Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), degree \(2\), 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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.3 | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.l.508.3 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.19245 | + | 2.06538i | −0.843188 | + | 1.46044i | 0.0439980 | + | 0.999032i | \(0.485990\pi\) |
−0.887186 | + | 0.461412i | \(0.847343\pi\) | |||||||
\(3\) | −0.352721 | − | 0.610931i | −0.203644 | − | 0.352721i | 0.746056 | − | 0.665883i | \(-0.231945\pi\) |
−0.949700 | + | 0.313162i | \(0.898612\pi\) | |||||||
\(4\) | −1.84386 | − | 3.19366i | −0.921931 | − | 1.59683i | ||||
\(5\) | 0.384905 | − | 0.666675i | 0.172135 | − | 0.298146i | −0.767031 | − | 0.641610i | \(-0.778267\pi\) |
0.939166 | + | 0.343464i | \(0.111600\pi\) | |||||||
\(6\) | 1.68241 | 0.686839 | ||||||||
\(7\) | −2.49409 | + | 0.882891i | −0.942679 | + | 0.333701i | ||||
\(8\) | 4.02505 | 1.42307 | ||||||||
\(9\) | 1.25118 | − | 2.16710i | 0.417059 | − | 0.722367i | ||||
\(10\) | 0.917958 | + | 1.58995i | 0.290284 | + | 0.502786i | ||||
\(11\) | −0.556434 | − | 0.963772i | −0.167771 | − | 0.290588i | 0.769865 | − | 0.638207i | \(-0.220324\pi\) |
−0.937636 | + | 0.347619i | \(0.886990\pi\) | |||||||
\(12\) | −1.30074 | + | 2.25294i | −0.375491 | + | 0.650369i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.15057 | − | 6.20405i | 0.307503 | − | 1.65810i | ||||
\(15\) | −0.543056 | −0.140216 | ||||||||
\(16\) | −1.11193 | + | 1.92592i | −0.277983 | + | 0.481481i | ||||
\(17\) | −3.52812 | − | 6.11088i | −0.855695 | − | 1.48211i | −0.875999 | − | 0.482313i | \(-0.839797\pi\) |
0.0203041 | − | 0.999794i | \(-0.493537\pi\) | |||||||
\(18\) | 2.98392 | + | 5.16831i | 0.703317 | + | 1.21818i | ||||
\(19\) | −1.86064 | + | 3.22273i | −0.426861 | + | 0.739344i | −0.996592 | − | 0.0824865i | \(-0.973714\pi\) |
0.569731 | + | 0.821831i | \(0.307047\pi\) | |||||||
\(20\) | −2.83885 | −0.634785 | ||||||||
\(21\) | 1.41910 | + | 1.21230i | 0.309674 | + | 0.264546i | ||||
\(22\) | 2.65407 | 0.565851 | ||||||||
\(23\) | −3.01206 | + | 5.21703i | −0.628057 | + | 1.08783i | 0.359884 | + | 0.932997i | \(0.382816\pi\) |
−0.987941 | + | 0.154830i | \(0.950517\pi\) | |||||||
\(24\) | −1.41972 | − | 2.45902i | −0.289799 | − | 0.501946i | ||||
\(25\) | 2.20370 | + | 3.81691i | 0.440739 | + | 0.763383i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.88159 | −0.747012 | ||||||||
\(28\) | 7.41842 | + | 6.33737i | 1.40195 | + | 1.19765i | ||||
\(29\) | 4.31164 | 0.800651 | 0.400326 | − | 0.916373i | \(-0.368897\pi\) | ||||
0.400326 | + | 0.916373i | \(0.368897\pi\) | |||||||
\(30\) | 0.647566 | − | 1.12162i | 0.118229 | − | 0.204778i | ||||
\(31\) | 1.26887 | + | 2.19775i | 0.227896 | + | 0.394728i | 0.957184 | − | 0.289479i | \(-0.0934820\pi\) |
−0.729288 | + | 0.684207i | \(0.760149\pi\) | |||||||
\(32\) | 1.37320 | + | 2.37846i | 0.242750 | + | 0.420456i | ||||
\(33\) | −0.392532 | + | 0.679886i | −0.0683311 | + | 0.118353i | ||||
\(34\) | 16.8284 | 2.88605 | ||||||||
\(35\) | −0.371388 | + | 2.00258i | −0.0627760 | + | 0.338497i | ||||
\(36\) | −9.22798 | −1.53800 | ||||||||
\(37\) | 0.0519393 | − | 0.0899614i | 0.00853876 | − | 0.0147896i | −0.861724 | − | 0.507377i | \(-0.830615\pi\) |
0.870263 | + | 0.492587i | \(0.163949\pi\) | |||||||
\(38\) | −4.43744 | − | 7.68587i | −0.719847 | − | 1.24681i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.54926 | − | 2.68340i | 0.244960 | − | 0.424282i | ||||
\(41\) | 8.12661 | 1.26916 | 0.634582 | − | 0.772856i | \(-0.281172\pi\) | ||||
0.634582 | + | 0.772856i | \(0.281172\pi\) | |||||||
\(42\) | −4.19608 | + | 1.48538i | −0.647469 | + | 0.229199i | ||||
\(43\) | −2.53454 | −0.386513 | −0.193257 | − | 0.981148i | \(-0.561905\pi\) | ||||
−0.193257 | + | 0.981148i | \(0.561905\pi\) | |||||||
\(44\) | −2.05198 | + | 3.55413i | −0.309347 | + | 0.535805i | ||||
\(45\) | −0.963167 | − | 1.66825i | −0.143580 | − | 0.248689i | ||||
\(46\) | −7.18344 | − | 12.4421i | −1.05914 | − | 1.83448i | ||||
\(47\) | −4.69122 | + | 8.12544i | −0.684285 | + | 1.18522i | 0.289376 | + | 0.957216i | \(0.406552\pi\) |
−0.973661 | + | 0.228001i | \(0.926781\pi\) | |||||||
\(48\) | 1.56881 | 0.226438 | ||||||||
\(49\) | 5.44101 | − | 4.40402i | 0.777287 | − | 0.629146i | ||||
\(50\) | −10.5112 | −1.48650 | ||||||||
\(51\) | −2.48888 | + | 4.31087i | −0.348513 | + | 0.603643i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.73721 | + | 9.93714i | 0.788067 | + | 1.36497i | 0.927150 | + | 0.374691i | \(0.122251\pi\) |
−0.139083 | + | 0.990281i | \(0.544415\pi\) | |||||||
\(54\) | 4.62859 | − | 8.01696i | 0.629872 | − | 1.09097i | ||||
\(55\) | −0.856697 | −0.115517 | ||||||||
\(56\) | −10.0388 | + | 3.55368i | −1.34150 | + | 0.474880i | ||||
\(57\) | 2.62515 | 0.347710 | ||||||||
\(58\) | −5.14140 | + | 8.90517i | −0.675100 | + | 1.16931i | ||||
\(59\) | 4.54100 | + | 7.86524i | 0.591187 | + | 1.02397i | 0.994073 | + | 0.108716i | \(0.0346740\pi\) |
−0.402885 | + | 0.915250i | \(0.631993\pi\) | |||||||
\(60\) | 1.00132 | + | 1.73434i | 0.129270 | + | 0.223902i | ||||
\(61\) | −7.69656 | + | 13.3308i | −0.985443 | + | 1.70684i | −0.345494 | + | 0.938421i | \(0.612289\pi\) |
−0.639950 | + | 0.768417i | \(0.721045\pi\) | |||||||
\(62\) | −6.05226 | −0.768637 | ||||||||
\(63\) | −1.20724 | + | 6.50960i | −0.152098 | + | 0.820133i | ||||
\(64\) | −10.9976 | −1.37470 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.936148 | − | 1.62146i | −0.115232 | − | 0.199587i | ||||
\(67\) | −6.79763 | − | 11.7738i | −0.830463 | − | 1.43840i | −0.897671 | − | 0.440665i | \(-0.854743\pi\) |
0.0672083 | − | 0.997739i | \(-0.478591\pi\) | |||||||
\(68\) | −13.0107 | + | 22.5353i | −1.57778 | + | 2.73280i | ||||
\(69\) | 4.24966 | 0.511599 | ||||||||
\(70\) | −3.69322 | − | 3.15503i | −0.441425 | − | 0.377098i | ||||
\(71\) | 1.13421 | 0.134606 | 0.0673028 | − | 0.997733i | \(-0.478561\pi\) | ||||
0.0673028 | + | 0.997733i | \(0.478561\pi\) | |||||||
\(72\) | 5.03604 | − | 8.72268i | 0.593503 | − | 1.02798i | ||||
\(73\) | −3.83796 | − | 6.64755i | −0.449200 | − | 0.778037i | 0.549134 | − | 0.835734i | \(-0.314958\pi\) |
−0.998334 | + | 0.0576973i | \(0.981624\pi\) | |||||||
\(74\) | 0.123870 | + | 0.214549i | 0.0143996 | + | 0.0249408i | ||||
\(75\) | 1.55458 | − | 2.69261i | 0.179507 | − | 0.310916i | ||||
\(76\) | 13.7231 | 1.57414 | ||||||||
\(77\) | 2.23870 | + | 1.91247i | 0.255124 | + | 0.217946i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.75598 | + | 4.77350i | −0.310072 | + | 0.537061i | −0.978378 | − | 0.206826i | \(-0.933687\pi\) |
0.668306 | + | 0.743887i | \(0.267020\pi\) | |||||||
\(80\) | 0.855977 | + | 1.48259i | 0.0957011 | + | 0.165759i | ||||
\(81\) | −2.38441 | − | 4.12992i | −0.264934 | − | 0.458880i | ||||
\(82\) | −9.69056 | + | 16.7845i | −1.07014 | + | 1.85354i | ||||
\(83\) | −5.42111 | −0.595044 | −0.297522 | − | 0.954715i | \(-0.596160\pi\) | ||||
−0.297522 | + | 0.954715i | \(0.596160\pi\) | |||||||
\(84\) | 1.25506 | − | 6.76746i | 0.136938 | − | 0.738391i | ||||
\(85\) | −5.43196 | −0.589179 | ||||||||
\(86\) | 3.02230 | − | 5.23478i | 0.325903 | − | 0.564481i | ||||
\(87\) | −1.52081 | − | 2.63411i | −0.163048 | − | 0.282407i | ||||
\(88\) | −2.23967 | − | 3.87923i | −0.238750 | − | 0.413527i | ||||
\(89\) | −7.64141 | + | 13.2353i | −0.809988 | + | 1.40294i | 0.102884 | + | 0.994693i | \(0.467193\pi\) |
−0.912872 | + | 0.408247i | \(0.866140\pi\) | |||||||
\(90\) | 4.59411 | 0.484261 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 22.2153 | 2.31610 | ||||||||
\(93\) | 0.895116 | − | 1.55039i | 0.0928192 | − | 0.160768i | ||||
\(94\) | −11.1881 | − | 19.3783i | −1.15396 | − | 1.99872i | ||||
\(95\) | 1.43234 | + | 2.48089i | 0.146955 | + | 0.254534i | ||||
\(96\) | 0.968716 | − | 1.67786i | 0.0988691 | − | 0.171246i | ||||
\(97\) | −12.1661 | −1.23528 | −0.617641 | − | 0.786460i | \(-0.711912\pi\) | ||||
−0.617641 | + | 0.786460i | \(0.711912\pi\) | |||||||
\(98\) | 2.60787 | + | 16.4893i | 0.263434 | + | 1.66567i | ||||
\(99\) | −2.78479 | −0.279882 | ||||||||
\(100\) | 8.12663 | − | 14.0757i | 0.812663 | − | 1.40757i | ||||
\(101\) | −0.201680 | − | 0.349320i | −0.0200679 | − | 0.0347586i | 0.855817 | − | 0.517279i | \(-0.173055\pi\) |
−0.875885 | + | 0.482520i | \(0.839722\pi\) | |||||||
\(102\) | −5.93573 | − | 10.2810i | −0.587725 | − | 1.01797i | ||||
\(103\) | −1.90020 | + | 3.29124i | −0.187232 | + | 0.324296i | −0.944326 | − | 0.329010i | \(-0.893285\pi\) |
0.757094 | + | 0.653306i | \(0.226618\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.35443 | − | 0.479459i | 0.132179 | − | 0.0467904i | ||||
\(106\) | −27.3653 | −2.65795 | ||||||||
\(107\) | 4.32973 | − | 7.49932i | 0.418571 | − | 0.724986i | −0.577225 | − | 0.816585i | \(-0.695864\pi\) |
0.995796 | + | 0.0915988i | \(0.0291977\pi\) | |||||||
\(108\) | 7.15712 | + | 12.3965i | 0.688694 | + | 1.19285i | ||||
\(109\) | 2.00744 | + | 3.47699i | 0.192278 | + | 0.333036i | 0.946005 | − | 0.324152i | \(-0.105079\pi\) |
−0.753727 | + | 0.657188i | \(0.771746\pi\) | |||||||
\(110\) | 1.02157 | − | 1.76940i | 0.0974025 | − | 0.168706i | ||||
\(111\) | −0.0732803 | −0.00695546 | ||||||||
\(112\) | 1.07288 | − | 5.78515i | 0.101378 | − | 0.546645i | ||||
\(113\) | 4.01288 | 0.377500 | 0.188750 | − | 0.982025i | \(-0.439556\pi\) | ||||
