Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(64,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.c (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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.6 | ||
Root | \(-0.854638 + 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.64 |
Dual form | 273.2.c.b.64.1 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.17009i | 1.53448i | 0.641358 | + | 0.767241i | \(0.278371\pi\) | ||||
−0.641358 | + | 0.767241i | \(0.721629\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −2.70928 | −1.35464 | ||||||||
\(5\) | − | 0.630898i | − | 0.282146i | −0.989999 | − | 0.141073i | \(-0.954945\pi\) | ||
0.989999 | − | 0.141073i | \(-0.0450552\pi\) | |||||||
\(6\) | 2.17009i | 0.885934i | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − | 1.53919i | − | 0.544185i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.36910 | 0.432948 | ||||||||
\(11\) | 5.70928i | 1.72141i | 0.509103 | + | 0.860706i | \(0.329977\pi\) | ||||
−0.509103 | + | 0.860706i | \(0.670023\pi\) | |||||||
\(12\) | −2.70928 | −0.782100 | ||||||||
\(13\) | −2.17009 | + | 2.87936i | −0.601874 | + | 0.798591i | ||||
\(14\) | −2.17009 | −0.579980 | ||||||||
\(15\) | − | 0.630898i | − | 0.162897i | ||||||
\(16\) | −2.07838 | −0.519594 | ||||||||
\(17\) | 1.07838 | 0.261545 | 0.130773 | − | 0.991412i | \(-0.458254\pi\) | ||||
0.130773 | + | 0.991412i | \(0.458254\pi\) | |||||||
\(18\) | 2.17009i | 0.511494i | ||||||||
\(19\) | − | 7.41855i | − | 1.70193i | −0.525221 | − | 0.850966i | \(-0.676017\pi\) | ||
0.525221 | − | 0.850966i | \(-0.323983\pi\) | |||||||
\(20\) | 1.70928i | 0.382206i | ||||||||
\(21\) | 1.00000i | 0.218218i | ||||||||
\(22\) | −12.3896 | −2.64148 | ||||||||
\(23\) | 5.41855 | 1.12985 | 0.564923 | − | 0.825144i | \(-0.308906\pi\) | ||||
0.564923 | + | 0.825144i | \(0.308906\pi\) | |||||||
\(24\) | − | 1.53919i | − | 0.314186i | ||||||
\(25\) | 4.60197 | 0.920394 | ||||||||
\(26\) | −6.24846 | − | 4.70928i | −1.22542 | − | 0.923565i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − | 2.70928i | − | 0.512005i | ||||||
\(29\) | 6.68035 | 1.24051 | 0.620255 | − | 0.784401i | \(-0.287029\pi\) | ||||
0.620255 | + | 0.784401i | \(0.287029\pi\) | |||||||
\(30\) | 1.36910 | 0.249963 | ||||||||
\(31\) | − | 6.15676i | − | 1.10579i | −0.833252 | − | 0.552893i | \(-0.813524\pi\) | ||
0.833252 | − | 0.552893i | \(-0.186476\pi\) | |||||||
\(32\) | − | 7.58864i | − | 1.34149i | ||||||
\(33\) | 5.70928i | 0.993857i | ||||||||
\(34\) | 2.34017i | 0.401336i | ||||||||
\(35\) | 0.630898 | 0.106641 | ||||||||
\(36\) | −2.70928 | −0.451546 | ||||||||
\(37\) | − | 3.41855i | − | 0.562006i | −0.959707 | − | 0.281003i | \(-0.909333\pi\) | ||
0.959707 | − | 0.281003i | \(-0.0906671\pi\) | |||||||
\(38\) | 16.0989 | 2.61159 | ||||||||
\(39\) | −2.17009 | + | 2.87936i | −0.347492 | + | 0.461067i | ||||
\(40\) | −0.971071 | −0.153540 | ||||||||
\(41\) | − | 1.21235i | − | 0.189337i | −0.995509 | − | 0.0946684i | \(-0.969821\pi\) | ||
0.995509 | − | 0.0946684i | \(-0.0301791\pi\) | |||||||
\(42\) | −2.17009 | −0.334852 | ||||||||
\(43\) | −12.6803 | −1.93373 | −0.966867 | − | 0.255279i | \(-0.917833\pi\) | ||||
−0.966867 | + | 0.255279i | \(0.917833\pi\) | |||||||
\(44\) | − | 15.4680i | − | 2.33189i | ||||||
\(45\) | − | 0.630898i | − | 0.0940487i | ||||||
\(46\) | 11.7587i | 1.73373i | ||||||||
\(47\) | − | 6.04945i | − | 0.882403i | −0.897408 | − | 0.441201i | \(-0.854552\pi\) | ||
0.897408 | − | 0.441201i | \(-0.145448\pi\) | |||||||
\(48\) | −2.07838 | −0.299988 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 9.98667i | 1.41233i | ||||||||
\(51\) | 1.07838 | 0.151003 | ||||||||
\(52\) | 5.87936 | − | 7.80098i | 0.815321 | − | 1.08180i | ||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 2.17009i | 0.295311i | ||||||||
\(55\) | 3.60197 | 0.485689 | ||||||||
\(56\) | 1.53919 | 0.205683 | ||||||||
\(57\) | − | 7.41855i | − | 0.982611i | ||||||
\(58\) | 14.4969i | 1.90354i | ||||||||
\(59\) | 1.36910i | 0.178242i | 0.996021 | + | 0.0891210i | \(0.0284058\pi\) | ||||
−0.996021 | + | 0.0891210i | \(0.971594\pi\) | |||||||
\(60\) | 1.70928i | 0.220667i | ||||||||
\(61\) | 12.6537 | 1.62014 | 0.810069 | − | 0.586334i | \(-0.199430\pi\) | ||||
0.810069 | + | 0.586334i | \(0.199430\pi\) | |||||||
\(62\) | 13.3607 | 1.69681 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 12.3112 | 1.53891 | ||||||||
\(65\) | 1.81658 | + | 1.36910i | 0.225319 | + | 0.169816i | ||||
\(66\) | −12.3896 | −1.52506 | ||||||||
\(67\) | − | 0.581449i | − | 0.0710353i | −0.999369 | − | 0.0355177i | \(-0.988692\pi\) | ||
0.999369 | − | 0.0355177i | \(-0.0113080\pi\) | |||||||
\(68\) | −2.92162 | −0.354299 | ||||||||
\(69\) | 5.41855 | 0.652317 | ||||||||
\(70\) | 1.36910i | 0.163639i | ||||||||
\(71\) | 4.81432i | 0.571354i | 0.958326 | + | 0.285677i | \(0.0922185\pi\) | ||||
−0.958326 | + | 0.285677i | \(0.907782\pi\) | |||||||
\(72\) | − | 1.53919i | − | 0.181395i | ||||||
\(73\) | 3.81658i | 0.446697i | 0.974739 | + | 0.223349i | \(0.0716988\pi\) | ||||
−0.974739 | + | 0.223349i | \(0.928301\pi\) | |||||||
\(74\) | 7.41855 | 0.862389 | ||||||||
\(75\) | 4.60197 | 0.531390 | ||||||||
\(76\) | 20.0989i | 2.30550i | ||||||||
\(77\) | −5.70928 | −0.650632 | ||||||||
\(78\) | −6.24846 | − | 4.70928i | −0.707499 | − | 0.533220i | ||||
\(79\) | −1.65983 | −0.186745 | −0.0933726 | − | 0.995631i | \(-0.529765\pi\) | ||||
−0.0933726 | + | 0.995631i | \(0.529765\pi\) | |||||||
\(80\) | 1.31124i | 0.146601i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.63090 | 0.290534 | ||||||||
\(83\) | 12.8865i | 1.41448i | 0.706972 | + | 0.707241i | \(0.250061\pi\) | ||||
−0.706972 | + | 0.707241i | \(0.749939\pi\) | |||||||
\(84\) | − | 2.70928i | − | 0.295606i | ||||||
\(85\) | − | 0.680346i | − | 0.0737939i | ||||||
\(86\) | − | 27.5174i | − | 2.96728i | ||||||
\(87\) | 6.68035 | 0.716208 | ||||||||
\(88\) | 8.78765 | 0.936767 | ||||||||
\(89\) | − | 6.20620i | − | 0.657856i | −0.944355 | − | 0.328928i | \(-0.893313\pi\) | ||
0.944355 | − | 0.328928i | \(-0.106687\pi\) | |||||||
\(90\) | 1.36910 | 0.144316 | ||||||||
\(91\) | −2.87936 | − | 2.17009i | −0.301839 | − | 0.227487i | ||||
\(92\) | −14.6803 | −1.53053 | ||||||||
\(93\) | − | 6.15676i | − | 0.638426i | ||||||
\(94\) | 13.1278 | 1.35403 | ||||||||
\(95\) | −4.68035 | −0.480193 | ||||||||
\(96\) | − | 7.58864i | − | 0.774512i | ||||||
\(97\) | 1.07838i | 0.109493i | 0.998500 | + | 0.0547463i | \(0.0174350\pi\) | ||||
−0.998500 | + | 0.0547463i | \(0.982565\pi\) | |||||||
\(98\) | − | 2.17009i | − | 0.219212i | ||||||
\(99\) | 5.70928i | 0.573804i | ||||||||
\(100\) | −12.4680 | −1.24680 | ||||||||
\(101\) | −7.23513 | −0.719923 | −0.359961 | − | 0.932967i | \(-0.617210\pi\) | ||||
−0.359961 | + | 0.932967i | \(0.617210\pi\) | |||||||
\(102\) | 2.34017i | 0.231712i | ||||||||
\(103\) | 13.7587 | 1.35569 | 0.677844 | − | 0.735206i | \(-0.262915\pi\) | ||||
0.677844 | + | 0.735206i | \(0.262915\pi\) | |||||||
\(104\) | 4.43188 | + | 3.34017i | 0.434582 | + | 0.327531i | ||||
\(105\) | 0.630898 | 0.0615693 | ||||||||
\(106\) | − | 13.0205i | − | 1.26466i | ||||||
\(107\) | −10.0989 | −0.976297 | −0.488149 | − | 0.872761i | \(-0.662328\pi\) | ||||
−0.488149 | + | 0.872761i | \(0.662328\pi\) | |||||||
\(108\) | −2.70928 | −0.260700 | ||||||||
\(109\) | − | 17.9421i | − | 1.71855i | −0.511518 | − | 0.859273i | \(-0.670917\pi\) | ||
0.511518 | − | 0.859273i | \(-0.329083\pi\) | |||||||
\(110\) | 7.81658i | 0.745282i | ||||||||
\(111\) | − | 3.41855i | − | 0.324474i | ||||||
\(112\) | − | 2.07838i | − | 0.196388i | ||||||
\(113\) | 10.6803 | 1.00472 | 0.502361 | − | 0.864658i | \(-0.332465\pi\) | ||||
