Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(117,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.117");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.h (of order \(4\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 3x^{8} - 8x^{7} - 26x^{6} + 12x^{5} + 24x^{4} + 166x^{3} + 113x^{2} - 152x + 160 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 117.1 | ||
Root | \(-0.287871 + 2.59703i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.117 |
Dual form | 370.2.h.d.253.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.70160 | − | 1.70160i | −0.982418 | − | 0.982418i | 0.0174300 | − | 0.999848i | \(-0.494452\pi\) |
−0.999848 | + | 0.0174300i | \(0.994452\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.73245 | − | 1.41373i | 0.774774 | − | 0.632238i | ||||
\(6\) | −1.70160 | − | 1.70160i | −0.694674 | − | 0.694674i | ||||
\(7\) | 2.82745 | + | 2.82745i | 1.06868 | + | 1.06868i | 0.997461 | + | 0.0712163i | \(0.0226881\pi\) |
0.0712163 | + | 0.997461i | \(0.477312\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.79087i | 0.930291i | ||||||||
\(10\) | 1.73245 | − | 1.41373i | 0.547848 | − | 0.447060i | ||||
\(11\) | − | 2.94236i | − | 0.887153i | −0.896236 | − | 0.443577i | \(-0.853709\pi\) | ||
0.896236 | − | 0.443577i | \(-0.146291\pi\) | |||||||
\(12\) | −1.70160 | − | 1.70160i | −0.491209 | − | 0.491209i | ||||
\(13\) | −0.738730 | −0.204887 | −0.102443 | − | 0.994739i | \(-0.532666\pi\) | ||||
−0.102443 | + | 0.994739i | \(0.532666\pi\) | |||||||
\(14\) | 2.82745 | + | 2.82745i | 0.755669 | + | 0.755669i | ||||
\(15\) | −5.35353 | − | 0.542335i | −1.38227 | − | 0.140030i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 6.61833i | − | 1.60518i | −0.596531 | − | 0.802590i | \(-0.703455\pi\) | ||
0.596531 | − | 0.802590i | \(-0.296545\pi\) | |||||||
\(18\) | 2.79087i | 0.657815i | ||||||||
\(19\) | −5.03108 | + | 5.03108i | −1.15421 | + | 1.15421i | −0.168509 | + | 0.985700i | \(0.553895\pi\) |
−0.985700 | + | 0.168509i | \(0.946105\pi\) | |||||||
\(20\) | 1.73245 | − | 1.41373i | 0.387387 | − | 0.316119i | ||||
\(21\) | − | 9.62238i | − | 2.09978i | ||||||
\(22\) | − | 2.94236i | − | 0.627312i | ||||||
\(23\) | 6.39364 | 1.33317 | 0.666583 | − | 0.745431i | \(-0.267756\pi\) | ||||
0.666583 | + | 0.745431i | \(0.267756\pi\) | |||||||
\(24\) | −1.70160 | − | 1.70160i | −0.347337 | − | 0.347337i | ||||
\(25\) | 1.00275 | − | 4.89842i | 0.200550 | − | 0.979683i | ||||
\(26\) | −0.738730 | −0.144877 | ||||||||
\(27\) | −0.355853 | + | 0.355853i | −0.0684839 | + | 0.0684839i | ||||
\(28\) | 2.82745 | + | 2.82745i | 0.534339 | + | 0.534339i | ||||
\(29\) | −2.49797 | − | 2.49797i | −0.463862 | − | 0.463862i | 0.436057 | − | 0.899919i | \(-0.356375\pi\) |
−0.899919 | + | 0.436057i | \(0.856375\pi\) | |||||||
\(30\) | −5.35353 | − | 0.542335i | −0.977415 | − | 0.0990163i | ||||
\(31\) | −1.48171 | + | 1.48171i | −0.266123 | + | 0.266123i | −0.827536 | − | 0.561413i | \(-0.810258\pi\) |
0.561413 | + | 0.827536i | \(0.310258\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.00671 | + | 5.00671i | −0.871556 | + | 0.871556i | ||||
\(34\) | − | 6.61833i | − | 1.13503i | ||||||
\(35\) | 8.89567 | + | 0.901168i | 1.50364 | + | 0.152325i | ||||
\(36\) | 2.79087i | 0.465145i | ||||||||
\(37\) | −6.07917 | + | 0.209128i | −0.999409 | + | 0.0343805i | ||||
\(38\) | −5.03108 | + | 5.03108i | −0.816149 | + | 0.816149i | ||||
\(39\) | 1.25702 | + | 1.25702i | 0.201284 | + | 0.201284i | ||||
\(40\) | 1.73245 | − | 1.41373i | 0.273924 | − | 0.223530i | ||||
\(41\) | 7.39769i | 1.15533i | 0.816276 | + | 0.577663i | \(0.196035\pi\) | ||||
−0.816276 | + | 0.577663i | \(0.803965\pi\) | |||||||
\(42\) | − | 9.62238i | − | 1.48477i | ||||||
\(43\) | 6.98494 | 1.06519 | 0.532597 | − | 0.846369i | \(-0.321216\pi\) | ||||
0.532597 | + | 0.846369i | \(0.321216\pi\) | |||||||
\(44\) | − | 2.94236i | − | 0.443577i | ||||||
\(45\) | 3.94553 | + | 4.83504i | 0.588165 | + | 0.720765i | ||||
\(46\) | 6.39364 | 0.942691 | ||||||||
\(47\) | 7.56618 | + | 7.56618i | 1.10364 | + | 1.10364i | 0.993968 | + | 0.109674i | \(0.0349806\pi\) |
0.109674 | + | 0.993968i | \(0.465019\pi\) | |||||||
\(48\) | −1.70160 | − | 1.70160i | −0.245605 | − | 0.245605i | ||||
\(49\) | 8.98899i | 1.28414i | ||||||||
\(50\) | 1.00275 | − | 4.89842i | 0.141810 | − | 0.692741i | ||||
\(51\) | −11.2617 | + | 11.2617i | −1.57696 | + | 1.57696i | ||||
\(52\) | −0.738730 | −0.102443 | ||||||||
\(53\) | 1.94236 | − | 1.94236i | 0.266803 | − | 0.266803i | −0.561008 | − | 0.827811i | \(-0.689586\pi\) |
0.827811 | + | 0.561008i | \(0.189586\pi\) | |||||||
\(54\) | −0.355853 | + | 0.355853i | −0.0484254 | + | 0.0484254i | ||||
\(55\) | −4.15969 | − | 5.09748i | −0.560892 | − | 0.687344i | ||||
\(56\) | 2.82745 | + | 2.82745i | 0.377834 | + | 0.377834i | ||||
\(57\) | 17.1218 | 2.26783 | ||||||||
\(58\) | −2.49797 | − | 2.49797i | −0.328000 | − | 0.328000i | ||||
\(59\) | −8.34044 | + | 8.34044i | −1.08583 | + | 1.08583i | −0.0898798 | + | 0.995953i | \(0.528648\pi\) |
−0.995953 | + | 0.0898798i | \(0.971352\pi\) | |||||||
\(60\) | −5.35353 | − | 0.542335i | −0.691137 | − | 0.0700151i | ||||
\(61\) | −2.31872 | + | 2.31872i | −0.296882 | + | 0.296882i | −0.839791 | − | 0.542909i | \(-0.817323\pi\) |
0.542909 | + | 0.839791i | \(0.317323\pi\) | |||||||
\(62\) | −1.48171 | + | 1.48171i | −0.188177 | + | 0.188177i | ||||
\(63\) | −7.89106 | + | 7.89106i | −0.994180 | + | 0.994180i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.27981 | + | 1.04436i | −0.158741 | + | 0.129537i | ||||
\(66\) | −5.00671 | + | 5.00671i | −0.616283 | + | 0.616283i | ||||
\(67\) | 2.10003 | − | 2.10003i | 0.256560 | − | 0.256560i | −0.567093 | − | 0.823653i | \(-0.691932\pi\) |
0.823653 | + | 0.567093i | \(0.191932\pi\) | |||||||
\(68\) | − | 6.61833i | − | 0.802590i | ||||||
\(69\) | −10.8794 | − | 10.8794i | −1.30973 | − | 1.30973i | ||||
\(70\) | 8.89567 | + | 0.901168i | 1.06324 | + | 0.107710i | ||||
\(71\) | −2.52254 | −0.299370 | −0.149685 | − | 0.988734i | \(-0.547826\pi\) | ||||
−0.149685 | + | 0.988734i | \(0.547826\pi\) | |||||||
\(72\) | 2.79087i | 0.328907i | ||||||||
\(73\) | 7.18876 | + | 7.18876i | 0.841381 | + | 0.841381i | 0.989038 | − | 0.147658i | \(-0.0471735\pi\) |
−0.147658 | + | 0.989038i | \(0.547173\pi\) | |||||||
\(74\) | −6.07917 | + | 0.209128i | −0.706689 | + | 0.0243107i | ||||
\(75\) | −10.0414 | + | 6.62886i | −1.15948 | + | 0.765434i | ||||
\(76\) | −5.03108 | + | 5.03108i | −0.577104 | + | 0.577104i | ||||
\(77\) | 8.31937 | − | 8.31937i | 0.948081 | − | 0.948081i | ||||
\(78\) | 1.25702 | + | 1.25702i | 0.142330 | + | 0.142330i | ||||
\(79\) | −5.69610 | + | 5.69610i | −0.640861 | + | 0.640861i | −0.950767 | − | 0.309906i | \(-0.899702\pi\) |
0.309906 | + | 0.950767i | \(0.399702\pi\) | |||||||
\(80\) | 1.73245 | − | 1.41373i | 0.193694 | − | 0.158059i | ||||
\(81\) | 9.58365 | 1.06485 | ||||||||
\(82\) | 7.39769i | 0.816939i | ||||||||
\(83\) | −2.72617 | + | 2.72617i | −0.299236 | + | 0.299236i | −0.840714 | − | 0.541479i | \(-0.817865\pi\) |
0.541479 | + | 0.840714i | \(0.317865\pi\) | |||||||
\(84\) | − | 9.62238i | − | 1.04989i | ||||||
\(85\) | −9.35651 | − | 11.4659i | −1.01486 | − | 1.24365i | ||||
\(86\) | 6.98494 | 0.753205 | ||||||||
\(87\) | 8.50109i | 0.911413i | ||||||||
\(88\) | − | 2.94236i | − | 0.313656i | ||||||
\(89\) | −4.25577 | − | 4.25577i | −0.451110 | − | 0.451110i | 0.444613 | − | 0.895723i | \(-0.353341\pi\) |
−0.895723 | + | 0.444613i | \(0.853341\pi\) | |||||||
\(90\) | 3.94553 | + | 4.83504i | 0.415895 | + | 0.509658i | ||||
\(91\) | −2.08872 | − | 2.08872i | −0.218958 | − | 0.218958i | ||||
\(92\) | 6.39364 | 0.666583 | ||||||||
\(93\) | 5.04255 | 0.522888 | ||||||||
\(94\) | 7.56618 | + | 7.56618i | 0.780392 | + | 0.780392i | ||||
\(95\) | −1.60351 | + | 15.8287i | −0.164517 | + | 1.62399i | ||||
\(96\) | −1.70160 | − | 1.70160i | −0.173669 | − | 0.173669i | ||||
\(97\) | 3.40320i | 0.345542i | 0.984962 | + | 0.172771i | \(0.0552721\pi\) | ||||
−0.984962 | + | 0.172771i | \(0.944728\pi\) | |||||||
\(98\) | 8.98899i | 0.908026i | ||||||||
\(99\) | 8.21174 | 0.825310 | ||||||||
\(100\) | 1.00275 | − | 4.89842i | 0.100275 | − | 0.489842i | ||||
\(101\) | 4.21918i | 0.419825i | 0.977720 | + | 0.209912i | \(0.0673178\pi\) | ||||
−0.977720 | + | 0.209912i | \(0.932682\pi\) | |||||||
\(102\) | −11.2617 | + | 11.2617i | −1.11508 | + | 1.11508i | ||||
\(103\) | − | 8.10234i | − | 0.798347i | −0.916875 | − | 0.399174i | \(-0.869297\pi\) | ||
0.916875 | − | 0.399174i | \(-0.130703\pi\) | |||||||
\(104\) | −0.738730 | −0.0724384 | ||||||||
\(105\) | −13.6034 | − | 16.6703i | −1.32756 | − | 1.62685i | ||||
\(106\) | 1.94236 | − | 1.94236i | 0.188658 | − | 0.188658i | ||||
\(107\) | −11.7919 | − | 11.7919i | −1.13996 | − | 1.13996i | −0.988456 | − | 0.151508i | \(-0.951587\pi\) |
−0.151508 | − | 0.988456i | \(-0.548413\pi\) | |||||||
\(108\) | −0.355853 | + | 0.355853i | −0.0342419 | + | 0.0342419i | ||||
\(109\) | 9.81489 | − | 9.81489i | 0.940096 | − | 0.940096i | −0.0582084 | − | 0.998304i | \(-0.518539\pi\) |
0.998304 | + | 0.0582084i | \(0.0185388\pi\) | |||||||
\(110\) | −4.15969 | − | 5.09748i | −0.396611 | − | 0.486025i | ||||
\(111\) | 10.7002 | + | 9.98845i | 1.01561 | + | 0.948061i | ||||
\(112\) | 2.82745 | + | 2.82745i | 0.267169 | + | 0.267169i | ||||
