Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,4,Mod(81,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.81");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.k (of order \(4\), degree \(2\), 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: | \(8.02425976078\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 119x^{12} + 5319x^{10} + 112122x^{8} + 1120191x^{6} + 4382607x^{4} + 1699337x^{2} + 2704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 81.4 | ||
Root | \(-0.0399724i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.81 |
Dual form | 136.4.k.b.89.4 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.0399724 | + | 0.0399724i | 0.00769269 | + | 0.00769269i | 0.710943 | − | 0.703250i | \(-0.248269\pi\) |
−0.703250 | + | 0.710943i | \(0.748269\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.97903 | − | 1.97903i | −0.177010 | − | 0.177010i | 0.613041 | − | 0.790051i | \(-0.289946\pi\) |
−0.790051 | + | 0.613041i | \(0.789946\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.30175 | + | 4.30175i | −0.232273 | + | 0.232273i | −0.813641 | − | 0.581368i | \(-0.802518\pi\) |
0.581368 | + | 0.813641i | \(0.302518\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 26.9968i | − | 0.999882i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.5044 | − | 36.5044i | 1.00059 | − | 1.00059i | 0.000590210 | − | 1.00000i | \(-0.499812\pi\) |
1.00000 | 0.000590210i | \(-0.000187870\pi\) | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.2351 | 0.410373 | 0.205187 | − | 0.978723i | \(-0.434220\pi\) | ||||
0.205187 | + | 0.978723i | \(0.434220\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.158213i | − | 0.00272337i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −57.9167 | − | 39.4798i | −0.826286 | − | 0.563250i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 25.0096i | − | 0.301979i | −0.988535 | − | 0.150989i | \(-0.951754\pi\) | ||
0.988535 | − | 0.150989i | \(-0.0482459\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.343902 | −0.00357360 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 105.841 | − | 105.841i | 0.959540 | − | 0.959540i | −0.0396723 | − | 0.999213i | \(-0.512631\pi\) |
0.999213 | + | 0.0396723i | \(0.0126314\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 117.167i | − | 0.937335i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.15838 | − | 2.15838i | 0.0153845 | − | 0.0153845i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −14.6850 | − | 14.6850i | −0.0940322 | − | 0.0940322i | 0.658526 | − | 0.752558i | \(-0.271180\pi\) |
−0.752558 | + | 0.658526i | \(0.771180\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 161.487 | + | 161.487i | 0.935608 | + | 0.935608i | 0.998049 | − | 0.0624410i | \(-0.0198885\pi\) |
−0.0624410 | + | 0.998049i | \(0.519889\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.91833 | 0.0153944 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 17.0266 | 0.0822292 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −249.300 | − | 249.300i | −1.10769 | − | 1.10769i | −0.993453 | − | 0.114240i | \(-0.963557\pi\) |
−0.114240 | − | 0.993453i | \(-0.536443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.768872 | + | 0.768872i | 0.00315687 | + | 0.00315687i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −155.469 | + | 155.469i | −0.592199 | + | 0.592199i | −0.938225 | − | 0.346026i | \(-0.887531\pi\) |
0.346026 | + | 0.938225i | \(0.387531\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 51.0771i | 0.181144i | 0.995890 | + | 0.0905719i | \(0.0288695\pi\) | ||||
−0.995890 | + | 0.0905719i | \(0.971131\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −53.4276 | + | 53.4276i | −0.176989 | + | 0.176989i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 261.156 | 0.810501 | 0.405250 | − | 0.914206i | \(-0.367184\pi\) | ||||
0.405250 | + | 0.914206i | \(0.367184\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 305.990i | 0.892099i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.736967 | − | 3.89317i | −0.00202345 | − | 0.0106893i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 102.139i | 0.264713i | 0.991202 | + | 0.132357i | \(0.0422544\pi\) | ||||
−0.991202 | + | 0.132357i | \(0.957746\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −144.487 | −0.354229 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.999693 | − | 0.999693i | 0.00232303 | − | 0.00232303i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 694.356i | 1.53216i | 0.642745 | + | 0.766080i | \(0.277796\pi\) | ||||
−0.642745 | + | 0.766080i | \(0.722204\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −154.454 | + | 154.454i | −0.324194 | + | 0.324194i | −0.850374 | − | 0.526179i | \(-0.823624\pi\) |
0.526179 | + | 0.850374i | \(0.323624\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 116.133 | + | 116.133i | 0.232245 | + | 0.232245i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −38.0669 | − | 38.0669i | −0.0726403 | − | 0.0726403i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −442.817 | −0.807444 | −0.403722 | − | 0.914882i | \(-0.632284\pi\) | ||||
−0.403722 | + | 0.914882i | \(0.632284\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.46145 | 0.0147629 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 382.069 | + | 382.069i | 0.638638 | + | 0.638638i | 0.950219 | − | 0.311582i | \(-0.100859\pi\) |
−0.311582 | + | 0.950219i | \(0.600859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −190.365 | − | 190.365i | −0.305212 | − | 0.305212i | 0.537837 | − | 0.843049i | \(-0.319242\pi\) |
−0.843049 | + | 0.537837i | \(0.819242\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.68344 | − | 4.68344i | 0.00721062 | − | 0.00721062i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 314.065i | 0.464819i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −22.3403 | + | 22.3403i | −0.0318162 | + | 0.0318162i | −0.722836 | − | 0.691020i | \(-0.757162\pi\) |
0.691020 | + | 0.722836i | \(0.257162\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −728.741 | −0.999645 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 669.427i | − | 0.885291i | −0.896697 | − | 0.442645i | \(-0.854040\pi\) | ||
0.896697 | − | 0.442645i | \(-0.145960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 36.4873 | + | 192.751i | 0.0465600 | + | 0.245962i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.17399i | − | 0.00144672i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1184.49 | 1.41074 | 0.705371 | − | 0.708839i | \(-0.250781\pi\) | ||||
0.705371 | + | 0.708839i | \(0.250781\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −82.7445 | + | 82.7445i | −0.0953185 | + | 0.0953185i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.9100i | 0.0143947i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −49.4948 | + | 49.4948i | −0.0534533 | + | 0.0534533i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 218.714 | + | 218.714i | 0.228939 | + | 0.228939i | 0.812249 | − | 0.583310i | \(-0.198243\pi\) |
−0.583310 | + | 0.812249i | \(0.698243\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −985.502 | − | 985.502i | −1.00047 | − | 1.00047i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 805.995 | 0.794054 | 0.397027 | − | 0.917807i | \(-0.370042\pi\) | ||||
0.397027 | + | 0.917807i | \(0.370042\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 531.840 | 0.508774 | 0.254387 | − | 0.967102i | \(-0.418126\pi\) | ||||
0.254387 | + | 0.967102i | \(0.418126\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.680594 | + | 0.680594i | 0.000632563 | + | 0.000632563i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −849.213 | − | 849.213i | −0.767257 | − | 0.767257i | 0.210366 | − | 0.977623i | \(-0.432535\pi\) |