0.188750 | + | 0.982025i | \(0.439556\pi\) | |||||||
\(114\) | −3.13036 | + | 5.42193i | −0.293185 | + | 0.507811i | ||||
\(115\) | 2.31871 | + | 4.01612i | 0.216221 | + | 0.374505i | ||||
\(116\) | −7.95007 | − | 13.7699i | −0.738146 | − | 1.27851i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −21.6596 | −1.99393 | ||||||||
\(119\) | 14.1947 | + | 12.1262i | 1.30123 | + | 1.11160i | ||||
\(120\) | −2.18583 | −0.199538 | ||||||||
\(121\) | 4.88076 | − | 8.45373i | 0.443706 | − | 0.768521i | ||||
\(122\) | −18.3555 | − | 31.7926i | −1.66183 | − | 2.87837i | ||||
\(123\) | −2.86643 | − | 4.96480i | −0.258457 | − | 0.447661i | ||||
\(124\) | 4.67925 | − | 8.10471i | 0.420209 | − | 0.727824i | ||||
\(125\) | 7.24190 | 0.647735 | ||||||||
\(126\) | −12.0052 | − | 10.2558i | −1.06951 | − | 0.913656i | ||||
\(127\) | −3.95166 | −0.350654 | −0.175327 | − | 0.984510i | \(-0.556098\pi\) | ||||
−0.175327 | + | 0.984510i | \(0.556098\pi\) | |||||||
\(128\) | 10.3677 | − | 17.9574i | 0.916383 | − | 1.58722i | ||||
\(129\) | 0.893984 | + | 1.54843i | 0.0787109 | + | 0.136331i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.62906 | + | 2.82161i | −0.142331 | + | 0.246525i | −0.928374 | − | 0.371647i | \(-0.878793\pi\) |
0.786043 | + | 0.618172i | \(0.212127\pi\) | |||||||
\(132\) | 2.89510 | 0.251986 | ||||||||
\(133\) | 1.79530 | − | 9.68053i | 0.155672 | − | 0.839408i | ||||
\(134\) | 32.4233 | 2.80095 | ||||||||
\(135\) | −1.49404 | + | 2.58776i | −0.128587 | + | 0.222719i | ||||
\(136\) | −14.2008 | − | 24.5966i | −1.21771 | − | 2.10914i | ||||
\(137\) | 4.42794 | + | 7.66941i | 0.378304 | + | 0.655242i | 0.990816 | − | 0.135220i | \(-0.0431740\pi\) |
−0.612511 | + | 0.790462i | \(0.709841\pi\) | |||||||
\(138\) | −5.06750 | + | 8.77716i | −0.431374 | + | 0.747162i | ||||
\(139\) | 21.8559 | 1.85379 | 0.926895 | − | 0.375321i | \(-0.122467\pi\) | ||||
0.926895 | + | 0.375321i | \(0.122467\pi\) | |||||||
\(140\) | 7.08035 | − | 2.50639i | 0.598399 | − | 0.211829i | ||||
\(141\) | 6.61877 | 0.557401 | ||||||||
\(142\) | −1.35248 | + | 2.34257i | −0.113498 | + | 0.196584i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.78245 | + | 4.81934i | 0.231871 | + | 0.401612i | ||||
\(145\) | 1.65957 | − | 2.87446i | 0.137820 | − | 0.238711i | ||||
\(146\) | 18.3063 | 1.51504 | ||||||||
\(147\) | −4.60971 | − | 1.77069i | −0.380203 | − | 0.146044i | ||||
\(148\) | −0.383075 | −0.0314886 | ||||||||
\(149\) | −1.18111 | + | 2.04574i | −0.0967601 | + | 0.167593i | −0.910342 | − | 0.413857i | \(-0.864181\pi\) |
0.813582 | + | 0.581451i | \(0.197515\pi\) | |||||||
\(150\) | 3.70751 | + | 6.42160i | 0.302717 | + | 0.524321i | ||||
\(151\) | −6.01843 | − | 10.4242i | −0.489773 | − | 0.848312i | 0.510158 | − | 0.860081i | \(-0.329587\pi\) |
−0.999931 | + | 0.0117692i | \(0.996254\pi\) | |||||||
\(152\) | −7.48917 | + | 12.9716i | −0.607452 | + | 1.05214i | ||||
\(153\) | −17.6572 | −1.42750 | ||||||||
\(154\) | −6.61951 | + | 2.34326i | −0.533415 | + | 0.188825i | ||||
\(155\) | 1.95358 | 0.156915 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.22684 | + | 2.12494i | 0.0979121 | + | 0.169589i | 0.910820 | − | 0.412803i | \(-0.135450\pi\) |
−0.812908 | + | 0.582392i | \(0.802117\pi\) | |||||||
\(158\) | −6.57273 | − | 11.3843i | −0.522898 | − | 0.905686i | ||||
\(159\) | 4.04727 | − | 7.01008i | 0.320969 | − | 0.555935i | ||||
\(160\) | 2.11421 | 0.167143 | ||||||||
\(161\) | 2.90628 | − | 15.6711i | 0.229047 | − | 1.23505i | ||||
\(162\) | 11.3731 | 0.893558 | ||||||||
\(163\) | −8.95038 | + | 15.5025i | −0.701048 | + | 1.21425i | 0.267051 | + | 0.963682i | \(0.413951\pi\) |
−0.968099 | + | 0.250569i | \(0.919382\pi\) | |||||||
\(164\) | −14.9844 | − | 25.9537i | −1.17008 | − | 2.02664i | ||||
\(165\) | 0.302175 | + | 0.523382i | 0.0235243 | + | 0.0407453i | ||||
\(166\) | 6.46439 | − | 11.1966i | 0.501734 | − | 0.869029i | ||||
\(167\) | 0.741807 | 0.0574028 | 0.0287014 | − | 0.999588i | \(-0.490863\pi\) | ||||
0.0287014 | + | 0.999588i | \(0.490863\pi\) | |||||||
\(168\) | 5.71196 | + | 4.87958i | 0.440687 | + | 0.376468i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 6.47733 | − | 11.2191i | 0.496789 | − | 0.860463i | ||||
\(171\) | 4.65598 | + | 8.06440i | 0.356052 | + | 0.616700i | ||||
\(172\) | 4.67334 | + | 8.09446i | 0.356339 | + | 0.617197i | ||||
\(173\) | −0.807878 | + | 1.39929i | −0.0614219 | + | 0.106386i | −0.895101 | − | 0.445863i | \(-0.852897\pi\) |
0.833679 | + | 0.552249i | \(0.186230\pi\) | |||||||
\(174\) | 7.25393 | 0.549919 | ||||||||
\(175\) | −8.86614 | − | 7.57412i | −0.670218 | − | 0.572550i | ||||
\(176\) | 2.47487 | 0.186550 | ||||||||
\(177\) | 3.20341 | − | 5.54847i | 0.240783 | − | 0.417048i | ||||
\(178\) | −18.2240 | − | 31.5648i | −1.36594 | − | 2.36588i | ||||
\(179\) | 6.77841 | + | 11.7406i | 0.506642 | + | 0.877530i | 0.999970 | + | 0.00768695i | \(0.00244686\pi\) |
−0.493328 | + | 0.869843i | \(0.664220\pi\) | |||||||
\(180\) | −3.55190 | + | 6.15206i | −0.264743 | + | 0.458548i | ||||
\(181\) | −7.15326 | −0.531698 | −0.265849 | − | 0.964015i | \(-0.585652\pi\) | ||||
−0.265849 | + | 0.964015i | \(0.585652\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.8590 | 0.802717 | ||||||||
\(184\) | −12.1237 | + | 20.9988i | −0.893769 | + | 1.54805i | ||||
\(185\) | −0.0399833 | − | 0.0692532i | −0.00293963 | − | 0.00509160i | ||||
\(186\) | 2.13476 | + | 3.69751i | 0.156528 | + | 0.271115i | ||||
\(187\) | −3.92633 | + | 6.80061i | −0.287122 | + | 0.497310i | ||||
\(188\) | 34.5999 | 2.52346 | ||||||||
\(189\) | 9.68105 | − | 3.42702i | 0.704193 | − | 0.249279i | ||||
\(190\) | −6.83197 | −0.495643 | ||||||||
\(191\) | −8.13226 | + | 14.0855i | −0.588430 | + | 1.01919i | 0.406009 | + | 0.913869i | \(0.366920\pi\) |
−0.994438 | + | 0.105321i | \(0.966413\pi\) | |||||||
\(192\) | 3.87909 | + | 6.71879i | 0.279949 | + | 0.484887i | ||||
\(193\) | 6.85969 | + | 11.8813i | 0.493771 | + | 0.855237i | 0.999974 | − | 0.00717736i | \(-0.00228464\pi\) |
−0.506203 | + | 0.862414i | \(0.668951\pi\) | |||||||
\(194\) | 14.5075 | − | 25.1277i | 1.04157 | − | 1.80406i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.0974 | − | 9.25633i | −1.72125 | − | 0.661167i | ||||
\(197\) | −8.00113 | −0.570057 | −0.285028 | − | 0.958519i | \(-0.592003\pi\) | ||||
−0.285028 | + | 0.958519i | \(0.592003\pi\) | |||||||
\(198\) | 3.32071 | − | 5.75165i | 0.235993 | − | 0.408752i | ||||
\(199\) | 2.31688 | + | 4.01295i | 0.164239 | + | 0.284470i | 0.936385 | − | 0.350975i | \(-0.114150\pi\) |
−0.772146 | + | 0.635445i | \(0.780817\pi\) | |||||||
\(200\) | 8.86998 | + | 15.3633i | 0.627202 | + | 1.08635i | ||||
\(201\) | −4.79534 | + | 8.30577i | −0.338237 | + | 0.585844i | ||||
\(202\) | 0.961970 | 0.0676840 | ||||||||
\(203\) | −10.7536 | + | 3.80671i | −0.754757 | + | 0.267178i | ||||
\(204\) | 18.3566 | 1.28522 | ||||||||
\(205\) | 3.12797 | − | 5.41781i | 0.218467 | − | 0.378396i | ||||
\(206\) | −4.53177 | − | 7.84926i | −0.315744 | − | 0.546884i | ||||
\(207\) | 7.53722 | + | 13.0549i | 0.523873 | + | 0.907375i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.14130 | 0.286460 | ||||||||
\(210\) | −0.624825 | + | 3.36915i | −0.0431170 | + | 0.232493i | ||||
\(211\) | 6.47571 | 0.445806 | 0.222903 | − | 0.974841i | \(-0.428447\pi\) | ||||
0.222903 | + | 0.974841i | \(0.428447\pi\) | |||||||
\(212\) | 21.1573 | − | 36.6455i | 1.45309 | − | 2.51682i | ||||
\(213\) | −0.400058 | − | 0.692922i | −0.0274116 | − | 0.0474782i | ||||
\(214\) | 10.3260 | + | 17.8851i | 0.705868 | + | 1.22260i | ||||
\(215\) | −0.975556 | + | 1.68971i | −0.0665323 | + | 0.115237i | ||||
\(216\) | −15.6236 | −1.06305 | ||||||||
\(217\) | −5.10506 | − | 4.36112i | −0.346554 | − | 0.296052i | ||||
\(218\) | −9.57508 | −0.648506 | ||||||||
\(219\) | −2.70746 | + | 4.68946i | −0.182953 | + | 0.316884i | ||||
\(220\) | 1.57963 | + | 2.73600i | 0.106499 | + | 0.184461i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.0873829 | − | 0.151352i | 0.00586476 | − | 0.0101581i | ||||
\(223\) | −10.7063 | −0.716948 | −0.358474 | − | 0.933540i | \(-0.616703\pi\) | ||||
−0.358474 | + | 0.933540i | \(0.616703\pi\) | |||||||
\(224\) | −5.52482 | − | 4.71971i | −0.369142 | − | 0.315349i | ||||
\(225\) | 11.0288 | 0.735256 | ||||||||
\(226\) | −4.78515 | + | 8.28813i | −0.318304 | + | 0.551318i | ||||
\(227\) | −5.67410 | − | 9.82784i | −0.376604 | − | 0.652296i | 0.613962 | − | 0.789335i | \(-0.289575\pi\) |
−0.990566 | + | 0.137039i | \(0.956241\pi\) | |||||||
\(228\) | −4.84042 | − | 8.38385i | −0.320564 | − | 0.555234i | ||||
\(229\) | −7.32801 | + | 12.6925i | −0.484248 | + | 0.838743i | −0.999836 | − | 0.0180939i | \(-0.994240\pi\) |
0.515588 | + | 0.856837i | \(0.327574\pi\) | |||||||
\(230\) | −11.0598 | −0.729259 | ||||||||
\(231\) | 0.378747 | − | 2.04226i | 0.0249197 | − | 0.134371i | ||||
\(232\) | 17.3546 | 1.13938 | ||||||||
\(233\) | 4.31684 | − | 7.47698i | 0.282805 | − | 0.489833i | −0.689269 | − | 0.724505i | \(-0.742068\pi\) |
0.972075 | + | 0.234672i | \(0.0754016\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.61135 | + | 6.25504i | 0.235578 | + | 0.408034i | ||||
\(236\) | 16.7459 | − | 29.0048i | 1.09007 | − | 1.88805i | ||||
\(237\) | 3.88837 | 0.252577 | ||||||||
\(238\) | −41.9716 | + | 14.8576i | −2.72061 | + | 0.963077i | ||||
\(239\) | 12.7158 | 0.822514 | 0.411257 | − | 0.911519i | \(-0.365090\pi\) | ||||
