Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,3,Mod(551,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.551");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.d (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: | \(31.3352304014\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 551.4 | ||
Root | \(2.26343i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.551 |
Dual form | 1150.3.d.b.551.3 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | −1.43837 | −0.479458 | −0.239729 | − | 0.970840i | \(-0.577059\pi\) | ||||
−0.239729 | + | 0.970840i | \(0.577059\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.03417 | 0.339028 | ||||||||
\(7\) | 10.1866i | 1.45522i | 0.685989 | + | 0.727612i | \(0.259370\pi\) | ||||
−0.685989 | + | 0.727612i | \(0.740630\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −6.93108 | −0.770120 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 13.0237i | − | 1.18397i | −0.805947 | − | 0.591987i | \(-0.798343\pi\) | ||
0.805947 | − | 0.591987i | \(-0.201657\pi\) | |||||||
\(12\) | −2.87675 | −0.239729 | ||||||||
\(13\) | −23.2154 | −1.78580 | −0.892900 | − | 0.450255i | \(-0.851333\pi\) | ||||
−0.892900 | + | 0.450255i | \(0.851333\pi\) | |||||||
\(14\) | − | 14.4060i | − | 1.02900i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 28.2228i | − | 1.66016i | −0.557641 | − | 0.830082i | \(-0.688293\pi\) | ||
0.557641 | − | 0.830082i | \(-0.311707\pi\) | |||||||
\(18\) | 9.80202 | 0.544557 | ||||||||
\(19\) | 11.6665i | 0.614027i | 0.951705 | + | 0.307013i | \(0.0993297\pi\) | ||||
−0.951705 | + | 0.307013i | \(0.900670\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 14.6521i | − | 0.697719i | ||||||
\(22\) | 18.4183i | 0.837197i | ||||||||
\(23\) | 17.3999 | − | 15.0414i | 0.756516 | − | 0.653976i | ||||
\(24\) | 4.06834 | 0.169514 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 32.8315 | 1.26275 | ||||||||
\(27\) | 22.9149 | 0.848699 | ||||||||
\(28\) | 20.3731i | 0.727612i | ||||||||
\(29\) | 42.4794 | 1.46481 | 0.732404 | − | 0.680870i | \(-0.238398\pi\) | ||||
0.732404 | + | 0.680870i | \(0.238398\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.7683 | 0.605428 | 0.302714 | − | 0.953082i | \(-0.402107\pi\) | ||||
0.302714 | + | 0.953082i | \(0.402107\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 18.7330i | 0.567667i | ||||||||
\(34\) | 39.9131i | 1.17391i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −13.8622 | −0.385060 | ||||||||
\(37\) | − | 1.14094i | − | 0.0308363i | −0.999881 | − | 0.0154182i | \(-0.995092\pi\) | ||
0.999881 | − | 0.0154182i | \(-0.00490795\pi\) | |||||||
\(38\) | − | 16.4989i | − | 0.434183i | ||||||
\(39\) | 33.3924 | 0.856217 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −72.8198 | −1.77609 | −0.888046 | − | 0.459755i | \(-0.847937\pi\) | ||||
−0.888046 | + | 0.459755i | \(0.847937\pi\) | |||||||
\(42\) | 20.7212i | 0.493362i | ||||||||
\(43\) | − | 4.96573i | − | 0.115482i | −0.998332 | − | 0.0577411i | \(-0.981610\pi\) | ||
0.998332 | − | 0.0577411i | \(-0.0183898\pi\) | |||||||
\(44\) | − | 26.0474i | − | 0.591987i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −24.6071 | + | 21.2718i | −0.534937 | + | 0.462431i | ||||
\(47\) | 0.813360 | 0.0173055 | 0.00865277 | − | 0.999963i | \(-0.497246\pi\) | ||||
0.00865277 | + | 0.999963i | \(0.497246\pi\) | |||||||
\(48\) | −5.75350 | −0.119865 | ||||||||
\(49\) | −54.7661 | −1.11768 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 40.5950i | 0.795980i | ||||||||
\(52\) | −46.4308 | −0.892900 | ||||||||
\(53\) | 26.7286i | 0.504313i | 0.967686 | + | 0.252157i | \(0.0811398\pi\) | ||||
−0.967686 | + | 0.252157i | \(0.918860\pi\) | |||||||
\(54\) | −32.4065 | −0.600121 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 28.8120i | − | 0.514499i | ||||||
\(57\) | − | 16.7808i | − | 0.294400i | ||||||
\(58\) | −60.0750 | −1.03578 | ||||||||
\(59\) | 94.0845 | 1.59465 | 0.797326 | − | 0.603549i | \(-0.206247\pi\) | ||||
0.797326 | + | 0.603549i | \(0.206247\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 74.5293i | 1.22179i | 0.791711 | + | 0.610896i | \(0.209191\pi\) | ||||
−0.791711 | + | 0.610896i | \(0.790809\pi\) | |||||||
\(62\) | −26.5423 | −0.428102 | ||||||||
\(63\) | − | 70.6039i | − | 1.12070i | ||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 26.4925i | − | 0.401401i | ||||||
\(67\) | 80.0906i | 1.19538i | 0.801727 | + | 0.597691i | \(0.203915\pi\) | ||||
−0.801727 | + | 0.597691i | \(0.796085\pi\) | |||||||
\(68\) | − | 56.4456i | − | 0.830082i | ||||||
\(69\) | −25.0275 | + | 21.6352i | −0.362718 | + | 0.313554i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −83.5303 | −1.17648 | −0.588241 | − | 0.808686i | \(-0.700179\pi\) | ||||
−0.588241 | + | 0.808686i | \(0.700179\pi\) | |||||||
\(72\) | 19.6040 | 0.272278 | ||||||||
\(73\) | 8.98897 | 0.123137 | 0.0615683 | − | 0.998103i | \(-0.480390\pi\) | ||||
0.0615683 | + | 0.998103i | \(0.480390\pi\) | |||||||
\(74\) | 1.61354i | 0.0218046i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 23.3330i | 0.307013i | ||||||||
\(77\) | 132.667 | 1.72295 | ||||||||
\(78\) | −47.2241 | −0.605437 | ||||||||
\(79\) | 80.2841i | 1.01626i | 0.861282 | + | 0.508128i | \(0.169662\pi\) | ||||
−0.861282 | + | 0.508128i | \(0.830338\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.4195 | 0.363204 | ||||||||
\(82\) | 102.983 | 1.25589 | ||||||||
\(83\) | − | 94.6451i | − | 1.14030i | −0.821540 | − | 0.570151i | \(-0.806885\pi\) | ||
0.821540 | − | 0.570151i | \(-0.193115\pi\) | |||||||
\(84\) | − | 29.3042i | − | 0.348859i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.02261i | 0.0816582i | ||||||||
\(87\) | −61.1014 | −0.702315 | ||||||||
\(88\) | 36.8367i | 0.418598i | ||||||||
\(89\) | 136.812i | 1.53722i | 0.639720 | + | 0.768608i | \(0.279050\pi\) | ||||
−0.639720 | + | 0.768608i | \(0.720950\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 236.485i | − | 2.59874i | ||||||
\(92\) | 34.7997 | − | 30.0829i | 0.378258 | − | 0.326988i | ||||
\(93\) | −26.9958 | −0.290277 | ||||||||
\(94\) | −1.15026 | −0.0122369 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.13668 | 0.0847571 | ||||||||
\(97\) | − | 2.32666i | − | 0.0239862i | −0.999928 | − | 0.0119931i | \(-0.996182\pi\) | ||
0.999928 | − | 0.0119931i | \(-0.00381761\pi\) | |||||||
\(98\) | 77.4509 | 0.790316 | ||||||||
\(99\) | 90.2684i | 0.911802i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.9918 | 0.128632 | 0.0643161 | − | 0.997930i | \(-0.479513\pi\) | ||||
0.0643161 | + | 0.997930i | \(0.479513\pi\) | |||||||
\(102\) | − | 57.4100i | − | 0.562843i | ||||||
\(103\) | 90.3165i | 0.876859i | 0.898766 | + | 0.438430i | \(0.144465\pi\) | ||||
−0.898766 | + | 0.438430i | \(0.855535\pi\) | |||||||
\(104\) | 65.6631 | 0.631376 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 37.7999i | − | 0.356603i | ||||||
\(107\) | 185.173i | 1.73059i | 0.501264 | + | 0.865294i | \(0.332869\pi\) | ||||
−0.501264 | + | 0.865294i | \(0.667131\pi\) | |||||||
\(108\) | 45.8297 | 0.424349 | ||||||||
\(109\) | − | 13.8248i | − | 0.126833i | −0.997987 | − | 0.0634167i | \(-0.979800\pi\) | ||
0.997987 | − | 0.0634167i | \(-0.0201997\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.64110i | 0.0147847i | ||||||||
\(112\) | 40.7463i | 0.363806i | ||||||||
