Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(383,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.383");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.f (of order \(2\), degree \(1\), 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: | \(45.3134668844\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.12960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 12) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.4 | ||
Root | \(0.535233 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.383 |
Dual form | 768.4.f.c.383.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −3.87298 | + | 3.46410i | −0.745356 | + | 0.666667i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.94427 | 0.800000 | 0.400000 | − | 0.916515i | \(-0.369010\pi\) | ||||
0.400000 | + | 0.916515i | \(0.369010\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.74597i | − | 0.418243i | −0.977890 | − | 0.209121i | \(-0.932940\pi\) | ||
0.977890 | − | 0.209121i | \(-0.0670604\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | − | 26.8328i | 0.111111 | − | 0.993808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 34.6410i | 0.949514i | 0.880117 | + | 0.474757i | \(0.157464\pi\) | ||||
−0.880117 | + | 0.474757i | \(0.842536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.0000i | 0.213346i | 0.994294 | + | 0.106673i | \(0.0340198\pi\) | ||||
−0.994294 | + | 0.106673i | \(0.965980\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −34.6410 | + | 30.9839i | −0.596285 | + | 0.533333i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 35.7771i | − | 0.510425i | −0.966885 | − | 0.255212i | \(-0.917855\pi\) | ||
0.966885 | − | 0.255212i | \(-0.0821454\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −69.7137 | −0.841759 | −0.420879 | − | 0.907117i | \(-0.638278\pi\) | ||||
−0.420879 | + | 0.907117i | \(0.638278\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 26.8328 | + | 30.0000i | 0.278829 | + | 0.311740i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 96.9948 | 0.879340 | 0.439670 | − | 0.898159i | \(-0.355095\pi\) | ||||
0.439670 | + | 0.898159i | \(0.355095\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −45.0000 | −0.360000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 81.3327 | + | 114.315i | 0.579721 | + | 0.814815i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 152.053 | 0.973637 | 0.486818 | − | 0.873503i | \(-0.338157\pi\) | ||||
0.486818 | + | 0.873503i | \(0.338157\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 224.633i | 1.30146i | 0.759309 | + | 0.650730i | \(0.225537\pi\) | ||||
−0.759309 | + | 0.650730i | \(0.774463\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −120.000 | − | 134.164i | −0.633010 | − | 0.707726i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 69.2820i | − | 0.334594i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 130.000i | − | 0.577618i | −0.957387 | − | 0.288809i | \(-0.906741\pi\) | ||
0.957387 | − | 0.288809i | \(-0.0932593\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −34.6410 | − | 38.7298i | −0.142231 | − | 0.159019i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 125.220i | − | 0.476977i | −0.971145 | − | 0.238488i | \(-0.923348\pi\) | ||
0.971145 | − | 0.238488i | \(-0.0766519\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 224.633 | 0.796656 | 0.398328 | − | 0.917243i | \(-0.369591\pi\) | ||||
0.398328 | + | 0.917243i | \(0.369591\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 26.8328 | − | 240.000i | 0.0888889 | − | 0.795046i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −193.990 | −0.602049 | −0.301025 | − | 0.953616i | \(-0.597329\pi\) | ||||
−0.301025 | + | 0.953616i | \(0.597329\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 283.000 | 0.825073 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 123.935 | + | 138.564i | 0.340283 | + | 0.380448i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 545.601 | 1.41404 | 0.707019 | − | 0.707195i | \(-0.250040\pi\) | ||||
0.707019 | + | 0.707195i | \(0.250040\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 309.839i | 0.759612i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 270.000 | − | 241.495i | 0.627410 | − | 0.561173i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 173.205i | 0.382193i | 0.981571 | + | 0.191096i | \(0.0612043\pi\) | ||||
−0.981571 | + | 0.191096i | \(0.938796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 442.000i | 0.927743i | 0.885903 | + | 0.463871i | \(0.153540\pi\) | ||||
−0.885903 | + | 0.463871i | \(0.846460\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −207.846 | − | 23.2379i | −0.415653 | − | 0.0464714i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 89.4427i | 0.170677i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 735.867 | 1.34180 | 0.670899 | − | 0.741549i | \(-0.265908\pi\) | ||||
0.670899 | + | 0.741549i | \(0.265908\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −375.659 | + | 336.000i | −0.655421 | + | 0.586227i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1039.23 | −1.73710 | −0.868549 | − | 0.495603i | \(-0.834947\pi\) | ||||
−0.868549 | + | 0.495603i | \(0.834947\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −410.000 | −0.657354 | −0.328677 | − | 0.944442i | \(-0.606603\pi\) | ||||
−0.328677 | + | 0.944442i | \(0.606603\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 174.284 | − | 155.885i | 0.268328 | − | 0.240000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 268.328 | 0.397128 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 85.2056i | − | 0.121347i | −0.998158 | − | 0.0606733i | \(-0.980675\pi\) | ||
0.998158 | − | 0.0606733i | \(-0.0193248\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −711.000 | − | 160.997i | −0.975309 | − | 0.220846i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1254.00i | 1.65837i | 0.558973 | + | 0.829186i | \(0.311196\pi\) | ||||
−0.558973 | + | 0.829186i | \(0.688804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 320.000i | − | 0.408340i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −588.897 | + | 526.726i | −0.725706 | + | 0.649091i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 840.762i | 1.00135i | 0.865634 | + | 0.500677i | \(0.166916\pi\) | ||||
−0.865634 | + | 0.500677i | \(0.833084\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 77.4597 | 0.0892305 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −778.152 | − | 870.000i | −0.867641 | − | 0.970052i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −623.538 | −0.673407 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 770.000 | 0.805996 | 0.402998 | − | 0.915201i | \(-0.367968\pi\) | ||||
0.402998 | + | 0.915201i | \(0.367968\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 929.516 | + | 103.923i | 0.943635 | + | 0.105502i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1493.69 | −1.47156 | −0.735782 | − | 0.677218i | \(-0.763185\pi\) | ||||
−0.735782 | + | 0.677218i | \(0.763185\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1355.54i | 1.29675i | 0.761319 | + | 0.648377i | \(0.224552\pi\) | ||||
−0.761319 | + | 0.648377i | \(0.775448\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 240.000 | + | 268.328i | 0.223063 | + | 0.249392i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 644.323i | 0.582141i | 0.956702 | + | 0.291070i | \(0.0940114\pi\) | ||||
