Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(129,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 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("400.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.y (of order \(10\), degree \(4\), 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: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.58140625.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 369.2 | ||
Root | \(-0.983224 + 0.644389i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.369 |
Dual form | 400.2.y.c.129.2 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.865190 | + | 1.19083i | 0.499518 | + | 0.687527i | 0.982108 | − | 0.188319i | \(-0.0603039\pi\) |
−0.482590 | + | 0.875846i | \(0.660304\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.107666 | + | 2.23347i | 0.0481496 | + | 0.998840i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.26086i | 1.23249i | 0.787555 | + | 0.616244i | \(0.211346\pi\) | ||||
−0.787555 | + | 0.616244i | \(0.788654\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.257524 | − | 0.792578i | 0.0858414 | − | 0.264193i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.618034 | − | 1.90211i | −0.186344 | − | 0.573509i | 0.813625 | − | 0.581390i | \(-0.197491\pi\) |
−0.999969 | + | 0.00788181i | \(0.997491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.281873 | + | 0.0915860i | 0.0781775 | + | 0.0254014i | 0.347845 | − | 0.937552i | \(-0.386914\pi\) |
−0.269667 | + | 0.962954i | \(0.586914\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.56654 | + | 2.06059i | −0.662678 | + | 0.532042i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.03472 | + | 4.17693i | −0.736027 | + | 1.01305i | 0.262810 | + | 0.964847i | \(0.415351\pi\) |
−0.998837 | + | 0.0482067i | \(0.984649\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.39991 | − | 1.01709i | −0.321161 | − | 0.233337i | 0.415510 | − | 0.909589i | \(-0.363603\pi\) |
−0.736671 | + | 0.676252i | \(0.763603\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.88313 | + | 2.82126i | −0.847369 | + | 0.615649i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.836161 | + | 0.271685i | −0.174352 | + | 0.0566503i | −0.394892 | − | 0.918728i | \(-0.629218\pi\) |
0.220540 | + | 0.975378i | \(0.429218\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.97682 | + | 0.480938i | −0.995363 | + | 0.0961876i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.36635 | − | 1.74363i | 1.03276 | − | 0.335563i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.78304 | − | 3.47508i | 0.888188 | − | 0.645306i | −0.0472171 | − | 0.998885i | \(-0.515035\pi\) |
0.935405 | + | 0.353578i | \(0.115035\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.93462 | + | 3.58521i | 0.886285 | + | 0.643923i | 0.934907 | − | 0.354894i | \(-0.115483\pi\) |
−0.0486220 | + | 0.998817i | \(0.515483\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.73038 | − | 2.38166i | 0.301220 | − | 0.414594i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.28304 | + | 0.351083i | −1.23106 | + | 0.0593438i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.69215 | + | 2.49933i | 1.26458 | + | 0.410887i | 0.863125 | − | 0.504991i | \(-0.168504\pi\) |
0.401457 | + | 0.915878i | \(0.368504\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.134810 | + | 0.414902i | 0.0215869 | + | 0.0664376i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.313697 | + | 0.965461i | −0.0489913 | + | 0.150780i | −0.972559 | − | 0.232655i | \(-0.925259\pi\) |
0.923568 | + | 0.383434i | \(0.125259\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.24199i | − | 0.494399i | −0.968965 | − | 0.247200i | \(-0.920490\pi\) | ||
0.968965 | − | 0.247200i | \(-0.0795103\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.79793 | + | 0.489840i | 0.268019 | + | 0.0730210i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.48043 | + | 3.41402i | 0.361808 | + | 0.497986i | 0.950651 | − | 0.310261i | \(-0.100417\pi\) |
−0.588844 | + | 0.808247i | \(0.700417\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.63318 | −0.519026 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.59963 | −1.06416 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.76148 | − | 6.55362i | −0.654040 | − | 0.900209i | 0.345226 | − | 0.938520i | \(-0.387802\pi\) |
−0.999266 | + | 0.0383106i | \(0.987802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.18178 | − | 1.58516i | 0.563871 | − | 0.213742i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.54703i | − | 0.337363i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.83443 | − | 5.64581i | 0.238823 | − | 0.735021i | −0.757768 | − | 0.652524i | \(-0.773710\pi\) |
0.996591 | − | 0.0824976i | \(-0.0262897\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.282941 | + | 0.870802i | 0.0362268 | + | 0.111495i | 0.967535 | − | 0.252738i | \(-0.0813312\pi\) |
−0.931308 | + | 0.364233i | \(0.881331\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.58448 | + | 0.839749i | 0.325614 | + | 0.105798i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.174207 | + | 0.639416i | −0.0216077 | + | 0.0793099i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.04870 | + | 5.57255i | −0.494627 | + | 0.680796i | −0.981233 | − | 0.192826i | \(-0.938235\pi\) |
0.486606 | + | 0.873622i | \(0.338235\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.04697 | − | 0.760668i | −0.126040 | − | 0.0915737i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.82884 | + | 3.50836i | −0.573078 | + | 0.416366i | −0.836222 | − | 0.548391i | \(-0.815241\pi\) |
0.263144 | + | 0.964757i | \(0.415241\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.40107 | − | 2.72967i | 0.983271 | − | 0.319484i | 0.227110 | − | 0.973869i | \(-0.427072\pi\) |
0.756161 | + | 0.654385i | \(0.227072\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.87861 | − | 5.51045i | −0.563333 | − | 0.636292i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.20252 | − | 2.01532i | 0.706842 | − | 0.229667i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.27851 | − | 4.56161i | 0.706388 | − | 0.513221i | −0.175618 | − | 0.984458i | \(-0.556192\pi\) |
0.882006 | + | 0.471237i | \(0.156192\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.69667 | + | 3.41233i | 0.521852 | + | 0.379148i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.53192 | − | 11.7432i | 0.936500 | − | 1.28898i | −0.0207694 | − | 0.999784i | \(-0.506612\pi\) |
0.957269 | − | 0.289197i | \(-0.0933884\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.65580 | − | 6.32825i | −1.04732 | − | 0.686395i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.27647 | + | 2.68919i | 0.887331 | + | 0.288311i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.32579 | − | 7.15805i | −0.246534 | − | 0.758752i | −0.995380 | − | 0.0960092i | \(-0.969392\pi\) |
0.748847 | − | 0.662743i | \(-0.230608\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.298649 | + | 0.919147i | −0.0313069 | + | 0.0963528i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.97820i | 0.930996i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.12093 | − | 3.23616i | 0.217602 | − | 0.332023i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.95373 | + | 5.44184i | 0.401440 | + | 0.552535i | 0.961105 | − | 0.276184i | \(-0.0890699\pi\) |
−0.559664 | + | 0.828719i | \(0.689070\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.66673 | −0.167513 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.1955 | −1.21350 | −0.606748 | − | 0.794894i | \(-0.707526\pi\) | ||||
−0.606748 | + | 0.794894i | \(0.707526\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.811969 | − | 1.11758i | −0.0800057 | − | 0.110118i | 0.767138 | − | 0.641482i | \(-0.221680\pi\) |
−0.847144 | + | 0.531363i | \(0.821680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.71929 | − | 8.36912i | −0.655736 | − | 0.816742i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.8285i | − | 1.53020i | −0.643911 | − | 0.765101i | \(-0.722689\pi\) | ||
0.643911 | − | 0.765101i | \(-0.277311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.619199 | − | 1.90570i | 0.0593085 | − | 0.182533i | −0.917013 | − | 0.398857i | \(-0.869407\pi\) |