\(113\) | − | 178.530i | − | 1.57991i | −0.613164 | − | 0.789956i | \(-0.710103\pi\) | ||
0.613164 | − | 0.789956i | \(-0.289897\pi\) | |||||||
\(114\) | 23.7317i | 0.208172i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 84.9589 | 0.732404 | ||||||||
\(117\) | 160.908 | 1.37528 | ||||||||
\(118\) | −133.056 | −1.12759 | ||||||||
\(119\) | 287.493 | 2.41591 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −48.6174 | −0.401797 | ||||||||
\(122\) | − | 105.400i | − | 0.863938i | ||||||
\(123\) | 104.742 | 0.851562 | ||||||||
\(124\) | 37.5365 | 0.302714 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 99.8489i | 0.792452i | ||||||||
\(127\) | 112.959 | 0.889442 | 0.444721 | − | 0.895669i | \(-0.353303\pi\) | ||||
0.444721 | + | 0.895669i | \(0.353303\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 7.14258i | 0.0553689i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.1419 | −0.0926860 | −0.0463430 | − | 0.998926i | \(-0.514757\pi\) | ||||
−0.0463430 | + | 0.998926i | \(0.514757\pi\) | |||||||
\(132\) | 37.4660i | 0.283833i | ||||||||
\(133\) | −118.842 | −0.893546 | ||||||||
\(134\) | − | 113.265i | − | 0.845263i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 79.8261i | 0.586957i | ||||||||
\(137\) | 170.543i | 1.24484i | 0.782685 | + | 0.622418i | \(0.213850\pi\) | ||||
−0.782685 | + | 0.622418i | \(0.786150\pi\) | |||||||
\(138\) | 35.3943 | − | 30.5968i | 0.256480 | − | 0.221716i | ||||
\(139\) | 38.5478 | 0.277322 | 0.138661 | − | 0.990340i | \(-0.455720\pi\) | ||||
0.138661 | + | 0.990340i | \(0.455720\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.16992 | −0.00829728 | ||||||||
\(142\) | 118.130 | 0.831899 | ||||||||
\(143\) | 302.351i | 2.11434i | ||||||||
\(144\) | −27.7243 | −0.192530 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.7123 | −0.0870707 | ||||||||
\(147\) | 78.7742 | 0.535879 | ||||||||
\(148\) | − | 2.28189i | − | 0.0154182i | ||||||
\(149\) | 81.4125i | 0.546393i | 0.961958 | + | 0.273196i | \(0.0880808\pi\) | ||||
−0.961958 | + | 0.273196i | \(0.911919\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 159.680 | 1.05748 | 0.528742 | − | 0.848782i | \(-0.322664\pi\) | ||||
0.528742 | + | 0.848782i | \(0.322664\pi\) | |||||||
\(152\) | − | 32.9979i | − | 0.217091i | ||||||
\(153\) | 195.614i | 1.27853i | ||||||||
\(154\) | −187.619 | −1.21831 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 66.7849 | 0.428108 | ||||||||
\(157\) | 38.5953i | 0.245830i | 0.992417 | + | 0.122915i | \(0.0392242\pi\) | ||||
−0.992417 | + | 0.122915i | \(0.960776\pi\) | |||||||
\(158\) | − | 113.539i | − | 0.718601i | ||||||
\(159\) | − | 38.4457i | − | 0.241797i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 153.221 | + | 177.245i | 0.951681 | + | 1.10090i | ||||
\(162\) | −41.6055 | −0.256824 | ||||||||
\(163\) | −150.291 | −0.922028 | −0.461014 | − | 0.887393i | \(-0.652514\pi\) | ||||
−0.461014 | + | 0.887393i | \(0.652514\pi\) | |||||||
\(164\) | −145.640 | −0.888046 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 133.848i | 0.806316i | ||||||||
\(167\) | −27.7604 | −0.166230 | −0.0831149 | − | 0.996540i | \(-0.526487\pi\) | ||||
−0.0831149 | + | 0.996540i | \(0.526487\pi\) | |||||||
\(168\) | 41.4424i | 0.246681i | ||||||||
\(169\) | 369.955 | 2.18908 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 80.8615i | − | 0.472874i | ||||||
\(172\) | − | 9.93146i | − | 0.0577411i | ||||||
\(173\) | 24.0064 | 0.138765 | 0.0693826 | − | 0.997590i | \(-0.477897\pi\) | ||||
0.0693826 | + | 0.997590i | \(0.477897\pi\) | |||||||
\(174\) | 86.4104 | 0.496611 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 52.0949i | − | 0.295994i | ||||||
\(177\) | −135.329 | −0.764569 | ||||||||
\(178\) | − | 193.482i | − | 1.08698i | ||||||
\(179\) | −201.178 | −1.12390 | −0.561949 | − | 0.827172i | \(-0.689948\pi\) | ||||
−0.561949 | + | 0.827172i | \(0.689948\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 202.358i | − | 1.11800i | −0.829168 | − | 0.558999i | \(-0.811186\pi\) | ||
0.829168 | − | 0.558999i | \(-0.188814\pi\) | |||||||
\(182\) | 334.441i | 1.83759i | ||||||||
\(183\) | − | 107.201i | − | 0.585798i | ||||||
\(184\) | −49.2142 | + | 42.5436i | −0.267469 | + | 0.231215i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 38.1778 | 0.205257 | ||||||||
\(187\) | −367.566 | −1.96559 | ||||||||
\(188\) | 1.62672 | 0.00865277 | ||||||||
\(189\) | 233.424i | 1.23505i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 111.302i | 0.582735i | 0.956611 | + | 0.291368i | \(0.0941103\pi\) | ||||
−0.956611 | + | 0.291368i | \(0.905890\pi\) | |||||||
\(192\) | −11.5070 | −0.0599323 | ||||||||
\(193\) | 164.081 | 0.850163 | 0.425081 | − | 0.905155i | \(-0.360246\pi\) | ||||
0.425081 | + | 0.905155i | \(0.360246\pi\) | |||||||
\(194\) | 3.29040i | 0.0169608i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −109.532 | −0.558838 | ||||||||
\(197\) | 329.562 | 1.67290 | 0.836451 | − | 0.548042i | \(-0.184627\pi\) | ||||
0.836451 | + | 0.548042i | \(0.184627\pi\) | |||||||
\(198\) | − | 127.659i | − | 0.644742i | ||||||
\(199\) | − | 337.886i | − | 1.69792i | −0.528455 | − | 0.848961i | \(-0.677229\pi\) | ||
0.528455 | − | 0.848961i | \(-0.322771\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 115.200i | − | 0.573136i | ||||||
\(202\) | −18.3732 | −0.0909566 | ||||||||
\(203\) | 432.720i | 2.13162i | ||||||||
\(204\) | 81.1899i | 0.397990i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 127.727i | − | 0.620033i | ||||||
\(207\) | −120.600 | + | 104.253i | −0.582608 | + | 0.503640i | ||||
\(208\) | −92.8616 | −0.446450 | ||||||||
\(209\) | 151.941 | 0.726992 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 111.656 | 0.529173 | 0.264587 | − | 0.964362i | \(-0.414765\pi\) | ||||
0.264587 | + | 0.964362i | \(0.414765\pi\) | |||||||
\(212\) | 53.4572i | 0.252157i | ||||||||
\(213\) | 120.148 | 0.564074 | ||||||||
\(214\) | − | 261.874i | − | 1.22371i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −64.8130 | −0.300060 | ||||||||
\(217\) | 191.184i | 0.881032i | ||||||||
\(218\) | 19.5513i | 0.0896847i | ||||||||
\(219\) | −12.9295 | −0.0590389 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 655.204i | 2.96472i | ||||||||
\(222\) | − | 2.32087i | − | 0.0104544i | ||||||
\(223\) | 363.545 | 1.63025 | 0.815123 | − | 0.579288i | \(-0.196669\pi\) | ||||
0.815123 | + | 0.579288i | \(0.196669\pi\) | |||||||
\(224\) | − | 57.6239i | − | 0.257250i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 252.480i | 1.11717i | ||||||||
\(227\) | − | 11.3368i | − | 0.0499418i | −0.999688 | − | 0.0249709i | \(-0.992051\pi\) | ||
0.999688 | − | 0.0249709i | \(-0.00794931\pi\) | |||||||
\(228\) | − | 33.5616i | − | 0.147200i | ||||||
\(229\) | − | 112.509i | − | 0.491306i | −0.969358 | − | 0.245653i | \(-0.920998\pi\) | ||
0.969358 | − | 0.245653i | \(-0.0790024\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −190.825 | −0.826082 | ||||||||
\(232\) | −120.150 | −0.517888 | ||||||||
\(233\) | 381.634 | 1.63791 | 0.818957 | − | 0.573855i | \(-0.194553\pi\) | ||||
0.818957 | + | 0.573855i | \(0.194553\pi\) | |||||||
\(234\) | −227.558 | −0.972470 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 188.169 | 0.797326 | ||||||||
\(237\) | − | 115.479i | − | 0.487252i | ||||||
\(238\) | −406.577 | −1.70831 | ||||||||
