Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(626,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.626");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.f (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: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 626.8 | ||
Character | \(\chi\) | \(=\) | 1045.626 |
Dual form | 1045.2.f.a.626.7 |
$q$-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 \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.04337 | −1.44488 | −0.722439 | − | 0.691434i | \(-0.756979\pi\) | ||||
−0.722439 | + | 0.691434i | \(0.756979\pi\) | |||||||
\(3\) | 0.838315i | 0.484002i | 0.970276 | + | 0.242001i | \(0.0778037\pi\) | ||||
−0.970276 | + | 0.242001i | \(0.922196\pi\) | |||||||
\(4\) | 2.17535 | 1.08768 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | − | 1.71299i | − | 0.699324i | ||||||
\(7\) | 4.78057i | 1.80688i | 0.428710 | + | 0.903442i | \(0.358968\pi\) | ||||
−0.428710 | + | 0.903442i | \(0.641032\pi\) | |||||||
\(8\) | −0.358306 | −0.126680 | ||||||||
\(9\) | 2.29723 | 0.765742 | ||||||||
\(10\) | 2.04337 | 0.646170 | ||||||||
\(11\) | −2.69484 | + | 1.93335i | −0.812524 | + | 0.582928i | ||||
\(12\) | 1.82363i | 0.526437i | ||||||||
\(13\) | −4.24020 | −1.17602 | −0.588010 | − | 0.808854i | \(-0.700088\pi\) | ||||
−0.588010 | + | 0.808854i | \(0.700088\pi\) | |||||||
\(14\) | − | 9.76845i | − | 2.61073i | ||||||
\(15\) | − | 0.838315i | − | 0.216452i | ||||||
\(16\) | −3.61855 | −0.904638 | ||||||||
\(17\) | 3.99629i | 0.969243i | 0.874724 | + | 0.484621i | \(0.161043\pi\) | ||||
−0.874724 | + | 0.484621i | \(0.838957\pi\) | |||||||
\(18\) | −4.69408 | −1.10641 | ||||||||
\(19\) | −4.34129 | − | 0.391440i | −0.995960 | − | 0.0898026i | ||||
\(20\) | −2.17535 | −0.486423 | ||||||||
\(21\) | −4.00762 | −0.874535 | ||||||||
\(22\) | 5.50654 | − | 3.95055i | 1.17400 | − | 0.842260i | ||||
\(23\) | 5.80780 | 1.21101 | 0.605505 | − | 0.795841i | \(-0.292971\pi\) | ||||
0.605505 | + | 0.795841i | \(0.292971\pi\) | |||||||
\(24\) | − | 0.300373i | − | 0.0613134i | ||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.66428 | 1.69921 | ||||||||
\(27\) | 4.44075i | 0.854622i | ||||||||
\(28\) | 10.3994i | 1.96530i | ||||||||
\(29\) | 0.280948 | 0.0521707 | 0.0260854 | − | 0.999660i | \(-0.491696\pi\) | ||||
0.0260854 | + | 0.999660i | \(0.491696\pi\) | |||||||
\(30\) | 1.71299i | 0.312747i | ||||||||
\(31\) | − | 1.69878i | − | 0.305110i | −0.988295 | − | 0.152555i | \(-0.951250\pi\) | ||
0.988295 | − | 0.152555i | \(-0.0487501\pi\) | |||||||
\(32\) | 8.11064 | 1.43377 | ||||||||
\(33\) | −1.62076 | − | 2.25912i | −0.282138 | − | 0.393263i | ||||
\(34\) | − | 8.16589i | − | 1.40044i | ||||||
\(35\) | − | 4.78057i | − | 0.808063i | ||||||
\(36\) | 4.99727 | 0.832879 | ||||||||
\(37\) | 2.87696i | 0.472969i | 0.971635 | + | 0.236484i | \(0.0759952\pi\) | ||||
−0.971635 | + | 0.236484i | \(0.924005\pi\) | |||||||
\(38\) | 8.87084 | + | 0.799856i | 1.43904 | + | 0.129754i | ||||
\(39\) | − | 3.55462i | − | 0.569195i | ||||||
\(40\) | 0.358306 | 0.0566531 | ||||||||
\(41\) | 5.74842 | 0.897752 | 0.448876 | − | 0.893594i | \(-0.351824\pi\) | ||||
0.448876 | + | 0.893594i | \(0.351824\pi\) | |||||||
\(42\) | 8.18905 | 1.26360 | ||||||||
\(43\) | − | 5.09337i | − | 0.776731i | −0.921505 | − | 0.388365i | \(-0.873040\pi\) | ||
0.921505 | − | 0.388365i | \(-0.126960\pi\) | |||||||
\(44\) | −5.86222 | + | 4.20572i | −0.883762 | + | 0.634036i | ||||
\(45\) | −2.29723 | −0.342450 | ||||||||
\(46\) | −11.8675 | −1.74976 | ||||||||
\(47\) | −1.73791 | −0.253500 | −0.126750 | − | 0.991935i | \(-0.540455\pi\) | ||||
−0.126750 | + | 0.991935i | \(0.540455\pi\) | |||||||
\(48\) | − | 3.03349i | − | 0.437846i | ||||||
\(49\) | −15.8538 | −2.26483 | ||||||||
\(50\) | −2.04337 | −0.288976 | ||||||||
\(51\) | −3.35015 | −0.469115 | ||||||||
\(52\) | −9.22392 | −1.27913 | ||||||||
\(53\) | 10.5567i | 1.45008i | 0.688708 | + | 0.725039i | \(0.258178\pi\) | ||||
−0.688708 | + | 0.725039i | \(0.741822\pi\) | |||||||
\(54\) | − | 9.07408i | − | 1.23483i | ||||||
\(55\) | 2.69484 | − | 1.93335i | 0.363372 | − | 0.260693i | ||||
\(56\) | − | 1.71290i | − | 0.228896i | ||||||
\(57\) | 0.328151 | − | 3.63937i | 0.0434646 | − | 0.482046i | ||||
\(58\) | −0.574080 | −0.0753803 | ||||||||
\(59\) | 1.61310i | 0.210007i | 0.994472 | + | 0.105004i | \(0.0334854\pi\) | ||||
−0.994472 | + | 0.105004i | \(0.966515\pi\) | |||||||
\(60\) | − | 1.82363i | − | 0.235430i | ||||||
\(61\) | 1.50074i | 0.192150i | 0.995374 | + | 0.0960748i | \(0.0306288\pi\) | ||||
−0.995374 | + | 0.0960748i | \(0.969371\pi\) | |||||||
\(62\) | 3.47123i | 0.440847i | ||||||||
\(63\) | 10.9820i | 1.38361i | ||||||||
\(64\) | −9.33592 | −1.16699 | ||||||||
\(65\) | 4.24020 | 0.525932 | ||||||||
\(66\) | 3.31181 | + | 4.61622i | 0.407655 | + | 0.568217i | ||||
\(67\) | − | 12.0842i | − | 1.47632i | −0.674624 | − | 0.738161i | \(-0.735694\pi\) | ||
0.674624 | − | 0.738161i | \(-0.264306\pi\) | |||||||
\(68\) | 8.69333i | 1.05422i | ||||||||
\(69\) | 4.86877i | 0.586131i | ||||||||
\(70\) | 9.76845i | 1.16755i | ||||||||
\(71\) | − | 12.3578i | − | 1.46660i | −0.679904 | − | 0.733302i | \(-0.737978\pi\) | ||
0.679904 | − | 0.733302i | \(-0.262022\pi\) | |||||||
\(72\) | −0.823109 | −0.0970043 | ||||||||
\(73\) | 0.489478i | 0.0572891i | 0.999590 | + | 0.0286445i | \(0.00911909\pi\) | ||||
−0.999590 | + | 0.0286445i | \(0.990881\pi\) | |||||||
\(74\) | − | 5.87868i | − | 0.683383i | ||||||
\(75\) | 0.838315i | 0.0968003i | ||||||||
\(76\) | −9.44382 | − | 0.851520i | −1.08328 | − | 0.0976760i | ||||
\(77\) | −9.24252 | − | 12.8828i | −1.05328 | − | 1.46814i | ||||
\(78\) | 7.26340i | 0.822418i | ||||||||
\(79\) | −6.76671 | −0.761315 | −0.380657 | − | 0.924716i | \(-0.624302\pi\) | ||||
−0.380657 | + | 0.924716i | \(0.624302\pi\) | |||||||
\(80\) | 3.61855 | 0.404566 | ||||||||
\(81\) | 3.16893 | 0.352104 | ||||||||
\(82\) | −11.7461 | −1.29714 | ||||||||
\(83\) | − | 14.7552i | − | 1.61960i | −0.586708 | − | 0.809799i | \(-0.699576\pi\) | ||
0.586708 | − | 0.809799i | \(-0.300424\pi\) | |||||||
\(84\) | −8.71798 | −0.951210 | ||||||||
\(85\) | − | 3.99629i | − | 0.433459i | ||||||
\(86\) | 10.4076i | 1.12228i | ||||||||
\(87\) | 0.235523i | 0.0252507i | ||||||||
\(88\) | 0.965575 | − | 0.692731i | 0.102931 | − | 0.0738454i | ||||
\(89\) | − | 4.01878i | − | 0.425990i | −0.977053 | − | 0.212995i | \(-0.931678\pi\) | ||
0.977053 | − | 0.212995i | \(-0.0683218\pi\) | |||||||
\(90\) | 4.69408 | 0.494799 | ||||||||
\(91\) | − | 20.2706i | − | 2.12493i | ||||||
\(92\) | 12.6340 | 1.31719 | ||||||||
\(93\) | 1.42411 | 0.147674 | ||||||||
\(94\) | 3.55118 | 0.366276 | ||||||||
\(95\) | 4.34129 | + | 0.391440i | 0.445407 | + | 0.0401609i | ||||
\(96\) | 6.79928i | 0.693948i | ||||||||
\(97\) | 11.2670i | 1.14399i | 0.820257 | + | 0.571996i | \(0.193831\pi\) | ||||
−0.820257 | + | 0.571996i | \(0.806169\pi\) | |||||||
\(98\) | 32.3952 | 3.27241 | ||||||||
\(99\) | −6.19065 | + | 4.44135i | −0.622184 | + | 0.446372i | ||||
\(100\) | 2.17535 | 0.217535 | ||||||||
\(101\) | 7.47740i | 0.744029i | 0.928227 | + | 0.372015i | \(0.121333\pi\) | ||||
−0.928227 | + | 0.372015i | \(0.878667\pi\) | |||||||
\(102\) | 6.84559 | 0.677815 | ||||||||
\(103\) | − | 2.84871i | − | 0.280691i | −0.990103 | − | 0.140346i | \(-0.955179\pi\) | ||
0.990103 | − | 0.140346i | \(-0.0448214\pi\) | |||||||
\(104\) | 1.51929 | 0.148978 | ||||||||
\(105\) | 4.00762 | 0.391104 | ||||||||
\(106\) | − | 21.5713i | − | 2.09519i | ||||||
\(107\) | −5.91167 | −0.571503 | −0.285751 | − | 0.958304i | \(-0.592243\pi\) | ||||
−0.285751 | + | 0.958304i | \(0.592243\pi\) | |||||||
\(108\) | 9.66018i | 0.929551i | ||||||||
\(109\) | −17.3818 | −1.66488 | −0.832439 | − | 0.554117i | \(-0.813056\pi\) | ||||
−0.832439 | + | 0.554117i | \(0.813056\pi\) | |||||||
