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 | 97.4 | ||
Root | \(0.932438 + 1.76934i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.97 |
Dual form | 128.4.e.a.33.4 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.98356 | − | 1.98356i | 0.381737 | − | 0.381737i | −0.489991 | − | 0.871728i | \(-0.663000\pi\) |
0.871728 | + | 0.489991i | \(0.163000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.596848 | + | 0.596848i | 0.0533837 | + | 0.0533837i | 0.733295 | − | 0.679911i | \(-0.237982\pi\) |
−0.679911 | + | 0.733295i | \(0.737982\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 29.0828i | 1.57033i | 0.619289 | + | 0.785163i | \(0.287421\pi\) | ||||
−0.619289 | + | 0.785163i | \(0.712579\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 19.1310i | 0.708554i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.1291 | + | 12.1291i | 0.332461 | + | 0.332461i | 0.853520 | − | 0.521059i | \(-0.174463\pi\) |
−0.521059 | + | 0.853520i | \(0.674463\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 48.5658 | − | 48.5658i | 1.03613 | − | 1.03613i | 0.0368113 | − | 0.999322i | \(-0.488280\pi\) |
0.999322 | − | 0.0368113i | \(-0.0117200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.36777 | 0.0407570 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 86.7193 | 1.23721 | 0.618604 | − | 0.785703i | \(-0.287699\pi\) | ||||
0.618604 | + | 0.785703i | \(0.287699\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −54.8442 | + | 54.8442i | −0.662217 | + | 0.662217i | −0.955902 | − | 0.293685i | \(-0.905118\pi\) |
0.293685 | + | 0.955902i | \(0.405118\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 57.6876 | + | 57.6876i | 0.599451 | + | 0.599451i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 70.2145i | 0.636554i | 0.947998 | + | 0.318277i | \(0.103104\pi\) | ||||
−0.947998 | + | 0.318277i | \(0.896896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 124.288i | − | 0.994300i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 91.5036 | + | 91.5036i | 0.652218 | + | 0.652218i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −63.4021 | + | 63.4021i | −0.405982 | + | 0.405982i | −0.880335 | − | 0.474353i | \(-0.842682\pi\) |
0.474353 | + | 0.880335i | \(0.342682\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.86868 | 0.0513826 | 0.0256913 | − | 0.999670i | \(-0.491821\pi\) | ||||
0.0256913 | + | 0.999670i | \(0.491821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 48.1178 | 0.253825 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −17.3580 | + | 17.3580i | −0.0838298 | + | 0.0838298i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 21.7145 | + | 21.7145i | 0.0964820 | + | 0.0964820i | 0.753700 | − | 0.657218i | \(-0.228267\pi\) |
−0.657218 | + | 0.753700i | \(0.728267\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 192.667i | − | 0.791060i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 153.274i | 0.583840i | 0.956443 | + | 0.291920i | \(0.0942941\pi\) | ||||
−0.956443 | + | 0.291920i | \(0.905706\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −120.951 | − | 120.951i | −0.428949 | − | 0.428949i | 0.459322 | − | 0.888270i | \(-0.348093\pi\) |
−0.888270 | + | 0.459322i | \(0.848093\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.4183 | + | 11.4183i | −0.0378253 | + | 0.0378253i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 99.9792 | 0.310286 | 0.155143 | − | 0.987892i | \(-0.450416\pi\) | ||||
0.155143 | + | 0.987892i | \(0.450416\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −502.812 | −1.46592 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 172.013 | − | 172.013i | 0.472287 | − | 0.472287i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −389.132 | − | 389.132i | −1.00852 | − | 1.00852i | −0.999963 | − | 0.00855213i | \(-0.997278\pi\) |
−0.00855213 | − | 0.999963i | \(-0.502722\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.4785i | 0.0354960i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 217.574i | 0.505585i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −324.819 | − | 324.819i | −0.716744 | − | 0.716744i | 0.251193 | − | 0.967937i | \(-0.419177\pi\) |
−0.967937 | + | 0.251193i | \(0.919177\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.339194 | − | 0.339194i | 0.000711957 | − | 0.000711957i | −0.706751 | − | 0.707463i | \(-0.749840\pi\) |
0.707463 | + | 0.706751i | \(0.249840\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −556.383 | −1.11266 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 57.9728 | 0.110625 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 565.288 | − | 565.288i | 1.03076 | − | 1.03076i | 0.0312478 | − | 0.999512i | \(-0.490052\pi\) |
0.999512 | − | 0.0312478i | \(-0.00994810\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 139.275 | + | 139.275i | 0.242996 | + | 0.242996i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 419.500i | − | 0.701205i | −0.936524 | − | 0.350602i | \(-0.885977\pi\) | ||
0.936524 | − | 0.350602i | \(-0.114023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 374.833i | − | 0.600971i | −0.953786 | − | 0.300485i | \(-0.902851\pi\) | ||
0.953786 | − | 0.300485i | \(-0.0971487\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −246.532 | − | 246.532i | −0.379561 | − | 0.379561i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −352.750 | + | 352.750i | −0.522072 | + | 0.522072i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 705.750 | 1.00510 | 0.502551 | − | 0.864547i | \(-0.332395\pi\) | ||||
0.502551 | + | 0.864547i | \(0.332395\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −153.530 | −0.210604 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −947.092 | + | 947.092i | −1.25249 | + | 1.25249i | −0.297893 | + | 0.954599i | \(0.596284\pi\) |
−0.954599 | + | 0.297893i | \(0.903716\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 51.7582 | + | 51.7582i | 0.0660467 | + | 0.0660467i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 251.524i | 0.309956i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.72918i | 0.00563249i | 0.999996 | + | 0.00281625i | \(0.000896440\pi\) | ||||
−0.999996 | + | 0.00281625i | \(0.999104\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1412.43 | + | 1412.43i | 1.62707 | + | 1.62707i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.5916 | − | 17.5916i | 0.0196146 | − | 0.0196146i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −65.4673 | −0.0707032 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 379.542 | 0.397285 | 0.198643 | − | 0.980072i | \(-0.436347\pi\) | ||||
0.198643 | + | 0.980072i | \(0.436347\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −232.042 | + | 232.042i | −0.235567 | + | 0.235567i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 391.005 | + | 391.005i | 0.385212 | + | 0.385212i | 0.872976 | − | 0.487764i | \(-0.162187\pi\) |
−0.487764 | + | 0.872976i | \(0.662187\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 307.935i | − | 0.294580i | −0.989093 | − | 0.147290i | \(-0.952945\pi\) | ||
0.989093 | − | 0.147290i | \(-0.0470551\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 68.8615i | 0.0640018i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −601.607 | − | 601.607i | −0.543548 | − | 0.543548i | 0.381019 | − | 0.924567i | \(-0.375573\pi\) |
−0.924567 | + | 0.381019i | \(0.875573\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 948.890 | − | 948.890i | 0.833827 | − | 0.833827i | −0.154211 | − | 0.988038i | \(-0.549283\pi\) |
0.988038 | + | 0.154211i | \(0.0492835\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 86.1439 | 0.0736614 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1824.02 | 1.51849 | 0.759244 | − | 0.650807i | \(-0.225569\pi\) | ||||
