ||||||||
\(371\) | −12.2446 | −0.635707 | ||||||||
\(372\) | −5.97823 | −0.309957 | ||||||||
\(373\) | −9.60686 | −0.497424 | −0.248712 | − | 0.968577i | \(-0.580007\pi\) | ||||
−0.248712 | + | 0.968577i | \(0.580007\pi\) | |||||||
\(374\) | −4.82371 | −0.249428 | ||||||||
\(375\) | −1.35690 | −0.0700698 | ||||||||
\(376\) | 4.15452 | 0.214253 | ||||||||
\(377\) | −26.4504 | −1.36227 | ||||||||
\(378\) | −12.6799 | −0.652186 | ||||||||
\(379\) | 3.00969 | 0.154597 | 0.0772987 | − | 0.997008i | \(-0.475371\pi\) | ||||
0.0772987 | + | 0.997008i | \(0.475371\pi\) | |||||||
\(380\) | −3.19806 | −0.164057 | ||||||||
\(381\) | 26.3521 | 1.35006 | ||||||||
\(382\) | −1.87263 | −0.0958118 | ||||||||
\(383\) | 22.0344 | 1.12591 | 0.562954 | − | 0.826488i | \(-0.309665\pi\) | ||||
0.562954 | + | 0.826488i | \(0.309665\pi\) | |||||||
\(384\) | 22.0659 | 1.12605 | ||||||||
\(385\) | −0.753020 | −0.0383775 | ||||||||
\(386\) | −27.0127 | −1.37491 | ||||||||
\(387\) | −2.60388 | −0.132362 | ||||||||
\(388\) | −1.70841 | −0.0867316 | ||||||||
\(389\) | 14.3478 | 0.727462 | 0.363731 | − | 0.931504i | \(-0.381503\pi\) | ||||
0.363731 | + | 0.931504i | \(0.381503\pi\) | |||||||
\(390\) | 10.9215 | 0.553034 | ||||||||
\(391\) | 2.85086 | 0.144174 | ||||||||
\(392\) | −2.35690 | −0.119041 | ||||||||
\(393\) | 19.6668 | 0.992058 | ||||||||
\(394\) | −53.8340 | −2.71212 | ||||||||
\(395\) | 11.0761 | 0.557297 | ||||||||
\(396\) | 2.66056 | 0.133698 | ||||||||
\(397\) | −5.44803 | −0.273429 | −0.136714 | − | 0.990611i | \(-0.543654\pi\) | ||||
−0.136714 | + | 0.990611i | \(0.543654\pi\) | |||||||
\(398\) | 48.2180 | 2.41695 | ||||||||
\(399\) | −1.42327 | −0.0712527 | ||||||||
\(400\) | −0.801938 | −0.0400969 | ||||||||
\(401\) | −4.68127 | −0.233771 | −0.116886 | − | 0.993145i | \(-0.537291\pi\) | ||||
−0.116886 | + | 0.993145i | \(0.537291\pi\) | |||||||
\(402\) | −19.7332 | −0.984201 | ||||||||
\(403\) | −5.17629 | −0.257849 | ||||||||
\(404\) | −12.9782 | −0.645691 | ||||||||
\(405\) | 4.18060 | 0.207736 | ||||||||
\(406\) | −16.5918 | −0.823437 | ||||||||
\(407\) | 2.81700 | 0.139634 | ||||||||
\(408\) | 9.11721 | 0.451369 | ||||||||
\(409\) | 30.4480 | 1.50556 | 0.752779 | − | 0.658273i | \(-0.228713\pi\) | ||||
0.752779 | + | 0.658273i | \(0.228713\pi\) | |||||||
\(410\) | −19.5526 | −0.965632 | ||||||||
\(411\) | −6.84356 | −0.337568 | ||||||||
\(412\) | −17.7192 | −0.872961 | ||||||||
\(413\) | 2.59419 | 0.127652 | ||||||||
\(414\) | −2.60388 | −0.127973 | ||||||||
\(415\) | 13.6256 | 0.668857 | ||||||||
\(416\) | 23.3400 | 1.14434 | ||||||||
\(417\) | 9.78746 | 0.479294 | ||||||||
\(418\) | 1.77479 | 0.0868078 | ||||||||
\(419\) | −5.81833 | −0.284244 | −0.142122 | − | 0.989849i | \(-0.545393\pi\) | ||||
−0.142122 | + | 0.989849i | \(0.545393\pi\) | |||||||
\(420\) | 4.13706 | 0.201868 | ||||||||
\(421\) | −17.7603 | −0.865585 | −0.432792 | − | 0.901494i | \(-0.642472\pi\) | ||||
−0.432792 | + | 0.901494i | \(0.642472\pi\) | |||||||
\(422\) | −30.9584 | −1.50703 | ||||||||
\(423\) | 2.04269 | 0.0993188 | ||||||||
\(424\) | −28.8592 | −1.40153 | ||||||||
\(425\) | −2.85086 | −0.138287 | ||||||||
\(426\) | 45.5109 | 2.20501 | ||||||||
\(427\) | 8.76271 | 0.424057 | ||||||||
\(428\) | −41.9778 | −2.02907 | ||||||||
\(429\) | −3.66009 | −0.176711 | ||||||||
\(430\) | 5.04892 | 0.243480 | ||||||||
\(431\) | −6.67696 | −0.321618 | −0.160809 | − | 0.986986i | \(-0.551410\pi\) | ||||
−0.160809 | + | 0.986986i | \(0.551410\pi\) | |||||||
\(432\) | 4.52542 | 0.217729 | ||||||||
\(433\) | −32.8388 | −1.57813 | −0.789065 | − | 0.614309i | \(-0.789435\pi\) | ||||
−0.789065 | + | 0.614309i | \(0.789435\pi\) | |||||||
\(434\) | −3.24698 | −0.155860 | ||||||||
\(435\) | 10.0194 | 0.480392 | ||||||||
\(436\) | 11.1371 | 0.533369 | ||||||||
\(437\) | −1.04892 | −0.0501765 | ||||||||
\(438\) | −8.42327 | −0.402479 | ||||||||
\(439\) | −0.624318 | −0.0297971 | −0.0148985 | − | 0.999889i | \(-0.504743\pi\) | ||||
−0.0148985 | + | 0.999889i | \(0.504743\pi\) | |||||||
\(440\) | −1.77479 | −0.0846098 | ||||||||
\(441\) | −1.15883 | −0.0551826 | ||||||||
\(442\) | 22.9463 | 1.09144 | ||||||||
\(443\) | −18.3666 | −0.872623 | −0.436311 | − | 0.899796i | \(-0.643715\pi\) | ||||
−0.436311 | + | 0.899796i | \(0.643715\pi\) | |||||||
\(444\) | −15.4765 | −0.734482 | ||||||||
\(445\) | −3.46681 | −0.164343 | ||||||||
\(446\) | −8.85623 | −0.419355 | ||||||||
