Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(33,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, 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("128.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.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: | \(7.55224448073\) |
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 | 33.1 | ||
Root | \(1.97476 + 0.316760i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.33 |
Dual form | 128.4.e.a.97.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | \(-0.948514\pi\) |
−0.161043 | − | 0.986947i | \(-0.551486\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.67959 | + | 8.67959i | −0.776326 | + | 0.776326i | −0.979204 | − | 0.202878i | \(-0.934971\pi\) |
0.202878 | + | 0.979204i | \(0.434971\pi\) | |||||||
\(6\) | 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 | −0.412181 | − | 0.911102i | \(-0.635233\pi\) |
0.911102 | + | 0.412181i | \(0.135233\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.34700 | + | 9.34700i | 0.199415 | + | 0.199415i | 0.799749 | − | 0.600334i | \(-0.204966\pi\) |
−0.600334 | + | 0.799749i | \(0.704966\pi\) | |||||||
\(14\) | 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 | 0.990999 | − | 0.133866i | \(-0.0427392\pi\) |
−0.133866 | + | 0.990999i | \(0.542739\pi\) | |||||||
\(20\) | 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 | \(0.0560031\pi\) |
0.175033 | + | 0.984563i | \(0.443997\pi\) | |||||||
\(30\) | 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 | −0.979319 | − | 0.202324i | \(-0.935151\pi\) |
0.202324 | + | 0.979319i | \(0.435151\pi\) | |||||||
\(38\) | 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 | \(0.504258\pi\) |
−0.999911 | + | 0.0133770i | \(0.995742\pi\) | |||||||
\(44\) | 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 | \(-0.336214\pi\) |
0.870515 | − | 0.492143i | \(-0.163786\pi\) | |||||||
\(54\) | 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 | −0.653904 | − | 0.756577i | \(-0.726870\pi\) |
0.756577 | + | 0.653904i | \(0.226870\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −193.318 | − | 193.318i | −0.405767 | − | 0.405767i | 0.474493 | − | 0.880259i | \(-0.342632\pi\) |
−0.880259 | + | 0.474493i | \(0.842632\pi\) | |||||||
\(62\) | 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 | 0.915914 | − | 0.401375i | \(-0.131468\pi\) |
−0.401375 | + | 0.915914i | \(0.631468\pi\) | |||||||
\(68\) | 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 | 0.381821 | − | 0.924236i | \(-0.375297\pi\) |
−0.924236 | + | 0.381821i | \(0.875297\pi\) | |||||||
\(84\) | 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 | −0.541806 | − | 0.840504i | \(-0.682259\pi\) |
0.840504 | + | 0.541806i | \(0.182259\pi\) | |||||||
\(102\) | 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 | −0.296871 | − | 0.954918i | \(-0.595943\pi\) |
0.954918 | + | 0.296871i | \(0.0959432\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 593.258 | + | 593.258i | 0.521319 | + | 0.521319i | 0.917970 | − | 0.396651i | \(-0.129828\pi\) |
−0.396651 | + | 0.917970i | \(0.629828\pi\) | |||||||
\(110\) | 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 | 0.828731 | − | 0.559647i | \(-0.189063\pi\) |
−0.559647 | + | 0.828731i | \(0.689063\pi\) | |||||||
\(132\) | 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 | \(0.509976\pi\) |
−0.999509 | + | 0.0313345i | \(0.990024\pi\) | |||||||
\(140\) | 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 | −0.698193 | − | 0.715909i | \(-0.746012\pi\) |
0.715909 | + | 0.698193i | \(0.246012\pi\) | |||||||
\(150\) | 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 | 0.0308332 | − | 0.999525i | \(-0.490184\pi\) |
−0.999525 | + | 0.0308332i | \(0.990184\pi\) | |||||||
\(158\) | 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 | 0.856778 | − | 0.515686i | \(-0.172463\pi\) |
−0.515686 | + | 0.856778i | \(0.672463\pi\) | |||||||
\(164\) | 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 | 0.932930 | − | 0.360059i | \(-0.117243\pi\) |
−0.360059 | + | 0.932930i | \(0.617243\pi\) | |||||||
\(174\) | 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 | 0.444054 | − | 0.896000i | \(-0.353540\pi\) |