0.759244 | + | 0.650807i | \(0.225569\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −41.9074 | + | 41.9074i | −0.0339816 | + | 0.0339816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 929.111 | + | 929.111i | 0.734157 | + | 0.734157i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2522.04i | 1.94282i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1036.77i | − | 0.778939i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 304.029 | + | 304.029i | 0.222873 | + | 0.222873i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 148.787 | − | 148.787i | 0.106463 | − | 0.106463i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −988.748 | −0.690844 | −0.345422 | − | 0.938447i | \(-0.612264\pi\) | ||||
−0.345422 | + | 0.938447i | \(0.612264\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −479.826 | −0.327491 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 793.572 | − | 793.572i | 0.529273 | − | 0.529273i | −0.391083 | − | 0.920356i | \(-0.627899\pi\) |
0.920356 | + | 0.391083i | \(0.127899\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1595.03 | − | 1595.03i | −1.03990 | − | 1.03990i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 109.227i | 0.0696356i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1595.30i | 0.994856i | 0.867505 | + | 0.497428i | \(0.165722\pi\) | ||||
−0.867505 | + | 0.497428i | \(0.834278\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −277.696 | − | 277.696i | −0.169452 | − | 0.169452i | 0.617286 | − | 0.786738i | \(-0.288232\pi\) |
−0.786738 | + | 0.617286i | \(0.788232\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 198.315 | − | 198.315i | 0.118448 | − | 0.118448i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1178.12 | 0.688948 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −75.6828 | −0.0433456 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −997.359 | + | 997.359i | −0.559597 | + | 0.559597i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 593.272 | + | 593.272i | 0.326193 | + | 0.326193i | 0.851137 | − | 0.524944i | \(-0.175914\pi\) |
−0.524944 | + | 0.851137i | \(0.675914\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 160.655i | − | 0.0865821i | −0.999063 | − | 0.0432911i | \(-0.986216\pi\) | ||
0.999063 | − | 0.0432911i | \(-0.0137843\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1659.02i | 0.876629i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.29325 | + | 5.29325i | 0.00274299 | + | 0.00274299i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 705.762 | − | 705.762i | 0.358764 | − | 0.358764i | −0.504593 | − | 0.863357i | \(-0.668358\pi\) |
0.863357 | + | 0.504593i | \(0.168358\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1543.73 | −0.769975 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2042.04 | −0.999598 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1872.64 | − | 1872.64i | 0.899855 | − | 0.899855i | −0.0955676 | − | 0.995423i | \(-0.530467\pi\) |
0.995423 | + | 0.0955676i | \(0.0304666\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 28.7190 | + | 28.7190i | 0.0135501 | + | 0.0135501i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3852.19i | − | 1.78498i | −0.451066 | − | 0.892490i | \(-0.648956\pi\) | ||
0.451066 | − | 0.892490i | \(-0.351044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2520.28i | − | 1.14715i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1049.22 | − | 1049.22i | −0.469217 | − | 0.469217i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2625.61 | + | 2625.61i | −1.15388 | + | 1.15388i | −0.168112 | + | 0.985768i | \(0.553767\pi\) |
−0.985768 | + | 0.168112i | \(0.946233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3614.64 | 1.56138 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1288.60 | −0.547215 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1236.73 | + | 1236.73i | −0.516413 | + | 0.516413i | −0.916484 | − | 0.400071i | \(-0.868985\pi\) |
0.400071 | + | 0.916484i | \(0.368985\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1574.90 | − | 1574.90i | −0.646748 | − | 0.646748i | 0.305458 | − | 0.952206i | \(-0.401191\pi\) |
−0.952206 | + | 0.305458i | \(0.901191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.34563i | − | 0.000543560i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.9204i | 0.0103011i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1051.83 | + | 1051.83i | 0.411323 | + | 0.411323i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2661.19 | + | 2661.19i | −1.02419 | + | 1.02419i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3585.92 | −1.35847 | −0.679236 | − | 0.733920i | \(-0.737689\pi\) | ||||
−0.679236 | + | 0.733920i | \(0.737689\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 523.601 | 0.195283 | 0.0976415 | − | 0.995222i | \(-0.468870\pi\) | ||||
0.0976415 | + | 0.995222i | \(0.468870\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 114.993 | − | 114.993i | 0.0422297 | − | 0.0422297i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1125.64 | + | 1125.64i | 0.407098 | + | 0.407098i | 0.880725 | − | 0.473627i | \(-0.157056\pi\) |
−0.473627 | + | 0.880725i | \(0.657056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2312.48i | − | 0.823757i | −0.911239 | − | 0.411878i | \(-0.864873\pi\) | ||
0.911239 | − | 0.411878i | \(-0.135127\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2242.57i | − | 0.786957i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1843.91 | − | 1843.91i | −0.637524 | − | 0.637524i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −91.4815 | + | 91.4815i | −0.0311675 | + | 0.0311675i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1343.27 | −0.451033 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1330.43 | −0.440323 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1418.59 | − | 1418.59i | 0.462842 | − | 0.462842i | −0.436744 | − | 0.899586i | \(-0.643868\pi\) |
0.899586 | + | 0.436744i | \(0.143868\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −832.105 | − | 832.105i | −0.267675 | − | 0.267675i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 144.378i | − | 0.0457977i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 257.926i | 0.0806875i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −743.504 | − | 743.504i | −0.229413 | − | 0.229413i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4211.60 | − | 4211.60i | 1.28191 | − | 1.28191i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4315.08 | 1.29578 | 0.647890 | − | 0.761734i | \(-0.275651\pi\) | ||||
0.647890 | + | 0.761734i | \(0.275651\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2377.74 | 0.704516 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 701.203 | − | 701.203i | 0.205024 | − | 0.205024i | −0.597124 | − | 0.802149i | \(-0.703690\pi\) |
0.802149 | + | 0.597124i | \(0.203690\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 663.351 | + | 663.351i | 0.191421 | + | 0.191421i | 0.796310 | − | 0.604889i | \(-0.206782\pi\) |
−0.604889 | + | 0.796310i | \(0.706782\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1399.40i | 0.398588i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3490.15i | 0.981318i | 0.871352 | + | 0.490659i | \(0.163244\pi\) | ||||
−0.871352 | + | 0.490659i | \(0.836756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 59.6724 | + | 59.6724i | 0.0165642 | + | 0.0165642i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1399.90 | − | 1399.90i | 0.383684 | − | 0.383684i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2950.43 | −0.798525 | −0.399263 | − | 0.916837i | \(-0.630734\pi\) | ||||