\(447\) | −8.19460 | −0.387591 | ||||||||
\(448\) | 13.0368 | 0.615933 | ||||||||
\(449\) | 18.3491 | 0.865949 | 0.432974 | − | 0.901406i | \(-0.357464\pi\) | ||||
0.432974 | + | 0.901406i | \(0.357464\pi\) | |||||||
\(450\) | 2.60388 | 0.122748 | ||||||||
\(451\) | 6.55257 | 0.308548 | ||||||||
\(452\) | −55.6999 | −2.61990 | ||||||||
\(453\) | 13.1215 | 0.616503 | ||||||||
\(454\) | 38.7754 | 1.81982 | ||||||||
\(455\) | 3.58211 | 0.167932 | ||||||||
\(456\) | −3.35450 | −0.157089 | ||||||||
\(457\) | 27.0901 | 1.26722 | 0.633610 | − | 0.773653i | \(-0.281572\pi\) | ||||
0.633610 | + | 0.773653i | \(0.281572\pi\) | |||||||
\(458\) | −28.0562 | −1.31098 | ||||||||
\(459\) | 16.0877 | 0.750908 | ||||||||
\(460\) | 3.04892 | 0.142157 | ||||||||
\(461\) | 41.6708 | 1.94080 | 0.970402 | − | 0.241494i | \(-0.0776374\pi\) | ||||
0.970402 | + | 0.241494i | \(0.0776374\pi\) | |||||||
\(462\) | −2.29590 | −0.106815 | ||||||||
\(463\) | 3.67456 | 0.170771 | 0.0853857 | − | 0.996348i | \(-0.472788\pi\) | ||||
0.0853857 | + | 0.996348i | \(0.472788\pi\) | |||||||
\(464\) | 5.92154 | 0.274901 | ||||||||
\(465\) | 1.96077 | 0.0909286 | ||||||||
\(466\) | −32.0954 | −1.48679 | ||||||||
\(467\) | −14.6679 | −0.678748 | −0.339374 | − | 0.940652i | \(-0.610215\pi\) | ||||
−0.339374 | + | 0.940652i | \(0.610215\pi\) | |||||||
\(468\) | −12.6563 | −0.585035 | ||||||||
\(469\) | −6.47219 | −0.298858 | ||||||||
\(470\) | −3.96077 | −0.182697 | ||||||||
\(471\) | −10.3045 | −0.474807 | ||||||||
\(472\) | 6.11423 | 0.281430 | ||||||||
\(473\) | −1.69202 | −0.0777992 | ||||||||
\(474\) | 33.7700 | 1.55111 | ||||||||
\(475\) | 1.04892 | 0.0481276 | ||||||||
\(476\) | 8.69202 | 0.398398 | ||||||||
\(477\) | −14.1894 | −0.649690 | ||||||||
\(478\) | −17.9705 | −0.821950 | ||||||||
\(479\) | −10.9933 | −0.502296 | −0.251148 | − | 0.967949i | \(-0.580808\pi\) | ||||
−0.251148 | + | 0.967949i | \(0.580808\pi\) | |||||||
\(480\) | −8.84117 | −0.403542 | ||||||||
\(481\) | −13.4004 | −0.611007 | ||||||||
\(482\) | −18.9584 | −0.863530 | ||||||||
\(483\) | 1.35690 | 0.0617409 | ||||||||
\(484\) | −31.8092 | −1.44587 | ||||||||
\(485\) | 0.560335 | 0.0254435 | ||||||||
\(486\) | −25.2935 | −1.14734 | ||||||||
\(487\) | −21.9476 | −0.994542 | −0.497271 | − | 0.867595i | \(-0.665664\pi\) | ||||
−0.497271 | + | 0.867595i | \(0.665664\pi\) | |||||||
\(488\) | 20.6528 | 0.934908 | ||||||||
\(489\) | 6.99270 | 0.316221 | ||||||||
\(490\) | 2.24698 | 0.101508 | ||||||||
\(491\) | 18.9245 | 0.854052 | 0.427026 | − | 0.904239i | \(-0.359561\pi\) | ||||
0.427026 | + | 0.904239i | \(0.359561\pi\) | |||||||
\(492\) | −35.9995 | −1.62298 | ||||||||
\(493\) | 21.0508 | 0.948082 | ||||||||
\(494\) | −8.44265 | −0.379853 | ||||||||
\(495\) | −0.872625 | −0.0392216 | ||||||||
\(496\) | 1.15883 | 0.0520332 | ||||||||
\(497\) | 14.9269 | 0.669564 | ||||||||
\(498\) | 41.5435 | 1.86161 | ||||||||
\(499\) | −12.6407 | −0.565876 | −0.282938 | − | 0.959138i | \(-0.591309\pi\) | ||||
−0.282938 | + | 0.959138i | \(0.591309\pi\) | |||||||
\(500\) | −3.04892 | −0.136352 | ||||||||
\(501\) | 24.2276 | 1.08241 | ||||||||
\(502\) | −7.95539 | −0.355067 | ||||||||
\(503\) | 34.3400 | 1.53115 | 0.765573 | − | 0.643349i | \(-0.222456\pi\) | ||||
0.765573 | + | 0.643349i | \(0.222456\pi\) | |||||||
\(504\) | −2.73125 | −0.121660 | ||||||||
\(505\) | 4.25667 | 0.189419 | ||||||||
\(506\) | −1.69202 | −0.0752195 | ||||||||
\(507\) | −0.228667 | −0.0101555 | ||||||||
\(508\) | 59.2127 | 2.62714 | ||||||||
\(509\) | 9.30260 | 0.412331 | 0.206165 | − | 0.978517i | \(-0.433902\pi\) | ||||
0.206165 | + | 0.978517i | \(0.433902\pi\) | |||||||
\(510\) | −8.69202 | −0.384889 | ||||||||
\(511\) | −2.76271 | −0.122215 | ||||||||
\(512\) | −9.00538 | −0.397985 | ||||||||
\(513\) | −5.91915 | −0.261337 | ||||||||
\(514\) | 10.3961 | 0.458553 | ||||||||
\(515\) | 5.81163 | 0.256091 | ||||||||
\(516\) | 9.29590 | 0.409229 | ||||||||
\(517\) | 1.32736 | 0.0583770 | ||||||||
\(518\) | −8.40581 | −0.369330 | ||||||||
\(519\) | 2.95885 | 0.129879 | ||||||||
\(520\) | 8.44265 | 0.370235 | ||||||||
\(521\) | 22.8780 | 1.00230 | 0.501152 | − | 0.865359i | \(-0.332910\pi\) | ||||
0.501152 | + | 0.865359i | \(0.332910\pi\) | |||||||
\(522\) | −19.2271 | −0.841549 | ||||||||
\(523\) | −17.4746 | −0.764110 | −0.382055 | − | 0.924140i | \(-0.624784\pi\) | ||||
−0.382055 | + | 0.924140i | \(0.624784\pi\) | |||||||
\(524\) | 44.1909 | 1.93049 | ||||||||