0.411257 | + | 0.911519i | \(0.365090\pi\) | |||||||
\(240\) | 0.603842 | − | 1.04588i | 0.0389778 | − | 0.0675116i | ||||
\(241\) | −8.00758 | − | 13.8695i | −0.515814 | − | 0.893415i | −0.999831 | − | 0.0183573i | \(-0.994156\pi\) |
0.484018 | − | 0.875058i | \(-0.339177\pi\) | |||||||
\(242\) | 11.6401 | + | 20.1613i | 0.748254 | + | 1.29601i | ||||
\(243\) | −7.50445 | + | 12.9981i | −0.481411 | + | 0.833827i | ||||
\(244\) | 56.7656 | 3.63404 | ||||||||
\(245\) | −0.841781 | − | 5.32251i | −0.0537794 | − | 0.340043i | ||||
\(246\) | 13.6723 | 0.871711 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.10727 | + | 8.84606i | 0.324312 | + | 0.561725i | ||||
\(249\) | 1.91214 | + | 3.31192i | 0.121177 | + | 0.209885i | ||||
\(250\) | −8.63559 | + | 14.9573i | −0.546163 | + | 0.945981i | ||||
\(251\) | −22.9647 | −1.44952 | −0.724758 | − | 0.689003i | \(-0.758049\pi\) | ||||
−0.724758 | + | 0.689003i | \(0.758049\pi\) | |||||||
\(252\) | 23.0155 | − | 8.14730i | 1.44984 | − | 0.513232i | ||||
\(253\) | 6.70404 | 0.421480 | ||||||||
\(254\) | 4.71215 | − | 8.16169i | 0.295667 | − | 0.512110i | ||||
\(255\) | 1.91597 | + | 3.31855i | 0.119983 | + | 0.207816i | ||||
\(256\) | 13.7282 | + | 23.7780i | 0.858013 | + | 1.48612i | ||||
\(257\) | 10.1200 | − | 17.5283i | 0.631268 | − | 1.09339i | −0.356025 | − | 0.934476i | \(-0.615868\pi\) |
0.987293 | − | 0.158911i | \(-0.0507984\pi\) | |||||||
\(258\) | −4.26412 | −0.265472 | ||||||||
\(259\) | −0.0501153 | + | 0.270229i | −0.00311401 | + | 0.0167912i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.39462 | − | 9.34376i | 0.333919 | − | 0.578364i | ||||
\(262\) | −3.88513 | − | 6.72924i | −0.240024 | − | 0.415734i | ||||
\(263\) | 13.3147 | + | 23.0618i | 0.821021 | + | 1.42205i | 0.904923 | + | 0.425575i | \(0.139928\pi\) |
−0.0839024 | + | 0.996474i | \(0.526738\pi\) | |||||||
\(264\) | −1.57996 | + | 2.73657i | −0.0972398 | + | 0.168424i | ||||
\(265\) | 8.83312 | 0.542614 | ||||||||
\(266\) | 17.8532 | + | 15.2515i | 1.09465 | + | 0.935130i | ||||
\(267\) | 10.7811 | 0.659795 | ||||||||
\(268\) | −25.0678 | + | 43.4187i | −1.53126 | + | 2.65222i | ||||
\(269\) | 6.25774 | + | 10.8387i | 0.381541 | + | 0.660849i | 0.991283 | − | 0.131751i | \(-0.0420600\pi\) |
−0.609741 | + | 0.792600i | \(0.708727\pi\) | |||||||
\(270\) | −3.56314 | − | 6.17153i | −0.216845 | − | 0.375587i | ||||
\(271\) | 8.50396 | − | 14.7293i | 0.516579 | − | 0.894741i | −0.483236 | − | 0.875490i | \(-0.660539\pi\) |
0.999815 | − | 0.0192505i | \(-0.00612799\pi\) | |||||||
\(272\) | 15.6921 | 0.951475 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.1203 | −1.27593 | ||||||||
\(275\) | 2.45242 | − | 4.24772i | 0.147887 | − | 0.256147i | ||||
\(276\) | −7.83579 | − | 13.5720i | −0.471659 | − | 0.816938i | ||||
\(277\) | −6.58600 | − | 11.4073i | −0.395715 | − | 0.685398i | 0.597478 | − | 0.801886i | \(-0.296170\pi\) |
−0.993192 | + | 0.116488i | \(0.962836\pi\) | |||||||
\(278\) | −26.0620 | + | 45.1407i | −1.56309 | + | 2.70736i | ||||
\(279\) | 6.35033 | 0.380184 | ||||||||
\(280\) | −1.49485 | + | 8.06047i | −0.0893346 | + | 0.481705i | ||||
\(281\) | 8.92658 | 0.532515 | 0.266258 | − | 0.963902i | \(-0.414213\pi\) | ||||
0.266258 | + | 0.963902i | \(0.414213\pi\) | |||||||
\(282\) | −7.89254 | + | 13.6703i | −0.469994 | + | 0.814053i | ||||
\(283\) | 5.77071 | + | 9.99516i | 0.343033 | + | 0.594151i | 0.984994 | − | 0.172586i | \(-0.0552124\pi\) |
−0.641961 | + | 0.766737i | \(0.721879\pi\) | |||||||
\(284\) | −2.09132 | − | 3.62227i | −0.124097 | − | 0.214942i | ||||
\(285\) | 1.01043 | − | 1.75012i | 0.0598529 | − | 0.103668i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.2685 | + | 7.17491i | −1.19641 | + | 0.423521i | ||||
\(288\) | 6.87248 | 0.404965 | ||||||||
\(289\) | −16.3953 | + | 28.3974i | −0.964427 | + | 1.67044i | ||||
\(290\) | 3.95790 | + | 6.85529i | 0.232416 | + | 0.402556i | ||||
\(291\) | 4.29125 | + | 7.43265i | 0.251557 | + | 0.435710i | ||||
\(292\) | −14.1534 | + | 24.5143i | −0.828263 | + | 1.43459i | ||||
\(293\) | −0.750227 | −0.0438287 | −0.0219144 | − | 0.999760i | \(-0.506976\pi\) | ||||
−0.0219144 | + | 0.999760i | \(0.506976\pi\) | |||||||
\(294\) | 9.15398 | − | 7.40935i | 0.533871 | − | 0.432122i | ||||
\(295\) | 6.99141 | 0.407055 | ||||||||
\(296\) | 0.209058 | − | 0.362099i | 0.0121512 | − | 0.0210466i | ||||
\(297\) | 2.15985 | + | 3.74097i | 0.125327 | + | 0.217073i | ||||
\(298\) | −2.81682 | − | 4.87887i | −0.163174 | − | 0.282626i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −11.4657 | −0.661974 | ||||||||
\(301\) | 6.32137 | − | 2.23772i | 0.364358 | − | 0.128980i | ||||
\(302\) | 28.7067 | 1.65188 | ||||||||
\(303\) | −0.142273 | + | 0.246425i | −0.00817339 | + | 0.0141567i | ||||
\(304\) | −4.13782 | − | 7.16691i | −0.237320 | − | 0.411051i | ||||
\(305\) | 5.92489 | + | 10.2622i | 0.339258 | + | 0.587612i | ||||
\(306\) | 21.0553 | − | 36.4688i | 1.20365 | − | 2.08478i | ||||
\(307\) | 8.68971 | 0.495948 | 0.247974 | − | 0.968767i | \(-0.420235\pi\) | ||||
0.247974 | + | 0.968767i | \(0.420235\pi\) | |||||||
\(308\) | 1.97992 | − | 10.6760i | 0.112816 | − | 0.608321i | ||||
\(309\) | 2.68096 | 0.152514 | ||||||||
\(310\) | −2.32954 | + | 4.03489i | −0.132309 | + | 0.229166i | ||||
\(311\) | 11.8543 | + | 20.5323i | 0.672198 | + | 1.16428i | 0.977279 | + | 0.211955i | \(0.0679829\pi\) |
−0.305082 | + | 0.952326i | \(0.598684\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.7850 | + | 20.4122i | −0.666125 | + | 1.15376i | 0.312854 | + | 0.949801i | \(0.398715\pi\) |
−0.978979 | + | 0.203962i | \(0.934618\pi\) | |||||||
\(314\) | −5.85175 | −0.330233 | ||||||||
\(315\) | 3.87512 | + | 3.31041i | 0.218338 | + | 0.186521i | ||||
\(316\) | 20.3266 | 1.14346 | ||||||||
\(317\) | −6.08017 | + | 10.5312i | −0.341497 | + | 0.591489i | −0.984711 | − | 0.174197i | \(-0.944267\pi\) |
0.643214 | + | 0.765686i | \(0.277600\pi\) | |||||||
\(318\) | 9.65232 | + | 16.7183i | 0.541275 | + | 0.937516i | ||||
\(319\) | −2.39914 | − | 4.15544i | −0.134326 | − | 0.232660i | ||||
\(320\) | −4.23304 | + | 7.33184i | −0.236634 | + | 0.409862i | ||||
\(321\) | −6.10875 | −0.340957 | ||||||||
\(322\) | 28.9012 | + | 24.6895i | 1.61060 | + | 1.37589i | ||||
\(323\) | 26.2583 | 1.46105 | ||||||||
\(324\) | −8.79305 | + | 15.2300i | −0.488503 | + | 0.846111i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.3457 | − | 36.9719i | −1.18223 | − | 2.04768i | ||||
\(327\) | 1.41613 | − | 2.45282i | 0.0783124 | − | 0.135641i | ||||
\(328\) | 32.7100 | 1.80611 | ||||||||
\(329\) | 4.52648 | − | 24.4074i | 0.249553 | − | 1.34563i | ||||
\(330\) | −1.44131 | −0.0793416 | ||||||||
\(331\) | 0.716230 | − | 1.24055i | 0.0393676 | − | 0.0681866i | −0.845670 | − | 0.533706i | \(-0.820799\pi\) |
0.885038 | + | 0.465519i | \(0.154132\pi\) | |||||||
\(332\) | 9.99578 | + | 17.3132i | 0.548590 | + | 0.950185i | ||||
\(333\) | −0.129970 | − | 0.225115i | −0.00712233 | − | 0.0123362i | ||||
\(334\) | −0.884566 | + | 1.53211i | −0.0484013 | + | 0.0838335i | ||||
\(335\) | −10.4658 | −0.571806 | ||||||||
\(336\) | −3.91275 | + | 1.38509i | −0.213458 | + | 0.0755626i | ||||
\(337\) | 9.39905 | 0.511999 | 0.255999 | − | 0.966677i | \(-0.417595\pi\) | ||||
0.255999 | + | 0.966677i | \(0.417595\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.41543 | − | 2.45159i | −0.0768755 | − | 0.133152i | ||||
\(340\) | 10.0158 | + | 17.3479i | 0.543183 | + | 0.940820i | ||||
\(341\) | 1.41209 | − | 2.44581i | 0.0764689 | − | 0.132448i | ||||
\(342\) | −22.2081 | −1.20087 | ||||||||
\(343\) | −9.68211 | + | 15.7879i | −0.522785 | + | 0.852465i | ||||
\(344\) | −10.2016 | −0.550035 | ||||||||
\(345\) | 1.63572 | − | 2.83314i | 0.0880639 | − | 0.152531i | ||||
\(346\) | −1.92671 | − | 3.33715i | −0.103580 | − | 0.179406i | ||||
\(347\) | 4.91015 | + | 8.50463i | 0.263591 | + | 0.456552i | 0.967193 | − | 0.254041i | \(-0.0817599\pi\) |
−0.703603 | + | 0.710593i | \(0.748427\pi\) | |||||||
\(348\) | −5.60831 | + | 9.71389i | −0.300637 | + | 0.520719i | ||||
\(349\) | −34.1355 | −1.82723 | −0.913616 | − | 0.406578i | \(-0.866722\pi\) | ||||
−0.913616 | + | 0.406578i | \(0.866722\pi\) | |||||||
\(350\) | 26.2158 | − | 9.28021i | 1.40130 | − | 0.496048i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.52820 | − | 2.64691i | 0.0814531 | − | 0.141081i | ||||
\(353\) | 5.92702 | + | 10.2659i | 0.315463 | + | 0.546399i | 0.979536 | − | 0.201270i | \(-0.0645067\pi\) |
−0.664073 | + | 0.747668i | \(0.731173\pi\) | |||||||
\(354\) | 7.63980 | + | 13.2325i | 0.406051 | + | 0.703300i | ||||
\(355\) | 0.436562 | − | 0.756147i | 0.0231703 | − | 0.0401321i | ||||
\(356\) | 56.3588 | 2.98701 | ||||||||
\(357\) | 2.40148 | − | 12.9491i | 0.127100 | − | 0.685341i | ||||
\(358\) | −32.3316 | −1.70878 | ||||||||
\(359\) | 6.51543 | − | 11.2851i | 0.343871 | − | 0.595603i | −0.641277 | − | 0.767310i | \(-0.721595\pi\) |
0.985148 | + | 0.171707i | \(0.0549283\pi\) | |||||||
\(360\) | −3.87679 | − | 6.71480i | −0.204325 | − | 0.353901i | ||||
\(361\) | 2.57602 | + | 4.46179i | 0.135580 | + | 0.234831i | ||||
\(362\) | 8.52989 | − | 14.7742i | 0.448321 | − | 0.776515i | ||||
\(363\) | −6.88619 | −0.361431 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.90900 | −0.309291 | ||||||||
\(366\) | −12.9487 | + | 22.4279i | −0.676841 | + | 1.17232i | ||||
