Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,4,Mod(17,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.e (of order \(4\), 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: | \(3.77612224037\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.5 | ||
Root | \(1.97476 + 0.316760i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 64.17 |
Dual form | 64.4.e.a.49.5 |
$q$-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 \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(63\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 5.96513 | + | 5.96513i | 1.14799 | + | 1.14799i | 0.986947 | + | 0.161043i | \(0.0514857\pi\) |
0.161043 | + | 0.986947i | \(0.448514\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.67959 | − | 8.67959i | 0.776326 | − | 0.776326i | −0.202878 | − | 0.979204i | \(-0.565029\pi\) |
0.979204 | + | 0.202878i | \(0.0650295\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.63924i | 0.0885109i | 0.999020 | + | 0.0442554i | \(0.0140915\pi\) | ||||
−0.999020 | + | 0.0442554i | \(0.985908\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 44.1656i | 1.63576i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.2021 | + | 18.2021i | −0.498921 | + | 0.498921i | −0.911102 | − | 0.412181i | \(-0.864767\pi\) |
0.412181 | + | 0.911102i | \(0.364767\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.34700 | − | 9.34700i | −0.199415 | − | 0.199415i | 0.600334 | − | 0.799749i | \(-0.295034\pi\) |
−0.799749 | + | 0.600334i | \(0.795034\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 103.550 | 1.78243 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 53.6113 | 0.764862 | 0.382431 | − | 0.923984i | \(-0.375087\pi\) | ||||
0.382431 | + | 0.923984i | \(0.375087\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −70.9870 | − | 70.9870i | −0.857133 | − | 0.857133i | 0.133866 | − | 0.990999i | \(-0.457261\pi\) |
−0.990999 | + | 0.133866i | \(0.957261\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.77831 | + | 9.77831i | −0.101610 | + | 0.101610i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 25.1189i | − | 0.227724i | −0.993497 | − | 0.113862i | \(-0.963678\pi\) | ||
0.993497 | − | 0.113862i | \(-0.0363222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 25.6706i | − | 0.205365i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −102.395 | + | 102.395i | −0.729850 | + | 0.729850i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −181.094 | − | 181.094i | −1.15960 | − | 1.15960i | −0.984563 | − | 0.175033i | \(-0.943997\pi\) |
−0.175033 | − | 0.984563i | \(-0.556003\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −132.684 | −0.768733 | −0.384367 | − | 0.923180i | \(-0.625580\pi\) | ||||
−0.384367 | + | 0.923180i | \(0.625580\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −217.155 | −1.14551 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.2280 | + | 14.2280i | 0.0687133 | + | 0.0687133i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 174.872 | − | 174.872i | 0.776994 | − | 0.776994i | −0.202324 | − | 0.979319i | \(-0.564849\pi\) |
0.979319 | + | 0.202324i | \(0.0648495\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 111.512i | − | 0.457853i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 198.660i | 0.756720i | 0.925658 | + | 0.378360i | \(0.123512\pi\) | ||||
−0.925658 | + | 0.378360i | \(0.876488\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 285.717 | − | 285.717i | 1.01329 | − | 1.01329i | 0.0133770 | − | 0.999911i | \(-0.495742\pi\) |
0.999911 | − | 0.0133770i | \(-0.00425815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 383.339 | + | 383.339i | 1.26989 | + | 1.26989i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −78.3629 | −0.243200 | −0.121600 | − | 0.992579i | \(-0.538803\pi\) | ||||
−0.121600 | + | 0.992579i | \(0.538803\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 340.313 | 0.992166 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 319.799 | + | 319.799i | 0.878054 | + | 0.878054i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −525.776 | + | 525.776i | −1.36266 | + | 1.36266i | −0.492143 | + | 0.870515i | \(0.663786\pi\) |
−0.870515 | + | 0.492143i | \(0.836214\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 315.973i | 0.774650i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 846.894i | − | 1.96796i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −46.5301 | + | 46.5301i | −0.102673 | + | 0.102673i | −0.756577 | − | 0.653904i | \(-0.773130\pi\) |
0.653904 | + | 0.756577i | \(0.273130\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 193.318 | + | 193.318i | 0.405767 | + | 0.405767i | 0.880259 | − | 0.474493i | \(-0.157368\pi\) |
−0.474493 | + | 0.880259i | \(0.657368\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −72.3982 | −0.144783 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −162.256 | −0.309622 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −282.182 | − | 282.182i | −0.514538 | − | 0.514538i | 0.401375 | − | 0.915914i | \(-0.368532\pi\) |
−0.915914 | + | 0.401375i | \(0.868532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 149.838 | − | 149.838i | 0.261425 | − | 0.261425i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 727.536i | 1.21609i | 0.793901 | + | 0.608046i | \(0.208047\pi\) | ||||
−0.793901 | + | 0.608046i | \(0.791953\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 106.065i | 0.170054i | 0.996379 | + | 0.0850270i | \(0.0270977\pi\) | ||||
−0.996379 | + | 0.0850270i | \(0.972902\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 153.128 | − | 153.128i | 0.235757 | − | 0.235757i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −29.8376 | − | 29.8376i | −0.0441599 | − | 0.0441599i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58.9970 | 0.0840213 | 0.0420107 | − | 0.999117i | \(-0.486624\pi\) | ||||
0.0420107 | + | 0.999117i | \(0.486624\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −29.1298 | −0.0399586 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 410.156 | + | 410.156i | 0.542416 | + | 0.542416i | 0.924236 | − | 0.381821i | \(-0.124703\pi\) |
−0.381821 | + | 0.924236i | \(0.624703\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 465.324 | − | 465.324i | 0.593783 | − | 0.593783i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2160.50i | − | 2.66241i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 768.959i | 0.915837i | 0.888994 | + | 0.457918i | \(0.151405\pi\) | ||||
−0.888994 | + | 0.457918i | \(0.848595\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.3220 | − | 15.3220i | 0.0176504 | − | 0.0176504i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −791.477 | − | 791.477i | −0.882499 | − | 0.882499i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1232.28 | −1.33083 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −809.953 | −0.847817 | −0.423908 | − | 0.905705i | \(-0.639342\pi\) | ||||
−0.423908 | + | 0.905705i | \(0.639342\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −803.905 | − | 803.905i | −0.816116 | − | 0.816116i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −303.189 | + | 303.189i | −0.298698 | + | 0.298698i | −0.840504 | − | 0.541806i | \(-0.817741\pi\) |
0.541806 | + | 0.840504i | \(0.317741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 962.201i | 0.920471i | 0.887797 | + | 0.460235i | \(0.152235\pi\) | ||||
−0.887797 | + | 0.460235i | \(0.847765\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 169.743i | 0.157764i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −728.337 | + | 728.337i | −0.658046 | + | 0.658046i | −0.954918 | − | 0.296871i | \(-0.904057\pi\) |