−0.399263 | + | 0.916837i | \(0.630734\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1128.96 | −0.301755 | −0.150877 | − | 0.988552i | \(-0.548210\pi\) | ||||
−0.150877 | + | 0.988552i | \(0.548210\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2775.13 | + | 2775.13i | −0.732613 | + | 0.732613i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −300.102 | − | 300.102i | −0.0782565 | − | 0.0782565i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5327.11i | 1.37229i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3757.23i | 0.956244i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4621.86 | + | 4621.86i | 1.16227 | + | 1.16227i | 0.983978 | + | 0.178291i | \(0.0570569\pi\) |
0.178291 | + | 0.983978i | \(0.442943\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −851.642 | + | 851.642i | −0.211630 | + | 0.211630i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 205.331 | 0.0504249 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 610.977 | 0.148295 | 0.0741473 | − | 0.997247i | \(-0.476377\pi\) | ||||
0.0741473 | + | 0.997247i | \(0.476377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −631.518 | + | 631.518i | −0.151508 | + | 0.151508i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1212.94 | − | 1212.94i | −0.287660 | − | 0.287660i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4973.57i | 1.16610i | 0.812438 | + | 0.583048i | \(0.198140\pi\) | ||||
−0.812438 | + | 0.583048i | \(0.801860\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 464.505i | − | 0.107677i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.38061 | + | 9.38061i | 0.00215013 | + | 0.00215013i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 938.415 | − | 938.415i | 0.212700 | − | 0.212700i | −0.592714 | − | 0.805413i | \(-0.701943\pi\) |
0.805413 | + | 0.592714i | \(0.201943\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4010.64 | 0.898999 | 0.449500 | − | 0.893280i | \(-0.351602\pi\) | ||||
0.449500 | + | 0.893280i | \(0.351602\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5603.29 | 1.24222 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1507.50 | − | 1507.50i | 0.330566 | − | 0.330566i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3534.99 | + | 3534.99i | 0.766776 | + | 0.766776i | 0.977538 | − | 0.210762i | \(-0.0675943\pi\) |
−0.210762 | + | 0.977538i | \(0.567594\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 169.666i | 0.0364074i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7468.35i | − | 1.58550i | −0.609550 | − | 0.792748i | \(-0.708650\pi\) | ||
0.609550 | − | 0.792748i | \(-0.291350\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2249.22 | − | 2249.22i | −0.472447 | − | 0.472447i | 0.430259 | − | 0.902705i | \(-0.358422\pi\) |
−0.902705 | + | 0.430259i | \(0.858422\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −129.858 | + | 129.858i | −0.0269900 | + | 0.0269900i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4457.66 | −0.916819 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2607.24 | 0.530682 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 752.845 | − | 752.845i | 0.151658 | − | 0.151658i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3952.79 | + | 3952.79i | 0.788139 | + | 0.788139i | 0.981189 | − | 0.193050i | \(-0.0618381\pi\) |
−0.193050 | + | 0.981189i | \(0.561838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 387.736i | − | 0.0765249i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2219.72i | 0.433674i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3410.03 | + | 3410.03i | 0.659555 | + | 0.659555i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3517.59 | − | 3517.59i | 0.673589 | − | 0.673589i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1551.16 | 0.294099 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.404895 | 7.60138e−5 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3855.24 | + | 3855.24i | −0.716711 | + | 0.716711i | −0.967930 | − | 0.251219i | \(-0.919168\pi\) |
0.251219 | + | 0.967930i | \(0.419168\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −610.809 | − | 610.809i | −0.112452 | − | 0.112452i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5194.39i | − | 0.947096i | −0.880768 | − | 0.473548i | \(-0.842973\pi\) | ||
0.880768 | − | 0.473548i | \(-0.157027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4710.01i | − | 0.850561i | −0.905062 | − | 0.425281i | \(-0.860175\pi\) | ||
0.905062 | − | 0.425281i | \(-0.139825\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −332.076 | − | 332.076i | −0.0593980 | − | 0.0593980i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5680.21 | + | 5680.21i | −1.00641 | + | 1.00641i | −0.00643263 | + | 0.999979i | \(0.502048\pi\) |
−0.999979 | + | 0.00643263i | \(0.997952\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1538.03 | −0.269946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2386.65 | −0.414984 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4756.05 | + | 4756.05i | −0.819300 | + | 0.819300i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6036.13 | − | 6036.13i | −1.03023 | − | 1.03023i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 3764.36i | − | 0.636605i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2907.68i | 0.487251i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1815.80 | + | 1815.80i | 0.301526 | + | 0.301526i | 0.841611 | − | 0.540084i | \(-0.181608\pi\) |
−0.540084 | + | 0.841611i | \(0.681608\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −415.418 | + | 415.418i | −0.0683627 | + | 0.0683627i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 674.782 | 0.110052 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2683.29 | −0.433733 | −0.216867 | − | 0.976201i | \(-0.569584\pi\) | ||||
−0.216867 | + | 0.976201i | \(0.569584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3618.05 | − | 3618.05i | 0.579662 | − | 0.579662i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 107.569 | + | 107.569i | 0.0170827 | + | 0.0170827i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4647.79i | − | 0.731653i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 166.252i | 0.0259440i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5291.81 | − | 5291.81i | −0.818671 | − | 0.818671i | 0.167244 | − | 0.985916i | \(-0.446513\pi\) |
−0.985916 | + | 0.167244i | \(0.946513\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −73.7084 | + | 73.7084i | −0.0113052 | + | 0.0113052i | −0.712737 | − | 0.701432i | \(-0.752545\pi\) |
0.701432 | + | 0.712737i | \(0.252545\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8887.90 | 1.35157 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5067.25 | −0.764030 | −0.382015 | − | 0.924156i | \(-0.624770\pi\) | ||||
−0.382015 | + | 0.924156i | \(0.624770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 250.378 | − | 250.378i | 0.0374329 | − | 0.0374329i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5002.63 | + | 5002.63i | 0.741645 | + | 0.741645i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 970.230i | 0.142637i | 0.997454 | + | 0.0713186i | \(0.0227207\pi\) | ||||
−0.997454 | + | 0.0713186i | \(0.977279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 843.224i | 0.122937i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2056.49 | − | 2056.49i | −0.297350 | − | 0.297350i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 223.718 | − | 223.718i | 0.0320821 | − | 0.0320821i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13451.4 | −1.91323 | −0.956617 | − | 0.291347i | \(-0.905896\pi\) | ||||