−0.977623 | + | 0.210366i | \(0.932535\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 952.659 | − | 952.659i | 0.837139 | − | 0.837139i | −0.151342 | − | 0.988481i | \(-0.548360\pi\) |
0.988481 | + | 0.151342i | \(0.0483596\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 19.9302i | − | 0.0170423i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 161.682 | − | 161.682i | 0.134600 | − | 0.134600i | −0.636597 | − | 0.771197i | \(-0.719658\pi\) |
0.771197 | + | 0.636597i | \(0.219658\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −418.927 | −0.339697 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 519.286i | − | 0.410325i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 418.975 | − | 79.3110i | 0.322751 | − | 0.0610960i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1334.14i | − | 1.00236i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.4289 | −0.00911119 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −479.256 | + | 479.256i | −0.342928 | + | 0.342928i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 140.286i | 0.0980189i | 0.998798 | + | 0.0490095i | \(0.0156064\pi\) | ||||
−0.998798 | + | 0.0490095i | \(0.984394\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.04167 | + | 2.04167i | −0.00139348 | + | 0.00139348i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −288.058 | − | 288.058i | −0.192120 | − | 0.192120i | 0.604491 | − | 0.796612i | \(-0.293376\pi\) |
−0.796612 | + | 0.604491i | \(0.793376\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 107.585 | + | 107.585i | 0.0701414 | + | 0.0701414i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.54301 | −0.00544641 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2753.80 | 1.71732 | 0.858661 | − | 0.512545i | \(-0.171297\pi\) | ||||
0.858661 | + | 0.512545i | \(0.171297\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1595.40 | − | 1595.40i | −0.973523 | − | 0.973523i | 0.0261350 | − | 0.999658i | \(-0.491680\pi\) |
−0.999658 | + | 0.0261350i | \(0.991680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.4390 | + | 10.4390i | 0.00623493 | + | 0.00623493i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 702.166 | − | 702.166i | 0.410616 | − | 0.410616i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 58.1241i | 0.0332893i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.2311 | + | 12.2311i | −0.00686264 | + | 0.00686264i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1689.36 | 0.928843 | 0.464422 | − | 0.885614i | \(-0.346262\pi\) | ||||
0.464422 | + | 0.885614i | \(0.346262\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 658.964i | − | 0.355137i | −0.984108 | − | 0.177569i | \(-0.943177\pi\) | ||
0.984108 | − | 0.177569i | \(-0.0568232\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1065.83 | + | 1563.57i | −0.563184 | + | 0.826188i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 639.175i | − | 0.331224i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1725.60 | −0.877186 | −0.438593 | − | 0.898686i | \(-0.644523\pi\) | ||||
−0.438593 | + | 0.898686i | \(0.644523\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.08272 | + | 4.08272i | −0.00203636 | + | 0.00203636i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 910.605i | 0.445750i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1603.92 | + | 1603.92i | −0.770728 | + | 0.770728i | −0.978234 | − | 0.207505i | \(-0.933466\pi\) |
0.207505 | + | 0.978234i | \(0.433466\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.77548 | − | 5.77548i | −0.00272497 | − | 0.00272497i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1736.33 | + | 1736.33i | 0.804559 | + | 0.804559i | 0.983804 | − | 0.179246i | \(-0.0573657\pi\) |
−0.179246 | + | 0.983804i | \(0.557366\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1827.01 | −0.831594 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −675.179 | −0.301943 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 216.659 | + | 216.659i | 0.0952153 | + | 0.0952153i | 0.753110 | − | 0.657895i | \(-0.228553\pi\) |
−0.657895 | + | 0.753110i | \(0.728553\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 504.022 | + | 504.022i | 0.217717 | + | 0.217717i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.7551 | + | 27.7551i | −0.0117864 | + | 0.0117864i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2741.86i | 1.14490i | 0.819941 | + | 0.572448i | \(0.194006\pi\) | ||||
−0.819941 | + | 0.572448i | \(0.805994\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1097.33 | − | 1097.33i | 0.450628 | − | 0.450628i | −0.444935 | − | 0.895563i | \(-0.646773\pi\) |
0.895563 | + | 0.444935i | \(0.146773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.3478 | −0.00498785 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 986.746i | 0.392146i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3555.40 | + | 673.029i | −1.39036 | + | 0.263191i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.5696i | 0.00714678i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3861.44 | 1.46285 | 0.731424 | − | 0.681923i | \(-0.238856\pi\) | ||||
0.731424 | + | 0.681923i | \(0.238856\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1043.68 | − | 1043.68i | 0.389251 | − | 0.389251i | −0.485169 | − | 0.874420i | \(-0.661242\pi\) |
0.874420 | + | 0.485169i | \(0.161242\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 3.04325i | − | 0.00111760i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3782.22 | + | 3782.22i | −1.36788 | + | 1.36788i | −0.504416 | + | 0.863460i | \(0.668292\pi\) |
−0.863460 | + | 0.504416i | \(0.831708\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2619.61 | + | 2619.61i | 0.933162 | + | 0.933162i | 0.997902 | − | 0.0647402i | \(-0.0206219\pi\) |
−0.0647402 | + | 0.997902i | \(0.520622\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.7005 | − | 17.7005i | −0.00621141 | − | 0.00621141i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 126.342 | 0.0436822 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 615.356 | 0.209650 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2857.38 | − | 2857.38i | −0.959427 | − | 0.959427i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −912.960 | − | 912.960i | −0.302157 | − | 0.302157i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −708.196 | + | 708.196i | −0.231063 | + | 0.231063i | −0.813136 | − | 0.582074i | \(-0.802242\pi\) |
0.582074 | + | 0.813136i | \(0.302242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 30.5444i | 0.00982568i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 101.083 | − | 101.083i | 0.0320643 | − | 0.0320643i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1389.35 | −0.434632 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 15.2187i | − | 0.00469581i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1114.03 | − | 759.398i | −0.339086 | − | 0.231143i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4456.87i | 1.33836i | 0.743101 | + | 0.669180i | \(0.233354\pi\) | ||||
−0.743101 | + | 0.669180i | \(0.766646\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3163.13 | −0.937224 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2485.09 | − | 2485.09i | 0.726613 | − | 0.726613i | −0.243331 | − | 0.969943i | \(-0.578240\pi\) |
0.969943 | + | 0.243331i | \(0.0782401\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4609.76i | 1.33023i | 0.746743 | + | 0.665113i | \(0.231617\pi\) | ||||