0.296871 | + | 0.954918i | \(0.404057\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −593.258 | − | 593.258i | −0.521319 | − | 0.521319i | 0.396651 | − | 0.917970i | \(-0.370172\pi\) |
−0.917970 | + | 0.396651i | \(0.870172\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2086.27 | 1.78396 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 351.938 | 0.292987 | 0.146493 | − | 0.989212i | \(-0.453201\pi\) | ||||
0.146493 | + | 0.989212i | \(0.453201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −218.022 | − | 218.022i | −0.176788 | − | 0.176788i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 412.816 | − | 412.816i | 0.326195 | − | 0.326195i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 87.8821i | 0.0676986i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 668.370i | 0.502157i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1185.04 | + | 1185.04i | −0.868707 | + | 0.868707i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 862.139 | + | 862.139i | 0.616896 | + | 0.616896i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2365.81 | 1.65301 | 0.826504 | − | 0.562931i | \(-0.190326\pi\) | ||||
0.826504 | + | 0.562931i | \(0.190326\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3408.67 | 2.32649 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −403.454 | − | 403.454i | −0.269083 | − | 0.269083i | 0.559647 | − | 0.828731i | \(-0.310937\pi\) |
−0.828731 | + | 0.559647i | \(0.810937\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 116.365 | − | 116.365i | 0.0758656 | − | 0.0758656i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1777.50i | 1.13320i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 856.850i | − | 0.534348i | −0.963648 | − | 0.267174i | \(-0.913910\pi\) | ||
0.963648 | − | 0.267174i | \(-0.0860898\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1689.33 | − | 1689.33i | 1.03084 | − | 1.03084i | 0.0313345 | − | 0.999509i | \(-0.490024\pi\) |
0.999509 | − | 0.0313345i | \(-0.00997572\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −467.445 | − | 467.445i | −0.279191 | − | 0.279191i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 340.269 | 0.198984 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3143.64 | −1.80045 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2030.01 | + | 2030.01i | 1.13900 | + | 1.13900i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −32.2208 | + | 32.2208i | −0.0177156 | + | 0.0177156i | −0.715909 | − | 0.698193i | \(-0.753988\pi\) |
0.698193 | + | 0.715909i | \(0.253988\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1077.06i | − | 0.580460i | −0.956957 | − | 0.290230i | \(-0.906268\pi\) | ||
0.956957 | − | 0.290230i | \(-0.0937319\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2367.78i | 1.25113i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1151.64 | + | 1151.64i | −0.596788 | + | 0.596788i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1905.61 | + | 1905.61i | 0.968691 | + | 0.968691i | 0.999525 | − | 0.0308332i | \(-0.00981607\pi\) |
−0.0308332 | + | 0.999525i | \(0.509816\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6272.64 | −3.12863 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 41.1761 | 0.0201561 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −709.828 | − | 709.828i | −0.341092 | − | 0.341092i | 0.515686 | − | 0.856778i | \(-0.327537\pi\) |
−0.856778 | + | 0.515686i | \(0.827537\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1884.82 | + | 1884.82i | −0.889291 | + | 0.889291i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3460.66i | − | 1.60356i | −0.597623 | − | 0.801778i | \(-0.703888\pi\) | ||
0.597623 | − | 0.801778i | \(-0.296112\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2022.27i | − | 0.920467i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3135.18 | − | 3135.18i | 1.40207 | − | 1.40207i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1303.54 | − | 1303.54i | −0.572871 | − | 0.572871i | 0.360059 | − | 0.932930i | \(-0.382757\pi\) |
−0.932930 | + | 0.360059i | \(0.882757\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 42.0803 | 0.0181770 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −555.117 | −0.235735 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1082.35 | + | 1082.35i | 0.451947 | + | 0.451947i | 0.896000 | − | 0.444054i | \(-0.146460\pi\) |
−0.444054 | + | 0.896000i | \(0.646460\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2943.93 | − | 2943.93i | 1.20895 | − | 1.20895i | 0.237588 | − | 0.971366i | \(-0.423643\pi\) |
0.971366 | − | 0.237588i | \(-0.0763567\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2306.33i | 0.931633i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3035.64i | − | 1.20640i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −975.837 | + | 975.837i | −0.381606 | + | 0.381606i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −167.851 | − | 167.851i | −0.0645997 | − | 0.0645997i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 430.650 | 0.163145 | 0.0815726 | − | 0.996667i | \(-0.474006\pi\) | ||||
0.0815726 | + | 0.996667i | \(0.474006\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2266.98 | −0.845497 | −0.422749 | − | 0.906247i | \(-0.638935\pi\) | ||||
−0.422749 | + | 0.906247i | \(0.638935\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −967.881 | − | 967.881i | −0.355443 | − | 0.355443i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1039.41 | + | 1039.41i | −0.375913 | + | 0.375913i | −0.869625 | − | 0.493712i | \(-0.835640\pi\) |
0.493712 | + | 0.869625i | \(0.335640\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4989.44i | 1.77735i | 0.458540 | + | 0.888674i | \(0.348373\pi\) | ||||
−0.458540 | + | 0.888674i | \(0.651627\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 3366.51i | − | 1.18137i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 296.857 | − | 296.857i | 0.102637 | − | 0.102637i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1724.29 | + | 1724.29i | 0.587462 | + | 0.587462i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1109.39 | 0.372503 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2584.22 | 0.855283 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2651.50 | − | 2651.50i | −0.865103 | − | 0.865103i | 0.126823 | − | 0.991925i | \(-0.459522\pi\) |
−0.991925 | + | 0.126823i | \(0.959522\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4339.85 | + | 4339.85i | −1.39606 | + | 1.39606i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4959.80i | − | 1.57328i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 217.501i | − | 0.0680413i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −632.691 | + | 632.691i | −0.195220 | + | 0.195220i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −501.105 | − | 501.105i | −0.152525 | − | 0.152525i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3690.85 | −1.10833 | −0.554165 | − | 0.832407i | \(-0.686962\pi\) | ||||
−0.554165 | + | 0.832407i | \(0.686962\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1133.76 | 0.335928 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1710.42 | + | 1710.42i | 0.500108 | + | 0.500108i | 0.911471 | − | 0.411363i | \(-0.134947\pi\) |
−0.411363 | + | 0.911471i | \(0.634947\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −91.8012 | + | 91.8012i | −0.0264908 | + | 0.0264908i | −0.720228 | − | 0.693737i | \(-0.755963\pi\) |
0.693737 | + | 0.720228i | \(0.255963\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 355.971i | − | 0.101390i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4259.71i | 1.19769i | 0.800863 | + | 0.598847i | \(0.204374\pi\) | ||||