\(110\) | −5.50654 | + | 3.95055i | −0.525028 | + | 0.376670i | ||||
\(111\) | −2.41180 | −0.228918 | ||||||||
\(112\) | − | 17.2987i | − | 1.63458i | ||||||
\(113\) | 12.2517i | 1.15254i | 0.817260 | + | 0.576270i | \(0.195492\pi\) | ||||
−0.817260 | + | 0.576270i | \(0.804508\pi\) | |||||||
\(114\) | −0.670532 | + | 7.43657i | −0.0628011 | + | 0.696498i | ||||
\(115\) | −5.80780 | −0.541580 | ||||||||
\(116\) | 0.611160 | 0.0567448 | ||||||||
\(117\) | −9.74070 | −0.900528 | ||||||||
\(118\) | − | 3.29615i | − | 0.303435i | ||||||
\(119\) | −19.1045 | −1.75131 | ||||||||
\(120\) | 0.300373i | 0.0274202i | ||||||||
\(121\) | 3.52430 | − | 10.4201i | 0.320391 | − | 0.947286i | ||||
\(122\) | − | 3.06655i | − | 0.277633i | ||||||
\(123\) | 4.81899i | 0.434514i | ||||||||
\(124\) | − | 3.69544i | − | 0.331860i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | − | 22.4404i | − | 1.99915i | ||||||
\(127\) | 1.70223 | 0.151049 | 0.0755243 | − | 0.997144i | \(-0.475937\pi\) | ||||
0.0755243 | + | 0.997144i | \(0.475937\pi\) | |||||||
\(128\) | 2.85543 | 0.252386 | ||||||||
\(129\) | 4.26985 | 0.375939 | ||||||||
\(130\) | −8.66428 | −0.759908 | ||||||||
\(131\) | 6.07917i | 0.531140i | 0.964092 | + | 0.265570i | \(0.0855601\pi\) | ||||
−0.964092 | + | 0.265570i | \(0.914440\pi\) | |||||||
\(132\) | −3.52572 | − | 4.91439i | −0.306875 | − | 0.427742i | ||||
\(133\) | 1.87131 | − | 20.7538i | 0.162263 | − | 1.79958i | ||||
\(134\) | 24.6925i | 2.13311i | ||||||||
\(135\) | − | 4.44075i | − | 0.382199i | ||||||
\(136\) | − | 1.43189i | − | 0.122784i | ||||||
\(137\) | −19.5811 | −1.67293 | −0.836465 | − | 0.548020i | \(-0.815382\pi\) | ||||
−0.836465 | + | 0.548020i | \(0.815382\pi\) | |||||||
\(138\) | − | 9.94868i | − | 0.846888i | ||||||
\(139\) | − | 14.8952i | − | 1.26339i | −0.775216 | − | 0.631696i | \(-0.782359\pi\) | ||
0.775216 | − | 0.631696i | \(-0.217641\pi\) | |||||||
\(140\) | − | 10.3994i | − | 0.878910i | ||||||
\(141\) | − | 1.45691i | − | 0.122694i | ||||||
\(142\) | 25.2516i | 2.11906i | ||||||||
\(143\) | 11.4266 | − | 8.19780i | 0.955544 | − | 0.685534i | ||||
\(144\) | −8.31263 | −0.692720 | ||||||||
\(145\) | −0.280948 | −0.0233314 | ||||||||
\(146\) | − | 1.00018i | − | 0.0827758i | ||||||
\(147\) | − | 13.2905i | − | 1.09618i | ||||||
\(148\) | 6.25839i | 0.514436i | ||||||||
\(149\) | − | 23.1713i | − | 1.89826i | −0.314878 | − | 0.949132i | \(-0.601964\pi\) | ||
0.314878 | − | 0.949132i | \(-0.398036\pi\) | |||||||
\(150\) | − | 1.71299i | − | 0.139865i | ||||||
\(151\) | −2.62018 | −0.213227 | −0.106614 | − | 0.994301i | \(-0.534001\pi\) | ||||
−0.106614 | + | 0.994301i | \(0.534001\pi\) | |||||||
\(152\) | 1.55551 | + | 0.140255i | 0.126168 | + | 0.0113762i | ||||
\(153\) | 9.18039i | 0.742190i | ||||||||
\(154\) | 18.8859 | + | 26.3244i | 1.52187 | + | 2.12128i | ||||
\(155\) | 1.69878i | 0.136449i | ||||||||
\(156\) | − | 7.73255i | − | 0.619100i | ||||||
\(157\) | −0.859743 | −0.0686150 | −0.0343075 | − | 0.999411i | \(-0.510923\pi\) | ||||
−0.0343075 | + | 0.999411i | \(0.510923\pi\) | |||||||
\(158\) | 13.8269 | 1.10001 | ||||||||
\(159\) | −8.84987 | −0.701840 | ||||||||
\(160\) | −8.11064 | −0.641202 | ||||||||
\(161\) | 27.7646i | 2.18816i | ||||||||
\(162\) | −6.47530 | −0.508747 | ||||||||
\(163\) | −4.37921 | −0.343006 | −0.171503 | − | 0.985184i | \(-0.554862\pi\) | ||||
−0.171503 | + | 0.985184i | \(0.554862\pi\) | |||||||
\(164\) | 12.5048 | 0.976463 | ||||||||
\(165\) | 1.62076 | + | 2.25912i | 0.126176 | + | 0.175873i | ||||
\(166\) | 30.1504i | 2.34012i | ||||||||
\(167\) | 9.39022 | 0.726637 | 0.363319 | − | 0.931665i | \(-0.381644\pi\) | ||||
0.363319 | + | 0.931665i | \(0.381644\pi\) | |||||||
\(168\) | 1.43595 | 0.110786 | ||||||||
\(169\) | 4.97928 | 0.383022 | ||||||||
\(170\) | 8.16589i | 0.626295i | ||||||||
\(171\) | −9.97292 | − | 0.899227i | −0.762648 | − | 0.0687656i | ||||
\(172\) | − | 11.0799i | − | 0.844831i | ||||||
\(173\) | 12.6812 | 0.964136 | 0.482068 | − | 0.876134i | \(-0.339886\pi\) | ||||
0.482068 | + | 0.876134i | \(0.339886\pi\) | |||||||
\(174\) | − | 0.481260i | − | 0.0364842i | ||||||
\(175\) | 4.78057i | 0.361377i | ||||||||
\(176\) | 9.75141 | − | 6.99593i | 0.735040 | − | 0.527338i | ||||
\(177\) | −1.35228 | −0.101644 | ||||||||
\(178\) | 8.21185i | 0.615504i | ||||||||
\(179\) | 0.803768i | 0.0600764i | 0.999549 | + | 0.0300382i | \(0.00956290\pi\) | ||||
−0.999549 | + | 0.0300382i | \(0.990437\pi\) | |||||||
\(180\) | −4.99727 | −0.372475 | ||||||||
\(181\) | 24.2956i | 1.80588i | 0.429770 | + | 0.902939i | \(0.358595\pi\) | ||||
−0.429770 | + | 0.902939i | \(0.641405\pi\) | |||||||
\(182\) | 41.4202i | 3.07027i | ||||||||
\(183\) | −1.25809 | −0.0930007 | ||||||||
\(184\) | −2.08097 | −0.153411 | ||||||||
\(185\) | − | 2.87696i | − | 0.211518i | ||||||
\(186\) | −2.90999 | −0.213371 | ||||||||
\(187\) | −7.72624 | − | 10.7694i | −0.564999 | − | 0.787533i | ||||
\(188\) | −3.78055 | −0.275725 | ||||||||
\(189\) | −21.2293 | −1.54420 | ||||||||
\(190\) | −8.87084 | − | 0.799856i | −0.643559 | − | 0.0580277i | ||||
\(191\) | 3.48103 | 0.251879 | 0.125939 | − | 0.992038i | \(-0.459806\pi\) | ||||
0.125939 | + | 0.992038i | \(0.459806\pi\) | |||||||
\(192\) | − | 7.82644i | − | 0.564825i | ||||||
\(193\) | −12.9504 | −0.932187 | −0.466094 | − | 0.884735i | \(-0.654339\pi\) | ||||
−0.466094 | + | 0.884735i | \(0.654339\pi\) | |||||||
\(194\) | − | 23.0226i | − | 1.65293i | ||||||
\(195\) | 3.55462i | 0.254552i | ||||||||
\(196\) | −34.4876 | −2.46340 | ||||||||
\(197\) | 10.8525i | 0.773210i | 0.922245 | + | 0.386605i | \(0.126352\pi\) | ||||
−0.922245 | + | 0.386605i | \(0.873648\pi\) | |||||||
\(198\) | 12.6498 | − | 9.07531i | 0.898981 | − | 0.644954i | ||||
\(199\) | 21.8885 | 1.55163 | 0.775816 | − | 0.630959i | \(-0.217338\pi\) | ||||
0.775816 | + | 0.630959i | \(0.217338\pi\) | |||||||
\(200\) | −0.358306 | −0.0253360 | ||||||||
\(201\) | 10.1304 | 0.714543 | ||||||||
\(202\) | − | 15.2791i | − | 1.07503i | ||||||
\(203\) | 1.34309i | 0.0942664i | ||||||||
\(204\) | −7.28776 | −0.510245 | ||||||||
\(205\) | −5.74842 | −0.401487 | ||||||||
\(206\) | 5.82096i | 0.405565i | ||||||||
\(207\) | 13.3418 | 0.927322 | ||||||||
\(208\) | 15.3434 | 1.06387 | ||||||||
\(209\) | 12.4559 | − | 7.33837i | 0.861590 | − | 0.507606i | ||||
\(210\) | −8.18905 | −0.565098 | ||||||||
\(211\) | −13.9828 | −0.962618 | −0.481309 | − | 0.876551i | \(-0.659839\pi\) | ||||
−0.481309 | + | 0.876551i | \(0.659839\pi\) | |||||||
\(212\) | 22.9646i | 1.57721i | ||||||||
\(213\) | 10.3598 | 0.709838 | ||||||||
\(214\) | 12.0797 | 0.825753 | ||||||||
\(215\) | 5.09337i | 0.347365i | ||||||||
\(216\) | − | 1.59114i | − | 0.108264i | ||||||
\(217\) | 8.12113 | 0.551298 | ||||||||
\(218\) | 35.5175 | 2.40555 | ||||||||
\(219\) | −0.410337 | −0.0277280 | ||||||||
\(220\) | 5.86222 | − | 4.20572i | 0.395231 | − | 0.283550i | ||||
\(221\) | − | 16.9451i | − | 1.13985i | ||||||
\(222\) | 4.92819 | 0.330758 | ||||||||
\(223\) | 3.15124i | 0.211022i | 0.994418 | + | 0.105511i | \(0.0336479\pi\) | ||||
−0.994418 | + | 0.105511i | \(0.966352\pi\) | |||||||
\(224\) | 38.7735i | 2.59066i | ||||||||
\(225\) | 2.29723 | 0.153148 | ||||||||
\(226\) | − | 25.0346i | − | 1.66528i | ||||||
\(227\) | −7.54188 | −0.500572 | −0.250286 | − | 0.968172i | \(-0.580525\pi\) | ||||
−0.250286 | + | 0.968172i | \(0.580525\pi\) | |||||||
\(228\) | 0.713842 | − | 7.91690i | 0.0472754 | − | 0.524310i | ||||
\(229\) | −12.1719 | −0.804341 | −0.402170 | − | 0.915565i | \(-0.631744\pi\) | ||||
−0.402170 | + | 0.915565i | \(0.631744\pi\) | |||||||
\(230\) | 11.8675 | 0.782518 | ||||||||
\(231\) | 10.7999 | − | 7.74815i | 0.710581 | − | 0.509791i | ||||
\(232\) | −0.100665 | −0.00660899 | ||||||||
\(233\) | 9.79180i | 0.641482i | 0.947167 | + | 0.320741i | \(0.103932\pi\) | ||||
−0.947167 | + | 0.320741i | \(0.896068\pi\) | |||||||