−0.956702 | + | 0.291070i | \(0.905989\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1066.00i | 0.936737i | 0.883533 | + | 0.468368i | \(0.155158\pi\) | ||||
−0.883533 | + | 0.468368i | \(0.844842\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 450.333 | + | 503.488i | 0.385079 | + | 0.430531i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1037.54i | 0.863745i | 0.901935 | + | 0.431872i | \(0.142147\pi\) | ||||
−0.901935 | + | 0.431872i | \(0.857853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 867.548 | 0.703472 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 268.328 | + | 30.0000i | 0.212025 | + | 0.0237051i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −277.128 | −0.213481 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 131.000 | 0.0984222 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 433.774 | + | 484.974i | 0.317985 | + | 0.355518i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1520.53 | −1.08800 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1835.79i | 1.28268i | 0.767257 | + | 0.641340i | \(0.221621\pi\) | ||||
−0.767257 | + | 0.641340i | \(0.778379\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −870.000 | + | 778.152i | −0.593792 | + | 0.531104i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 450.333i | 0.300350i | 0.988659 | + | 0.150175i | \(0.0479836\pi\) | ||||
−0.988659 | + | 0.150175i | \(0.952016\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 540.000i | 0.352060i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 727.461 | + | 1022.47i | 0.463777 | + | 0.651852i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 89.4427i | 0.0557782i | 0.999611 | + | 0.0278891i | \(0.00887852\pi\) | ||||
−0.999611 | + | 0.0278891i | \(0.991121\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1959.73 | 1.19584 | 0.597921 | − | 0.801555i | \(-0.295994\pi\) | ||||
0.597921 | + | 0.801555i | \(0.295994\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 751.319 | − | 672.000i | 0.448741 | − | 0.401366i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −346.410 | −0.202575 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1360.00 | 0.778909 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1096.05 | + | 980.341i | −0.614973 | + | 0.550049i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1618.91 | 0.890111 | 0.445055 | − | 0.895503i | \(-0.353184\pi\) | ||||
0.445055 | + | 0.895503i | \(0.353184\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 565.456i | − | 0.304743i | −0.988323 | − | 0.152371i | \(-0.951309\pi\) | ||
0.988323 | − | 0.152371i | \(-0.0486909\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −960.000 | − | 107.331i | −0.507264 | − | 0.0567138i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2009.18i | 1.04117i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 730.000i | 0.371085i | 0.982636 | + | 0.185542i | \(0.0594042\pi\) | ||||
−0.982636 | + | 0.185542i | \(0.940596\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2113.10 | + | 1890.02i | −1.05396 | + | 0.942692i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 751.319i | − | 0.367778i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −255.617 | −0.122831 | −0.0614155 | − | 0.998112i | \(-0.519561\pi\) | ||||
−0.0614155 | + | 0.998112i | \(0.519561\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1073.31 | − | 1200.00i | −0.506408 | − | 0.566181i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.8564 | 0.00642060 | 0.00321030 | − | 0.999995i | \(-0.498978\pi\) | ||||
0.00321030 | + | 0.999995i | \(0.498978\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2097.00 | 0.954483 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −209.141 | + | 1870.61i | −0.0935288 | + | 0.836547i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1118.03 | 0.491344 | 0.245672 | − | 0.969353i | \(-0.420991\pi\) | ||||
0.245672 | + | 0.969353i | \(0.420991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 348.569i | 0.150567i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −600.000 | − | 670.820i | −0.254795 | − | 0.284870i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1351.00i | − | 0.564125i | −0.959396 | − | 0.282063i | \(-0.908981\pi\) | ||
0.959396 | − | 0.282063i | \(-0.0910186\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1262.00i | 0.518253i | 0.965843 | + | 0.259126i | \(0.0834346\pi\) | ||||
−0.965843 | + | 0.259126i | \(0.916565\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1531.13 | − | 1711.86i | −0.618495 | − | 0.691499i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1162.76i | − | 0.462094i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1239.35 | 0.484656 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 885.483 | − | 630.000i | 0.340791 | − | 0.242464i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2771.28 | −1.04986 | −0.524929 | − | 0.851146i | \(-0.675908\pi\) | ||||
−0.524929 | + | 0.851146i | \(0.675908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −190.000 | −0.0708627 | −0.0354313 | − | 0.999372i | \(-0.511281\pi\) | ||||
−0.0354313 | + | 0.999372i | \(0.511281\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −309.839 | − | 346.410i | −0.113785 | − | 0.127215i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2137.68 | −0.773114 | −0.386557 | − | 0.922266i | \(-0.626336\pi\) | ||||
−0.386557 | + | 0.922266i | \(0.626336\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 255.617i | − | 0.0910563i | −0.998963 | − | 0.0455281i | \(-0.985503\pi\) | ||
0.998963 | − | 0.0455281i | \(-0.0144971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2850.00 | + | 2549.12i | −1.00012 | + | 0.894532i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1177.79i | − | 0.407217i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1120.00i | − | 0.381581i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 290.985 | − | 2602.64i | 0.0977045 | − | 0.873895i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2414.95i | − | 0.799262i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 549.964 | 0.179436 | 0.0897181 | − | 0.995967i | \(-0.471403\pi\) | ||||
0.0897181 | + | 0.995967i | \(0.471403\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4024.92 | − | 3600.00i | 1.29476 | − | 1.15807i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2009.18 | 0.637325 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1740.00 | 0.544327 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1587.92 | − | 1420.28i | 0.489963 | − | 0.438236i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 357.771 | 0.108897 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 472.504i | 0.141889i | 0.997480 | + | 0.0709444i | \(0.0226013\pi\) | ||||
−0.997480 | + | 0.0709444i | \(0.977399\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −135.000 | + | 1207.48i | −0.0400000 | + | 0.357771i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 505.759i | 0.147878i | 0.997263 | + | 0.0739392i | \(0.0235571\pi\) | ||||
−0.997263 | + | 0.0739392i | \(0.976443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4094.00i | 1.18139i | 0.806894 | + | 0.590697i | \(0.201147\pi\) | ||||
−0.806894 | + | 0.590697i | \(0.798853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1039.23 | + | 929.516i | −0.296001 | + | 0.264752i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5277.12i | − | 1.48376i | −0.670534 | − | 0.741879i | \(-0.733935\pi\) | ||
