Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(99,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.u (of order \(18\), degree \(6\), not 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 549.6 | ||
Character | \(\chi\) | \(=\) | 950.549 |
Dual form | 950.2.u.g.199.6 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.984808 | + | 0.173648i | 0.696364 | + | 0.122788i | ||||
\(3\) | 1.49114 | − | 1.77707i | 0.860909 | − | 1.02599i | −0.138456 | − | 0.990369i | \(-0.544214\pi\) |
0.999365 | − | 0.0356229i | \(-0.0113415\pi\) | |||||||
\(4\) | 0.939693 | + | 0.342020i | 0.469846 | + | 0.171010i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.77707 | − | 1.49114i | 0.725486 | − | 0.608755i | ||||
\(7\) | 4.25802 | − | 2.45837i | 1.60938 | − | 0.929177i | 0.619873 | − | 0.784702i | \(-0.287184\pi\) |
0.989508 | − | 0.144475i | \(-0.0461494\pi\) | |||||||
\(8\) | 0.866025 | + | 0.500000i | 0.306186 | + | 0.176777i | ||||
\(9\) | −0.413538 | − | 2.34529i | −0.137846 | − | 0.781763i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.42329 | + | 2.46520i | −0.429137 | + | 0.743287i | −0.996797 | − | 0.0799763i | \(-0.974516\pi\) |
0.567660 | + | 0.823263i | \(0.307849\pi\) | |||||||
\(12\) | 2.00901 | − | 1.15990i | 0.579950 | − | 0.334834i | ||||
\(13\) | −4.21784 | − | 5.02662i | −1.16982 | − | 1.39413i | −0.902590 | − | 0.430500i | \(-0.858337\pi\) |
−0.267227 | − | 0.963634i | \(-0.586107\pi\) | |||||||
\(14\) | 4.62023 | − | 1.68163i | 1.23481 | − | 0.449433i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.766044 | + | 0.642788i | 0.191511 | + | 0.160697i | ||||
\(17\) | 2.15794 | + | 0.380503i | 0.523377 | + | 0.0922855i | 0.429094 | − | 0.903260i | \(-0.358833\pi\) |
0.0942832 | + | 0.995545i | \(0.469944\pi\) | |||||||
\(18\) | − | 2.38147i | − | 0.561317i | ||||||
\(19\) | −4.17271 | + | 1.26036i | −0.957285 | + | 0.289146i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.98061 | − | 11.2326i | 0.432204 | − | 2.45115i | ||||
\(22\) | −1.82974 | + | 2.18060i | −0.390102 | + | 0.464906i | ||||
\(23\) | −0.908934 | + | 2.49728i | −0.189526 | + | 0.520718i | −0.997667 | − | 0.0682711i | \(-0.978252\pi\) |
0.808141 | + | 0.588989i | \(0.200474\pi\) | |||||||
\(24\) | 2.17990 | − | 0.793418i | 0.444970 | − | 0.161956i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.28089 | − | 5.68268i | −0.643436 | − | 1.11446i | ||||
\(27\) | 1.24263 | + | 0.717435i | 0.239145 | + | 0.138070i | ||||
\(28\) | 4.84205 | − | 0.853783i | 0.915061 | − | 0.161350i | ||||
\(29\) | 1.32004 | + | 7.48630i | 0.245125 | + | 1.39017i | 0.820203 | + | 0.572072i | \(0.193860\pi\) |
−0.575079 | + | 0.818098i | \(0.695029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.70769 | + | 4.68986i | 0.486316 | + | 0.842324i | 0.999876 | − | 0.0157295i | \(-0.00500705\pi\) |
−0.513560 | + | 0.858054i | \(0.671674\pi\) | |||||||
\(32\) | 0.642788 | + | 0.766044i | 0.113630 | + | 0.135419i | ||||
\(33\) | 2.25852 | + | 6.20524i | 0.393158 | + | 1.08019i | ||||
\(34\) | 2.05908 | + | 0.749444i | 0.353130 | + | 0.128529i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.413538 | − | 2.34529i | 0.0689229 | − | 0.390881i | ||||
\(37\) | 2.06252i | 0.339076i | 0.985524 | + | 0.169538i | \(0.0542276\pi\) | ||||
−0.985524 | + | 0.169538i | \(0.945772\pi\) | |||||||
\(38\) | −4.32817 | + | 0.516628i | −0.702123 | + | 0.0838081i | ||||
\(39\) | −15.2220 | −2.43748 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.16810 | − | 6.01475i | −1.11947 | − | 0.939346i | −0.120892 | − | 0.992666i | \(-0.538575\pi\) |
−0.998578 | + | 0.0533193i | \(0.983020\pi\) | |||||||
\(42\) | 3.90103 | − | 10.7180i | 0.601942 | − | 1.65382i | ||||
\(43\) | −0.593093 | − | 1.62951i | −0.0904459 | − | 0.248498i | 0.886219 | − | 0.463266i | \(-0.153323\pi\) |
−0.976665 | + | 0.214768i | \(0.931100\pi\) | |||||||
\(44\) | −2.18060 | + | 1.82974i | −0.328738 | + | 0.275844i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.32877 | + | 2.30150i | −0.195917 | + | 0.339338i | ||||
\(47\) | −2.95934 | + | 0.521812i | −0.431664 | + | 0.0761140i | −0.385259 | − | 0.922809i | \(-0.625888\pi\) |
−0.0464056 | + | 0.998923i | \(0.514777\pi\) | |||||||
\(48\) | 2.28456 | − | 0.402829i | 0.329747 | − | 0.0581433i | ||||
\(49\) | 8.58718 | − | 14.8734i | 1.22674 | − | 2.12478i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.89396 | − | 3.26742i | 0.545264 | − | 0.457531i | ||||
\(52\) | −2.24426 | − | 6.16606i | −0.311223 | − | 0.855079i | ||||
\(53\) | −1.44406 | + | 3.96752i | −0.198357 | + | 0.544981i | −0.998495 | − | 0.0548340i | \(-0.982537\pi\) |
0.800139 | + | 0.599815i | \(0.204759\pi\) | |||||||
\(54\) | 1.09917 | + | 0.922316i | 0.149579 | + | 0.125511i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.91674 | 0.657027 | ||||||||
\(57\) | −3.98234 | + | 9.29456i | −0.527474 | + | 1.23109i | ||||
\(58\) | 7.60179i | 0.998163i | ||||||||
\(59\) | 0.167500 | − | 0.949937i | 0.0218066 | − | 0.123671i | −0.971961 | − | 0.235141i | \(-0.924445\pi\) |
0.993768 | + | 0.111470i | \(0.0355559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.04727 | + | 2.56500i | 0.902311 | + | 0.328414i | 0.751178 | − | 0.660099i | \(-0.229486\pi\) |
0.151132 | + | 0.988514i | \(0.451708\pi\) | |||||||
\(62\) | 1.85217 | + | 5.08880i | 0.235226 | + | 0.646278i | ||||
\(63\) | −7.52644 | − | 8.96967i | −0.948243 | − | 1.13007i | ||||
\(64\) | 0.500000 | + | 0.866025i | 0.0625000 | + | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.14668 | + | 6.50315i | 0.141147 | + | 0.800483i | ||||
\(67\) | 1.89039 | − | 0.333326i | 0.230948 | − | 0.0407223i | −0.0569765 | − | 0.998376i | \(-0.518146\pi\) |
0.287924 | + | 0.957653i | \(0.407035\pi\) | |||||||
\(68\) | 1.89766 | + | 1.09561i | 0.230125 | + | 0.132863i | ||||
\(69\) | 3.08249 | + | 5.33902i | 0.371088 | + | 0.642743i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.79354 | − | 2.10868i | 0.687567 | − | 0.250254i | 0.0254738 | − | 0.999675i | \(-0.491891\pi\) |
0.662093 | + | 0.749422i | \(0.269668\pi\) | |||||||
\(72\) | 0.814510 | − | 2.23785i | 0.0959909 | − | 0.263733i | ||||
\(73\) | 2.55639 | − | 3.04659i | 0.299203 | − | 0.356576i | −0.595407 | − | 0.803424i | \(-0.703009\pi\) |
0.894610 | + | 0.446848i | \(0.147454\pi\) | |||||||
\(74\) | −0.358153 | + | 2.03119i | −0.0416344 | + | 0.236121i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.35213 | − | 0.242800i | −0.499224 | − | 0.0278511i | ||||
\(77\) | 13.9959i | 1.59498i | ||||||||
\(78\) | −14.9908 | − | 2.64328i | −1.69737 | − | 0.299292i | ||||
\(79\) | −11.7380 | − | 9.84938i | −1.32063 | − | 1.10814i | −0.986171 | − | 0.165732i | \(-0.947001\pi\) |
−0.334461 | − | 0.942409i | \(-0.608554\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.84141 | − | 3.58198i | 1.09349 | − | 0.397998i | ||||
\(82\) | −6.01475 | − | 7.16810i | −0.664218 | − | 0.791584i | ||||
\(83\) | −1.13628 | + | 0.656032i | −0.124723 | + | 0.0720089i | −0.561064 | − | 0.827773i | \(-0.689608\pi\) |
0.436340 | + | 0.899782i | \(0.356274\pi\) | |||||||
\(84\) | 5.70293 | − | 9.87776i | 0.622240 | − | 1.07775i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.301121 | − | 1.70774i | −0.0324708 | − | 0.184151i | ||||
\(87\) | 15.2720 | + | 8.81731i | 1.63733 | + | 0.945315i | ||||
\(88\) | −2.46520 | + | 1.42329i | −0.262792 | + | 0.151723i | ||||
\(89\) | 8.25512 | − | 6.92687i | 0.875041 | − | 0.734247i | −0.0901123 | − | 0.995932i | \(-0.528723\pi\) |
0.965153 | + | 0.261685i | \(0.0842782\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −30.3170 | − | 11.0345i | −3.17808 | − | 1.15673i | ||||
\(92\) | −1.70824 | + | 2.03580i | −0.178096 | + | 0.212247i | ||||
\(93\) | 12.3718 | + | 2.18147i | 1.28289 | + | 0.226208i | ||||
\(94\) | −3.00499 | −0.309941 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.31980 | 0.236764 | ||||||||
\(97\) | −2.02308 | − | 0.356724i | −0.205413 | − | 0.0362198i | 0.0699948 | − | 0.997547i | \(-0.477702\pi\) |
−0.275408 | + | 0.961328i | \(0.588813\pi\) | |||||||
\(98\) | 11.0395 | − | 13.1563i | 1.11515 | − | 1.32899i | ||||
\(99\) | 6.37020 | + | 2.31856i | 0.640229 | + | 0.233024i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.83762 | + | 3.22015i | −0.381857 | + | 0.320416i | −0.813431 | − | 0.581661i | \(-0.802403\pi\) |
0.431574 | + | 0.902078i | \(0.357959\pi\) | |||||||
\(102\) | 4.40219 | − | 2.54161i | 0.435882 | − | 0.251656i | ||||
\(103\) | 7.82444 | + | 4.51744i | 0.770965 | + | 0.445117i | 0.833219 | − | 0.552943i | \(-0.186495\pi\) |
−0.0622537 | + | 0.998060i | \(0.519829\pi\) | |||||||
\(104\) | −1.13944 | − | 6.46210i | −0.111732 | − | 0.633661i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.11108 | + | 3.65649i | −0.205046 | + | 0.355150i | ||||
\(107\) | −5.16829 | + | 2.98391i | −0.499637 | + | 0.288466i | −0.728564 | − | 0.684978i | \(-0.759812\pi\) |
0.228926 | + | 0.973444i | \(0.426478\pi\) | |||||||
\(108\) | 0.922316 | + | 1.09917i | 0.0887499 | + | 0.105768i | ||||
\(109\) | −14.8753 | + | 5.41417i | −1.42480 | + | 0.518583i | −0.935435 | − | 0.353499i | \(-0.884992\pi\) |
−0.489360 | + | 0.872082i | \(0.662770\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.66524 | + | 3.07550i | 0.347889 | + | 0.291914i | ||||
\(112\) | 4.84205 | + | 0.853783i | 0.457530 | + | 0.0806750i | ||||
\(113\) | 18.2051i | 1.71259i | 0.516485 | + | 0.856296i | \(0.327240\pi\) | ||||
−0.516485 | + | 0.856296i | \(0.672760\pi\) | |||||||