0.502361 | + | 0.864658i | \(0.332465\pi\) | |||||||
\(114\) | 16.0989 | 1.50780 | ||||||||
\(115\) | − | 3.41855i | − | 0.318781i | ||||||
\(116\) | −18.0989 | −1.68044 | ||||||||
\(117\) | −2.17009 | + | 2.87936i | −0.200625 | + | 0.266197i | ||||
\(118\) | −2.97107 | −0.273509 | ||||||||
\(119\) | 1.07838i | 0.0988547i | ||||||||
\(120\) | −0.971071 | −0.0886462 | ||||||||
\(121\) | −21.5958 | −1.96326 | ||||||||
\(122\) | 27.4596i | 2.48607i | ||||||||
\(123\) | − | 1.21235i | − | 0.109314i | ||||||
\(124\) | 16.6803i | 1.49794i | ||||||||
\(125\) | − | 6.05786i | − | 0.541831i | ||||||
\(126\) | −2.17009 | −0.193327 | ||||||||
\(127\) | 6.34017 | 0.562599 | 0.281300 | − | 0.959620i | \(-0.409235\pi\) | ||||
0.281300 | + | 0.959620i | \(0.409235\pi\) | |||||||
\(128\) | 11.5392i | 1.01993i | ||||||||
\(129\) | −12.6803 | −1.11644 | ||||||||
\(130\) | −2.97107 | + | 3.94214i | −0.260580 | + | 0.345749i | ||||
\(131\) | −7.51745 | −0.656802 | −0.328401 | − | 0.944538i | \(-0.606510\pi\) | ||||
−0.328401 | + | 0.944538i | \(0.606510\pi\) | |||||||
\(132\) | − | 15.4680i | − | 1.34632i | ||||||
\(133\) | 7.41855 | 0.643270 | ||||||||
\(134\) | 1.26180 | 0.109003 | ||||||||
\(135\) | − | 0.630898i | − | 0.0542990i | ||||||
\(136\) | − | 1.65983i | − | 0.142329i | ||||||
\(137\) | 4.47414i | 0.382252i | 0.981566 | + | 0.191126i | \(0.0612139\pi\) | ||||
−0.981566 | + | 0.191126i | \(0.938786\pi\) | |||||||
\(138\) | 11.7587i | 1.00097i | ||||||||
\(139\) | −9.75872 | −0.827724 | −0.413862 | − | 0.910340i | \(-0.635820\pi\) | ||||
−0.413862 | + | 0.910340i | \(0.635820\pi\) | |||||||
\(140\) | −1.70928 | −0.144460 | ||||||||
\(141\) | − | 6.04945i | − | 0.509455i | ||||||
\(142\) | −10.4475 | −0.876733 | ||||||||
\(143\) | −16.4391 | − | 12.3896i | −1.37470 | − | 1.03607i | ||||
\(144\) | −2.07838 | −0.173198 | ||||||||
\(145\) | − | 4.21461i | − | 0.350005i | ||||||
\(146\) | −8.28231 | −0.685449 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 9.26180i | 0.761315i | ||||||||
\(149\) | − | 1.46800i | − | 0.120263i | −0.998190 | − | 0.0601316i | \(-0.980848\pi\) | ||
0.998190 | − | 0.0601316i | \(-0.0191520\pi\) | |||||||
\(150\) | 9.98667i | 0.815408i | ||||||||
\(151\) | 13.3607i | 1.08728i | 0.839319 | + | 0.543639i | \(0.182954\pi\) | ||||
−0.839319 | + | 0.543639i | \(0.817046\pi\) | |||||||
\(152\) | −11.4186 | −0.926167 | ||||||||
\(153\) | 1.07838 | 0.0871817 | ||||||||
\(154\) | − | 12.3896i | − | 0.998384i | ||||||
\(155\) | −3.88428 | −0.311993 | ||||||||
\(156\) | 5.87936 | − | 7.80098i | 0.470726 | − | 0.624579i | ||||
\(157\) | −8.15676 | −0.650980 | −0.325490 | − | 0.945545i | \(-0.605529\pi\) | ||||
−0.325490 | + | 0.945545i | \(0.605529\pi\) | |||||||
\(158\) | − | 3.60197i | − | 0.286557i | ||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | −4.78765 | −0.378497 | ||||||||
\(161\) | 5.41855i | 0.427042i | ||||||||
\(162\) | 2.17009i | 0.170498i | ||||||||
\(163\) | 4.58145i | 0.358847i | 0.983772 | + | 0.179423i | \(0.0574232\pi\) | ||||
−0.983772 | + | 0.179423i | \(0.942577\pi\) | |||||||
\(164\) | 3.28458i | 0.256483i | ||||||||
\(165\) | 3.60197 | 0.280413 | ||||||||
\(166\) | −27.9649 | −2.17050 | ||||||||
\(167\) | 7.31124i | 0.565761i | 0.959155 | + | 0.282881i | \(0.0912900\pi\) | ||||
−0.959155 | + | 0.282881i | \(0.908710\pi\) | |||||||
\(168\) | 1.53919 | 0.118751 | ||||||||
\(169\) | −3.58145 | − | 12.4969i | −0.275496 | − | 0.961302i | ||||
\(170\) | 1.47641 | 0.113235 | ||||||||
\(171\) | − | 7.41855i | − | 0.567311i | ||||||
\(172\) | 34.3545 | 2.61951 | ||||||||
\(173\) | 7.60197 | 0.577967 | 0.288983 | − | 0.957334i | \(-0.406683\pi\) | ||||
0.288983 | + | 0.957334i | \(0.406683\pi\) | |||||||
\(174\) | 14.4969i | 1.09901i | ||||||||
\(175\) | 4.60197i | 0.347876i | ||||||||
\(176\) | − | 11.8660i | − | 0.894436i | ||||||
\(177\) | 1.36910i | 0.102908i | ||||||||
\(178\) | 13.4680 | 1.00947 | ||||||||
\(179\) | 9.10504 | 0.680543 | 0.340271 | − | 0.940327i | \(-0.389481\pi\) | ||||
0.340271 | + | 0.940327i | \(0.389481\pi\) | |||||||
\(180\) | 1.70928i | 0.127402i | ||||||||
\(181\) | 15.3607 | 1.14175 | 0.570876 | − | 0.821037i | \(-0.306604\pi\) | ||||
0.570876 | + | 0.821037i | \(0.306604\pi\) | |||||||
\(182\) | 4.70928 | − | 6.24846i | 0.349075 | − | 0.463167i | ||||
\(183\) | 12.6537 | 0.935387 | ||||||||
\(184\) | − | 8.34017i | − | 0.614846i | ||||||
\(185\) | −2.15676 | −0.158568 | ||||||||
\(186\) | 13.3607 | 0.979653 | ||||||||
\(187\) | 6.15676i | 0.450227i | ||||||||
\(188\) | 16.3896i | 1.19534i | ||||||||
\(189\) | 1.00000i | 0.0727393i | ||||||||
\(190\) | − | 10.1568i | − | 0.736848i | ||||||
\(191\) | −24.5692 | −1.77776 | −0.888881 | − | 0.458138i | \(-0.848517\pi\) | ||||
−0.888881 | + | 0.458138i | \(0.848517\pi\) | |||||||
\(192\) | 12.3112 | 0.888487 | ||||||||
\(193\) | 13.5753i | 0.977172i | 0.872516 | + | 0.488586i | \(0.162487\pi\) | ||||
−0.872516 | + | 0.488586i | \(0.837513\pi\) | |||||||
\(194\) | −2.34017 | −0.168015 | ||||||||
\(195\) | 1.81658 | + | 1.36910i | 0.130088 | + | 0.0980435i | ||||
\(196\) | 2.70928 | 0.193520 | ||||||||
\(197\) | 2.94441i | 0.209780i | 0.994484 | + | 0.104890i | \(0.0334491\pi\) | ||||
−0.994484 | + | 0.104890i | \(0.966551\pi\) | |||||||
\(198\) | −12.3896 | −0.880492 | ||||||||
\(199\) | −10.5236 | −0.745998 | −0.372999 | − | 0.927832i | \(-0.621670\pi\) | ||||
−0.372999 | + | 0.927832i | \(0.621670\pi\) | |||||||
\(200\) | − | 7.08330i | − | 0.500865i | ||||||
\(201\) | − | 0.581449i | − | 0.0410123i | ||||||
\(202\) | − | 15.7009i | − | 1.10471i | ||||||
\(203\) | 6.68035i | 0.468868i | ||||||||
\(204\) | −2.92162 | −0.204554 | ||||||||
\(205\) | −0.764867 | −0.0534206 | ||||||||
\(206\) | 29.8576i | 2.08028i | ||||||||
\(207\) | 5.41855 | 0.376615 | ||||||||
\(208\) | 4.51026 | − | 5.98440i | 0.312730 | − | 0.414944i | ||||
\(209\) | 42.3545 | 2.92973 | ||||||||
\(210\) | 1.36910i | 0.0944770i | ||||||||
\(211\) | −3.02052 | −0.207941 | −0.103971 | − | 0.994580i | \(-0.533155\pi\) | ||||
−0.103971 | + | 0.994580i | \(0.533155\pi\) | |||||||
\(212\) | 16.2557 | 1.11644 | ||||||||
\(213\) | 4.81432i | 0.329871i | ||||||||
\(214\) | − | 21.9155i | − | 1.49811i | ||||||
\(215\) | 8.00000i | 0.545595i | ||||||||
\(216\) | − | 1.53919i | − | 0.104729i | ||||||
\(217\) | 6.15676 | 0.417948 | ||||||||
\(218\) | 38.9360 | 2.63708 | ||||||||
\(219\) | 3.81658i | 0.257901i | ||||||||
\(220\) | −9.75872 | −0.657933 | ||||||||
\(221\) | −2.34017 | + | 3.10504i | −0.157417 | + | 0.208868i | ||||
\(222\) | 7.41855 | 0.497901 | ||||||||
\(223\) | − | 22.6225i | − | 1.51491i | −0.652885 | − | 0.757457i | \(-0.726442\pi\) | ||
0.652885 | − | 0.757457i | \(-0.273558\pi\) | |||||||
\(224\) | 7.58864 | 0.507037 | ||||||||
\(225\) | 4.60197 | 0.306798 | ||||||||
\(226\) | 23.1773i | 1.54173i | ||||||||
\(227\) | 22.9444i | 1.52287i | 0.648239 | + | 0.761437i | \(0.275506\pi\) | ||||
−0.648239 | + | 0.761437i | \(0.724494\pi\) | |||||||
\(228\) | 20.0989i | 1.33108i | ||||||||
\(229\) | − | 21.5441i | − | 1.42367i | −0.702344 | − | 0.711837i | \(-0.747863\pi\) | ||
0.702344 | − | 0.711837i | \(-0.252137\pi\) | |||||||
\(230\) | 7.41855 | 0.489165 | ||||||||
\(231\) | −5.70928 | −0.375643 | ||||||||
\(232\) | − | 10.2823i | − | 0.675067i | ||||||
\(233\) | 7.36069 | 0.482215 | 0.241107 | − | 0.970498i | \(-0.422489\pi\) | ||||
0.241107 | + | 0.970498i | \(0.422489\pi\) | |||||||
\(234\) | −6.24846 | − | 4.70928i | −0.408475 | − | 0.307855i | ||||
\(235\) | −3.81658 | −0.248966 | ||||||||
\(236\) | − | 3.70928i | − | 0.241453i | ||||||
\(237\) | −1.65983 | −0.107817 | ||||||||
\(238\) | −2.34017 | −0.151691 | ||||||||
\(239\) | − | 15.5525i | − | 1.00601i | −0.864284 | − | 0.503004i | \(-0.832228\pi\) | ||