−0.800863 | + | 0.598847i | \(0.795626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −680.158 | + | 680.158i | −0.188803 | + | 0.188803i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 351.925 | + | 351.925i | 0.0964556 | + | 0.0964556i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5053.12 | 1.36761 | 0.683806 | − | 0.729664i | \(-0.260324\pi\) | ||||
0.683806 | + | 0.729664i | \(0.260324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 48.8379 | 0.0130536 | 0.00652681 | − | 0.999979i | \(-0.497922\pi\) | ||||
0.00652681 | + | 0.999979i | \(0.497922\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2590.91 | + | 2590.91i | 0.683978 | + | 0.683978i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2953.78 | − | 2953.78i | 0.770244 | − | 0.770244i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1327.03i | 0.341850i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4893.28i | 1.24538i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2604.76 | − | 2604.76i | 0.655025 | − | 0.655025i | −0.299174 | − | 0.954199i | \(-0.596711\pi\) |
0.954199 | + | 0.299174i | \(0.0967111\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 457.216 | + | 457.216i | 0.113616 | + | 0.113616i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5551.44 | 1.36331 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 739.054 | 0.179381 | 0.0896905 | − | 0.995970i | \(-0.471412\pi\) | ||||
0.0896905 | + | 0.995970i | \(0.471412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 286.658 | + | 286.658i | 0.0687724 | + | 0.0687724i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7998.12 | − | 7998.12i | 1.89682 | − | 1.89682i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2448.30i | 0.574025i | 0.957927 | + | 0.287012i | \(0.0926621\pi\) | ||||
−0.957927 | + | 0.287012i | \(0.907338\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9127.03i | 2.11573i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4586.94 | + | 4586.94i | −1.05137 | + | 1.05137i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −829.952 | − | 829.952i | −0.188116 | − | 0.188116i | 0.606765 | − | 0.794881i | \(-0.292467\pi\) |
−0.794881 | + | 0.606765i | \(0.792467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1404.85 | −0.314902 | −0.157451 | − | 0.987527i | \(-0.550328\pi\) | ||||
−0.157451 | + | 0.987527i | \(0.550328\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 182.796 | 0.0405249 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 467.257 | + | 467.257i | 0.102461 | + | 0.102461i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2245.69 | + | 2245.69i | −0.487112 | + | 0.487112i | −0.907394 | − | 0.420281i | \(-0.861931\pi\) |
0.420281 | + | 0.907394i | \(0.361931\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 5860.07i | − | 1.25747i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6045.97i | − | 1.28353i | −0.766900 | − | 0.641766i | \(-0.778202\pi\) | ||
0.766900 | − | 0.641766i | \(-0.221798\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2459.63 | + | 2459.63i | −0.516643 | + | 0.516643i | −0.916554 | − | 0.399911i | \(-0.869041\pi\) |
0.399911 | + | 0.916554i | \(0.369041\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7350.69 | − | 7350.69i | −1.52778 | − | 1.52778i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −325.653 | −0.0669780 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2038.82 | −0.414986 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4831.48 | − | 4831.48i | −0.973286 | − | 0.973286i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1852.49 | + | 1852.49i | −0.369364 | + | 0.369364i | −0.867245 | − | 0.497881i | \(-0.834112\pi\) |
0.497881 | + | 0.867245i | \(0.334112\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 807.725i | 0.159415i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3727.60i | − | 0.728275i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −234.787 | + | 234.787i | −0.0454116 | + | 0.0454116i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 468.359 | + | 468.359i | 0.0896870 | + | 0.0896870i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3617.13 | −0.685804 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3355.83 | 0.630015 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2107.35 | − | 2107.35i | −0.391768 | − | 0.391768i | 0.483549 | − | 0.875317i | \(-0.339347\pi\) |
−0.875317 | + | 0.483549i | \(0.839347\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5739.66 | + | 5739.66i | −1.05669 | + | 1.05669i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5294.90i | 0.965422i | 0.875780 | + | 0.482711i | \(0.160348\pi\) | ||||
−0.875780 | + | 0.482711i | \(0.839652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4005.87i | − | 0.723403i | −0.932294 | − | 0.361702i | \(-0.882196\pi\) | ||
0.932294 | − | 0.361702i | \(-0.117804\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −628.387 | + | 628.387i | −0.112399 | + | 0.112399i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 809.240 | + | 809.240i | 0.143380 | + | 0.143380i | 0.775153 | − | 0.631773i | \(-0.217673\pi\) |
−0.631773 | + | 0.775153i | \(0.717673\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6592.56 | 1.15709 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8689.25 | −1.51086 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3805.71 | − | 3805.71i | −0.655589 | − | 0.655589i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −239.943 | + | 239.943i | −0.0409527 | + | 0.0409527i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 7077.72i | − | 1.19694i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 128.456i | − | 0.0215259i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4229.66 | − | 4229.66i | 0.702366 | − | 0.702366i | −0.262552 | − | 0.964918i | \(-0.584564\pi\) |
0.964918 | + | 0.262552i | \(0.0845641\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7723.33 | + | 7723.33i | 1.27098 | + | 1.27098i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4898.46 | −0.798899 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10002.6 | 1.61684 | 0.808419 | − | 0.588607i | \(-0.200323\pi\) | ||||
0.808419 | + | 0.588607i | \(0.200323\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2099.36 | + | 2099.36i | 0.336346 | + | 0.336346i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2415.12 | − | 2415.12i | 0.383537 | − | 0.383537i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1120.12i | 0.176328i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 2601.06i | − | 0.405903i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6409.49 | − | 6409.49i | 0.991583 | − | 0.991583i | −0.00838198 | − | 0.999965i | \(-0.502668\pi\) |
0.999965 | + | 0.00838198i | \(0.00266810\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5503.23 | − | 5503.23i | −0.844071 | − | 0.844071i | 0.145314 | − | 0.989386i | \(-0.453581\pi\) |
−0.989386 | + | 0.145314i | \(0.953581\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1914.18 | 0.291086 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1411.35 | −0.212800 | −0.106400 | − | 0.994323i | \(-0.533932\pi\) | ||||
−0.106400 | + | 0.994323i | \(0.533932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6314.71 | + | 6314.71i | 0.944085 | + | 0.944085i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −524.228 | + | 524.228i | −0.0777174 | + | 0.0777174i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2160.73i | − | 0.317658i | −0.987306 | − | 0.158829i | \(-0.949228\pi\) | ||
0.987306 | − | 0.158829i | \(-0.0507718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3219.31i | 0.469355i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3986.92 | + | 3986.92i | −0.576471 | + | 0.576471i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 920.599 | + | 920.599i | 0.132017 | + | 0.132017i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10757.7 | −1.53010 | −0.765052 | − | 0.643969i | \(-0.777287\pi\) | ||||
