Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(316,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.m (of order \(6\), degree \(2\), 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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 316.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.316 |
Dual form | 845.2.m.a.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | − | 0.866025i | −1.06066 | − | 0.612372i | −0.135045 | − | 0.990839i | \(-0.543118\pi\) |
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | −1.36603 | + | 2.36603i | −0.788675 | + | 1.36603i | 0.138104 | + | 0.990418i | \(0.455899\pi\) |
−0.926779 | + | 0.375608i | \(0.877434\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 4.09808 | − | 2.36603i | 1.67303 | − | 0.965926i | ||||
\(7\) | 1.73205 | − | 1.00000i | 0.654654 | − | 0.377964i | −0.135583 | − | 0.990766i | \(-0.543291\pi\) |
0.790237 | + | 0.612801i | \(0.209957\pi\) | |||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | −2.23205 | − | 3.86603i | −0.744017 | − | 1.28868i | ||||
\(10\) | 0.866025 | − | 1.50000i | 0.273861 | − | 0.474342i | ||||
\(11\) | 4.09808 | + | 2.36603i | 1.23562 | + | 0.713384i | 0.968195 | − | 0.250196i | \(-0.0804951\pi\) |
0.267421 | + | 0.963580i | \(0.413828\pi\) | |||||||
\(12\) | −2.73205 | −0.788675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −3.46410 | −0.925820 | ||||||||
\(15\) | −2.36603 | − | 1.36603i | −0.610905 | − | 0.352706i | ||||
\(16\) | 2.50000 | − | 4.33013i | 0.625000 | − | 1.08253i | ||||
\(17\) | −1.73205 | − | 3.00000i | −0.420084 | − | 0.727607i | 0.575863 | − | 0.817546i | \(-0.304666\pi\) |
−0.995947 | + | 0.0899392i | \(0.971333\pi\) | |||||||
\(18\) | 7.73205i | 1.82246i | ||||||||
\(19\) | 5.36603 | − | 3.09808i | 1.23105 | − | 0.710747i | 0.263802 | − | 0.964577i | \(-0.415024\pi\) |
0.967249 | + | 0.253830i | \(0.0816902\pi\) | |||||||
\(20\) | −0.866025 | + | 0.500000i | −0.193649 | + | 0.111803i | ||||
\(21\) | 5.46410i | 1.19236i | ||||||||
\(22\) | −4.09808 | − | 7.09808i | −0.873713 | − | 1.51331i | ||||
\(23\) | 0.633975 | − | 1.09808i | 0.132193 | − | 0.228965i | −0.792329 | − | 0.610094i | \(-0.791132\pi\) |
0.924522 | + | 0.381130i | \(0.124465\pi\) | |||||||
\(24\) | −4.09808 | − | 2.36603i | −0.836516 | − | 0.482963i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 1.73205 | + | 1.00000i | 0.327327 | + | 0.188982i | ||||
\(29\) | 1.26795 | − | 2.19615i | 0.235452 | − | 0.407815i | −0.723952 | − | 0.689851i | \(-0.757676\pi\) |
0.959404 | + | 0.282035i | \(0.0910095\pi\) | |||||||
\(30\) | 2.36603 | + | 4.09808i | 0.431975 | + | 0.748203i | ||||
\(31\) | − | 10.1962i | − | 1.83128i | −0.401996 | − | 0.915642i | \(-0.631683\pi\) | ||
0.401996 | − | 0.915642i | \(-0.368317\pi\) | |||||||
\(32\) | −4.50000 | + | 2.59808i | −0.795495 | + | 0.459279i | ||||
\(33\) | −11.1962 | + | 6.46410i | −1.94900 | + | 1.12526i | ||||
\(34\) | 6.00000i | 1.02899i | ||||||||
\(35\) | 1.00000 | + | 1.73205i | 0.169031 | + | 0.292770i | ||||
\(36\) | 2.23205 | − | 3.86603i | 0.372008 | − | 0.644338i | ||||
\(37\) | 3.46410 | + | 2.00000i | 0.569495 | + | 0.328798i | 0.756948 | − | 0.653476i | \(-0.226690\pi\) |
−0.187453 | + | 0.982274i | \(0.560023\pi\) | |||||||
\(38\) | −10.7321 | −1.74097 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.73205 | −0.273861 | ||||||||
\(41\) | 3.00000 | + | 1.73205i | 0.468521 | + | 0.270501i | 0.715621 | − | 0.698489i | \(-0.246144\pi\) |
−0.247099 | + | 0.968990i | \(0.579477\pi\) | |||||||
\(42\) | 4.73205 | − | 8.19615i | 0.730171 | − | 1.26469i | ||||
\(43\) | −0.0980762 | − | 0.169873i | −0.0149565 | − | 0.0259054i | 0.858450 | − | 0.512897i | \(-0.171428\pi\) |
−0.873407 | + | 0.486991i | \(0.838094\pi\) | |||||||
\(44\) | 4.73205i | 0.713384i | ||||||||
\(45\) | 3.86603 | − | 2.23205i | 0.576313 | − | 0.332734i | ||||
\(46\) | −1.90192 | + | 1.09808i | −0.280423 | + | 0.161903i | ||||
\(47\) | 6.00000i | 0.875190i | 0.899172 | + | 0.437595i | \(0.144170\pi\) | ||||
−0.899172 | + | 0.437595i | \(0.855830\pi\) | |||||||
\(48\) | 6.83013 | + | 11.8301i | 0.985844 | + | 1.70753i | ||||
\(49\) | −1.50000 | + | 2.59808i | −0.214286 | + | 0.371154i | ||||
\(50\) | 1.50000 | + | 0.866025i | 0.212132 | + | 0.122474i | ||||
\(51\) | 9.46410 | 1.32524 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3923 | 1.42749 | 0.713746 | − | 0.700404i | \(-0.246997\pi\) | ||||
0.713746 | + | 0.700404i | \(0.246997\pi\) | |||||||
\(54\) | −6.00000 | − | 3.46410i | −0.816497 | − | 0.471405i | ||||
\(55\) | −2.36603 | + | 4.09808i | −0.319035 | + | 0.552584i | ||||
\(56\) | 1.73205 | + | 3.00000i | 0.231455 | + | 0.400892i | ||||
\(57\) | 16.9282i | 2.24220i | ||||||||
\(58\) | −3.80385 | + | 2.19615i | −0.499470 | + | 0.288369i | ||||
\(59\) | 7.90192 | − | 4.56218i | 1.02874 | − | 0.593945i | 0.112119 | − | 0.993695i | \(-0.464236\pi\) |
0.916624 | + | 0.399750i | \(0.130903\pi\) | |||||||
\(60\) | − | 2.73205i | − | 0.352706i | ||||||
\(61\) | 4.19615 | + | 7.26795i | 0.537262 | + | 0.930566i | 0.999050 | + | 0.0435752i | \(0.0138748\pi\) |
−0.461788 | + | 0.886990i | \(0.652792\pi\) | |||||||
\(62\) | −8.83013 | + | 15.2942i | −1.12143 | + | 1.94237i | ||||
\(63\) | −7.73205 | − | 4.46410i | −0.974147 | − | 0.562424i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 22.3923 | 2.75630 | ||||||||
\(67\) | 5.53590 | + | 3.19615i | 0.676318 | + | 0.390472i | 0.798466 | − | 0.602040i | \(-0.205645\pi\) |
−0.122149 | + | 0.992512i | \(0.538978\pi\) | |||||||
\(68\) | 1.73205 | − | 3.00000i | 0.210042 | − | 0.363803i | ||||
\(69\) | 1.73205 | + | 3.00000i | 0.208514 | + | 0.361158i | ||||
\(70\) | − | 3.46410i | − | 0.414039i | ||||||
\(71\) | −4.09808 | + | 2.36603i | −0.486352 | + | 0.280796i | −0.723060 | − | 0.690785i | \(-0.757265\pi\) |
0.236708 | + | 0.971581i | \(0.423932\pi\) | |||||||
\(72\) | 6.69615 | − | 3.86603i | 0.789149 | − | 0.455615i | ||||
\(73\) | − | 4.00000i | − | 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | −3.46410 | − | 6.00000i | −0.402694 | − | 0.697486i | ||||
\(75\) | 1.36603 | − | 2.36603i | 0.157735 | − | 0.273205i | ||||
\(76\) | 5.36603 | + | 3.09808i | 0.615525 | + | 0.355374i | ||||
\(77\) | 9.46410 | 1.07853 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.39230 | −0.944208 | −0.472104 | − | 0.881543i | \(-0.656505\pi\) | ||||
−0.472104 | + | 0.881543i | \(0.656505\pi\) | |||||||
\(80\) | 4.33013 | + | 2.50000i | 0.484123 | + | 0.279508i | ||||
\(81\) | 1.23205 | − | 2.13397i | 0.136895 | − | 0.237108i | ||||
\(82\) | −3.00000 | − | 5.19615i | −0.331295 | − | 0.573819i | ||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | −4.73205 | + | 2.73205i | −0.516309 | + | 0.298091i | ||||
\(85\) | 3.00000 | − | 1.73205i | 0.325396 | − | 0.187867i | ||||
\(86\) | 0.339746i | 0.0366357i | ||||||||
\(87\) | 3.46410 | + | 6.00000i | 0.371391 | + | 0.643268i | ||||
\(88\) | −4.09808 | + | 7.09808i | −0.436856 | + | 0.756657i | ||||
\(89\) | 11.1962 | + | 6.46410i | 1.18679 | + | 0.685193i | 0.957575 | − | 0.288183i | \(-0.0930510\pi\) |
0.229214 | + | 0.973376i | \(0.426384\pi\) | |||||||
\(90\) | −7.73205 | −0.815030 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.26795 | 0.132193 | ||||||||
\(93\) | 24.1244 | + | 13.9282i | 2.50158 | + | 1.44429i | ||||
\(94\) | 5.19615 | − | 9.00000i | 0.535942 | − | 0.928279i | ||||
\(95\) | 3.09808 | + | 5.36603i | 0.317856 | + | 0.550543i | ||||
\(96\) | − | 14.1962i | − | 1.44889i | ||||||
\(97\) | −1.73205 | + | 1.00000i | −0.175863 | + | 0.101535i | −0.585348 | − | 0.810782i | \(-0.699042\pi\) |
0.409484 | + | 0.912317i | \(0.365709\pi\) | |||||||
\(98\) | 4.50000 | − | 2.59808i | 0.454569 | − | 0.262445i | ||||
\(99\) | − | 21.1244i | − | 2.12308i | ||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −0.464102 | + | 0.803848i | −0.0461798 | + | 0.0799858i | −0.888191 | − | 0.459474i | \(-0.848038\pi\) |
0.842012 | + | 0.539459i | \(0.181371\pi\) | |||||||
\(102\) | −14.1962 | − | 8.19615i | −1.40563 | − | 0.811540i | ||||
\(103\) | 0.196152 | 0.0193275 | 0.00966374 | − | 0.999953i | \(-0.496924\pi\) | ||||
0.00966374 | + | 0.999953i | \(0.496924\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.46410 | −0.533242 | ||||||||
\(106\) | −15.5885 | − | 9.00000i | −1.51408 | − | 0.874157i | ||||
\(107\) | −8.83013 | + | 15.2942i | −0.853641 | + | 1.47855i | 0.0242598 | + | 0.999706i | \(0.492277\pi\) |
−0.877900 | + | 0.478843i | \(0.841056\pi\) | |||||||
\(108\) | 2.00000 | + | 3.46410i | 0.192450 | + | 0.333333i | ||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | 7.09808 | − | 4.09808i | 0.676775 | − | 0.390736i | ||||
\(111\) | −9.46410 | + | 5.46410i | −0.898293 | + | 0.518630i | ||||
\(112\) | − | 10.0000i | − | 0.944911i | ||||||
\(113\) | −4.26795 | − | 7.39230i | −0.401495 | − | 0.695410i | 0.592412 | − | 0.805635i | \(-0.298176\pi\) |
−0.993907 | + | 0.110226i | \(0.964843\pi\) | |||||||
\(114\) | 14.6603 | − | 25.3923i | 1.37306 | − | 2.37821i | ||||
\(115\) | 1.09808 | + | 0.633975i | 0.102396 | + | 0.0591184i | ||||
\(116\) | 2.53590 | 0.235452 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.8038 | −1.45486 | ||||||||
\(119\) | −6.00000 | − | 3.46410i | −0.550019 | − | 0.317554i | ||||
\(120\) | 2.36603 | − | 4.09808i | 0.215988 | − | 0.374101i | ||||
