Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(191,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, 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("384.191");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.f (of order \(2\), degree \(1\), 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: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{26})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.2 | ||
Root | \(-2.54951 + 2.54951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.191 |
Dual form | 384.4.f.f.191.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −5.09902 | + | 1.00000i | −0.981307 | + | 0.192450i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.1980 | −0.912140 | −0.456070 | − | 0.889944i | \(-0.650743\pi\) | ||||
−0.456070 | + | 0.889944i | \(0.650743\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.1980i | 0.550642i | 0.961352 | + | 0.275321i | \(0.0887842\pi\) | ||||
−0.961352 | + | 0.275321i | \(0.911216\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 25.0000 | − | 10.1980i | 0.925926 | − | 0.377705i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 46.0000i | 1.26087i | 0.776244 | + | 0.630433i | \(0.217123\pi\) | ||||
−0.776244 | + | 0.630433i | \(0.782877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 44.0000i | 0.938723i | 0.883006 | + | 0.469362i | \(0.155516\pi\) | ||||
−0.883006 | + | 0.469362i | \(0.844484\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 52.0000 | − | 10.1980i | 0.895089 | − | 0.175541i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 20.3961i | − | 0.290987i | −0.989359 | − | 0.145493i | \(-0.953523\pi\) | ||
0.989359 | − | 0.145493i | \(-0.0464770\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.1980 | 0.123136 | 0.0615682 | − | 0.998103i | \(-0.480390\pi\) | ||||
0.0615682 | + | 0.998103i | \(0.480390\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.1980 | − | 52.0000i | −0.105971 | − | 0.540349i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 88.0000 | 0.797794 | 0.398897 | − | 0.916996i | \(-0.369393\pi\) | ||||
0.398897 | + | 0.916996i | \(0.369393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.0000 | −0.168000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −117.277 | + | 77.0000i | −0.835928 | + | 0.548839i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −254.951 | −1.63252 | −0.816262 | − | 0.577682i | \(-0.803958\pi\) | ||||
−0.816262 | + | 0.577682i | \(0.803958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 214.159i | 1.24078i | 0.784295 | + | 0.620388i | \(0.213025\pi\) | ||||
−0.784295 | + | 0.620388i | \(0.786975\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −46.0000 | − | 234.555i | −0.242654 | − | 1.23730i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 104.000i | − | 0.502263i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 332.000i | − | 1.47515i | −0.675266 | − | 0.737574i | \(-0.735971\pi\) | ||
0.675266 | − | 0.737574i | \(-0.264029\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −44.0000 | − | 224.357i | −0.180657 | − | 0.921176i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 489.506i | − | 1.86458i | −0.361706 | − | 0.932292i | \(-0.617805\pi\) | ||
0.361706 | − | 0.932292i | \(-0.382195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 234.555 | 0.831844 | 0.415922 | − | 0.909400i | \(-0.363459\pi\) | ||||
0.415922 | + | 0.909400i | \(0.363459\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −254.951 | + | 104.000i | −0.844574 | + | 0.344520i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −384.000 | −1.19175 | −0.595874 | − | 0.803078i | \(-0.703194\pi\) | ||||
−0.595874 | + | 0.803078i | \(0.703194\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 239.000 | 0.696793 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.3961 | + | 104.000i | 0.0560004 | + | 0.285547i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −458.912 | −1.18937 | −0.594683 | − | 0.803960i | \(-0.702722\pi\) | ||||
−0.594683 | + | 0.803960i | \(0.702722\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 469.110i | − | 1.15009i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −52.0000 | + | 10.1980i | −0.120835 | + | 0.0236976i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 630.000i | − | 1.39015i | −0.718936 | − | 0.695076i | \(-0.755371\pi\) | ||
0.718936 | − | 0.695076i | \(-0.244629\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 236.000i | 0.495356i | 0.968842 | + | 0.247678i | \(0.0796675\pi\) | ||||
−0.968842 | + | 0.247678i | \(0.920333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 104.000 | + | 254.951i | 0.207980 | + | 0.509854i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 448.714i | − | 0.856247i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −50.9902 | −0.0929768 | −0.0464884 | − | 0.998919i | \(-0.514803\pi\) | ||||
−0.0464884 | + | 0.998919i | \(0.514803\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −448.714 | + | 88.0000i | −0.782881 | + | 0.153536i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −680.000 | −1.13664 | −0.568318 | − | 0.822809i | \(-0.692406\pi\) | ||||
−0.568318 | + | 0.822809i | \(0.692406\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 422.000 | 0.676594 | 0.338297 | − | 0.941039i | \(-0.390149\pi\) | ||||
0.338297 | + | 0.941039i | \(0.390149\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 107.079 | − | 21.0000i | 0.164860 | − | 0.0323316i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −469.110 | −0.694286 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 744.457i | 1.06023i | 0.847927 | + | 0.530114i | \(0.177851\pi\) | ||||
−0.847927 | + | 0.530114i | \(0.822149\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 521.000 | − | 509.902i | 0.714678 | − | 0.699454i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 186.000i | − | 0.245978i | −0.992408 | − | 0.122989i | \(-0.960752\pi\) | ||
0.992408 | − | 0.122989i | \(-0.0392479\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 208.000i | 0.265421i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1300.00 | − | 254.951i | 1.60201 | − | 0.314179i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 958.616i | − | 1.14172i | −0.821048 | − | 0.570860i | \(-0.806610\pi\) | ||
0.821048 | − | 0.570860i | \(-0.193390\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −448.714 | −0.516901 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −214.159 | − | 1092.00i | −0.238787 | − | 1.21758i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −104.000 | −0.112318 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1062.00 | −1.11165 | −0.555824 | − | 0.831300i | \(-0.687597\pi\) | ||||
−0.555824 | + | 0.831300i | \(0.687597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 469.110 | + | 1150.00i | 0.476235 | + | 1.16747i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1980 | −0.0100470 | −0.00502348 | − | 0.999987i | \(-0.501599\pi\) | ||||
−0.00502348 | + | 0.999987i | \(0.501599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1988.62i | − | 1.90237i | −0.308618 | − | 0.951186i | \(-0.599867\pi\) | ||
0.308618 | − | 0.951186i | \(-0.400133\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 104.000 | + | 530.298i | 0.0966606 | + | 0.492874i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 234.000i | 0.211417i | 0.994397 | + | 0.105709i | \(0.0337111\pi\) | ||||