−0.765052 | + | 0.643969i | \(0.777287\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8773.95 | −1.23782 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −861.875 | − | 861.875i | −0.120610 | − | 0.120610i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1406.99 | − | 1406.99i | 0.195312 | − | 0.195312i | −0.602675 | − | 0.797987i | \(-0.705898\pi\) |
0.797987 | + | 0.602675i | \(0.205898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10285.5i | 1.41638i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3385.37i | 0.462481i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1146.95 | − | 1146.95i | 0.155449 | − | 0.155449i | −0.625098 | − | 0.780547i | \(-0.714941\pi\) |
0.780547 | + | 0.625098i | \(0.214941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14112.4 | + | 14112.4i | 1.89764 | + | 1.89764i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9042.17 | −1.20635 | −0.603176 | − | 0.797608i | \(-0.706098\pi\) | ||||
−0.603176 | + | 0.797608i | \(0.706098\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −517.957 | −0.0685650 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12618.8 | + | 12618.8i | 1.65750 | + | 1.65750i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2575.34 | − | 2575.34i | 0.335668 | − | 0.335668i | −0.519066 | − | 0.854734i | \(-0.673720\pi\) |
0.854734 | + | 0.519066i | \(0.173720\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1346.66i | − | 0.174178i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4813.31i | − | 0.617810i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 512.070 | − | 512.070i | 0.0652279 | − | 0.0652279i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7121.46 | − | 7121.46i | −0.900292 | − | 0.900292i | 0.0951695 | − | 0.995461i | \(-0.469661\pi\) |
−0.995461 | + | 0.0951695i | \(0.969661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1388.27 | 0.174186 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3025.14 | −0.376729 | −0.188365 | − | 0.982099i | \(-0.560319\pi\) | ||||
−0.188365 | + | 0.982099i | \(0.560319\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1240.20 | + | 1240.20i | 0.153297 | + | 0.153297i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −252.835 | + | 252.835i | −0.0310209 | + | 0.0310209i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6366.06i | 0.775317i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9440.21i | − | 1.14129i | −0.821196 | − | 0.570646i | \(-0.806693\pi\) | ||
0.821196 | − | 0.570646i | \(-0.193307\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5111.22 | − | 5111.22i | 0.613426 | − | 0.613426i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −76.2743 | − | 76.2743i | −0.00908768 | − | 0.00908768i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7119.98 | 0.842183 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20154.2 | 2.36680 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3255.69 | + | 3255.69i | 0.379597 | + | 0.379597i | 0.870957 | − | 0.491360i | \(-0.163500\pi\) |
−0.491360 | + | 0.870957i | \(0.663500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9438.04 | + | 9438.04i | −1.09259 | + | 1.09259i | −0.0973423 | + | 0.995251i | \(0.531034\pi\) |
−0.995251 | + | 0.0973423i | \(0.968966\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3460.95i | − | 0.397818i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1376.23i | − | 0.157076i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −316.895 | + | 316.895i | −0.0359148 | + | 0.0359148i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2029.75 | + | 2029.75i | 0.228432 | + | 0.228432i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10617.7 | 1.18663 | 0.593314 | − | 0.804971i | \(-0.297819\pi\) | ||||
0.593314 | + | 0.804971i | \(0.297819\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 706.479 | 0.0784093 | 0.0392046 | − | 0.999231i | \(-0.487518\pi\) | ||||
0.0392046 | + | 0.999231i | \(0.487518\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18752.2 | − | 18752.2i | −2.06690 | − | 2.06690i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1783.12 | + | 1783.12i | −0.195190 | + | 0.195190i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13611.8i | − | 1.47985i | −0.672688 | − | 0.739926i | \(-0.734860\pi\) | ||
0.672688 | − | 0.739926i | \(-0.265140\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15030.1i | 1.62295i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3126.97 | + | 3126.97i | −0.335366 | + | 0.335366i | −0.854620 | − | 0.519254i | \(-0.826210\pi\) |
0.519254 | + | 0.854620i | \(0.326210\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6674.25 | + | 6674.25i | 0.710988 | + | 0.710988i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −384.403 | −0.0406748 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5231.76 | −0.549893 | −0.274947 | − | 0.961460i | \(-0.588660\pi\) | ||||
−0.274947 | + | 0.961460i | \(0.588660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3616.03 | − | 3616.03i | −0.377543 | − | 0.377543i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6424.78 | − | 6424.78i | 0.666363 | − | 0.666363i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 265.978i | − | 0.0274049i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6833.10i | − | 0.699429i | −0.936856 | − | 0.349715i | \(-0.886279\pi\) | ||
0.936856 | − | 0.349715i | \(-0.113721\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5489.54 | + | 5489.54i | −0.558235 | + | 0.558235i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5975.90 | − | 5975.90i | −0.603742 | − | 0.603742i | 0.337561 | − | 0.941304i | \(-0.390398\pi\) |
−0.941304 | + | 0.337561i | \(0.890398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4273.38 | 0.428943 | 0.214472 | − | 0.976730i | \(-0.431197\pi\) | ||||
0.214472 | + | 0.976730i | \(0.431197\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13739.4 | −1.37021 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12245.6 | − | 12245.6i | −1.21340 | − | 1.21340i | −0.969901 | − | 0.243500i | \(-0.921704\pi\) |
−0.243500 | − | 0.969901i | \(-0.578296\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 462.566 | − | 462.566i | 0.0455422 | − | 0.0455422i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22734.5i | 2.22410i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10401.3i | 1.01110i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1822.28 | + | 1822.28i | −0.176025 | + | 0.176025i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23221.2 | − | 23221.2i | −2.22898 | − | 2.22898i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4067.97 | 0.388038 | 0.194019 | − | 0.980998i | \(-0.437848\pi\) | ||||
0.194019 | + | 0.980998i | \(0.437848\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3269.06 | −0.309888 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 245.621 | + | 245.621i | 0.0231390 | + | 0.0231390i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7030.06 | + | 7030.06i | −0.658182 | + | 0.658182i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16174.3i | − | 1.50499i | −0.658600 | − | 0.752493i | \(-0.728851\pi\) | ||
0.658600 | − | 0.752493i | \(-0.271149\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 8468.44i | − | 0.783141i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13596.7 | + | 13596.7i | −1.24971 | + | 1.24971i | −0.293866 | + | 0.955847i | \(0.594942\pi\) |