\(114\) | −5.53582 | + | 8.46183i | −0.518477 | + | 0.792523i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.32004 | + | 7.48630i | −0.122562 | + | 0.695085i | ||||
\(117\) | −10.0446 | + | 11.9707i | −0.928628 | + | 1.10670i | ||||
\(118\) | 0.329910 | − | 0.906420i | 0.0303707 | − | 0.0834427i | ||||
\(119\) | 10.1240 | − | 3.68482i | 0.928063 | − | 0.337787i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.44851 | + | 2.50890i | 0.131683 | + | 0.228082i | ||||
\(122\) | 6.49480 | + | 3.74977i | 0.588012 | + | 0.339489i | ||||
\(123\) | −21.3773 | + | 3.76939i | −1.92752 | + | 0.339874i | ||||
\(124\) | 0.940372 | + | 5.33311i | 0.0844479 | + | 0.478928i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.85453 | − | 10.1404i | −0.521563 | − | 0.903374i | ||||
\(127\) | −4.91703 | − | 5.85989i | −0.436316 | − | 0.519981i | 0.502418 | − | 0.864625i | \(-0.332444\pi\) |
−0.938733 | + | 0.344644i | \(0.888000\pi\) | |||||||
\(128\) | 0.342020 | + | 0.939693i | 0.0302306 | + | 0.0830579i | ||||
\(129\) | −3.78014 | − | 1.37586i | −0.332823 | − | 0.121137i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.31209 | + | 13.1125i | −0.202008 | + | 1.14564i | 0.700071 | + | 0.714073i | \(0.253152\pi\) |
−0.902079 | + | 0.431571i | \(0.857960\pi\) | |||||||
\(132\) | 6.60347i | 0.574759i | ||||||||
\(133\) | −14.6691 | + | 15.6247i | −1.27197 | + | 1.35483i | ||||
\(134\) | 1.91955 | 0.165824 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.67858 | + | 1.40849i | 0.143937 | + | 0.120777i | ||||
\(137\) | 2.47153 | − | 6.79047i | 0.211157 | − | 0.580149i | −0.788222 | − | 0.615391i | \(-0.788998\pi\) |
0.999379 | + | 0.0352423i | \(0.0112203\pi\) | |||||||
\(138\) | 2.10854 | + | 5.79318i | 0.179491 | + | 0.493148i | ||||
\(139\) | 1.84752 | − | 1.55026i | 0.156705 | − | 0.131491i | −0.561064 | − | 0.827772i | \(-0.689608\pi\) |
0.717769 | + | 0.696281i | \(0.245163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.48549 | + | 6.03705i | −0.293531 | + | 0.508411i | ||||
\(142\) | 6.07169 | − | 1.07060i | 0.509525 | − | 0.0898430i | ||||
\(143\) | 18.3948 | − | 3.24351i | 1.53825 | − | 0.271236i | ||||
\(144\) | 1.19073 | − | 2.06241i | 0.0992279 | − | 0.171868i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.04659 | − | 2.55639i | 0.252137 | − | 0.211568i | ||||
\(147\) | −13.6264 | − | 37.4384i | −1.12389 | − | 3.08786i | ||||
\(148\) | −0.705424 | + | 1.93814i | −0.0579855 | + | 0.159314i | ||||
\(149\) | 5.34602 | + | 4.48584i | 0.437963 | + | 0.367495i | 0.834946 | − | 0.550331i | \(-0.185499\pi\) |
−0.396983 | + | 0.917826i | \(0.629943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.69362 | −0.463340 | −0.231670 | − | 0.972794i | \(-0.574419\pi\) | ||||
−0.231670 | + | 0.972794i | \(0.574419\pi\) | |||||||
\(152\) | −4.24385 | − | 0.994851i | −0.344222 | − | 0.0806931i | ||||
\(153\) | − | 5.21834i | − | 0.421878i | ||||||
\(154\) | −2.43036 | + | 13.7832i | −0.195844 | + | 1.11068i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −14.3040 | − | 5.20624i | −1.14524 | − | 0.416833i | ||||
\(157\) | −1.81744 | − | 4.99337i | −0.145047 | − | 0.398514i | 0.845800 | − | 0.533500i | \(-0.179123\pi\) |
−0.990848 | + | 0.134985i | \(0.956901\pi\) | |||||||
\(158\) | −9.84938 | − | 11.7380i | −0.783575 | − | 0.933828i | ||||
\(159\) | 4.89727 | + | 8.48232i | 0.388379 | + | 0.672692i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.26897 | + | 12.8680i | 0.178820 | + | 1.01414i | ||||
\(162\) | 10.3139 | − | 1.81862i | 0.810337 | − | 0.142884i | ||||
\(163\) | 3.87424 | + | 2.23679i | 0.303454 | + | 0.175199i | 0.643993 | − | 0.765031i | \(-0.277276\pi\) |
−0.340540 | + | 0.940230i | \(0.610610\pi\) | |||||||
\(164\) | −4.67865 | − | 8.10365i | −0.365341 | − | 0.632789i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.23294 | + | 0.448753i | −0.0956945 | + | 0.0348300i | ||||
\(167\) | −1.24795 | + | 3.42872i | −0.0965694 | + | 0.265322i | −0.978566 | − | 0.205934i | \(-0.933977\pi\) |
0.881997 | + | 0.471256i | \(0.156199\pi\) | |||||||
\(168\) | 7.33154 | − | 8.73739i | 0.565641 | − | 0.674104i | ||||
\(169\) | −5.21936 | + | 29.6004i | −0.401489 | + | 2.27696i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.68148 | + | 9.26500i | 0.358002 | + | 0.708512i | ||||
\(172\) | − | 1.73409i | − | 0.132223i | ||||||
\(173\) | −1.15844 | − | 0.204264i | −0.0880746 | − | 0.0155299i | 0.129437 | − | 0.991588i | \(-0.458683\pi\) |
−0.217512 | + | 0.976058i | \(0.569794\pi\) | |||||||
\(174\) | 13.5089 | + | 11.3353i | 1.02411 | + | 0.859328i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.67490 | + | 0.973585i | −0.201628 | + | 0.0733867i | ||||
\(177\) | −1.43834 | − | 1.71415i | −0.108112 | − | 0.128843i | ||||
\(178\) | 9.33254 | − | 5.38815i | 0.699504 | − | 0.403859i | ||||
\(179\) | 2.16529 | − | 3.75038i | 0.161841 | − | 0.280317i | −0.773688 | − | 0.633567i | \(-0.781590\pi\) |
0.935529 | + | 0.353250i | \(0.114923\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.237758 | + | 1.34839i | 0.0176724 | + | 0.100225i | 0.992368 | − | 0.123311i | \(-0.0393511\pi\) |
−0.974696 | + | 0.223536i | \(0.928240\pi\) | |||||||
\(182\) | −27.9403 | − | 16.1313i | −2.07107 | − | 1.19573i | ||||
\(183\) | 15.0666 | − | 8.69872i | 1.11376 | − | 0.643028i | ||||
\(184\) | −2.03580 | + | 1.70824i | −0.150081 | + | 0.125933i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.8050 | + | 4.29667i | 0.865584 | + | 0.315047i | ||||
\(187\) | −4.00938 | + | 4.77819i | −0.293195 | + | 0.349416i | ||||
\(188\) | −2.95934 | − | 0.521812i | −0.215832 | − | 0.0380570i | ||||
\(189\) | 7.05488 | 0.513167 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6338 | 0.986505 | 0.493252 | − | 0.869886i | \(-0.335808\pi\) | ||||
0.493252 | + | 0.869886i | \(0.335808\pi\) | |||||||
\(192\) | 2.28456 | + | 0.402829i | 0.164874 | + | 0.0290717i | ||||
\(193\) | 3.35501 | − | 3.99835i | 0.241499 | − | 0.287807i | −0.631657 | − | 0.775248i | \(-0.717625\pi\) |
0.873156 | + | 0.487441i | \(0.162069\pi\) | |||||||
\(194\) | −1.93040 | − | 0.702609i | −0.138595 | − | 0.0504444i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.1563 | − | 11.0395i | 0.939737 | − | 0.788533i | ||||
\(197\) | −2.47286 | + | 1.42771i | −0.176184 | + | 0.101720i | −0.585498 | − | 0.810674i | \(-0.699101\pi\) |
0.409315 | + | 0.912393i | \(0.365768\pi\) | |||||||
\(198\) | 5.87080 | + | 3.38951i | 0.417220 | + | 0.240882i | ||||
\(199\) | 0.254330 | + | 1.44238i | 0.0180290 | + | 0.102247i | 0.992494 | − | 0.122290i | \(-0.0390239\pi\) |
−0.974465 | + | 0.224538i | \(0.927913\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.22649 | − | 3.85639i | 0.157044 | − | 0.272009i | ||||
\(202\) | −4.33849 | + | 2.50483i | −0.305255 | + | 0.176239i | ||||
\(203\) | 24.0248 | + | 28.6317i | 1.68621 | + | 2.00955i | ||||
\(204\) | 4.77666 | − | 1.73856i | 0.334433 | − | 0.121724i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.92112 | + | 5.80751i | 0.482218 | + | 0.404629i | ||||
\(207\) | 6.23271 | + | 1.09900i | 0.433203 | + | 0.0763855i | ||||
\(208\) | − | 6.56179i | − | 0.454978i | ||||||
\(209\) | 2.83192 | − | 12.0804i | 0.195888 | − | 0.835621i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.227567 | − | 1.29059i | 0.0156663 | − | 0.0888482i | −0.975972 | − | 0.217896i | \(-0.930081\pi\) |
0.991638 | + | 0.129047i | \(0.0411919\pi\) | |||||||
\(212\) | −2.71395 | + | 3.23435i | −0.186395 | + | 0.222136i | ||||
\(213\) | 4.89171 | − | 13.4399i | 0.335174 | − | 0.920883i | ||||
\(214\) | −5.60792 | + | 2.04112i | −0.383350 | + | 0.139528i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.717435 | + | 1.24263i | 0.0488152 | + | 0.0845505i | ||||
\(217\) | 23.0588 | + | 13.3130i | 1.56534 | + | 0.903747i | ||||
\(218\) | −15.5895 | + | 2.74884i | −1.05585 | + | 0.186175i | ||||
\(219\) | −1.60206 | − | 9.08576i | −0.108257 | − | 0.613959i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.18919 | − | 12.4520i | −0.483597 | − | 0.837615i | ||||
\(222\) | 3.07550 | + | 3.66524i | 0.206414 | + | 0.245995i | ||||
\(223\) | −9.62115 | − | 26.4339i | −0.644280 | − | 1.77014i | −0.637846 | − | 0.770164i | \(-0.720174\pi\) |
−0.00643379 | − | 0.999979i | \(-0.502048\pi\) | |||||||
\(224\) | 4.62023 | + | 1.68163i | 0.308702 | + | 0.112358i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.16128 | + | 17.9285i | −0.210285 | + | 1.19259i | ||||
\(227\) | − | 12.6466i | − | 0.839382i | −0.907667 | − | 0.419691i | \(-0.862138\pi\) | ||
0.907667 | − | 0.419691i | \(-0.137862\pi\) | |||||||
\(228\) | −6.92110 | + | 7.37199i | −0.458361 | + | 0.488222i | ||||
\(229\) | −13.7440 | −0.908227 | −0.454113 | − | 0.890944i | \(-0.650044\pi\) | ||||
−0.454113 | + | 0.890944i | \(0.650044\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.8716 | + | 20.8698i | 1.63643 | + | 1.37313i | ||||
\(232\) | −2.59996 | + | 7.14334i | −0.170696 | + | 0.468983i | ||||
\(233\) | −8.41990 | − | 23.1335i | −0.551606 | − | 1.51552i | −0.831517 | − | 0.555499i | \(-0.812527\pi\) |
0.279911 | − | 0.960026i | \(-0.409695\pi\) | |||||||
\(234\) | −11.9707 | + | 10.0446i | −0.782552 | + | 0.656639i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.482296 | − | 0.835361i | 0.0313948 | − | 0.0543774i | ||||
\(237\) | −35.0061 | + | 6.17251i | −2.27389 | + | 0.400948i | ||||
\(238\) | 10.6100 | − | 1.87083i | 0.687746 | − | 0.121268i | ||||
\(239\) | −8.14698 | + | 14.1110i | −0.526984 | + | 0.912763i | 0.472522 | + | 0.881319i | \(0.343344\pi\) |