\(121\) | 5.69615 | + | 9.86603i | 0.517832 | + | 0.896911i | ||||
\(122\) | − | 14.5359i | − | 1.31602i | ||||||
\(123\) | −8.19615 | + | 4.73205i | −0.739022 | + | 0.426675i | ||||
\(124\) | 8.83013 | − | 5.09808i | 0.792969 | − | 0.457821i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 7.73205 | + | 13.3923i | 0.688826 | + | 1.19308i | ||||
\(127\) | 8.09808 | − | 14.0263i | 0.718588 | − | 1.24463i | −0.242971 | − | 0.970034i | \(-0.578122\pi\) |
0.961559 | − | 0.274598i | \(-0.0885446\pi\) | |||||||
\(128\) | 10.5000 | + | 6.06218i | 0.928078 | + | 0.535826i | ||||
\(129\) | 0.535898 | 0.0471832 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −11.1962 | − | 6.46410i | −0.974500 | − | 0.562628i | ||||
\(133\) | 6.19615 | − | 10.7321i | 0.537275 | − | 0.930587i | ||||
\(134\) | −5.53590 | − | 9.58846i | −0.478229 | − | 0.828317i | ||||
\(135\) | 4.00000i | 0.344265i | ||||||||
\(136\) | 5.19615 | − | 3.00000i | 0.445566 | − | 0.257248i | ||||
\(137\) | 0.803848 | − | 0.464102i | 0.0686773 | − | 0.0396509i | −0.465268 | − | 0.885170i | \(-0.654042\pi\) |
0.533945 | + | 0.845519i | \(0.320709\pi\) | |||||||
\(138\) | − | 6.00000i | − | 0.510754i | ||||||
\(139\) | −6.19615 | − | 10.7321i | −0.525551 | − | 0.910281i | −0.999557 | − | 0.0297592i | \(-0.990526\pi\) |
0.474006 | − | 0.880521i | \(-0.342807\pi\) | |||||||
\(140\) | −1.00000 | + | 1.73205i | −0.0845154 | + | 0.146385i | ||||
\(141\) | −14.1962 | − | 8.19615i | −1.19553 | − | 0.690241i | ||||
\(142\) | 8.19615 | 0.687806 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −22.3205 | −1.86004 | ||||||||
\(145\) | 2.19615 | + | 1.26795i | 0.182381 | + | 0.105297i | ||||
\(146\) | −3.46410 | + | 6.00000i | −0.286691 | + | 0.496564i | ||||
\(147\) | −4.09808 | − | 7.09808i | −0.338004 | − | 0.585439i | ||||
\(148\) | 4.00000i | 0.328798i | ||||||||
\(149\) | 6.80385 | − | 3.92820i | 0.557393 | − | 0.321811i | −0.194706 | − | 0.980862i | \(-0.562375\pi\) |
0.752098 | + | 0.659051i | \(0.229042\pi\) | |||||||
\(150\) | −4.09808 | + | 2.36603i | −0.334607 | + | 0.193185i | ||||
\(151\) | − | 1.80385i | − | 0.146795i | −0.997303 | − | 0.0733975i | \(-0.976616\pi\) | ||
0.997303 | − | 0.0733975i | \(-0.0233842\pi\) | |||||||
\(152\) | 5.36603 | + | 9.29423i | 0.435242 | + | 0.753861i | ||||
\(153\) | −7.73205 | + | 13.3923i | −0.625099 | + | 1.08270i | ||||
\(154\) | −14.1962 | − | 8.19615i | −1.14396 | − | 0.660465i | ||||
\(155\) | 10.1962 | 0.818975 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 12.5885 | + | 7.26795i | 1.00148 | + | 0.578207i | ||||
\(159\) | −14.1962 | + | 24.5885i | −1.12583 | + | 1.94999i | ||||
\(160\) | −2.59808 | − | 4.50000i | −0.205396 | − | 0.355756i | ||||
\(161\) | − | 2.53590i | − | 0.199857i | ||||||
\(162\) | −3.69615 | + | 2.13397i | −0.290397 | + | 0.167661i | ||||
\(163\) | −12.4641 | + | 7.19615i | −0.976264 | + | 0.563646i | −0.901140 | − | 0.433528i | \(-0.857269\pi\) |
−0.0751237 | + | 0.997174i | \(0.523935\pi\) | |||||||
\(164\) | 3.46410i | 0.270501i | ||||||||
\(165\) | −6.46410 | − | 11.1962i | −0.503230 | − | 0.871619i | ||||
\(166\) | 5.19615 | − | 9.00000i | 0.403300 | − | 0.698535i | ||||
\(167\) | 0.803848 | + | 0.464102i | 0.0622036 | + | 0.0359133i | 0.530779 | − | 0.847510i | \(-0.321899\pi\) |
−0.468576 | + | 0.883423i | \(0.655233\pi\) | |||||||
\(168\) | −9.46410 | −0.730171 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.00000 | −0.460179 | ||||||||
\(171\) | −23.9545 | − | 13.8301i | −1.83185 | − | 1.05762i | ||||
\(172\) | 0.0980762 | − | 0.169873i | 0.00747824 | − | 0.0129527i | ||||
\(173\) | 4.26795 | + | 7.39230i | 0.324486 | + | 0.562027i | 0.981408 | − | 0.191932i | \(-0.0614753\pi\) |
−0.656922 | + | 0.753958i | \(0.728142\pi\) | |||||||
\(174\) | − | 12.0000i | − | 0.909718i | ||||||
\(175\) | −1.73205 | + | 1.00000i | −0.130931 | + | 0.0755929i | ||||
\(176\) | 20.4904 | − | 11.8301i | 1.54452 | − | 0.891729i | ||||
\(177\) | 24.9282i | 1.87372i | ||||||||
\(178\) | −11.1962 | − | 19.3923i | −0.839187 | − | 1.45351i | ||||
\(179\) | −9.46410 | + | 16.3923i | −0.707380 | + | 1.22522i | 0.258446 | + | 0.966026i | \(0.416790\pi\) |
−0.965826 | + | 0.259193i | \(0.916544\pi\) | |||||||
\(180\) | 3.86603 | + | 2.23205i | 0.288157 | + | 0.166367i | ||||
\(181\) | −0.392305 | −0.0291598 | −0.0145799 | − | 0.999894i | \(-0.504641\pi\) | ||||
−0.0145799 | + | 0.999894i | \(0.504641\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.9282 | −1.69490 | ||||||||
\(184\) | 1.90192 | + | 1.09808i | 0.140212 | + | 0.0809513i | ||||
\(185\) | −2.00000 | + | 3.46410i | −0.147043 | + | 0.254686i | ||||
\(186\) | −24.1244 | − | 41.7846i | −1.76888 | − | 3.06380i | ||||
\(187\) | − | 16.3923i | − | 1.19872i | ||||||
\(188\) | −5.19615 | + | 3.00000i | −0.378968 | + | 0.218797i | ||||
\(189\) | 6.92820 | − | 4.00000i | 0.503953 | − | 0.290957i | ||||
\(190\) | − | 10.7321i | − | 0.778585i | ||||||
\(191\) | 2.53590 | + | 4.39230i | 0.183491 | + | 0.317816i | 0.943067 | − | 0.332603i | \(-0.107927\pi\) |
−0.759576 | + | 0.650419i | \(0.774593\pi\) | |||||||
\(192\) | 1.36603 | − | 2.36603i | 0.0985844 | − | 0.170753i | ||||
\(193\) | 8.66025 | + | 5.00000i | 0.623379 | + | 0.359908i | 0.778183 | − | 0.628037i | \(-0.216141\pi\) |
−0.154805 | + | 0.987945i | \(0.549475\pi\) | |||||||
\(194\) | 3.46410 | 0.248708 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | −11.1962 | − | 6.46410i | −0.797693 | − | 0.460548i | 0.0449709 | − | 0.998988i | \(-0.485680\pi\) |
−0.842664 | + | 0.538440i | \(0.819014\pi\) | |||||||
\(198\) | −18.2942 | + | 31.6865i | −1.30011 | + | 2.25186i | ||||
\(199\) | 10.0000 | + | 17.3205i | 0.708881 | + | 1.22782i | 0.965272 | + | 0.261245i | \(0.0841331\pi\) |
−0.256391 | + | 0.966573i | \(0.582534\pi\) | |||||||
\(200\) | − | 1.73205i | − | 0.122474i | ||||||
\(201\) | −15.1244 | + | 8.73205i | −1.06679 | + | 0.615911i | ||||
\(202\) | 1.39230 | − | 0.803848i | 0.0979622 | − | 0.0565585i | ||||
\(203\) | − | 5.07180i | − | 0.355970i | ||||||
\(204\) | 4.73205 | + | 8.19615i | 0.331310 | + | 0.573845i | ||||
\(205\) | −1.73205 | + | 3.00000i | −0.120972 | + | 0.209529i | ||||
\(206\) | −0.294229 | − | 0.169873i | −0.0204999 | − | 0.0118356i | ||||
\(207\) | −5.66025 | −0.393415 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.3205 | 2.02814 | ||||||||
\(210\) | 8.19615 | + | 4.73205i | 0.565588 | + | 0.326543i | ||||
\(211\) | −4.00000 | + | 6.92820i | −0.275371 | + | 0.476957i | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | 5.19615 | + | 9.00000i | 0.356873 | + | 0.618123i | ||||
\(213\) | − | 12.9282i | − | 0.885826i | ||||||
\(214\) | 26.4904 | − | 15.2942i | 1.81085 | − | 1.04549i | ||||
\(215\) | 0.169873 | − | 0.0980762i | 0.0115852 | − | 0.00668874i | ||||
\(216\) | 6.92820i | 0.471405i | ||||||||
\(217\) | −10.1962 | − | 17.6603i | −0.692160 | − | 1.19886i | ||||
\(218\) | −1.73205 | + | 3.00000i | −0.117309 | + | 0.203186i | ||||
\(219\) | 9.46410 | + | 5.46410i | 0.639525 | + | 0.369230i | ||||
\(220\) | −4.73205 | −0.319035 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 18.9282 | 1.27038 | ||||||||
\(223\) | 1.73205 | + | 1.00000i | 0.115987 | + | 0.0669650i | 0.556871 | − | 0.830599i | \(-0.312002\pi\) |
−0.440884 | + | 0.897564i | \(0.645335\pi\) | |||||||
\(224\) | −5.19615 | + | 9.00000i | −0.347183 | + | 0.601338i | ||||
\(225\) | 2.23205 | + | 3.86603i | 0.148803 | + | 0.257735i | ||||
\(226\) | 14.7846i | 0.983458i | ||||||||
\(227\) | 3.00000 | − | 1.73205i | 0.199117 | − | 0.114960i | −0.397127 | − | 0.917764i | \(-0.629993\pi\) |
0.596244 | + | 0.802804i | \(0.296659\pi\) | |||||||
\(228\) | −14.6603 | + | 8.46410i | −0.970899 | + | 0.560549i | ||||
\(229\) | 6.39230i | 0.422415i | 0.977441 | + | 0.211208i | \(0.0677396\pi\) | ||||
−0.977441 | + | 0.211208i | \(0.932260\pi\) | |||||||
\(230\) | −1.09808 | − | 1.90192i | −0.0724050 | − | 0.125409i | ||||
\(231\) | −12.9282 | + | 22.3923i | −0.850613 | + | 1.47331i | ||||
\(232\) | 3.80385 | + | 2.19615i | 0.249735 | + | 0.144184i | ||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 7.90192 | + | 4.56218i | 0.514371 | + | 0.296972i | ||||
\(237\) | 11.4641 | − | 19.8564i | 0.744673 | − | 1.28981i | ||||
\(238\) | 6.00000 | + | 10.3923i | 0.388922 | + | 0.673633i | ||||
\(239\) | 14.1962i | 0.918273i | 0.888366 | + | 0.459136i | \(0.151841\pi\) | ||||
−0.888366 | + | 0.459136i | \(0.848159\pi\) | |||||||
\(240\) | −11.8301 | + | 6.83013i | −0.763631 | + | 0.440883i | ||||
\(241\) | −2.07180 | + | 1.19615i | −0.133456 | + | 0.0770510i | −0.565242 | − | 0.824925i | \(-0.691217\pi\) |
0.431785 | + | 0.901976i | \(0.357884\pi\) | |||||||
\(242\) | − | 19.7321i | − | 1.26842i | ||||||
\(243\) | 9.36603 | + | 16.2224i | 0.600831 | + | 1.04067i | ||||
\(244\) | −4.19615 | + | 7.26795i | −0.268631 | + | 0.465283i | ||||
\(245\) | −2.59808 | − | 1.50000i | −0.165985 | − | 0.0958315i | ||||
\(246\) | 16.3923 | 1.04514 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 17.6603 | 1.12143 | ||||||||
\(249\) | −14.1962 | − | 8.19615i | −0.899645 | − | 0.519410i | ||||
\(250\) | −0.866025 | + | 1.50000i | −0.0547723 | + | 0.0948683i | ||||
\(251\) | −10.7321 | − | 18.5885i | −0.677401 | − | 1.17329i | −0.975761 | − | 0.218840i | \(-0.929773\pi\) |
