Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 11x^{14} + 85x^{12} + 334x^{10} + 952x^{8} + 1050x^{6} + 853x^{4} + 93x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.7 | ||
Root | \(1.06275 + 1.84073i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.i.508.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.06275 | − | 1.84073i | 0.751474 | − | 1.30159i | −0.195634 | − | 0.980677i | \(-0.562676\pi\) |
0.947108 | − | 0.320915i | \(-0.103990\pi\) | |||||||
\(3\) | 0.0894272 | + | 0.154892i | 0.0516308 | + | 0.0894272i | 0.890686 | − | 0.454620i | \(-0.150225\pi\) |
−0.839055 | + | 0.544047i | \(0.816891\pi\) | |||||||
\(4\) | −1.25885 | − | 2.18040i | −0.629427 | − | 1.09020i | ||||
\(5\) | −1.80301 | + | 3.12291i | −0.806332 | + | 1.39661i | 0.109056 | + | 0.994036i | \(0.465217\pi\) |
−0.915388 | + | 0.402572i | \(0.868116\pi\) | |||||||
\(6\) | 0.380153 | 0.155197 | ||||||||
\(7\) | −2.35320 | + | 1.20931i | −0.889428 | + | 0.457076i | ||||
\(8\) | −1.10038 | −0.389044 | ||||||||
\(9\) | 1.48401 | − | 2.57037i | 0.494669 | − | 0.856791i | ||||
\(10\) | 3.83229 | + | 6.63772i | 1.21188 | + | 2.09903i | ||||
\(11\) | −1.99618 | − | 3.45748i | −0.601871 | − | 1.04247i | −0.992538 | − | 0.121939i | \(-0.961089\pi\) |
0.390667 | − | 0.920532i | \(-0.372244\pi\) | |||||||
\(12\) | 0.225152 | − | 0.389974i | 0.0649957 | − | 0.112576i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.274848 | + | 5.61680i | −0.0734563 | + | 1.50115i | ||||
\(15\) | −0.644954 | −0.166526 | ||||||||
\(16\) | 1.34828 | − | 2.33529i | 0.337070 | − | 0.583823i | ||||
\(17\) | −2.39458 | − | 4.14753i | −0.580771 | − | 1.00592i | −0.995388 | − | 0.0959284i | \(-0.969418\pi\) |
0.414618 | − | 0.909996i | \(-0.363915\pi\) | |||||||
\(18\) | −3.15424 | − | 5.46330i | −0.743461 | − | 1.28771i | ||||
\(19\) | 1.57530 | − | 2.72850i | 0.361398 | − | 0.625960i | −0.626793 | − | 0.779186i | \(-0.715633\pi\) |
0.988191 | + | 0.153226i | \(0.0489662\pi\) | |||||||
\(20\) | 9.07892 | 2.03011 | ||||||||
\(21\) | −0.397753 | − | 0.256349i | −0.0867969 | − | 0.0559398i | ||||
\(22\) | −8.48572 | −1.80916 | ||||||||
\(23\) | 1.08943 | − | 1.88694i | 0.227161 | − | 0.393455i | −0.729804 | − | 0.683656i | \(-0.760389\pi\) |
0.956966 | + | 0.290201i | \(0.0937222\pi\) | |||||||
\(24\) | −0.0984042 | − | 0.170441i | −0.0200867 | − | 0.0347911i | ||||
\(25\) | −4.00171 | − | 6.93117i | −0.800343 | − | 1.38623i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.06740 | 0.205422 | ||||||||
\(28\) | 5.59912 | + | 3.60858i | 1.05813 | + | 0.681958i | ||||
\(29\) | −6.57198 | −1.22039 | −0.610193 | − | 0.792253i | \(-0.708908\pi\) | ||||
−0.610193 | + | 0.792253i | \(0.708908\pi\) | |||||||
\(30\) | −0.685421 | + | 1.18718i | −0.125140 | + | 0.216749i | ||||
\(31\) | −0.743358 | − | 1.28753i | −0.133511 | − | 0.231248i | 0.791517 | − | 0.611148i | \(-0.209292\pi\) |
−0.925028 | + | 0.379900i | \(0.875958\pi\) | |||||||
\(32\) | −3.96614 | − | 6.86956i | −0.701121 | − | 1.21438i | ||||
\(33\) | 0.357025 | − | 0.618386i | 0.0621502 | − | 0.107647i | ||||
\(34\) | −10.1793 | −1.74574 | ||||||||
\(35\) | 0.466298 | − | 9.52925i | 0.0788187 | − | 1.61074i | ||||
\(36\) | −7.47259 | −1.24543 | ||||||||
\(37\) | −2.48252 | + | 4.29984i | −0.408123 | + | 0.706890i | −0.994679 | − | 0.103019i | \(-0.967150\pi\) |
0.586556 | + | 0.809908i | \(0.300483\pi\) | |||||||
\(38\) | −3.34828 | − | 5.79939i | −0.543163 | − | 0.940786i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.98401 | − | 3.43640i | 0.313699 | − | 0.543342i | ||||
\(41\) | −2.11931 | −0.330981 | −0.165490 | − | 0.986211i | \(-0.552921\pi\) | ||||
−0.165490 | + | 0.986211i | \(0.552921\pi\) | |||||||
\(42\) | −0.894578 | + | 0.459722i | −0.138036 | + | 0.0709367i | ||||
\(43\) | 1.43145 | 0.218294 | 0.109147 | − | 0.994026i | \(-0.465188\pi\) | ||||
0.109147 | + | 0.994026i | \(0.465188\pi\) | |||||||
\(44\) | −5.02580 | + | 8.70494i | −0.757667 | + | 1.31232i | ||||
\(45\) | 5.35136 | + | 9.26883i | 0.797734 | + | 1.38172i | ||||
\(46\) | −2.31557 | − | 4.01068i | −0.341412 | − | 0.591342i | ||||
\(47\) | −0.509464 | + | 0.882417i | −0.0743129 | + | 0.128714i | −0.900787 | − | 0.434261i | \(-0.857010\pi\) |
0.826474 | + | 0.562974i | \(0.190343\pi\) | |||||||
\(48\) | 0.482292 | 0.0696129 | ||||||||
\(49\) | 4.07515 | − | 5.69150i | 0.582164 | − | 0.813072i | ||||
\(50\) | −17.0112 | −2.40575 | ||||||||
\(51\) | 0.428281 | − | 0.741804i | 0.0599713 | − | 0.103873i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.01771 | − | 5.22682i | −0.414514 | − | 0.717959i | 0.580863 | − | 0.814001i | \(-0.302715\pi\) |
−0.995377 | + | 0.0960417i | \(0.969382\pi\) | |||||||
\(54\) | 1.13438 | − | 1.96480i | 0.154369 | − | 0.267376i | ||||
\(55\) | 14.3966 | 1.94123 | ||||||||
\(56\) | 2.58943 | − | 1.33070i | 0.346027 | − | 0.177823i | ||||
\(57\) | 0.563498 | 0.0746371 | ||||||||
\(58\) | −6.98434 | + | 12.0972i | −0.917089 | + | 1.58844i | ||||
\(59\) | 2.45161 | + | 4.24631i | 0.319172 | + | 0.552823i | 0.980316 | − | 0.197437i | \(-0.0632618\pi\) |
−0.661143 | + | 0.750260i | \(0.729928\pi\) | |||||||
\(60\) | 0.811902 | + | 1.40626i | 0.104816 | + | 0.181547i | ||||
\(61\) | 1.01771 | − | 1.76272i | 0.130304 | − | 0.225693i | −0.793490 | − | 0.608584i | \(-0.791738\pi\) |
0.923794 | + | 0.382890i | \(0.125071\pi\) | |||||||
\(62\) | −3.16000 | −0.401320 | ||||||||
\(63\) | −0.383795 | + | 7.84323i | −0.0483537 | + | 0.988155i | ||||
\(64\) | −11.4669 | −1.43336 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.758854 | − | 1.31437i | −0.0934085 | − | 0.161788i | ||||
\(67\) | −1.95545 | − | 3.38694i | −0.238896 | − | 0.413781i | 0.721501 | − | 0.692413i | \(-0.243452\pi\) |
−0.960398 | + | 0.278632i | \(0.910119\pi\) | |||||||
\(68\) | −6.02885 | + | 10.4423i | −0.731105 | + | 1.26631i | ||||
\(69\) | 0.389698 | 0.0469141 | ||||||||
\(70\) | −17.0452 | − | 10.9855i | −2.03729 | − | 1.31302i | ||||
\(71\) | −8.80684 | −1.04518 | −0.522590 | − | 0.852584i | \(-0.675034\pi\) | ||||
−0.522590 | + | 0.852584i | \(0.675034\pi\) | |||||||
\(72\) | −1.63297 | + | 2.82840i | −0.192448 | + | 0.333330i | ||||
\(73\) | −1.54439 | − | 2.67497i | −0.180757 | − | 0.313081i | 0.761381 | − | 0.648304i | \(-0.224522\pi\) |
−0.942139 | + | 0.335223i | \(0.891188\pi\) | |||||||
\(74\) | 5.27656 | + | 9.13927i | 0.613388 | + | 1.06242i | ||||
\(75\) | 0.715724 | − | 1.23967i | 0.0826447 | − | 0.143145i | ||||
\(76\) | −7.93228 | −0.909895 | ||||||||
\(77\) | 8.87858 | + | 5.72217i | 1.01181 | + | 0.652102i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.984006 | + | 1.70435i | −0.110709 | + | 0.191754i | −0.916056 | − | 0.401049i | \(-0.868646\pi\) |
0.805347 | + | 0.592803i | \(0.201979\pi\) | |||||||
\(80\) | 4.86194 | + | 8.42112i | 0.543581 | + | 0.941510i | ||||
\(81\) | −4.35656 | − | 7.54579i | −0.484062 | − | 0.838421i | ||||
\(82\) | −2.25229 | + | 3.90108i | −0.248724 | + | 0.430802i | ||||
\(83\) | 7.66020 | 0.840816 | 0.420408 | − | 0.907335i | \(-0.361887\pi\) | ||||
0.420408 | + | 0.907335i | \(0.361887\pi\) | |||||||
\(84\) | −0.0582290 | + | 1.18997i | −0.00635330 | + | 0.129836i | ||||
\(85\) | 17.2698 | 1.87318 | ||||||||
\(86\) | 1.52126 | − | 2.63491i | 0.164042 | − | 0.284129i | ||||
\(87\) | −0.587714 | − | 1.01795i | −0.0630095 | − | 0.109136i | ||||
\(88\) | 2.19656 | + | 3.80456i | 0.234154 | + | 0.405567i | ||||
\(89\) | 6.39960 | − | 11.0844i | 0.678356 | − | 1.17495i | −0.297120 | − | 0.954840i | \(-0.596026\pi\) |
0.975476 | − | 0.220107i | \(-0.0706406\pi\) | |||||||
\(90\) | 22.7485 | 2.39791 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.48572 | −0.571926 | ||||||||
\(93\) | 0.132953 | − | 0.230281i | 0.0137866 | − | 0.0238790i | ||||
\(94\) | 1.08286 | + | 1.87557i | 0.111689 | + | 0.193450i | ||||
\(95\) | 5.68057 | + | 9.83903i | 0.582814 | + | 1.00946i | ||||
\(96\) | 0.709362 | − | 1.22865i | 0.0723989 | − | 0.125399i | ||||
\(97\) | 1.35900 | 0.137986 | 0.0689930 | − | 0.997617i | \(-0.478021\pi\) | ||||
0.0689930 | + | 0.997617i | \(0.478021\pi\) | |||||||
\(98\) | −6.14567 | − | 13.5499i | −0.620806 | − | 1.36874i | ||||
\(99\) | −11.8494 | −1.19091 | ||||||||
\(100\) | −10.0751 | + | 17.4507i | −1.00751 | + | 1.74507i | ||||
\(101\) | −2.14400 | − | 3.71353i | −0.213336 | − | 0.369510i | 0.739420 | − | 0.673244i | \(-0.235100\pi\) |
−0.952757 | + | 0.303735i | \(0.901766\pi\) | |||||||
\(102\) | −0.910307 | − | 1.57670i | −0.0901338 | − | 0.156116i | ||||
\(103\) | −7.21744 | + | 12.5010i | −0.711155 | + | 1.23176i | 0.253269 | + | 0.967396i | \(0.418494\pi\) |
−0.964424 | + | 0.264361i | \(0.914839\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.51771 | − | 0.779948i | 0.148113 | − | 0.0761151i | ||||
\(106\) | −12.8282 | −1.24599 | ||||||||
\(107\) | 4.85942 | − | 8.41677i | 0.469778 | − | 0.813680i | −0.529625 | − | 0.848232i | \(-0.677667\pi\) |
0.999403 | + | 0.0345525i | \(0.0110006\pi\) | |||||||
\(108\) | −1.34371 | − | 2.32737i | −0.129298 | − | 0.223951i | ||||
\(109\) | 3.32428 | + | 5.75782i | 0.318408 | + | 0.551499i | 0.980156 | − | 0.198227i | \(-0.0635185\pi\) |
−0.661748 | + | 0.749726i | \(0.730185\pi\) | |||||||
\(110\) | 15.2999 | − | 26.5001i | 1.45878 | − | 2.52669i | ||||
\(111\) | −0.888018 | −0.0842869 | ||||||||
\(112\) | −0.348694 | + | 7.12591i | −0.0329485 | + | 0.673335i | ||||
\(113\) | 17.5434 | 1.65035 | 0.825173 | − | 0.564880i | \(-0.191078\pi\) | ||||
0.825173 | + | 0.564880i | \(0.191078\pi\) | |||||||
\(114\) | 0.598855 | − | 1.03725i | 0.0560879 | − | 0.0971471i | ||||
\(115\) | 3.92850 | + | 6.80437i | 0.366335 | + | 0.634511i | ||||