−0.994397 | + | 0.105709i | \(0.966289\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 724.000i | − | 0.636208i | −0.948056 | − | 0.318104i | \(-0.896954\pi\) | ||
0.948056 | − | 0.318104i | \(-0.103046\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 332.000 | + | 1692.87i | 0.283892 | + | 1.44757i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1019.80i | 0.848983i | 0.905432 | + | 0.424492i | \(0.139547\pi\) | ||||
−0.905432 | + | 0.424492i | \(0.860453\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −897.427 | −0.727700 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 448.714 | + | 1100.00i | 0.354561 | + | 0.869188i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 208.000 | 0.160230 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −785.000 | −0.589782 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 489.506 | + | 2496.00i | 0.358839 | + | 1.82973i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1488.91 | 1.06538 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2253.77i | 1.57472i | 0.616493 | + | 0.787360i | \(0.288553\pi\) | ||||
−0.616493 | + | 0.787360i | \(0.711447\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1196.00 | + | 234.555i | −0.816294 | + | 0.160088i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1742.00i | − | 1.16183i | −0.813966 | − | 0.580913i | \(-0.802696\pi\) | ||
0.813966 | − | 0.580913i | \(-0.197304\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 104.000i | 0.0678041i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1196.00 | − | 785.249i | 0.762484 | − | 0.500618i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2406.74i | 1.50089i | 0.660935 | + | 0.750443i | \(0.270160\pi\) | ||||
−0.660935 | + | 0.750443i | \(0.729840\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −764.853 | −0.466719 | −0.233360 | − | 0.972390i | \(-0.574972\pi\) | ||||
−0.233360 | + | 0.972390i | \(0.574972\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1958.02 | − | 384.000i | 1.16947 | − | 0.229352i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2024.00 | −1.18360 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2600.00 | 1.48909 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1218.67 | + | 239.000i | −0.683768 | + | 0.134098i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 479.308 | 0.263533 | 0.131767 | − | 0.991281i | \(-0.457935\pi\) | ||||
0.131767 | + | 0.991281i | \(0.457935\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1499.11i | − | 0.807920i | −0.914777 | − | 0.403960i | \(-0.867633\pi\) | ||
0.914777 | − | 0.403960i | \(-0.132367\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −208.000 | − | 509.902i | −0.109907 | − | 0.269432i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2184.00i | − | 1.13176i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1948.00i | 0.990238i | 0.868825 | + | 0.495119i | \(0.164875\pi\) | ||||
−0.868825 | + | 0.495119i | \(0.835125\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2340.00 | − | 458.912i | 1.16713 | − | 0.228894i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 897.427i | 0.439299i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3395.95 | 1.63185 | 0.815924 | − | 0.578160i | \(-0.196229\pi\) | ||||
0.815924 | + | 0.578160i | \(0.196229\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 469.110 | + | 2392.00i | 0.221334 | + | 1.12859i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2008.00 | −0.930441 | −0.465221 | − | 0.885195i | \(-0.654025\pi\) | ||||
−0.465221 | + | 0.885195i | \(0.654025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 261.000 | 0.118798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 254.951 | − | 104.000i | 0.114015 | − | 0.0465092i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1213.57 | 0.533328 | 0.266664 | − | 0.963790i | \(-0.414079\pi\) | ||||
0.266664 | + | 0.963790i | \(0.414079\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 214.159i | − | 0.0925079i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 630.000 | + | 3212.38i | 0.267535 | + | 1.36417i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 2382.00i | − | 0.994632i | −0.867570 | − | 0.497316i | \(-0.834319\pi\) | ||
0.867570 | − | 0.497316i | \(-0.165681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2652.00i | − | 1.08907i | −0.838738 | − | 0.544535i | \(-0.816706\pi\) | ||
0.838738 | − | 0.544535i | \(-0.183294\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −236.000 | − | 1203.37i | −0.0953313 | − | 0.486096i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3385.75i | 1.34554i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 938.220 | 0.366895 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −785.249 | − | 1196.00i | −0.302214 | − | 0.460297i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4784.00 | −1.81235 | −0.906173 | − | 0.422907i | \(-0.861010\pi\) | ||||
−0.906173 | + | 0.422907i | \(0.861010\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3074.00 | −1.14648 | −0.573242 | − | 0.819386i | \(-0.694314\pi\) | ||||
−0.573242 | + | 0.819386i | \(0.694314\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 448.714 | + | 2288.00i | 0.164785 | + | 0.840241i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4844.07 | 1.75191 | 0.875953 | − | 0.482396i | \(-0.160233\pi\) | ||||
0.875953 | + | 0.482396i | \(0.160233\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1927.43i | 0.686592i | 0.939227 | + | 0.343296i | \(0.111543\pi\) | ||||
−0.939227 | + | 0.343296i | \(0.888457\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 260.000 | − | 50.9902i | 0.0912387 | − | 0.0178934i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2600.00i | − | 0.898937i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4992.00i | 1.70076i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2200.00 | − | 897.427i | 0.738698 | − | 0.301331i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 469.110i | 0.155258i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3436.74 | −1.12130 | −0.560651 | − | 0.828052i | \(-0.689449\pi\) | ||||
−0.560651 | + | 0.828052i | \(0.689449\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3467.33 | − | 680.000i | 1.11539 | − | 0.218746i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2392.00 | −0.758758 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2184.00 | −0.683224 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2151.79 | + | 422.000i | −0.663946 | + | 0.130211i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 897.427 | 0.273156 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1233.96i | 0.370548i | 0.982687 | + | 0.185274i | \(0.0593173\pi\) | ||||
−0.982687 | + | 0.185274i | \(0.940683\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −525.000 | + | 214.159i | −0.155556 | + | 0.0634545i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1270.00i | 0.371334i | 0.982613 | + | 0.185667i | \(0.0594446\pi\) | ||||
−0.982613 | + | 0.185667i | \(0.940555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4556.00i | − | 1.31471i | −0.753580 | − | 0.657356i | \(-0.771675\pi\) | ||
0.753580 | − | 0.657356i | \(-0.228325\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2392.00 | − | 469.110i | 0.681308 | − | 0.133615i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 877.031i | − | 0.246593i | −0.992370 | − | 0.123297i | \(-0.960653\pi\) | ||