−0.999506 | + | 0.0314439i | \(0.989989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.7500 | + | 12.3767i | −0.950133 | + | 0.797256i | −0.979320 | − | 0.202318i | \(-0.935153\pi\) |
0.0291873 | + | 0.999574i | \(0.490708\pi\) | |||||||
\(242\) | 0.990842 | + | 2.72232i | 0.0636938 | + | 0.174997i | ||||
\(243\) | 6.83722 | − | 18.7851i | 0.438608 | − | 1.20506i | ||||
\(244\) | 5.74499 | + | 4.82062i | 0.367785 | + | 0.308608i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −21.7070 | −1.38399 | ||||||||
\(247\) | 23.9351 | + | 15.6586i | 1.52296 | + | 0.996335i | ||||
\(248\) | 5.41539i | 0.343877i | ||||||||
\(249\) | −0.528538 | + | 2.99749i | −0.0334947 | + | 0.189958i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.0953 | + | 9.49792i | 1.64712 | + | 0.599504i | 0.988263 | − | 0.152762i | \(-0.0488169\pi\) |
0.658860 | + | 0.752266i | \(0.271039\pi\) | |||||||
\(252\) | −4.00474 | − | 11.0029i | −0.252275 | − | 0.693119i | ||||
\(253\) | −4.86262 | − | 5.79505i | −0.305710 | − | 0.364331i | ||||
\(254\) | −3.82477 | − | 6.62470i | −0.239987 | − | 0.415671i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.173648 | + | 0.984808i | 0.0108530 | + | 0.0615505i | ||||
\(257\) | 12.8717 | − | 2.26963i | 0.802915 | − | 0.141576i | 0.242893 | − | 0.970053i | \(-0.421904\pi\) |
0.560022 | + | 0.828478i | \(0.310793\pi\) | |||||||
\(258\) | −3.48379 | − | 2.01137i | −0.216891 | − | 0.125222i | ||||
\(259\) | 5.07044 | + | 8.78226i | 0.315062 | + | 0.545703i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.0116 | − | 6.19173i | 1.05299 | − | 0.383259i | ||||
\(262\) | −4.55392 | + | 12.5118i | −0.281342 | + | 0.772981i | ||||
\(263\) | −9.67780 | + | 11.5336i | −0.596759 | + | 0.711190i | −0.976890 | − | 0.213743i | \(-0.931434\pi\) |
0.380131 | + | 0.924933i | \(0.375879\pi\) | |||||||
\(264\) | −1.14668 | + | 6.50315i | −0.0705734 | + | 0.400241i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −17.1594 | + | 12.8401i | −1.05211 | + | 0.787276i | ||||
\(267\) | − | 24.9988i | − | 1.52990i | ||||||
\(268\) | 1.89039 | + | 0.333326i | 0.115474 | + | 0.0203612i | ||||
\(269\) | −18.7339 | − | 15.7196i | −1.14222 | − | 0.958439i | −0.142714 | − | 0.989764i | \(-0.545583\pi\) |
−0.999509 | + | 0.0313248i | \(0.990027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.41094 | + | 3.06133i | −0.510928 | + | 0.185963i | −0.584603 | − | 0.811320i | \(-0.698750\pi\) |
0.0736745 | + | 0.997282i | \(0.476527\pi\) | |||||||
\(272\) | 1.40849 | + | 1.67858i | 0.0854025 | + | 0.101779i | ||||
\(273\) | −64.8158 | + | 37.4214i | −3.92283 | + | 2.26485i | ||||
\(274\) | 3.61313 | − | 6.25813i | 0.218277 | − | 0.378067i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.07054 | + | 6.07131i | 0.0644387 | + | 0.365450i | ||||
\(277\) | −6.75622 | − | 3.90071i | −0.405942 | − | 0.234371i | 0.283103 | − | 0.959090i | \(-0.408636\pi\) |
−0.689045 | + | 0.724719i | \(0.741970\pi\) | |||||||
\(278\) | 2.08866 | − | 1.20589i | 0.125269 | − | 0.0723242i | ||||
\(279\) | 9.87935 | − | 8.28976i | 0.591461 | − | 0.496295i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.1947 | − | 6.25837i | −1.02575 | − | 0.373343i | −0.226290 | − | 0.974060i | \(-0.572660\pi\) |
−0.799462 | + | 0.600717i | \(0.794882\pi\) | |||||||
\(282\) | −4.48086 | + | 5.34008i | −0.266831 | + | 0.317997i | ||||
\(283\) | 7.11822 | + | 1.25513i | 0.423134 | + | 0.0746100i | 0.381161 | − | 0.924509i | \(-0.375524\pi\) |
0.0419735 | + | 0.999119i | \(0.486635\pi\) | |||||||
\(284\) | 6.16536 | 0.365847 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.6786 | 1.10449 | ||||||||
\(287\) | −45.3084 | − | 7.98910i | −2.67447 | − | 0.471582i | ||||
\(288\) | 1.53078 | − | 1.82431i | 0.0902020 | − | 0.107499i | ||||
\(289\) | −11.4629 | − | 4.17214i | −0.674286 | − | 0.245420i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.65062 | + | 3.06323i | −0.214003 | + | 0.179570i | ||||
\(292\) | 3.44421 | − | 1.98852i | 0.201557 | − | 0.116369i | ||||
\(293\) | −9.86109 | − | 5.69330i | −0.576091 | − | 0.332606i | 0.183488 | − | 0.983022i | \(-0.441261\pi\) |
−0.759578 | + | 0.650416i | \(0.774595\pi\) | |||||||
\(294\) | −6.91833 | − | 39.2358i | −0.403485 | − | 2.28828i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.03126 | + | 1.78620i | −0.0599408 | + | 0.103821i | ||||
\(297\) | −3.53724 | + | 2.04223i | −0.205252 | + | 0.118502i | ||||
\(298\) | 4.48584 | + | 5.34602i | 0.259858 | + | 0.309687i | ||||
\(299\) | 16.3866 | − | 5.96423i | 0.947662 | − | 0.344921i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.53135 | − | 5.48045i | −0.376461 | − | 0.315888i | ||||
\(302\) | −5.60712 | − | 0.988686i | −0.322653 | − | 0.0568925i | ||||
\(303\) | 11.6214i | 0.667632i | ||||||||
\(304\) | −4.00662 | − | 1.71667i | −0.229796 | − | 0.0984580i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.906156 | − | 5.13906i | 0.0518015 | − | 0.293781i | ||||
\(307\) | 3.17725 | − | 3.78649i | 0.181335 | − | 0.216107i | −0.667718 | − | 0.744414i | \(-0.732729\pi\) |
0.849053 | + | 0.528308i | \(0.177173\pi\) | |||||||
\(308\) | −4.78687 | + | 13.1518i | −0.272757 | + | 0.749394i | ||||
\(309\) | 19.6951 | − | 7.16844i | 1.12042 | − | 0.407798i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0586 | − | 20.8861i | −0.683782 | − | 1.18434i | −0.973818 | − | 0.227329i | \(-0.927001\pi\) |
0.290036 | − | 0.957016i | \(-0.406333\pi\) | |||||||
\(312\) | −13.1827 | − | 7.61102i | −0.746322 | − | 0.430889i | ||||
\(313\) | 30.5050 | − | 5.37886i | 1.72424 | − | 0.304031i | 0.778188 | − | 0.628031i | \(-0.216139\pi\) |
0.946057 | + | 0.324001i | \(0.105028\pi\) | |||||||
\(314\) | −0.922737 | − | 5.23310i | −0.0520731 | − | 0.295321i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.66146 | − | 13.2700i | −0.430991 | − | 0.746498i | ||||
\(317\) | 4.44201 | + | 5.29378i | 0.249488 | + | 0.297328i | 0.876225 | − | 0.481903i | \(-0.160054\pi\) |
−0.626737 | + | 0.779231i | \(0.715610\pi\) | |||||||
\(318\) | 3.34993 | + | 9.20386i | 0.187855 | + | 0.516127i | ||||
\(319\) | −20.3340 | − | 7.40098i | −1.13849 | − | 0.414376i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.40401 | + | 13.6338i | −0.134179 | + | 0.760966i | ||||
\(322\) | 13.0665i | 0.728166i | ||||||||
\(323\) | −9.48402 | + | 1.13205i | −0.527705 | + | 0.0629890i | ||||
\(324\) | 10.4730 | 0.581834 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.42697 | + | 2.87557i | 0.189802 | + | 0.159263i | ||||
\(327\) | −12.5598 | + | 34.5077i | −0.694557 | + | 1.90828i | ||||
\(328\) | −3.20038 | − | 8.79298i | −0.176712 | − | 0.485511i | ||||
\(329\) | −11.3181 | + | 9.49705i | −0.623989 | + | 0.523589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.08943 | + | 3.61900i | −0.114845 | + | 0.198918i | −0.917718 | − | 0.397233i | \(-0.869971\pi\) |
0.802873 | + | 0.596151i | \(0.203304\pi\) | |||||||
\(332\) | −1.29213 | + | 0.227838i | −0.0709149 | + | 0.0125042i | ||||
\(333\) | 4.83721 | − | 0.852930i | 0.265077 | − | 0.0467403i | ||||
\(334\) | −1.82438 | + | 3.15992i | −0.0998258 | + | 0.172903i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.73739 | − | 7.33154i | 0.476664 | − | 0.399968i | ||||
\(337\) | 5.88315 | + | 16.1638i | 0.320476 | + | 0.880500i | 0.990420 | + | 0.138088i | \(0.0440958\pi\) |
−0.669944 | + | 0.742411i | \(0.733682\pi\) | |||||||
\(338\) | −10.2801 | + | 28.2444i | −0.559165 | + | 1.53629i | ||||
\(339\) | 32.3517 | + | 27.1463i | 1.75710 | + | 1.47439i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.4153 | −0.834784 | ||||||||
\(342\) | 3.00151 | + | 9.93717i | 0.162303 | + | 0.537341i | ||||
\(343\) | − | 50.0247i | − | 2.70108i | ||||||
\(344\) | 0.301121 | − | 1.70774i | 0.0162354 | − | 0.0920754i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.10537 | − | 0.402322i | −0.0594251 | − | 0.0216290i | ||||
\(347\) | 6.31466 | + | 17.3494i | 0.338989 | + | 0.931364i | 0.985682 | + | 0.168614i | \(0.0539291\pi\) |
−0.646693 | + | 0.762750i | \(0.723849\pi\) | |||||||
\(348\) | 11.3353 | + | 13.5089i | 0.607637 | + | 0.724153i | ||||
\(349\) | 12.3704 | + | 21.4262i | 0.662174 | + | 1.14692i | 0.980043 | + | 0.198784i | \(0.0636992\pi\) |
−0.317870 | + | 0.948134i | \(0.602967\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.63495 | − | 9.27227i | −0.0872672 | − | 0.494917i | ||||
\(352\) | −2.80333 | + | 0.494302i | −0.149418 | + | 0.0263464i | ||||
\(353\) | 5.55115 | + | 3.20496i | 0.295458 | + | 0.170583i | 0.640401 | − | 0.768041i | \(-0.278768\pi\) |
−0.344943 | + | 0.938624i | \(0.612102\pi\) | |||||||
\(354\) | −1.11883 | − | 1.93787i | −0.0594651 | − | 0.102997i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.1264 | − | 3.68571i | 0.536698 | − | 0.195342i | ||||
\(357\) | 8.54805 | − | 23.4856i | 0.452411 | − | 1.24299i | ||||
\(358\) | 2.78364 | − | 3.31741i | 0.147120 | − | 0.175331i | ||||
\(359\) | 6.39293 | − | 36.2561i | 0.337406 | − | 1.91353i | −0.0646449 | − | 0.997908i | \(-0.520591\pi\) |
0.402051 | − | 0.915617i | \(-0.368297\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.8230 | − | 10.5182i | 0.832789 | − | 0.553591i | ||||
\(362\) | 1.36920i | 0.0719633i | ||||||||
\(363\) | 6.61843 | + | 1.16701i | 0.347377 | + | 0.0612520i | ||||
\(364\) | −24.7146 | − | 20.7380i | −1.29540 | − | 1.08697i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 16.3483 | − | 5.95028i | 0.854537 | − | 0.311026i | ||||
\(367\) | −9.39999 | − | 11.2025i | −0.490676 | − | 0.584764i | 0.462714 | − | 0.886508i | \(-0.346876\pi\) |