\(525\) | −1.35690 | −0.0592198 | ||||||||
\(526\) | 26.9215 | 1.17384 | ||||||||
\(527\) | 4.11960 | 0.179453 | ||||||||
\(528\) | 0.819396 | 0.0356596 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 27.5133 | 1.19510 | ||||||||
\(531\) | 3.00623 | 0.130459 | ||||||||
\(532\) | −3.19806 | −0.138654 | ||||||||
\(533\) | −31.1704 | −1.35014 | ||||||||
\(534\) | −10.5700 | −0.457410 | ||||||||
\(535\) | 13.7681 | 0.595246 | ||||||||
\(536\) | −15.2543 | −0.658884 | ||||||||
\(537\) | −4.57135 | −0.197268 | ||||||||
\(538\) | −54.5139 | −2.35026 | ||||||||
\(539\) | −0.753020 | −0.0324349 | ||||||||
\(540\) | 17.2054 | 0.740401 | ||||||||
\(541\) | 8.64981 | 0.371884 | 0.185942 | − | 0.982561i | \(-0.440466\pi\) | ||||
0.185942 | + | 0.982561i | \(0.440466\pi\) | |||||||
\(542\) | 27.0586 | 1.16227 | ||||||||
\(543\) | 2.19269 | 0.0940971 | ||||||||
\(544\) | −18.5754 | −0.796414 | ||||||||
\(545\) | −3.65279 | −0.156468 | ||||||||
\(546\) | 10.9215 | 0.467399 | ||||||||
\(547\) | 21.4349 | 0.916489 | 0.458245 | − | 0.888826i | \(-0.348478\pi\) | ||||
0.458245 | + | 0.888826i | \(0.348478\pi\) | |||||||
\(548\) | −15.3773 | −0.656887 | ||||||||
\(549\) | 10.1545 | 0.433384 | ||||||||
\(550\) | 1.69202 | 0.0721480 | ||||||||
\(551\) | −7.74525 | −0.329959 | ||||||||
\(552\) | 3.19806 | 0.136119 | ||||||||
\(553\) | 11.0761 | 0.471002 | ||||||||
\(554\) | 24.3207 | 1.03329 | ||||||||
\(555\) | 5.07606 | 0.215467 | ||||||||
\(556\) | 21.9922 | 0.932678 | ||||||||
\(557\) | −33.0471 | −1.40025 | −0.700126 | − | 0.714020i | \(-0.746873\pi\) | ||||
−0.700126 | + | 0.714020i | \(0.746873\pi\) | |||||||
\(558\) | −3.76271 | −0.159288 | ||||||||
\(559\) | 8.04892 | 0.340433 | ||||||||
\(560\) | −0.801938 | −0.0338881 | ||||||||
\(561\) | 2.91292 | 0.122984 | ||||||||
\(562\) | −33.2054 | −1.40068 | ||||||||
\(563\) | 24.0006 | 1.01150 | 0.505752 | − | 0.862679i | \(-0.331215\pi\) | ||||
0.505752 | + | 0.862679i | \(0.331215\pi\) | |||||||
\(564\) | −7.29244 | −0.307067 | ||||||||
\(565\) | 18.2687 | 0.768572 | ||||||||
\(566\) | −28.4547 | −1.19604 | ||||||||
\(567\) | 4.18060 | 0.175569 | ||||||||
\(568\) | 35.1812 | 1.47617 | ||||||||
\(569\) | −24.3991 | −1.02286 | −0.511432 | − | 0.859324i | \(-0.670885\pi\) | ||||
−0.511432 | + | 0.859324i | \(0.670885\pi\) | |||||||
\(570\) | 3.19806 | 0.133952 | ||||||||
\(571\) | −33.4209 | −1.39862 | −0.699310 | − | 0.714818i | \(-0.746509\pi\) | ||||
−0.699310 | + | 0.714818i | \(0.746509\pi\) | |||||||
\(572\) | −8.22414 | −0.343869 | ||||||||
\(573\) | 1.13083 | 0.0472412 | ||||||||
\(574\) | −19.5526 | −0.816108 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 15.1075 | 0.629480 | ||||||||
\(577\) | 2.31873 | 0.0965301 | 0.0482650 | − | 0.998835i | \(-0.484631\pi\) | ||||
0.0482650 | + | 0.998835i | \(0.484631\pi\) | |||||||
\(578\) | 19.9366 | 0.829254 | ||||||||
\(579\) | 16.3123 | 0.677916 | ||||||||
\(580\) | 22.5133 | 0.934815 | ||||||||
\(581\) | 13.6256 | 0.565287 | ||||||||
\(582\) | 1.70841 | 0.0708161 | ||||||||
\(583\) | −9.22042 | −0.381871 | ||||||||
\(584\) | −6.51142 | −0.269444 | ||||||||
\(585\) | 4.15106 | 0.171625 | ||||||||
\(586\) | −64.2398 | −2.65372 | ||||||||
\(587\) | 1.25906 | 0.0519670 | 0.0259835 | − | 0.999662i | \(-0.491728\pi\) | ||||
0.0259835 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(588\) | 4.13706 | 0.170610 | ||||||||
\(589\) | −1.51573 | −0.0624545 | ||||||||
\(590\) | −5.82908 | −0.239980 | ||||||||
\(591\) | 32.5090 | 1.33724 | ||||||||
\(592\) | 3.00000 | 0.123299 | ||||||||
\(593\) | 34.0422 | 1.39795 | 0.698973 | − | 0.715148i | \(-0.253641\pi\) | ||||
0.698973 | + | 0.715148i | \(0.253641\pi\) | |||||||
\(594\) | −9.54825 | −0.391770 | ||||||||
\(595\) | −2.85086 | −0.116874 | ||||||||
\(596\) | −18.4131 | −0.754230 | ||||||||
\(597\) | −29.1177 | −1.19171 | ||||||||
\(598\) | 8.04892 | 0.329145 | ||||||||
\(599\) | −11.1631 | −0.456114 | −0.228057 | − | 0.973648i | \(-0.573237\pi\) | ||||
−0.228057 | + | 0.973648i | \(0.573237\pi\) | |||||||
\(600\) | −3.19806 | −0.130560 | ||||||||
\(601\) | −21.1323 | −0.862004 | −0.431002 | − | 0.902351i | \(-0.641840\pi\) | ||||
−0.431002 | + | 0.902351i | \(0.641840\pi\) | |||||||
\(602\) | 5.04892 | 0.205779 | ||||||||
\(603\) | −7.50019 | −0.305431 | ||||||||
\(604\) | 29.4838 | 1.19968 | ||||||||
\(605\) | 10.4330 | 0.424160 | ||||||||
\(606\) | 12.9782 | 0.527205 | ||||||||