−0.746743 | + | 0.665113i | \(0.768383\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.5539 | + | 12.5539i | −0.00357571 | + | 0.00357571i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2019.71 | + | 2019.71i | 0.567877 | + | 0.567877i | 0.931533 | − | 0.363656i | \(-0.118472\pi\) |
−0.363656 | + | 0.931533i | \(0.618472\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −516.837 | − | 516.837i | −0.143467 | − | 0.143467i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.78599 | −0.000489504 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6534.60 | 1.76857 | 0.884285 | − | 0.466947i | \(-0.154646\pi\) | ||||
0.884285 | + | 0.466947i | \(0.154646\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2360.27 | − | 2360.27i | −0.630863 | − | 0.630863i | 0.317421 | − | 0.948285i | \(-0.397183\pi\) |
−0.948285 | + | 0.317421i | \(0.897183\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −87.4058 | − | 87.4058i | −0.0230744 | − | 0.0230744i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 605.564 | − | 605.564i | 0.157911 | − | 0.157911i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 481.062i | − | 0.123924i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 26.7586 | − | 26.7586i | 0.00681026 | − | 0.00681026i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2225.36 | 0.559616 | 0.279808 | − | 0.960056i | \(-0.409729\pi\) | ||||
0.279808 | + | 0.960056i | \(0.409729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7727.34i | − | 1.92021i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.24623 | + | 9.16320i | −0.00153394 | + | 0.00225028i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 4927.60i | − | 1.19601i | −0.801491 | − | 0.598006i | \(-0.795960\pi\) | ||
0.801491 | − | 0.598006i | \(-0.204040\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2144.85 | 0.514574 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −396.448 | + | 396.448i | −0.0940210 | + | 0.0940210i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5423.64i | 1.27162i | 0.771846 | + | 0.635810i | \(0.219334\pi\) | ||||
−0.771846 | + | 0.635810i | \(0.780666\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 202.136 | − | 202.136i | 0.0468570 | − | 0.0468570i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 47.3470 | + | 47.3470i | 0.0108524 | + | 0.0108524i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1401.41 | − | 1401.41i | −0.317641 | − | 0.317641i | 0.530220 | − | 0.847860i | \(-0.322109\pi\) |
−0.847860 | + | 0.530220i | \(0.822109\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3510.15 | −0.786812 | −0.393406 | − | 0.919365i | \(-0.628703\pi\) | ||||
−0.393406 | + | 0.919365i | \(0.628703\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.61499 | −0.00146651 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4277.11 | − | 4277.11i | −0.937888 | − | 0.937888i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5410.58 | − | 5410.58i | −1.17361 | − | 1.17361i | −0.981342 | − | 0.192270i | \(-0.938415\pi\) |
−0.192270 | − | 0.981342i | \(-0.561585\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4359.62 | − | 4359.62i | 0.935497 | − | 0.935497i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4519.42i | 0.959451i | 0.877419 | + | 0.479726i | \(0.159264\pi\) | ||||
−0.877419 | + | 0.479726i | \(0.840736\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3295.00 | − | 3295.00i | 0.692111 | − | 0.692111i | −0.270585 | − | 0.962696i | \(-0.587217\pi\) |
0.962696 | + | 0.270585i | \(0.0872171\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.95685 | −0.000822399 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1337.57i | − | 0.275103i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1795.69 | + | 4573.08i | 0.365498 | + | 0.930812i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.4851i | 0.00352231i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6222.10 | 1.24061 | 0.620305 | − | 0.784360i | \(-0.287009\pi\) | ||||
0.620305 | + | 0.784360i | \(0.287009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1374.15 | − | 1374.15i | 0.271208 | − | 0.271208i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 157.581i | − | 0.0307871i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2035.87 | − | 2035.87i | 0.393770 | − | 0.393770i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −219.721 | − | 219.721i | −0.0420747 | − | 0.0420747i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.2175 | + | 32.2175i | 0.00610841 | + | 0.00610841i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 611.341 | 0.114771 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 478.173 | 0.0888951 | 0.0444475 | − | 0.999012i | \(-0.485847\pi\) | ||||
0.0444475 | + | 0.999012i | \(0.485847\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.2589 | + | 21.2589i | 0.00391384 | + | 0.00391384i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5088.61 | − | 5088.61i | −0.927809 | − | 0.927809i | 0.0697553 | − | 0.997564i | \(-0.477778\pi\) |
−0.997564 | + | 0.0697553i | \(0.977778\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6588.67 | − | 6588.67i | 1.18982 | − | 1.18982i | 0.212703 | − | 0.977117i | \(-0.431773\pi\) |
0.977117 | − | 0.212703i | \(-0.0682268\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 459.664i | − | 0.0822195i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −939.884 | + | 939.884i | −0.166527 | + | 0.166527i | −0.785451 | − | 0.618924i | \(-0.787569\pi\) |
0.618924 | + | 0.785451i | \(0.287569\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1072.13 | −0.188175 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 67.8901i | − | 0.0118045i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −987.374 | + | 1448.47i | −0.170090 | + | 0.249521i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2253.72i | − | 0.384657i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 76.1600 | 0.0128797 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1123.43 | + | 1123.43i | −0.188257 | + | 0.188257i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10372.7i | 1.72246i | 0.508218 | + | 0.861229i | \(0.330305\pi\) | ||||
−0.508218 | + | 0.861229i | \(0.669695\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6730.30 | + | 6730.30i | −1.10756 | + | 1.10756i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 876.350 | + | 876.350i | 0.142926 | + | 0.142926i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5162.49 | − | 5162.49i | −0.834476 | − | 0.834476i | 0.153649 | − | 0.988125i | \(-0.450897\pi\) |
−0.988125 | + | 0.153649i | \(0.950897\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.9256 | 0.00207087 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11789.9 | 1.87232 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2791.79 | − | 2791.79i | −0.439483 | − | 0.439483i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.7455 | − | 16.7455i | −0.00261318 | − | 0.00261318i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3136.83 | + | 3136.83i | −0.485285 | + | 0.485285i | −0.906815 | − | 0.421529i | \(-0.861493\pi\) |
0.421529 | + | 0.906815i | \(0.361493\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3795.57i | 0.582155i | 0.956699 | + | 0.291078i | \(0.0940138\pi\) | ||||
−0.956699 | + | 0.291078i | \(0.905986\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 41.5166 | − | 41.5166i | 0.00631337 | − | 0.00631337i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6298.80 | −0.949721 | −0.474860 | − | 0.880061i | \(-0.657501\pi\) | ||||
−0.474860 | + | 0.880061i | \(0.657501\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1512.26i | − | 0.226091i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.9177 | + | 13.5772i | 0.00295282 | + | 0.00201283i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 4063.54i | − | 0.597397i | −0.954348 | − | 0.298699i | \(-0.903447\pi\) | ||