\(234\) | 19.9038 | 1.30115 | ||||||||
\(235\) | 1.73791 | 0.113368 | ||||||||
\(236\) | 3.50905i | 0.228420i | ||||||||
\(237\) | − | 5.67264i | − | 0.368478i | ||||||
\(238\) | 39.0376 | 2.53043 | ||||||||
\(239\) | − | 21.3790i | − | 1.38289i | −0.722428 | − | 0.691446i | \(-0.756974\pi\) | ||
0.722428 | − | 0.691446i | \(-0.243026\pi\) | |||||||
\(240\) | 3.03349i | 0.195811i | ||||||||
\(241\) | 23.5429 | 1.51653 | 0.758266 | − | 0.651945i | \(-0.226047\pi\) | ||||
0.758266 | + | 0.651945i | \(0.226047\pi\) | |||||||
\(242\) | −7.20143 | + | 21.2922i | −0.462926 | + | 1.36871i | ||||
\(243\) | 15.9788i | 1.02504i | ||||||||
\(244\) | 3.26463i | 0.208996i | ||||||||
\(245\) | 15.8538 | 1.01286 | ||||||||
\(246\) | − | 9.84696i | − | 0.627819i | ||||||
\(247\) | 18.4079 | + | 1.65978i | 1.17127 | + | 0.105610i | ||||
\(248\) | 0.608682i | 0.0386513i | ||||||||
\(249\) | 12.3695 | 0.783888 | ||||||||
\(250\) | 2.04337 | 0.129234 | ||||||||
\(251\) | 5.60396 | 0.353719 | 0.176860 | − | 0.984236i | \(-0.443406\pi\) | ||||
0.176860 | + | 0.984236i | \(0.443406\pi\) | |||||||
\(252\) | 23.8898i | 1.50492i | ||||||||
\(253\) | −15.6511 | + | 11.2285i | −0.983975 | + | 0.705931i | ||||
\(254\) | −3.47829 | −0.218247 | ||||||||
\(255\) | 3.35015 | 0.209795 | ||||||||
\(256\) | 12.8371 | 0.802322 | ||||||||
\(257\) | 17.9270i | 1.11826i | 0.829081 | + | 0.559128i | \(0.188864\pi\) | ||||
−0.829081 | + | 0.559128i | \(0.811136\pi\) | |||||||
\(258\) | −8.72487 | −0.543186 | ||||||||
\(259\) | −13.7535 | −0.854600 | ||||||||
\(260\) | 9.22392 | 0.572043 | ||||||||
\(261\) | 0.645401 | 0.0399493 | ||||||||
\(262\) | − | 12.4220i | − | 0.767433i | ||||||
\(263\) | − | 4.35904i | − | 0.268790i | −0.990928 | − | 0.134395i | \(-0.957091\pi\) | ||
0.990928 | − | 0.134395i | \(-0.0429090\pi\) | |||||||
\(264\) | 0.580727 | + | 0.809457i | 0.0357413 | + | 0.0498186i | ||||
\(265\) | − | 10.5567i | − | 0.648495i | ||||||
\(266\) | −3.82377 | + | 42.4077i | −0.234450 | + | 2.60018i | ||||
\(267\) | 3.36901 | 0.206180 | ||||||||
\(268\) | − | 26.2874i | − | 1.60576i | ||||||
\(269\) | 21.1595i | 1.29012i | 0.764133 | + | 0.645059i | \(0.223167\pi\) | ||||
−0.764133 | + | 0.645059i | \(0.776833\pi\) | |||||||
\(270\) | 9.07408i | 0.552231i | ||||||||
\(271\) | 0.512638i | 0.0311405i | 0.999879 | + | 0.0155703i | \(0.00495637\pi\) | ||||
−0.999879 | + | 0.0155703i | \(0.995044\pi\) | |||||||
\(272\) | − | 14.4608i | − | 0.876814i | ||||||
\(273\) | 16.9931 | 1.02847 | ||||||||
\(274\) | 40.0115 | 2.41718 | ||||||||
\(275\) | −2.69484 | + | 1.93335i | −0.162505 | + | 0.116586i | ||||
\(276\) | 10.5913i | 0.637520i | ||||||||
\(277\) | − | 2.99976i | − | 0.180238i | −0.995931 | − | 0.0901191i | \(-0.971275\pi\) | ||
0.995931 | − | 0.0901191i | \(-0.0287248\pi\) | |||||||
\(278\) | 30.4363i | 1.82545i | ||||||||
\(279\) | − | 3.90248i | − | 0.233636i | ||||||
\(280\) | 1.71290i | 0.102366i | ||||||||
\(281\) | −18.2144 | −1.08658 | −0.543291 | − | 0.839544i | \(-0.682822\pi\) | ||||
−0.543291 | + | 0.839544i | \(0.682822\pi\) | |||||||
\(282\) | 2.97701i | 0.177278i | ||||||||
\(283\) | 31.9641i | 1.90007i | 0.312148 | + | 0.950034i | \(0.398952\pi\) | ||||
−0.312148 | + | 0.950034i | \(0.601048\pi\) | |||||||
\(284\) | − | 26.8826i | − | 1.59519i | ||||||
\(285\) | −0.328151 | + | 3.63937i | −0.0194380 | + | 0.215578i | ||||
\(286\) | −23.3488 | + | 16.7511i | −1.38065 | + | 0.990514i | ||||
\(287\) | 27.4807i | 1.62213i | ||||||||
\(288\) | 18.6320 | 1.09790 | ||||||||
\(289\) | 1.02966 | 0.0605682 | ||||||||
\(290\) | 0.574080 | 0.0337111 | ||||||||
\(291\) | −9.44531 | −0.553694 | ||||||||
\(292\) | 1.06479i | 0.0623119i | ||||||||
\(293\) | 27.4990 | 1.60651 | 0.803253 | − | 0.595638i | \(-0.203101\pi\) | ||||
0.803253 | + | 0.595638i | \(0.203101\pi\) | |||||||
\(294\) | 27.1574i | 1.58385i | ||||||||
\(295\) | − | 1.61310i | − | 0.0939181i | ||||||
\(296\) | − | 1.03083i | − | 0.0599157i | ||||||
\(297\) | −8.58553 | − | 11.9671i | −0.498183 | − | 0.694401i | ||||
\(298\) | 47.3474i | 2.74276i | ||||||||
\(299\) | −24.6262 | −1.42417 | ||||||||
\(300\) | 1.82363i | 0.105287i | ||||||||
\(301\) | 24.3492 | 1.40346 | ||||||||
\(302\) | 5.35399 | 0.308087 | ||||||||
\(303\) | −6.26842 | −0.360111 | ||||||||
\(304\) | 15.7092 | + | 1.41645i | 0.900983 | + | 0.0812388i | ||||
\(305\) | − | 1.50074i | − | 0.0859319i | ||||||
\(306\) | − | 18.7589i | − | 1.07238i | ||||||
\(307\) | 12.2286 | 0.697924 | 0.348962 | − | 0.937137i | \(-0.386534\pi\) | ||||
0.348962 | + | 0.937137i | \(0.386534\pi\) | |||||||
\(308\) | −20.1057 | − | 28.0247i | −1.14563 | − | 1.59686i | ||||
\(309\) | 2.38812 | 0.135855 | ||||||||
\(310\) | − | 3.47123i | − | 0.197153i | ||||||
\(311\) | 21.3158 | 1.20871 | 0.604355 | − | 0.796715i | \(-0.293431\pi\) | ||||
0.604355 | + | 0.796715i | \(0.293431\pi\) | |||||||
\(312\) | 1.27364i | 0.0721057i | ||||||||
\(313\) | −6.70861 | −0.379193 | −0.189596 | − | 0.981862i | \(-0.560718\pi\) | ||||
−0.189596 | + | 0.981862i | \(0.560718\pi\) | |||||||
\(314\) | 1.75677 | 0.0991404 | ||||||||
\(315\) | − | 10.9820i | − | 0.618768i | ||||||
\(316\) | −14.7200 | −0.828063 | ||||||||
\(317\) | − | 23.0700i | − | 1.29574i | −0.761750 | − | 0.647871i | \(-0.775660\pi\) | ||
0.761750 | − | 0.647871i | \(-0.224340\pi\) | |||||||
\(318\) | 18.0835 | 1.01407 | ||||||||
\(319\) | −0.757109 | + | 0.543171i | −0.0423899 | + | 0.0304117i | ||||
\(320\) | 9.33592 | 0.521894 | ||||||||
\(321\) | − | 4.95585i | − | 0.276608i | ||||||
\(322\) | − | 56.7332i | − | 3.16162i | ||||||
\(323\) | 1.56431 | − | 17.3490i | 0.0870405 | − | 0.965327i | ||||
\(324\) | 6.89354 | 0.382975 | ||||||||
\(325\) | −4.24020 | −0.235204 | ||||||||
\(326\) | 8.94833 | 0.495602 | ||||||||
\(327\) | − | 14.5715i | − | 0.805804i | ||||||
\(328\) | −2.05969 | −0.113727 | ||||||||
\(329\) | − | 8.30817i | − | 0.458044i | ||||||
\(330\) | −3.31181 | − | 4.61622i | −0.182309 | − | 0.254115i | ||||
\(331\) | − | 8.86321i | − | 0.487166i | −0.969880 | − | 0.243583i | \(-0.921677\pi\) | ||
0.969880 | − | 0.243583i | \(-0.0783228\pi\) | |||||||
\(332\) | − | 32.0978i | − | 1.76160i | ||||||
\(333\) | 6.60902i | 0.362172i | ||||||||
\(334\) | −19.1877 | −1.04990 | ||||||||
\(335\) | 12.0842i | 0.660232i | ||||||||
\(336\) | 14.5018 | 0.791137 | ||||||||
\(337\) | −26.1314 | −1.42347 | −0.711733 | − | 0.702450i | \(-0.752090\pi\) | ||||
−0.711733 | + | 0.702450i | \(0.752090\pi\) | |||||||
\(338\) | −10.1745 | −0.553420 | ||||||||
\(339\) | −10.2708 | −0.557831 | ||||||||
\(340\) | − | 8.69333i | − | 0.471462i | ||||||
\(341\) | 3.28434 | + | 4.57793i | 0.177857 | + | 0.247909i | ||||
\(342\) | 20.3783 | + | 1.83745i | 1.10193 | + | 0.0993580i | ||||
\(343\) | − | 42.3263i | − | 2.28540i | ||||||
\(344\) | 1.82498i | 0.0983964i | ||||||||
\(345\) | − | 4.86877i | − | 0.262126i | ||||||
\(346\) | −25.9124 | −1.39306 | ||||||||
\(347\) | 6.17525i | 0.331505i | 0.986167 | + | 0.165752i | \(0.0530052\pi\) | ||||
−0.986167 | + | 0.165752i | \(0.946995\pi\) | |||||||
\(348\) | 0.512345i | 0.0274646i | ||||||||
\(349\) | 24.6872i | 1.32147i | 0.750617 | + | 0.660737i | \(0.229756\pi\) | ||||
−0.750617 | + | 0.660737i | \(0.770244\pi\) | |||||||
\(350\) | − | 9.76845i | − | 0.522146i | ||||||
\(351\) | − | 18.8297i | − | 1.00505i | ||||||
\(352\) | −21.8569 | + | 15.6807i | −1.16497 | + | 0.835786i | ||||
\(353\) | −14.3112 | −0.761711 | −0.380855 | − | 0.924635i | \(-0.624370\pi\) | ||||
−0.380855 | + | 0.924635i | \(0.624370\pi\) | |||||||
\(354\) | 2.76321 | 0.146863 | ||||||||
\(355\) | 12.3578i | 0.655885i | ||||||||
\(356\) | − | 8.74226i | − | 0.463339i | ||||||
\(357\) | − | 16.0156i | − | 0.847637i | ||||||
\(358\) | − | 1.64239i | − | 0.0868032i | ||||||
\(359\) | 33.9044i | 1.78941i | 0.446662 | + | 0.894703i | \(0.352613\pi\) | ||||
−0.446662 | + | 0.894703i | \(0.647387\pi\) | |||||||