0.864284 | − | 0.503004i | \(-0.167772\pi\) | |||||||
\(240\) | 1.31124i | 0.0846404i | ||||||||
\(241\) | − | 7.33403i | − | 0.472426i | −0.971701 | − | 0.236213i | \(-0.924094\pi\) | ||
0.971701 | − | 0.236213i | \(-0.0759064\pi\) | |||||||
\(242\) | − | 46.8648i | − | 3.01258i | ||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −34.2823 | −2.19470 | ||||||||
\(245\) | 0.630898i | 0.0403066i | ||||||||
\(246\) | 2.63090 | 0.167740 | ||||||||
\(247\) | 21.3607 | + | 16.0989i | 1.35915 | + | 1.02435i | ||||
\(248\) | −9.47641 | −0.601753 | ||||||||
\(249\) | 12.8865i | 0.816652i | ||||||||
\(250\) | 13.1461 | 0.831431 | ||||||||
\(251\) | −13.6742 | −0.863108 | −0.431554 | − | 0.902087i | \(-0.642035\pi\) | ||||
−0.431554 | + | 0.902087i | \(0.642035\pi\) | |||||||
\(252\) | − | 2.70928i | − | 0.170668i | ||||||
\(253\) | 30.9360i | 1.94493i | ||||||||
\(254\) | 13.7587i | 0.863299i | ||||||||
\(255\) | − | 0.680346i | − | 0.0426049i | ||||||
\(256\) | −0.418551 | −0.0261594 | ||||||||
\(257\) | −26.1256 | −1.62967 | −0.814834 | − | 0.579695i | \(-0.803172\pi\) | ||||
−0.814834 | + | 0.579695i | \(0.803172\pi\) | |||||||
\(258\) | − | 27.5174i | − | 1.71316i | ||||||
\(259\) | 3.41855 | 0.212418 | ||||||||
\(260\) | −4.92162 | − | 3.70928i | −0.305226 | − | 0.230039i | ||||
\(261\) | 6.68035 | 0.413503 | ||||||||
\(262\) | − | 16.3135i | − | 1.00785i | ||||||
\(263\) | −30.7792 | −1.89793 | −0.948965 | − | 0.315382i | \(-0.897867\pi\) | ||||
−0.948965 | + | 0.315382i | \(0.897867\pi\) | |||||||
\(264\) | 8.78765 | 0.540843 | ||||||||
\(265\) | 3.78539i | 0.232534i | ||||||||
\(266\) | 16.0989i | 0.987087i | ||||||||
\(267\) | − | 6.20620i | − | 0.379814i | ||||||
\(268\) | 1.57531i | 0.0962271i | ||||||||
\(269\) | 5.39189 | 0.328749 | 0.164375 | − | 0.986398i | \(-0.447439\pi\) | ||||
0.164375 | + | 0.986398i | \(0.447439\pi\) | |||||||
\(270\) | 1.36910 | 0.0833209 | ||||||||
\(271\) | − | 11.4186i | − | 0.693628i | −0.937934 | − | 0.346814i | \(-0.887264\pi\) | ||
0.937934 | − | 0.346814i | \(-0.112736\pi\) | |||||||
\(272\) | −2.24128 | −0.135897 | ||||||||
\(273\) | −2.87936 | − | 2.17009i | −0.174267 | − | 0.131340i | ||||
\(274\) | −9.70928 | −0.586559 | ||||||||
\(275\) | 26.2739i | 1.58438i | ||||||||
\(276\) | −14.6803 | −0.883653 | ||||||||
\(277\) | 13.1506 | 0.790144 | 0.395072 | − | 0.918650i | \(-0.370720\pi\) | ||||
0.395072 | + | 0.918650i | \(0.370720\pi\) | |||||||
\(278\) | − | 21.1773i | − | 1.27013i | ||||||
\(279\) | − | 6.15676i | − | 0.368595i | ||||||
\(280\) | − | 0.971071i | − | 0.0580326i | ||||||
\(281\) | 2.14834i | 0.128160i | 0.997945 | + | 0.0640798i | \(0.0204112\pi\) | ||||
−0.997945 | + | 0.0640798i | \(0.979589\pi\) | |||||||
\(282\) | 13.1278 | 0.781751 | ||||||||
\(283\) | −12.1978 | −0.725084 | −0.362542 | − | 0.931968i | \(-0.618091\pi\) | ||||
−0.362542 | + | 0.931968i | \(0.618091\pi\) | |||||||
\(284\) | − | 13.0433i | − | 0.773978i | ||||||
\(285\) | −4.68035 | −0.277240 | ||||||||
\(286\) | 26.8865 | − | 35.6742i | 1.58984 | − | 2.10946i | ||||
\(287\) | 1.21235 | 0.0715626 | ||||||||
\(288\) | − | 7.58864i | − | 0.447165i | ||||||
\(289\) | −15.8371 | −0.931594 | ||||||||
\(290\) | 9.14608 | 0.537076 | ||||||||
\(291\) | 1.07838i | 0.0632156i | ||||||||
\(292\) | − | 10.3402i | − | 0.605113i | ||||||
\(293\) | − | 7.15449i | − | 0.417970i | −0.977919 | − | 0.208985i | \(-0.932984\pi\) | ||
0.977919 | − | 0.208985i | \(-0.0670159\pi\) | |||||||
\(294\) | − | 2.17009i | − | 0.126562i | ||||||
\(295\) | 0.863763 | 0.0502903 | ||||||||
\(296\) | −5.26180 | −0.305836 | ||||||||
\(297\) | 5.70928i | 0.331286i | ||||||||
\(298\) | 3.18568 | 0.184542 | ||||||||
\(299\) | −11.7587 | + | 15.6020i | −0.680025 | + | 0.902285i | ||||
\(300\) | −12.4680 | −0.719840 | ||||||||
\(301\) | − | 12.6803i | − | 0.730883i | ||||||
\(302\) | −28.9939 | −1.66841 | ||||||||
\(303\) | −7.23513 | −0.415648 | ||||||||
\(304\) | 15.4186i | 0.884315i | ||||||||
\(305\) | − | 7.98318i | − | 0.457116i | ||||||
\(306\) | 2.34017i | 0.133779i | ||||||||
\(307\) | 21.8432i | 1.24666i | 0.781959 | + | 0.623330i | \(0.214221\pi\) | ||||
−0.781959 | + | 0.623330i | \(0.785779\pi\) | |||||||
\(308\) | 15.4680 | 0.881371 | ||||||||
\(309\) | 13.7587 | 0.782706 | ||||||||
\(310\) | − | 8.42923i | − | 0.478748i | ||||||
\(311\) | −7.51745 | −0.426275 | −0.213138 | − | 0.977022i | \(-0.568368\pi\) | ||||
−0.213138 | + | 0.977022i | \(0.568368\pi\) | |||||||
\(312\) | 4.43188 | + | 3.34017i | 0.250906 | + | 0.189100i | ||||
\(313\) | 25.7009 | 1.45270 | 0.726349 | − | 0.687326i | \(-0.241215\pi\) | ||||
0.726349 | + | 0.687326i | \(0.241215\pi\) | |||||||
\(314\) | − | 17.7009i | − | 0.998918i | ||||||
\(315\) | 0.630898 | 0.0355471 | ||||||||
\(316\) | 4.49693 | 0.252972 | ||||||||
\(317\) | − | 9.36910i | − | 0.526221i | −0.964766 | − | 0.263111i | \(-0.915252\pi\) | ||
0.964766 | − | 0.263111i | \(-0.0847484\pi\) | |||||||
\(318\) | − | 13.0205i | − | 0.730154i | ||||||
\(319\) | 38.1399i | 2.13543i | ||||||||
\(320\) | − | 7.76713i | − | 0.434196i | ||||||
\(321\) | −10.0989 | −0.563665 | ||||||||
\(322\) | −11.7587 | −0.655288 | ||||||||
\(323\) | − | 8.00000i | − | 0.445132i | ||||||
\(324\) | −2.70928 | −0.150515 | ||||||||
\(325\) | −9.98667 | + | 13.2507i | −0.553961 | + | 0.735018i | ||||
\(326\) | −9.94214 | −0.550644 | ||||||||
\(327\) | − | 17.9421i | − | 0.992203i | ||||||
\(328\) | −1.86603 | −0.103034 | ||||||||
\(329\) | 6.04945 | 0.333517 | ||||||||
\(330\) | 7.81658i | 0.430289i | ||||||||
\(331\) | − | 21.0472i | − | 1.15686i | −0.815733 | − | 0.578429i | \(-0.803666\pi\) | ||
0.815733 | − | 0.578429i | \(-0.196334\pi\) | |||||||
\(332\) | − | 34.9132i | − | 1.91611i | ||||||
\(333\) | − | 3.41855i | − | 0.187335i | ||||||
\(334\) | −15.8660 | −0.868151 | ||||||||
\(335\) | −0.366835 | −0.0200423 | ||||||||
\(336\) | − | 2.07838i | − | 0.113385i | ||||||
\(337\) | 15.4452 | 0.841354 | 0.420677 | − | 0.907210i | \(-0.361793\pi\) | ||||
0.420677 | + | 0.907210i | \(0.361793\pi\) | |||||||
\(338\) | 27.1194 | − | 7.77205i | 1.47510 | − | 0.422744i | ||||
\(339\) | 10.6803 | 0.580077 | ||||||||
\(340\) | 1.84324i | 0.0999640i | ||||||||
\(341\) | 35.1506 | 1.90351 | ||||||||
\(342\) | 16.0989 | 0.870529 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 19.5174i | 1.05231i | ||||||||
\(345\) | − | 3.41855i | − | 0.184049i | ||||||
\(346\) | 16.4969i | 0.886880i | ||||||||
\(347\) | 21.7321 | 1.16664 | 0.583319 | − | 0.812243i | \(-0.301754\pi\) | ||||
0.583319 | + | 0.812243i | \(0.301754\pi\) | |||||||
\(348\) | −18.0989 | −0.970203 | ||||||||
\(349\) | 5.65983i | 0.302964i | 0.988460 | + | 0.151482i | \(0.0484045\pi\) | ||||
−0.988460 | + | 0.151482i | \(0.951596\pi\) | |||||||
\(350\) | −9.98667 | −0.533810 | ||||||||
\(351\) | −2.17009 | + | 2.87936i | −0.115831 | + | 0.153689i | ||||
\(352\) | 43.3256 | 2.30926 | ||||||||
\(353\) | − | 33.7237i | − | 1.79493i | −0.441087 | − | 0.897464i | \(-0.645407\pi\) | ||
0.441087 | − | 0.897464i | \(-0.354593\pi\) | |||||||
\(354\) | −2.97107 | −0.157911 | ||||||||
\(355\) | 3.03734 | 0.161205 | ||||||||
\(356\) | 16.8143i | 0.891157i | ||||||||
\(357\) | 1.07838i | 0.0570738i | ||||||||
\(358\) | 19.7587i | 1.04428i | ||||||||
\(359\) | 18.7031i | 0.987114i | 0.869714 | + | 0.493557i | \(0.164303\pi\) | ||||
−0.869714 | + | 0.493557i | \(0.835697\pi\) | |||||||
\(360\) | −0.971071 | −0.0511799 | ||||||||
\(361\) | −36.0349 | −1.89657 | ||||||||
\(362\) | 33.3340i | 1.75200i | ||||||||
\(363\) | −21.5958 | −1.13349 | ||||||||
\(364\) | 7.80098 | + | 5.87936i | 0.408883 | + | 0.308162i | ||||
\(365\) | 2.40787 | 0.126034 | ||||||||
\(366\) | 27.4596i | 1.43534i | ||||||||