\(116\) | 8.27316 | + | 14.3295i | 0.768144 | + | 1.33046i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.4217 | 0.959399 | ||||||||
\(119\) | 10.6506 | + | 6.86421i | 0.976337 | + | 0.629241i | ||||
\(120\) | 0.709696 | 0.0647861 | ||||||||
\(121\) | −2.46946 | + | 4.27724i | −0.224497 | + | 0.388840i | ||||
\(122\) | −2.16313 | − | 3.74665i | −0.195840 | − | 0.339206i | ||||
\(123\) | −0.189524 | − | 0.328265i | −0.0170888 | − | 0.0295987i | ||||
\(124\) | −1.87156 | + | 3.24163i | −0.168071 | + | 0.291107i | ||||
\(125\) | 10.8304 | 0.968704 | ||||||||
\(126\) | 14.0294 | + | 9.04182i | 1.24984 | + | 0.805510i | ||||
\(127\) | 19.5143 | 1.73162 | 0.865809 | − | 0.500375i | \(-0.166805\pi\) | ||||
0.865809 | + | 0.500375i | \(0.166805\pi\) | |||||||
\(128\) | −4.25407 | + | 7.36826i | −0.376010 | + | 0.651269i | ||||
\(129\) | 0.128010 | + | 0.221720i | 0.0112707 | + | 0.0195214i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.53713 | + | 16.5188i | −0.833263 | + | 1.44325i | 0.0621741 | + | 0.998065i | \(0.480197\pi\) |
−0.895437 | + | 0.445188i | \(0.853137\pi\) | |||||||
\(132\) | −1.79777 | −0.156476 | ||||||||
\(133\) | −0.407406 | + | 8.32573i | −0.0353266 | + | 0.721933i | ||||
\(134\) | −8.31259 | −0.718098 | ||||||||
\(135\) | −1.92455 | + | 3.33341i | −0.165638 | + | 0.286894i | ||||
\(136\) | 2.63495 | + | 4.56387i | 0.225945 | + | 0.391349i | ||||
\(137\) | 3.21445 | + | 5.56759i | 0.274629 | + | 0.475672i | 0.970042 | − | 0.242939i | \(-0.0781116\pi\) |
−0.695412 | + | 0.718611i | \(0.744778\pi\) | |||||||
\(138\) | 0.414149 | − | 0.717328i | 0.0352547 | − | 0.0610630i | ||||
\(139\) | −2.42854 | −0.205986 | −0.102993 | − | 0.994682i | \(-0.532842\pi\) | ||||
−0.102993 | + | 0.994682i | \(0.532842\pi\) | |||||||
\(140\) | −21.3646 | + | 10.9792i | −1.80564 | + | 0.927913i | ||||
\(141\) | −0.182240 | −0.0153473 | ||||||||
\(142\) | −9.35942 | + | 16.2110i | −0.785425 | + | 1.36040i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.00171 | − | 6.93117i | −0.333476 | − | 0.577598i | ||||
\(145\) | 11.8494 | − | 20.5237i | 0.984036 | − | 1.70440i | ||||
\(146\) | −6.56518 | −0.543338 | ||||||||
\(147\) | 1.24600 | + | 0.122234i | 0.102768 | + | 0.0100817i | ||||
\(148\) | 12.5005 | 1.02753 | ||||||||
\(149\) | 0.0576764 | − | 0.0998984i | 0.00472503 | − | 0.00818400i | −0.863653 | − | 0.504086i | \(-0.831829\pi\) |
0.868378 | + | 0.495902i | \(0.165163\pi\) | |||||||
\(150\) | −1.52126 | − | 2.63491i | −0.124211 | − | 0.215139i | ||||
\(151\) | −5.90155 | − | 10.2218i | −0.480262 | − | 0.831838i | 0.519482 | − | 0.854481i | \(-0.326125\pi\) |
−0.999744 | + | 0.0226438i | \(0.992792\pi\) | |||||||
\(152\) | −1.73343 | + | 3.00239i | −0.140600 | + | 0.243526i | ||||
\(153\) | −14.2143 | −1.14916 | ||||||||
\(154\) | 19.9686 | − | 10.2619i | 1.60912 | − | 0.826924i | ||||
\(155\) | 5.36114 | 0.430617 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.57343 | + | 11.3855i | 0.524617 | + | 0.908663i | 0.999589 | + | 0.0286625i | \(0.00912481\pi\) |
−0.474972 | + | 0.880001i | \(0.657542\pi\) | |||||||
\(158\) | 2.09149 | + | 3.62257i | 0.166390 | + | 0.288197i | ||||
\(159\) | 0.539730 | − | 0.934840i | 0.0428034 | − | 0.0741377i | ||||
\(160\) | 28.6040 | 2.26135 | ||||||||
\(161\) | −0.281749 | + | 5.75782i | −0.0222049 | + | 0.453780i | ||||
\(162\) | −18.5197 | −1.45504 | ||||||||
\(163\) | −9.32424 | + | 16.1501i | −0.730331 | + | 1.26497i | 0.226411 | + | 0.974032i | \(0.427301\pi\) |
−0.956742 | + | 0.290938i | \(0.906033\pi\) | |||||||
\(164\) | 2.66790 | + | 4.62094i | 0.208328 | + | 0.360835i | ||||
\(165\) | 1.28744 | + | 2.22992i | 0.100227 | + | 0.173599i | ||||
\(166\) | 8.14084 | − | 14.1003i | 0.631852 | − | 1.09440i | ||||
\(167\) | 0.972672 | 0.0752676 | 0.0376338 | − | 0.999292i | \(-0.488018\pi\) | ||||
0.0376338 | + | 0.999292i | \(0.488018\pi\) | |||||||
\(168\) | 0.437681 | + | 0.282082i | 0.0337678 | + | 0.0217631i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 18.3534 | − | 31.7891i | 1.40764 | − | 2.43811i | ||||
\(171\) | −4.67550 | − | 8.09821i | −0.357545 | − | 0.619286i | ||||
\(172\) | −1.80198 | − | 3.12113i | −0.137400 | − | 0.237984i | ||||
\(173\) | −1.22855 | + | 2.12791i | −0.0934050 | + | 0.161782i | −0.908942 | − | 0.416923i | \(-0.863108\pi\) |
0.815537 | + | 0.578705i | \(0.196442\pi\) | |||||||
\(174\) | −2.49836 | −0.189400 | ||||||||
\(175\) | 17.7988 | + | 11.4712i | 1.34546 | + | 0.867138i | ||||
\(176\) | −10.7656 | −0.811491 | ||||||||
\(177\) | −0.438481 | + | 0.759471i | −0.0329583 | + | 0.0570854i | ||||
\(178\) | −13.6023 | − | 23.5598i | −1.01953 | − | 1.76588i | ||||
\(179\) | −7.23629 | − | 12.5336i | −0.540866 | − | 0.936807i | −0.998855 | − | 0.0478492i | \(-0.984763\pi\) |
0.457989 | − | 0.888958i | \(-0.348570\pi\) | |||||||
\(180\) | 13.4732 | − | 23.3362i | 1.00423 | − | 1.73938i | ||||
\(181\) | 9.17885 | 0.682259 | 0.341129 | − | 0.940016i | \(-0.389191\pi\) | ||||
0.341129 | + | 0.940016i | \(0.389191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.364043 | 0.0269108 | ||||||||
\(184\) | −1.19879 | + | 2.07636i | −0.0883758 | + | 0.153071i | ||||
\(185\) | −8.95202 | − | 15.5053i | −0.658165 | − | 1.13998i | ||||
\(186\) | −0.282590 | − | 0.489460i | −0.0207205 | − | 0.0358889i | ||||
\(187\) | −9.56002 | + | 16.5584i | −0.699098 | + | 1.21087i | ||||
\(188\) | 2.56536 | 0.187098 | ||||||||
\(189\) | −2.51182 | + | 1.29082i | −0.182708 | + | 0.0938935i | ||||
\(190\) | 24.1480 | 1.75188 | ||||||||
\(191\) | −8.79202 | + | 15.2282i | −0.636168 | + | 1.10188i | 0.350098 | + | 0.936713i | \(0.386148\pi\) |
−0.986266 | + | 0.165162i | \(0.947185\pi\) | |||||||
\(192\) | −1.02545 | − | 1.77613i | −0.0740054 | − | 0.128181i | ||||
\(193\) | −9.87791 | − | 17.1090i | −0.711028 | − | 1.23154i | −0.964472 | − | 0.264186i | \(-0.914897\pi\) |
0.253444 | − | 0.967350i | \(-0.418437\pi\) | |||||||
\(194\) | 1.44428 | − | 2.50156i | 0.103693 | − | 0.179601i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −17.5398 | − | 1.72068i | −1.25284 | − | 0.122905i | ||||
\(197\) | −7.66020 | −0.545767 | −0.272883 | − | 0.962047i | \(-0.587977\pi\) | ||||
−0.272883 | + | 0.962047i | \(0.587977\pi\) | |||||||
\(198\) | −12.5929 | + | 21.8115i | −0.894935 | + | 1.55007i | ||||
\(199\) | 3.27171 | + | 5.66677i | 0.231925 | + | 0.401706i | 0.958375 | − | 0.285514i | \(-0.0921642\pi\) |
−0.726449 | + | 0.687220i | \(0.758831\pi\) | |||||||
\(200\) | 4.40342 | + | 7.62694i | 0.311369 | + | 0.539306i | ||||
\(201\) | 0.349741 | − | 0.605769i | 0.0246688 | − | 0.0427277i | ||||
\(202\) | −9.11412 | −0.641267 | ||||||||
\(203\) | 15.4652 | − | 7.94755i | 1.08545 | − | 0.557809i | ||||
\(204\) | −2.15657 | −0.150990 | ||||||||
\(205\) | 3.82115 | − | 6.61842i | 0.266880 | − | 0.462250i | ||||
\(206\) | 15.3406 | + | 26.5707i | 1.06883 | + | 1.85127i | ||||
\(207\) | −3.23343 | − | 5.60047i | −0.224739 | − | 0.389259i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.5783 | −0.870060 | ||||||||
\(210\) | 0.177265 | − | 3.62257i | 0.0122324 | − | 0.249981i | ||||
\(211\) | 20.0452 | 1.37997 | 0.689983 | − | 0.723825i | \(-0.257618\pi\) | ||||
0.689983 | + | 0.723825i | \(0.257618\pi\) | |||||||
\(212\) | −7.59771 | + | 13.1596i | −0.521813 | + | 0.903806i | ||||
\(213\) | −0.787571 | − | 1.36411i | −0.0539635 | − | 0.0934674i | ||||
\(214\) | −10.3287 | − | 17.8898i | −0.706052 | − | 1.22292i | ||||
\(215\) | −2.58092 | + | 4.47028i | −0.176017 | + | 0.304871i | ||||
\(216\) | −1.17455 | −0.0799183 | ||||||||
\(217\) | 3.30630 | + | 2.13088i | 0.224446 | + | 0.144654i | ||||
\(218\) | 14.1314 | 0.957102 | ||||||||
\(219\) | 0.276221 | − | 0.478429i | 0.0186653 | − | 0.0323293i | ||||
\(220\) | −18.1232 | − | 31.3902i | −1.22186 | − | 2.11633i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.943736 | + | 1.63460i | −0.0633394 | + | 0.109707i | ||||
\(223\) | −27.7139 | −1.85586 | −0.927931 | − | 0.372752i | \(-0.878414\pi\) | ||||
−0.927931 | + | 0.372752i | \(0.878414\pi\) | |||||||
\(224\) | 17.6406 | + | 11.3692i | 1.17866 | + | 0.759636i | ||||
\(225\) | −23.7543 | −1.58362 | ||||||||
\(226\) | 18.6442 | − | 32.2927i | 1.24019 | − | 2.14808i | ||||
\(227\) | 5.68555 | + | 9.84766i | 0.377363 | + | 0.653612i | 0.990678 | − | 0.136227i | \(-0.0434976\pi\) |
−0.613315 | + | 0.789839i | \(0.710164\pi\) | |||||||
\(228\) | −0.709362 | − | 1.22865i | −0.0469786 | − | 0.0813694i | ||||
\(229\) | −4.35556 | + | 7.54406i | −0.287824 | + | 0.498525i | −0.973290 | − | 0.229579i | \(-0.926265\pi\) |
0.685466 | + | 0.728104i | \(0.259598\pi\) | |||||||
\(230\) | 16.7000 | 1.10116 | ||||||||
\(231\) | −0.0923344 | + | 1.88694i | −0.00607516 | + | 0.124152i | ||||
\(232\) | 7.23170 | 0.474784 | ||||||||
\(233\) | 1.68228 | − | 2.91380i | 0.110210 | − | 0.190889i | −0.805645 | − | 0.592399i | \(-0.798181\pi\) |
0.915855 | + | 0.401510i | \(0.131514\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.83714 | − | 3.18202i | −0.119842 | − | 0.207572i | ||||
\(236\) | 6.17244 | − | 10.6910i | 0.401791 | − | 0.695923i | ||||
\(237\) | −0.351987 | −0.0228640 | ||||||||
\(238\) | 23.9540 | − | 12.3099i | 1.55271 | − | 0.797934i | ||||
\(239\) | 19.8798 | 1.28592 | 0.642958 | − | 0.765902i | \(-0.277707\pi\) | ||||
0.642958 | + | 0.765902i | \(0.277707\pi\) | |||||||
\(240\) | −0.869579 | + | 1.50615i | −0.0561311 | + | 0.0972219i | ||||
\(241\) | −9.43595 | − | 16.3435i | −0.607823 | − | 1.05278i | −0.991599 | − | 0.129354i | \(-0.958710\pi\) |
0.383776 | − | 0.923426i | \(-0.374624\pi\) | |||||||
\(242\) | 5.24882 | + | 9.09123i | 0.337407 | + | 0.584406i | ||||
