Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,5,Mod(22,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.22");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.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: | \(7.13252745279\) |
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: | \( x^{16} + 5598 x^{14} + 11369517 x^{12} + 11272666128 x^{10} + 5958872960073 x^{8} + \cdots + 13\!\cdots\!52 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.6 | ||
Root | \(19.7839i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.22 |
Dual form | 69.5.d.a.22.5 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.02014 | −0.505034 | −0.252517 | − | 0.967592i | \(-0.581258\pi\) | ||||
−0.252517 | + | 0.967592i | \(0.581258\pi\) | |||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | −11.9191 | −0.744941 | ||||||||
\(5\) | 11.8600i | 0.474401i | 0.971461 | + | 0.237201i | \(0.0762299\pi\) | ||||
−0.971461 | + | 0.237201i | \(0.923770\pi\) | |||||||
\(6\) | −10.4969 | −0.291581 | ||||||||
\(7\) | − | 49.3562i | − | 1.00727i | −0.863917 | − | 0.503634i | \(-0.831996\pi\) | ||
0.863917 | − | 0.503634i | \(-0.168004\pi\) | |||||||
\(8\) | 56.4003 | 0.881254 | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | − | 23.9589i | − | 0.239589i | ||||||
\(11\) | − | 138.760i | − | 1.14678i | −0.819283 | − | 0.573389i | \(-0.805628\pi\) | ||
0.819283 | − | 0.573389i | \(-0.194372\pi\) | |||||||
\(12\) | −61.9332 | −0.430092 | ||||||||
\(13\) | 1.54329 | 0.00913189 | 0.00456595 | − | 0.999990i | \(-0.498547\pi\) | ||||
0.00456595 | + | 0.999990i | \(0.498547\pi\) | |||||||
\(14\) | 99.7061i | 0.508705i | ||||||||
\(15\) | 61.6265i | 0.273896i | ||||||||
\(16\) | 76.7686 | 0.299878 | ||||||||
\(17\) | − | 442.918i | − | 1.53259i | −0.642489 | − | 0.766295i | \(-0.722098\pi\) | ||
0.642489 | − | 0.766295i | \(-0.277902\pi\) | |||||||
\(18\) | −54.5437 | −0.168345 | ||||||||
\(19\) | − | 136.903i | − | 0.379232i | −0.981858 | − | 0.189616i | \(-0.939276\pi\) | ||
0.981858 | − | 0.189616i | \(-0.0607244\pi\) | |||||||
\(20\) | − | 141.360i | − | 0.353401i | ||||||
\(21\) | − | 256.462i | − | 0.581547i | ||||||
\(22\) | 280.314i | 0.579162i | ||||||||
\(23\) | −111.696 | − | 517.074i | −0.211145 | − | 0.977455i | ||||
\(24\) | 293.064 | 0.508792 | ||||||||
\(25\) | 484.340 | 0.774943 | ||||||||
\(26\) | −3.11765 | −0.00461191 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | 588.279i | 0.750356i | ||||||||
\(29\) | 799.586 | 0.950756 | 0.475378 | − | 0.879782i | \(-0.342311\pi\) | ||||
0.475378 | + | 0.879782i | \(0.342311\pi\) | |||||||
\(30\) | − | 124.494i | − | 0.138327i | ||||||
\(31\) | −1832.70 | −1.90708 | −0.953540 | − | 0.301265i | \(-0.902591\pi\) | ||||
−0.953540 | + | 0.301265i | \(0.902591\pi\) | |||||||
\(32\) | −1057.49 | −1.03270 | ||||||||
\(33\) | − | 721.019i | − | 0.662092i | ||||||
\(34\) | 894.755i | 0.774010i | ||||||||
\(35\) | 585.366 | 0.477850 | ||||||||
\(36\) | −321.814 | −0.248314 | ||||||||
\(37\) | 2680.48i | 1.95798i | 0.203906 | + | 0.978990i | \(0.434636\pi\) | ||||
−0.203906 | + | 0.978990i | \(0.565364\pi\) | |||||||
\(38\) | 276.562i | 0.191525i | ||||||||