\(113\) | 5.85257i | 0.550564i | 0.961364 | + | 0.275282i | \(0.0887712\pi\) | ||||
−0.961364 | + | 0.275282i | \(0.911229\pi\) | |||||||
\(114\) | 17.1218 | 1.60360 | ||||||||
\(115\) | 11.0766 | − | 9.03886i | 1.03290 | − | 0.842878i | ||||
\(116\) | −2.49797 | − | 2.49797i | −0.231931 | − | 0.231931i | ||||
\(117\) | − | 2.06170i | − | 0.190604i | ||||||
\(118\) | −8.34044 | + | 8.34044i | −0.767799 | + | 0.767799i | ||||
\(119\) | 18.7130 | − | 18.7130i | 1.71542 | − | 1.71542i | ||||
\(120\) | −5.35353 | − | 0.542335i | −0.488708 | − | 0.0495082i | ||||
\(121\) | 2.34255 | 0.212959 | ||||||||
\(122\) | −2.31872 | + | 2.31872i | −0.209927 | + | 0.209927i | ||||
\(123\) | 12.5879 | − | 12.5879i | 1.13501 | − | 1.13501i | ||||
\(124\) | −1.48171 | + | 1.48171i | −0.133061 | + | 0.133061i | ||||
\(125\) | −5.18781 | − | 9.90387i | −0.464012 | − | 0.885829i | ||||
\(126\) | −7.89106 | + | 7.89106i | −0.702992 | + | 0.702992i | ||||
\(127\) | 1.49192 | + | 1.49192i | 0.132387 | + | 0.132387i | 0.770195 | − | 0.637808i | \(-0.220159\pi\) |
−0.637808 | + | 0.770195i | \(0.720159\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −11.8856 | − | 11.8856i | −1.04647 | − | 1.04647i | ||||
\(130\) | −1.27981 | + | 1.04436i | −0.112247 | + | 0.0915966i | ||||
\(131\) | −11.9137 | + | 11.9137i | −1.04090 | + | 1.04090i | −0.0417762 | + | 0.999127i | \(0.513302\pi\) |
−0.999127 | + | 0.0417762i | \(0.986698\pi\) | |||||||
\(132\) | −5.00671 | + | 5.00671i | −0.435778 | + | 0.435778i | ||||
\(133\) | −28.4503 | −2.46695 | ||||||||
\(134\) | 2.10003 | − | 2.10003i | 0.181415 | − | 0.181415i | ||||
\(135\) | −0.113418 | + | 1.11957i | −0.00976143 | + | 0.0963576i | ||||
\(136\) | − | 6.61833i | − | 0.567517i | ||||||
\(137\) | 5.09297 | + | 5.09297i | 0.435122 | + | 0.435122i | 0.890367 | − | 0.455244i | \(-0.150448\pi\) |
−0.455244 | + | 0.890367i | \(0.650448\pi\) | |||||||
\(138\) | −10.8794 | − | 10.8794i | −0.926116 | − | 0.926116i | ||||
\(139\) | 1.23936 | 0.105121 | 0.0525606 | − | 0.998618i | \(-0.483262\pi\) | ||||
0.0525606 | + | 0.998618i | \(0.483262\pi\) | |||||||
\(140\) | 8.89567 | + | 0.901168i | 0.751821 | + | 0.0761626i | ||||
\(141\) | − | 25.7492i | − | 2.16847i | ||||||
\(142\) | −2.52254 | −0.211687 | ||||||||
\(143\) | 2.17361i | 0.181766i | ||||||||
\(144\) | 2.79087i | 0.232573i | ||||||||
\(145\) | −7.85906 | − | 0.796156i | −0.652659 | − | 0.0661171i | ||||
\(146\) | 7.18876 | + | 7.18876i | 0.594946 | + | 0.594946i | ||||
\(147\) | 15.2957 | − | 15.2957i | 1.26156 | − | 1.26156i | ||||
\(148\) | −6.07917 | + | 0.209128i | −0.499704 | + | 0.0171903i | ||||
\(149\) | 0.292738i | 0.0239821i | 0.999928 | + | 0.0119910i | \(0.00381696\pi\) | ||||
−0.999928 | + | 0.0119910i | \(0.996183\pi\) | |||||||
\(150\) | −10.0414 | + | 6.62886i | −0.819878 | + | 0.541244i | ||||
\(151\) | − | 16.1449i | − | 1.31386i | −0.753954 | − | 0.656928i | \(-0.771856\pi\) | ||
0.753954 | − | 0.656928i | \(-0.228144\pi\) | |||||||
\(152\) | −5.03108 | + | 5.03108i | −0.408074 | + | 0.408074i | ||||
\(153\) | 18.4709 | 1.49328 | ||||||||
\(154\) | 8.31937 | − | 8.31937i | 0.670394 | − | 0.670394i | ||||
\(155\) | −0.472251 | + | 4.66171i | −0.0379321 | + | 0.374438i | ||||
\(156\) | 1.25702 | + | 1.25702i | 0.100642 | + | 0.100642i | ||||
\(157\) | −3.24426 | − | 3.24426i | −0.258920 | − | 0.258920i | 0.565695 | − | 0.824615i | \(-0.308608\pi\) |
−0.824615 | + | 0.565695i | \(0.808608\pi\) | |||||||
\(158\) | −5.69610 | + | 5.69610i | −0.453157 | + | 0.453157i | ||||
\(159\) | −6.61022 | −0.524224 | ||||||||
\(160\) | 1.73245 | − | 1.41373i | 0.136962 | − | 0.111765i | ||||
\(161\) | 18.0777 | + | 18.0777i | 1.42472 | + | 1.42472i | ||||
\(162\) | 9.58365 | 0.752963 | ||||||||
\(163\) | 23.5099i | 1.84144i | 0.390228 | + | 0.920718i | \(0.372396\pi\) | ||||
−0.390228 | + | 0.920718i | \(0.627604\pi\) | |||||||
\(164\) | 7.39769i | 0.577663i | ||||||||
\(165\) | −1.59574 | + | 15.7520i | −0.124228 | + | 1.22629i | ||||
\(166\) | −2.72617 | + | 2.72617i | −0.211592 | + | 0.211592i | ||||
\(167\) | 11.4543i | 0.886359i | 0.896433 | + | 0.443179i | \(0.146150\pi\) | ||||
−0.896433 | + | 0.443179i | \(0.853850\pi\) | |||||||
\(168\) | − | 9.62238i | − | 0.742383i | ||||||
\(169\) | −12.4543 | −0.958021 | ||||||||
\(170\) | −9.35651 | − | 11.4659i | −0.717611 | − | 0.879395i | ||||
\(171\) | −14.0411 | − | 14.0411i | −1.07375 | − | 1.07375i | ||||
\(172\) | 6.98494 | 0.532597 | ||||||||
\(173\) | 2.14087 | + | 2.14087i | 0.162767 | + | 0.162767i | 0.783791 | − | 0.621024i | \(-0.213283\pi\) |
−0.621024 | + | 0.783791i | \(0.713283\pi\) | |||||||
\(174\) | 8.50109i | 0.644466i | ||||||||
\(175\) | 16.6853 | − | 11.0148i | 1.26129 | − | 0.832642i | ||||
\(176\) | − | 2.94236i | − | 0.221788i | ||||||
\(177\) | 28.3841 | 2.13348 | ||||||||
\(178\) | −4.25577 | − | 4.25577i | −0.318983 | − | 0.318983i | ||||
\(179\) | 14.9428 | + | 14.9428i | 1.11688 | + | 1.11688i | 0.992197 | + | 0.124682i | \(0.0397909\pi\) |
0.124682 | + | 0.992197i | \(0.460209\pi\) | |||||||
\(180\) | 3.94553 | + | 4.83504i | 0.294082 | + | 0.360383i | ||||
\(181\) | 12.0625 | 0.896602 | 0.448301 | − | 0.893883i | \(-0.352029\pi\) | ||||
0.448301 | + | 0.893883i | \(0.352029\pi\) | |||||||
\(182\) | −2.08872 | − | 2.08872i | −0.154827 | − | 0.154827i | ||||
\(183\) | 7.89106 | 0.583324 | ||||||||
\(184\) | 6.39364 | 0.471345 | ||||||||
\(185\) | −10.2362 | + | 8.95659i | −0.752580 | + | 0.658501i | ||||
\(186\) | 5.04255 | 0.369737 | ||||||||
\(187\) | −19.4735 | −1.42404 | ||||||||
\(188\) | 7.56618 | + | 7.56618i | 0.551821 | + | 0.551821i | ||||
\(189\) | −2.01231 | −0.146374 | ||||||||
\(190\) | −1.60351 | + | 15.8287i | −0.116331 | + | 1.14833i | ||||
\(191\) | −10.7383 | − | 10.7383i | −0.776998 | − | 0.776998i | 0.202321 | − | 0.979319i | \(-0.435151\pi\) |
−0.979319 | + | 0.202321i | \(0.935151\pi\) | |||||||
\(192\) | −1.70160 | − | 1.70160i | −0.122802 | − | 0.122802i | ||||
\(193\) | −9.09024 | −0.654330 | −0.327165 | − | 0.944967i | \(-0.606093\pi\) | ||||
−0.327165 | + | 0.944967i | \(0.606093\pi\) | |||||||
\(194\) | 3.40320i | 0.244335i | ||||||||
\(195\) | 3.95481 | + | 0.400639i | 0.283210 | + | 0.0286903i | ||||
\(196\) | 8.98899i | 0.642071i | ||||||||
\(197\) | −7.91262 | − | 7.91262i | −0.563751 | − | 0.563751i | 0.366620 | − | 0.930371i | \(-0.380515\pi\) |
−0.930371 | + | 0.366620i | \(0.880515\pi\) | |||||||
\(198\) | 8.21174 | 0.583583 | ||||||||
\(199\) | −9.14683 | − | 9.14683i | −0.648402 | − | 0.648402i | 0.304205 | − | 0.952607i | \(-0.401609\pi\) |
−0.952607 | + | 0.304205i | \(0.901609\pi\) | |||||||
\(200\) | 1.00275 | − | 4.89842i | 0.0709052 | − | 0.346370i | ||||
\(201\) | −7.14683 | −0.504098 | ||||||||
\(202\) | 4.21918i | 0.296861i | ||||||||
\(203\) | − | 14.1258i | − | 0.991437i | ||||||
\(204\) | −11.2617 | + | 11.2617i | −0.788479 | + | 0.788479i | ||||
\(205\) | 10.4583 | + | 12.8161i | 0.730441 | + | 0.895117i | ||||
\(206\) | − | 8.10234i | − | 0.564517i | ||||||
\(207\) | 17.8438i | 1.24023i | ||||||||
\(208\) | −0.738730 | −0.0512217 | ||||||||
\(209\) | 14.8032 | + | 14.8032i | 1.02396 | + | 1.02396i | ||||
\(210\) | −13.6034 | − | 16.6703i | −0.938725 | − | 1.15036i | ||||
\(211\) | −12.2667 | −0.844473 | −0.422237 | − | 0.906486i | \(-0.638755\pi\) | ||||
−0.422237 | + | 0.906486i | \(0.638755\pi\) | |||||||
\(212\) | 1.94236 | − | 1.94236i | 0.133402 | − | 0.133402i | ||||
\(213\) | 4.29235 | + | 4.29235i | 0.294107 | + | 0.294107i | ||||
\(214\) | −11.7919 | − | 11.7919i | −0.806076 | − | 0.806076i | ||||
\(215\) | 12.1010 | − | 9.87480i | 0.825284 | − | 0.673456i | ||||
\(216\) | −0.355853 | + | 0.355853i | −0.0242127 | + | 0.0242127i | ||||
\(217\) | −8.37893 | −0.568799 | ||||||||
\(218\) | 9.81489 | − | 9.81489i | 0.664748 | − | 0.664748i | ||||
\(219\) | − | 24.4648i | − | 1.65317i | ||||||
\(220\) | −4.15969 | − | 5.09748i | −0.280446 | − | 0.343672i | ||||
\(221\) | 4.88915i | 0.328880i | ||||||||
\(222\) | 10.7002 | + | 9.98845i | 0.718147 | + | 0.670381i | ||||
\(223\) | −8.70510 | + | 8.70510i | −0.582937 | + | 0.582937i | −0.935709 | − | 0.352772i | \(-0.885239\pi\) |
0.352772 | + | 0.935709i | \(0.385239\pi\) | |||||||
\(224\) | 2.82745 | + | 2.82745i | 0.188917 | + | 0.188917i | ||||
\(225\) | 13.6709 | + | 2.79855i | 0.911390 | + | 0.186570i | ||||
\(226\) | 5.85257i | 0.389307i | ||||||||
\(227\) | − | 22.3785i | − | 1.48532i | −0.669671 | − | 0.742658i | \(-0.733565\pi\) | ||
0.669671 | − | 0.742658i | \(-0.266435\pi\) | |||||||
\(228\) | 17.1218 | 1.13392 | ||||||||
\(229\) | − | 6.97332i | − | 0.460810i | −0.973095 | − | 0.230405i | \(-0.925995\pi\) | ||
0.973095 | − | 0.230405i | \(-0.0740051\pi\) | |||||||
\(230\) | 11.0766 | − | 9.03886i | 0.730372 | − | 0.596005i | ||||
\(231\) | −28.3125 | −1.86282 | ||||||||
\(232\) | −2.49797 | − | 2.49797i | −0.164000 | − | 0.164000i | ||||
\(233\) | 15.1891 | + | 15.1891i | 0.995069 | + | 0.995069i | 0.999988 | − | 0.00491851i | \(-0.00156562\pi\) |
−0.00491851 | + | 0.999988i | \(0.501566\pi\) | |||||||
\(234\) | − | 2.06170i | − | 0.134778i | ||||||
\(235\) | 23.8045 | + | 2.41150i | 1.55284 | + | 0.157309i | ||||
\(236\) | −8.34044 | + | 8.34044i | −0.542916 | + | 0.542916i | ||||
\(237\) | 19.3849 | 1.25919 | ||||||||
\(238\) | 18.7130 | − | 18.7130i | 1.21298 | − | 1.21298i | ||||