\(239\) | 139.296 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 82.3347i | − | 0.341638i | −0.985302 | − | 0.170819i | \(-0.945359\pi\) | ||
0.985302 | − | 0.170819i | \(-0.0546413\pi\) | |||||||
\(242\) | 68.7554 | 0.284113 | ||||||||
\(243\) | −248.550 | −1.02284 | ||||||||
\(244\) | 149.059i | 0.610896i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −148.128 | −0.602145 | ||||||||
\(247\) | − | 270.843i | − | 1.09653i | ||||||
\(248\) | −53.0846 | −0.214051 | ||||||||
\(249\) | 136.135i | 0.546728i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 323.924i | − | 1.29054i | −0.763957 | − | 0.645268i | \(-0.776746\pi\) | ||
0.763957 | − | 0.645268i | \(-0.223254\pi\) | |||||||
\(252\) | − | 141.208i | − | 0.560348i | ||||||
\(253\) | −195.896 | − | 226.611i | −0.774291 | − | 0.895695i | ||||
\(254\) | −159.748 | −0.628931 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 250.796 | 0.975858 | 0.487929 | − | 0.872883i | \(-0.337752\pi\) | ||||
0.487929 | + | 0.872883i | \(0.337752\pi\) | |||||||
\(258\) | − | 10.1011i | − | 0.0391517i | ||||||
\(259\) | 11.6223 | 0.0448737 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −294.428 | −1.12808 | ||||||||
\(262\) | 17.1712 | 0.0655389 | ||||||||
\(263\) | − | 276.878i | − | 1.05277i | −0.850247 | − | 0.526384i | \(-0.823548\pi\) | ||
0.850247 | − | 0.526384i | \(-0.176452\pi\) | |||||||
\(264\) | − | 52.9849i | − | 0.200700i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 168.067 | 0.631833 | ||||||||
\(267\) | − | 196.787i | − | 0.737031i | ||||||
\(268\) | 160.181i | 0.597691i | ||||||||
\(269\) | −78.1002 | −0.290335 | −0.145168 | − | 0.989407i | \(-0.546372\pi\) | ||||
−0.145168 | + | 0.989407i | \(0.546372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 331.551 | 1.22343 | 0.611717 | − | 0.791076i | \(-0.290479\pi\) | ||||
0.611717 | + | 0.791076i | \(0.290479\pi\) | |||||||
\(272\) | − | 112.891i | − | 0.415041i | ||||||
\(273\) | 340.154i | 1.24599i | ||||||||
\(274\) | − | 241.184i | − | 0.880232i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −50.0550 | + | 43.2705i | −0.181359 | + | 0.156777i | ||||
\(277\) | 355.974 | 1.28511 | 0.642553 | − | 0.766241i | \(-0.277875\pi\) | ||||
0.642553 | + | 0.766241i | \(0.277875\pi\) | |||||||
\(278\) | −54.5148 | −0.196097 | ||||||||
\(279\) | −130.084 | −0.466252 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 391.437i | 1.39301i | 0.717550 | + | 0.696507i | \(0.245264\pi\) | ||||
−0.717550 | + | 0.696507i | \(0.754736\pi\) | |||||||
\(282\) | 1.65451 | 0.00586706 | ||||||||
\(283\) | − | 133.616i | − | 0.472143i | −0.971736 | − | 0.236071i | \(-0.924140\pi\) | ||
0.971736 | − | 0.236071i | \(-0.0758599\pi\) | |||||||
\(284\) | −167.061 | −0.588241 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 427.589i | − | 1.49507i | ||||||
\(287\) | − | 741.783i | − | 2.58461i | ||||||
\(288\) | 39.2081 | 0.136139 | ||||||||
\(289\) | −507.527 | −1.75615 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.34661i | 0.0115004i | ||||||||
\(292\) | 17.9779 | 0.0615683 | ||||||||
\(293\) | − | 533.454i | − | 1.82066i | −0.413880 | − | 0.910331i | \(-0.635827\pi\) | ||
0.413880 | − | 0.910331i | \(-0.364173\pi\) | |||||||
\(294\) | −111.403 | −0.378923 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.22708i | 0.0109023i | ||||||||
\(297\) | − | 298.437i | − | 1.00484i | ||||||
\(298\) | − | 115.135i | − | 0.386358i | ||||||
\(299\) | −403.945 | + | 349.193i | −1.35099 | + | 1.16787i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 50.5837 | 0.168052 | ||||||||
\(302\) | −225.822 | −0.747755 | ||||||||
\(303\) | −18.6871 | −0.0616737 | ||||||||
\(304\) | 46.6660i | 0.153507i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 276.641i | − | 0.904054i | ||||||
\(307\) | −282.656 | −0.920705 | −0.460352 | − | 0.887736i | \(-0.652277\pi\) | ||||
−0.460352 | + | 0.887736i | \(0.652277\pi\) | |||||||
\(308\) | 265.334 | 0.861474 | ||||||||
\(309\) | − | 129.909i | − | 0.420417i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −193.206 | −0.621241 | −0.310620 | − | 0.950534i | \(-0.600537\pi\) | ||||
−0.310620 | + | 0.950534i | \(0.600537\pi\) | |||||||
\(312\) | −94.4481 | −0.302718 | ||||||||
\(313\) | 399.279i | 1.27565i | 0.770181 | + | 0.637826i | \(0.220166\pi\) | ||||
−0.770181 | + | 0.637826i | \(0.779834\pi\) | |||||||
\(314\) | − | 54.5820i | − | 0.173828i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 160.568i | 0.508128i | ||||||||
\(317\) | 36.5297 | 0.115236 | 0.0576178 | − | 0.998339i | \(-0.481650\pi\) | ||||
0.0576178 | + | 0.998339i | \(0.481650\pi\) | |||||||
\(318\) | 54.3705i | 0.170976i | ||||||||
\(319\) | − | 553.241i | − | 1.73430i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 266.348i | − | 0.829745i | ||||||
\(322\) | −216.687 | − | 250.662i | −0.672940 | − | 0.778453i | ||||
\(323\) | 329.262 | 1.01939 | ||||||||
\(324\) | 58.8391 | 0.181602 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 212.543 | 0.651973 | ||||||||
\(327\) | 19.8853i | 0.0608113i | ||||||||
\(328\) | 205.965 | 0.627943 | ||||||||
\(329\) | 8.28534i | 0.0251834i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 85.9406 | 0.259639 | 0.129820 | − | 0.991538i | \(-0.458560\pi\) | ||||
0.129820 | + | 0.991538i | \(0.458560\pi\) | |||||||
\(332\) | − | 189.290i | − | 0.570151i | ||||||
\(333\) | 7.90797i | 0.0237476i | ||||||||
\(334\) | 39.2591 | 0.117542 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 58.6084i | − | 0.174430i | ||||||
\(337\) | 548.713i | 1.62823i | 0.580706 | + | 0.814114i | \(0.302777\pi\) | ||||
−0.580706 | + | 0.814114i | \(0.697223\pi\) | |||||||
\(338\) | −523.195 | −1.54791 | ||||||||
\(339\) | 256.793i | 0.757502i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 244.433i | − | 0.716811i | ||||||
\(342\) | 114.355i | 0.334373i | ||||||||
\(343\) | − | 58.7366i | − | 0.171244i | ||||||
\(344\) | 14.0452i | 0.0408291i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −33.9502 | −0.0981219 | ||||||||
\(347\) | −62.0036 | −0.178685 | −0.0893424 | − | 0.996001i | \(-0.528477\pi\) | ||||
−0.0893424 | + | 0.996001i | \(0.528477\pi\) | |||||||
\(348\) | −122.203 | −0.351157 | ||||||||
\(349\) | −131.393 | −0.376485 | −0.188242 | − | 0.982123i | \(-0.560279\pi\) | ||||
−0.188242 | + | 0.982123i | \(0.560279\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −531.978 | −1.51561 | ||||||||
\(352\) | 73.6733i | 0.209299i | ||||||||
\(353\) | 176.990 | 0.501389 | 0.250694 | − | 0.968066i | \(-0.419341\pi\) | ||||
0.250694 | + | 0.968066i | \(0.419341\pi\) | |||||||
\(354\) | 191.384 | 0.540632 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 273.624i | 0.768608i | ||||||||
\(357\) | −413.523 | −1.15833 | ||||||||
\(358\) | 284.508 | 0.794716 | ||||||||
\(359\) | 187.851i | 0.523260i | 0.965168 | + | 0.261630i | \(0.0842601\pi\) | ||||
−0.965168 | + | 0.261630i | \(0.915740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 224.893 | 0.622971 | ||||||||
\(362\) | 286.177i | 0.790544i | ||||||||
\(363\) | 69.9300 | 0.192645 | ||||||||
\(364\) | − | 472.970i | − | 1.29937i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 151.605i | 0.414222i | ||||||||
\(367\) | − | 128.510i | − | 0.350162i | −0.984554 | − | 0.175081i | \(-0.943981\pi\) | ||
0.984554 | − | 0.175081i | \(-0.0560188\pi\) | |||||||