−0.955847 | + | 0.293866i | \(0.905058\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9708.68 | − | 9708.68i | −0.886931 | − | 0.886931i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13955.1 | −1.26714 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1192.61 | −0.107637 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14646.7 | + | 14646.7i | 1.31398 | + | 1.31398i | 0.918453 | + | 0.395530i | \(0.129439\pi\) |
0.395530 | + | 0.918453i | \(0.370561\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20643.3 | − | 20643.3i | 1.84087 | − | 1.84087i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 9828.84i | − | 0.871265i | −0.900125 | − | 0.435632i | \(-0.856525\pi\) | ||
0.900125 | − | 0.435632i | \(-0.143475\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5263.12i | 0.463774i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12063.1 | − | 12063.1i | 1.05669 | − | 1.05669i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13456.1 | + | 13456.1i | 1.17177 | + | 1.17177i | 0.981787 | + | 0.189985i | \(0.0608439\pi\) |
0.189985 | + | 0.981787i | \(0.439156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −173.866 | −0.0150516 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14537.5 | 1.25116 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8351.51 | + | 8351.51i | 0.714585 | + | 0.714585i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1426.37 | − | 1426.37i | 0.121338 | − | 0.121338i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 15551.6i | − | 1.31530i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10607.1i | 0.891950i | 0.895045 | + | 0.445975i | \(0.147143\pi\) | ||||
−0.895045 | + | 0.445975i | \(0.852857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3903.15 | + | 3903.15i | −0.326334 | + | 0.326334i | −0.851191 | − | 0.524857i | \(-0.824119\pi\) |
0.524857 | + | 0.851191i | \(0.324119\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 251.015 | + | 251.015i | 0.0208670 | + | 0.0208670i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7113.36 | −0.587975 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11536.0 | 0.948142 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2055.03 | − | 2055.03i | −0.167949 | − | 0.167949i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1856.88 | − | 1856.88i | 0.150901 | − | 0.150901i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12643.3i | 1.02172i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12912.7i | 1.03766i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6194.39 | + | 6194.39i | −0.495012 | + | 0.495012i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9532.77 | + | 9532.77i | 0.757570 | + | 0.757570i | 0.975880 | − | 0.218309i | \(-0.0700541\pi\) |
−0.218309 | + | 0.975880i | \(0.570054\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35121.9 | 2.77573 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10298.5 | −0.809427 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1232.88 | + | 1232.88i | 0.0963693 | + | 0.0963693i | 0.753648 | − | 0.657278i | \(-0.228292\pi\) |
−0.657278 | + | 0.753648i | \(0.728292\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8537.99 | + | 8537.99i | −0.663739 | + | 0.663739i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25710.6i | 1.98786i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 96.7105i | 0.00743680i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18108.0 | − | 18108.0i | 1.38494 | − | 1.38494i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2889.57 | − | 2889.57i | −0.219812 | − | 0.219812i | 0.588607 | − | 0.808419i | \(-0.299676\pi\) |
−0.808419 | + | 0.588607i | \(0.799676\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5341.19 | −0.404129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11642.0 | −0.876159 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −70.0753 | − | 70.0753i | −0.00524569 | − | 0.00524569i | 0.704479 | − | 0.709725i | \(-0.251181\pi\) |
−0.709725 | + | 0.704479i | \(0.751181\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3054.68 | − | 3054.68i | 0.227453 | − | 0.227453i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 47.7509i | − | 0.00353677i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 8915.23i | − | 0.656847i | −0.944531 | − | 0.328423i | \(-0.893483\pi\) | ||
0.944531 | − | 0.328423i | \(-0.106517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4946.30 | + | 4946.30i | −0.362515 | + | 0.362515i | −0.864738 | − | 0.502223i | \(-0.832516\pi\) |
0.502223 | + | 0.864738i | \(0.332516\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2568.89 | + | 2568.89i | 0.187289 | + | 0.187289i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −644.818 | −0.0467665 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17911.5 | 1.29232 | 0.646159 | − | 0.763203i | \(-0.276374\pi\) | ||||
0.646159 | + | 0.763203i | \(0.276374\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13522.8 | − | 13522.8i | −0.970622 | − | 0.970622i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −672.347 | + | 672.347i | −0.0480097 | + | 0.0480097i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 19140.4i | − | 1.35972i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 7166.15i | − | 0.506468i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7940.26 | + | 7940.26i | −0.558312 | + | 0.558312i | −0.928827 | − | 0.370514i | \(-0.879181\pi\) |
0.370514 | + | 0.928827i | \(0.379181\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9418.83 | + | 9418.83i | 0.658907 | + | 0.658907i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12400.4 | −0.863088 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7006.26 | −0.485181 | −0.242591 | − | 0.970129i | \(-0.577997\pi\) | ||||
−0.242591 | + | 0.970129i | \(0.577997\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 762.780 | + | 762.780i | 0.0525562 | + | 0.0525562i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29762.7 | + | 29762.7i | −2.04038 | + | 2.04038i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8502.74i | 0.579987i | 0.957029 | + | 0.289994i | \(0.0936532\pi\) | ||||
−0.957029 | + | 0.289994i | \(0.906347\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 11936.2i | − | 0.810127i | −0.914289 | − | 0.405063i | \(-0.867249\pi\) | ||
0.914289 | − | 0.405063i | \(-0.132751\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12462.8 | − | 12462.8i | 0.841663 | − | 0.841663i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5801.18 | + | 5801.18i | 0.389837 | + | 0.389837i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3850.00 | 0.257441 | 0.128721 | − | 0.991681i | \(-0.458913\pi\) | ||||
0.128721 | + | 0.991681i | \(0.458913\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3541.58 | 0.235652 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 732.459 | + | 732.459i | 0.0484977 | + | 0.0484977i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6320.36 | + | 6320.36i | −0.416439 | + | 0.416439i | −0.883974 | − | 0.467536i | \(-0.845142\pi\) |
0.467536 | + | 0.883974i | \(0.345142\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20571.2i | 1.34880i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2585.09i | − | 0.168674i | −0.996437 | − | 0.0843370i | \(-0.973123\pi\) | ||
0.996437 | − | 0.0843370i | \(-0.0268772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7325.02 | + | 7325.02i | −0.475634 | + | 0.475634i | −0.903732 | − | 0.428098i | \(-0.859184\pi\) |
0.428098 | + | 0.903732i | \(0.359184\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2572.06 | + | 2572.06i | 0.166205 | + | 0.166205i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1260.51 | −0.0810615 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18174.8 | 1.16319 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15415.2 | + | 15415.2i | 0.981857 | + | 0.981857i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9375.13 | − | 9375.13i | 0.594294 | − | 0.594294i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14411.5i | − | 0.909210i | −0.890693 | − | 0.454605i | \(-0.849780\pi\) | ||