\(239\) | 1.35831 | − | 1.35831i | 0.0878617 | − | 0.0878617i | −0.661810 | − | 0.749672i | \(-0.730211\pi\) |
0.749672 | + | 0.661810i | \(0.230211\pi\) | |||||||
\(240\) | −5.35353 | − | 0.542335i | −0.345569 | − | 0.0350076i | ||||
\(241\) | −9.55663 | − | 9.55663i | −0.615596 | − | 0.615596i | 0.328802 | − | 0.944399i | \(-0.393355\pi\) |
−0.944399 | + | 0.328802i | \(0.893355\pi\) | |||||||
\(242\) | 2.34255 | 0.150585 | ||||||||
\(243\) | −15.2400 | − | 15.2400i | −0.977644 | − | 0.977644i | ||||
\(244\) | −2.31872 | + | 2.31872i | −0.148441 | + | 0.148441i | ||||
\(245\) | 12.7080 | + | 15.5730i | 0.811883 | + | 0.994920i | ||||
\(246\) | 12.5879 | − | 12.5879i | 0.802575 | − | 0.802575i | ||||
\(247\) | 3.71661 | − | 3.71661i | 0.236482 | − | 0.236482i | ||||
\(248\) | −1.48171 | + | 1.48171i | −0.0940886 | + | 0.0940886i | ||||
\(249\) | 9.27768 | 0.587949 | ||||||||
\(250\) | −5.18781 | − | 9.90387i | −0.328106 | − | 0.626376i | ||||
\(251\) | 11.4900 | − | 11.4900i | 0.725241 | − | 0.725241i | −0.244427 | − | 0.969668i | \(-0.578600\pi\) |
0.969668 | + | 0.244427i | \(0.0785998\pi\) | |||||||
\(252\) | −7.89106 | + | 7.89106i | −0.497090 | + | 0.497090i | ||||
\(253\) | − | 18.8124i | − | 1.18272i | ||||||
\(254\) | 1.49192 | + | 1.49192i | 0.0936114 | + | 0.0936114i | ||||
\(255\) | −3.58935 | + | 35.4314i | −0.224774 | + | 2.21880i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 31.7662i | − | 1.98152i | −0.135622 | − | 0.990761i | \(-0.543303\pi\) | ||
0.135622 | − | 0.990761i | \(-0.456697\pi\) | |||||||
\(258\) | −11.8856 | − | 11.8856i | −0.739963 | − | 0.739963i | ||||
\(259\) | −17.7799 | − | 16.5973i | −1.10479 | − | 1.03130i | ||||
\(260\) | −1.27981 | + | 1.04436i | −0.0793705 | + | 0.0647686i | ||||
\(261\) | 6.97152 | − | 6.97152i | 0.431526 | − | 0.431526i | ||||
\(262\) | −11.9137 | + | 11.9137i | −0.736030 | + | 0.736030i | ||||
\(263\) | −18.8716 | − | 18.8716i | −1.16367 | − | 1.16367i | −0.983665 | − | 0.180007i | \(-0.942388\pi\) |
−0.180007 | − | 0.983665i | \(-0.557612\pi\) | |||||||
\(264\) | −5.00671 | + | 5.00671i | −0.308141 | + | 0.308141i | ||||
\(265\) | 0.619069 | − | 6.11099i | 0.0380291 | − | 0.375395i | ||||
\(266\) | −28.4503 | −1.74440 | ||||||||
\(267\) | 14.4832i | 0.886358i | ||||||||
\(268\) | 2.10003 | − | 2.10003i | 0.128280 | − | 0.128280i | ||||
\(269\) | 5.87409i | 0.358150i | 0.983835 | + | 0.179075i | \(0.0573104\pi\) | ||||
−0.983835 | + | 0.179075i | \(0.942690\pi\) | |||||||
\(270\) | −0.113418 | + | 1.11957i | −0.00690238 | + | 0.0681351i | ||||
\(271\) | 2.68158 | 0.162895 | 0.0814473 | − | 0.996678i | \(-0.474046\pi\) | ||||
0.0814473 | + | 0.996678i | \(0.474046\pi\) | |||||||
\(272\) | − | 6.61833i | − | 0.401295i | ||||||
\(273\) | 7.10834i | 0.430216i | ||||||||
\(274\) | 5.09297 | + | 5.09297i | 0.307678 | + | 0.307678i | ||||
\(275\) | −14.4129 | − | 2.95045i | −0.869130 | − | 0.177919i | ||||
\(276\) | −10.8794 | − | 10.8794i | −0.654863 | − | 0.654863i | ||||
\(277\) | −8.90912 | −0.535297 | −0.267649 | − | 0.963517i | \(-0.586247\pi\) | ||||
−0.267649 | + | 0.963517i | \(0.586247\pi\) | |||||||
\(278\) | 1.23936 | 0.0743319 | ||||||||
\(279\) | −4.13526 | − | 4.13526i | −0.247571 | − | 0.247571i | ||||
\(280\) | 8.89567 | + | 0.901168i | 0.531618 | + | 0.0538551i | ||||
\(281\) | −3.03708 | − | 3.03708i | −0.181177 | − | 0.181177i | 0.610692 | − | 0.791869i | \(-0.290892\pi\) |
−0.791869 | + | 0.610692i | \(0.790892\pi\) | |||||||
\(282\) | − | 25.7492i | − | 1.53334i | ||||||
\(283\) | 5.36256i | 0.318771i | 0.987216 | + | 0.159386i | \(0.0509513\pi\) | ||||
−0.987216 | + | 0.159386i | \(0.949049\pi\) | |||||||
\(284\) | −2.52254 | −0.149685 | ||||||||
\(285\) | 29.6625 | − | 24.2055i | 1.75706 | − | 1.43381i | ||||
\(286\) | 2.17361i | 0.128528i | ||||||||
\(287\) | −20.9166 | + | 20.9166i | −1.23467 | + | 1.23467i | ||||
\(288\) | 2.79087i | 0.164454i | ||||||||
\(289\) | −26.8022 | −1.57660 | ||||||||
\(290\) | −7.85906 | − | 0.796156i | −0.461500 | − | 0.0467519i | ||||
\(291\) | 5.79087 | − | 5.79087i | 0.339467 | − | 0.339467i | ||||
\(292\) | 7.18876 | + | 7.18876i | 0.420690 | + | 0.420690i | ||||
\(293\) | 13.2752 | − | 13.2752i | 0.775544 | − | 0.775544i | −0.203525 | − | 0.979070i | \(-0.565240\pi\) |
0.979070 | + | 0.203525i | \(0.0652399\pi\) | |||||||
\(294\) | 15.2957 | − | 15.2957i | 0.892061 | − | 0.892061i | ||||
\(295\) | −2.65827 | + | 26.2405i | −0.154771 | + | 1.52778i | ||||
\(296\) | −6.07917 | + | 0.209128i | −0.353344 | + | 0.0121553i | ||||
\(297\) | 1.04704 | + | 1.04704i | 0.0607557 | + | 0.0607557i | ||||
\(298\) | 0.292738i | 0.0169579i | ||||||||
\(299\) | −4.72317 | −0.273148 | ||||||||
\(300\) | −10.0414 | + | 6.62886i | −0.579741 | + | 0.382717i | ||||
\(301\) | 19.7496 | + | 19.7496i | 1.13835 | + | 1.13835i | ||||
\(302\) | − | 16.1449i | − | 0.929036i | ||||||
\(303\) | 7.17936 | − | 7.17936i | 0.412443 | − | 0.412443i | ||||
\(304\) | −5.03108 | + | 5.03108i | −0.288552 | + | 0.288552i | ||||
\(305\) | −0.739025 | + | 7.29510i | −0.0423164 | + | 0.417716i | ||||
\(306\) | 18.4709 | 1.05591 | ||||||||
\(307\) | 3.46389 | − | 3.46389i | 0.197694 | − | 0.197694i | −0.601316 | − | 0.799011i | \(-0.705357\pi\) |
0.799011 | + | 0.601316i | \(0.205357\pi\) | |||||||
\(308\) | 8.31937 | − | 8.31937i | 0.474040 | − | 0.474040i | ||||
\(309\) | −13.7869 | + | 13.7869i | −0.784311 | + | 0.784311i | ||||
\(310\) | −0.472251 | + | 4.66171i | −0.0268221 | + | 0.264768i | ||||
\(311\) | 10.6674 | − | 10.6674i | 0.604894 | − | 0.604894i | −0.336713 | − | 0.941607i | \(-0.609315\pi\) |
0.941607 | + | 0.336713i | \(0.109315\pi\) | |||||||
\(312\) | 1.25702 | + | 1.25702i | 0.0711648 | + | 0.0711648i | ||||
\(313\) | −23.2451 | −1.31389 | −0.656947 | − | 0.753937i | \(-0.728152\pi\) | ||||
−0.656947 | + | 0.753937i | \(0.728152\pi\) | |||||||
\(314\) | −3.24426 | − | 3.24426i | −0.183084 | − | 0.183084i | ||||
\(315\) | −2.51505 | + | 24.8267i | −0.141707 | + | 1.39882i | ||||
\(316\) | −5.69610 | + | 5.69610i | −0.320430 | + | 0.320430i | ||||
\(317\) | 7.42086 | − | 7.42086i | 0.416797 | − | 0.416797i | −0.467301 | − | 0.884098i | \(-0.654774\pi\) |
0.884098 | + | 0.467301i | \(0.154774\pi\) | |||||||
\(318\) | −6.61022 | −0.370682 | ||||||||
\(319\) | −7.34992 | + | 7.34992i | −0.411517 | + | 0.411517i | ||||
\(320\) | 1.73245 | − | 1.41373i | 0.0968468 | − | 0.0790297i | ||||
\(321\) | 40.1301i | 2.23984i | ||||||||
\(322\) | 18.0777 | + | 18.0777i | 1.00743 | + | 1.00743i | ||||
\(323\) | 33.2973 | + | 33.2973i | 1.85271 | + | 1.85271i | ||||
\(324\) | 9.58365 | 0.532425 | ||||||||
\(325\) | −0.740762 | + | 3.61861i | −0.0410901 | + | 0.200724i | ||||
\(326\) | 23.5099i | 1.30209i | ||||||||
\(327\) | −33.4020 | −1.84713 | ||||||||
\(328\) | 7.39769i | 0.408469i | ||||||||
\(329\) | 42.7861i | 2.35887i | ||||||||
\(330\) | −1.59574 | + | 15.7520i | −0.0878427 | + | 0.867118i | ||||
\(331\) | 13.2492 | + | 13.2492i | 0.728243 | + | 0.728243i | 0.970270 | − | 0.242027i | \(-0.0778122\pi\) |
−0.242027 | + | 0.970270i | \(0.577812\pi\) | |||||||
\(332\) | −2.72617 | + | 2.72617i | −0.149618 | + | 0.149618i | ||||
\(333\) | −0.583651 | − | 16.9662i | −0.0319839 | − | 0.929741i | ||||
\(334\) | 11.4543i | 0.626750i | ||||||||
\(335\) | 0.669325 | − | 6.60708i | 0.0365691 | − | 0.360983i | ||||
\(336\) | − | 9.62238i | − | 0.524944i | ||||||
\(337\) | 3.84828 | − | 3.84828i | 0.209629 | − | 0.209629i | −0.594481 | − | 0.804110i | \(-0.702642\pi\) |
0.804110 | + | 0.594481i | \(0.202642\pi\) | |||||||
\(338\) | −12.4543 | −0.677423 | ||||||||
\(339\) | 9.95872 | − | 9.95872i | 0.540884 | − | 0.540884i | ||||
\(340\) | −9.35651 | − | 11.4659i | −0.507428 | − | 0.621826i | ||||
\(341\) | 4.35971 | + | 4.35971i | 0.236092 | + | 0.236092i | ||||
\(342\) | −14.0411 | − | 14.0411i | −0.759256 | − | 0.759256i | ||||
\(343\) | −5.62379 | + | 5.62379i | −0.303656 | + | 0.303656i | ||||
\(344\) | 6.98494 | 0.376603 | ||||||||
\(345\) | −34.2285 | − | 3.46749i | −1.84280 | − | 0.186683i | ||||
\(346\) | 2.14087 | + | 2.14087i | 0.115094 | + | 0.115094i | ||||
\(347\) | 20.7126 | 1.11191 | 0.555956 | − | 0.831212i | \(-0.312352\pi\) | ||||
0.555956 | + | 0.831212i | \(0.312352\pi\) | |||||||
\(348\) | 8.50109i | 0.455706i | ||||||||
\(349\) | 29.0891i | 1.55711i | 0.627579 | + | 0.778553i | \(0.284046\pi\) | ||||
−0.627579 | + | 0.778553i | \(0.715954\pi\) | |||||||
\(350\) | 16.6853 | − | 11.0148i | 0.891866 | − | 0.588767i | ||||
\(351\) | 0.262879 | − | 0.262879i | 0.0140314 | − | 0.0140314i | ||||
\(352\) | − | 2.94236i | − | 0.156828i | ||||||
\(353\) | − | 22.8767i | − | 1.21760i | −0.793323 | − | 0.608801i | \(-0.791651\pi\) | ||
0.793323 | − | 0.608801i | \(-0.208349\pi\) | |||||||
\(354\) | 28.3841 | 1.50860 | ||||||||
\(355\) | −4.37017 | + | 3.56618i | −0.231945 | + | 0.189273i | ||||
\(356\) | −4.25577 | − | 4.25577i | −0.225555 | − | 0.225555i | ||||
\(357\) | −63.6841 | −3.37052 | ||||||||
\(358\) | 14.9428 | + | 14.9428i | 0.789752 | + | 0.789752i | ||||
\(359\) | 25.7577i | 1.35944i | 0.733472 | + | 0.679720i | \(0.237899\pi\) | ||||
−0.733472 | + | 0.679720i | \(0.762101\pi\) | |||||||
\(360\) | 3.94553 | + | 4.83504i | 0.207948 | + | 0.254829i | ||||
\(361\) | − | 31.6235i | − | 1.66440i | ||||||
\(362\) | 12.0625 | 0.633993 | ||||||||
\(363\) | −3.98607 | − | 3.98607i | −0.209214 | − | 0.209214i | ||||