\(607\) | 11.6112 | 0.471283 | 0.235641 | − | 0.971840i | \(-0.424281\pi\) | ||||
0.235641 | + | 0.971840i | \(0.424281\pi\) | |||||||
\(608\) | 6.83446 | 0.277174 | ||||||||
\(609\) | 10.0194 | 0.406006 | ||||||||
\(610\) | −19.6896 | −0.797210 | ||||||||
\(611\) | −6.31421 | −0.255446 | ||||||||
\(612\) | 10.0726 | 0.407161 | ||||||||
\(613\) | −8.34481 | −0.337044 | −0.168522 | − | 0.985698i | \(-0.553899\pi\) | ||||
−0.168522 | + | 0.985698i | \(0.553899\pi\) | |||||||
\(614\) | 21.0925 | 0.851222 | ||||||||
\(615\) | 11.8073 | 0.476117 | ||||||||
\(616\) | −1.77479 | −0.0715084 | ||||||||
\(617\) | −1.55197 | −0.0624801 | −0.0312401 | − | 0.999512i | \(-0.509946\pi\) | ||||
−0.0312401 | + | 0.999512i | \(0.509946\pi\) | |||||||
\(618\) | 17.7192 | 0.712769 | ||||||||
\(619\) | −37.0388 | −1.48871 | −0.744357 | − | 0.667782i | \(-0.767244\pi\) | ||||
−0.744357 | + | 0.667782i | \(0.767244\pi\) | |||||||
\(620\) | 4.40581 | 0.176942 | ||||||||
\(621\) | 5.64310 | 0.226450 | ||||||||
\(622\) | −3.82371 | −0.153317 | ||||||||
\(623\) | −3.46681 | −0.138895 | ||||||||
\(624\) | −3.89785 | −0.156039 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 71.3226 | 2.85062 | ||||||||
\(627\) | −1.07175 | −0.0428017 | ||||||||
\(628\) | −23.1540 | −0.923947 | ||||||||
\(629\) | 10.6649 | 0.425236 | ||||||||
\(630\) | 2.60388 | 0.103741 | ||||||||
\(631\) | −9.07547 | −0.361289 | −0.180644 | − | 0.983548i | \(-0.557818\pi\) | ||||
−0.180644 | + | 0.983548i | \(0.557818\pi\) | |||||||
\(632\) | 26.1051 | 1.03841 | ||||||||
\(633\) | 18.6950 | 0.743060 | ||||||||
\(634\) | −46.5013 | −1.84680 | ||||||||
\(635\) | −19.4209 | −0.770694 | ||||||||
\(636\) | 50.6566 | 2.00867 | ||||||||
\(637\) | 3.58211 | 0.141928 | ||||||||
\(638\) | −12.4940 | −0.494641 | ||||||||
\(639\) | 17.2978 | 0.684291 | ||||||||
\(640\) | −16.2620 | −0.642814 | ||||||||
\(641\) | 6.99090 | 0.276124 | 0.138062 | − | 0.990424i | \(-0.455913\pi\) | ||||
0.138062 | + | 0.990424i | \(0.455913\pi\) | |||||||
\(642\) | 41.9778 | 1.65673 | ||||||||
\(643\) | −23.8907 | −0.942156 | −0.471078 | − | 0.882091i | \(-0.656135\pi\) | ||||
−0.471078 | + | 0.882091i | \(0.656135\pi\) | |||||||
\(644\) | 3.04892 | 0.120144 | ||||||||
\(645\) | −3.04892 | −0.120051 | ||||||||
\(646\) | 6.71917 | 0.264362 | ||||||||
\(647\) | −39.2295 | −1.54227 | −0.771136 | − | 0.636671i | \(-0.780311\pi\) | ||||
−0.771136 | + | 0.636671i | \(0.780311\pi\) | |||||||
\(648\) | 9.85325 | 0.387072 | ||||||||
\(649\) | 1.95348 | 0.0766806 | ||||||||
\(650\) | −8.04892 | −0.315705 | ||||||||
\(651\) | 1.96077 | 0.0768487 | ||||||||
\(652\) | 15.7125 | 0.615348 | ||||||||
\(653\) | −35.0151 | −1.37025 | −0.685123 | − | 0.728428i | \(-0.740251\pi\) | ||||
−0.685123 | + | 0.728428i | \(0.740251\pi\) | |||||||
\(654\) | −11.1371 | −0.435494 | ||||||||
\(655\) | −14.4940 | −0.566326 | ||||||||
\(656\) | 6.97823 | 0.272454 | ||||||||
\(657\) | −3.20152 | −0.124903 | ||||||||
\(658\) | −3.96077 | −0.154407 | ||||||||
\(659\) | −38.7391 | −1.50906 | −0.754531 | − | 0.656264i | \(-0.772136\pi\) | ||||
−0.754531 | + | 0.656264i | \(0.772136\pi\) | |||||||
\(660\) | 3.11529 | 0.121263 | ||||||||
\(661\) | −13.9769 | −0.543638 | −0.271819 | − | 0.962348i | \(-0.587625\pi\) | ||||
−0.271819 | + | 0.962348i | \(0.587625\pi\) | |||||||
\(662\) | 0.246980 | 0.00959913 | ||||||||
\(663\) | −13.8567 | −0.538150 | ||||||||
\(664\) | 32.1142 | 1.24627 | ||||||||
\(665\) | 1.04892 | 0.0406753 | ||||||||
\(666\) | −9.74094 | −0.377454 | ||||||||
\(667\) | 7.38404 | 0.285911 | ||||||||
\(668\) | 54.4389 | 2.10631 | ||||||||
\(669\) | 5.34806 | 0.206768 | ||||||||
\(670\) | 14.5429 | 0.561840 | ||||||||
\(671\) | 6.59850 | 0.254732 | ||||||||
\(672\) | −8.84117 | −0.341055 | ||||||||
\(673\) | −1.82430 | −0.0703216 | −0.0351608 | − | 0.999382i | \(-0.511194\pi\) | ||||
−0.0351608 | + | 0.999382i | \(0.511194\pi\) | |||||||
\(674\) | 42.8461 | 1.65037 | ||||||||
\(675\) | −5.64310 | −0.217203 | ||||||||
\(676\) | −0.513811 | −0.0197619 | ||||||||
\(677\) | 44.7982 | 1.72174 | 0.860868 | − | 0.508829i | \(-0.169921\pi\) | ||||
0.860868 | + | 0.508829i | \(0.169921\pi\) | |||||||
\(678\) | 55.6999 | 2.13914 | ||||||||
\(679\) | 0.560335 | 0.0215037 | ||||||||
\(680\) | −6.71917 | −0.257668 | ||||||||
\(681\) | −23.4155 | −0.897284 | ||||||||
\(682\) | −2.44504 | −0.0936255 | ||||||||