\(367\) | 0.425803 | + | 0.737512i | 0.0222267 | + | 0.0384978i | 0.876925 | − | 0.480628i | \(-0.159591\pi\) |
−0.854698 | + | 0.519125i | \(0.826258\pi\) | |||||||
\(368\) | −6.69841 | − | 11.6020i | −0.349179 | − | 0.604795i | ||||
\(369\) | 10.1678 | − | 17.6112i | 0.529316 | − | 0.916801i | ||||
\(370\) | 0.190712 | 0.00991465 | ||||||||
\(371\) | −23.0826 | − | 19.7188i | −1.19839 | − | 1.02375i | ||||
\(372\) | −6.60188 | −0.342292 | ||||||||
\(373\) | 16.2998 | − | 28.2320i | 0.843970 | − | 1.46180i | −0.0425432 | − | 0.999095i | \(-0.513546\pi\) |
0.886513 | − | 0.462704i | \(-0.153121\pi\) | |||||||
\(374\) | −9.36389 | − | 16.2187i | −0.484195 | − | 0.838651i | ||||
\(375\) | −2.55437 | − | 4.42430i | −0.131907 | − | 0.228470i | ||||
\(376\) | −18.8824 | + | 32.7053i | −0.973785 | + | 1.68665i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.46605 | + | 24.0816i | −0.229709 | + | 1.23862i | ||||
\(379\) | −19.1587 | −0.984116 | −0.492058 | − | 0.870562i | \(-0.663755\pi\) | ||||
−0.492058 | + | 0.870562i | \(0.663755\pi\) | |||||||
\(380\) | 5.28208 | − | 9.14883i | 0.270965 | − | 0.469325i | ||||
\(381\) | 1.39384 | + | 2.41419i | 0.0714083 | + | 0.123683i | ||||
\(382\) | −19.3946 | − | 33.5924i | −0.992313 | − | 1.71874i | ||||
\(383\) | 14.0203 | − | 24.2839i | 0.716404 | − | 1.24085i | −0.246012 | − | 0.969267i | \(-0.579120\pi\) |
0.962416 | − | 0.271581i | \(-0.0875465\pi\) | |||||||
\(384\) | −14.6276 | −0.746462 | ||||||||
\(385\) | 2.13668 | − | 0.756370i | 0.108895 | − | 0.0385482i | ||||
\(386\) | −32.7193 | −1.66537 | ||||||||
\(387\) | −3.17115 | + | 5.49260i | −0.161199 | + | 0.279204i | ||||
\(388\) | 22.4326 | + | 38.8545i | 1.13885 | + | 1.97254i | ||||
\(389\) | 3.79850 | + | 6.57919i | 0.192591 | + | 0.333578i | 0.946108 | − | 0.323850i | \(-0.104977\pi\) |
−0.753517 | + | 0.657429i | \(0.771644\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.5076 | 2.14970 | ||||||||
\(392\) | 21.9003 | − | 17.7264i | 1.10613 | − | 0.895319i | ||||
\(393\) | 2.29841 | 0.115939 | ||||||||
\(394\) | 9.54093 | − | 16.5254i | 0.480665 | − | 0.832536i | ||||
\(395\) | 2.12158 | + | 3.67469i | 0.106748 | + | 0.184894i | ||||
\(396\) | 5.13477 | + | 8.89368i | 0.258032 | + | 0.446924i | ||||
\(397\) | 5.74428 | − | 9.94938i | 0.288297 | − | 0.499345i | −0.685106 | − | 0.728443i | \(-0.740244\pi\) |
0.973403 | + | 0.229098i | \(0.0735776\pi\) | |||||||
\(398\) | −11.0510 | −0.553937 | ||||||||
\(399\) | −6.54737 | + | 2.31772i | −0.327779 | + | 0.116031i | ||||
\(400\) | −9.80145 | −0.490073 | ||||||||
\(401\) | −2.82547 | + | 4.89385i | −0.141097 | + | 0.244387i | −0.927910 | − | 0.372804i | \(-0.878396\pi\) |
0.786813 | + | 0.617192i | \(0.211730\pi\) | |||||||
\(402\) | −11.4364 | − | 19.8084i | −0.570395 | − | 0.987952i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.743740 | + | 1.28819i | −0.0370024 | + | 0.0640901i | ||||
\(405\) | −3.67108 | −0.182418 | ||||||||
\(406\) | 4.96085 | − | 26.7496i | 0.246203 | − | 1.32756i | ||||
\(407\) | −0.115603 | −0.00573024 | ||||||||
\(408\) | −10.0179 | + | 17.3515i | −0.495959 | + | 0.859026i | ||||
\(409\) | −14.3539 | − | 24.8616i | −0.709752 | − | 1.22933i | −0.964949 | − | 0.262438i | \(-0.915474\pi\) |
0.255197 | − | 0.966889i | \(-0.417860\pi\) | |||||||
\(410\) | 7.45988 | + | 12.9209i | 0.368417 | + | 0.638118i | ||||
\(411\) | 3.12365 | − | 5.41033i | 0.154078 | − | 0.266872i | ||||
\(412\) | 14.0148 | 0.690461 | ||||||||
\(413\) | −18.2698 | − | 15.6074i | −0.898999 | − | 0.767992i | ||||
\(414\) | −35.9510 | −1.76689 | ||||||||
\(415\) | −2.08661 | + | 3.61412i | −0.102428 | + | 0.177410i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.70902 | − | 13.3524i | −0.377512 | − | 0.653871i | ||||
\(418\) | −4.93829 | + | 8.55336i | −0.241539 | + | 0.418359i | ||||
\(419\) | −31.0913 | −1.51891 | −0.759454 | − | 0.650561i | \(-0.774534\pi\) | ||||
−0.759454 | + | 0.650561i | \(0.774534\pi\) | |||||||
\(420\) | −4.02862 | − | 3.44155i | −0.196576 | − | 0.167930i | ||||
\(421\) | −11.7143 | −0.570922 | −0.285461 | − | 0.958390i | \(-0.592147\pi\) | ||||
−0.285461 | + | 0.958390i | \(0.592147\pi\) | |||||||
\(422\) | −7.72195 | + | 13.3748i | −0.375898 | + | 0.651075i | ||||
\(423\) | 11.7391 | + | 20.3327i | 0.570774 | + | 0.988610i | ||||
\(424\) | 23.0926 | + | 39.9975i | 1.12147 | + | 1.94245i | ||||
\(425\) | 15.5498 | − | 26.9331i | 0.754277 | − | 1.30645i | ||||
\(426\) | 1.90819 | 0.0924523 | ||||||||
\(427\) | 7.42627 | − | 40.0436i | 0.359383 | − | 1.93784i | ||||
\(428\) | −31.9337 | −1.54358 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.32660 | − | 4.02979i | −0.112199 | − | 0.194334i | ||||
\(431\) | 3.86105 | + | 6.68753i | 0.185980 | + | 0.322127i | 0.943906 | − | 0.330213i | \(-0.107121\pi\) |
−0.757926 | + | 0.652340i | \(0.773787\pi\) | |||||||
\(432\) | 4.31607 | − | 7.47565i | 0.207657 | − | 0.359672i | ||||
\(433\) | −22.7946 | −1.09544 | −0.547718 | − | 0.836663i | \(-0.684503\pi\) | ||||
−0.547718 | + | 0.836663i | \(0.684503\pi\) | |||||||
\(434\) | 15.0949 | − | 5.34348i | 0.724578 | − | 0.256495i | ||||
\(435\) | −2.34146 | −0.112265 | ||||||||
\(436\) | 7.40290 | − | 12.8222i | 0.354535 | − | 0.614072i | ||||
\(437\) | −11.2087 | − | 19.4141i | −0.536186 | − | 0.928701i | ||||
\(438\) | −6.45701 | − | 11.1839i | −0.308528 | − | 0.534386i | ||||
\(439\) | −7.19363 | + | 12.4597i | −0.343333 | + | 0.594670i | −0.985049 | − | 0.172272i | \(-0.944889\pi\) |
0.641716 | + | 0.766942i | \(0.278223\pi\) | |||||||
\(440\) | −3.44825 | −0.164389 | ||||||||
\(441\) | −2.73630 | − | 17.3014i | −0.130300 | − | 0.823877i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.1347 | − | 29.6782i | 0.814094 | − | 1.41005i | −0.0958830 | − | 0.995393i | \(-0.530567\pi\) |
0.909977 | − | 0.414659i | \(-0.136099\pi\) | |||||||
\(444\) | 0.135119 | + | 0.234033i | 0.00641245 | + | 0.0111067i | ||||
\(445\) | 5.88243 | + | 10.1887i | 0.278854 | + | 0.482989i | ||||
\(446\) | 12.7667 | − | 22.1126i | 0.604522 | − | 1.04706i | ||||
\(447\) | 1.66641 | 0.0788183 | ||||||||
\(448\) | 27.4291 | − | 9.70970i | 1.29590 | − | 0.458740i | ||||
\(449\) | 25.5552 | 1.20602 | 0.603012 | − | 0.797732i | \(-0.293967\pi\) | ||||
0.603012 | + | 0.797732i | \(0.293967\pi\) | |||||||
\(450\) | −13.1513 | + | 22.7788i | −0.619959 | + | 1.07380i | ||||
\(451\) | −4.52192 | − | 7.83220i | −0.212929 | − | 0.368804i | ||||
\(452\) | −7.39921 | − | 12.8158i | −0.348029 | − | 0.602805i | ||||
\(453\) | −4.24565 | + | 7.35369i | −0.199478 | + | 0.345506i | ||||
\(454\) | 27.0643 | 1.27019 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.5664 | 0.494815 | ||||||||
\(457\) | −13.7310 | + | 23.7828i | −0.642309 | + | 1.11251i | 0.342607 | + | 0.939479i | \(0.388690\pi\) |
−0.984916 | + | 0.173033i | \(0.944643\pi\) | |||||||
\(458\) | −17.4765 | − | 30.2702i | −0.816625 | − | 1.41444i | ||||
\(459\) | 13.6947 | + | 23.7199i | 0.639215 | + | 1.10715i | ||||
\(460\) | 8.55076 | − | 14.8104i | 0.398681 | − | 0.690536i | ||||
\(461\) | −5.85152 | −0.272533 | −0.136266 | − | 0.990672i | \(-0.543510\pi\) | ||||
−0.136266 | + | 0.990672i | \(0.543510\pi\) | |||||||
\(462\) | 3.76641 | + | 3.21755i | 0.175229 | + | 0.149694i | ||||
\(463\) | −18.9046 | −0.878570 | −0.439285 | − | 0.898348i | \(-0.644768\pi\) | ||||
−0.439285 | + | 0.898348i | \(0.644768\pi\) | |||||||
\(464\) | −4.79425 | + | 8.30389i | −0.222568 | + | 0.385498i | ||||
\(465\) | −0.689069 | − | 1.19350i | −0.0319548 | − | 0.0553474i | ||||
\(466\) | 10.2952 | + | 17.8318i | 0.476916 | + | 0.826043i | ||||
\(467\) | 5.13106 | − | 8.88725i | 0.237437 | − | 0.411253i | −0.722541 | − | 0.691328i | \(-0.757026\pi\) |
0.959978 | + | 0.280075i | \(0.0903593\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.3490 | + | 23.3635i | 1.26286 | + | 1.07883i | ||||
\(470\) | −17.2254 | −0.794547 | ||||||||
\(471\) | 0.865461 | − | 1.49902i | 0.0398783 | − | 0.0690713i | ||||
\(472\) | 18.2777 | + | 31.6580i | 0.841301 | + | 1.45718i | ||||
\(473\) | 1.41030 | + | 2.44272i | 0.0648458 | + | 0.112316i | ||||
\(474\) | −4.63668 | + | 8.03096i | −0.212970 | + | 0.368874i | ||||
\(475\) | −16.4012 | −0.752537 | ||||||||
\(476\) | 12.5538 | − | 67.6921i | 0.575404 | − | 3.10266i | ||||
\(477\) | 28.7130 | 1.31468 | ||||||||
\(478\) | −15.1629 | + | 26.2629i | −0.693534 | + | 1.20124i | ||||
\(479\) | −14.7056 | − | 25.4709i | −0.671918 | − | 1.16380i | −0.977360 | − | 0.211585i | \(-0.932137\pi\) |
0.305442 | − | 0.952211i | \(-0.401196\pi\) | |||||||
\(480\) | −0.745727 | − | 1.29164i | −0.0340376 | − | 0.0589549i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 38.1945 | 1.73971 | ||||||||
\(483\) | −10.5991 | + | 3.75199i | −0.482274 | + | 0.170721i | ||||
\(484\) | −35.9978 | −1.63626 | ||||||||
\(485\) | −4.68280 | + | 8.11084i | −0.212635 | + | 0.368294i | ||||
\(486\) | −17.8973 | − | 30.9991i | −0.811839 | − | 1.40615i | ||||
\(487\) | 8.29480 | + | 14.3670i | 0.375873 | + | 0.651031i | 0.990457 | − | 0.137820i | \(-0.0440095\pi\) |
−0.614584 | + | 0.788851i | \(0.710676\pi\) | |||||||
\(488\) | −30.9790 | + | 53.6572i | −1.40235 | + | 2.42895i | ||||
\(489\) | 12.6280 | 0.571056 | ||||||||
\(490\) | 11.9968 | + | 4.60822i | 0.541960 | + | 0.208178i | ||||
\(491\) | 6.25288 | 0.282189 | 0.141094 | − | 0.989996i | \(-0.454938\pi\) | ||||
0.141094 | + | 0.989996i | \(0.454938\pi\) | |||||||