0.298360 | − | 0.954453i | \(-0.403560\pi\) | |||||||
\(252\) | − | 8.92820i | − | 0.562424i | ||||||
\(253\) | 5.19615 | − | 3.00000i | 0.326679 | − | 0.188608i | ||||
\(254\) | −24.2942 | + | 14.0263i | −1.52436 | + | 0.880087i | ||||
\(255\) | 9.46410i | 0.592665i | ||||||||
\(256\) | −9.50000 | − | 16.4545i | −0.593750 | − | 1.02841i | ||||
\(257\) | 9.92820 | − | 17.1962i | 0.619304 | − | 1.07267i | −0.370309 | − | 0.928909i | \(-0.620748\pi\) |
0.989613 | − | 0.143758i | \(-0.0459186\pi\) | |||||||
\(258\) | −0.803848 | − | 0.464102i | −0.0500454 | − | 0.0288937i | ||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.3205 | −0.700722 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.633975 | + | 1.09808i | −0.0390925 | + | 0.0677103i | −0.884910 | − | 0.465763i | \(-0.845780\pi\) |
0.845817 | + | 0.533473i | \(0.179113\pi\) | |||||||
\(264\) | −11.1962 | − | 19.3923i | −0.689076 | − | 1.19351i | ||||
\(265\) | 10.3923i | 0.638394i | ||||||||
\(266\) | −18.5885 | + | 10.7321i | −1.13973 | + | 0.658024i | ||||
\(267\) | −30.5885 | + | 17.6603i | −1.87198 | + | 1.08079i | ||||
\(268\) | 6.39230i | 0.390472i | ||||||||
\(269\) | 9.92820 | + | 17.1962i | 0.605333 | + | 1.04847i | 0.991999 | + | 0.126248i | \(0.0402935\pi\) |
−0.386665 | + | 0.922220i | \(0.626373\pi\) | |||||||
\(270\) | 3.46410 | − | 6.00000i | 0.210819 | − | 0.365148i | ||||
\(271\) | −26.8301 | − | 15.4904i | −1.62981 | − | 0.940974i | −0.984147 | − | 0.177355i | \(-0.943246\pi\) |
−0.645667 | − | 0.763619i | \(-0.723421\pi\) | |||||||
\(272\) | −17.3205 | −1.05021 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.60770 | −0.0971244 | ||||||||
\(275\) | −4.09808 | − | 2.36603i | −0.247123 | − | 0.142677i | ||||
\(276\) | −1.73205 | + | 3.00000i | −0.104257 | + | 0.180579i | ||||
\(277\) | −13.1962 | − | 22.8564i | −0.792880 | − | 1.37331i | −0.924177 | − | 0.381965i | \(-0.875247\pi\) |
0.131297 | − | 0.991343i | \(-0.458086\pi\) | |||||||
\(278\) | 21.4641i | 1.28733i | ||||||||
\(279\) | −39.4186 | + | 22.7583i | −2.35993 | + | 1.36251i | ||||
\(280\) | −3.00000 | + | 1.73205i | −0.179284 | + | 0.103510i | ||||
\(281\) | 22.3923i | 1.33581i | 0.744245 | + | 0.667906i | \(0.232809\pi\) | ||||
−0.744245 | + | 0.667906i | \(0.767191\pi\) | |||||||
\(282\) | 14.1962 | + | 24.5885i | 0.845369 | + | 1.46422i | ||||
\(283\) | 16.2942 | − | 28.2224i | 0.968591 | − | 1.67765i | 0.268952 | − | 0.963154i | \(-0.413323\pi\) |
0.699640 | − | 0.714496i | \(-0.253344\pi\) | |||||||
\(284\) | −4.09808 | − | 2.36603i | −0.243176 | − | 0.140398i | ||||
\(285\) | −16.9282 | −1.00274 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.92820 | 0.408959 | ||||||||
\(288\) | 20.0885 | + | 11.5981i | 1.18372 | + | 0.683423i | ||||
\(289\) | 2.50000 | − | 4.33013i | 0.147059 | − | 0.254713i | ||||
\(290\) | −2.19615 | − | 3.80385i | −0.128963 | − | 0.223370i | ||||
\(291\) | − | 5.46410i | − | 0.320311i | ||||||
\(292\) | 3.46410 | − | 2.00000i | 0.202721 | − | 0.117041i | ||||
\(293\) | −4.39230 | + | 2.53590i | −0.256601 | + | 0.148149i | −0.622783 | − | 0.782395i | \(-0.713998\pi\) |
0.366182 | + | 0.930543i | \(0.380665\pi\) | |||||||
\(294\) | 14.1962i | 0.827936i | ||||||||
\(295\) | 4.56218 | + | 7.90192i | 0.265620 | + | 0.460068i | ||||
\(296\) | −3.46410 | + | 6.00000i | −0.201347 | + | 0.348743i | ||||
\(297\) | 16.3923 | + | 9.46410i | 0.951178 | + | 0.549163i | ||||
\(298\) | −13.6077 | −0.788273 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.73205 | 0.157735 | ||||||||
\(301\) | −0.339746 | − | 0.196152i | −0.0195826 | − | 0.0113060i | ||||
\(302\) | −1.56218 | + | 2.70577i | −0.0898932 | + | 0.155700i | ||||
\(303\) | −1.26795 | − | 2.19615i | −0.0728418 | − | 0.126166i | ||||
\(304\) | − | 30.9808i | − | 1.77687i | ||||||
\(305\) | −7.26795 | + | 4.19615i | −0.416162 | + | 0.240271i | ||||
\(306\) | 23.1962 | − | 13.3923i | 1.32604 | − | 0.765587i | ||||
\(307\) | − | 18.7846i | − | 1.07209i | −0.844188 | − | 0.536047i | \(-0.819917\pi\) | ||
0.844188 | − | 0.536047i | \(-0.180083\pi\) | |||||||
\(308\) | 4.73205 | + | 8.19615i | 0.269634 | + | 0.467019i | ||||
\(309\) | −0.267949 | + | 0.464102i | −0.0152431 | + | 0.0264018i | ||||
\(310\) | −15.2942 | − | 8.83013i | −0.868654 | − | 0.501518i | ||||
\(311\) | 16.3923 | 0.929522 | 0.464761 | − | 0.885436i | \(-0.346140\pi\) | ||||
0.464761 | + | 0.885436i | \(0.346140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.3923 | −0.813501 | −0.406751 | − | 0.913539i | \(-0.633338\pi\) | ||||
−0.406751 | + | 0.913539i | \(0.633338\pi\) | |||||||
\(314\) | 15.0000 | + | 8.66025i | 0.846499 | + | 0.488726i | ||||
\(315\) | 4.46410 | − | 7.73205i | 0.251524 | − | 0.435652i | ||||
\(316\) | −4.19615 | − | 7.26795i | −0.236052 | − | 0.408854i | ||||
\(317\) | − | 24.0000i | − | 1.34797i | −0.738743 | − | 0.673987i | \(-0.764580\pi\) | ||
0.738743 | − | 0.673987i | \(-0.235420\pi\) | |||||||
\(318\) | 42.5885 | − | 24.5885i | 2.38824 | − | 1.37885i | ||||
\(319\) | 10.3923 | − | 6.00000i | 0.581857 | − | 0.335936i | ||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | −24.1244 | − | 41.7846i | −1.34649 | − | 2.33219i | ||||
\(322\) | −2.19615 | + | 3.80385i | −0.122387 | + | 0.211980i | ||||
\(323\) | −18.5885 | − | 10.7321i | −1.03429 | − | 0.597147i | ||||
\(324\) | 2.46410 | 0.136895 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.9282 | 1.38065 | ||||||||
\(327\) | 4.73205 | + | 2.73205i | 0.261683 | + | 0.151083i | ||||
\(328\) | −3.00000 | + | 5.19615i | −0.165647 | + | 0.286910i | ||||
\(329\) | 6.00000 | + | 10.3923i | 0.330791 | + | 0.572946i | ||||
\(330\) | 22.3923i | 1.23266i | ||||||||
\(331\) | −2.24167 | + | 1.29423i | −0.123213 | + | 0.0711372i | −0.560340 | − | 0.828263i | \(-0.689329\pi\) |
0.437127 | + | 0.899400i | \(0.355996\pi\) | |||||||
\(332\) | −5.19615 | + | 3.00000i | −0.285176 | + | 0.164646i | ||||
\(333\) | − | 17.8564i | − | 0.978525i | ||||||
\(334\) | −0.803848 | − | 1.39230i | −0.0439846 | − | 0.0761835i | ||||
\(335\) | −3.19615 | + | 5.53590i | −0.174624 | + | 0.302458i | ||||
\(336\) | 23.6603 | + | 13.6603i | 1.29077 | + | 0.745228i | ||||
\(337\) | 26.3923 | 1.43768 | 0.718840 | − | 0.695175i | \(-0.244673\pi\) | ||||
0.718840 | + | 0.695175i | \(0.244673\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.3205 | 1.26660 | ||||||||
\(340\) | 3.00000 | + | 1.73205i | 0.162698 | + | 0.0939336i | ||||
\(341\) | 24.1244 | − | 41.7846i | 1.30641 | − | 2.26276i | ||||
\(342\) | 23.9545 | + | 41.4904i | 1.29531 | + | 2.24354i | ||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 0.294229 | − | 0.169873i | 0.0158637 | − | 0.00915894i | ||||
\(345\) | −3.00000 | + | 1.73205i | −0.161515 | + | 0.0932505i | ||||
\(346\) | − | 14.7846i | − | 0.794826i | ||||||
\(347\) | 2.83013 | + | 4.90192i | 0.151929 | + | 0.263149i | 0.931937 | − | 0.362621i | \(-0.118118\pi\) |
−0.780007 | + | 0.625770i | \(0.784785\pi\) | |||||||
\(348\) | −3.46410 | + | 6.00000i | −0.185695 | + | 0.321634i | ||||
\(349\) | 12.4641 | + | 7.19615i | 0.667188 | + | 0.385201i | 0.795010 | − | 0.606596i | \(-0.207465\pi\) |
−0.127822 | + | 0.991797i | \(0.540799\pi\) | |||||||
\(350\) | 3.46410 | 0.185164 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −24.5885 | −1.31057 | ||||||||
\(353\) | −24.0000 | − | 13.8564i | −1.27739 | − | 0.737502i | −0.301023 | − | 0.953617i | \(-0.597328\pi\) |
−0.976368 | + | 0.216115i | \(0.930661\pi\) | |||||||
\(354\) | 21.5885 | − | 37.3923i | 1.14741 | − | 1.98738i | ||||
\(355\) | −2.36603 | − | 4.09808i | −0.125576 | − | 0.217503i | ||||
\(356\) | 12.9282i | 0.685193i | ||||||||
\(357\) | 16.3923 | − | 9.46410i | 0.867573 | − | 0.500893i | ||||
\(358\) | 28.3923 | − | 16.3923i | 1.50058 | − | 0.866360i | ||||
\(359\) | − | 2.19615i | − | 0.115908i | −0.998319 | − | 0.0579542i | \(-0.981542\pi\) | ||
0.998319 | − | 0.0579542i | \(-0.0184578\pi\) | |||||||
\(360\) | 3.86603 | + | 6.69615i | 0.203757 | + | 0.352918i | ||||
\(361\) | 9.69615 | − | 16.7942i | 0.510324 | − | 0.883907i | ||||
\(362\) | 0.588457 | + | 0.339746i | 0.0309286 | + | 0.0178567i | ||||
\(363\) | −31.1244 | −1.63361 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00000 | 0.209370 | ||||||||
\(366\) | 34.3923 | + | 19.8564i | 1.79771 | + | 1.03791i | ||||
\(367\) | −5.90192 | + | 10.2224i | −0.308078 | + | 0.533607i | −0.977942 | − | 0.208877i | \(-0.933019\pi\) |
0.669864 | + | 0.742484i | \(0.266352\pi\) | |||||||
\(368\) | −3.16987 | − | 5.49038i | −0.165241 | − | 0.286206i | ||||
\(369\) | − | 15.4641i | − | 0.805029i | ||||||
\(370\) | 6.00000 | − | 3.46410i | 0.311925 | − | 0.180090i | ||||
\(371\) | 18.0000 | − | 10.3923i | 0.934513 | − | 0.539542i | ||||
\(372\) | 27.8564i | 1.44429i | ||||||||
\(373\) | 5.00000 | + | 8.66025i | 0.258890 | + | 0.448411i | 0.965945 | − | 0.258748i | \(-0.0833099\pi\) |
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(374\) | −14.1962 | + | 24.5885i | −0.734066 | + | 1.27144i | ||||
\(375\) | 2.36603 | + | 1.36603i | 0.122181 | + | 0.0705412i | ||||
\(376\) | −10.3923 | −0.535942 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −13.8564 | −0.712697 | ||||||||
\(379\) | 16.4378 | + | 9.49038i | 0.844354 | + | 0.487488i | 0.858742 | − | 0.512408i | \(-0.171247\pi\) |
−0.0143877 | + | 0.999896i | \(0.504580\pi\) | |||||||
