Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,2,Mod(71,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.e (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(0.670743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.2593100598870016.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.12 | ||
Root | \(-0.430469 + 1.34711i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.71 |
Dual form | 84.2.e.a.71.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34711 | + | 0.430469i | 0.952548 | + | 0.304388i | ||||
\(3\) | −0.916638 | − | 1.46962i | −0.529221 | − | 0.848484i | ||||
\(4\) | 1.62939 | + | 1.15978i | 0.814696 | + | 0.579888i | ||||
\(5\) | 0.348612i | 0.155904i | 0.996957 | + | 0.0779520i | \(0.0248381\pi\) | ||||
−0.996957 | + | 0.0779520i | \(0.975162\pi\) | |||||||
\(6\) | −0.602184 | − | 2.37432i | −0.245841 | − | 0.969310i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 1.69572 | + | 2.26374i | 0.599527 | + | 0.800354i | ||||
\(9\) | −1.31955 | + | 2.69421i | −0.439850 | + | 0.898071i | ||||
\(10\) | −0.150067 | + | 0.469617i | −0.0474552 | + | 0.148506i | ||||
\(11\) | −3.90376 | −1.17703 | −0.588514 | − | 0.808487i | \(-0.700287\pi\) | ||||
−0.588514 | + | 0.808487i | \(0.700287\pi\) | |||||||
\(12\) | 0.210863 | − | 3.45768i | 0.0608710 | − | 0.998146i | ||||
\(13\) | −2.93923 | −0.815197 | −0.407599 | − | 0.913161i | \(-0.633634\pi\) | ||||
−0.407599 | + | 0.913161i | \(0.633634\pi\) | |||||||
\(14\) | 0.430469 | − | 1.34711i | 0.115048 | − | 0.360029i | ||||
\(15\) | 0.512326 | − | 0.319551i | 0.132282 | − | 0.0825077i | ||||
\(16\) | 1.30984 | + | 3.77946i | 0.327461 | + | 0.944865i | ||||
\(17\) | − | 3.90376i | − | 0.946802i | −0.880847 | − | 0.473401i | \(-0.843026\pi\) | ||
0.880847 | − | 0.473401i | \(-0.156974\pi\) | |||||||
\(18\) | −2.93735 | + | 3.06137i | −0.692340 | + | 0.721571i | ||||
\(19\) | 5.57834i | 1.27976i | 0.768476 | + | 0.639879i | \(0.221016\pi\) | ||||
−0.768476 | + | 0.639879i | \(0.778984\pi\) | |||||||
\(20\) | −0.404312 | + | 0.568026i | −0.0904068 | + | 0.127014i | ||||
\(21\) | −1.46962 | + | 0.916638i | −0.320697 | + | 0.200027i | ||||
\(22\) | −5.25879 | − | 1.68045i | −1.12118 | − | 0.358273i | ||||
\(23\) | 2.18189 | 0.454955 | 0.227477 | − | 0.973783i | \(-0.426952\pi\) | ||||
0.227477 | + | 0.973783i | \(0.426952\pi\) | |||||||
\(24\) | 1.77248 | − | 4.56709i | 0.361806 | − | 0.932254i | ||||
\(25\) | 4.87847 | 0.975694 | ||||||||
\(26\) | −3.95946 | − | 1.26525i | −0.776515 | − | 0.248136i | ||||
\(27\) | 5.16901 | − | 0.530383i | 0.994777 | − | 0.102072i | ||||
\(28\) | 1.15978 | − | 1.62939i | 0.219177 | − | 0.307926i | ||||
\(29\) | − | 9.75220i | − | 1.81094i | −0.424412 | − | 0.905469i | \(-0.639519\pi\) | ||
0.424412 | − | 0.905469i | \(-0.360481\pi\) | |||||||
\(30\) | 0.827715 | − | 0.209928i | 0.151119 | − | 0.0383275i | ||||
\(31\) | − | 2.63910i | − | 0.473997i | −0.971510 | − | 0.236998i | \(-0.923836\pi\) | ||
0.971510 | − | 0.236998i | \(-0.0761636\pi\) | |||||||
\(32\) | 0.137557 | + | 5.65518i | 0.0243168 | + | 0.999704i | ||||
\(33\) | 3.57834 | + | 5.73704i | 0.622908 | + | 0.998690i | ||||
\(34\) | 1.68045 | − | 5.25879i | 0.288195 | − | 0.901874i | ||||
\(35\) | 0.348612 | 0.0589262 | ||||||||
\(36\) | −5.27475 | + | 2.85955i | −0.879125 | + | 0.476592i | ||||
\(37\) | 0.639102 | 0.105068 | 0.0525338 | − | 0.998619i | \(-0.483270\pi\) | ||||
0.0525338 | + | 0.998619i | \(0.483270\pi\) | |||||||
\(38\) | −2.40130 | + | 7.51461i | −0.389542 | + | 1.21903i | ||||
\(39\) | 2.69421 | + | 4.31955i | 0.431419 | + | 0.691682i | ||||
\(40\) | −0.789168 | + | 0.591148i | −0.124778 | + | 0.0934687i | ||||
\(41\) | 7.57031i | 1.18228i | 0.806567 | + | 0.591142i | \(0.201323\pi\) | ||||
−0.806567 | + | 0.591142i | \(0.798677\pi\) | |||||||
\(42\) | −2.37432 | + | 0.602184i | −0.366365 | + | 0.0929190i | ||||
\(43\) | − | 2.51757i | − | 0.383926i | −0.981402 | − | 0.191963i | \(-0.938515\pi\) | ||
0.981402 | − | 0.191963i | \(-0.0614854\pi\) | |||||||
\(44\) | −6.36076 | − | 4.52749i | −0.958921 | − | 0.682545i | ||||
\(45\) | −0.939235 | − | 0.460011i | −0.140013 | − | 0.0685744i | ||||
\(46\) | 2.93923 | + | 0.939235i | 0.433367 | + | 0.138483i | ||||
\(47\) | 4.36377 | 0.636522 | 0.318261 | − | 0.948003i | \(-0.396901\pi\) | ||||
0.318261 | + | 0.948003i | \(0.396901\pi\) | |||||||
\(48\) | 4.35371 | − | 5.38936i | 0.628404 | − | 0.777887i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 6.57182 | + | 2.10003i | 0.929396 | + | 0.296989i | ||||
\(51\) | −5.73704 | + | 3.57834i | −0.803346 | + | 0.501067i | ||||
\(52\) | −4.78917 | − | 3.40885i | −0.664138 | − | 0.472723i | ||||
\(53\) | 1.72188i | 0.236518i | 0.992983 | + | 0.118259i | \(0.0377313\pi\) | ||||
−0.992983 | + | 0.118259i | \(0.962269\pi\) | |||||||
\(54\) | 7.19153 | + | 1.51062i | 0.978643 | + | 0.205569i | ||||
\(55\) | − | 1.36090i | − | 0.183504i | ||||||
\(56\) | 2.26374 | − | 1.69572i | 0.302506 | − | 0.226600i | ||||
\(57\) | 8.19802 | − | 5.11331i | 1.08585 | − | 0.677275i | ||||
\(58\) | 4.19802 | − | 13.1373i | 0.551227 | − | 1.72501i | ||||
\(59\) | 8.24635 | 1.07358 | 0.536792 | − | 0.843715i | \(-0.319636\pi\) | ||||
0.536792 | + | 0.843715i | \(0.319636\pi\) | |||||||
\(60\) | 1.20539 | + | 0.0735095i | 0.155615 | + | 0.00949003i | ||||
\(61\) | −14.0959 | −1.80480 | −0.902398 | − | 0.430903i | \(-0.858195\pi\) | ||||
−0.902398 | + | 0.430903i | \(0.858195\pi\) | |||||||
\(62\) | 1.13605 | − | 3.55515i | 0.144279 | − | 0.451505i | ||||
\(63\) | 2.69421 | + | 1.31955i | 0.339439 | + | 0.166248i | ||||
\(64\) | −2.24908 | + | 7.67735i | −0.281135 | + | 0.959668i | ||||
\(65\) | − | 1.02465i | − | 0.127092i | ||||||
\(66\) | 2.35078 | + | 9.26877i | 0.289361 | + | 1.14091i | ||||
\(67\) | − | 0.639102i | − | 0.0780787i | −0.999238 | − | 0.0390393i | \(-0.987570\pi\) | ||
0.999238 | − | 0.0390393i | \(-0.0124298\pi\) | |||||||
\(68\) | 4.52749 | − | 6.36076i | 0.549039 | − | 0.771356i | ||||
\(69\) | −2.00000 | − | 3.20654i | −0.240772 | − | 0.386022i | ||||
\(70\) | 0.469617 | + | 0.150067i | 0.0561300 | + | 0.0179364i | ||||
\(71\) | −11.9341 | −1.41632 | −0.708158 | − | 0.706054i | \(-0.750474\pi\) | ||||
−0.708158 | + | 0.706054i | \(0.750474\pi\) | |||||||
\(72\) | −8.33660 | + | 1.58150i | −0.982477 | + | 0.186382i | ||||
\(73\) | 7.87847 | 0.922105 | 0.461053 | − | 0.887373i | \(-0.347472\pi\) | ||||
0.461053 | + | 0.887373i | \(0.347472\pi\) | |||||||
\(74\) | 0.860938 | + | 0.275113i | 0.100082 | + | 0.0319813i | ||||
\(75\) | −4.47179 | − | 7.16948i | −0.516358 | − | 0.827861i | ||||
\(76\) | −6.46962 | + | 9.08930i | −0.742116 | + | 1.04261i | ||||
\(77\) | 3.90376i | 0.444875i | ||||||||
\(78\) | 1.76996 | + | 6.97867i | 0.200409 | + | 0.790179i | ||||
\(79\) | − | 4.00000i | − | 0.450035i | −0.974355 | − | 0.225018i | \(-0.927756\pi\) | ||
0.974355 | − | 0.225018i | \(-0.0722440\pi\) | |||||||
\(80\) | −1.31756 | + | 0.456627i | −0.147308 | + | 0.0510524i | ||||
\(81\) | −5.51757 | − | 7.11030i | −0.613063 | − | 0.790034i | ||||
\(82\) | −3.25879 | + | 10.1980i | −0.359873 | + | 1.12618i | ||||
\(83\) | −8.94358 | −0.981685 | −0.490843 | − | 0.871248i | \(-0.663311\pi\) | ||||
−0.490843 | + | 0.871248i | \(0.663311\pi\) | |||||||
\(84\) | −3.45768 | − | 0.210863i | −0.377264 | − | 0.0230071i | ||||
\(85\) | 1.36090 | 0.147610 | ||||||||
\(86\) | 1.08374 | − | 3.39144i | 0.116862 | − | 0.365708i | ||||
\(87\) | −14.3320 | + | 8.93923i | −1.53655 | + | 0.958387i | ||||
\(88\) | −6.61968 | − | 8.83712i | −0.705661 | − | 0.942040i | ||||
\(89\) | 10.5396i | 1.11720i | 0.829437 | + | 0.558600i | \(0.188661\pi\) | ||||
−0.829437 | + | 0.558600i | \(0.811339\pi\) | |||||||
\(90\) | −1.06723 | − | 1.02400i | −0.112496 | − | 0.107939i | ||||
\(91\) | 2.93923i | 0.308116i | ||||||||
\(92\) | 3.55515 | + | 2.53050i | 0.370650 | + | 0.263823i | ||||
\(93\) | −3.87847 | + | 2.41910i | −0.402179 | + | 0.250849i | ||||
\(94\) | 5.87847 | + | 1.87847i | 0.606318 | + | 0.193749i | ||||
\(95\) | −1.94467 | −0.199519 | ||||||||
\(96\) | 8.18486 | − | 5.38591i | 0.835364 | − | 0.549697i | ||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | −1.34711 | − | 0.430469i | −0.136078 | − | 0.0434839i | ||||
\(99\) | 5.15121 | − | 10.5176i | 0.517716 | − | 1.05706i | ||||
\(100\) | 7.94894 | + | 5.65793i | 0.794894 | + | 0.565793i | ||||
\(101\) | − | 3.09514i | − | 0.307978i | −0.988073 | − | 0.153989i | \(-0.950788\pi\) | ||
0.988073 | − | 0.153989i | \(-0.0492120\pi\) | |||||||
\(102\) | −9.26877 | + | 2.35078i | −0.917745 | + | 0.232762i | ||||
\(103\) | − | 7.23937i | − | 0.713316i | −0.934235 | − | 0.356658i | \(-0.883916\pi\) | ||
0.934235 | − | 0.356658i | \(-0.116084\pi\) | |||||||
\(104\) | −4.98412 | − | 6.65368i | −0.488733 | − | 0.652447i | ||||
\(105\) | −0.319551 | − | 0.512326i | −0.0311850 | − | 0.0499979i | ||||
\(106\) | −0.741214 | + | 2.31955i | −0.0719931 | + | 0.225295i | ||||
\(107\) | 11.0141 | 1.06477 | 0.532385 | − | 0.846502i | \(-0.321296\pi\) | ||||
0.532385 | + | 0.846502i | \(0.321296\pi\) | |||||||
\(108\) | 9.03748 | + | 5.13069i | 0.869632 | + | 0.493701i | ||||
\(109\) | 1.39973 | 0.134070 | 0.0670351 | − | 0.997751i | \(-0.478646\pi\) | ||||
0.0670351 | + | 0.997751i | \(0.478646\pi\) | |||||||
\(110\) | 0.585825 | − | 1.83328i | 0.0558562 | − | 0.174796i | ||||
\(111\) | −0.585825 | − | 0.939235i | −0.0556040 | − | 0.0891482i | ||||
\(112\) | 3.77946 | − | 1.30984i | 0.357125 | − | 0.123768i | ||||
\(113\) | 8.83218i | 0.830862i | 0.909625 | + | 0.415431i | \(0.136369\pi\) | ||||
−0.909625 | + | 0.415431i | \(0.863631\pi\) | |||||||
\(114\) | 13.2447 | − | 3.35918i | 1.24048 | − | 0.314616i | ||||
\(115\) | 0.760632i | 0.0709293i | ||||||||
\(116\) | 11.3104 | − | 15.8902i | 1.05014 | − | 1.47536i | ||||
\(117\) | 3.87847 | − | 7.91893i | 0.358565 | − | 0.732105i | ||||