\(492\) | −10.5706 | + | 18.3088i | −0.476559 | + | 0.825425i | ||||
\(493\) | −15.2120 | − | 26.3479i | −0.685113 | − | 1.18665i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.07188 | + | 1.85655i | −0.0481774 | + | 0.0834456i | ||||
\(496\) | −5.64361 | −0.253405 | ||||||||
\(497\) | −2.82882 | + | 1.00138i | −0.126890 | + | 0.0449180i | ||||
\(498\) | −9.12050 | −0.408699 | ||||||||
\(499\) | 13.0888 | − | 22.6705i | 0.585935 | − | 1.01487i | −0.408823 | − | 0.912614i | \(-0.634061\pi\) |
0.994758 | − | 0.102256i | \(-0.0326061\pi\) | |||||||
\(500\) | −13.3531 | − | 23.1282i | −0.597168 | − | 1.03432i | ||||
\(501\) | −0.261651 | − | 0.453193i | −0.0116897 | − | 0.0202472i | ||||
\(502\) | 27.3842 | − | 47.4307i | 1.22221 | − | 2.11694i | ||||
\(503\) | −20.5184 | −0.914870 | −0.457435 | − | 0.889243i | \(-0.651232\pi\) | ||||
−0.457435 | + | 0.889243i | \(0.651232\pi\) | |||||||
\(504\) | −4.85919 | + | 26.2015i | −0.216445 | + | 1.16711i | ||||
\(505\) | −0.310510 | −0.0138175 | ||||||||
\(506\) | −7.99422 | + | 13.8464i | −0.355386 | + | 0.615547i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.28633 | + | 12.6203i | 0.323278 | + | 0.559935i | ||||
\(509\) | 6.76903 | − | 11.7243i | 0.300032 | − | 0.519670i | −0.676111 | − | 0.736800i | \(-0.736336\pi\) |
0.976143 | + | 0.217129i | \(0.0696694\pi\) | |||||||
\(510\) | −9.13876 | −0.404671 | ||||||||
\(511\) | 15.4413 | + | 13.1911i | 0.683083 | + | 0.583540i | ||||
\(512\) | −24.0100 | −1.06110 | ||||||||
\(513\) | 7.22225 | − | 12.5093i | 0.318870 | − | 0.552299i | ||||
\(514\) | 24.1351 | + | 41.8032i | 1.06455 | + | 1.84386i | ||||
\(515\) | 1.46279 | + | 2.53363i | 0.0644583 | + | 0.111645i | ||||
\(516\) | 3.29677 | − | 5.71017i | 0.145132 | − | 0.251376i | ||||
\(517\) | 10.4414 | 0.459214 | ||||||||
\(518\) | −0.498366 | − | 0.425741i | −0.0218969 | − | 0.0187060i | ||||
\(519\) | 1.13982 | 0.0500327 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0622 | − | 20.8924i | −0.528457 | − | 0.915314i | −0.999449 | − | 0.0331769i | \(-0.989438\pi\) |
0.470993 | − | 0.882137i | \(-0.343896\pi\) | |||||||
\(522\) | 12.8656 | + | 22.2839i | 0.563112 | + | 0.975339i | ||||
\(523\) | 12.6491 | − | 21.9090i | 0.553109 | − | 0.958012i | −0.444939 | − | 0.895561i | \(-0.646775\pi\) |
0.998048 | − | 0.0624515i | \(-0.0198919\pi\) | |||||||
\(524\) | 12.0150 | 0.524879 | ||||||||
\(525\) | −1.49999 | + | 8.08815i | −0.0654648 | + | 0.352996i | ||||
\(526\) | −63.5084 | −2.76910 | ||||||||
\(527\) | 8.95347 | − | 15.5079i | 0.390019 | − | 0.675533i | ||||
\(528\) | −0.872939 | − | 1.51197i | −0.0379898 | − | 0.0658002i | ||||
\(529\) | −6.64496 | − | 11.5094i | −0.288911 | − | 0.500409i | ||||
\(530\) | −10.5330 | + | 18.2438i | −0.457526 | + | 0.792458i | ||||
\(531\) | 22.7263 | 0.986239 | ||||||||
\(532\) | −34.2266 | + | 12.1160i | −1.48391 | + | 0.525294i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −12.8559 | + | 22.2672i | −0.556331 | + | 0.963594i | ||||
\(535\) | −3.33307 | − | 5.77305i | −0.144101 | − | 0.249591i | ||||
\(536\) | −27.3608 | − | 47.3903i | −1.18181 | − | 2.04695i | ||||
\(537\) | 4.78178 | − | 8.28228i | 0.206349 | − | 0.357407i | ||||
\(538\) | −29.8481 | −1.28684 | ||||||||
\(539\) | −7.27204 | − | 2.79334i | −0.313229 | − | 0.120318i | ||||
\(540\) | 11.0192 | 0.474192 | ||||||||
\(541\) | 13.1582 | − | 22.7907i | 0.565716 | − | 0.979848i | −0.431267 | − | 0.902224i | \(-0.641933\pi\) |
0.996983 | − | 0.0776240i | \(-0.0247334\pi\) | |||||||
\(542\) | 20.2811 | + | 35.1278i | 0.871146 | + | 1.50887i | ||||
\(543\) | 2.52310 | + | 4.37015i | 0.108277 | + | 0.187541i | ||||
\(544\) | 9.68966 | − | 16.7830i | 0.415441 | − | 0.719564i | ||||
\(545\) | 3.09070 | 0.132391 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.4439 | −0.831362 | −0.415681 | − | 0.909510i | \(-0.636457\pi\) | ||||
−0.415681 | + | 0.909510i | \(0.636457\pi\) | |||||||
\(548\) | 16.3290 | − | 28.2827i | 0.697541 | − | 1.20818i | ||||
\(549\) | 19.2595 | + | 33.3584i | 0.821975 | + | 1.42370i | ||||
\(550\) | 5.84878 | + | 10.1304i | 0.249393 | + | 0.431961i | ||||
\(551\) | −8.02242 | + | 13.8952i | −0.341767 | + | 0.591957i | ||||
\(552\) | 17.1051 | 0.728041 | ||||||||
\(553\) | 2.65920 | − | 14.3388i | 0.113081 | − | 0.609747i | ||||
\(554\) | 31.4138 | 1.33465 | ||||||||
\(555\) | −0.0282059 | + | 0.0488541i | −0.00119728 | + | 0.00207374i | ||||
\(556\) | −40.2992 | − | 69.8003i | −1.70907 | − | 2.96019i | ||||
\(557\) | 20.5119 | + | 35.5276i | 0.869117 | + | 1.50535i | 0.862901 | + | 0.505374i | \(0.168645\pi\) |
0.00621596 | + | 0.999981i | \(0.498021\pi\) | |||||||
\(558\) | −7.57244 | + | 13.1158i | −0.320567 | + | 0.555238i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.44386 | − | 2.94200i | −0.145529 | − | 0.124322i | ||||
\(561\) | 5.53960 | 0.233882 | ||||||||
\(562\) | −10.6445 | + | 18.4368i | −0.449010 | + | 0.777709i | ||||
\(563\) | 15.1356 | + | 26.2156i | 0.637888 | + | 1.10485i | 0.985895 | + | 0.167363i | \(0.0535252\pi\) |
−0.348007 | + | 0.937492i | \(0.613141\pi\) | |||||||
\(564\) | −12.2041 | − | 21.1381i | −0.513886 | − | 0.890076i | ||||
\(565\) | 1.54458 | − | 2.67529i | 0.0649809 | − | 0.112550i | ||||
\(566\) | −27.5251 | −1.15697 | ||||||||
\(567\) | 9.59321 | + | 8.19523i | 0.402877 | + | 0.344167i | ||||
\(568\) | 4.56523 | 0.191553 | ||||||||
\(569\) | 6.54938 | − | 11.3439i | 0.274564 | − | 0.475559i | −0.695461 | − | 0.718564i | \(-0.744800\pi\) |
0.970025 | + | 0.243005i | \(0.0781331\pi\) | |||||||
\(570\) | 2.40978 | + | 4.17386i | 0.100934 | + | 0.174824i | ||||
\(571\) | 5.98580 | + | 10.3677i | 0.250498 | + | 0.433875i | 0.963663 | − | 0.267121i | \(-0.0860723\pi\) |
−0.713165 | + | 0.700996i | \(0.752739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.4737 | 0.479320 | ||||||||
\(574\) | 9.35025 | − | 50.4179i | 0.390272 | − | 2.10440i | ||||
\(575\) | −26.5506 | −1.10724 | ||||||||
\(576\) | −13.7600 | + | 23.8330i | −0.573332 | + | 0.993040i | ||||
\(577\) | 1.00752 | + | 1.74507i | 0.0419435 | + | 0.0726483i | 0.886235 | − | 0.463236i | \(-0.153312\pi\) |
−0.844292 | + | 0.535884i | \(0.819978\pi\) | |||||||
\(578\) | −39.1010 | − | 67.7249i | −1.62639 | − | 2.81698i | ||||
\(579\) | 4.83911 | − | 8.38159i | 0.201107 | − | 0.348327i | ||||
\(580\) | −12.2401 | −0.508242 | ||||||||
\(581\) | 13.5208 | − | 4.78625i | 0.560935 | − | 0.198567i | ||||
\(582\) | −20.4683 | −0.848440 | ||||||||
\(583\) | 6.38476 | − | 11.0587i | 0.264430 | − | 0.458006i | ||||
\(584\) | −15.4480 | − | 26.7567i | −0.639242 | − | 1.10720i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.894606 | − | 1.54950i | 0.0369558 | − | 0.0640094i | ||||
\(587\) | 17.7652 | 0.733247 | 0.366624 | − | 0.930369i | \(-0.380514\pi\) | ||||
0.366624 | + | 0.930369i | \(0.380514\pi\) | |||||||
\(588\) | 2.84470 | + | 17.9868i | 0.117313 | + | 0.741762i | ||||
\(589\) | −9.44368 | −0.389120 | ||||||||
\(590\) | −8.33689 | + | 14.4399i | −0.343224 | + | 0.594482i | ||||
\(591\) | 2.82217 | + | 4.88814i | 0.116088 | + | 0.201071i | ||||
\(592\) | 0.115506 | + | 0.200062i | 0.00474727 | + | 0.00822250i | ||||
\(593\) | −14.5652 | + | 25.2277i | −0.598121 | + | 1.03598i | 0.394978 | + | 0.918691i | \(0.370752\pi\) |
−0.993098 | + | 0.117285i | \(0.962581\pi\) | |||||||
\(594\) | −10.3020 | −0.422697 | ||||||||
\(595\) | 13.5478 | − | 4.79583i | 0.555407 | − | 0.196610i | ||||
\(596\) | 8.71120 | 0.356825 | ||||||||
\(597\) | 1.63442 | − | 2.83090i | 0.0668924 | − | 0.115861i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.7659 | − | 22.1111i | −0.521600 | − | 0.903437i | −0.999684 | − | 0.0251232i | \(-0.992002\pi\) |
0.478085 | − | 0.878314i | \(-0.341331\pi\) | |||||||
\(600\) | 6.25726 | − | 10.8379i | 0.255451 | − | 0.442455i | ||||
\(601\) | −34.4411 | −1.40488 | −0.702441 | − | 0.711742i | \(-0.747907\pi\) | ||||
−0.702441 | + | 0.711742i | \(0.747907\pi\) | |||||||
\(602\) | −2.91617 | + | 15.7244i | −0.118854 | + | 0.640879i | ||||
\(603\) | −34.0201 | −1.38541 | ||||||||
\(604\) | −22.1943 | + | 38.4417i | −0.903074 | + | 1.56417i | ||||
\(605\) | −3.75726 | − | 6.50776i | −0.152754 | − | 0.264578i | ||||
\(606\) | −0.339307 | − | 0.587697i | −0.0137834 | − | 0.0238736i | ||||
\(607\) | −10.4819 | + | 18.1552i | −0.425449 | + | 0.736898i | −0.996462 | − | 0.0840421i | \(-0.973217\pi\) |
0.571014 | + | 0.820941i | \(0.306550\pi\) | |||||||
\(608\) | −10.2202 | −0.414483 | ||||||||
\(609\) | 6.11867 | + | 5.22702i | 0.247941 | + | 0.211810i | ||||
\(610\) | −28.2605 | −1.14423 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 32.5574 | + | 56.3911i | 1.31606 | + | 2.27948i | ||||
\(613\) | −6.06480 | − | 10.5045i | −0.244955 | − | 0.424275i | 0.717164 | − | 0.696904i | \(-0.245440\pi\) |
−0.962119 | + | 0.272630i | \(0.912107\pi\) | |||||||
\(614\) | −10.3620 | + | 17.9475i | −0.418177 | + | 0.724304i | ||||
\(615\) | −4.41321 | −0.177958 | ||||||||
\(616\) | 9.01089 | + | 7.69777i | 0.363059 | + | 0.310152i | ||||
\(617\) | −5.46234 | −0.219906 | −0.109953 | − | 0.993937i | \(-0.535070\pi\) | ||||
−0.109953 | + | 0.993937i | \(0.535070\pi\) | |||||||
\(618\) | −3.19690 | + | 5.53720i | −0.128598 | + | 0.222739i | ||||
\(619\) | −6.63530 | − | 11.4927i | −0.266695 | − | 0.461930i | 0.701311 | − | 0.712855i | \(-0.252598\pi\) |
−0.968006 | + | 0.250926i | \(0.919265\pi\) | |||||||
\(620\) | −3.60213 | − | 6.23908i | −0.144665 | − | 0.250568i | ||||