−0.953389 | + | 0.301743i | \(0.902431\pi\) | |||||||
\(368\) | −2.30150 | + | 1.32877i | −0.119974 | + | 0.0692671i | ||||
\(369\) | −11.1420 | + | 19.2986i | −0.580032 | + | 1.00464i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.60480 | + | 20.4438i | 0.187152 | + | 1.06139i | ||||
\(372\) | 10.8795 | + | 6.28130i | 0.564078 | + | 0.325670i | ||||
\(373\) | −11.7411 | + | 6.77871i | −0.607930 | + | 0.350989i | −0.772155 | − | 0.635434i | \(-0.780821\pi\) |
0.164225 | + | 0.986423i | \(0.447488\pi\) | |||||||
\(374\) | −4.77819 | + | 4.00938i | −0.247075 | + | 0.207320i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.82377 | − | 1.02777i | −0.145625 | − | 0.0530031i | ||||
\(377\) | 32.0631 | − | 38.2113i | 1.65133 | − | 1.96798i | ||||
\(378\) | 6.94770 | + | 1.22507i | 0.357351 | + | 0.0630107i | ||||
\(379\) | −30.2899 | −1.55589 | −0.777944 | − | 0.628333i | \(-0.783738\pi\) | ||||
−0.777944 | + | 0.628333i | \(0.783738\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.7454 | −0.909124 | ||||||||
\(382\) | 13.4266 | + | 2.36748i | 0.686967 | + | 0.121131i | ||||
\(383\) | 18.4242 | − | 21.9571i | 0.941433 | − | 1.12196i | −0.0509425 | − | 0.998702i | \(-0.516223\pi\) |
0.992375 | − | 0.123254i | \(-0.0393330\pi\) | |||||||
\(384\) | 2.17990 | + | 0.793418i | 0.111242 | + | 0.0404889i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.99835 | − | 3.35501i | 0.203511 | − | 0.170766i | ||||
\(387\) | −3.57641 | + | 2.06484i | −0.181799 | + | 0.104962i | ||||
\(388\) | −1.77907 | − | 1.02715i | −0.0903186 | − | 0.0521454i | ||||
\(389\) | −2.97395 | − | 16.8661i | −0.150785 | − | 0.855145i | −0.962539 | − | 0.271145i | \(-0.912598\pi\) |
0.811754 | − | 0.584000i | \(-0.198513\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.91165 | + | 5.04312i | −0.147248 | + | 0.255041i | ||||
\(392\) | 14.8734 | − | 8.58718i | 0.751222 | − | 0.433718i | ||||
\(393\) | 19.8542 | + | 23.6613i | 1.00151 | + | 1.19355i | ||||
\(394\) | −2.68321 | + | 0.976608i | −0.135178 | + | 0.0492008i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.19303 | + | 4.35747i | 0.260960 | + | 0.218971i | ||||
\(397\) | −25.7084 | − | 4.53308i | −1.29027 | − | 0.227509i | −0.513932 | − | 0.857831i | \(-0.671812\pi\) |
−0.776334 | + | 0.630322i | \(0.782923\pi\) | |||||||
\(398\) | 1.46463i | 0.0734151i | ||||||||
\(399\) | 5.89259 | + | 49.3665i | 0.294998 | + | 2.47142i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.61683 | + | 9.16948i | −0.0807405 | + | 0.457902i | 0.917454 | + | 0.397841i | \(0.130241\pi\) |
−0.998195 | + | 0.0600607i | \(0.980871\pi\) | |||||||
\(402\) | 2.86232 | − | 3.41117i | 0.142759 | − | 0.170134i | ||||
\(403\) | 12.1536 | − | 33.3916i | 0.605412 | − | 1.66336i | ||||
\(404\) | −4.70754 | + | 1.71340i | −0.234209 | + | 0.0852450i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.6880 | + | 32.3686i | 0.927471 | + | 1.60643i | ||||
\(407\) | −5.08453 | − | 2.93556i | −0.252031 | − | 0.145510i | ||||
\(408\) | 5.00598 | − | 0.882690i | 0.247833 | − | 0.0436997i | ||||
\(409\) | −2.53175 | − | 14.3583i | −0.125187 | − | 0.709972i | −0.981196 | − | 0.193012i | \(-0.938175\pi\) |
0.856009 | − | 0.516960i | \(-0.172937\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.38174 | − | 14.5176i | −0.413441 | − | 0.716101i | ||||
\(412\) | 5.80751 | + | 6.92112i | 0.286116 | + | 0.340979i | ||||
\(413\) | −1.62208 | − | 4.45663i | −0.0798174 | − | 0.219297i | ||||
\(414\) | 5.94718 | + | 2.16460i | 0.292288 | + | 0.106384i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.13944 | − | 6.46210i | 0.0558658 | − | 0.316831i | ||||
\(417\) | − | 5.59483i | − | 0.273980i | ||||||
\(418\) | 4.88664 | − | 11.4051i | 0.239013 | − | 0.557844i | ||||
\(419\) | −14.5969 | −0.713103 | −0.356552 | − | 0.934276i | \(-0.616048\pi\) | ||||
−0.356552 | + | 0.934276i | \(0.616048\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.0605 | − | 25.2237i | −1.46506 | − | 1.22933i | −0.920580 | − | 0.390554i | \(-0.872283\pi\) |
−0.544478 | − | 0.838775i | \(-0.683272\pi\) | |||||||
\(422\) | 0.448219 | − | 1.23147i | 0.0218190 | − | 0.0599471i | ||||
\(423\) | 2.44760 | + | 6.72472i | 0.119006 | + | 0.326967i | ||||
\(424\) | −3.23435 | + | 2.71395i | −0.157074 | + | 0.131801i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.15120 | − | 12.3862i | 0.346477 | − | 0.600115i | ||||
\(427\) | 36.3132 | − | 6.40299i | 1.75732 | − | 0.309862i | ||||
\(428\) | −5.87716 | + | 1.03630i | −0.284083 | + | 0.0500916i | ||||
\(429\) | 21.6653 | − | 37.5254i | 1.04601 | − | 1.81174i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.7585 | − | 14.0620i | 0.807228 | − | 0.677345i | −0.142716 | − | 0.989764i | \(-0.545584\pi\) |
0.949944 | + | 0.312419i | \(0.101139\pi\) | |||||||
\(432\) | 0.490754 | + | 1.34834i | 0.0236114 | + | 0.0648718i | ||||
\(433\) | −0.376798 | + | 1.03524i | −0.0181078 | + | 0.0497507i | −0.948417 | − | 0.317025i | \(-0.897316\pi\) |
0.930309 | + | 0.366776i | \(0.119538\pi\) | |||||||
\(434\) | 20.3967 | + | 17.1149i | 0.979075 | + | 0.821542i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.8300 | −0.758118 | ||||||||
\(437\) | 0.645253 | − | 11.5660i | 0.0308666 | − | 0.553276i | ||||
\(438\) | − | 9.22592i | − | 0.440832i | ||||||
\(439\) | 0.732304 | − | 4.15310i | 0.0349510 | − | 0.198217i | −0.962333 | − | 0.271875i | \(-0.912356\pi\) |
0.997284 | + | 0.0736582i | \(0.0234674\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −38.4336 | − | 13.9887i | −1.83017 | − | 0.666128i | ||||
\(442\) | −4.91770 | − | 13.5113i | −0.233911 | − | 0.642665i | ||||
\(443\) | 4.87432 | + | 5.80899i | 0.231586 | + | 0.275993i | 0.869305 | − | 0.494275i | \(-0.164567\pi\) |
−0.637719 | + | 0.770269i | \(0.720122\pi\) | |||||||
\(444\) | 2.39232 | + | 4.14362i | 0.113534 | + | 0.196647i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.88478 | − | 27.7030i | −0.231301 | − | 1.31177i | ||||
\(447\) | 15.9433 | − | 2.81124i | 0.754093 | − | 0.132967i | ||||
\(448\) | 4.25802 | + | 2.45837i | 0.201173 | + | 0.116147i | ||||
\(449\) | 14.8487 | + | 25.7188i | 0.700756 | + | 1.21374i | 0.968202 | + | 0.250171i | \(0.0804870\pi\) |
−0.267446 | + | 0.963573i | \(0.586180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.0298 | − | 9.11012i | 1.17861 | − | 0.428979i | ||||
\(452\) | −6.22651 | + | 17.1072i | −0.292871 | + | 0.804655i | ||||
\(453\) | −8.48997 | + | 10.1180i | −0.398894 | + | 0.475383i | ||||
\(454\) | 2.19605 | − | 12.4544i | 0.103066 | − | 0.584515i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.09609 | + | 6.05816i | −0.379134 | + | 0.283699i | ||||
\(457\) | − | 9.12576i | − | 0.426885i | −0.976956 | − | 0.213442i | \(-0.931532\pi\) | ||
0.976956 | − | 0.213442i | \(-0.0684676\pi\) | |||||||
\(458\) | −13.5352 | − | 2.38661i | −0.632456 | − | 0.111519i | ||||
\(459\) | 2.40854 | + | 2.02101i | 0.112421 | + | 0.0943324i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.7943 | − | 9.02439i | 1.15479 | − | 0.420308i | 0.307554 | − | 0.951531i | \(-0.400490\pi\) |
0.847232 | + | 0.531223i | \(0.178267\pi\) | |||||||
\(462\) | 20.8698 | + | 24.8716i | 0.970949 | + | 1.15713i | ||||
\(463\) | −13.6156 | + | 7.86094i | −0.632768 | + | 0.365329i | −0.781823 | − | 0.623500i | \(-0.785710\pi\) |
0.149055 | + | 0.988829i | \(0.452377\pi\) | |||||||
\(464\) | −3.80089 | + | 6.58334i | −0.176452 | + | 0.305624i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.27489 | − | 24.2441i | −0.198031 | − | 1.12309i | ||||
\(467\) | −5.97499 | − | 3.44966i | −0.276490 | − | 0.159631i | 0.355344 | − | 0.934736i | \(-0.384364\pi\) |
−0.631833 | + | 0.775104i | \(0.717697\pi\) | |||||||
\(468\) | −13.5331 | + | 7.81335i | −0.625568 | + | 0.361172i | ||||
\(469\) | 7.22988 | − | 6.06659i | 0.333845 | − | 0.280129i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.5836 | − | 4.21609i | −0.533745 | − | 0.194267i | ||||
\(472\) | 0.620028 | − | 0.738920i | 0.0285391 | − | 0.0340116i | ||||
\(473\) | 4.86122 | + | 0.857164i | 0.223519 | + | 0.0394124i | ||||
\(474\) | −35.5461 | −1.63269 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.7737 | 0.493812 | ||||||||
\(477\) | 9.90216 | + | 1.74602i | 0.453389 | + | 0.0799447i | ||||
\(478\) | −10.4735 | + | 12.4819i | −0.479049 | + | 0.570908i | ||||
\(479\) | −3.42858 | − | 1.24790i | −0.156656 | − | 0.0570180i | 0.262502 | − | 0.964931i | \(-0.415452\pi\) |
−0.419158 | + | 0.907913i | \(0.637675\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.3675 | − | 8.69938i | 0.472718 | − | 0.396657i | ||||
\(482\) | −16.6751 | + | 9.62739i | −0.759532 | + | 0.438516i | ||||
\(483\) | 26.2506 | + | 15.1558i | 1.19444 | + | 0.689612i | ||||
\(484\) | 0.503064 | + | 2.85302i | 0.0228665 | + | 0.129683i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.99534 | − | 17.3124i | 0.453398 | − | 0.785308i | ||||
\(487\) | 19.4986 | − | 11.2575i | 0.883568 | − | 0.510128i | 0.0117346 | − | 0.999931i | \(-0.496265\pi\) |
0.871833 | + | 0.489803i | \(0.162931\pi\) | |||||||
\(488\) | 4.82062 | + | 5.74499i | 0.218219 | + | 0.260063i | ||||
\(489\) | 9.75196 | − | 3.54942i | 0.440999 | − | 0.160510i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.2746 | + | 16.1733i | 0.869849 | + | 0.729890i | 0.964066 | − | 0.265662i | \(-0.0855905\pi\) |
−0.0942175 | + | 0.995552i | \(0.530035\pi\) | |||||||
\(492\) | −21.3773 | − | 3.76939i | −0.963761 | − | 0.169937i | ||||
\(493\) | 16.6573i | 0.750205i | ||||||||