0.890693 | − | 0.454605i | \(-0.150220\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 31633.1i | − | 1.98626i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20534.3 | − | 20534.3i | 1.28327 | − | 1.28327i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3180.91 | − | 3180.91i | −0.197853 | − | 0.197853i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −32132.1 | −1.98924 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25724.0 | −1.58508 | −0.792542 | − | 0.609818i | \(-0.791243\pi\) | ||||
−0.792542 | + | 0.609818i | \(0.791243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7835.74 | + | 7835.74i | 0.480578 | + | 0.480578i | 0.905316 | − | 0.424738i | \(-0.139634\pi\) |
−0.424738 | + | 0.905316i | \(0.639634\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29585.9 | − | 29585.9i | 1.80611 | − | 1.80611i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1247.43i | 0.0757981i | 0.999282 | + | 0.0378991i | \(0.0120665\pi\) | ||||
−0.999282 | + | 0.0378991i | \(0.987933\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1693.89i | − | 0.102451i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1297.42 | − | 1297.42i | 0.0781107 | − | 0.0781107i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8302.21 | + | 8302.21i | 0.497535 | + | 0.497535i | 0.910670 | − | 0.413135i | \(-0.135566\pi\) |
−0.413135 | + | 0.910670i | \(0.635566\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7003.63 | −0.417793 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4684.42 | −0.278168 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1696.16 | − | 1696.16i | −0.100262 | − | 0.100262i | 0.655196 | − | 0.755459i | \(-0.272586\pi\) |
−0.755459 | + | 0.655196i | \(0.772586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8788.30 | + | 8788.30i | −0.517134 | + | 0.517134i | −0.916703 | − | 0.399569i | \(-0.869160\pi\) |
0.399569 | + | 0.916703i | \(0.369160\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 5978.32i | − | 0.350194i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2020.00i | − | 0.117793i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4548.88 | + | 4548.88i | −0.264068 | + | 0.264068i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22016.4 | − | 22016.4i | −1.27235 | − | 1.27235i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7037.56 | −0.404891 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23869.3 | −1.36716 | −0.683578 | − | 0.729878i | \(-0.739577\pi\) | ||||
−0.683578 | + | 0.729878i | \(0.739577\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2628.54 | + | 2628.54i | 0.149885 | + | 0.149885i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5663.30 | + | 5663.30i | −0.321504 | + | 0.321504i | −0.849344 | − | 0.527840i | \(-0.823002\pi\) |
0.527840 | + | 0.849344i | \(0.323002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1327.71i | − | 0.0750410i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20405.8i | 1.14824i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9152.80 | − | 9152.80i | 0.512770 | − | 0.512770i | −0.402604 | − | 0.915374i | \(-0.631895\pi\) |
0.915374 | + | 0.402604i | \(0.131895\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7437.11 | − | 7437.11i | −0.414828 | − | 0.414828i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1095.21 | −0.0608224 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9828.85 | 0.543468 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17057.9 | − | 17057.9i | −0.939091 | − | 0.939091i | 0.0591580 | − | 0.998249i | \(-0.481158\pi\) |
−0.998249 | + | 0.0591580i | \(0.981158\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1317.80 | − | 1317.80i | 0.0722351 | − | 0.0722351i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 29325.4i | − | 1.60054i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10650.4i | 0.578787i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25409.7 | + | 25409.7i | −1.37494 | + | 1.37494i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7720.44 | − | 7720.44i | −0.415973 | − | 0.415973i | 0.467840 | − | 0.883813i | \(-0.345032\pi\) |
−0.883813 | + | 0.467840i | \(0.845032\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24827.3 | −1.33198 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8114.47 | −0.433487 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −497.001 | − | 497.001i | −0.0264380 | − | 0.0264380i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4577.66 | − | 4577.66i | 0.242479 | − | 0.242479i | −0.575396 | − | 0.817875i | \(-0.695152\pi\) |
0.817875 | + | 0.575396i | \(0.195152\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2605.64i | 0.137439i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3332.88i | 0.175059i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2953.40 | − | 2953.40i | 0.154477 | − | 0.154477i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 30142.5 | + | 30142.5i | 1.57000 | + | 1.57000i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30210.0 | 1.56696 | 0.783479 | − | 0.621418i | \(-0.213443\pi\) | ||||
0.783479 | + | 0.621418i | \(0.213443\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1577.28 | −0.0814717 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 291.324 | + | 291.324i | 0.0149854 | + | 0.0149854i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4648.78 | + | 4648.78i | −0.238140 | + | 0.238140i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20721.3i | 1.05710i | 0.848903 | + | 0.528549i | \(0.177264\pi\) | ||||
−0.848903 | + | 0.528549i | \(0.822736\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 31696.7i | 1.61036i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15317.6 | − | 15317.6i | 0.775025 | − | 0.775025i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13879.8 | − | 13879.8i | −0.699404 | − | 0.699404i | 0.264878 | − | 0.964282i | \(-0.414668\pi\) |
−0.964282 | + | 0.264878i | \(0.914668\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35239.3 | 1.76847 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10272.6 | 0.513428 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8793.93 | − | 8793.93i | −0.437740 | − | 0.437740i | 0.453511 | − | 0.891251i | \(-0.350171\pi\) |
−0.891251 | + | 0.453511i | \(0.850171\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7915.92 | + | 7915.92i | −0.392441 | + | 0.392441i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7669.27i | 0.378678i | 0.981912 | + | 0.189339i | \(0.0606346\pi\) | ||||
−0.981912 | + | 0.189339i | \(0.939365\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 559.327i | 0.0275062i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18114.8 | + | 18114.8i | −0.887264 | + | 0.887264i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1193.92 | − | 1193.92i | −0.0582443 | − | 0.0582443i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26531.8 | 1.28916 | 0.644580 | − | 0.764537i | \(-0.277032\pi\) | ||||
0.644580 | + | 0.764537i | \(0.277032\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31075.5 | 1.50392 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9348.40 | − | 9348.40i | −0.450627 | − | 0.450627i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −79.4192 | + | 79.4192i | −0.00381313 | + | 0.00381313i | −0.709011 | − | 0.705198i | \(-0.750858\pi\) |
0.705198 | + | 0.709011i | \(0.250858\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5454.71i | 0.260861i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 36991.3i | − | 1.76207i | −0.473055 | − | 0.881033i | \(-0.656849\pi\) | ||