\(380\) | −3.09808 | + | 5.36603i | −0.158928 | + | 0.275271i | ||||
\(381\) | 22.1244 | + | 38.3205i | 1.13347 | + | 1.96322i | ||||
\(382\) | − | 8.78461i | − | 0.449460i | ||||||
\(383\) | −11.1962 | + | 6.46410i | −0.572097 | + | 0.330300i | −0.757986 | − | 0.652270i | \(-0.773817\pi\) |
0.185890 | + | 0.982571i | \(0.440483\pi\) | |||||||
\(384\) | −28.6865 | + | 16.5622i | −1.46390 | + | 0.845185i | ||||
\(385\) | 9.46410i | 0.482335i | ||||||||
\(386\) | −8.66025 | − | 15.0000i | −0.440795 | − | 0.763480i | ||||
\(387\) | −0.437822 | + | 0.758330i | −0.0222558 | + | 0.0385481i | ||||
\(388\) | −1.73205 | − | 1.00000i | −0.0879316 | − | 0.0507673i | ||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.39230 | −0.222128 | ||||||||
\(392\) | −4.50000 | − | 2.59808i | −0.227284 | − | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.1962 | + | 19.3923i | 0.564054 | + | 0.976970i | ||||
\(395\) | − | 8.39230i | − | 0.422263i | ||||||
\(396\) | 18.2942 | − | 10.5622i | 0.919320 | − | 0.530769i | ||||
\(397\) | 24.9282 | − | 14.3923i | 1.25111 | − | 0.722329i | 0.279781 | − | 0.960064i | \(-0.409738\pi\) |
0.971330 | + | 0.237735i | \(0.0764049\pi\) | |||||||
\(398\) | − | 34.6410i | − | 1.73640i | ||||||
\(399\) | 16.9282 | + | 29.3205i | 0.847470 | + | 1.46786i | ||||
\(400\) | −2.50000 | + | 4.33013i | −0.125000 | + | 0.216506i | ||||
\(401\) | 31.9808 | + | 18.4641i | 1.59704 | + | 0.922053i | 0.992053 | + | 0.125820i | \(0.0401562\pi\) |
0.604990 | + | 0.796233i | \(0.293177\pi\) | |||||||
\(402\) | 30.2487 | 1.50867 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.928203 | −0.0461798 | ||||||||
\(405\) | 2.13397 | + | 1.23205i | 0.106038 | + | 0.0612211i | ||||
\(406\) | −4.39230 | + | 7.60770i | −0.217986 | + | 0.377564i | ||||
\(407\) | 9.46410 | + | 16.3923i | 0.469118 | + | 0.812536i | ||||
\(408\) | 16.3923i | 0.811540i | ||||||||
\(409\) | 15.2487 | − | 8.80385i | 0.754000 | − | 0.435322i | −0.0731372 | − | 0.997322i | \(-0.523301\pi\) |
0.827137 | + | 0.562000i | \(0.189968\pi\) | |||||||
\(410\) | 5.19615 | − | 3.00000i | 0.256620 | − | 0.148159i | ||||
\(411\) | 2.53590i | 0.125087i | ||||||||
\(412\) | 0.0980762 | + | 0.169873i | 0.00483187 | + | 0.00836904i | ||||
\(413\) | 9.12436 | − | 15.8038i | 0.448980 | − | 0.777657i | ||||
\(414\) | 8.49038 | + | 4.90192i | 0.417279 | + | 0.240916i | ||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.8564 | 1.65796 | ||||||||
\(418\) | −43.9808 | − | 25.3923i | −2.15117 | − | 1.24198i | ||||
\(419\) | 1.26795 | − | 2.19615i | 0.0619434 | − | 0.107289i | −0.833391 | − | 0.552684i | \(-0.813604\pi\) |
0.895334 | + | 0.445395i | \(0.146937\pi\) | |||||||
\(420\) | −2.73205 | − | 4.73205i | −0.133310 | − | 0.230900i | ||||
\(421\) | 30.7846i | 1.50035i | 0.661239 | + | 0.750175i | \(0.270031\pi\) | ||||
−0.661239 | + | 0.750175i | \(0.729969\pi\) | |||||||
\(422\) | 12.0000 | − | 6.92820i | 0.584151 | − | 0.337260i | ||||
\(423\) | 23.1962 | − | 13.3923i | 1.12784 | − | 0.651156i | ||||
\(424\) | 18.0000i | 0.874157i | ||||||||
\(425\) | 1.73205 | + | 3.00000i | 0.0840168 | + | 0.145521i | ||||
\(426\) | −11.1962 | + | 19.3923i | −0.542455 | + | 0.939560i | ||||
\(427\) | 14.5359 | + | 8.39230i | 0.703441 | + | 0.406132i | ||||
\(428\) | −17.6603 | −0.853641 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.339746 | −0.0163840 | ||||||||
\(431\) | −22.0981 | − | 12.7583i | −1.06443 | − | 0.614547i | −0.137773 | − | 0.990464i | \(-0.543995\pi\) |
−0.926653 | + | 0.375917i | \(0.877328\pi\) | |||||||
\(432\) | 10.0000 | − | 17.3205i | 0.481125 | − | 0.833333i | ||||
\(433\) | 17.3923 | + | 30.1244i | 0.835821 | + | 1.44768i | 0.893360 | + | 0.449341i | \(0.148341\pi\) |
−0.0575395 | + | 0.998343i | \(0.518326\pi\) | |||||||
\(434\) | 35.3205i | 1.69544i | ||||||||
\(435\) | −6.00000 | + | 3.46410i | −0.287678 | + | 0.166091i | ||||
\(436\) | 1.73205 | − | 1.00000i | 0.0829502 | − | 0.0478913i | ||||
\(437\) | − | 7.85641i | − | 0.375823i | ||||||
\(438\) | −9.46410 | − | 16.3923i | −0.452212 | − | 0.783255i | ||||
\(439\) | 16.0000 | − | 27.7128i | 0.763638 | − | 1.32266i | −0.177325 | − | 0.984152i | \(-0.556744\pi\) |
0.940963 | − | 0.338508i | \(-0.109922\pi\) | |||||||
\(440\) | −7.09808 | − | 4.09808i | −0.338388 | − | 0.195368i | ||||
\(441\) | 13.3923 | 0.637729 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.9808 | −0.806780 | −0.403390 | − | 0.915028i | \(-0.632168\pi\) | ||||
−0.403390 | + | 0.915028i | \(0.632168\pi\) | |||||||
\(444\) | −9.46410 | − | 5.46410i | −0.449146 | − | 0.259315i | ||||
\(445\) | −6.46410 | + | 11.1962i | −0.306428 | + | 0.530749i | ||||
\(446\) | −1.73205 | − | 3.00000i | −0.0820150 | − | 0.142054i | ||||
\(447\) | 21.4641i | 1.01522i | ||||||||
\(448\) | −1.73205 | + | 1.00000i | −0.0818317 | + | 0.0472456i | ||||
\(449\) | 17.7846 | − | 10.2679i | 0.839308 | − | 0.484574i | −0.0177212 | − | 0.999843i | \(-0.505641\pi\) |
0.857029 | + | 0.515268i | \(0.172308\pi\) | |||||||
\(450\) | − | 7.73205i | − | 0.364492i | ||||||
\(451\) | 8.19615 | + | 14.1962i | 0.385942 | + | 0.668471i | ||||
\(452\) | 4.26795 | − | 7.39230i | 0.200747 | − | 0.347705i | ||||
\(453\) | 4.26795 | + | 2.46410i | 0.200526 | + | 0.115774i | ||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −29.3205 | −1.37306 | ||||||||
\(457\) | 9.33975 | + | 5.39230i | 0.436895 | + | 0.252241i | 0.702280 | − | 0.711901i | \(-0.252166\pi\) |
−0.265385 | + | 0.964143i | \(0.585499\pi\) | |||||||
\(458\) | 5.53590 | − | 9.58846i | 0.258676 | − | 0.448039i | ||||
\(459\) | −6.92820 | − | 12.0000i | −0.323381 | − | 0.560112i | ||||
\(460\) | 1.26795i | 0.0591184i | ||||||||
\(461\) | 3.00000 | − | 1.73205i | 0.139724 | − | 0.0806696i | −0.428508 | − | 0.903538i | \(-0.640961\pi\) |
0.568232 | + | 0.822868i | \(0.307627\pi\) | |||||||
\(462\) | 38.7846 | − | 22.3923i | 1.80442 | − | 1.04178i | ||||
\(463\) | − | 2.39230i | − | 0.111180i | −0.998454 | − | 0.0555899i | \(-0.982296\pi\) | ||
0.998454 | − | 0.0555899i | \(-0.0177039\pi\) | |||||||
\(464\) | −6.33975 | − | 10.9808i | −0.294315 | − | 0.509769i | ||||
\(465\) | −13.9282 | + | 24.1244i | −0.645905 | + | 1.11874i | ||||
\(466\) | −9.00000 | − | 5.19615i | −0.416917 | − | 0.240707i | ||||
\(467\) | −27.8038 | −1.28661 | −0.643304 | − | 0.765611i | \(-0.722437\pi\) | ||||
−0.643304 | + | 0.765611i | \(0.722437\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.7846 | 0.590338 | ||||||||
\(470\) | 9.00000 | + | 5.19615i | 0.415139 | + | 0.239681i | ||||
\(471\) | 13.6603 | − | 23.6603i | 0.629431 | − | 1.09021i | ||||
\(472\) | 7.90192 | + | 13.6865i | 0.363716 | + | 0.629974i | ||||
\(473\) | − | 0.928203i | − | 0.0426788i | ||||||
\(474\) | −34.3923 | + | 19.8564i | −1.57969 | + | 0.912035i | ||||
\(475\) | −5.36603 | + | 3.09808i | −0.246210 | + | 0.142149i | ||||
\(476\) | − | 6.92820i | − | 0.317554i | ||||||
\(477\) | −23.1962 | − | 40.1769i | −1.06208 | − | 1.83957i | ||||
\(478\) | 12.2942 | − | 21.2942i | 0.562325 | − | 0.973975i | ||||
\(479\) | −30.8827 | − | 17.8301i | −1.41107 | − | 0.814679i | −0.415577 | − | 0.909558i | \(-0.636420\pi\) |
−0.995489 | + | 0.0948787i | \(0.969754\pi\) | |||||||
\(480\) | 14.1962 | 0.647963 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.14359 | 0.188736 | ||||||||
\(483\) | 6.00000 | + | 3.46410i | 0.273009 | + | 0.157622i | ||||
\(484\) | −5.69615 | + | 9.86603i | −0.258916 | + | 0.448456i | ||||
\(485\) | −1.00000 | − | 1.73205i | −0.0454077 | − | 0.0786484i | ||||
\(486\) | − | 32.4449i | − | 1.47173i | ||||||
\(487\) | 22.8564 | − | 13.1962i | 1.03572 | − | 0.597975i | 0.117104 | − | 0.993120i | \(-0.462639\pi\) |
0.918619 | + | 0.395145i | \(0.129306\pi\) | |||||||
\(488\) | −12.5885 | + | 7.26795i | −0.569853 | + | 0.329005i | ||||
\(489\) | − | 39.3205i | − | 1.77813i | ||||||
\(490\) | 2.59808 | + | 4.50000i | 0.117369 | + | 0.203289i | ||||
\(491\) | −1.26795 | + | 2.19615i | −0.0572217 | + | 0.0991110i | −0.893217 | − | 0.449625i | \(-0.851558\pi\) |
0.835996 | + | 0.548736i | \(0.184891\pi\) | |||||||
\(492\) | −8.19615 | − | 4.73205i | −0.369511 | − | 0.213337i | ||||
\(493\) | −8.78461 | −0.395639 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.1244 | 0.949469 | ||||||||
\(496\) | −44.1506 | − | 25.4904i | −1.98242 | − | 1.14455i | ||||
\(497\) | −4.73205 | + | 8.19615i | −0.212261 | + | 0.367648i | ||||
\(498\) | 14.1962 | + | 24.5885i | 0.636145 | + | 1.10184i | ||||
\(499\) | 38.9808i | 1.74502i | 0.488598 | + | 0.872509i | \(0.337509\pi\) | ||||
−0.488598 | + | 0.872509i | \(0.662491\pi\) | |||||||
\(500\) | 0.866025 | − | 0.500000i | 0.0387298 | − | 0.0223607i | ||||
\(501\) | −2.19615 | + | 1.26795i | −0.0981169 | + | 0.0566478i | ||||
\(502\) | 37.1769i | 1.65929i | ||||||||
\(503\) | −9.75833 | − | 16.9019i | −0.435102 | − | 0.753620i | 0.562202 | − | 0.827000i | \(-0.309955\pi\) |
−0.997304 | + | 0.0733807i | \(0.976621\pi\) | |||||||
\(504\) | 7.73205 | − | 13.3923i | 0.344413 | − | 0.596541i | ||||
\(505\) | −0.803848 | − | 0.464102i | −0.0357707 | − | 0.0206523i | ||||
\(506\) | −10.3923 | −0.461994 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.1962 | 0.718588 | ||||||||
\(509\) | 34.1769 | + | 19.7321i | 1.51487 | + | 0.874608i | 0.999848 | + | 0.0174278i | \(0.00554772\pi\) |