0.992370 | − | 0.123297i | \(-0.0393467\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3916.05 | 1.08704 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −744.457 | − | 3796.00i | −0.204041 | − | 1.04041i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1920.00 | 0.519642 | 0.259821 | − | 0.965657i | \(-0.416336\pi\) | ||||
0.259821 | + | 0.965657i | \(0.416336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1618.00 | −0.432467 | −0.216233 | − | 0.976342i | \(-0.569377\pi\) | ||||
−0.216233 | + | 0.976342i | \(0.569377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2146.69 | + | 3121.00i | −0.566708 | + | 0.823919i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2437.33 | −0.635573 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 448.714i | 0.115591i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 186.000 | + | 948.418i | 0.0473384 | + | 0.241380i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1586.00i | − | 0.398834i | −0.979915 | − | 0.199417i | \(-0.936095\pi\) | ||
0.979915 | − | 0.199417i | \(-0.0639049\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4048.00i | 1.00591i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −208.000 | − | 1060.60i | −0.0510803 | − | 0.260459i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3956.84i | − | 0.960392i | −0.877161 | − | 0.480196i | \(-0.840565\pi\) | ||
0.877161 | − | 0.480196i | \(-0.159435\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3385.75 | 0.812279 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6373.77 | + | 2600.00i | −1.51160 | + | 0.616613i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4344.00 | 1.01849 | 0.509244 | − | 0.860622i | \(-0.329925\pi\) | ||||
0.509244 | + | 0.860622i | \(0.329925\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4680.00 | 1.08487 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 958.616 | + | 4888.00i | 0.219724 | + | 1.12038i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2743.27 | −0.621785 | −0.310893 | − | 0.950445i | \(-0.600628\pi\) | ||||
−0.310893 | + | 0.950445i | \(0.600628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3253.17i | − | 0.729211i | −0.931162 | − | 0.364606i | \(-0.881204\pi\) | ||
0.931162 | − | 0.364606i | \(-0.118796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2288.00 | − | 448.714i | 0.507238 | − | 0.0994776i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 966.000i | − | 0.211825i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4956.00i | − | 1.07501i | −0.843261 | − | 0.537504i | \(-0.819367\pi\) | ||
0.843261 | − | 0.537504i | \(-0.180633\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2184.00 | + | 5353.97i | 0.468648 | + | 1.14887i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1978.42i | − | 0.420009i | −0.977700 | − | 0.210005i | \(-0.932652\pi\) | ||
0.977700 | − | 0.210005i | \(-0.0673479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7985.06 | −1.67725 | −0.838627 | − | 0.544706i | \(-0.816641\pi\) | ||||
−0.838627 | + | 0.544706i | \(0.816641\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 530.298 | − | 104.000i | 0.110218 | − | 0.0216155i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4992.00 | 1.02672 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4497.00 | 0.915327 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5415.16 | − | 1062.00i | 1.09087 | − | 0.213937i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1845.85 | −0.368039 | −0.184019 | − | 0.982923i | \(-0.558911\pi\) | ||||
−0.184019 | + | 0.982923i | \(0.558911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6424.76i | 1.26801i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3542.00 | − | 5394.76i | −0.692012 | − | 1.05399i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3872.00i | 0.748908i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2392.00i | 0.458048i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 52.0000 | − | 10.1980i | 0.00985915 | − | 0.00193354i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2406.74i | − | 0.451834i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8291.01 | −1.54134 | −0.770672 | − | 0.637232i | \(-0.780079\pi\) | ||||
−0.770672 | + | 0.637232i | \(0.780079\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1988.62 | + | 10140.0i | 0.366112 | + | 1.86681i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10104.0 | −1.84227 | −0.921134 | − | 0.389246i | \(-0.872736\pi\) | ||||
−0.921134 | + | 0.389246i | \(0.872736\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1198.00 | 0.216342 | 0.108171 | − | 0.994132i | \(-0.465501\pi\) | ||||
0.108171 | + | 0.994132i | \(0.465501\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1060.60 | − | 2600.00i | −0.189707 | − | 0.465058i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5027.63 | −0.890789 | −0.445394 | − | 0.895335i | \(-0.646937\pi\) | ||||
−0.445394 | + | 0.895335i | \(0.646937\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 11727.7i | − | 2.05839i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −234.000 | − | 1193.17i | −0.0406872 | − | 0.207465i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 208.000i | − | 0.0358311i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 924.000i | − | 0.157706i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 724.000 | + | 3691.69i | 0.122438 | + | 0.624315i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3916.05i | − | 0.656227i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6129.02 | 1.01777 | 0.508884 | − | 0.860835i | \(-0.330058\pi\) | ||||
0.508884 | + | 0.860835i | \(0.330058\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3385.75 | − | 8300.00i | −0.557171 | − | 1.36588i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 520.000 | 0.0848079 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 390.000 | 0.0630405 | 0.0315203 | − | 0.999503i | \(-0.489965\pi\) | ||||
0.0315203 | + | 0.999503i | \(0.489965\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1019.80 | − | 5200.00i | −0.163387 | − | 0.833113i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9851.31 | −1.56445 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5935.26i | 0.934326i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4576.00 | − | 897.427i | 0.714097 | − | 0.140046i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4366.00i | 0.675444i | 0.941246 | + | 0.337722i | \(0.109656\pi\) | ||||
−0.941246 | + | 0.337722i | \(0.890344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5492.00i | − | 0.842350i | −0.906979 | − | 0.421175i | \(-0.861618\pi\) | ||
0.906979 | − | 0.421175i | \(-0.138382\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3388.00 | − | 5160.21i | −0.515208 | − | 0.784705i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 81.5843i | 0.0123011i | 0.999981 | + | 0.00615056i | \(0.00195780\pi\) | ||||
−0.999981 | + | 0.00615056i | \(0.998042\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6934.67 | 1.03677 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1060.60 | + | 208.000i | −0.157234 | + | 0.0308362i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2216.00 | −0.325783 | −0.162891 | − | 0.986644i | \(-0.552082\pi\) | ||||
−0.162891 | + | 0.986644i | \(0.552082\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6755.00 | −0.984837 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4002.73 | − | 785.000i | 0.578757 | − | 0.113504i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4303.57 | −0.617149 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7128.43i | − | 1.01390i | −0.861976 | − | 0.506950i | \(-0.830773\pi\) | ||