\(243\) | 2.38030 | − | 4.12280i | 0.152696 | − | 0.264477i | ||||
\(244\) | −5.12458 | −0.328068 | ||||||||
\(245\) | 10.4265 | + | 22.9882i | 0.666125 | + | 1.46866i | ||||
\(246\) | −0.805663 | −0.0513672 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.817978 | + | 1.41678i | 0.0519417 | + | 0.0899656i | ||||
\(249\) | 0.685030 | + | 1.18651i | 0.0434120 | + | 0.0751918i | ||||
\(250\) | 11.5100 | − | 19.9359i | 0.727956 | − | 1.26086i | ||||
\(251\) | −9.79601 | −0.618319 | −0.309159 | − | 0.951010i | \(-0.600048\pi\) | ||||
−0.309159 | + | 0.951010i | \(0.600048\pi\) | |||||||
\(252\) | 17.5845 | − | 9.03666i | 1.10772 | − | 0.569256i | ||||
\(253\) | −8.69877 | −0.546887 | ||||||||
\(254\) | 20.7388 | − | 35.9206i | 1.30127 | − | 2.25386i | ||||
\(255\) | 1.54439 | + | 2.67497i | 0.0967136 | + | 0.167513i | ||||
\(256\) | −2.42488 | − | 4.20002i | −0.151555 | − | 0.262501i | ||||
\(257\) | −10.4697 | + | 18.1341i | −0.653083 | + | 1.13117i | 0.329287 | + | 0.944230i | \(0.393192\pi\) |
−0.982371 | + | 0.186944i | \(0.940142\pi\) | |||||||
\(258\) | 0.544170 | 0.0338785 | ||||||||
\(259\) | 0.642031 | − | 13.1205i | 0.0398939 | − | 0.815271i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.75285 | + | 16.8924i | −0.603686 | + | 1.04562i | ||||
\(262\) | 20.2711 | + | 35.1105i | 1.25235 | + | 2.16914i | ||||
\(263\) | 3.69340 | + | 6.39715i | 0.227745 | + | 0.394465i | 0.957139 | − | 0.289628i | \(-0.0935316\pi\) |
−0.729395 | + | 0.684093i | \(0.760198\pi\) | |||||||
\(264\) | −0.392865 | + | 0.680462i | −0.0241792 | + | 0.0418795i | ||||
\(265\) | 21.7639 | 1.33694 | ||||||||
\(266\) | 14.8924 | + | 9.59806i | 0.913114 | + | 0.588495i | ||||
\(267\) | 2.28919 | 0.140096 | ||||||||
\(268\) | −4.92326 | + | 8.52733i | −0.300736 | + | 0.520890i | ||||
\(269\) | −11.3946 | − | 19.7360i | −0.694740 | − | 1.20332i | −0.970268 | − | 0.242032i | \(-0.922186\pi\) |
0.275529 | − | 0.961293i | \(-0.411147\pi\) | |||||||
\(270\) | 4.09060 | + | 7.08513i | 0.248946 | + | 0.431187i | ||||
\(271\) | −2.08316 | + | 3.60814i | −0.126543 | + | 0.219179i | −0.922335 | − | 0.386391i | \(-0.873722\pi\) |
0.795792 | + | 0.605570i | \(0.207055\pi\) | |||||||
\(272\) | −12.9143 | −0.783042 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.6646 | 0.825507 | ||||||||
\(275\) | −15.9763 | + | 27.6717i | −0.963406 | + | 1.66867i | ||||
\(276\) | −0.490572 | − | 0.849696i | −0.0295290 | − | 0.0511457i | ||||
\(277\) | −0.388551 | − | 0.672989i | −0.0233457 | − | 0.0404360i | 0.854116 | − | 0.520082i | \(-0.174099\pi\) |
−0.877462 | + | 0.479646i | \(0.840765\pi\) | |||||||
\(278\) | −2.58092 | + | 4.47028i | −0.154793 | + | 0.268110i | ||||
\(279\) | −4.41259 | −0.264175 | ||||||||
\(280\) | −0.513106 | + | 10.4858i | −0.0306639 | + | 0.626648i | ||||
\(281\) | −11.8988 | −0.709824 | −0.354912 | − | 0.934900i | \(-0.615489\pi\) | ||||
−0.354912 | + | 0.934900i | \(0.615489\pi\) | |||||||
\(282\) | −0.193674 | + | 0.335454i | −0.0115331 | + | 0.0199760i | ||||
\(283\) | 7.95202 | + | 13.7733i | 0.472698 | + | 0.818738i | 0.999512 | − | 0.0312434i | \(-0.00994670\pi\) |
−0.526813 | + | 0.849981i | \(0.676613\pi\) | |||||||
\(284\) | 11.0865 | + | 19.2024i | 0.657864 | + | 1.13945i | ||||
\(285\) | −1.01599 | + | 1.75975i | −0.0601823 | + | 0.104239i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.98717 | − | 2.56290i | 0.294383 | − | 0.151283i | ||||
\(288\) | −23.5431 | −1.38729 | ||||||||
\(289\) | −2.96801 | + | 5.14075i | −0.174589 | + | 0.302397i | ||||
\(290\) | −25.1857 | − | 43.6229i | −1.47896 | − | 2.56163i | ||||
\(291\) | 0.121532 | + | 0.210500i | 0.00712433 | + | 0.0123397i | ||||
\(292\) | −3.88833 | + | 6.73478i | −0.227547 | + | 0.394123i | ||||
\(293\) | −6.73698 | −0.393579 | −0.196789 | − | 0.980446i | \(-0.563051\pi\) | ||||
−0.196789 | + | 0.980446i | \(0.563051\pi\) | |||||||
\(294\) | 1.54918 | − | 2.16364i | 0.0903500 | − | 0.126186i | ||||
\(295\) | −17.6811 | −1.02944 | ||||||||
\(296\) | 2.73172 | − | 4.73148i | 0.158778 | − | 0.275011i | ||||
\(297\) | −2.13073 | − | 3.69054i | −0.123638 | − | 0.214147i | ||||
\(298\) | −0.122591 | − | 0.212333i | −0.00710148 | − | 0.0123001i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.60397 | −0.208075 | ||||||||
\(301\) | −3.36849 | + | 1.73106i | −0.194157 | + | 0.0997768i | ||||
\(302\) | −25.0874 | −1.44362 | ||||||||
\(303\) | 0.383465 | − | 0.664180i | 0.0220295 | − | 0.0381562i | ||||
\(304\) | −4.24789 | − | 7.35756i | −0.243633 | − | 0.421985i | ||||
\(305\) | 3.66988 | + | 6.35642i | 0.210137 | + | 0.363968i | ||||
\(306\) | −15.1061 | + | 26.1646i | −0.863561 | + | 1.49573i | ||||
\(307\) | 14.7179 | 0.839996 | 0.419998 | − | 0.907525i | \(-0.362031\pi\) | ||||
0.419998 | + | 0.907525i | \(0.362031\pi\) | |||||||
\(308\) | 1.29978 | − | 26.5622i | 0.0740617 | − | 1.51352i | ||||
\(309\) | −2.58174 | −0.146870 | ||||||||
\(310\) | 5.69752 | − | 9.86840i | 0.323597 | − | 0.560487i | ||||
\(311\) | −14.3289 | − | 24.8184i | −0.812517 | − | 1.40732i | −0.911097 | − | 0.412191i | \(-0.864764\pi\) |
0.0985808 | − | 0.995129i | \(-0.468570\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.4125 | − | 28.4274i | 0.927692 | − | 1.60681i | 0.140518 | − | 0.990078i | \(-0.455123\pi\) |
0.787174 | − | 0.616732i | \(-0.211544\pi\) | |||||||
\(314\) | 27.9435 | 1.57694 | ||||||||
\(315\) | −23.8017 | − | 15.3400i | −1.34108 | − | 0.864312i | ||||
\(316\) | 4.95488 | 0.278734 | ||||||||
\(317\) | 5.20605 | − | 9.01715i | 0.292401 | − | 0.506453i | −0.681976 | − | 0.731375i | \(-0.738879\pi\) |
0.974377 | + | 0.224921i | \(0.0722125\pi\) | |||||||
\(318\) | −1.14719 | − | 1.98699i | −0.0643313 | − | 0.111425i | ||||
\(319\) | 13.1188 | + | 22.7225i | 0.734515 | + | 1.27222i | ||||
\(320\) | 20.6749 | − | 35.8100i | 1.15576 | − | 2.00184i | ||||
\(321\) | 1.73826 | 0.0970201 | ||||||||
\(322\) | 10.2992 | + | 6.63772i | 0.573949 | + | 0.369905i | ||||
\(323\) | −15.0887 | −0.839558 | ||||||||
\(324\) | −10.9686 | + | 18.9981i | −0.609364 | + | 1.05545i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.8186 | + | 34.3268i | 1.09765 | + | 1.90118i | ||||
\(327\) | −0.594562 | + | 1.02981i | −0.0328793 | + | 0.0569487i | ||||
\(328\) | 2.33205 | 0.128766 | ||||||||
\(329\) | 0.131758 | − | 2.69261i | 0.00726406 | − | 0.148448i | ||||
\(330\) | 5.47290 | 0.301273 | ||||||||
\(331\) | −2.23007 | + | 3.86260i | −0.122576 | + | 0.212308i | −0.920783 | − | 0.390076i | \(-0.872449\pi\) |
0.798207 | + | 0.602383i | \(0.205782\pi\) | |||||||
\(332\) | −9.64307 | − | 16.7023i | −0.529232 | − | 0.916657i | ||||
\(333\) | 7.36813 | + | 12.7620i | 0.403771 | + | 0.699352i | ||||
\(334\) | 1.03370 | − | 1.79043i | 0.0565617 | − | 0.0979677i | ||||
\(335\) | 14.1028 | 0.770519 | ||||||||
\(336\) | −1.13493 | + | 0.583240i | −0.0619156 | + | 0.0318183i | ||||
\(337\) | −10.7949 | −0.588034 | −0.294017 | − | 0.955800i | \(-0.594992\pi\) | ||||
−0.294017 | + | 0.955800i | \(0.594992\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.56886 | + | 2.71734i | 0.0852087 | + | 0.147586i | ||||
\(340\) | −21.7402 | − | 37.6551i | −1.17903 | − | 2.04214i | ||||
\(341\) | −2.96775 | + | 5.14030i | −0.160713 | + | 0.278363i | ||||
\(342\) | −19.8755 | −1.07474 | ||||||||
\(343\) | −2.70687 | + | 18.3214i | −0.146157 | + | 0.989261i | ||||
\(344\) | −1.57514 | −0.0849259 | ||||||||
\(345\) | −0.702630 | + | 1.21699i | −0.0378283 | + | 0.0655206i | ||||
\(346\) | 2.61127 | + | 4.52286i | 0.140383 | + | 0.243150i | ||||
\(347\) | 2.03516 | + | 3.52499i | 0.109253 | + | 0.189232i | 0.915468 | − | 0.402391i | \(-0.131821\pi\) |
−0.806215 | + | 0.591623i | \(0.798487\pi\) | |||||||
\(348\) | −1.47969 | + | 2.56290i | −0.0793198 | + | 0.137386i | ||||
\(349\) | 23.8727 | 1.27788 | 0.638938 | − | 0.769258i | \(-0.279374\pi\) | ||||
0.638938 | + | 0.769258i | \(0.279374\pi\) | |||||||
\(350\) | 40.0309 | − | 20.5718i | 2.13974 | − | 1.09961i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15.8343 | + | 27.4257i | −0.843969 | + | 1.46180i | ||||
\(353\) | −13.0420 | − | 22.5894i | −0.694154 | − | 1.20231i | −0.970465 | − | 0.241242i | \(-0.922445\pi\) |
0.276311 | − | 0.961068i | \(-0.410888\pi\) | |||||||
\(354\) | 0.931987 | + | 1.61425i | 0.0495346 | + | 0.0857964i | ||||
\(355\) | 15.8788 | − | 27.5030i | 0.842762 | − | 1.45971i | ||||
\(356\) | −32.2246 | −1.70790 | ||||||||
\(357\) | −0.110763 | + | 2.26354i | −0.00586217 | + | 0.119799i | ||||
\(358\) | −30.7613 | −1.62579 | ||||||||
\(359\) | 11.4472 | − | 19.8271i | 0.604160 | − | 1.04644i | −0.388024 | − | 0.921649i | \(-0.626842\pi\) |
0.992184 | − | 0.124786i | \(-0.0398244\pi\) | |||||||
\(360\) | −5.88855 | − | 10.1993i | −0.310354 | − | 0.537549i | ||||
\(361\) | 4.53687 | + | 7.85809i | 0.238783 | + | 0.413584i | ||||
\(362\) | 9.75478 | − | 16.8958i | 0.512700 | − | 0.888022i | ||||
\(363\) | −0.883349 | −0.0463638 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.1382 | 0.583002 | ||||||||
\(366\) | 0.386885 | − | 0.670104i | 0.0202228 | − | 0.0350269i | ||||
\(367\) | 9.08003 | + | 15.7271i | 0.473974 | + | 0.820946i | 0.999556 | − | 0.0297964i | \(-0.00948589\pi\) |
−0.525582 | + | 0.850743i | \(0.676153\pi\) | |||||||
\(368\) | −2.93771 | − | 5.08826i | −0.153139 | − | 0.265244i | ||||
\(369\) | −3.14507 | + | 5.44742i | −0.163726 | + | 0.283581i | ||||
\(370\) | −38.0548 | −1.97838 | ||||||||
\(371\) | 13.4221 | + | 8.65045i | 0.696842 | + | 0.449109i | ||||
\(372\) | −0.669473 | −0.0347105 | ||||||||
\(373\) | 7.93457 | − | 13.7431i | 0.410836 | − | 0.711590i | −0.584145 | − | 0.811649i | \(-0.698570\pi\) |