\(364\) | −2.08872 | − | 2.08872i | −0.109479 | − | 0.109479i | ||||
\(365\) | 22.6171 | + | 2.29121i | 1.18383 | + | 0.119927i | ||||
\(366\) | 7.89106 | 0.412472 | ||||||||
\(367\) | −17.7447 | − | 17.7447i | −0.926265 | − | 0.926265i | 0.0711974 | − | 0.997462i | \(-0.477318\pi\) |
−0.997462 | + | 0.0711974i | \(0.977318\pi\) | |||||||
\(368\) | 6.39364 | 0.333291 | ||||||||
\(369\) | −20.6460 | −1.07479 | ||||||||
\(370\) | −10.2362 | + | 8.95659i | −0.532154 | + | 0.465631i | ||||
\(371\) | 10.9838 | 0.570253 | ||||||||
\(372\) | 5.04255 | 0.261444 | ||||||||
\(373\) | 22.7050 | + | 22.7050i | 1.17562 | + | 1.17562i | 0.980848 | + | 0.194773i | \(0.0623969\pi\) |
0.194773 | + | 0.980848i | \(0.437603\pi\) | |||||||
\(374\) | −19.4735 | −1.00695 | ||||||||
\(375\) | −8.02484 | + | 25.6800i | −0.414401 | + | 1.32611i | ||||
\(376\) | 7.56618 | + | 7.56618i | 0.390196 | + | 0.390196i | ||||
\(377\) | 1.84533 | + | 1.84533i | 0.0950392 | + | 0.0950392i | ||||
\(378\) | −2.01231 | −0.103502 | ||||||||
\(379\) | − | 27.5341i | − | 1.41433i | −0.707047 | − | 0.707166i | \(-0.749973\pi\) | ||
0.707047 | − | 0.707166i | \(-0.250027\pi\) | |||||||
\(380\) | −1.60351 | + | 15.8287i | −0.0822583 | + | 0.811993i | ||||
\(381\) | − | 5.07730i | − | 0.260118i | ||||||
\(382\) | −10.7383 | − | 10.7383i | −0.549420 | − | 0.549420i | ||||
\(383\) | 4.93269 | 0.252049 | 0.126024 | − | 0.992027i | \(-0.459778\pi\) | ||||
0.126024 | + | 0.992027i | \(0.459778\pi\) | |||||||
\(384\) | −1.70160 | − | 1.70160i | −0.0868343 | − | 0.0868343i | ||||
\(385\) | 2.65156 | − | 26.1742i | 0.135136 | − | 1.33396i | ||||
\(386\) | −9.09024 | −0.462681 | ||||||||
\(387\) | 19.4941i | 0.990939i | ||||||||
\(388\) | 3.40320i | 0.172771i | ||||||||
\(389\) | −4.25176 | + | 4.25176i | −0.215573 | + | 0.215573i | −0.806630 | − | 0.591057i | \(-0.798711\pi\) |
0.591057 | + | 0.806630i | \(0.298711\pi\) | |||||||
\(390\) | 3.95481 | + | 0.400639i | 0.200259 | + | 0.0202871i | ||||
\(391\) | − | 42.3152i | − | 2.13997i | ||||||
\(392\) | 8.98899i | 0.454013i | ||||||||
\(393\) | 40.5446 | 2.04520 | ||||||||
\(394\) | −7.91262 | − | 7.91262i | −0.398632 | − | 0.398632i | ||||
\(395\) | −1.81546 | + | 17.9209i | −0.0913459 | + | 0.901699i | ||||
\(396\) | 8.21174 | 0.412655 | ||||||||
\(397\) | −6.85748 | + | 6.85748i | −0.344167 | + | 0.344167i | −0.857931 | − | 0.513764i | \(-0.828251\pi\) |
0.513764 | + | 0.857931i | \(0.328251\pi\) | |||||||
\(398\) | −9.14683 | − | 9.14683i | −0.458489 | − | 0.458489i | ||||
\(399\) | 48.4110 | + | 48.4110i | 2.42358 | + | 2.42358i | ||||
\(400\) | 1.00275 | − | 4.89842i | 0.0501376 | − | 0.244921i | ||||
\(401\) | 4.52089 | − | 4.52089i | 0.225763 | − | 0.225763i | −0.585157 | − | 0.810920i | \(-0.698967\pi\) |
0.810920 | + | 0.585157i | \(0.198967\pi\) | |||||||
\(402\) | −7.14683 | −0.356451 | ||||||||
\(403\) | 1.09458 | − | 1.09458i | 0.0545250 | − | 0.0545250i | ||||
\(404\) | 4.21918i | 0.209912i | ||||||||
\(405\) | 16.6032 | − | 13.5487i | 0.825018 | − | 0.673239i | ||||
\(406\) | − | 14.1258i | − | 0.701052i | ||||||
\(407\) | 0.615330 | + | 17.8871i | 0.0305008 | + | 0.886629i | ||||
\(408\) | −11.2617 | + | 11.2617i | −0.557539 | + | 0.557539i | ||||
\(409\) | 12.6409 | + | 12.6409i | 0.625053 | + | 0.625053i | 0.946819 | − | 0.321766i | \(-0.104277\pi\) |
−0.321766 | + | 0.946819i | \(0.604277\pi\) | |||||||
\(410\) | 10.4583 | + | 12.8161i | 0.516500 | + | 0.632943i | ||||
\(411\) | − | 17.3324i | − | 0.854944i | ||||||
\(412\) | − | 8.10234i | − | 0.399174i | ||||||
\(413\) | −47.1644 | −2.32081 | ||||||||
\(414\) | 17.8438i | 0.876976i | ||||||||
\(415\) | −0.868886 | + | 8.57700i | −0.0426519 | + | 0.421028i | ||||
\(416\) | −0.738730 | −0.0362192 | ||||||||
\(417\) | −2.10889 | − | 2.10889i | −0.103273 | − | 0.103273i | ||||
\(418\) | 14.8032 | + | 14.8032i | 0.724049 | + | 0.724049i | ||||
\(419\) | − | 18.0818i | − | 0.883353i | −0.897174 | − | 0.441676i | \(-0.854384\pi\) | ||
0.897174 | − | 0.441676i | \(-0.145616\pi\) | |||||||
\(420\) | −13.6034 | − | 16.6703i | −0.663779 | − | 0.813426i | ||||
\(421\) | −2.11385 | + | 2.11385i | −0.103023 | + | 0.103023i | −0.756739 | − | 0.653717i | \(-0.773209\pi\) |
0.653717 | + | 0.756739i | \(0.273209\pi\) | |||||||
\(422\) | −12.2667 | −0.597133 | ||||||||
\(423\) | −21.1162 | + | 21.1162i | −1.02671 | + | 1.02671i | ||||
\(424\) | 1.94236 | − | 1.94236i | 0.0943291 | − | 0.0943291i | ||||
\(425\) | −32.4193 | − | 6.63654i | −1.57257 | − | 0.321919i | ||||
\(426\) | 4.29235 | + | 4.29235i | 0.207965 | + | 0.207965i | ||||
\(427\) | −13.1122 | −0.634542 | ||||||||
\(428\) | −11.7919 | − | 11.7919i | −0.569982 | − | 0.569982i | ||||
\(429\) | 3.69860 | − | 3.69860i | 0.178570 | − | 0.178570i | ||||
\(430\) | 12.1010 | − | 9.87480i | 0.583564 | − | 0.476205i | ||||
\(431\) | −2.69254 | + | 2.69254i | −0.129695 | + | 0.129695i | −0.768975 | − | 0.639279i | \(-0.779233\pi\) |
0.639279 | + | 0.768975i | \(0.279233\pi\) | |||||||
\(432\) | −0.355853 | + | 0.355853i | −0.0171210 | + | 0.0171210i | ||||
\(433\) | −13.9527 | + | 13.9527i | −0.670524 | + | 0.670524i | −0.957837 | − | 0.287312i | \(-0.907238\pi\) |
0.287312 | + | 0.957837i | \(0.407238\pi\) | |||||||
\(434\) | −8.37893 | −0.402201 | ||||||||
\(435\) | 12.0182 | + | 14.7277i | 0.576230 | + | 0.706139i | ||||
\(436\) | 9.81489 | − | 9.81489i | 0.470048 | − | 0.470048i | ||||
\(437\) | −32.1669 | + | 32.1669i | −1.53875 | + | 1.53875i | ||||
\(438\) | − | 24.4648i | − | 1.16897i | ||||||
\(439\) | −22.9884 | − | 22.9884i | −1.09718 | − | 1.09718i | −0.994739 | − | 0.102437i | \(-0.967336\pi\) |
−0.102437 | − | 0.994739i | \(-0.532664\pi\) | |||||||
\(440\) | −4.15969 | − | 5.09748i | −0.198305 | − | 0.243013i | ||||
\(441\) | −25.0871 | −1.19463 | ||||||||
\(442\) | 4.88915i | 0.232553i | ||||||||
\(443\) | −7.06197 | − | 7.06197i | −0.335524 | − | 0.335524i | 0.519156 | − | 0.854680i | \(-0.326247\pi\) |
−0.854680 | + | 0.519156i | \(0.826247\pi\) | |||||||
\(444\) | 10.7002 | + | 9.98845i | 0.507807 | + | 0.474031i | ||||
\(445\) | −13.3894 | − | 1.35640i | −0.634718 | − | 0.0642996i | ||||
\(446\) | −8.70510 | + | 8.70510i | −0.412199 | + | 0.412199i | ||||
\(447\) | 0.498123 | − | 0.498123i | 0.0235604 | − | 0.0235604i | ||||
\(448\) | 2.82745 | + | 2.82745i | 0.133585 | + | 0.133585i | ||||
\(449\) | 2.65135 | − | 2.65135i | 0.125125 | − | 0.125125i | −0.641771 | − | 0.766896i | \(-0.721800\pi\) |
0.766896 | + | 0.641771i | \(0.221800\pi\) | |||||||
\(450\) | 13.6709 | + | 2.79855i | 0.644450 | + | 0.131925i | ||||
\(451\) | 21.7666 | 1.02495 | ||||||||
\(452\) | 5.85257i | 0.275282i | ||||||||
\(453\) | −27.4722 | + | 27.4722i | −1.29075 | + | 1.29075i | ||||
\(454\) | − | 22.3785i | − | 1.05028i | ||||||
\(455\) | −6.57149 | − | 0.665720i | −0.308076 | − | 0.0312094i | ||||
\(456\) | 17.1218 | 0.801799 | ||||||||
\(457\) | − | 6.35811i | − | 0.297420i | −0.988881 | − | 0.148710i | \(-0.952488\pi\) | ||
0.988881 | − | 0.148710i | \(-0.0475121\pi\) | |||||||
\(458\) | − | 6.97332i | − | 0.325842i | ||||||
\(459\) | 2.35515 | + | 2.35515i | 0.109929 | + | 0.109929i | ||||
\(460\) | 11.0766 | − | 9.03886i | 0.516451 | − | 0.421439i | ||||
\(461\) | 13.5522 | + | 13.5522i | 0.631188 | + | 0.631188i | 0.948366 | − | 0.317178i | \(-0.102735\pi\) |
−0.317178 | + | 0.948366i | \(0.602735\pi\) | |||||||
\(462\) | −28.3125 | −1.31721 | ||||||||
\(463\) | 6.65144 | 0.309119 | 0.154559 | − | 0.987983i | \(-0.450604\pi\) | ||||
0.154559 | + | 0.987983i | \(0.450604\pi\) | |||||||
\(464\) | −2.49797 | − | 2.49797i | −0.115965 | − | 0.115965i | ||||
\(465\) | 8.73595 | − | 7.12878i | 0.405120 | − | 0.330589i | ||||
\(466\) | 15.1891 | + | 15.1891i | 0.703620 | + | 0.703620i | ||||
\(467\) | − | 18.5636i | − | 0.859019i | −0.903062 | − | 0.429510i | \(-0.858686\pi\) | ||
0.903062 | − | 0.429510i | \(-0.141314\pi\) | |||||||
\(468\) | − | 2.06170i | − | 0.0953021i | ||||||
\(469\) | 11.8755 | 0.548360 | ||||||||
\(470\) | 23.8045 | + | 2.41150i | 1.09802 | + | 0.111234i | ||||
\(471\) | 11.0409i | 0.508736i | ||||||||
\(472\) | −8.34044 | + | 8.34044i | −0.383900 | + | 0.383900i | ||||
\(473\) | − | 20.5522i | − | 0.944990i | ||||||
\(474\) | 19.3849 | 0.890379 | ||||||||
\(475\) | 19.5994 | + | 29.6892i | 0.899282 | + | 1.36224i | ||||
\(476\) | 18.7130 | − | 18.7130i | 0.857710 | − | 0.857710i | ||||
\(477\) | 5.42086 | + | 5.42086i | 0.248204 | + | 0.248204i | ||||
\(478\) | 1.35831 | − | 1.35831i | 0.0621276 | − | 0.0621276i | ||||
\(479\) | −3.71611 | + | 3.71611i | −0.169793 | + | 0.169793i | −0.786889 | − | 0.617095i | \(-0.788309\pi\) |
0.617095 | + | 0.786889i | \(0.288309\pi\) | |||||||
\(480\) | −5.35353 | − | 0.542335i | −0.244354 | − | 0.0247541i | ||||
\(481\) | 4.49086 | − | 0.154489i | 0.204766 | − | 0.00704411i | ||||
\(482\) | −9.55663 | − | 9.55663i | −0.435292 | − | 0.435292i | ||||
\(483\) | − | 61.5220i | − | 2.79935i | ||||||
\(484\) | 2.34255 | 0.106479 | ||||||||
\(485\) | 4.81119 | + | 5.89586i | 0.218465 | + | 0.267717i | ||||
\(486\) | −15.2400 | − | 15.2400i | −0.691299 | − | 0.691299i | ||||
\(487\) | 0.818395i | 0.0370850i | 0.999828 | + | 0.0185425i | \(0.00590260\pi\) | ||||
−0.999828 | + | 0.0185425i | \(0.994097\pi\) | |||||||
\(488\) | −2.31872 | + | 2.31872i | −0.104964 | + | 0.104964i | ||||
\(489\) | 40.0044 | − | 40.0044i | 1.80906 | − | 1.80906i | ||||