0.861976 | − | 0.506950i | \(-0.169227\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4992.00 | − | 12237.6i | −0.704263 | − | 1.72647i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4680.00i | − | 0.654915i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2028.00i | − | 0.281517i | −0.990044 | − | 0.140759i | \(-0.955046\pi\) | ||
0.990044 | − | 0.140759i | \(-0.0449541\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7592.00 | + | 1488.91i | −1.04546 | + | 0.205032i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 11217.8i | − | 1.53249i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1315.55 | −0.178298 | −0.0891492 | − | 0.996018i | \(-0.528415\pi\) | ||||
−0.0891492 | + | 0.996018i | \(0.528415\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2253.77 | − | 11492.0i | −0.303055 | − | 1.54528i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2128.00 | −0.283905 | −0.141953 | − | 0.989873i | \(-0.545338\pi\) | ||||
−0.141953 | + | 0.989873i | \(0.545338\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4784.00 | 0.633286 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5863.87 | − | 2392.00i | 0.770226 | − | 0.314192i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1927.43 | −0.251220 | −0.125610 | − | 0.992080i | \(-0.540089\pi\) | ||||
−0.125610 | + | 0.992080i | \(0.540089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1794.85i | − | 0.232148i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1742.00 | + | 8882.49i | 0.223594 | + | 1.14011i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 7592.00i | − | 0.967076i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6220.00i | 0.786330i | 0.919468 | + | 0.393165i | \(0.128620\pi\) | ||||
−0.919468 | + | 0.393165i | \(0.871380\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −104.000 | − | 530.298i | −0.0130489 | − | 0.0665366i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1937.63i | − | 0.241298i | −0.992695 | − | 0.120649i | \(-0.961502\pi\) | ||
0.992695 | − | 0.120649i | \(-0.0384976\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9422.99 | −1.16475 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5313.18 | + | 5200.00i | −0.651886 | + | 0.638000i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15272.0 | 1.85996 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1270.00 | −0.153539 | −0.0767695 | − | 0.997049i | \(-0.524461\pi\) | ||||
−0.0767695 | + | 0.997049i | \(0.524461\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2406.74 | − | 12272.0i | −0.288846 | − | 1.47283i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6424.76 | 0.765477 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1896.84i | 0.224366i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3900.00 | − | 764.853i | 0.457995 | − | 0.0898202i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9126.00i | 1.06404i | 0.846731 | + | 0.532022i | \(0.178568\pi\) | ||||
−0.846731 | + | 0.532022i | \(0.821432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3436.00i | − | 0.397768i | −0.980023 | − | 0.198884i | \(-0.936268\pi\) | ||
0.980023 | − | 0.198884i | \(-0.0637317\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9600.00 | + | 3916.05i | −1.10347 | + | 0.450129i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 428.318i | 0.0488858i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2406.74 | −0.272764 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10320.4 | − | 2024.00i | 1.16148 | − | 0.227785i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1920.00 | 0.214578 | 0.107289 | − | 0.994228i | \(-0.465783\pi\) | ||||
0.107289 | + | 0.994228i | \(0.465783\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15766.0 | −1.74981 | −0.874903 | − | 0.484299i | \(-0.839075\pi\) | ||||
−0.874903 | + | 0.484299i | \(0.839075\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13257.5 | + | 2600.00i | −1.46126 | + | 0.286576i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 897.427 | 0.0982375 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7311.99i | 0.794949i | 0.917613 | + | 0.397474i | \(0.130113\pi\) | ||||
−0.917613 | + | 0.397474i | \(0.869887\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5975.00 | − | 2437.33i | 0.645179 | − | 0.263182i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8190.00i | 0.878372i | 0.898396 | + | 0.439186i | \(0.144733\pi\) | ||||
−0.898396 | + | 0.439186i | \(0.855267\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9776.00i | 1.04141i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2444.00 | + | 479.308i | −0.258607 | + | 0.0507170i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13767.4i | 1.44704i | 0.690303 | + | 0.723521i | \(0.257477\pi\) | ||||
−0.690303 | + | 0.723521i | \(0.742523\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22517.3 | 2.35099 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1499.11 | + | 7644.00i | 0.155484 | + | 0.792818i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4576.00 | 0.471486 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10682.0 | 1.09340 | 0.546699 | − | 0.837329i | \(-0.315884\pi\) | ||||
0.546699 | + | 0.837329i | \(0.315884\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1570.50 | + | 2392.00i | 0.159705 | + | 0.243244i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3090.01 | 0.312182 | 0.156091 | − | 0.987743i | \(-0.450111\pi\) | ||||
0.156091 | + | 0.987743i | \(0.450111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2661.69i | 0.267169i | 0.991037 | + | 0.133584i | \(0.0426487\pi\) | ||||
−0.991037 | + | 0.133584i | \(0.957351\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2184.00 | + | 11136.3i | 0.217808 | + | 1.11061i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12246.0i | 1.21344i | 0.794915 | + | 0.606721i | \(0.207515\pi\) | ||||
−0.794915 | + | 0.606721i | \(0.792485\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 520.000i | − | 0.0511969i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1948.00 | − | 9932.89i | −0.190571 | − | 0.971727i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10789.5i | 1.04884i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −214.159 | −0.0206869 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11472.8 | + | 4680.00i | −1.10126 | + | 0.449230i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15008.0 | 1.43159 | 0.715796 | − | 0.698309i | \(-0.246064\pi\) | ||||
0.715796 | + | 0.698309i | \(0.246064\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14608.0 | 1.38476 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −897.427 | − | 4576.00i | −0.0845432 | − | 0.431087i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10830.3 | 1.01398 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5721.10i | 0.532336i | 0.963927 | + | 0.266168i | \(0.0857576\pi\) | ||||
−0.963927 | + | 0.266168i | \(0.914242\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17316.0 | + | 3395.95i | −1.60134 | + | 0.314049i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5018.00i | 0.461220i | 0.973046 | + | 0.230610i | \(0.0740722\pi\) | ||||