0.994981 | + | 0.100060i | \(0.0319034\pi\) | |||||||
\(374\) | 20.3197 | + | 35.1948i | 1.05071 | + | 1.81988i | ||||
\(375\) | 0.968536 | + | 1.67755i | 0.0500150 | + | 0.0866285i | ||||
\(376\) | 0.560605 | − | 0.970997i | 0.0289110 | − | 0.0500754i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.293375 | + | 5.99540i | −0.0150896 | + | 0.308370i | ||||
\(379\) | 27.7634 | 1.42611 | 0.713055 | − | 0.701108i | \(-0.247311\pi\) | ||||
0.713055 | + | 0.701108i | \(0.247311\pi\) | |||||||
\(380\) | 14.3020 | − | 24.7718i | 0.733678 | − | 1.27077i | ||||
\(381\) | 1.74511 | + | 3.02262i | 0.0894048 | + | 0.154854i | ||||
\(382\) | 18.6873 | + | 32.3674i | 0.956128 | + | 1.65606i | ||||
\(383\) | 13.1234 | − | 22.7304i | 0.670576 | − | 1.16147i | −0.307165 | − | 0.951656i | \(-0.599380\pi\) |
0.977741 | − | 0.209815i | \(-0.0672863\pi\) | |||||||
\(384\) | −1.52172 | −0.0776548 | ||||||||
\(385\) | −33.8780 | + | 17.4099i | −1.72658 | + | 0.887289i | ||||
\(386\) | −41.9908 | −2.13728 | ||||||||
\(387\) | 2.12428 | − | 3.67936i | 0.107983 | − | 0.187032i | ||||
\(388\) | −1.71079 | − | 2.96317i | −0.0868521 | − | 0.150432i | ||||
\(389\) | 12.6277 | + | 21.8718i | 0.640250 | + | 1.10895i | 0.985377 | + | 0.170389i | \(0.0545026\pi\) |
−0.345127 | + | 0.938556i | \(0.612164\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.4349 | −0.527714 | ||||||||
\(392\) | −4.48422 | + | 6.26283i | −0.226487 | + | 0.316321i | ||||
\(393\) | −3.41151 | −0.172088 | ||||||||
\(394\) | −8.14084 | + | 14.1003i | −0.410129 | + | 0.710365i | ||||
\(395\) | −3.54835 | − | 6.14592i | −0.178537 | − | 0.309235i | ||||
\(396\) | 14.9166 | + | 25.8363i | 0.749588 | + | 1.29833i | ||||
\(397\) | 7.48827 | − | 12.9701i | 0.375826 | − | 0.650949i | −0.614625 | − | 0.788820i | \(-0.710692\pi\) |
0.990450 | + | 0.137871i | \(0.0440258\pi\) | |||||||
\(398\) | 13.9080 | 0.697143 | ||||||||
\(399\) | −1.32603 | + | 0.681443i | −0.0663843 | + | 0.0341148i | ||||
\(400\) | −21.5817 | −1.07909 | ||||||||
\(401\) | 2.67204 | − | 4.62811i | 0.133435 | − | 0.231117i | −0.791563 | − | 0.611087i | \(-0.790733\pi\) |
0.924999 | + | 0.379970i | \(0.124066\pi\) | |||||||
\(402\) | −0.743371 | − | 1.28756i | −0.0370760 | − | 0.0642175i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.39798 | + | 9.34957i | −0.268559 | + | 0.465159i | ||||
\(405\) | 31.4198 | 1.56126 | ||||||||
\(406\) | 1.80630 | − | 36.9135i | 0.0896451 | − | 1.83199i | ||||
\(407\) | 19.8222 | 0.982549 | ||||||||
\(408\) | −0.471273 | + | 0.816269i | −0.0233315 | + | 0.0404113i | ||||
\(409\) | 1.68259 | + | 2.91433i | 0.0831985 | + | 0.144104i | 0.904622 | − | 0.426214i | \(-0.140153\pi\) |
−0.821424 | + | 0.570319i | \(0.806820\pi\) | |||||||
\(410\) | −8.12181 | − | 14.0674i | −0.401107 | − | 0.694739i | ||||
\(411\) | −0.574919 | + | 0.995789i | −0.0283587 | + | 0.0491186i | ||||
\(412\) | 36.3428 | 1.79048 | ||||||||
\(413\) | −10.9042 | − | 7.02769i | −0.536562 | − | 0.345810i | ||||
\(414\) | −13.7453 | −0.675542 | ||||||||
\(415\) | −13.8114 | + | 23.9221i | −0.677977 | + | 1.17429i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.217178 | − | 0.376163i | −0.0106352 | − | 0.0184208i | ||||
\(418\) | −13.3675 | + | 23.1533i | −0.653828 | + | 1.13246i | ||||
\(419\) | −28.8639 | −1.41010 | −0.705048 | − | 0.709160i | \(-0.749074\pi\) | ||||
−0.705048 | + | 0.709160i | \(0.749074\pi\) | |||||||
\(420\) | −3.61117 | − | 2.32737i | −0.176207 | − | 0.113564i | ||||
\(421\) | −16.6125 | −0.809644 | −0.404822 | − | 0.914395i | \(-0.632667\pi\) | ||||
−0.404822 | + | 0.914395i | \(0.632667\pi\) | |||||||
\(422\) | 21.3029 | − | 36.8977i | 1.03701 | − | 1.79615i | ||||
\(423\) | 1.51209 | + | 2.61902i | 0.0735205 | + | 0.127341i | ||||
\(424\) | 3.32064 | + | 5.75151i | 0.161264 | + | 0.279318i | ||||
\(425\) | −19.1648 | + | 33.1945i | −0.929631 | + | 1.61017i | ||||
\(426\) | −3.34795 | −0.162209 | ||||||||
\(427\) | −0.263201 | + | 5.37877i | −0.0127372 | + | 0.260297i | ||||
\(428\) | −24.4692 | −1.18276 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.48572 | + | 9.50154i | 0.264545 | + | 0.458205i | ||||
\(431\) | −10.2777 | − | 17.8015i | −0.495060 | − | 0.857469i | 0.504924 | − | 0.863164i | \(-0.331521\pi\) |
−0.999984 | + | 0.00569505i | \(0.998187\pi\) | |||||||
\(432\) | 1.43916 | − | 2.49270i | 0.0692417 | − | 0.119930i | ||||
\(433\) | 19.4092 | 0.932748 | 0.466374 | − | 0.884588i | \(-0.345560\pi\) | ||||
0.466374 | + | 0.884588i | \(0.345560\pi\) | |||||||
\(434\) | 7.43613 | − | 3.82141i | 0.356945 | − | 0.183434i | ||||
\(435\) | 4.23862 | 0.203226 | ||||||||
\(436\) | 8.36956 | − | 14.4965i | 0.400829 | − | 0.694257i | ||||
\(437\) | −3.43235 | − | 5.94500i | −0.164191 | − | 0.284388i | ||||
\(438\) | −0.587106 | − | 1.01690i | −0.0280530 | − | 0.0485892i | ||||
\(439\) | −6.71256 | + | 11.6265i | −0.320373 | + | 0.554902i | −0.980565 | − | 0.196195i | \(-0.937142\pi\) |
0.660192 | + | 0.751097i | \(0.270475\pi\) | |||||||
\(440\) | −15.8417 | −0.755225 | ||||||||
\(441\) | −8.58174 | − | 18.9209i | −0.408654 | − | 0.900994i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.7766 | − | 29.0579i | 0.797080 | − | 1.38058i | −0.124430 | − | 0.992228i | \(-0.539710\pi\) |
0.921510 | − | 0.388354i | \(-0.126956\pi\) | |||||||
\(444\) | 1.11788 | + | 1.93623i | 0.0530524 | + | 0.0918895i | ||||
\(445\) | 23.0771 | + | 39.9707i | 1.09396 | + | 1.89479i | ||||
\(446\) | −29.4528 | + | 51.0138i | −1.39463 | + | 2.41557i | ||||
\(447\) | 0.0206313 | 0.000975829 | ||||||||
\(448\) | 26.9839 | − | 13.8670i | 1.27487 | − | 0.655153i | ||||
\(449\) | 34.4284 | 1.62478 | 0.812388 | − | 0.583117i | \(-0.198167\pi\) | ||||
0.812388 | + | 0.583117i | \(0.198167\pi\) | |||||||
\(450\) | −25.2447 | + | 43.7251i | −1.19005 | + | 2.06122i | ||||
\(451\) | 4.23052 | + | 7.32748i | 0.199208 | + | 0.345038i | ||||
\(452\) | −22.0846 | − | 38.2517i | −1.03877 | − | 1.79921i | ||||
\(453\) | 1.05552 | − | 1.82821i | 0.0495926 | − | 0.0858969i | ||||
\(454\) | 24.1691 | 1.13431 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.620064 | −0.0290371 | ||||||||
\(457\) | 6.73967 | − | 11.6735i | 0.315269 | − | 0.546061i | −0.664226 | − | 0.747532i | \(-0.731239\pi\) |
0.979495 | + | 0.201471i | \(0.0645720\pi\) | |||||||
\(458\) | 9.25771 | + | 16.0348i | 0.432584 | + | 0.749258i | ||||
\(459\) | −2.55598 | − | 4.42710i | −0.119303 | − | 0.206639i | ||||
\(460\) | 9.89082 | − | 17.1314i | 0.461162 | − | 0.798756i | ||||
\(461\) | −1.35900 | −0.0632951 | −0.0316476 | − | 0.999499i | \(-0.510075\pi\) | ||||
−0.0316476 | + | 0.999499i | \(0.510075\pi\) | |||||||
\(462\) | 3.37522 | + | 2.17530i | 0.157030 | + | 0.101204i | ||||
\(463\) | 2.49836 | 0.116109 | 0.0580543 | − | 0.998313i | \(-0.481510\pi\) | ||||
0.0580543 | + | 0.998313i | \(0.481510\pi\) | |||||||
\(464\) | −8.86088 | + | 15.3475i | −0.411356 | + | 0.712489i | ||||
\(465\) | 0.479431 | + | 0.830399i | 0.0222331 | + | 0.0385088i | ||||
\(466\) | −3.57567 | − | 6.19325i | −0.165640 | − | 0.286897i | ||||
\(467\) | 13.1091 | − | 22.7056i | 0.606617 | − | 1.05069i | −0.385176 | − | 0.922843i | \(-0.625859\pi\) |
0.991794 | − | 0.127849i | \(-0.0408072\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.69744 | + | 5.60542i | 0.401610 | + | 0.258834i | ||||
\(470\) | −7.80965 | −0.360232 | ||||||||
\(471\) | −1.17569 | + | 2.03635i | −0.0541728 | + | 0.0938301i | ||||
\(472\) | −2.69771 | − | 4.67257i | −0.124172 | − | 0.215072i | ||||
\(473\) | −2.85743 | − | 4.94921i | −0.131385 | − | 0.227565i | ||||
\(474\) | −0.374073 | + | 0.647913i | −0.0171817 | + | 0.0297596i | ||||
\(475\) | −25.2156 | −1.15697 | ||||||||
\(476\) | 1.55919 | − | 31.8635i | 0.0714653 | − | 1.46046i | ||||
\(477\) | −17.9132 | −0.820188 | ||||||||
\(478\) | 21.1271 | − | 36.5933i | 0.966332 | − | 1.67374i | ||||
\(479\) | −11.9230 | − | 20.6513i | −0.544778 | − | 0.943583i | −0.998621 | − | 0.0525011i | \(-0.983281\pi\) |
0.453843 | − | 0.891082i | \(-0.350053\pi\) | |||||||
\(480\) | 2.55798 | + | 4.43055i | 0.116755 | + | 0.202226i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −40.1120 | −1.82705 | ||||||||
\(483\) | −0.917038 | + | 0.471265i | −0.0417267 | + | 0.0214433i | ||||
\(484\) | 12.4348 | 0.565217 | ||||||||
\(485\) | −2.45030 | + | 4.24405i | −0.111263 | + | 0.192712i | ||||
\(486\) | −5.05930 | − | 8.76296i | −0.229494 | − | 0.397496i | ||||
\(487\) | −5.29733 | − | 9.17524i | −0.240045 | − | 0.415770i | 0.720682 | − | 0.693266i | \(-0.243829\pi\) |
−0.960727 | + | 0.277496i | \(0.910496\pi\) | |||||||
\(488\) | −1.11987 | + | 1.93967i | −0.0506941 | + | 0.0878047i | ||||
\(489\) | −3.33536 | −0.150830 | ||||||||
\(490\) | 53.3957 | + | 5.23820i | 2.41217 | + | 0.236638i | ||||
\(491\) | −19.7704 | −0.892224 | −0.446112 | − | 0.894977i | \(-0.647192\pi\) | ||||
−0.446112 | + | 0.894977i | \(0.647192\pi\) | |||||||
\(492\) | −0.477166 | + | 0.826476i | −0.0215123 | + | 0.0372604i | ||||
\(493\) | 15.7371 | + | 27.2575i | 0.708764 | + | 1.22762i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.3646 | − | 37.0045i | 0.960266 | − | 1.66323i | ||||
\(496\) | −4.00902 | −0.180010 | ||||||||
\(497\) | 20.7243 | − | 10.6502i | 0.929612 | − | 0.477726i | ||||
\(498\) | 2.91205 | 0.130492 | ||||||||
\(499\) | 6.59530 | − | 11.4234i | 0.295246 | − | 0.511381i | −0.679796 | − | 0.733401i | \(-0.737932\pi\) |
0.975042 | + | 0.222020i | \(0.0712650\pi\) | |||||||
\(500\) | −13.6339 | − | 23.6147i | −0.609728 | − | 1.05608i | ||||
\(501\) | 0.0869833 | + | 0.150660i | 0.00388613 | + | 0.00673097i | ||||