\(367\) | 10.0722 | 0.525766 | 0.262883 | − | 0.964828i | \(-0.415327\pi\) | ||||
0.262883 | + | 0.964828i | \(0.415327\pi\) | |||||||
\(368\) | −11.2618 | −0.587062 | ||||||||
\(369\) | − | 1.21235i | − | 0.0631123i | ||||||
\(370\) | − | 4.68035i | − | 0.243320i | ||||||
\(371\) | − | 6.00000i | − | 0.311504i | ||||||
\(372\) | 16.6803i | 0.864836i | ||||||||
\(373\) | 4.24128 | 0.219605 | 0.109802 | − | 0.993953i | \(-0.464978\pi\) | ||||
0.109802 | + | 0.993953i | \(0.464978\pi\) | |||||||
\(374\) | −13.3607 | −0.690865 | ||||||||
\(375\) | − | 6.05786i | − | 0.312826i | ||||||
\(376\) | −9.31124 | −0.480191 | ||||||||
\(377\) | −14.4969 | + | 19.2351i | −0.746630 | + | 0.990660i | ||||
\(378\) | −2.17009 | −0.111617 | ||||||||
\(379\) | 20.1978i | 1.03749i | 0.854929 | + | 0.518745i | \(0.173601\pi\) | ||||
−0.854929 | + | 0.518745i | \(0.826399\pi\) | |||||||
\(380\) | 12.6803 | 0.650488 | ||||||||
\(381\) | 6.34017 | 0.324817 | ||||||||
\(382\) | − | 53.3172i | − | 2.72795i | ||||||
\(383\) | − | 7.04331i | − | 0.359896i | −0.983676 | − | 0.179948i | \(-0.942407\pi\) | ||
0.983676 | − | 0.179948i | \(-0.0575930\pi\) | |||||||
\(384\) | 11.5392i | 0.588857i | ||||||||
\(385\) | 3.60197i | 0.183573i | ||||||||
\(386\) | −29.4596 | −1.49945 | ||||||||
\(387\) | −12.6803 | −0.644578 | ||||||||
\(388\) | − | 2.92162i | − | 0.148323i | ||||||
\(389\) | −3.84324 | −0.194860 | −0.0974301 | − | 0.995242i | \(-0.531062\pi\) | ||||
−0.0974301 | + | 0.995242i | \(0.531062\pi\) | |||||||
\(390\) | −2.97107 | + | 3.94214i | −0.150446 | + | 0.199618i | ||||
\(391\) | 5.84324 | 0.295506 | ||||||||
\(392\) | 1.53919i | 0.0777408i | ||||||||
\(393\) | −7.51745 | −0.379205 | ||||||||
\(394\) | −6.38962 | −0.321904 | ||||||||
\(395\) | 1.04718i | 0.0526894i | ||||||||
\(396\) | − | 15.4680i | − | 0.777296i | ||||||
\(397\) | 14.4391i | 0.724676i | 0.932047 | + | 0.362338i | \(0.118021\pi\) | ||||
−0.932047 | + | 0.362338i | \(0.881979\pi\) | |||||||
\(398\) | − | 22.8371i | − | 1.14472i | ||||||
\(399\) | 7.41855 | 0.371392 | ||||||||
\(400\) | −9.56463 | −0.478231 | ||||||||
\(401\) | − | 9.83483i | − | 0.491128i | −0.969380 | − | 0.245564i | \(-0.921027\pi\) | ||
0.969380 | − | 0.245564i | \(-0.0789732\pi\) | |||||||
\(402\) | 1.26180 | 0.0629326 | ||||||||
\(403\) | 17.7275 | + | 13.3607i | 0.883071 | + | 0.665543i | ||||
\(404\) | 19.6020 | 0.975234 | ||||||||
\(405\) | − | 0.630898i | − | 0.0313496i | ||||||
\(406\) | −14.4969 | −0.719470 | ||||||||
\(407\) | 19.5174 | 0.967444 | ||||||||
\(408\) | − | 1.65983i | − | 0.0821737i | ||||||
\(409\) | − | 7.54864i | − | 0.373256i | −0.982431 | − | 0.186628i | \(-0.940244\pi\) | ||
0.982431 | − | 0.186628i | \(-0.0597560\pi\) | |||||||
\(410\) | − | 1.65983i | − | 0.0819730i | ||||||
\(411\) | 4.47414i | 0.220693i | ||||||||
\(412\) | −37.2762 | −1.83647 | ||||||||
\(413\) | −1.36910 | −0.0673691 | ||||||||
\(414\) | 11.7587i | 0.577910i | ||||||||
\(415\) | 8.13009 | 0.399091 | ||||||||
\(416\) | 21.8504 | + | 16.4680i | 1.07131 | + | 0.807410i | ||||
\(417\) | −9.75872 | −0.477887 | ||||||||
\(418\) | 91.9130i | 4.49561i | ||||||||
\(419\) | −35.1506 | −1.71722 | −0.858610 | − | 0.512630i | \(-0.828671\pi\) | ||||
−0.858610 | + | 0.512630i | \(0.828671\pi\) | |||||||
\(420\) | −1.70928 | −0.0834041 | ||||||||
\(421\) | 25.6742i | 1.25128i | 0.780110 | + | 0.625642i | \(0.215163\pi\) | ||||
−0.780110 | + | 0.625642i | \(0.784837\pi\) | |||||||
\(422\) | − | 6.55479i | − | 0.319082i | ||||||
\(423\) | − | 6.04945i | − | 0.294134i | ||||||
\(424\) | 9.23513i | 0.448498i | ||||||||
\(425\) | 4.96266 | 0.240724 | ||||||||
\(426\) | −10.4475 | −0.506182 | ||||||||
\(427\) | 12.6537i | 0.612355i | ||||||||
\(428\) | 27.3607 | 1.32253 | ||||||||
\(429\) | −16.4391 | − | 12.3896i | −0.793686 | − | 0.598177i | ||||
\(430\) | −17.3607 | −0.837207 | ||||||||
\(431\) | 16.2329i | 0.781910i | 0.920410 | + | 0.390955i | \(0.127855\pi\) | ||||
−0.920410 | + | 0.390955i | \(0.872145\pi\) | |||||||
\(432\) | −2.07838 | −0.0999960 | ||||||||
\(433\) | −5.38735 | −0.258900 | −0.129450 | − | 0.991586i | \(-0.541321\pi\) | ||||
−0.129450 | + | 0.991586i | \(0.541321\pi\) | |||||||
\(434\) | 13.3607i | 0.641334i | ||||||||
\(435\) | − | 4.21461i | − | 0.202075i | ||||||
\(436\) | 48.6102i | 2.32801i | ||||||||
\(437\) | − | 40.1978i | − | 1.92292i | ||||||
\(438\) | −8.28231 | −0.395744 | ||||||||
\(439\) | −10.2413 | −0.488789 | −0.244395 | − | 0.969676i | \(-0.578589\pi\) | ||||
−0.244395 | + | 0.969676i | \(0.578589\pi\) | |||||||
\(440\) | − | 5.54411i | − | 0.264305i | ||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | −6.73820 | − | 5.07838i | −0.320504 | − | 0.241554i | ||||
\(443\) | 15.9421 | 0.757434 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(444\) | 9.26180i | 0.439545i | ||||||||
\(445\) | −3.91548 | −0.185612 | ||||||||
\(446\) | 49.0928 | 2.32461 | ||||||||
\(447\) | − | 1.46800i | − | 0.0694340i | ||||||
\(448\) | 12.3112i | 0.581652i | ||||||||
\(449\) | 13.2001i | 0.622949i | 0.950254 | + | 0.311475i | \(0.100823\pi\) | ||||
−0.950254 | + | 0.311475i | \(0.899177\pi\) | |||||||
\(450\) | 9.98667i | 0.470776i | ||||||||
\(451\) | 6.92162 | 0.325926 | ||||||||
\(452\) | −28.9360 | −1.36103 | ||||||||
\(453\) | 13.3607i | 0.627740i | ||||||||
\(454\) | −49.7914 | −2.33682 | ||||||||
\(455\) | −1.36910 | + | 1.81658i | −0.0641845 | + | 0.0851627i | ||||
\(456\) | −11.4186 | −0.534723 | ||||||||
\(457\) | − | 18.3090i | − | 0.856458i | −0.903670 | − | 0.428229i | \(-0.859138\pi\) | ||
0.903670 | − | 0.428229i | \(-0.140862\pi\) | |||||||
\(458\) | 46.7526 | 2.18460 | ||||||||
\(459\) | 1.07838 | 0.0503344 | ||||||||
\(460\) | 9.26180i | 0.431833i | ||||||||
\(461\) | 18.9399i | 0.882118i | 0.897478 | + | 0.441059i | \(0.145397\pi\) | ||||
−0.897478 | + | 0.441059i | \(0.854603\pi\) | |||||||
\(462\) | − | 12.3896i | − | 0.576417i | ||||||
\(463\) | 1.74435i | 0.0810667i | 0.999178 | + | 0.0405334i | \(0.0129057\pi\) | ||||
−0.999178 | + | 0.0405334i | \(0.987094\pi\) | |||||||
\(464\) | −13.8843 | −0.644562 | ||||||||
\(465\) | −3.88428 | −0.180129 | ||||||||
\(466\) | 15.9733i | 0.739951i | ||||||||
\(467\) | −18.1568 | −0.840194 | −0.420097 | − | 0.907479i | \(-0.638004\pi\) | ||||
−0.420097 | + | 0.907479i | \(0.638004\pi\) | |||||||
\(468\) | 5.87936 | − | 7.80098i | 0.271774 | − | 0.360601i | ||||
\(469\) | 0.581449 | 0.0268488 | ||||||||
\(470\) | − | 8.28231i | − | 0.382035i | ||||||
\(471\) | −8.15676 | −0.375843 | ||||||||
\(472\) | 2.10731 | 0.0969967 | ||||||||
\(473\) | − | 72.3956i | − | 3.32875i | ||||||
\(474\) | − | 3.60197i | − | 0.165444i | ||||||
\(475\) | − | 34.1399i | − | 1.56645i | ||||||
\(476\) | − | 2.92162i | − | 0.133912i | ||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 33.7503 | 1.54370 | ||||||||
\(479\) | − | 30.4619i | − | 1.39184i | −0.718120 | − | 0.695919i | \(-0.754997\pi\) | ||
0.718120 | − | 0.695919i | \(-0.245003\pi\) | |||||||
\(480\) | −4.78765 | −0.218525 | ||||||||
\(481\) | 9.84324 | + | 7.41855i | 0.448813 | + | 0.338257i | ||||
\(482\) | 15.9155 | 0.724930 | ||||||||
\(483\) | 5.41855i | 0.246553i | ||||||||
\(484\) | 58.5090 | 2.65950 | ||||||||
\(485\) | 0.680346 | 0.0308929 | ||||||||
\(486\) | 2.17009i | 0.0984371i | ||||||||
\(487\) | 0.313511i | 0.0142065i | 0.999975 | + | 0.00710327i | \(0.00226106\pi\) | ||||
−0.999975 | + | 0.00710327i | \(0.997739\pi\) | |||||||
\(488\) | − | 19.4764i | − | 0.881656i | ||||||
\(489\) | 4.58145i | 0.207180i | ||||||||
\(490\) | −1.36910 | −0.0618497 | ||||||||
\(491\) | −8.93600 | −0.403276 | −0.201638 | − | 0.979460i | \(-0.564626\pi\) | ||||
−0.201638 | + | 0.979460i | \(0.564626\pi\) | |||||||
\(492\) | 3.28458i | 0.148080i | ||||||||