\(360\) | 0.823109 | 0.0433817 | ||||||||
\(361\) | 18.6935 | + | 3.39871i | 0.983871 | + | 0.178879i | ||||
\(362\) | − | 49.6448i | − | 2.60927i | ||||||
\(363\) | 8.73537 | + | 2.95447i | 0.458488 | + | 0.155070i | ||||
\(364\) | − | 44.0956i | − | 2.31124i | ||||||
\(365\) | − | 0.489478i | − | 0.0256205i | ||||||
\(366\) | 2.57074 | 0.134375 | ||||||||
\(367\) | 12.2487 | 0.639375 | 0.319687 | − | 0.947523i | \(-0.396422\pi\) | ||||
0.319687 | + | 0.947523i | \(0.396422\pi\) | |||||||
\(368\) | −21.0158 | −1.09553 | ||||||||
\(369\) | 13.2054 | 0.687447 | ||||||||
\(370\) | 5.87868i | 0.305618i | ||||||||
\(371\) | −50.4672 | −2.62012 | ||||||||
\(372\) | 3.09795 | 0.160621 | ||||||||
\(373\) | −35.2303 | −1.82416 | −0.912078 | − | 0.410016i | \(-0.865523\pi\) | ||||
−0.912078 | + | 0.410016i | \(0.865523\pi\) | |||||||
\(374\) | 15.7875 | + | 22.0057i | 0.816354 | + | 1.13789i | ||||
\(375\) | − | 0.838315i | − | 0.0432904i | ||||||
\(376\) | 0.622701 | 0.0321133 | ||||||||
\(377\) | −1.19127 | −0.0613538 | ||||||||
\(378\) | 43.3792 | 2.23119 | ||||||||
\(379\) | − | 22.4583i | − | 1.15360i | −0.816884 | − | 0.576802i | \(-0.804300\pi\) | ||
0.816884 | − | 0.576802i | \(-0.195700\pi\) | |||||||
\(380\) | 9.44382 | + | 0.851520i | 0.484458 | + | 0.0436821i | ||||
\(381\) | 1.42701i | 0.0731078i | ||||||||
\(382\) | −7.11302 | −0.363934 | ||||||||
\(383\) | 25.4026i | 1.29801i | 0.760783 | + | 0.649006i | \(0.224815\pi\) | ||||
−0.760783 | + | 0.649006i | \(0.775185\pi\) | |||||||
\(384\) | 2.39375i | 0.122155i | ||||||||
\(385\) | 9.24252 | + | 12.8828i | 0.471042 | + | 0.656571i | ||||
\(386\) | 26.4623 | 1.34690 | ||||||||
\(387\) | − | 11.7006i | − | 0.594776i | ||||||
\(388\) | 24.5097i | 1.24429i | ||||||||
\(389\) | 16.7386 | 0.848679 | 0.424339 | − | 0.905503i | \(-0.360506\pi\) | ||||
0.424339 | + | 0.905503i | \(0.360506\pi\) | |||||||
\(390\) | − | 7.26340i | − | 0.367797i | ||||||
\(391\) | 23.2097i | 1.17376i | ||||||||
\(392\) | 5.68051 | 0.286909 | ||||||||
\(393\) | −5.09626 | −0.257073 | ||||||||
\(394\) | − | 22.1757i | − | 1.11720i | ||||||
\(395\) | 6.76671 | 0.340470 | ||||||||
\(396\) | −13.4668 | + | 9.66149i | −0.676734 | + | 0.485508i | ||||
\(397\) | −29.2161 | −1.46632 | −0.733158 | − | 0.680058i | \(-0.761955\pi\) | ||||
−0.733158 | + | 0.680058i | \(0.761955\pi\) | |||||||
\(398\) | −44.7262 | −2.24192 | ||||||||
\(399\) | 17.3982 | + | 1.56875i | 0.871002 | + | 0.0785355i | ||||
\(400\) | −3.61855 | −0.180928 | ||||||||
\(401\) | 4.43897i | 0.221671i | 0.993839 | + | 0.110836i | \(0.0353527\pi\) | ||||
−0.993839 | + | 0.110836i | \(0.964647\pi\) | |||||||
\(402\) | −20.7001 | −1.03243 | ||||||||
\(403\) | 7.20316i | 0.358815i | ||||||||
\(404\) | 16.2660i | 0.809262i | ||||||||
\(405\) | −3.16893 | −0.157466 | ||||||||
\(406\) | − | 2.74443i | − | 0.136204i | ||||||
\(407\) | −5.56217 | − | 7.75293i | −0.275707 | − | 0.384299i | ||||
\(408\) | 1.20038 | 0.0594276 | ||||||||
\(409\) | 18.3611 | 0.907897 | 0.453949 | − | 0.891028i | \(-0.350015\pi\) | ||||
0.453949 | + | 0.891028i | \(0.350015\pi\) | |||||||
\(410\) | 11.7461 | 0.580100 | ||||||||
\(411\) | − | 16.4152i | − | 0.809701i | ||||||
\(412\) | − | 6.19694i | − | 0.305301i | ||||||
\(413\) | −7.71151 | −0.379459 | ||||||||
\(414\) | −27.2623 | −1.33987 | ||||||||
\(415\) | 14.7552i | 0.724306i | ||||||||
\(416\) | −34.3907 | −1.68614 | ||||||||
\(417\) | 12.4869 | 0.611484 | ||||||||
\(418\) | −25.4519 | + | 14.9950i | −1.24489 | + | 0.733429i | ||||
\(419\) | 14.5981 | 0.713162 | 0.356581 | − | 0.934264i | \(-0.383942\pi\) | ||||
0.356581 | + | 0.934264i | \(0.383942\pi\) | |||||||
\(420\) | 8.71798 | 0.425394 | ||||||||
\(421\) | 32.5038i | 1.58414i | 0.610430 | + | 0.792070i | \(0.290997\pi\) | ||||
−0.610430 | + | 0.792070i | \(0.709003\pi\) | |||||||
\(422\) | 28.5721 | 1.39087 | ||||||||
\(423\) | −3.99236 | −0.194115 | ||||||||
\(424\) | − | 3.78253i | − | 0.183696i | ||||||
\(425\) | 3.99629i | 0.193849i | ||||||||
\(426\) | −21.1688 | −1.02563 | ||||||||
\(427\) | −7.17437 | −0.347192 | ||||||||
\(428\) | −12.8600 | −0.621610 | ||||||||
\(429\) | 6.87234 | + | 9.57913i | 0.331800 | + | 0.462485i | ||||
\(430\) | − | 10.4076i | − | 0.501900i | ||||||
\(431\) | 38.6568 | 1.86203 | 0.931016 | − | 0.364979i | \(-0.118924\pi\) | ||||
0.931016 | + | 0.364979i | \(0.118924\pi\) | |||||||
\(432\) | − | 16.0691i | − | 0.773124i | ||||||
\(433\) | 4.08511i | 0.196318i | 0.995171 | + | 0.0981590i | \(0.0312954\pi\) | ||||
−0.995171 | + | 0.0981590i | \(0.968705\pi\) | |||||||
\(434\) | −16.5945 | −0.796559 | ||||||||
\(435\) | − | 0.235523i | − | 0.0112925i | ||||||
\(436\) | −37.8116 | −1.81085 | ||||||||
\(437\) | −25.2133 | − | 2.27341i | −1.20612 | − | 0.108752i | ||||
\(438\) | 0.838469 | 0.0400636 | ||||||||
\(439\) | −17.0748 | −0.814937 | −0.407468 | − | 0.913219i | \(-0.633588\pi\) | ||||
−0.407468 | + | 0.913219i | \(0.633588\pi\) | |||||||
\(440\) | −0.965575 | + | 0.692731i | −0.0460320 | + | 0.0330246i | ||||
\(441\) | −36.4198 | −1.73428 | ||||||||
\(442\) | 34.6250i | 1.64694i | ||||||||
\(443\) | 1.35565 | 0.0644090 | 0.0322045 | − | 0.999481i | \(-0.489747\pi\) | ||||
0.0322045 | + | 0.999481i | \(0.489747\pi\) | |||||||
\(444\) | −5.24650 | −0.248988 | ||||||||
\(445\) | 4.01878i | 0.190509i | ||||||||
\(446\) | − | 6.43913i | − | 0.304902i | ||||||
\(447\) | 19.4248 | 0.918763 | ||||||||
\(448\) | − | 44.6310i | − | 2.10862i | ||||||
\(449\) | − | 32.3293i | − | 1.52571i | −0.646568 | − | 0.762857i | \(-0.723796\pi\) | ||
0.646568 | − | 0.762857i | \(-0.276204\pi\) | |||||||
\(450\) | −4.69408 | −0.221281 | ||||||||
\(451\) | −15.4911 | + | 11.1137i | −0.729445 | + | 0.523325i | ||||
\(452\) | 26.6517i | 1.25359i | ||||||||
\(453\) | − | 2.19654i | − | 0.103202i | ||||||
\(454\) | 15.4108 | 0.723266 | ||||||||
\(455\) | 20.2706i | 0.950298i | ||||||||
\(456\) | −0.117578 | + | 1.30401i | −0.00550610 | + | 0.0610657i | ||||
\(457\) | − | 8.90740i | − | 0.416671i | −0.978057 | − | 0.208335i | \(-0.933195\pi\) | ||
0.978057 | − | 0.208335i | \(-0.0668045\pi\) | |||||||
\(458\) | 24.8716 | 1.16218 | ||||||||
\(459\) | −17.7465 | −0.828337 | ||||||||
\(460\) | −12.6340 | −0.589063 | ||||||||
\(461\) | − | 24.1691i | − | 1.12567i | −0.826570 | − | 0.562833i | \(-0.809711\pi\) | ||
0.826570 | − | 0.562833i | \(-0.190289\pi\) | |||||||
\(462\) | −22.0681 | + | 15.8323i | −1.02670 | + | 0.736586i | ||||
\(463\) | −35.5508 | −1.65218 | −0.826092 | − | 0.563536i | \(-0.809441\pi\) | ||||
−0.826092 | + | 0.563536i | \(0.809441\pi\) | |||||||
\(464\) | −1.01662 | −0.0471956 | ||||||||
\(465\) | −1.42411 | −0.0660417 | ||||||||
\(466\) | − | 20.0082i | − | 0.926864i | ||||||
\(467\) | −26.5304 | −1.22768 | −0.613840 | − | 0.789430i | \(-0.710376\pi\) | ||||
−0.613840 | + | 0.789430i | \(0.710376\pi\) | |||||||
\(468\) | −21.1894 | −0.979482 | ||||||||
\(469\) | 57.7694 | 2.66754 | ||||||||
\(470\) | −3.55118 | −0.163804 | ||||||||
\(471\) | − | 0.720736i | − | 0.0332098i | ||||||
\(472\) | − | 0.577981i | − | 0.0266037i | ||||||
\(473\) | 9.84727 | + | 13.7258i | 0.452778 | + | 0.631113i | ||||
\(474\) | 11.5913i | 0.532406i | ||||||||
\(475\) | −4.34129 | − | 0.391440i | −0.199192 | − | 0.0179605i | ||||
\(476\) | −41.5591 | −1.90486 | ||||||||
\(477\) | 24.2512i | 1.11039i | ||||||||
\(478\) | 43.6851i | 1.99811i | ||||||||
\(479\) | 17.7512i | 0.811073i | 0.914079 | + | 0.405536i | \(0.132915\pi\) | ||||
−0.914079 | + | 0.405536i | \(0.867085\pi\) | |||||||
\(480\) | − | 6.79928i | − | 0.310343i | ||||||
\(481\) | − | 12.1989i | − | 0.556221i | ||||||
\(482\) | −48.1068 | −2.19120 | ||||||||
\(483\) | −23.2755 | −1.05907 | ||||||||
\(484\) | 7.66658 | − | 22.6675i | 0.348481 | − | 1.03034i | ||||
\(485\) | − | 11.2670i | − | 0.511608i | ||||||
\(486\) | − | 32.6506i | − | 1.48106i | ||||||
\(487\) | 16.5288i | 0.748989i | 0.927229 | + | 0.374495i | \(0.122184\pi\) | ||||