\(39\) | 8.01917 | 0.00527230 | ||||||||
\(40\) | 668.909i | 0.418068i | ||||||||
\(41\) | 1129.66 | 0.672017 | 0.336009 | − | 0.941859i | \(-0.390923\pi\) | ||||
0.336009 | + | 0.941859i | \(0.390923\pi\) | |||||||
\(42\) | 518.088i | 0.293701i | ||||||||
\(43\) | 1149.16i | 0.621506i | 0.950491 | + | 0.310753i | \(0.100581\pi\) | ||||
−0.950491 | + | 0.310753i | \(0.899419\pi\) | |||||||
\(44\) | 1653.89i | 0.854281i | ||||||||
\(45\) | 320.221i | 0.158134i | ||||||||
\(46\) | 225.641 | + | 1044.56i | 0.106636 | + | 0.493648i | ||||
\(47\) | −1549.99 | −0.701669 | −0.350834 | − | 0.936438i | \(-0.614102\pi\) | ||||
−0.350834 | + | 0.936438i | \(0.614102\pi\) | |||||||
\(48\) | 398.902 | 0.173134 | ||||||||
\(49\) | −35.0313 | −0.0145903 | ||||||||
\(50\) | −978.432 | −0.391373 | ||||||||
\(51\) | − | 2301.47i | − | 0.884841i | ||||||
\(52\) | −18.3945 | −0.00680272 | ||||||||
\(53\) | − | 1245.11i | − | 0.443258i | −0.975131 | − | 0.221629i | \(-0.928863\pi\) | ||
0.975131 | − | 0.221629i | \(-0.0711374\pi\) | |||||||
\(54\) | −283.417 | −0.0971938 | ||||||||
\(55\) | 1645.70 | 0.544033 | ||||||||
\(56\) | − | 2783.70i | − | 0.887660i | ||||||
\(57\) | − | 711.368i | − | 0.218950i | ||||||
\(58\) | −1615.27 | −0.480164 | ||||||||
\(59\) | −272.245 | −0.0782087 | −0.0391044 | − | 0.999235i | \(-0.512450\pi\) | ||||
−0.0391044 | + | 0.999235i | \(0.512450\pi\) | |||||||
\(60\) | − | 734.530i | − | 0.204036i | ||||||
\(61\) | − | 6172.94i | − | 1.65895i | −0.558546 | − | 0.829474i | \(-0.688641\pi\) | ||
0.558546 | − | 0.829474i | \(-0.311359\pi\) | |||||||
\(62\) | 3702.31 | 0.963140 | ||||||||
\(63\) | − | 1332.62i | − | 0.335756i | ||||||
\(64\) | 907.970 | 0.221672 | ||||||||
\(65\) | 18.3035i | 0.00433218i | ||||||||
\(66\) | 1456.56i | 0.334379i | ||||||||
\(67\) | 653.333i | 0.145541i | 0.997349 | + | 0.0727705i | \(0.0231840\pi\) | ||||
−0.997349 | + | 0.0727705i | \(0.976816\pi\) | |||||||
\(68\) | 5279.17i | 1.14169i | ||||||||
\(69\) | −580.389 | − | 2686.79i | −0.121905 | − | 0.564334i | ||||
\(70\) | −1182.52 | −0.241330 | ||||||||
\(71\) | 1628.32 | 0.323016 | 0.161508 | − | 0.986871i | \(-0.448364\pi\) | ||||
0.161508 | + | 0.986871i | \(0.448364\pi\) | |||||||
\(72\) | 1522.81 | 0.293751 | ||||||||
\(73\) | −830.928 | −0.155926 | −0.0779628 | − | 0.996956i | \(-0.524842\pi\) | ||||
−0.0779628 | + | 0.996956i | \(0.524842\pi\) | |||||||
\(74\) | − | 5414.92i | − | 0.988847i | ||||||
\(75\) | 2516.70 | 0.447414 | ||||||||
\(76\) | 1631.75i | 0.282506i | ||||||||
\(77\) | −6848.67 | −1.15511 | ||||||||
\(78\) | −16.1998 | −0.00266269 | ||||||||
\(79\) | 4359.86i | 0.698584i | 0.937014 | + | 0.349292i | \(0.113578\pi\) | ||||
−0.937014 | + | 0.349292i | \(0.886422\pi\) | |||||||
\(80\) | 910.478i | 0.142262i | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | −2282.07 | −0.339391 | ||||||||
\(83\) | − | 5180.44i | − | 0.751987i | −0.926622 | − | 0.375994i | \(-0.877301\pi\) | ||
0.926622 | − | 0.375994i | \(-0.122699\pi\) | |||||||
\(84\) | 3056.79i | 0.433218i | ||||||||
\(85\) | 5253.03 | 0.727062 | ||||||||
\(86\) | − | 2321.47i | − | 0.313882i | ||||||
\(87\) | 4154.77 | 0.548920 | ||||||||
\(88\) | − | 7826.11i | − | 1.01060i | ||||||