\(118\) | 11.1087 | + | 3.54980i | 1.02264 | + | 0.326786i | ||||
\(119\) | −3.90376 | −0.357857 | ||||||||
\(120\) | 1.59214 | + | 0.617907i | 0.145342 | + | 0.0564069i | ||||
\(121\) | 4.23937 | 0.385397 | ||||||||
\(122\) | −18.9887 | − | 6.06785i | −1.71916 | − | 0.549357i | ||||
\(123\) | 11.1255 | − | 6.93923i | 1.00315 | − | 0.625690i | ||||
\(124\) | 3.06077 | − | 4.30013i | 0.274865 | − | 0.386163i | ||||
\(125\) | 3.44375i | 0.308019i | ||||||||
\(126\) | 3.06137 | + | 2.93735i | 0.272728 | + | 0.261680i | ||||
\(127\) | 12.3960i | 1.09997i | 0.835174 | + | 0.549985i | \(0.185367\pi\) | ||||
−0.835174 | + | 0.549985i | \(0.814633\pi\) | |||||||
\(128\) | −6.33461 | + | 9.37405i | −0.559905 | + | 0.828557i | ||||
\(129\) | −3.69987 | + | 2.30770i | −0.325755 | + | 0.203182i | ||||
\(130\) | 0.441081 | − | 1.38032i | 0.0386854 | − | 0.121062i | ||||
\(131\) | 1.61048 | 0.140708 | 0.0703540 | − | 0.997522i | \(-0.477587\pi\) | ||||
0.0703540 | + | 0.997522i | \(0.477587\pi\) | |||||||
\(132\) | −0.823160 | + | 13.4980i | −0.0716469 | + | 1.17485i | ||||
\(133\) | 5.57834 | 0.483703 | ||||||||
\(134\) | 0.275113 | − | 0.860938i | 0.0237662 | − | 0.0743737i | ||||
\(135\) | 0.184898 | + | 1.80198i | 0.0159135 | + | 0.155090i | ||||
\(136\) | 8.83712 | − | 6.61968i | 0.757777 | − | 0.567633i | ||||
\(137\) | − | 4.36377i | − | 0.372822i | −0.982472 | − | 0.186411i | \(-0.940314\pi\) | ||
0.982472 | − | 0.186411i | \(-0.0596857\pi\) | |||||||
\(138\) | −1.31390 | − | 5.18049i | −0.111846 | − | 0.440992i | ||||
\(139\) | 16.8177i | 1.42646i | 0.700931 | + | 0.713230i | \(0.252768\pi\) | ||||
−0.700931 | + | 0.713230i | \(0.747232\pi\) | |||||||
\(140\) | 0.568026 | + | 0.404312i | 0.0480069 | + | 0.0341706i | ||||
\(141\) | −4.00000 | − | 6.41308i | −0.336861 | − | 0.540079i | ||||
\(142\) | −16.0765 | − | 5.13726i | −1.34911 | − | 0.431109i | ||||
\(143\) | 11.4741 | 0.959511 | ||||||||
\(144\) | −11.9111 | − | 1.45819i | −0.992589 | − | 0.121516i | ||||
\(145\) | 3.39973 | 0.282332 | ||||||||
\(146\) | 10.6131 | + | 3.39144i | 0.878350 | + | 0.280677i | ||||
\(147\) | 0.916638 | + | 1.46962i | 0.0756030 | + | 0.121212i | ||||
\(148\) | 1.04135 | + | 0.741214i | 0.0855982 | + | 0.0609274i | ||||
\(149\) | 7.66053i | 0.627575i | 0.949493 | + | 0.313788i | \(0.101598\pi\) | ||||
−0.949493 | + | 0.313788i | \(0.898402\pi\) | |||||||
\(150\) | −2.93774 | − | 11.5830i | −0.239865 | − | 0.945750i | ||||
\(151\) | − | 12.6391i | − | 1.02856i | −0.857624 | − | 0.514278i | \(-0.828060\pi\) | ||
0.857624 | − | 0.514278i | \(-0.171940\pi\) | |||||||
\(152\) | −12.6279 | + | 9.45929i | −1.02426 | + | 0.767250i | ||||
\(153\) | 10.5176 | + | 5.15121i | 0.850295 | + | 0.416451i | ||||
\(154\) | −1.68045 | + | 5.25879i | −0.135414 | + | 0.423765i | ||||
\(155\) | 0.920022 | 0.0738980 | ||||||||
\(156\) | −0.619777 | + | 10.1629i | −0.0496219 | + | 0.813685i | ||||
\(157\) | 0.217438 | 0.0173534 | 0.00867672 | − | 0.999962i | \(-0.497238\pi\) | ||||
0.00867672 | + | 0.999962i | \(0.497238\pi\) | |||||||
\(158\) | 1.72188 | − | 5.38843i | 0.136985 | − | 0.428680i | ||||
\(159\) | 2.53050 | − | 1.57834i | 0.200682 | − | 0.125170i | ||||
\(160\) | −1.97146 | + | 0.0479539i | −0.155858 | + | 0.00379109i | ||||
\(161\) | − | 2.18189i | − | 0.171957i | ||||||
\(162\) | −4.37199 | − | 11.9535i | −0.343496 | − | 0.939154i | ||||
\(163\) | 5.23937i | 0.410379i | 0.978722 | + | 0.205189i | \(0.0657811\pi\) | ||||
−0.978722 | + | 0.205189i | \(0.934219\pi\) | |||||||
\(164\) | −8.77986 | + | 12.3350i | −0.685592 | + | 0.963203i | ||||
\(165\) | −2.00000 | + | 1.24745i | −0.155700 | + | 0.0971139i | ||||
\(166\) | −12.0480 | − | 3.84993i | −0.935103 | − | 0.298813i | ||||
\(167\) | 11.4741 | 0.887891 | 0.443945 | − | 0.896054i | \(-0.353578\pi\) | ||||
0.443945 | + | 0.896054i | \(0.353578\pi\) | |||||||
\(168\) | −4.56709 | − | 1.77248i | −0.352359 | − | 0.136750i | ||||
\(169\) | −4.36090 | −0.335454 | ||||||||
\(170\) | 1.83328 | + | 0.585825i | 0.140606 | + | 0.0449307i | ||||
\(171\) | −15.0292 | − | 7.36090i | −1.14931 | − | 0.562902i | ||||
\(172\) | 2.91982 | − | 4.10211i | 0.222634 | − | 0.312783i | ||||
\(173\) | − | 21.2051i | − | 1.61219i | −0.591784 | − | 0.806097i | \(-0.701576\pi\) | ||
0.591784 | − | 0.806097i | \(-0.298424\pi\) | |||||||
\(174\) | −23.1548 | + | 5.87262i | −1.75536 | + | 0.445202i | ||||
\(175\) | − | 4.87847i | − | 0.368778i | ||||||
\(176\) | −5.11331 | − | 14.7541i | −0.385430 | − | 1.11213i | ||||
\(177\) | −7.55892 | − | 12.1190i | −0.568163 | − | 0.910919i | ||||
\(178\) | −4.53699 | + | 14.1980i | −0.340062 | + | 1.06419i | ||||
\(179\) | −1.81209 | −0.135442 | −0.0677211 | − | 0.997704i | \(-0.521573\pi\) | ||||
−0.0677211 | + | 0.997704i | \(0.521573\pi\) | |||||||
\(180\) | −0.996873 | − | 1.83884i | −0.0743025 | − | 0.137059i | ||||
\(181\) | 7.53950 | 0.560407 | 0.280203 | − | 0.959941i | \(-0.409598\pi\) | ||||
0.280203 | + | 0.959941i | \(0.409598\pi\) | |||||||
\(182\) | −1.26525 | + | 3.95946i | −0.0937865 | + | 0.293495i | ||||
\(183\) | 12.9208 | + | 20.7156i | 0.955136 | + | 1.53134i | ||||
\(184\) | 3.69987 | + | 4.93923i | 0.272758 | + | 0.364125i | ||||
\(185\) | 0.222798i | 0.0163805i | ||||||||
\(186\) | −6.26606 | + | 1.58922i | −0.459450 | + | 0.116528i | ||||
\(187\) | 15.2394i | 1.11441i | ||||||||
\(188\) | 7.11030 | + | 5.06100i | 0.518572 | + | 0.369111i | ||||
\(189\) | −0.530383 | − | 5.16901i | −0.0385797 | − | 0.375990i | ||||
\(190\) | −2.61968 | − | 0.837122i | −0.190052 | − | 0.0607312i | ||||
\(191\) | −1.63166 | −0.118063 | −0.0590314 | − | 0.998256i | \(-0.518801\pi\) | ||||
−0.0590314 | + | 0.998256i | \(0.518801\pi\) | |||||||
\(192\) | 13.3444 | − | 3.73206i | 0.963046 | − | 0.269338i | ||||
\(193\) | −15.1567 | −1.09100 | −0.545501 | − | 0.838110i | \(-0.683660\pi\) | ||||
−0.545501 | + | 0.838110i | \(0.683660\pi\) | |||||||
\(194\) | −2.69421 | − | 0.860938i | −0.193433 | − | 0.0618117i | ||||
\(195\) | −1.50585 | + | 0.939235i | −0.107836 | + | 0.0672600i | ||||
\(196\) | −1.62939 | − | 1.15978i | −0.116385 | − | 0.0828411i | ||||
\(197\) | 21.2263i | 1.51231i | 0.654393 | + | 0.756155i | \(0.272924\pi\) | ||||
−0.654393 | + | 0.756155i | \(0.727076\pi\) | |||||||
\(198\) | 11.4667 | − | 11.9509i | 0.814905 | − | 0.849310i | ||||
\(199\) | 3.75694i | 0.266322i | 0.991094 | + | 0.133161i | \(0.0425128\pi\) | ||||
−0.991094 | + | 0.133161i | \(0.957487\pi\) | |||||||
\(200\) | 8.27251 | + | 11.0436i | 0.584955 | + | 0.780901i | ||||
\(201\) | −0.939235 | + | 0.585825i | −0.0662485 | + | 0.0413209i | ||||
\(202\) | 1.33236 | − | 4.16948i | 0.0937447 | − | 0.293364i | ||||
\(203\) | −9.75220 | −0.684470 | ||||||||
\(204\) | −13.4980 | − | 0.823160i | −0.945046 | − | 0.0576328i | ||||
\(205\) | −2.63910 | −0.184323 | ||||||||
\(206\) | 3.11632 | − | 9.75220i | 0.217125 | − | 0.679468i | ||||
\(207\) | −2.87911 | + | 5.87847i | −0.200112 | + | 0.408582i | ||||
\(208\) | −3.84993 | − | 11.1087i | −0.266945 | − | 0.770251i | ||||
\(209\) | − | 21.7765i | − | 1.50631i | ||||||
\(210\) | −0.209928 | − | 0.827715i | −0.0144864 | − | 0.0571177i | ||||
\(211\) | − | 9.83963i | − | 0.677388i | −0.940897 | − | 0.338694i | \(-0.890015\pi\) | ||
0.940897 | − | 0.338694i | \(-0.109985\pi\) | |||||||
\(212\) | −1.99699 | + | 2.80561i | −0.137154 | + | 0.192690i | ||||
\(213\) | 10.9392 | + | 17.5385i | 0.749544 | + | 1.20172i | ||||
\(214\) | 14.8371 | + | 4.74121i | 1.01424 | + | 0.324103i | ||||
\(215\) | 0.877655 | 0.0598556 | ||||||||
\(216\) | 9.96584 | + | 10.8019i | 0.678090 | + | 0.734979i | ||||
\(217\) | −2.63910 | −0.179154 | ||||||||
\(218\) | 1.88559 | + | 0.602542i | 0.127708 | + | 0.0408093i | ||||
\(219\) | −7.22170 | − | 11.5783i | −0.487997 | − | 0.782391i | ||||
\(220\) | 1.57834 | − | 2.21744i | 0.106411 | − | 0.149500i | ||||
\(221\) | 11.4741i | 0.771830i | ||||||||
\(222\) | −0.384857 | − | 1.51743i | −0.0258299 | − | 0.101843i | ||||
\(223\) | − | 22.9136i | − | 1.53441i | −0.641403 | − | 0.767204i | \(-0.721647\pi\) | ||
0.641403 | − | 0.767204i | \(-0.278353\pi\) | |||||||
\(224\) | 5.65518 | − | 0.137557i | 0.377853 | − | 0.00919090i | ||||
\(225\) | −6.43739 | + | 13.1436i | −0.429159 | + | 0.876243i | ||||
\(226\) | −3.80198 | + | 11.8979i | −0.252904 | + | 0.791436i | ||||
\(227\) | 13.5302 | 0.898028 | 0.449014 | − | 0.893525i | \(-0.351775\pi\) | ||||
0.449014 | + | 0.893525i | \(0.351775\pi\) | |||||||
\(228\) | 19.2881 | + | 1.17627i | 1.27739 | + | 0.0779002i | ||||
\(229\) | 14.6962 | 0.971151 | 0.485575 | − | 0.874195i | \(-0.338610\pi\) | ||||
0.485575 | + | 0.874195i | \(0.338610\pi\) | |||||||
\(230\) | −0.327428 | + | 1.02465i | −0.0215900 | + | 0.0675636i | ||||
\(231\) | 5.73704 | − | 3.57834i | 0.377469 | − | 0.235437i | ||||
\(232\) | 22.0765 | − | 16.5370i | 1.44939 | − | 1.08571i | ||||
\(233\) | − | 17.1899i | − | 1.12615i | −0.826406 | − | 0.563075i | \(-0.809618\pi\) | ||
0.826406 | − | 0.563075i | \(-0.190382\pi\) | |||||||
\(234\) | 8.63356 | − | 8.99808i | 0.564394 | − | 0.588223i | ||||
\(235\) | 1.52126i | 0.0992363i | ||||||||
\(236\) | 13.4366 | + | 9.56392i | 0.874645 | + | 0.622558i | ||||
\(237\) | −5.87847 | + | 3.66655i | −0.381848 | + | 0.238168i | ||||
\(238\) | −5.25879 | − | 1.68045i | −0.340876 | − | 0.108927i | ||||
\(239\) | −14.5336 | −0.940102 | −0.470051 | − | 0.882639i | \(-0.655764\pi\) | ||||
−0.470051 | + | 0.882639i | \(0.655764\pi\) | |||||||
\(240\) | 1.87880 | + | 1.51775i | 0.121276 | + | 0.0979707i | ||||
\(241\) | −18.7921 | −1.21050 | −0.605252 | − | 0.796034i | \(-0.706928\pi\) | ||||
−0.605252 | + | 0.796034i | \(0.706928\pi\) | |||||||
\(242\) | 5.71088 | + | 1.82492i | 0.367109 | + | 0.117310i | ||||
\(243\) | −5.39181 | + | 14.6263i | −0.345885 | + | 0.938277i | ||||
\(244\) | −22.9678 | − | 16.3481i | −1.47036 | − | 1.04658i | ||||