\(493\) | 7.20394 | 0.324449 | ||||||||
\(494\) | −34.9360 | + | 46.3545i | −1.57184 | + | 2.08559i | ||||
\(495\) | 3.60197 | 0.161896 | ||||||||
\(496\) | 12.7961i | 0.574560i | ||||||||
\(497\) | −4.81432 | −0.215952 | ||||||||
\(498\) | −27.9649 | −1.25314 | ||||||||
\(499\) | − | 33.9877i | − | 1.52150i | −0.649046 | − | 0.760750i | \(-0.724832\pi\) | ||
0.649046 | − | 0.760750i | \(-0.275168\pi\) | |||||||
\(500\) | 16.4124i | 0.733985i | ||||||||
\(501\) | 7.31124i | 0.326642i | ||||||||
\(502\) | − | 29.6742i | − | 1.32442i | ||||||
\(503\) | 33.5585 | 1.49630 | 0.748149 | − | 0.663530i | \(-0.230943\pi\) | ||||
0.748149 | + | 0.663530i | \(0.230943\pi\) | |||||||
\(504\) | 1.53919 | 0.0685609 | ||||||||
\(505\) | 4.56463i | 0.203123i | ||||||||
\(506\) | −67.1338 | −2.98446 | ||||||||
\(507\) | −3.58145 | − | 12.4969i | −0.159058 | − | 0.555008i | ||||
\(508\) | −17.1773 | −0.762118 | ||||||||
\(509\) | − | 24.8287i | − | 1.10051i | −0.834996 | − | 0.550256i | \(-0.814530\pi\) | ||
0.834996 | − | 0.550256i | \(-0.185470\pi\) | |||||||
\(510\) | 1.47641 | 0.0653765 | ||||||||
\(511\) | −3.81658 | −0.168836 | ||||||||
\(512\) | 22.1701i | 0.979789i | ||||||||
\(513\) | − | 7.41855i | − | 0.327537i | ||||||
\(514\) | − | 56.6947i | − | 2.50070i | ||||||
\(515\) | − | 8.68035i | − | 0.382502i | ||||||
\(516\) | 34.3545 | 1.51237 | ||||||||
\(517\) | 34.5380 | 1.51898 | ||||||||
\(518\) | 7.41855i | 0.325952i | ||||||||
\(519\) | 7.60197 | 0.333689 | ||||||||
\(520\) | 2.10731 | − | 2.79606i | 0.0924115 | − | 0.122616i | ||||
\(521\) | 20.2290 | 0.886248 | 0.443124 | − | 0.896460i | \(-0.353870\pi\) | ||||
0.443124 | + | 0.896460i | \(0.353870\pi\) | |||||||
\(522\) | 14.4969i | 0.634513i | ||||||||
\(523\) | −40.1666 | −1.75636 | −0.878181 | − | 0.478328i | \(-0.841243\pi\) | ||||
−0.878181 | + | 0.478328i | \(0.841243\pi\) | |||||||
\(524\) | 20.3668 | 0.889729 | ||||||||
\(525\) | 4.60197i | 0.200846i | ||||||||
\(526\) | − | 66.7936i | − | 2.91234i | ||||||
\(527\) | − | 6.63931i | − | 0.289213i | ||||||
\(528\) | − | 11.8660i | − | 0.516403i | ||||||
\(529\) | 6.36069 | 0.276552 | ||||||||
\(530\) | −8.21461 | −0.356820 | ||||||||
\(531\) | 1.36910i | 0.0594140i | ||||||||
\(532\) | −20.0989 | −0.871398 | ||||||||
\(533\) | 3.49079 | + | 2.63090i | 0.151203 | + | 0.113957i | ||||
\(534\) | 13.4680 | 0.582817 | ||||||||
\(535\) | 6.37137i | 0.275458i | ||||||||
\(536\) | −0.894960 | −0.0386564 | ||||||||
\(537\) | 9.10504 | 0.392911 | ||||||||
\(538\) | 11.7009i | 0.504460i | ||||||||
\(539\) | − | 5.70928i | − | 0.245916i | ||||||
\(540\) | 1.70928i | 0.0735555i | ||||||||
\(541\) | 18.2101i | 0.782912i | 0.920197 | + | 0.391456i | \(0.128029\pi\) | ||||
−0.920197 | + | 0.391456i | \(0.871971\pi\) | |||||||
\(542\) | 24.7792 | 1.06436 | ||||||||
\(543\) | 15.3607 | 0.659190 | ||||||||
\(544\) | − | 8.18342i | − | 0.350861i | ||||||
\(545\) | −11.3197 | −0.484881 | ||||||||
\(546\) | 4.70928 | − | 6.24846i | 0.201538 | − | 0.267410i | ||||
\(547\) | −6.32580 | −0.270472 | −0.135236 | − | 0.990813i | \(-0.543179\pi\) | ||||
−0.135236 | + | 0.990813i | \(0.543179\pi\) | |||||||
\(548\) | − | 12.1217i | − | 0.517813i | ||||||
\(549\) | 12.6537 | 0.540046 | ||||||||
\(550\) | −57.0166 | −2.43120 | ||||||||
\(551\) | − | 49.5585i | − | 2.11126i | ||||||
\(552\) | − | 8.34017i | − | 0.354981i | ||||||
\(553\) | − | 1.65983i | − | 0.0705830i | ||||||
\(554\) | 28.5380i | 1.21246i | ||||||||
\(555\) | −2.15676 | −0.0915492 | ||||||||
\(556\) | 26.4391 | 1.12127 | ||||||||
\(557\) | 10.6309i | 0.450446i | 0.974307 | + | 0.225223i | \(0.0723110\pi\) | ||||
−0.974307 | + | 0.225223i | \(0.927689\pi\) | |||||||
\(558\) | 13.3607 | 0.565603 | ||||||||
\(559\) | 27.5174 | − | 36.5113i | 1.16386 | − | 1.54426i | ||||
\(560\) | −1.31124 | −0.0554102 | ||||||||
\(561\) | 6.15676i | 0.259938i | ||||||||
\(562\) | −4.66209 | −0.196659 | ||||||||
\(563\) | −37.0472 | −1.56135 | −0.780676 | − | 0.624936i | \(-0.785125\pi\) | ||||
−0.780676 | + | 0.624936i | \(0.785125\pi\) | |||||||
\(564\) | 16.3896i | 0.690128i | ||||||||
\(565\) | − | 6.73820i | − | 0.283478i | ||||||
\(566\) | − | 26.4703i | − | 1.11263i | ||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 7.41014 | 0.310923 | ||||||||
\(569\) | 25.7152 | 1.07804 | 0.539019 | − | 0.842293i | \(-0.318795\pi\) | ||||
0.539019 | + | 0.842293i | \(0.318795\pi\) | |||||||
\(570\) | − | 10.1568i | − | 0.425420i | ||||||
\(571\) | −12.4969 | −0.522980 | −0.261490 | − | 0.965206i | \(-0.584214\pi\) | ||||
−0.261490 | + | 0.965206i | \(0.584214\pi\) | |||||||
\(572\) | 44.5380 | + | 33.5669i | 1.86223 | + | 1.40350i | ||||
\(573\) | −24.5692 | −1.02639 | ||||||||
\(574\) | 2.63090i | 0.109812i | ||||||||
\(575\) | 24.9360 | 1.03990 | ||||||||
\(576\) | 12.3112 | 0.512968 | ||||||||
\(577\) | 3.91548i | 0.163004i | 0.996673 | + | 0.0815018i | \(0.0259716\pi\) | ||||
−0.996673 | + | 0.0815018i | \(0.974028\pi\) | |||||||
\(578\) | − | 34.3679i | − | 1.42952i | ||||||
\(579\) | 13.5753i | 0.564170i | ||||||||
\(580\) | 11.4186i | 0.474130i | ||||||||
\(581\) | −12.8865 | −0.534624 | ||||||||
\(582\) | −2.34017 | −0.0970033 | ||||||||
\(583\) | − | 34.2557i | − | 1.41872i | ||||||
\(584\) | 5.87444 | 0.243086 | ||||||||
\(585\) | 1.81658 | + | 1.36910i | 0.0751064 | + | 0.0566054i | ||||
\(586\) | 15.5259 | 0.641367 | ||||||||
\(587\) | − | 6.94441i | − | 0.286626i | −0.989677 | − | 0.143313i | \(-0.954224\pi\) | ||
0.989677 | − | 0.143313i | \(-0.0457756\pi\) | |||||||
\(588\) | 2.70928 | 0.111729 | ||||||||
\(589\) | −45.6742 | −1.88197 | ||||||||
\(590\) | 1.87444i | 0.0771695i | ||||||||
\(591\) | 2.94441i | 0.121117i | ||||||||
\(592\) | 7.10504i | 0.292015i | ||||||||
\(593\) | 29.9383i | 1.22942i | 0.788754 | + | 0.614709i | \(0.210726\pi\) | ||||
−0.788754 | + | 0.614709i | \(0.789274\pi\) | |||||||
\(594\) | −12.3896 | −0.508352 | ||||||||
\(595\) | 0.680346 | 0.0278915 | ||||||||
\(596\) | 3.97721i | 0.162913i | ||||||||
\(597\) | −10.5236 | −0.430702 | ||||||||
\(598\) | −33.8576 | − | 25.5174i | −1.38454 | − | 1.04349i | ||||
\(599\) | 43.2905 | 1.76880 | 0.884402 | − | 0.466726i | \(-0.154567\pi\) | ||||
0.884402 | + | 0.466726i | \(0.154567\pi\) | |||||||
\(600\) | − | 7.08330i | − | 0.289174i | ||||||
\(601\) | −31.2306 | −1.27392 | −0.636961 | − | 0.770896i | \(-0.719809\pi\) | ||||
−0.636961 | + | 0.770896i | \(0.719809\pi\) | |||||||
\(602\) | 27.5174 | 1.12153 | ||||||||
\(603\) | − | 0.581449i | − | 0.0236784i | ||||||
\(604\) | − | 36.1978i | − | 1.47287i | ||||||
\(605\) | 13.6248i | 0.553925i | ||||||||
\(606\) | − | 15.7009i | − | 0.637804i | ||||||
\(607\) | 4.96266 | 0.201428 | 0.100714 | − | 0.994915i | \(-0.467887\pi\) | ||||
0.100714 | + | 0.994915i | \(0.467887\pi\) | |||||||
\(608\) | −56.2967 | −2.28313 | ||||||||
\(609\) | 6.68035i | 0.270701i | ||||||||
\(610\) | 17.3242 | 0.701436 | ||||||||
\(611\) | 17.4186 | + | 13.1278i | 0.704679 | + | 0.531095i | ||||
\(612\) | −2.92162 | −0.118100 | ||||||||
\(613\) | 0.366835i | 0.0148163i | 0.999973 | + | 0.00740816i | \(0.00235811\pi\) | ||||
−0.999973 | + | 0.00740816i | \(0.997642\pi\) | |||||||
\(614\) | −47.4017 | −1.91298 | ||||||||
\(615\) | −0.764867 | −0.0308424 | ||||||||
\(616\) | 8.78765i | 0.354065i | ||||||||
\(617\) | 47.7237i | 1.92128i | 0.277793 | + | 0.960641i | \(0.410397\pi\) | ||||
−0.277793 | + | 0.960641i | \(0.589603\pi\) | |||||||
\(618\) | 29.8576i | 1.20105i | ||||||||
\(619\) | 19.7854i | 0.795242i | 0.917550 | + | 0.397621i | \(0.130164\pi\) | ||||
−0.917550 | + | 0.397621i | \(0.869836\pi\) | |||||||
\(620\) | 10.5236 | 0.422638 | ||||||||
\(621\) | 5.41855 | 0.217439 | ||||||||
\(622\) | − | 16.3135i | − | 0.654112i | ||||||