−0.956617 | + | 0.291347i | \(0.905896\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2932.29 | −0.413682 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11317.1 | − | 11317.1i | 1.58370 | − | 1.58370i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5898.22 | − | 5898.22i | −0.818762 | − | 0.818762i | 0.167167 | − | 0.985929i | \(-0.446538\pi\) |
−0.985929 | + | 0.167167i | \(0.946538\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 590.255i | − | 0.0812817i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6158.35i | 0.841302i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4446.72 | − | 4446.72i | −0.602673 | − | 0.602673i | 0.338348 | − | 0.941021i | \(-0.390132\pi\) |
−0.941021 | + | 0.338348i | \(0.890132\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1961.24 | + | 1961.24i | −0.263721 | + | 0.263721i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6417.68 | 0.856209 | 0.428105 | − | 0.903729i | \(-0.359181\pi\) | ||||
0.428105 | + | 0.903729i | \(0.359181\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −421.076 | −0.0557403 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2313.90 | − | 2313.90i | 0.303933 | − | 0.303933i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6555.61 | − | 6555.61i | −0.854455 | − | 0.854455i | 0.136223 | − | 0.990678i | \(-0.456503\pi\) |
−0.990678 | + | 0.136223i | \(0.956503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6088.96i | 0.787549i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3148.20i | − | 0.404086i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 421.226 | + | 421.226i | 0.0536561 | + | 0.0536561i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8902.51 | + | 8902.51i | −1.12545 | + | 1.12545i | −0.134543 | + | 0.990908i | \(0.542957\pi\) |
−0.990908 | + | 0.134543i | \(0.957043\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6327.66 | −0.793933 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6425.77 | −0.800218 | −0.400109 | − | 0.916468i | \(-0.631028\pi\) | ||||
−0.400109 | + | 0.916468i | \(0.631028\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 430.715 | − | 430.715i | 0.0532393 | − | 0.0532393i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −91.6341 | − | 91.6341i | −0.0112428 | − | 0.0112428i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 526.755i | 0.0641530i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12796.0i | 1.54699i | 0.633801 | + | 0.773496i | \(0.281494\pi\) | ||||
−0.633801 | + | 0.773496i | \(0.718506\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3164.37 | + | 3164.37i | 0.379773 | + | 0.379773i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9446.67 | − | 9446.67i | 1.12552 | − | 1.12552i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1130.54 | −0.133725 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1101.65 | −0.129372 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6545.21 | + | 6545.21i | −0.763137 | + | 0.763137i | −0.976888 | − | 0.213751i | \(-0.931432\pi\) |
0.213751 | + | 0.976888i | \(0.431432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6390.00 | + | 6390.00i | 0.739738 | + | 0.739738i | 0.972527 | − | 0.232789i | \(-0.0747852\pi\) |
−0.232789 | + | 0.972527i | \(0.574785\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1912.70i | 0.219855i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 10778.1i | − | 1.23016i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.86474 | + | 9.86474i | 0.00111801 | + | 0.00111801i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2336.88 | − | 2336.88i | 0.262997 | − | 0.262997i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10639.3 | 1.18904 | 0.594519 | − | 0.804081i | \(-0.297342\pi\) | ||||
0.594519 | + | 0.804081i | \(0.297342\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3806.14 | 0.422428 | 0.211214 | − | 0.977440i | \(-0.432258\pi\) | ||||
0.211214 | + | 0.977440i | \(0.432258\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −150.121 | + | 150.121i | −0.0165466 | + | 0.0165466i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3850.86 | − | 3850.86i | −0.421537 | − | 0.421537i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14102.8i | − | 1.53323i | −0.642106 | − | 0.766616i | \(-0.721939\pi\) | ||
0.642106 | − | 0.766616i | \(-0.278061\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 9619.28i | − | 1.03869i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7662.45 | − | 7662.45i | −0.821792 | − | 0.821792i | 0.164573 | − | 0.986365i | \(-0.447375\pi\) |
−0.986365 | + | 0.164573i | \(0.947375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.82260 | + | 2.82260i | −0.000300683 | + | 0.000300683i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2353.58 | 0.249040 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13679.4 | 1.43779 | 0.718897 | − | 0.695117i | \(-0.244647\pi\) | ||||
0.718897 | + | 0.695117i | \(0.244647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1859.09 | + | 1859.09i | −0.194104 | + | 0.194104i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −318.669 | − | 318.669i | −0.0330516 | − | 0.0330516i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1686.01i | 0.173718i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7913.48i | 0.810016i | 0.914313 | + | 0.405008i | \(0.132731\pi\) | ||||
−0.914313 | + | 0.405008i | \(0.867269\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7935.13 | + | 7935.13i | 0.806929 | + | 0.806929i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 580.215 | − | 580.215i | 0.0586189 | − | 0.0586189i | −0.677190 | − | 0.735809i | \(-0.736802\pi\) |
0.735809 | + | 0.677190i | \(0.236802\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14236.5 | −1.42899 | −0.714497 | − | 0.699638i | \(-0.753344\pi\) | ||||
−0.714497 | + | 0.699638i | \(0.753344\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.9990 | 0.00209420 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8344.57 | + | 8344.57i | −0.826853 | + | 0.826853i | −0.987080 | − | 0.160227i | \(-0.948777\pi\) |
0.160227 | + | 0.987080i | \(0.448777\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16440.2 | + | 16440.2i | 1.61863 | + | 1.61863i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 2799.85i | − | 0.273907i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2934.05i | − | 0.285217i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6816.45 | + | 6816.45i | 0.658443 | + | 0.658443i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7444.46 | − | 7444.46i | 0.714588 | − | 0.714588i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5563.77 | 0.530720 | 0.265360 | − | 0.964149i | \(-0.414509\pi\) | ||||
0.265360 | + | 0.964149i | \(0.414509\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2109.16 | 0.199936 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4050.51 | + | 4050.51i | −0.381583 | + | 0.381583i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 226.529 | + | 226.529i | 0.0212085 | + | 0.0212085i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18150.5i | 1.68886i | 0.535662 | + | 0.844432i | \(0.320062\pi\) | ||||
−0.535662 | + | 0.844432i | \(0.679938\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7428.99i | − | 0.687015i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11593.0 | + | 11593.0i | 1.06555 | + | 1.06555i | 0.997695 | + | 0.0678570i | \(0.0216162\pi\) |
0.0678570 | + | 0.997695i | \(0.478384\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5498.18 | + | 5498.18i | −0.502284 | + | 0.502284i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −276.988 | −0.0251509 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12200.3 | 1.10112 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3109.58 | − | 3109.58i | 0.278966 | − | 0.278966i | −0.553730 | − | 0.832696i | \(-0.686796\pi\) |