\(245\) | − | 0.348612i | − | 0.0222720i | ||||||
\(246\) | 17.9743 | − | 4.55872i | 1.14600 | − | 0.290653i | ||||
\(247\) | − | 16.3960i | − | 1.04326i | ||||||
\(248\) | 5.97425 | − | 4.47517i | 0.379365 | − | 0.284174i | ||||
\(249\) | 8.19802 | + | 13.1436i | 0.519528 | + | 0.832944i | ||||
\(250\) | −1.48243 | + | 4.63910i | −0.0937570 | + | 0.293403i | ||||
\(251\) | −20.6405 | −1.30281 | −0.651407 | − | 0.758729i | \(-0.725821\pi\) | ||||
−0.651407 | + | 0.758729i | \(0.725821\pi\) | |||||||
\(252\) | 2.85955 | + | 5.27475i | 0.180135 | + | 0.332278i | ||||
\(253\) | −8.51757 | −0.535495 | ||||||||
\(254\) | −5.33611 | + | 16.6988i | −0.334817 | + | 1.04778i | ||||
\(255\) | −1.24745 | − | 2.00000i | −0.0781184 | − | 0.125245i | ||||
\(256\) | −12.5686 | + | 9.90099i | −0.785539 | + | 0.618812i | ||||
\(257\) | − | 4.82379i | − | 0.300899i | −0.988618 | − | 0.150450i | \(-0.951928\pi\) | ||
0.988618 | − | 0.150450i | \(-0.0480722\pi\) | |||||||
\(258\) | −5.97751 | + | 1.51604i | −0.372143 | + | 0.0943846i | ||||
\(259\) | − | 0.639102i | − | 0.0397118i | ||||||
\(260\) | 1.18837 | − | 1.66956i | 0.0736994 | − | 0.103542i | ||||
\(261\) | 26.2745 | + | 12.8685i | 1.62635 | + | 0.796542i | ||||
\(262\) | 2.16948 | + | 0.693260i | 0.134031 | + | 0.0428298i | ||||
\(263\) | −14.4578 | −0.891507 | −0.445754 | − | 0.895156i | \(-0.647064\pi\) | ||||
−0.445754 | + | 0.895156i | \(0.647064\pi\) | |||||||
\(264\) | −6.91934 | + | 17.8288i | −0.425856 | + | 1.09729i | ||||
\(265\) | −0.600267 | −0.0368741 | ||||||||
\(266\) | 7.51461 | + | 2.40130i | 0.460751 | + | 0.147233i | ||||
\(267\) | 15.4892 | − | 9.66103i | 0.947926 | − | 0.591246i | ||||
\(268\) | 0.741214 | − | 1.04135i | 0.0452769 | − | 0.0636104i | ||||
\(269\) | 4.71239i | 0.287319i | 0.989627 | + | 0.143660i | \(0.0458871\pi\) | ||||
−0.989627 | + | 0.143660i | \(0.954113\pi\) | |||||||
\(270\) | −0.526619 | + | 2.50705i | −0.0320490 | + | 0.152574i | ||||
\(271\) | − | 15.6742i | − | 0.952143i | −0.879407 | − | 0.476071i | \(-0.842060\pi\) | ||
0.879407 | − | 0.476071i | \(-0.157940\pi\) | |||||||
\(272\) | 14.7541 | − | 5.11331i | 0.894600 | − | 0.310040i | ||||
\(273\) | 4.31955 | − | 2.69421i | 0.261431 | − | 0.163061i | ||||
\(274\) | 1.87847 | − | 5.87847i | 0.113483 | − | 0.355131i | ||||
\(275\) | −19.0444 | −1.14842 | ||||||||
\(276\) | 0.460080 | − | 7.54426i | 0.0276936 | − | 0.454111i | ||||
\(277\) | 16.9963 | 1.02121 | 0.510605 | − | 0.859816i | \(-0.329422\pi\) | ||||
0.510605 | + | 0.859816i | \(0.329422\pi\) | |||||||
\(278\) | −7.23950 | + | 22.6552i | −0.434196 | + | 1.35877i | ||||
\(279\) | 7.11030 | + | 3.48243i | 0.425683 | + | 0.208488i | ||||
\(280\) | 0.591148 | + | 0.789168i | 0.0353278 | + | 0.0471618i | ||||
\(281\) | 5.75822i | 0.343507i | 0.985140 | + | 0.171753i | \(0.0549432\pi\) | ||||
−0.985140 | + | 0.171753i | \(0.945057\pi\) | |||||||
\(282\) | −2.62779 | − | 10.3610i | −0.156483 | − | 0.616987i | ||||
\(283\) | − | 5.57834i | − | 0.331598i | −0.986160 | − | 0.165799i | \(-0.946980\pi\) | ||
0.986160 | − | 0.165799i | \(-0.0530202\pi\) | |||||||
\(284\) | −19.4453 | − | 13.8409i | −1.15387 | − | 0.821304i | ||||
\(285\) | 1.78256 | + | 2.85793i | 0.105590 | + | 0.169289i | ||||
\(286\) | 15.4568 | + | 4.93923i | 0.913980 | + | 0.292063i | ||||
\(287\) | 7.57031 | 0.446862 | ||||||||
\(288\) | −15.4178 | − | 7.09169i | −0.908501 | − | 0.417882i | ||||
\(289\) | 1.76063 | 0.103567 | ||||||||
\(290\) | 4.57980 | + | 1.46348i | 0.268935 | + | 0.0859385i | ||||
\(291\) | 1.83328 | + | 2.93923i | 0.107469 | + | 0.172301i | ||||
\(292\) | 12.8371 | + | 9.13726i | 0.751236 | + | 0.534717i | ||||
\(293\) | − | 23.7712i | − | 1.38873i | −0.719624 | − | 0.694364i | \(-0.755686\pi\) | ||
0.719624 | − | 0.694364i | \(-0.244314\pi\) | |||||||
\(294\) | 0.602184 | + | 2.37432i | 0.0351201 | + | 0.138473i | ||||
\(295\) | 2.87478i | 0.167376i | ||||||||
\(296\) | 1.08374 | + | 1.44676i | 0.0629909 | + | 0.0840914i | ||||
\(297\) | −20.1786 | + | 2.07049i | −1.17088 | + | 0.120142i | ||||
\(298\) | −3.29762 | + | 10.3196i | −0.191026 | + | 0.597796i | ||||
\(299\) | −6.41308 | −0.370878 | ||||||||
\(300\) | 1.02869 | − | 16.8682i | 0.0593915 | − | 0.973885i | ||||
\(301\) | −2.51757 | −0.145110 | ||||||||
\(302\) | 5.44074 | − | 17.0262i | 0.313080 | − | 0.979749i | ||||
\(303\) | −4.54867 | + | 2.83712i | −0.261314 | + | 0.162988i | ||||
\(304\) | −21.0831 | + | 7.30674i | −1.20920 | + | 0.419070i | ||||
\(305\) | − | 4.91400i | − | 0.281375i | ||||||
\(306\) | 11.9509 | + | 11.4667i | 0.683185 | + | 0.655509i | ||||
\(307\) | − | 3.69987i | − | 0.211163i | −0.994411 | − | 0.105581i | \(-0.966330\pi\) | ||
0.994411 | − | 0.105581i | \(-0.0336703\pi\) | |||||||
\(308\) | −4.52749 | + | 6.36076i | −0.257978 | + | 0.362438i | ||||
\(309\) | −10.6391 | + | 6.63588i | −0.605237 | + | 0.377502i | ||||
\(310\) | 1.23937 | + | 0.396041i | 0.0703914 | + | 0.0224936i | ||||
\(311\) | 7.58473 | 0.430090 | 0.215045 | − | 0.976604i | \(-0.431010\pi\) | ||||
0.215045 | + | 0.976604i | \(0.431010\pi\) | |||||||
\(312\) | −5.20973 | + | 13.4238i | −0.294943 | + | 0.759970i | ||||
\(313\) | 15.6354 | 0.883766 | 0.441883 | − | 0.897073i | \(-0.354311\pi\) | ||||
0.441883 | + | 0.897073i | \(0.354311\pi\) | |||||||
\(314\) | 0.292912 | + | 0.0936004i | 0.0165300 | + | 0.00528217i | ||||
\(315\) | −0.460011 | + | 0.939235i | −0.0259187 | + | 0.0529199i | ||||
\(316\) | 4.63910 | − | 6.51757i | 0.260970 | − | 0.366642i | ||||
\(317\) | − | 13.8932i | − | 0.780319i | −0.920747 | − | 0.390159i | \(-0.872420\pi\) | ||
0.920747 | − | 0.390159i | \(-0.127580\pi\) | |||||||
\(318\) | 4.08828 | − | 1.03689i | 0.229259 | − | 0.0581457i | ||||
\(319\) | 38.0703i | 2.13153i | ||||||||
\(320\) | −2.67641 | − | 0.784055i | −0.149616 | − | 0.0438300i | ||||
\(321\) | −10.0959 | − | 16.1865i | −0.563499 | − | 0.903440i | ||||
\(322\) | 0.939235 | − | 2.93923i | 0.0523415 | − | 0.163797i | ||||
\(323\) | 21.7765 | 1.21168 | ||||||||
\(324\) | −0.743937 | − | 17.9846i | −0.0413298 | − | 0.999146i | ||||
\(325\) | −14.3390 | −0.795383 | ||||||||
\(326\) | −2.25539 | + | 7.05799i | −0.124914 | + | 0.390906i | ||||
\(327\) | −1.28305 | − | 2.05707i | −0.0709527 | − | 0.113756i | ||||
\(328\) | −17.1373 | + | 12.8371i | −0.946247 | + | 0.708811i | ||||
\(329\) | − | 4.36377i | − | 0.240583i | ||||||
\(330\) | −3.23120 | + | 0.819511i | −0.177872 | + | 0.0451126i | ||||
\(331\) | 31.7958i | 1.74765i | 0.486237 | + | 0.873827i | \(0.338369\pi\) | ||||
−0.486237 | + | 0.873827i | \(0.661631\pi\) | |||||||
\(332\) | −14.5726 | − | 10.3725i | −0.799775 | − | 0.569267i | ||||
\(333\) | −0.843327 | + | 1.72188i | −0.0462140 | + | 0.0943582i | ||||
\(334\) | 15.4568 | + | 4.93923i | 0.845759 | + | 0.270263i | ||||
\(335\) | 0.222798 | 0.0121728 | ||||||||
\(336\) | −5.38936 | − | 4.35371i | −0.294014 | − | 0.237514i | ||||
\(337\) | −17.1178 | −0.932468 | −0.466234 | − | 0.884661i | \(-0.654390\pi\) | ||||
−0.466234 | + | 0.884661i | \(0.654390\pi\) | |||||||
\(338\) | −5.87460 | − | 1.87723i | −0.319536 | − | 0.102108i | ||||
\(339\) | 12.9799 | − | 8.09591i | 0.704973 | − | 0.439709i | ||||
\(340\) | 2.21744 | + | 1.57834i | 0.120257 | + | 0.0855973i | ||||
\(341\) | 10.3024i | 0.557908i | ||||||||
\(342\) | −17.0773 | − | 16.3855i | −0.923437 | − | 0.886028i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 5.69914 | − | 4.26909i | 0.307277 | − | 0.230174i | ||||
\(345\) | 1.11784 | − | 0.697224i | 0.0601824 | − | 0.0375373i | ||||
\(346\) | 9.12814 | − | 28.5655i | 0.490732 | − | 1.53569i | ||||
\(347\) | 8.44797 | 0.453511 | 0.226755 | − | 0.973952i | \(-0.427188\pi\) | ||||
0.226755 | + | 0.973952i | \(0.427188\pi\) | |||||||
\(348\) | −33.7200 | − | 2.05638i | −1.80758 | − | 0.110234i | ||||
\(349\) | 17.4956 | 0.936520 | 0.468260 | − | 0.883591i | \(-0.344881\pi\) | ||||
0.468260 | + | 0.883591i | \(0.344881\pi\) | |||||||
\(350\) | 2.10003 | − | 6.57182i | 0.112251 | − | 0.351279i | ||||
\(351\) | −15.1929 | + | 1.55892i | −0.810939 | + | 0.0832089i | ||||
\(352\) | −0.536989 | − | 22.0765i | −0.0286216 | − | 1.17668i | ||||
\(353\) | − | 8.26754i | − | 0.440037i | −0.975496 | − | 0.220018i | \(-0.929388\pi\) | ||
0.975496 | − | 0.220018i | \(-0.0706117\pi\) | |||||||
\(354\) | −4.96582 | − | 19.5794i | −0.263930 | − | 1.04064i | ||||
\(355\) | − | 4.16037i | − | 0.220809i | ||||||
\(356\) | −12.2236 | + | 17.1732i | −0.647850 | + | 0.910179i | ||||
\(357\) | 3.57834 | + | 5.73704i | 0.189386 | + | 0.303636i | ||||
\(358\) | −2.44108 | − | 0.780049i | −0.129015 | − | 0.0412269i | ||||
\(359\) | 25.1300 | 1.32631 | 0.663156 | − | 0.748481i | \(-0.269216\pi\) | ||||
0.663156 | + | 0.748481i | \(0.269216\pi\) | |||||||
\(360\) | −0.551330 | − | 2.90624i | −0.0290577 | − | 0.153172i | ||||
\(361\) | −12.1178 | −0.637781 | ||||||||
\(362\) | 10.1565 | + | 3.24552i | 0.533814 | + | 0.170581i | ||||
\(363\) | −3.88596 | − | 6.23025i | −0.203960 | − | 0.327003i | ||||
\(364\) | −3.40885 | + | 4.78917i | −0.178672 | + | 0.251021i | ||||
\(365\) | 2.74653i | 0.143760i | ||||||||
\(366\) | 8.48833 | + | 33.4681i | 0.443692 | + | 1.74941i | ||||
\(367\) | 21.7131i | 1.13341i | 0.823920 | + | 0.566707i | \(0.191783\pi\) | ||||
−0.823920 | + | 0.566707i | \(0.808217\pi\) | |||||||
\(368\) | 2.85793 | + | 8.24635i | 0.148980 | + | 0.429871i | ||||
\(369\) | −20.3960 | − | 9.98941i | −1.06178 | − | 0.520028i | ||||
\(370\) | −0.0959078 | + | 0.300133i | −0.00498601 | + | 0.0156032i | ||||
\(371\) | 1.72188 | 0.0893954 | ||||||||
\(372\) | −9.12516 | − | 0.556490i | −0.473118 | − | 0.0288526i | ||||
\(373\) | −0.721797 | −0.0373732 | −0.0186866 | − | 0.999825i | \(-0.505948\pi\) | ||||
−0.0186866 | + | 0.999825i | \(0.505948\pi\) | |||||||
\(374\) | −6.56008 | + | 20.5291i | −0.339213 | + | 1.06153i | ||||