\(490\) | 12.7080 | + | 15.5730i | 0.574088 | + | 0.703515i | ||||
\(491\) | 5.21815 | 0.235492 | 0.117746 | − | 0.993044i | \(-0.462433\pi\) | ||||
0.117746 | + | 0.993044i | \(0.462433\pi\) | |||||||
\(492\) | 12.5879 | − | 12.5879i | 0.567506 | − | 0.567506i | ||||
\(493\) | −16.5324 | + | 16.5324i | −0.744582 | + | 0.744582i | ||||
\(494\) | 3.71661 | − | 3.71661i | 0.167218 | − | 0.167218i | ||||
\(495\) | 14.2264 | − | 11.6092i | 0.639429 | − | 0.521793i | ||||
\(496\) | −1.48171 | + | 1.48171i | −0.0665307 | + | 0.0665307i | ||||
\(497\) | −7.13237 | − | 7.13237i | −0.319930 | − | 0.319930i | ||||
\(498\) | 9.27768 | 0.415743 | ||||||||
\(499\) | −17.1758 | − | 17.1758i | −0.768894 | − | 0.768894i | 0.209018 | − | 0.977912i | \(-0.432973\pi\) |
−0.977912 | + | 0.209018i | \(0.932973\pi\) | |||||||
\(500\) | −5.18781 | − | 9.90387i | −0.232006 | − | 0.442914i | ||||
\(501\) | 19.4906 | − | 19.4906i | 0.870775 | − | 0.870775i | ||||
\(502\) | 11.4900 | − | 11.4900i | 0.512823 | − | 0.512823i | ||||
\(503\) | 26.2211 | 1.16914 | 0.584569 | − | 0.811344i | \(-0.301263\pi\) | ||||
0.584569 | + | 0.811344i | \(0.301263\pi\) | |||||||
\(504\) | −7.89106 | + | 7.89106i | −0.351496 | + | 0.351496i | ||||
\(505\) | 5.96478 | + | 7.30952i | 0.265429 | + | 0.325269i | ||||
\(506\) | − | 18.8124i | − | 0.836311i | ||||||
\(507\) | 21.1922 | + | 21.1922i | 0.941178 | + | 0.941178i | ||||
\(508\) | 1.49192 | + | 1.49192i | 0.0661933 | + | 0.0661933i | ||||
\(509\) | −5.42333 | −0.240385 | −0.120192 | − | 0.992751i | \(-0.538351\pi\) | ||||
−0.120192 | + | 0.992751i | \(0.538351\pi\) | |||||||
\(510\) | −3.58935 | + | 35.4314i | −0.158939 | + | 1.56893i | ||||
\(511\) | 40.6518i | 1.79833i | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | − | 3.58064i | − | 0.158089i | ||||||
\(514\) | − | 31.7662i | − | 1.40115i | ||||||
\(515\) | −11.4545 | − | 14.0369i | −0.504745 | − | 0.618539i | ||||
\(516\) | −11.8856 | − | 11.8856i | −0.523233 | − | 0.523233i | ||||
\(517\) | 22.2624 | − | 22.2624i | 0.979099 | − | 0.979099i | ||||
\(518\) | −17.7799 | − | 16.5973i | −0.781202 | − | 0.729242i | ||||
\(519\) | − | 7.28579i | − | 0.319811i | ||||||
\(520\) | −1.27981 | + | 1.04436i | −0.0561234 | + | 0.0457983i | ||||
\(521\) | − | 20.3630i | − | 0.892120i | −0.895003 | − | 0.446060i | \(-0.852827\pi\) | ||
0.895003 | − | 0.446060i | \(-0.147173\pi\) | |||||||
\(522\) | 6.97152 | − | 6.97152i | 0.305135 | − | 0.305135i | ||||
\(523\) | −3.41343 | −0.149259 | −0.0746293 | − | 0.997211i | \(-0.523777\pi\) | ||||
−0.0746293 | + | 0.997211i | \(0.523777\pi\) | |||||||
\(524\) | −11.9137 | + | 11.9137i | −0.520452 | + | 0.520452i | ||||
\(525\) | −47.1344 | − | 9.64886i | −2.05712 | − | 0.421111i | ||||
\(526\) | −18.8716 | − | 18.8716i | −0.822841 | − | 0.822841i | ||||
\(527\) | 9.80643 | + | 9.80643i | 0.427175 | + | 0.427175i | ||||
\(528\) | −5.00671 | + | 5.00671i | −0.217889 | + | 0.217889i | ||||
\(529\) | 17.8786 | 0.777331 | ||||||||
\(530\) | 0.619069 | − | 6.11099i | 0.0268906 | − | 0.265444i | ||||
\(531\) | −23.2771 | − | 23.2771i | −1.01014 | − | 1.01014i | ||||
\(532\) | −28.4503 | −1.23348 | ||||||||
\(533\) | − | 5.46490i | − | 0.236711i | ||||||
\(534\) | 14.4832i | 0.626750i | ||||||||
\(535\) | −37.0993 | − | 3.75832i | −1.60394 | − | 0.162486i | ||||
\(536\) | 2.10003 | − | 2.10003i | 0.0907077 | − | 0.0907077i | ||||
\(537\) | − | 50.8533i | − | 2.19448i | ||||||
\(538\) | 5.87409i | 0.253250i | ||||||||
\(539\) | 26.4488 | 1.13923 | ||||||||
\(540\) | −0.113418 | + | 1.11957i | −0.00488072 | + | 0.0481788i | ||||
\(541\) | 1.72146 | + | 1.72146i | 0.0740112 | + | 0.0740112i | 0.743143 | − | 0.669132i | \(-0.233334\pi\) |
−0.669132 | + | 0.743143i | \(0.733334\pi\) | |||||||
\(542\) | 2.68158 | 0.115184 | ||||||||
\(543\) | −20.5256 | − | 20.5256i | −0.880838 | − | 0.880838i | ||||
\(544\) | − | 6.61833i | − | 0.283758i | ||||||
\(545\) | 3.12821 | − | 30.8794i | 0.133998 | − | 1.32273i | ||||
\(546\) | 7.10834i | 0.304209i | ||||||||
\(547\) | 38.3283 | 1.63880 | 0.819400 | − | 0.573223i | \(-0.194307\pi\) | ||||
0.819400 | + | 0.573223i | \(0.194307\pi\) | |||||||
\(548\) | 5.09297 | + | 5.09297i | 0.217561 | + | 0.217561i | ||||
\(549\) | −6.47125 | − | 6.47125i | −0.276186 | − | 0.276186i | ||||
\(550\) | −14.4129 | − | 2.95045i | −0.614567 | − | 0.125808i | ||||
\(551\) | 25.1350 | 1.07079 | ||||||||
\(552\) | −10.8794 | − | 10.8794i | −0.463058 | − | 0.463058i | ||||
\(553\) | −32.2109 | −1.36975 | ||||||||
\(554\) | −8.90912 | −0.378512 | ||||||||
\(555\) | 32.6584 | + | 2.17737i | 1.38627 | + | 0.0924242i | ||||
\(556\) | 1.23936 | 0.0525606 | ||||||||
\(557\) | −14.2458 | −0.603613 | −0.301806 | − | 0.953369i | \(-0.597590\pi\) | ||||
−0.301806 | + | 0.953369i | \(0.597590\pi\) | |||||||
\(558\) | −4.13526 | − | 4.13526i | −0.175059 | − | 0.175059i | ||||
\(559\) | −5.15998 | −0.218244 | ||||||||
\(560\) | 8.89567 | + | 0.901168i | 0.375910 | + | 0.0380813i | ||||
\(561\) | 33.1360 | + | 33.1360i | 1.39900 | + | 1.39900i | ||||
\(562\) | −3.03708 | − | 3.03708i | −0.128112 | − | 0.128112i | ||||
\(563\) | −4.87106 | −0.205291 | −0.102645 | − | 0.994718i | \(-0.532731\pi\) | ||||
−0.102645 | + | 0.994718i | \(0.532731\pi\) | |||||||
\(564\) | − | 25.7492i | − | 1.08424i | ||||||
\(565\) | 8.27394 | + | 10.1393i | 0.348087 | + | 0.426563i | ||||
\(566\) | 5.36256i | 0.225405i | ||||||||
\(567\) | 27.0973 | + | 27.0973i | 1.13798 | + | 1.13798i | ||||
\(568\) | −2.52254 | −0.105843 | ||||||||
\(569\) | 15.2311 | + | 15.2311i | 0.638521 | + | 0.638521i | 0.950191 | − | 0.311669i | \(-0.100888\pi\) |
−0.311669 | + | 0.950191i | \(0.600888\pi\) | |||||||
\(570\) | 29.6625 | − | 24.2055i | 1.24243 | − | 1.01386i | ||||
\(571\) | 10.5691 | 0.442302 | 0.221151 | − | 0.975240i | \(-0.429019\pi\) | ||||
0.221151 | + | 0.975240i | \(0.429019\pi\) | |||||||
\(572\) | 2.17361i | 0.0908830i | ||||||||
\(573\) | 36.5446i | 1.52667i | ||||||||
\(574\) | −20.9166 | + | 20.9166i | −0.873044 | + | 0.873044i | ||||
\(575\) | 6.41123 | − | 31.3187i | 0.267367 | − | 1.30608i | ||||
\(576\) | 2.79087i | 0.116286i | ||||||||
\(577\) | 27.8591i | 1.15979i | 0.814691 | + | 0.579895i | \(0.196906\pi\) | ||||
−0.814691 | + | 0.579895i | \(0.803094\pi\) | |||||||
\(578\) | −26.8022 | −1.11483 | ||||||||
\(579\) | 15.4679 | + | 15.4679i | 0.642826 | + | 0.642826i | ||||
\(580\) | −7.85906 | − | 0.796156i | −0.326330 | − | 0.0330586i | ||||
\(581\) | −15.4162 | −0.639573 | ||||||||
\(582\) | 5.79087 | − | 5.79087i | 0.240039 | − | 0.240039i | ||||
\(583\) | −5.71510 | − | 5.71510i | −0.236695 | − | 0.236695i | ||||
\(584\) | 7.18876 | + | 7.18876i | 0.297473 | + | 0.297473i | ||||
\(585\) | −2.91468 | − | 3.57179i | −0.120507 | − | 0.147675i | ||||
\(586\) | 13.2752 | − | 13.2752i | 0.548393 | − | 0.548393i | ||||
\(587\) | −1.53471 | −0.0633441 | −0.0316720 | − | 0.999498i | \(-0.510083\pi\) | ||||
−0.0316720 | + | 0.999498i | \(0.510083\pi\) | |||||||
\(588\) | 15.2957 | − | 15.2957i | 0.630782 | − | 0.630782i | ||||
\(589\) | − | 14.9092i | − | 0.614322i | ||||||
\(590\) | −2.65827 | + | 26.2405i | −0.109439 | + | 1.08030i | ||||
\(591\) | 26.9282i | 1.10768i | ||||||||
\(592\) | −6.07917 | + | 0.209128i | −0.249852 | + | 0.00859513i | ||||
\(593\) | 33.9424 | − | 33.9424i | 1.39385 | − | 1.39385i | 0.577353 | − | 0.816495i | \(-0.304086\pi\) |
0.816495 | − | 0.577353i | \(-0.195914\pi\) | |||||||
\(594\) | 1.04704 | + | 1.04704i | 0.0429608 | + | 0.0429608i | ||||
\(595\) | 5.96423 | − | 58.8744i | 0.244509 | − | 2.41362i | ||||
\(596\) | 0.292738i | 0.0119910i | ||||||||
\(597\) | 31.1285i | 1.27400i | ||||||||
\(598\) | −4.72317 | −0.193145 | ||||||||
\(599\) | − | 3.02066i | − | 0.123421i | −0.998094 | − | 0.0617105i | \(-0.980344\pi\) | ||
0.998094 | − | 0.0617105i | \(-0.0196555\pi\) | |||||||
\(600\) | −10.0414 | + | 6.62886i | −0.409939 | + | 0.270622i | ||||
\(601\) | 19.6569 | 0.801820 | 0.400910 | − | 0.916117i | \(-0.368694\pi\) | ||||
0.400910 | + | 0.916117i | \(0.368694\pi\) | |||||||
\(602\) | 19.7496 | + | 19.7496i | 0.804933 | + | 0.804933i | ||||
\(603\) | 5.86093 | + | 5.86093i | 0.238675 | + | 0.238675i | ||||
\(604\) | − | 16.1449i | − | 0.656928i | ||||||
\(605\) | 4.05834 | − | 3.31172i | 0.164995 | − | 0.134641i | ||||
\(606\) | 7.17936 | − | 7.17936i | 0.291641 | − | 0.291641i | ||||
\(607\) | −2.50292 | −0.101590 | −0.0507951 | − | 0.998709i | \(-0.516176\pi\) | ||||
−0.0507951 | + | 0.998709i | \(0.516176\pi\) | |||||||
\(608\) | −5.03108 | + | 5.03108i | −0.204037 | + | 0.204037i | ||||
\(609\) | −24.0364 | + | 24.0364i | −0.974006 | + | 0.974006i | ||||
\(610\) | −0.739025 | + | 7.29510i | −0.0299222 | + | 0.295370i | ||||
\(611\) | −5.58936 | − | 5.58936i | −0.226122 | − | 0.226122i | ||||
\(612\) | 18.4709 | 0.746642 | ||||||||
\(613\) | 26.8961 | + | 26.8961i | 1.08632 | + | 1.08632i | 0.995904 | + | 0.0904205i | \(0.0288211\pi\) |
0.0904205 | + | 0.995904i | \(0.471179\pi\) | |||||||
\(614\) | 3.46389 | − | 3.46389i | 0.139791 | − | 0.139791i | ||||
\(615\) | 4.01203 | − | 39.6037i | 0.161780 | − | 1.59698i | ||||
\(616\) | 8.31937 | − | 8.31937i | 0.335197 | − | 0.335197i | ||||
\(617\) | −4.81845 | + | 4.81845i | −0.193983 | + | 0.193983i | −0.797415 | − | 0.603432i | \(-0.793800\pi\) |
0.603432 | + | 0.797415i | \(0.293800\pi\) | |||||||