\(368\) | 69.5994 | − | 60.1658i | 0.189129 | − | 0.163494i | ||||
\(369\) | 504.719 | 1.36780 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −272.273 | −0.733888 | ||||||||
\(372\) | −53.9916 | −0.145139 | ||||||||
\(373\) | − | 79.2928i | − | 0.212581i | −0.994335 | − | 0.106291i | \(-0.966103\pi\) | ||
0.994335 | − | 0.106291i | \(-0.0338974\pi\) | |||||||
\(374\) | 519.817 | 1.38988 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.30053 | −0.00611843 | ||||||||
\(377\) | −986.177 | −2.61585 | ||||||||
\(378\) | − | 330.111i | − | 0.873309i | ||||||
\(379\) | 402.569i | 1.06219i | 0.847313 | + | 0.531094i | \(0.178219\pi\) | ||||
−0.847313 | + | 0.531094i | \(0.821781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −162.478 | −0.426450 | ||||||||
\(382\) | − | 157.405i | − | 0.412056i | ||||||
\(383\) | 370.198i | 0.966575i | 0.875462 | + | 0.483288i | \(0.160557\pi\) | ||||
−0.875462 | + | 0.483288i | \(0.839443\pi\) | |||||||
\(384\) | 16.2734 | 0.0423785 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −232.046 | −0.601156 | ||||||||
\(387\) | 34.4179i | 0.0889351i | ||||||||
\(388\) | − | 4.65332i | − | 0.0119931i | ||||||
\(389\) | 12.0598i | 0.0310021i | 0.999880 | + | 0.0155011i | \(0.00493434\pi\) | ||||
−0.999880 | + | 0.0155011i | \(0.995066\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −424.512 | − | 491.073i | −1.08571 | − | 1.25594i | ||||
\(392\) | 154.902 | 0.395158 | ||||||||
\(393\) | 17.4645 | 0.0444391 | ||||||||
\(394\) | −466.071 | −1.18292 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 180.537i | 0.455901i | ||||||||
\(397\) | −233.543 | −0.588270 | −0.294135 | − | 0.955764i | \(-0.595032\pi\) | ||||
−0.294135 | + | 0.955764i | \(0.595032\pi\) | |||||||
\(398\) | 477.844i | 1.20061i | ||||||||
\(399\) | 170.939 | 0.428418 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 114.072i | 0.284469i | 0.989833 | + | 0.142235i | \(0.0454287\pi\) | ||||
−0.989833 | + | 0.142235i | \(0.954571\pi\) | |||||||
\(402\) | 162.918i | 0.405268i | ||||||||
\(403\) | −435.713 | −1.08117 | ||||||||
\(404\) | 25.9837 | 0.0643161 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 611.958i | − | 1.50729i | ||||||
\(407\) | −14.8593 | −0.0365094 | ||||||||
\(408\) | − | 114.820i | − | 0.281421i | ||||||
\(409\) | 125.952 | 0.307950 | 0.153975 | − | 0.988075i | \(-0.450792\pi\) | ||||
0.153975 | + | 0.988075i | \(0.450792\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 245.304i | − | 0.596847i | ||||||
\(412\) | 180.633i | 0.438430i | ||||||||
\(413\) | 958.397i | 2.32057i | ||||||||
\(414\) | 170.554 | − | 147.437i | 0.411966 | − | 0.356127i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 131.326 | 0.315688 | ||||||||
\(417\) | −55.4462 | −0.132965 | ||||||||
\(418\) | −214.878 | −0.514061 | ||||||||
\(419\) | − | 135.868i | − | 0.324268i | −0.986769 | − | 0.162134i | \(-0.948162\pi\) | ||
0.986769 | − | 0.162134i | \(-0.0518377\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 194.111i | − | 0.461070i | −0.973064 | − | 0.230535i | \(-0.925952\pi\) | ||
0.973064 | − | 0.230535i | \(-0.0740477\pi\) | |||||||
\(422\) | −157.905 | −0.374182 | ||||||||
\(423\) | −5.63746 | −0.0133273 | ||||||||
\(424\) | − | 75.5999i | − | 0.178302i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −169.915 | −0.398861 | ||||||||
\(427\) | −759.198 | −1.77798 | ||||||||
\(428\) | 370.346i | 0.865294i | ||||||||
\(429\) | − | 434.894i | − | 1.01374i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 421.699i | − | 0.978420i | −0.872166 | − | 0.489210i | \(-0.837285\pi\) | ||
0.872166 | − | 0.489210i | \(-0.162715\pi\) | |||||||
\(432\) | 91.6595 | 0.212175 | ||||||||
\(433\) | 3.78505i | 0.00874144i | 0.999990 | + | 0.00437072i | \(0.00139125\pi\) | ||||
−0.999990 | + | 0.00437072i | \(0.998609\pi\) | |||||||
\(434\) | − | 270.375i | − | 0.622984i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 27.6497i | − | 0.0634167i | ||||||
\(437\) | 175.481 | + | 202.996i | 0.401559 | + | 0.464521i | ||||
\(438\) | 18.2851 | 0.0417468 | ||||||||
\(439\) | −6.17744 | −0.0140716 | −0.00703581 | − | 0.999975i | \(-0.502240\pi\) | ||||
−0.00703581 | + | 0.999975i | \(0.502240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 379.588 | 0.860744 | ||||||||
\(442\) | − | 926.598i | − | 2.09638i | ||||||
\(443\) | 406.821 | 0.918331 | 0.459166 | − | 0.888351i | \(-0.348148\pi\) | ||||
0.459166 | + | 0.888351i | \(0.348148\pi\) | |||||||
\(444\) | 3.28221i | 0.00739236i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −514.130 | −1.15276 | ||||||||
\(447\) | − | 117.102i | − | 0.261972i | ||||||
\(448\) | 81.4925i | 0.181903i | ||||||||
\(449\) | −289.981 | −0.645837 | −0.322918 | − | 0.946427i | \(-0.604664\pi\) | ||||
−0.322918 | + | 0.946427i | \(0.604664\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 948.385i | 2.10285i | ||||||||
\(452\) | − | 357.060i | − | 0.789956i | ||||||
\(453\) | −229.680 | −0.507020 | ||||||||
\(454\) | 16.0326i | 0.0353142i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 47.4633i | 0.104086i | ||||||||
\(457\) | 224.430i | 0.491094i | 0.969385 | + | 0.245547i | \(0.0789676\pi\) | ||||
−0.969385 | + | 0.245547i | \(0.921032\pi\) | |||||||
\(458\) | 159.112i | 0.347406i | ||||||||
\(459\) | − | 646.722i | − | 1.40898i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 534.660 | 1.15978 | 0.579891 | − | 0.814694i | \(-0.303095\pi\) | ||||
0.579891 | + | 0.814694i | \(0.303095\pi\) | |||||||
\(462\) | 269.867 | 0.584128 | ||||||||
\(463\) | −166.226 | −0.359019 | −0.179509 | − | 0.983756i | \(-0.557451\pi\) | ||||
−0.179509 | + | 0.983756i | \(0.557451\pi\) | |||||||
\(464\) | 169.918 | 0.366202 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −539.712 | −1.15818 | ||||||||
\(467\) | − | 113.755i | − | 0.243587i | −0.992555 | − | 0.121794i | \(-0.961135\pi\) | ||
0.992555 | − | 0.121794i | \(-0.0388646\pi\) | |||||||
\(468\) | 321.815 | 0.687640 | ||||||||
\(469\) | −815.848 | −1.73955 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 55.5145i | − | 0.117865i | ||||||
\(472\) | −266.111 | −0.563795 | ||||||||
\(473\) | −64.6723 | −0.136728 | ||||||||
\(474\) | 163.312i | 0.344539i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 574.987 | 1.20796 | ||||||||
\(477\) | − | 185.258i | − | 0.388382i | ||||||
\(478\) | −196.994 | −0.412121 | ||||||||
\(479\) | − | 156.314i | − | 0.326334i | −0.986598 | − | 0.163167i | \(-0.947829\pi\) | ||
0.986598 | − | 0.163167i | \(-0.0521710\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.4875i | 0.0550675i | ||||||||
\(482\) | 116.439i | 0.241574i | ||||||||
\(483\) | −220.389 | − | 254.944i | −0.456291 | − | 0.527835i | ||||
\(484\) | −97.2348 | −0.200898 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 351.503 | 0.723257 | ||||||||
\(487\) | 207.919 | 0.426938 | 0.213469 | − | 0.976950i | \(-0.431524\pi\) | ||||
0.213469 | + | 0.976950i | \(0.431524\pi\) | |||||||
\(488\) | − | 210.801i | − | 0.431969i | ||||||
\(489\) | 216.174 | 0.442074 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −463.345 | −0.943676 | −0.471838 | − | 0.881685i | \(-0.656409\pi\) | ||||
−0.471838 | + | 0.881685i | \(0.656409\pi\) | |||||||
\(492\) | 209.484 | 0.425781 | ||||||||
\(493\) | − | 1198.89i | − | 2.43182i | ||||||