−0.927229 | + | 0.374495i | \(0.877816\pi\) | |||||||
\(488\) | − | 0.537722i | − | 0.0243415i | ||||||
\(489\) | − | 3.67116i | − | 0.166015i | ||||||
\(490\) | −32.3952 | −1.46346 | ||||||||
\(491\) | 2.95440i | 0.133330i | 0.997775 | + | 0.0666651i | \(0.0212359\pi\) | ||||
−0.997775 | + | 0.0666651i | \(0.978764\pi\) | |||||||
\(492\) | 10.4830i | 0.472610i | ||||||||
\(493\) | 1.12275i | 0.0505661i | ||||||||
\(494\) | −37.6141 | − | 3.39155i | −1.69234 | − | 0.152593i | ||||
\(495\) | 6.19065 | − | 4.44135i | 0.278249 | − | 0.199624i | ||||
\(496\) | 6.14712i | 0.276014i | ||||||||
\(497\) | 59.0774 | 2.64998 | ||||||||
\(498\) | −25.2755 | −1.13262 | ||||||||
\(499\) | −5.61842 | −0.251515 | −0.125757 | − | 0.992061i | \(-0.540136\pi\) | ||||
−0.125757 | + | 0.992061i | \(0.540136\pi\) | |||||||
\(500\) | −2.17535 | −0.0972846 | ||||||||
\(501\) | 7.87197i | 0.351694i | ||||||||
\(502\) | −11.4510 | −0.511081 | ||||||||
\(503\) | − | 6.36857i | − | 0.283960i | −0.989870 | − | 0.141980i | \(-0.954653\pi\) | ||
0.989870 | − | 0.141980i | \(-0.0453469\pi\) | |||||||
\(504\) | − | 3.93493i | − | 0.175276i | ||||||
\(505\) | − | 7.47740i | − | 0.332740i | ||||||
\(506\) | 31.9809 | − | 22.9440i | 1.42172 | − | 1.01999i | ||||
\(507\) | 4.17421i | 0.185383i | ||||||||
\(508\) | 3.70295 | 0.164292 | ||||||||
\(509\) | − | 37.1203i | − | 1.64533i | −0.568527 | − | 0.822665i | \(-0.692486\pi\) | ||
0.568527 | − | 0.822665i | \(-0.307514\pi\) | |||||||
\(510\) | −6.84559 | −0.303128 | ||||||||
\(511\) | −2.33998 | −0.103515 | ||||||||
\(512\) | −31.9419 | −1.41164 | ||||||||
\(513\) | 1.73829 | − | 19.2786i | 0.0767473 | − | 0.851169i | ||||
\(514\) | − | 36.6315i | − | 1.61574i | ||||||
\(515\) | 2.84871i | 0.125529i | ||||||||
\(516\) | 9.28841 | 0.408900 | ||||||||
\(517\) | 4.68337 | − | 3.35998i | 0.205974 | − | 0.147772i | ||||
\(518\) | 28.1034 | 1.23479 | ||||||||
\(519\) | 10.6309i | 0.466644i | ||||||||
\(520\) | −1.51929 | −0.0666251 | ||||||||
\(521\) | − | 28.8890i | − | 1.26565i | −0.774294 | − | 0.632826i | \(-0.781895\pi\) | ||
0.774294 | − | 0.632826i | \(-0.218105\pi\) | |||||||
\(522\) | −1.31879 | −0.0577219 | ||||||||
\(523\) | 9.81873 | 0.429343 | 0.214671 | − | 0.976686i | \(-0.431132\pi\) | ||||
0.214671 | + | 0.976686i | \(0.431132\pi\) | |||||||
\(524\) | 13.2243i | 0.577708i | ||||||||
\(525\) | −4.00762 | −0.174907 | ||||||||
\(526\) | 8.90711i | 0.388369i | ||||||||
\(527\) | 6.78882 | 0.295726 | ||||||||
\(528\) | 5.86480 | + | 8.17476i | 0.255233 | + | 0.355761i | ||||
\(529\) | 10.7305 | 0.466546 | ||||||||
\(530\) | 21.5713i | 0.936996i | ||||||||
\(531\) | 3.70565i | 0.160811i | ||||||||
\(532\) | 4.07075 | − | 45.1468i | 0.176489 | − | 1.95736i | ||||
\(533\) | −24.3744 | −1.05577 | ||||||||
\(534\) | −6.88412 | −0.297905 | ||||||||
\(535\) | 5.91167 | 0.255584 | ||||||||
\(536\) | 4.32984i | 0.187021i | ||||||||
\(537\) | −0.673811 | −0.0290771 | ||||||||
\(538\) | − | 43.2367i | − | 1.86406i | ||||||
\(539\) | 42.7235 | − | 30.6510i | 1.84023 | − | 1.32023i | ||||
\(540\) | − | 9.66018i | − | 0.415708i | ||||||
\(541\) | 23.4115i | 1.00654i | 0.864129 | + | 0.503270i | \(0.167870\pi\) | ||||
−0.864129 | + | 0.503270i | \(0.832130\pi\) | |||||||
\(542\) | − | 1.04751i | − | 0.0449943i | ||||||
\(543\) | −20.3674 | −0.874048 | ||||||||
\(544\) | 32.4125i | 1.38967i | ||||||||
\(545\) | 17.3818 | 0.744556 | ||||||||
\(546\) | −34.7232 | −1.48602 | ||||||||
\(547\) | −9.02603 | −0.385925 | −0.192963 | − | 0.981206i | \(-0.561810\pi\) | ||||
−0.192963 | + | 0.981206i | \(0.561810\pi\) | |||||||
\(548\) | −42.5959 | −1.81961 | ||||||||
\(549\) | 3.44753i | 0.147137i | ||||||||
\(550\) | 5.50654 | − | 3.95055i | 0.234800 | − | 0.168452i | ||||
\(551\) | −1.21968 | − | 0.109974i | −0.0519599 | − | 0.00468506i | ||||
\(552\) | − | 1.74451i | − | 0.0742511i | ||||||
\(553\) | − | 32.3487i | − | 1.37561i | ||||||
\(554\) | 6.12961i | 0.260422i | ||||||||
\(555\) | 2.41180 | 0.102375 | ||||||||
\(556\) | − | 32.4022i | − | 1.37416i | ||||||
\(557\) | − | 4.62806i | − | 0.196097i | −0.995182 | − | 0.0980485i | \(-0.968740\pi\) | ||
0.995182 | − | 0.0980485i | \(-0.0312600\pi\) | |||||||
\(558\) | 7.97421i | 0.337575i | ||||||||
\(559\) | 21.5969i | 0.913451i | ||||||||
\(560\) | 17.2987i | 0.731005i | ||||||||
\(561\) | 9.02812 | − | 6.47703i | 0.381167 | − | 0.273460i | ||||
\(562\) | 37.2188 | 1.56998 | ||||||||
\(563\) | 6.88954 | 0.290359 | 0.145180 | − | 0.989405i | \(-0.453624\pi\) | ||||
0.145180 | + | 0.989405i | \(0.453624\pi\) | |||||||
\(564\) | − | 3.16930i | − | 0.133451i | ||||||
\(565\) | − | 12.2517i | − | 0.515431i | ||||||
\(566\) | − | 65.3144i | − | 2.74537i | ||||||
\(567\) | 15.1493i | 0.636211i | ||||||||
\(568\) | 4.42787i | 0.185789i | ||||||||
\(569\) | 9.45500 | 0.396374 | 0.198187 | − | 0.980164i | \(-0.436495\pi\) | ||||
0.198187 | + | 0.980164i | \(0.436495\pi\) | |||||||
\(570\) | 0.670532 | − | 7.43657i | 0.0280855 | − | 0.311484i | ||||
\(571\) | 38.5665i | 1.61396i | 0.590581 | + | 0.806979i | \(0.298899\pi\) | ||||
−0.590581 | + | 0.806979i | \(0.701101\pi\) | |||||||
\(572\) | 24.8570 | − | 17.8331i | 1.03932 | − | 0.745639i | ||||
\(573\) | 2.91820i | 0.121910i | ||||||||
\(574\) | − | 56.1532i | − | 2.34379i | ||||||
\(575\) | 5.80780 | 0.242202 | ||||||||
\(576\) | −21.4467 | −0.893613 | ||||||||
\(577\) | −17.0872 | −0.711349 | −0.355674 | − | 0.934610i | \(-0.615749\pi\) | ||||
−0.355674 | + | 0.934610i | \(0.615749\pi\) | |||||||
\(578\) | −2.10397 | −0.0875138 | ||||||||
\(579\) | − | 10.8565i | − | 0.451180i | ||||||
\(580\) | −0.611160 | −0.0253770 | ||||||||
\(581\) | 70.5384 | 2.92643 | ||||||||
\(582\) | 19.3002 | 0.800020 | ||||||||
\(583\) | −20.4099 | − | 28.4487i | −0.845291 | − | 1.17822i | ||||
\(584\) | − | 0.175383i | − | 0.00725739i | ||||||
\(585\) | 9.74070 | 0.402728 | ||||||||
\(586\) | −56.1905 | −2.32121 | ||||||||
\(587\) | 4.62095 | 0.190727 | 0.0953636 | − | 0.995443i | \(-0.469599\pi\) | ||||
0.0953636 | + | 0.995443i | \(0.469599\pi\) | |||||||
\(588\) | − | 28.9115i | − | 1.19229i | ||||||
\(589\) | −0.664971 | + | 7.37489i | −0.0273996 | + | 0.303877i | ||||
\(590\) | 3.29615i | 0.135700i | ||||||||
\(591\) | −9.09784 | −0.374235 | ||||||||
\(592\) | − | 10.4104i | − | 0.427865i | ||||||
\(593\) | 24.1621i | 0.992216i | 0.868261 | + | 0.496108i | \(0.165238\pi\) | ||||
−0.868261 | + | 0.496108i | \(0.834762\pi\) | |||||||
\(594\) | 17.5434 | + | 24.4532i | 0.719814 | + | 1.00333i | ||||
\(595\) | 19.1045 | 0.783210 | ||||||||
\(596\) | − | 50.4056i | − | 2.06469i | ||||||
\(597\) | 18.3494i | 0.750993i | ||||||||
\(598\) | 50.3204 | 2.05776 | ||||||||
\(599\) | 18.4185i | 0.752559i | 0.926506 | + | 0.376280i | \(0.122797\pi\) | ||||
−0.926506 | + | 0.376280i | \(0.877203\pi\) | |||||||
\(600\) | − | 0.300373i | − | 0.0122627i | ||||||
\(601\) | 21.9532 | 0.895489 | 0.447744 | − | 0.894162i | \(-0.352227\pi\) | ||||
0.447744 | + | 0.894162i | \(0.352227\pi\) | |||||||
\(602\) | −49.7543 | −2.02783 | ||||||||
\(603\) | − | 27.7602i | − | 1.13048i | ||||||
\(604\) | −5.69981 | −0.231922 | ||||||||
\(605\) | −3.52430 | + | 10.4201i | −0.143283 | + | 0.423639i | ||||
\(606\) | 12.8087 | 0.520318 | ||||||||
\(607\) | −8.55737 | −0.347333 | −0.173666 | − | 0.984805i | \(-0.555561\pi\) | ||||
−0.173666 | + | 0.984805i | \(0.555561\pi\) | |||||||
\(608\) | −35.2106 | − | 3.17483i | −1.42798 | − | 0.128756i | ||||
\(609\) | −1.12593 | −0.0456251 | ||||||||
\(610\) | 3.06655i | 0.124161i | ||||||||
\(611\) | 7.36906 | 0.298120 | ||||||||
\(612\) | 19.9706i | 0.807262i | ||||||||
\(613\) | 2.23422i | 0.0902395i | 0.998982 | + | 0.0451197i | \(0.0143669\pi\) | ||||
−0.998982 | + | 0.0451197i | \(0.985633\pi\) | |||||||
\(614\) | −24.9876 | −1.00842 | ||||||||
\(615\) | − | 4.81899i | − | 0.194320i | ||||||