\(618\) | −13.7869 | + | 13.7869i | −0.554591 | + | 0.554591i | ||||
\(619\) | −10.4774 | −0.421121 | −0.210560 | − | 0.977581i | \(-0.567529\pi\) | ||||
−0.210560 | + | 0.977581i | \(0.567529\pi\) | |||||||
\(620\) | −0.472251 | + | 4.66171i | −0.0189661 | + | 0.187219i | ||||
\(621\) | −2.27519 | + | 2.27519i | −0.0913003 | + | 0.0913003i | ||||
\(622\) | 10.6674 | − | 10.6674i | 0.427725 | − | 0.427725i | ||||
\(623\) | − | 24.0660i | − | 0.964183i | ||||||
\(624\) | 1.25702 | + | 1.25702i | 0.0503211 | + | 0.0503211i | ||||
\(625\) | −22.9890 | − | 9.82379i | −0.919559 | − | 0.392952i | ||||
\(626\) | −23.2451 | −0.929063 | ||||||||
\(627\) | − | 50.3783i | − | 2.01191i | ||||||
\(628\) | −3.24426 | − | 3.24426i | −0.129460 | − | 0.129460i | ||||
\(629\) | 1.38408 | + | 40.2339i | 0.0551869 | + | 1.60423i | ||||
\(630\) | −2.51505 | + | 24.8267i | −0.100202 | + | 0.989118i | ||||
\(631\) | −20.7491 | + | 20.7491i | −0.826008 | + | 0.826008i | −0.986962 | − | 0.160954i | \(-0.948543\pi\) |
0.160954 | + | 0.986962i | \(0.448543\pi\) | |||||||
\(632\) | −5.69610 | + | 5.69610i | −0.226578 | + | 0.226578i | ||||
\(633\) | 20.8730 | + | 20.8730i | 0.829626 | + | 0.829626i | ||||
\(634\) | 7.42086 | − | 7.42086i | 0.294720 | − | 0.294720i | ||||
\(635\) | 4.69384 | + | 0.475506i | 0.186269 | + | 0.0188699i | ||||
\(636\) | −6.61022 | −0.262112 | ||||||||
\(637\) | − | 6.64044i | − | 0.263104i | ||||||
\(638\) | −7.34992 | + | 7.34992i | −0.290986 | + | 0.290986i | ||||
\(639\) | − | 7.04009i | − | 0.278502i | ||||||
\(640\) | 1.73245 | − | 1.41373i | 0.0684810 | − | 0.0558825i | ||||
\(641\) | −31.3975 | −1.24013 | −0.620064 | − | 0.784552i | \(-0.712893\pi\) | ||||
−0.620064 | + | 0.784552i | \(0.712893\pi\) | |||||||
\(642\) | 40.1301i | 1.58381i | ||||||||
\(643\) | − | 39.2482i | − | 1.54780i | −0.633309 | − | 0.773899i | \(-0.718304\pi\) | ||
0.633309 | − | 0.773899i | \(-0.281696\pi\) | |||||||
\(644\) | 18.0777 | + | 18.0777i | 0.712362 | + | 0.712362i | ||||
\(645\) | −37.3940 | − | 3.78817i | −1.47239 | − | 0.149159i | ||||
\(646\) | 33.2973 | + | 33.2973i | 1.31007 | + | 1.31007i | ||||
\(647\) | 33.5881 | 1.32048 | 0.660242 | − | 0.751053i | \(-0.270454\pi\) | ||||
0.660242 | + | 0.751053i | \(0.270454\pi\) | |||||||
\(648\) | 9.58365 | 0.376481 | ||||||||
\(649\) | 24.5405 | + | 24.5405i | 0.963300 | + | 0.963300i | ||||
\(650\) | −0.740762 | + | 3.61861i | −0.0290551 | + | 0.141933i | ||||
\(651\) | 14.2576 | + | 14.2576i | 0.558798 | + | 0.558798i | ||||
\(652\) | 23.5099i | 0.920718i | ||||||||
\(653\) | − | 32.2571i | − | 1.26232i | −0.775653 | − | 0.631159i | \(-0.782579\pi\) | ||
0.775653 | − | 0.631159i | \(-0.217421\pi\) | |||||||
\(654\) | −33.4020 | −1.30612 | ||||||||
\(655\) | −3.79714 | + | 37.4825i | −0.148366 | + | 1.46456i | ||||
\(656\) | 7.39769i | 0.288831i | ||||||||
\(657\) | −20.0629 | + | 20.0629i | −0.782728 | + | 0.782728i | ||||
\(658\) | 42.7861i | 1.66797i | ||||||||
\(659\) | 28.7104 | 1.11840 | 0.559199 | − | 0.829033i | \(-0.311109\pi\) | ||||
0.559199 | + | 0.829033i | \(0.311109\pi\) | |||||||
\(660\) | −1.59574 | + | 15.7520i | −0.0621141 | + | 0.613145i | ||||
\(661\) | 5.46781 | − | 5.46781i | 0.212673 | − | 0.212673i | −0.592729 | − | 0.805402i | \(-0.701949\pi\) |
0.805402 | + | 0.592729i | \(0.201949\pi\) | |||||||
\(662\) | 13.2492 | + | 13.2492i | 0.514945 | + | 0.514945i | ||||
\(663\) | 8.31937 | − | 8.31937i | 0.323098 | − | 0.323098i | ||||
\(664\) | −2.72617 | + | 2.72617i | −0.105796 | + | 0.105796i | ||||
\(665\) | −49.2887 | + | 40.2210i | −1.91133 | + | 1.55970i | ||||
\(666\) | −0.583651 | − | 16.9662i | −0.0226160 | − | 0.657426i | ||||
\(667\) | −15.9711 | − | 15.9711i | −0.618405 | − | 0.618405i | ||||
\(668\) | 11.4543i | 0.443179i | ||||||||
\(669\) | 29.6252 | 1.14538 | ||||||||
\(670\) | 0.669325 | − | 6.60708i | 0.0258583 | − | 0.255254i | ||||
\(671\) | 6.82250 | + | 6.82250i | 0.263380 | + | 0.263380i | ||||
\(672\) | − | 9.62238i | − | 0.371191i | ||||||
\(673\) | 15.3921 | − | 15.3921i | 0.593323 | − | 0.593323i | −0.345204 | − | 0.938528i | \(-0.612190\pi\) |
0.938528 | + | 0.345204i | \(0.112190\pi\) | |||||||
\(674\) | 3.84828 | − | 3.84828i | 0.148230 | − | 0.148230i | ||||
\(675\) | 1.38628 | + | 2.09995i | 0.0533580 | + | 0.0808269i | ||||
\(676\) | −12.4543 | −0.479011 | ||||||||
\(677\) | 8.46595 | − | 8.46595i | 0.325373 | − | 0.325373i | −0.525451 | − | 0.850824i | \(-0.676103\pi\) |
0.850824 | + | 0.525451i | \(0.176103\pi\) | |||||||
\(678\) | 9.95872 | − | 9.95872i | 0.382462 | − | 0.382462i | ||||
\(679\) | −9.62238 | + | 9.62238i | −0.369273 | + | 0.369273i | ||||
\(680\) | −9.35651 | − | 11.4659i | −0.358806 | − | 0.439697i | ||||
\(681\) | −38.0793 | + | 38.0793i | −1.45920 | + | 1.45920i | ||||
\(682\) | 4.35971 | + | 4.35971i | 0.166942 | + | 0.166942i | ||||
\(683\) | −42.2105 | −1.61514 | −0.807570 | − | 0.589772i | \(-0.799218\pi\) | ||||
−0.807570 | + | 0.589772i | \(0.799218\pi\) | |||||||
\(684\) | −14.0411 | − | 14.0411i | −0.536875 | − | 0.536875i | ||||
\(685\) | 16.0234 | + | 1.62324i | 0.612222 | + | 0.0620207i | ||||
\(686\) | −5.62379 | + | 5.62379i | −0.214717 | + | 0.214717i | ||||
\(687\) | −11.8658 | + | 11.8658i | −0.452708 | + | 0.452708i | ||||
\(688\) | 6.98494 | 0.266298 | ||||||||
\(689\) | −1.43488 | + | 1.43488i | −0.0546644 | + | 0.0546644i | ||||
\(690\) | −34.2285 | − | 3.46749i | −1.30306 | − | 0.132005i | ||||
\(691\) | 7.77112i | 0.295627i | 0.989015 | + | 0.147814i | \(0.0472236\pi\) | ||||
−0.989015 | + | 0.147814i | \(0.952776\pi\) | |||||||
\(692\) | 2.14087 | + | 2.14087i | 0.0813835 | + | 0.0813835i | ||||
\(693\) | 23.2183 | + | 23.2183i | 0.881991 | + | 0.881991i | ||||
\(694\) | 20.7126 | 0.786240 | ||||||||
\(695\) | 2.14713 | − | 1.75212i | 0.0814452 | − | 0.0664616i | ||||
\(696\) | 8.50109i | 0.322233i | ||||||||
\(697\) | 48.9603 | 1.85451 | ||||||||
\(698\) | 29.0891i | 1.10104i | ||||||||
\(699\) | − | 51.6914i | − | 1.95515i | ||||||
\(700\) | 16.6853 | − | 11.0148i | 0.630644 | − | 0.416321i | ||||
\(701\) | −36.6175 | − | 36.6175i | −1.38302 | − | 1.38302i | −0.839197 | − | 0.543828i | \(-0.816974\pi\) |
−0.543828 | − | 0.839197i | \(-0.683026\pi\) | |||||||
\(702\) | 0.262879 | − | 0.262879i | 0.00992172 | − | 0.00992172i | ||||
\(703\) | 29.5326 | − | 31.6369i | 1.11384 | − | 1.19321i | ||||
\(704\) | − | 2.94236i | − | 0.110894i | ||||||
\(705\) | −36.4024 | − | 44.6092i | −1.37099 | − | 1.68008i | ||||
\(706\) | − | 22.8767i | − | 0.860975i | ||||||
\(707\) | −11.9296 | + | 11.9296i | −0.448657 | + | 0.448657i | ||||
\(708\) | 28.3841 | 1.06674 | ||||||||
\(709\) | 33.4953 | − | 33.4953i | 1.25794 | − | 1.25794i | 0.305869 | − | 0.952074i | \(-0.401053\pi\) |
0.952074 | − | 0.305869i | \(-0.0989469\pi\) | |||||||
\(710\) | −4.37017 | + | 3.56618i | −0.164010 | + | 0.133836i | ||||
\(711\) | −15.8971 | − | 15.8971i | −0.596187 | − | 0.596187i | ||||
\(712\) | −4.25577 | − | 4.25577i | −0.159492 | − | 0.159492i | ||||
\(713\) | −9.47351 | + | 9.47351i | −0.354786 | + | 0.354786i | ||||
\(714\) | −63.6841 | −2.38332 | ||||||||
\(715\) | 3.07288 | + | 3.76566i | 0.114919 | + | 0.140828i | ||||
\(716\) | 14.9428 | + | 14.9428i | 0.558439 | + | 0.558439i | ||||
\(717\) | −4.62259 | −0.172634 | ||||||||
\(718\) | 25.7577i | 0.961269i | ||||||||
\(719\) | 7.36568i | 0.274693i | 0.990523 | + | 0.137347i | \(0.0438574\pi\) | ||||
−0.990523 | + | 0.137347i | \(0.956143\pi\) | |||||||
\(720\) | 3.94553 | + | 4.83504i | 0.147041 | + | 0.180191i | ||||
\(721\) | 22.9090 | − | 22.9090i | 0.853175 | − | 0.853175i | ||||
\(722\) | − | 31.6235i | − | 1.17691i | ||||||
\(723\) | 32.5231i | 1.20955i | ||||||||
\(724\) | 12.0625 | 0.448301 | ||||||||
\(725\) | −14.7410 | + | 9.73127i | −0.547465 | + | 0.361410i | ||||
\(726\) | −3.98607 | − | 3.98607i | −0.147937 | − | 0.147937i | ||||
\(727\) | −49.6628 | −1.84189 | −0.920945 | − | 0.389692i | \(-0.872581\pi\) | ||||
−0.920945 | + | 0.389692i | \(0.872581\pi\) | |||||||
\(728\) | −2.08872 | − | 2.08872i | −0.0774133 | − | 0.0774133i | ||||
\(729\) | 23.1136i | 0.856060i | ||||||||
\(730\) | 22.6171 | + | 2.29121i | 0.837096 | + | 0.0848014i | ||||
\(731\) | − | 46.2286i | − | 1.70983i | ||||||
\(732\) | 7.89106 | 0.291662 | ||||||||
\(733\) | −1.72578 | − | 1.72578i | −0.0637431 | − | 0.0637431i | 0.674517 | − | 0.738260i | \(-0.264352\pi\) |
−0.738260 | + | 0.674517i | \(0.764352\pi\) | |||||||
\(734\) | −17.7447 | − | 17.7447i | −0.654968 | − | 0.654968i | ||||
\(735\) | 4.87504 | − | 48.1228i | 0.179819 | − | 1.77504i | ||||
\(736\) | 6.39364 | 0.235673 | ||||||||
\(737\) | −6.17905 | − | 6.17905i | −0.227608 | − | 0.227608i | ||||
\(738\) | −20.6460 | −0.759990 | ||||||||
\(739\) | −34.0153 | −1.25127 | −0.625636 | − | 0.780115i | \(-0.715160\pi\) | ||||
−0.625636 | + | 0.780115i | \(0.715160\pi\) | |||||||
\(740\) | −10.2362 | + | 8.95659i | −0.376290 | + | 0.329251i | ||||
\(741\) | −12.6483 | −0.464649 | ||||||||
\(742\) | 10.9838 | 0.403229 | ||||||||
\(743\) | 11.8640 | + | 11.8640i | 0.435249 | + | 0.435249i | 0.890410 | − | 0.455160i | \(-0.150418\pi\) |
−0.455160 | + | 0.890410i | \(0.650418\pi\) | |||||||
\(744\) | 5.04255 | 0.184869 | ||||||||
\(745\) | 0.413852 | + | 0.507154i | 0.0151624 | + | 0.0185807i | ||||
\(746\) | 22.7050 | + | 22.7050i | 0.831290 | + | 0.831290i | ||||