−0.896000 | + | 0.444054i | \(0.853540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2943.93 | + | 2943.93i | −1.20895 | + | 1.20895i | −0.237588 | + | 0.971366i | \(0.576357\pi\) |
−0.971366 | + | 0.237588i | \(0.923643\pi\) | |||||||
\(182\) | 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 | −0.493712 | − | 0.869625i | \(-0.664360\pi\) |
0.869625 | + | 0.493712i | \(0.164360\pi\) | |||||||
\(198\) | 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 | 0.991925 | − | 0.126823i | \(-0.0404779\pi\) |
−0.126823 | + | 0.991925i | \(0.540478\pi\) | |||||||
\(212\) | 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 | 0.411363 | − | 0.911471i | \(-0.365053\pi\) |
−0.911471 | + | 0.411363i | \(0.865053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 91.8012 | − | 91.8012i | 0.0264908 | − | 0.0264908i | −0.693737 | − | 0.720228i | \(-0.744037\pi\) |
0.720228 | + | 0.693737i | \(0.244037\pi\) | |||||||
\(230\) | 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 | −0.954199 | − | 0.299174i | \(-0.903289\pi\) |
0.299174 | + | 0.954199i | \(0.403289\pi\) | |||||||
\(252\) | 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 | 0.794881 | − | 0.606765i | \(-0.207533\pi\) |
−0.606765 | + | 0.794881i | \(0.707533\pi\) | |||||||
\(270\) | 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 | −0.420281 | − | 0.907394i | \(-0.638069\pi\) |
0.907394 | + | 0.420281i | \(0.138069\pi\) | |||||||
\(278\) | 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 | −0.399911 | − | 0.916554i | \(-0.630959\pi\) |
0.916554 | + | 0.399911i | \(0.130959\pi\) | |||||||
\(284\) | 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 | −0.497881 | − | 0.867245i | \(-0.665888\pi\) |
0.867245 | + | 0.497881i | \(0.165888\pi\) | |||||||
\(294\) | 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 | 0.875317 | − | 0.483549i | \(-0.160653\pi\) |
−0.483549 | + | 0.875317i | \(0.660653\pi\) | |||||||
\(308\) | 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 | 0.631773 | − | 0.775153i | \(-0.282327\pi\) |
−0.775153 | + | 0.631773i | \(0.782327\pi\) | |||||||
\(318\) | 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 | −0.964918 | − | 0.262552i | \(-0.915436\pi\) |
0.262552 | + | 0.964918i | \(0.415436\pi\) | |||||||
\(332\) | 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 | −0.999965 | − | 0.00838198i | \(-0.997332\pi\) |
0.00838198 | + | 0.999965i | \(0.497332\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5503.23 | + | 5503.23i | 0.844071 | + | 0.844071i | 0.989386 | − | 0.145314i | \(-0.0464193\pi\) |
−0.145314 | + | 0.989386i | \(0.546419\pi\) | |||||||
\(350\) | 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 | −0.797987 | − | 0.602675i | \(-0.794102\pi\) |
0.602675 | + | 0.797987i | \(0.294102\pi\) | |||||||
\(374\) | 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 | −0.780547 | − | 0.625098i | \(-0.785059\pi\) |
0.625098 | + | 0.780547i | \(0.285059\pi\) | |||||||
\(380\) | 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 | −0.854734 | − | 0.519066i | \(-0.826280\pi\) |
0.519066 | + | 0.854734i | \(0.326280\pi\) | |||||||
\(390\) | 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 | 0.995461 | − | 0.0951695i | \(-0.0303393\pi\) |
−0.0951695 | + | 0.995461i | \(0.530339\pi\) | |||||||
\(398\) | 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 | 0.491360 | − | 0.870957i | \(-0.336500\pi\) |
−0.870957 | + | 0.491360i | \(0.836500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9438.04 | − | 9438.04i | 1.09259 | − | 1.09259i | 0.0973423 | − | 0.995251i | \(-0.468966\pi\) |
0.995251 | − | 0.0973423i | \(-0.0310342\pi\) | |||||||
\(422\) | 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 | −0.519254 | − | 0.854620i | \(-0.673790\pi\) |
0.854620 | + | 0.519254i | \(0.173790\pi\) | |||||||
\(444\) | 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 | 0.941304 | − | 0.337561i | \(-0.109602\pi\) |
−0.337561 | + | 0.941304i | \(0.609602\pi\) | |||||||
\(462\) | 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 | \(0.0782956\pi\) |
0.243500 | + | 0.969901i | \(0.421704\pi\) | |||||||
\(468\) | 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 | \(-0.405058\pi\) |