\(621\) | 11.6916 | − | 20.2504i | 0.469166 | − | 0.812620i | ||||
\(622\) | −56.5427 | −2.26716 | ||||||||
\(623\) | 7.37306 | − | 39.7566i | 0.295395 | − | 1.59282i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.23104 | + | 14.2566i | −0.329242 | + | 0.570263i | ||||
\(626\) | −28.1059 | − | 48.6808i | −1.12334 | − | 1.94568i | ||||
\(627\) | −1.46072 | − | 2.53005i | −0.0583357 | − | 0.101040i | ||||
\(628\) | 4.52423 | − | 7.83620i | 0.180536 | − | 0.312698i | ||||
\(629\) | −0.732992 | −0.0292263 | ||||||||
\(630\) | −11.4581 | + | 4.05609i | −0.456503 | + | 0.161599i | ||||
\(631\) | 27.6525 | 1.10083 | 0.550414 | − | 0.834892i | \(-0.314470\pi\) | ||||
0.550414 | + | 0.834892i | \(0.314470\pi\) | |||||||
\(632\) | −11.0930 | + | 19.2136i | −0.441254 | + | 0.764274i | ||||
\(633\) | −2.28412 | − | 3.95621i | −0.0907856 | − | 0.157245i | ||||
\(634\) | −14.5006 | − | 25.1157i | −0.575891 | − | 0.997473i | ||||
\(635\) | −1.52101 | + | 2.63447i | −0.0603596 | + | 0.104546i | ||||
\(636\) | −29.8504 | −1.18365 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11.4434 | 0.453049 | ||||||||
\(639\) | 1.41909 | − | 2.45794i | 0.0561384 | − | 0.0972346i | ||||
\(640\) | −7.98114 | − | 13.8237i | −0.315482 | − | 0.546432i | ||||
\(641\) | 7.27920 | + | 12.6079i | 0.287511 | + | 0.497984i | 0.973215 | − | 0.229897i | \(-0.0738388\pi\) |
−0.685704 | + | 0.727881i | \(0.740506\pi\) | |||||||
\(642\) | 7.28437 | − | 12.6169i | 0.287491 | − | 0.497949i | ||||
\(643\) | −5.35888 | −0.211334 | −0.105667 | − | 0.994402i | \(-0.533698\pi\) | ||||
−0.105667 | + | 0.994402i | \(0.533698\pi\) | |||||||
\(644\) | −55.4070 | + | 19.6137i | −2.18334 | + | 0.772886i | ||||
\(645\) | 1.37640 | 0.0541955 | ||||||||
\(646\) | −31.3116 | + | 54.2333i | −1.23194 | + | 2.13378i | ||||
\(647\) | −9.04617 | − | 15.6684i | −0.355641 | − | 0.615989i | 0.631586 | − | 0.775306i | \(-0.282404\pi\) |
−0.987228 | + | 0.159317i | \(0.949071\pi\) | |||||||
\(648\) | −9.59736 | − | 16.6231i | −0.377020 | − | 0.653018i | ||||
\(649\) | 5.05353 | − | 8.75298i | 0.198369 | − | 0.343584i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.863682 | + | 4.65710i | −0.0338504 | + | 0.182526i | ||||
\(652\) | 66.0131 | 2.58527 | ||||||||
\(653\) | −19.9819 | + | 34.6096i | −0.781951 | + | 1.35438i | 0.148853 | + | 0.988859i | \(0.452442\pi\) |
−0.930804 | + | 0.365519i | \(0.880891\pi\) | |||||||
\(654\) | 3.37733 | + | 5.84971i | 0.132064 | + | 0.228742i | ||||
\(655\) | 1.25406 | + | 2.17210i | 0.0490003 | + | 0.0848710i | ||||
\(656\) | −9.03625 | + | 15.6512i | −0.352806 | + | 0.611078i | ||||
\(657\) | −19.2079 | −0.749370 | ||||||||
\(658\) | 45.0130 | + | 38.4535i | 1.75479 | + | 1.49907i | ||||
\(659\) | −40.8081 | −1.58966 | −0.794828 | − | 0.606834i | \(-0.792439\pi\) | ||||
−0.794828 | + | 0.606834i | \(0.792439\pi\) | |||||||
\(660\) | 1.11434 | − | 1.93009i | 0.0433756 | − | 0.0751287i | ||||
\(661\) | −4.74488 | − | 8.21837i | −0.184554 | − | 0.319658i | 0.758872 | − | 0.651240i | \(-0.225751\pi\) |
−0.943426 | + | 0.331582i | \(0.892418\pi\) | |||||||
\(662\) | 1.70813 | + | 2.95858i | 0.0663885 | + | 0.114988i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.8202 | −0.846789 | ||||||||
\(665\) | −5.76274 | − | 4.92296i | −0.223470 | − | 0.190904i | ||||
\(666\) | 0.619931 | 0.0240218 | ||||||||
\(667\) | −12.9869 | + | 22.4940i | −0.502855 | + | 0.870970i | ||||
\(668\) | −1.36779 | − | 2.36908i | −0.0529214 | − | 0.0916626i | ||||
\(669\) | 3.77634 | + | 6.54082i | 0.146002 | + | 0.252883i | ||||
\(670\) | 12.4799 | − | 21.6158i | 0.482140 | − | 0.835091i | ||||
\(671\) | 17.1305 | 0.661316 | ||||||||
\(672\) | −0.934697 | + | 5.04002i | −0.0360567 | + | 0.194423i | ||||
\(673\) | −5.64510 | −0.217603 | −0.108801 | − | 0.994064i | \(-0.534701\pi\) | ||||
−0.108801 | + | 0.994064i | \(0.534701\pi\) | |||||||
\(674\) | −11.2079 | + | 19.4126i | −0.431711 | + | 0.747746i | ||||
\(675\) | −8.55385 | − | 14.8157i | −0.329238 | − | 0.570256i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.71924 | + | 8.17396i | −0.181375 | + | 0.314151i | −0.942349 | − | 0.334632i | \(-0.891388\pi\) |
0.760974 | + | 0.648782i | \(0.224721\pi\) | |||||||
\(678\) | 6.75130 | 0.259282 | ||||||||
\(679\) | 30.3434 | − | 10.7414i | 1.16447 | − | 0.412215i | ||||
\(680\) | −21.8639 | −0.838442 | ||||||||
\(681\) | −4.00275 | + | 6.93297i | −0.153386 | + | 0.265672i | ||||
\(682\) | 3.36768 | + | 5.83300i | 0.128955 | + | 0.223357i | ||||
\(683\) | 8.30765 | + | 14.3893i | 0.317883 | + | 0.550590i | 0.980046 | − | 0.198770i | \(-0.0636946\pi\) |
−0.662163 | + | 0.749360i | \(0.730361\pi\) | |||||||
\(684\) | 17.1700 | − | 29.7393i | 0.656511 | − | 1.13711i | ||||
\(685\) | 6.81734 | 0.260477 | ||||||||
\(686\) | −21.0625 | − | 38.8234i | −0.804171 | − | 1.48229i | ||||
\(687\) | 10.3390 | 0.394456 | ||||||||
\(688\) | 2.81823 | − | 4.88133i | 0.107444 | − | 0.186099i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.90101 | + | 6.75675i | 0.148509 | + | 0.257225i | ||||
\(691\) | −18.1380 | + | 31.4160i | −0.690003 | + | 1.19512i | 0.281833 | + | 0.959463i | \(0.409058\pi\) |
−0.971836 | + | 0.235657i | \(0.924276\pi\) | |||||||
\(692\) | 5.95847 | 0.226507 | ||||||||
\(693\) | 6.94552 | − | 2.45866i | 0.263839 | − | 0.0933969i | ||||
\(694\) | −23.4204 | −0.889025 | ||||||||
\(695\) | 8.41243 | − | 14.5707i | 0.319102 | − | 0.552700i | ||||
\(696\) | −6.12132 | − | 10.6024i | −0.232028 | − | 0.401884i | ||||
\(697\) | −28.6717 | − | 49.6608i | −1.08602 | − | 1.88104i | ||||
\(698\) | 40.7048 | − | 70.5028i | 1.54070 | − | 2.66857i | ||||
\(699\) | −6.09056 | −0.230366 | ||||||||
\(700\) | −7.84124 | + | 42.2811i | −0.296371 | + | 1.59808i | ||||
\(701\) | 14.8413 | 0.560547 | 0.280273 | − | 0.959920i | \(-0.409575\pi\) | ||||
0.280273 | + | 0.959920i | \(0.409575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.193281 | + | 0.334772i | 0.00728973 | + | 0.0126262i | ||||
\(704\) | 6.11946 | + | 10.5992i | 0.230636 | + | 0.399473i | ||||
\(705\) | 2.54760 | − | 4.41257i | 0.0959481 | − | 0.166187i | ||||
\(706\) | −28.2706 | −1.06398 | ||||||||
\(707\) | 0.811419 | + | 0.693175i | 0.0305166 | + | 0.0260695i | ||||
\(708\) | −23.6266 | −0.887942 | ||||||||
\(709\) | 11.2020 | − | 19.4025i | 0.420701 | − | 0.728676i | −0.575307 | − | 0.817938i | \(-0.695117\pi\) |
0.996008 | + | 0.0892614i | \(0.0284507\pi\) | |||||||
\(710\) | 1.04115 | + | 1.80333i | 0.0390738 | + | 0.0676778i | ||||
\(711\) | 6.89643 | + | 11.9450i | 0.258636 | + | 0.447972i | ||||
\(712\) | −30.7570 | + | 53.2728i | −1.15267 | + | 1.99648i | ||||
\(713\) | −15.2877 | −0.572527 | ||||||||
\(714\) | 23.8812 | + | 20.4011i | 0.893733 | + | 0.763493i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.9969 | − | 43.2959i | 0.934179 | − | 1.61805i | ||||
\(717\) | −4.48512 | − | 7.76845i | −0.167500 | − | 0.290118i | ||||
\(718\) | 15.5386 | + | 26.9137i | 0.579896 | + | 1.00441i | ||||
\(719\) | −3.96850 | + | 6.87365i | −0.148000 | + | 0.256344i | −0.930488 | − | 0.366322i | \(-0.880617\pi\) |
0.782488 | + | 0.622666i | \(0.213950\pi\) | |||||||
\(720\) | 4.28391 | 0.159652 | ||||||||
\(721\) | 1.83347 | − | 9.88633i | 0.0682819 | − | 0.368186i | ||||
\(722\) | −12.2871 | −0.457277 | ||||||||
\(723\) | −5.64888 | + | 9.78415i | −0.210084 | + | 0.363877i | ||||
\(724\) | 13.1896 | + | 22.8451i | 0.490189 | + | 0.849032i | ||||
\(725\) | 9.50155 | + | 16.4572i | 0.352879 | + | 0.611204i | ||||
\(726\) | 8.21142 | − | 14.2226i | 0.304754 | − | 0.527850i | ||||
\(727\) | −52.6516 | −1.95274 | −0.976370 | − | 0.216106i | \(-0.930664\pi\) | ||||
−0.976370 | + | 0.216106i | \(0.930664\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.71855 | −0.137724 | ||||||||
\(730\) | 7.04618 | − | 12.2043i | 0.260791 | − | 0.451703i | ||||
\(731\) | 8.94215 | + | 15.4883i | 0.330737 | + | 0.572854i | ||||
\(732\) | −20.0224 | − | 34.6798i | −0.740050 | − | 1.28180i | ||||
\(733\) | 12.1309 | − | 21.0113i | 0.448065 | − | 0.776071i | −0.550195 | − | 0.835036i | \(-0.685447\pi\) |
0.998260 | + | 0.0589649i | \(0.0187800\pi\) | |||||||
\(734\) | −2.03099 | −0.0749652 | ||||||||
\(735\) | −2.95477 | + | 2.39163i | −0.108988 | + | 0.0882167i | ||||
\(736\) | −16.5447 | −0.609845 | ||||||||
\(737\) | −7.56487 | + | 13.1027i | −0.278656 | + | 0.482646i | ||||
\(738\) | 24.2492 | + | 42.0008i | 0.892625 | + | 1.54607i | ||||
\(739\) | −15.1742 | − | 26.2826i | −0.558193 | − | 0.966819i | −0.997647 | − | 0.0685542i | \(-0.978161\pi\) |
0.439454 | − | 0.898265i | \(-0.355172\pi\) | |||||||
\(740\) | −0.147448 | + | 0.255387i | −0.00542028 | + | 0.00938820i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 68.2516 | − | 24.1606i | 2.50560 | − | 0.886962i | ||||
\(743\) | 22.0992 | 0.810743 | 0.405371 | − | 0.914152i | \(-0.367142\pi\) | ||||
0.405371 | + | 0.914152i | \(0.367142\pi\) | |||||||
\(744\) | 3.60288 | − | 6.24038i | 0.132088 | − | 0.228783i | ||||
\(745\) | 0.909228 | + | 1.57483i | 0.0333115 | + | 0.0576973i | ||||
\(746\) | 38.8732 | + | 67.3304i | 1.42325 | + | 2.46514i | ||||
\(747\) | −6.78276 | + | 11.7481i | −0.248168 | + | 0.429840i | ||||
\(748\) | 28.9585 | 1.05883 | ||||||||
\(749\) | −4.17768 | + | 22.5267i | −0.152649 | + | 0.823107i | ||||
\(750\) | 12.1838 | 0.444890 | ||||||||
\(751\) | −17.5833 | + | 30.4552i | −0.641624 | + | 1.11132i | 0.343447 | + | 0.939172i | \(0.388406\pi\) |