0.670534 | − | 0.741879i | \(-0.266065\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1735.10 | −0.481639 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 295.161 | + | 330.000i | 0.0808977 | + | 0.0904464i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5681.13 | 1.53758 | 0.768790 | − | 0.639502i | \(-0.220859\pi\) | ||||
0.768790 | + | 0.639502i | \(0.220859\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1198.00 | −0.320207 | −0.160104 | − | 0.987100i | \(-0.551183\pi\) | ||||
−0.160104 | + | 0.987100i | \(0.551183\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3311.40 | − | 1839.44i | 0.874183 | − | 0.485597i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2531.23 | 0.660058 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 697.137i | − | 0.179586i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4344.00 | − | 4856.74i | −1.10558 | − | 1.23608i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4260.84i | − | 1.07148i | −0.844382 | − | 0.535741i | \(-0.820032\pi\) | ||
0.844382 | − | 0.535741i | \(-0.179968\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3360.00i | 0.834946i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1108.51 | + | 1239.35i | 0.272226 | + | 0.304358i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3148.38i | − | 0.764166i | −0.924128 | − | 0.382083i | \(-0.875207\pi\) | ||
0.924128 | − | 0.382083i | \(-0.124793\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1006.98 | −0.241585 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 456.158 | − | 4080.00i | 0.108182 | − | 0.967608i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4253.92 | −0.997368 | −0.498684 | − | 0.866784i | \(-0.666183\pi\) | ||||
−0.498684 | + | 0.866784i | \(0.666183\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4880.00 | 1.13123 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2912.48 | − | 3256.26i | −0.667570 | − | 0.746366i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 44.7214 | 0.0101365 | 0.00506823 | − | 0.999987i | \(-0.498387\pi\) | ||||
0.00506823 | + | 0.999987i | \(0.498387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8760.69i | − | 1.96374i | −0.189552 | − | 0.981871i | \(-0.560704\pi\) | ||
0.189552 | − | 0.981871i | \(-0.439296\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −300.000 | + | 268.328i | −0.0665085 | + | 0.0594870i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1558.85i | − | 0.341825i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6350.00i | 1.37738i | 0.725055 | + | 0.688690i | \(0.241814\pi\) | ||||
−0.725055 | + | 0.688690i | \(0.758186\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6027.54 | + | 673.899i | 1.29340 | + | 0.144607i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5563.34i | 1.18107i | 0.807012 | + | 0.590535i | \(0.201083\pi\) | ||||
−0.807012 | + | 0.590535i | \(0.798917\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6777.72 | −1.42365 | −0.711826 | − | 0.702356i | \(-0.752132\pi\) | ||||
−0.711826 | + | 0.702356i | \(0.752132\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2414.95 | − | 2160.00i | 0.501928 | − | 0.448938i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −969.948 | −0.199492 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3633.00 | 0.739467 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2982.20 | + | 2667.36i | −0.600754 | + | 0.537331i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 652.932 | 0.130187 | 0.0650933 | − | 0.997879i | \(-0.479265\pi\) | ||||
0.0650933 | + | 0.997879i | \(0.479265\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1549.19i | 0.305754i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3960.00 | + | 2817.45i | −0.773678 | + | 0.550454i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 969.948i | 0.187604i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1740.00i | − | 0.333196i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5785.05 | − | 5174.31i | 1.09684 | − | 0.981043i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3953.37i | 0.742194i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1556.94 | −0.289444 | −0.144722 | − | 0.989472i | \(-0.546229\pi\) | ||||
−0.144722 | + | 0.989472i | \(0.546229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4695.74 | − | 5250.00i | −0.864503 | − | 0.966544i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3256.26 | 0.593715 | 0.296857 | − | 0.954922i | \(-0.404061\pi\) | ||||
0.296857 | + | 0.954922i | \(0.404061\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7030.00 | 1.26952 | 0.634759 | − | 0.772710i | \(-0.281099\pi\) | ||||
0.634759 | + | 0.772710i | \(0.281099\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1859.03 | − | 207.846i | −0.332522 | − | 0.0371771i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −491.935 | −0.0871603 | −0.0435802 | − | 0.999050i | \(-0.513876\pi\) | ||||
−0.0435802 | + | 0.999050i | \(0.513876\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5267.26i | 0.924482i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2232.00 | − | 2495.45i | −0.388094 | − | 0.433902i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2494.15i | 0.429654i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 450.000i | − | 0.0768046i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3692.73 | − | 4128.60i | −0.624491 | − | 0.698202i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1502.64i | 0.251803i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4237.04 | −0.703592 | −0.351796 | − | 0.936077i | \(-0.614429\pi\) | ||||
−0.351796 | + | 0.936077i | \(0.614429\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3488.27 | − | 390.000i | −0.574041 | − | 0.0641798i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6581.79 | 1.07344 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1490.00 | 0.240847 | 0.120424 | − | 0.992723i | \(-0.461575\pi\) | ||||
0.120424 | + | 0.992723i | \(0.461575\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3594.13 | − | 4018.36i | −0.575830 | − | 0.643797i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7781.52 | −1.23576 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4848.98i | − | 0.763324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3360.00 | + | 3005.28i | −0.524337 | + | 0.468981i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 1988.39i | − | 0.307616i | −0.988101 | − | 0.153808i | \(-0.950846\pi\) | ||
0.988101 | − | 0.153808i | \(-0.0491537\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2074.00i | 0.318105i | 0.987270 | + | 0.159053i | \(0.0508439\pi\) | ||||
−0.987270 | + | 0.159053i | \(0.949156\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1143.15 | + | 813.327i | −0.173838 | + | 0.123681i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8658.06i | 1.30544i | 0.757597 | + | 0.652722i | \(0.226373\pi\) | ||||
−0.757597 | + | 0.652722i | \(0.773627\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9295.16 | −1.38968 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1073.31 | − | 960.000i | 0.159120 | − | 0.142321i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8106.00 | 1.19169 | 0.595847 | − | 0.803098i | \(-0.296816\pi\) | ||||
0.595847 | + | 0.803098i | \(0.296816\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1999.00 | −0.291442 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −507.361 | + | 453.797i | −0.0733596 | + | 0.0656148i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3667.15 | −0.525884 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7893.14i | − | 1.12267i | −0.827590 | − | 0.561333i | \(-0.810289\pi\) | ||
