Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.941592 | −0.543629 | −0.271814 | − | 0.962350i | \(-0.587624\pi\) | ||||
−0.271814 | + | 0.962350i | \(0.587624\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.129713 | −0.0580095 | −0.0290047 | − | 0.999579i | \(-0.509234\pi\) | ||||
−0.0290047 | + | 0.999579i | \(0.509234\pi\) | |||||||
\(6\) | 0.941592 | 0.384403 | ||||||||
\(7\) | 0.350515 | 0.132482 | 0.0662411 | − | 0.997804i | \(-0.478899\pi\) | ||||
0.0662411 | + | 0.997804i | \(0.478899\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.11340 | −0.704468 | ||||||||
\(10\) | 0.129713 | 0.0410189 | ||||||||
\(11\) | 3.66879 | 1.10618 | 0.553091 | − | 0.833121i | \(-0.313448\pi\) | ||||
0.553091 | + | 0.833121i | \(0.313448\pi\) | |||||||
\(12\) | −0.941592 | −0.271814 | ||||||||
\(13\) | −0.342580 | −0.0950146 | −0.0475073 | − | 0.998871i | \(-0.515128\pi\) | ||||
−0.0475073 | + | 0.998871i | \(0.515128\pi\) | |||||||
\(14\) | −0.350515 | −0.0936791 | ||||||||
\(15\) | 0.122137 | 0.0315356 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.324847 | −0.0787871 | −0.0393935 | − | 0.999224i | \(-0.512543\pi\) | ||||
−0.0393935 | + | 0.999224i | \(0.512543\pi\) | |||||||
\(18\) | 2.11340 | 0.498134 | ||||||||
\(19\) | −0.916569 | −0.210275 | −0.105138 | − | 0.994458i | \(-0.533528\pi\) | ||||
−0.105138 | + | 0.994458i | \(0.533528\pi\) | |||||||
\(20\) | −0.129713 | −0.0290047 | ||||||||
\(21\) | −0.330042 | −0.0720212 | ||||||||
\(22\) | −3.66879 | −0.782189 | ||||||||
\(23\) | 1.25046 | 0.260739 | 0.130369 | − | 0.991466i | \(-0.458384\pi\) | ||||
0.130369 | + | 0.991466i | \(0.458384\pi\) | |||||||
\(24\) | 0.941592 | 0.192202 | ||||||||
\(25\) | −4.98317 | −0.996635 | ||||||||
\(26\) | 0.342580 | 0.0671855 | ||||||||
\(27\) | 4.81474 | 0.926598 | ||||||||
\(28\) | 0.350515 | 0.0662411 | ||||||||
\(29\) | 2.88923 | 0.536516 | 0.268258 | − | 0.963347i | \(-0.413552\pi\) | ||||
0.268258 | + | 0.963347i | \(0.413552\pi\) | |||||||
\(30\) | −0.122137 | −0.0222990 | ||||||||
\(31\) | −8.36762 | −1.50287 | −0.751434 | − | 0.659808i | \(-0.770638\pi\) | ||||
−0.751434 | + | 0.659808i | \(0.770638\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.45450 | −0.601352 | ||||||||
\(34\) | 0.324847 | 0.0557109 | ||||||||
\(35\) | −0.0454664 | −0.00768523 | ||||||||
\(36\) | −2.11340 | −0.352234 | ||||||||
\(37\) | 10.3336 | 1.69884 | 0.849419 | − | 0.527719i | \(-0.176953\pi\) | ||||
0.849419 | + | 0.527719i | \(0.176953\pi\) | |||||||
\(38\) | 0.916569 | 0.148687 | ||||||||
\(39\) | 0.322571 | 0.0516527 | ||||||||
\(40\) | 0.129713 | 0.0205094 | ||||||||
\(41\) | −1.92216 | −0.300190 | −0.150095 | − | 0.988672i | \(-0.547958\pi\) | ||||
−0.150095 | + | 0.988672i | \(0.547958\pi\) | |||||||
\(42\) | 0.330042 | 0.0509266 | ||||||||
\(43\) | −8.00424 | −1.22063 | −0.610317 | − | 0.792157i | \(-0.708958\pi\) | ||||
−0.610317 | + | 0.792157i | \(0.708958\pi\) | |||||||
\(44\) | 3.66879 | 0.553091 | ||||||||
\(45\) | 0.274136 | 0.0408658 | ||||||||
\(46\) | −1.25046 | −0.184370 | ||||||||
\(47\) | −2.84720 | −0.415306 | −0.207653 | − | 0.978203i | \(-0.566583\pi\) | ||||
−0.207653 | + | 0.978203i | \(0.566583\pi\) | |||||||
\(48\) | −0.941592 | −0.135907 | ||||||||
\(49\) | −6.87714 | −0.982448 | ||||||||
\(50\) | 4.98317 | 0.704727 | ||||||||
\(51\) | 0.305874 | 0.0428309 | ||||||||
\(52\) | −0.342580 | −0.0475073 | ||||||||
\(53\) | 7.31739 | 1.00512 | 0.502560 | − | 0.864542i | \(-0.332391\pi\) | ||||
0.502560 | + | 0.864542i | \(0.332391\pi\) | |||||||
\(54\) | −4.81474 | −0.655203 | ||||||||
\(55\) | −0.475890 | −0.0641690 | ||||||||
\(56\) | −0.350515 | −0.0468396 | ||||||||
\(57\) | 0.863034 | 0.114312 | ||||||||
\(58\) | −2.88923 | −0.379374 | ||||||||
\(59\) | 3.01002 | 0.391871 | 0.195935 | − | 0.980617i | \(-0.437226\pi\) | ||||
0.195935 | + | 0.980617i | \(0.437226\pi\) | |||||||
\(60\) | 0.122137 | 0.0157678 | ||||||||
\(61\) | 10.1935 | 1.30515 | 0.652574 | − | 0.757725i | \(-0.273689\pi\) | ||||
0.652574 | + | 0.757725i | \(0.273689\pi\) | |||||||
\(62\) | 8.36762 | 1.06269 | ||||||||
\(63\) | −0.740780 | −0.0933295 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0444371 | 0.00551175 | ||||||||
\(66\) | 3.45450 | 0.425220 | ||||||||
\(67\) | 2.69312 | 0.329017 | 0.164508 | − | 0.986376i | \(-0.447396\pi\) | ||||
0.164508 | + | 0.986376i | \(0.447396\pi\) | |||||||
\(68\) | −0.324847 | −0.0393935 | ||||||||
\(69\) | −1.17742 | −0.141745 | ||||||||
\(70\) | 0.0454664 | 0.00543428 | ||||||||
\(71\) | 5.69491 | 0.675862 | 0.337931 | − | 0.941171i | \(-0.390273\pi\) | ||||
0.337931 | + | 0.941171i | \(0.390273\pi\) | |||||||
\(72\) | 2.11340 | 0.249067 | ||||||||
\(73\) | −10.4653 | −1.22487 | −0.612436 | − | 0.790520i | \(-0.709810\pi\) | ||||
−0.612436 | + | 0.790520i | \(0.709810\pi\) | |||||||
\(74\) | −10.3336 | −1.20126 | ||||||||
\(75\) | 4.69212 | 0.541799 | ||||||||
\(76\) | −0.916569 | −0.105138 | ||||||||
\(77\) | 1.28597 | 0.146549 | ||||||||
\(78\) | −0.322571 | −0.0365239 | ||||||||
\(79\) | 1.47461 | 0.165907 | 0.0829535 | − | 0.996553i | \(-0.473565\pi\) | ||||
0.0829535 | + | 0.996553i | \(0.473565\pi\) | |||||||
\(80\) | −0.129713 | −0.0145024 | ||||||||
\(81\) | 1.80669 | 0.200743 | ||||||||
\(82\) | 1.92216 | 0.212267 | ||||||||
\(83\) | −10.6060 | −1.16416 | −0.582078 | − | 0.813133i | \(-0.697760\pi\) | ||||
−0.582078 | + | 0.813133i | \(0.697760\pi\) | |||||||
\(84\) | −0.330042 | −0.0360106 | ||||||||
\(85\) | 0.0421370 | 0.00457040 | ||||||||
\(86\) | 8.00424 | 0.863119 | ||||||||
\(87\) | −2.72047 | −0.291665 | ||||||||
\(88\) | −3.66879 | −0.391094 | ||||||||
\(89\) | −17.5017 | −1.85518 | −0.927588 | − | 0.373604i | \(-0.878122\pi\) | ||||
−0.927588 | + | 0.373604i | \(0.878122\pi\) | |||||||
\(90\) | −0.274136 | −0.0288965 | ||||||||
\(91\) | −0.120080 | −0.0125878 | ||||||||
\(92\) | 1.25046 | 0.130369 | ||||||||
\(93\) | 7.87888 | 0.817002 | ||||||||
\(94\) | 2.84720 | 0.293666 | ||||||||
\(95\) | 0.118891 | 0.0121980 | ||||||||
\(96\) | 0.941592 | 0.0961009 | ||||||||
\(97\) | −15.5913 | −1.58306 | −0.791530 | − | 0.611130i | \(-0.790715\pi\) | ||||
−0.791530 | + | 0.611130i | \(0.790715\pi\) | |||||||
\(98\) | 6.87714 | 0.694696 | ||||||||
\(99\) | −7.75363 | −0.779270 | ||||||||
\(100\) | −4.98317 | −0.498317 | ||||||||
\(101\) | 6.78412 | 0.675046 | 0.337523 | − | 0.941317i | \(-0.390411\pi\) | ||||
0.337523 | + | 0.941317i | \(0.390411\pi\) | |||||||
\(102\) | −0.305874 | −0.0302860 | ||||||||
\(103\) | 11.3369 | 1.11706 | 0.558528 | − | 0.829485i | \(-0.311366\pi\) | ||||
0.558528 | + | 0.829485i | \(0.311366\pi\) | |||||||
\(104\) | 0.342580 | 0.0335927 | ||||||||
\(105\) | 0.0428108 | 0.00417791 | ||||||||
\(106\) | −7.31739 | −0.710728 | ||||||||
\(107\) | −11.4350 | −1.10547 | −0.552733 | − | 0.833358i | \(-0.686415\pi\) | ||||
−0.552733 | + | 0.833358i | \(0.686415\pi\) | |||||||
\(108\) | 4.81474 | 0.463299 | ||||||||
\(109\) | 18.1642 | 1.73982 | 0.869909 | − | 0.493212i | \(-0.164177\pi\) | ||||
0.869909 | + | 0.493212i | \(0.164177\pi\) | |||||||
\(110\) | 0.475890 | 0.0453743 | ||||||||
\(111\) | −9.73007 | −0.923537 | ||||||||
\(112\) | 0.350515 | 0.0331206 | ||||||||