0.976322 | + | 0.216324i | \(0.0694069\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.67889 | + | 11.3225i | 0.349185 | + | 1.07468i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.91713 | + | 3.22227i | 0.932925 | + | 0.303126i | 0.735758 | − | 0.677244i | \(-0.236826\pi\) |
0.197167 | + | 0.980370i | \(0.436826\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.696828 | − | 1.83829i | −0.0649795 | − | 0.171422i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.145178 | − | 0.199821i | 0.0134217 | − | 0.0184734i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.6204 | − | 9.89577i | −1.24858 | − | 0.907144i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.66312 | − | 4.11450i | 0.514829 | − | 0.374045i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.42111 | + | 0.461746i | −0.128137 | + | 0.0416343i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.61000 | − | 11.0638i | −0.144002 | − | 0.989577i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.56375 | + | 1.80777i | −0.493703 | + | 0.160414i | −0.545278 | − | 0.838255i | \(-0.683576\pi\) |
0.0515752 | + | 0.998669i | \(0.483576\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.86067 | − | 2.80494i | 0.339913 | − | 0.246961i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.21081 | − | 0.879704i | −0.105789 | − | 0.0768601i | 0.533633 | − | 0.845716i | \(-0.320826\pi\) |
−0.639422 | + | 0.768856i | \(0.720826\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.31659 | − | 4.56489i | 0.287585 | − | 0.395827i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.47214 | + | 11.7979i | 0.384900 | + | 1.01540i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.46472 | − | 2.42543i | −0.637754 | − | 0.207219i | −0.0277472 | − | 0.999615i | \(-0.508833\pi\) |
−0.610007 | + | 0.792396i | \(0.708833\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.66607 | + | 5.12764i | 0.141314 | + | 0.434921i | 0.996519 | − | 0.0833702i | \(-0.0265684\pi\) |
−0.855204 | + | 0.518291i | \(0.826568\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.91948 | + | 5.90755i | −0.161649 | + | 0.497505i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.592757i | − | 0.0495689i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.27647 | + | 10.3086i | 0.687324 | + | 0.856086i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.14339 | − | 4.32651i | −0.259262 | − | 0.356844i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.8229 | −1.54203 | −0.771015 | − | 0.636817i | \(-0.780251\pi\) | ||||
−0.771015 | + | 0.636817i | \(0.780251\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.88797 | 0.316398 | 0.158199 | − | 0.987407i | \(-0.449431\pi\) | ||||
0.158199 | + | 0.987407i | \(0.449431\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.52903 | + | 3.48091i | 0.204460 | + | 0.281415i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.47619 | + | 11.4074i | −0.600502 | + | 0.916261i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.28378i | 0.341883i | 0.985281 | + | 0.170941i | \(0.0546808\pi\) | ||||
−0.985281 | + | 0.170941i | \(0.945319\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.68467 | − | 11.3403i | 0.292214 | − | 0.899341i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.885926 | − | 2.72660i | −0.0698208 | − | 0.214886i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.9566 | + | 4.85970i | 1.17149 | + | 0.380641i | 0.829200 | − | 0.558952i | \(-0.188796\pi\) |
0.342293 | + | 0.939593i | \(0.388796\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.50569 | + | 3.60834i | 0.428617 | + | 0.280909i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.3629 | + | 17.0161i | −0.956670 | + | 1.31674i | −0.00816967 | + | 0.999967i | \(0.502601\pi\) |
−0.948500 | + | 0.316777i | \(0.897399\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4462 | − | 7.58958i | −0.803551 | − | 0.583814i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.16663 | + | 0.847609i | −0.0892148 | + | 0.0648183i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.81587 | − | 2.21461i | 0.518201 | − | 0.168374i | −0.0382277 | − | 0.999269i | \(-0.512171\pi\) |
0.556429 | + | 0.830895i | \(0.312171\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.56827 | − | 16.2287i | −0.118550 | − | 1.22677i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.31034 | − | 2.70019i | 0.624643 | − | 0.202959i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.50396 | + | 4.72540i | −0.486129 | + | 0.353193i | −0.803694 | − | 0.595043i | \(-0.797135\pi\) |
0.317565 | + | 0.948237i | \(0.397135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6796 | + | 12.1184i | 1.23978 | + | 0.900756i | 0.997584 | − | 0.0694707i | \(-0.0221310\pi\) |
0.242200 | + | 0.970226i | \(0.422131\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.792181 | + | 1.09034i | −0.0585597 | + | 0.0806005i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.75401 | + | 17.4493i | −0.349522 | + | 1.28290i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.82055 | + | 3.19089i | 0.718150 | + | 0.233341i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.68574 | + | 17.4989i | 0.413577 | + | 1.27286i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.57167 | + | 17.1478i | −0.403152 | + | 1.24077i | 0.519277 | + | 0.854606i | \(0.326201\pi\) |
−0.922429 | + | 0.386167i | \(0.873799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.78859i | − | 0.488653i | −0.969693 | − | 0.244327i | \(-0.921433\pi\) | ||
0.969693 | − | 0.244327i | \(-0.0785669\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.912160 | + | 0.345766i | −0.0653211 | + | 0.0247608i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.69956 | − | 6.46839i | −0.334830 | − | 0.460854i | 0.608092 | − | 0.793866i | \(-0.291935\pi\) |
−0.942923 | + | 0.333012i | \(0.891935\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.20485 | −0.368962 | −0.184481 | − | 0.982836i | \(-0.559060\pi\) | ||||
−0.184481 | + | 0.982836i | \(0.559060\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.1389 | −0.715141 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.3317 | + | 15.5968i | 0.795332 | + | 1.09468i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.19011 | − | 0.596687i | −0.152964 | − | 0.0416745i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.732688i | 0.0509254i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.06943 | + | 3.29138i | −0.0739743 | + | 0.227669i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.13029 | − | 15.7894i | −0.353184 | − | 1.08699i | −0.957055 | − | 0.289906i | \(-0.906376\pi\) |
0.603872 | − | 0.797082i | \(-0.293624\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.35573 | − | 2.71494i | −0.572525 | − | 0.186025i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.24091 | − | 0.349052i | 0.493826 | − | 0.0238051i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.6909 | + | 16.0911i | −0.793628 | + | 1.09233i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5191 | + | 7.64258i | 0.710815 | + | 0.516438i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.23795 | + | 0.899425i | −0.0832737 | + | 0.0605019i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.30368 | + | 2.04819i | −0.422126 | + | 0.137157i | −0.512374 | − | 0.858762i | \(-0.671234\pi\) |
0.0902485 | + | 0.995919i | \(0.471234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.900470 | + | 4.06837i | −0.0600313 | + | 0.271224i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.7365 | − | 4.13833i | 0.845350 | − | 0.274671i | 0.145853 | − | 0.989306i | \(-0.453407\pi\) |
0.699497 | + | 0.714636i | \(0.253407\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.16032 | − | 5.92882i | 0.539249 | − | 0.391788i | −0.284557 | − | 0.958659i | \(-0.591846\pi\) |
0.823806 | + | 0.566872i | \(0.191846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.76626 | + | 5.64252i | 0.510983 | + | 0.371251i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.9345 | + | 17.8028i | −0.847368 | + | 1.16630i | 0.137069 | + | 0.990562i | \(0.456232\pi\) |
−0.984437 | + | 0.175740i | \(0.943768\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.35806 | + | 5.90755i | −0.479987 | + | 0.385366i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.8642 | + | 3.53000i | 0.705707 | + | 0.229298i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.33626 | + | 7.19026i | 0.151120 | + | 0.465099i | 0.997747 | − | 0.0670870i | \(-0.0213705\pi\) |