0.832696 | + | 0.553730i | \(0.186796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7641.07 | − | 7641.07i | −0.681393 | − | 0.681393i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6221.21i | 0.551471i | 0.961233 | + | 0.275736i | \(0.0889215\pi\) | ||||
−0.961233 | + | 0.275736i | \(0.911079\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 466.740i | 0.0411281i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4999.13 | − | 4999.13i | −0.437907 | − | 0.437907i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13800.4 | + | 13800.4i | −1.20176 | + | 1.20176i | −0.228124 | + | 0.973632i | \(0.573259\pi\) |
−0.973632 | + | 0.228124i | \(0.926741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10901.2 | 0.943720 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10036.9 | −0.863820 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 183.791 | − | 183.791i | 0.0157258 | − | 0.0157258i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1212.66 | + | 1212.66i | 0.103158 | + | 0.103158i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10416.1i | 0.880957i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6874.63i | − | 0.578086i | −0.957316 | − | 0.289043i | \(-0.906663\pi\) | ||
0.957316 | − | 0.289043i | \(-0.0933371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2306.52 | + | 2306.52i | 0.192843 | + | 0.192843i | 0.796924 | − | 0.604080i | \(-0.206459\pi\) |
−0.604080 | + | 0.796924i | \(0.706459\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7169.85 | − | 7169.85i | 0.596034 | − | 0.596034i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 769.086 | 0.0635710 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7236.92 | 0.594799 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6214.11 | − | 6214.11i | 0.507852 | − | 0.507852i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7443.90 | + | 7443.90i | 0.604936 | + | 0.604936i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 718.136i | − | 0.0580332i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4906.28i | 0.394267i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6098.68 | − | 6098.68i | −0.487363 | − | 0.487363i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13240.0 | − | 13240.0i | 1.05218 | − | 1.05218i | 0.0536210 | − | 0.998561i | \(-0.482924\pi\) |
0.998561 | − | 0.0536210i | \(-0.0170763\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6247.82 | −0.493775 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1132.69 | 0.0890256 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13271.3 | + | 13271.3i | −1.03737 | + | 1.03737i | −0.0380940 | + | 0.999274i | \(0.512129\pi\) |
−0.999274 | + | 0.0380940i | \(0.987871\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.48912 | + | 6.48912i | 0.000504460 | + | 0.000504460i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6954.47i | − | 0.537696i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20525.2i | 1.57834i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 51.4148 | + | 51.4148i | 0.00393232 | + | 0.00393232i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8500.61 | − | 8500.61i | 0.646647 | − | 0.646647i | −0.305534 | − | 0.952181i | \(-0.598835\pi\) |
0.952181 | + | 0.305534i | \(0.0988349\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11748.1 | −0.888896 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4172.74 | 0.314034 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17327.2 | − | 17327.2i | 1.29708 | − | 1.29708i | 0.366763 | − | 0.930314i | \(-0.380466\pi\) |
0.930314 | − | 0.366763i | \(-0.119534\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1088.66 | + | 1088.66i | 0.0810625 | + | 0.0810625i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 4465.09i | − | 0.330716i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8998.54i | 0.662985i | 0.943458 | + | 0.331492i | \(0.107552\pi\) | ||||
−0.943458 | + | 0.331492i | \(0.892448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9849.25 | − | 9849.25i | −0.721853 | − | 0.721853i | 0.247129 | − | 0.968983i | \(-0.420513\pi\) |
−0.968983 | + | 0.247129i | \(0.920513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7112.89 | + | 7112.89i | −0.518578 | + | 0.518578i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8726.79 | 0.632926 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20584.4 | −1.48516 | −0.742580 | − | 0.669757i | \(-0.766398\pi\) | ||||
−0.742580 | + | 0.669757i | \(0.766398\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1038.59 | − | 1038.59i | 0.0745467 | − | 0.0745467i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27544.1 | − | 27544.1i | −1.96682 | − | 1.96682i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 9439.66i | − | 0.670585i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1109.08i | 0.0783840i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2586.77 | − | 2586.77i | −0.181887 | − | 0.181887i | 0.610291 | − | 0.792177i | \(-0.291053\pi\) |
−0.792177 | + | 0.610291i | \(0.791053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −486.396 | + | 486.396i | −0.0340265 | + | 0.0340265i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4465.54 | 0.310809 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6035.89 | −0.417984 | −0.208992 | − | 0.977917i | \(-0.567018\pi\) | ||||
−0.208992 | + | 0.977917i | \(0.567018\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1505.28 | + | 1505.28i | −0.103715 | + | 0.103715i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4586.95 | − | 4586.95i | −0.314458 | − | 0.314458i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5427.20i | 0.370199i | 0.982720 | + | 0.185100i | \(0.0592608\pi\) | ||||
−0.982720 | + | 0.185100i | \(0.940739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17725.7i | − | 1.20307i | −0.798847 | − | 0.601535i | \(-0.794556\pi\) | ||
0.798847 | − | 0.601535i | \(-0.205444\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10814.5 | + | 10814.5i | 0.730349 | + | 0.730349i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 618.793 | − | 618.793i | 0.0415827 | − | 0.0415827i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13487.6 | −0.901884 | −0.450942 | − | 0.892553i | \(-0.648912\pi\) | ||||
−0.450942 | + | 0.892553i | \(0.648912\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7315.03 | −0.486732 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4855.57 | − | 4855.57i | 0.321498 | − | 0.321498i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16850.4 | + | 16850.4i | 1.11025 | + | 1.11025i | 0.993117 | + | 0.117129i | \(0.0373691\pi\) |
0.117129 | + | 0.993117i | \(0.462631\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 362.918i | 0.0237956i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 535.243i | 0.0349239i | 0.999848 | + | 0.0174620i | \(0.00555860\pi\) | ||||
−0.999848 | + | 0.0174620i | \(0.994441\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19691.0 | − | 19691.0i | −1.27859 | − | 1.27859i | −0.941458 | − | 0.337130i | \(-0.890544\pi\) |
−0.337130 | − | 0.941458i | \(-0.609456\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6424.88 | + | 6424.88i | −0.415172 | + | 0.415172i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −137.538 | −0.00884485 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15358.3 | −0.982934 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2638.98 | + | 2638.98i | −0.168087 | + | 0.168087i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1883.06 | + | 1883.06i | 0.119368 | + | 0.119368i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 11880.2i | − | 0.749511i | −0.927124 | − | 0.374755i | \(-0.877727\pi\) | ||