0.515017 | + | 0.857180i | \(0.327786\pi\) | |||||||
\(510\) | 8.19615 | − | 14.1962i | 0.362932 | − | 0.628616i | ||||
\(511\) | −4.00000 | − | 6.92820i | −0.176950 | − | 0.306486i | ||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | 21.4641 | − | 12.3923i | 0.947663 | − | 0.547134i | ||||
\(514\) | −29.7846 | + | 17.1962i | −1.31374 | + | 0.758490i | ||||
\(515\) | 0.196152i | 0.00864351i | ||||||||
\(516\) | 0.267949 | + | 0.464102i | 0.0117958 | + | 0.0204309i | ||||
\(517\) | −14.1962 | + | 24.5885i | −0.624346 | + | 1.08140i | ||||
\(518\) | −12.0000 | − | 6.92820i | −0.527250 | − | 0.304408i | ||||
\(519\) | −23.3205 | −1.02366 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.3923 | −1.24389 | −0.621945 | − | 0.783061i | \(-0.713657\pi\) | ||||
−0.621945 | + | 0.783061i | \(0.713657\pi\) | |||||||
\(522\) | 16.9808 | + | 9.80385i | 0.743228 | + | 0.429103i | ||||
\(523\) | 12.0981 | − | 20.9545i | 0.529012 | − | 0.916276i | −0.470416 | − | 0.882445i | \(-0.655896\pi\) |
0.999428 | − | 0.0338306i | \(-0.0107707\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 5.46410i | − | 0.238473i | ||||||
\(526\) | 1.90192 | − | 1.09808i | 0.0829278 | − | 0.0478784i | ||||
\(527\) | −30.5885 | + | 17.6603i | −1.33245 | + | 0.769293i | ||||
\(528\) | 64.6410i | 2.81314i | ||||||||
\(529\) | 10.6962 | + | 18.5263i | 0.465050 | + | 0.805490i | ||||
\(530\) | 9.00000 | − | 15.5885i | 0.390935 | − | 0.677119i | ||||
\(531\) | −35.2750 | − | 20.3660i | −1.53080 | − | 0.883810i | ||||
\(532\) | 12.3923 | 0.537275 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 61.1769 | 2.64738 | ||||||||
\(535\) | −15.2942 | − | 8.83013i | −0.661227 | − | 0.381760i | ||||
\(536\) | −5.53590 | + | 9.58846i | −0.239114 | + | 0.414158i | ||||
\(537\) | −25.8564 | − | 44.7846i | −1.11579 | − | 1.93260i | ||||
\(538\) | − | 34.3923i | − | 1.48276i | ||||||
\(539\) | −12.2942 | + | 7.09808i | −0.529550 | + | 0.305736i | ||||
\(540\) | −3.46410 | + | 2.00000i | −0.149071 | + | 0.0860663i | ||||
\(541\) | − | 26.3923i | − | 1.13469i | −0.823479 | − | 0.567347i | \(-0.807970\pi\) | ||
0.823479 | − | 0.567347i | \(-0.192030\pi\) | |||||||
\(542\) | 26.8301 | + | 46.4711i | 1.15245 | + | 1.99611i | ||||
\(543\) | 0.535898 | − | 0.928203i | 0.0229976 | − | 0.0398330i | ||||
\(544\) | 15.5885 | + | 9.00000i | 0.668350 | + | 0.385872i | ||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.1962 | −0.521470 | −0.260735 | − | 0.965410i | \(-0.583965\pi\) | ||||
−0.260735 | + | 0.965410i | \(0.583965\pi\) | |||||||
\(548\) | 0.803848 | + | 0.464102i | 0.0343387 | + | 0.0198254i | ||||
\(549\) | 18.7321 | − | 32.4449i | 0.799464 | − | 1.38471i | ||||
\(550\) | 4.09808 | + | 7.09808i | 0.174743 | + | 0.302663i | ||||
\(551\) | − | 15.7128i | − | 0.669388i | ||||||
\(552\) | −5.19615 | + | 3.00000i | −0.221163 | + | 0.127688i | ||||
\(553\) | −14.5359 | + | 8.39230i | −0.618129 | + | 0.356877i | ||||
\(554\) | 45.7128i | 1.94215i | ||||||||
\(555\) | −5.46410 | − | 9.46410i | −0.231938 | − | 0.401729i | ||||
\(556\) | 6.19615 | − | 10.7321i | 0.262775 | − | 0.455140i | ||||
\(557\) | −1.60770 | − | 0.928203i | −0.0681202 | − | 0.0393292i | 0.465553 | − | 0.885020i | \(-0.345855\pi\) |
−0.533673 | + | 0.845691i | \(0.679189\pi\) | |||||||
\(558\) | 78.8372 | 3.33744 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 10.0000 | 0.422577 | ||||||||
\(561\) | 38.7846 | + | 22.3923i | 1.63749 | + | 0.945404i | ||||
\(562\) | 19.3923 | − | 33.5885i | 0.818015 | − | 1.41684i | ||||
\(563\) | −11.0263 | − | 19.0981i | −0.464702 | − | 0.804888i | 0.534486 | − | 0.845177i | \(-0.320505\pi\) |
−0.999188 | + | 0.0402895i | \(0.987172\pi\) | |||||||
\(564\) | − | 16.3923i | − | 0.690241i | ||||||
\(565\) | 7.39230 | − | 4.26795i | 0.310997 | − | 0.179554i | ||||
\(566\) | −48.8827 | + | 28.2224i | −2.05469 | + | 1.18628i | ||||
\(567\) | − | 4.92820i | − | 0.206965i | ||||||
\(568\) | −4.09808 | − | 7.09808i | −0.171951 | − | 0.297829i | ||||
\(569\) | −1.26795 | + | 2.19615i | −0.0531552 | + | 0.0920675i | −0.891379 | − | 0.453259i | \(-0.850261\pi\) |
0.838223 | + | 0.545327i | \(0.183594\pi\) | |||||||
\(570\) | 25.3923 | + | 14.6603i | 1.06357 | + | 0.614050i | ||||
\(571\) | −36.3923 | −1.52297 | −0.761485 | − | 0.648182i | \(-0.775530\pi\) | ||||
−0.761485 | + | 0.648182i | \(0.775530\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.8564 | −0.578860 | ||||||||
\(574\) | −10.3923 | − | 6.00000i | −0.433766 | − | 0.250435i | ||||
\(575\) | −0.633975 | + | 1.09808i | −0.0264386 | + | 0.0457929i | ||||
\(576\) | 2.23205 | + | 3.86603i | 0.0930021 | + | 0.161084i | ||||
\(577\) | 4.00000i | 0.166522i | 0.996528 | + | 0.0832611i | \(0.0265335\pi\) | ||||
−0.996528 | + | 0.0832611i | \(0.973466\pi\) | |||||||
\(578\) | −7.50000 | + | 4.33013i | −0.311959 | + | 0.180110i | ||||
\(579\) | −23.6603 | + | 13.6603i | −0.983287 | + | 0.567701i | ||||
\(580\) | 2.53590i | 0.105297i | ||||||||
\(581\) | 6.00000 | + | 10.3923i | 0.248922 | + | 0.431145i | ||||
\(582\) | −4.73205 | + | 8.19615i | −0.196150 | + | 0.339741i | ||||
\(583\) | 42.5885 | + | 24.5885i | 1.76383 | + | 1.01835i | ||||
\(584\) | 6.92820 | 0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.78461 | 0.362889 | ||||||||
\(587\) | −7.39230 | − | 4.26795i | −0.305113 | − | 0.176157i | 0.339624 | − | 0.940561i | \(-0.389700\pi\) |
−0.644738 | + | 0.764404i | \(0.723033\pi\) | |||||||
\(588\) | 4.09808 | − | 7.09808i | 0.169002 | − | 0.292720i | ||||
\(589\) | −31.5885 | − | 54.7128i | −1.30158 | − | 2.25440i | ||||
\(590\) | − | 15.8038i | − | 0.650634i | ||||||
\(591\) | 30.5885 | − | 17.6603i | 1.25824 | − | 0.726446i | ||||
\(592\) | 17.3205 | − | 10.0000i | 0.711868 | − | 0.410997i | ||||
\(593\) | 26.7846i | 1.09991i | 0.835194 | + | 0.549956i | \(0.185356\pi\) | ||||
−0.835194 | + | 0.549956i | \(0.814644\pi\) | |||||||
\(594\) | −16.3923 | − | 28.3923i | −0.672584 | − | 1.16495i | ||||
\(595\) | 3.46410 | − | 6.00000i | 0.142014 | − | 0.245976i | ||||
\(596\) | 6.80385 | + | 3.92820i | 0.278696 | + | 0.160905i | ||||
\(597\) | −54.6410 | −2.23631 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.60770 | −0.310842 | −0.155421 | − | 0.987848i | \(-0.549673\pi\) | ||||
−0.155421 | + | 0.987848i | \(0.549673\pi\) | |||||||
\(600\) | 4.09808 | + | 2.36603i | 0.167303 | + | 0.0965926i | ||||
\(601\) | −21.7846 | + | 37.7321i | −0.888613 | + | 1.53912i | −0.0470967 | + | 0.998890i | \(0.514997\pi\) |
−0.841516 | + | 0.540232i | \(0.818336\pi\) | |||||||
\(602\) | 0.339746 | + | 0.588457i | 0.0138470 | + | 0.0239837i | ||||
\(603\) | − | 28.5359i | − | 1.16207i | ||||||
\(604\) | 1.56218 | − | 0.901924i | 0.0635641 | − | 0.0366988i | ||||
\(605\) | −9.86603 | + | 5.69615i | −0.401111 | + | 0.231582i | ||||
\(606\) | 4.39230i | 0.178425i | ||||||||
\(607\) | −12.4904 | − | 21.6340i | −0.506969 | − | 0.878096i | −0.999967 | − | 0.00806581i | \(-0.997433\pi\) |
0.492999 | − | 0.870030i | \(-0.335901\pi\) | |||||||
\(608\) | −16.0981 | + | 27.8827i | −0.652863 | + | 1.13079i | ||||
\(609\) | 12.0000 | + | 6.92820i | 0.486265 | + | 0.280745i | ||||
\(610\) | 14.5359 | 0.588541 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −15.4641 | −0.625099 | ||||||||
\(613\) | 22.5167 | + | 13.0000i | 0.909439 | + | 0.525065i | 0.880251 | − | 0.474509i | \(-0.157374\pi\) |
0.0291886 | + | 0.999574i | \(0.490708\pi\) | |||||||
\(614\) | −16.2679 | + | 28.1769i | −0.656521 | + | 1.13713i | ||||
\(615\) | −4.73205 | − | 8.19615i | −0.190815 | − | 0.330501i | ||||
\(616\) | 16.3923i | 0.660465i | ||||||||
\(617\) | −29.1962 | + | 16.8564i | −1.17539 | + | 0.678613i | −0.954944 | − | 0.296785i | \(-0.904085\pi\) |
−0.220449 | + | 0.975399i | \(0.570752\pi\) | |||||||
\(618\) | 0.803848 | − | 0.464102i | 0.0323355 | − | 0.0186689i | ||||
\(619\) | 6.98076i | 0.280581i | 0.990110 | + | 0.140290i | \(0.0448036\pi\) | ||||
−0.990110 | + | 0.140290i | \(0.955196\pi\) | |||||||
\(620\) | 5.09808 | + | 8.83013i | 0.204744 | + | 0.354626i | ||||
\(621\) | 2.53590 | − | 4.39230i | 0.101762 | − | 0.176257i | ||||
\(622\) | −24.5885 | − | 14.1962i | −0.985907 | − | 0.569214i | ||||
\(623\) | 25.8564 | 1.03592 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 21.5885 | + | 12.4641i | 0.862848 | + | 0.498166i | ||||
\(627\) | −40.0526 | + | 69.3731i | −1.59955 | + | 2.77049i | ||||
\(628\) | −5.00000 | − | 8.66025i | −0.199522 | − | 0.345582i | ||||
\(629\) | − | 13.8564i | − | 0.552491i | ||||||
\(630\) | −13.3923 | + | 7.73205i | −0.533562 | + | 0.308052i | ||||
\(631\) | 5.02628 | − | 2.90192i | 0.200093 | − | 0.115524i | −0.396606 | − | 0.917989i | \(-0.629812\pi\) |
0.596699 | + | 0.802465i | \(0.296479\pi\) | |||||||
\(632\) | − | 14.5359i | − | 0.578207i | ||||||
\(633\) | −10.9282 | − | 18.9282i | −0.434357 | − | 0.752329i | ||||
\(634\) | −20.7846 | + | 36.0000i | −0.825462 | + | 1.42974i | ||||
\(635\) | 14.0263 | + | 8.09808i | 0.556616 | + | 0.321362i | ||||
\(636\) | −28.3923 | −1.12583 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −20.7846 | −0.822871 | ||||||||
\(639\) | 18.2942 | + | 10.5622i | 0.723708 | + | 0.417833i | ||||
\(640\) | −6.06218 | + | 10.5000i | −0.239629 | + | 0.415049i | ||||
\(641\) | 6.46410 | + | 11.1962i | 0.255317 | + | 0.442221i | 0.964981 | − | 0.262318i | \(-0.0844869\pi\) |