\(89\) | − | 4715.91i | − | 0.595367i | −0.954665 | − | 0.297684i | \(-0.903786\pi\) | ||
0.954665 | − | 0.297684i | \(-0.0962141\pi\) | |||||||
\(90\) | − | 646.889i | − | 0.0798629i | ||||||
\(91\) | − | 76.1709i | − | 0.00919827i | ||||||
\(92\) | 1331.31 | + | 6163.03i | 0.157291 | + | 0.728146i | ||||
\(93\) | −9523.01 | −1.10105 | ||||||||
\(94\) | 3131.18 | 0.354366 | ||||||||
\(95\) | 1623.67 | 0.179908 | ||||||||
\(96\) | −5494.87 | −0.596231 | ||||||||
\(97\) | 7546.72i | 0.802075i | 0.916062 | + | 0.401037i | \(0.131350\pi\) | ||||
−0.916062 | + | 0.401037i | \(0.868650\pi\) | |||||||
\(98\) | 70.7680 | 0.00736860 | ||||||||
\(99\) | − | 3746.52i | − | 0.382259i | ||||||
\(100\) | −5772.87 | −0.577287 | ||||||||
\(101\) | 12320.4 | 1.20776 | 0.603880 | − | 0.797075i | \(-0.293621\pi\) | ||||
0.603880 | + | 0.797075i | \(0.293621\pi\) | |||||||
\(102\) | 4649.28i | 0.446875i | ||||||||
\(103\) | − | 15454.2i | − | 1.45671i | −0.685200 | − | 0.728355i | \(-0.740285\pi\) | ||
0.685200 | − | 0.728355i | \(-0.259715\pi\) | |||||||
\(104\) | 87.0419 | 0.00804752 | ||||||||
\(105\) | 3041.65 | 0.275887 | ||||||||
\(106\) | 2515.30i | 0.223860i | ||||||||
\(107\) | 8600.42i | 0.751194i | 0.926783 | + | 0.375597i | \(0.122562\pi\) | ||||
−0.926783 | + | 0.375597i | \(0.877438\pi\) | |||||||
\(108\) | −1672.20 | −0.143364 | ||||||||
\(109\) | 1914.39i | 0.161131i | 0.996749 | + | 0.0805653i | \(0.0256726\pi\) | ||||
−0.996749 | + | 0.0805653i | \(0.974327\pi\) | |||||||
\(110\) | −3324.53 | −0.274755 | ||||||||
\(111\) | 13928.2i | 1.13044i | ||||||||
\(112\) | − | 3789.01i | − | 0.302057i | ||||||
\(113\) | 8842.41i | 0.692490i | 0.938144 | + | 0.346245i | \(0.112543\pi\) | ||||
−0.938144 | + | 0.346245i | \(0.887457\pi\) | |||||||
\(114\) | 1437.06i | 0.110577i | ||||||||
\(115\) | 6132.51 | − | 1324.72i | 0.463706 | − | 0.100168i | ||||
\(116\) | −9530.31 | −0.708257 | ||||||||
\(117\) | 41.6688 | 0.00304396 | ||||||||
\(118\) | 549.971 | 0.0394981 | ||||||||
\(119\) | −21860.8 | −1.54373 | ||||||||
\(120\) | 3475.75i | 0.241372i | ||||||||
\(121\) | −4613.36 | −0.315099 | ||||||||
\(122\) | 12470.2i | 0.837825i | ||||||||
\(123\) | 5869.89 | 0.387989 | ||||||||
\(124\) | 21844.1 | 1.42066 | ||||||||
\(125\) | 13156.8i | 0.842035i | ||||||||
\(126\) | 2692.07i | 0.169568i | ||||||||
\(127\) | −16086.6 | −0.997372 | −0.498686 | − | 0.866783i | \(-0.666184\pi\) | ||||
−0.498686 | + | 0.866783i | \(0.666184\pi\) | |||||||
\(128\) | 15085.6 | 0.920751 | ||||||||
\(129\) | 5971.23i | 0.358827i | ||||||||
\(130\) | − | 36.9755i | − | 0.00218790i | ||||||
\(131\) | 9411.82 | 0.548443 | 0.274221 | − | 0.961667i | \(-0.411580\pi\) | ||||
0.274221 | + | 0.961667i | \(0.411580\pi\) | |||||||
\(132\) | 8593.86i | 0.493220i | ||||||||
\(133\) | −6757.00 | −0.381989 | ||||||||
\(134\) | − | 1319.82i | − | 0.0735031i | ||||||
\(135\) | 1663.92i | 0.0912986i | ||||||||
\(136\) | − | 24980.7i | − | 1.35060i | ||||||
\(137\) | − | 20606.2i | − | 1.09788i | −0.835860 | − | 0.548942i | \(-0.815031\pi\) | ||
0.835860 | − | 0.548942i | \(-0.184969\pi\) | |||||||
\(138\) | 1172.46 | + | 5427.69i | 0.0615661 | + | 0.285008i | ||||