\(683\) | −51.7193 | −1.97898 | −0.989492 | − | 0.144589i | \(-0.953814\pi\) | ||||
−0.989492 | + | 0.144589i | \(0.953814\pi\) | |||||||
\(684\) | −3.70602 | −0.141703 | ||||||||
\(685\) | 5.04354 | 0.192704 | ||||||||
\(686\) | 2.24698 | 0.0857901 | ||||||||
\(687\) | 16.9425 | 0.646395 | ||||||||
\(688\) | −1.80194 | −0.0686982 | ||||||||
\(689\) | 43.8614 | 1.67099 | ||||||||
\(690\) | −3.04892 | −0.116070 | ||||||||
\(691\) | −24.9511 | −0.949184 | −0.474592 | − | 0.880206i | \(-0.657404\pi\) | ||||
−0.474592 | + | 0.880206i | \(0.657404\pi\) | |||||||
\(692\) | 6.64848 | 0.252737 | ||||||||
\(693\) | −0.872625 | −0.0331483 | ||||||||
\(694\) | 63.0253 | 2.39241 | ||||||||
\(695\) | −7.21313 | −0.273610 | ||||||||
\(696\) | 23.6146 | 0.895110 | ||||||||
\(697\) | 24.8073 | 0.939644 | ||||||||
\(698\) | −65.0930 | −2.46381 | ||||||||
\(699\) | 19.3817 | 0.733081 | ||||||||
\(700\) | −3.04892 | −0.115238 | ||||||||
\(701\) | 38.7090 | 1.46202 | 0.731009 | − | 0.682367i | \(-0.239050\pi\) | ||||
0.731009 | + | 0.682367i | \(0.239050\pi\) | |||||||
\(702\) | 45.4209 | 1.71430 | ||||||||
\(703\) | −3.92394 | −0.147994 | ||||||||
\(704\) | 9.81700 | 0.369992 | ||||||||
\(705\) | 2.39181 | 0.0900809 | ||||||||
\(706\) | −37.2054 | −1.40024 | ||||||||
\(707\) | 4.25667 | 0.160088 | ||||||||
\(708\) | −10.7323 | −0.403345 | ||||||||
\(709\) | −27.9004 | −1.04782 | −0.523910 | − | 0.851774i | \(-0.675527\pi\) | ||||
−0.523910 | + | 0.851774i | \(0.675527\pi\) | |||||||
\(710\) | −33.5405 | −1.25875 | ||||||||
\(711\) | 12.8353 | 0.481362 | ||||||||
\(712\) | −8.17092 | −0.306218 | ||||||||
\(713\) | 1.44504 | 0.0541172 | ||||||||
\(714\) | −8.69202 | −0.325291 | ||||||||
\(715\) | 2.69740 | 0.100877 | ||||||||
\(716\) | −10.2717 | −0.383873 | ||||||||
\(717\) | 10.8519 | 0.405272 | ||||||||
\(718\) | 33.7144 | 1.25821 | ||||||||
\(719\) | −26.8310 | −1.00063 | −0.500314 | − | 0.865844i | \(-0.666782\pi\) | ||||
−0.500314 | + | 0.865844i | \(0.666782\pi\) | |||||||
\(720\) | −0.929312 | −0.0346334 | ||||||||
\(721\) | 5.81163 | 0.216436 | ||||||||
\(722\) | 40.2204 | 1.49685 | ||||||||
\(723\) | 11.4485 | 0.425774 | ||||||||
\(724\) | 4.92692 | 0.183108 | ||||||||
\(725\) | −7.38404 | −0.274236 | ||||||||
\(726\) | 31.8092 | 1.18055 | ||||||||
\(727\) | −19.1172 | −0.709018 | −0.354509 | − | 0.935053i | \(-0.615352\pi\) | ||||
−0.354509 | + | 0.935053i | \(0.615352\pi\) | |||||||
\(728\) | 8.44265 | 0.312905 | ||||||||
\(729\) | 27.8159 | 1.03022 | ||||||||
\(730\) | 6.20775 | 0.229759 | ||||||||
\(731\) | −6.40581 | −0.236928 | ||||||||
\(732\) | −36.2519 | −1.33991 | ||||||||
\(733\) | 49.2170 | 1.81787 | 0.908935 | − | 0.416938i | \(-0.136897\pi\) | ||||
0.908935 | + | 0.416938i | \(0.136897\pi\) | |||||||
\(734\) | −6.85623 | −0.253068 | ||||||||
\(735\) | −1.35690 | −0.0500499 | ||||||||
\(736\) | −6.51573 | −0.240173 | ||||||||
\(737\) | −4.87369 | −0.179525 | ||||||||
\(738\) | −22.6582 | −0.834059 | ||||||||
\(739\) | 12.7928 | 0.470592 | 0.235296 | − | 0.971924i | \(-0.424394\pi\) | ||||
0.235296 | + | 0.971924i | \(0.424394\pi\) | |||||||
\(740\) | 11.4058 | 0.419286 | ||||||||
\(741\) | 5.09831 | 0.187291 | ||||||||
\(742\) | 27.5133 | 1.01005 | ||||||||
\(743\) | 19.2687 | 0.706902 | 0.353451 | − | 0.935453i | \(-0.385008\pi\) | ||||
0.353451 | + | 0.935453i | \(0.385008\pi\) | |||||||
\(744\) | 4.62133 | 0.169426 | ||||||||
\(745\) | 6.03923 | 0.221260 | ||||||||
\(746\) | 21.5864 | 0.790335 | ||||||||
\(747\) | 15.7899 | 0.577721 | ||||||||
\(748\) | 6.54527 | 0.239319 | ||||||||
\(749\) | 13.7681 | 0.503075 | ||||||||
\(750\) | 3.04892 | 0.111331 | ||||||||
\(751\) | −36.1353 | −1.31859 | −0.659297 | − | 0.751882i | \(-0.729146\pi\) | ||||
−0.659297 | + | 0.751882i | \(0.729146\pi\) | |||||||
\(752\) | 1.41358 | 0.0515481 | ||||||||
\(753\) | 4.80407 | 0.175070 | ||||||||
\(754\) | 59.4336 | 2.16444 | ||||||||
\(755\) | −9.67025 | −0.351936 | ||||||||
\(756\) | 17.2054 | 0.625753 | ||||||||
\(757\) | −37.0471 | −1.34650 | −0.673250 | − | 0.739415i | \(-0.735102\pi\) | ||||
−0.673250 | + | 0.739415i | \(0.735102\pi\) | |||||||
\(758\) | −6.76271 | −0.245633 | ||||||||
\(759\) | 1.02177 | 0.0370879 | ||||||||
\(760\) | 2.47219 | 0.0896757 | ||||||||
\(761\) | −32.8842 | −1.19205 | −0.596026 | − | 0.802965i | \(-0.703255\pi\) | ||||
−0.596026 | + | 0.802965i | \(0.703255\pi\) | |||||||
\(762\) | −59.2127 | −2.14505 | ||||||||
\(763\) | −3.65279 | −0.132240 | ||||||||