\(502\) | −10.4107 | + | 18.0318i | −0.464651 | + | 0.804798i | ||||
\(503\) | 37.9046 | 1.69008 | 0.845040 | − | 0.534703i | \(-0.179576\pi\) | ||||
0.845040 | + | 0.534703i | \(0.179576\pi\) | |||||||
\(504\) | 0.422322 | − | 8.63056i | 0.0188117 | − | 0.384436i | ||||
\(505\) | 15.4627 | 0.688080 | ||||||||
\(506\) | −9.24457 | + | 16.0121i | −0.410971 | + | 0.711823i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −24.5657 | − | 42.5490i | −1.08993 | − | 1.88781i | ||||
\(509\) | 13.8313 | − | 23.9565i | 0.613062 | − | 1.06185i | −0.377660 | − | 0.925944i | \(-0.623271\pi\) |
0.990721 | − | 0.135909i | \(-0.0433956\pi\) | |||||||
\(510\) | 6.56518 | 0.290711 | ||||||||
\(511\) | 6.86913 | + | 4.42710i | 0.303872 | + | 0.195843i | ||||
\(512\) | −27.3244 | −1.20758 | ||||||||
\(513\) | 1.68148 | − | 2.91241i | 0.0742392 | − | 0.128586i | ||||
\(514\) | 22.2533 | + | 38.5438i | 0.981551 | + | 1.70010i | ||||
\(515\) | −26.0263 | − | 45.0788i | −1.14685 | − | 1.98641i | ||||
\(516\) | 0.322293 | − | 0.558227i | 0.0141881 | − | 0.0245746i | ||||
\(517\) | 4.06792 | 0.178907 | ||||||||
\(518\) | −23.4690 | − | 15.1256i | −1.03117 | − | 0.664580i | ||||
\(519\) | −0.439464 | −0.0192903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.78339 | − | 13.4812i | −0.340996 | − | 0.590623i | 0.643622 | − | 0.765344i | \(-0.277431\pi\) |
−0.984618 | + | 0.174721i | \(0.944098\pi\) | |||||||
\(522\) | 20.7296 | + | 35.9047i | 0.907310 | + | 1.57151i | ||||
\(523\) | −13.6169 | + | 23.5852i | −0.595425 | + | 1.03131i | 0.398061 | + | 0.917359i | \(0.369683\pi\) |
−0.993487 | + | 0.113948i | \(0.963650\pi\) | |||||||
\(524\) | 48.0234 | 2.09791 | ||||||||
\(525\) | −0.185101 | + | 3.78273i | −0.00807849 | + | 0.165092i | ||||
\(526\) | 15.7005 | 0.684577 | ||||||||
\(527\) | −3.56006 | + | 6.16620i | −0.155079 | + | 0.268604i | ||||
\(528\) | −0.962741 | − | 1.66752i | −0.0418979 | − | 0.0725694i | ||||
\(529\) | 9.12630 | + | 15.8072i | 0.396796 | + | 0.687270i | ||||
\(530\) | 23.1294 | − | 40.0614i | 1.00468 | − | 1.74015i | ||||
\(531\) | 14.5528 | 0.631538 | ||||||||
\(532\) | 18.6663 | − | 9.59258i | 0.809286 | − | 0.415891i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.43283 | − | 4.21378i | 0.105279 | − | 0.182348i | ||||
\(535\) | 17.5232 | + | 30.3511i | 0.757594 | + | 1.31219i | ||||
\(536\) | 2.15175 | + | 3.72693i | 0.0929413 | + | 0.160979i | ||||
\(537\) | 1.29424 | − | 2.24169i | 0.0558507 | − | 0.0967362i | ||||
\(538\) | −48.4381 | −2.08832 | ||||||||
\(539\) | −27.8130 | − | 2.72850i | −1.19799 | − | 0.117525i | ||||
\(540\) | 9.69089 | 0.417029 | ||||||||
\(541\) | 12.1027 | − | 20.9626i | 0.520338 | − | 0.901251i | −0.479383 | − | 0.877606i | \(-0.659139\pi\) |
0.999720 | − | 0.0236453i | \(-0.00752724\pi\) | |||||||
\(542\) | 4.42774 | + | 7.66907i | 0.190188 | + | 0.329415i | ||||
\(543\) | 0.820839 | + | 1.42174i | 0.0352256 | + | 0.0610125i | ||||
\(544\) | −18.9945 | + | 32.8994i | −0.814381 | + | 1.41055i | ||||
\(545\) | −23.9749 | −1.02697 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.2177 | −0.949960 | −0.474980 | − | 0.879997i | \(-0.657545\pi\) | ||||
−0.474980 | + | 0.879997i | \(0.657545\pi\) | |||||||
\(548\) | 8.09305 | − | 14.0176i | 0.345718 | − | 0.598801i | ||||
\(549\) | −3.02057 | − | 5.23178i | −0.128915 | − | 0.223287i | ||||
\(550\) | 33.9574 | + | 58.8160i | 1.44795 | + | 2.50792i | ||||
\(551\) | −10.3528 | + | 17.9316i | −0.441045 | + | 0.763913i | ||||
\(552\) | −0.428817 | −0.0182517 | ||||||||
\(553\) | 0.254485 | − | 5.20065i | 0.0108218 | − | 0.221154i | ||||
\(554\) | −1.65172 | −0.0701749 | ||||||||
\(555\) | 1.60111 | − | 2.77320i | 0.0679632 | − | 0.117716i | ||||
\(556\) | 3.05718 | + | 5.29519i | 0.129653 | + | 0.224566i | ||||
\(557\) | −11.1602 | − | 19.3300i | −0.472873 | − | 0.819040i | 0.526645 | − | 0.850085i | \(-0.323450\pi\) |
−0.999518 | + | 0.0310455i | \(0.990116\pi\) | |||||||
\(558\) | −4.68946 | + | 8.12238i | −0.198521 | + | 0.343848i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −21.6249 | − | 13.9370i | −0.913818 | − | 0.588948i | ||||
\(561\) | −3.41970 | −0.144380 | ||||||||
\(562\) | −12.6454 | + | 21.9025i | −0.533415 | + | 0.923901i | ||||
\(563\) | −13.3519 | − | 23.1262i | −0.562717 | − | 0.974655i | −0.997258 | − | 0.0740027i | \(-0.976423\pi\) |
0.434541 | − | 0.900652i | \(-0.356911\pi\) | |||||||
\(564\) | 0.229413 | + | 0.397355i | 0.00966004 | + | 0.0167317i | ||||
\(565\) | −31.6310 | + | 54.7865i | −1.33073 | + | 2.30489i | ||||
\(566\) | 33.8039 | 1.42088 | ||||||||
\(567\) | 19.3771 | + | 12.4884i | 0.813760 | + | 0.524462i | ||||
\(568\) | 9.69090 | 0.406621 | ||||||||
\(569\) | −3.30510 | + | 5.72461i | −0.138557 | + | 0.239988i | −0.926951 | − | 0.375183i | \(-0.877580\pi\) |
0.788393 | + | 0.615171i | \(0.210913\pi\) | |||||||
\(570\) | 2.15949 | + | 3.74034i | 0.0904509 | + | 0.156666i | ||||
\(571\) | 21.0643 | + | 36.4844i | 0.881513 | + | 1.52683i | 0.849659 | + | 0.527333i | \(0.176808\pi\) |
0.0318546 | + | 0.999493i | \(0.489859\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.14498 | −0.131383 | ||||||||
\(574\) | 0.582489 | − | 11.9037i | 0.0243126 | − | 0.496853i | ||||
\(575\) | −17.4383 | −0.727227 | ||||||||
\(576\) | −17.0169 | + | 29.4741i | −0.709037 | + | 1.22809i | ||||
\(577\) | 7.94195 | + | 13.7559i | 0.330628 | + | 0.572664i | 0.982635 | − | 0.185549i | \(-0.0594063\pi\) |
−0.652007 | + | 0.758213i | \(0.726073\pi\) | |||||||
\(578\) | 6.30848 | + | 10.9266i | 0.262398 | + | 0.454487i | ||||
\(579\) | 1.76671 | − | 3.06003i | 0.0734219 | − | 0.127170i | ||||
\(580\) | −59.6665 | −2.47752 | ||||||||
\(581\) | −18.0260 | + | 9.26354i | −0.747845 | + | 0.384316i | ||||
\(582\) | 0.516630 | 0.0214150 | ||||||||
\(583\) | −12.0478 | + | 20.8674i | −0.498968 | + | 0.864238i | ||||
\(584\) | 1.69942 | + | 2.94349i | 0.0703226 | + | 0.121802i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.15969 | + | 12.4010i | −0.295764 | + | 0.512279i | ||||
\(587\) | −18.5676 | −0.766366 | −0.383183 | − | 0.923672i | \(-0.625172\pi\) | ||||
−0.383183 | + | 0.923672i | \(0.625172\pi\) | |||||||
\(588\) | −1.30201 | − | 2.87065i | −0.0536940 | − | 0.118384i | ||||
\(589\) | −4.68404 | −0.193003 | ||||||||
\(590\) | −18.7905 | + | 32.5462i | −0.773594 | + | 1.33990i | ||||
\(591\) | −0.685030 | − | 1.18651i | −0.0281784 | − | 0.0488064i | ||||
\(592\) | 6.69426 | + | 11.5948i | 0.275132 | + | 0.476543i | ||||
\(593\) | −10.3050 | + | 17.8487i | −0.423175 | + | 0.732960i | −0.996248 | − | 0.0865442i | \(-0.972418\pi\) |
0.573073 | + | 0.819504i | \(0.305751\pi\) | |||||||
\(594\) | −9.05770 | −0.371642 | ||||||||
\(595\) | −40.6394 | + | 20.8845i | −1.66605 | + | 0.856183i | ||||
\(596\) | −0.290425 | −0.0118963 | ||||||||
\(597\) | −0.585159 | + | 1.01353i | −0.0239490 | + | 0.0414809i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.80224 | + | 11.7818i | 0.277932 | + | 0.481393i | 0.970871 | − | 0.239604i | \(-0.0770176\pi\) |
−0.692939 | + | 0.720997i | \(0.743684\pi\) | |||||||
\(600\) | −0.787571 | + | 1.36411i | −0.0321524 | + | 0.0556897i | ||||
\(601\) | −12.1503 | −0.495621 | −0.247810 | − | 0.968809i | \(-0.579711\pi\) | ||||
−0.247810 | + | 0.968809i | \(0.579711\pi\) | |||||||
\(602\) | −0.393431 | + | 8.04015i | −0.0160351 | + | 0.327692i | ||||
\(603\) | −11.6076 | −0.472698 | ||||||||
\(604\) | −14.8584 | + | 25.7355i | −0.604579 | + | 1.04716i | ||||
\(605\) | −8.90496 | − | 15.4238i | −0.362038 | − | 0.627068i | ||||
\(606\) | −0.815050 | − | 1.41171i | −0.0331092 | − | 0.0573467i | ||||
\(607\) | −17.6166 | + | 30.5128i | −0.715035 | + | 1.23848i | 0.247911 | + | 0.968783i | \(0.420256\pi\) |
−0.962946 | + | 0.269695i | \(0.913077\pi\) | |||||||
\(608\) | −24.9914 | −1.01354 | ||||||||
\(609\) | 2.61403 | + | 1.68472i | 0.105926 | + | 0.0682682i | ||||
\(610\) | 15.6006 | 0.631650 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 17.8937 | + | 30.9928i | 0.723310 | + | 1.25281i | ||||
\(613\) | 15.0310 | + | 26.0345i | 0.607097 | + | 1.05152i | 0.991716 | + | 0.128448i | \(0.0409996\pi\) |
−0.384619 | + | 0.923075i | \(0.625667\pi\) | |||||||
\(614\) | 15.6414 | − | 27.0917i | 0.631236 | − | 1.09333i | ||||
\(615\) | 1.36686 | 0.0551170 | ||||||||
\(616\) | −9.76984 | − | 6.29658i | −0.393638 | − | 0.253697i | ||||
\(617\) | 7.01712 | 0.282499 | 0.141249 | − | 0.989974i | \(-0.454888\pi\) | ||||
0.141249 | + | 0.989974i | \(0.454888\pi\) | |||||||
\(618\) | −2.74373 | + | 4.75228i | −0.110369 | + | 0.191165i | ||||
\(619\) | 21.9241 | + | 37.9736i | 0.881203 | + | 1.52629i | 0.850004 | + | 0.526776i | \(0.176599\pi\) |
0.0311993 | + | 0.999513i | \(0.490067\pi\) | |||||||
\(620\) | −6.74889 | − | 11.6894i | −0.271042 | − | 0.469458i | ||||
\(621\) | 1.16286 | − | 2.01413i | 0.0466640 | − | 0.0808244i | ||||
\(622\) | −60.9118 | −2.44234 | ||||||||
\(623\) | −1.65507 | + | 33.8230i | −0.0663091 | + | 1.35509i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.481145 | − | 0.833367i | 0.0192458 | − | 0.0333347i | ||||
\(626\) | −34.8847 | − | 60.4221i | −1.39427 | − | 2.41495i | ||||
\(627\) | −1.12484 | − | 1.94829i | −0.0449219 | − | 0.0778070i | ||||
\(628\) | 16.5500 | − | 28.6654i | 0.660416 | − | 1.14387i | ||||
\(629\) | 23.7783 | 0.948103 | ||||||||
\(630\) | −53.5320 | + | 27.5100i | −2.13276 | + | 1.09602i | ||||
\(631\) | −23.4936 | −0.935267 | −0.467634 | − | 0.883922i | \(-0.654893\pi\) | ||||
−0.467634 | + | 0.883922i | \(0.654893\pi\) | |||||||
\(632\) | 1.08278 | − | 1.87544i | 0.0430708 | − | 0.0746008i | ||||
\(633\) | 1.79258 | + | 3.10485i | 0.0712488 | + | 0.123407i | ||||