\(623\) | 6.20620 | 0.248646 | ||||||||
\(624\) | 4.51026 | − | 5.98440i | 0.180555 | − | 0.239568i | ||||
\(625\) | 19.1880 | 0.767518 | ||||||||
\(626\) | 55.7731i | 2.22914i | ||||||||
\(627\) | 42.3545 | 1.69148 | ||||||||
\(628\) | 22.0989 | 0.881842 | ||||||||
\(629\) | − | 3.68649i | − | 0.146990i | ||||||
\(630\) | 1.36910i | 0.0545463i | ||||||||
\(631\) | − | 20.1522i | − | 0.802247i | −0.916024 | − | 0.401124i | \(-0.868620\pi\) | ||
0.916024 | − | 0.401124i | \(-0.131380\pi\) | |||||||
\(632\) | 2.55479i | 0.101624i | ||||||||
\(633\) | −3.02052 | −0.120055 | ||||||||
\(634\) | 20.3318 | 0.807477 | ||||||||
\(635\) | − | 4.00000i | − | 0.158735i | ||||||
\(636\) | 16.2557 | 0.644579 | ||||||||
\(637\) | 2.17009 | − | 2.87936i | 0.0859820 | − | 0.114084i | ||||
\(638\) | −82.7670 | −3.27678 | ||||||||
\(639\) | 4.81432i | 0.190451i | ||||||||
\(640\) | 7.28005 | 0.287769 | ||||||||
\(641\) | −12.1034 | −0.478057 | −0.239028 | − | 0.971013i | \(-0.576829\pi\) | ||||
−0.239028 | + | 0.971013i | \(0.576829\pi\) | |||||||
\(642\) | − | 21.9155i | − | 0.864935i | ||||||
\(643\) | − | 20.6803i | − | 0.815553i | −0.913082 | − | 0.407777i | \(-0.866304\pi\) | ||
0.913082 | − | 0.407777i | \(-0.133696\pi\) | |||||||
\(644\) | − | 14.6803i | − | 0.578487i | ||||||
\(645\) | 8.00000i | 0.315000i | ||||||||
\(646\) | 17.3607 | 0.683047 | ||||||||
\(647\) | 40.8781 | 1.60709 | 0.803543 | − | 0.595247i | \(-0.202946\pi\) | ||||
0.803543 | + | 0.595247i | \(0.202946\pi\) | |||||||
\(648\) | − | 1.53919i | − | 0.0604650i | ||||||
\(649\) | −7.81658 | −0.306828 | ||||||||
\(650\) | −28.7552 | − | 21.6719i | −1.12787 | − | 0.850043i | ||||
\(651\) | 6.15676 | 0.241302 | ||||||||
\(652\) | − | 12.4124i | − | 0.486107i | ||||||
\(653\) | 6.31351 | 0.247067 | 0.123533 | − | 0.992340i | \(-0.460577\pi\) | ||||
0.123533 | + | 0.992340i | \(0.460577\pi\) | |||||||
\(654\) | 38.9360 | 1.52252 | ||||||||
\(655\) | 4.74274i | 0.185314i | ||||||||
\(656\) | 2.51971i | 0.0983783i | ||||||||
\(657\) | 3.81658i | 0.148899i | ||||||||
\(658\) | 13.1278i | 0.511776i | ||||||||
\(659\) | −20.9360 | −0.815551 | −0.407775 | − | 0.913082i | \(-0.633695\pi\) | ||||
−0.407775 | + | 0.913082i | \(0.633695\pi\) | |||||||
\(660\) | −9.75872 | −0.379858 | ||||||||
\(661\) | − | 22.2245i | − | 0.864431i | −0.901770 | − | 0.432216i | \(-0.857732\pi\) | ||
0.901770 | − | 0.432216i | \(-0.142268\pi\) | |||||||
\(662\) | 45.6742 | 1.77518 | ||||||||
\(663\) | −2.34017 | + | 3.10504i | −0.0908848 | + | 0.120590i | ||||
\(664\) | 19.8348 | 0.769741 | ||||||||
\(665\) | − | 4.68035i | − | 0.181496i | ||||||
\(666\) | 7.41855 | 0.287463 | ||||||||
\(667\) | 36.1978 | 1.40158 | ||||||||
\(668\) | − | 19.8082i | − | 0.766401i | ||||||
\(669\) | − | 22.6225i | − | 0.874636i | ||||||
\(670\) | − | 0.796064i | − | 0.0307546i | ||||||
\(671\) | 72.2434i | 2.78892i | ||||||||
\(672\) | 7.58864 | 0.292738 | ||||||||
\(673\) | −1.15061 | −0.0443528 | −0.0221764 | − | 0.999754i | \(-0.507060\pi\) | ||||
−0.0221764 | + | 0.999754i | \(0.507060\pi\) | |||||||
\(674\) | 33.5174i | 1.29104i | ||||||||
\(675\) | 4.60197 | 0.177130 | ||||||||
\(676\) | 9.70313 | + | 33.8576i | 0.373197 | + | 1.30222i | ||||
\(677\) | −33.5897 | −1.29096 | −0.645478 | − | 0.763779i | \(-0.723342\pi\) | ||||
−0.645478 | + | 0.763779i | \(0.723342\pi\) | |||||||
\(678\) | 23.1773i | 0.890118i | ||||||||
\(679\) | −1.07838 | −0.0413843 | ||||||||
\(680\) | −1.04718 | −0.0401576 | ||||||||
\(681\) | 22.9444i | 0.879232i | ||||||||
\(682\) | 76.2799i | 2.92091i | ||||||||
\(683\) | 25.1110i | 0.960846i | 0.877037 | + | 0.480423i | \(0.159517\pi\) | ||||
−0.877037 | + | 0.480423i | \(0.840483\pi\) | |||||||
\(684\) | 20.0989i | 0.768501i | ||||||||
\(685\) | 2.82273 | 0.107851 | ||||||||
\(686\) | 2.17009 | 0.0828543 | ||||||||
\(687\) | − | 21.5441i | − | 0.821959i | ||||||
\(688\) | 26.3545 | 1.00476 | ||||||||
\(689\) | 13.0205 | − | 17.2762i | 0.496042 | − | 0.658170i | ||||
\(690\) | 7.41855 | 0.282419 | ||||||||
\(691\) | 6.30898i | 0.240005i | 0.992774 | + | 0.120002i | \(0.0382902\pi\) | ||||
−0.992774 | + | 0.120002i | \(0.961710\pi\) | |||||||
\(692\) | −20.5958 | −0.782936 | ||||||||
\(693\) | −5.70928 | −0.216877 | ||||||||
\(694\) | 47.1605i | 1.79019i | ||||||||
\(695\) | 6.15676i | 0.233539i | ||||||||
\(696\) | − | 10.2823i | − | 0.389750i | ||||||
\(697\) | − | 1.30737i | − | 0.0495201i | ||||||
\(698\) | −12.2823 | −0.464892 | ||||||||
\(699\) | 7.36069 | 0.278407 | ||||||||
\(700\) | − | 12.4680i | − | 0.471246i | ||||||
\(701\) | 45.8843 | 1.73303 | 0.866513 | − | 0.499155i | \(-0.166356\pi\) | ||||
0.866513 | + | 0.499155i | \(0.166356\pi\) | |||||||
\(702\) | −6.24846 | − | 4.70928i | −0.235833 | − | 0.177740i | ||||
\(703\) | −25.3607 | −0.956497 | ||||||||
\(704\) | 70.2883i | 2.64909i | ||||||||
\(705\) | −3.81658 | −0.143741 | ||||||||
\(706\) | 73.1832 | 2.75429 | ||||||||
\(707\) | − | 7.23513i | − | 0.272105i | ||||||
\(708\) | − | 3.70928i | − | 0.139403i | ||||||
\(709\) | − | 46.4534i | − | 1.74460i | −0.488975 | − | 0.872298i | \(-0.662629\pi\) | ||
0.488975 | − | 0.872298i | \(-0.337371\pi\) | |||||||
\(710\) | 6.59129i | 0.247367i | ||||||||
\(711\) | −1.65983 | −0.0622484 | ||||||||
\(712\) | −9.55252 | −0.357996 | ||||||||
\(713\) | − | 33.3607i | − | 1.24937i | ||||||
\(714\) | −2.34017 | −0.0875788 | ||||||||
\(715\) | −7.81658 | + | 10.3714i | −0.292324 | + | 0.387867i | ||||
\(716\) | −24.6681 | −0.921889 | ||||||||
\(717\) | − | 15.5525i | − | 0.580819i | ||||||
\(718\) | −40.5874 | −1.51471 | ||||||||
\(719\) | −7.20394 | −0.268661 | −0.134331 | − | 0.990937i | \(-0.542888\pi\) | ||||
−0.134331 | + | 0.990937i | \(0.542888\pi\) | |||||||
\(720\) | 1.31124i | 0.0488672i | ||||||||
\(721\) | 13.7587i | 0.512402i | ||||||||
\(722\) | − | 78.1988i | − | 2.91026i | ||||||
\(723\) | − | 7.33403i | − | 0.272756i | ||||||
\(724\) | −41.6163 | −1.54666 | ||||||||
\(725\) | 30.7427 | 1.14176 | ||||||||
\(726\) | − | 46.8648i | − | 1.73932i | ||||||
\(727\) | 13.6742 | 0.507148 | 0.253574 | − | 0.967316i | \(-0.418394\pi\) | ||||
0.253574 | + | 0.967316i | \(0.418394\pi\) | |||||||
\(728\) | −3.34017 | + | 4.43188i | −0.123795 | + | 0.164256i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.22529i | 0.193397i | ||||||||
\(731\) | −13.6742 | −0.505759 | ||||||||
\(732\) | −34.2823 | −1.26711 | ||||||||
\(733\) | 7.70086i | 0.284438i | 0.989835 | + | 0.142219i | \(0.0454237\pi\) | ||||
−0.989835 | + | 0.142219i | \(0.954576\pi\) | |||||||
\(734\) | 21.8576i | 0.806779i | ||||||||
\(735\) | 0.630898i | 0.0232710i | ||||||||
\(736\) | − | 41.1194i | − | 1.51568i | ||||||
\(737\) | 3.31965 | 0.122281 | ||||||||
\(738\) | 2.63090 | 0.0968447 | ||||||||
\(739\) | − | 24.5814i | − | 0.904243i | −0.891956 | − | 0.452122i | \(-0.850667\pi\) | ||
0.891956 | − | 0.452122i | \(-0.149333\pi\) | |||||||
\(740\) | 5.84324 | 0.214802 | ||||||||
\(741\) | 21.3607 | + | 16.0989i | 0.784705 | + | 0.591408i | ||||
\(742\) | 13.0205 | 0.477998 | ||||||||
\(743\) | − | 24.3773i | − | 0.894318i | −0.894455 | − | 0.447159i | \(-0.852436\pi\) | ||
0.894455 | − | 0.447159i | \(-0.147564\pi\) | |||||||
\(744\) | −9.47641 | −0.347422 | ||||||||
\(745\) | −0.926157 | −0.0339318 | ||||||||
\(746\) | 9.20394i | 0.336980i | ||||||||
\(747\) | 12.8865i | 0.471494i | ||||||||
\(748\) | − | 16.6803i | − | 0.609894i | ||||||
\(749\) | − | 10.0989i | − | 0.369006i | ||||||
\(750\) | 13.1461 | 0.480027 | ||||||||
\(751\) | −24.6803 | −0.900599 | −0.450299 | − | 0.892878i | \(-0.648683\pi\) | ||||
−0.450299 | + | 0.892878i | \(0.648683\pi\) | |||||||
\(752\) | 12.5730i | 0.458492i | ||||||||
\(753\) | −13.6742 | −0.498316 | ||||||||