0.954348 | − | 0.298699i | \(-0.0965525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6233.52 | 0.908809 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 53.3288 | − | 53.3288i | 0.00771085 | − | 0.00771085i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 753.476i | 0.108051i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6960.90 | + | 6960.90i | −0.990071 | + | 0.990071i | −0.999951 | − | 0.00987975i | \(-0.996855\pi\) |
0.00987975 | + | 0.999951i | \(0.496855\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4197.16 | + | 4197.16i | 0.592128 | + | 0.592128i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −439.374 | − | 439.374i | −0.0614856 | − | 0.0614856i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10995.7 | 1.52638 | 0.763188 | − | 0.646177i | \(-0.223633\pi\) | ||||
0.763188 | + | 0.646177i | \(0.223633\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −38.3140 | −0.00527607 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −282.467 | − | 282.467i | −0.0385883 | − | 0.0385883i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 57.7292 | + | 57.7292i | 0.00782415 | + | 0.00782415i | 0.711008 | − | 0.703184i | \(-0.248239\pi\) |
−0.703184 | + | 0.711008i | \(0.748239\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.60758 | + | 5.60758i | −0.000754029 | + | 0.000754029i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1528.32i | 0.203899i | 0.994790 | + | 0.101949i | \(0.0325080\pi\) | ||||
−0.994790 | + | 0.101949i | \(0.967492\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 621.546 | − | 621.546i | 0.0822777 | − | 0.0822777i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1378.92 | 0.181122 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7868.90i | 1.02563i | 0.858500 | + | 0.512813i | \(0.171397\pi\) | ||||
−0.858500 | + | 0.512813i | \(0.828603\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10308.6 | + | 1951.39i | −1.33332 | + | 0.252394i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 23.0287i | − | 0.00295584i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 88.4244 | 0.0112636 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7541.37 | + | 7541.37i | −0.953376 | + | 0.953376i | −0.998961 | − | 0.0455841i | \(-0.985485\pi\) |
0.0455841 | + | 0.998961i | \(0.485485\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.60085i | 0.00107915i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9284.96 | + | 9284.96i | −1.15628 | + | 1.15628i | −0.171013 | + | 0.985269i | \(0.554704\pi\) |
−0.985269 | + | 0.171013i | \(0.945296\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3106.21 | + | 3106.21i | 0.383949 | + | 0.383949i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1442.20 | + | 1442.20i | 0.176947 | + | 0.176947i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18201.1 | −2.21669 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12487.9 | 1.50975 | 0.754877 | − | 0.655867i | \(-0.227697\pi\) | ||||
0.754877 | + | 0.655867i | \(0.227697\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 110.076 | + | 110.076i | 0.0132108 | + | 0.0132108i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2986.95 | − | 2986.95i | −0.355879 | − | 0.355879i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1324.82 | + | 1324.82i | −0.156705 | + | 0.156705i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 127.544i | − | 0.0149780i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1686.42 | − | 1686.42i | 0.196628 | − | 0.196628i | −0.601925 | − | 0.798553i | \(-0.705599\pi\) |
0.798553 | + | 0.601925i | \(0.205599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4179.68 | 0.483860 | 0.241930 | − | 0.970294i | \(-0.422220\pi\) | ||||
0.241930 | + | 0.970294i | \(0.422220\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 7050.38i | − | 0.810405i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4625.72 | + | 6785.92i | −0.527954 | + | 0.774507i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1328.85i | − | 0.150603i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 56.1344 | 0.00631747 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5546.33 | − | 5546.33i | 0.619854 | − | 0.619854i | −0.325640 | − | 0.945494i | \(-0.605580\pi\) |
0.945494 | + | 0.325640i | \(0.105580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1323.79i | 0.146922i | 0.997298 | + | 0.0734610i | \(0.0234044\pi\) | ||||
−0.997298 | + | 0.0734610i | \(0.976596\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.32336 | + | 2.32336i | −0.000256084 | + | 0.000256084i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2647.05 | − | 2647.05i | −0.289761 | − | 0.289761i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10146.7 | + | 10146.7i | 1.10313 | + | 1.10313i | 0.994030 | + | 0.109103i | \(0.0347979\pi\) |
0.109103 | + | 0.994030i | \(0.465202\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8260.75 | 0.891993 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5281.03 | 0.566387 | 0.283193 | − | 0.959063i | \(-0.408606\pi\) | ||||
0.283193 | + | 0.959063i | \(0.408606\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2344.15 | − | 2344.15i | −0.249716 | − | 0.249716i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 67.5277 | + | 67.5277i | 0.00714530 | + | 0.00714530i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2107.89 | − | 2107.89i | 0.221553 | − | 0.221553i | −0.587599 | − | 0.809152i | \(-0.699927\pi\) |
0.809152 | + | 0.587599i | \(0.199927\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11350.6i | 1.18510i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.3404 | − | 26.3404i | 0.00273196 | − | 0.00273196i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 327.508 | 0.0337447 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1746.31i | − | 0.178750i | −0.995998 | − | 0.0893750i | \(-0.971513\pi\) | ||
0.995998 | − | 0.0893750i | \(-0.0284870\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −210.219 | + | 39.7939i | −0.0213773 | + | 0.00404666i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 12493.9i | − | 1.26226i | −0.775679 | − | 0.631128i | \(-0.782592\pi\) | ||
0.775679 | − | 0.631128i | \(-0.217408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9171.67 | −0.920612 | −0.460306 | − | 0.887760i | \(-0.652260\pi\) | ||||
−0.460306 | + | 0.887760i | \(0.652260\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.5493 | − | 25.5493i | 0.00254800 | − | 0.00254800i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2173.91i | 0.215410i | 0.994183 | + | 0.107705i | \(0.0343502\pi\) | ||||
−0.994183 | + | 0.107705i | \(0.965650\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1904.89 | − | 1904.89i | 0.187547 | − | 0.187547i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −68.9765 | − | 68.9765i | −0.00674792 | − | 0.00674792i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1864.54 | + | 1864.54i | 0.181251 | + | 0.181251i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2930.30 | −0.283055 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2757.41 | 0.264682 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11222.9 | − | 11222.9i | −1.07054 | − | 1.07054i | −0.997316 | − | 0.0732221i | \(-0.976672\pi\) |
−0.0732221 | − | 0.997316i | \(-0.523328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4795.31 | − | 4795.31i | −0.454568 | − | 0.454568i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −36.3990 | + | 36.3990i | −0.00342901 | + | 0.00342901i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 865.686i | − | 0.0810491i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 210.075 | − | 210.075i | 0.0195470 | − | 0.0195470i | −0.697266 | − | 0.716813i | \(-0.745600\pi\) |