\(113\) | −1.75797 | −0.165376 | −0.0826881 | − | 0.996575i | \(-0.526351\pi\) | ||||
−0.0826881 | + | 0.996575i | \(0.526351\pi\) | |||||||
\(114\) | −0.863034 | −0.0808306 | ||||||||
\(115\) | −0.162201 | −0.0151253 | ||||||||
\(116\) | 2.88923 | 0.268258 | ||||||||
\(117\) | 0.724010 | 0.0669348 | ||||||||
\(118\) | −3.01002 | −0.277094 | ||||||||
\(119\) | −0.113864 | −0.0104379 | ||||||||
\(120\) | −0.122137 | −0.0111495 | ||||||||
\(121\) | 2.46002 | 0.223638 | ||||||||
\(122\) | −10.1935 | −0.922879 | ||||||||
\(123\) | 1.80989 | 0.163192 | ||||||||
\(124\) | −8.36762 | −0.751434 | ||||||||
\(125\) | 1.29495 | 0.115824 | ||||||||
\(126\) | 0.740780 | 0.0659939 | ||||||||
\(127\) | 19.0525 | 1.69064 | 0.845320 | − | 0.534261i | \(-0.179410\pi\) | ||||
0.845320 | + | 0.534261i | \(0.179410\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 7.53673 | 0.663572 | ||||||||
\(130\) | −0.0444371 | −0.00389739 | ||||||||
\(131\) | −12.1222 | −1.05912 | −0.529562 | − | 0.848271i | \(-0.677644\pi\) | ||||
−0.529562 | + | 0.848271i | \(0.677644\pi\) | |||||||
\(132\) | −3.45450 | −0.300676 | ||||||||
\(133\) | −0.321271 | −0.0278578 | ||||||||
\(134\) | −2.69312 | −0.232650 | ||||||||
\(135\) | −0.624535 | −0.0537514 | ||||||||
\(136\) | 0.324847 | 0.0278554 | ||||||||
\(137\) | −9.76659 | −0.834416 | −0.417208 | − | 0.908811i | \(-0.636991\pi\) | ||||
−0.417208 | + | 0.908811i | \(0.636991\pi\) | |||||||
\(138\) | 1.17742 | 0.100229 | ||||||||
\(139\) | −0.211615 | −0.0179490 | −0.00897448 | − | 0.999960i | \(-0.502857\pi\) | ||||
−0.00897448 | + | 0.999960i | \(0.502857\pi\) | |||||||
\(140\) | −0.0454664 | −0.00384261 | ||||||||
\(141\) | 2.68090 | 0.225772 | ||||||||
\(142\) | −5.69491 | −0.477907 | ||||||||
\(143\) | −1.25685 | −0.105103 | ||||||||
\(144\) | −2.11340 | −0.176117 | ||||||||
\(145\) | −0.374771 | −0.0311230 | ||||||||
\(146\) | 10.4653 | 0.866116 | ||||||||
\(147\) | 6.47546 | 0.534087 | ||||||||
\(148\) | 10.3336 | 0.849419 | ||||||||
\(149\) | −0.581612 | −0.0476475 | −0.0238238 | − | 0.999716i | \(-0.507584\pi\) | ||||
−0.0238238 | + | 0.999716i | \(0.507584\pi\) | |||||||
\(150\) | −4.69212 | −0.383110 | ||||||||
\(151\) | −2.43880 | −0.198466 | −0.0992332 | − | 0.995064i | \(-0.531639\pi\) | ||||
−0.0992332 | + | 0.995064i | \(0.531639\pi\) | |||||||
\(152\) | 0.916569 | 0.0743436 | ||||||||
\(153\) | 0.686534 | 0.0555030 | ||||||||
\(154\) | −1.28597 | −0.103626 | ||||||||
\(155\) | 1.08539 | 0.0871806 | ||||||||
\(156\) | 0.322571 | 0.0258263 | ||||||||
\(157\) | 20.0875 | 1.60315 | 0.801577 | − | 0.597891i | \(-0.203994\pi\) | ||||
0.801577 | + | 0.597891i | \(0.203994\pi\) | |||||||
\(158\) | −1.47461 | −0.117314 | ||||||||
\(159\) | −6.89000 | −0.546412 | ||||||||
\(160\) | 0.129713 | 0.0102547 | ||||||||
\(161\) | 0.438304 | 0.0345432 | ||||||||
\(162\) | −1.80669 | −0.141947 | ||||||||
\(163\) | 6.78425 | 0.531384 | 0.265692 | − | 0.964058i | \(-0.414400\pi\) | ||||
0.265692 | + | 0.964058i | \(0.414400\pi\) | |||||||
\(164\) | −1.92216 | −0.150095 | ||||||||
\(165\) | 0.448095 | 0.0348841 | ||||||||
\(166\) | 10.6060 | 0.823182 | ||||||||
\(167\) | −18.7317 | −1.44950 | −0.724752 | − | 0.689009i | \(-0.758046\pi\) | ||||
−0.724752 | + | 0.689009i | \(0.758046\pi\) | |||||||
\(168\) | 0.330042 | 0.0254633 | ||||||||
\(169\) | −12.8826 | −0.990972 | ||||||||
\(170\) | −0.0421370 | −0.00323176 | ||||||||
\(171\) | 1.93708 | 0.148132 | ||||||||
\(172\) | −8.00424 | −0.610317 | ||||||||
\(173\) | −25.2897 | −1.92274 | −0.961370 | − | 0.275258i | \(-0.911237\pi\) | ||||
−0.961370 | + | 0.275258i | \(0.911237\pi\) | |||||||
\(174\) | 2.72047 | 0.206239 | ||||||||
\(175\) | −1.74668 | −0.132036 | ||||||||
\(176\) | 3.66879 | 0.276545 | ||||||||
\(177\) | −2.83421 | −0.213032 | ||||||||
\(178\) | 17.5017 | 1.31181 | ||||||||
\(179\) | −14.2700 | −1.06659 | −0.533296 | − | 0.845929i | \(-0.679047\pi\) | ||||
−0.533296 | + | 0.845929i | \(0.679047\pi\) | |||||||
\(180\) | 0.274136 | 0.0204329 | ||||||||
\(181\) | −1.28838 | −0.0957645 | −0.0478823 | − | 0.998853i | \(-0.515247\pi\) | ||||
−0.0478823 | + | 0.998853i | \(0.515247\pi\) | |||||||
\(182\) | 0.120080 | 0.00890089 | ||||||||
\(183\) | −9.59815 | −0.709516 | ||||||||
\(184\) | −1.25046 | −0.0921850 | ||||||||
\(185\) | −1.34041 | −0.0985487 | ||||||||
\(186\) | −7.87888 | −0.577708 | ||||||||
\(187\) | −1.19180 | −0.0871528 | ||||||||
\(188\) | −2.84720 | −0.207653 | ||||||||
\(189\) | 1.68764 | 0.122758 | ||||||||
\(190\) | −0.118891 | −0.00862526 | ||||||||
\(191\) | −7.65560 | −0.553940 | −0.276970 | − | 0.960879i | \(-0.589330\pi\) | ||||
−0.276970 | + | 0.960879i | \(0.589330\pi\) | |||||||
\(192\) | −0.941592 | −0.0679536 | ||||||||
\(193\) | 15.6131 | 1.12386 | 0.561930 | − | 0.827185i | \(-0.310059\pi\) | ||||
0.561930 | + | 0.827185i | \(0.310059\pi\) | |||||||
\(194\) | 15.5913 | 1.11939 | ||||||||
\(195\) | −0.0418417 | −0.00299634 | ||||||||
\(196\) | −6.87714 | −0.491224 | ||||||||
\(197\) | −2.44421 | −0.174142 | −0.0870712 | − | 0.996202i | \(-0.527751\pi\) | ||||
−0.0870712 | + | 0.996202i | \(0.527751\pi\) | |||||||
\(198\) | 7.75363 | 0.551027 | ||||||||
\(199\) | −27.3011 | −1.93532 | −0.967661 | − | 0.252255i | \(-0.918828\pi\) | ||||
−0.967661 | + | 0.252255i | \(0.918828\pi\) | |||||||
\(200\) | 4.98317 | 0.352364 | ||||||||
\(201\) | −2.53582 | −0.178863 | ||||||||
\(202\) | −6.78412 | −0.477329 | ||||||||
\(203\) | 1.01272 | 0.0710788 | ||||||||
\(204\) | 0.305874 | 0.0214155 | ||||||||
\(205\) | 0.249329 | 0.0174139 | ||||||||
\(206\) | −11.3369 | −0.789878 | ||||||||
\(207\) | −2.64272 | −0.183682 | ||||||||
\(208\) | −0.342580 | −0.0237537 | ||||||||
\(209\) | −3.36270 | −0.232603 | ||||||||
\(210\) | −0.0428108 | −0.00295423 | ||||||||
\(211\) | 4.19124 | 0.288537 | 0.144269 | − | 0.989539i | \(-0.453917\pi\) | ||||
0.144269 | + | 0.989539i | \(0.453917\pi\) | |||||||
\(212\) | 7.31739 | 0.502560 | ||||||||
\(213\) | −5.36229 | −0.367418 | ||||||||
\(214\) | 11.4350 | 0.781683 | ||||||||
\(215\) | 1.03825 | 0.0708084 | ||||||||
\(216\) | −4.81474 | −0.327602 | ||||||||
\(217\) | −2.93298 | −0.199103 | ||||||||
\(218\) | −18.1642 | −1.23024 | ||||||||
\(219\) | 9.85406 | 0.665876 | ||||||||
\(220\) | −0.475890 | −0.0320845 | ||||||||
\(221\) | 0.111286 | 0.00748592 | ||||||||
\(222\) | 9.73007 | 0.653039 | ||||||||
\(223\) | 4.63209 | 0.310188 | 0.155094 | − | 0.987900i | \(-0.450432\pi\) | ||||
0.155094 | + | 0.987900i | \(0.450432\pi\) | |||||||
\(224\) | −0.350515 | −0.0234198 | ||||||||
\(225\) | 10.5315 | 0.702097 | ||||||||
\(226\) | 1.75797 | 0.116939 | ||||||||
\(227\) | 10.4114 | 0.691027 | 0.345513 | − | 0.938414i | \(-0.387705\pi\) | ||||
0.345513 | + | 0.938414i | \(0.387705\pi\) | |||||||
\(228\) | 0.863034 | 0.0571558 | ||||||||
\(229\) | −8.95876 | −0.592012 | −0.296006 | − | 0.955186i | \(-0.595655\pi\) | ||||
−0.296006 | + | 0.955186i | \(0.595655\pi\) | |||||||
\(230\) | 0.162201 | 0.0106952 | ||||||||
\(231\) | −1.21086 | −0.0796685 | ||||||||
\(232\) | −2.88923 | −0.189687 | ||||||||
\(233\) | 21.0993 | 1.38226 | 0.691132 | − | 0.722729i | \(-0.257113\pi\) | ||||
0.691132 | + | 0.722729i | \(0.257113\pi\) | |||||||
\(234\) | −0.724010 | −0.0473300 | ||||||||