0.473055 | − | 0.881033i | \(-0.343151\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 972.494 | − | 972.494i | 0.0461424 | − | 0.0461424i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20551.3 | + | 20551.3i | 0.971288 | + | 0.971288i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 869.835 | 0.0409490 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26637.0 | 1.24910 | 0.624548 | − | 0.780987i | \(-0.285283\pi\) | ||||
0.624548 | + | 0.780987i | \(0.285283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4408.55 | + | 4408.55i | 0.205928 | + | 0.205928i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19743.6 | − | 19743.6i | 0.918667 | − | 0.918667i | −0.0782657 | − | 0.996933i | \(-0.524938\pi\) |
0.996933 | + | 0.0782657i | \(0.0249382\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3406.07i | 0.157871i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3419.91i | 0.157900i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14102.3 | − | 14102.3i | 0.648610 | − | 0.648610i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13242.6 | − | 13242.6i | −0.606734 | − | 0.606734i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 37086.2 | 1.69266 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33079.9 | 1.50404 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28878.1 | + | 28878.1i | 1.30800 | + | 1.30800i | 0.922860 | + | 0.385136i | \(0.125845\pi\) |
0.385136 | + | 0.922860i | \(0.374155\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14604.4 | + | 14604.4i | −0.658975 | + | 0.658975i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 576.912i | 0.0259325i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3613.88i | − | 0.161832i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −54444.0 | + | 54444.0i | −2.42884 | + | 2.42884i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16656.0 | − | 16656.0i | −0.740257 | − | 0.740257i | 0.232371 | − | 0.972627i | \(-0.425352\pi\) |
−0.972627 | + | 0.232371i | \(0.925352\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4201.14 | −0.186015 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33961.5 | −1.49809 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1930.60 | − | 1930.60i | −0.0848435 | − | 0.0848435i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 357.391 | − | 357.391i | 0.0156477 | − | 0.0156477i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9901.55i | − | 0.431910i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34940.4i | 1.51847i | 0.650819 | + | 0.759233i | \(0.274426\pi\) | ||||
−0.650819 | + | 0.759233i | \(0.725574\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15168.2 | − | 15168.2i | 0.656753 | − | 0.656753i | −0.297857 | − | 0.954610i | \(-0.596272\pi\) |
0.954610 | + | 0.297857i | \(0.0962719\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8380.10 | − | 8380.10i | −0.361504 | − | 0.361504i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12322.0 | −0.529597 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40564.3 | −1.73705 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 676.707 | + | 676.707i | 0.0288718 | + | 0.0288718i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8710.55 | − | 8710.55i | 0.370280 | − | 0.370280i | −0.497299 | − | 0.867579i | \(-0.665675\pi\) |
0.867579 | + | 0.497299i | \(0.165675\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24493.5i | 1.03741i | 0.854952 | + | 0.518707i | \(0.173586\pi\) | ||||
−0.854952 | + | 0.518707i | \(0.826414\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5574.50i | 0.235248i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26328.0 | + | 26328.0i | −1.10703 | + | 1.10703i | −0.113492 | + | 0.993539i | \(0.536204\pi\) |
−0.993539 | + | 0.113492i | \(0.963796\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9108.25 | + | 9108.25i | 0.381596 | + | 0.381596i | 0.871677 | − | 0.490081i | \(-0.163033\pi\) |
−0.490081 | + | 0.871677i | \(0.663033\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26791.6 | −1.11840 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18244.6 | 0.758870 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30037.1 | − | 30037.1i | −1.24488 | − | 1.24488i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13586.2 | − | 13586.2i | 0.561060 | − | 0.561060i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1394.89i | 0.0573982i | 0.999588 | + | 0.0286991i | \(0.00913646\pi\) | ||||
−0.999588 | + | 0.0286991i | \(0.990864\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41200.9i | 1.68932i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 36065.0 | − | 36065.0i | 1.47348 | − | 1.47348i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17552.4 | − | 17552.4i | −0.714583 | − | 0.714583i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1095.62 | −0.0444463 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29344.1 | −1.18620 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4392.60 | − | 4392.60i | −0.176941 | − | 0.176941i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15284.7 | − | 15284.7i | 0.613527 | − | 0.613527i | −0.330337 | − | 0.943863i | \(-0.607162\pi\) |
0.943863 | + | 0.330337i | \(0.107162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 54424.2i | − | 2.17692i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2273.70i | 0.0906277i | 0.998973 | + | 0.0453139i | \(0.0144288\pi\) | ||||
−0.998973 | + | 0.0453139i | \(0.985571\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21674.3 | − | 21674.3i | 0.860905 | − | 0.860905i | −0.130538 | − | 0.991443i | \(-0.541671\pi\) |
0.991443 | + | 0.130538i | \(0.0416706\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1942.56 | − | 1942.56i | −0.0768900 | − | 0.0768900i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23721.7 | −0.935686 | −0.467843 | − | 0.883812i | \(-0.654969\pi\) | ||||
−0.467843 | + | 0.883812i | \(0.654969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22628.5 | −0.889469 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12161.9 | − | 12161.9i | −0.476400 | − | 0.476400i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1073.87 | + | 1073.87i | −0.0419200 | + | 0.0419200i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5275.12i | 0.205213i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 35772.1i | − | 1.38683i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1413.26 | + | 1413.26i | −0.0546020 | + | 0.0546020i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22429.6 | + | 22429.6i | 0.863617 | + | 0.863617i | 0.991756 | − | 0.128139i | \(-0.0409004\pi\) |
−0.128139 | + | 0.991756i | \(0.540900\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22100.7 | −0.848054 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24603.0 | 0.940859 | 0.470429 | − | 0.882438i | \(-0.344099\pi\) | ||||
0.470429 | + | 0.882438i | \(0.344099\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23486.7 | + | 23486.7i | 0.895120 | + | 0.895120i | 0.995000 | − | 0.0998799i | \(-0.0318459\pi\) |
−0.0998799 | + | 0.995000i | \(0.531846\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4818.19 | + | 4818.19i | −0.183007 | + | 0.183007i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 39722.9i | − | 1.50368i | −0.659345 | − | 0.751841i | \(-0.729166\pi\) | ||