\(616\) | 3.31165 | + | 4.61600i | 0.133430 | + | 0.185984i | ||||
\(617\) | 6.18327 | 0.248929 | 0.124464 | − | 0.992224i | \(-0.460279\pi\) | ||||
0.124464 | + | 0.992224i | \(0.460279\pi\) | |||||||
\(618\) | −4.87980 | −0.196294 | ||||||||
\(619\) | 30.0279 | 1.20692 | 0.603462 | − | 0.797392i | \(-0.293788\pi\) | ||||
0.603462 | + | 0.797392i | \(0.293788\pi\) | |||||||
\(620\) | 3.69544i | 0.148412i | ||||||||
\(621\) | 25.7910i | 1.03496i | ||||||||
\(622\) | −43.5560 | −1.74644 | ||||||||
\(623\) | 19.2121 | 0.769715 | ||||||||
\(624\) | 12.8626i | 0.514916i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 13.7082 | 0.547888 | ||||||||
\(627\) | 6.15187 | + | 10.4419i | 0.245682 | + | 0.417011i | ||||
\(628\) | −1.87024 | −0.0746308 | ||||||||
\(629\) | −11.4972 | −0.458422 | ||||||||
\(630\) | 22.4404i | 0.894045i | ||||||||
\(631\) | −35.1837 | −1.40064 | −0.700320 | − | 0.713829i | \(-0.746959\pi\) | ||||
−0.700320 | + | 0.713829i | \(0.746959\pi\) | |||||||
\(632\) | 2.42455 | 0.0964435 | ||||||||
\(633\) | − | 11.7220i | − | 0.465909i | ||||||
\(634\) | 47.1405i | 1.87219i | ||||||||
\(635\) | −1.70223 | −0.0675510 | ||||||||
\(636\) | −19.2516 | −0.763374 | ||||||||
\(637\) | 67.2233 | 2.66349 | ||||||||
\(638\) | 1.54705 | − | 1.10990i | 0.0612483 | − | 0.0439413i | ||||
\(639\) | − | 28.3887i | − | 1.12304i | ||||||
\(640\) | −2.85543 | −0.112871 | ||||||||
\(641\) | − | 18.9080i | − | 0.746821i | −0.927666 | − | 0.373411i | \(-0.878188\pi\) | ||
0.927666 | − | 0.373411i | \(-0.121812\pi\) | |||||||
\(642\) | 10.1266i | 0.399666i | ||||||||
\(643\) | 11.4234 | 0.450495 | 0.225248 | − | 0.974302i | \(-0.427681\pi\) | ||||
0.225248 | + | 0.974302i | \(0.427681\pi\) | |||||||
\(644\) | 60.3977i | 2.38000i | ||||||||
\(645\) | −4.26985 | −0.168125 | ||||||||
\(646\) | −3.19646 | + | 35.4505i | −0.125763 | + | 1.39478i | ||||
\(647\) | −6.93587 | −0.272677 | −0.136339 | − | 0.990662i | \(-0.543534\pi\) | ||||
−0.136339 | + | 0.990662i | \(0.543534\pi\) | |||||||
\(648\) | −1.13545 | −0.0446046 | ||||||||
\(649\) | −3.11868 | − | 4.34703i | −0.122419 | − | 0.170636i | ||||
\(650\) | 8.66428 | 0.339841 | ||||||||
\(651\) | 6.80807i | 0.266829i | ||||||||
\(652\) | −9.52631 | −0.373079 | ||||||||
\(653\) | −10.1523 | −0.397289 | −0.198645 | − | 0.980072i | \(-0.563654\pi\) | ||||
−0.198645 | + | 0.980072i | \(0.563654\pi\) | |||||||
\(654\) | 29.7748i | 1.16429i | ||||||||
\(655\) | − | 6.07917i | − | 0.237533i | ||||||
\(656\) | −20.8009 | −0.812141 | ||||||||
\(657\) | 1.12444i | 0.0438687i | ||||||||
\(658\) | 16.9766i | 0.661819i | ||||||||
\(659\) | −37.0084 | −1.44164 | −0.720822 | − | 0.693121i | \(-0.756235\pi\) | ||||
−0.720822 | + | 0.693121i | \(0.756235\pi\) | |||||||
\(660\) | 3.52572 | + | 4.91439i | 0.137238 | + | 0.191292i | ||||
\(661\) | 29.2224i | 1.13662i | 0.822815 | + | 0.568309i | \(0.192402\pi\) | ||||
−0.822815 | + | 0.568309i | \(0.807598\pi\) | |||||||
\(662\) | 18.1108i | 0.703896i | ||||||||
\(663\) | 14.2053 | 0.551689 | ||||||||
\(664\) | 5.28688i | 0.205171i | ||||||||
\(665\) | −1.87131 | + | 20.7538i | −0.0725662 | + | 0.804798i | ||||
\(666\) | − | 13.5047i | − | 0.523295i | ||||||
\(667\) | 1.63169 | 0.0631792 | ||||||||
\(668\) | 20.4270 | 0.790345 | ||||||||
\(669\) | −2.64173 | −0.102135 | ||||||||
\(670\) | − | 24.6925i | − | 0.953955i | ||||||
\(671\) | −2.90145 | − | 4.04424i | −0.112009 | − | 0.156126i | ||||
\(672\) | −32.5044 | −1.25388 | ||||||||
\(673\) | −32.3665 | −1.24764 | −0.623818 | − | 0.781570i | \(-0.714419\pi\) | ||||
−0.623818 | + | 0.781570i | \(0.714419\pi\) | |||||||
\(674\) | 53.3960 | 2.05674 | ||||||||
\(675\) | 4.44075i | 0.170924i | ||||||||
\(676\) | 10.8317 | 0.416603 | ||||||||
\(677\) | 36.1224 | 1.38830 | 0.694148 | − | 0.719832i | \(-0.255781\pi\) | ||||
0.694148 | + | 0.719832i | \(0.255781\pi\) | |||||||
\(678\) | 20.9869 | 0.805998 | ||||||||
\(679\) | −53.8627 | −2.06706 | ||||||||
\(680\) | 1.43189i | 0.0549106i | ||||||||
\(681\) | − | 6.32247i | − | 0.242278i | ||||||
\(682\) | −6.71111 | − | 9.35440i | −0.256982 | − | 0.358199i | ||||
\(683\) | 7.52944i | 0.288106i | 0.989570 | + | 0.144053i | \(0.0460136\pi\) | ||||
−0.989570 | + | 0.144053i | \(0.953986\pi\) | |||||||
\(684\) | −21.6946 | − | 1.95613i | −0.829514 | − | 0.0747947i | ||||
\(685\) | 19.5811 | 0.748157 | ||||||||
\(686\) | 86.4881i | 3.30213i | ||||||||
\(687\) | − | 10.2039i | − | 0.389302i | ||||||
\(688\) | 18.4306i | 0.702660i | ||||||||
\(689\) | − | 44.7626i | − | 1.70532i | ||||||
\(690\) | 9.94868i | 0.378740i | ||||||||
\(691\) | 31.3023 | 1.19080 | 0.595398 | − | 0.803431i | \(-0.296995\pi\) | ||||
0.595398 | + | 0.803431i | \(0.296995\pi\) | |||||||
\(692\) | 27.5861 | 1.04867 | ||||||||
\(693\) | −21.2322 | − | 29.5948i | −0.806543 | − | 1.12421i | ||||
\(694\) | − | 12.6183i | − | 0.478984i | ||||||
\(695\) | 14.8952i | 0.565006i | ||||||||
\(696\) | − | 0.0843892i | − | 0.00319876i | ||||||
\(697\) | 22.9724i | 0.870140i | ||||||||
\(698\) | − | 50.4450i | − | 1.90937i | ||||||
\(699\) | −8.20862 | −0.310478 | ||||||||
\(700\) | 10.3994i | 0.393061i | ||||||||
\(701\) | − | 3.29429i | − | 0.124424i | −0.998063 | − | 0.0622118i | \(-0.980185\pi\) | ||
0.998063 | − | 0.0622118i | \(-0.0198154\pi\) | |||||||
\(702\) | 38.4759i | 1.45218i | ||||||||
\(703\) | 1.12616 | − | 12.4897i | 0.0424738 | − | 0.471058i | ||||
\(704\) | 25.1588 | − | 18.0496i | 0.948207 | − | 0.680271i | ||||
\(705\) | 1.45691i | 0.0548705i | ||||||||
\(706\) | 29.2431 | 1.10058 | ||||||||
\(707\) | −35.7462 | −1.34438 | ||||||||
\(708\) | −2.94169 | −0.110555 | ||||||||
\(709\) | −13.3297 | −0.500607 | −0.250303 | − | 0.968167i | \(-0.580530\pi\) | ||||
−0.250303 | + | 0.968167i | \(0.580530\pi\) | |||||||
\(710\) | − | 25.2516i | − | 0.947674i | ||||||
\(711\) | −15.5447 | −0.582971 | ||||||||
\(712\) | 1.43995i | 0.0539645i | ||||||||
\(713\) | − | 9.86617i | − | 0.369491i | ||||||
\(714\) | 32.7258i | 1.22473i | ||||||||
\(715\) | −11.4266 | + | 8.19780i | −0.427332 | + | 0.306580i | ||||
\(716\) | 1.74848i | 0.0653437i | ||||||||
\(717\) | 17.9223 | 0.669322 | ||||||||
\(718\) | − | 69.2791i | − | 2.58547i | ||||||
\(719\) | −18.2514 | −0.680662 | −0.340331 | − | 0.940306i | \(-0.610539\pi\) | ||||
−0.340331 | + | 0.940306i | \(0.610539\pi\) | |||||||
\(720\) | 8.31263 | 0.309794 | ||||||||
\(721\) | 13.6184 | 0.507177 | ||||||||
\(722\) | −38.1978 | − | 6.94481i | −1.42157 | − | 0.258459i | ||||
\(723\) | 19.7364i | 0.734004i | ||||||||
\(724\) | 52.8514i | 1.96421i | ||||||||
\(725\) | 0.280948 | 0.0104341 | ||||||||
\(726\) | −17.8496 | − | 6.03707i | −0.662459 | − | 0.224057i | ||||
\(727\) | −5.73117 | −0.212557 | −0.106279 | − | 0.994336i | \(-0.533894\pi\) | ||||
−0.106279 | + | 0.994336i | \(0.533894\pi\) | |||||||
\(728\) | 7.26305i | 0.269187i | ||||||||
\(729\) | −3.88848 | −0.144018 | ||||||||
\(730\) | 1.00018i | 0.0370185i | ||||||||
\(731\) | 20.3546 | 0.752841 | ||||||||
\(732\) | −2.73679 | −0.101155 | ||||||||
\(733\) | − | 42.2696i | − | 1.56126i | −0.624991 | − | 0.780632i | \(-0.714897\pi\) | ||
0.624991 | − | 0.780632i | \(-0.285103\pi\) | |||||||
\(734\) | −25.0285 | −0.923819 | ||||||||
\(735\) | 13.2905i | 0.490228i | ||||||||
\(736\) | 47.1050 | 1.73631 | ||||||||
\(737\) | 23.3631 | + | 32.5650i | 0.860590 | + | 1.19955i | ||||
\(738\) | −26.9835 | −0.993277 | ||||||||
\(739\) | 46.6279i | 1.71524i | 0.514287 | + | 0.857618i | \(0.328057\pi\) | ||||
−0.514287 | + | 0.857618i | \(0.671943\pi\) | |||||||
\(740\) | − | 6.25839i | − | 0.230063i | ||||||
\(741\) | −1.39142 | + | 15.4316i | −0.0511152 | + | 0.566896i | ||||
\(742\) | 103.123 | 3.78576 | ||||||||
\(743\) | 2.67695 | 0.0982077 | 0.0491038 | − | 0.998794i | \(-0.484363\pi\) | ||||
0.0491038 | + | 0.998794i | \(0.484363\pi\) | |||||||
\(744\) | −0.510268 | −0.0187073 | ||||||||
\(745\) | 23.1713i | 0.848930i | ||||||||