\(634\) | −11.0654 | − | 19.1659i | −0.439464 | − | 0.761173i | ||||
\(635\) | −35.1846 | + | 60.9415i | −1.39626 | + | 2.41839i | ||||
\(636\) | −2.71777 | −0.107766 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 55.7680 | 2.20788 | ||||||||
\(639\) | −13.0694 | + | 22.6369i | −0.517017 | + | 0.895500i | ||||
\(640\) | −15.3403 | − | 26.5702i | −0.606378 | − | 1.05028i | ||||
\(641\) | −3.70233 | − | 6.41262i | −0.146233 | − | 0.253283i | 0.783599 | − | 0.621267i | \(-0.213382\pi\) |
−0.929832 | + | 0.367983i | \(0.880048\pi\) | |||||||
\(642\) | 1.84732 | − | 3.19966i | 0.0729081 | − | 0.126281i | ||||
\(643\) | 39.9607 | 1.57590 | 0.787948 | − | 0.615742i | \(-0.211144\pi\) | ||||
0.787948 | + | 0.615742i | \(0.211144\pi\) | |||||||
\(644\) | 12.9090 | − | 6.63393i | 0.508687 | − | 0.261413i | ||||
\(645\) | −0.923218 | −0.0363517 | ||||||||
\(646\) | −16.0354 | + | 27.7742i | −0.630906 | + | 1.09276i | ||||
\(647\) | −13.6234 | − | 23.5964i | −0.535591 | − | 0.927670i | −0.999134 | − | 0.0415963i | \(-0.986756\pi\) |
0.463544 | − | 0.886074i | \(-0.346578\pi\) | |||||||
\(648\) | 4.79389 | + | 8.30326i | 0.188322 | + | 0.326183i | ||||
\(649\) | 9.78770 | − | 16.9528i | 0.384201 | − | 0.665456i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0343844 | + | 0.702679i | −0.00134763 | + | 0.0275402i | ||||
\(652\) | 46.9514 | 1.83876 | ||||||||
\(653\) | −9.57255 | + | 16.5801i | −0.374603 | + | 0.648831i | −0.990267 | − | 0.139177i | \(-0.955554\pi\) |
0.615665 | + | 0.788008i | \(0.288888\pi\) | |||||||
\(654\) | 1.26373 | + | 2.18885i | 0.0494159 | + | 0.0855909i | ||||
\(655\) | −34.3911 | − | 59.5672i | −1.34377 | − | 2.32748i | ||||
\(656\) | −2.85743 | + | 4.94921i | −0.111564 | + | 0.193234i | ||||
\(657\) | −9.16755 | −0.357660 | ||||||||
\(658\) | −4.81633 | − | 3.10409i | −0.187760 | − | 0.121010i | ||||
\(659\) | 41.5725 | 1.61943 | 0.809717 | − | 0.586820i | \(-0.199620\pi\) | ||||
0.809717 | + | 0.586820i | \(0.199620\pi\) | |||||||
\(660\) | 3.24141 | − | 5.61428i | 0.126172 | − | 0.218536i | ||||
\(661\) | −17.1023 | − | 29.6221i | −0.665203 | − | 1.15217i | −0.979230 | − | 0.202752i | \(-0.935012\pi\) |
0.314027 | − | 0.949414i | \(-0.398322\pi\) | |||||||
\(662\) | 4.74000 | + | 8.20992i | 0.184225 | + | 0.319088i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.42915 | −0.327115 | ||||||||
\(665\) | −25.2660 | − | 16.2837i | −0.979772 | − | 0.631455i | ||||
\(666\) | 31.3218 | 1.21369 | ||||||||
\(667\) | −7.15969 | + | 12.4010i | −0.277224 | + | 0.480167i | ||||
\(668\) | −1.22445 | − | 2.12081i | −0.0473755 | − | 0.0820567i | ||||
\(669\) | −2.47838 | − | 4.29268i | −0.0958197 | − | 0.165965i | ||||
\(670\) | 14.9877 | − | 25.9595i | 0.579025 | − | 1.00290i | ||||
\(671\) | −8.12611 | −0.313705 | ||||||||
\(672\) | −0.183456 | + | 3.74910i | −0.00707697 | + | 0.144625i | ||||
\(673\) | 21.4308 | 0.826098 | 0.413049 | − | 0.910709i | \(-0.364464\pi\) | ||||
0.413049 | + | 0.910709i | \(0.364464\pi\) | |||||||
\(674\) | −11.4722 | + | 19.8704i | −0.441893 | + | 0.765381i | ||||
\(675\) | −4.27145 | − | 7.39837i | −0.164408 | − | 0.284763i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.89083 | + | 8.47117i | −0.187970 | + | 0.325573i | −0.944573 | − | 0.328301i | \(-0.893524\pi\) |
0.756603 | + | 0.653874i | \(0.226857\pi\) | |||||||
\(678\) | 6.66919 | 0.256129 | ||||||||
\(679\) | −3.19802 | + | 1.64346i | −0.122729 | + | 0.0630700i | ||||
\(680\) | −19.0034 | −0.728748 | ||||||||
\(681\) | −1.01688 | + | 1.76130i | −0.0389671 | + | 0.0674930i | ||||
\(682\) | 6.30793 | + | 10.9256i | 0.241543 | + | 0.418365i | ||||
\(683\) | −7.63818 | − | 13.2297i | −0.292267 | − | 0.506221i | 0.682079 | − | 0.731279i | \(-0.261076\pi\) |
−0.974345 | + | 0.225058i | \(0.927743\pi\) | |||||||
\(684\) | −11.7716 | + | 20.3889i | −0.450097 | + | 0.779590i | ||||
\(685\) | −23.1828 | −0.885769 | ||||||||
\(686\) | 30.8480 | + | 24.4536i | 1.17778 | + | 0.933642i | ||||
\(687\) | −1.55802 | −0.0594423 | ||||||||
\(688\) | 1.92999 | − | 3.34285i | 0.0735803 | − | 0.127445i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.49343 | + | 2.58670i | 0.0568540 | + | 0.0984741i | ||||
\(691\) | −21.2286 | + | 36.7690i | −0.807573 | + | 1.39876i | 0.106967 | + | 0.994263i | \(0.465886\pi\) |
−0.914540 | + | 0.404496i | \(0.867447\pi\) | |||||||
\(692\) | 6.18627 | 0.235167 | ||||||||
\(693\) | 27.8840 | − | 14.3295i | 1.05922 | − | 0.544334i | ||||
\(694\) | 8.65141 | 0.328403 | ||||||||
\(695\) | 4.37869 | − | 7.58412i | 0.166093 | − | 0.287682i | ||||
\(696\) | 0.646710 | + | 1.12013i | 0.0245135 | + | 0.0424586i | ||||
\(697\) | 5.07486 | + | 8.78991i | 0.192224 | + | 0.332942i | ||||
\(698\) | 25.3706 | − | 43.9432i | 0.960291 | − | 1.66327i | ||||
\(699\) | 0.601767 | 0.0227609 | ||||||||
\(700\) | 2.60565 | − | 53.2489i | 0.0984842 | − | 2.01262i | ||||
\(701\) | −2.79985 | −0.105749 | −0.0528744 | − | 0.998601i | \(-0.516838\pi\) | ||||
−0.0528744 | + | 0.998601i | \(0.516838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.82141 | + | 13.5471i | 0.294990 | + | 0.510937i | ||||
\(704\) | 22.8899 | + | 39.6465i | 0.862696 | + | 1.49423i | ||||
\(705\) | 0.328581 | − | 0.569118i | 0.0123751 | − | 0.0214342i | ||||
\(706\) | −55.4412 | −2.08656 | ||||||||
\(707\) | 9.53608 | + | 6.14592i | 0.358641 | + | 0.231141i | ||||
\(708\) | 2.20793 | 0.0829793 | ||||||||
\(709\) | 7.28319 | − | 12.6149i | 0.273526 | − | 0.473761i | −0.696236 | − | 0.717813i | \(-0.745143\pi\) |
0.969762 | + | 0.244052i | \(0.0784767\pi\) | |||||||
\(710\) | −33.7503 | − | 58.4573i | −1.26663 | − | 2.19386i | ||||
\(711\) | 2.92054 | + | 5.05852i | 0.109529 | + | 0.189709i | ||||
\(712\) | −7.04201 | + | 12.1971i | −0.263910 | + | 0.457106i | ||||
\(713\) | −3.23934 | −0.121314 | ||||||||
\(714\) | 4.04885 | + | 2.60945i | 0.151524 | + | 0.0976562i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.2189 | + | 31.5560i | −0.680871 | + | 1.17930i | ||||
\(717\) | 1.77779 | + | 3.07923i | 0.0663928 | + | 0.114996i | ||||
\(718\) | −24.3309 | − | 42.1423i | −0.908021 | − | 1.57274i | ||||
\(719\) | −17.2529 | + | 29.8828i | −0.643423 | + | 1.11444i | 0.341240 | + | 0.939976i | \(0.389153\pi\) |
−0.984663 | + | 0.174465i | \(0.944180\pi\) | |||||||
\(720\) | 28.8606 | 1.07557 | ||||||||
\(721\) | 1.86658 | − | 38.1454i | 0.0695152 | − | 1.42061i | ||||
\(722\) | 19.2861 | 0.717756 | ||||||||
\(723\) | 1.68766 | − | 2.92311i | 0.0627648 | − | 0.108712i | ||||
\(724\) | −11.5548 | − | 20.0136i | −0.429432 | − | 0.743798i | ||||
\(725\) | 26.2992 | + | 45.5515i | 0.976727 | + | 1.69174i | ||||
\(726\) | −0.938775 | + | 1.62601i | −0.0348412 | + | 0.0603467i | ||||
\(727\) | 35.7571 | 1.32616 | 0.663078 | − | 0.748550i | \(-0.269250\pi\) | ||||
0.663078 | + | 0.748550i | \(0.269250\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.2879 | −0.936590 | ||||||||
\(730\) | 11.8371 | − | 20.5025i | 0.438111 | − | 0.758830i | ||||
\(731\) | −3.42771 | − | 5.93698i | −0.126779 | − | 0.219587i | ||||
\(732\) | −0.458277 | − | 0.793759i | −0.0169384 | − | 0.0293382i | ||||
\(733\) | 20.5250 | − | 35.5504i | 0.758108 | − | 1.31308i | −0.185706 | − | 0.982605i | \(-0.559457\pi\) |
0.943814 | − | 0.330477i | \(-0.107210\pi\) | |||||||
\(734\) | 38.5990 | 1.42472 | ||||||||
\(735\) | −2.62828 | + | 3.67075i | −0.0969456 | + | 0.135398i | ||||
\(736\) | −17.2833 | −0.637071 | ||||||||
\(737\) | −7.80686 | + | 13.5219i | −0.287570 | + | 0.498085i | ||||
\(738\) | 6.68481 | + | 11.5784i | 0.246071 | + | 0.426208i | ||||
\(739\) | 0.363205 | + | 0.629089i | 0.0133607 | + | 0.0231414i | 0.872628 | − | 0.488385i | \(-0.162414\pi\) |
−0.859268 | + | 0.511526i | \(0.829080\pi\) | |||||||
\(740\) | −22.5386 | + | 39.0379i | −0.828534 | + | 1.43506i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30.1874 | − | 15.5133i | 1.10822 | − | 0.569510i | ||||
\(743\) | 16.4547 | 0.603664 | 0.301832 | − | 0.953361i | \(-0.402402\pi\) | ||||
0.301832 | + | 0.953361i | \(0.402402\pi\) | |||||||
\(744\) | −0.146299 | + | 0.253397i | −0.00536358 | + | 0.00929000i | ||||
\(745\) | 0.207983 | + | 0.360236i | 0.00761989 | + | 0.0131980i | ||||
\(746\) | −16.8648 | − | 29.2108i | −0.617466 | − | 1.06948i | ||||
\(747\) | 11.3678 | − | 19.6896i | 0.415925 | − | 0.720404i | ||||
\(748\) | 48.1387 | 1.76012 | ||||||||
\(749\) | −1.25675 | + | 25.6829i | −0.0459206 | + | 0.938433i | ||||
\(750\) | 4.11723 | 0.150340 | ||||||||
\(751\) | −12.5854 | + | 21.7985i | −0.459247 | + | 0.795439i | −0.998921 | − | 0.0464350i | \(-0.985214\pi\) |
0.539675 | + | 0.841874i | \(0.318547\pi\) | |||||||
\(752\) | 1.37380 | + | 2.37949i | 0.0500974 | + | 0.0867712i | ||||
\(753\) | −0.876030 | − | 1.51733i | −0.0319243 | − | 0.0552945i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 42.5623 | 1.54900 | ||||||||
\(756\) | 5.97652 | + | 3.85182i | 0.217364 | + | 0.140089i | ||||
\(757\) | 44.0743 | 1.60191 | 0.800953 | − | 0.598727i | \(-0.204327\pi\) | ||||
0.800953 | + | 0.598727i | \(0.204327\pi\) | |||||||
\(758\) | 29.5054 | − | 51.1049i | 1.07168 | − | 1.85621i | ||||
\(759\) | −0.777906 | − | 1.34737i | −0.0282362 | − | 0.0489066i | ||||
\(760\) | −6.25080 | − | 10.8267i | −0.226740 | − | 0.392726i | ||||
\(761\) | 19.3511 | − | 33.5171i | 0.701477 | − | 1.21499i | −0.266471 | − | 0.963843i | \(-0.585858\pi\) |
0.967948 | − | 0.251151i | \(-0.0808090\pi\) | |||||||
\(762\) | 7.41844 | 0.268742 | ||||||||
\(763\) | −14.7857 | − | 9.52925i | −0.535278 | − | 0.344982i | ||||
\(764\) | 44.2715 | 1.60169 | ||||||||
\(765\) | 25.6285 | − | 44.3899i | 0.926601 | − | 1.60492i | ||||