0.955847 | − | 0.293866i | \(-0.0949420\pi\) | |||||||
\(492\) | 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 | \(-0.870561\pi\) |
−0.395530 | − | 0.918453i | \(-0.629439\pi\) | |||||||
\(500\) | 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 | \(-0.939156\pi\) |
−0.189985 | − | 0.981787i | \(-0.560844\pi\) | |||||||
\(510\) | 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 | −0.524857 | − | 0.851191i | \(-0.675881\pi\) |
0.851191 | + | 0.524857i | \(0.175881\pi\) | |||||||
\(524\) | 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 | 0.218309 | − | 0.975880i | \(-0.429946\pi\) |
−0.975880 | + | 0.218309i | \(0.929946\pi\) | |||||||
\(542\) | 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 | 0.657278 | − | 0.753648i | \(-0.271708\pi\) |
−0.753648 | + | 0.657278i | \(0.771708\pi\) | |||||||
\(548\) | 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 | 0.808419 | − | 0.588607i | \(-0.200324\pi\) |
−0.588607 | + | 0.808419i | \(0.700324\pi\) | |||||||
\(558\) | 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 | 0.709725 | − | 0.704479i | \(-0.248819\pi\) |
−0.704479 | + | 0.709725i | \(0.748819\pi\) | |||||||
\(564\) | 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 | −0.502223 | − | 0.864738i | \(-0.667484\pi\) |
0.864738 | + | 0.502223i | \(0.167484\pi\) | |||||||
\(572\) | 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 | −0.370514 | − | 0.928827i | \(-0.620819\pi\) |
0.928827 | + | 0.370514i | \(0.120819\pi\) | |||||||
\(588\) | 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 | −0.467536 | − | 0.883974i | \(-0.654858\pi\) |
0.883974 | + | 0.467536i | \(0.154858\pi\) | |||||||
\(614\) | 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 | −0.428098 | − | 0.903732i | \(-0.640816\pi\) |
0.903732 | + | 0.428098i | \(0.140816\pi\) | |||||||
\(620\) | 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 | 0.424738 | − | 0.905316i | \(-0.360366\pi\) |
−0.905316 | + | 0.424738i | \(0.860366\pi\) | |||||||
\(644\) | 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 | 0.413135 | − | 0.910670i | \(-0.364434\pi\) |
−0.910670 | + | 0.413135i | \(0.864434\pi\) | |||||||
\(654\) | 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 | 0.755459 | − | 0.655196i | \(-0.227414\pi\) |
−0.655196 | + | 0.755459i | \(0.727414\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8788.30 | − | 8788.30i | 0.517134 | − | 0.517134i | −0.399569 | − | 0.916703i | \(-0.630840\pi\) |
0.916703 | + | 0.399569i | \(0.130840\pi\) | |||||||
\(662\) | 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 | −0.527840 | − | 0.849344i | \(-0.676998\pi\) |
0.849344 | + | 0.527840i | \(0.176998\pi\) | |||||||
\(678\) | 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 | −0.915374 | − | 0.402604i | \(-0.868105\pi\) |
0.402604 | + | 0.915374i | \(0.368105\pi\) | |||||||
\(684\) | 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 | 0.998249 | − | 0.0591580i | \(-0.0188416\pi\) |
−0.0591580 | + | 0.998249i | \(0.518842\pi\) | |||||||
\(692\) | 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 | 0.883813 | − | 0.467840i | \(-0.154968\pi\) |
−0.467840 | + | 0.883813i | \(0.654968\pi\) | |||||||
\(702\) | 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 | −0.817875 | − | 0.575396i | \(-0.804848\pi\) |
0.575396 | + | 0.817875i | \(0.304848\pi\) | |||||||
\(710\) | 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 | 0.964282 | − | 0.264878i | \(-0.0853316\pi\) |
−0.264878 | + | 0.964282i | \(0.585332\pi\) | |||||||
\(734\) | 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 | 0.891251 | − | 0.453511i | \(-0.149829\pi\) |
−0.453511 | + | 0.891251i | \(0.649829\pi\) | |||||||
\(740\) | 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 | −0.705198 | − | 0.709011i | \(-0.749142\pi\) |
0.709011 | + | 0.705198i | \(0.249142\pi\) | |||||||
\(758\) | 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 | −0.996933 | − | 0.0782657i | \(-0.975062\pi\) |
0.0782657 | + | 0.996933i | \(0.475062\pi\) | |||||||
\(774\) | 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 | \(-0.874155\pi\) |
−0.385136 | − | 0.922860i | \(-0.625845\pi\) | |||||||