\(375\) | 5.06100 | − | 3.15667i | 0.261349 | − | 0.163010i | ||||
\(376\) | 7.39973 | + | 9.87847i | 0.381612 | + | 0.509443i | ||||
\(377\) | 28.6640i | 1.47627i | ||||||||
\(378\) | 1.51062 | − | 7.19153i | 0.0776978 | − | 0.369892i | ||||
\(379\) | − | 18.2745i | − | 0.938699i | −0.883013 | − | 0.469349i | \(-0.844489\pi\) | ||
0.883013 | − | 0.469349i | \(-0.155511\pi\) | |||||||
\(380\) | −3.16864 | − | 2.25539i | −0.162548 | − | 0.115699i | ||||
\(381\) | 18.2174 | − | 11.3627i | 0.933308 | − | 0.582128i | ||||
\(382\) | −2.19802 | − | 0.702379i | −0.112461 | − | 0.0359368i | ||||
\(383\) | −2.04930 | −0.104715 | −0.0523573 | − | 0.998628i | \(-0.516673\pi\) | ||||
−0.0523573 | + | 0.998628i | \(0.516673\pi\) | |||||||
\(384\) | 19.5828 | + | 0.716843i | 0.999331 | + | 0.0365813i | ||||
\(385\) | −1.36090 | −0.0693578 | ||||||||
\(386\) | −20.4177 | − | 6.52448i | −1.03923 | − | 0.332087i | ||||
\(387\) | 6.78287 | + | 3.32206i | 0.344793 | + | 0.168870i | ||||
\(388\) | −3.25879 | − | 2.31955i | −0.165440 | − | 0.117757i | ||||
\(389\) | 11.1466i | 0.565158i | 0.959244 | + | 0.282579i | \(0.0911899\pi\) | ||||
−0.959244 | + | 0.282579i | \(0.908810\pi\) | |||||||
\(390\) | −2.43285 | + | 0.617029i | −0.123192 | + | 0.0312445i | ||||
\(391\) | − | 8.51757i | − | 0.430752i | ||||||
\(392\) | −1.69572 | − | 2.26374i | −0.0856467 | − | 0.114336i | ||||
\(393\) | −1.47622 | − | 2.36678i | −0.0744656 | − | 0.119389i | ||||
\(394\) | −9.13726 | + | 28.5941i | −0.460328 | + | 1.44055i | ||||
\(395\) | 1.39445 | 0.0701623 | ||||||||
\(396\) | 20.5914 | − | 11.1630i | 1.03476 | − | 0.560962i | ||||
\(397\) | 7.97438 | 0.400223 | 0.200111 | − | 0.979773i | \(-0.435870\pi\) | ||||
0.200111 | + | 0.979773i | \(0.435870\pi\) | |||||||
\(398\) | −1.61725 | + | 5.06100i | −0.0810652 | + | 0.253685i | ||||
\(399\) | −5.11331 | − | 8.19802i | −0.255986 | − | 0.410414i | ||||
\(400\) | 6.39002 | + | 18.4380i | 0.319501 | + | 0.921899i | ||||
\(401\) | 21.4779i | 1.07256i | 0.844042 | + | 0.536278i | \(0.180170\pi\) | ||||
−0.844042 | + | 0.536278i | \(0.819830\pi\) | |||||||
\(402\) | −1.51743 | + | 0.384857i | −0.0756825 | + | 0.0191949i | ||||
\(403\) | 7.75694i | 0.386401i | ||||||||
\(404\) | 3.58967 | − | 5.04320i | 0.178593 | − | 0.250909i | ||||
\(405\) | 2.47874 | − | 1.92349i | 0.123169 | − | 0.0955790i | ||||
\(406\) | −13.1373 | − | 4.19802i | −0.651991 | − | 0.208344i | ||||
\(407\) | −2.49490 | −0.123668 | ||||||||
\(408\) | −17.8288 | − | 6.91934i | −0.882659 | − | 0.342558i | ||||
\(409\) | 36.9136 | 1.82526 | 0.912630 | − | 0.408786i | \(-0.134048\pi\) | ||||
0.912630 | + | 0.408786i | \(0.134048\pi\) | |||||||
\(410\) | −3.55515 | − | 1.13605i | −0.175576 | − | 0.0561056i | ||||
\(411\) | −6.41308 | + | 4.00000i | −0.316334 | + | 0.197305i | ||||
\(412\) | 8.39604 | − | 11.7958i | 0.413643 | − | 0.581136i | ||||
\(413\) | − | 8.24635i | − | 0.405777i | ||||||
\(414\) | −6.40897 | + | 6.67956i | −0.314984 | + | 0.328282i | ||||
\(415\) | − | 3.11784i | − | 0.153049i | ||||||
\(416\) | −0.404312 | − | 16.6219i | −0.0198230 | − | 0.814956i | ||||
\(417\) | 24.7156 | − | 15.4157i | 1.21033 | − | 0.754912i | ||||
\(418\) | 9.37411 | − | 29.3353i | 0.458503 | − | 1.43484i | ||||
\(419\) | 29.5773 | 1.44494 | 0.722472 | − | 0.691400i | \(-0.243006\pi\) | ||||
0.722472 | + | 0.691400i | \(0.243006\pi\) | |||||||
\(420\) | 0.0735095 | − | 1.20539i | 0.00358689 | − | 0.0588169i | ||||
\(421\) | 36.8309 | 1.79503 | 0.897515 | − | 0.440985i | \(-0.145371\pi\) | ||||
0.897515 | + | 0.440985i | \(0.145371\pi\) | |||||||
\(422\) | 4.23566 | − | 13.2550i | 0.206189 | − | 0.645245i | ||||
\(423\) | −5.75822 | + | 11.7569i | −0.279974 | + | 0.571642i | ||||
\(424\) | −3.89789 | + | 2.91982i | −0.189298 | + | 0.141799i | ||||
\(425\) | − | 19.0444i | − | 0.923789i | ||||||
\(426\) | 7.18652 | + | 28.3353i | 0.348188 | + | 1.37285i | ||||
\(427\) | 14.0959i | 0.682149i | ||||||||
\(428\) | 17.9462 | + | 12.7738i | 0.867464 | + | 0.617447i | ||||
\(429\) | −10.5176 | − | 16.8625i | −0.507793 | − | 0.814129i | ||||
\(430\) | 1.18230 | + | 0.377803i | 0.0570153 | + | 0.0182193i | ||||
\(431\) | −4.67679 | −0.225273 | −0.112636 | − | 0.993636i | \(-0.535930\pi\) | ||||
−0.112636 | + | 0.993636i | \(0.535930\pi\) | |||||||
\(432\) | 8.77515 | + | 18.8414i | 0.422195 | + | 0.906505i | ||||
\(433\) | −16.5564 | −0.795650 | −0.397825 | − | 0.917461i | \(-0.630235\pi\) | ||||
−0.397825 | + | 0.917461i | \(0.630235\pi\) | |||||||
\(434\) | −3.55515 | − | 1.13605i | −0.170653 | − | 0.0545322i | ||||
\(435\) | −3.11632 | − | 4.99631i | −0.149416 | − | 0.239555i | ||||
\(436\) | 2.28072 | + | 1.62338i | 0.109226 | + | 0.0777456i | ||||
\(437\) | 12.1713i | 0.582232i | ||||||||
\(438\) | −4.74429 | − | 18.7060i | −0.226691 | − | 0.893806i | ||||
\(439\) | − | 26.4787i | − | 1.26376i | −0.775066 | − | 0.631881i | \(-0.782283\pi\) | ||
0.775066 | − | 0.631881i | \(-0.217717\pi\) | |||||||
\(440\) | 3.08073 | − | 2.30770i | 0.146868 | − | 0.110015i | ||||
\(441\) | 1.31955 | − | 2.69421i | 0.0628358 | − | 0.128296i | ||||
\(442\) | −4.93923 | + | 15.4568i | −0.234935 | + | 0.735205i | ||||
\(443\) | 4.60099 | 0.218599 | 0.109300 | − | 0.994009i | \(-0.465139\pi\) | ||||
0.109300 | + | 0.994009i | \(0.465139\pi\) | |||||||
\(444\) | 0.134763 | − | 2.20981i | 0.00639557 | − | 0.104873i | ||||
\(445\) | −3.67424 | −0.174176 | ||||||||
\(446\) | 9.86360 | − | 30.8671i | 0.467055 | − | 1.46160i | ||||
\(447\) | 11.2580 | − | 7.02193i | 0.532487 | − | 0.332126i | ||||
\(448\) | 7.67735 | + | 2.24908i | 0.362721 | + | 0.106259i | ||||
\(449\) | − | 17.0095i | − | 0.802728i | −0.915919 | − | 0.401364i | \(-0.868536\pi\) | ||
0.915919 | − | 0.401364i | \(-0.131464\pi\) | |||||||
\(450\) | −14.3298 | + | 14.9348i | −0.675512 | + | 0.704033i | ||||
\(451\) | − | 29.5527i | − | 1.39158i | ||||||
\(452\) | −10.2433 | + | 14.3911i | −0.481806 | + | 0.676900i | ||||
\(453\) | −18.5746 | + | 11.5855i | −0.872713 | + | 0.544333i | ||||
\(454\) | 18.2266 | + | 5.82431i | 0.855415 | + | 0.273348i | ||||
\(455\) | −1.02465 | −0.0480364 | ||||||||
\(456\) | 25.4768 | + | 9.88748i | 1.19306 | + | 0.463024i | ||||
\(457\) | −15.4312 | −0.721840 | −0.360920 | − | 0.932597i | \(-0.617537\pi\) | ||||
−0.360920 | + | 0.932597i | \(0.617537\pi\) | |||||||
\(458\) | 19.7973 | + | 6.32625i | 0.925068 | + | 0.295606i | ||||
\(459\) | −2.07049 | − | 20.1786i | −0.0966421 | − | 0.941857i | ||||
\(460\) | −0.882162 | + | 1.23937i | −0.0411310 | + | 0.0577858i | ||||
\(461\) | 33.3764i | 1.55449i | 0.629196 | + | 0.777247i | \(0.283384\pi\) | ||||
−0.629196 | + | 0.777247i | \(0.716616\pi\) | |||||||
\(462\) | 9.26877 | − | 2.35078i | 0.431222 | − | 0.109368i | ||||
\(463\) | 26.4787i | 1.23057i | 0.788304 | + | 0.615286i | \(0.210959\pi\) | ||||
−0.788304 | + | 0.615286i | \(0.789041\pi\) | |||||||
\(464\) | 36.8580 | − | 12.7738i | 1.71109 | − | 0.593011i | ||||
\(465\) | −0.843327 | − | 1.35208i | −0.0391084 | − | 0.0627012i | ||||
\(466\) | 7.39973 | − | 23.1567i | 0.342786 | − | 1.07271i | ||||
\(467\) | −18.5911 | −0.860296 | −0.430148 | − | 0.902758i | \(-0.641539\pi\) | ||||
−0.430148 | + | 0.902758i | \(0.641539\pi\) | |||||||
\(468\) | 15.5037 | − | 8.40489i | 0.716660 | − | 0.388516i | ||||
\(469\) | −0.639102 | −0.0295110 | ||||||||
\(470\) | −0.654857 | + | 2.04930i | −0.0302063 | + | 0.0945274i | ||||
\(471\) | −0.199312 | − | 0.319551i | −0.00918381 | − | 0.0147241i | ||||
\(472\) | 13.9835 | + | 18.6676i | 0.643643 | + | 0.859248i | ||||
\(473\) | 9.82800i | 0.451892i | ||||||||
\(474\) | −9.49726 | + | 2.40874i | −0.436224 | + | 0.110637i | ||||
\(475\) | 27.2137i | 1.24865i | ||||||||
\(476\) | −6.36076 | − | 4.52749i | −0.291545 | − | 0.207517i | ||||
\(477\) | −4.63910 | − | 2.27210i | −0.212410 | − | 0.104032i | ||||
\(478\) | −19.5783 | − | 6.25627i | −0.895492 | − | 0.286155i | ||||
\(479\) | −40.8777 | −1.86775 | −0.933874 | − | 0.357601i | \(-0.883595\pi\) | ||||
−0.933874 | + | 0.357601i | \(0.883595\pi\) | |||||||
\(480\) | 1.87759 | + | 2.85334i | 0.0856999 | + | 0.130237i | ||||
\(481\) | −1.87847 | −0.0856508 | ||||||||
\(482\) | −25.3149 | − | 8.08941i | −1.15306 | − | 0.368462i | ||||
\(483\) | −3.20654 | + | 2.00000i | −0.145903 | + | 0.0910032i | ||||
\(484\) | 6.90760 | + | 4.91671i | 0.313982 | + | 0.223487i | ||||
\(485\) | − | 0.697224i | − | 0.0316593i | ||||||
\(486\) | −13.5595 | + | 17.3822i | −0.615072 | + | 0.788471i | ||||
\(487\) | − | 21.4312i | − | 0.971140i | −0.874198 | − | 0.485570i | \(-0.838612\pi\) | ||
0.874198 | − | 0.485570i | \(-0.161388\pi\) | |||||||
\(488\) | −23.9027 | − | 31.9095i | −1.08202 | − | 1.44448i | ||||
\(489\) | 7.69987 | − | 4.80260i | 0.348200 | − | 0.217181i | ||||
\(490\) | 0.150067 | − | 0.469617i | 0.00677932 | − | 0.0212152i | ||||
\(491\) | −1.63166 | −0.0736358 | −0.0368179 | − | 0.999322i | \(-0.511722\pi\) | ||||
−0.0368179 | + | 0.999322i | \(0.511722\pi\) | |||||||
\(492\) | 26.1757 | + | 1.59630i | 1.18009 | + | 0.0719668i | ||||
\(493\) | −38.0703 | −1.71460 | ||||||||
\(494\) | 7.05799 | − | 22.0872i | 0.317554 | − | 0.993751i | ||||
\(495\) | 3.66655 | + | 1.79577i | 0.164799 | + | 0.0807141i | ||||
\(496\) | 9.97438 | − | 3.45681i | 0.447863 | − | 0.155215i | ||||
\(497\) | 11.9341i | 0.535317i | ||||||||
\(498\) | 5.38568 | + | 21.2349i | 0.241338 | + | 0.951558i | ||||
\(499\) | − | 8.88216i | − | 0.397620i | −0.980038 | − | 0.198810i | \(-0.936292\pi\) | ||
0.980038 | − | 0.198810i | \(-0.0637077\pi\) | |||||||
\(500\) | −3.99398 | + | 5.61123i | −0.178616 | + | 0.250942i | ||||
\(501\) | −10.5176 | − | 16.8625i | −0.469890 | − | 0.753361i | ||||
\(502\) | −27.8049 | − | 8.88508i | −1.24099 | − | 0.396560i | ||||
\(503\) | −34.8967 | −1.55597 | −0.777983 | − | 0.628286i | \(-0.783757\pi\) | ||||
−0.777983 | + | 0.628286i | \(0.783757\pi\) | |||||||