0.827590 | − | 0.561333i | \(-0.189711\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3360.00 | − | 375.659i | −0.474023 | − | 0.0529974i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4226.20i | − | 0.591411i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4910.00i | 0.681582i | 0.940139 | + | 0.340791i | \(0.110695\pi\) | ||||
−0.940139 | + | 0.340791i | \(0.889305\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5888.97 | − | 5267.26i | 0.810947 | − | 0.725333i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1520.53i | 0.207722i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3137.12 | 0.425179 | 0.212590 | − | 0.977142i | \(-0.431810\pi\) | ||||
0.212590 | + | 0.977142i | \(0.431810\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6359.38 | − | 7110.00i | −0.855120 | − | 0.956053i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6207.67 | −0.828191 | −0.414095 | − | 0.910233i | \(-0.635902\pi\) | ||||
−0.414095 | + | 0.910233i | \(0.635902\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2400.00 | 0.317702 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 673.899 | − | 6027.54i | 0.0885174 | − | 0.791723i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9454.10 | 1.23224 | 0.616120 | − | 0.787652i | \(-0.288703\pi\) | ||||
0.616120 | + | 0.787652i | \(0.288703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3470.19i | − | 0.448837i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1560.00 | − | 1744.13i | −0.200233 | − | 0.223867i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 762.102i | − | 0.0970773i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10570.0i | 1.33625i | 0.744047 | + | 0.668127i | \(0.232904\pi\) | ||||
−0.744047 | + | 0.668127i | \(0.767096\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1870.61 | − | 2091.41i | −0.234706 | − | 0.262410i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1681.52i | 0.209405i | 0.994504 | + | 0.104702i | \(0.0333890\pi\) | ||||
−0.994504 | + | 0.104702i | \(0.966611\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2246.33 | −0.277662 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6359.38 | − | 1440.00i | −0.780247 | − | 0.176677i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4503.33 | 0.548457 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3574.00 | 0.432085 | 0.216043 | − | 0.976384i | \(-0.430685\pi\) | ||||
0.216043 | + | 0.976384i | \(0.430685\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −309.839 | − | 346.410i | −0.0371854 | − | 0.0415746i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1341.64 | 0.159849 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11216.2i | 1.32670i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7590.00 | + | 6788.70i | −0.891328 | + | 0.797228i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 15346.0i | − | 1.78926i | −0.446808 | − | 0.894630i | \(-0.647439\pi\) | ||
0.446808 | − | 0.894630i | \(-0.352561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3518.00i | 0.407261i | 0.979048 | + | 0.203630i | \(0.0652741\pi\) | ||||
−0.979048 | + | 0.203630i | \(0.934726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −581.969 | + | 5205.29i | −0.0668943 | + | 0.598321i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1609.97i | 0.183753i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3423.72 | 0.388022 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1341.64 | − | 1200.00i | 0.150991 | − | 0.135050i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12886.5 | 1.44018 | 0.720091 | − | 0.693879i | \(-0.244100\pi\) | ||||
0.720091 | + | 0.693879i | \(0.244100\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14450.0 | 1.60375 | 0.801874 | − | 0.597493i | \(-0.203837\pi\) | ||||
0.801874 | + | 0.597493i | \(0.203837\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5267.26 | + | 4711.18i | −0.580565 | + | 0.519273i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6761.87 | −0.740192 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15065.9i | − | 1.63794i | −0.573835 | − | 0.818971i | \(-0.694545\pi\) | ||
0.573835 | − | 0.818971i | \(-0.305455\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 849.000 | − | 7593.69i | 0.0916748 | − | 0.819964i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 3041.48i | − | 0.326197i | −0.986610 | − | 0.163098i | \(-0.947851\pi\) | ||
0.986610 | − | 0.163098i | \(-0.0521488\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7520.00i | 0.801084i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6270.02 | + | 5608.08i | −0.663450 | + | 0.593407i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14310.8i | − | 1.50416i | −0.659069 | − | 0.752082i | \(-0.729049\pi\) | ||
0.659069 | − | 0.752082i | \(-0.270951\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4337.74 | 0.452896 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1958.80 | + | 2190.00i | 0.203162 | + | 0.227142i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 692.820 | 0.0713844 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3430.00 | 0.351091 | 0.175546 | − | 0.984471i | \(-0.443831\pi\) | ||||
0.175546 | + | 0.984471i | \(0.443831\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4089.87 | − | 2909.85i | 0.415902 | − | 0.295904i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3908.65 | 0.394889 | 0.197445 | − | 0.980314i | \(-0.436736\pi\) | ||||
0.197445 | + | 0.980314i | \(0.436736\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 18179.8i | − | 1.82481i | −0.409291 | − | 0.912404i | \(-0.634224\pi\) | ||
0.409291 | − | 0.912404i | \(-0.365776\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6960.00 | − | 7781.52i | −0.694112 | − | 0.776041i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1849.83i | − | 0.183298i | −0.995791 | − | 0.0916488i | \(-0.970786\pi\) | ||
0.995791 | − | 0.0916488i | \(-0.0292137\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5700.00i | − | 0.561197i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2528.79 | − | 2827.28i | −0.247390 | − | 0.276590i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7781.52i | 0.756437i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3137.12 | 0.303033 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1636.80 | − | 14640.0i | 0.157115 | − | 1.40528i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15242.0 | −1.45392 | −0.726959 | − | 0.686681i | \(-0.759067\pi\) | ||||
−0.726959 | + | 0.686681i | \(0.759067\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1300.00 | 0.123233 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2602.64 | + | 2909.85i | 0.245185 | + | 0.274125i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6887.09 | 0.644797 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9783.16i | 0.910302i | 0.890414 | + | 0.455151i | \(0.150415\pi\) | ||||
−0.890414 | + | 0.455151i | \(0.849585\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 990.000 | − | 885.483i | 0.0915529 | − | 0.0818874i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6893.56i | − | 0.633609i | −0.948491 | − | 0.316805i | \(-0.897390\pi\) | ||