\(235\) | 0.369319 | 0.0240917 | ||||||||
\(236\) | 3.01002 | 0.195935 | ||||||||
\(237\) | −1.38849 | −0.0901918 | ||||||||
\(238\) | 0.113864 | 0.00738070 | ||||||||
\(239\) | 4.13040 | 0.267174 | 0.133587 | − | 0.991037i | \(-0.457350\pi\) | ||||
0.133587 | + | 0.991037i | \(0.457350\pi\) | |||||||
\(240\) | 0.122137 | 0.00788390 | ||||||||
\(241\) | −13.0441 | −0.840242 | −0.420121 | − | 0.907468i | \(-0.638012\pi\) | ||||
−0.420121 | + | 0.907468i | \(0.638012\pi\) | |||||||
\(242\) | −2.46002 | −0.158136 | ||||||||
\(243\) | −16.1454 | −1.03573 | ||||||||
\(244\) | 10.1935 | 0.652574 | ||||||||
\(245\) | 0.892055 | 0.0569913 | ||||||||
\(246\) | −1.80989 | −0.115394 | ||||||||
\(247\) | 0.313998 | 0.0199792 | ||||||||
\(248\) | 8.36762 | 0.531344 | ||||||||
\(249\) | 9.98649 | 0.632868 | ||||||||
\(250\) | −1.29495 | −0.0818998 | ||||||||
\(251\) | 20.2778 | 1.27992 | 0.639962 | − | 0.768406i | \(-0.278950\pi\) | ||||
0.639962 | + | 0.768406i | \(0.278950\pi\) | |||||||
\(252\) | −0.740780 | −0.0466648 | ||||||||
\(253\) | 4.58767 | 0.288424 | ||||||||
\(254\) | −19.0525 | −1.19546 | ||||||||
\(255\) | −0.0396759 | −0.00248460 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.336181 | −0.0209704 | −0.0104852 | − | 0.999945i | \(-0.503338\pi\) | ||||
−0.0104852 | + | 0.999945i | \(0.503338\pi\) | |||||||
\(258\) | −7.53673 | −0.469216 | ||||||||
\(259\) | 3.62209 | 0.225066 | ||||||||
\(260\) | 0.0444371 | 0.00275587 | ||||||||
\(261\) | −6.10610 | −0.377958 | ||||||||
\(262\) | 12.1222 | 0.748914 | ||||||||
\(263\) | −24.0852 | −1.48516 | −0.742578 | − | 0.669759i | \(-0.766397\pi\) | ||||
−0.742578 | + | 0.669759i | \(0.766397\pi\) | |||||||
\(264\) | 3.45450 | 0.212610 | ||||||||
\(265\) | −0.949161 | −0.0583065 | ||||||||
\(266\) | 0.321271 | 0.0196984 | ||||||||
\(267\) | 16.4795 | 1.00853 | ||||||||
\(268\) | 2.69312 | 0.164508 | ||||||||
\(269\) | −8.89648 | −0.542428 | −0.271214 | − | 0.962519i | \(-0.587425\pi\) | ||||
−0.271214 | + | 0.962519i | \(0.587425\pi\) | |||||||
\(270\) | 0.624535 | 0.0380080 | ||||||||
\(271\) | −15.9456 | −0.968624 | −0.484312 | − | 0.874895i | \(-0.660930\pi\) | ||||
−0.484312 | + | 0.874895i | \(0.660930\pi\) | |||||||
\(272\) | −0.324847 | −0.0196968 | ||||||||
\(273\) | 0.113066 | 0.00684306 | ||||||||
\(274\) | 9.76659 | 0.590021 | ||||||||
\(275\) | −18.2822 | −1.10246 | ||||||||
\(276\) | −1.17742 | −0.0708725 | ||||||||
\(277\) | −24.6530 | −1.48125 | −0.740626 | − | 0.671917i | \(-0.765471\pi\) | ||||
−0.740626 | + | 0.671917i | \(0.765471\pi\) | |||||||
\(278\) | 0.211615 | 0.0126918 | ||||||||
\(279\) | 17.6842 | 1.05872 | ||||||||
\(280\) | 0.0454664 | 0.00271714 | ||||||||
\(281\) | −12.2409 | −0.730233 | −0.365116 | − | 0.930962i | \(-0.618971\pi\) | ||||
−0.365116 | + | 0.930962i | \(0.618971\pi\) | |||||||
\(282\) | −2.68090 | −0.159645 | ||||||||
\(283\) | 21.5413 | 1.28050 | 0.640249 | − | 0.768168i | \(-0.278831\pi\) | ||||
0.640249 | + | 0.768168i | \(0.278831\pi\) | |||||||
\(284\) | 5.69491 | 0.337931 | ||||||||
\(285\) | −0.111947 | −0.00663116 | ||||||||
\(286\) | 1.25685 | 0.0743193 | ||||||||
\(287\) | −0.673745 | −0.0397699 | ||||||||
\(288\) | 2.11340 | 0.124534 | ||||||||
\(289\) | −16.8945 | −0.993793 | ||||||||
\(290\) | 0.374771 | 0.0220073 | ||||||||
\(291\) | 14.6807 | 0.860597 | ||||||||
\(292\) | −10.4653 | −0.612436 | ||||||||
\(293\) | −22.8468 | −1.33473 | −0.667363 | − | 0.744733i | \(-0.732577\pi\) | ||||
−0.667363 | + | 0.744733i | \(0.732577\pi\) | |||||||
\(294\) | −6.47546 | −0.377657 | ||||||||
\(295\) | −0.390439 | −0.0227322 | ||||||||
\(296\) | −10.3336 | −0.600630 | ||||||||
\(297\) | 17.6643 | 1.02499 | ||||||||
\(298\) | 0.581612 | 0.0336919 | ||||||||
\(299\) | −0.428382 | −0.0247740 | ||||||||
\(300\) | 4.69212 | 0.270900 | ||||||||
\(301\) | −2.80561 | −0.161712 | ||||||||
\(302\) | 2.43880 | 0.140337 | ||||||||
\(303\) | −6.38788 | −0.366974 | ||||||||
\(304\) | −0.916569 | −0.0525688 | ||||||||
\(305\) | −1.32223 | −0.0757109 | ||||||||
\(306\) | −0.686534 | −0.0392465 | ||||||||
\(307\) | −9.56090 | −0.545670 | −0.272835 | − | 0.962061i | \(-0.587961\pi\) | ||||
−0.272835 | + | 0.962061i | \(0.587961\pi\) | |||||||
\(308\) | 1.28597 | 0.0732747 | ||||||||
\(309\) | −10.6747 | −0.607264 | ||||||||
\(310\) | −1.08539 | −0.0616460 | ||||||||
\(311\) | −10.2196 | −0.579501 | −0.289750 | − | 0.957102i | \(-0.593572\pi\) | ||||
−0.289750 | + | 0.957102i | \(0.593572\pi\) | |||||||
\(312\) | −0.322571 | −0.0182620 | ||||||||
\(313\) | −10.7607 | −0.608229 | −0.304114 | − | 0.952636i | \(-0.598360\pi\) | ||||
−0.304114 | + | 0.952636i | \(0.598360\pi\) | |||||||
\(314\) | −20.0875 | −1.13360 | ||||||||
\(315\) | 0.0960889 | 0.00541400 | ||||||||
\(316\) | 1.47461 | 0.0829535 | ||||||||
\(317\) | 14.7775 | 0.829985 | 0.414993 | − | 0.909825i | \(-0.363784\pi\) | ||||
0.414993 | + | 0.909825i | \(0.363784\pi\) | |||||||
\(318\) | 6.89000 | 0.386372 | ||||||||
\(319\) | 10.6000 | 0.593484 | ||||||||
\(320\) | −0.129713 | −0.00725118 | ||||||||
\(321\) | 10.7671 | 0.600963 | ||||||||
\(322\) | −0.438304 | −0.0244258 | ||||||||
\(323\) | 0.297745 | 0.0165670 | ||||||||
\(324\) | 1.80669 | 0.100372 | ||||||||
\(325\) | 1.70714 | 0.0946949 | ||||||||
\(326\) | −6.78425 | −0.375745 | ||||||||
\(327\) | −17.1033 | −0.945815 | ||||||||
\(328\) | 1.92216 | 0.106133 | ||||||||
\(329\) | −0.997985 | −0.0550207 | ||||||||
\(330\) | −0.448095 | −0.0246668 | ||||||||
\(331\) | 4.76669 | 0.262001 | 0.131000 | − | 0.991382i | \(-0.458181\pi\) | ||||
0.131000 | + | 0.991382i | \(0.458181\pi\) | |||||||
\(332\) | −10.6060 | −0.582078 | ||||||||
\(333\) | −21.8391 | −1.19678 | ||||||||
\(334\) | 18.7317 | 1.02495 | ||||||||
\(335\) | −0.349333 | −0.0190861 | ||||||||
\(336\) | −0.330042 | −0.0180053 | ||||||||
\(337\) | −0.980382 | −0.0534048 | −0.0267024 | − | 0.999643i | \(-0.508501\pi\) | ||||
−0.0267024 | + | 0.999643i | \(0.508501\pi\) | |||||||
\(338\) | 12.8826 | 0.700723 | ||||||||
\(339\) | 1.65529 | 0.0899033 | ||||||||
\(340\) | 0.0421370 | 0.00228520 | ||||||||
\(341\) | −30.6990 | −1.66245 | ||||||||
\(342\) | −1.93708 | −0.104745 | ||||||||
\(343\) | −4.86415 | −0.262639 | ||||||||
\(344\) | 8.00424 | 0.431560 | ||||||||
\(345\) | 0.152727 | 0.00822255 | ||||||||
\(346\) | 25.2897 | 1.35958 | ||||||||
\(347\) | −23.2784 | −1.24965 | −0.624826 | − | 0.780764i | \(-0.714830\pi\) | ||||
−0.624826 | + | 0.780764i | \(0.714830\pi\) | |||||||
\(348\) | −2.72047 | −0.145833 | ||||||||
\(349\) | 5.88858 | 0.315208 | 0.157604 | − | 0.987502i | \(-0.449623\pi\) | ||||
0.157604 | + | 0.987502i | \(0.449623\pi\) | |||||||
\(350\) | 1.74668 | 0.0933639 | ||||||||
\(351\) | −1.64943 | −0.0880403 | ||||||||
\(352\) | −3.66879 | −0.195547 | ||||||||
\(353\) | −17.0303 | −0.906434 | −0.453217 | − | 0.891400i | \(-0.649724\pi\) | ||||
−0.453217 | + | 0.891400i | \(0.649724\pi\) | |||||||
\(354\) | 2.83421 | 0.150636 | ||||||||
\(355\) | −0.738705 | −0.0392064 | ||||||||
\(356\) | −17.5017 | −0.927588 | ||||||||
\(357\) | 0.107213 | 0.00567434 | ||||||||
\(358\) | 14.2700 | 0.754195 | ||||||||
\(359\) | −15.5151 | −0.818855 | −0.409428 | − | 0.912343i | \(-0.634272\pi\) | ||||
−0.409428 | + | 0.912343i | \(0.634272\pi\) | |||||||