\(504\) | 1.58150 | + | 8.33660i | 0.0704457 | + | 0.371342i | ||||
\(505\) | 1.07900 | 0.0480150 | ||||||||
\(506\) | −11.4741 | − | 3.66655i | −0.510085 | − | 0.162998i | ||||
\(507\) | 3.99736 | + | 6.40885i | 0.177529 | + | 0.284627i | ||||
\(508\) | −14.3766 | + | 20.1980i | −0.637860 | + | 0.896142i | ||||
\(509\) | 23.7712i | 1.05364i | 0.849977 | + | 0.526820i | \(0.176616\pi\) | ||||
−0.849977 | + | 0.526820i | \(0.823384\pi\) | |||||||
\(510\) | −0.819511 | − | 3.23120i | −0.0362886 | − | 0.143080i | ||||
\(511\) | − | 7.87847i | − | 0.348523i | ||||||
\(512\) | −21.1934 | + | 7.92728i | −0.936623 | + | 0.350340i | ||||
\(513\) | 2.95865 | + | 28.8345i | 0.130628 | + | 1.27307i | ||||
\(514\) | 2.07649 | − | 6.49815i | 0.0915901 | − | 0.286621i | ||||
\(515\) | 2.52373 | 0.111209 | ||||||||
\(516\) | −8.70495 | − | 0.530863i | −0.383214 | − | 0.0233700i | ||||
\(517\) | −17.0351 | −0.749205 | ||||||||
\(518\) | 0.275113 | − | 0.860938i | 0.0120878 | − | 0.0378274i | ||||
\(519\) | −31.1634 | + | 19.4374i | −1.36792 | + | 0.853207i | ||||
\(520\) | 2.31955 | − | 1.73752i | 0.101719 | − | 0.0761954i | ||||
\(521\) | 5.73027i | 0.251048i | 0.992091 | + | 0.125524i | \(0.0400612\pi\) | ||||
−0.992091 | + | 0.125524i | \(0.959939\pi\) | |||||||
\(522\) | 29.8551 | + | 28.6456i | 1.30672 | + | 1.25379i | ||||
\(523\) | 4.81770i | 0.210664i | 0.994437 | + | 0.105332i | \(0.0335904\pi\) | ||||
−0.994437 | + | 0.105332i | \(0.966410\pi\) | |||||||
\(524\) | 2.62410 | + | 1.86779i | 0.114634 | + | 0.0815948i | ||||
\(525\) | −7.16948 | + | 4.47179i | −0.312902 | + | 0.195165i | ||||
\(526\) | −19.4762 | − | 6.22364i | −0.849204 | − | 0.271364i | ||||
\(527\) | −10.3024 | −0.448781 | ||||||||
\(528\) | −16.9958 | + | 21.0388i | −0.739649 | + | 0.915596i | ||||
\(529\) | −18.2394 | −0.793016 | ||||||||
\(530\) | −0.808623 | − | 0.258396i | −0.0351243 | − | 0.0112240i | ||||
\(531\) | −10.8815 | + | 22.2174i | −0.472216 | + | 0.964155i | ||||
\(532\) | 9.08930 | + | 6.46962i | 0.394071 | + | 0.280493i | ||||
\(533\) | − | 22.2509i | − | 0.963795i | ||||||
\(534\) | 25.0244 | − | 6.34680i | 1.08291 | − | 0.274653i | ||||
\(535\) | 3.83963i | 0.166002i | ||||||||
\(536\) | 1.44676 | − | 1.08374i | 0.0624906 | − | 0.0468103i | ||||
\(537\) | 1.66103 | + | 2.66308i | 0.0716788 | + | 0.114920i | ||||
\(538\) | −2.02854 | + | 6.34809i | −0.0874564 | + | 0.273685i | ||||
\(539\) | 3.90376 | 0.168147 | ||||||||
\(540\) | −1.78862 | + | 3.15057i | −0.0769700 | + | 0.135579i | ||||
\(541\) | −12.0388 | −0.517590 | −0.258795 | − | 0.965932i | \(-0.583325\pi\) | ||||
−0.258795 | + | 0.965932i | \(0.583325\pi\) | |||||||
\(542\) | 6.74728 | − | 21.1149i | 0.289820 | − | 0.906962i | ||||
\(543\) | −6.91099 | − | 11.0802i | −0.296579 | − | 0.475496i | ||||
\(544\) | 22.0765 | − | 0.536989i | 0.946522 | − | 0.0230232i | ||||
\(545\) | 0.487964i | 0.0209021i | ||||||||
\(546\) | 6.97867 | − | 1.76996i | 0.298660 | − | 0.0757473i | ||||
\(547\) | − | 35.3097i | − | 1.50973i | −0.655879 | − | 0.754866i | \(-0.727702\pi\) | ||
0.655879 | − | 0.754866i | \(-0.272298\pi\) | |||||||
\(548\) | 5.06100 | − | 7.11030i | 0.216195 | − | 0.303737i | ||||
\(549\) | 18.6003 | − | 37.9774i | 0.793840 | − | 1.62084i | ||||
\(550\) | −25.6548 | − | 8.19802i | −1.09393 | − | 0.349565i | ||||
\(551\) | 54.4011 | 2.31756 | ||||||||
\(552\) | 3.86735 | − | 9.96488i | 0.164605 | − | 0.424133i | ||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 22.8958 | + | 7.31638i | 0.972751 | + | 0.310843i | ||||
\(555\) | 0.327428 | − | 0.204225i | 0.0138986 | − | 0.00866889i | ||||
\(556\) | −19.5048 | + | 27.4026i | −0.827186 | + | 1.16213i | ||||
\(557\) | − | 34.7920i | − | 1.47419i | −0.675792 | − | 0.737093i | \(-0.736198\pi\) | ||
0.675792 | − | 0.737093i | \(-0.263802\pi\) | |||||||
\(558\) | 8.07926 | + | 7.75197i | 0.342022 | + | 0.328167i | ||||
\(559\) | 7.39973i | 0.312975i | ||||||||
\(560\) | 0.456627 | + | 1.31756i | 0.0192960 | + | 0.0556773i | ||||
\(561\) | 22.3960 | − | 13.9690i | 0.945562 | − | 0.589771i | ||||
\(562\) | −2.47874 | + | 7.75694i | −0.104559 | + | 0.327207i | ||||
\(563\) | −12.8618 | −0.542058 | −0.271029 | − | 0.962571i | \(-0.587364\pi\) | ||||
−0.271029 | + | 0.962571i | \(0.587364\pi\) | |||||||
\(564\) | 0.920160 | − | 15.0885i | 0.0387457 | − | 0.635342i | ||||
\(565\) | −3.07900 | −0.129535 | ||||||||
\(566\) | 2.40130 | − | 7.51461i | 0.100934 | − | 0.315863i | ||||
\(567\) | −7.11030 | + | 5.51757i | −0.298605 | + | 0.231716i | ||||
\(568\) | −20.2369 | − | 27.0157i | −0.849120 | − | 1.13355i | ||||
\(569\) | 15.6909i | 0.657795i | 0.944366 | + | 0.328897i | \(0.106677\pi\) | ||||
−0.944366 | + | 0.328897i | \(0.893323\pi\) | |||||||
\(570\) | 1.17105 | + | 4.61727i | 0.0490500 | + | 0.193396i | ||||
\(571\) | − | 42.0315i | − | 1.75896i | −0.475935 | − | 0.879481i | \(-0.657890\pi\) | ||
0.475935 | − | 0.879481i | \(-0.342110\pi\) | |||||||
\(572\) | 18.6958 | + | 13.3074i | 0.781710 | + | 0.556408i | ||||
\(573\) | 1.49564 | + | 2.39792i | 0.0624813 | + | 0.100174i | ||||
\(574\) | 10.1980 | + | 3.25879i | 0.425657 | + | 0.136019i | ||||
\(575\) | 10.6443 | 0.443897 | ||||||||
\(576\) | −17.7166 | − | 16.1901i | −0.738193 | − | 0.674589i | ||||
\(577\) | 38.7921 | 1.61494 | 0.807468 | − | 0.589912i | \(-0.200837\pi\) | ||||
0.807468 | + | 0.589912i | \(0.200837\pi\) | |||||||
\(578\) | 2.37176 | + | 0.757897i | 0.0986522 | + | 0.0315244i | ||||
\(579\) | 13.8932 | + | 22.2745i | 0.577381 | + | 0.925697i | ||||
\(580\) | 5.53950 | + | 3.94293i | 0.230015 | + | 0.163721i | ||||
\(581\) | 8.94358i | 0.371042i | ||||||||
\(582\) | 1.20437 | + | 4.74863i | 0.0499227 | + | 0.196837i | ||||
\(583\) | − | 6.72180i | − | 0.278388i | ||||||
\(584\) | 13.3597 | + | 17.8348i | 0.552827 | + | 0.738011i | ||||
\(585\) | 2.76063 | + | 1.35208i | 0.114138 | + | 0.0559017i | ||||
\(586\) | 10.2328 | − | 32.0223i | 0.422711 | − | 1.32283i | ||||
\(587\) | −7.07471 | −0.292004 | −0.146002 | − | 0.989284i | \(-0.546641\pi\) | ||||
−0.146002 | + | 0.989284i | \(0.546641\pi\) | |||||||
\(588\) | −0.210863 | + | 3.45768i | −0.00869586 | + | 0.142592i | ||||
\(589\) | 14.7218 | 0.606601 | ||||||||
\(590\) | −1.23750 | + | 3.87263i | −0.0509472 | + | 0.159434i | ||||
\(591\) | 31.1945 | − | 19.4568i | 1.28317 | − | 0.800346i | ||||
\(592\) | 0.837122 | + | 2.41546i | 0.0344055 | + | 0.0992747i | ||||
\(593\) | 18.3895i | 0.755168i | 0.925975 | + | 0.377584i | \(0.123245\pi\) | ||||
−0.925975 | + | 0.377584i | \(0.876755\pi\) | |||||||
\(594\) | −28.0740 | − | 5.89710i | −1.15189 | − | 0.241961i | ||||
\(595\) | − | 1.36090i | − | 0.0557914i | ||||||
\(596\) | −8.88449 | + | 12.4820i | −0.363923 | + | 0.511283i | ||||
\(597\) | 5.52126 | − | 3.44375i | 0.225970 | − | 0.140943i | ||||
\(598\) | −8.63910 | − | 2.76063i | −0.353279 | − | 0.112891i | ||||
\(599\) | 37.8516 | 1.54657 | 0.773287 | − | 0.634057i | \(-0.218611\pi\) | ||||
0.773287 | + | 0.634057i | \(0.218611\pi\) | |||||||
\(600\) | 8.64698 | − | 22.2804i | 0.353012 | − | 0.909594i | ||||
\(601\) | 21.9488 | 0.895308 | 0.447654 | − | 0.894207i | \(-0.352260\pi\) | ||||
0.447654 | + | 0.894207i | \(0.352260\pi\) | |||||||
\(602\) | −3.39144 | − | 1.08374i | −0.138225 | − | 0.0441698i | ||||
\(603\) | 1.72188 | + | 0.843327i | 0.0701202 | + | 0.0343429i | ||||
\(604\) | 14.6585 | − | 20.5941i | 0.596447 | − | 0.837960i | ||||
\(605\) | 1.47789i | 0.0600849i | ||||||||
\(606\) | −7.34884 | + | 1.86384i | −0.298526 | + | 0.0757135i | ||||
\(607\) | 25.8785i | 1.05037i | 0.850987 | + | 0.525187i | \(0.176005\pi\) | ||||
−0.850987 | + | 0.525187i | \(0.823995\pi\) | |||||||
\(608\) | −31.5465 | + | 0.767338i | −1.27938 | + | 0.0311197i | ||||
\(609\) | 8.93923 | + | 14.3320i | 0.362236 | + | 0.580762i | ||||
\(610\) | 2.11533 | − | 6.61968i | 0.0856470 | − | 0.268023i | ||||
\(611\) | −12.8262 | −0.518891 | ||||||||
\(612\) | 11.1630 | + | 20.5914i | 0.451238 | + | 0.832357i | ||||
\(613\) | −12.9136 | −0.521576 | −0.260788 | − | 0.965396i | \(-0.583982\pi\) | ||||
−0.260788 | + | 0.965396i | \(0.583982\pi\) | |||||||
\(614\) | 1.59268 | − | 4.98412i | 0.0642753 | − | 0.201143i | ||||
\(615\) | 2.41910 | + | 3.87847i | 0.0975475 | + | 0.156395i | ||||
\(616\) | −8.83712 | + | 6.61968i | −0.356058 | + | 0.266715i | ||||
\(617\) | − | 26.4677i | − | 1.06555i | −0.846257 | − | 0.532775i | \(-0.821149\pi\) | ||
0.846257 | − | 0.532775i | \(-0.178851\pi\) | |||||||
\(618\) | −17.1885 | + | 4.35943i | −0.691425 | + | 0.175362i | ||||
\(619\) | 34.3390i | 1.38020i | 0.723714 | + | 0.690100i | \(0.242433\pi\) | ||||
−0.723714 | + | 0.690100i | \(0.757567\pi\) | |||||||
\(620\) | 1.49908 | + | 1.06702i | 0.0602044 | + | 0.0428525i | ||||
\(621\) | 11.2782 | − | 1.15723i | 0.452579 | − | 0.0464382i | ||||
\(622\) | 10.2174 | + | 3.26499i | 0.409682 | + | 0.130914i | ||||
\(623\) | 10.5396 | 0.422262 | ||||||||
\(624\) | −12.7966 | + | 15.8406i | −0.512273 | + | 0.634131i | ||||
\(625\) | 23.1918 | 0.927673 | ||||||||
\(626\) | 21.0626 | + | 6.73056i | 0.841829 | + | 0.269007i | ||||
\(627\) | −32.0031 | + | 19.9612i | −1.27808 | + | 0.797172i | ||||
\(628\) | 0.354292 | + | 0.252179i | 0.0141378 | + | 0.0100631i | ||||
\(629\) | − | 2.49490i | − | 0.0994782i | ||||||
\(630\) | −1.02400 | + | 1.06723i | −0.0407970 | + | 0.0425194i | ||||
\(631\) | 27.7569i | 1.10499i | 0.833517 | + | 0.552493i | \(0.186323\pi\) | ||||
−0.833517 | + | 0.552493i | \(0.813677\pi\) | |||||||
\(632\) | 9.05498 | − | 6.78287i | 0.360188 | − | 0.269808i | ||||
\(633\) | −14.4605 | + | 9.01938i | −0.574753 | + | 0.358488i | ||||
\(634\) | 5.98058 | − | 18.7156i | 0.237519 | − | 0.743291i | ||||
\(635\) | −4.32141 | −0.171490 | ||||||||
\(636\) | 5.95369 | + | 0.363081i | 0.236079 | + | 0.0143971i | ||||
\(637\) | 2.93923 | 0.116457 | ||||||||