\(494\) | 383.029i | 0.775363i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 75.0730 | 0.151357 | ||||||||
\(497\) | − | 850.886i | − | 1.71204i | ||||||
\(498\) | − | 192.524i | − | 0.386595i | ||||||
\(499\) | −50.7777 | −0.101759 | −0.0508794 | − | 0.998705i | \(-0.516202\pi\) | ||||
−0.0508794 | + | 0.998705i | \(0.516202\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 39.9298 | 0.0797003 | ||||||||
\(502\) | 458.098i | 0.912546i | ||||||||
\(503\) | 91.1857i | 0.181284i | 0.995884 | + | 0.0906419i | \(0.0288919\pi\) | ||||
−0.995884 | + | 0.0906419i | \(0.971108\pi\) | |||||||
\(504\) | 199.698i | 0.396226i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 277.038 | + | 320.476i | 0.547506 | + | 0.633352i | ||||
\(507\) | −532.134 | −1.04957 | ||||||||
\(508\) | 225.918 | 0.444721 | ||||||||
\(509\) | 317.681 | 0.624128 | 0.312064 | − | 0.950061i | \(-0.398980\pi\) | ||||
0.312064 | + | 0.950061i | \(0.398980\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 91.5667i | 0.179191i | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 267.337i | 0.521124i | ||||||||
\(514\) | −354.678 | −0.690036 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14.2852i | 0.0276844i | ||||||||
\(517\) | − | 10.5930i | − | 0.0204893i | ||||||
\(518\) | −16.4364 | −0.0317305 | ||||||||
\(519\) | −34.5302 | −0.0665322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 522.346i | − | 1.00258i | −0.865279 | − | 0.501291i | \(-0.832858\pi\) | ||
0.865279 | − | 0.501291i | \(-0.167142\pi\) | |||||||
\(522\) | 416.385 | 0.797671 | ||||||||
\(523\) | − | 245.926i | − | 0.470221i | −0.971969 | − | 0.235111i | \(-0.924455\pi\) | ||
0.971969 | − | 0.235111i | \(-0.0755452\pi\) | |||||||
\(524\) | −24.2837 | −0.0463430 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 391.564i | 0.744419i | ||||||||
\(527\) | − | 529.693i | − | 1.00511i | ||||||
\(528\) | 74.9320i | 0.141917i | ||||||||
\(529\) | 76.5101 | − | 523.438i | 0.144632 | − | 0.989486i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −652.107 | −1.22807 | ||||||||
\(532\) | −237.683 | −0.446773 | ||||||||
\(533\) | 1690.54 | 3.17174 | ||||||||
\(534\) | 278.299i | 0.521160i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 226.530i | − | 0.422631i | ||||||
\(537\) | 289.369 | 0.538862 | ||||||||
\(538\) | 110.450 | 0.205298 | ||||||||
\(539\) | 713.258i | 1.32330i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −307.138 | −0.567723 | −0.283861 | − | 0.958865i | \(-0.591616\pi\) | ||||
−0.283861 | + | 0.958865i | \(0.591616\pi\) | |||||||
\(542\) | −468.884 | −0.865099 | ||||||||
\(543\) | 291.066i | 0.536033i | ||||||||
\(544\) | 159.652i | 0.293478i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 481.051i | − | 0.881046i | ||||||
\(547\) | 712.547 | 1.30265 | 0.651323 | − | 0.758801i | \(-0.274214\pi\) | ||||
0.651323 | + | 0.758801i | \(0.274214\pi\) | |||||||
\(548\) | 341.085i | 0.622418i | ||||||||
\(549\) | − | 516.569i | − | 0.940926i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 495.587i | 0.899432i | ||||||||
\(552\) | 70.7885 | − | 61.1937i | 0.128240 | − | 0.110858i | ||||
\(553\) | −817.820 | −1.47888 | ||||||||
\(554\) | −503.424 | −0.908707 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 77.0956 | 0.138661 | ||||||||
\(557\) | 1.17109i | 0.00210250i | 0.999999 | + | 0.00105125i | \(0.000334623\pi\) | ||||
−0.999999 | + | 0.00105125i | \(0.999665\pi\) | |||||||
\(558\) | 183.967 | 0.329690 | ||||||||
\(559\) | 115.281i | 0.206228i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 528.698 | 0.942420 | ||||||||
\(562\) | − | 553.575i | − | 0.985010i | ||||||
\(563\) | 900.058i | 1.59868i | 0.600878 | + | 0.799341i | \(0.294818\pi\) | ||||
−0.600878 | + | 0.799341i | \(0.705182\pi\) | |||||||
\(564\) | −2.33983 | −0.00414864 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 188.962i | 0.333855i | ||||||||
\(567\) | 299.684i | 0.528543i | ||||||||
\(568\) | 236.259 | 0.415949 | ||||||||
\(569\) | 589.836i | 1.03662i | 0.855193 | + | 0.518309i | \(0.173438\pi\) | ||||
−0.855193 | + | 0.518309i | \(0.826562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 117.755i | − | 0.206225i | −0.994670 | − | 0.103113i | \(-0.967120\pi\) | ||
0.994670 | − | 0.103113i | \(-0.0328802\pi\) | |||||||
\(572\) | 604.702i | 1.05717i | ||||||||
\(573\) | − | 160.095i | − | 0.279397i | ||||||
\(574\) | 1049.04i | 1.82760i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −55.4486 | −0.0962650 | ||||||||
\(577\) | 403.533 | 0.699365 | 0.349682 | − | 0.936868i | \(-0.386290\pi\) | ||||
0.349682 | + | 0.936868i | \(0.386290\pi\) | |||||||
\(578\) | 717.751 | 1.24178 | ||||||||
\(579\) | −236.011 | −0.407618 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 964.109 | 1.65940 | ||||||||
\(582\) | − | 4.73282i | − | 0.00813200i | ||||||
\(583\) | 348.106 | 0.597094 | ||||||||
\(584\) | −25.4246 | −0.0435354 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 754.418i | 1.28740i | ||||||||
\(587\) | −607.731 | −1.03532 | −0.517659 | − | 0.855587i | \(-0.673196\pi\) | ||||
−0.517659 | + | 0.855587i | \(0.673196\pi\) | |||||||
\(588\) | 157.548 | 0.267939 | ||||||||
\(589\) | 218.960i | 0.371749i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −474.033 | −0.802087 | ||||||||
\(592\) | − | 4.56377i | − | 0.00770908i | ||||||
\(593\) | −428.555 | −0.722690 | −0.361345 | − | 0.932432i | \(-0.617682\pi\) | ||||
−0.361345 | + | 0.932432i | \(0.617682\pi\) | |||||||
\(594\) | 422.053i | 0.710528i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 162.825i | 0.273196i | ||||||||
\(597\) | 486.007i | 0.814083i | ||||||||
\(598\) | 571.264 | − | 493.834i | 0.955291 | − | 0.825809i | ||||
\(599\) | −162.171 | −0.270736 | −0.135368 | − | 0.990795i | \(-0.543222\pi\) | ||||
−0.135368 | + | 0.990795i | \(0.543222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 957.407 | 1.59302 | 0.796512 | − | 0.604623i | \(-0.206676\pi\) | ||||
0.796512 | + | 0.604623i | \(0.206676\pi\) | |||||||
\(602\) | −71.5362 | −0.118831 | ||||||||
\(603\) | − | 555.114i | − | 0.920587i | ||||||
\(604\) | 319.360 | 0.528742 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 26.4276 | 0.0436099 | ||||||||
\(607\) | 989.893 | 1.63080 | 0.815398 | − | 0.578901i | \(-0.196518\pi\) | ||||
0.815398 | + | 0.578901i | \(0.196518\pi\) | |||||||
\(608\) | − | 65.9958i | − | 0.108546i | ||||||
\(609\) | − | 622.413i | − | 1.02202i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.8825 | −0.0309042 | ||||||||
\(612\) | 391.229i | 0.639263i | ||||||||
\(613\) | − | 134.181i | − | 0.218892i | −0.993993 | − | 0.109446i | \(-0.965092\pi\) | ||
0.993993 | − | 0.109446i | \(-0.0349076\pi\) | |||||||
\(614\) | 399.736 | 0.651037 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −375.239 | −0.609154 | ||||||||
\(617\) | 151.269i | 0.245168i | 0.992458 | + | 0.122584i | \(0.0391181\pi\) | ||||
−0.992458 | + | 0.122584i | \(0.960882\pi\) | |||||||
\(618\) | 183.719i | 0.297280i | ||||||||
\(619\) | 115.852i | 0.187159i | 0.995612 | + | 0.0935797i | \(0.0298310\pi\) | ||||
−0.995612 | + | 0.0935797i | \(0.970169\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 398.715 | − | 344.673i | 0.642054 | − | 0.555028i | ||||
\(622\) | 273.234 | 0.439284 | ||||||||
\(623\) | −1393.65 | −2.23699 | ||||||||
\(624\) | 133.570 | 0.214054 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 564.665i | − | 0.902022i | ||||||