\(494\) | 20.8524 | + | 19.5770i | 0.938195 | + | 0.880813i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.940372 | + | 5.33311i | −0.0422239 | + | 0.239464i | ||||
\(497\) | 19.4851 | − | 23.2215i | 0.874027 | − | 1.04163i | ||||
\(498\) | −1.04102 | + | 2.86017i | −0.0466490 | + | 0.128167i | ||||
\(499\) | 29.8561 | − | 10.8667i | 1.33654 | − | 0.486461i | 0.427819 | − | 0.903864i | \(-0.359282\pi\) |
0.908721 | + | 0.417403i | \(0.137060\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.23220 | + | 7.33039i | 0.189081 | + | 0.327498i | ||||
\(502\) | 24.0496 | + | 13.8850i | 1.07339 | + | 0.619719i | ||||
\(503\) | 25.1737 | − | 4.43880i | 1.12244 | − | 0.197917i | 0.418528 | − | 0.908204i | \(-0.362546\pi\) |
0.703912 | + | 0.710287i | \(0.251435\pi\) | |||||||
\(504\) | −2.03326 | − | 11.5312i | −0.0905685 | − | 0.513640i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.78245 | − | 6.55139i | −0.168150 | − | 0.291245i | ||||
\(507\) | 44.8192 | + | 53.4135i | 1.99049 | + | 2.37218i | ||||
\(508\) | −2.61630 | − | 7.18822i | −0.116079 | − | 0.318926i | ||||
\(509\) | 9.28595 | + | 3.37981i | 0.411592 | + | 0.149807i | 0.539513 | − | 0.841977i | \(-0.318608\pi\) |
−0.127921 | + | 0.991784i | \(0.540830\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.39553 | − | 19.2570i | 0.150209 | − | 0.851879i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −6.08937 | − | 1.42748i | −0.268852 | − | 0.0630248i | ||||
\(514\) | 13.0703 | 0.576505 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.08160 | − | 2.58577i | −0.135660 | − | 0.113832i | ||||
\(517\) | 2.92562 | − | 8.03806i | 0.128668 | − | 0.353514i | ||||
\(518\) | 3.46839 | + | 9.52932i | 0.152392 | + | 0.418694i | ||||
\(519\) | −2.09039 | + | 1.75404i | −0.0917578 | + | 0.0769940i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.14888 | − | 3.72196i | 0.0941440 | − | 0.163062i | −0.815107 | − | 0.579310i | \(-0.803322\pi\) |
0.909251 | + | 0.416248i | \(0.136655\pi\) | |||||||
\(522\) | 17.8284 | − | 3.14362i | 0.780327 | − | 0.137593i | ||||
\(523\) | −24.5247 | + | 4.32437i | −1.07239 | + | 0.189092i | −0.681849 | − | 0.731493i | \(-0.738824\pi\) |
−0.390543 | + | 0.920585i | \(0.627713\pi\) | |||||||
\(524\) | −6.65739 | + | 11.5309i | −0.290829 | + | 0.503731i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.5336 | + | 9.67780i | −0.502887 | + | 0.421972i | ||||
\(527\) | 4.05853 | + | 11.1507i | 0.176792 | + | 0.485733i | ||||
\(528\) | −2.25852 | + | 6.20524i | −0.0982895 | + | 0.270048i | ||||
\(529\) | 12.2088 | + | 10.2444i | 0.530817 | + | 0.445408i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.29714 | −0.0996876 | ||||||||
\(532\) | −19.1284 | + | 9.66531i | −0.829320 | + | 0.419044i | ||||
\(533\) | 61.4006i | 2.65955i | ||||||||
\(534\) | 4.34100 | − | 24.6191i | 0.187854 | − | 1.06537i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.80379 | + | 0.656525i | 0.0779118 | + | 0.0283576i | ||||
\(537\) | −3.43595 | − | 9.44020i | −0.148272 | − | 0.407375i | ||||
\(538\) | −15.7196 | − | 18.7339i | −0.677719 | − | 0.807674i | ||||
\(539\) | 24.4440 | + | 42.3383i | 1.05288 | + | 1.82364i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.80139 | − | 21.5587i | −0.163434 | − | 0.926882i | −0.950664 | − | 0.310222i | \(-0.899596\pi\) |
0.787230 | − | 0.616660i | \(-0.211515\pi\) | |||||||
\(542\) | −8.81475 | + | 1.55428i | −0.378626 | + | 0.0667620i | ||||
\(543\) | 2.75072 | + | 1.58813i | 0.118045 | + | 0.0681531i | ||||
\(544\) | 1.09561 | + | 1.89766i | 0.0469741 | + | 0.0813615i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −70.3292 | + | 25.5978i | −3.00981 | + | 1.09548i | ||||
\(547\) | −1.01317 | + | 2.78367i | −0.0433202 | + | 0.119021i | −0.959466 | − | 0.281823i | \(-0.909061\pi\) |
0.916146 | + | 0.400844i | \(0.131283\pi\) | |||||||
\(548\) | 4.64495 | − | 5.53564i | 0.198423 | − | 0.236471i | ||||
\(549\) | 3.10135 | − | 17.5886i | 0.132362 | − | 0.750663i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.9435 | − | 29.5744i | −0.636617 | − | 1.25991i | ||||
\(552\) | 6.16497i | 0.262399i | ||||||||
\(553\) | −74.1943 | − | 13.0825i | −3.15506 | − | 0.556322i | ||||
\(554\) | −5.97623 | − | 5.01465i | −0.253906 | − | 0.213052i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.26632 | − | 0.824874i | 0.0961135 | − | 0.0349825i | ||||
\(557\) | 19.7784 | + | 23.5710i | 0.838038 | + | 0.998734i | 0.999929 | + | 0.0119259i | \(0.00379621\pi\) |
−0.161891 | + | 0.986809i | \(0.551759\pi\) | |||||||
\(558\) | 11.1688 | − | 6.44829i | 0.472811 | − | 0.272978i | ||||
\(559\) | −5.68936 | + | 9.85426i | −0.240634 | + | 0.416791i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.51264 | + | 14.2499i | 0.106084 | + | 0.601631i | ||||
\(562\) | −15.8467 | − | 9.14912i | −0.668455 | − | 0.385933i | ||||
\(563\) | −30.7518 | + | 17.7546i | −1.29603 | + | 0.748266i | −0.979717 | − | 0.200387i | \(-0.935780\pi\) |
−0.316318 | + | 0.948653i | \(0.602447\pi\) | |||||||
\(564\) | −5.34008 | + | 4.48086i | −0.224858 | + | 0.188678i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.79213 | + | 2.47213i | 0.285494 | + | 0.103911i | ||||
\(567\) | 33.0991 | − | 39.4460i | 1.39003 | − | 1.65658i | ||||
\(568\) | 6.07169 | + | 1.07060i | 0.254763 | + | 0.0449215i | ||||
\(569\) | −33.0813 | −1.38684 | −0.693421 | − | 0.720533i | \(-0.743897\pi\) | ||||
−0.693421 | + | 0.720533i | \(0.743897\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.29342 | 0.0959766 | 0.0479883 | − | 0.998848i | \(-0.484719\pi\) | ||||
0.0479883 | + | 0.998848i | \(0.484719\pi\) | |||||||
\(572\) | 18.3948 | + | 3.24351i | 0.769127 | + | 0.135618i | ||||
\(573\) | 20.3298 | − | 24.2282i | 0.849291 | − | 1.01215i | ||||
\(574\) | −43.2328 | − | 15.7355i | −1.80450 | − | 0.656785i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.82431 | − | 1.53078i | 0.0760129 | − | 0.0637824i | ||||
\(577\) | 13.5997 | − | 7.85178i | 0.566162 | − | 0.326874i | −0.189453 | − | 0.981890i | \(-0.560671\pi\) |
0.755615 | + | 0.655016i | \(0.227338\pi\) | |||||||
\(578\) | −10.5642 | − | 6.09926i | −0.439414 | − | 0.253696i | ||||
\(579\) | −2.10255 | − | 11.9242i | −0.0873792 | − | 0.495552i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.22554 | + | 5.58680i | −0.133818 | + | 0.231780i | ||||
\(582\) | −4.12708 | + | 2.38277i | −0.171073 | + | 0.0987691i | ||||
\(583\) | −7.72544 | − | 9.20682i | −0.319955 | − | 0.381308i | ||||
\(584\) | 3.73719 | − | 1.36023i | 0.154646 | − | 0.0562865i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.72264 | − | 7.31917i | −0.360329 | − | 0.302352i | ||||
\(587\) | 26.1082 | + | 4.60359i | 1.07760 | + | 0.190010i | 0.684155 | − | 0.729337i | \(-0.260171\pi\) |
0.393448 | + | 0.919347i | \(0.371282\pi\) | |||||||
\(588\) | − | 39.8411i | − | 1.64302i | ||||||
\(589\) | −17.2093 | − | 16.1568i | −0.709098 | − | 0.665728i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.15024 | + | 6.52335i | −0.0473146 | + | 0.268335i | ||||
\(592\) | −1.32576 | + | 1.57998i | −0.0544885 | + | 0.0649369i | ||||
\(593\) | −1.00184 | + | 2.75254i | −0.0411408 | + | 0.113033i | −0.958562 | − | 0.284884i | \(-0.908045\pi\) |
0.917421 | + | 0.397918i | \(0.130267\pi\) | |||||||
\(594\) | −3.83813 | + | 1.39697i | −0.157481 | + | 0.0573182i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.48937 | + | 6.04376i | 0.142930 | + | 0.247562i | ||||
\(597\) | 2.94244 | + | 1.69882i | 0.120426 | + | 0.0695281i | ||||
\(598\) | 17.1733 | − | 3.02812i | 0.702270 | − | 0.123829i | ||||
\(599\) | −6.43428 | − | 36.4906i | −0.262897 | − | 1.49097i | −0.774956 | − | 0.632015i | \(-0.782228\pi\) |
0.512059 | − | 0.858950i | \(-0.328883\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.84799 | + | 8.39697i | 0.197754 | + | 0.342520i | 0.947800 | − | 0.318866i | \(-0.103302\pi\) |
−0.750046 | + | 0.661386i | \(0.769969\pi\) | |||||||
\(602\) | −5.48045 | − | 6.53135i | −0.223367 | − | 0.266198i | ||||
\(603\) | −1.56349 | − | 4.29566i | −0.0636704 | − | 0.174933i | ||||
\(604\) | −5.35025 | − | 1.94733i | −0.217699 | − | 0.0792358i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.01803 | + | 11.4448i | −0.0819771 | + | 0.464915i | ||||
\(607\) | 38.0294i | 1.54357i | 0.635886 | + | 0.771783i | \(0.280635\pi\) | ||||
−0.635886 | + | 0.771783i | \(0.719365\pi\) | |||||||
\(608\) | −3.64766 | − | 2.38634i | −0.147932 | − | 0.0967787i | ||||
\(609\) | 86.7049 | 3.51346 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.1050 | + | 12.6746i | 0.611081 | + | 0.512758i | ||||
\(612\) | 1.78478 | − | 4.90364i | 0.0721454 | − | 0.198218i | ||||
\(613\) | 7.81429 | + | 21.4696i | 0.315616 | + | 0.867149i | 0.991496 | + | 0.130137i | \(0.0415416\pi\) |
−0.675880 | + | 0.737012i | \(0.736236\pi\) | |||||||
\(614\) | 3.78649 | − | 3.17725i | 0.152810 | − | 0.128223i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.99793 | + | 12.1208i | −0.281955 | + | 0.488360i | ||||
\(617\) | −25.0606 | + | 4.41886i | −1.00890 | + | 0.177896i | −0.653588 | − | 0.756851i | \(-0.726737\pi\) |
−0.355313 | + | 0.934747i | \(0.615626\pi\) | |||||||
\(618\) | 20.6407 | − | 3.63951i | 0.830291 | − | 0.146403i | ||||
\(619\) | 7.95778 | − | 13.7833i | 0.319850 | − | 0.553997i | −0.660606 | − | 0.750733i | \(-0.729701\pi\) |
0.980457 | + | 0.196736i | \(0.0630341\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.92110 | + | 2.45110i | −0.117220 | + | 0.0983591i | ||||