−0.846627 | + | 0.532187i | \(0.821371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.30226 | + | 19.3964i | −0.405964 | + | 1.24943i | 0.514123 | + | 0.857716i | \(0.328117\pi\) |
−0.920087 | + | 0.391713i | \(0.871883\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 8.38230i | − | 0.537725i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.391169 | − | 8.11461i | −0.0249909 | − | 0.518424i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.301444 | − | 0.414902i | −0.0191804 | − | 0.0263996i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.3659 | 1.35401 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5717 | −0.667278 | −0.333639 | − | 0.942701i | \(-0.608277\pi\) | ||||
−0.333639 | + | 0.942701i | \(0.608277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.03355 | + | 1.42256i | 0.0649789 | + | 0.0894357i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.818220 | − | 16.9736i | −0.0512389 | − | 1.06293i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 20.2700i | − | 1.26441i | −0.774801 | − | 0.632205i | \(-0.782150\pi\) | ||
0.774801 | − | 0.632205i | \(-0.217850\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.14996 | + | 25.0830i | −0.506414 | + | 1.55858i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.52252 | − | 4.68585i | −0.0942419 | − | 0.290047i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.7160 | − | 8.68056i | −1.64738 | − | 0.535267i | −0.669211 | − | 0.743072i | \(-0.733368\pi\) |
−0.978170 | + | 0.207806i | \(0.933368\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.1247 | − | 11.3403i | 0.867673 | − | 0.696626i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.51179 | − | 8.96271i | 0.398515 | − | 0.548509i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.4416 | + | 11.9455i | 1.00246 | + | 0.728333i | 0.962615 | − | 0.270873i | \(-0.0873123\pi\) |
0.0398490 | + | 0.999206i | \(0.487312\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.4409 | − | 18.4839i | 1.54543 | − | 1.12282i | 0.598610 | − | 0.801041i | \(-0.295720\pi\) |
0.946816 | − | 0.321777i | \(-0.104280\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.35294 | + | 0.439596i | −0.0818835 | + | 0.0266056i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.99064 | + | 9.16923i | 0.240645 | + | 0.552925i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.2487 | + | 4.30475i | −0.796035 | + | 0.258648i | −0.678672 | − | 0.734441i | \(-0.737444\pi\) |
−0.117363 | + | 0.993089i | \(0.537444\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.11235 | − | 2.98779i | 0.246200 | − | 0.178875i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.9355 | − | 15.2105i | −1.24891 | − | 0.907383i | −0.250748 | − | 0.968052i | \(-0.580677\pi\) |
−0.998158 | + | 0.0606690i | \(0.980677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9491 | + | 19.1993i | −0.829188 | + | 1.14128i | 0.158885 | + | 0.987297i | \(0.449210\pi\) |
−0.988074 | + | 0.153983i | \(0.950790\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.68873 | − | 0.274228i | 0.336971 | − | 0.0162439i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.14823 | − | 1.02292i | −0.185834 | − | 0.0603811i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.98394 | − | 9.18363i | −0.175526 | − | 0.540214i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.05959 | + | 9.41645i | −0.179356 | + | 0.552002i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 12.3029i | − | 0.718742i | −0.933195 | − | 0.359371i | \(-0.882991\pi\) | ||
0.933195 | − | 0.359371i | \(-0.117009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.8073 | + | 3.48930i | 0.745668 | + | 0.203155i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.63318 | − | 9.12979i | −0.384896 | − | 0.529764i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.260574 | −0.0150694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.5717 | 0.609341 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.5514 | − | 14.5228i | −0.606163 | − | 0.834311i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.91445 | + | 0.725696i | −0.109621 | + | 0.0415532i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.28249i | 0.244415i | 0.992505 | + | 0.122207i | \(0.0389973\pi\) | ||||
−0.992505 | + | 0.122207i | \(0.961003\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.628342 | − | 1.93384i | 0.0357451 | − | 0.110012i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.92526 | − | 24.3915i | −0.449400 | − | 1.38311i | −0.877585 | − | 0.479421i | \(-0.840847\pi\) |
0.428185 | − | 0.903691i | \(-0.359153\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.2573 | − | 6.90692i | −1.20153 | − | 0.390402i | −0.361209 | − | 0.932485i | \(-0.617636\pi\) |
−0.840325 | + | 0.542083i | \(0.817636\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.59730 | + | 5.86279i | −0.0899975 | + | 0.330331i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.8859 | + | 17.7360i | −0.723746 | + | 0.996151i | 0.275645 | + | 0.961259i | \(0.411108\pi\) |
−0.999391 | + | 0.0348911i | \(0.988892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.56608 | − | 6.95016i | −0.535597 | − | 0.389134i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.8491 | − | 13.6947i | 1.05205 | − | 0.764363i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.49664 | − | 2.76073i | 0.472766 | − | 0.153611i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.44688 | − | 0.320244i | −0.0802583 | − | 0.0177639i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.80509 | − | 0.911429i | 0.155122 | − | 0.0504021i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.1326 | + | 8.08832i | −0.613761 | + | 0.445923i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.25121 | − | 5.26831i | −0.398563 | − | 0.289573i | 0.370393 | − | 0.928875i | \(-0.379223\pi\) |
−0.768955 | + | 0.639303i | \(0.779223\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.96183 | − | 5.45299i | 0.217107 | − | 0.298822i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.8821 | − | 8.44269i | −0.703822 | − | 0.461273i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.6601 | + | 8.98731i | 1.50674 | + | 0.489570i | 0.941976 | − | 0.335681i | \(-0.108966\pi\) |
0.564766 | + | 0.825251i | \(0.308966\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.74302 | + | 14.5975i | 0.257605 | + | 0.792828i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.76972 | − | 11.6020i | 0.204142 | − | 0.628283i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.9787i | 0.592795i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.58621 | − | 2.42028i | 0.0853987 | − | 0.130303i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.40368 | − | 11.5667i | −0.451133 | − | 0.620931i | 0.521508 | − | 0.853247i | \(-0.325370\pi\) |
−0.972641 | + | 0.232315i | \(0.925370\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.62382 | −0.301036 | −0.150518 | − | 0.988607i | \(-0.548094\pi\) | ||||
−0.150518 | + | 0.988607i | \(0.548094\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.67232 | 0.0892620 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.12265 | − | 1.54520i | −0.0597529 | − | 0.0822427i | 0.778095 | − | 0.628147i | \(-0.216186\pi\) |
−0.837848 | + | 0.545904i | \(0.816186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.35573 | − | 10.4074i | −0.443476 | − | 0.552366i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 24.7813i | − | 1.31156i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.86161 | − | 21.1179i | 0.362142 | − | 1.11456i | −0.589609 | − | 0.807689i | \(-0.700718\pi\) |
0.951751 | − | 0.306870i | \(-0.0992818\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.94606 | − | 15.2224i | −0.260319 | − | 0.801179i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.79935 | + | 3.18400i | 0.514332 | + | 0.167117i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.00116 | + | 18.4697i | 0.366458 | + | 0.966748i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.6050 | + | 17.3493i | −0.657978 | + | 0.905629i | −0.999412 | − | 0.0342768i | \(-0.989087\pi\) |
0.341435 | + | 0.939906i | \(0.389087\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.684418 | + | 0.497259i | 0.0356294 | + | 0.0258863i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.3704 | − | 15.5265i | 1.10950 | − | 0.806096i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0074 | + | 7.15063i | −1.13950 | + | 0.370245i | −0.817178 | − | 0.576385i | \(-0.804463\pi\) |