\(764\) | 2.54096 | 0.0919286 | ||||||||
\(765\) | −3.30367 | −0.119444 | ||||||||
\(766\) | −49.5109 | −1.78890 | ||||||||
\(767\) | −9.29265 | −0.335538 | ||||||||
\(768\) | −14.2024 | −0.512484 | ||||||||
\(769\) | 38.2258 | 1.37846 | 0.689229 | − | 0.724544i | \(-0.257949\pi\) | ||||
0.689229 | + | 0.724544i | \(0.257949\pi\) | |||||||
\(770\) | 1.69202 | 0.0609762 | ||||||||
\(771\) | −6.27796 | −0.226095 | ||||||||
\(772\) | 36.6534 | 1.31918 | ||||||||
\(773\) | 53.4470 | 1.92235 | 0.961177 | − | 0.275933i | \(-0.0889869\pi\) | ||||
0.961177 | + | 0.275933i | \(0.0889869\pi\) | |||||||
\(774\) | 5.85086 | 0.210305 | ||||||||
\(775\) | −1.44504 | −0.0519074 | ||||||||
\(776\) | 1.32065 | 0.0474086 | ||||||||
\(777\) | 5.07606 | 0.182103 | ||||||||
\(778\) | −32.2392 | −1.15583 | ||||||||
\(779\) | −9.12737 | −0.327022 | ||||||||
\(780\) | −14.8194 | −0.530619 | ||||||||
\(781\) | 11.2403 | 0.402209 | ||||||||
\(782\) | −6.40581 | −0.229071 | ||||||||
\(783\) | 41.6689 | 1.48913 | ||||||||
\(784\) | −0.801938 | −0.0286406 | ||||||||
\(785\) | 7.59419 | 0.271048 | ||||||||
\(786\) | −44.1909 | −1.57624 | ||||||||
\(787\) | −32.6568 | −1.16409 | −0.582045 | − | 0.813156i | \(-0.697747\pi\) | ||||
−0.582045 | + | 0.813156i | \(0.697747\pi\) | |||||||
\(788\) | 73.0471 | 2.60220 | ||||||||
\(789\) | −16.2573 | −0.578774 | ||||||||
\(790\) | −24.8877 | −0.885464 | ||||||||
\(791\) | 18.2687 | 0.649562 | ||||||||
\(792\) | −2.05669 | −0.0730812 | ||||||||
\(793\) | −31.3889 | −1.11465 | ||||||||
\(794\) | 12.2416 | 0.434438 | ||||||||
\(795\) | −16.6146 | −0.589260 | ||||||||
\(796\) | −65.4268 | −2.31899 | ||||||||
\(797\) | 9.12498 | 0.323223 | 0.161612 | − | 0.986854i | \(-0.448331\pi\) | ||||
0.161612 | + | 0.986854i | \(0.448331\pi\) | |||||||
\(798\) | 3.19806 | 0.113210 | ||||||||
\(799\) | 5.02523 | 0.177780 | ||||||||
\(800\) | 6.51573 | 0.230366 | ||||||||
\(801\) | −4.01746 | −0.141950 | ||||||||
\(802\) | 10.5187 | 0.371429 | ||||||||
\(803\) | −2.08038 | −0.0734149 | ||||||||
\(804\) | 26.7759 | 0.944312 | ||||||||
\(805\) | −1.00000 | −0.0352454 | ||||||||
\(806\) | 11.6310 | 0.409685 | ||||||||
\(807\) | 32.9196 | 1.15883 | ||||||||
\(808\) | 10.0325 | 0.352943 | ||||||||
\(809\) | −29.2127 | −1.02706 | −0.513531 | − | 0.858071i | \(-0.671663\pi\) | ||||
−0.513531 | + | 0.858071i | \(0.671663\pi\) | |||||||
\(810\) | −9.39373 | −0.330062 | ||||||||
\(811\) | −27.4892 | −0.965275 | −0.482638 | − | 0.875820i | \(-0.660321\pi\) | ||||
−0.482638 | + | 0.875820i | \(0.660321\pi\) | |||||||
\(812\) | 22.5133 | 0.790063 | ||||||||
\(813\) | −16.3400 | −0.573070 | ||||||||
\(814\) | −6.32975 | −0.221858 | ||||||||
\(815\) | −5.15346 | −0.180518 | ||||||||
\(816\) | 3.10215 | 0.108597 | ||||||||
\(817\) | 2.35690 | 0.0824573 | ||||||||
\(818\) | −68.4161 | −2.39211 | ||||||||
\(819\) | 4.15106 | 0.145050 | ||||||||
\(820\) | 26.5308 | 0.926496 | ||||||||
\(821\) | −43.6249 | −1.52252 | −0.761260 | − | 0.648447i | \(-0.775419\pi\) | ||||
−0.761260 | + | 0.648447i | \(0.775419\pi\) | |||||||
\(822\) | 15.3773 | 0.536346 | ||||||||
\(823\) | −37.9154 | −1.32165 | −0.660824 | − | 0.750541i | \(-0.729793\pi\) | ||||
−0.660824 | + | 0.750541i | \(0.729793\pi\) | |||||||
\(824\) | 13.6974 | 0.477171 | ||||||||
\(825\) | −1.02177 | −0.0355735 | ||||||||
\(826\) | −5.82908 | −0.202820 | ||||||||
\(827\) | −32.6765 | −1.13627 | −0.568136 | − | 0.822934i | \(-0.692335\pi\) | ||||
−0.568136 | + | 0.822934i | \(0.692335\pi\) | |||||||
\(828\) | 3.53319 | 0.122787 | ||||||||
\(829\) | 53.0998 | 1.84423 | 0.922115 | − | 0.386915i | \(-0.126459\pi\) | ||||
0.922115 | + | 0.386915i | \(0.126459\pi\) | |||||||
\(830\) | −30.6165 | −1.06272 | ||||||||
\(831\) | −14.6866 | −0.509474 | ||||||||
\(832\) | −46.6993 | −1.61901 | ||||||||
\(833\) | −2.85086 | −0.0987763 | ||||||||
\(834\) | −21.9922 | −0.761529 | ||||||||
\(835\) | −17.8552 | −0.617904 | ||||||||
\(836\) | −2.40821 | −0.0832896 | ||||||||
\(837\) | 8.15452 | 0.281862 | ||||||||
\(838\) | 13.0737 | 0.451622 | ||||||||
\(839\) | −46.2881 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(840\) | −3.19806 | −0.110344 | ||||||||
\(841\) | 25.5241 | 0.880141 | ||||||||
\(842\) | 39.9071 | 1.37529 | ||||||||
\(843\) | 20.0519 | 0.690624 | ||||||||
\(844\) | 42.0073 | 1.44595 | ||||||||
\(845\) | 0.168522 | 0.00579734 | ||||||||
\(846\) | −4.58987 | −0.157803 | ||||||||