\(360\) | −0.274136 | −0.0144482 | ||||||||
\(361\) | −18.1599 | −0.955784 | ||||||||
\(362\) | 1.28838 | 0.0677158 | ||||||||
\(363\) | −2.31633 | −0.121576 | ||||||||
\(364\) | −0.120080 | −0.00629388 | ||||||||
\(365\) | 1.35749 | 0.0710542 | ||||||||
\(366\) | 9.59815 | 0.501703 | ||||||||
\(367\) | 26.9568 | 1.40714 | 0.703568 | − | 0.710628i | \(-0.251589\pi\) | ||||
0.703568 | + | 0.710628i | \(0.251589\pi\) | |||||||
\(368\) | 1.25046 | 0.0651846 | ||||||||
\(369\) | 4.06229 | 0.211474 | ||||||||
\(370\) | 1.34041 | 0.0696845 | ||||||||
\(371\) | 2.56486 | 0.133161 | ||||||||
\(372\) | 7.87888 | 0.408501 | ||||||||
\(373\) | −5.36389 | −0.277732 | −0.138866 | − | 0.990311i | \(-0.544346\pi\) | ||||
−0.138866 | + | 0.990311i | \(0.544346\pi\) | |||||||
\(374\) | 1.19180 | 0.0616263 | ||||||||
\(375\) | −1.21931 | −0.0629651 | ||||||||
\(376\) | 2.84720 | 0.146833 | ||||||||
\(377\) | −0.989791 | −0.0509768 | ||||||||
\(378\) | −1.68764 | −0.0868028 | ||||||||
\(379\) | −13.8038 | −0.709056 | −0.354528 | − | 0.935045i | \(-0.615358\pi\) | ||||
−0.354528 | + | 0.935045i | \(0.615358\pi\) | |||||||
\(380\) | 0.118891 | 0.00609898 | ||||||||
\(381\) | −17.9397 | −0.919080 | ||||||||
\(382\) | 7.65560 | 0.391694 | ||||||||
\(383\) | −23.4129 | −1.19634 | −0.598171 | − | 0.801369i | \(-0.704105\pi\) | ||||
−0.598171 | + | 0.801369i | \(0.704105\pi\) | |||||||
\(384\) | 0.941592 | 0.0480504 | ||||||||
\(385\) | −0.166807 | −0.00850126 | ||||||||
\(386\) | −15.6131 | −0.794688 | ||||||||
\(387\) | 16.9162 | 0.859898 | ||||||||
\(388\) | −15.5913 | −0.791530 | ||||||||
\(389\) | −23.9313 | −1.21336 | −0.606682 | − | 0.794945i | \(-0.707500\pi\) | ||||
−0.606682 | + | 0.794945i | \(0.707500\pi\) | |||||||
\(390\) | 0.0418417 | 0.00211874 | ||||||||
\(391\) | −0.406208 | −0.0205428 | ||||||||
\(392\) | 6.87714 | 0.347348 | ||||||||
\(393\) | 11.4142 | 0.575770 | ||||||||
\(394\) | 2.44421 | 0.123137 | ||||||||
\(395\) | −0.191277 | −0.00962418 | ||||||||
\(396\) | −7.75363 | −0.389635 | ||||||||
\(397\) | −4.43559 | −0.222616 | −0.111308 | − | 0.993786i | \(-0.535504\pi\) | ||||
−0.111308 | + | 0.993786i | \(0.535504\pi\) | |||||||
\(398\) | 27.3011 | 1.36848 | ||||||||
\(399\) | 0.302507 | 0.0151443 | ||||||||
\(400\) | −4.98317 | −0.249159 | ||||||||
\(401\) | −6.81431 | −0.340290 | −0.170145 | − | 0.985419i | \(-0.554424\pi\) | ||||
−0.170145 | + | 0.985419i | \(0.554424\pi\) | |||||||
\(402\) | 2.53582 | 0.126475 | ||||||||
\(403\) | 2.86658 | 0.142794 | ||||||||
\(404\) | 6.78412 | 0.337523 | ||||||||
\(405\) | −0.234351 | −0.0116450 | ||||||||
\(406\) | −1.01272 | −0.0502603 | ||||||||
\(407\) | 37.9119 | 1.87922 | ||||||||
\(408\) | −0.305874 | −0.0151430 | ||||||||
\(409\) | −24.3559 | −1.20432 | −0.602161 | − | 0.798375i | \(-0.705693\pi\) | ||||
−0.602161 | + | 0.798375i | \(0.705693\pi\) | |||||||
\(410\) | −0.249329 | −0.0123135 | ||||||||
\(411\) | 9.19615 | 0.453612 | ||||||||
\(412\) | 11.3369 | 0.558528 | ||||||||
\(413\) | 1.05506 | 0.0519159 | ||||||||
\(414\) | 2.64272 | 0.129883 | ||||||||
\(415\) | 1.37573 | 0.0675320 | ||||||||
\(416\) | 0.342580 | 0.0167964 | ||||||||
\(417\) | 0.199255 | 0.00975757 | ||||||||
\(418\) | 3.36270 | 0.164475 | ||||||||
\(419\) | 29.0451 | 1.41894 | 0.709472 | − | 0.704734i | \(-0.248933\pi\) | ||||
0.709472 | + | 0.704734i | \(0.248933\pi\) | |||||||
\(420\) | 0.0428108 | 0.00208895 | ||||||||
\(421\) | −14.3006 | −0.696968 | −0.348484 | − | 0.937315i | \(-0.613303\pi\) | ||||
−0.348484 | + | 0.937315i | \(0.613303\pi\) | |||||||
\(422\) | −4.19124 | −0.204027 | ||||||||
\(423\) | 6.01727 | 0.292570 | ||||||||
\(424\) | −7.31739 | −0.355364 | ||||||||
\(425\) | 1.61877 | 0.0785219 | ||||||||
\(426\) | 5.36229 | 0.259804 | ||||||||
\(427\) | 3.57299 | 0.172909 | ||||||||
\(428\) | −11.4350 | −0.552733 | ||||||||
\(429\) | 1.18344 | 0.0571372 | ||||||||
\(430\) | −1.03825 | −0.0500691 | ||||||||
\(431\) | −22.7210 | −1.09443 | −0.547217 | − | 0.836991i | \(-0.684313\pi\) | ||||
−0.547217 | + | 0.836991i | \(0.684313\pi\) | |||||||
\(432\) | 4.81474 | 0.231649 | ||||||||
\(433\) | −35.0246 | −1.68317 | −0.841587 | − | 0.540121i | \(-0.818378\pi\) | ||||
−0.841587 | + | 0.540121i | \(0.818378\pi\) | |||||||
\(434\) | 2.93298 | 0.140787 | ||||||||
\(435\) | 0.352881 | 0.0169194 | ||||||||
\(436\) | 18.1642 | 0.869909 | ||||||||
\(437\) | −1.14613 | −0.0548269 | ||||||||
\(438\) | −9.85406 | −0.470845 | ||||||||
\(439\) | 3.41021 | 0.162761 | 0.0813803 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813803 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(440\) | 0.475890 | 0.0226872 | ||||||||
\(441\) | 14.5342 | 0.692103 | ||||||||
\(442\) | −0.111286 | −0.00529335 | ||||||||
\(443\) | −2.49849 | −0.118707 | −0.0593535 | − | 0.998237i | \(-0.518904\pi\) | ||||
−0.0593535 | + | 0.998237i | \(0.518904\pi\) | |||||||
\(444\) | −9.73007 | −0.461768 | ||||||||
\(445\) | 2.27020 | 0.107618 | ||||||||
\(446\) | −4.63209 | −0.219336 | ||||||||
\(447\) | 0.547642 | 0.0259026 | ||||||||
\(448\) | 0.350515 | 0.0165603 | ||||||||
\(449\) | −16.2151 | −0.765237 | −0.382619 | − | 0.923906i | \(-0.624978\pi\) | ||||
−0.382619 | + | 0.923906i | \(0.624978\pi\) | |||||||
\(450\) | −10.5315 | −0.496458 | ||||||||
\(451\) | −7.05199 | −0.332065 | ||||||||
\(452\) | −1.75797 | −0.0826881 | ||||||||
\(453\) | 2.29635 | 0.107892 | ||||||||
\(454\) | −10.4114 | −0.488630 | ||||||||
\(455\) | 0.0155759 | 0.000730209 0 | ||||||||
\(456\) | −0.863034 | −0.0404153 | ||||||||
\(457\) | 13.4972 | 0.631372 | 0.315686 | − | 0.948864i | \(-0.397765\pi\) | ||||
0.315686 | + | 0.948864i | \(0.397765\pi\) | |||||||
\(458\) | 8.95876 | 0.418615 | ||||||||
\(459\) | −1.56406 | −0.0730039 | ||||||||
\(460\) | −0.162201 | −0.00756265 | ||||||||
\(461\) | −37.6469 | −1.75339 | −0.876696 | − | 0.481046i | \(-0.840257\pi\) | ||||
−0.876696 | + | 0.481046i | \(0.840257\pi\) | |||||||
\(462\) | 1.21086 | 0.0563341 | ||||||||
\(463\) | 31.4858 | 1.46327 | 0.731635 | − | 0.681697i | \(-0.238758\pi\) | ||||
0.731635 | + | 0.681697i | \(0.238758\pi\) | |||||||
\(464\) | 2.88923 | 0.134129 | ||||||||
\(465\) | −1.02199 | −0.0473939 | ||||||||
\(466\) | −21.0993 | −0.977408 | ||||||||
\(467\) | 6.12073 | 0.283233 | 0.141617 | − | 0.989922i | \(-0.454770\pi\) | ||||
0.141617 | + | 0.989922i | \(0.454770\pi\) | |||||||
\(468\) | 0.724010 | 0.0334674 | ||||||||
\(469\) | 0.943979 | 0.0435889 | ||||||||
\(470\) | −0.369319 | −0.0170354 | ||||||||
\(471\) | −18.9142 | −0.871521 | ||||||||
\(472\) | −3.01002 | −0.138547 | ||||||||
\(473\) | −29.3659 | −1.35024 | ||||||||
\(474\) | 1.38849 | 0.0637753 | ||||||||
\(475\) | 4.56742 | 0.209568 | ||||||||
\(476\) | −0.113864 | −0.00521895 | ||||||||
\(477\) | −15.4646 | −0.708075 | ||||||||
\(478\) | −4.13040 | −0.188920 | ||||||||
\(479\) | 17.8974 | 0.817752 | 0.408876 | − | 0.912590i | \(-0.365921\pi\) | ||||
0.408876 | + | 0.912590i | \(0.365921\pi\) | |||||||
\(480\) | −0.122137 | −0.00557476 | ||||||||
\(481\) | −3.54010 | −0.161414 | ||||||||
\(482\) | 13.0441 | 0.594141 | ||||||||
\(483\) | −0.412704 | −0.0187787 | ||||||||
\(484\) | 2.46002 | 0.111819 | ||||||||
\(485\) | 2.02240 | 0.0918325 | ||||||||