−0.322320 | + | 0.946631i | \(0.604463\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.7822 | − | 11.4895i | 0.608430 | − | 0.593317i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.66648 | − | 0.541471i | 0.0858279 | − | 0.0278872i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.5153 | − | 12.7256i | 0.899702 | − | 0.653672i | −0.0386872 | − | 0.999251i | \(-0.512318\pi\) |
0.938390 | + | 0.345579i | \(0.112318\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.96645 | − | 5.06142i | −0.356902 | − | 0.259304i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.32381 | + | 4.57484i | −0.169839 | + | 0.233763i | −0.885449 | − | 0.464737i | \(-0.846149\pi\) |
0.715610 | + | 0.698500i | \(0.246149\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.16896 | + | 13.6362i | 0.263435 | + | 0.694964i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.56953 | − | 0.834891i | −0.130617 | − | 0.0424399i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.51109 | + | 7.72833i | 0.127317 | + | 0.391842i | 0.994316 | − | 0.106468i | \(-0.0339541\pi\) |
−0.866999 | + | 0.498310i | \(0.833954\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.40270 | − | 4.31707i | 0.0709377 | − | 0.218324i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.20298i | − | 0.111126i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.8642 | + | 13.5318i | 0.546638 | + | 0.680857i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.2076 | − | 16.8024i | −0.612684 | − | 0.843287i | 0.384111 | − | 0.923287i | \(-0.374508\pi\) |
−0.996795 | + | 0.0799998i | \(0.974508\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.30550 | 0.415795 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.1195 | 1.50410 | 0.752049 | − | 0.659107i | \(-0.229066\pi\) | ||||
0.752049 | + | 0.659107i | \(0.229066\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.06258 | + | 1.46252i | 0.0529309 | + | 0.0728532i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.11568 | + | 10.8573i | −0.353581 | + | 0.539503i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 16.1760i | − | 0.801815i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.41317 | + | 10.5046i | −0.168770 | + | 0.519421i | −0.999294 | − | 0.0375613i | \(-0.988041\pi\) |
0.830524 | + | 0.556983i | \(0.188041\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.57012 | − | 10.9877i | −0.176101 | − | 0.541983i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.4102 | + | 5.98182i | 0.905905 | + | 0.294346i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.1467 | + | 17.7915i | 1.33258 | + | 0.873350i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.66469 | + | 6.42039i | −0.228431 | + | 0.314408i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.6338 | + | 19.3506i | 1.30115 | + | 0.945337i | 0.999966 | − | 0.00823011i | \(-0.00261975\pi\) |
0.301179 | + | 0.953568i | \(0.402620\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.3945 | − | 11.9113i | 0.799019 | − | 0.580522i | −0.111607 | − | 0.993752i | \(-0.535600\pi\) |
0.910626 | + | 0.413231i | \(0.135600\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.34464 | − | 1.08674i | 0.162622 | − | 0.0528392i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.0944 | − | 22.2473i | 0.635171 | − | 1.07915i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.83956 | + | 0.922629i | −0.137416 | + | 0.0446491i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.705874 | − | 0.512848i | 0.0340799 | − | 0.0247605i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.78873 | + | 4.20576i | 0.278833 | + | 0.202584i | 0.718408 | − | 0.695622i | \(-0.244871\pi\) |
−0.439575 | + | 0.898206i | \(0.644871\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.22262 | + | 4.43555i | −0.154869 | + | 0.213159i | −0.879400 | − | 0.476083i | \(-0.842056\pi\) |
0.724531 | + | 0.689242i | \(0.242056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.11514 | + | 18.7748i | −0.245252 | + | 0.900184i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.44688 | + | 0.470119i | 0.0692135 | + | 0.0224888i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.50415 | − | 29.2508i | −0.453609 | − | 1.39606i | −0.872761 | − | 0.488148i | \(-0.837673\pi\) |
0.419153 | − | 0.907916i | \(-0.362327\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.935631 | + | 2.87958i | −0.0445539 | + | 0.137123i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 11.3527i | − | 0.539381i | −0.962947 | − | 0.269691i | \(-0.913079\pi\) | ||
0.962947 | − | 0.269691i | \(-0.0869214\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.7369 | − | 5.96528i | 0.746002 | − | 0.282781i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.2854 | − | 22.4149i | −0.770271 | − | 1.06019i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7661 | 0.744050 | 0.372025 | − | 0.928223i | \(-0.378664\pi\) | ||||
0.372025 | + | 0.928223i | \(0.378664\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.03029 | 0.0956027 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.36383 | + | 4.62992i | 0.158047 | + | 0.217532i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.08504 | − | 0.568064i | −0.0977484 | − | 0.0266312i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.16714i | 0.194931i | 0.995239 | + | 0.0974653i | \(0.0310735\pi\) | ||||
−0.995239 | + | 0.0974653i | \(0.968926\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.00233 | + | 27.7063i | −0.420193 | + | 1.29322i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.40758 | − | 22.7982i | −0.345005 | − | 1.06182i | −0.961581 | − | 0.274521i | \(-0.911481\pi\) |
0.616576 | − | 0.787296i | \(-0.288519\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.3021 | − | 12.7700i | −1.82652 | − | 0.593473i | −0.999510 | − | 0.0312899i | \(-0.990038\pi\) |
−0.827013 | − | 0.562183i | \(-0.809962\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.0526 | + | 0.966645i | −0.929916 | + | 0.0448271i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.11096 | + | 8.41102i | −0.282782 | + | 0.389216i | −0.926653 | − | 0.375918i | \(-0.877327\pi\) |
0.643871 | + | 0.765134i | \(0.277327\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.1713 | − | 13.2022i | −0.839072 | − | 0.609622i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.10126 | + | 3.70628i | −0.235054 | + | 0.170776i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.16663 | + | 2.00366i | −0.283542 | + | 0.0921284i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.45624 | + | 4.38861i | 0.342116 | + | 0.201363i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.42045 | + | 2.08613i | −0.293972 | + | 0.0955174i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.1312 | + | 21.1650i | −1.33104 | + | 0.967055i | −0.331314 | + | 0.943520i | \(0.607492\pi\) |
−0.999723 | + | 0.0235349i | \(0.992508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.93930 | + | 1.40899i | 0.0884246 | + | 0.0642443i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.48043 | − | 3.41402i | 0.112863 | − | 0.155343i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.7285 | + | 9.41645i | −0.532565 | + | 0.427579i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.1172 | + | 3.28726i | 0.458452 | + | 0.148960i | 0.529133 | − | 0.848539i | \(-0.322517\pi\) |
−0.0706809 | + | 0.997499i | \(0.522517\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.15323 | + | 22.0154i | 0.323480 | + | 0.995570i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.46010 | − | 16.8045i | 0.246411 | − | 0.758375i | −0.748990 | − | 0.662581i | \(-0.769461\pi\) |
0.995401 | − | 0.0957938i | \(-0.0305389\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.5243i | 1.37475i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.179450 | − | 3.72260i | −0.00806568 | − | 0.167319i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.4403 | − | 15.7462i | −0.513166 | − | 0.706312i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.41734 | −0.421578 | −0.210789 | − | 0.977532i | \(-0.567603\pi\) | ||||
−0.210789 | + | 0.977532i | \(0.567603\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.9595 | −1.38317 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.5879 | − | 14.5730i | −0.472093 | − | 0.649780i | 0.504869 | − | 0.863196i | \(-0.331541\pi\) |