\(754\) | −41.7419 | − | 31.4596i | −1.52015 | − | 1.14569i | ||||
\(755\) | 8.42923 | 0.306771 | ||||||||
\(756\) | − | 2.70928i | − | 0.0985354i | ||||||
\(757\) | −41.3172 | −1.50170 | −0.750850 | − | 0.660473i | \(-0.770356\pi\) | ||||
−0.750850 | + | 0.660473i | \(0.770356\pi\) | |||||||
\(758\) | −43.8310 | −1.59201 | ||||||||
\(759\) | 30.9360i | 1.12291i | ||||||||
\(760\) | 7.20394i | 0.261314i | ||||||||
\(761\) | − | 15.9506i | − | 0.578207i | −0.957298 | − | 0.289104i | \(-0.906643\pi\) | ||
0.957298 | − | 0.289104i | \(-0.0933572\pi\) | |||||||
\(762\) | 13.7587i | 0.498426i | ||||||||
\(763\) | 17.9421 | 0.649549 | ||||||||
\(764\) | 66.5646 | 2.40822 | ||||||||
\(765\) | − | 0.680346i | − | 0.0245980i | ||||||
\(766\) | 15.2846 | 0.552254 | ||||||||
\(767\) | −3.94214 | − | 2.97107i | −0.142342 | − | 0.107279i | ||||
\(768\) | −0.418551 | −0.0151031 | ||||||||
\(769\) | 6.22446i | 0.224460i | 0.993682 | + | 0.112230i | \(0.0357993\pi\) | ||||
−0.993682 | + | 0.112230i | \(0.964201\pi\) | |||||||
\(770\) | −7.81658 | −0.281690 | ||||||||
\(771\) | −26.1256 | −0.940889 | ||||||||
\(772\) | − | 36.7792i | − | 1.32371i | ||||||
\(773\) | 39.1545i | 1.40829i | 0.710057 | + | 0.704145i | \(0.248669\pi\) | ||||
−0.710057 | + | 0.704145i | \(0.751331\pi\) | |||||||
\(774\) | − | 27.5174i | − | 0.989094i | ||||||
\(775\) | − | 28.3332i | − | 1.01776i | ||||||
\(776\) | 1.65983 | 0.0595843 | ||||||||
\(777\) | 3.41855 | 0.122640 | ||||||||
\(778\) | − | 8.34017i | − | 0.299010i | ||||||
\(779\) | −8.99386 | −0.322238 | ||||||||
\(780\) | −4.92162 | − | 3.70928i | −0.176222 | − | 0.132813i | ||||
\(781\) | −27.4863 | −0.983535 | ||||||||
\(782\) | 12.6803i | 0.453448i | ||||||||
\(783\) | 6.68035 | 0.238736 | ||||||||
\(784\) | 2.07838 | 0.0742278 | ||||||||
\(785\) | 5.14608i | 0.183671i | ||||||||
\(786\) | − | 16.3135i | − | 0.581884i | ||||||
\(787\) | 32.2967i | 1.15125i | 0.817713 | + | 0.575626i | \(0.195242\pi\) | ||||
−0.817713 | + | 0.575626i | \(0.804758\pi\) | |||||||
\(788\) | − | 7.97721i | − | 0.284176i | ||||||
\(789\) | −30.7792 | −1.09577 | ||||||||
\(790\) | −2.27247 | −0.0808510 | ||||||||
\(791\) | 10.6803i | 0.379749i | ||||||||
\(792\) | 8.78765 | 0.312256 | ||||||||
\(793\) | −27.4596 | + | 36.4345i | −0.975119 | + | 1.29383i | ||||
\(794\) | −31.3340 | −1.11200 | ||||||||
\(795\) | 3.78539i | 0.134254i | ||||||||
\(796\) | 28.5113 | 1.01056 | ||||||||
\(797\) | −30.2700 | −1.07222 | −0.536110 | − | 0.844148i | \(-0.680107\pi\) | ||||
−0.536110 | + | 0.844148i | \(0.680107\pi\) | |||||||
\(798\) | 16.0989i | 0.569895i | ||||||||
\(799\) | − | 6.52359i | − | 0.230788i | ||||||
\(800\) | − | 34.9227i | − | 1.23470i | ||||||
\(801\) | − | 6.20620i | − | 0.219285i | ||||||
\(802\) | 21.3424 | 0.753628 | ||||||||
\(803\) | −21.7899 | −0.768950 | ||||||||
\(804\) | 1.57531i | 0.0555568i | ||||||||
\(805\) | 3.41855 | 0.120488 | ||||||||
\(806\) | −28.9939 | + | 38.4703i | −1.02127 | + | 1.35506i | ||||
\(807\) | 5.39189 | 0.189803 | ||||||||
\(808\) | 11.1362i | 0.391771i | ||||||||
\(809\) | 39.5585 | 1.39080 | 0.695401 | − | 0.718622i | \(-0.255227\pi\) | ||||
0.695401 | + | 0.718622i | \(0.255227\pi\) | |||||||
\(810\) | 1.36910 | 0.0481054 | ||||||||
\(811\) | 34.4079i | 1.20822i | 0.796899 | + | 0.604112i | \(0.206472\pi\) | ||||
−0.796899 | + | 0.604112i | \(0.793528\pi\) | |||||||
\(812\) | − | 18.0989i | − | 0.635147i | ||||||
\(813\) | − | 11.4186i | − | 0.400466i | ||||||
\(814\) | 42.3545i | 1.48453i | ||||||||
\(815\) | 2.89043 | 0.101247 | ||||||||
\(816\) | −2.24128 | −0.0784604 | ||||||||
\(817\) | 94.0698i | 3.29109i | ||||||||
\(818\) | 16.3812 | 0.572756 | ||||||||
\(819\) | −2.87936 | − | 2.17009i | −0.100613 | − | 0.0758290i | ||||
\(820\) | 2.07223 | 0.0723656 | ||||||||
\(821\) | 7.89269i | 0.275457i | 0.990470 | + | 0.137728i | \(0.0439801\pi\) | ||||
−0.990470 | + | 0.137728i | \(0.956020\pi\) | |||||||
\(822\) | −9.70928 | −0.338650 | ||||||||
\(823\) | 29.6742 | 1.03438 | 0.517189 | − | 0.855871i | \(-0.326978\pi\) | ||||
0.517189 | + | 0.855871i | \(0.326978\pi\) | |||||||
\(824\) | − | 21.1773i | − | 0.737745i | ||||||
\(825\) | 26.2739i | 0.914740i | ||||||||
\(826\) | − | 2.97107i | − | 0.103377i | ||||||
\(827\) | 14.1918i | 0.493498i | 0.969079 | + | 0.246749i | \(0.0793624\pi\) | ||||
−0.969079 | + | 0.246749i | \(0.920638\pi\) | |||||||
\(828\) | −14.6803 | −0.510177 | ||||||||
\(829\) | 3.71315 | 0.128963 | 0.0644815 | − | 0.997919i | \(-0.479461\pi\) | ||||
0.0644815 | + | 0.997919i | \(0.479461\pi\) | |||||||
\(830\) | 17.6430i | 0.612398i | ||||||||
\(831\) | 13.1506 | 0.456190 | ||||||||
\(832\) | −26.7165 | + | 35.4485i | −0.926227 | + | 1.22896i | ||||
\(833\) | −1.07838 | −0.0373636 | ||||||||
\(834\) | − | 21.1773i | − | 0.733309i | ||||||
\(835\) | 4.61265 | 0.159627 | ||||||||
\(836\) | −114.750 | −3.96872 | ||||||||
\(837\) | − | 6.15676i | − | 0.212809i | ||||||
\(838\) | − | 76.2799i | − | 2.63504i | ||||||
\(839\) | − | 48.6719i | − | 1.68034i | −0.542322 | − | 0.840171i | \(-0.682455\pi\) | ||
0.542322 | − | 0.840171i | \(-0.317545\pi\) | |||||||
\(840\) | − | 0.971071i | − | 0.0335051i | ||||||
\(841\) | 15.6270 | 0.538863 | ||||||||
\(842\) | −55.7152 | −1.92007 | ||||||||
\(843\) | 2.14834i | 0.0739929i | ||||||||
\(844\) | 8.18342 | 0.281685 | ||||||||
\(845\) | −7.88428 | + | 2.25953i | −0.271228 | + | 0.0777301i | ||||
\(846\) | 13.1278 | 0.451344 | ||||||||
\(847\) | − | 21.5958i | − | 0.742041i | ||||||
\(848\) | 12.4703 | 0.428231 | ||||||||
\(849\) | −12.1978 | −0.418627 | ||||||||
\(850\) | 10.7694i | 0.369387i | ||||||||
\(851\) | − | 18.5236i | − | 0.634981i | ||||||
\(852\) | − | 13.0433i | − | 0.446856i | ||||||
\(853\) | − | 1.92777i | − | 0.0660054i | −0.999455 | − | 0.0330027i | \(-0.989493\pi\) | ||
0.999455 | − | 0.0330027i | \(-0.0105070\pi\) | |||||||
\(854\) | −27.4596 | −0.939648 | ||||||||
\(855\) | −4.68035 | −0.160064 | ||||||||
\(856\) | 15.5441i | 0.531287i | ||||||||
\(857\) | 24.3980 | 0.833421 | 0.416710 | − | 0.909039i | \(-0.363183\pi\) | ||||
0.416710 | + | 0.909039i | \(0.363183\pi\) | |||||||
\(858\) | 26.8865 | − | 35.6742i | 0.917892 | − | 1.21790i | ||||
\(859\) | −15.1506 | −0.516932 | −0.258466 | − | 0.966020i | \(-0.583217\pi\) | ||||
−0.258466 | + | 0.966020i | \(0.583217\pi\) | |||||||
\(860\) | − | 21.6742i | − | 0.739084i | ||||||
\(861\) | 1.21235 | 0.0413167 | ||||||||
\(862\) | −35.2267 | −1.19983 | ||||||||
\(863\) | 49.7380i | 1.69310i | 0.532308 | + | 0.846551i | \(0.321325\pi\) | ||||
−0.532308 | + | 0.846551i | \(0.678675\pi\) | |||||||
\(864\) | − | 7.58864i | − | 0.258171i | ||||||
\(865\) | − | 4.79606i | − | 0.163071i | ||||||
\(866\) | − | 11.6910i | − | 0.397277i | ||||||
\(867\) | −15.8371 | −0.537856 | ||||||||
\(868\) | −16.6803 | −0.566168 | ||||||||
\(869\) | − | 9.47641i | − | 0.321465i | ||||||
\(870\) | 9.14608 | 0.310081 | ||||||||
\(871\) | 1.67420 | + | 1.26180i | 0.0567282 | + | 0.0427543i | ||||
\(872\) | −27.6163 | −0.935207 | ||||||||
\(873\) | 1.07838i | 0.0364976i | ||||||||
\(874\) | 87.2327 | 2.95069 | ||||||||
\(875\) | 6.05786 | 0.204793 | ||||||||
\(876\) | − | 10.3402i | − | 0.349362i | ||||||
\(877\) | − | 9.72753i | − | 0.328475i | −0.986421 | − | 0.164238i | \(-0.947484\pi\) | ||
0.986421 | − | 0.164238i | \(-0.0525164\pi\) | |||||||
\(878\) | − | 22.2245i | − | 0.750039i | ||||||
\(879\) | − | 7.15449i | − | 0.241315i | ||||||
\(880\) | −7.48625 | −0.252361 | ||||||||
\(881\) | 6.12556 | 0.206375 | 0.103188 | − | 0.994662i | \(-0.467096\pi\) | ||||
0.103188 | + | 0.994662i | \(0.467096\pi\) | |||||||
\(882\) | − | 2.17009i | − | 0.0730706i | ||||||
\(883\) | 1.03281 | 0.0347567 | 0.0173783 | − | 0.999849i | \(-0.494468\pi\) | ||||