\(746\) | 71.9885 | 2.63569 | ||||||||
\(747\) | − | 33.8961i | − | 1.24019i | ||||||
\(748\) | −16.8073 | − | 23.4271i | −0.614535 | − | 0.856580i | ||||
\(749\) | − | 28.2611i | − | 1.03264i | ||||||
\(750\) | 1.71299i | 0.0625494i | ||||||||
\(751\) | − | 29.4294i | − | 1.07389i | −0.843616 | − | 0.536946i | \(-0.819578\pi\) | ||
0.843616 | − | 0.536946i | \(-0.180422\pi\) | |||||||
\(752\) | 6.28870 | 0.229325 | ||||||||
\(753\) | 4.69789i | 0.171201i | ||||||||
\(754\) | 2.43421 | 0.0886488 | ||||||||
\(755\) | 2.62018 | 0.0953580 | ||||||||
\(756\) | −46.1811 | −1.67959 | ||||||||
\(757\) | 41.2088 | 1.49776 | 0.748879 | − | 0.662707i | \(-0.230592\pi\) | ||||
0.748879 | + | 0.662707i | \(0.230592\pi\) | |||||||
\(758\) | 45.8905i | 1.66682i | ||||||||
\(759\) | −9.41305 | − | 13.1205i | −0.341672 | − | 0.476245i | ||||
\(760\) | −1.55551 | − | 0.140255i | −0.0564242 | − | 0.00508759i | ||||
\(761\) | 21.4284i | 0.776778i | 0.921496 | + | 0.388389i | \(0.126968\pi\) | ||||
−0.921496 | + | 0.388389i | \(0.873032\pi\) | |||||||
\(762\) | − | 2.91590i | − | 0.105632i | ||||||
\(763\) | − | 83.0950i | − | 3.00824i | ||||||
\(764\) | 7.57246 | 0.273962 | ||||||||
\(765\) | − | 9.18039i | − | 0.331918i | ||||||
\(766\) | − | 51.9069i | − | 1.87547i | ||||||
\(767\) | − | 6.83985i | − | 0.246973i | ||||||
\(768\) | 10.7616i | 0.388325i | ||||||||
\(769\) | 40.2910i | 1.45293i | 0.687203 | + | 0.726466i | \(0.258838\pi\) | ||||
−0.687203 | + | 0.726466i | \(0.741162\pi\) | |||||||
\(770\) | −18.8859 | − | 26.3244i | −0.680599 | − | 0.948665i | ||||
\(771\) | −15.0285 | −0.541238 | ||||||||
\(772\) | −28.1716 | −1.01392 | ||||||||
\(773\) | 45.7752i | 1.64642i | 0.567738 | + | 0.823209i | \(0.307819\pi\) | ||||
−0.567738 | + | 0.823209i | \(0.692181\pi\) | |||||||
\(774\) | 23.9087i | 0.859379i | ||||||||
\(775\) | − | 1.69878i | − | 0.0610220i | ||||||
\(776\) | − | 4.03703i | − | 0.144921i | ||||||
\(777\) | − | 11.5298i | − | 0.413628i | ||||||
\(778\) | −34.2030 | −1.22624 | ||||||||
\(779\) | −24.9555 | − | 2.25016i | −0.894125 | − | 0.0806205i | ||||
\(780\) | 7.73255i | 0.276870i | ||||||||
\(781\) | 23.8920 | + | 33.3023i | 0.854924 | + | 1.19165i | ||||
\(782\) | − | 47.4259i | − | 1.69595i | ||||||
\(783\) | 1.24762i | 0.0445862i | ||||||||
\(784\) | 57.3679 | 2.04885 | ||||||||
\(785\) | 0.859743 | 0.0306856 | ||||||||
\(786\) | 10.4135 | 0.371439 | ||||||||
\(787\) | −26.4863 | −0.944135 | −0.472068 | − | 0.881562i | \(-0.656492\pi\) | ||||
−0.472068 | + | 0.881562i | \(0.656492\pi\) | |||||||
\(788\) | 23.6080i | 0.841002i | ||||||||
\(789\) | 3.65425 | 0.130095 | ||||||||
\(790\) | −13.8269 | −0.491938 | ||||||||
\(791\) | −58.5699 | −2.08251 | ||||||||
\(792\) | 2.21815 | − | 1.59136i | 0.0788184 | − | 0.0565465i | ||||
\(793\) | − | 6.36342i | − | 0.225972i | ||||||
\(794\) | 59.6993 | 2.11865 | ||||||||
\(795\) | 8.84987 | 0.313873 | ||||||||
\(796\) | 47.6151 | 1.68767 | ||||||||
\(797\) | 25.5522i | 0.905107i | 0.891737 | + | 0.452553i | \(0.149487\pi\) | ||||
−0.891737 | + | 0.452553i | \(0.850513\pi\) | |||||||
\(798\) | −35.5510 | − | 3.20552i | −1.25849 | − | 0.113474i | ||||
\(799\) | − | 6.94517i | − | 0.245703i | ||||||
\(800\) | 8.11064 | 0.286754 | ||||||||
\(801\) | − | 9.23206i | − | 0.326199i | ||||||
\(802\) | − | 9.07044i | − | 0.320288i | ||||||
\(803\) | −0.946334 | − | 1.31906i | −0.0333954 | − | 0.0465488i | ||||
\(804\) | 22.0372 | 0.777190 | ||||||||
\(805\) | − | 27.7646i | − | 0.978573i | ||||||
\(806\) | − | 14.7187i | − | 0.518444i | ||||||
\(807\) | −17.7383 | −0.624419 | ||||||||
\(808\) | − | 2.67919i | − | 0.0942537i | ||||||
\(809\) | 16.4494i | 0.578329i | 0.957279 | + | 0.289165i | \(0.0933775\pi\) | ||||
−0.957279 | + | 0.289165i | \(0.906623\pi\) | |||||||
\(810\) | 6.47530 | 0.227519 | ||||||||
\(811\) | 10.1198 | 0.355353 | 0.177676 | − | 0.984089i | \(-0.443142\pi\) | ||||
0.177676 | + | 0.984089i | \(0.443142\pi\) | |||||||
\(812\) | 2.92169i | 0.102531i | ||||||||
\(813\) | −0.429752 | −0.0150721 | ||||||||
\(814\) | 11.3656 | + | 15.8421i | 0.398363 | + | 0.555265i | ||||
\(815\) | 4.37921 | 0.153397 | ||||||||
\(816\) | 12.1227 | 0.424379 | ||||||||
\(817\) | −1.99375 | + | 22.1118i | −0.0697524 | + | 0.773593i | ||||
\(818\) | −37.5185 | −1.31180 | ||||||||
\(819\) | − | 46.5661i | − | 1.62715i | ||||||
\(820\) | −12.5048 | −0.436687 | ||||||||
\(821\) | 15.5106i | 0.541324i | 0.962674 | + | 0.270662i | \(0.0872425\pi\) | ||||
−0.962674 | + | 0.270662i | \(0.912757\pi\) | |||||||
\(822\) | 33.5422i | 1.16992i | ||||||||
\(823\) | 39.7706 | 1.38632 | 0.693158 | − | 0.720786i | \(-0.256219\pi\) | ||||
0.693158 | + | 0.720786i | \(0.256219\pi\) | |||||||
\(824\) | 1.02071i | 0.0355580i | ||||||||
\(825\) | −1.62076 | − | 2.25912i | −0.0564276 | − | 0.0786526i | ||||
\(826\) | 15.7575 | 0.548272 | ||||||||
\(827\) | 22.2810 | 0.774785 | 0.387393 | − | 0.921915i | \(-0.373376\pi\) | ||||
0.387393 | + | 0.921915i | \(0.373376\pi\) | |||||||
\(828\) | 29.0232 | 1.00862 | ||||||||
\(829\) | 27.9389i | 0.970358i | 0.874415 | + | 0.485179i | \(0.161246\pi\) | ||||
−0.874415 | + | 0.485179i | \(0.838754\pi\) | |||||||
\(830\) | − | 30.1504i | − | 1.04653i | ||||||
\(831\) | 2.51475 | 0.0872356 | ||||||||
\(832\) | 39.5861 | 1.37240 | ||||||||
\(833\) | − | 63.3565i | − | 2.19517i | ||||||
\(834\) | −25.5152 | −0.883520 | ||||||||
\(835\) | −9.39022 | −0.324962 | ||||||||
\(836\) | 27.0959 | − | 15.9635i | 0.937130 | − | 0.552110i | ||||
\(837\) | 7.54385 | 0.260754 | ||||||||
\(838\) | −29.8292 | −1.03043 | ||||||||
\(839\) | 38.1453i | 1.31692i | 0.752616 | + | 0.658460i | \(0.228792\pi\) | ||||
−0.752616 | + | 0.658460i | \(0.771208\pi\) | |||||||
\(840\) | −1.43595 | −0.0495451 | ||||||||
\(841\) | −28.9211 | −0.997278 | ||||||||
\(842\) | − | 66.4173i | − | 2.28889i | ||||||
\(843\) | − | 15.2695i | − | 0.525908i | ||||||
\(844\) | −30.4176 | −1.04702 | ||||||||
\(845\) | −4.97928 | −0.171293 | ||||||||
\(846\) | 8.15786 | 0.280473 | ||||||||
\(847\) | 49.8142 | + | 16.8481i | 1.71164 | + | 0.578909i | ||||
\(848\) | − | 38.2001i | − | 1.31180i | ||||||
\(849\) | −26.7960 | −0.919636 | ||||||||
\(850\) | − | 8.16589i | − | 0.280088i | ||||||
\(851\) | 16.7088i | 0.572770i | ||||||||
\(852\) | 22.5361 | 0.772074 | ||||||||
\(853\) | 18.2159i | 0.623700i | 0.950131 | + | 0.311850i | \(0.100949\pi\) | ||||
−0.950131 | + | 0.311850i | \(0.899051\pi\) | |||||||
\(854\) | 14.6599 | 0.501650 | ||||||||
\(855\) | 9.97292 | + | 0.899227i | 0.341067 | + | 0.0307529i | ||||
\(856\) | 2.11818 | 0.0723981 | ||||||||
\(857\) | 7.16167 | 0.244638 | 0.122319 | − | 0.992491i | \(-0.460967\pi\) | ||||
0.122319 | + | 0.992491i | \(0.460967\pi\) | |||||||
\(858\) | −14.0427 | − | 19.5737i | −0.479411 | − | 0.668235i | ||||
\(859\) | −28.9464 | −0.987638 | −0.493819 | − | 0.869565i | \(-0.664400\pi\) | ||||
−0.493819 | + | 0.869565i | \(0.664400\pi\) | |||||||
\(860\) | 11.0799i | 0.377820i | ||||||||
\(861\) | −23.0375 | −0.785116 | ||||||||
\(862\) | −78.9900 | −2.69041 | ||||||||
\(863\) | − | 25.5181i | − | 0.868646i | −0.900757 | − | 0.434323i | \(-0.856988\pi\) | ||
0.900757 | − | 0.434323i | \(-0.143012\pi\) | |||||||
\(864\) | 36.0173i | 1.22533i | ||||||||
\(865\) | −12.6812 | −0.431175 | ||||||||
\(866\) | − | 8.34739i | − | 0.283656i | ||||||
\(867\) | 0.863180i | 0.0293151i | ||||||||
\(868\) | 17.6663 | 0.599633 | ||||||||
\(869\) | 18.2352 | − | 13.0824i | 0.618587 | − | 0.443791i | ||||
\(870\) | 0.481260i | 0.0163162i | ||||||||
\(871\) | 51.2395i | 1.73618i | ||||||||
\(872\) | 6.22801 | 0.210907 | ||||||||
\(873\) | 25.8829i | 0.876003i | ||||||||
\(874\) | 51.5201 | + | 4.64541i | 1.74269 | + | 0.157133i | ||||
\(875\) | − | 4.78057i | − | 0.161613i | ||||||
\(876\) | −0.892627 | −0.0301591 | ||||||||
\(877\) | 14.0400 | 0.474098 | 0.237049 | − | 0.971498i | \(-0.423820\pi\) | ||||