−0.976961 | + | 0.213416i | \(0.931541\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.31304 | − | 27.2383i | −0.0584294 | − | 1.21209i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 19.0060i | − | 0.844088i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.95926 | − | 15.2630i | 0.219815 | − | 0.676522i | −0.778961 | − | 0.627072i | \(-0.784253\pi\) |
0.998777 | − | 0.0494500i | \(-0.0157469\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.90107 | + | 27.3947i | 0.393760 | + | 1.21187i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.28583 | − | 3.01715i | −0.409980 | − | 0.133210i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.40867 | − | 1.93384i | 0.106138 | − | 0.0852151i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.96086 | − | 6.82803i | 0.218178 | − | 0.300297i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.53425 | + | 6.20050i | 0.374612 | + | 0.272172i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.78040 | − | 1.29354i | 0.0780007 | − | 0.0566708i | −0.548102 | − | 0.836412i | \(-0.684649\pi\) |
0.626102 | + | 0.779741i | \(0.284649\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.07194 | + | 2.29781i | −0.309234 | + | 0.100476i | −0.459523 | − | 0.888166i | \(-0.651980\pi\) |
0.150289 | + | 0.988642i | \(0.451980\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.9688 | − | 15.9084i | 0.784222 | − | 0.694301i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.9504 | + | 9.73147i | −1.30466 | + | 0.423909i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.9820 | + | 13.0647i | −0.781828 | + | 0.568031i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00233 | − | 2.90786i | −0.173686 | − | 0.126190i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.176845 | + | 0.243407i | −0.00766003 | + | 0.0105431i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.3526 | − | 1.70419i | 1.52843 | − | 0.0736786i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.2543 | − | 3.65675i | −0.485660 | − | 0.157800i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.24543 | + | 6.91072i | 0.0967174 | + | 0.297666i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.38040 | − | 19.6368i | 0.274315 | − | 0.844254i | −0.715085 | − | 0.699037i | \(-0.753612\pi\) |
0.989400 | − | 0.145216i | \(-0.0463878\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.3473i | 1.30233i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.32299 | + | 1.17779i | 0.185177 | + | 0.0504508i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.4424 | − | 25.3839i | −0.788542 | − | 1.08534i | −0.994288 | − | 0.106730i | \(-0.965962\pi\) |
0.205746 | − | 0.978605i | \(-0.434038\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.763042 | 0.0325658 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.2303 | −0.435825 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.8747 | + | 20.4733i | 0.632538 | + | 0.870615i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.8923 | + | 9.43574i | −1.05662 | + | 0.400525i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.3515i | 0.947064i | 0.880776 | + | 0.473532i | \(0.157021\pi\) | ||||
−0.880776 | + | 0.473532i | \(0.842979\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.296921 | − | 0.913829i | 0.0125584 | − | 0.0386509i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.69683 | + | 14.4554i | 0.198300 | + | 0.610305i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.6843 | + | 10.6198i | 1.37748 | + | 0.447570i | 0.901840 | − | 0.432070i | \(-0.142217\pi\) |
0.475639 | + | 0.879640i | \(0.342217\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.12912 | + | 22.4966i | −0.257854 | + | 0.946438i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.1271 | + | 15.3152i | −0.467295 | + | 0.643177i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.0230 | + | 18.9068i | 1.09094 | + | 0.792615i | 0.979558 | − | 0.201162i | \(-0.0644718\pi\) |
0.111383 | + | 0.993778i | \(0.464472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.9784 | + | 15.9683i | −0.919768 | + | 0.668251i | −0.943466 | − | 0.331468i | \(-0.892456\pi\) |
0.0236979 | + | 0.999719i | \(0.492456\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.2407 | + | 8.20121i | −1.05445 | + | 0.342610i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.03076 | − | 1.75427i | 0.168094 | − | 0.0731581i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.1724 | − | 4.27998i | 0.548375 | − | 0.178178i | −0.0217089 | − | 0.999764i | \(-0.506911\pi\) |
0.570084 | + | 0.821586i | \(0.306911\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.08407 | − | 5.87342i | 0.335963 | − | 0.244091i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.2928 | + | 27.8214i | 1.58865 | + | 1.15422i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.52297 | + | 13.1072i | −0.394401 | + | 0.542847i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.461925 | + | 0.302738i | 0.0190982 | + | 0.0125167i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.9890 | + | 13.6431i | 1.73307 | + | 0.563110i | 0.993888 | − | 0.110392i | \(-0.0352107\pi\) |
0.739185 | + | 0.673502i | \(0.235211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.26152 | − | 10.0379i | −0.134389 | − | 0.413606i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.63675 | − | 11.1928i | 0.149596 | − | 0.460409i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 16.2531i | − | 0.667437i | −0.942673 | − | 0.333718i | \(-0.891697\pi\) | ||
0.942673 | − | 0.333718i | \(-0.108303\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.6355 | − | 31.4862i | 0.845973 | − | 1.29081i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.50318 | − | 6.19810i | −0.184303 | − | 0.253671i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.4822 | 1.24547 | 0.622734 | − | 0.782433i | \(-0.286022\pi\) | ||||
0.622734 | + | 0.782433i | \(0.286022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.9162 | −1.17952 | −0.589758 | − | 0.807580i | \(-0.700777\pi\) | ||||
−0.589758 | + | 0.807580i | \(0.700777\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.37405 | + | 4.64398i | 0.137402 | + | 0.189117i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.79935 | + | 12.2054i | 0.398400 | + | 0.496222i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.23276i | 0.334157i | 0.985944 | + | 0.167079i | \(0.0534334\pi\) | ||||
−0.985944 | + | 0.167079i | \(0.946567\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.76906 | + | 26.9884i | −0.355340 | + | 1.09362i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.386489 | + | 1.18949i | 0.0156357 | + | 0.0481217i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.56327 | + | 1.48270i | 0.184309 | + | 0.0598856i | 0.399717 | − | 0.916638i | \(-0.369108\pi\) |
−0.215408 | + | 0.976524i | \(0.569108\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.18430 | − | 3.12430i | −0.0477557 | − | 0.125984i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.19428 | − | 1.64379i | 0.0480800 | − | 0.0661765i | −0.784300 | − | 0.620382i | \(-0.786978\pi\) |
0.832380 | + | 0.554205i | \(0.186978\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.58621 | − | 4.78516i | −0.264722 | − | 0.192332i | 0.447504 | − | 0.894282i | \(-0.352313\pi\) |
−0.712226 | + | 0.701950i | \(0.752313\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.01342 | + | 2.91592i | −0.161053 | + | 0.117012i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.3414 | − | 7.58408i | 0.935153 | − | 0.303850i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.5374 | − | 4.78708i | 0.981496 | − | 0.191483i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.84474 | + | 1.57415i | −0.193480 | + | 0.0628656i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.7830 | + | 24.5448i | −1.34702 | + | 0.978665i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.9279 | + | 19.5643i | 1.07198 | + | 0.778841i | 0.976268 | − | 0.216567i | \(-0.0694861\pi\) |
0.0957154 | + | 0.995409i | \(0.469486\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.3638 | − | 19.7701i | 0.570912 | − | 0.785793i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.63663 | − | 12.2318i | −0.183999 | − | 0.485406i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.02409 | − | 0.332749i | −0.0405761 | − | 0.0131840i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.53710 | + | 4.73072i | 0.0608069 | + | 0.187144i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.3755 | + | 38.0880i | −0.488804 | + | 1.50439i | 0.337590 | + | 0.941293i | \(0.390388\pi\) |