\(627\) | −218.549 | −0.348563 | ||||||||
\(628\) | 77.1906i | 0.122915i | ||||||||
\(629\) | −32.2006 | −0.0511934 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 730.187i | 1.15719i | 0.815615 | + | 0.578595i | \(0.196399\pi\) | ||||
−0.815615 | + | 0.578595i | \(0.803601\pi\) | |||||||
\(632\) | − | 227.078i | − | 0.359300i | ||||||
\(633\) | −160.602 | −0.253716 | ||||||||
\(634\) | −51.6608 | −0.0814839 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 76.8915i | − | 0.120899i | ||||||
\(637\) | 1271.42 | 1.99594 | ||||||||
\(638\) | 782.400i | 1.22633i | ||||||||
\(639\) | 578.955 | 0.906032 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 725.551i | − | 1.13190i | −0.824438 | − | 0.565952i | \(-0.808509\pi\) | ||
0.824438 | − | 0.565952i | \(-0.191491\pi\) | |||||||
\(642\) | 376.673i | 0.586718i | ||||||||
\(643\) | − | 505.908i | − | 0.786792i | −0.919369 | − | 0.393396i | \(-0.871300\pi\) | ||
0.919369 | − | 0.393396i | \(-0.128700\pi\) | |||||||
\(644\) | 306.441 | + | 354.490i | 0.475840 | + | 0.550450i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −465.646 | −0.720815 | ||||||||
\(647\) | 324.943 | 0.502230 | 0.251115 | − | 0.967957i | \(-0.419203\pi\) | ||||
0.251115 | + | 0.967957i | \(0.419203\pi\) | |||||||
\(648\) | −83.2110 | −0.128412 | ||||||||
\(649\) | − | 1225.33i | − | 1.88803i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 274.994i | − | 0.422418i | ||||||
\(652\) | −300.581 | −0.461014 | ||||||||
\(653\) | 146.801 | 0.224810 | 0.112405 | − | 0.993662i | \(-0.464145\pi\) | ||||
0.112405 | + | 0.993662i | \(0.464145\pi\) | |||||||
\(654\) | − | 28.1220i | − | 0.0430001i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −291.279 | −0.444023 | ||||||||
\(657\) | −62.3033 | −0.0948299 | ||||||||
\(658\) | − | 11.7172i | − | 0.0178074i | ||||||
\(659\) | 366.667i | 0.556399i | 0.960523 | + | 0.278200i | \(0.0897377\pi\) | ||||
−0.960523 | + | 0.278200i | \(0.910262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1241.87i | 1.87878i | 0.342852 | + | 0.939389i | \(0.388607\pi\) | ||||
−0.342852 | + | 0.939389i | \(0.611393\pi\) | |||||||
\(662\) | −121.538 | −0.183593 | ||||||||
\(663\) | − | 942.428i | − | 1.42146i | ||||||
\(664\) | 267.697i | 0.403158i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 11.1836i | − | 0.0167921i | ||||||
\(667\) | 739.136 | − | 638.952i | 1.10815 | − | 0.957949i | ||||
\(668\) | −55.5208 | −0.0831149 | ||||||||
\(669\) | −522.914 | −0.781635 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 970.649 | 1.44657 | ||||||||
\(672\) | 82.8848i | 0.123340i | ||||||||
\(673\) | −812.966 | −1.20797 | −0.603987 | − | 0.796994i | \(-0.706422\pi\) | ||||
−0.603987 | + | 0.796994i | \(0.706422\pi\) | |||||||
\(674\) | − | 775.997i | − | 1.15133i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 739.910 | 1.09454 | ||||||||
\(677\) | 1053.03i | 1.55544i | 0.628610 | + | 0.777721i | \(0.283624\pi\) | ||||
−0.628610 | + | 0.777721i | \(0.716376\pi\) | |||||||
\(678\) | − | 363.160i | − | 0.535635i | ||||||
\(679\) | 23.7007 | 0.0349053 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.3066i | 0.0239450i | ||||||||
\(682\) | 345.680i | 0.506862i | ||||||||
\(683\) | −947.718 | −1.38758 | −0.693791 | − | 0.720177i | \(-0.744061\pi\) | ||||
−0.693791 | + | 0.720177i | \(0.744061\pi\) | |||||||
\(684\) | − | 161.723i | − | 0.236437i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 83.0661i | 0.121088i | ||||||||
\(687\) | 161.830i | 0.235561i | ||||||||
\(688\) | − | 19.8629i | − | 0.0288705i | ||||||
\(689\) | − | 620.515i | − | 0.900602i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −600.541 | −0.869090 | −0.434545 | − | 0.900650i | \(-0.643091\pi\) | ||||
−0.434545 | + | 0.900650i | \(0.643091\pi\) | |||||||
\(692\) | 48.0128 | 0.0693826 | ||||||||
\(693\) | −919.525 | −1.32688 | ||||||||
\(694\) | 87.6863 | 0.126349 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 172.821 | 0.248306 | ||||||||
\(697\) | 2055.18i | 2.94861i | ||||||||
\(698\) | 185.818 | 0.266215 | ||||||||
\(699\) | −548.932 | −0.785311 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 907.376i | 1.29440i | 0.762319 | + | 0.647201i | \(0.224061\pi\) | ||||
−0.762319 | + | 0.647201i | \(0.775939\pi\) | |||||||
\(702\) | 752.330 | 1.07170 | ||||||||
\(703\) | 13.3108 | 0.0189343 | ||||||||
\(704\) | − | 104.190i | − | 0.147997i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −250.302 | −0.354536 | ||||||||
\(707\) | 132.342i | 0.187188i | ||||||||
\(708\) | −270.657 | −0.382285 | ||||||||
\(709\) | 657.300i | 0.927081i | 0.886076 | + | 0.463540i | \(0.153421\pi\) | ||||
−0.886076 | + | 0.463540i | \(0.846579\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 556.456i | − | 0.782638i | ||||||
\(712\) | − | 386.963i | − | 0.543488i | ||||||
\(713\) | 326.565 | − | 282.302i | 0.458015 | − | 0.395935i | ||||
\(714\) | 584.810 | 0.819062 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −402.356 | −0.561949 | ||||||||
\(717\) | −200.360 | −0.279442 | ||||||||
\(718\) | − | 265.661i | − | 0.370001i | ||||||
\(719\) | 1095.72 | 1.52395 | 0.761975 | − | 0.647606i | \(-0.224230\pi\) | ||||
0.761975 | + | 0.647606i | \(0.224230\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −920.015 | −1.27603 | ||||||||
\(722\) | −318.046 | −0.440507 | ||||||||
\(723\) | 118.428i | 0.163801i | ||||||||
\(724\) | − | 404.715i | − | 0.558999i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −98.8960 | −0.136220 | ||||||||
\(727\) | − | 814.942i | − | 1.12097i | −0.828166 | − | 0.560483i | \(-0.810616\pi\) | ||
0.828166 | − | 0.560483i | \(-0.189384\pi\) | |||||||
\(728\) | 668.881i | 0.918793i | ||||||||
\(729\) | 92.7324 | 0.127205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −140.147 | −0.191719 | ||||||||
\(732\) | − | 214.402i | − | 0.292899i | ||||||
\(733\) | 742.293i | 1.01268i | 0.862335 | + | 0.506339i | \(0.169001\pi\) | ||||
−0.862335 | + | 0.506339i | \(0.830999\pi\) | |||||||
\(734\) | 181.740i | 0.247602i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −98.4285 | + | 85.0872i | −0.133734 | + | 0.115608i | ||||
\(737\) | 1043.08 | 1.41530 | ||||||||
\(738\) | −713.781 | −0.967183 | ||||||||
\(739\) | −288.013 | −0.389733 | −0.194866 | − | 0.980830i | \(-0.562427\pi\) | ||||
−0.194866 | + | 0.980830i | \(0.562427\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 389.573i | 0.525740i | ||||||||
\(742\) | 385.052 | 0.518937 | ||||||||
\(743\) | − | 199.651i | − | 0.268709i | −0.990933 | − | 0.134354i | \(-0.957104\pi\) | ||
0.990933 | − | 0.134354i | \(-0.0428961\pi\) | |||||||
\(744\) | 76.3556 | 0.102629 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 112.137i | 0.150318i | ||||||||
\(747\) | 655.993i | 0.878170i | ||||||||
\(748\) | −735.132 | −0.982797 | ||||||||
\(749\) | −1886.28 | −2.51839 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 610.667i | 0.813138i | 0.913620 | + | 0.406569i | \(0.133275\pi\) | ||||
−0.913620 | + | 0.406569i | \(0.866725\pi\) | |||||||
\(752\) | 3.25344 | 0.00432638 | ||||||||
\(753\) | 465.925i | 0.618758i | ||||||||
\(754\) | 1394.67 | 1.84969 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 466.847i | 0.617523i | ||||||||
\(757\) | − | 241.235i | − | 0.318672i | −0.987224 | − | 0.159336i | \(-0.949065\pi\) | ||