0.237049 | + | 0.971498i | \(0.423820\pi\) | |||||||
\(878\) | 34.8901 | 1.17748 | ||||||||
\(879\) | 23.0528i | 0.777552i | ||||||||
\(880\) | −9.75141 | + | 6.99593i | −0.328720 | + | 0.235833i | ||||
\(881\) | −20.6744 | −0.696537 | −0.348269 | − | 0.937395i | \(-0.613230\pi\) | ||||
−0.348269 | + | 0.937395i | \(0.613230\pi\) | |||||||
\(882\) | 74.4191 | 2.50582 | ||||||||
\(883\) | −32.0849 | −1.07974 | −0.539871 | − | 0.841748i | \(-0.681527\pi\) | ||||
−0.539871 | + | 0.841748i | \(0.681527\pi\) | |||||||
\(884\) | − | 36.8615i | − | 1.23979i | ||||||
\(885\) | 1.35228 | 0.0454565 | ||||||||
\(886\) | −2.77010 | −0.0930632 | ||||||||
\(887\) | 14.4663 | 0.485730 | 0.242865 | − | 0.970060i | \(-0.421913\pi\) | ||||
0.242865 | + | 0.970060i | \(0.421913\pi\) | |||||||
\(888\) | 0.864160 | 0.0289993 | ||||||||
\(889\) | 8.13763i | 0.272928i | ||||||||
\(890\) | − | 8.21185i | − | 0.275262i | ||||||
\(891\) | −8.53976 | + | 6.12667i | −0.286093 | + | 0.205251i | ||||
\(892\) | 6.85504i | 0.229524i | ||||||||
\(893\) | 7.54474 | + | 0.680286i | 0.252475 | + | 0.0227649i | ||||
\(894\) | −39.6921 | −1.32750 | ||||||||
\(895\) | − | 0.803768i | − | 0.0268670i | ||||||
\(896\) | 13.6506i | 0.456033i | ||||||||
\(897\) | − | 20.6445i | − | 0.689301i | ||||||
\(898\) | 66.0606i | 2.20447i | ||||||||
\(899\) | − | 0.477268i | − | 0.0159178i | ||||||
\(900\) | 4.99727 | 0.166576 | ||||||||
\(901\) | −42.1878 | −1.40548 | ||||||||
\(902\) | 31.6539 | − | 22.7094i | 1.05396 | − | 0.756141i | ||||
\(903\) | 20.4123i | 0.679278i | ||||||||
\(904\) | − | 4.38984i | − | 0.146004i | ||||||
\(905\) | − | 24.2956i | − | 0.807613i | ||||||
\(906\) | 4.48833i | 0.149115i | ||||||||
\(907\) | − | 39.0709i | − | 1.29733i | −0.761074 | − | 0.648665i | \(-0.775328\pi\) | ||
0.761074 | − | 0.648665i | \(-0.224672\pi\) | |||||||
\(908\) | −16.4062 | −0.544460 | ||||||||
\(909\) | 17.1773i | 0.569735i | ||||||||
\(910\) | − | 41.4202i | − | 1.37307i | ||||||
\(911\) | 18.7047i | 0.619715i | 0.950783 | + | 0.309857i | \(0.100281\pi\) | ||||
−0.950783 | + | 0.309857i | \(0.899719\pi\) | |||||||
\(912\) | −1.18743 | + | 13.1692i | −0.0393197 | + | 0.436077i | ||||
\(913\) | 28.5271 | + | 39.7630i | 0.944108 | + | 1.31596i | ||||
\(914\) | 18.2011i | 0.602039i | ||||||||
\(915\) | 1.25809 | 0.0415912 | ||||||||
\(916\) | −26.4781 | −0.874862 | ||||||||
\(917\) | −29.0619 | −0.959708 | ||||||||
\(918\) | 36.2627 | 1.19685 | ||||||||
\(919\) | 25.1876i | 0.830863i | 0.909624 | + | 0.415432i | \(0.136369\pi\) | ||||
−0.909624 | + | 0.415432i | \(0.863631\pi\) | |||||||
\(920\) | 2.08097 | 0.0686074 | ||||||||
\(921\) | 10.2514i | 0.337796i | ||||||||
\(922\) | 49.3863i | 1.62645i | ||||||||
\(923\) | 52.3996i | 1.72475i | ||||||||
\(924\) | 23.4936 | − | 16.8549i | 0.772881 | − | 0.554487i | ||||
\(925\) | 2.87696i | 0.0945938i | ||||||||
\(926\) | 72.6433 | 2.38721 | ||||||||
\(927\) | − | 6.54413i | − | 0.214937i | ||||||
\(928\) | 2.27867 | 0.0748009 | ||||||||
\(929\) | −58.4083 | −1.91631 | −0.958156 | − | 0.286245i | \(-0.907593\pi\) | ||||
−0.958156 | + | 0.286245i | \(0.907593\pi\) | |||||||
\(930\) | 2.90999 | 0.0954222 | ||||||||
\(931\) | 68.8260 | + | 6.20582i | 2.25568 | + | 0.203388i | ||||
\(932\) | 21.3006i | 0.697724i | ||||||||
\(933\) | 17.8694i | 0.585017i | ||||||||
\(934\) | 54.2114 | 1.77385 | ||||||||
\(935\) | 7.72624 | + | 10.7694i | 0.252675 | + | 0.352196i | ||||
\(936\) | 3.49015 | 0.114079 | ||||||||
\(937\) | 41.7955i | 1.36540i | 0.730700 | + | 0.682699i | \(0.239194\pi\) | ||||
−0.730700 | + | 0.682699i | \(0.760806\pi\) | |||||||
\(938\) | −118.044 | −3.85428 | ||||||||
\(939\) | − | 5.62393i | − | 0.183530i | ||||||
\(940\) | 3.78055 | 0.123308 | ||||||||
\(941\) | 28.4760 | 0.928292 | 0.464146 | − | 0.885759i | \(-0.346361\pi\) | ||||
0.464146 | + | 0.885759i | \(0.346361\pi\) | |||||||
\(942\) | 1.47273i | 0.0479841i | ||||||||
\(943\) | 33.3857 | 1.08719 | ||||||||
\(944\) | − | 5.83707i | − | 0.189980i | ||||||
\(945\) | 21.2293 | 0.690589 | ||||||||
\(946\) | −20.1216 | − | 28.0468i | −0.654209 | − | 0.911881i | ||||
\(947\) | −32.9022 | −1.06918 | −0.534589 | − | 0.845112i | \(-0.679534\pi\) | ||||
−0.534589 | + | 0.845112i | \(0.679534\pi\) | |||||||
\(948\) | − | 12.3400i | − | 0.400784i | ||||||
\(949\) | − | 2.07548i | − | 0.0673731i | ||||||
\(950\) | 8.87084 | + | 0.799856i | 0.287808 | + | 0.0259508i | ||||
\(951\) | 19.3400 | 0.627141 | ||||||||
\(952\) | 6.84526 | 0.221856 | ||||||||
\(953\) | −3.54330 | −0.114779 | −0.0573894 | − | 0.998352i | \(-0.518278\pi\) | ||||
−0.0573894 | + | 0.998352i | \(0.518278\pi\) | |||||||
\(954\) | − | 49.5541i | − | 1.60437i | ||||||
\(955\) | −3.48103 | −0.112644 | ||||||||
\(956\) | − | 46.5068i | − | 1.50414i | ||||||
\(957\) | −0.455349 | − | 0.634696i | −0.0147193 | − | 0.0205168i | ||||
\(958\) | − | 36.2722i | − | 1.17190i | ||||||
\(959\) | − | 93.6090i | − | 3.02279i | ||||||
\(960\) | 7.82644i | 0.252597i | ||||||||
\(961\) | 28.1141 | 0.906908 | ||||||||
\(962\) | 24.9268i | 0.803671i | ||||||||
\(963\) | −13.5805 | −0.437624 | ||||||||
\(964\) | 51.2141 | 1.64949 | ||||||||
\(965\) | 12.9504 | 0.416887 | ||||||||
\(966\) | 47.5604 | 1.53023 | ||||||||
\(967\) | − | 17.8620i | − | 0.574402i | −0.957870 | − | 0.287201i | \(-0.907275\pi\) | ||
0.957870 | − | 0.287201i | \(-0.0927248\pi\) | |||||||
\(968\) | −1.26277 | + | 3.73359i | −0.0405871 | + | 0.120002i | ||||
\(969\) | 14.5440 | + | 1.31138i | 0.467220 | + | 0.0421278i | ||||
\(970\) | 23.0226i | 0.739212i | ||||||||
\(971\) | − | 47.0160i | − | 1.50882i | −0.656406 | − | 0.754408i | \(-0.727924\pi\) | ||
0.656406 | − | 0.754408i | \(-0.272076\pi\) | |||||||
\(972\) | 34.7595i | 1.11491i | ||||||||
\(973\) | 71.2073 | 2.28280 | ||||||||
\(974\) | − | 33.7743i | − | 1.08220i | ||||||
\(975\) | − | 3.55462i | − | 0.113839i | ||||||
\(976\) | − | 5.43049i | − | 0.173826i | ||||||
\(977\) | 60.2471i | 1.92747i | 0.266852 | + | 0.963737i | \(0.414016\pi\) | ||||
−0.266852 | + | 0.963737i | \(0.585984\pi\) | |||||||
\(978\) | 7.50152i | 0.239872i | ||||||||
\(979\) | 7.76972 | + | 10.8300i | 0.248321 | + | 0.346127i | ||||
\(980\) | 34.4876 | 1.10167 | ||||||||
\(981\) | −39.9300 | −1.27487 | ||||||||
\(982\) | − | 6.03692i | − | 0.192646i | ||||||
\(983\) | 52.9616i | 1.68921i | 0.535388 | + | 0.844607i | \(0.320166\pi\) | ||||
−0.535388 | + | 0.844607i | \(0.679834\pi\) | |||||||
\(984\) | − | 1.72667i | − | 0.0550442i | ||||||
\(985\) | − | 10.8525i | − | 0.345790i | ||||||
\(986\) | − | 2.29419i | − | 0.0730619i | ||||||
\(987\) | 6.96487 | 0.221694 | ||||||||
\(988\) | 40.0437 | + | 3.61061i | 1.27396 | + | 0.114869i | ||||
\(989\) | − | 29.5813i | − | 0.940629i | ||||||
\(990\) | −12.6498 | + | 9.07531i | −0.402036 | + | 0.288432i | ||||
\(991\) | 13.9302i | 0.442508i | 0.975216 | + | 0.221254i | \(0.0710150\pi\) | ||||
−0.975216 | + | 0.221254i | \(0.928985\pi\) | |||||||
\(992\) | − | 13.7782i | − | 0.437458i | ||||||
\(993\) | 7.43017 | 0.235789 | ||||||||
\(994\) | −120.717 | −3.82890 | ||||||||
\(995\) | −21.8885 | −0.693911 | ||||||||
\(996\) | 26.9081 | 0.852616 | ||||||||
\(997\) | 44.1823i | 1.39927i | 0.714501 | + | 0.699634i | \(0.246654\pi\) | ||||
−0.714501 | + | 0.699634i | \(0.753346\pi\) | |||||||
\(998\) | 11.4805 | 0.363409 | ||||||||
\(999\) | −12.7758 | −0.404210 |
(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 | 1045.2.f.a.626.8 | yes | 40 | |
11.10 | odd | 2 | inner | 1045.2.f.a.626.34 | yes | 40 | |
19.18 | odd | 2 | inner | 1045.2.f.a.626.33 | yes | 40 | |
209.208 | even | 2 | inner | 1045.2.f.a.626.7 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.f.a.626.7 | ✓ | 40 | 209.208 | even | 2 | inner | |
1045.2.f.a.626.8 | yes | 40 | 1.1 | even | 1 | trivial | |
1045.2.f.a.626.33 | yes | 40 | 19.18 | odd | 2 | inner | |
1045.2.f.a.626.34 | yes | 40 | 11.10 | odd | 2 | inner |