\(847\) | 10.4330 | 0.358481 | ||||||||
\(848\) | −9.81940 | −0.337199 | ||||||||
\(849\) | 17.1831 | 0.589723 | ||||||||
\(850\) | 6.40581 | 0.219718 | ||||||||
\(851\) | 3.74094 | 0.128238 | ||||||||
\(852\) | −61.7536 | −2.11564 | ||||||||
\(853\) | −31.2006 | −1.06829 | −0.534144 | − | 0.845394i | \(-0.679366\pi\) | ||||
−0.534144 | + | 0.845394i | \(0.679366\pi\) | |||||||
\(854\) | −19.6896 | −0.673765 | ||||||||
\(855\) | 1.21552 | 0.0415699 | ||||||||
\(856\) | 32.4499 | 1.10912 | ||||||||
\(857\) | −20.6950 | −0.706928 | −0.353464 | − | 0.935448i | \(-0.614996\pi\) | ||||
−0.353464 | + | 0.935448i | \(0.614996\pi\) | |||||||
\(858\) | 8.22414 | 0.280768 | ||||||||
\(859\) | −52.3618 | −1.78656 | −0.893281 | − | 0.449499i | \(-0.851602\pi\) | ||||
−0.893281 | + | 0.449499i | \(0.851602\pi\) | |||||||
\(860\) | −6.85086 | −0.233612 | ||||||||
\(861\) | 11.8073 | 0.402392 | ||||||||
\(862\) | 15.0030 | 0.511004 | ||||||||
\(863\) | 50.4760 | 1.71822 | 0.859112 | − | 0.511788i | \(-0.171017\pi\) | ||||
0.859112 | + | 0.511788i | \(0.171017\pi\) | |||||||
\(864\) | −36.7689 | −1.25090 | ||||||||
\(865\) | −2.18060 | −0.0741428 | ||||||||
\(866\) | 73.7881 | 2.50742 | ||||||||
\(867\) | −12.0392 | −0.408874 | ||||||||
\(868\) | 4.40581 | 0.149543 | ||||||||
\(869\) | 8.34050 | 0.282932 | ||||||||
\(870\) | −22.5133 | −0.763274 | ||||||||
\(871\) | 23.1841 | 0.785562 | ||||||||
\(872\) | −8.60925 | −0.291546 | ||||||||
\(873\) | 0.649335 | 0.0219767 | ||||||||
\(874\) | 2.35690 | 0.0797232 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 11.4295 | 0.386167 | ||||||||
\(877\) | 0.157769 | 0.00532747 | 0.00266373 | − | 0.999996i | \(-0.499152\pi\) | ||||
0.00266373 | + | 0.999996i | \(0.499152\pi\) | |||||||
\(878\) | 1.40283 | 0.0473432 | ||||||||
\(879\) | 38.7928 | 1.30845 | ||||||||
\(880\) | −0.603875 | −0.0203566 | ||||||||
\(881\) | −37.4185 | −1.26066 | −0.630330 | − | 0.776327i | \(-0.717081\pi\) | ||||
−0.630330 | + | 0.776327i | \(0.717081\pi\) | |||||||
\(882\) | 2.60388 | 0.0876770 | ||||||||
\(883\) | 19.1675 | 0.645036 | 0.322518 | − | 0.946563i | \(-0.395471\pi\) | ||||
0.322518 | + | 0.946563i | \(0.395471\pi\) | |||||||
\(884\) | −31.1357 | −1.04721 | ||||||||
\(885\) | 3.52004 | 0.118325 | ||||||||
\(886\) | 41.2693 | 1.38647 | ||||||||
\(887\) | −9.89141 | −0.332121 | −0.166061 | − | 0.986116i | \(-0.553105\pi\) | ||||
−0.166061 | + | 0.986116i | \(0.553105\pi\) | |||||||
\(888\) | 11.9638 | 0.401477 | ||||||||
\(889\) | −19.4209 | −0.651355 | ||||||||
\(890\) | 7.78986 | 0.261117 | ||||||||
\(891\) | 3.14808 | 0.105465 | ||||||||
\(892\) | 12.0170 | 0.402358 | ||||||||
\(893\) | −1.84894 | −0.0618723 | ||||||||
\(894\) | 18.4131 | 0.615826 | ||||||||
\(895\) | 3.36898 | 0.112612 | ||||||||
\(896\) | −16.2620 | −0.543277 | ||||||||
\(897\) | −4.86054 | −0.162289 | ||||||||
\(898\) | −41.2301 | −1.37587 | ||||||||
\(899\) | 10.6703 | 0.355873 | ||||||||
\(900\) | −3.53319 | −0.117773 | ||||||||
\(901\) | −34.9075 | −1.16294 | ||||||||
\(902\) | −14.7235 | −0.490238 | ||||||||
\(903\) | −3.04892 | −0.101462 | ||||||||
\(904\) | 43.0575 | 1.43207 | ||||||||
\(905\) | −1.61596 | −0.0537162 | ||||||||
\(906\) | −29.4838 | −0.979534 | ||||||||
\(907\) | −0.0163935 | −0.000544336 0 | −0.000272168 | − | 1.00000i | \(-0.500087\pi\) | ||||
−0.000272168 | 1.00000i | \(0.500087\pi\) | ||||||||
\(908\) | −52.6142 | −1.74606 | ||||||||
\(909\) | 4.93277 | 0.163610 | ||||||||
\(910\) | −8.04892 | −0.266819 | ||||||||
\(911\) | −12.8817 | −0.426791 | −0.213395 | − | 0.976966i | \(-0.568452\pi\) | ||||
−0.213395 | + | 0.976966i | \(0.568452\pi\) | |||||||
\(912\) | −1.14138 | −0.0377947 | ||||||||
\(913\) | 10.2604 | 0.339569 | ||||||||
\(914\) | −60.8708 | −2.01343 | ||||||||
\(915\) | 11.8901 | 0.393074 | ||||||||
\(916\) | 38.0694 | 1.25785 | ||||||||
\(917\) | −14.4940 | −0.478633 | ||||||||
\(918\) | −36.1487 | −1.19308 | ||||||||
\(919\) | −21.3321 | −0.703682 | −0.351841 | − | 0.936060i | \(-0.614444\pi\) | ||||
−0.351841 | + | 0.936060i | \(0.614444\pi\) | |||||||
\(920\) | −2.35690 | −0.0777046 | ||||||||
\(921\) | −12.7372 | −0.419706 | ||||||||
\(922\) | −93.6335 | −3.08366 | ||||||||
\(923\) | −53.4698 | −1.75998 | ||||||||
\(924\) | 3.11529 | 0.102486 | ||||||||
\(925\) | −3.74094 | −0.123001 | ||||||||
\(926\) | −8.25667 | −0.271331 | ||||||||
\(927\) | 6.73471 | 0.221197 | ||||||||
\(928\) | −48.1124 | −1.57937 | ||||||||