0.987224 | − | 0.159336i | \(-0.0509354\pi\) | |||||||
\(758\) | − | 569.319i | − | 0.751080i | ||||||
\(759\) | 281.771 | + | 325.952i | 0.371240 | + | 0.429449i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 568.126 | 0.746552 | 0.373276 | − | 0.927720i | \(-0.378235\pi\) | ||||
0.373276 | + | 0.927720i | \(0.378235\pi\) | |||||||
\(762\) | 229.778 | 0.301546 | ||||||||
\(763\) | 140.828 | 0.184571 | ||||||||
\(764\) | 222.605i | 0.291368i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 523.539i | − | 0.683472i | ||||||
\(767\) | −2184.21 | −2.84773 | ||||||||
\(768\) | −23.0140 | −0.0299661 | ||||||||
\(769\) | − | 425.966i | − | 0.553922i | −0.960881 | − | 0.276961i | \(-0.910673\pi\) | ||
0.960881 | − | 0.276961i | \(-0.0893273\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −360.738 | −0.467883 | ||||||||
\(772\) | 328.163 | 0.425081 | ||||||||
\(773\) | − | 849.417i | − | 1.09886i | −0.835540 | − | 0.549429i | \(-0.814845\pi\) | ||
0.835540 | − | 0.549429i | \(-0.185155\pi\) | |||||||
\(774\) | − | 48.6742i | − | 0.0628866i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.58079i | 0.00848040i | ||||||||
\(777\) | −16.7172 | −0.0215151 | ||||||||
\(778\) | − | 17.0552i | − | 0.0219218i | ||||||
\(779\) | − | 849.553i | − | 1.09057i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1087.87i | 1.39293i | ||||||||
\(782\) | 600.350 | + | 694.482i | 0.767711 | + | 0.888084i | ||||
\(783\) | 973.411 | 1.24318 | ||||||||
\(784\) | −219.064 | −0.279419 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −24.6986 | −0.0314232 | ||||||||
\(787\) | 1448.81i | 1.84093i | 0.390828 | + | 0.920464i | \(0.372189\pi\) | ||||
−0.390828 | + | 0.920464i | \(0.627811\pi\) | |||||||
\(788\) | 659.123 | 0.836451 | ||||||||
\(789\) | 398.254i | 0.504758i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1818.61 | 2.29912 | ||||||||
\(792\) | − | 255.318i | − | 0.322371i | ||||||
\(793\) | − | 1730.23i | − | 2.18188i | ||||||
\(794\) | 330.280 | 0.415970 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 675.773i | − | 0.848961i | ||||||
\(797\) | − | 405.786i | − | 0.509141i | −0.967054 | − | 0.254571i | \(-0.918066\pi\) | ||
0.967054 | − | 0.254571i | \(-0.0819342\pi\) | |||||||
\(798\) | −241.744 | −0.302937 | ||||||||
\(799\) | − | 22.9553i | − | 0.0287300i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 948.256i | − | 1.18384i | ||||||
\(802\) | − | 161.322i | − | 0.201150i | ||||||
\(803\) | − | 117.070i | − | 0.145791i | ||||||
\(804\) | − | 230.401i | − | 0.286568i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 616.191 | 0.764504 | ||||||||
\(807\) | 112.337 | 0.139204 | ||||||||
\(808\) | −36.7465 | −0.0454783 | ||||||||
\(809\) | 755.183 | 0.933477 | 0.466739 | − | 0.884395i | \(-0.345429\pi\) | ||||
0.466739 | + | 0.884395i | \(0.345429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1132.66 | −1.39662 | −0.698311 | − | 0.715795i | \(-0.746065\pi\) | ||||
−0.698311 | + | 0.715795i | \(0.746065\pi\) | |||||||
\(812\) | 865.439i | 1.06581i | ||||||||
\(813\) | −476.894 | −0.586586 | ||||||||
\(814\) | 21.0143 | 0.0258161 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 162.380i | 0.198995i | ||||||||
\(817\) | 57.9328 | 0.0709091 | ||||||||
\(818\) | −178.122 | −0.217754 | ||||||||
\(819\) | 1639.10i | 2.00134i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 167.684 | 0.204244 | 0.102122 | − | 0.994772i | \(-0.467437\pi\) | ||||
0.102122 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(822\) | 346.913i | 0.422035i | ||||||||
\(823\) | 403.176 | 0.489886 | 0.244943 | − | 0.969538i | \(-0.421231\pi\) | ||||
0.244943 | + | 0.969538i | \(0.421231\pi\) | |||||||
\(824\) | − | 255.454i | − | 0.310016i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 1355.38i | − | 1.64089i | ||||||
\(827\) | 901.234i | 1.08976i | 0.838513 | + | 0.544881i | \(0.183425\pi\) | ||||
−0.838513 | + | 0.544881i | \(0.816575\pi\) | |||||||
\(828\) | −241.200 | + | 208.507i | −0.291304 | + | 0.251820i | ||||
\(829\) | −455.150 | −0.549034 | −0.274517 | − | 0.961582i | \(-0.588518\pi\) | ||||
−0.274517 | + | 0.961582i | \(0.588518\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −512.024 | −0.616155 | ||||||||
\(832\) | −185.723 | −0.223225 | ||||||||
\(833\) | 1545.65i | 1.85553i | ||||||||
\(834\) | 78.4128 | 0.0940201 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 303.883 | 0.363496 | ||||||||
\(837\) | 430.072 | 0.513826 | ||||||||
\(838\) | 192.147i | 0.229292i | ||||||||
\(839\) | 150.136i | 0.178946i | 0.995989 | + | 0.0894730i | \(0.0285183\pi\) | ||||
−0.995989 | + | 0.0894730i | \(0.971482\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 963.503 | 1.14566 | ||||||||
\(842\) | 274.514i | 0.326026i | ||||||||
\(843\) | − | 563.033i | − | 0.667892i | ||||||
\(844\) | 223.311 | 0.264587 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.97257 | 0.00942385 | ||||||||
\(847\) | − | 495.244i | − | 0.584704i | ||||||
\(848\) | 106.914i | 0.126078i | ||||||||
\(849\) | 192.190i | 0.226373i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.1614 | − | 19.8523i | −0.0201662 | − | 0.0233281i | ||||
\(852\) | 240.296 | 0.282037 | ||||||||
\(853\) | −582.826 | −0.683266 | −0.341633 | − | 0.939833i | \(-0.610980\pi\) | ||||
−0.341633 | + | 0.939833i | \(0.610980\pi\) | |||||||
\(854\) | 1073.67 | 1.25722 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 523.748i | − | 0.611856i | ||||||
\(857\) | 435.647 | 0.508339 | 0.254170 | − | 0.967160i | \(-0.418198\pi\) | ||||
0.254170 | + | 0.967160i | \(0.418198\pi\) | |||||||
\(858\) | 615.033i | 0.716822i | ||||||||
\(859\) | −427.848 | −0.498076 | −0.249038 | − | 0.968494i | \(-0.580114\pi\) | ||||
−0.249038 | + | 0.968494i | \(0.580114\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1066.96i | 1.23921i | ||||||||
\(862\) | 596.373i | 0.691848i | ||||||||
\(863\) | 698.719 | 0.809640 | 0.404820 | − | 0.914396i | \(-0.367334\pi\) | ||||
0.404820 | + | 0.914396i | \(0.367334\pi\) | |||||||
\(864\) | −129.626 | −0.150030 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 5.35286i | − | 0.00618113i | ||||||
\(867\) | 730.013 | 0.841999 | ||||||||
\(868\) | 382.368i | 0.440516i | ||||||||
\(869\) | 1045.60 | 1.20322 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1859.34i | − | 2.13471i | ||||||
\(872\) | 39.1025i | 0.0448424i | ||||||||
\(873\) | 16.1263i | 0.0184722i | ||||||||
\(874\) | −248.168 | − | 287.079i | −0.283945 | − | 0.328466i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −25.8590 | −0.0295194 | ||||||||
\(877\) | −779.272 | −0.888566 | −0.444283 | − | 0.895887i | \(-0.646541\pi\) | ||||
−0.444283 | + | 0.895887i | \(0.646541\pi\) | |||||||
\(878\) | 8.73622 | 0.00995014 | ||||||||
\(879\) | 767.307i | 0.872932i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1612.85i | 1.83070i | 0.402659 | + | 0.915350i | \(0.368086\pi\) | ||||
−0.402659 | + | 0.915350i | \(0.631914\pi\) | |||||||
\(882\) | −536.818 | −0.608638 | ||||||||
\(883\) | 336.489 | 0.381075 | 0.190537 | − | 0.981680i | \(-0.438977\pi\) | ||||
0.190537 | + | 0.981680i | \(0.438977\pi\) | |||||||
\(884\) | 1310.41i | 1.48236i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −575.331 | −0.649358 | ||||||||
\(887\) | 12.5177 | 0.0141124 | 0.00705619 | − | 0.999975i | \(-0.497754\pi\) | ||||