\(747\) | −7.60838 | − | 7.60838i | −0.278376 | − | 0.278376i | ||||
\(748\) | −19.4735 | −0.712020 | ||||||||
\(749\) | − | 66.6820i | − | 2.43651i | ||||||
\(750\) | −8.02484 | + | 25.6800i | −0.293026 | + | 0.937700i | ||||
\(751\) | 18.1038i | 0.660617i | 0.943873 | + | 0.330308i | \(0.107153\pi\) | ||||
−0.943873 | + | 0.330308i | \(0.892847\pi\) | |||||||
\(752\) | 7.56618 | + | 7.56618i | 0.275910 | + | 0.275910i | ||||
\(753\) | −39.1026 | −1.42498 | ||||||||
\(754\) | 1.84533 | + | 1.84533i | 0.0672028 | + | 0.0672028i | ||||
\(755\) | −22.8245 | − | 27.9702i | −0.830669 | − | 1.01794i | ||||
\(756\) | −2.01231 | −0.0731871 | ||||||||
\(757\) | − | 25.2565i | − | 0.917964i | −0.888445 | − | 0.458982i | \(-0.848214\pi\) | ||
0.888445 | − | 0.458982i | \(-0.151786\pi\) | |||||||
\(758\) | − | 27.5341i | − | 1.00008i | ||||||
\(759\) | −32.0111 | + | 32.0111i | −1.16193 | + | 1.16193i | ||||
\(760\) | −1.60351 | + | 15.8287i | −0.0581654 | + | 0.574166i | ||||
\(761\) | 45.4777i | 1.64856i | 0.566179 | + | 0.824282i | \(0.308421\pi\) | ||||
−0.566179 | + | 0.824282i | \(0.691579\pi\) | |||||||
\(762\) | − | 5.07730i | − | 0.183931i | ||||||
\(763\) | 55.5023 | 2.00932 | ||||||||
\(764\) | −10.7383 | − | 10.7383i | −0.388499 | − | 0.388499i | ||||
\(765\) | 31.9999 | − | 26.1128i | 1.15696 | − | 0.944111i | ||||
\(766\) | 4.93269 | 0.178225 | ||||||||
\(767\) | 6.16133 | − | 6.16133i | 0.222473 | − | 0.222473i | ||||
\(768\) | −1.70160 | − | 1.70160i | −0.0614011 | − | 0.0614011i | ||||
\(769\) | 5.30402 | + | 5.30402i | 0.191268 | + | 0.191268i | 0.796244 | − | 0.604976i | \(-0.206817\pi\) |
−0.604976 | + | 0.796244i | \(0.706817\pi\) | |||||||
\(770\) | 2.65156 | − | 26.1742i | 0.0955555 | − | 0.943253i | ||||
\(771\) | −54.0533 | + | 54.0533i | −1.94668 | + | 1.94668i | ||||
\(772\) | −9.09024 | −0.327165 | ||||||||
\(773\) | −21.8164 | + | 21.8164i | −0.784681 | + | 0.784681i | −0.980617 | − | 0.195935i | \(-0.937226\pi\) |
0.195935 | + | 0.980617i | \(0.437226\pi\) | |||||||
\(774\) | 19.4941i | 0.700700i | ||||||||
\(775\) | 5.77224 | + | 8.74381i | 0.207345 | + | 0.314087i | ||||
\(776\) | 3.40320i | 0.122168i | ||||||||
\(777\) | 2.01231 | + | 58.4961i | 0.0721913 | + | 2.09853i | ||||
\(778\) | −4.25176 | + | 4.25176i | −0.152433 | + | 0.152433i | ||||
\(779\) | −37.2184 | − | 37.2184i | −1.33349 | − | 1.33349i | ||||
\(780\) | 3.95481 | + | 0.400639i | 0.141605 | + | 0.0143452i | ||||
\(781\) | 7.42221i | 0.265588i | ||||||||
\(782\) | − | 42.3152i | − | 1.51319i | ||||||
\(783\) | 1.77782 | 0.0635341 | ||||||||
\(784\) | 8.98899i | 0.321036i | ||||||||
\(785\) | −10.2070 | − | 1.03401i | −0.364304 | − | 0.0369055i | ||||
\(786\) | 40.5446 | 1.44618 | ||||||||
\(787\) | −29.6710 | − | 29.6710i | −1.05766 | − | 1.05766i | −0.998233 | − | 0.0594240i | \(-0.981074\pi\) |
−0.0594240 | − | 0.998233i | \(-0.518926\pi\) | |||||||
\(788\) | −7.91262 | − | 7.91262i | −0.281875 | − | 0.281875i | ||||
\(789\) | 64.2237i | 2.28643i | ||||||||
\(790\) | −1.81546 | + | 17.9209i | −0.0645913 | + | 0.637597i | ||||
\(791\) | −16.5479 | + | 16.5479i | −0.588375 | + | 0.588375i | ||||
\(792\) | 8.21174 | 0.291791 | ||||||||
\(793\) | 1.71291 | − | 1.71291i | 0.0608271 | − | 0.0608271i | ||||
\(794\) | −6.85748 | + | 6.85748i | −0.243363 | + | 0.243363i | ||||
\(795\) | −11.4519 | + | 9.34504i | −0.406155 | + | 0.331434i | ||||
\(796\) | −9.14683 | − | 9.14683i | −0.324201 | − | 0.324201i | ||||
\(797\) | −12.5492 | −0.444515 | −0.222257 | − | 0.974988i | \(-0.571343\pi\) | ||||
−0.222257 | + | 0.974988i | \(0.571343\pi\) | |||||||
\(798\) | 48.4110 | + | 48.4110i | 1.71373 | + | 1.71373i | ||||
\(799\) | 50.0755 | − | 50.0755i | 1.77154 | − | 1.77154i | ||||
\(800\) | 1.00275 | − | 4.89842i | 0.0354526 | − | 0.173185i | ||||
\(801\) | 11.8773 | − | 11.8773i | 0.419664 | − | 0.419664i | ||||
\(802\) | 4.52089 | − | 4.52089i | 0.159638 | − | 0.159638i | ||||
\(803\) | 21.1519 | − | 21.1519i | 0.746434 | − | 0.746434i | ||||
\(804\) | −7.14683 | −0.252049 | ||||||||
\(805\) | 56.8757 | + | 5.76175i | 2.00460 | + | 0.203075i | ||||
\(806\) | 1.09458 | − | 1.09458i | 0.0385550 | − | 0.0385550i | ||||
\(807\) | 9.99535 | − | 9.99535i | 0.351853 | − | 0.351853i | ||||
\(808\) | 4.21918i | 0.148430i | ||||||||
\(809\) | −19.1078 | − | 19.1078i | −0.671796 | − | 0.671796i | 0.286334 | − | 0.958130i | \(-0.407563\pi\) |
−0.958130 | + | 0.286334i | \(0.907563\pi\) | |||||||
\(810\) | 16.6032 | − | 13.5487i | 0.583376 | − | 0.476052i | ||||
\(811\) | 9.22121 | 0.323801 | 0.161900 | − | 0.986807i | \(-0.448238\pi\) | ||||
0.161900 | + | 0.986807i | \(0.448238\pi\) | |||||||
\(812\) | − | 14.1258i | − | 0.495719i | ||||||
\(813\) | −4.56298 | − | 4.56298i | −0.160031 | − | 0.160031i | ||||
\(814\) | 0.615330 | + | 17.8871i | 0.0215673 | + | 0.626941i | ||||
\(815\) | 33.2366 | + | 40.7297i | 1.16423 | + | 1.42670i | ||||
\(816\) | −11.2617 | + | 11.2617i | −0.394239 | + | 0.394239i | ||||
\(817\) | −35.1418 | + | 35.1418i | −1.22946 | + | 1.22946i | ||||
\(818\) | 12.6409 | + | 12.6409i | 0.441979 | + | 0.441979i | ||||
\(819\) | 5.82936 | − | 5.82936i | 0.203694 | − | 0.203694i | ||||
\(820\) | 10.4583 | + | 12.8161i | 0.365220 | + | 0.447558i | ||||
\(821\) | 1.92924 | 0.0673310 | 0.0336655 | − | 0.999433i | \(-0.489282\pi\) | ||||
0.0336655 | + | 0.999433i | \(0.489282\pi\) | |||||||
\(822\) | − | 17.3324i | − | 0.604536i | ||||||
\(823\) | −14.9775 | + | 14.9775i | −0.522084 | + | 0.522084i | −0.918200 | − | 0.396116i | \(-0.870358\pi\) |
0.396116 | + | 0.918200i | \(0.370358\pi\) | |||||||
\(824\) | − | 8.10234i | − | 0.282258i | ||||||
\(825\) | 19.5045 | + | 29.5454i | 0.679058 | + | 1.02864i | ||||
\(826\) | −47.1644 | −1.64106 | ||||||||
\(827\) | 46.1448i | 1.60461i | 0.596913 | + | 0.802306i | \(0.296394\pi\) | ||||
−0.596913 | + | 0.802306i | \(0.703606\pi\) | |||||||
\(828\) | 17.8438i | 0.620116i | ||||||||
\(829\) | −10.2967 | − | 10.2967i | −0.357619 | − | 0.357619i | 0.505315 | − | 0.862935i | \(-0.331376\pi\) |
−0.862935 | + | 0.505315i | \(0.831376\pi\) | |||||||
\(830\) | −0.868886 | + | 8.57700i | −0.0301595 | + | 0.297712i | ||||
\(831\) | 15.1597 | + | 15.1597i | 0.525885 | + | 0.525885i | ||||
\(832\) | −0.738730 | −0.0256108 | ||||||||
\(833\) | 59.4921 | 2.06128 | ||||||||
\(834\) | −2.10889 | − | 2.10889i | −0.0730250 | − | 0.0730250i | ||||
\(835\) | 16.1932 | + | 19.8439i | 0.560390 | + | 0.686728i | ||||
\(836\) | 14.8032 | + | 14.8032i | 0.511980 | + | 0.511980i | ||||
\(837\) | − | 1.05454i | − | 0.0364502i | ||||||
\(838\) | − | 18.0818i | − | 0.624625i | ||||||
\(839\) | 32.5351 | 1.12324 | 0.561619 | − | 0.827396i | \(-0.310179\pi\) | ||||
0.561619 | + | 0.827396i | \(0.310179\pi\) | |||||||
\(840\) | −13.6034 | − | 16.6703i | −0.469363 | − | 0.575179i | ||||
\(841\) | − | 16.5203i | − | 0.569664i | ||||||
\(842\) | −2.11385 | + | 2.11385i | −0.0728482 | + | 0.0728482i | ||||
\(843\) | 10.3358i | 0.355983i | ||||||||
\(844\) | −12.2667 | −0.422237 | ||||||||
\(845\) | −21.5764 | + | 17.6070i | −0.742250 | + | 0.605698i | ||||
\(846\) | −21.1162 | + | 21.1162i | −0.725992 | + | 0.725992i | ||||
\(847\) | 6.62344 | + | 6.62344i | 0.227584 | + | 0.227584i | ||||
\(848\) | 1.94236 | − | 1.94236i | 0.0667008 | − | 0.0667008i | ||||
\(849\) | 9.12492 | − | 9.12492i | 0.313166 | − | 0.313166i | ||||
\(850\) | −32.4193 | − | 6.63654i | −1.11197 | − | 0.227631i | ||||
\(851\) | −38.8680 | + | 1.33709i | −1.33238 | + | 0.0458349i | ||||
\(852\) | 4.29235 | + | 4.29235i | 0.147053 | + | 0.147053i | ||||
\(853\) | 42.8714i | 1.46789i | 0.679209 | + | 0.733945i | \(0.262323\pi\) | ||||
−0.679209 | + | 0.733945i | \(0.737677\pi\) | |||||||
\(854\) | −13.1122 | −0.448689 | ||||||||
\(855\) | −44.1757 | − | 4.47519i | −1.51078 | − | 0.153048i | ||||
\(856\) | −11.7919 | − | 11.7919i | −0.403038 | − | 0.403038i | ||||
\(857\) | − | 3.29400i | − | 0.112521i | −0.998416 | − | 0.0562604i | \(-0.982082\pi\) | ||
0.998416 | − | 0.0562604i | \(-0.0179177\pi\) | |||||||
\(858\) | 3.69860 | − | 3.69860i | 0.126268 | − | 0.126268i | ||||
\(859\) | −18.0550 | + | 18.0550i | −0.616030 | + | 0.616030i | −0.944511 | − | 0.328481i | \(-0.893463\pi\) |
0.328481 | + | 0.944511i | \(0.393463\pi\) | |||||||
\(860\) | 12.1010 | − | 9.87480i | 0.412642 | − | 0.336728i | ||||
\(861\) | 71.1834 | 2.42592 | ||||||||
\(862\) | −2.69254 | + | 2.69254i | −0.0917083 | + | 0.0917083i | ||||
\(863\) | −18.6224 | + | 18.6224i | −0.633913 | + | 0.633913i | −0.949047 | − | 0.315134i | \(-0.897950\pi\) |
0.315134 | + | 0.949047i | \(0.397950\pi\) | |||||||
\(864\) | −0.355853 | + | 0.355853i | −0.0121063 | + | 0.0121063i | ||||
\(865\) | 6.73554 | + | 0.682339i | 0.229015 | + | 0.0232002i | ||||
\(866\) | −13.9527 | + | 13.9527i | −0.474132 | + | 0.474132i | ||||
\(867\) | 45.6066 | + | 45.6066i | 1.54888 | + | 1.54888i | ||||
\(868\) | −8.37893 | −0.284399 | ||||||||
\(869\) | 16.7599 | + | 16.7599i | 0.568542 | + | 0.568542i | ||||
\(870\) | 12.0182 | + | 14.7277i | 0.407456 | + | 0.499316i | ||||
\(871\) | −1.55136 | + | 1.55136i | −0.0525658 | + | 0.0525658i | ||||
\(872\) | 9.81489 | − | 9.81489i | 0.332374 | − | 0.332374i | ||||
\(873\) | −9.49788 | −0.321455 | ||||||||
\(874\) | −32.1669 | + | 32.1669i | −1.08806 | + | 1.08806i | ||||
\(875\) | 13.3344 | − | 42.6710i | 0.450786 | − | 1.44254i | ||||