\(788\) | 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 | 0.972627 | − | 0.232371i | \(-0.0746483\pi\) |
−0.232371 | + | 0.972627i | \(0.574648\pi\) | |||||||
\(798\) | 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 | −0.954610 | − | 0.297857i | \(-0.903728\pi\) |
0.297857 | + | 0.954610i | \(0.403728\pi\) | |||||||
\(812\) | 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 | −0.867579 | − | 0.497299i | \(-0.834325\pi\) |
0.497299 | + | 0.867579i | \(0.334325\pi\) | |||||||
\(822\) | 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 | \(-0.463796\pi\) |
0.993539 | − | 0.113492i | \(-0.0362037\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9108.25 | − | 9108.25i | −0.381596 | − | 0.381596i | 0.490081 | − | 0.871677i | \(-0.336967\pi\) |
−0.871677 | + | 0.490081i | \(0.836967\pi\) | |||||||
\(830\) | 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 | −0.943863 | − | 0.330337i | \(-0.892838\pi\) |
0.330337 | + | 0.943863i | \(0.392838\pi\) | |||||||
\(854\) | 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 | −0.991443 | − | 0.130538i | \(-0.958329\pi\) |
0.130538 | + | 0.991443i | \(0.458329\pi\) | |||||||
\(860\) | 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 | 0.128139 | − | 0.991756i | \(-0.459100\pi\) |
−0.991756 | + | 0.128139i | \(0.959100\pi\) | |||||||
\(878\) | 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 | 0.0998799 | − | 0.995000i | \(-0.468154\pi\) |
−0.995000 | + | 0.0998799i | \(0.968154\pi\) | |||||||
\(884\) | 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 | −0.618583 | − | 0.785719i | \(-0.712293\pi\) |
0.785719 | + | 0.618583i | \(0.212293\pi\) | |||||||
\(908\) | 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 | 0.396012 | − | 0.918246i | \(-0.370394\pi\) |
−0.918246 | + | 0.396012i | \(0.870394\pi\) | |||||||
\(942\) | 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 | 0.911400 | − | 0.411521i | \(-0.135002\pi\) |
−0.411521 | + | 0.911400i | \(0.635002\pi\) | |||||||
\(948\) | 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 | \(-0.435873\pi\) |
0.979775 | − | 0.200101i | \(-0.0641270\pi\) | |||||||
\(972\) | 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 | −0.964038 | − | 0.265764i | \(-0.914376\pi\) |
0.265764 | + | 0.964038i | \(0.414376\pi\) | |||||||
\(998\) | 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 | 128.4.e.a.33.1 | 10 | ||
4.3 | odd | 2 | 128.4.e.b.33.5 | 10 | |||
8.3 | odd | 2 | 16.4.e.a.13.2 | yes | 10 | ||
8.5 | even | 2 | 64.4.e.a.17.5 | 10 | |||
16.3 | odd | 4 | 16.4.e.a.5.2 | ✓ | 10 | ||
16.5 | even | 4 | inner | 128.4.e.a.97.1 | 10 | ||
16.11 | odd | 4 | 128.4.e.b.97.5 | 10 | |||
16.13 | even | 4 | 64.4.e.a.49.5 | 10 | |||
24.5 | odd | 2 | 576.4.k.a.145.1 | 10 | |||
24.11 | even | 2 | 144.4.k.a.109.4 | 10 | |||
32.3 | odd | 8 | 1024.4.b.j.513.10 | 10 | |||
32.5 | even | 8 | 1024.4.a.m.1.10 | 10 | |||
32.11 | odd | 8 | 1024.4.a.n.1.10 | 10 | |||
32.13 | even | 8 | 1024.4.b.k.513.10 | 10 | |||
32.19 | odd | 8 | 1024.4.b.j.513.1 | 10 | |||
32.21 | even | 8 | 1024.4.a.m.1.1 | 10 | |||
32.27 | odd | 8 | 1024.4.a.n.1.1 | 10 | |||
32.29 | even | 8 | 1024.4.b.k.513.1 | 10 | |||
48.29 | odd | 4 | 576.4.k.a.433.1 | 10 | |||
48.35 | 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 | 16.3 | odd | 4 | ||
16.4.e.a.13.2 | yes | 10 | 8.3 | odd | 2 | ||
64.4.e.a.17.5 | 10 | 8.5 | even | 2 | |||
64.4.e.a.49.5 | 10 | 16.13 | even | 4 | |||
128.4.e.a.33.1 | 10 | 1.1 | even | 1 | trivial | ||
128.4.e.a.97.1 | 10 | 16.5 | even | 4 | inner | ||
128.4.e.b.33.5 | 10 | 4.3 | odd | 2 | |||
128.4.e.b.97.5 | 10 | 16.11 | odd | 4 | |||
144.4.k.a.37.4 | 10 | 48.35 | even | 4 | |||
144.4.k.a.109.4 | 10 | 24.11 | even | 2 | |||
576.4.k.a.145.1 | 10 | 24.5 | odd | 2 | |||
576.4.k.a.433.1 | 10 | 48.29 | odd | 4 | |||
1024.4.a.m.1.1 | 10 | 32.21 | even | 8 | |||
1024.4.a.m.1.10 | 10 | 32.5 | even | 8 | |||
1024.4.a.n.1.1 | 10 | 32.27 | odd | 8 | |||
1024.4.a.n.1.10 | 10 | 32.11 | odd | 8 | |||
1024.4.b.j.513.1 | 10 | 32.19 | odd | 8 | |||
1024.4.b.j.513.10 | 10 | 32.3 | odd | 8 | |||
1024.4.b.k.513.1 | 10 | 32.29 | even | 8 | |||
1024.4.b.k.513.10 | 10 | 32.13 | even | 8 |