0.948491 | − | 0.316805i | \(-0.102610\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5440.00i | − | 0.496968i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8313.84 | + | 929.516i | 0.754908 | + | 0.0844013i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8049.84i | 0.726529i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1309.07 | −0.117439 | −0.0587194 | − | 0.998275i | \(-0.518702\pi\) | ||||
−0.0587194 | + | 0.998275i | \(0.518702\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −53.6656 | + | 48.0000i | −0.00478564 | + | 0.00428040i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7939.72 | −0.703806 | −0.351903 | − | 0.936036i | \(-0.614465\pi\) | ||||
−0.351903 | + | 0.936036i | \(0.614465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13360.0 | −1.17725 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8121.65 | + | 7264.22i | −0.711430 | + | 0.636322i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14534.4 | 1.26567 | 0.632837 | − | 0.774285i | \(-0.281890\pi\) | ||||
0.632837 | + | 0.774285i | \(0.281890\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3175.85i | 0.274934i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5670.00 | − | 7969.35i | −0.487986 | − | 0.685878i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12124.4i | 1.03740i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6720.00i | − | 0.571654i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4330.13 | + | 3872.98i | −0.366226 | + | 0.327563i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9355.71i | − | 0.786720i | −0.919385 | − | 0.393360i | \(-0.871313\pi\) | ||
0.919385 | − | 0.393360i | \(-0.128687\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10062.0 | −0.841264 | −0.420632 | − | 0.907231i | \(-0.638192\pi\) | ||||
−0.420632 | + | 0.907231i | \(0.638192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1207.48 | − | 1350.00i | −0.100378 | − | 0.112226i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8036.72 | 0.664298 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2759.00 | −0.226761 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4647.58 | + | 519.615i | 0.379826 | + | 0.0424659i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1252.20 | 0.101761 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5763.00i | 0.465712i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4680.00 | + | 5232.40i | 0.376084 | + | 0.420474i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9803.41i | 0.783419i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23962.0i | 1.90426i | 0.305687 | + | 0.952132i | \(0.401114\pi\) | ||||
−0.305687 | + | 0.952132i | \(0.598886\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4371.70 | − | 4887.70i | −0.345502 | − | 0.386283i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9534.59i | 0.749389i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15112.4 | 1.18128 | 0.590639 | − | 0.806936i | \(-0.298876\pi\) | ||||
0.590639 | + | 0.806936i | \(0.298876\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11860.1 | + | 1326.00i | 0.921998 | + | 0.103083i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10600.2 | −0.819567 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −660.000 | −0.0507524 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4027.90 | + | 4503.33i | 0.308063 | + | 0.344425i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16055.0 | −1.22131 | −0.610656 | − | 0.791896i | \(-0.709094\pi\) | ||||
−0.610656 | + | 0.791896i | \(0.709094\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2246.33i | 0.169964i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4800.00 | + | 4293.25i | −0.361241 | + | 0.323104i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25142.4i | 1.88211i | 0.338254 | + | 0.941055i | \(0.390164\pi\) | ||||
−0.338254 | + | 0.941055i | \(0.609836\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9280.00i | 0.690996i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1247.08 | + | 5507.38i | −0.0923674 | + | 0.407916i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 23416.1i | − | 1.72523i | −0.505864 | − | 0.862613i | \(-0.668826\pi\) | ||
0.505864 | − | 0.862613i | \(-0.331174\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4918.69 | −0.360492 | −0.180246 | − | 0.983622i | \(-0.557689\pi\) | ||||
−0.180246 | + | 0.983622i | \(0.557689\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10733.1 | − | 9600.00i | 0.782518 | − | 0.699905i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4364.77 | −0.316562 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19490.0 | 1.40620 | 0.703102 | − | 0.711089i | \(-0.251798\pi\) | ||||
0.703102 | + | 0.711089i | \(0.251798\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 735.867 | − | 658.179i | 0.0528179 | − | 0.0472418i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9713.48 | 0.693602 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18900.2i | 1.34265i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2400.00 | + | 268.328i | 0.169620 | + | 0.0189641i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1364.86i | 0.0959687i | 0.998848 | + | 0.0479844i | \(0.0152798\pi\) | ||||
−0.998848 | + | 0.0479844i | \(0.984720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 15660.0i | − | 1.09552i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8279.20 | − | 7405.14i | 0.576245 | − | 0.515409i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25795.3i | − | 1.78632i | −0.449743 | − | 0.893158i | \(-0.648485\pi\) | ||
0.449743 | − | 0.893158i | \(-0.351515\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2478.71 | −0.170785 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 885.483 | + | 990.000i | 0.0607042 | + | 0.0678694i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2424.87 | 0.165405 | 0.0827025 | − | 0.996574i | \(-0.473645\pi\) | ||||
0.0827025 | + | 0.996574i | \(0.473645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8758.00 | 0.594420 | 0.297210 | − | 0.954812i | \(-0.403944\pi\) | ||||
0.297210 | + | 0.954812i | \(0.403944\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2207.60 | − | 19745.4i | 0.149089 | − | 1.33349i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1171.70 | 0.0787378 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19558.6i | 1.30784i | 0.756565 | + | 0.653919i | \(0.226876\pi\) | ||||
−0.756565 | + | 0.653919i | \(0.773124\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4080.00 | + | 4561.58i | 0.271478 | + | 0.303521i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1939.90i | − | 0.128445i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 16450.0i | − | 1.08386i | −0.840422 | − | 0.541932i | \(-0.817693\pi\) | ||
0.840422 | − | 0.541932i | \(-0.182307\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3879.79 | + | 4337.74i | 0.254388 | + | 0.284414i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8461.28i | 0.552088i | 0.961145 | + | 0.276044i | \(0.0890236\pi\) | ||||
−0.961145 | + | 0.276044i | \(0.910976\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19930.4 | 1.29413 | 0.647067 | − | 0.762433i | \(-0.275995\pi\) | ||||
0.647067 | + | 0.762433i | \(0.275995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7888.85 | + | 11088.0i | 0.509772 | + | 0.716499i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6512.51 | 0.418809 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7975.00 | −0.510400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8365.64 | + | 9353.07i | 0.532842 | + | 0.595735i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4651.02 | −0.294830 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12199.9i | 0.769683i | 0.922983 | + | 0.384842i | \(0.125744\pi\) | ||||