\(766\) | −27.8937 | − | 48.3133i | −1.00784 | − | 1.74563i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.433701 | − | 0.751191i | 0.0156498 | − | 0.0271063i | ||||
\(769\) | −36.1506 | −1.30362 | −0.651811 | − | 0.758381i | \(-0.725991\pi\) | ||||
−0.651811 | + | 0.758381i | \(0.725991\pi\) | |||||||
\(770\) | −3.95687 | + | 80.8625i | −0.142596 | + | 2.91408i | ||||
\(771\) | −3.74511 | −0.134877 | ||||||||
\(772\) | −24.8697 | + | 43.0756i | −0.895080 | + | 1.55032i | ||||
\(773\) | −15.0366 | − | 26.0441i | −0.540827 | − | 0.936740i | −0.998857 | − | 0.0478033i | \(-0.984778\pi\) |
0.458030 | − | 0.888937i | \(-0.348555\pi\) | |||||||
\(774\) | −4.51513 | − | 7.82043i | −0.162293 | − | 0.281100i | ||||
\(775\) | −5.94941 | + | 10.3047i | −0.213709 | + | 0.370155i | ||||
\(776\) | −1.49543 | −0.0536827 | ||||||||
\(777\) | 2.08969 | − | 1.07389i | 0.0749671 | − | 0.0385255i | ||||
\(778\) | 53.6801 | 1.92453 | ||||||||
\(779\) | −3.33855 | + | 5.78253i | −0.119616 | + | 0.207181i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.5800 | + | 30.4495i | 0.629063 | + | 1.08957i | ||||
\(782\) | −11.0896 | + | 19.2078i | −0.396564 | + | 0.686868i | ||||
\(783\) | −7.01496 | −0.250694 | ||||||||
\(784\) | −7.79687 | − | 17.1904i | −0.278460 | − | 0.613943i | ||||
\(785\) | −47.4079 | −1.69206 | ||||||||
\(786\) | −3.62557 | + | 6.27967i | −0.129320 | + | 0.223988i | ||||
\(787\) | 18.4236 | + | 31.9106i | 0.656730 | + | 1.13749i | 0.981457 | + | 0.191682i | \(0.0613943\pi\) |
−0.324727 | + | 0.945808i | \(0.605272\pi\) | |||||||
\(788\) | 9.64307 | + | 16.7023i | 0.343520 | + | 0.594994i | ||||
\(789\) | −0.660580 | + | 1.14416i | −0.0235173 | + | 0.0407331i | ||||
\(790\) | −15.0840 | −0.536663 | ||||||||
\(791\) | −41.2833 | + | 21.2154i | −1.46786 | + | 0.754333i | ||||
\(792\) | 13.0388 | 0.463315 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −15.9163 | − | 27.5678i | −0.564847 | − | 0.978343i | ||||
\(795\) | 1.94628 | + | 3.37106i | 0.0690275 | + | 0.119559i | ||||
\(796\) | 8.23721 | − | 14.2673i | 0.291960 | − | 0.505690i | ||||
\(797\) | 27.5910 | 0.977323 | 0.488661 | − | 0.872474i | \(-0.337485\pi\) | ||||
0.488661 | + | 0.872474i | \(0.337485\pi\) | |||||||
\(798\) | −0.154877 | + | 3.16505i | −0.00548257 | + | 0.112042i | ||||
\(799\) | 4.87980 | 0.172635 | ||||||||
\(800\) | −31.7427 | + | 54.9800i | −1.12227 | + | 1.94384i | ||||
\(801\) | −18.9941 | − | 32.8987i | −0.671123 | − | 1.16242i | ||||
\(802\) | −5.67939 | − | 9.83700i | −0.200546 | − | 0.347356i | ||||
\(803\) | −6.16577 | + | 10.6794i | −0.217585 | + | 0.376869i | ||||
\(804\) | −1.76109 | −0.0621089 | ||||||||
\(805\) | −17.4732 | − | 11.2613i | −0.615848 | − | 0.396909i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.03797 | − | 3.52987i | 0.0717399 | − | 0.124257i | ||||
\(808\) | 2.35923 | + | 4.08630i | 0.0829973 | + | 0.143756i | ||||
\(809\) | −17.8551 | − | 30.9260i | −0.627752 | − | 1.08730i | −0.988002 | − | 0.154443i | \(-0.950642\pi\) |
0.360250 | − | 0.932856i | \(-0.382692\pi\) | |||||||
\(810\) | 33.3912 | − | 57.8352i | 1.17325 | − | 2.03212i | ||||
\(811\) | 2.22418 | 0.0781015 | 0.0390508 | − | 0.999237i | \(-0.487567\pi\) | ||||
0.0390508 | + | 0.999237i | \(0.487567\pi\) | |||||||
\(812\) | −36.7973 | − | 23.7155i | −1.29133 | − | 0.832252i | ||||
\(813\) | −0.745166 | −0.0261341 | ||||||||
\(814\) | 21.0659 | − | 36.4873i | 0.738360 | − | 1.27888i | ||||
\(815\) | −33.6234 | − | 58.2375i | −1.17778 | − | 2.03997i | ||||
\(816\) | −1.15489 | − | 2.00032i | −0.0404291 | − | 0.0700252i | ||||
\(817\) | 2.25496 | − | 3.90570i | 0.0788910 | − | 0.136643i | ||||
\(818\) | 7.15264 | 0.250086 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.2411 | −0.671927 | ||||||||
\(821\) | 26.6847 | − | 46.2192i | 0.931302 | − | 1.61306i | 0.150203 | − | 0.988655i | \(-0.452007\pi\) |
0.781099 | − | 0.624407i | \(-0.214659\pi\) | |||||||
\(822\) | 1.22198 | + | 2.11654i | 0.0426216 | + | 0.0738228i | ||||
\(823\) | −25.6043 | − | 44.3479i | −0.892509 | − | 1.54587i | −0.836857 | − | 0.547421i | \(-0.815610\pi\) |
−0.0556519 | − | 0.998450i | \(-0.517724\pi\) | |||||||
\(824\) | 7.94195 | − | 13.7559i | 0.276671 | − | 0.479208i | ||||
\(825\) | −5.71485 | −0.198966 | ||||||||
\(826\) | −24.5245 | + | 12.6031i | −0.853316 | + | 0.438518i | ||||
\(827\) | 8.97196 | 0.311986 | 0.155993 | − | 0.987758i | \(-0.450142\pi\) | ||||
0.155993 | + | 0.987758i | \(0.450142\pi\) | |||||||
\(828\) | −8.14084 | + | 14.1003i | −0.282914 | + | 0.490021i | ||||
\(829\) | −20.2858 | − | 35.1360i | −0.704554 | − | 1.22032i | −0.966852 | − | 0.255337i | \(-0.917814\pi\) |
0.262298 | − | 0.964987i | \(-0.415520\pi\) | |||||||
\(830\) | 29.3561 | + | 50.8462i | 1.01896 | + | 1.76490i | ||||
\(831\) | 0.0694940 | − | 0.120367i | 0.00241072 | − | 0.00417549i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.3639 | − | 3.27305i | −1.15599 | − | 0.113405i | ||||
\(834\) | −0.923218 | −0.0319684 | ||||||||
\(835\) | −1.75374 | + | 3.03757i | −0.0606907 | + | 0.105119i | ||||
\(836\) | 15.8343 | + | 27.4257i | 0.547639 | + | 0.948539i | ||||
\(837\) | −0.793464 | − | 1.37432i | −0.0274261 | − | 0.0475034i | ||||
\(838\) | −30.6750 | + | 53.1307i | −1.05965 | + | 1.83537i | ||||
\(839\) | −32.3005 | −1.11514 | −0.557568 | − | 0.830131i | \(-0.688266\pi\) | ||||
−0.557568 | + | 0.830131i | \(0.688266\pi\) | |||||||
\(840\) | −1.67006 | + | 0.858242i | −0.0576226 | + | 0.0296121i | ||||
\(841\) | 14.1909 | 0.489342 | ||||||||
\(842\) | −17.6549 | + | 30.5791i | −0.608427 | + | 1.05383i | ||||
\(843\) | −1.06408 | − | 1.84304i | −0.0366488 | − | 0.0634776i | ||||
\(844\) | −25.2340 | − | 43.7065i | −0.868588 | − | 1.50444i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.42788 | 0.220995 | ||||||||
\(847\) | 0.638656 | − | 13.0516i | 0.0219445 | − | 0.448457i | ||||
\(848\) | −16.2749 | −0.558882 | ||||||||
\(849\) | −1.42225 | + | 2.46341i | −0.0488116 | + | 0.0845442i | ||||
\(850\) | 40.7347 | + | 70.5545i | 1.39719 | + | 2.42000i | ||||
\(851\) | 5.40904 | + | 9.36873i | 0.185419 | + | 0.321156i | ||||
\(852\) | −1.98287 | + | 3.43444i | −0.0679321 | + | 0.117662i | ||||
\(853\) | 35.5887 | 1.21853 | 0.609267 | − | 0.792965i | \(-0.291464\pi\) | ||||
0.609267 | + | 0.792965i | \(0.291464\pi\) | |||||||
\(854\) | 9.62114 | + | 6.20074i | 0.329229 | + | 0.212185i | ||||
\(855\) | 33.7200 | 1.15320 | ||||||||
\(856\) | −5.34723 | + | 9.26167i | −0.182764 | + | 0.316557i | ||||
\(857\) | −23.0114 | − | 39.8570i | −0.786055 | − | 1.36149i | −0.928367 | − | 0.371666i | \(-0.878787\pi\) |
0.142311 | − | 0.989822i | \(-0.454547\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6229 | + | 21.8635i | −0.430689 | + | 0.745975i | −0.996933 | − | 0.0782630i | \(-0.975063\pi\) |
0.566244 | + | 0.824238i | \(0.308396\pi\) | |||||||
\(860\) | 12.9960 | 0.443160 | ||||||||
\(861\) | 0.842963 | + | 0.543282i | 0.0287281 | + | 0.0185150i | ||||
\(862\) | −43.6903 | −1.48810 | ||||||||
\(863\) | −6.91684 | + | 11.9803i | −0.235452 | + | 0.407815i | −0.959404 | − | 0.282036i | \(-0.908990\pi\) |
0.723952 | + | 0.689850i | \(0.242324\pi\) | |||||||
\(864\) | −4.23348 | − | 7.33260i | −0.144026 | − | 0.249460i | ||||
\(865\) | −4.43019 | − | 7.67331i | −0.150631 | − | 0.260900i | ||||
\(866\) | 20.6271 | − | 35.7271i | 0.700936 | − | 1.21406i | ||||
\(867\) | −1.06168 | −0.0360567 | ||||||||
\(868\) | 0.484025 | − | 9.89152i | 0.0164289 | − | 0.335740i | ||||
\(869\) | 7.85701 | 0.266531 | ||||||||
\(870\) | 4.50457 | − | 7.80215i | 0.152719 | − | 0.264518i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.65798 | − | 6.33581i | −0.123875 | − | 0.214557i | ||||
\(873\) | 2.01677 | − | 3.49315i | 0.0682573 | − | 0.118225i | ||||
\(874\) | −14.5908 | −0.493542 | ||||||||
\(875\) | −25.4862 | + | 13.0973i | −0.861592 | + | 0.442771i | ||||
\(876\) | −1.39089 | −0.0469938 | ||||||||
\(877\) | 1.82708 | − | 3.16459i | 0.0616961 | − | 0.106861i | −0.833528 | − | 0.552478i | \(-0.813682\pi\) |
0.895224 | + | 0.445617i | \(0.147016\pi\) | |||||||
\(878\) | 14.2675 | + | 24.7120i | 0.481504 | + | 0.833989i | ||||
\(879\) | −0.602469 | − | 1.04351i | −0.0203208 | − | 0.0351966i | ||||
\(880\) | 19.4106 | − | 33.6201i | 0.654331 | − | 1.13333i | ||||
\(881\) | 36.6320 | 1.23416 | 0.617082 | − | 0.786899i | \(-0.288315\pi\) | ||||
0.617082 | + | 0.786899i | \(0.288315\pi\) | |||||||
\(882\) | −43.9484 | − | 4.31140i | −1.47982 | − | 0.145172i | ||||
\(883\) | −7.11145 | −0.239319 | −0.119660 | − | 0.992815i | \(-0.538180\pi\) | ||||
−0.119660 | + | 0.992815i | \(0.538180\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.58117 | − | 2.73867i | −0.0531506 | − | 0.0920595i | ||||
\(886\) | −35.6585 | − | 61.7623i | −1.19797 | − | 2.07494i | ||||
\(887\) | 3.36773 | − | 5.83308i | 0.113077 | − | 0.195856i | −0.803932 | − | 0.594721i | \(-0.797263\pi\) |
0.917010 | + | 0.398865i | \(0.130596\pi\) | |||||||
\(888\) | 0.977160 | 0.0327913 | ||||||||
\(889\) | −45.9212 | + | 23.5989i | −1.54015 | + | 0.791480i | ||||
\(890\) | 98.1004 | 3.28833 | ||||||||
\(891\) | −17.3930 | + | 30.1255i | −0.582686 | + | 1.00924i | ||||
\(892\) | 34.8878 | + | 60.4274i | 1.16813 | + | 2.02326i | ||||
\(893\) | 1.60512 | + | 2.78014i | 0.0537131 | + | 0.0930339i | ||||
\(894\) | 0.0219259 | − | 0.0379767i | 0.000733311 | − | 0.00127013i | ||||
\(895\) | 52.1885 | 1.74447 | ||||||||
\(896\) | 1.10019 | − | 22.4835i | 0.0367549 | − | 0.751122i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36.5886 | − | 63.3733i | 1.22098 | − | 2.11479i | ||||