0.716813 | + | 0.697266i | \(0.245600\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −128.225 | −0.0118579 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8812.02i | − | 0.809941i | −0.914330 | − | 0.404970i | \(-0.867282\pi\) | ||
0.914330 | − | 0.404970i | \(-0.132718\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 270.746 | + | 1430.27i | 0.0247338 | + | 0.130661i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3900.68i | 0.354187i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3287.13 | −0.296676 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13173.4 | − | 13173.4i | 1.18180 | − | 1.18180i | 0.202529 | − | 0.979276i | \(-0.435084\pi\) |
0.979276 | − | 0.202529i | \(-0.0649159\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 138.810i | 0.0123784i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 239.890 | − | 239.890i | 0.0212647 | − | 0.0212647i | −0.696394 | − | 0.717659i | \(-0.745214\pi\) |
0.717659 | + | 0.696394i | \(0.245214\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1595.09 | − | 1595.09i | −0.140556 | − | 0.140556i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −73.0300 | − | 73.0300i | −0.00639719 | − | 0.00639719i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9045.53 | −0.787693 | −0.393847 | − | 0.919176i | \(-0.628856\pi\) | ||||
−0.393847 | + | 0.919176i | \(0.628856\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1637.80 | 0.141785 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −53.9802 | − | 53.9802i | −0.00464578 | − | 0.00464578i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1052.53 | − | 1052.53i | −0.0900583 | − | 0.0900583i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9533.35 | − | 9533.35i | 0.810979 | − | 0.810979i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.3207i | 0.00146492i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2882.23 | − | 2882.23i | 0.242366 | − | 0.242366i | −0.575462 | − | 0.817828i | \(-0.695178\pi\) |
0.817828 | + | 0.575462i | \(0.195178\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22649.5 | 1.89368 | 0.946839 | − | 0.321707i | \(-0.104257\pi\) | ||||
0.946839 | + | 0.321707i | \(0.104257\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 40.2939i | 0.00334966i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2977.31 | − | 15728.2i | −0.246098 | − | 1.30006i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 10237.7i | − | 0.841436i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18745.4 | 1.53198 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2990.46 | + | 2990.46i | −0.243023 | + | 0.243023i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3361.24i | 0.271625i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −109.599 | + | 109.599i | −0.00880733 | + | 0.00880733i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11170.0 | + | 11170.0i | 0.892625 | + | 0.892625i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8794.59 | − | 8794.59i | −0.698908 | − | 0.698908i | 0.265267 | − | 0.964175i | \(-0.414540\pi\) |
−0.964175 | + | 0.265267i | \(0.914540\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 87.7256 | 0.00693308 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3770.69 | −0.296364 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9867.73 | − | 9867.73i | −0.771323 | − | 0.771323i | 0.207015 | − | 0.978338i | \(-0.433625\pi\) |
−0.978338 | + | 0.207015i | \(0.933625\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4169.78 | + | 4169.78i | 0.324156 | + | 0.324156i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −367.265 | + | 367.265i | −0.0283957 | + | 0.0283957i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 192.205i | − | 0.0147801i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −39.4426 | + | 39.4426i | −0.00301666 | + | 0.00301666i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17027.0 | −1.29526 | −0.647629 | − | 0.761956i | \(-0.724239\pi\) | ||||
−0.647629 | + | 0.761956i | \(0.724239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 982.473i | 0.0743366i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −169.020 | − | 115.215i | −0.0127202 | − | 0.00867093i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23996.7i | 1.79634i | 0.439649 | + | 0.898170i | \(0.355103\pi\) | ||||
−0.439649 | + | 0.898170i | \(0.644897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −639.949 | −0.0476510 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3134.86 | − | 3134.86i | 0.232190 | − | 0.232190i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 442.338i | 0.0325901i | 0.999867 | + | 0.0162951i | \(0.00518711\pi\) | ||||
−0.999867 | + | 0.0162951i | \(0.994813\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4060.36 | − | 4060.36i | 0.297584 | − | 0.297584i | −0.542483 | − | 0.840067i | \(-0.682516\pi\) |
0.840067 | + | 0.542483i | \(0.182516\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 154.351 | + | 154.351i | 0.0112532 | + | 0.0112532i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12401.1 | − | 12401.1i | −0.899411 | − | 0.899411i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6432.83 | −0.464129 | −0.232064 | − | 0.972700i | \(-0.574548\pi\) | ||||
−0.232064 | + | 0.972700i | \(0.574548\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 83.4363 | 0.00598877 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2879.71 | + | 2879.71i | 0.205629 | + | 0.205629i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3728.51 | + | 3728.51i | 0.264870 | + | 0.264870i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1027.68 | + | 1027.68i | −0.0726317 | + | 0.0726317i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 5080.96i | − | 0.357264i | −0.983916 | − | 0.178632i | \(-0.942833\pi\) | ||
0.983916 | − | 0.178632i | \(-0.0571671\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4038.71 | − | 4038.71i | 0.282534 | − | 0.282534i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −302.368 | −0.0210453 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15267.6i | − | 1.05727i | −0.848848 | − | 0.528637i | \(-0.822703\pi\) | ||
0.848848 | − | 0.528637i | \(-0.177297\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −986.125 | − | 672.207i | −0.0679449 | − | 0.0463156i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 209.424i | 0.0143570i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14852.3 | 1.01310 | 0.506551 | − | 0.862210i | \(-0.330920\pi\) | ||||
0.506551 | + | 0.862210i | \(0.330920\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6958.91 | + | 6958.91i | −0.472313 | + | 0.472313i | −0.902662 | − | 0.430349i | \(-0.858390\pi\) |
0.430349 | + | 0.902662i | \(0.358390\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11954.7i | 0.807348i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2640.31 | + | 2640.31i | −0.177428 | + | 0.177428i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2781.06 | + | 2781.06i | 0.185964 | + | 0.185964i | 0.793949 | − | 0.607985i | \(-0.208022\pi\) |
−0.607985 | + | 0.793949i | \(0.708022\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.05020 | + | 5.05020i | 0.000336033 | + | 0.000336033i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5023.36 | 0.332608 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3388.18 | 0.223242 | 0.111621 | − | 0.993751i | \(-0.464396\pi\) | ||||
0.111621 | + | 0.993751i | \(0.464396\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.5972 | + | 24.5972i | 0.00161277 | + | 0.00161277i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8426.48 | − | 8426.48i | −0.549818 | − | 0.549818i | 0.376570 | − | 0.926388i | \(-0.377103\pi\) |