−0.826394 | + | 0.563092i | \(0.809612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.6870i | 0.460890i | 0.973085 | + | 0.230445i | \(0.0740182\pi\) | ||||
−0.973085 | + | 0.230445i | \(0.925982\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.68042 | + | 8.32070i | 0.263041 | + | 0.327627i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.67252 | + | 6.43117i | 0.183696 | + | 0.252835i | 0.890927 | − | 0.454147i | \(-0.150056\pi\) |
−0.707231 | + | 0.706982i | \(0.750056\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.8727 | −0.466044 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.2766 | −1.14744 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.96165 | − | 2.69998i | −0.0767653 | − | 0.105658i | 0.768908 | − | 0.639360i | \(-0.220801\pi\) |
−0.845673 | + | 0.533702i | \(0.820801\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.83443 | − | 2.79902i | 0.0716772 | − | 0.109367i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 7.36146i | − | 0.287198i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.28621 | + | 28.5800i | −0.361739 | + | 1.11332i | 0.590259 | + | 0.807214i | \(0.299026\pi\) |
−0.951998 | + | 0.306105i | \(0.900974\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.03462 | − | 6.26192i | −0.0791375 | − | 0.243560i | 0.903659 | − | 0.428253i | \(-0.140871\pi\) |
−0.982796 | + | 0.184693i | \(0.940871\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.14213 | − | 0.696020i | −0.0831934 | − | 0.0270312i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.5527 | + | 6.91604i | 0.409215 | + | 0.268192i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.05526 | + | 4.20521i | −0.118300 | + | 0.162826i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.89293 | − | 5.73455i | −0.305158 | − | 0.221711i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.48150 | − | 1.07637i | 0.0571925 | − | 0.0415528i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.40194 | + | 2.08012i | −0.246777 | + | 0.0801826i | −0.429794 | − | 0.902927i | \(-0.641414\pi\) |
0.183017 | + | 0.983110i | \(0.441414\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.8688 | + | 11.2586i | −0.995690 | + | 0.433345i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.9799 | − | 4.21741i | 0.498857 | − | 0.162088i | −0.0487718 | − | 0.998810i | \(-0.515531\pi\) |
0.547629 | + | 0.836722i | \(0.315531\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.7451 | + | 12.8925i | −0.680993 | + | 0.494770i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.9475 | + | 11.5866i | 0.611111 | + | 0.443998i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.689001 | + | 0.948329i | −0.0263639 | + | 0.0362868i | −0.821995 | − | 0.569494i | \(-0.807139\pi\) |
0.795632 | + | 0.605781i | \(0.207139\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.61345 | − | 16.9334i | 0.176271 | − | 0.646992i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.1205 | + | 4.58802i | 0.538729 | + | 0.175044i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.741913 | − | 2.28337i | −0.0282646 | − | 0.0869896i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.79083 | + | 11.6670i | −0.144210 | + | 0.443832i | −0.996909 | − | 0.0785709i | \(-0.974964\pi\) |
0.852699 | + | 0.522403i | \(0.174964\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 5.43497i | − | 0.206457i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.2731 | + | 4.27320i | −0.427612 | + | 0.162092i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.08068 | − | 4.24019i | −0.116689 | − | 0.160609i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −32.3910 | −1.22514 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.0271 | −0.756415 | −0.378207 | − | 0.925721i | \(-0.623459\pi\) | ||||
−0.378207 | + | 0.925721i | \(0.623459\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.22624 | − | 11.3225i | −0.310259 | − | 0.427034i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.4010 | − | 3.65106i | −0.504711 | − | 0.137507i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 39.7677i | − | 1.49562i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.35816 | − | 4.17998i | 0.0510067 | − | 0.156983i | −0.922309 | − | 0.386454i | \(-0.873700\pi\) |
0.973315 | + | 0.229471i | \(0.0736998\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.99856 | − | 6.15094i | −0.0749519 | − | 0.230678i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.10019 | − | 1.65715i | −0.191004 | − | 0.0620608i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.32391 | − | 0.0638197i | 0.0495114 | − | 0.00238672i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.54109 | + | 9.00303i | −0.244281 | + | 0.336224i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.84119 | + | 6.42350i | 0.329721 | + | 0.239556i | 0.740312 | − | 0.672263i | \(-0.234678\pi\) |
−0.410591 | + | 0.911819i | \(0.634678\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.64427 | − | 2.64772i | 0.135720 | − | 0.0986061i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.5505 | + | 9.27661i | −1.06180 | + | 0.345001i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.1330 | + | 19.5952i | −0.821999 | + | 0.727747i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.2928 | − | 10.1677i | 1.16059 | − | 0.377097i | 0.335465 | − | 0.942053i | \(-0.391107\pi\) |
0.825122 | + | 0.564955i | \(0.191107\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.0719 | − | 17.4893i | 0.891553 | − | 0.647751i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.5416 | + | 9.83853i | 0.500853 | + | 0.363891i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.08190 | + | 11.1238i | −0.298512 | + | 0.410866i | −0.931756 | − | 0.363086i | \(-0.881723\pi\) |
0.633244 | + | 0.773952i | \(0.281723\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.32470 | − | 7.48650i | 0.343947 | − | 0.276144i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.1019 | + | 4.25705i | 0.482613 | + | 0.156811i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.3462 | − | 41.0754i | −0.490949 | − | 1.51098i | −0.823177 | − | 0.567785i | \(-0.807800\pi\) |
0.332228 | − | 0.943199i | \(-0.392200\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.233273 | − | 0.717939i | 0.00856948 | − | 0.0263741i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.8479i | 1.16838i | 0.811615 | + | 0.584192i | \(0.198589\pi\) | ||||
−0.811615 | + | 0.584192i | \(0.801411\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.02658 | − | 42.0404i | −0.0742482 | − | 1.54024i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.11021 | − | 9.78637i | −0.260149 | − | 0.358064i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 51.6145 | 1.88595 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.5952 | 1.07995 | 0.539973 | − | 0.841682i | \(-0.318435\pi\) | ||||
0.539973 | + | 0.841682i | \(0.318435\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.14650 | − | 12.5891i | −0.333317 | − | 0.458771i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.418601 | + | 8.68368i | 0.0152345 | + | 0.316031i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 0.0984401i | − | 0.00357786i | −0.999998 | − | 0.00178893i | \(-0.999431\pi\) | ||
0.999998 | − | 0.00178893i | \(-0.000569435\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.799814 | + | 2.46157i | −0.0290314 | + | 0.0893495i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.09516 | − | 3.37056i | −0.0396996 | − | 0.122183i | 0.929243 | − | 0.369470i | \(-0.120461\pi\) |
−0.968942 | + | 0.247287i | \(0.920461\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.21421 | + | 2.01912i | 0.224969 | + | 0.0730970i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.50223 | + | 6.02330i | −0.271244 | + | 0.217773i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.03415 | − | 1.42339i | 0.0373411 | − | 0.0513957i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.15494 | + | 0.839116i | 0.0416484 | + | 0.0302593i | 0.608415 | − | 0.793619i | \(-0.291806\pi\) |