−0.709665 | + | 0.704539i | \(0.751154\pi\) | |||||||
\(642\) | 83.5692i | 3.29821i | ||||||||
\(643\) | 5.87564 | − | 3.39230i | 0.231713 | − | 0.133779i | −0.379649 | − | 0.925131i | \(-0.623955\pi\) |
0.611362 | + | 0.791351i | \(0.290622\pi\) | |||||||
\(644\) | 2.19615 | − | 1.26795i | 0.0865405 | − | 0.0499642i | ||||
\(645\) | 0.535898i | 0.0211010i | ||||||||
\(646\) | 18.5885 | + | 32.1962i | 0.731353 | + | 1.26674i | ||||
\(647\) | 11.0263 | − | 19.0981i | 0.433488 | − | 0.750823i | −0.563683 | − | 0.825991i | \(-0.690616\pi\) |
0.997171 | + | 0.0751683i | \(0.0239494\pi\) | |||||||
\(648\) | 3.69615 | + | 2.13397i | 0.145199 | + | 0.0838304i | ||||
\(649\) | 43.1769 | 1.69484 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 55.7128 | 2.18356 | ||||||||
\(652\) | −12.4641 | − | 7.19615i | −0.488132 | − | 0.281823i | ||||
\(653\) | −3.92820 | + | 6.80385i | −0.153722 | + | 0.266255i | −0.932593 | − | 0.360929i | \(-0.882460\pi\) |
0.778871 | + | 0.627185i | \(0.215793\pi\) | |||||||
\(654\) | −4.73205 | − | 8.19615i | −0.185038 | − | 0.320495i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15.0000 | − | 8.66025i | 0.585652 | − | 0.338126i | ||||
\(657\) | −15.4641 | + | 8.92820i | −0.603312 | + | 0.348322i | ||||
\(658\) | − | 20.7846i | − | 0.810268i | ||||||
\(659\) | 10.7321 | + | 18.5885i | 0.418061 | + | 0.724103i | 0.995744 | − | 0.0921577i | \(-0.0293764\pi\) |
−0.577683 | + | 0.816261i | \(0.696043\pi\) | |||||||
\(660\) | 6.46410 | − | 11.1962i | 0.251615 | − | 0.435810i | ||||
\(661\) | −9.33975 | − | 5.39230i | −0.363274 | − | 0.209736i | 0.307242 | − | 0.951631i | \(-0.400594\pi\) |
−0.670516 | + | 0.741895i | \(0.733927\pi\) | |||||||
\(662\) | 4.48334 | 0.174250 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.3923 | −0.403300 | ||||||||
\(665\) | 10.7321 | + | 6.19615i | 0.416171 | + | 0.240276i | ||||
\(666\) | −15.4641 | + | 26.7846i | −0.599222 | + | 1.03788i | ||||
\(667\) | −1.60770 | − | 2.78461i | −0.0622502 | − | 0.107821i | ||||
\(668\) | 0.928203i | 0.0359133i | ||||||||
\(669\) | −4.73205 | + | 2.73205i | −0.182952 | + | 0.105627i | ||||
\(670\) | 9.58846 | − | 5.53590i | 0.370434 | − | 0.213870i | ||||
\(671\) | 39.7128i | 1.53310i | ||||||||
\(672\) | −14.1962 | − | 24.5885i | −0.547628 | − | 0.948520i | ||||
\(673\) | −7.19615 | + | 12.4641i | −0.277391 | + | 0.480456i | −0.970736 | − | 0.240151i | \(-0.922803\pi\) |
0.693344 | + | 0.720606i | \(0.256137\pi\) | |||||||
\(674\) | −39.5885 | − | 22.8564i | −1.52489 | − | 0.880396i | ||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.3923 | 0.399409 | 0.199704 | − | 0.979856i | \(-0.436002\pi\) | ||||
0.199704 | + | 0.979856i | \(0.436002\pi\) | |||||||
\(678\) | −34.9808 | − | 20.1962i | −1.34343 | − | 0.775629i | ||||
\(679\) | −2.00000 | + | 3.46410i | −0.0767530 | + | 0.132940i | ||||
\(680\) | 3.00000 | + | 5.19615i | 0.115045 | + | 0.199263i | ||||
\(681\) | 9.46410i | 0.362665i | ||||||||
\(682\) | −72.3731 | + | 41.7846i | −2.77131 | + | 1.60002i | ||||
\(683\) | 28.1769 | − | 16.2679i | 1.07816 | − | 0.622476i | 0.147760 | − | 0.989023i | \(-0.452794\pi\) |
0.930399 | + | 0.366547i | \(0.119460\pi\) | |||||||
\(684\) | − | 27.6603i | − | 1.05762i | ||||||
\(685\) | 0.464102 | + | 0.803848i | 0.0177324 | + | 0.0307134i | ||||
\(686\) | 17.3205 | − | 30.0000i | 0.661300 | − | 1.14541i | ||||
\(687\) | −15.1244 | − | 8.73205i | −0.577030 | − | 0.333149i | ||||
\(688\) | −0.980762 | −0.0373912 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 6.00000 | 0.228416 | ||||||||
\(691\) | −41.3660 | − | 23.8827i | −1.57364 | − | 0.908540i | −0.995718 | − | 0.0924469i | \(-0.970531\pi\) |
−0.577920 | − | 0.816093i | \(-0.696135\pi\) | |||||||
\(692\) | −4.26795 | + | 7.39230i | −0.162243 | + | 0.281013i | ||||
\(693\) | −21.1244 | − | 36.5885i | −0.802448 | − | 1.38988i | ||||
\(694\) | − | 9.80385i | − | 0.372149i | ||||||
\(695\) | 10.7321 | − | 6.19615i | 0.407090 | − | 0.235033i | ||||
\(696\) | −10.3923 | + | 6.00000i | −0.393919 | + | 0.227429i | ||||
\(697\) | − | 12.0000i | − | 0.454532i | ||||||
\(698\) | −12.4641 | − | 21.5885i | −0.471773 | − | 0.817135i | ||||
\(699\) | −8.19615 | + | 14.1962i | −0.310007 | + | 0.536948i | ||||
\(700\) | −1.73205 | − | 1.00000i | −0.0654654 | − | 0.0377964i | ||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.7846 | 0.934769 | ||||||||
\(704\) | −4.09808 | − | 2.36603i | −0.154452 | − | 0.0891729i | ||||
\(705\) | 8.19615 | − | 14.1962i | 0.308685 | − | 0.534658i | ||||
\(706\) | 24.0000 | + | 41.5692i | 0.903252 | + | 1.56448i | ||||
\(707\) | 1.85641i | 0.0698174i | ||||||||
\(708\) | −21.5885 | + | 12.4641i | −0.811344 | + | 0.468430i | ||||
\(709\) | 26.3205 | − | 15.1962i | 0.988487 | − | 0.570703i | 0.0836656 | − | 0.996494i | \(-0.473337\pi\) |
0.904822 | + | 0.425790i | \(0.140004\pi\) | |||||||
\(710\) | 8.19615i | 0.307596i | ||||||||
\(711\) | 18.7321 | + | 32.4449i | 0.702507 | + | 1.21678i | ||||
\(712\) | −11.1962 | + | 19.3923i | −0.419594 | + | 0.726757i | ||||
\(713\) | −11.1962 | − | 6.46410i | −0.419299 | − | 0.242083i | ||||
\(714\) | −32.7846 | −1.22693 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.9282 | −0.707380 | ||||||||
\(717\) | −33.5885 | − | 19.3923i | −1.25438 | − | 0.724219i | ||||
\(718\) | −1.90192 | + | 3.29423i | −0.0709792 | + | 0.122940i | ||||
\(719\) | −12.9282 | − | 22.3923i | −0.482141 | − | 0.835092i | 0.517649 | − | 0.855593i | \(-0.326807\pi\) |
−0.999790 | + | 0.0205009i | \(0.993474\pi\) | |||||||
\(720\) | − | 22.3205i | − | 0.831836i | ||||||
\(721\) | 0.339746 | − | 0.196152i | 0.0126528 | − | 0.00730510i | ||||
\(722\) | −29.0885 | + | 16.7942i | −1.08256 | + | 0.625016i | ||||
\(723\) | − | 6.53590i | − | 0.243073i | ||||||
\(724\) | −0.196152 | − | 0.339746i | −0.00728995 | − | 0.0126266i | ||||
\(725\) | −1.26795 | + | 2.19615i | −0.0470905 | + | 0.0815631i | ||||
\(726\) | 46.6865 | + | 26.9545i | 1.73270 | + | 1.00037i | ||||
\(727\) | −44.5885 | −1.65369 | −0.826847 | − | 0.562427i | \(-0.809868\pi\) | ||||
−0.826847 | + | 0.562427i | \(0.809868\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | −6.00000 | − | 3.46410i | −0.222070 | − | 0.128212i | ||||
\(731\) | −0.339746 | + | 0.588457i | −0.0125660 | + | 0.0217649i | ||||
\(732\) | −11.4641 | − | 19.8564i | −0.423725 | − | 0.733914i | ||||
\(733\) | − | 38.0000i | − | 1.40356i | −0.712393 | − | 0.701781i | \(-0.752388\pi\) | ||
0.712393 | − | 0.701781i | \(-0.247612\pi\) | |||||||
\(734\) | 17.7058 | − | 10.2224i | 0.653532 | − | 0.377317i | ||||
\(735\) | 7.09808 | − | 4.09808i | 0.261816 | − | 0.151160i | ||||
\(736\) | 6.58846i | 0.242854i | ||||||||
\(737\) | 15.1244 | + | 26.1962i | 0.557113 | + | 0.964948i | ||||
\(738\) | −13.3923 | + | 23.1962i | −0.492978 | + | 0.853862i | ||||
\(739\) | 15.7583 | + | 9.09808i | 0.579680 | + | 0.334678i | 0.761006 | − | 0.648745i | \(-0.224706\pi\) |
−0.181326 | + | 0.983423i | \(0.558039\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −36.0000 | −1.32160 | ||||||||
\(743\) | −13.9808 | − | 8.07180i | −0.512904 | − | 0.296126i | 0.221122 | − | 0.975246i | \(-0.429028\pi\) |
−0.734027 | + | 0.679121i | \(0.762361\pi\) | |||||||
\(744\) | −24.1244 | + | 41.7846i | −0.884442 | + | 1.53190i | ||||
\(745\) | 3.92820 | + | 6.80385i | 0.143918 | + | 0.249274i | ||||
\(746\) | − | 17.3205i | − | 0.634149i | ||||||
\(747\) | 23.1962 | − | 13.3923i | 0.848703 | − | 0.489999i | ||||
\(748\) | 14.1962 | − | 8.19615i | 0.519063 | − | 0.299681i | ||||
\(749\) | 35.3205i | 1.29058i | ||||||||
\(750\) | −2.36603 | − | 4.09808i | −0.0863950 | − | 0.149641i | ||||
\(751\) | 18.1962 | − | 31.5167i | 0.663987 | − | 1.15006i | −0.315572 | − | 0.948902i | \(-0.602196\pi\) |
0.979559 | − | 0.201158i | \(-0.0644703\pi\) | |||||||
\(752\) | 25.9808 | + | 15.0000i | 0.947421 | + | 0.546994i | ||||
\(753\) | 58.6410 | 2.13700 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.80385 | 0.0656487 | ||||||||
\(756\) | 6.92820 | + | 4.00000i | 0.251976 | + | 0.145479i | ||||
\(757\) | 1.19615 | − | 2.07180i | 0.0434749 | − | 0.0753007i | −0.843469 | − | 0.537178i | \(-0.819490\pi\) |
0.886944 | + | 0.461877i | \(0.152824\pi\) | |||||||
\(758\) | −16.4378 | − | 28.4711i | −0.597049 | − | 1.03412i | ||||
\(759\) | 16.3923i | 0.595003i | ||||||||
\(760\) | −9.29423 | + | 5.36603i | −0.337137 | + | 0.194646i | ||||
\(761\) | −17.1962 | + | 9.92820i | −0.623360 | + | 0.359897i | −0.778176 | − | 0.628046i | \(-0.783855\pi\) |
0.154816 | + | 0.987943i | \(0.450522\pi\) | |||||||
\(762\) | − | 76.6410i | − | 2.77641i | ||||||
\(763\) | −2.00000 | − | 3.46410i | −0.0724049 | − | 0.125409i | ||||
\(764\) | −2.53590 | + | 4.39230i | −0.0917456 | + | 0.158908i | ||||
\(765\) | −13.3923 | − | 7.73205i | −0.484200 | − | 0.279553i | ||||
\(766\) | 22.3923 | 0.809067 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 51.9090 | 1.87310 | ||||||||
\(769\) | 30.1244 | + | 17.3923i | 1.08631 | + | 0.627183i | 0.932592 | − | 0.360932i | \(-0.117541\pi\) |
0.153720 | + | 0.988114i | \(0.450875\pi\) | |||||||
\(770\) | 8.19615 | − | 14.1962i | 0.295369 | − | 0.511594i | ||||
\(771\) | 27.1244 | + | 46.9808i | 0.976860 | + | 1.69197i | ||||
\(772\) | 10.0000i | 0.359908i | ||||||||