−0.926388 | + | 0.376570i | \(0.877103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5634.61 | + | 5634.61i | −0.365871 | + | 0.365871i | −0.865969 | − | 0.500098i | \(-0.833297\pi\) |
0.500098 | + | 0.865969i | \(0.333297\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 456.891i | − | 0.0295240i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5095.39 | + | 5095.39i | −0.327677 | + | 0.327677i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12748.9 | −0.815931 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 72.9864i | − | 0.00464879i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4596.32 | + | 24280.9i | 0.291363 | + | 1.53918i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15781.0i | 0.995612i | 0.867288 | + | 0.497806i | \(0.165861\pi\) | ||||
−0.867288 | + | 0.497806i | \(0.834139\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −56.6165 | −0.00355498 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 277.631 | − | 277.631i | 0.0173503 | − | 0.0173503i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5885.75i | 0.366094i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10314.6 | − | 10314.6i | 0.638562 | − | 0.638562i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13468.8 | − | 13468.8i | −0.829930 | − | 0.829930i | 0.157577 | − | 0.987507i | \(-0.449632\pi\) |
−0.987507 | + | 0.157577i | \(0.949632\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18993.3 | + | 18993.3i | 1.16489 | + | 1.16489i | 0.983391 | + | 0.181499i | \(0.0580949\pi\) |
0.181499 | + | 0.983391i | \(0.441905\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.08108 | 0.000493321 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22573.9 | −1.37167 | −0.685835 | − | 0.727757i | \(-0.740563\pi\) | ||||
−0.685835 | + | 0.727757i | \(0.740563\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25347.1 | + | 25347.1i | 1.53306 | + | 1.53306i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −55.5356 | − | 55.5356i | −0.00334349 | − | 0.00334349i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3162.80 | − | 3162.80i | 0.189540 | − | 0.189540i | −0.605957 | − | 0.795497i | \(-0.707210\pi\) |
0.795497 | + | 0.605957i | \(0.207210\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1140.15i | 0.0680145i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5139.24 | + | 5139.24i | −0.305176 | + | 0.305176i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11439.0 | −0.676174 | −0.338087 | − | 0.941115i | \(-0.609780\pi\) | ||||
−0.338087 | + | 0.941115i | \(0.609780\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11381.6i | 0.669730i | 0.942266 | + | 0.334865i | \(0.108691\pi\) | ||||
−0.942266 | + | 0.334865i | \(0.891309\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.1756 | − | 74.8855i | −0.000830371 | − | 0.00438659i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 425.829i | − | 0.0248315i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3108.55 | −0.180455 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −178.152 | + | 178.152i | −0.0102956 | + | 0.0102956i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11276.5i | 0.648771i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8821.52 | + | 8821.52i | −0.505267 | + | 0.505267i | −0.913070 | − | 0.407803i | \(-0.866295\pi\) |
0.407803 | + | 0.913070i | \(0.366295\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −252.891 | − | 252.891i | −0.0144204 | − | 0.0144204i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8725.07 | − | 8725.07i | −0.495320 | − | 0.495320i | 0.414657 | − | 0.909978i | \(-0.363901\pi\) |
−0.909978 | + | 0.414657i | \(0.863901\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1881.71 | −0.106352 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 198.670 | 0.0111792 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12158.3 | − | 12158.3i | −0.681146 | − | 0.681146i | 0.279113 | − | 0.960258i | \(-0.409960\pi\) |
−0.960258 | + | 0.279113i | \(0.909960\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5449.86 | − | 5449.86i | −0.303983 | − | 0.303983i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −184.263 | + | 184.263i | −0.0102330 | + | 0.0102330i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1964.64i | 0.108631i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2132.44 | − | 2132.44i | 0.117398 | − | 0.117398i | −0.645967 | − | 0.763365i | \(-0.723546\pi\) |
0.763365 | + | 0.645967i | \(0.223546\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8478.76 | 0.464764 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6314.69i | 0.344647i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15142.1 | − | 2866.36i | 0.822882 | − | 0.155769i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 161.465i | 0.00873700i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31729.0 | −1.70954 | −0.854770 | − | 0.519007i | \(-0.826302\pi\) | ||||
−0.854770 | + | 0.519007i | \(0.826302\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6234.89 | + | 6234.89i | −0.334500 | + | 0.334500i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 41.3184i | − | 0.00220729i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3467.19 | + | 3467.19i | −0.184437 | + | 0.184437i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18575.2 | + | 18575.2i | 0.983930 | + | 0.983930i | 0.999873 | − | 0.0159433i | \(-0.00507512\pi\) |
−0.0159433 | + | 0.999873i | \(0.505075\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 603.117 | + | 603.117i | 0.0318124 | + | 0.0318124i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34183.9 | 1.79551 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2779.22 | −0.145366 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 261.204 | + | 261.204i | 0.0136051 | + | 0.0136051i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17278.6 | + | 17278.6i | 0.896222 | + | 0.896222i | 0.995100 | − | 0.0988778i | \(-0.0315253\pi\) |
−0.0988778 | + | 0.995100i | \(0.531525\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2287.84 | + | 2287.84i | −0.118174 | + | 0.118174i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 188.691i | − | 0.00970607i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1720.59 | + | 1720.59i | −0.0881396 | + | 0.0881396i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7209.98 | −0.367818 | −0.183909 | − | 0.982943i | \(-0.558875\pi\) | ||||
−0.183909 | + | 0.982943i | \(0.558875\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19669.0i | 0.999290i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2016.51 | − | 2958.22i | 0.102029 | − | 0.149677i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21640.2i | − | 1.09045i | −0.838290 | − | 0.545225i | \(-0.816444\pi\) | ||
0.838290 | − | 0.545225i | \(-0.183556\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 48.4117 | 0.00242951 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16164.8 | + | 16164.8i | −0.807920 | + | 0.807920i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 34704.0i | − | 1.72748i | −0.503940 | − | 0.863738i | \(-0.668117\pi\) | ||
0.503940 | − | 0.863738i | \(-0.331883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19.2292 | − | 19.2292i | 0.000953309 | − | 0.000953309i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23978.2 | − | 23978.2i | −1.18395 | − | 1.18395i | −0.978712 | − | 0.205241i | \(-0.934202\pi\) |