−0.922983 | + | 0.384842i | \(0.874256\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2130.00 | + | 1905.13i | −0.133744 | + | 0.119624i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16419.8i | 1.02614i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2830.00i | 0.176026i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3117.69 | + | 27885.5i | −0.193011 | + | 1.72634i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 7012.31i | − | 0.432090i | −0.976383 | − | 0.216045i | \(-0.930684\pi\) | ||
0.976383 | − | 0.216045i | \(-0.0693158\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15979.9 | 0.980073 | 0.490036 | − | 0.871702i | \(-0.336983\pi\) | ||||
0.490036 | + | 0.871702i | \(0.336983\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7781.52 | + | 6960.00i | −0.475034 | + | 0.424883i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17999.5 | −1.09371 | −0.546856 | − | 0.837226i | \(-0.684176\pi\) | ||||
−0.546856 | + | 0.837226i | \(0.684176\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6000.00 | −0.362898 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6738.99 | + | 6027.54i | −0.405717 | + | 0.362884i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5196.62 | 0.311423 | 0.155712 | − | 0.987803i | \(-0.450233\pi\) | ||||
0.155712 | + | 0.987803i | \(0.450233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4027.90i | 0.240280i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1230.00 | + | 11001.5i | −0.0730394 | + | 0.653284i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 6062.18i | − | 0.358344i | −0.983818 | − | 0.179172i | \(-0.942658\pi\) | ||
0.983818 | − | 0.179172i | \(-0.0573419\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9422.00i | 0.554423i | 0.960809 | + | 0.277211i | \(0.0894102\pi\) | ||||
−0.960809 | + | 0.277211i | \(0.910590\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1385.64 | + | 1239.35i | −0.0811672 | + | 0.0725981i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4829.91i | 0.281648i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14748.3 | 0.856158 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1636.80 | − | 1830.00i | −0.0945925 | − | 0.105758i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15311.3 | −0.880905 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17470.0 | −1.00062 | −0.500311 | − | 0.865846i | \(-0.666781\pi\) | ||||
−0.500311 | + | 0.865846i | \(0.666781\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3659.97 | − | 5144.19i | −0.208700 | − | 0.293333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20813.3 | −1.18157 | −0.590784 | − | 0.806830i | \(-0.701181\pi\) | ||||
−0.590784 | + | 0.806830i | \(0.701181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5964.39i | − | 0.337102i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1752.00 | − | 1958.80i | −0.0985856 | − | 0.110222i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12616.3i | 0.706805i | 0.935471 | + | 0.353402i | \(0.114975\pi\) | ||||
−0.935471 | + | 0.353402i | \(0.885025\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 800.000i | 0.0446225i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14182.0 | − | 15856.0i | −0.787596 | − | 0.880559i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5456.01i | 0.301680i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3028.67 | 0.166738 | 0.0833691 | − | 0.996519i | \(-0.473432\pi\) | ||||
0.0833691 | + | 0.996519i | \(0.473432\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 804.984 | − | 7200.00i | 0.0441253 | − | 0.394669i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17528.4 | 0.956674 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4480.00 | −0.243461 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18280.5 | + | 20438.2i | 0.989172 | + | 1.10593i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17664.9 | −0.951777 | −0.475888 | − | 0.879506i | \(-0.657873\pi\) | ||||
−0.475888 | + | 0.879506i | \(0.657873\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9062.78i | 0.486215i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6720.00 | − | 6010.55i | 0.358993 | − | 0.321093i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11570.1i | 0.615472i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14174.0i | 0.750798i | 0.926863 | + | 0.375399i | \(0.122494\pi\) | ||||
−0.926863 | + | 0.375399i | \(0.877506\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2286.31 | − | 255.617i | −0.120595 | − | 0.0134830i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21788.2i | 1.14443i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3098.39 | −0.162060 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22002.9 | + | 19680.0i | −1.14604 | + | 1.02505i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32839.7 | −1.70336 | −0.851678 | − | 0.524065i | \(-0.824415\pi\) | ||||
−0.851678 | + | 0.524065i | \(0.824415\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10500.0 | 0.542358 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4639.83 | − | 4149.99i | 0.238668 | − | 0.213472i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6842.37 | −0.350509 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8001.58i | − | 0.408201i | −0.978950 | − | 0.204101i | \(-0.934573\pi\) | ||
0.978950 | − | 0.204101i | \(-0.0654270\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6453.00 | + | 18595.1i | −0.327846 | + | 0.944731i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 8036.72i | − | 0.406633i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 11750.0i | − | 0.592082i | −0.955175 | − | 0.296041i | \(-0.904333\pi\) | ||
0.955175 | − | 0.296041i | \(-0.0956665\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9803.41 | + | 8768.43i | −0.491978 | + | 0.440039i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25491.2i | 1.27406i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19961.4 | −0.993627 | −0.496814 | − | 0.867857i | \(-0.665497\pi\) | ||||
−0.496814 | + | 0.867857i | \(0.665497\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2414.95 | + | 2700.00i | 0.119724 | + | 0.133856i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25592.8 | −1.26367 | −0.631836 | − | 0.775102i | \(-0.717698\pi\) | ||||
−0.631836 | + | 0.775102i | \(0.717698\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14480.0 | 0.712089 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 33648.5 | + | 3762.01i | 1.64810 | + | 0.184264i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4990.90 | 0.243476 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5244.02i | 0.254803i | 0.991851 | + | 0.127401i | \(0.0406637\pi\) | ||||
−0.991851 | + | 0.127401i | \(0.959336\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14760.0 | + | 16502.2i | 0.714322 | + | 0.798636i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 5057.59i | − | 0.243794i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 14290.0i | − | 0.686102i | −0.939317 | − | 0.343051i | \(-0.888540\pi\) | ||