\(876\) | − | 24.4648i | − | 0.826587i | ||||||
\(877\) | 25.3664 | + | 25.3664i | 0.856561 | + | 0.856561i | 0.990931 | − | 0.134370i | \(-0.0429011\pi\) |
−0.134370 | + | 0.990931i | \(0.542901\pi\) | |||||||
\(878\) | −22.9884 | − | 22.9884i | −0.775821 | − | 0.775821i | ||||
\(879\) | −45.1780 | −1.52382 | ||||||||
\(880\) | −4.15969 | − | 5.09748i | −0.140223 | − | 0.171836i | ||||
\(881\) | − | 28.4586i | − | 0.958796i | −0.877598 | − | 0.479398i | \(-0.840855\pi\) | ||
0.877598 | − | 0.479398i | \(-0.159145\pi\) | |||||||
\(882\) | −25.0871 | −0.844728 | ||||||||
\(883\) | 17.5471i | 0.590508i | 0.955419 | + | 0.295254i | \(0.0954042\pi\) | ||||
−0.955419 | + | 0.295254i | \(0.904596\pi\) | |||||||
\(884\) | 4.88915i | 0.164440i | ||||||||
\(885\) | 49.1740 | − | 40.1274i | 1.65297 | − | 1.34887i | ||||
\(886\) | −7.06197 | − | 7.06197i | −0.237251 | − | 0.237251i | ||||
\(887\) | 25.1122 | − | 25.1122i | 0.843184 | − | 0.843184i | −0.146088 | − | 0.989272i | \(-0.546668\pi\) |
0.989272 | + | 0.146088i | \(0.0466683\pi\) | |||||||
\(888\) | 10.7002 | + | 9.98845i | 0.359074 | + | 0.335190i | ||||
\(889\) | 8.43667i | 0.282957i | ||||||||
\(890\) | −13.3894 | − | 1.35640i | −0.448813 | − | 0.0454667i | ||||
\(891\) | − | 28.1985i | − | 0.944685i | ||||||
\(892\) | −8.70510 | + | 8.70510i | −0.291468 | + | 0.291468i | ||||
\(893\) | −76.1321 | −2.54767 | ||||||||
\(894\) | 0.498123 | − | 0.498123i | 0.0166597 | − | 0.0166597i | ||||
\(895\) | 47.0127 | + | 4.76259i | 1.57146 | + | 0.159196i | ||||
\(896\) | 2.82745 | + | 2.82745i | 0.0944586 | + | 0.0944586i | ||||
\(897\) | 8.03694 | + | 8.03694i | 0.268346 | + | 0.268346i | ||||
\(898\) | 2.65135 | − | 2.65135i | 0.0884768 | − | 0.0884768i | ||||
\(899\) | 7.40254 | 0.246888 | ||||||||
\(900\) | 13.6709 | + | 2.79855i | 0.455695 | + | 0.0932850i | ||||
\(901\) | −12.8551 | − | 12.8551i | −0.428267 | − | 0.428267i | ||||
\(902\) | 21.7666 | 0.724750 | ||||||||
\(903\) | − | 67.2117i | − | 2.23667i | ||||||
\(904\) | 5.85257i | 0.194654i | ||||||||
\(905\) | 20.8977 | − | 17.0532i | 0.694664 | − | 0.566866i | ||||
\(906\) | −27.4722 | + | 27.4722i | −0.912702 | + | 0.912702i | ||||
\(907\) | 57.0816i | 1.89536i | 0.319215 | + | 0.947682i | \(0.396581\pi\) | ||||
−0.319215 | + | 0.947682i | \(0.603419\pi\) | |||||||
\(908\) | − | 22.3785i | − | 0.742658i | ||||||
\(909\) | −11.7752 | −0.390559 | ||||||||
\(910\) | −6.57149 | − | 0.665720i | −0.217843 | − | 0.0220684i | ||||
\(911\) | −22.4319 | − | 22.4319i | −0.743203 | − | 0.743203i | 0.229990 | − | 0.973193i | \(-0.426131\pi\) |
−0.973193 | + | 0.229990i | \(0.926131\pi\) | |||||||
\(912\) | 17.1218 | 0.566958 | ||||||||
\(913\) | 8.02135 | + | 8.02135i | 0.265468 | + | 0.265468i | ||||
\(914\) | − | 6.35811i | − | 0.210308i | ||||||
\(915\) | 13.6709 | − | 11.1558i | 0.451944 | − | 0.368800i | ||||
\(916\) | − | 6.97332i | − | 0.230405i | ||||||
\(917\) | −67.3708 | −2.22478 | ||||||||
\(918\) | 2.35515 | + | 2.35515i | 0.0777315 | + | 0.0777315i | ||||
\(919\) | 33.5651 | + | 33.5651i | 1.10721 | + | 1.10721i | 0.993516 | + | 0.113694i | \(0.0362684\pi\) |
0.113694 | + | 0.993516i | \(0.463732\pi\) | |||||||
\(920\) | 11.0766 | − | 9.03886i | 0.365186 | − | 0.298002i | ||||
\(921\) | −11.7883 | −0.388437 | ||||||||
\(922\) | 13.5522 | + | 13.5522i | 0.446317 | + | 0.446317i | ||||
\(923\) | 1.86348 | 0.0613370 | ||||||||
\(924\) | −28.3125 | −0.931412 | ||||||||
\(925\) | −5.07149 | + | 29.9880i | −0.166750 | + | 0.985999i | ||||
\(926\) | 6.65144 | 0.218580 | ||||||||
\(927\) | 22.6126 | 0.742695 | ||||||||
\(928\) | −2.49797 | − | 2.49797i | −0.0820000 | − | 0.0820000i | ||||
\(929\) | −58.2060 | −1.90968 | −0.954838 | − | 0.297127i | \(-0.903972\pi\) | ||||
−0.954838 | + | 0.297127i | \(0.903972\pi\) | |||||||
\(930\) | 8.73595 | − | 7.12878i | 0.286463 | − | 0.233762i | ||||
\(931\) | −45.2243 | − | 45.2243i | −1.48217 | − | 1.48217i | ||||
\(932\) | 15.1891 | + | 15.1891i | 0.497535 | + | 0.497535i | ||||
\(933\) | −36.3033 | −1.18852 | ||||||||
\(934\) | − | 18.5636i | − | 0.607418i | ||||||
\(935\) | −33.7368 | + | 27.5302i | −1.10331 | + | 0.900333i | ||||
\(936\) | − | 2.06170i | − | 0.0673888i | ||||||
\(937\) | 23.5283 | + | 23.5283i | 0.768637 | + | 0.768637i | 0.977867 | − | 0.209229i | \(-0.0670955\pi\) |
−0.209229 | + | 0.977867i | \(0.567095\pi\) | |||||||
\(938\) | 11.8755 | 0.387749 | ||||||||
\(939\) | 39.5539 | + | 39.5539i | 1.29079 | + | 1.29079i | ||||
\(940\) | 23.8045 | + | 2.41150i | 0.776418 | + | 0.0786545i | ||||
\(941\) | 23.9226 | 0.779853 | 0.389926 | − | 0.920846i | \(-0.372500\pi\) | ||||
0.389926 | + | 0.920846i | \(0.372500\pi\) | |||||||
\(942\) | 11.0409i | 0.359731i | ||||||||
\(943\) | 47.2982i | 1.54024i | ||||||||
\(944\) | −8.34044 | + | 8.34044i | −0.271458 | + | 0.271458i | ||||
\(945\) | −3.48623 | + | 2.84486i | −0.113407 | + | 0.0925434i | ||||
\(946\) | − | 20.5522i | − | 0.668209i | ||||||
\(947\) | − | 44.9073i | − | 1.45929i | −0.683826 | − | 0.729645i | \(-0.739685\pi\) | ||
0.683826 | − | 0.729645i | \(-0.260315\pi\) | |||||||
\(948\) | 19.3849 | 0.629593 | ||||||||
\(949\) | −5.31055 | − | 5.31055i | −0.172388 | − | 0.172388i | ||||
\(950\) | 19.5994 | + | 29.6892i | 0.635889 | + | 0.963246i | ||||
\(951\) | −25.2547 | −0.818938 | ||||||||
\(952\) | 18.7130 | − | 18.7130i | 0.606492 | − | 0.606492i | ||||
\(953\) | −6.57978 | − | 6.57978i | −0.213140 | − | 0.213140i | 0.592460 | − | 0.805600i | \(-0.298157\pi\) |
−0.805600 | + | 0.592460i | \(0.798157\pi\) | |||||||
\(954\) | 5.42086 | + | 5.42086i | 0.175507 | + | 0.175507i | ||||
\(955\) | −33.7846 | − | 3.42253i | −1.09325 | − | 0.110750i | ||||
\(956\) | 1.35831 | − | 1.35831i | 0.0439309 | − | 0.0439309i | ||||
\(957\) | 25.0132 | 0.808563 | ||||||||
\(958\) | −3.71611 | + | 3.71611i | −0.120062 | + | 0.120062i | ||||
\(959\) | 28.8003i | 0.930010i | ||||||||
\(960\) | −5.35353 | − | 0.542335i | −0.172784 | − | 0.0175038i | ||||
\(961\) | 26.6091i | 0.858357i | ||||||||
\(962\) | 4.49086 | − | 0.154489i | 0.144791 | − | 0.00498094i | ||||
\(963\) | 32.9096 | − | 32.9096i | 1.06050 | − | 1.06050i | ||||
\(964\) | −9.55663 | − | 9.55663i | −0.307798 | − | 0.307798i | ||||
\(965\) | −15.7484 | + | 12.8511i | −0.506958 | + | 0.413692i | ||||
\(966\) | − | 61.5220i | − | 1.97944i | ||||||
\(967\) | − | 37.1279i | − | 1.19395i | −0.802259 | − | 0.596977i | \(-0.796369\pi\) | ||
0.802259 | − | 0.596977i | \(-0.203631\pi\) | |||||||
\(968\) | 2.34255 | 0.0752923 | ||||||||
\(969\) | − | 113.317i | − | 3.64028i | ||||||
\(970\) | 4.81119 | + | 5.89586i | 0.154478 | + | 0.189305i | ||||
\(971\) | −12.7942 | −0.410586 | −0.205293 | − | 0.978701i | \(-0.565815\pi\) | ||||
−0.205293 | + | 0.978701i | \(0.565815\pi\) | |||||||
\(972\) | −15.2400 | − | 15.2400i | −0.488822 | − | 0.488822i | ||||
\(973\) | 3.50423 | + | 3.50423i | 0.112341 | + | 0.112341i | ||||
\(974\) | 0.818395i | 0.0262231i | ||||||||
\(975\) | 7.41789 | − | 4.89693i | 0.237563 | − | 0.156827i | ||||
\(976\) | −2.31872 | + | 2.31872i | −0.0742204 | + | 0.0742204i | ||||
\(977\) | −27.6004 | −0.883015 | −0.441507 | − | 0.897258i | \(-0.645556\pi\) | ||||
−0.441507 | + | 0.897258i | \(0.645556\pi\) | |||||||
\(978\) | 40.0044 | − | 40.0044i | 1.27920 | − | 1.27920i | ||||
\(979\) | −12.5220 | + | 12.5220i | −0.400204 | + | 0.400204i | ||||
\(980\) | 12.7080 | + | 15.5730i | 0.405942 | + | 0.497460i | ||||
\(981\) | 27.3921 | + | 27.3921i | 0.874562 | + | 0.874562i | ||||
\(982\) | 5.21815 | 0.166518 | ||||||||
\(983\) | −3.23105 | − | 3.23105i | −0.103054 | − | 0.103054i | 0.653700 | − | 0.756754i | \(-0.273216\pi\) |
−0.756754 | + | 0.653700i | \(0.773216\pi\) | |||||||
\(984\) | 12.5879 | − | 12.5879i | 0.401288 | − | 0.401288i | ||||
\(985\) | −24.8945 | − | 2.52192i | −0.793205 | − | 0.0803550i | ||||
\(986\) | −16.5324 | + | 16.5324i | −0.526499 | + | 0.526499i | ||||
\(987\) | 72.8047 | − | 72.8047i | 2.31740 | − | 2.31740i | ||||
\(988\) | 3.71661 | − | 3.71661i | 0.118241 | − | 0.118241i | ||||
\(989\) | 44.6592 | 1.42008 | ||||||||
\(990\) | 14.2264 | − | 11.6092i | 0.452145 | − | 0.368963i | ||||
\(991\) | −19.0174 | + | 19.0174i | −0.604108 | + | 0.604108i | −0.941400 | − | 0.337292i | \(-0.890489\pi\) |
0.337292 | + | 0.941400i | \(0.390489\pi\) | |||||||
\(992\) | −1.48171 | + | 1.48171i | −0.0470443 | + | 0.0470443i | ||||
\(993\) | − | 45.0897i | − | 1.43088i | ||||||
\(994\) | −7.13237 | − | 7.13237i | −0.226225 | − | 0.226225i | ||||
\(995\) | −28.7775 | − | 2.91528i | −0.912309 | − | 0.0924207i | ||||
\(996\) | 9.27768 | 0.293974 | ||||||||
\(997\) | − | 28.6699i | − | 0.907984i | −0.891006 | − | 0.453992i | \(-0.849999\pi\) | ||
0.891006 | − | 0.453992i | \(-0.150001\pi\) | |||||||
\(998\) | −17.1758 | − | 17.1758i | −0.543690 | − | 0.543690i | ||||
\(999\) | 2.08887 | − | 2.23771i | 0.0660889 | − | 0.0707979i |
(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 | 370.2.h.d.117.1 | yes | 10 | |
5.3 | odd | 4 | 370.2.g.d.43.5 | ✓ | 10 | ||
37.31 | odd | 4 | 370.2.g.d.327.5 | yes | 10 | ||
185.68 | even | 4 | inner | 370.2.h.d.253.1 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.d.43.5 | ✓ | 10 | 5.3 | odd | 4 | ||
370.2.g.d.327.5 | yes | 10 | 37.31 | odd | 4 | ||
370.2.h.d.117.1 | yes | 10 | 1.1 | even | 1 | trivial | |
370.2.h.d.253.1 | yes | 10 | 185.68 | even | 4 | inner |