−0.985070 | + | 0.172153i | \(0.944928\pi\) | |||||||
\(752\) | −10.4327 | − | 18.0699i | −0.380440 | − | 0.658941i | ||||
\(753\) | 8.10012 | + | 14.0298i | 0.295185 | + | 0.511275i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.26609 | −0.337228 | ||||||||
\(756\) | −28.7953 | − | 24.5991i | −1.04727 | − | 0.894659i | ||||
\(757\) | −23.3691 | −0.849365 | −0.424682 | − | 0.905342i | \(-0.639614\pi\) | ||||
−0.424682 | + | 0.905342i | \(0.639614\pi\) | |||||||
\(758\) | 22.8457 | − | 39.5700i | 0.829795 | − | 1.43725i | ||||
\(759\) | −2.36466 | − | 4.09571i | −0.0858316 | − | 0.148665i | ||||
\(760\) | 5.76524 | + | 9.98569i | 0.209127 | + | 0.362219i | ||||
\(761\) | −19.8951 | + | 34.4593i | −0.721196 | + | 1.24915i | 0.239324 | + | 0.970940i | \(0.423074\pi\) |
−0.960521 | + | 0.278209i | \(0.910259\pi\) | |||||||
\(762\) | −6.64830 | −0.240843 | ||||||||
\(763\) | −8.07656 | − | 6.89960i | −0.292391 | − | 0.249782i | ||||
\(764\) | 59.9791 | 2.16997 | ||||||||
\(765\) | −6.79634 | + | 11.7716i | −0.245722 | + | 0.425603i | ||||
\(766\) | 33.4369 | + | 57.9145i | 1.20813 | + | 2.09254i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 9.68446 | − | 16.7740i | 0.349458 | − | 0.605279i | ||||
\(769\) | 12.2562 | 0.441968 | 0.220984 | − | 0.975277i | \(-0.429073\pi\) | ||||
0.220984 | + | 0.975277i | \(0.429073\pi\) | |||||||
\(770\) | −0.985691 | + | 5.31499i | −0.0355218 | + | 0.191539i | ||||
\(771\) | −14.2781 | −0.514214 | ||||||||
\(772\) | 25.2967 | − | 43.8151i | 0.910446 | − | 1.57694i | ||||
\(773\) | 18.9964 | + | 32.9027i | 0.683252 | + | 1.18343i | 0.973983 | + | 0.226622i | \(0.0727682\pi\) |
−0.290731 | + | 0.956805i | \(0.593898\pi\) | |||||||
\(774\) | −7.56286 | − | 13.0993i | −0.271842 | − | 0.470843i | ||||
\(775\) | −5.59242 | + | 9.68636i | −0.200886 | + | 0.347944i | ||||
\(776\) | −48.9692 | −1.75789 | ||||||||
\(777\) | 0.182768 | − | 0.0646985i | 0.00655676 | − | 0.00232104i | ||||
\(778\) | −18.1180 | −0.649563 | ||||||||
\(779\) | −15.1207 | + | 26.1899i | −0.541756 | + | 0.938349i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.631111 | − | 1.09312i | −0.0225829 | − | 0.0391148i | ||||
\(782\) | −50.6881 | + | 87.7943i | −1.81260 | + | 3.13952i | ||||
\(783\) | −16.7360 | −0.598097 | ||||||||
\(784\) | 2.43178 | + | 15.3759i | 0.0868493 | + | 0.549141i | ||||
\(785\) | 1.88886 | 0.0674163 | ||||||||
\(786\) | −2.74073 | + | 4.74709i | −0.0977587 | + | 0.169323i | ||||
\(787\) | −18.8911 | − | 32.7203i | −0.673393 | − | 1.16635i | −0.976936 | − | 0.213533i | \(-0.931503\pi\) |
0.303543 | − | 0.952818i | \(-0.401831\pi\) | |||||||
\(788\) | 14.7530 | + | 25.5529i | 0.525553 | + | 0.910285i | ||||
\(789\) | 9.39276 | − | 16.2687i | 0.334391 | − | 0.579182i | ||||
\(790\) | −10.1195 | −0.360035 | ||||||||
\(791\) | −10.0085 | + | 3.54294i | −0.355862 | + | 0.125972i | ||||
\(792\) | −11.2089 | −0.398291 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.6995 | + | 23.7282i | 0.486177 | + | 0.842083i | ||||
\(795\) | −3.11563 | − | 5.39643i | −0.110500 | − | 0.191392i | ||||
\(796\) | 8.54400 | − | 14.7986i | 0.302834 | − | 0.524524i | ||||
\(797\) | 4.55614 | 0.161387 | 0.0806935 | − | 0.996739i | \(-0.474287\pi\) | ||||
0.0806935 | + | 0.996739i | \(0.474287\pi\) | |||||||
\(798\) | 3.02042 | − | 16.2866i | 0.106922 | − | 0.576538i | ||||
\(799\) | 66.2048 | 2.34216 | ||||||||
\(800\) | −6.05225 | + | 10.4828i | −0.213979 | + | 0.370623i | ||||
\(801\) | 19.1215 | + | 33.1194i | 0.675625 | + | 1.17022i | ||||
\(802\) | −6.73845 | − | 11.6713i | −0.237943 | − | 0.412129i | ||||
\(803\) | −4.27115 | + | 7.39785i | −0.150726 | + | 0.261064i | ||||
\(804\) | 35.3678 | 1.24732 | ||||||||
\(805\) | −9.32888 | − | 7.96942i | −0.328800 | − | 0.280885i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.41448 | − | 7.64610i | 0.155397 | − | 0.269155i | ||||
\(808\) | −0.811771 | − | 1.40603i | −0.0285580 | − | 0.0494639i | ||||
\(809\) | −13.3555 | − | 23.1325i | −0.469556 | − | 0.813295i | 0.529838 | − | 0.848099i | \(-0.322253\pi\) |
−0.999394 | + | 0.0348040i | \(0.988919\pi\) | |||||||
\(810\) | 4.37757 | − | 7.58218i | 0.153812 | − | 0.266411i | ||||
\(811\) | 5.89688 | 0.207068 | 0.103534 | − | 0.994626i | \(-0.466985\pi\) | ||||
0.103534 | + | 0.994626i | \(0.466985\pi\) | |||||||
\(812\) | 31.9856 | + | 27.3244i | 1.12247 | + | 0.958900i | ||||
\(813\) | −11.9981 | −0.420792 | ||||||||
\(814\) | 0.137851 | − | 0.238764i | 0.00483166 | − | 0.00836869i | ||||
\(815\) | 6.89009 | + | 11.9340i | 0.241349 | + | 0.418029i | ||||
\(816\) | −5.53494 | − | 9.58680i | −0.193762 | − | 0.335605i | ||||
\(817\) | 4.71587 | − | 8.16812i | 0.164987 | − | 0.285766i | ||||
\(818\) | 68.4649 | 2.39382 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −23.0702 | −0.805646 | ||||||||
\(821\) | 8.12138 | − | 14.0666i | 0.283438 | − | 0.490929i | −0.688791 | − | 0.724960i | \(-0.741858\pi\) |
0.972229 | + | 0.234031i | \(0.0751916\pi\) | |||||||
\(822\) | 7.44959 | + | 12.9031i | 0.259834 | + | 0.450046i | ||||
\(823\) | −19.2590 | − | 33.3576i | −0.671328 | − | 1.16277i | −0.977528 | − | 0.210807i | \(-0.932391\pi\) |
0.306199 | − | 0.951967i | \(-0.400943\pi\) | |||||||
\(824\) | −7.64839 | + | 13.2474i | −0.266444 | + | 0.461495i | ||||
\(825\) | −3.46009 | −0.120465 | ||||||||
\(826\) | 54.0211 | − | 19.1231i | 1.87963 | − | 0.665376i | ||||
\(827\) | 23.5064 | 0.817398 | 0.408699 | − | 0.912669i | \(-0.365983\pi\) | ||||
0.408699 | + | 0.912669i | \(0.365983\pi\) | |||||||
\(828\) | 27.7952 | − | 48.1427i | 0.965950 | − | 1.67307i | ||||
\(829\) | −0.306676 | − | 0.531178i | −0.0106513 | − | 0.0184486i | 0.860651 | − | 0.509196i | \(-0.170057\pi\) |
−0.871302 | + | 0.490747i | \(0.836724\pi\) | |||||||
\(830\) | −4.97635 | − | 8.61929i | −0.172732 | − | 0.299180i | ||||
\(831\) | −4.64604 | + | 8.04718i | −0.161169 | + | 0.279154i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −46.1090 | − | 17.7114i | −1.59758 | − | 0.613665i | ||||
\(834\) | 36.7704 | 1.27326 | ||||||||
\(835\) | 0.285525 | − | 0.494544i | 0.00988101 | − | 0.0171144i | ||||
\(836\) | −7.63599 | − | 13.2259i | −0.264096 | − | 0.457428i | ||||
\(837\) | −4.92524 | − | 8.53077i | −0.170241 | − | 0.294867i | ||||
\(838\) | 37.0747 | − | 64.2153i | 1.28072 | − | 2.21828i | ||||
\(839\) | 18.0433 | 0.622924 | 0.311462 | − | 0.950259i | \(-0.399181\pi\) | ||||
0.311462 | + | 0.950259i | \(0.399181\pi\) | |||||||
\(840\) | 5.45166 | − | 1.92985i | 0.188100 | − | 0.0665860i | ||||
\(841\) | −10.4098 | −0.358957 | ||||||||
\(842\) | 13.9687 | − | 24.1945i | 0.481394 | − | 0.833799i | ||||
\(843\) | −3.14859 | − | 5.45352i | −0.108443 | − | 0.187829i | ||||
\(844\) | −11.9403 | − | 20.6812i | −0.411003 | − | 0.711878i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −55.9930 | −1.92508 | ||||||||
\(847\) | −4.70936 | + | 25.3936i | −0.161816 | + | 0.872533i | ||||
\(848\) | −25.5176 | −0.876277 | ||||||||
\(849\) | 4.07090 | − | 7.05101i | 0.139713 | − | 0.241990i | ||||
\(850\) | 37.0847 | + | 64.2325i | 1.27199 | + | 2.20316i | ||||
\(851\) | 0.312888 | + | 0.541938i | 0.0107257 | + | 0.0185774i | ||||
\(852\) | −1.47531 | + | 2.55530i | −0.0505431 | + | 0.0875433i | ||||
\(853\) | 50.0142 | 1.71245 | 0.856227 | − | 0.516599i | \(-0.172802\pi\) | ||||
0.856227 | + | 0.516599i | \(0.172802\pi\) | |||||||
\(854\) | 73.8497 | + | 63.0879i | 2.52709 | + | 2.15882i | ||||
\(855\) | 7.16844 | 0.245155 | ||||||||
\(856\) | 17.4274 | − | 30.1851i | 0.595656 | − | 1.03171i | ||||
\(857\) | −6.20769 | − | 10.7520i | −0.212051 | − | 0.367283i | 0.740305 | − | 0.672271i | \(-0.234681\pi\) |
−0.952356 | + | 0.304988i | \(0.901348\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.5798 | − | 32.1811i | 0.633934 | − | 1.09801i | −0.352806 | − | 0.935696i | \(-0.614772\pi\) |
0.986740 | − | 0.162309i | \(-0.0518942\pi\) | |||||||
\(860\) | 7.19516 | 0.245353 | ||||||||
\(861\) | 11.5325 | + | 9.85193i | 0.393027 | + | 0.335753i | ||||
\(862\) | −18.4164 | −0.627265 | ||||||||
\(863\) | −13.0818 | + | 22.6584i | −0.445310 | + | 0.771300i | −0.998074 | − | 0.0620384i | \(-0.980240\pi\) |
0.552764 | + | 0.833338i | \(0.313573\pi\) | |||||||
\(864\) | −5.33021 | − | 9.23220i | −0.181338 | − | 0.314086i | ||||
\(865\) | 0.621913 | + | 1.07718i | 0.0211457 | + | 0.0366254i | ||||
\(866\) | 27.1813 | − | 47.0794i | 0.923659 | − | 1.59982i | ||||
\(867\) | 23.1318 | 0.785598 | ||||||||
\(868\) | −4.51493 | + | 24.3452i | −0.153247 | + | 0.826329i | ||||
\(869\) | 6.13409 | 0.208085 | ||||||||
\(870\) | 2.79207 | − | 4.83601i | 0.0946601 | − | 0.163956i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.08005 | + | 13.9951i | 0.273625 | + | 0.473933i | ||||
\(873\) | −15.2220 | + | 26.3652i | −0.515185 | + | 0.892327i | ||||
\(874\) | 53.4632 | 1.80842 | ||||||||
\(875\) | −18.0620 | + | 6.39381i | −0.610606 | + | 0.216150i | ||||
\(876\) | 19.9687 | 0.674681 | ||||||||
\(877\) | −27.7749 | + | 48.1075i | −0.937892 | + | 1.62448i | −0.168497 | + | 0.985702i | \(0.553891\pi\) |
−0.769394 | + | 0.638774i | \(0.779442\pi\) | |||||||
\(878\) | −17.1560 | − | 29.7151i | −0.578989 | − | 1.00284i | ||||
\(879\) | 0.264621 | + | 0.458337i | 0.00892544 | + | 0.0154593i | ||||
\(880\) | 0.952589 | − | 1.64993i | 0.0321118 | − | 0.0556192i | ||||