0.939317 | − | 0.343051i | \(-0.111460\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11639.4 | − | 13013.2i | −0.556631 | − | 0.622332i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 16976.2i | − | 0.808657i | −0.914614 | − | 0.404328i | \(-0.867505\pi\) | ||
0.914614 | − | 0.404328i | \(-0.132495\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8257.20 | 0.391783 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8586.50 | − | 960.000i | −0.405811 | − | 0.0453711i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1732.05 | −0.0815394 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29566.0 | −1.38645 | −0.693223 | − | 0.720723i | \(-0.743810\pi\) | ||||
−0.693223 | + | 0.720723i | \(0.743810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10906.3 | + | 12193.6i | 0.509444 | + | 0.569576i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21457.3 | −0.998403 | −0.499202 | − | 0.866486i | \(-0.666373\pi\) | ||||
−0.499202 | + | 0.866486i | \(0.666373\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10108.5i | − | 0.468526i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3900.00 | − | 3488.27i | 0.180067 | − | 0.161056i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8729.54i | 0.401499i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 36000.0i | − | 1.64940i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12366.8 | + | 17381.9i | 0.564438 | + | 0.793334i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6529.32i | 0.296868i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3896.22 | 0.176474 | 0.0882372 | − | 0.996099i | \(-0.471877\pi\) | ||||
0.0882372 | + | 0.996099i | \(0.471877\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16475.3 | − | 14736.0i | 0.743394 | − | 0.664912i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8036.72 | 0.361255 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4420.00 | −0.197930 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18900.2 | + | 16904.8i | −0.843169 | + | 0.754154i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30759.4 | −1.36707 | −0.683533 | − | 0.729919i | \(-0.739558\pi\) | ||||
−0.683533 | + | 0.729919i | \(0.739558\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6940.39i | 0.307301i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22560.0 | + | 2522.28i | 0.995154 | + | 0.111262i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 14202.8i | − | 0.624168i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 6720.00i | − | 0.294222i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −173.205 | + | 154.919i | −0.00755528 | + | 0.00675764i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 10429.0i | − | 0.453232i | −0.973984 | − | 0.226616i | \(-0.927234\pi\) | ||
0.973984 | − | 0.226616i | \(-0.0727663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8156.50 | 0.353161 | 0.176580 | − | 0.984286i | \(-0.443496\pi\) | ||||
0.176580 | + | 0.984286i | \(0.443496\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30347.9 | + | 33930.0i | 1.30916 | + | 1.46369i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2286.31 | −0.0982648 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15660.0 | −0.670592 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 232.379 | − | 2078.46i | 0.00991450 | − | 0.0886780i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35750.3 | 1.51972 | 0.759861 | − | 0.650085i | \(-0.225267\pi\) | ||||
0.759861 | + | 0.650085i | \(0.225267\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20875.4i | 0.884168i | 0.896974 | + | 0.442084i | \(0.145761\pi\) | ||||
−0.896974 | + | 0.442084i | \(0.854239\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5400.00 | + | 6037.38i | 0.227883 | + | 0.254781i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 12907.2i | − | 0.542719i | −0.962478 | − | 0.271360i | \(-0.912527\pi\) | ||
0.962478 | − | 0.271360i | \(-0.0874733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14074.0i | 0.589638i | 0.955553 | + | 0.294819i | \(0.0952594\pi\) | ||||
−0.955553 | + | 0.294819i | \(0.904741\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21997.0 | − | 24593.4i | −0.918254 | − | 1.02664i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 10124.9i | − | 0.421138i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 123.935 | 0.00513648 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25679.0 | + | 18270.0i | −1.06045 | + | 0.754485i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16697.0 | 0.687060 | 0.343530 | − | 0.939142i | \(-0.388377\pi\) | ||||
0.343530 | + | 0.939142i | \(0.388377\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1269.00 | −0.0520317 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19272.0 | − | 21546.7i | −0.787380 | − | 0.880318i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18756.1 | 0.763587 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1014.72i | − | 0.0411644i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26250.0 | − | 23478.7i | 1.06113 | − | 0.949102i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 12609.3i | − | 0.507923i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23630.0i | 0.948506i | 0.880389 | + | 0.474253i | \(0.157282\pi\) | ||||
−0.880389 | + | 0.474253i | \(0.842718\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1870.61 | + | 16731.3i | −0.0748230 | + | 0.669237i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31322.8i | 1.24850i | 0.781223 | + | 0.624252i | \(0.214596\pi\) | ||||
−0.781223 | + | 0.624252i | \(0.785404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13671.6 | 0.543038 | 0.271519 | − | 0.962433i | \(-0.412474\pi\) | ||||
0.271519 | + | 0.962433i | \(0.412474\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3756.59 | − | 3360.00i | 0.148693 | − | 0.132995i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25107.8 | 0.990359 | 0.495179 | − | 0.868791i | \(-0.335102\pi\) | ||||
0.495179 | + | 0.868791i | \(0.335102\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10000.0 | 0.393075 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14070.5 | + | 12585.1i | −0.551166 | + | 0.492978i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2951.61 | 0.115220 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7358.67i | 0.286267i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2310.00 | − | 20661.3i | 0.0895552 | − | 0.801006i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11777.9i | 0.455048i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 41750.0i | − | 1.60752i | −0.594952 | − | 0.803761i | \(-0.702829\pi\) | ||
0.594952 | − | 0.803761i | \(-0.297171\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2528.79 | + | 2261.82i | −0.0970354 | + | 0.0867911i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2397.06i | − | 0.0916676i | −0.998949 | − | 0.0458338i | \(-0.985406\pi\) | ||
0.998949 | − | 0.0458338i | \(-0.0145945\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43431.6 | 1.65526 | 0.827628 | − | 0.561277i | \(-0.189690\pi\) | ||||
0.827628 | + | 0.561277i | \(0.189690\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5366.56 | − | 6000.00i | −0.203836 | − | 0.227896i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6387.80 | −0.241805 | −0.120903 | − | 0.992664i | \(-0.538579\pi\) | ||||