0.659345 | − | 0.751841i | \(-0.270834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3878.15i | 0.146309i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 530.222 | − | 530.222i | 0.0199362 | − | 0.0199362i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5562.75 | + | 5562.75i | 0.208455 | + | 0.208455i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18788.7 | 0.701716 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2801.07 | −0.104264 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24028.2 | + | 24028.2i | 0.891420 | + | 0.891420i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28187.5 | + | 28187.5i | −1.04225 | + | 1.04225i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5587.65i | 0.205920i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 51104.2i | − | 1.87708i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4565.44 | + | 4565.44i | −0.167136 | + | 0.167136i | −0.785719 | − | 0.618583i | \(-0.787707\pi\) |
0.618583 | + | 0.785719i | \(0.287707\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13390.5 | − | 13390.5i | −0.488599 | − | 0.488599i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2013.95 | 0.0732438 | 0.0366219 | − | 0.999329i | \(-0.488340\pi\) | ||||
0.0366219 | + | 0.999329i | \(0.488340\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14931.4 | −0.541245 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20018.0 | + | 20018.0i | 0.723251 | + | 0.723251i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 661.359 | − | 661.359i | 0.0238168 | − | 0.0238168i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37746.5i | 1.35489i | 0.735575 | + | 0.677443i | \(0.236912\pi\) | ||||
−0.735575 | + | 0.677443i | \(0.763088\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 25141.2i | − | 0.899492i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6800.28 | − | 6800.28i | 0.242507 | − | 0.242507i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4489.07 | − | 4489.07i | −0.159567 | − | 0.159567i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −42496.2 | −1.50567 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45643.5 | 1.61197 | 0.805983 | − | 0.591939i | \(-0.201637\pi\) | ||||
0.805983 | + | 0.591939i | \(0.201637\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24157.8 | − | 24157.8i | −0.850418 | − | 0.850418i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31584.8 | + | 31584.8i | −1.10829 | + | 1.10829i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16939.7i | 0.592501i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 47317.5i | − | 1.64973i | −0.565331 | − | 0.824864i | \(-0.691252\pi\) | ||
0.565331 | − | 0.824864i | \(-0.308748\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23895.6 | − | 23895.6i | 0.830460 | − | 0.830460i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15074.7 | + | 15074.7i | 0.522234 | + | 0.522234i | 0.918246 | − | 0.396012i | \(-0.129606\pi\) |
−0.396012 | + | 0.918246i | \(0.629606\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4990.14 | 0.172324 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2913.75 | −0.100301 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14567.7 | − | 14567.7i | −0.499880 | − | 0.499880i | 0.411521 | − | 0.911400i | \(-0.364998\pi\) |
−0.911400 | + | 0.411521i | \(0.864998\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 991.388 | − | 991.388i | 0.0339113 | − | 0.0339113i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9654.45i | 0.329198i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42987.2i | 1.46117i | 0.682824 | + | 0.730583i | \(0.260752\pi\) | ||||
−0.682824 | + | 0.730583i | \(0.739248\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3737.87 | − | 3737.87i | 0.126654 | − | 0.126654i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 39325.5 | + | 39325.5i | 1.32833 | + | 1.32833i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1404.59 | 0.0472956 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12186.0 | −0.409049 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −32167.4 | − | 32167.4i | −1.07641 | − | 1.07641i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19676.5 | + | 19676.5i | −0.656381 | + | 0.656381i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44030.7i | 1.46425i | 0.681170 | + | 0.732126i | \(0.261472\pi\) | ||||
−0.681170 | + | 0.732126i | \(0.738528\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 45403.1i | − | 1.50522i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35699.8 | + | 35699.8i | −1.17988 | + | 1.17988i | −0.200101 | + | 0.979775i | \(0.564127\pi\) |
−0.979775 | + | 0.200101i | \(0.935873\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2769.23 | + | 2769.23i | 0.0912409 | + | 0.0912409i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2862.58 | −0.0940267 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49515.3 | −1.62143 | −0.810714 | − | 0.585442i | \(-0.800921\pi\) | ||||
−0.810714 | + | 0.585442i | \(0.800921\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13996.6 | − | 13996.6i | −0.456930 | − | 0.456930i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26201.6 | − | 26201.6i | 0.852755 | − | 0.852755i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 40046.2i | − | 1.29936i | −0.760206 | − | 0.649682i | \(-0.774902\pi\) | ||
0.760206 | − | 0.649682i | \(-0.225098\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18043.3i | 0.583662i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 766.257 | − | 766.257i | 0.0247115 | − | 0.0247115i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7176.90 | − | 7176.90i | −0.230750 | − | 0.230750i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18673.2 | −0.598560 | −0.299280 | − | 0.954165i | \(-0.596746\pi\) | ||||
−0.299280 | + | 0.954165i | \(0.596746\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 50460.9 | 1.61262 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43306.3 | + | 43306.3i | 1.37980 | + | 1.37980i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21982.1 | − | 21982.1i | 0.698274 | − | 0.698274i | −0.265764 | − | 0.964038i | \(-0.585624\pi\) |
0.964038 | + | 0.265764i | \(0.0856243\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 35812.1i | 1.13418i |
(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 | 64.4.e.a.17.5 | 10 | ||
3.2 | odd | 2 | 576.4.k.a.145.1 | 10 | |||
4.3 | odd | 2 | 16.4.e.a.13.2 | yes | 10 | ||
8.3 | odd | 2 | 128.4.e.b.33.5 | 10 | |||
8.5 | even | 2 | 128.4.e.a.33.1 | 10 | |||
12.11 | even | 2 | 144.4.k.a.109.4 | 10 | |||
16.3 | odd | 4 | 128.4.e.b.97.5 | 10 | |||
16.5 | even | 4 | inner | 64.4.e.a.49.5 | 10 | ||
16.11 | odd | 4 | 16.4.e.a.5.2 | ✓ | 10 | ||
16.13 | even | 4 | 128.4.e.a.97.1 | 10 | |||
32.3 | odd | 8 | 1024.4.b.j.513.1 | 10 | |||
32.5 | even | 8 | 1024.4.a.m.1.1 | 10 | |||
32.11 | odd | 8 | 1024.4.a.n.1.1 | 10 | |||
32.13 | even | 8 | 1024.4.b.k.513.1 | 10 | |||
32.19 | odd | 8 | 1024.4.b.j.513.10 | 10 | |||
32.21 | even | 8 | 1024.4.a.m.1.10 | 10 | |||
32.27 | odd | 8 | 1024.4.a.n.1.10 | 10 | |||
32.29 | even | 8 | 1024.4.b.k.513.10 | 10 | |||
48.5 | odd | 4 | 576.4.k.a.433.1 | 10 | |||
48.11 | even | 4 | 144.4.k.a.37.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.2 | ✓ | 10 | 16.11 | odd | 4 | ||
16.4.e.a.13.2 | yes | 10 | 4.3 | odd | 2 | ||
64.4.e.a.17.5 | 10 | 1.1 | even | 1 | trivial | ||
64.4.e.a.49.5 | 10 | 16.5 | even | 4 | inner | ||
128.4.e.a.33.1 | 10 | 8.5 | even | 2 | |||
128.4.e.a.97.1 | 10 | 16.13 | even | 4 | |||
128.4.e.b.33.5 | 10 | 8.3 | odd | 2 | |||
128.4.e.b.97.5 | 10 | 16.3 | odd | 4 | |||
144.4.k.a.37.4 | 10 | 48.11 | even | 4 | |||
144.4.k.a.109.4 | 10 | 12.11 | even | 2 | |||
576.4.k.a.145.1 | 10 | 3.2 | odd | 2 | |||
576.4.k.a.433.1 | 10 | 48.5 | odd | 4 | |||
1024.4.a.m.1.1 | 10 | 32.5 | even | 8 | |||
1024.4.a.m.1.10 | 10 | 32.21 | even | 8 | |||
1024.4.a.n.1.1 | 10 | 32.11 | odd | 8 | |||
1024.4.a.n.1.10 | 10 | 32.27 | odd | 8 | |||
1024.4.b.j.513.1 | 10 | 32.3 | odd | 8 | |||
1024.4.b.j.513.10 | 10 | 32.19 | odd | 8 | |||
1024.4.b.k.513.1 | 10 | 32.13 | even | 8 | |||
1024.4.b.k.513.10 | 10 | 32.29 | even | 8 |