\(486\) | 16.1454 | 0.732370 | ||||||||
\(487\) | −0.111862 | −0.00506897 | −0.00253448 | − | 0.999997i | \(-0.500807\pi\) | ||||
−0.00253448 | + | 0.999997i | \(0.500807\pi\) | |||||||
\(488\) | −10.1935 | −0.461439 | ||||||||
\(489\) | −6.38800 | −0.288875 | ||||||||
\(490\) | −0.892055 | −0.0402989 | ||||||||
\(491\) | −23.4744 | −1.05939 | −0.529693 | − | 0.848189i | \(-0.677693\pi\) | ||||
−0.529693 | + | 0.848189i | \(0.677693\pi\) | |||||||
\(492\) | 1.80989 | 0.0815960 | ||||||||
\(493\) | −0.938558 | −0.0422705 | ||||||||
\(494\) | −0.313998 | −0.0141274 | ||||||||
\(495\) | 1.00575 | 0.0452050 | ||||||||
\(496\) | −8.36762 | −0.375717 | ||||||||
\(497\) | 1.99615 | 0.0895397 | ||||||||
\(498\) | −9.98649 | −0.447505 | ||||||||
\(499\) | −5.14322 | −0.230242 | −0.115121 | − | 0.993351i | \(-0.536726\pi\) | ||||
−0.115121 | + | 0.993351i | \(0.536726\pi\) | |||||||
\(500\) | 1.29495 | 0.0579119 | ||||||||
\(501\) | 17.6377 | 0.787992 | ||||||||
\(502\) | −20.2778 | −0.905044 | ||||||||
\(503\) | −9.95795 | −0.444003 | −0.222002 | − | 0.975046i | \(-0.571259\pi\) | ||||
−0.222002 | + | 0.975046i | \(0.571259\pi\) | |||||||
\(504\) | 0.740780 | 0.0329970 | ||||||||
\(505\) | −0.879990 | −0.0391590 | ||||||||
\(506\) | −4.58767 | −0.203947 | ||||||||
\(507\) | 12.1302 | 0.538721 | ||||||||
\(508\) | 19.0525 | 0.845320 | ||||||||
\(509\) | −16.0954 | −0.713416 | −0.356708 | − | 0.934216i | \(-0.616101\pi\) | ||||
−0.356708 | + | 0.934216i | \(0.616101\pi\) | |||||||
\(510\) | 0.0396759 | 0.00175688 | ||||||||
\(511\) | −3.66825 | −0.162274 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.41304 | −0.194841 | ||||||||
\(514\) | 0.336181 | 0.0148283 | ||||||||
\(515\) | −1.47054 | −0.0647999 | ||||||||
\(516\) | 7.53673 | 0.331786 | ||||||||
\(517\) | −10.4458 | −0.459404 | ||||||||
\(518\) | −3.62209 | −0.159146 | ||||||||
\(519\) | 23.8126 | 1.04526 | ||||||||
\(520\) | −0.0444371 | −0.00194870 | ||||||||
\(521\) | 12.6857 | 0.555769 | 0.277884 | − | 0.960615i | \(-0.410367\pi\) | ||||
0.277884 | + | 0.960615i | \(0.410367\pi\) | |||||||
\(522\) | 6.10610 | 0.267257 | ||||||||
\(523\) | 29.4170 | 1.28632 | 0.643159 | − | 0.765733i | \(-0.277624\pi\) | ||||
0.643159 | + | 0.765733i | \(0.277624\pi\) | |||||||
\(524\) | −12.1222 | −0.529562 | ||||||||
\(525\) | 1.64466 | 0.0717788 | ||||||||
\(526\) | 24.0852 | 1.05016 | ||||||||
\(527\) | 2.71820 | 0.118407 | ||||||||
\(528\) | −3.45450 | −0.150338 | ||||||||
\(529\) | −21.4364 | −0.932015 | ||||||||
\(530\) | 0.949161 | 0.0412289 | ||||||||
\(531\) | −6.36138 | −0.276060 | ||||||||
\(532\) | −0.321271 | −0.0139289 | ||||||||
\(533\) | 0.658492 | 0.0285225 | ||||||||
\(534\) | −16.4795 | −0.713136 | ||||||||
\(535\) | 1.48327 | 0.0641276 | ||||||||
\(536\) | −2.69312 | −0.116325 | ||||||||
\(537\) | 13.4366 | 0.579830 | ||||||||
\(538\) | 8.89648 | 0.383555 | ||||||||
\(539\) | −25.2308 | −1.08677 | ||||||||
\(540\) | −0.624535 | −0.0268757 | ||||||||
\(541\) | 8.95639 | 0.385065 | 0.192533 | − | 0.981291i | \(-0.438330\pi\) | ||||
0.192533 | + | 0.981291i | \(0.438330\pi\) | |||||||
\(542\) | 15.9456 | 0.684921 | ||||||||
\(543\) | 1.21313 | 0.0520603 | ||||||||
\(544\) | 0.324847 | 0.0139277 | ||||||||
\(545\) | −2.35614 | −0.100926 | ||||||||
\(546\) | −0.113066 | −0.00483878 | ||||||||
\(547\) | 40.1406 | 1.71629 | 0.858145 | − | 0.513407i | \(-0.171617\pi\) | ||||
0.858145 | + | 0.513407i | \(0.171617\pi\) | |||||||
\(548\) | −9.76659 | −0.417208 | ||||||||
\(549\) | −21.5430 | −0.919435 | ||||||||
\(550\) | 18.2822 | 0.779556 | ||||||||
\(551\) | −2.64817 | −0.112816 | ||||||||
\(552\) | 1.17742 | 0.0501144 | ||||||||
\(553\) | 0.516875 | 0.0219797 | ||||||||
\(554\) | 24.6530 | 1.04740 | ||||||||
\(555\) | 1.26212 | 0.0535739 | ||||||||
\(556\) | −0.211615 | −0.00897448 | ||||||||
\(557\) | 26.0020 | 1.10174 | 0.550870 | − | 0.834591i | \(-0.314296\pi\) | ||||
0.550870 | + | 0.834591i | \(0.314296\pi\) | |||||||
\(558\) | −17.6842 | −0.748630 | ||||||||
\(559\) | 2.74209 | 0.115978 | ||||||||
\(560\) | −0.0454664 | −0.00192131 | ||||||||
\(561\) | 1.12219 | 0.0473788 | ||||||||
\(562\) | 12.2409 | 0.516352 | ||||||||
\(563\) | −16.9325 | −0.713621 | −0.356811 | − | 0.934177i | \(-0.616136\pi\) | ||||
−0.356811 | + | 0.934177i | \(0.616136\pi\) | |||||||
\(564\) | 2.68090 | 0.112886 | ||||||||
\(565\) | 0.228032 | 0.00959339 | ||||||||
\(566\) | −21.5413 | −0.905449 | ||||||||
\(567\) | 0.633271 | 0.0265949 | ||||||||
\(568\) | −5.69491 | −0.238953 | ||||||||
\(569\) | 4.85638 | 0.203590 | 0.101795 | − | 0.994805i | \(-0.467541\pi\) | ||||
0.101795 | + | 0.994805i | \(0.467541\pi\) | |||||||
\(570\) | 0.111947 | 0.00468894 | ||||||||
\(571\) | −28.5545 | −1.19497 | −0.597485 | − | 0.801880i | \(-0.703833\pi\) | ||||
−0.597485 | + | 0.801880i | \(0.703833\pi\) | |||||||
\(572\) | −1.25685 | −0.0525517 | ||||||||
\(573\) | 7.20845 | 0.301137 | ||||||||
\(574\) | 0.673745 | 0.0281216 | ||||||||
\(575\) | −6.23125 | −0.259861 | ||||||||
\(576\) | −2.11340 | −0.0880585 | ||||||||
\(577\) | −24.5989 | −1.02406 | −0.512032 | − | 0.858967i | \(-0.671107\pi\) | ||||
−0.512032 | + | 0.858967i | \(0.671107\pi\) | |||||||
\(578\) | 16.8945 | 0.702717 | ||||||||
\(579\) | −14.7012 | −0.610962 | ||||||||
\(580\) | −0.374771 | −0.0155615 | ||||||||
\(581\) | −3.71755 | −0.154230 | ||||||||
\(582\) | −14.6807 | −0.608534 | ||||||||
\(583\) | 26.8460 | 1.11185 | ||||||||
\(584\) | 10.4653 | 0.433058 | ||||||||
\(585\) | −0.0939136 | −0.00388285 | ||||||||
\(586\) | 22.8468 | 0.943794 | ||||||||
\(587\) | −14.0595 | −0.580296 | −0.290148 | − | 0.956982i | \(-0.593705\pi\) | ||||
−0.290148 | + | 0.956982i | \(0.593705\pi\) | |||||||
\(588\) | 6.47546 | 0.267044 | ||||||||
\(589\) | 7.66950 | 0.316016 | ||||||||
\(590\) | 0.390439 | 0.0160741 | ||||||||
\(591\) | 2.30145 | 0.0946688 | ||||||||
\(592\) | 10.3336 | 0.424710 | ||||||||
\(593\) | −12.9160 | −0.530395 | −0.265197 | − | 0.964194i | \(-0.585437\pi\) | ||||
−0.265197 | + | 0.964194i | \(0.585437\pi\) | |||||||
\(594\) | −17.6643 | −0.724774 | ||||||||
\(595\) | 0.0147696 | 0.000605497 0 | ||||||||
\(596\) | −0.581612 | −0.0238238 | ||||||||
\(597\) | 25.7065 | 1.05210 | ||||||||
\(598\) | 0.428382 | 0.0175178 | ||||||||
\(599\) | 25.1142 | 1.02614 | 0.513070 | − | 0.858347i | \(-0.328508\pi\) | ||||
0.513070 | + | 0.858347i | \(0.328508\pi\) | |||||||
\(600\) | −4.69212 | −0.191555 | ||||||||
\(601\) | 25.2372 | 1.02944 | 0.514722 | − | 0.857357i | \(-0.327895\pi\) | ||||
0.514722 | + | 0.857357i | \(0.327895\pi\) | |||||||
\(602\) | 2.80561 | 0.114348 | ||||||||
\(603\) | −5.69165 | −0.231782 | ||||||||
\(604\) | −2.43880 | −0.0992332 | ||||||||
\(605\) | −0.319096 | −0.0129731 | ||||||||
\(606\) | 6.38788 | 0.259490 | ||||||||
\(607\) | 47.4054 | 1.92413 | 0.962063 | − | 0.272827i | \(-0.0879587\pi\) | ||||
0.962063 | + | 0.272827i | \(0.0879587\pi\) | |||||||
\(608\) | 0.916569 | 0.0371718 | ||||||||
\(609\) | −0.953567 | −0.0386405 | ||||||||
\(610\) | 1.32223 | 0.0535357 | ||||||||
\(611\) | 0.975392 | 0.0394602 | ||||||||
\(612\) | 0.686534 | 0.0277515 | ||||||||
\(613\) | −18.9950 | −0.767200 | −0.383600 | − | 0.923499i | \(-0.625316\pi\) | ||||