\(929\) | 38.0411 | 1.24809 | 0.624045 | − | 0.781389i | \(-0.285488\pi\) | ||||
0.624045 | + | 0.781389i | \(0.285488\pi\) | |||||||
\(930\) | −4.40581 | −0.144472 | ||||||||
\(931\) | 1.04892 | 0.0343769 | ||||||||
\(932\) | 43.5502 | 1.42653 | ||||||||
\(933\) | 2.30904 | 0.0755947 | ||||||||
\(934\) | 32.9584 | 1.07843 | ||||||||
\(935\) | −2.14675 | −0.0702063 | ||||||||
\(936\) | 9.78363 | 0.319788 | ||||||||
\(937\) | 4.75196 | 0.155240 | 0.0776198 | − | 0.996983i | \(-0.475268\pi\) | ||||
0.0776198 | + | 0.996983i | \(0.475268\pi\) | |||||||
\(938\) | 14.5429 | 0.474842 | ||||||||
\(939\) | −43.0700 | −1.40553 | ||||||||
\(940\) | 5.37435 | 0.175292 | ||||||||
\(941\) | −8.23596 | −0.268485 | −0.134242 | − | 0.990949i | \(-0.542860\pi\) | ||||
−0.134242 | + | 0.990949i | \(0.542860\pi\) | |||||||
\(942\) | 23.1540 | 0.754400 | ||||||||
\(943\) | 8.70171 | 0.283367 | ||||||||
\(944\) | 2.08038 | 0.0677105 | ||||||||
\(945\) | −5.64310 | −0.183570 | ||||||||
\(946\) | 3.80194 | 0.123612 | ||||||||
\(947\) | −54.6437 | −1.77568 | −0.887841 | − | 0.460151i | \(-0.847795\pi\) | ||||
−0.887841 | + | 0.460151i | \(0.847795\pi\) | |||||||
\(948\) | −45.8224 | −1.48824 | ||||||||
\(949\) | 9.89631 | 0.321248 | ||||||||
\(950\) | −2.35690 | −0.0764678 | ||||||||
\(951\) | 28.0810 | 0.910588 | ||||||||
\(952\) | −6.71917 | −0.217770 | ||||||||
\(953\) | −28.2204 | −0.914149 | −0.457075 | − | 0.889428i | \(-0.651103\pi\) | ||||
−0.457075 | + | 0.889428i | \(0.651103\pi\) | |||||||
\(954\) | 31.8834 | 1.03226 | ||||||||
\(955\) | −0.833397 | −0.0269681 | ||||||||
\(956\) | 24.3840 | 0.788636 | ||||||||
\(957\) | 7.54480 | 0.243889 | ||||||||
\(958\) | 24.7017 | 0.798076 | ||||||||
\(959\) | 5.04354 | 0.162864 | ||||||||
\(960\) | 17.6896 | 0.570930 | ||||||||
\(961\) | −28.9119 | −0.932640 | ||||||||
\(962\) | 30.1105 | 0.970802 | ||||||||
\(963\) | 15.9549 | 0.514140 | ||||||||
\(964\) | 25.7245 | 0.828532 | ||||||||
\(965\) | −12.0218 | −0.386994 | ||||||||
\(966\) | −3.04892 | −0.0980973 | ||||||||
\(967\) | 36.7724 | 1.18252 | 0.591260 | − | 0.806481i | \(-0.298631\pi\) | ||||
0.591260 | + | 0.806481i | \(0.298631\pi\) | |||||||
\(968\) | 24.5894 | 0.790333 | ||||||||
\(969\) | −4.05754 | −0.130347 | ||||||||
\(970\) | −1.25906 | −0.0404260 | ||||||||
\(971\) | 30.1420 | 0.967302 | 0.483651 | − | 0.875261i | \(-0.339310\pi\) | ||||
0.483651 | + | 0.875261i | \(0.339310\pi\) | |||||||
\(972\) | 34.3207 | 1.10084 | ||||||||
\(973\) | −7.21313 | −0.231242 | ||||||||
\(974\) | 49.3159 | 1.58018 | ||||||||
\(975\) | 4.86054 | 0.155662 | ||||||||
\(976\) | 7.02715 | 0.224933 | ||||||||
\(977\) | −25.0568 | −0.801638 | −0.400819 | − | 0.916157i | \(-0.631274\pi\) | ||||
−0.400819 | + | 0.916157i | \(0.631274\pi\) | |||||||
\(978\) | −15.7125 | −0.502429 | ||||||||
\(979\) | −2.61058 | −0.0834345 | ||||||||
\(980\) | −3.04892 | −0.0973941 | ||||||||
\(981\) | −4.23298 | −0.135149 | ||||||||
\(982\) | −42.5230 | −1.35696 | ||||||||
\(983\) | 40.5284 | 1.29266 | 0.646328 | − | 0.763060i | \(-0.276304\pi\) | ||||
0.646328 | + | 0.763060i | \(0.276304\pi\) | |||||||
\(984\) | 27.8286 | 0.887144 | ||||||||
\(985\) | −23.9584 | −0.763377 | ||||||||
\(986\) | −47.3008 | −1.50636 | ||||||||
\(987\) | 2.39181 | 0.0761322 | ||||||||
\(988\) | 11.4558 | 0.364457 | ||||||||
\(989\) | −2.24698 | −0.0714498 | ||||||||
\(990\) | 1.96077 | 0.0623174 | ||||||||
\(991\) | 13.2228 | 0.420037 | 0.210018 | − | 0.977697i | \(-0.432648\pi\) | ||||
0.210018 | + | 0.977697i | \(0.432648\pi\) | |||||||
\(992\) | −9.41550 | −0.298942 | ||||||||
\(993\) | −0.149145 | −0.00473297 | ||||||||
\(994\) | −33.5405 | −1.06384 | ||||||||
\(995\) | 21.4590 | 0.680297 | ||||||||
\(996\) | −56.3702 | −1.78616 | ||||||||
\(997\) | 39.3793 | 1.24715 | 0.623577 | − | 0.781762i | \(-0.285679\pi\) | ||||
0.623577 | + | 0.781762i | \(0.285679\pi\) | |||||||
\(998\) | 28.4034 | 0.899095 | ||||||||
\(999\) | 21.1105 | 0.667907 |
(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 | 805.2.a.f.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 7245.2.a.ba.1.3 | 3 | |||
5.4 | even | 2 | 4025.2.a.k.1.3 | 3 | |||
7.6 | odd | 2 | 5635.2.a.r.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.a.f.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
4025.2.a.k.1.3 | 3 | 5.4 | even | 2 | |||
5635.2.a.r.1.1 | 3 | 7.6 | odd | 2 | |||
7245.2.a.ba.1.3 | 3 | 3.2 | odd | 2 |