−0.205241 | − | 0.978712i | \(-0.565798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3343.30 | − | 3343.30i | −0.164415 | − | 0.164415i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18072.4 | −0.885186 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7306.20 | 0.356426 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 431.344 | + | 431.344i | 0.0209587 | + | 0.0209587i | 0.717508 | − | 0.696550i | \(-0.245282\pi\) |
−0.696550 | + | 0.717508i | \(0.745282\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 88.9530 | + | 88.9530i | 0.00430495 | + | 0.00430495i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1304.11 | + | 1304.11i | −0.0628629 | + | 0.0628629i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 11527.3i | − | 0.553457i | −0.960948 | − | 0.276729i | \(-0.910750\pi\) | ||
0.960948 | − | 0.276729i | \(-0.0892503\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 308.880 | − | 308.880i | 0.0147716 | − | 0.0147716i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35908.5 | 1.71049 | 0.855246 | − | 0.518223i | \(-0.173406\pi\) | ||||
0.855246 | + | 0.518223i | \(0.173406\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8196.19i | 0.388889i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5203.66 | − | 985.040i | 0.245933 | − | 0.0465545i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13356.0i | 0.628758i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4159.74 | −0.195064 | −0.0975320 | − | 0.995232i | \(-0.531095\pi\) | ||||
−0.0975320 | + | 0.995232i | \(0.531095\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 196.968 | − | 196.968i | 0.00920055 | − | 0.00920055i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 38339.5i | − | 1.78393i | −0.452106 | − | 0.891964i | \(-0.649327\pi\) | ||
0.452106 | − | 0.891964i | \(-0.350673\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18920.9 | − | 18920.9i | 0.876978 | − | 0.876978i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 85.7348 | + | 85.7348i | 0.00395845 | + | 0.00395845i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3888.21 | + | 3888.21i | 0.178831 | + | 0.178831i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27894.4 | 1.27803 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −63.3915 | −0.00289327 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3415.03 | + | 3415.03i | 0.155271 | + | 0.155271i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10975.5 | − | 10975.5i | −0.497123 | − | 0.497123i | 0.413418 | − | 0.910541i | \(-0.364335\pi\) |
−0.910541 | + | 0.413418i | \(0.864335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −216.796 | + | 216.796i | −0.00978217 | + | 0.00978217i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1391.03i | 0.0625276i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2970.95 | + | 2970.95i | −0.133041 | + | 0.133041i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.1597 | 0.000720912 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 483.686i | 0.0214969i | 0.999942 | + | 0.0107484i | \(0.00342140\pi\) | ||||
−0.999942 | + | 0.0107484i | \(0.996579\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15125.3 | − | 10310.4i | −0.669706 | − | 0.456515i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 31977.5i | − | 1.41057i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13898.3 | −0.610785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1802.12 | − | 1802.12i | 0.0789023 | − | 0.0789023i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 112.035i | − | 0.00488702i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11349.9 | + | 11349.9i | −0.493252 | + | 0.493252i | −0.909329 | − | 0.416077i | \(-0.863405\pi\) |
0.416077 | + | 0.909329i | \(0.363405\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7111.36 | − | 7111.36i | −0.307908 | − | 0.307908i | 0.536189 | − | 0.844098i | \(-0.319863\pi\) |
−0.844098 | + | 0.536189i | \(0.819863\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −140.309 | − | 140.309i | −0.00605270 | − | 0.00605270i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6348.42 | 0.272854 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1277.42 | 0.0547016 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2233.84 | + | 2233.84i | 0.0953072 | + | 0.0953072i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29059.7 | + | 29059.7i | 1.23531 | + | 1.23531i | 0.961896 | + | 0.273415i | \(0.0881532\pi\) |
0.273415 | + | 0.961896i | \(0.411847\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3018.11 | + | 3018.11i | −0.127831 | + | 0.127831i | −0.768128 | − | 0.640297i | \(-0.778811\pi\) |
0.640297 | + | 0.768128i | \(0.278811\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 341.932i | − | 0.0144298i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9959.68 | − | 9959.68i | 0.418781 | − | 0.418781i | −0.466002 | − | 0.884783i | \(-0.654306\pi\) |
0.884783 | + | 0.466002i | \(0.154306\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42024.2 | −1.76063 | −0.880314 | − | 0.474391i | \(-0.842668\pi\) | ||||
−0.880314 | + | 0.474391i | \(0.842668\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 432.548i | − | 0.0180565i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12080.4 | − | 17721.9i | 0.502475 | − | 0.737129i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 6872.51i | − | 0.284830i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 697.099 | 0.0287876 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32650.7 | − | 32650.7i | 1.34354 | − | 1.34354i | 0.451024 | − | 0.892512i | \(-0.351059\pi\) |
0.892512 | − | 0.451024i | \(-0.148941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 23957.7i | − | 0.982316i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −180.652 | + | 180.652i | −0.00738076 | + | 0.00738076i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3615.72 | + | 3615.72i | 0.147201 | + | 0.147201i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5739.14 | + | 5739.14i | 0.232821 | + | 0.232821i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 263.418 | 0.0106484 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −52772.4 | −2.12575 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33363.7 | + | 33363.7i | 1.33922 | + | 1.33922i | 0.896819 | + | 0.442397i | \(0.145872\pi\) |
0.442397 | + | 0.896819i | \(0.354128\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1336.20 | + | 1336.20i | 0.0534470 | + | 0.0534470i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11067.4 | − | 11067.4i | 0.441139 | − | 0.441139i | −0.451255 | − | 0.892395i | \(-0.649024\pi\) |
0.892395 | + | 0.451255i | \(0.149024\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 34645.2i | − | 1.37611i | −0.725658 | − | 0.688056i | \(-0.758464\pi\) | ||
0.725658 | − | 0.688056i | \(-0.241536\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 53.4660 | − | 53.4660i | 0.00211628 | − | 0.00211628i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28318.9 | 1.11702 | 0.558508 | − | 0.829499i | \(-0.311374\pi\) | ||||
0.558508 | + | 0.829499i | \(0.311374\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 857.550i | − | 0.0337082i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −111.019 | + | 254.575i | −0.00434878 | + | 0.00997211i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1631.04i | 0.0636700i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8517.63 | −0.331354 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5904.59 | − | 5904.59i | 0.228912 | − | 0.228912i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 4123.28i | − | 0.159306i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9654.78 | − | 9654.78i | 0.371743 | − | 0.371743i | −0.496369 | − | 0.868112i | \(-0.665334\pi\) |