\(622\) | −8.24858 | − | 22.6628i | −0.330738 | − | 0.908695i | ||||
\(623\) | 18.1217 | − | 49.7889i | 0.726030 | − | 1.99475i | ||||
\(624\) | −11.6608 | − | 9.78453i | −0.466804 | − | 0.391695i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 30.9756 | 1.23803 | ||||||||
\(627\) | −17.2450 | − | 23.0461i | −0.688698 | − | 0.920372i | ||||
\(628\) | − | 5.31383i | − | 0.212045i | ||||||
\(629\) | −0.784795 | + | 4.45079i | −0.0312918 | + | 0.177465i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.7345 | + | 6.81880i | 0.745808 | + | 0.271452i | 0.686841 | − | 0.726808i | \(-0.258997\pi\) |
0.0589675 | + | 0.998260i | \(0.481219\pi\) | |||||||
\(632\) | −5.24075 | − | 14.3988i | −0.208466 | − | 0.572755i | ||||
\(633\) | −1.95414 | − | 2.32886i | −0.0776702 | − | 0.0925637i | ||||
\(634\) | 3.45527 | + | 5.98470i | 0.137226 | + | 0.237683i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.70080 | + | 9.64574i | 0.0674413 | + | 0.382478i | ||||
\(637\) | −110.982 | + | 19.5692i | −4.39728 | + | 0.775360i | ||||
\(638\) | −18.7399 | − | 10.8195i | −0.741922 | − | 0.428349i | ||||
\(639\) | −7.34130 | − | 12.7155i | −0.290417 | − | 0.503018i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.28156 | + | 0.830421i | −0.0901163 | + | 0.0327996i | −0.386685 | − | 0.922212i | \(-0.626380\pi\) |
0.296569 | + | 0.955012i | \(0.404158\pi\) | |||||||
\(642\) | −4.73498 | + | 13.0093i | −0.186875 | + | 0.513434i | ||||
\(643\) | 4.30313 | − | 5.12827i | 0.169699 | − | 0.202239i | −0.674492 | − | 0.738282i | \(-0.735637\pi\) |
0.844191 | + | 0.536043i | \(0.180082\pi\) | |||||||
\(644\) | −2.26897 | + | 12.8680i | −0.0894099 | + | 0.507069i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.53651 | − | 0.532031i | −0.375209 | − | 0.0209325i | ||||
\(647\) | − | 28.2280i | − | 1.10976i | −0.831932 | − | 0.554878i | \(-0.812765\pi\) | ||
0.831932 | − | 0.554878i | \(-0.187235\pi\) | |||||||
\(648\) | 10.3139 | + | 1.81862i | 0.405168 | + | 0.0714421i | ||||
\(649\) | 2.10339 | + | 1.76495i | 0.0825652 | + | 0.0692805i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 58.0421 | − | 21.1256i | 2.27485 | − | 0.827977i | ||||
\(652\) | 2.87557 | + | 3.42697i | 0.112616 | + | 0.134210i | ||||
\(653\) | 14.7075 | − | 8.49136i | 0.575548 | − | 0.332293i | −0.183814 | − | 0.982961i | \(-0.558844\pi\) |
0.759362 | + | 0.650668i | \(0.225511\pi\) | |||||||
\(654\) | −18.3612 | + | 31.8025i | −0.717978 | + | 1.24358i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.62488 | − | 9.21513i | −0.0634408 | − | 0.359791i | ||||
\(657\) | −8.20228 | − | 4.73559i | −0.320002 | − | 0.184753i | ||||
\(658\) | −12.7953 | + | 7.38739i | −0.498814 | + | 0.287990i | ||||
\(659\) | 14.0188 | − | 11.7632i | 0.546095 | − | 0.458228i | −0.327521 | − | 0.944844i | \(-0.606213\pi\) |
0.873616 | + | 0.486616i | \(0.161769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.11150 | − | 1.86043i | −0.198814 | − | 0.0723625i | 0.240694 | − | 0.970601i | \(-0.422625\pi\) |
−0.439508 | + | 0.898239i | \(0.644847\pi\) | |||||||
\(662\) | −2.68612 | + | 3.20119i | −0.104399 | + | 0.124418i | ||||
\(663\) | −32.8482 | − | 5.79203i | −1.27572 | − | 0.224944i | ||||
\(664\) | −1.31206 | −0.0509180 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.91183 | 0.190329 | ||||||||
\(667\) | −19.8952 | − | 3.50806i | −0.770344 | − | 0.135833i | ||||
\(668\) | −2.34538 | + | 2.79512i | −0.0907456 | + | 0.108146i | ||||
\(669\) | −61.3213 | − | 22.3191i | −2.37082 | − | 0.862907i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.3535 | + | 13.7222i | −0.631321 | + | 0.529741i | ||||
\(672\) | 9.87776 | − | 5.70293i | 0.381043 | − | 0.219995i | ||||
\(673\) | 25.9066 | + | 14.9572i | 0.998626 | + | 0.576557i | 0.907842 | − | 0.419313i | \(-0.137729\pi\) |
0.0907847 | + | 0.995871i | \(0.471062\pi\) | |||||||
\(674\) | 2.98695 | + | 16.9399i | 0.115053 | + | 0.652499i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.0285 | + | 26.0302i | −0.578021 | + | 1.00116i | ||||
\(677\) | 27.2420 | − | 15.7282i | 1.04700 | − | 0.604483i | 0.125189 | − | 0.992133i | \(-0.460046\pi\) |
0.921807 | + | 0.387650i | \(0.126713\pi\) | |||||||
\(678\) | 27.1463 | + | 32.3517i | 1.04255 | + | 1.24246i | ||||
\(679\) | −9.49130 | + | 3.45455i | −0.364243 | + | 0.132573i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.4738 | − | 18.8578i | −0.861199 | − | 0.722631i | ||||
\(682\) | −15.1811 | − | 2.67684i | −0.581314 | − | 0.102501i | ||||
\(683\) | − | 49.8920i | − | 1.90906i | −0.298109 | − | 0.954532i | \(-0.596356\pi\) | ||
0.298109 | − | 0.954532i | \(-0.403644\pi\) | |||||||
\(684\) | 1.23033 | + | 10.3074i | 0.0470430 | + | 0.394114i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.68670 | − | 49.2647i | 0.331660 | − | 1.88094i | ||||
\(687\) | −20.4941 | + | 24.4240i | −0.781900 | + | 0.931833i | ||||
\(688\) | 0.593093 | − | 1.62951i | 0.0226115 | − | 0.0621245i | ||||
\(689\) | 26.0341 | − | 9.47562i | 0.991818 | − | 0.360992i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.36370 | − | 16.2184i | −0.356212 | − | 0.616977i | 0.631113 | − | 0.775691i | \(-0.282599\pi\) |
−0.987325 | + | 0.158714i | \(0.949265\pi\) | |||||||
\(692\) | −1.01872 | − | 0.588156i | −0.0387258 | − | 0.0223583i | ||||
\(693\) | 32.8243 | − | 5.78782i | 1.24689 | − | 0.219861i | ||||
\(694\) | 3.20604 | + | 18.1823i | 0.121699 | + | 0.690192i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.81731 | + | 15.2720i | 0.334219 | + | 0.578885i | ||||
\(697\) | −13.1797 | − | 15.7069i | −0.499217 | − | 0.594943i | ||||
\(698\) | 8.46187 | + | 23.2488i | 0.320286 | + | 0.879980i | ||||
\(699\) | −53.6650 | − | 19.5325i | −2.02980 | − | 0.738786i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.10915 | + | 17.6329i | −0.117431 | + | 0.665984i | 0.868087 | + | 0.496412i | \(0.165350\pi\) |
−0.985518 | + | 0.169572i | \(0.945761\pi\) | |||||||
\(702\) | − | 9.41531i | − | 0.355358i | ||||||
\(703\) | −2.59952 | − | 8.60630i | −0.0980426 | − | 0.324593i | ||||
\(704\) | −2.84657 | −0.107284 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.91028 | + | 4.12021i | 0.184801 | + | 0.155066i | ||||
\(707\) | −8.42437 | + | 23.1458i | −0.316831 | + | 0.870486i | ||||
\(708\) | −0.765324 | − | 2.10271i | −0.0287627 | − | 0.0790247i | ||||
\(709\) | −20.6673 | + | 17.3419i | −0.776177 | + | 0.651290i | −0.942283 | − | 0.334818i | \(-0.891325\pi\) |
0.166106 | + | 0.986108i | \(0.446881\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.2455 | + | 31.6022i | −0.684260 | + | 1.18517i | ||||
\(712\) | 10.6126 | − | 1.87128i | 0.397723 | − | 0.0701293i | ||||
\(713\) | −14.1730 | + | 2.49908i | −0.530783 | + | 0.0935913i | ||||
\(714\) | 12.4964 | − | 21.6444i | 0.467667 | − | 0.810023i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.31741 | − | 2.78364i | 0.123977 | − | 0.104029i | ||||
\(717\) | 12.9279 | + | 35.5192i | 0.482802 | + | 1.32649i | ||||
\(718\) | 12.5916 | − | 34.5952i | 0.469915 | − | 1.29108i | ||||
\(719\) | −32.4936 | − | 27.2653i | −1.21180 | − | 1.01683i | −0.999212 | − | 0.0396842i | \(-0.987365\pi\) |
−0.212593 | − | 0.977141i | \(-0.568191\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.4222 | 1.65437 | ||||||||
\(722\) | 17.4091 | − | 7.61079i | 0.647899 | − | 0.283244i | ||||
\(723\) | 44.6672i | 1.66119i | ||||||||
\(724\) | −0.237758 | + | 1.34839i | −0.00883622 | + | 0.0501127i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.31523 | + | 2.29856i | 0.234380 | + | 0.0853074i | ||||
\(727\) | −14.7217 | − | 40.4476i | −0.545999 | − | 1.50012i | −0.839067 | − | 0.544028i | \(-0.816898\pi\) |
0.293068 | − | 0.956092i | \(-0.405324\pi\) | |||||||
\(728\) | −20.7380 | − | 24.7146i | −0.768602 | − | 0.915984i | ||||
\(729\) | −7.47766 | − | 12.9517i | −0.276950 | − | 0.479692i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.659826 | − | 3.74206i | −0.0244045 | − | 0.138405i | ||||
\(732\) | 17.1331 | − | 3.02104i | 0.633259 | − | 0.111661i | ||||
\(733\) | 26.3235 | + | 15.1979i | 0.972282 | + | 0.561347i | 0.899931 | − | 0.436032i | \(-0.143617\pi\) |
0.0723507 | + | 0.997379i | \(0.476950\pi\) | |||||||
\(734\) | −7.31190 | − | 12.6646i | −0.269887 | − | 0.467458i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.49728 | + | 0.908934i | −0.0920508 | + | 0.0335038i | ||||
\(737\) | −1.86885 | + | 5.13461i | −0.0688398 | + | 0.189136i | ||||
\(738\) | −14.3239 | + | 17.0706i | −0.527272 | + | 0.628378i | ||||
\(739\) | 6.40630 | − | 36.3319i | 0.235659 | − | 1.33649i | −0.605561 | − | 0.795799i | \(-0.707051\pi\) |
0.841221 | − | 0.540692i | \(-0.181838\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 63.5171 | − | 19.1852i | 2.33336 | − | 0.704787i | ||||
\(742\) | 20.7592i | 0.762095i | ||||||||
\(743\) | 24.1976 | + | 4.26670i | 0.887725 | + | 0.156530i | 0.598873 | − | 0.800844i | \(-0.295615\pi\) |
0.288852 | + | 0.957374i | \(0.406726\pi\) | |||||||
\(744\) | 9.62352 | + | 8.07509i | 0.352815 | + | 0.296047i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.7398 | + | 4.63691i | −0.466438 | + | 0.169769i | ||||
\(747\) | 2.00848 | + | 2.39361i | 0.0734865 | + | 0.0875778i | ||||
\(748\) | −5.40182 | + | 3.11874i | −0.197510 | + | 0.114033i | ||||
\(749\) | −14.6711 | + | 25.4112i | −0.536072 | + | 0.928503i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.64514 | + | 9.33008i | 0.0600322 | + | 0.340459i | 1.00000 | 0.000804564i | \(-0.000256101\pi\) | |
−0.939967 | + | 0.341264i | \(0.889145\pi\) | |||||||