−0.566766 | + | 0.823879i | \(0.691806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.1382 | − | 17.5374i | 0.869316 | − | 0.631595i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.1274 | − | 10.4388i | 1.15554 | − | 0.375458i | 0.332313 | − | 0.943169i | \(-0.392171\pi\) |
0.823228 | + | 0.567711i | \(0.192171\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.2830 | − | 15.4697i | −0.944113 | − | 0.555688i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −36.9209 | + | 11.9963i | −1.32453 | + | 0.430366i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.42111 | − | 1.03250i | 0.0509165 | − | 0.0369930i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.65769 | + | 7.01672i | 0.345579 | + | 0.251078i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.6082 | − | 26.9884i | 0.700740 | − | 0.964486i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.56771 | + | 0.461216i | −0.341486 | + | 0.0164615i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.07358 | − | 0.673749i | −0.0739153 | − | 0.0240165i | 0.271826 | − | 0.962346i | \(-0.412373\pi\) |
−0.345741 | + | 0.938330i | \(0.612373\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.7773 | − | 39.3246i | −0.454886 | − | 1.39999i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.5074 | + | 32.3383i | −0.373599 | + | 1.14982i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.271369i | 0.00963659i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.7249 | + | 7.00866i | 0.912368 | + | 0.248572i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.8082 | − | 19.0053i | −0.489110 | − | 0.673203i | 0.491113 | − | 0.871096i | \(-0.336590\pi\) |
−0.980224 | + | 0.197893i | \(0.936590\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.7875 | −0.770787 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.27226 | −0.221620 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.3843 | − | 14.2928i | −0.366454 | − | 0.504380i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.99441 | − | 2.27226i | 0.211275 | − | 0.0800865i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.9144i | 1.05304i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.7893 | − | 36.2837i | 0.414489 | − | 1.27567i | −0.498217 | − | 0.867052i | \(-0.666012\pi\) |
0.912707 | − | 0.408615i | \(-0.133988\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.8040 | − | 45.5622i | −0.519840 | − | 1.59990i | −0.774298 | − | 0.632821i | \(-0.781897\pi\) |
0.254458 | − | 0.967084i | \(-0.418103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 44.0224 | + | 14.3038i | 1.54393 | + | 0.501655i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.24370 | + | 33.9285i | −0.323793 | + | 1.18846i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.29740 | + | 4.53849i | −0.115362 | + | 0.158782i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.651586 | + | 0.473405i | 0.0227683 | + | 0.0165421i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.3558 | + | 11.1566i | −0.535920 | + | 0.389369i | −0.822568 | − | 0.568667i | \(-0.807459\pi\) |
0.286647 | + | 0.958036i | \(0.407459\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.0831 | − | 6.85033i | 0.734912 | − | 0.238787i | 0.0824356 | − | 0.996596i | \(-0.473730\pi\) |
0.652476 | + | 0.757809i | \(0.273730\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.46635 | + | 12.6853i | −0.259945 | + | 0.441646i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.49790 | + | 1.46146i | −0.156407 | + | 0.0508199i | −0.386174 | − | 0.922426i | \(-0.626204\pi\) |
0.229767 | + | 0.973246i | \(0.426204\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.3003 | − | 9.66320i | 0.461937 | − | 0.335617i | −0.332354 | − | 0.943155i | \(-0.607843\pi\) |
0.794291 | + | 0.607538i | \(0.207843\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.5889 | − | 12.0525i | −0.575461 | − | 0.418097i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.0257 | − | 15.1755i | 0.382017 | − | 0.525801i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39.3360 | − | 25.7802i | −1.36128 | − | 0.892160i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.7322 | + | 10.6354i | 1.13139 | + | 0.367611i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.73075 | − | 5.32671i | −0.0597522 | − | 0.183898i | 0.916725 | − | 0.399519i | \(-0.130823\pi\) |
−0.976477 | + | 0.215620i | \(0.930823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.83977 | − | 5.66224i | 0.0634405 | − | 0.195250i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 38.0906i | − | 1.31191i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.8264 | − | 24.1484i | 0.544446 | − | 0.830729i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.4168 | + | 18.4666i | 0.461006 | + | 0.634520i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.9318 | −1.19886 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.11091 | −0.243759 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.5158 | − | 14.4737i | −0.360053 | − | 0.495571i | 0.590110 | − | 0.807323i | \(-0.299084\pi\) |
−0.950164 | + | 0.311752i | \(0.899084\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.01872 | − | 2.51439i | −0.0690388 | − | 0.0859903i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.19536i | 0.109151i | 0.998510 | + | 0.0545757i | \(0.0173806\pi\) | ||||
−0.998510 | + | 0.0545757i | \(0.982619\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.4174 | − | 41.2945i | 0.457795 | − | 1.40895i | −0.410027 | − | 0.912073i | \(-0.634481\pi\) |
0.867822 | − | 0.496875i | \(-0.165519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.50569 | − | 4.63403i | −0.0513137 | − | 0.157927i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.1545 | + | 13.3719i | 1.40091 | + | 0.455185i | 0.909486 | − | 0.415734i | \(-0.136475\pi\) |
0.491428 | + | 0.870918i | \(0.336475\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.68011 | + | 14.9846i | 0.193130 | + | 0.509493i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.35449 | − | 11.4990i | 0.283733 | − | 0.390525i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.5570 | − | 9.12322i | −0.425968 | − | 0.309484i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.65159 | + | 1.19995i | −0.0559619 | + | 0.0406587i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.33126 | − | 1.73223i | 0.180436 | − | 0.0586272i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.0775 | − | 5.24996i | 1.21964 | − | 0.177481i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.5584 | + | 10.5789i | −1.09942 | + | 0.357223i | −0.801879 | − | 0.597487i | \(-0.796166\pi\) |
−0.297540 | + | 0.954709i | \(0.596166\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.6507 | − | 10.6443i | 0.494154 | − | 0.359024i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.3507 | − | 16.2388i | −0.753016 | − | 0.547098i | 0.143744 | − | 0.989615i | \(-0.454086\pi\) |
−0.896760 | + | 0.442517i | \(0.854086\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.2231 | − | 20.9527i | 0.512297 | − | 0.705116i | −0.472008 | − | 0.881594i | \(-0.656471\pi\) |
0.984305 | + | 0.176478i | \(0.0564706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.92555 | + | 18.2702i | 0.232800 | + | 0.614146i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.4009 | − | 5.32897i | −0.550688 | − | 0.178929i | 0.0204392 | − | 0.999791i | \(-0.493494\pi\) |
−0.571127 | + | 0.820862i | \(0.693494\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.89488 | − | 18.1426i | −0.197708 | − | 0.608482i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.58794 | − | 11.0425i | 0.120200 | − | 0.369939i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7.30213i | − | 0.244356i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.2543 | − | 14.0177i | −0.376191 | − | 0.468559i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.225446 | − | 0.310299i | −0.00752741 | − | 0.0103606i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36.0614 | 1.20271 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.8238 | 1.39335 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.14650 | + | 12.5891i | 0.304376 | + | 0.418938i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.2704 | + | 38.5582i | −0.840016 | + | 1.28172i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 57.0465i | 1.89420i | 0.320940 | + | 0.947099i | \(0.396001\pi\) | ||||