−0.383600 | + | 0.923499i | \(0.625316\pi\) | |||||||
\(614\) | 9.56090 | 0.385847 | ||||||||
\(615\) | −0.234766 | −0.00946668 | ||||||||
\(616\) | −1.28597 | −0.0518131 | ||||||||
\(617\) | 44.5007 | 1.79153 | 0.895766 | − | 0.444525i | \(-0.146628\pi\) | ||||
0.895766 | + | 0.444525i | \(0.146628\pi\) | |||||||
\(618\) | 10.6747 | 0.429400 | ||||||||
\(619\) | −23.2897 | −0.936091 | −0.468045 | − | 0.883704i | \(-0.655042\pi\) | ||||
−0.468045 | + | 0.883704i | \(0.655042\pi\) | |||||||
\(620\) | 1.08539 | 0.0435903 | ||||||||
\(621\) | 6.02063 | 0.241600 | ||||||||
\(622\) | 10.2196 | 0.409769 | ||||||||
\(623\) | −6.13461 | −0.245778 | ||||||||
\(624\) | 0.322571 | 0.0129132 | ||||||||
\(625\) | 24.7479 | 0.989916 | ||||||||
\(626\) | 10.7607 | 0.430083 | ||||||||
\(627\) | 3.16629 | 0.126449 | ||||||||
\(628\) | 20.0875 | 0.801577 | ||||||||
\(629\) | −3.35685 | −0.133846 | ||||||||
\(630\) | −0.0960889 | −0.00382827 | ||||||||
\(631\) | −19.2637 | −0.766874 | −0.383437 | − | 0.923567i | \(-0.625260\pi\) | ||||
−0.383437 | + | 0.923567i | \(0.625260\pi\) | |||||||
\(632\) | −1.47461 | −0.0586570 | ||||||||
\(633\) | −3.94644 | −0.156857 | ||||||||
\(634\) | −14.7775 | −0.586888 | ||||||||
\(635\) | −2.47136 | −0.0980731 | ||||||||
\(636\) | −6.89000 | −0.273206 | ||||||||
\(637\) | 2.35597 | 0.0933470 | ||||||||
\(638\) | −10.6000 | −0.419657 | ||||||||
\(639\) | −12.0357 | −0.476123 | ||||||||
\(640\) | 0.129713 | 0.00512736 | ||||||||
\(641\) | 3.98859 | 0.157540 | 0.0787699 | − | 0.996893i | \(-0.474901\pi\) | ||||
0.0787699 | + | 0.996893i | \(0.474901\pi\) | |||||||
\(642\) | −10.7671 | −0.424945 | ||||||||
\(643\) | 39.6773 | 1.56472 | 0.782360 | − | 0.622827i | \(-0.214016\pi\) | ||||
0.782360 | + | 0.622827i | \(0.214016\pi\) | |||||||
\(644\) | 0.438304 | 0.0172716 | ||||||||
\(645\) | −0.977613 | −0.0384935 | ||||||||
\(646\) | −0.297745 | −0.0117146 | ||||||||
\(647\) | 39.8399 | 1.56627 | 0.783135 | − | 0.621852i | \(-0.213619\pi\) | ||||
0.783135 | + | 0.621852i | \(0.213619\pi\) | |||||||
\(648\) | −1.80669 | −0.0709734 | ||||||||
\(649\) | 11.0431 | 0.433480 | ||||||||
\(650\) | −1.70714 | −0.0669594 | ||||||||
\(651\) | 2.76167 | 0.108238 | ||||||||
\(652\) | 6.78425 | 0.265692 | ||||||||
\(653\) | −14.6957 | −0.575088 | −0.287544 | − | 0.957768i | \(-0.592839\pi\) | ||||
−0.287544 | + | 0.957768i | \(0.592839\pi\) | |||||||
\(654\) | 17.1033 | 0.668792 | ||||||||
\(655\) | 1.57241 | 0.0614392 | ||||||||
\(656\) | −1.92216 | −0.0750476 | ||||||||
\(657\) | 22.1174 | 0.862884 | ||||||||
\(658\) | 0.997985 | 0.0389055 | ||||||||
\(659\) | −18.1529 | −0.707137 | −0.353569 | − | 0.935409i | \(-0.615032\pi\) | ||||
−0.353569 | + | 0.935409i | \(0.615032\pi\) | |||||||
\(660\) | 0.448095 | 0.0174421 | ||||||||
\(661\) | −8.74244 | −0.340042 | −0.170021 | − | 0.985440i | \(-0.554383\pi\) | ||||
−0.170021 | + | 0.985440i | \(0.554383\pi\) | |||||||
\(662\) | −4.76669 | −0.185263 | ||||||||
\(663\) | −0.104786 | −0.00406956 | ||||||||
\(664\) | 10.6060 | 0.411591 | ||||||||
\(665\) | 0.0416731 | 0.00161601 | ||||||||
\(666\) | 21.8391 | 0.846249 | ||||||||
\(667\) | 3.61286 | 0.139890 | ||||||||
\(668\) | −18.7317 | −0.724752 | ||||||||
\(669\) | −4.36154 | −0.168627 | ||||||||
\(670\) | 0.349333 | 0.0134959 | ||||||||
\(671\) | 37.3979 | 1.44373 | ||||||||
\(672\) | 0.330042 | 0.0127317 | ||||||||
\(673\) | 6.40280 | 0.246810 | 0.123405 | − | 0.992356i | \(-0.460619\pi\) | ||||
0.123405 | + | 0.992356i | \(0.460619\pi\) | |||||||
\(674\) | 0.980382 | 0.0377629 | ||||||||
\(675\) | −23.9927 | −0.923479 | ||||||||
\(676\) | −12.8826 | −0.495486 | ||||||||
\(677\) | −16.2493 | −0.624510 | −0.312255 | − | 0.949998i | \(-0.601084\pi\) | ||||
−0.312255 | + | 0.949998i | \(0.601084\pi\) | |||||||
\(678\) | −1.65529 | −0.0635712 | ||||||||
\(679\) | −5.46500 | −0.209727 | ||||||||
\(680\) | −0.0421370 | −0.00161588 | ||||||||
\(681\) | −9.80326 | −0.375662 | ||||||||
\(682\) | 30.6990 | 1.17553 | ||||||||
\(683\) | 19.7004 | 0.753815 | 0.376908 | − | 0.926251i | \(-0.376987\pi\) | ||||
0.376908 | + | 0.926251i | \(0.376987\pi\) | |||||||
\(684\) | 1.93708 | 0.0740661 | ||||||||
\(685\) | 1.26686 | 0.0484040 | ||||||||
\(686\) | 4.86415 | 0.185714 | ||||||||
\(687\) | 8.43550 | 0.321834 | ||||||||
\(688\) | −8.00424 | −0.305159 | ||||||||
\(689\) | −2.50679 | −0.0955012 | ||||||||
\(690\) | −0.152727 | −0.00581422 | ||||||||
\(691\) | −16.9280 | −0.643971 | −0.321986 | − | 0.946745i | \(-0.604350\pi\) | ||||
−0.321986 | + | 0.946745i | \(0.604350\pi\) | |||||||
\(692\) | −25.2897 | −0.961370 | ||||||||
\(693\) | −2.71777 | −0.103239 | ||||||||
\(694\) | 23.2784 | 0.883637 | ||||||||
\(695\) | 0.0274493 | 0.00104121 | ||||||||
\(696\) | 2.72047 | 0.103119 | ||||||||
\(697\) | 0.624407 | 0.0236511 | ||||||||
\(698\) | −5.88858 | −0.222886 | ||||||||
\(699\) | −19.8670 | −0.751438 | ||||||||
\(700\) | −1.74668 | −0.0660182 | ||||||||
\(701\) | 14.6088 | 0.551768 | 0.275884 | − | 0.961191i | \(-0.411029\pi\) | ||||
0.275884 | + | 0.961191i | \(0.411029\pi\) | |||||||
\(702\) | 1.64943 | 0.0622539 | ||||||||
\(703\) | −9.47148 | −0.357224 | ||||||||
\(704\) | 3.66879 | 0.138273 | ||||||||
\(705\) | −0.347748 | −0.0130969 | ||||||||
\(706\) | 17.0303 | 0.640945 | ||||||||
\(707\) | 2.37794 | 0.0894316 | ||||||||
\(708\) | −2.83421 | −0.106516 | ||||||||
\(709\) | −24.6702 | −0.926507 | −0.463254 | − | 0.886226i | \(-0.653318\pi\) | ||||
−0.463254 | + | 0.886226i | \(0.653318\pi\) | |||||||
\(710\) | 0.738705 | 0.0277231 | ||||||||
\(711\) | −3.11646 | −0.116876 | ||||||||
\(712\) | 17.5017 | 0.655904 | ||||||||
\(713\) | −10.4634 | −0.391856 | ||||||||
\(714\) | −0.107213 | −0.00401236 | ||||||||
\(715\) | 0.163030 | 0.00609699 | ||||||||
\(716\) | −14.2700 | −0.533296 | ||||||||
\(717\) | −3.88916 | −0.145243 | ||||||||
\(718\) | 15.5151 | 0.579018 | ||||||||
\(719\) | 13.8705 | 0.517283 | 0.258642 | − | 0.965973i | \(-0.416725\pi\) | ||||
0.258642 | + | 0.965973i | \(0.416725\pi\) | |||||||
\(720\) | 0.274136 | 0.0102165 | ||||||||
\(721\) | 3.97375 | 0.147990 | ||||||||
\(722\) | 18.1599 | 0.675842 | ||||||||
\(723\) | 12.2822 | 0.456780 | ||||||||
\(724\) | −1.28838 | −0.0478823 | ||||||||
\(725\) | −14.3975 | −0.534710 | ||||||||
\(726\) | 2.31633 | 0.0859672 | ||||||||
\(727\) | −7.88316 | −0.292370 | −0.146185 | − | 0.989257i | \(-0.546699\pi\) | ||||
−0.146185 | + | 0.989257i | \(0.546699\pi\) | |||||||
\(728\) | 0.120080 | 0.00445044 | ||||||||
\(729\) | 9.78231 | 0.362308 | ||||||||
\(730\) | −1.35749 | −0.0502429 | ||||||||
\(731\) | 2.60016 | 0.0961703 | ||||||||
\(732\) | −9.59815 | −0.354758 | ||||||||
\(733\) | 37.1659 | 1.37275 | 0.686377 | − | 0.727246i | \(-0.259200\pi\) | ||||
0.686377 | + | 0.727246i | \(0.259200\pi\) | |||||||
\(734\) | −26.9568 | −0.994995 | ||||||||
\(735\) | −0.839952 | −0.0309821 | ||||||||
\(736\) | −1.25046 | −0.0460925 | ||||||||
\(737\) | 9.88048 | 0.363952 | ||||||||
\(738\) | −4.06229 | −0.149535 | ||||||||
\(739\) | 32.2183 | 1.18517 | 0.592585 | − | 0.805508i | \(-0.298108\pi\) | ||||
0.592585 | + | 0.805508i | \(0.298108\pi\) | |||||||
\(740\) | −1.34041 | −0.0492744 | ||||||||
\(741\) | −0.295658 | −0.0108613 | ||||||||