\(752\) | −2.60240 | − | 1.50250i | −0.0948998 | − | 0.0547904i | ||||
\(753\) | 55.7902 | − | 32.2105i | 2.03311 | − | 1.17382i | ||||
\(754\) | 38.2113 | − | 32.0631i | 1.39157 | − | 1.16767i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.62942 | + | 2.41291i | 0.241110 | + | 0.0877568i | ||||
\(757\) | −4.54780 | + | 5.41985i | −0.165292 | + | 0.196988i | −0.842332 | − | 0.538958i | \(-0.818818\pi\) |
0.677040 | + | 0.735946i | \(0.263262\pi\) | |||||||
\(758\) | −29.8298 | − | 5.25979i | −1.08347 | − | 0.191044i | ||||
\(759\) | −17.5490 | −0.636990 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.9880 | −1.66706 | −0.833531 | − | 0.552472i | \(-0.813684\pi\) | ||||
−0.833531 | + | 0.552472i | \(0.813684\pi\) | |||||||
\(762\) | −17.4758 | − | 3.08146i | −0.633082 | − | 0.111629i | ||||
\(763\) | −50.0293 | + | 59.6227i | −1.81118 | + | 2.15849i | ||||
\(764\) | 12.8116 | + | 4.66302i | 0.463506 | + | 0.168702i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.9571 | − | 18.4242i | 0.793342 | − | 0.665693i | ||||
\(767\) | −5.48146 | + | 3.16472i | −0.197924 | + | 0.114272i | ||||
\(768\) | 2.00901 | + | 1.15990i | 0.0724937 | + | 0.0418543i | ||||
\(769\) | 7.83899 | + | 44.4571i | 0.282681 | + | 1.60317i | 0.713452 | + | 0.700704i | \(0.247131\pi\) |
−0.430771 | + | 0.902461i | \(0.641758\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.1602 | − | 26.2582i | 0.545981 | − | 0.945667i | ||||
\(772\) | 4.52019 | − | 2.60974i | 0.162685 | − | 0.0939264i | ||||
\(773\) | −0.495905 | − | 0.590996i | −0.0178364 | − | 0.0212567i | 0.757052 | − | 0.653354i | \(-0.226639\pi\) |
−0.774889 | + | 0.632097i | \(0.782194\pi\) | |||||||
\(774\) | −3.88063 | + | 1.41243i | −0.139486 | + | 0.0507689i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.57368 | − | 1.32047i | −0.0564918 | − | 0.0474022i | ||||
\(777\) | 23.1674 | + | 4.08504i | 0.831127 | + | 0.146550i | ||||
\(778\) | − | 17.1263i | − | 0.614007i | ||||||
\(779\) | 37.4911 | + | 16.0634i | 1.34326 | + | 0.575532i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.04755 | + | 17.2835i | −0.109050 | + | 0.618452i | ||||
\(782\) | −3.74314 | + | 4.46090i | −0.133854 | + | 0.159521i | ||||
\(783\) | −3.73061 | + | 10.2498i | −0.133321 | + | 0.366297i | ||||
\(784\) | 16.1386 | − | 5.87398i | 0.576379 | − | 0.209785i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.4438 | + | 26.7494i | 0.550862 | + | 0.954121i | ||||
\(787\) | −11.7149 | − | 6.76358i | −0.417590 | − | 0.241095i | 0.276456 | − | 0.961027i | \(-0.410840\pi\) |
−0.694045 | + | 0.719931i | \(0.744173\pi\) | |||||||
\(788\) | −2.81203 | + | 0.495837i | −0.100174 | + | 0.0176635i | ||||
\(789\) | 6.06499 | + | 34.3963i | 0.215919 | + | 1.22454i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.7549 | + | 77.5178i | 1.59130 | + | 2.75621i | ||||
\(792\) | 4.35747 | + | 5.19303i | 0.154836 | + | 0.184526i | ||||
\(793\) | −16.8310 | − | 46.2427i | −0.597685 | − | 1.64213i | ||||
\(794\) | −24.5306 | − | 8.92842i | −0.870560 | − | 0.316858i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.254330 | + | 1.44238i | −0.00901448 | + | 0.0511237i | ||||
\(797\) | 33.8026i | 1.19735i | 0.800992 | + | 0.598674i | \(0.204306\pi\) | ||||
−0.800992 | + | 0.598674i | \(0.795694\pi\) | |||||||
\(798\) | −2.76935 | + | 49.6398i | −0.0980338 | + | 1.75723i | ||||
\(799\) | −6.58463 | −0.232947 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.6593 | − | 16.4961i | −0.694628 | − | 0.582862i | ||||
\(802\) | −3.18453 | + | 8.74942i | −0.112450 | + | 0.308953i | ||||
\(803\) | 3.87198 | + | 10.6382i | 0.136639 | + | 0.375413i | ||||
\(804\) | 3.41117 | − | 2.86232i | 0.120303 | − | 0.100946i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.7673 | − | 30.7739i | 0.625827 | − | 1.08396i | ||||
\(807\) | −55.8695 | + | 9.85131i | −1.96670 | + | 0.346782i | ||||
\(808\) | −4.93355 | + | 0.869918i | −0.173562 | + | 0.0306036i | ||||
\(809\) | −6.45477 | + | 11.1800i | −0.226938 | + | 0.393068i | −0.956899 | − | 0.290421i | \(-0.906205\pi\) |
0.729961 | + | 0.683488i | \(0.239538\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.3134 | − | 35.5052i | 1.48582 | − | 1.24675i | 0.586143 | − | 0.810208i | \(-0.300646\pi\) |
0.899681 | − | 0.436547i | \(-0.143799\pi\) | |||||||
\(812\) | 12.7834 | + | 35.1220i | 0.448608 | + | 1.23254i | ||||
\(813\) | −7.10168 | + | 19.5117i | −0.249067 | + | 0.684305i | ||||
\(814\) | −4.49753 | − | 3.77388i | −0.157638 | − | 0.132274i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.08321 | 0.177948 | ||||||||
\(817\) | 4.52857 | + | 6.05196i | 0.158435 | + | 0.211731i | ||||
\(818\) | − | 14.5798i | − | 0.509771i | ||||||
\(819\) | −13.3418 | + | 75.6652i | −0.466201 | + | 2.64396i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.4375 | − | 17.6298i | −1.69048 | − | 0.615285i | −0.695796 | − | 0.718240i | \(-0.744948\pi\) |
−0.994686 | + | 0.102955i | \(0.967170\pi\) | |||||||
\(822\) | −5.73345 | − | 15.7525i | −0.199977 | − | 0.549432i | ||||
\(823\) | −17.2160 | − | 20.5172i | −0.600112 | − | 0.715186i | 0.377403 | − | 0.926049i | \(-0.376817\pi\) |
−0.977516 | + | 0.210863i | \(0.932373\pi\) | |||||||
\(824\) | 4.51744 | + | 7.82444i | 0.157373 | + | 0.272577i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.823552 | − | 4.67060i | −0.0286551 | − | 0.162511i | ||||
\(827\) | −4.45430 | + | 0.785414i | −0.154891 | + | 0.0273115i | −0.250556 | − | 0.968102i | \(-0.580613\pi\) |
0.0956647 | + | 0.995414i | \(0.469502\pi\) | |||||||
\(828\) | 5.48096 | + | 3.16443i | 0.190476 | + | 0.109972i | ||||
\(829\) | −6.55868 | − | 11.3600i | −0.227792 | − | 0.394548i | 0.729361 | − | 0.684129i | \(-0.239817\pi\) |
−0.957154 | + | 0.289581i | \(0.906484\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.0063 | + | 6.18978i | −0.589941 | + | 0.214721i | ||||
\(832\) | 2.24426 | − | 6.16606i | 0.0778059 | − | 0.213770i | ||||
\(833\) | 24.1900 | − | 28.8285i | 0.838134 | − | 0.998849i | ||||
\(834\) | 0.971531 | − | 5.50983i | 0.0336414 | − | 0.190790i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.79288 | − | 10.3833i | 0.234937 | − | 0.359114i | ||||
\(837\) | 7.77037i | 0.268583i | ||||||||
\(838\) | −14.3751 | − | 2.53472i | −0.496580 | − | 0.0875604i | ||||
\(839\) | 19.2974 | + | 16.1924i | 0.666220 | + | 0.559025i | 0.911944 | − | 0.410315i | \(-0.134581\pi\) |
−0.245724 | + | 0.969340i | \(0.579026\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0511 | + | 9.84578i | −0.932796 | + | 0.339510i | ||||
\(842\) | −25.2237 | − | 30.0605i | −0.869267 | − | 1.03595i | ||||
\(843\) | −36.7613 | + | 21.2241i | −1.26613 | + | 0.730998i | ||||
\(844\) | 0.655252 | − | 1.13493i | 0.0225547 | − | 0.0390659i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.24268 | + | 7.04758i | 0.0427241 | + | 0.242301i | ||||
\(847\) | 12.3356 | + | 7.12197i | 0.423857 | + | 0.244714i | ||||
\(848\) | −3.65649 | + | 2.11108i | −0.125564 | + | 0.0724946i | ||||
\(849\) | 12.8447 | − | 10.7780i | 0.440829 | − | 0.369900i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.15068 | − | 1.87470i | −0.176563 | − | 0.0642638i | ||||
\(852\) | 9.19340 | − | 10.9563i | 0.314961 | − | 0.375356i | ||||
\(853\) | −33.5124 | − | 5.90914i | −1.14744 | − | 0.202325i | −0.432583 | − | 0.901594i | \(-0.642398\pi\) |
−0.714859 | + | 0.699269i | \(0.753509\pi\) | |||||||
\(854\) | 36.8734 | 1.26178 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.96783 | −0.203976 | ||||||||
\(857\) | 1.06558 | + | 0.187890i | 0.0363994 | + | 0.00641819i | 0.191818 | − | 0.981430i | \(-0.438562\pi\) |
−0.155419 | + | 0.987849i | \(0.549673\pi\) | |||||||
\(858\) | 27.8524 | − | 33.1932i | 0.950864 | − | 1.13320i | ||||
\(859\) | 32.0734 | + | 11.6737i | 1.09433 | + | 0.398303i | 0.825223 | − | 0.564807i | \(-0.191050\pi\) |
0.269106 | + | 0.963111i | \(0.413272\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −81.7583 | + | 68.6034i | −2.78632 | + | 2.33800i | ||||
\(862\) | 18.9457 | − | 10.9383i | 0.645294 | − | 0.372561i | ||||
\(863\) | 29.7233 | + | 17.1608i | 1.01179 | + | 0.584160i | 0.911716 | − | 0.410820i | \(-0.134758\pi\) |
0.100078 | + | 0.994980i | \(0.468091\pi\) | |||||||
\(864\) | 0.249162 | + | 1.41307i | 0.00847668 | + | 0.0480736i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.550842 | + | 0.954087i | −0.0187184 | + | 0.0324212i | ||||
\(867\) | −24.5069 | + | 14.1491i | −0.832297 | + | 0.480527i | ||||
\(868\) | 17.1149 | + | 20.3967i | 0.580918 | + | 0.692311i | ||||
\(869\) | 40.9873 | − | 14.9182i | 1.39040 | − | 0.506064i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.64886 | − | 8.09635i | −0.326939 | − | 0.274334i | ||||
\(872\) | −15.5895 | − | 2.74884i | −0.527926 | − | 0.0930876i | ||||
\(873\) | 4.89223i | 0.165577i | ||||||||
\(874\) | 2.64386 | − | 11.2782i | 0.0894300 | − | 0.381492i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.60206 | − | 9.08576i | 0.0541287 | − | 0.306979i | ||||
\(877\) | 1.01903 | − | 1.21443i | 0.0344102 | − | 0.0410084i | −0.748565 | − | 0.663062i | \(-0.769257\pi\) |
0.782975 | + | 0.622053i | \(0.213701\pi\) | |||||||
\(878\) | 1.44236 | − | 3.96284i | 0.0486772 | − | 0.133740i | ||||
\(879\) | −24.8216 | + | 9.03434i | −0.837213 | + | 0.304721i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.41502 | + | 14.5752i | 0.283509 | + | 0.491052i | 0.972247 | − | 0.233959i | \(-0.0751680\pi\) |
−0.688737 | + | 0.725011i | \(0.741835\pi\) | |||||||
\(882\) | −35.4206 | − | 20.4501i | −1.19267 | − | 0.688591i | ||||