−0.973046 | + | 0.230610i | \(0.925928\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5200.00i | 0.475043i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4784.00 | − | 11727.7i | −0.434394 | − | 1.06489i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6934.67i | − | 0.625880i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16082.3 | −1.44277 | −0.721386 | − | 0.692533i | \(-0.756494\pi\) | ||||
−0.721386 | + | 0.692533i | \(0.756494\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10238.8 | − | 2008.00i | 0.913048 | − | 0.179064i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10632.0 | 0.942460 | 0.471230 | − | 0.882010i | \(-0.343810\pi\) | ||||
0.471230 | + | 0.882010i | \(0.343810\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 104.000 | 0.00916424 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1330.84 | + | 261.000i | −0.116578 | + | 0.0228628i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3579.51 | 0.311707 | 0.155854 | − | 0.987780i | \(-0.450187\pi\) | ||||
0.155854 | + | 0.987780i | \(0.450187\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4303.57i | 0.372561i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1196.00 | + | 785.249i | −0.102933 | + | 0.0675820i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20280.0i | 1.73523i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 17664.0i | − | 1.50263i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6188.00 | + | 1213.57i | −0.523358 | + | 0.102639i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1590.89i | − | 0.133778i | −0.997760 | − | 0.0668890i | \(-0.978693\pi\) | ||
0.997760 | − | 0.0668890i | \(-0.0213073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4109.81 | 0.343613 | 0.171806 | − | 0.985131i | \(-0.445040\pi\) | ||||
0.171806 | + | 0.985131i | \(0.445040\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 214.159 | + | 1092.00i | 0.0178032 | + | 0.0907786i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4368.00 | 0.361049 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4423.00 | −0.363524 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6424.76 | − | 15750.0i | −0.525068 | − | 1.28718i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21538.3 | 1.75033 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2386.34i | − | 0.192842i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2382.00 | + | 12145.9i | 0.191417 | + | 0.976039i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10994.0i | 0.878562i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9484.00i | 0.753695i | 0.926275 | + | 0.376848i | \(0.122992\pi\) | ||||
−0.926275 | + | 0.376848i | \(0.877008\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2652.00 | + | 13522.6i | 0.209592 | + | 1.06871i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7383.38i | 0.580311i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5476.35 | 0.428065 | 0.214033 | − | 0.976827i | \(-0.431340\pi\) | ||||
0.214033 | + | 0.976827i | \(0.431340\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2406.74 | + | 5900.00i | 0.187098 | + | 0.458663i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2600.00 | −0.201023 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7592.00 | −0.583806 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3385.75 | − | 17264.0i | −0.258950 | − | 1.32039i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1091.19 | 0.0830076 | 0.0415038 | − | 0.999138i | \(-0.486785\pi\) | ||||
0.0415038 | + | 0.999138i | \(0.486785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10320.4i | 0.780871i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4784.00 | + | 938.220i | −0.360037 | + | 0.0706090i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 17898.0i | − | 1.33981i | −0.742449 | − | 0.669903i | \(-0.766336\pi\) | ||
0.742449 | − | 0.669903i | \(-0.233664\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 10400.0i | − | 0.774392i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5200.00 | + | 5313.18i | 0.385149 | + | 0.393532i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21089.5i | 1.55381i | 0.629616 | + | 0.776907i | \(0.283212\pi\) | ||||
−0.629616 | + | 0.776907i | \(0.716788\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3334.76 | −0.244405 | −0.122203 | − | 0.992505i | \(-0.538996\pi\) | ||||
−0.122203 | + | 0.992505i | \(0.538996\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24393.7 | − | 4784.00i | 1.77847 | − | 0.348786i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1848.00 | −0.134029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5066.00 | −0.365512 | −0.182756 | − | 0.983158i | \(-0.558502\pi\) | ||||
−0.182756 | + | 0.983158i | \(0.558502\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15674.4 | − | 3074.00i | 1.12505 | − | 0.220641i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1896.84 | 0.135446 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 21109.9i | − | 1.49963i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4576.00 | − | 11217.8i | −0.323409 | − | 0.792822i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20042.0i | 1.40924i | 0.709587 | + | 0.704618i | \(0.248882\pi\) | ||||
−0.709587 | + | 0.704618i | \(0.751118\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2184.00i | 0.152785i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24700.0 | + | 4844.07i | −1.71916 | + | 0.337155i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26351.7i | 1.82485i | 0.409244 | + | 0.912425i | \(0.365792\pi\) | ||||
−0.409244 | + | 0.912425i | \(0.634208\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2121.19 | −0.146152 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1927.43 | − | 9828.00i | −0.132135 | − | 0.673758i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4344.00 | 0.296312 | 0.148156 | − | 0.988964i | \(-0.452666\pi\) | ||||
0.148156 | + | 0.988964i | \(0.452666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18250.0 | −1.23866 | −0.619329 | − | 0.785132i | \(-0.712595\pi\) | ||||
−0.619329 | + | 0.785132i | \(0.712595\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1274.75 | + | 520.000i | −0.0860896 | + | 0.0351178i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8005.46 | 0.537964 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5272.39i | 0.352553i | 0.984341 | + | 0.176276i | \(0.0564053\pi\) | ||||
−0.984341 | + | 0.176276i | \(0.943595\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2600.00 | + | 13257.5i | 0.173001 | + | 0.882133i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 16896.0i | − | 1.11872i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11748.0i | 0.774058i | 0.922068 | + | 0.387029i | \(0.126499\pi\) | ||||
−0.922068 | + | 0.387029i | \(0.873501\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4992.00 | − | 25454.3i | −0.327312 | − | 1.66897i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3895.65i | 0.254186i | 0.991891 | + | 0.127093i | \(0.0405647\pi\) | ||||
−0.991891 | + | 0.127093i | \(0.959435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7189.62 | 0.466842 | 0.233421 | − | 0.972376i | \(-0.425008\pi\) | ||||
0.233421 | + | 0.972376i | \(0.425008\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10320.4 | + | 6776.00i | −0.666899 | + | 0.437861i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9776.00 | 0.628679 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12559.0 | −0.803776 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −469.110 | − | 2392.00i | −0.0298795 | − | 0.152356i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6771.50 | −0.429248 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 26831.0i | − | 1.69275i | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||