\(638\) | −16.3881 | + | 51.2847i | −0.648810 | + | 2.03038i | ||||
\(639\) | 15.7476 | − | 32.1530i | 0.622967 | − | 1.27195i | ||||
\(640\) | −3.26790 | − | 2.20832i | −0.129175 | − | 0.0872915i | ||||
\(641\) | 6.96331i | 0.275034i | 0.990499 | + | 0.137517i | \(0.0439122\pi\) | ||||
−0.990499 | + | 0.137517i | \(0.956088\pi\) | |||||||
\(642\) | −6.63249 | − | 26.1509i | −0.261764 | − | 1.03209i | ||||
\(643\) | − | 9.74373i | − | 0.384255i | −0.981370 | − | 0.192128i | \(-0.938461\pi\) | ||
0.981370 | − | 0.192128i | \(-0.0615387\pi\) | |||||||
\(644\) | 2.53050 | − | 3.55515i | 0.0997156 | − | 0.140093i | ||||
\(645\) | −0.804492 | − | 1.28982i | −0.0316768 | − | 0.0507865i | ||||
\(646\) | 29.3353 | + | 9.37411i | 1.15418 | + | 0.368819i | ||||
\(647\) | −28.1896 | −1.10825 | −0.554123 | − | 0.832434i | \(-0.686946\pi\) | ||||
−0.554123 | + | 0.832434i | \(0.686946\pi\) | |||||||
\(648\) | 6.73966 | − | 24.5474i | 0.264759 | − | 0.964315i | ||||
\(649\) | −32.1918 | −1.26364 | ||||||||
\(650\) | −19.3161 | − | 6.17248i | −0.757641 | − | 0.242105i | ||||
\(651\) | 2.41910 | + | 3.87847i | 0.0948120 | + | 0.152009i | ||||
\(652\) | −6.07649 | + | 8.53699i | −0.237974 | + | 0.334334i | ||||
\(653\) | − | 10.8527i | − | 0.424697i | −0.977194 | − | 0.212349i | \(-0.931889\pi\) | ||
0.977194 | − | 0.212349i | \(-0.0681112\pi\) | |||||||
\(654\) | −0.842897 | − | 3.32341i | −0.0329599 | − | 0.129956i | ||||
\(655\) | 0.561431i | 0.0219369i | ||||||||
\(656\) | −28.6117 | + | 9.91592i | −1.11710 | + | 0.387151i | ||||
\(657\) | −10.3960 | + | 21.2263i | −0.405588 | + | 0.828116i | ||||
\(658\) | 1.87847 | − | 5.87847i | 0.0732304 | − | 0.229167i | ||||
\(659\) | 19.2248 | 0.748893 | 0.374446 | − | 0.927249i | \(-0.377833\pi\) | ||||
0.374446 | + | 0.927249i | \(0.377833\pi\) | |||||||
\(660\) | −4.70555 | − | 0.286964i | −0.183163 | − | 0.0111700i | ||||
\(661\) | −2.74742 | −0.106862 | −0.0534311 | − | 0.998572i | \(-0.517016\pi\) | ||||
−0.0534311 | + | 0.998572i | \(0.517016\pi\) | |||||||
\(662\) | −13.6871 | + | 42.8323i | −0.531964 | + | 1.66472i | ||||
\(663\) | 16.8625 | − | 10.5176i | 0.654885 | − | 0.408469i | ||||
\(664\) | −15.1658 | − | 20.2460i | −0.588547 | − | 0.785696i | ||||
\(665\) | 1.94467i | 0.0754112i | ||||||||
\(666\) | −1.87727 | + | 1.95652i | −0.0727426 | + | 0.0758138i | ||||
\(667\) | − | 21.2782i | − | 0.823895i | ||||||
\(668\) | 18.6958 | + | 13.3074i | 0.723361 | + | 0.514877i | ||||
\(669\) | −33.6742 | + | 21.0035i | −1.30192 | + | 0.812041i | ||||
\(670\) | 0.300133 | + | 0.0959078i | 0.0115952 | + | 0.00370524i | ||||
\(671\) | 55.0271 | 2.12430 | ||||||||
\(672\) | −5.38591 | − | 8.18486i | −0.207766 | − | 0.315738i | ||||
\(673\) | 31.3097 | 1.20690 | 0.603449 | − | 0.797401i | \(-0.293793\pi\) | ||||
0.603449 | + | 0.797401i | \(0.293793\pi\) | |||||||
\(674\) | −23.0596 | − | 7.36870i | −0.888221 | − | 0.283832i | ||||
\(675\) | 25.2169 | − | 2.58746i | 0.970598 | − | 0.0995912i | ||||
\(676\) | −7.10562 | − | 5.05766i | −0.273293 | − | 0.194525i | ||||
\(677\) | 20.9823i | 0.806415i | 0.915109 | + | 0.403208i | \(0.132105\pi\) | ||||
−0.915109 | + | 0.403208i | \(0.867895\pi\) | |||||||
\(678\) | 20.9704 | − | 5.31860i | 0.805363 | − | 0.204259i | ||||
\(679\) | 2.00000i | 0.0767530i | ||||||||
\(680\) | 2.30770 | + | 3.08073i | 0.0884963 | + | 0.118140i | ||||
\(681\) | −12.4022 | − | 19.8841i | −0.475255 | − | 0.761962i | ||||
\(682\) | −4.43488 | + | 13.8785i | −0.169820 | + | 0.531434i | ||||
\(683\) | 15.8234 | 0.605467 | 0.302734 | − | 0.953075i | \(-0.402101\pi\) | ||||
0.302734 | + | 0.953075i | \(0.402101\pi\) | |||||||
\(684\) | −15.9515 | − | 29.4243i | −0.609922 | − | 1.12507i | ||||
\(685\) | 1.52126 | 0.0581245 | ||||||||
\(686\) | −0.430469 | + | 1.34711i | −0.0164354 | + | 0.0514328i | ||||
\(687\) | −13.4711 | − | 21.5978i | −0.513953 | − | 0.824006i | ||||
\(688\) | 9.51506 | − | 3.29762i | 0.362758 | − | 0.125721i | ||||
\(689\) | − | 5.06100i | − | 0.192809i | ||||||
\(690\) | 1.80598 | − | 0.458040i | 0.0687525 | − | 0.0174373i | ||||
\(691\) | 24.4093i | 0.928572i | 0.885685 | + | 0.464286i | \(0.153689\pi\) | ||||
−0.885685 | + | 0.464286i | \(0.846311\pi\) | |||||||
\(692\) | 24.5931 | − | 34.5514i | 0.934891 | − | 1.31345i | ||||
\(693\) | −10.5176 | − | 5.15121i | −0.399529 | − | 0.195678i | ||||
\(694\) | 11.3803 | + | 3.63659i | 0.431991 | + | 0.138043i | ||||
\(695\) | −5.86285 | −0.222391 | ||||||||
\(696\) | −44.5392 | − | 17.2856i | −1.68825 | − | 0.655208i | ||||
\(697\) | 29.5527 | 1.11939 | ||||||||
\(698\) | 23.5685 | + | 7.53133i | 0.892081 | + | 0.285065i | ||||
\(699\) | −25.2626 | + | 15.7569i | −0.955520 | + | 0.595982i | ||||
\(700\) | 5.65793 | − | 7.94894i | 0.213850 | − | 0.300442i | ||||
\(701\) | − | 21.4779i | − | 0.811209i | −0.914049 | − | 0.405605i | \(-0.867061\pi\) | ||
0.914049 | − | 0.405605i | \(-0.132939\pi\) | |||||||
\(702\) | −21.1376 | − | 4.44006i | −0.797787 | − | 0.167579i | ||||
\(703\) | 3.56512i | 0.134461i | ||||||||
\(704\) | 8.77986 | − | 29.9705i | 0.330904 | − | 1.12956i | ||||
\(705\) | 2.23568 | − | 1.39445i | 0.0842004 | − | 0.0525179i | ||||
\(706\) | 3.55892 | − | 11.1373i | 0.133942 | − | 0.419156i | ||||
\(707\) | −3.09514 | −0.116405 | ||||||||
\(708\) | 1.73885 | − | 28.5132i | 0.0653501 | − | 1.07159i | ||||
\(709\) | −42.1918 | −1.58455 | −0.792273 | − | 0.610166i | \(-0.791103\pi\) | ||||
−0.792273 | + | 0.610166i | \(0.791103\pi\) | |||||||
\(710\) | 1.79091 | − | 5.60446i | 0.0672116 | − | 0.210331i | ||||
\(711\) | 10.7769 | + | 5.27820i | 0.404164 | + | 0.197948i | ||||
\(712\) | −23.8591 | + | 17.8723i | −0.894156 | + | 0.669791i | ||||
\(713\) | − | 5.75822i | − | 0.215647i | ||||||
\(714\) | 2.35078 | + | 9.26877i | 0.0879759 | + | 0.346875i | ||||
\(715\) | 4.00000i | 0.149592i | ||||||||
\(716\) | −2.95261 | − | 2.10162i | −0.110344 | − | 0.0785412i | ||||
\(717\) | 13.3221 | + | 21.3589i | 0.497522 | + | 0.797661i | ||||
\(718\) | 33.8528 | + | 10.8177i | 1.26338 | + | 0.403713i | ||||
\(719\) | −19.0588 | −0.710774 | −0.355387 | − | 0.934719i | \(-0.615651\pi\) | ||||
−0.355387 | + | 0.934719i | \(0.615651\pi\) | |||||||
\(720\) | 0.508344 | − | 4.15234i | 0.0189449 | − | 0.154749i | ||||
\(721\) | −7.23937 | −0.269608 | ||||||||
\(722\) | −16.3240 | − | 5.21635i | −0.607517 | − | 0.194133i | ||||
\(723\) | 17.2255 | + | 27.6172i | 0.640624 | + | 1.02709i | ||||
\(724\) | 12.2848 | + | 8.74413i | 0.456561 | + | 0.324973i | ||||
\(725\) | − | 47.5758i | − | 1.76692i | ||||||
\(726\) | −2.55288 | − | 10.0656i | −0.0947462 | − | 0.373569i | ||||
\(727\) | − | 3.72549i | − | 0.138171i | −0.997611 | − | 0.0690854i | \(-0.977992\pi\) | ||
0.997611 | − | 0.0690854i | \(-0.0220081\pi\) | |||||||
\(728\) | −6.65368 | + | 4.98412i | −0.246602 | + | 0.184724i | ||||
\(729\) | 26.4374 | − | 5.48311i | 0.979163 | − | 0.203078i | ||||
\(730\) | −1.18230 | + | 3.69987i | −0.0437587 | + | 0.136938i | ||||
\(731\) | −9.82800 | −0.363502 | ||||||||
\(732\) | −2.97231 | + | 48.7391i | −0.109860 | + | 1.80145i | ||||
\(733\) | −25.4180 | −0.938834 | −0.469417 | − | 0.882977i | \(-0.655536\pi\) | ||||
−0.469417 | + | 0.882977i | \(0.655536\pi\) | |||||||
\(734\) | −9.34681 | + | 29.2498i | −0.344997 | + | 1.07963i | ||||
\(735\) | −0.512326 | + | 0.319551i | −0.0188974 | + | 0.0117868i | ||||
\(736\) | 0.300133 | + | 12.3390i | 0.0110631 | + | 0.454820i | ||||
\(737\) | 2.49490i | 0.0919009i | ||||||||
\(738\) | −23.1755 | − | 22.2367i | −0.853102 | − | 0.818543i | ||||
\(739\) | 23.3097i | 0.857459i | 0.903433 | + | 0.428730i | \(0.141039\pi\) | ||||
−0.903433 | + | 0.428730i | \(0.858961\pi\) | |||||||
\(740\) | −0.258396 | + | 0.363026i | −0.00949883 | + | 0.0133451i | ||||
\(741\) | −24.0959 | + | 15.0292i | −0.885185 | + | 0.552113i | ||||
\(742\) | 2.31955 | + | 0.741214i | 0.0851534 | + | 0.0272108i | ||||
\(743\) | −33.8576 | −1.24211 | −0.621057 | − | 0.783765i | \(-0.713297\pi\) | ||||
−0.621057 | + | 0.783765i | \(0.713297\pi\) | |||||||
\(744\) | −12.0530 | − | 4.67775i | −0.441885 | − | 0.171495i | ||||
\(745\) | −2.67055 | −0.0978415 | ||||||||
\(746\) | −0.972337 | − | 0.310711i | −0.0355998 | − | 0.0113759i | ||||
\(747\) | 11.8015 | − | 24.0959i | 0.431795 | − | 0.881623i | ||||
\(748\) | −17.6742 | + | 24.8309i | −0.646234 | + | 0.907908i | ||||
\(749\) | − | 11.0141i | − | 0.402445i | ||||||
\(750\) | 8.17655 | − | 2.07377i | 0.298566 | − | 0.0757235i | ||||
\(751\) | 48.1530i | 1.75713i | 0.477625 | + | 0.878564i | \(0.341498\pi\) | ||||
−0.477625 | + | 0.878564i | \(0.658502\pi\) | |||||||
\(752\) | 5.71586 | + | 16.4927i | 0.208436 | + | 0.601427i | ||||
\(753\) | 18.9198 | + | 30.3336i | 0.689476 | + | 1.10542i | ||||
\(754\) | −12.3390 | + | 38.6135i | −0.449359 | + | 1.40622i | ||||
\(755\) | 4.40614 | 0.160356 | ||||||||
\(756\) | 5.13069 | − | 9.03748i | 0.186601 | − | 0.328690i | ||||
\(757\) | −11.3923 | −0.414062 | −0.207031 | − | 0.978334i | \(-0.566380\pi\) | ||||
−0.207031 | + | 0.978334i | \(0.566380\pi\) | |||||||
\(758\) | 7.86661 | − | 24.6177i | 0.285728 | − | 0.894156i | ||||
\(759\) | 7.80753 | + | 12.5176i | 0.283395 | + | 0.454359i | ||||
\(760\) | −3.29762 | − | 4.40225i | −0.119617 | − | 0.159686i | ||||
\(761\) | − | 27.5491i | − | 0.998656i | −0.866413 | − | 0.499328i | \(-0.833580\pi\) | ||
0.866413 | − | 0.499328i | \(-0.166420\pi\) | |||||||
\(762\) | 29.4321 | − | 7.46470i | 1.06621 | − | 0.270417i | ||||
\(763\) | − | 1.39973i | − | 0.0506738i | ||||||
\(764\) | −2.65862 | − | 1.89236i | −0.0961853 | − | 0.0684632i | ||||
\(765\) | −1.79577 | + | 3.66655i | −0.0649264 | + | 0.132564i | ||||
\(766\) | −2.76063 | − | 0.882162i | −0.0997457 | − | 0.0318738i | ||||
\(767\) | −24.2380 | −0.875182 | ||||||||
\(768\) | 26.0715 | + | 9.39545i | 0.940776 | + | 0.339029i | ||||