\(773\) | −6.00000 | + | 3.46410i | −0.215805 | + | 0.124595i | −0.604006 | − | 0.796980i | \(-0.706430\pi\) |
0.388201 | + | 0.921575i | \(0.373097\pi\) | |||||||
\(774\) | 1.31347 | − | 0.758330i | 0.0472116 | − | 0.0272576i | ||||
\(775\) | 10.1962i | 0.366257i | ||||||||
\(776\) | −1.73205 | − | 3.00000i | −0.0621770 | − | 0.107694i | ||||
\(777\) | −10.9282 | + | 18.9282i | −0.392047 | + | 0.679046i | ||||
\(778\) | 9.00000 | + | 5.19615i | 0.322666 | + | 0.186291i | ||||
\(779\) | 21.4641 | 0.769031 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.3923 | −0.801260 | ||||||||
\(782\) | 6.58846 | + | 3.80385i | 0.235603 | + | 0.136025i | ||||
\(783\) | 5.07180 | − | 8.78461i | 0.181251 | − | 0.313936i | ||||
\(784\) | 7.50000 | + | 12.9904i | 0.267857 | + | 0.463942i | ||||
\(785\) | − | 10.0000i | − | 0.356915i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.3397 | − | 15.7846i | 0.974557 | − | 0.562661i | 0.0739343 | − | 0.997263i | \(-0.476444\pi\) |
0.900622 | + | 0.434603i | \(0.143111\pi\) | |||||||
\(788\) | − | 12.9282i | − | 0.460548i | ||||||
\(789\) | −1.73205 | − | 3.00000i | −0.0616626 | − | 0.106803i | ||||
\(790\) | −7.26795 | + | 12.5885i | −0.258582 | + | 0.447877i | ||||
\(791\) | −14.7846 | − | 8.53590i | −0.525680 | − | 0.303502i | ||||
\(792\) | 36.5885 | 1.30011 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −49.8564 | −1.76934 | ||||||||
\(795\) | −24.5885 | − | 14.1962i | −0.872063 | − | 0.503486i | ||||
\(796\) | −10.0000 | + | 17.3205i | −0.354441 | + | 0.613909i | ||||
\(797\) | −20.3205 | − | 35.1962i | −0.719789 | − | 1.24671i | −0.961083 | − | 0.276260i | \(-0.910905\pi\) |
0.241294 | − | 0.970452i | \(-0.422428\pi\) | |||||||
\(798\) | − | 58.6410i | − | 2.07587i | ||||||
\(799\) | 18.0000 | − | 10.3923i | 0.636794 | − | 0.367653i | ||||
\(800\) | 4.50000 | − | 2.59808i | 0.159099 | − | 0.0918559i | ||||
\(801\) | − | 57.7128i | − | 2.03918i | ||||||
\(802\) | −31.9808 | − | 55.3923i | −1.12928 | − | 1.95597i | ||||
\(803\) | 9.46410 | − | 16.3923i | 0.333981 | − | 0.578472i | ||||
\(804\) | −15.1244 | − | 8.73205i | −0.533395 | − | 0.307956i | ||||
\(805\) | 2.53590 | 0.0893787 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −54.2487 | −1.90965 | ||||||||
\(808\) | −1.39230 | − | 0.803848i | −0.0489811 | − | 0.0282793i | ||||
\(809\) | 1.26795 | − | 2.19615i | 0.0445787 | − | 0.0772126i | −0.842875 | − | 0.538109i | \(-0.819139\pi\) |
0.887454 | + | 0.460897i | \(0.152472\pi\) | |||||||
\(810\) | −2.13397 | − | 3.69615i | −0.0749802 | − | 0.129870i | ||||
\(811\) | − | 17.8038i | − | 0.625178i | −0.949889 | − | 0.312589i | \(-0.898804\pi\) | ||
0.949889 | − | 0.312589i | \(-0.101196\pi\) | |||||||
\(812\) | 4.39230 | − | 2.53590i | 0.154140 | − | 0.0889926i | ||||
\(813\) | 73.3013 | − | 42.3205i | 2.57079 | − | 1.48425i | ||||
\(814\) | − | 32.7846i | − | 1.14910i | ||||||
\(815\) | −7.19615 | − | 12.4641i | −0.252070 | − | 0.436598i | ||||
\(816\) | 23.6603 | − | 40.9808i | 0.828275 | − | 1.43461i | ||||
\(817\) | −1.05256 | − | 0.607695i | −0.0368244 | − | 0.0212606i | ||||
\(818\) | −30.4974 | −1.06632 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.46410 | −0.120972 | ||||||||
\(821\) | 24.8038 | + | 14.3205i | 0.865660 | + | 0.499789i | 0.865904 | − | 0.500211i | \(-0.166744\pi\) |
−0.000243419 | 1.00000i | \(0.500077\pi\) | ||||||||
\(822\) | 2.19615 | − | 3.80385i | 0.0765996 | − | 0.132674i | ||||
\(823\) | −7.70577 | − | 13.3468i | −0.268606 | − | 0.465240i | 0.699896 | − | 0.714245i | \(-0.253230\pi\) |
−0.968502 | + | 0.249005i | \(0.919896\pi\) | |||||||
\(824\) | 0.339746i | 0.0118356i | ||||||||
\(825\) | 11.1962 | − | 6.46410i | 0.389800 | − | 0.225051i | ||||
\(826\) | −27.3731 | + | 15.8038i | −0.952431 | + | 0.549886i | ||||
\(827\) | 18.0000i | 0.625921i | 0.949766 | + | 0.312961i | \(0.101321\pi\) | ||||
−0.949766 | + | 0.312961i | \(0.898679\pi\) | |||||||
\(828\) | −2.83013 | − | 4.90192i | −0.0983537 | − | 0.170354i | ||||
\(829\) | 0.196152 | − | 0.339746i | 0.00681266 | − | 0.0117999i | −0.862599 | − | 0.505888i | \(-0.831165\pi\) |
0.869412 | + | 0.494088i | \(0.164498\pi\) | |||||||
\(830\) | 9.00000 | + | 5.19615i | 0.312395 | + | 0.180361i | ||||
\(831\) | 72.1051 | 2.50130 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.3923 | 0.360072 | ||||||||
\(834\) | −50.7846 | − | 29.3205i | −1.75853 | − | 1.01529i | ||||
\(835\) | −0.464102 | + | 0.803848i | −0.0160609 | + | 0.0278183i | ||||
\(836\) | 14.6603 | + | 25.3923i | 0.507035 | + | 0.878211i | ||||
\(837\) | − | 40.7846i | − | 1.40972i | ||||||
\(838\) | −3.80385 | + | 2.19615i | −0.131402 | + | 0.0758648i | ||||
\(839\) | 0.294229 | − | 0.169873i | 0.0101579 | − | 0.00586467i | −0.494912 | − | 0.868943i | \(-0.664800\pi\) |
0.505070 | + | 0.863078i | \(0.331467\pi\) | |||||||
\(840\) | − | 9.46410i | − | 0.326543i | ||||||
\(841\) | 11.2846 | + | 19.5455i | 0.389124 | + | 0.673983i | ||||
\(842\) | 26.6603 | − | 46.1769i | 0.918773 | − | 1.59136i | ||||
\(843\) | −52.9808 | − | 30.5885i | −1.82475 | − | 1.05352i | ||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −46.3923 | −1.59500 | ||||||||
\(847\) | 19.7321 | + | 11.3923i | 0.678001 | + | 0.391444i | ||||
\(848\) | 25.9808 | − | 45.0000i | 0.892183 | − | 1.54531i | ||||
\(849\) | 44.5167 | + | 77.1051i | 1.52781 | + | 2.64624i | ||||
\(850\) | − | 6.00000i | − | 0.205798i | ||||||
\(851\) | 4.39230 | − | 2.53590i | 0.150566 | − | 0.0869295i | ||||
\(852\) | 11.1962 | − | 6.46410i | 0.383574 | − | 0.221456i | ||||
\(853\) | 8.00000i | 0.273915i | 0.990577 | + | 0.136957i | \(0.0437323\pi\) | ||||
−0.990577 | + | 0.136957i | \(0.956268\pi\) | |||||||
\(854\) | −14.5359 | − | 25.1769i | −0.497408 | − | 0.861536i | ||||
\(855\) | 13.8301 | − | 23.9545i | 0.472980 | − | 0.819226i | ||||
\(856\) | −26.4904 | − | 15.2942i | −0.905423 | − | 0.522746i | ||||
\(857\) | 35.5692 | 1.21502 | 0.607511 | − | 0.794311i | \(-0.292168\pi\) | ||||
0.607511 | + | 0.794311i | \(0.292168\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.1769 | −0.586069 | −0.293034 | − | 0.956102i | \(-0.594665\pi\) | ||||
−0.293034 | + | 0.956102i | \(0.594665\pi\) | |||||||
\(860\) | 0.169873 | + | 0.0980762i | 0.00579262 | + | 0.00334437i | ||||
\(861\) | −9.46410 | + | 16.3923i | −0.322536 | + | 0.558648i | ||||
\(862\) | 22.0981 | + | 38.2750i | 0.752663 | + | 1.30365i | ||||
\(863\) | 38.7846i | 1.32024i | 0.751159 | + | 0.660122i | \(0.229495\pi\) | ||||
−0.751159 | + | 0.660122i | \(0.770505\pi\) | |||||||
\(864\) | −18.0000 | + | 10.3923i | −0.612372 | + | 0.353553i | ||||
\(865\) | −7.39230 | + | 4.26795i | −0.251346 | + | 0.145115i | ||||
\(866\) | − | 60.2487i | − | 2.04733i | ||||||
\(867\) | 6.83013 | + | 11.8301i | 0.231963 | + | 0.401772i | ||||
\(868\) | 10.1962 | − | 17.6603i | 0.346080 | − | 0.599428i | ||||
\(869\) | −34.3923 | − | 19.8564i | −1.16668 | − | 0.673582i | ||||
\(870\) | 12.0000 | 0.406838 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 3.46410 | 0.117309 | ||||||||
\(873\) | 7.73205 | + | 4.46410i | 0.261690 | + | 0.151087i | ||||
\(874\) | −6.80385 | + | 11.7846i | −0.230144 | + | 0.398620i | ||||
\(875\) | −1.00000 | − | 1.73205i | −0.0338062 | − | 0.0585540i | ||||
\(876\) | 10.9282i | 0.369230i | ||||||||
\(877\) | −1.73205 | + | 1.00000i | −0.0584872 | + | 0.0337676i | −0.528958 | − | 0.848648i | \(-0.677417\pi\) |
0.470471 | + | 0.882415i | \(0.344084\pi\) | |||||||
\(878\) | −48.0000 | + | 27.7128i | −1.61992 | + | 0.935262i | ||||
\(879\) | − | 13.8564i | − | 0.467365i | ||||||
\(880\) | 11.8301 | + | 20.4904i | 0.398794 | + | 0.690731i | ||||
\(881\) | −23.6603 | + | 40.9808i | −0.797134 | + | 1.38068i | 0.124341 | + | 0.992240i | \(0.460318\pi\) |
−0.921475 | + | 0.388437i | \(0.873015\pi\) | |||||||
\(882\) | −20.0885 | − | 11.5981i | −0.676414 | − | 0.390528i | ||||
\(883\) | −23.8038 | −0.801063 | −0.400532 | − | 0.916283i | \(-0.631175\pi\) | ||||
−0.400532 | + | 0.916283i | \(0.631175\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.9282 | −0.837952 | ||||||||
\(886\) | 25.4711 | + | 14.7058i | 0.855720 | + | 0.494050i | ||||
\(887\) | 23.9545 | − | 41.4904i | 0.804313 | − | 1.39311i | −0.112441 | − | 0.993658i | \(-0.535867\pi\) |
0.916754 | − | 0.399452i | \(-0.130800\pi\) | |||||||
\(888\) | −9.46410 | − | 16.3923i | −0.317594 | − | 0.550090i | ||||
\(889\) | − | 32.3923i | − | 1.08640i | ||||||
\(890\) | 19.3923 | − | 11.1962i | 0.650032 | − | 0.375296i | ||||
\(891\) | 10.0981 | − | 5.83013i | 0.338298 | − | 0.195317i | ||||
\(892\) | 2.00000i | 0.0669650i | ||||||||
\(893\) | 18.5885 | + | 32.1962i | 0.622039 | + | 1.07740i | ||||
\(894\) | 18.5885 | − | 32.1962i | 0.621691 | − | 1.07680i | ||||
\(895\) | −16.3923 | − | 9.46410i | −0.547934 | − | 0.316350i | ||||
\(896\) | 24.2487 | 0.810093 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −35.5692 | −1.18696 | ||||||||
\(899\) | −22.3923 | − | 12.9282i | −0.746825 | − | 0.431180i | ||||
\(900\) | −2.23205 | + | 3.86603i | −0.0744017 | + | 0.128868i | ||||
\(901\) | −18.0000 | − | 31.1769i | −0.599667 | − | 1.03865i | ||||
\(902\) | − | 28.3923i | − | 0.945360i | ||||||
\(903\) | 0.928203 | − | 0.535898i | 0.0308887 | − | 0.0178336i | ||||
\(904\) | 12.8038 | − | 7.39230i | 0.425850 | − | 0.245864i | ||||