0.0173783 | + | 0.999849i | \(0.494468\pi\) | |||||||
\(884\) | 6.34017 | − | 8.41241i | 0.213243 | − | 0.282940i | ||||
\(885\) | 0.863763 | 0.0290351 | ||||||||
\(886\) | 34.5958i | 1.16227i | ||||||||
\(887\) | 39.0882 | 1.31245 | 0.656227 | − | 0.754564i | \(-0.272151\pi\) | ||||
0.656227 | + | 0.754564i | \(0.272151\pi\) | |||||||
\(888\) | −5.26180 | −0.176574 | ||||||||
\(889\) | 6.34017i | 0.212643i | ||||||||
\(890\) | − | 8.49693i | − | 0.284818i | ||||||
\(891\) | 5.70928i | 0.191268i | ||||||||
\(892\) | 61.2905i | 2.05216i | ||||||||
\(893\) | −44.8781 | −1.50179 | ||||||||
\(894\) | 3.18568 | 0.106545 | ||||||||
\(895\) | − | 5.74435i | − | 0.192012i | ||||||
\(896\) | −11.5392 | −0.385497 | ||||||||
\(897\) | −11.7587 | + | 15.6020i | −0.392612 | + | 0.520935i | ||||
\(898\) | −28.6453 | −0.955905 | ||||||||
\(899\) | − | 41.1293i | − | 1.37174i | ||||||
\(900\) | −12.4680 | −0.415600 | ||||||||
\(901\) | −6.47027 | −0.215556 | ||||||||
\(902\) | 15.0205i | 0.500129i | ||||||||
\(903\) | − | 12.6803i | − | 0.421975i | ||||||
\(904\) | − | 16.4391i | − | 0.546755i | ||||||
\(905\) | − | 9.69102i | − | 0.322141i | ||||||
\(906\) | −28.9939 | −0.963256 | ||||||||
\(907\) | 45.3751 | 1.50665 | 0.753327 | − | 0.657646i | \(-0.228448\pi\) | ||||
0.753327 | + | 0.657646i | \(0.228448\pi\) | |||||||
\(908\) | − | 62.1627i | − | 2.06294i | ||||||
\(909\) | −7.23513 | −0.239974 | ||||||||
\(910\) | −3.94214 | − | 2.97107i | −0.130681 | − | 0.0984900i | ||||
\(911\) | −24.3090 | −0.805392 | −0.402696 | − | 0.915334i | \(-0.631927\pi\) | ||||
−0.402696 | + | 0.915334i | \(0.631927\pi\) | |||||||
\(912\) | 15.4186i | 0.510559i | ||||||||
\(913\) | −73.5729 | −2.43491 | ||||||||
\(914\) | 39.7321 | 1.31422 | ||||||||
\(915\) | − | 7.98318i | − | 0.263916i | ||||||
\(916\) | 58.3689i | 1.92856i | ||||||||
\(917\) | − | 7.51745i | − | 0.248248i | ||||||
\(918\) | 2.34017i | 0.0772372i | ||||||||
\(919\) | 55.8453 | 1.84217 | 0.921084 | − | 0.389364i | \(-0.127305\pi\) | ||||
0.921084 | + | 0.389364i | \(0.127305\pi\) | |||||||
\(920\) | −5.26180 | −0.173476 | ||||||||
\(921\) | 21.8432i | 0.719759i | ||||||||
\(922\) | −41.1012 | −1.35359 | ||||||||
\(923\) | −13.8622 | − | 10.4475i | −0.456278 | − | 0.343883i | ||||
\(924\) | 15.4680 | 0.508860 | ||||||||
\(925\) | − | 15.7321i | − | 0.517267i | ||||||
\(926\) | −3.78539 | −0.124395 | ||||||||
\(927\) | 13.7587 | 0.451896 | ||||||||
\(928\) | − | 50.6947i | − | 1.66414i | ||||||
\(929\) | 39.4680i | 1.29490i | 0.762107 | + | 0.647452i | \(0.224165\pi\) | ||||
−0.762107 | + | 0.647452i | \(0.775835\pi\) | |||||||
\(930\) | − | 8.42923i | − | 0.276405i | ||||||
\(931\) | 7.41855i | 0.243133i | ||||||||
\(932\) | −19.9421 | −0.653227 | ||||||||
\(933\) | −7.51745 | −0.246110 | ||||||||
\(934\) | − | 39.4017i | − | 1.28926i | ||||||
\(935\) | 3.88428 | 0.127030 | ||||||||
\(936\) | 4.43188 | + | 3.34017i | 0.144861 | + | 0.109177i | ||||
\(937\) | −22.2122 | −0.725640 | −0.362820 | − | 0.931859i | \(-0.618186\pi\) | ||||
−0.362820 | + | 0.931859i | \(0.618186\pi\) | |||||||
\(938\) | 1.26180i | 0.0411991i | ||||||||
\(939\) | 25.7009 | 0.838716 | ||||||||
\(940\) | 10.3402 | 0.337259 | ||||||||
\(941\) | 32.1483i | 1.04801i | 0.851716 | + | 0.524003i | \(0.175562\pi\) | ||||
−0.851716 | + | 0.524003i | \(0.824438\pi\) | |||||||
\(942\) | − | 17.7009i | − | 0.576725i | ||||||
\(943\) | − | 6.56916i | − | 0.213921i | ||||||
\(944\) | − | 2.84551i | − | 0.0926135i | ||||||
\(945\) | 0.630898 | 0.0205231 | ||||||||
\(946\) | 157.105 | 5.10791 | ||||||||
\(947\) | − | 19.2390i | − | 0.625184i | −0.949888 | − | 0.312592i | \(-0.898803\pi\) | ||
0.949888 | − | 0.312592i | \(-0.101197\pi\) | |||||||
\(948\) | 4.49693 | 0.146053 | ||||||||
\(949\) | −10.9893 | − | 8.28231i | −0.356728 | − | 0.268855i | ||||
\(950\) | 74.0866 | 2.40369 | ||||||||
\(951\) | − | 9.36910i | − | 0.303814i | ||||||
\(952\) | 1.65983 | 0.0537953 | ||||||||
\(953\) | 54.3423 | 1.76032 | 0.880159 | − | 0.474678i | \(-0.157436\pi\) | ||||
0.880159 | + | 0.474678i | \(0.157436\pi\) | |||||||
\(954\) | − | 13.0205i | − | 0.421555i | ||||||
\(955\) | 15.5006i | 0.501588i | ||||||||
\(956\) | 42.1361i | 1.36278i | ||||||||
\(957\) | 38.1399i | 1.23289i | ||||||||
\(958\) | 66.1049 | 2.13575 | ||||||||
\(959\) | −4.47414 | −0.144478 | ||||||||
\(960\) | − | 7.76713i | − | 0.250683i | ||||||
\(961\) | −6.90564 | −0.222763 | ||||||||
\(962\) | −16.0989 | + | 21.3607i | −0.519049 | + | 0.688696i | ||||
\(963\) | −10.0989 | −0.325432 | ||||||||
\(964\) | 19.8699i | 0.639967i | ||||||||
\(965\) | 8.56463 | 0.275705 | ||||||||
\(966\) | −11.7587 | −0.378331 | ||||||||
\(967\) | 1.43084i | 0.0460126i | 0.999735 | + | 0.0230063i | \(0.00732378\pi\) | ||||
−0.999735 | + | 0.0230063i | \(0.992676\pi\) | |||||||
\(968\) | 33.2401i | 1.06838i | ||||||||
\(969\) | − | 8.00000i | − | 0.256997i | ||||||
\(970\) | 1.47641i | 0.0474047i | ||||||||
\(971\) | −25.2450 | −0.810150 | −0.405075 | − | 0.914284i | \(-0.632755\pi\) | ||||
−0.405075 | + | 0.914284i | \(0.632755\pi\) | |||||||
\(972\) | −2.70928 | −0.0869000 | ||||||||
\(973\) | − | 9.75872i | − | 0.312850i | ||||||
\(974\) | −0.680346 | −0.0217997 | ||||||||
\(975\) | −9.98667 | + | 13.2507i | −0.319829 | + | 0.424363i | ||||
\(976\) | −26.2991 | −0.841815 | ||||||||
\(977\) | 7.31124i | 0.233907i | 0.993137 | + | 0.116954i | \(0.0373129\pi\) | ||||
−0.993137 | + | 0.116954i | \(0.962687\pi\) | |||||||
\(978\) | −9.94214 | −0.317915 | ||||||||
\(979\) | 35.4329 | 1.13244 | ||||||||
\(980\) | − | 1.70928i | − | 0.0546008i | ||||||
\(981\) | − | 17.9421i | − | 0.572848i | ||||||
\(982\) | − | 19.3919i | − | 0.618820i | ||||||
\(983\) | 21.0556i | 0.671569i | 0.941939 | + | 0.335785i | \(0.109001\pi\) | ||||
−0.941939 | + | 0.335785i | \(0.890999\pi\) | |||||||
\(984\) | −1.86603 | −0.0594869 | ||||||||
\(985\) | 1.85762 | 0.0591887 | ||||||||
\(986\) | 15.6332i | 0.497861i | ||||||||
\(987\) | 6.04945 | 0.192556 | ||||||||
\(988\) | −57.8720 | − | 43.6163i | −1.84115 | − | 1.38762i | ||||
\(989\) | −68.7091 | −2.18482 | ||||||||
\(990\) | 7.81658i | 0.248427i | ||||||||
\(991\) | 42.0410 | 1.33548 | 0.667739 | − | 0.744396i | \(-0.267262\pi\) | ||||
0.667739 | + | 0.744396i | \(0.267262\pi\) | |||||||
\(992\) | −46.7214 | −1.48341 | ||||||||
\(993\) | − | 21.0472i | − | 0.667912i | ||||||
\(994\) | − | 10.4475i | − | 0.331374i | ||||||
\(995\) | 6.63931i | 0.210480i | ||||||||
\(996\) | − | 34.9132i | − | 1.10627i | ||||||
\(997\) | −9.20394 | −0.291492 | −0.145746 | − | 0.989322i | \(-0.546558\pi\) | ||||
−0.145746 | + | 0.989322i | \(0.546558\pi\) | |||||||
\(998\) | 73.7563 | 2.33471 | ||||||||
\(999\) | − | 3.41855i | − | 0.108158i |
(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 | 273.2.c.b.64.6 | yes | 6 | |
3.2 | odd | 2 | 819.2.c.c.64.1 | 6 | |||
4.3 | odd | 2 | 4368.2.h.o.337.3 | 6 | |||
7.6 | odd | 2 | 1911.2.c.h.883.6 | 6 | |||
13.5 | odd | 4 | 3549.2.a.q.1.3 | 3 | |||
13.8 | odd | 4 | 3549.2.a.k.1.1 | 3 | |||
13.12 | even | 2 | inner | 273.2.c.b.64.1 | ✓ | 6 | |
39.38 | odd | 2 | 819.2.c.c.64.6 | 6 | |||
52.51 | odd | 2 | 4368.2.h.o.337.4 | 6 | |||
91.90 | odd | 2 | 1911.2.c.h.883.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.c.b.64.1 | ✓ | 6 | 13.12 | even | 2 | inner | |
273.2.c.b.64.6 | yes | 6 | 1.1 | even | 1 | trivial | |
819.2.c.c.64.1 | 6 | 3.2 | odd | 2 | |||
819.2.c.c.64.6 | 6 | 39.38 | odd | 2 | |||
1911.2.c.h.883.1 | 6 | 91.90 | odd | 2 | |||
1911.2.c.h.883.6 | 6 | 7.6 | odd | 2 | |||
3549.2.a.k.1.1 | 3 | 13.8 | odd | 4 | |||
3549.2.a.q.1.3 | 3 | 13.5 | odd | 4 | |||
4368.2.h.o.337.3 | 6 | 4.3 | odd | 2 | |||
4368.2.h.o.337.4 | 6 | 52.51 | odd | 2 |