−0.320940 | + | 0.947099i | \(0.603999\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.14063 | + | 9.66587i | −0.104168 | + | 0.320597i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.13965 | − | 18.8959i | −0.203416 | − | 0.626049i | −0.999775 | − | 0.0212248i | \(-0.993243\pi\) |
0.796359 | − | 0.604824i | \(-0.206757\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.6099 | − | 8.97099i | −0.913754 | − | 0.296897i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.52055 | − | 1.65192i | −0.0833267 | − | 0.0546109i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.86859 | − | 3.94827i | 0.0947291 | − | 0.130383i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.6350 | − | 16.4453i | −0.746661 | − | 0.542481i | 0.148129 | − | 0.988968i | \(-0.452675\pi\) |
−0.894790 | + | 0.446487i | \(0.852675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.09972 | + | 3.70517i | −0.168042 | + | 0.122089i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.68244 | + | 0.546657i | −0.0553781 | + | 0.0179934i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.4844 | − | 8.73926i | −1.29824 | − | 0.287345i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.09487 | + | 0.355745i | −0.0359603 | + | 0.0116842i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.4273 | + | 8.30242i | −0.374918 | + | 0.272394i | −0.759247 | − | 0.650802i | \(-0.774433\pi\) |
0.384329 | + | 0.923196i | \(0.374433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.08611 | + | 3.69528i | 0.166691 | + | 0.121108i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.1893 | − | 30.5409i | 0.726444 | − | 0.999864i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.06943 | + | 22.2775i | −0.198492 | + | 0.728552i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.1949 | + | 11.1106i | 1.11710 | + | 0.362967i | 0.808659 | − | 0.588277i | \(-0.200194\pi\) |
0.308438 | + | 0.951244i | \(0.400194\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.1666 | − | 31.2897i | −0.331776 | − | 1.02110i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.25011 | − | 25.3912i | 0.268946 | − | 0.827730i | −0.721812 | − | 0.692089i | \(-0.756691\pi\) |
0.990758 | − | 0.135641i | \(-0.0433094\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 0.892508i | − | 0.0290640i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −38.4712 | + | 14.5830i | −1.25147 | + | 0.474385i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.1747 | + | 14.0042i | 0.330633 | + | 0.455077i | 0.941676 | − | 0.336520i | \(-0.109250\pi\) |
−0.611044 | + | 0.791597i | \(0.709250\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.61803 | 0.0849850 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.2693 | −1.04640 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.2610 | + | 19.6286i | 0.461959 | + | 0.635831i | 0.974913 | − | 0.222584i | \(-0.0714492\pi\) |
−0.512955 | + | 0.858416i | \(0.671449\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.8991 | − | 10.5979i | −1.25875 | − | 0.342941i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 17.4048i | − | 0.562617i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.90899 | − | 24.3414i | 0.255395 | − | 0.786024i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.91722 | + | 5.90061i | 0.0618460 | + | 0.190342i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.5453 | − | 4.07623i | −0.404268 | − | 0.131355i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.1621 | − | 0.730899i | 0.488087 | − | 0.0235285i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.2885 | − | 25.1720i | 0.588120 | − | 0.809477i | −0.406437 | − | 0.913679i | \(-0.633229\pi\) |
0.994556 | + | 0.104202i | \(0.0332288\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.6388 | + | 7.72952i | 0.341767 | + | 0.248308i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.0543 | + | 10.2111i | −0.451025 | + | 0.327689i | −0.790000 | − | 0.613106i | \(-0.789920\pi\) |
0.338975 | + | 0.940795i | \(0.389920\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.7205 | + | 5.43282i | −0.536034 | + | 0.174168i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.870467 | − | 2.00006i | −0.0278773 | − | 0.0640531i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.7936 | − | 13.2546i | 1.30510 | − | 0.424054i | 0.427749 | − | 0.903898i | \(-0.359307\pi\) |
0.877354 | + | 0.479844i | \(0.159307\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.1780 | + | 8.84784i | −0.389211 | + | 0.282778i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.35096 | − | 0.981527i | −0.0431327 | − | 0.0313377i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.0145 | + | 30.3003i | −0.702153 | + | 0.966431i | 0.297777 | + | 0.954635i | \(0.403755\pi\) |
−0.999930 | + | 0.0117954i | \(0.996245\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.9410 | − | 11.1928i | 0.444198 | − | 0.356632i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.2637 | − | 6.25914i | −0.613169 | − | 0.199231i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.880801 | + | 2.71083i | 0.0280078 | + | 0.0861993i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.17987 | + | 15.9420i | −0.164544 | + | 0.506415i | −0.999002 | − | 0.0446564i | \(-0.985781\pi\) |
0.834458 | + | 0.551071i | \(0.185781\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 13.1931i | − | 0.418669i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.560384 | − | 11.6249i | −0.0177654 | − | 0.368534i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.1845 | + | 48.4273i | 1.11430 | + | 1.53371i | 0.814917 | + | 0.579577i | \(0.196782\pi\) |
0.299388 | + | 0.954132i | \(0.403218\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 45.6367 | 1.44388 |
(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 | 400.2.y.c.369.2 | 8 | ||
4.3 | odd | 2 | 25.2.e.a.19.2 | yes | 8 | ||
12.11 | even | 2 | 225.2.m.a.19.1 | 8 | |||
20.3 | even | 4 | 125.2.d.b.26.2 | 16 | |||
20.7 | even | 4 | 125.2.d.b.26.3 | 16 | |||
20.19 | odd | 2 | 125.2.e.b.99.1 | 8 | |||
25.2 | odd | 20 | 10000.2.a.bj.1.3 | 8 | |||
25.4 | even | 10 | inner | 400.2.y.c.129.2 | 8 | ||
25.23 | odd | 20 | 10000.2.a.bj.1.6 | 8 | |||
100.3 | even | 20 | 125.2.d.b.101.2 | 16 | |||
100.11 | odd | 10 | 625.2.b.c.624.4 | 8 | |||
100.19 | odd | 10 | 625.2.e.a.249.2 | 8 | |||
100.23 | even | 20 | 625.2.a.f.1.4 | 8 | |||
100.27 | even | 20 | 625.2.a.f.1.5 | 8 | |||
100.31 | odd | 10 | 625.2.e.i.249.1 | 8 | |||
100.39 | odd | 10 | 625.2.b.c.624.5 | 8 | |||
100.47 | even | 20 | 125.2.d.b.101.3 | 16 | |||
100.59 | odd | 10 | 625.2.e.i.374.1 | 8 | |||
100.63 | even | 20 | 625.2.d.o.251.3 | 16 | |||
100.67 | even | 20 | 625.2.d.o.376.2 | 16 | |||
100.71 | odd | 10 | 125.2.e.b.24.1 | 8 | |||
100.79 | odd | 10 | 25.2.e.a.4.2 | ✓ | 8 | ||
100.83 | even | 20 | 625.2.d.o.376.3 | 16 | |||
100.87 | even | 20 | 625.2.d.o.251.2 | 16 | |||
100.91 | odd | 10 | 625.2.e.a.374.2 | 8 | |||
300.23 | odd | 20 | 5625.2.a.x.1.5 | 8 | |||
300.179 | even | 10 | 225.2.m.a.154.1 | 8 | |||
300.227 | odd | 20 | 5625.2.a.x.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.e.a.4.2 | ✓ | 8 | 100.79 | odd | 10 | ||
25.2.e.a.19.2 | yes | 8 | 4.3 | odd | 2 | ||
125.2.d.b.26.2 | 16 | 20.3 | even | 4 | |||
125.2.d.b.26.3 | 16 | 20.7 | even | 4 | |||
125.2.d.b.101.2 | 16 | 100.3 | even | 20 | |||
125.2.d.b.101.3 | 16 | 100.47 | even | 20 | |||
125.2.e.b.24.1 | 8 | 100.71 | odd | 10 | |||
125.2.e.b.99.1 | 8 | 20.19 | odd | 2 | |||
225.2.m.a.19.1 | 8 | 12.11 | even | 2 | |||
225.2.m.a.154.1 | 8 | 300.179 | even | 10 | |||
400.2.y.c.129.2 | 8 | 25.4 | even | 10 | inner | ||
400.2.y.c.369.2 | 8 | 1.1 | even | 1 | trivial | ||
625.2.a.f.1.4 | 8 | 100.23 | even | 20 | |||
625.2.a.f.1.5 | 8 | 100.27 | even | 20 | |||
625.2.b.c.624.4 | 8 | 100.11 | odd | 10 | |||
625.2.b.c.624.5 | 8 | 100.39 | odd | 10 | |||
625.2.d.o.251.2 | 16 | 100.87 | even | 20 | |||
625.2.d.o.251.3 | 16 | 100.63 | even | 20 | |||
625.2.d.o.376.2 | 16 | 100.67 | even | 20 | |||
625.2.d.o.376.3 | 16 | 100.83 | even | 20 | |||
625.2.e.a.249.2 | 8 | 100.19 | odd | 10 | |||
625.2.e.a.374.2 | 8 | 100.91 | odd | 10 | |||
625.2.e.i.249.1 | 8 | 100.31 | odd | 10 | |||
625.2.e.i.374.1 | 8 | 100.59 | odd | 10 | |||
5625.2.a.x.1.4 | 8 | 300.227 | odd | 20 | |||
5625.2.a.x.1.5 | 8 | 300.23 | odd | 20 | |||
10000.2.a.bj.1.3 | 8 | 25.2 | odd | 20 | |||
10000.2.a.bj.1.6 | 8 | 25.23 | odd | 20 |