−0.120903 | + | 0.992664i | \(0.538579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14220.0 | 0.536472 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5577.10 | − | 24629.8i | 0.209697 | − | 0.926070i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13523.7 | 0.506780 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 12083.7i | − | 0.451300i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3360.00 | − | 3756.59i | −0.125069 | − | 0.139832i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34156.0i | 1.26715i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 19520.0i | − | 0.721760i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6027.54 | + | 6738.99i | 0.222131 | + | 0.248349i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11287.7i | 0.414602i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37327.8 | −1.36654 | −0.683269 | − | 0.730167i | \(-0.739442\pi\) | ||||
−0.683269 | + | 0.730167i | \(0.739442\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4481.08 | + | 40080.0i | −0.163507 | + | 1.46245i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50853.0 | 1.84944 | 0.924718 | − | 0.380654i | \(-0.124301\pi\) | ||||
0.924718 | + | 0.380654i | \(0.124301\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43440.0 | −1.57465 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13694.9 | − | 15311.3i | −0.494796 | − | 0.553199i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3488.27 | 0.125619 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 14198.4i | − | 0.509642i | −0.966988 | − | 0.254821i | \(-0.917984\pi\) | ||
0.966988 | − | 0.254821i | \(-0.0820165\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6030.00 | − | 5393.40i | 0.215739 | − | 0.192962i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 10392.3i | − | 0.370603i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5850.00i | 0.207943i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36373.1 | + | 4066.63i | 1.28873 | + | 0.144084i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 10232.2i | − | 0.361366i | −0.983541 | − | 0.180683i | \(-0.942169\pi\) | ||
0.983541 | − | 0.180683i | \(-0.0578308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19729.0 | −0.694512 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12611.4 | + | 11280.0i | −0.442529 | + | 0.395810i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11085.1 | 0.387724 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37850.0 | −1.31964 | −0.659822 | − | 0.751422i | \(-0.729368\pi\) | ||||
−0.659822 | + | 0.751422i | \(0.729368\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27227.1 | + | 24352.6i | −0.946243 | + | 0.846345i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13997.8 | 0.484925 | 0.242463 | − | 0.970161i | \(-0.422045\pi\) | ||||
0.242463 | + | 0.970161i | \(0.422045\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 12145.7i | − | 0.419425i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7920.00 | − | 5634.89i | 0.272632 | − | 0.193971i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7738.80i | 0.265552i | 0.991146 | + | 0.132776i | \(0.0423890\pi\) | ||||
−0.991146 | + | 0.132776i | \(0.957611\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4100.00i | − | 0.140244i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1905.26 | − | 1704.11i | 0.0649655 | − | 0.0581069i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 44882.4i | − | 1.52558i | −0.646644 | − | 0.762792i | \(-0.723828\pi\) | ||
0.646644 | − | 0.762792i | \(-0.276172\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24787.1 | −0.839886 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18246.3 | − | 20400.0i | −0.616321 | − | 0.689068i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 692.820 | 0.0233288 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20669.0 | −0.693800 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17289.0 | + | 1932.97i | 0.578536 | + | 0.0646823i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1699.41 | −0.0566902 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15856.0i | 0.527295i | 0.964619 | + | 0.263648i | \(0.0849256\pi\) | ||||
−0.964619 | + | 0.263648i | \(0.915074\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8640.00 | − | 9659.81i | −0.286436 | − | 0.320246i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 40426.1i | − | 1.33608i | −0.744125 | − | 0.668040i | \(-0.767133\pi\) | ||
0.744125 | − | 0.668040i | \(-0.232867\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 15180.0i | − | 0.500153i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1558.85 | + | 1742.84i | 0.0512031 | + | 0.0572468i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6404.10i | 0.209709i | 0.994488 | + | 0.104854i | \(0.0334376\pi\) | ||||
−0.994488 | + | 0.104854i | \(0.966562\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29124.8 | −0.950801 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28603.8 | + | 3198.00i | 0.930936 | + | 0.104082i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25953.0 | −0.842089 | −0.421045 | − | 0.907040i | \(-0.638336\pi\) | ||||
−0.421045 | + | 0.907040i | \(0.638336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19120.0 | −0.618491 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5205.29 | − | 5819.69i | −0.167868 | − | 0.187683i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21788.2 | 0.700532 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 48358.1i | − | 1.55010i | −0.631903 | − | 0.775048i | \(-0.717726\pi\) | ||
0.631903 | − | 0.775048i | \(-0.282274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16410.0 | − | 14677.6i | 0.524427 | − | 0.469061i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2286.31i | − | 0.0728450i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 18370.0i | − | 0.583534i | −0.956489 | − | 0.291767i | \(-0.905757\pi\) | ||
0.956489 | − | 0.291767i | \(-0.0942432\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14861.0 | − | 10573.2i | 0.470652 | − | 0.334858i |
(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 | 768.4.f.c.383.4 | 8 | ||
3.2 | odd | 2 | inner | 768.4.f.c.383.1 | 8 | ||
4.3 | odd | 2 | inner | 768.4.f.c.383.6 | 8 | ||
8.3 | odd | 2 | inner | 768.4.f.c.383.3 | 8 | ||
8.5 | even | 2 | inner | 768.4.f.c.383.5 | 8 | ||
12.11 | even | 2 | inner | 768.4.f.c.383.7 | 8 | ||
16.3 | odd | 4 | 12.4.b.a.11.2 | yes | 4 | ||
16.5 | even | 4 | 192.4.c.b.191.4 | 4 | |||
16.11 | odd | 4 | 192.4.c.b.191.1 | 4 | |||
16.13 | even | 4 | 12.4.b.a.11.4 | yes | 4 | ||
24.5 | odd | 2 | inner | 768.4.f.c.383.8 | 8 | ||
24.11 | even | 2 | inner | 768.4.f.c.383.2 | 8 | ||
48.5 | odd | 4 | 192.4.c.b.191.2 | 4 | |||
48.11 | even | 4 | 192.4.c.b.191.3 | 4 | |||
48.29 | odd | 4 | 12.4.b.a.11.1 | ✓ | 4 | ||
48.35 | even | 4 | 12.4.b.a.11.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.4.b.a.11.1 | ✓ | 4 | 48.29 | odd | 4 | ||
12.4.b.a.11.2 | yes | 4 | 16.3 | odd | 4 | ||
12.4.b.a.11.3 | yes | 4 | 48.35 | even | 4 | ||
12.4.b.a.11.4 | yes | 4 | 16.13 | even | 4 | ||
192.4.c.b.191.1 | 4 | 16.11 | odd | 4 | |||
192.4.c.b.191.2 | 4 | 48.5 | odd | 4 | |||
192.4.c.b.191.3 | 4 | 48.11 | even | 4 | |||
192.4.c.b.191.4 | 4 | 16.5 | even | 4 | |||
768.4.f.c.383.1 | 8 | 3.2 | odd | 2 | inner | ||
768.4.f.c.383.2 | 8 | 24.11 | even | 2 | inner | ||
768.4.f.c.383.3 | 8 | 8.3 | odd | 2 | inner | ||
768.4.f.c.383.4 | 8 | 1.1 | even | 1 | trivial | ||
768.4.f.c.383.5 | 8 | 8.5 | even | 2 | inner | ||
768.4.f.c.383.6 | 8 | 4.3 | odd | 2 | inner | ||
768.4.f.c.383.7 | 8 | 12.11 | even | 2 | inner | ||
768.4.f.c.383.8 | 8 | 24.5 | odd | 2 | inner |