0.927124 | − | 0.374755i | \(-0.122273\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 5627.72i | − | 0.353368i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −590.132 | − | 590.132i | −0.0368798 | − | 0.0368798i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24419.5 | + | 24419.5i | −1.51889 | + | 1.51889i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8025.45 | 0.496842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18341.0 | 1.13015 | 0.565074 | − | 0.825040i | \(-0.308848\pi\) | ||||
0.565074 | + | 0.825040i | \(0.308848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7026.21 | − | 7026.21i | 0.430928 | − | 0.430928i | −0.458016 | − | 0.888944i | \(-0.651440\pi\) |
0.888944 | + | 0.458016i | \(0.151440\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −286.383 | − | 286.383i | −0.0174827 | − | 0.0174827i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 21429.7i | − | 1.30215i | −0.759015 | − | 0.651073i | \(-0.774319\pi\) | ||
0.759015 | − | 0.651073i | \(-0.225681\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7879.56i | − | 0.476579i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 511.613 | + | 511.613i | 0.0308014 | + | 0.0308014i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8681.22 | + | 8681.22i | −0.520248 | + | 0.520248i | −0.917646 | − | 0.397398i | \(-0.869913\pi\) |
0.397398 | + | 0.917646i | \(0.369913\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 947.284 | 0.0565091 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7170.92 | 0.425821 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4151.60 | + | 4151.60i | −0.245407 | + | 0.245407i | −0.819083 | − | 0.573675i | \(-0.805517\pi\) |
0.573675 | + | 0.819083i | \(0.305517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12239.0 | − | 12239.0i | −0.720182 | − | 0.720182i | 0.248460 | − | 0.968642i | \(-0.420076\pi\) |
−0.968642 | + | 0.248460i | \(0.920076\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 16707.9i | − | 0.978706i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1903.98i | − | 0.111027i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4451.75 | − | 4451.75i | −0.258429 | − | 0.258429i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8559.23 | − | 8559.23i | 0.494647 | − | 0.494647i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.22827 | 0.000473396 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6528.62 | 0.373937 | 0.186969 | − | 0.982366i | \(-0.440134\pi\) | ||||
0.186969 | + | 0.982366i | \(0.440134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11372.8 | − | 11372.8i | 0.648500 | − | 0.648500i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14220.6 | + | 14220.6i | 0.807299 | + | 0.807299i | 0.984224 | − | 0.176925i | \(-0.0566151\pi\) |
−0.176925 | + | 0.984224i | \(0.556615\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11038.2i | 0.623867i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 2781.76i | − | 0.156530i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21419.5 | + | 21419.5i | 1.19999 | + | 1.19999i | 0.974167 | + | 0.225827i | \(0.0725084\pi\) |
0.225827 | + | 0.974167i | \(0.427492\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −952.149 | + | 952.149i | −0.0531091 | + | 0.0531091i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2631.60 | 0.146145 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37797.0 | −2.08991 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16537.1 | + | 16537.1i | −0.910423 | + | 0.910423i | −0.996305 | − | 0.0858818i | \(-0.972629\pi\) |
0.0858818 | + | 0.996305i | \(0.472629\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6748.45 | − | 6748.45i | −0.369917 | − | 0.369917i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 331.484i | − | 0.0180920i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13291.8i | 0.722331i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6922.92 | + | 6922.92i | 0.374605 | + | 0.374605i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3026.52 | − | 3026.52i | 0.163067 | − | 0.163067i | −0.620857 | − | 0.783924i | \(-0.713215\pi\) |
0.783924 | + | 0.620857i | \(0.213215\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2381.82 | −0.127784 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 236.728 | 0.0126464 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11371.5 | + | 11371.5i | −0.604908 | + | 0.604908i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3981.14 | − | 3981.14i | −0.210881 | − | 0.210881i | 0.593761 | − | 0.804642i | \(-0.297643\pi\) |
−0.804642 | + | 0.593761i | \(0.797643\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13501.7i | 0.712170i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 622.710i | 0.0327078i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 703.160 | + | 703.160i | 0.0367786 | + | 0.0367786i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5852.36 | + | 5852.36i | −0.304826 | + | 0.304826i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5682.25 | 0.294732 | 0.147366 | − | 0.989082i | \(-0.452921\pi\) | ||||
0.147366 | + | 0.989082i | \(0.452921\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8955.64 | 0.462587 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2239.37 | + | 2239.37i | −0.115191 | + | 0.115191i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7880.09 | + | 7880.09i | 0.403668 | + | 0.403668i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18883.0i | 0.963317i | 0.876359 | + | 0.481658i | \(0.159965\pi\) | ||||
−0.876359 | + | 0.481658i | \(0.840035\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6863.99i | 0.348727i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10488.8 | − | 10488.8i | −0.530698 | − | 0.530698i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24962.5 | − | 24962.5i | 1.25786 | − | 1.25786i | 0.305748 | − | 0.952113i | \(-0.401094\pi\) |
0.952113 | − | 0.305748i | \(-0.0989063\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1190.54 | −0.0597467 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13712.9 | 0.685375 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6202.38 | − | 6202.38i | 0.308739 | − | 0.308739i | −0.535681 | − | 0.844420i | \(-0.679945\pi\) |
0.844420 | + | 0.535681i | \(0.179945\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10566.6 | + | 10566.6i | 0.523854 | + | 0.523854i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 30.9140i | − | 0.00152641i | −1.00000 | 0.000763205i | \(-0.999757\pi\) | |||
1.00000 | 0.000763205i | \(-0.000242936\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 708.187i | 0.0348268i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18118.8 | − | 18118.8i | −0.887459 | − | 0.887459i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17496.5 | − | 17496.5i | 0.853547 | − | 0.853547i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16318.5 | 0.792905 | 0.396453 | − | 0.918055i | \(-0.370241\pi\) | ||||
0.396453 | + | 0.918055i | \(0.370241\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18335.5 | 0.887361 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 95.8865 | − | 95.8865i | 0.00462208 | − | 0.00462208i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9854.59 | − | 9854.59i | −0.473146 | − | 0.473146i | 0.429786 | − | 0.902931i | \(-0.358589\pi\) |
−0.902931 | + | 0.429786i | \(0.858589\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3378.57i | 0.161573i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3823.42i | − | 0.182127i | −0.995845 | − | 0.0910637i | \(-0.970973\pi\) | ||