\(742\) | −2.56486 | −0.0941588 | ||||||||
\(743\) | −37.0544 | −1.35939 | −0.679697 | − | 0.733493i | \(-0.737889\pi\) | ||||
−0.679697 | + | 0.733493i | \(0.737889\pi\) | |||||||
\(744\) | −7.87888 | −0.288854 | ||||||||
\(745\) | 0.0754427 | 0.00276401 | ||||||||
\(746\) | 5.36389 | 0.196386 | ||||||||
\(747\) | 22.4147 | 0.820110 | ||||||||
\(748\) | −1.19180 | −0.0435764 | ||||||||
\(749\) | −4.00815 | −0.146455 | ||||||||
\(750\) | 1.21931 | 0.0445230 | ||||||||
\(751\) | 49.6468 | 1.81164 | 0.905818 | − | 0.423667i | \(-0.139257\pi\) | ||||
0.905818 | + | 0.423667i | \(0.139257\pi\) | |||||||
\(752\) | −2.84720 | −0.103827 | ||||||||
\(753\) | −19.0934 | −0.695804 | ||||||||
\(754\) | 0.989791 | 0.0360461 | ||||||||
\(755\) | 0.316344 | 0.0115129 | ||||||||
\(756\) | 1.68764 | 0.0613789 | ||||||||
\(757\) | −48.3117 | −1.75592 | −0.877958 | − | 0.478737i | \(-0.841095\pi\) | ||||
−0.877958 | + | 0.478737i | \(0.841095\pi\) | |||||||
\(758\) | 13.8038 | 0.501378 | ||||||||
\(759\) | −4.31971 | −0.156796 | ||||||||
\(760\) | −0.118891 | −0.00431263 | ||||||||
\(761\) | 4.36062 | 0.158072 | 0.0790362 | − | 0.996872i | \(-0.474816\pi\) | ||||
0.0790362 | + | 0.996872i | \(0.474816\pi\) | |||||||
\(762\) | 17.9397 | 0.649888 | ||||||||
\(763\) | 6.36684 | 0.230495 | ||||||||
\(764\) | −7.65560 | −0.276970 | ||||||||
\(765\) | −0.0890524 | −0.00321970 | ||||||||
\(766\) | 23.4129 | 0.845941 | ||||||||
\(767\) | −1.03117 | −0.0372334 | ||||||||
\(768\) | −0.941592 | −0.0339768 | ||||||||
\(769\) | −15.4316 | −0.556478 | −0.278239 | − | 0.960512i | \(-0.589751\pi\) | ||||
−0.278239 | + | 0.960512i | \(0.589751\pi\) | |||||||
\(770\) | 0.166807 | 0.00601130 | ||||||||
\(771\) | 0.316546 | 0.0114001 | ||||||||
\(772\) | 15.6131 | 0.561930 | ||||||||
\(773\) | 34.7219 | 1.24886 | 0.624430 | − | 0.781081i | \(-0.285331\pi\) | ||||
0.624430 | + | 0.781081i | \(0.285331\pi\) | |||||||
\(774\) | −16.9162 | −0.608040 | ||||||||
\(775\) | 41.6973 | 1.49781 | ||||||||
\(776\) | 15.5913 | 0.559696 | ||||||||
\(777\) | −3.41054 | −0.122352 | ||||||||
\(778\) | 23.9313 | 0.857978 | ||||||||
\(779\) | 1.76179 | 0.0631226 | ||||||||
\(780\) | −0.0418417 | −0.00149817 | ||||||||
\(781\) | 20.8934 | 0.747626 | ||||||||
\(782\) | 0.406208 | 0.0145260 | ||||||||
\(783\) | 13.9109 | 0.497134 | ||||||||
\(784\) | −6.87714 | −0.245612 | ||||||||
\(785\) | −2.60561 | −0.0929982 | ||||||||
\(786\) | −11.4142 | −0.407131 | ||||||||
\(787\) | 13.5974 | 0.484696 | 0.242348 | − | 0.970189i | \(-0.422082\pi\) | ||||
0.242348 | + | 0.970189i | \(0.422082\pi\) | |||||||
\(788\) | −2.44421 | −0.0870712 | ||||||||
\(789\) | 22.6784 | 0.807374 | ||||||||
\(790\) | 0.191277 | 0.00680532 | ||||||||
\(791\) | −0.616197 | −0.0219094 | ||||||||
\(792\) | 7.75363 | 0.275513 | ||||||||
\(793\) | −3.49210 | −0.124008 | ||||||||
\(794\) | 4.43559 | 0.157413 | ||||||||
\(795\) | 0.893723 | 0.0316971 | ||||||||
\(796\) | −27.3011 | −0.967661 | ||||||||
\(797\) | 46.3988 | 1.64353 | 0.821765 | − | 0.569826i | \(-0.192989\pi\) | ||||
0.821765 | + | 0.569826i | \(0.192989\pi\) | |||||||
\(798\) | −0.302507 | −0.0107086 | ||||||||
\(799\) | 0.924904 | 0.0327208 | ||||||||
\(800\) | 4.98317 | 0.176182 | ||||||||
\(801\) | 36.9882 | 1.30691 | ||||||||
\(802\) | 6.81431 | 0.240622 | ||||||||
\(803\) | −38.3951 | −1.35493 | ||||||||
\(804\) | −2.53582 | −0.0894315 | ||||||||
\(805\) | −0.0568538 | −0.00200383 | ||||||||
\(806\) | −2.86658 | −0.100971 | ||||||||
\(807\) | 8.37686 | 0.294879 | ||||||||
\(808\) | −6.78412 | −0.238665 | ||||||||
\(809\) | −26.6972 | −0.938625 | −0.469313 | − | 0.883032i | \(-0.655498\pi\) | ||||
−0.469313 | + | 0.883032i | \(0.655498\pi\) | |||||||
\(810\) | 0.234351 | 0.00823426 | ||||||||
\(811\) | −6.42122 | −0.225480 | −0.112740 | − | 0.993625i | \(-0.535963\pi\) | ||||
−0.112740 | + | 0.993625i | \(0.535963\pi\) | |||||||
\(812\) | 1.01272 | 0.0355394 | ||||||||
\(813\) | 15.0142 | 0.526572 | ||||||||
\(814\) | −37.9119 | −1.32881 | ||||||||
\(815\) | −0.880007 | −0.0308253 | ||||||||
\(816\) | 0.305874 | 0.0107077 | ||||||||
\(817\) | 7.33644 | 0.256669 | ||||||||
\(818\) | 24.3559 | 0.851584 | ||||||||
\(819\) | 0.253776 | 0.00886767 | ||||||||
\(820\) | 0.249329 | 0.00870694 | ||||||||
\(821\) | 10.7889 | 0.376536 | 0.188268 | − | 0.982118i | \(-0.439713\pi\) | ||||
0.188268 | + | 0.982118i | \(0.439713\pi\) | |||||||
\(822\) | −9.19615 | −0.320752 | ||||||||
\(823\) | −27.6366 | −0.963351 | −0.481676 | − | 0.876350i | \(-0.659972\pi\) | ||||
−0.481676 | + | 0.876350i | \(0.659972\pi\) | |||||||
\(824\) | −11.3369 | −0.394939 | ||||||||
\(825\) | 17.2144 | 0.599328 | ||||||||
\(826\) | −1.05506 | −0.0367101 | ||||||||
\(827\) | 43.2078 | 1.50248 | 0.751242 | − | 0.660027i | \(-0.229455\pi\) | ||||
0.751242 | + | 0.660027i | \(0.229455\pi\) | |||||||
\(828\) | −2.64272 | −0.0918410 | ||||||||
\(829\) | −31.9777 | −1.11063 | −0.555316 | − | 0.831639i | \(-0.687403\pi\) | ||||
−0.555316 | + | 0.831639i | \(0.687403\pi\) | |||||||
\(830\) | −1.37573 | −0.0477524 | ||||||||
\(831\) | 23.2130 | 0.805251 | ||||||||
\(832\) | −0.342580 | −0.0118768 | ||||||||
\(833\) | 2.23402 | 0.0774042 | ||||||||
\(834\) | −0.199255 | −0.00689964 | ||||||||
\(835\) | 2.42975 | 0.0840850 | ||||||||
\(836\) | −3.36270 | −0.116301 | ||||||||
\(837\) | −40.2879 | −1.39255 | ||||||||
\(838\) | −29.0451 | −1.00334 | ||||||||
\(839\) | 6.33484 | 0.218703 | 0.109351 | − | 0.994003i | \(-0.465123\pi\) | ||||
0.109351 | + | 0.994003i | \(0.465123\pi\) | |||||||
\(840\) | −0.0428108 | −0.00147711 | ||||||||
\(841\) | −20.6524 | −0.712151 | ||||||||
\(842\) | 14.3006 | 0.492831 | ||||||||
\(843\) | 11.5260 | 0.396975 | ||||||||
\(844\) | 4.19124 | 0.144269 | ||||||||
\(845\) | 1.67105 | 0.0574858 | ||||||||
\(846\) | −6.01727 | −0.206878 | ||||||||
\(847\) | 0.862273 | 0.0296281 | ||||||||
\(848\) | 7.31739 | 0.251280 | ||||||||
\(849\) | −20.2831 | −0.696115 | ||||||||
\(850\) | −1.61877 | −0.0555234 | ||||||||
\(851\) | 12.9218 | 0.442953 | ||||||||
\(852\) | −5.36229 | −0.183709 | ||||||||
\(853\) | 28.2288 | 0.966534 | 0.483267 | − | 0.875473i | \(-0.339450\pi\) | ||||
0.483267 | + | 0.875473i | \(0.339450\pi\) | |||||||
\(854\) | −3.57299 | −0.122265 | ||||||||
\(855\) | −0.251265 | −0.00859307 | ||||||||
\(856\) | 11.4350 | 0.390842 | ||||||||
\(857\) | −31.8090 | −1.08657 | −0.543287 | − | 0.839547i | \(-0.682821\pi\) | ||||
−0.543287 | + | 0.839547i | \(0.682821\pi\) | |||||||
\(858\) | −1.18344 | −0.0404021 | ||||||||
\(859\) | 41.2690 | 1.40808 | 0.704041 | − | 0.710160i | \(-0.251377\pi\) | ||||
0.704041 | + | 0.710160i | \(0.251377\pi\) | |||||||
\(860\) | 1.03825 | 0.0354042 | ||||||||
\(861\) | 0.634393 | 0.0216201 | ||||||||
\(862\) | 22.7210 | 0.773881 | ||||||||
\(863\) | −40.4998 | −1.37863 | −0.689314 | − | 0.724463i | \(-0.742088\pi\) | ||||
−0.689314 | + | 0.724463i | \(0.742088\pi\) | |||||||
\(864\) | −4.81474 | −0.163801 | ||||||||
\(865\) | 3.28041 | 0.111537 | ||||||||
\(866\) | 35.0246 | 1.19018 | ||||||||
\(867\) | 15.9077 | 0.540254 | ||||||||
\(868\) | −2.93298 | −0.0995517 | ||||||||
\(869\) | 5.41005 | 0.183523 | ||||||||
\(870\) | −0.352881 | −0.0119638 | ||||||||