\(769\) | −5.83461 | −0.210401 | −0.105201 | − | 0.994451i | \(-0.533549\pi\) | ||||
−0.105201 | + | 0.994451i | \(0.533549\pi\) | |||||||
\(770\) | −1.83328 | − | 0.585825i | −0.0660667 | − | 0.0211117i | ||||
\(771\) | −7.08912 | + | 4.42166i | −0.255308 | + | 0.159242i | ||||
\(772\) | −24.6962 | − | 17.5783i | −0.888835 | − | 0.632658i | ||||
\(773\) | − | 47.5682i | − | 1.71091i | −0.517879 | − | 0.855454i | \(-0.673278\pi\) | ||
0.517879 | − | 0.855454i | \(-0.326722\pi\) | |||||||
\(774\) | 7.70721 | + | 7.39499i | 0.277030 | + | 0.265807i | ||||
\(775\) | − | 12.8748i | − | 0.462476i | ||||||
\(776\) | −3.39144 | − | 4.52749i | −0.121745 | − | 0.162527i | ||||
\(777\) | −0.939235 | + | 0.585825i | −0.0336949 | + | 0.0210163i | ||||
\(778\) | −4.79829 | + | 15.0157i | −0.172027 | + | 0.538340i | ||||
\(779\) | −42.2298 | −1.51304 | ||||||||
\(780\) | −3.54292 | − | 0.216062i | −0.126857 | − | 0.00773625i | ||||
\(781\) | 46.5879 | 1.66704 | ||||||||
\(782\) | 3.66655 | − | 11.4741i | 0.131116 | − | 0.410312i | ||||
\(783\) | −5.17240 | − | 50.4093i | −0.184846 | − | 1.80148i | ||||
\(784\) | −1.30984 | − | 3.77946i | −0.0467801 | − | 0.134981i | ||||
\(785\) | 0.0758015i | 0.00270547i | ||||||||
\(786\) | −0.969803 | − | 3.82378i | −0.0345917 | − | 0.136390i | ||||
\(787\) | − | 48.8177i | − | 1.74016i | −0.492908 | − | 0.870082i | \(-0.664066\pi\) | ||
0.492908 | − | 0.870082i | \(-0.335934\pi\) | |||||||
\(788\) | −24.6177 | + | 34.5859i | −0.876970 | + | 1.23207i | ||||
\(789\) | 13.2526 | + | 21.2475i | 0.471804 | + | 0.756430i | ||||
\(790\) | 1.87847 | + | 0.600267i | 0.0668330 | + | 0.0213565i | ||||
\(791\) | 8.83218 | 0.314036 | ||||||||
\(792\) | 32.5441 | − | 6.17381i | 1.15640 | − | 0.219377i | ||||
\(793\) | 41.4312 | 1.47126 | ||||||||
\(794\) | 10.7423 | + | 3.43272i | 0.381231 | + | 0.121823i | ||||
\(795\) | 0.550227 | + | 0.882162i | 0.0195145 | + | 0.0312871i | ||||
\(796\) | −4.35721 | + | 6.12153i | −0.154437 | + | 0.216972i | ||||
\(797\) | − | 12.7292i | − | 0.450890i | −0.974256 | − | 0.225445i | \(-0.927616\pi\) | ||
0.974256 | − | 0.225445i | \(-0.0723837\pi\) | |||||||
\(798\) | −3.35918 | − | 13.2447i | −0.118914 | − | 0.468858i | ||||
\(799\) | − | 17.0351i | − | 0.602660i | ||||||
\(800\) | 0.671066 | + | 27.5886i | 0.0237258 | + | 0.975405i | ||||
\(801\) | −28.3960 | − | 13.9076i | −1.00332 | − | 0.491401i | ||||
\(802\) | −9.24557 | + | 28.9330i | −0.326473 | + | 1.02166i | ||||
\(803\) | −30.7557 | −1.08534 | ||||||||
\(804\) | −2.20981 | − | 0.134763i | −0.0779339 | − | 0.00475273i | ||||
\(805\) | 0.760632 | 0.0268088 | ||||||||
\(806\) | −3.33912 | + | 10.4494i | −0.117616 | + | 0.368065i | ||||
\(807\) | 6.92541 | − | 4.31955i | 0.243786 | − | 0.152055i | ||||
\(808\) | 7.00661 | − | 5.24849i | 0.246492 | − | 0.184641i | ||||
\(809\) | 26.5813i | 0.934548i | 0.884113 | + | 0.467274i | \(0.154764\pi\) | ||||
−0.884113 | + | 0.467274i | \(0.845236\pi\) | |||||||
\(810\) | 4.16713 | − | 1.52413i | 0.146418 | − | 0.0535524i | ||||
\(811\) | 4.13977i | 0.145367i | 0.997355 | + | 0.0726835i | \(0.0231563\pi\) | ||||
−0.997355 | + | 0.0726835i | \(0.976844\pi\) | |||||||
\(812\) | −15.8902 | − | 11.3104i | −0.557636 | − | 0.396916i | ||||
\(813\) | −23.0351 | + | 14.3676i | −0.807878 | + | 0.503894i | ||||
\(814\) | −3.36090 | − | 1.07398i | −0.117799 | − | 0.0376429i | ||||
\(815\) | −1.82651 | −0.0639797 | ||||||||
\(816\) | −21.0388 | − | 16.9958i | −0.736505 | − | 0.594974i | ||||
\(817\) | 14.0439 | 0.491332 | ||||||||
\(818\) | 49.7266 | + | 15.8902i | 1.73865 | + | 0.555587i | ||||
\(819\) | −7.91893 | − | 3.87847i | −0.276710 | − | 0.135525i | ||||
\(820\) | −4.30013 | − | 3.06077i | −0.150167 | − | 0.106887i | ||||
\(821\) | 29.5082i | 1.02984i | 0.857237 | + | 0.514922i | \(0.172179\pi\) | ||||
−0.857237 | + | 0.514922i | \(0.827821\pi\) | |||||||
\(822\) | −10.3610 | + | 2.62779i | −0.361381 | + | 0.0916549i | ||||
\(823\) | 12.0777i | 0.421001i | 0.977594 | + | 0.210501i | \(0.0675094\pi\) | ||||
−0.977594 | + | 0.210501i | \(0.932491\pi\) | |||||||
\(824\) | 16.3881 | − | 12.2759i | 0.570906 | − | 0.427652i | ||||
\(825\) | 17.4568 | + | 27.9880i | 0.607768 | + | 0.974416i | ||||
\(826\) | 3.54980 | − | 11.1087i | 0.123513 | − | 0.386522i | ||||
\(827\) | 11.9341 | 0.414989 | 0.207494 | − | 0.978236i | \(-0.433469\pi\) | ||||
0.207494 | + | 0.978236i | \(0.433469\pi\) | |||||||
\(828\) | −11.5089 | + | 6.23921i | −0.399962 | + | 0.216828i | ||||
\(829\) | −2.50436 | −0.0869800 | −0.0434900 | − | 0.999054i | \(-0.513848\pi\) | ||||
−0.0434900 | + | 0.999054i | \(0.513848\pi\) | |||||||
\(830\) | 1.34213 | − | 4.20006i | 0.0465861 | − | 0.145786i | ||||
\(831\) | −15.5795 | − | 24.9781i | −0.540445 | − | 0.866480i | ||||
\(832\) | 6.61057 | − | 22.5655i | 0.229180 | − | 0.782319i | ||||
\(833\) | 3.90376i | 0.135257i | ||||||||
\(834\) | 39.9305 | − | 10.1274i | 1.38268 | − | 0.350682i | ||||
\(835\) | 4.00000i | 0.138426i | ||||||||
\(836\) | 25.2559 | − | 35.4825i | 0.873492 | − | 1.22719i | ||||
\(837\) | −1.39973 | − | 13.6416i | −0.0483819 | − | 0.471521i | ||||
\(838\) | 39.8437 | + | 12.7321i | 1.37638 | + | 0.439823i | ||||
\(839\) | 1.64607 | 0.0568288 | 0.0284144 | − | 0.999596i | \(-0.490954\pi\) | ||||
0.0284144 | + | 0.999596i | \(0.490954\pi\) | |||||||
\(840\) | 0.617907 | − | 1.59214i | 0.0213198 | − | 0.0549341i | ||||
\(841\) | −66.1054 | −2.27950 | ||||||||
\(842\) | 49.6152 | + | 15.8546i | 1.70985 | + | 0.546385i | ||||
\(843\) | 8.46238 | − | 5.27820i | 0.291460 | − | 0.181791i | ||||
\(844\) | 11.4118 | − | 16.0326i | 0.392809 | − | 0.551866i | ||||
\(845\) | − | 1.52026i | − | 0.0522986i | ||||||
\(846\) | −12.8179 | + | 13.3591i | −0.440690 | + | 0.459296i | ||||
\(847\) | − | 4.23937i | − | 0.145666i | ||||||
\(848\) | −6.50776 | + | 2.25539i | −0.223477 | + | 0.0774503i | ||||
\(849\) | −8.19802 | + | 5.11331i | −0.281355 | + | 0.175488i | ||||
\(850\) | 8.19802 | − | 25.6548i | 0.281190 | − | 0.879953i | ||||
\(851\) | 1.39445 | 0.0478010 | ||||||||
\(852\) | −2.51646 | + | 41.2642i | −0.0862125 | + | 1.41369i | ||||
\(853\) | −15.1311 | −0.518077 | −0.259039 | − | 0.965867i | \(-0.583406\pi\) | ||||
−0.259039 | + | 0.965867i | \(0.583406\pi\) | |||||||
\(854\) | −6.06785 | + | 18.9887i | −0.207638 | + | 0.649780i | ||||
\(855\) | 2.56610 | − | 5.23937i | 0.0877587 | − | 0.179183i | ||||
\(856\) | 18.6768 | + | 24.9330i | 0.638358 | + | 0.852193i | ||||
\(857\) | 48.9224i | 1.67116i | 0.549370 | + | 0.835579i | \(0.314868\pi\) | ||||
−0.549370 | + | 0.835579i | \(0.685132\pi\) | |||||||
\(858\) | −6.90950 | − | 27.2431i | −0.235887 | − | 0.930063i | ||||
\(859\) | − | 16.0571i | − | 0.547860i | −0.961750 | − | 0.273930i | \(-0.911676\pi\) | ||
0.961750 | − | 0.273930i | \(-0.0883237\pi\) | |||||||
\(860\) | 1.43005 | + | 1.01788i | 0.0487641 | + | 0.0347095i | ||||
\(861\) | −6.93923 | − | 11.1255i | −0.236488 | − | 0.379155i | ||||
\(862\) | −6.30013 | − | 2.01321i | −0.214583 | − | 0.0685703i | ||||
\(863\) | 14.9034 | 0.507318 | 0.253659 | − | 0.967294i | \(-0.418366\pi\) | ||||
0.253659 | + | 0.967294i | \(0.418366\pi\) | |||||||
\(864\) | 3.71044 | + | 29.1587i | 0.126232 | + | 0.992001i | ||||
\(865\) | 7.39235 | 0.251347 | ||||||||
\(866\) | −22.3032 | − | 7.12702i | −0.757895 | − | 0.242186i | ||||
\(867\) | −1.61386 | − | 2.58746i | −0.0548096 | − | 0.0878746i | ||||
\(868\) | −4.30013 | − | 3.06077i | −0.145956 | − | 0.103889i | ||||
\(869\) | 15.6151i | 0.529704i | ||||||||
\(870\) | −2.04726 | − | 8.07204i | −0.0694088 | − | 0.273668i | ||||
\(871\) | 1.87847i | 0.0636495i | ||||||||
\(872\) | 2.37355 | + | 3.16864i | 0.0803787 | + | 0.107304i | ||||
\(873\) | 2.63910 | − | 5.38843i | 0.0893201 | − | 0.182371i | ||||
\(874\) | −5.23937 | + | 16.3960i | −0.177224 | + | 0.554604i | ||||
\(875\) | 3.44375 | 0.116420 | ||||||||
\(876\) | 1.66128 | − | 27.2412i | 0.0561295 | − | 0.920395i | ||||
\(877\) | 11.8785 | 0.401107 | 0.200554 | − | 0.979683i | \(-0.435726\pi\) | ||||
0.200554 | + | 0.979683i | \(0.435726\pi\) | |||||||
\(878\) | 11.3983 | − | 35.6697i | 0.384673 | − | 1.20379i | ||||
\(879\) | −34.9346 | + | 21.7896i | −1.17831 | + | 0.734944i | ||||
\(880\) | 5.14346 | − | 1.78256i | 0.173386 | − | 0.0600901i | ||||
\(881\) | − | 36.4995i | − | 1.22970i | −0.788644 | − | 0.614850i | \(-0.789217\pi\) | ||
0.788644 | − | 0.614850i | \(-0.210783\pi\) | |||||||
\(882\) | 2.93735 | − | 3.06137i | 0.0989058 | − | 0.103082i | ||||
\(883\) | − | 31.1178i | − | 1.04720i | −0.851965 | − | 0.523599i | \(-0.824589\pi\) | ||
0.851965 | − | 0.523599i | \(-0.175411\pi\) | |||||||
\(884\) | −13.3074 | + | 18.6958i | −0.447575 | + | 0.628807i | ||||
\(885\) | 4.22482 | − | 2.63513i | 0.142016 | − | 0.0885789i | ||||
\(886\) | 6.19802 | + | 1.98058i | 0.208227 | + | 0.0665390i | ||||
\(887\) | −56.9248 | −1.91135 | −0.955674 | − | 0.294428i | \(-0.904871\pi\) | ||||
−0.955674 | + | 0.294428i | \(0.904871\pi\) | |||||||
\(888\) | 1.13279 | − | 2.91884i | 0.0380141 | − | 0.0979497i | ||||
\(889\) | 12.3960 | 0.415750 | ||||||||
\(890\) | −4.94960 | − | 1.58165i | −0.165911 | − | 0.0530170i | ||||
\(891\) | 21.5393 | + | 27.7569i | 0.721593 | + | 0.929892i | ||||
\(892\) | 26.5746 | − | 37.3353i | 0.889785 | − | 1.25008i | ||||
\(893\) | 24.3426i | 0.814594i | ||||||||
\(894\) | 18.1885 | − | 4.61305i | 0.608315 | − | 0.154283i | ||||
\(895\) | − | 0.631717i | − | 0.0211160i | ||||||
\(896\) | 9.37405 | + | 6.33461i | 0.313165 | + | 0.211624i | ||||
\(897\) | 5.87847 | + | 9.42477i | 0.196276 | + | 0.314684i | ||||
\(898\) | 7.32206 | − | 22.9136i | 0.244340 | − | 0.764637i | ||||
\(899\) | −25.7370 | −0.858379 | ||||||||
\(900\) | −25.7327 | + | 13.9502i | −0.857757 | + | 0.465008i | ||||
\(901\) | 6.72180 | 0.223936 | ||||||||
\(902\) | 12.7215 | − | 39.8107i | 0.423581 | − | 1.32555i | ||||