0.995845 | − | 0.0910637i | \(-0.0290267\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27596.4 | + | 27596.4i | 1.30938 | + | 1.30938i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −990.185 | + | 990.185i | −0.0467977 | + | 0.0467977i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31550.2 | −1.48528 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31689.1 | 1.48601 | 0.743003 | − | 0.669288i | \(-0.233401\pi\) | ||||
0.743003 | + | 0.669288i | \(0.233401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1211.91 | − | 1211.91i | 0.0566094 | − | 0.0566094i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1305.84 | + | 1305.84i | 0.0607604 | + | 0.0607604i | 0.736834 | − | 0.676074i | \(-0.236320\pi\) |
−0.676074 | + | 0.736834i | \(0.736320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1102.27i | − | 0.0510898i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2505.31i | 0.115672i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8406.21 | − | 8406.21i | −0.386629 | − | 0.386629i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5088.18 | − | 5088.18i | 0.233123 | − | 0.233123i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11603.0 | −0.529577 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 842.465 | 0.0383043 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14399.5 | − | 14399.5i | 0.652209 | − | 0.652209i | −0.301316 | − | 0.953524i | \(-0.597426\pi\) |
0.953524 | + | 0.301316i | \(0.0974258\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9865.37 | + | 9865.37i | 0.445141 | + | 0.445141i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 53047.6i | 2.38452i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 32.9465i | − | 0.00147537i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −921.374 | − | 921.374i | −0.0411041 | − | 0.0411041i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5572.19 | − | 5572.19i | 0.247650 | − | 0.247650i | −0.572356 | − | 0.820006i | \(-0.693970\pi\) |
0.820006 | + | 0.572356i | \(0.193970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8670.13 | 0.383889 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −90.4737 | −0.00399093 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4546.40 | − | 4546.40i | 0.199800 | − | 0.199800i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1218.79 | − | 1218.79i | −0.0533622 | − | 0.0533622i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 3722.81i | − | 0.162390i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5081.28i | − | 0.220826i | −0.993886 | − | 0.110413i | \(-0.964783\pi\) | ||
0.993886 | − | 0.110413i | \(-0.0352174\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4493.19 | + | 4493.19i | 0.194546 | + | 0.194546i | 0.797657 | − | 0.603111i | \(-0.206072\pi\) |
−0.603111 | + | 0.797657i | \(0.706072\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7955.35 | − | 7955.35i | 0.343181 | − | 0.343181i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2235.36 | 0.0960752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13266.9 | 0.568114 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −27021.2 | + | 27021.2i | −1.15287 | + | 1.15287i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2115.54 | − | 2115.54i | −0.0899304 | − | 0.0899304i | 0.660710 | − | 0.750641i | \(-0.270255\pi\) |
−0.750641 | + | 0.660710i | \(0.770255\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24432.6i | 1.03483i | 0.855734 | + | 0.517416i | \(0.173106\pi\) | ||||
−0.855734 | + | 0.517416i | \(0.826894\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5980.44i | − | 0.252378i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21051.4 | + | 21051.4i | 0.885162 | + | 0.885162i | 0.994054 | − | 0.108892i | \(-0.0347302\pi\) |
−0.108892 | + | 0.994054i | \(0.534730\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25442.0 | + | 25442.0i | −1.06591 | + | 1.06591i | −0.0682392 | + | 0.997669i | \(0.521738\pi\) |
−0.997669 | + | 0.0682392i | \(0.978262\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14023.7 | 0.585413 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −43603.5 | −1.81365 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2299.17 | − | 2299.17i | 0.0952889 | − | 0.0952889i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 811.516 | + | 811.516i | 0.0335127 | + | 0.0335127i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 18757.2i | − | 0.771837i | −0.922533 | − | 0.385919i | \(-0.873885\pi\) | ||
0.922533 | − | 0.385919i | \(-0.126115\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16349.4i | 0.670358i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14813.9 | − | 14813.9i | −0.605242 | − | 0.605242i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1504.22 | − | 1504.22i | 0.0612389 | − | 0.0612389i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30152.2 | 1.22319 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8922.94 | −0.360700 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1524.67 | + | 1524.67i | −0.0614160 | + | 0.0614160i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6100.17 | + | 6100.17i | 0.244860 | + | 0.244860i | 0.818857 | − | 0.573997i | \(-0.194608\pi\) |
−0.573997 | + | 0.818857i | \(0.694608\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1252.45i | − | 0.0500971i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2079.04i | − | 0.0828687i | −0.999141 | − | 0.0414344i | \(-0.986807\pi\) | ||
0.999141 | − | 0.0414344i | \(-0.0131927\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8301.95 | + | 8301.95i | 0.329754 | + | 0.329754i | 0.852493 | − | 0.522739i | \(-0.175090\pi\) |
−0.522739 | + | 0.852493i | \(0.675090\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8842.03 | + | 8842.03i | −0.349983 | + | 0.349983i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43830.8 | −1.72887 | −0.864436 | − | 0.502743i | \(-0.832324\pi\) | ||||
−0.864436 | + | 0.502743i | \(0.832324\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3134.18 | −0.123197 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5171.62 | − | 5171.62i | 0.202581 | − | 0.202581i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8560.14 | + | 8560.14i | 0.334158 | + | 0.334158i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 54907.3i | − | 2.13601i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7261.01i | 0.281498i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4327.14 | + | 4327.14i | 0.167182 | + | 0.167182i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2565.89 | − | 2565.89i | 0.0987958 | − | 0.0987958i | −0.655981 | − | 0.754777i | \(-0.727745\pi\) |
0.754777 | + | 0.655981i | \(0.227745\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15681.2 | 0.601723 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26429.8 | 1.01072 | 0.505360 | − | 0.862909i | \(-0.331360\pi\) | ||||
0.505360 | + | 0.862909i | \(0.331360\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20708.4 | + | 20708.4i | −0.789232 | + | 0.789232i | −0.981368 | − | 0.192136i | \(-0.938458\pi\) |
0.192136 | + | 0.981368i | \(0.438458\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −769.097 | − | 769.097i | −0.0292123 | − | 0.0292123i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 22350.0i | − | 0.846042i | −0.906120 | − | 0.423021i | \(-0.860970\pi\) | ||