0.532585 | − | 0.846376i | \(-0.321221\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17524.0 | − | 3436.74i | 1.10034 | − | 0.215795i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 22984.0i | − | 1.43637i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10516.0i | 0.654096i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17000.0 | + | 6934.67i | −1.05244 | + | 0.429313i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 23639.1i | − | 1.45661i | −0.685254 | − | 0.728305i | \(-0.740309\pi\) | ||
0.685254 | − | 0.728305i | \(-0.259691\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16245.5 | 0.996359 | 0.498180 | − | 0.867074i | \(-0.334002\pi\) | ||||
0.498180 | + | 0.867074i | \(0.334002\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12196.9 | − | 2392.00i | 0.744575 | − | 0.146023i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7384.00 | −0.448679 | −0.224339 | − | 0.974511i | \(-0.572022\pi\) | ||||
−0.224339 | + | 0.974511i | \(0.572022\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28980.0 | 1.75280 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11136.3 | − | 2184.00i | 0.670452 | − | 0.131486i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15082.9 | 0.903889 | 0.451944 | − | 0.892046i | \(-0.350731\pi\) | ||||
0.451944 | + | 0.892046i | \(0.350731\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17765.0i | 1.05975i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10550.0 | − | 4303.57i | 0.626476 | − | 0.255553i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20434.0i | 1.20788i | 0.797028 | + | 0.603942i | \(0.206404\pi\) | ||||
−0.797028 | + | 0.603942i | \(0.793596\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12148.0i | 0.714830i | 0.933946 | + | 0.357415i | \(0.116342\pi\) | ||||
−0.933946 | + | 0.357415i | \(0.883658\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4576.00 | + | 897.427i | −0.268050 | + | 0.0525689i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1060.60i | − | 0.0618468i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22435.7 | −1.30242 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1233.96 | − | 6292.00i | −0.0713120 | − | 0.363621i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10856.0 | −0.624577 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12730.0 | 0.729131 | 0.364566 | − | 0.931178i | \(-0.381217\pi\) | ||||
0.364566 | + | 0.931178i | \(0.381217\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2462.83 | − | 1617.00i | 0.140436 | − | 0.0922050i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19672.0 | −1.11678 | −0.558388 | − | 0.829580i | \(-0.688580\pi\) | ||||
−0.558388 | + | 0.829580i | \(0.688580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 10830.3i | − | 0.612120i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1270.00 | − | 6475.75i | −0.0714633 | − | 0.364393i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6558.00i | 0.367401i | 0.982982 | + | 0.183701i | \(0.0588077\pi\) | ||||
−0.982982 | + | 0.183701i | \(0.941192\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 24544.0i | − | 1.36902i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4556.00 | + | 23231.1i | 0.253016 | + | 1.29014i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 20192.1i | − | 1.11649i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30461.5 | −1.67701 | −0.838503 | − | 0.544896i | \(-0.816569\pi\) | ||||
−0.838503 | + | 0.544896i | \(0.816569\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11727.7 | + | 4784.00i | −0.642857 | + | 0.262235i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7800.00 | 0.425713 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9984.00 | −0.542570 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 877.031 | + | 4472.00i | 0.0474569 | + | 0.241984i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31461.0 | −1.69510 | −0.847549 | − | 0.530717i | \(-0.821923\pi\) | ||||
−0.847549 | + | 0.530717i | \(0.821923\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3385.75i | − | 0.181644i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19968.0 | + | 3916.05i | −1.06672 | + | 0.209201i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 104.000i | − | 0.00553228i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25396.0i | 1.34523i | 0.739993 | + | 0.672614i | \(0.234829\pi\) | ||||
−0.739993 | + | 0.672614i | \(0.765171\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7592.00 | + | 18611.4i | 0.400453 | + | 0.981692i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18846.0i | 0.989884i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20640.8 | 1.07961 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9790.12 | + | 1920.00i | −0.509928 | + | 0.100005i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7888.00 | −0.409142 | −0.204571 | − | 0.978852i | \(-0.565580\pi\) | ||||
−0.204571 | + | 0.978852i | \(0.565580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20280.0 | 1.04753 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8250.21 | − | 1618.00i | 0.424383 | − | 0.0832283i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5353.97 | 0.274264 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6475.75i | − | 0.330361i | −0.986263 | − | 0.165181i | \(-0.947179\pi\) | ||
0.986263 | − | 0.165181i | \(-0.0528207\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7825.00 | − | 18060.7i | 0.397551 | − | 0.917580i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 4784.00i | − | 0.242056i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 14772.0i | − | 0.744361i | −0.928160 | − | 0.372180i | \(-0.878610\pi\) | ||
0.928160 | − | 0.372180i | \(-0.121390\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12428.0 | − | 2437.33i | 0.623692 | − | 0.122316i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2345.55i | − | 0.117231i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22364.3 | −1.11324 | −0.556620 | − | 0.830767i | \(-0.687902\pi\) | ||||
−0.556620 | + | 0.830767i | \(0.687902\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −448.714 | − | 2288.00i | −0.0222455 | − | 0.113430i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19080.0 | 0.942096 | 0.471048 | − | 0.882108i | \(-0.343876\pi\) | ||||
0.471048 | + | 0.882108i | \(0.343876\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4888.00 | −0.240379 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1896.84 | − | 4650.00i | −0.0929071 | − | 0.227757i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2386.34 | −0.116415 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20324.7i | 0.987561i | 0.869586 | + | 0.493781i | \(0.164385\pi\) | ||||
−0.869586 | + | 0.493781i | \(0.835615\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1586.00 | + | 8087.04i | 0.0767557 | + | 0.391379i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15288.0i | 0.736937i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 4188.00i | − | 0.201077i | −0.994933 | − | 0.100539i | \(-0.967943\pi\) | ||