0.00705619 | + | 0.999975i | \(0.497754\pi\) | |||||||
\(888\) | − | 4.64174i | − | 0.00522719i | ||||||
\(889\) | 1150.67i | 1.29434i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 383.152i | − | 0.430025i | ||||||
\(892\) | 727.090 | 0.815123 | ||||||||
\(893\) | 9.48907i | 0.0106261i | ||||||||
\(894\) | 165.607i | 0.185242i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 115.248i | − | 0.128625i | ||||||
\(897\) | 581.024 | − | 502.271i | 0.647741 | − | 0.559945i | ||||
\(898\) | 410.095 | 0.456676 | ||||||||
\(899\) | 797.265 | 0.886835 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 754.356 | 0.837243 | ||||||||
\(902\) | − | 1341.22i | − | 1.48694i | ||||||
\(903\) | −72.7584 | −0.0805741 | ||||||||
\(904\) | 504.959i | 0.558583i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 324.817 | 0.358517 | ||||||||
\(907\) | − | 1320.74i | − | 1.45616i | −0.685492 | − | 0.728080i | \(-0.740413\pi\) | ||
0.685492 | − | 0.728080i | \(-0.259587\pi\) | |||||||
\(908\) | − | 22.6736i | − | 0.0249709i | ||||||
\(909\) | −90.0475 | −0.0990621 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1388.64i | − | 1.52430i | −0.647398 | − | 0.762152i | \(-0.724143\pi\) | ||
0.647398 | − | 0.762152i | \(-0.275857\pi\) | |||||||
\(912\) | − | 67.1233i | − | 0.0736001i | ||||||
\(913\) | −1232.63 | −1.35009 | ||||||||
\(914\) | − | 317.392i | − | 0.347256i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 225.018i | − | 0.245653i | ||||||
\(917\) | − | 123.684i | − | 0.134879i | ||||||
\(918\) | 914.602i | 0.996299i | ||||||||
\(919\) | − | 814.108i | − | 0.885863i | −0.896555 | − | 0.442932i | \(-0.853938\pi\) | ||
0.896555 | − | 0.442932i | \(-0.146062\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 406.566 | 0.441440 | ||||||||
\(922\) | −756.123 | −0.820090 | ||||||||
\(923\) | 1939.19 | 2.10096 | ||||||||
\(924\) | −381.650 | −0.413041 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 235.078 | 0.253864 | ||||||||
\(927\) | − | 625.991i | − | 0.675286i | ||||||
\(928\) | −240.300 | −0.258944 | ||||||||
\(929\) | 951.041 | 1.02373 | 0.511863 | − | 0.859067i | \(-0.328956\pi\) | ||||
0.511863 | + | 0.859067i | \(0.328956\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 638.929i | − | 0.686283i | ||||||
\(932\) | 763.268 | 0.818957 | ||||||||
\(933\) | 277.903 | 0.297859 | ||||||||
\(934\) | 160.874i | 0.172242i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −455.116 | −0.486235 | ||||||||
\(937\) | 25.4596i | 0.0271713i | 0.999908 | + | 0.0135857i | \(0.00432459\pi\) | ||||
−0.999908 | + | 0.0135857i | \(0.995675\pi\) | |||||||
\(938\) | 1153.78 | 1.23005 | ||||||||
\(939\) | − | 574.313i | − | 0.611622i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1304.69i | 1.38650i | 0.720698 | + | 0.693249i | \(0.243821\pi\) | ||||
−0.720698 | + | 0.693249i | \(0.756179\pi\) | |||||||
\(942\) | 78.5093i | 0.0833432i | ||||||||
\(943\) | −1267.05 | + | 1095.31i | −1.34364 | + | 1.16152i | ||||
\(944\) | 376.338 | 0.398663 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 91.4605 | 0.0966813 | ||||||||
\(947\) | 25.1178 | 0.0265236 | 0.0132618 | − | 0.999912i | \(-0.495779\pi\) | ||||
0.0132618 | + | 0.999912i | \(0.495779\pi\) | |||||||
\(948\) | − | 230.957i | − | 0.243626i | ||||||
\(949\) | −208.683 | −0.219897 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −52.5434 | −0.0552507 | ||||||||
\(952\) | −813.154 | −0.854153 | ||||||||
\(953\) | 663.560i | 0.696286i | 0.937442 | + | 0.348143i | \(0.113188\pi\) | ||||
−0.937442 | + | 0.348143i | \(0.886812\pi\) | |||||||
\(954\) | 261.994i | 0.274627i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 278.592 | 0.291414 | ||||||||
\(957\) | 795.767i | 0.831523i | ||||||||
\(958\) | 221.061i | 0.230753i | ||||||||
\(959\) | −1737.24 | −1.81152 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −608.753 | −0.633457 | ||||||||
\(962\) | − | 37.4589i | − | 0.0389386i | ||||||
\(963\) | − | 1283.45i | − | 1.33276i | ||||||
\(964\) | − | 164.669i | − | 0.170819i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 311.677 | + | 360.546i | 0.322647 | + | 0.373236i | ||||
\(967\) | 661.312 | 0.683880 | 0.341940 | − | 0.939722i | \(-0.388916\pi\) | ||||
0.341940 | + | 0.939722i | \(0.388916\pi\) | |||||||
\(968\) | 137.511 | 0.142057 | ||||||||
\(969\) | −473.602 | −0.488753 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1198.53i | − | 1.23433i | −0.786834 | − | 0.617165i | \(-0.788281\pi\) | ||
0.786834 | − | 0.617165i | \(-0.211719\pi\) | |||||||
\(972\) | −497.100 | −0.511420 | ||||||||
\(973\) | 392.670i | 0.403566i | ||||||||
\(974\) | −294.042 | −0.301891 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 298.117i | 0.305448i | ||||||||
\(977\) | − | 1156.31i | − | 1.18353i | −0.806110 | − | 0.591765i | \(-0.798431\pi\) | ||
0.806110 | − | 0.591765i | \(-0.201569\pi\) | |||||||
\(978\) | −305.717 | −0.312594 | ||||||||
\(979\) | 1781.80 | 1.82002 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 95.8210i | 0.0976768i | ||||||||
\(982\) | 655.268 | 0.667279 | ||||||||
\(983\) | − | 534.831i | − | 0.544080i | −0.962286 | − | 0.272040i | \(-0.912302\pi\) | ||
0.962286 | − | 0.272040i | \(-0.0876983\pi\) | |||||||
\(984\) | −296.255 | −0.301073 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1695.48i | 1.71956i | ||||||||
\(987\) | − | 11.9174i | − | 0.0120744i | ||||||
\(988\) | − | 541.685i | − | 0.548265i | ||||||
\(989\) | −74.6918 | − | 86.4030i | −0.0755225 | − | 0.0873640i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −217.485 | −0.219461 | −0.109730 | − | 0.993961i | \(-0.534999\pi\) | ||||
−0.109730 | + | 0.993961i | \(0.534999\pi\) | |||||||
\(992\) | −106.169 | −0.107025 | ||||||||
\(993\) | −123.615 | −0.124486 | ||||||||
\(994\) | 1203.33i | 1.21060i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 272.270i | 0.273364i | ||||||||
\(997\) | 248.055 | 0.248801 | 0.124400 | − | 0.992232i | \(-0.460299\pi\) | ||||
0.124400 | + | 0.992232i | \(0.460299\pi\) | |||||||
\(998\) | 71.8105 | 0.0719544 | ||||||||
\(999\) | − | 26.1446i | − | 0.0261707i |
(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 | 1150.3.d.b.551.4 | 16 | ||
5.2 | odd | 4 | 1150.3.c.c.1149.1 | 32 | |||
5.3 | odd | 4 | 1150.3.c.c.1149.32 | 32 | |||
5.4 | even | 2 | 230.3.d.a.91.13 | ✓ | 16 | ||
15.14 | odd | 2 | 2070.3.c.a.91.5 | 16 | |||
20.19 | odd | 2 | 1840.3.k.d.321.7 | 16 | |||
23.22 | odd | 2 | inner | 1150.3.d.b.551.3 | 16 | ||
115.22 | even | 4 | 1150.3.c.c.1149.31 | 32 | |||
115.68 | even | 4 | 1150.3.c.c.1149.2 | 32 | |||
115.114 | odd | 2 | 230.3.d.a.91.14 | yes | 16 | ||
345.344 | even | 2 | 2070.3.c.a.91.4 | 16 | |||
460.459 | even | 2 | 1840.3.k.d.321.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.13 | ✓ | 16 | 5.4 | even | 2 | ||
230.3.d.a.91.14 | yes | 16 | 115.114 | odd | 2 | ||
1150.3.c.c.1149.1 | 32 | 5.2 | odd | 4 | |||
1150.3.c.c.1149.2 | 32 | 115.68 | even | 4 | |||
1150.3.c.c.1149.31 | 32 | 115.22 | even | 4 | |||
1150.3.c.c.1149.32 | 32 | 5.3 | odd | 4 | |||
1150.3.d.b.551.3 | 16 | 23.22 | odd | 2 | inner | ||
1150.3.d.b.551.4 | 16 | 1.1 | even | 1 | trivial | ||
1840.3.k.d.321.7 | 16 | 20.19 | odd | 2 | |||
1840.3.k.d.321.8 | 16 | 460.459 | even | 2 | |||
2070.3.c.a.91.4 | 16 | 345.344 | even | 2 | |||
2070.3.c.a.91.5 | 16 | 15.14 | odd | 2 |