0.868112 | + | 0.496369i | \(0.165334\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 248.712 | + | 248.712i | 0.00954363 | + | 0.00954363i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4554.04 | + | 4554.04i | 0.174154 | + | 0.174154i | 0.788802 | − | 0.614648i | \(-0.210702\pi\) |
−0.614648 | + | 0.788802i | \(0.710702\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35594.1 | −1.35655 | −0.678277 | − | 0.734807i | \(-0.737273\pi\) | ||||
−0.678277 | + | 0.734807i | \(0.737273\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 109.856 | 0.00417264 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22055.1 | + | 22055.1i | 0.834881 | + | 0.834881i | 0.988180 | − | 0.153299i | \(-0.0489898\pi\) |
−0.153299 | + | 0.988180i | \(0.548990\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −603.477 | − | 603.477i | −0.0227671 | − | 0.0227671i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26602.3 | + | 26602.3i | −1.00023 | + | 1.00023i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 6531.41i | − | 0.244754i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5426.24 | − | 5426.24i | 0.202658 | − | 0.202658i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 162.757 | 0.00605830 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 4742.85i | − | 0.175954i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4032.41 | − | 5915.53i | 0.149100 | − | 0.218729i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 17.5655i | − | 0.000647335i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4343.30 | −0.159532 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13912.2 | + | 13912.2i | −0.509313 | + | 0.509313i | −0.914315 | − | 0.405003i | \(-0.867271\pi\) |
0.405003 | + | 0.914315i | \(0.367271\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 21759.3i | − | 0.793960i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25127.5 | − | 25127.5i | 0.913843 | − | 0.913843i | −0.0827295 | − | 0.996572i | \(-0.526364\pi\) |
0.996572 | + | 0.0827295i | \(0.0263638\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24437.0 | − | 24437.0i | −0.885813 | − | 0.885813i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.4367 | + | 24.4367i | 0.000882901 | + | 0.000882901i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2478.31 | 0.0892485 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 378.693 | 0.0135930 | 0.00679648 | − | 0.999977i | \(-0.497837\pi\) | ||||
0.00679648 | + | 0.999977i | \(0.497837\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.1137 | + | 19.1137i | 0.000683842 | + | 0.000683842i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7349.14 | + | 7349.14i | 0.262080 | + | 0.262080i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29209.7 | + | 29209.7i | −1.03828 | + | 1.03828i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 14358.0i | − | 0.508714i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9344.29 | + | 9344.29i | −0.330007 | + | 0.330007i | −0.852589 | − | 0.522582i | \(-0.824969\pi\) |
0.522582 | + | 0.852589i | \(0.324969\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7652.68 | 0.269395 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 406.808i | − | 0.0142747i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8368.21 | + | 5704.31i | 0.292695 | + | 0.199520i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34950.5i | 1.21855i | 0.792959 | + | 0.609275i | \(0.208540\pi\) | ||||
−0.792959 | + | 0.609275i | \(0.791460\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 526.730 | 0.0183058 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9450.53 | + | 9450.53i | −0.327395 | + | 0.327395i | −0.851595 | − | 0.524200i | \(-0.824364\pi\) |
0.524200 | + | 0.851595i | \(0.324364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32910.0i | 1.13648i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 36.7499 | − | 36.7499i | 0.00126505 | − | 0.00126505i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18549.3 | + | 18549.3i | 0.636506 | + | 0.636506i | 0.949692 | − | 0.313186i | \(-0.101396\pi\) |
−0.313186 | + | 0.949692i | \(0.601396\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3661.68 | − | 3661.68i | −0.125251 | − | 0.125251i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −75.1388 | −0.00256208 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19074.4 | −0.648352 | −0.324176 | − | 0.945997i | \(-0.605087\pi\) | ||||
−0.324176 | + | 0.945997i | \(0.605087\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7641.92 | − | 7641.92i | −0.258939 | − | 0.258939i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −42.8557 | − | 42.8557i | −0.00144757 | − | 0.00144757i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11846.2 | + | 11846.2i | −0.398887 | + | 0.398887i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22364.8i | 0.750724i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22926.0 | + | 22926.0i | −0.767166 | + | 0.767166i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4130.94 | −0.137803 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6142.31i | 0.204264i | 0.994771 | + | 0.102132i | \(0.0325664\pi\) | ||||
−0.994771 | + | 0.102132i | \(0.967434\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −97.3666 | + | 18.4312i | −0.00322793 | + | 0.000611039i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 56958.3i | 1.88247i | 0.337750 | + | 0.941236i | \(0.390334\pi\) | ||||
−0.337750 | + | 0.941236i | \(0.609666\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13726.0 | 0.452246 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 90.0863 | − | 90.0863i | 0.00295905 | − | 0.00295905i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 11185.4i | − | 0.366277i | −0.983087 | − | 0.183138i | \(-0.941374\pi\) | ||
0.983087 | − | 0.183138i | \(-0.0586257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43239.2 | − | 43239.2i | 1.41157 | − | 1.41157i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25718.7 | − | 25718.7i | −0.837040 | − | 0.837040i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20875.7 | + | 20875.7i | 0.677348 | + | 0.677348i | 0.959399 | − | 0.282052i | \(-0.0910150\pi\) |
−0.282052 | + | 0.959399i | \(0.591015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14970.3 | 0.484256 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −89.8121 | −0.00289641 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5406.06 | + | 5406.06i | 0.173815 | + | 0.173815i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30805.3 | + | 30805.3i | 0.987450 | + | 0.987450i | 0.999922 | − | 0.0124723i | \(-0.00397017\pi\) |
−0.0124723 | + | 0.999922i | \(0.503970\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −414.620 | + | 414.620i | −0.0132503 | + | 0.0132503i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 10368.6i | − | 0.330358i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28690.5 | + | 28690.5i | −0.911370 | + | 0.911370i | −0.996380 | − | 0.0850098i | \(-0.972908\pi\) |
0.0850098 | + | 0.996380i | \(0.472908\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1076.17 | −0.0340825 |
(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 | 136.4.k.b.81.4 | ✓ | 14 | |
4.3 | odd | 2 | 272.4.o.f.81.4 | 14 | |||
17.2 | even | 8 | 2312.4.a.l.1.8 | 14 | |||
17.4 | even | 4 | inner | 136.4.k.b.89.4 | yes | 14 | |
17.15 | even | 8 | 2312.4.a.l.1.7 | 14 | |||
68.55 | odd | 4 | 272.4.o.f.225.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.k.b.81.4 | ✓ | 14 | 1.1 | even | 1 | trivial | |
136.4.k.b.89.4 | yes | 14 | 17.4 | even | 4 | inner | |
272.4.o.f.81.4 | 14 | 4.3 | odd | 2 | |||
272.4.o.f.225.4 | 14 | 68.55 | odd | 4 | |||
2312.4.a.l.1.7 | 14 | 17.15 | even | 8 | |||
2312.4.a.l.1.8 | 14 | 17.2 | even | 8 |