0.994933 | − | 0.100539i | \(-0.0320566\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4048.00 | − | 20640.8i | −0.193588 | − | 0.987108i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 30757.3i | − | 1.46511i | −0.680706 | − | 0.732556i | \(-0.738327\pi\) | ||
0.680706 | − | 0.732556i | \(-0.261673\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7383.38 | 0.350323 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2121.19 | + | 5200.00i | 0.100251 | + | 0.245760i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27720.0 | 1.30497 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10370.0 | −0.486283 | −0.243142 | − | 0.969991i | \(-0.578178\pi\) | ||||
−0.243142 | + | 0.969991i | \(0.578178\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3956.84 | + | 20176.0i | 0.184828 | + | 0.942440i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10779.3 | −0.501559 | −0.250780 | − | 0.968044i | \(-0.580687\pi\) | ||||
−0.250780 | + | 0.968044i | \(0.580687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4497.34i | − | 0.208450i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17264.0 | + | 3385.75i | −0.797095 | + | 0.156323i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 4992.00i | − | 0.229598i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 31280.0i | − | 1.43315i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29900.0 | − | 19631.2i | 1.36467 | − | 0.895993i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 19865.8i | − | 0.903236i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23384.1 | 1.05915 | 0.529576 | − | 0.848262i | \(-0.322351\pi\) | ||||
0.529576 | + | 0.848262i | \(0.322351\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22150.1 | + | 4344.00i | −0.999450 | + | 0.196008i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10400.0 | −0.467486 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10384.0 | −0.465002 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23863.4 | + | 4680.00i | −1.06459 | + | 0.208783i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3232.78 | −0.143677 | −0.0718387 | − | 0.997416i | \(-0.522887\pi\) | ||||
−0.0718387 | + | 0.997416i | \(0.522887\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7832.09i | 0.346783i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9776.00 | − | 23965.4i | −0.431233 | − | 1.05715i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19412.0i | 0.853094i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 9152.00i | − | 0.400703i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13988.0 | − | 2743.27i | 0.610162 | − | 0.119663i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 33857.5i | − | 1.47140i | −0.677305 | − | 0.735702i | \(-0.736852\pi\) | ||
0.677305 | − | 0.735702i | \(-0.263148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10493.8 | −0.454361 | −0.227180 | − | 0.973853i | \(-0.572951\pi\) | ||||
−0.227180 | + | 0.973853i | \(0.572951\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3253.17 | + | 16588.0i | 0.140337 | + | 0.715580i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34632.0 | −1.48847 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2392.00 | 0.102430 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11217.8 | + | 4576.00i | −0.478612 | + | 0.195236i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15103.3 | −0.642032 | −0.321016 | − | 0.947074i | \(-0.604024\pi\) | ||||
−0.321016 | + | 0.947074i | \(0.604024\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17958.7i | 0.760635i | 0.924856 | + | 0.380317i | \(0.124185\pi\) | ||||
−0.924856 | + | 0.380317i | \(0.875815\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 966.000 | + | 4925.65i | 0.0407658 | + | 0.207866i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6598.00i | − | 0.277430i | −0.990332 | − | 0.138715i | \(-0.955703\pi\) | ||
0.990332 | − | 0.138715i | \(-0.0442973\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41028.0i | − | 1.71889i | −0.511227 | − | 0.859446i | \(-0.670809\pi\) | ||
0.511227 | − | 0.859446i | \(-0.329191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4956.00 | + | 25270.7i | 0.206885 | + | 1.05491i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 4874.66i | − | 0.202758i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20477.7 | 0.848693 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16490.2 | − | 25116.0i | −0.680987 | − | 1.03720i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17816.0 | 0.733107 | 0.366553 | − | 0.930397i | \(-0.380538\pi\) | ||||
0.366553 | + | 0.930397i | \(0.380538\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40611.0 | 1.66514 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1978.42 | + | 10088.0i | 0.0808308 | + | 0.412158i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2661.69 | −0.108361 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8005.46i | − | 0.324759i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40716.0 | − | 7985.06i | 1.64590 | − | 0.322788i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 29216.0i | − | 1.17686i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28308.0i | 1.13628i | 0.822932 | + | 0.568140i | \(0.192337\pi\) | ||||
−0.822932 | + | 0.568140i | \(0.807663\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2600.00 | + | 1060.60i | −0.103998 | + | 0.0424229i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 33735.1i | − | 1.34466i | −0.740254 | − | 0.672328i | \(-0.765295\pi\) | ||
0.740254 | − | 0.672328i | \(-0.234705\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −336.535 | −0.0133672 | −0.00668361 | − | 0.999978i | \(-0.502127\pi\) | ||||
−0.00668361 | + | 0.999978i | \(0.502127\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25454.3 | + | 4992.00i | −1.00753 | + | 0.197592i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48208.0 | −1.90153 | −0.950764 | − | 0.309915i | \(-0.899700\pi\) | ||||
−0.950764 | + | 0.309915i | \(0.899700\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12376.0 | −0.486470 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22930.3 | + | 4497.00i | −0.898216 | + | 0.176155i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34245.0 | −1.33680 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2243.57i | − | 0.0872795i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26550.0 | + | 10830.3i | −1.02930 | + | 0.419875i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15184.0i | 0.586643i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42844.0i | 1.64965i | 0.565391 | + | 0.824823i | \(0.308725\pi\) | ||||
−0.565391 | + | 0.824823i | \(0.691275\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9412.00 | − | 1845.85i | 0.361159 | − | 0.0708291i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6975.46i | 0.266753i | 0.991065 | + | 0.133376i | \(0.0425819\pi\) | ||||
−0.991065 | + | 0.133376i | \(0.957418\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4803.28 | −0.183061 | −0.0915306 | − | 0.995802i | \(-0.529176\pi\) | ||||
−0.0915306 | + | 0.995802i | \(0.529176\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6424.76 | − | 32760.0i | −0.244029 | − | 1.24431i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37336.0 | −1.41333 | −0.706663 | − | 0.707550i | \(-0.749800\pi\) | ||||