0.906120 | − | 0.423021i | \(-0.139030\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 28755.6i | − | 1.08485i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1862.19 | − | 1862.19i | −0.0700175 | − | 0.0700175i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5483.28 | + | 5483.28i | −0.205477 | + | 0.205477i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1476.28 | −0.0551360 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13528.0 | 0.503553 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −562.292 | + | 562.292i | −0.0208604 | + | 0.0208604i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33745.2 | − | 33745.2i | −1.24774 | − | 1.24774i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 13954.7i | − | 0.514267i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1879.95i | − | 0.0690516i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4086.93 | − | 4086.93i | −0.149619 | − | 0.149619i | 0.628329 | − | 0.777948i | \(-0.283739\pi\) |
−0.777948 | + | 0.628329i | \(0.783739\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7480.29 | + | 7480.29i | −0.272944 | + | 0.272944i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20024.6 | 0.728259 | 0.364130 | − | 0.931348i | \(-0.381367\pi\) | ||||
0.364130 | + | 0.931348i | \(0.381367\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22974.8 | −0.832810 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.803134 | − | 0.803134i | 2.90173e−5 | − | 2.90173e-5i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23079.3 | + | 23079.3i | 0.831131 | + | 0.831131i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 26977.7i | − | 0.968349i | −0.874971 | − | 0.484175i | \(-0.839120\pi\) | ||
0.874971 | − | 0.484175i | \(-0.160880\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15294.2i | 0.547189i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20373.4 | − | 20373.4i | −0.726542 | − | 0.726542i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2698.84 | − | 2698.84i | 0.0959321 | − | 0.0959321i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5891.10 | 0.208726 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34371.4 | −1.21387 | −0.606937 | − | 0.794750i | \(-0.707602\pi\) | ||||
−0.606937 | + | 0.794750i | \(0.707602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27576.3 | − | 27576.3i | 0.970760 | − | 0.970760i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10303.4 | − | 10303.4i | −0.361541 | − | 0.361541i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1255.57i | 0.0439159i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32901.8i | − | 1.14712i | −0.819163 | − | 0.573561i | \(-0.805561\pi\) | ||
0.819163 | − | 0.573561i | \(-0.194439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9342.60 | − | 9342.60i | −0.324690 | − | 0.324690i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33381.6 | + | 33381.6i | −1.15644 | + | 1.15644i | −0.171204 | + | 0.985236i | \(0.554766\pi\) |
−0.985236 | + | 0.171204i | \(0.945234\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10762.1 | −0.371646 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3176.65 | −0.109351 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13611.9 | − | 13611.9i | 0.467084 | − | 0.467084i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18204.1 | − | 18204.1i | −0.622686 | − | 0.622686i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22534.1i | 0.768369i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4572.49i | − | 0.155422i | −0.996976 | − | 0.0777112i | \(-0.975239\pi\) | ||
0.996976 | − | 0.0777112i | \(-0.0247612\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2140.25 | − | 2140.25i | −0.0725202 | − | 0.0725202i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3050.77 | + | 3050.77i | −0.103048 | + | 0.103048i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46395.7 | −1.56225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29712.3 | −0.997360 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11509.3 | − | 11509.3i | 0.385133 | − | 0.385133i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 312.510 | + | 312.510i | 0.0104249 | + | 0.0104249i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33060.9i | 1.09945i | 0.835346 | + | 0.549725i | \(0.185268\pi\) | ||||
−0.835346 | + | 0.549725i | \(0.814732\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18867.9i | 0.625514i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15553.4 | − | 15553.4i | −0.514041 | − | 0.514041i | 0.401721 | − | 0.915762i | \(-0.368412\pi\) |
−0.915762 | + | 0.401721i | \(0.868412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8076.18 | − | 8076.18i | 0.266095 | − | 0.266095i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23946.1 | −0.786551 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1241.54 | 0.0406555 | 0.0203277 | − | 0.999793i | \(-0.493529\pi\) | ||||
0.0203277 | + | 0.999793i | \(0.493529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −57.3608 | + | 57.3608i | −0.00187258 | + | 0.00187258i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18153.2 | + | 18153.2i | 0.590812 | + | 0.590812i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 10797.7i | − | 0.350349i | −0.984537 | − | 0.175175i | \(-0.943951\pi\) | ||
0.984537 | − | 0.175175i | \(-0.0560490\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1343.67i | 0.0434648i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5767.56 | + | 5767.56i | 0.186001 | + | 0.186001i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8492.49 | − | 8492.49i | 0.273049 | − | 0.273049i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10204.8 | 0.327112 | 0.163556 | − | 0.986534i | \(-0.447704\pi\) | ||||
0.163556 | + | 0.986534i | \(0.447704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7203.49 | 0.230207 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1380.20 | − | 1380.20i | 0.0439752 | − | 0.0439752i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15046.7 | − | 15046.7i | −0.477967 | − | 0.477967i | 0.426514 | − | 0.904481i | \(-0.359741\pi\) |
−0.904481 | + | 0.426514i | \(0.859741\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3973.90i | 0.125855i |
(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.97.4 | 10 | ||
4.3 | odd | 2 | 128.4.e.b.97.2 | 10 | |||
8.3 | odd | 2 | 16.4.e.a.5.4 | ✓ | 10 | ||
8.5 | even | 2 | 64.4.e.a.49.2 | 10 | |||
16.3 | odd | 4 | 128.4.e.b.33.2 | 10 | |||
16.5 | even | 4 | 64.4.e.a.17.2 | 10 | |||
16.11 | odd | 4 | 16.4.e.a.13.4 | yes | 10 | ||
16.13 | even | 4 | inner | 128.4.e.a.33.4 | 10 | ||
24.5 | odd | 2 | 576.4.k.a.433.3 | 10 | |||
24.11 | even | 2 | 144.4.k.a.37.2 | 10 | |||
32.3 | odd | 8 | 1024.4.a.n.1.4 | 10 | |||
32.5 | even | 8 | 1024.4.b.k.513.7 | 10 | |||
32.11 | odd | 8 | 1024.4.b.j.513.7 | 10 | |||
32.13 | even | 8 | 1024.4.a.m.1.4 | 10 | |||
32.19 | odd | 8 | 1024.4.a.n.1.7 | 10 | |||
32.21 | even | 8 | 1024.4.b.k.513.4 | 10 | |||
32.27 | odd | 8 | 1024.4.b.j.513.4 | 10 | |||
32.29 | even | 8 | 1024.4.a.m.1.7 | 10 | |||
48.5 | odd | 4 | 576.4.k.a.145.3 | 10 | |||
48.11 | even | 4 | 144.4.k.a.109.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.4 | ✓ | 10 | 8.3 | odd | 2 | ||
16.4.e.a.13.4 | yes | 10 | 16.11 | odd | 4 | ||
64.4.e.a.17.2 | 10 | 16.5 | even | 4 | |||
64.4.e.a.49.2 | 10 | 8.5 | even | 2 | |||
128.4.e.a.33.4 | 10 | 16.13 | even | 4 | inner | ||
128.4.e.a.97.4 | 10 | 1.1 | even | 1 | trivial | ||
128.4.e.b.33.2 | 10 | 16.3 | odd | 4 | |||
128.4.e.b.97.2 | 10 | 4.3 | odd | 2 | |||
144.4.k.a.37.2 | 10 | 24.11 | even | 2 | |||
144.4.k.a.109.2 | 10 | 48.11 | even | 4 | |||
576.4.k.a.145.3 | 10 | 48.5 | odd | 4 | |||
576.4.k.a.433.3 | 10 | 24.5 | odd | 2 | |||
1024.4.a.m.1.4 | 10 | 32.13 | even | 8 | |||
1024.4.a.m.1.7 | 10 | 32.29 | even | 8 | |||
1024.4.a.n.1.4 | 10 | 32.3 | odd | 8 | |||
1024.4.a.n.1.7 | 10 | 32.19 | odd | 8 | |||
1024.4.b.j.513.4 | 10 | 32.27 | odd | 8 | |||
1024.4.b.j.513.7 | 10 | 32.11 | odd | 8 | |||
1024.4.b.k.513.4 | 10 | 32.21 | even | 8 | |||
1024.4.b.k.513.7 | 10 | 32.5 | even | 8 |