\(883\) | 47.1138 | − | 8.30743i | 1.58550 | − | 0.279567i | 0.689727 | − | 0.724070i | \(-0.257731\pi\) |
0.895778 | + | 0.444503i | \(0.146620\pi\) | |||||||
\(884\) | −2.49678 | − | 14.1599i | −0.0839758 | − | 0.476250i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.79155 | + | 6.56715i | 0.127380 | + | 0.220628i | ||||
\(887\) | −19.8436 | − | 23.6487i | −0.666283 | − | 0.794045i | 0.321990 | − | 0.946743i | \(-0.395648\pi\) |
−0.988273 | + | 0.152698i | \(0.951204\pi\) | |||||||
\(888\) | 1.63644 | + | 4.49609i | 0.0549154 | + | 0.150879i | ||||
\(889\) | −35.3426 | − | 12.8637i | −1.18535 | − | 0.431433i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.17683 | + | 29.3593i | −0.173430 | + | 0.983573i | ||||
\(892\) | − | 28.1303i | − | 0.941874i | ||||||
\(893\) | 11.6908 | − | 5.90720i | 0.391218 | − | 0.197677i | ||||
\(894\) | 16.1893 | 0.541450 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.76644 | + | 3.16042i | 0.125828 | + | 0.105582i | ||||
\(897\) | 13.8358 | − | 38.0136i | 0.461965 | − | 1.26924i | ||||
\(898\) | 10.1571 | + | 27.9065i | 0.338948 | + | 0.931252i | ||||
\(899\) | −31.5354 | + | 26.4614i | −1.05177 | + | 0.882537i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.62585 | + | 8.01220i | −0.154109 | + | 0.266925i | ||||
\(902\) | 26.2315 | − | 4.62533i | 0.873415 | − | 0.154007i | ||||
\(903\) | −19.4783 | + | 3.43455i | −0.648197 | + | 0.114295i | ||||
\(904\) | −9.10255 | + | 15.7661i | −0.302746 | + | 0.524372i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.1180 | + | 8.48997i | −0.336146 | + | 0.282060i | ||||
\(907\) | −7.77328 | − | 21.3569i | −0.258108 | − | 0.709145i | −0.999284 | − | 0.0378346i | \(-0.987954\pi\) |
0.741176 | − | 0.671310i | \(-0.234268\pi\) | |||||||
\(908\) | 4.32538 | − | 11.8839i | 0.143543 | − | 0.394380i | ||||
\(909\) | 9.13917 | + | 7.66868i | 0.303127 | + | 0.254354i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −58.5516 | −1.93990 | −0.969950 | − | 0.243305i | \(-0.921768\pi\) | ||||
−0.969950 | + | 0.243305i | \(0.921768\pi\) | |||||||
\(912\) | −9.02508 | + | 4.56025i | −0.298850 | + | 0.151005i | ||||
\(913\) | − | 3.73489i | − | 0.123607i | ||||||
\(914\) | 1.58467 | − | 8.98712i | 0.0524163 | − | 0.297267i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.9151 | − | 4.70071i | −0.426727 | − | 0.155316i | ||||
\(917\) | 22.3905 | + | 61.5173i | 0.739398 | + | 2.03148i | ||||
\(918\) | 2.02101 | + | 2.40854i | 0.0667031 | + | 0.0794937i | ||||
\(919\) | 4.56100 | + | 7.89988i | 0.150454 | + | 0.260593i | 0.931394 | − | 0.364012i | \(-0.118593\pi\) |
−0.780941 | + | 0.624605i | \(0.785260\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.99115 | − | 11.2924i | −0.0656106 | − | 0.372096i | ||||
\(922\) | 25.9847 | − | 4.58180i | 0.855760 | − | 0.150894i | ||||
\(923\) | −35.0357 | − | 20.2279i | −1.15322 | − | 0.665809i | ||||
\(924\) | 16.2338 | + | 28.1178i | 0.534053 | + | 0.925006i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.7737 | + | 5.37720i | −0.485495 | + | 0.176706i | ||||
\(927\) | 7.35901 | − | 20.2187i | 0.241701 | − | 0.664069i | ||||
\(928\) | −4.88633 | + | 5.82331i | −0.160402 | + | 0.191159i | ||||
\(929\) | −9.58024 | + | 54.3323i | −0.314318 | + | 1.78258i | 0.261703 | + | 0.965148i | \(0.415716\pi\) |
−0.576021 | + | 0.817435i | \(0.695395\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.0859 | + | 72.8854i | −0.559969 | + | 2.38872i | ||||
\(932\) | − | 24.6181i | − | 0.806394i | ||||||
\(933\) | −55.0972 | − | 9.71512i | −1.80380 | − | 0.318059i | ||||
\(934\) | −5.28519 | − | 4.43480i | −0.172937 | − | 0.145111i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −14.6843 | + | 5.34464i | −0.479971 | + | 0.174695i | ||||
\(937\) | −29.7647 | − | 35.4722i | −0.972370 | − | 1.15883i | −0.987289 | − | 0.158937i | \(-0.949193\pi\) |
0.0149184 | − | 0.999889i | \(-0.495251\pi\) | |||||||
\(938\) | 8.17349 | − | 4.71897i | 0.266874 | − | 0.154080i | ||||
\(939\) | 35.9286 | − | 62.2301i | 1.17248 | − | 2.03080i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.80849 | − | 21.5990i | −0.124153 | − | 0.704107i | −0.981807 | − | 0.189880i | \(-0.939190\pi\) |
0.857654 | − | 0.514227i | \(-0.171921\pi\) | |||||||
\(942\) | −10.6755 | − | 6.16351i | −0.347827 | − | 0.200818i | ||||
\(943\) | 21.5358 | − | 12.4337i | 0.701303 | − | 0.404898i | ||||
\(944\) | 0.738920 | − | 0.620028i | 0.0240498 | − | 0.0201802i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.63852 | + | 1.68828i | 0.150811 | + | 0.0548908i | ||||
\(947\) | 9.40207 | − | 11.2050i | 0.305526 | − | 0.364112i | −0.591333 | − | 0.806427i | \(-0.701398\pi\) |
0.896860 | + | 0.442315i | \(0.145843\pi\) | |||||||
\(948\) | −35.0061 | − | 6.17251i | −1.13694 | − | 0.200474i | ||||
\(949\) | −26.0965 | −0.847127 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.0310 | 0.519842 | ||||||||
\(952\) | 10.6100 | + | 1.87083i | 0.343873 | + | 0.0606341i | ||||
\(953\) | −4.59886 | + | 5.48071i | −0.148972 | + | 0.177538i | −0.835370 | − | 0.549688i | \(-0.814746\pi\) |
0.686398 | + | 0.727226i | \(0.259191\pi\) | |||||||
\(954\) | 9.44853 | + | 3.43898i | 0.305908 | + | 0.111341i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.4819 | + | 10.4735i | −0.403693 | + | 0.338739i | ||||
\(957\) | −43.4729 | + | 25.0991i | −1.40528 | + | 0.811339i | ||||
\(958\) | −3.15979 | − | 1.82431i | −0.102088 | − | 0.0589407i | ||||
\(959\) | −6.16967 | − | 34.9899i | −0.199229 | − | 1.12988i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.836797 | − | 1.44938i | 0.0269935 | − | 0.0467540i | ||||
\(962\) | 11.7206 | − | 6.76691i | 0.377889 | − | 0.218174i | ||||
\(963\) | 9.13542 | + | 10.8872i | 0.294385 | + | 0.350834i | ||||
\(964\) | −18.0936 | + | 6.58553i | −0.582755 | + | 0.212105i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 23.2200 | + | 19.4839i | 0.747092 | + | 0.626885i | ||||
\(967\) | 10.6217 | + | 1.87290i | 0.341572 | + | 0.0602283i | 0.341803 | − | 0.939772i | \(-0.388963\pi\) |
−0.000231267 | 1.00000i | \(0.500074\pi\) | ||||||||
\(968\) | 2.89703i | 0.0931141i | ||||||||
\(969\) | −12.1303 | + | 18.5418i | −0.389680 | + | 0.595649i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.79260 | + | 55.5366i | −0.314260 | + | 1.78225i | 0.262082 | + | 0.965046i | \(0.415591\pi\) |
−0.576341 | + | 0.817209i | \(0.695520\pi\) | |||||||
\(972\) | 12.8498 | − | 15.3138i | 0.412156 | − | 0.491189i | ||||
\(973\) | 4.05570 | − | 11.1429i | 0.130020 | − | 0.357226i | ||||
\(974\) | 21.1573 | − | 7.70061i | 0.677922 | − | 0.246744i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.74977 | + | 6.49480i | 0.120027 | + | 0.207893i | ||||
\(977\) | 15.3500 | + | 8.86235i | 0.491091 | + | 0.283532i | 0.725027 | − | 0.688720i | \(-0.241827\pi\) |
−0.233936 | + | 0.972252i | \(0.575161\pi\) | |||||||
\(978\) | 10.2202 | − | 1.80209i | 0.326805 | − | 0.0576245i | ||||
\(979\) | 5.32674 | + | 30.2095i | 0.170243 | + | 0.965499i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.8493 | + | 32.6479i | 0.601811 | + | 1.04237i | ||||
\(982\) | 16.1733 | + | 19.2746i | 0.516110 | + | 0.615076i | ||||
\(983\) | 9.71721 | + | 26.6978i | 0.309931 | + | 0.851528i | 0.992669 | + | 0.120865i | \(0.0385669\pi\) |
−0.682738 | + | 0.730663i | \(0.739211\pi\) | |||||||
\(984\) | −20.3979 | − | 7.42424i | −0.650263 | − | 0.236676i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.89250 | + | 16.4042i | −0.0921160 | + | 0.522416i | ||||
\(987\) | 34.2745i | 1.09097i | ||||||||
\(988\) | 17.1361 | + | 22.9006i | 0.545172 | + | 0.728565i | ||||
\(989\) | 4.60842 | 0.146539 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7636 | − | 14.9054i | −0.564279 | − | 0.473487i | 0.315463 | − | 0.948938i | \(-0.397840\pi\) |
−0.879742 | + | 0.475451i | \(0.842285\pi\) | |||||||
\(992\) | −1.85217 | + | 5.08880i | −0.0588065 | + | 0.161570i | ||||
\(993\) | 3.31558 | + | 9.10948i | 0.105217 | + | 0.289081i | ||||
\(994\) | 23.2215 | − | 19.4851i | 0.736540 | − | 0.618031i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.52186 | + | 2.63595i | −0.0482221 | + | 0.0835231i | ||||
\(997\) | 30.0288 | − | 5.29489i | 0.951022 | − | 0.167691i | 0.323447 | − | 0.946246i | \(-0.395158\pi\) |
0.627576 | + | 0.778555i | \(0.284047\pi\) | |||||||
\(998\) | 31.2895 | − | 5.51718i | 0.990451 | − | 0.174643i | ||||
\(999\) | −1.47972 | + | 2.56296i | −0.0468164 | + | 0.0810884i |
(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 | 950.2.u.g.549.6 | 36 | ||
5.2 | odd | 4 | 190.2.k.d.131.1 | ✓ | 18 | ||
5.3 | odd | 4 | 950.2.l.i.701.3 | 18 | |||
5.4 | even | 2 | inner | 950.2.u.g.549.1 | 36 | ||
19.9 | even | 9 | inner | 950.2.u.g.199.1 | 36 | ||
95.9 | even | 18 | inner | 950.2.u.g.199.6 | 36 | ||
95.22 | even | 36 | 3610.2.a.bj.1.7 | 9 | |||
95.28 | odd | 36 | 950.2.l.i.351.3 | 18 | |||
95.47 | odd | 36 | 190.2.k.d.161.1 | yes | 18 | ||
95.92 | odd | 36 | 3610.2.a.bi.1.3 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.k.d.131.1 | ✓ | 18 | 5.2 | odd | 4 | ||
190.2.k.d.161.1 | yes | 18 | 95.47 | odd | 36 | ||
950.2.l.i.351.3 | 18 | 95.28 | odd | 36 | |||
950.2.l.i.701.3 | 18 | 5.3 | odd | 4 | |||
950.2.u.g.199.1 | 36 | 19.9 | even | 9 | inner | ||
950.2.u.g.199.6 | 36 | 95.9 | even | 18 | inner | ||
950.2.u.g.549.1 | 36 | 5.4 | even | 2 | inner | ||
950.2.u.g.549.6 | 36 | 1.1 | even | 1 | trivial | ||
3610.2.a.bi.1.3 | 9 | 95.92 | odd | 36 | |||
3610.2.a.bj.1.7 | 9 | 95.22 | even | 36 |