−0.706663 | + | 0.707550i | \(0.749800\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22984.0 | −0.867108 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23455.5 | + | 23966.0i | 0.881917 | + | 0.901112i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3916.05 | −0.146747 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24291.7i | 0.907244i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3872.00 | − | 19743.4i | −0.144127 | − | 0.734909i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 54600.0i | − | 2.02560i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9360.00i | 0.346090i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2392.00 | − | 12196.9i | −0.0881515 | − | 0.449486i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27045.2i | 0.993384i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16490.2 | −0.603692 | −0.301846 | − | 0.953357i | \(-0.597603\pi\) | ||||
−0.301846 | + | 0.953357i | \(0.597603\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −254.951 | + | 104.000i | −0.00930274 | + | 0.00379479i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35360.0 | 1.28598 | 0.642991 | − | 0.765874i | \(-0.277693\pi\) | ||||
0.642991 | + | 0.765874i | \(0.277693\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8556.00 | 0.310145 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2406.74 | + | 12272.0i | 0.0869555 | + | 0.443388i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17765.0 | 0.639751 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4395.35i | − | 0.157769i | −0.996884 | − | 0.0788843i | \(-0.974864\pi\) | ||
0.996884 | − | 0.0788843i | \(-0.0251358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42276.0 | − | 8291.01i | 1.51253 | − | 0.296632i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 29920.0i | − | 1.06699i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6972.00i | 0.247825i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20280.0 | − | 49715.4i | −0.718536 | − | 1.76146i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1815.25i | 0.0641081i | 0.999486 | + | 0.0320541i | \(0.0102049\pi\) | ||||
−0.999486 | + | 0.0320541i | \(0.989795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2437.33 | 0.0858005 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 51520.5 | − | 10104.0i | 1.80783 | − | 0.354545i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9568.00 | −0.334660 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34034.0 | 1.18660 | 0.593299 | − | 0.804982i | \(-0.297825\pi\) | ||||
0.593299 | + | 0.804982i | \(0.297825\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6108.63 | + | 1198.00i | −0.212298 | + | 0.0416350i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36967.9 | −1.28068 | −0.640339 | − | 0.768092i | \(-0.721206\pi\) | ||||
−0.640339 | + | 0.768092i | \(0.721206\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 43076.5i | − | 1.48756i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8008.00 | + | 12196.9i | 0.275662 | + | 0.419856i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 24862.0i | − | 0.853122i | −0.904459 | − | 0.426561i | \(-0.859725\pi\) | ||
0.904459 | − | 0.426561i | \(-0.140275\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18568.0i | 0.635135i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25636.0 | − | 5027.63i | 0.874137 | − | 0.171432i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22802.8i | 0.775085i | 0.921852 | + | 0.387542i | \(0.126676\pi\) | ||||
−0.921852 | + | 0.387542i | \(0.873324\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48787.4 | 1.65311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11727.7 | + | 59800.0i | 0.396138 | + | 2.01992i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24544.0 | −0.826452 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16073.0 | −0.539525 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2386.34 | + | 5850.00i | 0.0798533 | + | 0.195757i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31348.8 | 1.04575 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40068.1i | 1.33247i | 0.745740 | + | 0.666237i | \(0.232096\pi\) | ||||
−0.745740 | + | 0.666237i | \(0.767904\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 208.000 | + | 1060.60i | 0.00689569 | + | 0.0351613i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 43522.0i | − | 1.43840i | −0.694803 | − | 0.719201i | \(-0.744508\pi\) | ||
0.694803 | − | 0.719201i | \(-0.255492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 7800.00i | − | 0.256995i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 924.000 | + | 4711.49i | 0.0303504 | + | 0.154758i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17683.4i | 0.579060i | 0.957169 | + | 0.289530i | \(0.0934991\pi\) | ||||
−0.957169 | + | 0.289530i | \(0.906501\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44096.3 | 1.43956 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7383.38 | − | 18100.0i | −0.240299 | − | 0.589081i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42360.0 | −1.37444 | −0.687220 | − | 0.726450i | \(-0.741169\pi\) | ||||
−0.687220 | + | 0.726450i | \(0.741169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49400.0 | −1.59798 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3916.05 | + | 19968.0i | 0.126291 | + | 0.643960i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20640.8 | 0.663640 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 25199.4i | − | 0.807754i | −0.914813 | − | 0.403877i | \(-0.867662\pi\) | ||
0.914813 | − | 0.403877i | \(-0.132338\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31252.0 | + | 6129.02i | −0.998743 | + | 0.195870i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 19656.0i | − | 0.626268i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 5356.00i | − | 0.170137i | −0.996375 | − | 0.0850683i | \(-0.972889\pi\) | ||
0.996375 | − | 0.0850683i | \(-0.0271109\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25564.0 | + | 38936.1i | 0.809619 | + | 1.23312i |
(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 | 384.4.f.f.191.2 | yes | 4 | |
3.2 | odd | 2 | 384.4.f.e.191.1 | ✓ | 4 | ||
4.3 | odd | 2 | 384.4.f.e.191.3 | yes | 4 | ||
8.3 | odd | 2 | 384.4.f.e.191.2 | yes | 4 | ||
8.5 | even | 2 | inner | 384.4.f.f.191.3 | yes | 4 | |
12.11 | even | 2 | inner | 384.4.f.f.191.4 | yes | 4 | |
16.3 | odd | 4 | 768.4.c.f.767.2 | 2 | |||
16.5 | even | 4 | 768.4.c.g.767.2 | 2 | |||
16.11 | odd | 4 | 768.4.c.e.767.1 | 2 | |||
16.13 | even | 4 | 768.4.c.d.767.1 | 2 | |||
24.5 | odd | 2 | 384.4.f.e.191.4 | yes | 4 | ||
24.11 | even | 2 | inner | 384.4.f.f.191.1 | yes | 4 | |
48.5 | odd | 4 | 768.4.c.e.767.2 | 2 | |||
48.11 | even | 4 | 768.4.c.g.767.1 | 2 | |||
48.29 | odd | 4 | 768.4.c.f.767.1 | 2 | |||
48.35 | even | 4 | 768.4.c.d.767.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.f.e.191.1 | ✓ | 4 | 3.2 | odd | 2 | ||
384.4.f.e.191.2 | yes | 4 | 8.3 | odd | 2 | ||
384.4.f.e.191.3 | yes | 4 | 4.3 | odd | 2 | ||
384.4.f.e.191.4 | yes | 4 | 24.5 | odd | 2 | ||
384.4.f.f.191.1 | yes | 4 | 24.11 | even | 2 | inner | |
384.4.f.f.191.2 | yes | 4 | 1.1 | even | 1 | trivial | |
384.4.f.f.191.3 | yes | 4 | 8.5 | even | 2 | inner | |
384.4.f.f.191.4 | yes | 4 | 12.11 | even | 2 | inner | |
768.4.c.d.767.1 | 2 | 16.13 | even | 4 | |||
768.4.c.d.767.2 | 2 | 48.35 | even | 4 | |||
768.4.c.e.767.1 | 2 | 16.11 | odd | 4 | |||
768.4.c.e.767.2 | 2 | 48.5 | odd | 4 | |||
768.4.c.f.767.1 | 2 | 48.29 | odd | 4 | |||
768.4.c.f.767.2 | 2 | 16.3 | odd | 4 | |||
768.4.c.g.767.1 | 2 | 48.11 | even | 4 | |||
768.4.c.g.767.2 | 2 | 16.5 | even | 4 |