\(871\) | −0.922609 | −0.0312614 | ||||||||
\(872\) | −18.1642 | −0.615119 | ||||||||
\(873\) | 32.9508 | 1.11522 | ||||||||
\(874\) | 1.14613 | 0.0387685 | ||||||||
\(875\) | 0.453899 | 0.0153446 | ||||||||
\(876\) | 9.85406 | 0.332938 | ||||||||
\(877\) | 32.1167 | 1.08450 | 0.542252 | − | 0.840216i | \(-0.317572\pi\) | ||||
0.542252 | + | 0.840216i | \(0.317572\pi\) | |||||||
\(878\) | −3.41021 | −0.115089 | ||||||||
\(879\) | 21.5124 | 0.725595 | ||||||||
\(880\) | −0.475890 | −0.0160423 | ||||||||
\(881\) | 14.5979 | 0.491815 | 0.245908 | − | 0.969293i | \(-0.420914\pi\) | ||||
0.245908 | + | 0.969293i | \(0.420914\pi\) | |||||||
\(882\) | −14.5342 | −0.489391 | ||||||||
\(883\) | 13.3780 | 0.450206 | 0.225103 | − | 0.974335i | \(-0.427728\pi\) | ||||
0.225103 | + | 0.974335i | \(0.427728\pi\) | |||||||
\(884\) | 0.111286 | 0.00374296 | ||||||||
\(885\) | 0.367634 | 0.0123579 | ||||||||
\(886\) | 2.49849 | 0.0839385 | ||||||||
\(887\) | 45.1662 | 1.51653 | 0.758266 | − | 0.651945i | \(-0.226047\pi\) | ||||
0.758266 | + | 0.651945i | \(0.226047\pi\) | |||||||
\(888\) | 9.73007 | 0.326520 | ||||||||
\(889\) | 6.67820 | 0.223980 | ||||||||
\(890\) | −2.27020 | −0.0760973 | ||||||||
\(891\) | 6.62836 | 0.222058 | ||||||||
\(892\) | 4.63209 | 0.155094 | ||||||||
\(893\) | 2.60965 | 0.0873286 | ||||||||
\(894\) | −0.547642 | −0.0183159 | ||||||||
\(895\) | 1.85101 | 0.0618725 | ||||||||
\(896\) | −0.350515 | −0.0117099 | ||||||||
\(897\) | 0.403361 | 0.0134678 | ||||||||
\(898\) | 16.2151 | 0.541105 | ||||||||
\(899\) | −24.1759 | −0.806313 | ||||||||
\(900\) | 10.5315 | 0.351049 | ||||||||
\(901\) | −2.37703 | −0.0791905 | ||||||||
\(902\) | 7.05199 | 0.234805 | ||||||||
\(903\) | 2.64174 | 0.0879115 | ||||||||
\(904\) | 1.75797 | 0.0584693 | ||||||||
\(905\) | 0.167120 | 0.00555525 | ||||||||
\(906\) | −2.29635 | −0.0762911 | ||||||||
\(907\) | 10.5519 | 0.350370 | 0.175185 | − | 0.984536i | \(-0.443948\pi\) | ||||
0.175185 | + | 0.984536i | \(0.443948\pi\) | |||||||
\(908\) | 10.4114 | 0.345513 | ||||||||
\(909\) | −14.3376 | −0.475548 | ||||||||
\(910\) | −0.0155759 | −0.000516336 0 | ||||||||
\(911\) | 36.4848 | 1.20880 | 0.604398 | − | 0.796683i | \(-0.293414\pi\) | ||||
0.604398 | + | 0.796683i | \(0.293414\pi\) | |||||||
\(912\) | 0.863034 | 0.0285779 | ||||||||
\(913\) | −38.9110 | −1.28777 | ||||||||
\(914\) | −13.4972 | −0.446447 | ||||||||
\(915\) | 1.24501 | 0.0411586 | ||||||||
\(916\) | −8.95876 | −0.296006 | ||||||||
\(917\) | −4.24903 | −0.140315 | ||||||||
\(918\) | 1.56406 | 0.0516216 | ||||||||
\(919\) | 19.5171 | 0.643810 | 0.321905 | − | 0.946772i | \(-0.395677\pi\) | ||||
0.321905 | + | 0.946772i | \(0.395677\pi\) | |||||||
\(920\) | 0.162201 | 0.00534760 | ||||||||
\(921\) | 9.00247 | 0.296642 | ||||||||
\(922\) | 37.6469 | 1.23983 | ||||||||
\(923\) | −1.95096 | −0.0642168 | ||||||||
\(924\) | −1.21086 | −0.0398342 | ||||||||
\(925\) | −51.4943 | −1.69312 | ||||||||
\(926\) | −31.4858 | −1.03469 | ||||||||
\(927\) | −23.9594 | −0.786931 | ||||||||
\(928\) | −2.88923 | −0.0948435 | ||||||||
\(929\) | 8.12380 | 0.266533 | 0.133267 | − | 0.991080i | \(-0.457453\pi\) | ||||
0.133267 | + | 0.991080i | \(0.457453\pi\) | |||||||
\(930\) | 1.02199 | 0.0335125 | ||||||||
\(931\) | 6.30337 | 0.206585 | ||||||||
\(932\) | 21.0993 | 0.691132 | ||||||||
\(933\) | 9.62271 | 0.315033 | ||||||||
\(934\) | −6.12073 | −0.200276 | ||||||||
\(935\) | 0.154592 | 0.00505569 | ||||||||
\(936\) | −0.724010 | −0.0236650 | ||||||||
\(937\) | 45.0973 | 1.47326 | 0.736632 | − | 0.676294i | \(-0.236415\pi\) | ||||
0.736632 | + | 0.676294i | \(0.236415\pi\) | |||||||
\(938\) | −0.943979 | −0.0308220 | ||||||||
\(939\) | 10.1322 | 0.330651 | ||||||||
\(940\) | 0.369319 | 0.0120458 | ||||||||
\(941\) | −31.8845 | −1.03940 | −0.519702 | − | 0.854348i | \(-0.673957\pi\) | ||||
−0.519702 | + | 0.854348i | \(0.673957\pi\) | |||||||
\(942\) | 18.9142 | 0.616258 | ||||||||
\(943\) | −2.40358 | −0.0782712 | ||||||||
\(944\) | 3.01002 | 0.0979677 | ||||||||
\(945\) | −0.218909 | −0.00712111 | ||||||||
\(946\) | 29.3659 | 0.954767 | ||||||||
\(947\) | 59.1408 | 1.92182 | 0.960909 | − | 0.276866i | \(-0.0892957\pi\) | ||||
0.960909 | + | 0.276866i | \(0.0892957\pi\) | |||||||
\(948\) | −1.38849 | −0.0450959 | ||||||||
\(949\) | 3.58521 | 0.116381 | ||||||||
\(950\) | −4.56742 | −0.148187 | ||||||||
\(951\) | −13.9144 | −0.451204 | ||||||||
\(952\) | 0.113864 | 0.00369035 | ||||||||
\(953\) | 23.1786 | 0.750830 | 0.375415 | − | 0.926857i | \(-0.377500\pi\) | ||||
0.375415 | + | 0.926857i | \(0.377500\pi\) | |||||||
\(954\) | 15.4646 | 0.500685 | ||||||||
\(955\) | 0.993032 | 0.0321337 | ||||||||
\(956\) | 4.13040 | 0.133587 | ||||||||
\(957\) | −9.98084 | −0.322635 | ||||||||
\(958\) | −17.8974 | −0.578238 | ||||||||
\(959\) | −3.42334 | −0.110545 | ||||||||
\(960\) | 0.122137 | 0.00394195 | ||||||||
\(961\) | 39.0170 | 1.25861 | ||||||||
\(962\) | 3.54010 | 0.114137 | ||||||||
\(963\) | 24.1669 | 0.778766 | ||||||||
\(964\) | −13.0441 | −0.420121 | ||||||||
\(965\) | −2.02523 | −0.0651945 | ||||||||
\(966\) | 0.412704 | 0.0132785 | ||||||||
\(967\) | 30.2130 | 0.971586 | 0.485793 | − | 0.874074i | \(-0.338531\pi\) | ||||
0.485793 | + | 0.874074i | \(0.338531\pi\) | |||||||
\(968\) | −2.46002 | −0.0790679 | ||||||||
\(969\) | −0.280354 | −0.00900628 | ||||||||
\(970\) | −2.02240 | −0.0649354 | ||||||||
\(971\) | −13.9789 | −0.448603 | −0.224302 | − | 0.974520i | \(-0.572010\pi\) | ||||
−0.224302 | + | 0.974520i | \(0.572010\pi\) | |||||||
\(972\) | −16.1454 | −0.517864 | ||||||||
\(973\) | −0.0741743 | −0.00237792 | ||||||||
\(974\) | 0.111862 | 0.00358430 | ||||||||
\(975\) | −1.60743 | −0.0514788 | ||||||||
\(976\) | 10.1935 | 0.326287 | ||||||||
\(977\) | 30.2608 | 0.968129 | 0.484064 | − | 0.875032i | \(-0.339160\pi\) | ||||
0.484064 | + | 0.875032i | \(0.339160\pi\) | |||||||
\(978\) | 6.38800 | 0.204266 | ||||||||
\(979\) | −64.2101 | −2.05216 | ||||||||
\(980\) | 0.892055 | 0.0284957 | ||||||||
\(981\) | −38.3884 | −1.22565 | ||||||||
\(982\) | 23.4744 | 0.749099 | ||||||||
\(983\) | 28.7492 | 0.916956 | 0.458478 | − | 0.888706i | \(-0.348395\pi\) | ||||
0.458478 | + | 0.888706i | \(0.348395\pi\) | |||||||
\(984\) | −1.80989 | −0.0576971 | ||||||||
\(985\) | 0.317046 | 0.0101019 | ||||||||
\(986\) | 0.938558 | 0.0298898 | ||||||||
\(987\) | 0.939695 | 0.0299108 | ||||||||
\(988\) | 0.313998 | 0.00998962 | ||||||||
\(989\) | −10.0090 | −0.318267 | ||||||||
\(990\) | −1.00575 | −0.0319648 | ||||||||
\(991\) | 37.4492 | 1.18961 | 0.594806 | − | 0.803869i | \(-0.297229\pi\) | ||||
0.594806 | + | 0.803869i | \(0.297229\pi\) | |||||||
\(992\) | 8.36762 | 0.265672 | ||||||||
\(993\) | −4.48828 | −0.142431 | ||||||||
\(994\) | −1.99615 | −0.0633141 | ||||||||
\(995\) | 3.54131 | 0.112267 | ||||||||
\(996\) | 9.98649 | 0.316434 | ||||||||
\(997\) | −53.8516 | −1.70550 | −0.852748 | − | 0.522322i | \(-0.825066\pi\) | ||||
−0.852748 | + | 0.522322i | \(0.825066\pi\) | |||||||
\(998\) | 5.14322 | 0.162806 | ||||||||
\(999\) | 49.7538 | 1.57414 |
(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 | 4006.2.a.g.1.15 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.15 | ✓ | 40 | 1.1 | even | 1 | trivial |