\(881\) | −35.1270 | −1.18346 | −0.591730 | − | 0.806136i | \(-0.701555\pi\) | ||||
−0.591730 | + | 0.806136i | \(0.701555\pi\) | |||||||
\(882\) | 38.9969 | + | 14.9795i | 1.31309 | + | 0.504387i | ||||
\(883\) | 43.7616 | 1.47270 | 0.736348 | − | 0.676603i | \(-0.236549\pi\) | ||||
0.736348 | + | 0.676603i | \(0.236549\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.46602 | − | 4.27126i | −0.0828942 | − | 0.143577i | ||||
\(886\) | 40.8644 | + | 70.7793i | 1.37287 | + | 2.37788i | ||||
\(887\) | 19.8530 | − | 34.3865i | 0.666600 | − | 1.15458i | −0.312249 | − | 0.950000i | \(-0.601082\pi\) |
0.978849 | − | 0.204584i | \(-0.0655843\pi\) | |||||||
\(888\) | −0.294957 | −0.00989809 | ||||||||
\(889\) | 9.85582 | − | 3.48889i | 0.330554 | − | 0.117014i | ||||
\(890\) | −28.0580 | −0.940505 | ||||||||
\(891\) | −2.65353 | + | 4.59606i | −0.0888967 | + | 0.153974i | ||||
\(892\) | 19.7410 | + | 34.1924i | 0.660977 | + | 1.14485i | ||||
\(893\) | −17.4574 | − | 30.2371i | −0.584189 | − | 1.01185i | ||||
\(894\) | −1.98710 | + | 3.44176i | −0.0664586 | + | 0.115110i | ||||
\(895\) | 10.4362 | 0.348843 | ||||||||
\(896\) | −10.0036 | + | 53.9409i | −0.334197 | + | 1.80204i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.4732 | + | 52.7811i | −1.01690 | + | 1.76133i | ||||
\(899\) | 5.47092 | + | 9.47592i | 0.182465 | + | 0.316040i | ||||
\(900\) | −20.3357 | − | 35.2224i | −0.677856 | − | 1.17408i | ||||
\(901\) | 40.4832 | − | 70.1189i | 1.34869 | − | 2.33600i | ||||
\(902\) | 21.5686 | 0.718157 | ||||||||
\(903\) | −3.59677 | − | 3.07263i | −0.119693 | − | 0.102251i | ||||
\(904\) | 16.1520 | 0.537209 | ||||||||
\(905\) | −2.75332 | + | 4.76890i | −0.0915236 | + | 0.158523i | ||||
\(906\) | −10.1254 | − | 17.5378i | −0.336395 | − | 0.582654i | ||||
\(907\) | 23.8863 | + | 41.3722i | 0.793131 | + | 1.37374i | 0.924020 | + | 0.382345i | \(0.124884\pi\) |
−0.130889 | + | 0.991397i | \(0.541783\pi\) | |||||||
\(908\) | −20.9245 | + | 36.2424i | −0.694405 | + | 1.20274i | ||||
\(909\) | −1.00935 | −0.0334779 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.43817 | −0.113912 | −0.0569559 | − | 0.998377i | \(-0.518139\pi\) | ||||
−0.0569559 | + | 0.998377i | \(0.518139\pi\) | |||||||
\(912\) | −2.91899 | + | 5.05584i | −0.0966575 | + | 0.167416i | ||||
\(913\) | 3.01649 | + | 5.22472i | 0.0998313 | + | 0.172913i | ||||
\(914\) | −32.7470 | − | 56.7194i | −1.08317 | − | 1.87611i | ||||
\(915\) | 4.17966 | − | 7.23939i | 0.138175 | − | 0.239327i | ||||
\(916\) | 54.0473 | 1.78577 | ||||||||
\(917\) | 1.57185 | − | 8.47564i | 0.0519070 | − | 0.279890i | ||||
\(918\) | −65.3209 | −2.15591 | ||||||||
\(919\) | −3.62345 | + | 6.27599i | −0.119526 | + | 0.207026i | −0.919580 | − | 0.392903i | \(-0.871471\pi\) |
0.800054 | + | 0.599928i | \(0.204804\pi\) | |||||||
\(920\) | 9.33292 | + | 16.1651i | 0.307697 | + | 0.532947i | ||||
\(921\) | −3.06504 | − | 5.30881i | −0.100997 | − | 0.174931i | ||||
\(922\) | 6.97763 | − | 12.0856i | 0.229796 | − | 0.398019i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −7.22065 | + | 2.55606i | −0.237542 | + | 0.0840881i | ||||
\(925\) | 0.457834 | 0.0150535 | ||||||||
\(926\) | 22.5427 | − | 39.0451i | 0.740799 | − | 1.28310i | ||||
\(927\) | 4.75497 | + | 8.23584i | 0.156174 | + | 0.270501i | ||||
\(928\) | 5.92076 | + | 10.2551i | 0.194359 | + | 0.336639i | ||||
\(929\) | −11.4989 | + | 19.9167i | −0.377267 | + | 0.653445i | −0.990664 | − | 0.136330i | \(-0.956469\pi\) |
0.613397 | + | 0.789775i | \(0.289803\pi\) | |||||||
\(930\) | 3.28671 | 0.107776 | ||||||||
\(931\) | 4.06920 | + | 25.7292i | 0.133363 | + | 0.843241i | ||||
\(932\) | −31.8386 | −1.04291 | ||||||||
\(933\) | 8.36255 | − | 14.4844i | 0.273778 | − | 0.474197i | ||||
\(934\) | 12.2370 | + | 21.1952i | 0.400408 | + | 0.693527i | ||||
\(935\) | 3.02253 | + | 5.23517i | 0.0988473 | + | 0.171209i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.9823 | −0.358775 | −0.179387 | − | 0.983779i | \(-0.557412\pi\) | ||||
−0.179387 | + | 0.983779i | \(0.557412\pi\) | |||||||
\(938\) | −80.8667 | + | 28.6262i | −2.64039 | + | 0.934679i | ||||
\(939\) | 16.6272 | 0.542609 | ||||||||
\(940\) | 13.3177 | − | 23.0669i | 0.434374 | − | 0.752358i | ||||
\(941\) | −16.0847 | − | 27.8596i | −0.524347 | − | 0.908196i | −0.999598 | − | 0.0283458i | \(-0.990976\pi\) |
0.475251 | − | 0.879850i | \(-0.342357\pi\) | |||||||
\(942\) | 2.06403 | + | 3.57501i | 0.0672499 | + | 0.116480i | ||||
\(943\) | −24.4778 | + | 42.3968i | −0.797107 | + | 1.38063i | ||||
\(944\) | −20.1971 | −0.657361 | ||||||||
\(945\) | 1.44158 | − | 7.77319i | 0.0468944 | − | 0.252862i | ||||
\(946\) | −6.72685 | −0.218709 | ||||||||
\(947\) | 21.9413 | − | 38.0035i | 0.712998 | − | 1.23495i | −0.250729 | − | 0.968057i | \(-0.580670\pi\) |
0.963727 | − | 0.266891i | \(-0.0859964\pi\) | |||||||
\(948\) | −7.16962 | − | 12.4181i | −0.232858 | − | 0.403323i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 19.5575 | − | 33.8746i | 0.634530 | − | 1.09904i | ||||
\(951\) | 8.57842 | 0.278174 | ||||||||
\(952\) | 57.1344 | + | 48.8084i | 1.85174 | + | 1.58189i | ||||
\(953\) | −5.23257 | −0.169500 | −0.0847499 | − | 0.996402i | \(-0.527009\pi\) | ||||
−0.0847499 | + | 0.996402i | \(0.527009\pi\) | |||||||
\(954\) | −34.2388 | + | 59.3033i | −1.10852 | + | 1.92002i | ||||
\(955\) | 6.26029 | + | 10.8431i | 0.202578 | + | 0.350876i | ||||
\(956\) | −23.4461 | − | 40.6099i | −0.758301 | − | 1.31342i | ||||
\(957\) | −1.69246 | + | 2.93142i | −0.0547094 | + | 0.0947594i | ||||
\(958\) | 70.1428 | 2.26621 | ||||||||
\(959\) | −17.8149 | − | 15.2189i | −0.575275 | − | 0.491442i | ||||
\(960\) | 5.97233 | 0.192756 | ||||||||
\(961\) | 12.2799 | − | 21.2695i | 0.396127 | − | 0.686111i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.8345 | − | 18.7659i | −0.349137 | − | 0.604724i | ||||
\(964\) | −29.5298 | + | 51.1470i | −0.951089 | + | 1.64734i | ||||
\(965\) | 10.5613 | 0.339981 | ||||||||
\(966\) | 4.88954 | − | 26.3651i | 0.157318 | − | 0.848284i | ||||
\(967\) | 14.5514 | 0.467942 | 0.233971 | − | 0.972244i | \(-0.424828\pi\) | ||||
0.233971 | + | 0.972244i | \(0.424828\pi\) | |||||||
\(968\) | 19.6453 | − | 34.0267i | 0.631424 | − | 1.09366i | ||||
\(969\) | −9.26185 | − | 16.0420i | −0.297533 | − | 0.515343i | ||||
\(970\) | −11.1680 | − | 19.3435i | −0.358582 | − | 0.621083i | ||||
\(971\) | −4.62540 | + | 8.01143i | −0.148436 | + | 0.257099i | −0.930650 | − | 0.365911i | \(-0.880757\pi\) |
0.782213 | + | 0.623011i | \(0.214091\pi\) | |||||||
\(972\) | 55.3487 | 1.77531 | ||||||||
\(973\) | −54.5106 | + | 19.2963i | −1.74753 | + | 0.618612i | ||||
\(974\) | −39.5644 | −1.26773 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.1161 | − | 29.6460i | −0.547873 | − | 0.948945i | ||||
\(977\) | −10.9022 | − | 18.8831i | −0.348791 | − | 0.604124i | 0.637244 | − | 0.770662i | \(-0.280074\pi\) |
−0.986035 | + | 0.166538i | \(0.946741\pi\) | |||||||
\(978\) | −15.0582 | + | 26.0815i | −0.481507 | + | 0.833995i | ||||
\(979\) | 17.0078 | 0.543571 | ||||||||
\(980\) | −15.4462 | + | 12.5023i | −0.493410 | + | 0.399373i | ||||
\(981\) | 10.0467 | 0.320765 | ||||||||
\(982\) | −7.45624 | + | 12.9146i | −0.237938 | + | 0.412121i | ||||
\(983\) | −2.16580 | − | 3.75128i | −0.0690783 | − | 0.119647i | 0.829418 | − | 0.558629i | \(-0.188673\pi\) |
−0.898496 | + | 0.438982i | \(0.855339\pi\) | |||||||
\(984\) | −11.5375 | − | 19.9835i | −0.367802 | − | 0.637052i | ||||
\(985\) | −3.07967 | + | 5.33415i | −0.0981266 | + | 0.169960i | ||||
\(986\) | 72.5580 | 2.31072 | ||||||||
\(987\) | −16.5078 | + | 5.84365i | −0.525450 | + | 0.186006i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.63417 | − | 13.2228i | 0.242752 | − | 0.420459i | ||||
\(990\) | −2.55632 | − | 4.42767i | −0.0812451 | − | 0.140721i | ||||
\(991\) | −13.5810 | − | 23.5230i | −0.431415 | − | 0.747233i | 0.565580 | − | 0.824693i | \(-0.308652\pi\) |
−0.996995 | + | 0.0774601i | \(0.975319\pi\) | |||||||
\(992\) | −3.48484 | + | 6.03592i | −0.110644 | + | 0.191641i | ||||
\(993\) | −1.01052 | −0.0320678 | ||||||||
\(994\) | 1.30499 | − | 7.03668i | 0.0413916 | − | 0.223190i | ||||
\(995\) | 3.56711 | 0.113085 | ||||||||
\(996\) | 7.05144 | − | 12.2135i | 0.223434 | − | 0.386998i | ||||
\(997\) | −26.3294 | − | 45.6038i | −0.833860 | − | 1.44429i | −0.894955 | − | 0.446156i | \(-0.852793\pi\) |
0.0610957 | − | 0.998132i | \(-0.480541\pi\) | |||||||
\(998\) | 31.2154 | + | 54.0667i | 0.988107 | + | 1.71145i | ||||
\(999\) | −0.201607 | + | 0.349193i | −0.00637856 | + | 0.0110480i |
(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 | 1183.2.e.l.170.3 | yes | 48 | |
7.2 | even | 3 | 8281.2.a.cu.1.22 | 24 | |||
7.4 | even | 3 | inner | 1183.2.e.l.508.3 | yes | 48 | |
7.5 | odd | 6 | 8281.2.a.ct.1.22 | 24 | |||
13.12 | even | 2 | 1183.2.e.k.170.22 | ✓ | 48 | ||
91.12 | odd | 6 | 8281.2.a.cw.1.3 | 24 | |||
91.25 | even | 6 | 1183.2.e.k.508.22 | yes | 48 | ||
91.51 | even | 6 | 8281.2.a.cv.1.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.e.k.170.22 | ✓ | 48 | 13.12 | even | 2 | ||
1183.2.e.k.508.22 | yes | 48 | 91.25 | even | 6 | ||
1183.2.e.l.170.3 | yes | 48 | 1.1 | even | 1 | trivial | |
1183.2.e.l.508.3 | yes | 48 | 7.4 | even | 3 | inner | |
8281.2.a.ct.1.22 | 24 | 7.5 | odd | 6 | |||
8281.2.a.cu.1.22 | 24 | 7.2 | even | 3 | |||
8281.2.a.cv.1.3 | 24 | 91.51 | even | 6 | |||
8281.2.a.cw.1.3 | 24 | 91.12 | odd | 6 |