\(905\) | − | 0.392305i | − | 0.0130407i | ||||||
\(906\) | −4.26795 | − | 7.39230i | −0.141793 | − | 0.245593i | ||||
\(907\) | −26.8827 | + | 46.5622i | −0.892625 | + | 1.54607i | −0.0559081 | + | 0.998436i | \(0.517805\pi\) |
−0.836717 | + | 0.547636i | \(0.815528\pi\) | |||||||
\(908\) | 3.00000 | + | 1.73205i | 0.0995585 | + | 0.0574801i | ||||
\(909\) | 4.14359 | 0.137434 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | 73.3013 | + | 42.3205i | 2.42725 | + | 1.40137i | ||||
\(913\) | −14.1962 | + | 24.5885i | −0.469824 | + | 0.813759i | ||||
\(914\) | −9.33975 | − | 16.1769i | −0.308931 | − | 0.535085i | ||||
\(915\) | − | 22.9282i | − | 0.757983i | ||||||
\(916\) | −5.53590 | + | 3.19615i | −0.182911 | + | 0.105604i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 24.0000i | 0.792118i | ||||||||
\(919\) | −4.58846 | − | 7.94744i | −0.151359 | − | 0.262162i | 0.780368 | − | 0.625320i | \(-0.215032\pi\) |
−0.931727 | + | 0.363158i | \(0.881698\pi\) | |||||||
\(920\) | −1.09808 | + | 1.90192i | −0.0362025 | + | 0.0627046i | ||||
\(921\) | 44.4449 | + | 25.6603i | 1.46451 | + | 0.845534i | ||||
\(922\) | −6.00000 | −0.197599 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −25.8564 | −0.850613 | ||||||||
\(925\) | −3.46410 | − | 2.00000i | −0.113899 | − | 0.0657596i | ||||
\(926\) | −2.07180 | + | 3.58846i | −0.0680835 | + | 0.117924i | ||||
\(927\) | −0.437822 | − | 0.758330i | −0.0143800 | − | 0.0249068i | ||||
\(928\) | 13.1769i | 0.432553i | ||||||||
\(929\) | −38.5692 | + | 22.2679i | −1.26542 | + | 0.730588i | −0.974117 | − | 0.226045i | \(-0.927420\pi\) |
−0.291298 | + | 0.956632i | \(0.594087\pi\) | |||||||
\(930\) | 41.7846 | − | 24.1244i | 1.37017 | − | 0.791069i | ||||
\(931\) | 18.5885i | 0.609212i | ||||||||
\(932\) | 3.00000 | + | 5.19615i | 0.0982683 | + | 0.170206i | ||||
\(933\) | −22.3923 | + | 38.7846i | −0.733091 | + | 1.26975i | ||||
\(934\) | 41.7058 | + | 24.0788i | 1.36465 | + | 0.787884i | ||||
\(935\) | 16.3923 | 0.536086 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.7846 | 1.13636 | 0.568182 | − | 0.822903i | \(-0.307647\pi\) | ||||
0.568182 | + | 0.822903i | \(0.307647\pi\) | |||||||
\(938\) | −19.1769 | − | 11.0718i | −0.626148 | − | 0.361507i | ||||
\(939\) | 19.6603 | − | 34.0526i | 0.641588 | − | 1.11126i | ||||
\(940\) | −3.00000 | − | 5.19615i | −0.0978492 | − | 0.169480i | ||||
\(941\) | − | 31.1769i | − | 1.01634i | −0.861257 | − | 0.508169i | \(-0.830322\pi\) | ||
0.861257 | − | 0.508169i | \(-0.169678\pi\) | |||||||
\(942\) | −40.9808 | + | 23.6603i | −1.33523 | + | 0.770893i | ||||
\(943\) | 3.80385 | − | 2.19615i | 0.123870 | − | 0.0715166i | ||||
\(944\) | − | 45.6218i | − | 1.48486i | ||||||
\(945\) | 4.00000 | + | 6.92820i | 0.130120 | + | 0.225374i | ||||
\(946\) | −0.803848 | + | 1.39230i | −0.0261353 | + | 0.0452677i | ||||
\(947\) | −35.1962 | − | 20.3205i | −1.14372 | − | 0.660328i | −0.196372 | − | 0.980529i | \(-0.562916\pi\) |
−0.947349 | + | 0.320202i | \(0.896249\pi\) | |||||||
\(948\) | 22.9282 | 0.744673 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 10.7321 | 0.348194 | ||||||||
\(951\) | 56.7846 | + | 32.7846i | 1.84137 | + | 1.06311i | ||||
\(952\) | 6.00000 | − | 10.3923i | 0.194461 | − | 0.336817i | ||||
\(953\) | 0.464102 | + | 0.803848i | 0.0150337 | + | 0.0260392i | 0.873444 | − | 0.486924i | \(-0.161881\pi\) |
−0.858411 | + | 0.512963i | \(0.828548\pi\) | |||||||
\(954\) | 80.3538i | 2.60155i | ||||||||
\(955\) | −4.39230 | + | 2.53590i | −0.142132 | + | 0.0820597i | ||||
\(956\) | −12.2942 | + | 7.09808i | −0.397624 | + | 0.229568i | ||||
\(957\) | 32.7846i | 1.05978i | ||||||||
\(958\) | 30.8827 | + | 53.4904i | 0.997774 | + | 1.72820i | ||||
\(959\) | 0.928203 | − | 1.60770i | 0.0299732 | − | 0.0519152i | ||||
\(960\) | 2.36603 | + | 1.36603i | 0.0763631 | + | 0.0440883i | ||||
\(961\) | −72.9615 | −2.35360 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 78.8372 | 2.54049 | ||||||||
\(964\) | −2.07180 | − | 1.19615i | −0.0667281 | − | 0.0385255i | ||||
\(965\) | −5.00000 | + | 8.66025i | −0.160956 | + | 0.278783i | ||||
\(966\) | −6.00000 | − | 10.3923i | −0.193047 | − | 0.334367i | ||||
\(967\) | 50.3923i | 1.62051i | 0.586079 | + | 0.810254i | \(0.300671\pi\) | ||||
−0.586079 | + | 0.810254i | \(0.699329\pi\) | |||||||
\(968\) | −17.0885 | + | 9.86603i | −0.549244 | + | 0.317106i | ||||
\(969\) | 50.7846 | − | 29.3205i | 1.63144 | − | 0.941910i | ||||
\(970\) | 3.46410i | 0.111226i | ||||||||
\(971\) | −9.46410 | − | 16.3923i | −0.303717 | − | 0.526054i | 0.673257 | − | 0.739408i | \(-0.264895\pi\) |
−0.976975 | + | 0.213354i | \(0.931561\pi\) | |||||||
\(972\) | −9.36603 | + | 16.2224i | −0.300415 | + | 0.520335i | ||||
\(973\) | −21.4641 | − | 12.3923i | −0.688108 | − | 0.397279i | ||||
\(974\) | −45.7128 | −1.46473 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 41.9615 | 1.34316 | ||||||||
\(977\) | −13.6077 | − | 7.85641i | −0.435349 | − | 0.251349i | 0.266274 | − | 0.963897i | \(-0.414207\pi\) |
−0.701623 | + | 0.712549i | \(0.747541\pi\) | |||||||
\(978\) | −34.0526 | + | 58.9808i | −1.08888 | + | 1.88600i | ||||
\(979\) | 30.5885 | + | 52.9808i | 0.977611 | + | 1.69327i | ||||
\(980\) | − | 3.00000i | − | 0.0958315i | ||||||
\(981\) | −7.73205 | + | 4.46410i | −0.246865 | + | 0.142528i | ||||
\(982\) | 3.80385 | − | 2.19615i | 0.121386 | − | 0.0700820i | ||||
\(983\) | − | 34.3923i | − | 1.09694i | −0.836169 | − | 0.548472i | \(-0.815210\pi\) | ||
0.836169 | − | 0.548472i | \(-0.184790\pi\) | |||||||
\(984\) | −8.19615 | − | 14.1962i | −0.261284 | − | 0.452557i | ||||
\(985\) | 6.46410 | − | 11.1962i | 0.205963 | − | 0.356739i | ||||
\(986\) | 13.1769 | + | 7.60770i | 0.419638 | + | 0.242278i | ||||
\(987\) | −32.7846 | −1.04355 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.248711 | −0.00790856 | ||||||||
\(990\) | −31.6865 | − | 18.2942i | −1.00706 | − | 0.581429i | ||||
\(991\) | −4.00000 | + | 6.92820i | −0.127064 | + | 0.220082i | −0.922538 | − | 0.385906i | \(-0.873889\pi\) |
0.795474 | + | 0.605988i | \(0.207222\pi\) | |||||||
\(992\) | 26.4904 | + | 45.8827i | 0.841070 | + | 1.45678i | ||||
\(993\) | − | 7.07180i | − | 0.224417i | ||||||
\(994\) | 14.1962 | − | 8.19615i | 0.450275 | − | 0.259966i | ||||
\(995\) | −17.3205 | + | 10.0000i | −0.549097 | + | 0.317021i | ||||
\(996\) | − | 16.3923i | − | 0.519410i | ||||||
\(997\) | −16.8038 | − | 29.1051i | −0.532183 | − | 0.921768i | −0.999294 | − | 0.0375696i | \(-0.988038\pi\) |
0.467111 | − | 0.884199i | \(-0.345295\pi\) | |||||||
\(998\) | 33.7583 | − | 58.4711i | 1.06860 | − | 1.85087i | ||||
\(999\) | 13.8564 | + | 8.00000i | 0.438397 | + | 0.253109i |
(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 | 845.2.m.a.316.1 | 4 | ||
13.2 | odd | 12 | 845.2.e.f.146.1 | 4 | |||
13.3 | even | 3 | 845.2.m.c.361.1 | 4 | |||
13.4 | even | 6 | 845.2.c.e.506.2 | 4 | |||
13.5 | odd | 4 | 845.2.e.f.191.1 | 4 | |||
13.6 | odd | 12 | 845.2.a.d.1.2 | 2 | |||
13.7 | odd | 12 | 65.2.a.c.1.1 | ✓ | 2 | ||
13.8 | odd | 4 | 845.2.e.e.191.2 | 4 | |||
13.9 | even | 3 | 845.2.c.e.506.4 | 4 | |||
13.10 | even | 6 | inner | 845.2.m.a.361.1 | 4 | ||
13.11 | odd | 12 | 845.2.e.e.146.2 | 4 | |||
13.12 | even | 2 | 845.2.m.c.316.1 | 4 | |||
39.20 | even | 12 | 585.2.a.k.1.2 | 2 | |||
39.32 | even | 12 | 7605.2.a.be.1.1 | 2 | |||
52.7 | even | 12 | 1040.2.a.h.1.1 | 2 | |||
65.7 | even | 12 | 325.2.b.e.274.1 | 4 | |||
65.19 | odd | 12 | 4225.2.a.w.1.1 | 2 | |||
65.33 | even | 12 | 325.2.b.e.274.4 | 4 | |||
65.59 | odd | 12 | 325.2.a.g.1.2 | 2 | |||
91.20 | even | 12 | 3185.2.a.k.1.1 | 2 | |||
104.59 | even | 12 | 4160.2.a.bj.1.2 | 2 | |||
104.85 | odd | 12 | 4160.2.a.y.1.1 | 2 | |||
143.98 | even | 12 | 7865.2.a.h.1.2 | 2 | |||
156.59 | odd | 12 | 9360.2.a.cm.1.1 | 2 | |||
195.59 | even | 12 | 2925.2.a.z.1.1 | 2 | |||
195.98 | odd | 12 | 2925.2.c.v.2224.1 | 4 | |||
195.137 | odd | 12 | 2925.2.c.v.2224.4 | 4 | |||
260.59 | even | 12 | 5200.2.a.ca.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.c.1.1 | ✓ | 2 | 13.7 | odd | 12 | ||
325.2.a.g.1.2 | 2 | 65.59 | odd | 12 | |||
325.2.b.e.274.1 | 4 | 65.7 | even | 12 | |||
325.2.b.e.274.4 | 4 | 65.33 | even | 12 | |||
585.2.a.k.1.2 | 2 | 39.20 | even | 12 | |||
845.2.a.d.1.2 | 2 | 13.6 | odd | 12 | |||
845.2.c.e.506.2 | 4 | 13.4 | even | 6 | |||
845.2.c.e.506.4 | 4 | 13.9 | even | 3 | |||
845.2.e.e.146.2 | 4 | 13.11 | odd | 12 | |||
845.2.e.e.191.2 | 4 | 13.8 | odd | 4 | |||
845.2.e.f.146.1 | 4 | 13.2 | odd | 12 | |||
845.2.e.f.191.1 | 4 | 13.5 | odd | 4 | |||
845.2.m.a.316.1 | 4 | 1.1 | even | 1 | trivial | ||
845.2.m.a.361.1 | 4 | 13.10 | even | 6 | inner | ||
845.2.m.c.316.1 | 4 | 13.12 | even | 2 | |||
845.2.m.c.361.1 | 4 | 13.3 | even | 3 | |||
1040.2.a.h.1.1 | 2 | 52.7 | even | 12 | |||
2925.2.a.z.1.1 | 2 | 195.59 | even | 12 | |||
2925.2.c.v.2224.1 | 4 | 195.98 | odd | 12 | |||
2925.2.c.v.2224.4 | 4 | 195.137 | odd | 12 | |||
3185.2.a.k.1.1 | 2 | 91.20 | even | 12 | |||
4160.2.a.y.1.1 | 2 | 104.85 | odd | 12 | |||
4160.2.a.bj.1.2 | 2 | 104.59 | even | 12 | |||
4225.2.a.w.1.1 | 2 | 65.19 | odd | 12 | |||
5200.2.a.ca.1.2 | 2 | 260.59 | even | 12 | |||
7605.2.a.be.1.1 | 2 | 39.32 | even | 12 | |||
7865.2.a.h.1.2 | 2 | 143.98 | even | 12 | |||
9360.2.a.cm.1.1 | 2 | 156.59 | odd | 12 |