\(903\) | 2.30770 | + | 3.69987i | 0.0767955 | + | 0.123124i | ||||
\(904\) | −19.9938 | + | 14.9769i | −0.664984 | + | 0.498124i | ||||
\(905\) | 2.62836i | 0.0873696i | ||||||||
\(906\) | −30.0092 | + | 7.61106i | −0.996989 | + | 0.252861i | ||||
\(907\) | − | 6.70939i | − | 0.222782i | −0.993777 | − | 0.111391i | \(-0.964469\pi\) | ||
0.993777 | − | 0.111391i | \(-0.0355305\pi\) | |||||||
\(908\) | 22.0459 | + | 15.6919i | 0.731620 | + | 0.520755i | ||||
\(909\) | 8.33897 | + | 4.08419i | 0.276586 | + | 0.135464i | ||||
\(910\) | −1.38032 | − | 0.441081i | −0.0457570 | − | 0.0146217i | ||||
\(911\) | 50.1275 | 1.66080 | 0.830399 | − | 0.557169i | \(-0.188112\pi\) | ||||
0.830399 | + | 0.557169i | \(0.188112\pi\) | |||||||
\(912\) | 30.0637 | + | 24.2865i | 0.995508 | + | 0.804205i | ||||
\(913\) | 34.9136 | 1.15547 | ||||||||
\(914\) | −20.7875 | − | 6.64265i | −0.687588 | − | 0.219719i | ||||
\(915\) | −7.22170 | + | 4.50436i | −0.238742 | + | 0.148910i | ||||
\(916\) | 23.9458 | + | 17.0443i | 0.791193 | + | 0.563158i | ||||
\(917\) | − | 1.61048i | − | 0.0531826i | ||||||
\(918\) | 5.89710 | − | 28.0740i | 0.194633 | − | 0.926580i | ||||
\(919\) | − | 17.0351i | − | 0.561938i | −0.959717 | − | 0.280969i | \(-0.909344\pi\) | ||
0.959717 | − | 0.280969i | \(-0.0906557\pi\) | |||||||
\(920\) | −1.72188 | + | 1.28982i | −0.0567686 | + | 0.0425240i | ||||
\(921\) | −5.43739 | + | 3.39144i | −0.179168 | + | 0.111752i | ||||
\(922\) | −14.3675 | + | 44.9616i | −0.473169 | + | 1.48073i | ||||
\(923\) | 35.0771 | 1.15458 | ||||||||
\(924\) | 13.4980 | + | 0.823160i | 0.444050 | + | 0.0270800i | ||||
\(925\) | 3.11784 | 0.102514 | ||||||||
\(926\) | −11.3983 | + | 35.6697i | −0.374571 | + | 1.17218i | ||||
\(927\) | 19.5044 | + | 9.55271i | 0.640609 | + | 0.313752i | ||||
\(928\) | 55.1505 | − | 1.34148i | 1.81040 | − | 0.0440363i | ||||
\(929\) | 23.4082i | 0.767997i | 0.923334 | + | 0.383999i | \(0.125453\pi\) | ||||
−0.923334 | + | 0.383999i | \(0.874547\pi\) | |||||||
\(930\) | −0.554023 | − | 2.18442i | −0.0181671 | − | 0.0716301i | ||||
\(931\) | − | 5.57834i | − | 0.182823i | ||||||
\(932\) | 19.9365 | − | 28.0092i | 0.653040 | − | 0.917470i | ||||
\(933\) | −6.95245 | − | 11.1466i | −0.227613 | − | 0.364925i | ||||
\(934\) | −25.0443 | − | 8.00291i | −0.819473 | − | 0.261863i | ||||
\(935\) | −5.31263 | −0.173741 | ||||||||
\(936\) | 24.5032 | − | 4.64841i | 0.800913 | − | 0.151938i | ||||
\(937\) | −48.5929 | −1.58746 | −0.793730 | − | 0.608270i | \(-0.791864\pi\) | ||||
−0.793730 | + | 0.608270i | \(0.791864\pi\) | |||||||
\(938\) | −0.860938 | − | 0.275113i | −0.0281106 | − | 0.00898277i | ||||
\(939\) | −14.3320 | − | 22.9781i | −0.467707 | − | 0.749861i | ||||
\(940\) | −1.76432 | + | 2.47874i | −0.0575459 | + | 0.0808475i | ||||
\(941\) | − | 14.6116i | − | 0.476324i | −0.971225 | − | 0.238162i | \(-0.923455\pi\) | ||
0.971225 | − | 0.238162i | \(-0.0765449\pi\) | |||||||
\(942\) | −0.130938 | − | 0.516267i | −0.00426618 | − | 0.0168209i | ||||
\(943\) | 16.5176i | 0.537886i | ||||||||
\(944\) | 10.8014 | + | 31.1668i | 0.351556 | + | 1.01439i | ||||
\(945\) | 1.80198 | − | 0.184898i | 0.0586184 | − | 0.00601472i | ||||
\(946\) | −4.23065 | + | 13.2394i | −0.137550 | + | 0.430449i | ||||
\(947\) | 31.4250 | 1.02117 | 0.510587 | − | 0.859826i | \(-0.329428\pi\) | ||||
0.510587 | + | 0.859826i | \(0.329428\pi\) | |||||||
\(948\) | −13.8307 | − | 0.843453i | −0.449201 | − | 0.0273941i | ||||
\(949\) | −23.1567 | −0.751697 | ||||||||
\(950\) | −11.7147 | + | 36.6598i | −0.380074 | + | 1.18940i | ||||
\(951\) | −20.4177 | + | 12.7350i | −0.662088 | + | 0.412961i | ||||
\(952\) | −6.61968 | − | 8.83712i | −0.214545 | − | 0.286413i | ||||
\(953\) | 14.0113i | 0.453872i | 0.973910 | + | 0.226936i | \(0.0728708\pi\) | ||||
−0.973910 | + | 0.226936i | \(0.927129\pi\) | |||||||
\(954\) | −5.27129 | − | 5.05775i | −0.170664 | − | 0.163751i | ||||
\(955\) | − | 0.568816i | − | 0.0184065i | ||||||
\(956\) | −23.6810 | − | 16.8557i | −0.765898 | − | 0.545153i | ||||
\(957\) | 55.9488 | − | 34.8967i | 1.80857 | − | 1.12805i | ||||
\(958\) | −55.0666 | − | 17.5966i | −1.77912 | − | 0.568520i | ||||
\(959\) | −4.36377 | −0.140914 | ||||||||
\(960\) | 1.30104 | + | 4.65200i | 0.0419909 | + | 0.150143i | ||||
\(961\) | 24.0351 | 0.775327 | ||||||||
\(962\) | −2.53050 | − | 0.808623i | −0.0815866 | − | 0.0260711i | ||||
\(963\) | −14.5336 | + | 29.6742i | −0.468339 | + | 0.956239i | ||||
\(964\) | −30.6197 | − | 21.7946i | −0.986194 | − | 0.701957i | ||||
\(965\) | − | 5.28380i | − | 0.170091i | ||||||
\(966\) | −5.18049 | + | 1.31390i | −0.166679 | + | 0.0422740i | ||||
\(967\) | 35.9876i | 1.15728i | 0.815582 | + | 0.578641i | \(0.196417\pi\) | ||||
−0.815582 | + | 0.578641i | \(0.803583\pi\) | |||||||
\(968\) | 7.18878 | + | 9.59685i | 0.231056 | + | 0.308454i | ||||
\(969\) | −19.9612 | − | 32.0031i | −0.641245 | − | 1.02809i | ||||
\(970\) | 0.300133 | − | 0.939235i | 0.00963670 | − | 0.0301570i | ||||
\(971\) | 48.3844 | 1.55273 | 0.776365 | − | 0.630283i | \(-0.217061\pi\) | ||||
0.776365 | + | 0.630283i | \(0.217061\pi\) | |||||||
\(972\) | −25.7486 | + | 17.5787i | −0.825886 | + | 0.563837i | ||||
\(973\) | 16.8177 | 0.539151 | ||||||||
\(974\) | 9.22546 | − | 28.8701i | 0.295603 | − | 0.925057i | ||||
\(975\) | 13.1436 | + | 21.0728i | 0.420933 | + | 0.674870i | ||||
\(976\) | −18.4634 | − | 53.2749i | −0.590999 | − | 1.70529i | ||||
\(977\) | − | 37.6432i | − | 1.20431i | −0.798378 | − | 0.602156i | \(-0.794308\pi\) | ||
0.798378 | − | 0.602156i | \(-0.205692\pi\) | |||||||
\(978\) | 12.4399 | − | 3.15506i | 0.397785 | − | 0.100888i | ||||
\(979\) | − | 41.1443i | − | 1.31498i | ||||||
\(980\) | 0.404312 | − | 0.568026i | 0.0129153 | − | 0.0181449i | ||||
\(981\) | −1.84702 | + | 3.77118i | −0.0589708 | + | 0.120405i | ||||
\(982\) | −2.19802 | − | 0.702379i | −0.0701417 | − | 0.0224138i | ||||
\(983\) | 5.35499 | 0.170798 | 0.0853989 | − | 0.996347i | \(-0.472784\pi\) | ||||
0.0853989 | + | 0.996347i | \(0.472784\pi\) | |||||||
\(984\) | 34.5743 | + | 13.4182i | 1.10219 | + | 0.427757i | ||||
\(985\) | −7.39973 | −0.235775 | ||||||||
\(986\) | −51.2847 | − | 16.3881i | −1.63324 | − | 0.521903i | ||||
\(987\) | −6.41308 | + | 4.00000i | −0.204131 | + | 0.127321i | ||||
\(988\) | 19.0157 | − | 26.7156i | 0.604971 | − | 0.849936i | ||||
\(989\) | − | 5.49306i | − | 0.174669i | ||||||
\(990\) | 4.16621 | + | 3.99744i | 0.132411 | + | 0.127047i | ||||
\(991\) | 51.0278i | 1.62095i | 0.585773 | + | 0.810475i | \(0.300791\pi\) | ||||
−0.585773 | + | 0.810475i | \(0.699209\pi\) | |||||||
\(992\) | 14.9246 | − | 0.363026i | 0.473856 | − | 0.0115261i | ||||
\(993\) | 46.7276 | − | 29.1452i | 1.48286 | − | 0.924895i | ||||
\(994\) | −5.13726 | + | 16.0765i | −0.162944 | + | 0.509915i | ||||
\(995\) | −1.30971 | −0.0415207 | ||||||||
\(996\) | −1.88587 | + | 30.9240i | −0.0597562 | + | 0.979865i | ||||
\(997\) | −53.9305 | −1.70800 | −0.853998 | − | 0.520276i | \(-0.825829\pi\) | ||||
−0.853998 | + | 0.520276i | \(0.825829\pi\) | |||||||
\(998\) | 3.82350 | − | 11.9652i | 0.121031 | − | 0.378752i | ||||
\(999\) | 3.30352 | − | 0.338968i | 0.104519 | − | 0.0107245i |
(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 | 84.2.e.a.71.12 | yes | 12 | |
3.2 | odd | 2 | inner | 84.2.e.a.71.1 | ✓ | 12 | |
4.3 | odd | 2 | inner | 84.2.e.a.71.2 | yes | 12 | |
7.2 | even | 3 | 588.2.n.f.263.6 | 24 | |||
7.3 | odd | 6 | 588.2.n.g.275.3 | 24 | |||
7.4 | even | 3 | 588.2.n.f.275.3 | 24 | |||
7.5 | odd | 6 | 588.2.n.g.263.6 | 24 | |||
7.6 | odd | 2 | 588.2.e.c.491.12 | 12 | |||
8.3 | odd | 2 | 1344.2.h.h.575.3 | 12 | |||
8.5 | even | 2 | 1344.2.h.h.575.10 | 12 | |||
12.11 | even | 2 | inner | 84.2.e.a.71.11 | yes | 12 | |
21.2 | odd | 6 | 588.2.n.f.263.7 | 24 | |||
21.5 | even | 6 | 588.2.n.g.263.7 | 24 | |||
21.11 | odd | 6 | 588.2.n.f.275.10 | 24 | |||
21.17 | even | 6 | 588.2.n.g.275.10 | 24 | |||
21.20 | even | 2 | 588.2.e.c.491.1 | 12 | |||
24.5 | odd | 2 | 1344.2.h.h.575.4 | 12 | |||
24.11 | even | 2 | 1344.2.h.h.575.9 | 12 | |||
28.3 | even | 6 | 588.2.n.g.275.7 | 24 | |||
28.11 | odd | 6 | 588.2.n.f.275.7 | 24 | |||
28.19 | even | 6 | 588.2.n.g.263.10 | 24 | |||
28.23 | odd | 6 | 588.2.n.f.263.10 | 24 | |||
28.27 | even | 2 | 588.2.e.c.491.2 | 12 | |||
84.11 | even | 6 | 588.2.n.f.275.6 | 24 | |||
84.23 | even | 6 | 588.2.n.f.263.3 | 24 | |||
84.47 | odd | 6 | 588.2.n.g.263.3 | 24 | |||
84.59 | odd | 6 | 588.2.n.g.275.6 | 24 | |||
84.83 | odd | 2 | 588.2.e.c.491.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.e.a.71.1 | ✓ | 12 | 3.2 | odd | 2 | inner | |
84.2.e.a.71.2 | yes | 12 | 4.3 | odd | 2 | inner | |
84.2.e.a.71.11 | yes | 12 | 12.11 | even | 2 | inner | |
84.2.e.a.71.12 | yes | 12 | 1.1 | even | 1 | trivial | |
588.2.e.c.491.1 | 12 | 21.20 | even | 2 | |||
588.2.e.c.491.2 | 12 | 28.27 | even | 2 | |||
588.2.e.c.491.11 | 12 | 84.83 | odd | 2 | |||
588.2.e.c.491.12 | 12 | 7.6 | odd | 2 | |||
588.2.n.f.263.3 | 24 | 84.23 | even | 6 | |||
588.2.n.f.263.6 | 24 | 7.2 | even | 3 | |||
588.2.n.f.263.7 | 24 | 21.2 | odd | 6 | |||
588.2.n.f.263.10 | 24 | 28.23 | odd | 6 | |||
588.2.n.f.275.3 | 24 | 7.4 | even | 3 | |||
588.2.n.f.275.6 | 24 | 84.11 | even | 6 | |||
588.2.n.f.275.7 | 24 | 28.11 | odd | 6 | |||
588.2.n.f.275.10 | 24 | 21.11 | odd | 6 | |||
588.2.n.g.263.3 | 24 | 84.47 | odd | 6 | |||
588.2.n.g.263.6 | 24 | 7.5 | odd | 6 | |||
588.2.n.g.263.7 | 24 | 21.5 | even | 6 | |||
588.2.n.g.263.10 | 24 | 28.19 | even | 6 | |||
588.2.n.g.275.3 | 24 | 7.3 | odd | 6 | |||
588.2.n.g.275.6 | 24 | 84.59 | odd | 6 | |||
588.2.n.g.275.7 | 24 | 28.3 | even | 6 | |||
588.2.n.g.275.10 | 24 | 21.17 | even | 6 | |||
1344.2.h.h.575.3 | 12 | 8.3 | odd | 2 | |||
1344.2.h.h.575.4 | 12 | 24.5 | odd | 2 | |||
1344.2.h.h.575.9 | 12 | 24.11 | even | 2 | |||
1344.2.h.h.575.10 | 12 | 8.5 | even | 2 |