\(899\) | 4.88533 | + | 8.46164i | 0.162935 | + | 0.282212i | ||||
\(900\) | 29.9031 | + | 51.7938i | 0.996772 | + | 1.72646i | ||||
\(901\) | −14.4523 | + | 25.0321i | −0.481475 | + | 0.833939i | ||||
\(902\) | 17.9839 | 0.598798 | ||||||||
\(903\) | −0.569363 | − | 0.366950i | −0.0189472 | − | 0.0122113i | ||||
\(904\) | −19.3045 | −0.642058 | ||||||||
\(905\) | −16.5496 | + | 28.6647i | −0.550127 | + | 0.952848i | ||||
\(906\) | −2.24350 | − | 3.88585i | −0.0745351 | − | 0.129099i | ||||
\(907\) | 2.46630 | + | 4.27175i | 0.0818921 | + | 0.141841i | 0.904063 | − | 0.427400i | \(-0.140570\pi\) |
−0.822171 | + | 0.569241i | \(0.807237\pi\) | |||||||
\(908\) | 14.3145 | − | 24.7935i | 0.475045 | − | 0.822802i | ||||
\(909\) | −12.7269 | −0.422123 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.6258 | −0.882152 | −0.441076 | − | 0.897470i | \(-0.645403\pi\) | ||||
−0.441076 | + | 0.897470i | \(0.645403\pi\) | |||||||
\(912\) | 0.759754 | − | 1.31593i | 0.0251580 | − | 0.0435749i | ||||
\(913\) | −15.2911 | − | 26.4850i | −0.506063 | − | 0.876526i | ||||
\(914\) | −14.3251 | − | 24.8118i | −0.473833 | − | 0.820702i | ||||
\(915\) | −0.656374 | + | 1.13687i | −0.0216991 | + | 0.0375839i | ||||
\(916\) | 21.9321 | 0.724656 | ||||||||
\(917\) | 2.46650 | − | 50.4054i | 0.0814512 | − | 1.66453i | ||||
\(918\) | −10.8654 | −0.358613 | ||||||||
\(919\) | 16.1918 | − | 28.0450i | 0.534118 | − | 0.925119i | −0.465088 | − | 0.885265i | \(-0.653977\pi\) |
0.999205 | − | 0.0398544i | \(-0.0126894\pi\) | |||||||
\(920\) | −4.32286 | − | 7.48741i | −0.142520 | − | 0.246853i | ||||
\(921\) | 1.31618 | + | 2.27970i | 0.0433697 | + | 0.0751185i | ||||
\(922\) | −1.44428 | + | 2.50156i | −0.0475647 | + | 0.0823844i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.23052 | − | 2.17406i | 0.139174 | − | 0.0715213i | ||||
\(925\) | 39.7373 | 1.30655 | ||||||||
\(926\) | 2.65512 | − | 4.59880i | 0.0872526 | − | 0.151126i | ||||
\(927\) | 21.4214 | + | 37.1030i | 0.703572 | + | 1.21862i | ||||
\(928\) | 26.0654 | + | 45.1466i | 0.855639 | + | 1.48201i | ||||
\(929\) | −14.0135 | + | 24.2722i | −0.459769 | + | 0.796344i | −0.998948 | − | 0.0458472i | \(-0.985401\pi\) |
0.539179 | + | 0.842191i | \(0.318735\pi\) | |||||||
\(930\) | 2.03805 | 0.0668304 | ||||||||
\(931\) | −9.10967 | − | 20.0848i | −0.298557 | − | 0.658254i | ||||
\(932\) | −8.47099 | −0.277476 | ||||||||
\(933\) | 2.56278 | − | 4.43887i | 0.0839018 | − | 0.145322i | ||||
\(934\) | −27.8633 | − | 48.2606i | −0.911714 | − | 1.57914i | ||||
\(935\) | −34.4737 | − | 59.7102i | −1.12741 | − | 1.95273i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.1324 | 0.461686 | 0.230843 | − | 0.972991i | \(-0.425852\pi\) | ||||
0.230843 | + | 0.972991i | \(0.425852\pi\) | |||||||
\(938\) | 19.5612 | − | 10.0525i | 0.638696 | − | 0.328225i | ||||
\(939\) | 5.87091 | 0.191590 | ||||||||
\(940\) | −4.62538 | + | 8.01140i | −0.150863 | + | 0.261303i | ||||
\(941\) | −4.48647 | − | 7.77080i | −0.146255 | − | 0.253321i | 0.783586 | − | 0.621284i | \(-0.213389\pi\) |
−0.929840 | + | 0.367963i | \(0.880055\pi\) | |||||||
\(942\) | 2.49891 | + | 4.32824i | 0.0814189 | + | 0.141022i | ||||
\(943\) | −2.30883 | + | 3.99902i | −0.0751860 | + | 0.130226i | ||||
\(944\) | 13.2218 | 0.430334 | ||||||||
\(945\) | 0.497728 | − | 10.1716i | 0.0161911 | − | 0.330881i | ||||
\(946\) | −12.1469 | −0.394929 | ||||||||
\(947\) | 23.1479 | − | 40.0933i | 0.752205 | − | 1.30286i | −0.194546 | − | 0.980893i | \(-0.562324\pi\) |
0.946752 | − | 0.321964i | \(-0.104343\pi\) | |||||||
\(948\) | 0.443101 | + | 0.767473i | 0.0143912 | + | 0.0249264i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −26.7977 | + | 46.4150i | −0.869433 | + | 1.50590i | ||||
\(951\) | 1.86225 | 0.0603876 | ||||||||
\(952\) | −11.7197 | − | 7.55326i | −0.379838 | − | 0.244803i | ||||
\(953\) | 19.1097 | 0.619023 | 0.309512 | − | 0.950896i | \(-0.399834\pi\) | ||||
0.309512 | + | 0.950896i | \(0.399834\pi\) | |||||||
\(954\) | −19.0371 | + | 32.9733i | −0.616350 | + | 1.06755i | ||||
\(955\) | −31.7042 | − | 54.9134i | −1.02593 | − | 1.77695i | ||||
\(956\) | −25.0257 | − | 43.3458i | −0.809390 | − | 1.40190i | ||||
\(957\) | −2.34636 | + | 4.06402i | −0.0758472 | + | 0.131371i | ||||
\(958\) | −50.6846 | −1.63755 | ||||||||
\(959\) | −14.2972 | − | 9.21443i | −0.461681 | − | 0.297549i | ||||
\(960\) | 7.39560 | 0.238692 | ||||||||
\(961\) | 14.3948 | − | 24.9326i | 0.464350 | − | 0.804277i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.4228 | − | 24.9811i | −0.464769 | − | 0.805003i | ||||
\(964\) | −23.7570 | + | 41.1483i | −0.765160 | + | 1.32530i | ||||
\(965\) | 71.2400 | 2.29330 | ||||||||
\(966\) | −0.107108 | + | 2.18885i | −0.00344614 | + | 0.0704252i | ||||
\(967\) | 22.5432 | 0.724942 | 0.362471 | − | 0.931995i | \(-0.381933\pi\) | ||||
0.362471 | + | 0.931995i | \(0.381933\pi\) | |||||||
\(968\) | 2.71736 | − | 4.70660i | 0.0873392 | − | 0.151276i | ||||
\(969\) | −1.34934 | − | 2.33713i | −0.0433471 | − | 0.0750793i | ||||
\(970\) | 5.20809 | + | 9.02068i | 0.167222 | + | 0.289637i | ||||
\(971\) | −13.6429 | + | 23.6301i | −0.437820 | + | 0.758327i | −0.997521 | − | 0.0703679i | \(-0.977583\pi\) |
0.559701 | + | 0.828695i | \(0.310916\pi\) | |||||||
\(972\) | −11.9858 | −0.384444 | ||||||||
\(973\) | 5.71485 | − | 2.93685i | 0.183210 | − | 0.0941512i | ||||
\(974\) | −22.5188 | −0.721550 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.74431 | − | 4.75329i | −0.0878433 | − | 0.152149i | ||||
\(977\) | 28.0920 | + | 48.6568i | 0.898744 | + | 1.55667i | 0.829101 | + | 0.559098i | \(0.188853\pi\) |
0.0696427 | + | 0.997572i | \(0.477814\pi\) | |||||||
\(978\) | −3.54464 | + | 6.13949i | −0.113345 | + | 0.196319i | ||||
\(979\) | −51.0990 | −1.63313 | ||||||||
\(980\) | 36.9979 | − | 51.6727i | 1.18186 | − | 1.65062i | ||||
\(981\) | 19.7330 | 0.630026 | ||||||||
\(982\) | −21.0108 | + | 36.3919i | −0.670483 | + | 1.16131i | ||||
\(983\) | −13.2445 | − | 22.9402i | −0.422435 | − | 0.731678i | 0.573742 | − | 0.819036i | \(-0.305491\pi\) |
−0.996177 | + | 0.0873577i | \(0.972158\pi\) | |||||||
\(984\) | 0.208549 | + | 0.361218i | 0.00664830 | + | 0.0115152i | ||||
\(985\) | 13.8114 | − | 23.9221i | 0.440069 | − | 0.762222i | ||||
\(986\) | 66.8982 | 2.13047 | ||||||||
\(987\) | 0.428847 | − | 0.220384i | 0.0136504 | − | 0.00701490i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.55946 | − | 2.70106i | 0.0495879 | − | 0.0858887i | ||||
\(990\) | −45.4102 | − | 78.6527i | −1.44323 | − | 2.49975i | ||||
\(991\) | −2.55629 | − | 4.42763i | −0.0812033 | − | 0.140648i | 0.822564 | − | 0.568673i | \(-0.192543\pi\) |
−0.903767 | + | 0.428025i | \(0.859210\pi\) | |||||||
\(992\) | −5.89652 | + | 10.2131i | −0.187215 | + | 0.324266i | ||||
\(993\) | −0.797717 | −0.0253148 | ||||||||
\(994\) | 2.42055 | − | 49.4662i | 0.0767750 | − | 1.56897i | ||||
\(995\) | −23.5957 | −0.748035 | ||||||||
\(996\) | 1.72471 | − | 2.98728i | 0.0546494 | − | 0.0946555i | ||||
\(997\) | −1.01771 | − | 1.76272i | −0.0322311 | − | 0.0558260i | 0.849460 | − | 0.527653i | \(-0.176928\pi\) |
−0.881691 | + | 0.471827i | \(0.843595\pi\) | |||||||
\(998\) | −14.0182 | − | 24.2803i | −0.443740 | − | 0.768580i | ||||
\(999\) | −2.64985 | + | 4.58967i | −0.0838375 | + | 0.145211i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1183.2.e.i.170.7 | 16 | ||
7.2 | even | 3 | 8281.2.a.ck.1.2 | 8 | |||
7.4 | even | 3 | inner | 1183.2.e.i.508.7 | 16 | ||
7.5 | odd | 6 | 8281.2.a.cj.1.2 | 8 | |||
13.5 | odd | 4 | 91.2.r.a.51.2 | yes | 16 | ||
13.8 | odd | 4 | 91.2.r.a.51.7 | yes | 16 | ||
13.12 | even | 2 | inner | 1183.2.e.i.170.2 | 16 | ||
39.5 | even | 4 | 819.2.dl.e.415.7 | 16 | |||
39.8 | even | 4 | 819.2.dl.e.415.2 | 16 | |||
91.5 | even | 12 | 637.2.c.e.246.7 | 8 | |||
91.12 | odd | 6 | 8281.2.a.cj.1.7 | 8 | |||
91.18 | odd | 12 | 91.2.r.a.25.7 | yes | 16 | ||
91.25 | even | 6 | inner | 1183.2.e.i.508.2 | 16 | ||
91.31 | even | 12 | 637.2.r.f.116.7 | 16 | |||
91.34 | even | 4 | 637.2.r.f.324.7 | 16 | |||
91.44 | odd | 12 | 637.2.c.f.246.7 | 8 | |||
91.47 | even | 12 | 637.2.c.e.246.2 | 8 | |||
91.51 | even | 6 | 8281.2.a.ck.1.7 | 8 | |||
91.60 | odd | 12 | 91.2.r.a.25.2 | ✓ | 16 | ||
91.73 | even | 12 | 637.2.r.f.116.2 | 16 | |||
91.83 | even | 4 | 637.2.r.f.324.2 | 16 | |||
91.86 | odd | 12 | 637.2.c.f.246.2 | 8 | |||
273.200 | even | 12 | 819.2.dl.e.298.2 | 16 | |||
273.242 | even | 12 | 819.2.dl.e.298.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.2 | ✓ | 16 | 91.60 | odd | 12 | ||
91.2.r.a.25.7 | yes | 16 | 91.18 | odd | 12 | ||
91.2.r.a.51.2 | yes | 16 | 13.5 | odd | 4 | ||
91.2.r.a.51.7 | yes | 16 | 13.8 | odd | 4 | ||
637.2.c.e.246.2 | 8 | 91.47 | even | 12 | |||
637.2.c.e.246.7 | 8 | 91.5 | even | 12 | |||
637.2.c.f.246.2 | 8 | 91.86 | odd | 12 | |||
637.2.c.f.246.7 | 8 | 91.44 | odd | 12 | |||
637.2.r.f.116.2 | 16 | 91.73 | even | 12 | |||
637.2.r.f.116.7 | 16 | 91.31 | even | 12 | |||
637.2.r.f.324.2 | 16 | 91.83 | even | 4 | |||
637.2.r.f.324.7 | 16 | 91.34 | even | 4 | |||
819.2.dl.e.298.2 | 16 | 273.200 | even | 12 | |||
819.2.dl.e.298.7 | 16 | 273.242 | even | 12 | |||
819.2.dl.e.415.2 | 16 | 39.8 | even | 4 | |||
819.2.dl.e.415.7 | 16 | 39.5 | even | 4 | |||
1183.2.e.i.170.2 | 16 | 13.12 | even | 2 | inner | ||
1183.2.e.i.170.7 | 16 | 1.1 | even | 1 | trivial | ||
1183.2.e.i.508.2 | 16 | 91.25 | even | 6 | inner | ||
1183.2.e.i.508.7 | 16 | 7.4 | even | 3 | inner | ||
8281.2.a.cj.1.2 | 8 | 7.5 | odd | 6 | |||
8281.2.a.cj.1.7 | 8 | 91.12 | odd | 6 | |||
8281.2.a.ck.1.2 | 8 | 7.2 | even | 3 | |||
8281.2.a.ck.1.7 | 8 | 91.51 | even | 6 |