\(139\) | −9481.33 | −0.490727 | −0.245363 | − | 0.969431i | \(-0.578907\pi\) | ||||
−0.245363 | + | 0.969431i | \(0.578907\pi\) | |||||||
\(140\) | −6977.00 | −0.355970 | ||||||||
\(141\) | −8053.96 | −0.405109 | ||||||||
\(142\) | −3289.43 | −0.163134 | ||||||||
\(143\) | − | 214.147i | − | 0.0104722i | ||||||
\(144\) | 2072.75 | 0.0999592 | ||||||||
\(145\) | 9483.12i | 0.451040i | ||||||||
\(146\) | 1678.59 | 0.0787478 | ||||||||
\(147\) | −182.028 | −0.00842371 | ||||||||
\(148\) | − | 31948.7i | − | 1.45858i | ||||||
\(149\) | 34843.6i | 1.56946i | 0.619838 | + | 0.784730i | \(0.287198\pi\) | ||||
−0.619838 | + | 0.784730i | \(0.712802\pi\) | |||||||
\(150\) | −5084.08 | −0.225959 | ||||||||
\(151\) | 19394.8 | 0.850613 | 0.425307 | − | 0.905049i | \(-0.360166\pi\) | ||||
0.425307 | + | 0.905049i | \(0.360166\pi\) | |||||||
\(152\) | − | 7721.36i | − | 0.334200i | ||||||
\(153\) | − | 11958.8i | − | 0.510863i | ||||||
\(154\) | 13835.2 | 0.583371 | ||||||||
\(155\) | − | 21735.9i | − | 0.904721i | ||||||
\(156\) | −95.5809 | −0.00392755 | ||||||||
\(157\) | 22896.2i | 0.928891i | 0.885602 | + | 0.464446i | \(0.153746\pi\) | ||||
−0.885602 | + | 0.464446i | \(0.846254\pi\) | |||||||
\(158\) | − | 8807.51i | − | 0.352808i | ||||||
\(159\) | − | 6469.79i | − | 0.255915i | ||||||
\(160\) | − | 12541.8i | − | 0.489915i | ||||||
\(161\) | −25520.8 | + | 5512.88i | −0.984560 | + | 0.212680i | ||||
\(162\) | −1472.68 | −0.0561149 | ||||||||
\(163\) | 34238.6 | 1.28867 | 0.644333 | − | 0.764745i | \(-0.277135\pi\) | ||||
0.644333 | + | 0.764745i | \(0.277135\pi\) | |||||||
\(164\) | −13464.5 | −0.500613 | ||||||||
\(165\) | 8551.30 | 0.314097 | ||||||||
\(166\) | 10465.2i | 0.379779i | ||||||||
\(167\) | 44643.0 | 1.60074 | 0.800370 | − | 0.599506i | \(-0.204636\pi\) | ||||
0.800370 | + | 0.599506i | \(0.204636\pi\) | |||||||
\(168\) | − | 14464.5i | − | 0.512491i | ||||||
\(169\) | −28558.6 | −0.999917 | ||||||||
\(170\) | −10611.8 | −0.367191 | ||||||||
\(171\) | − | 3696.38i | − | 0.126411i | ||||||
\(172\) | − | 13696.9i | − | 0.462985i | ||||||
\(173\) | 26121.0 | 0.872765 | 0.436383 | − | 0.899761i | \(-0.356259\pi\) | ||||
0.436383 | + | 0.899761i | \(0.356259\pi\) | |||||||
\(174\) | −8393.20 | −0.277223 | ||||||||
\(175\) | − | 23905.2i | − | 0.780576i | ||||||
\(176\) | − | 10652.4i | − | 0.343893i | ||||||
\(177\) | −1414.62 | −0.0451538 | ||||||||
\(178\) | 9526.77i | 0.300681i | ||||||||
\(179\) | −18435.7 | −0.575379 | −0.287689 | − | 0.957724i | \(-0.592887\pi\) | ||||
−0.287689 | + | 0.957724i | \(0.592887\pi\) | |||||||
\(180\) | − | 3816.73i | − | 0.117800i | ||||||
\(181\) | 19820.1i | 0.604992i | 0.953151 | + | 0.302496i | \(0.0978199\pi\) | ||||
−0.953151 | + | 0.302496i | \(0.902180\pi\) | |||||||
\(182\) | 153.875i | 0.00464544i | ||||||||
\(183\) | − | 32075.6i | − | 0.957794i | ||||||
\(184\) | −6299.68 | − | 29163.1i | −0.186073 | − | 0.861386i | ||||
\(185\) | −31790.5 | −0.928869 | ||||||||
\(186\) | 19237.8 | 0.556069 | ||||||||
\(187\) | −61459.4 | −1.75754 | ||||||||
\(188\) | 18474.4 | 0.522702 | ||||||||
\(189\) | − | 6924.48i | − | 0.193849i | ||||||
\(190\) | −3280.04 | −0.0908598 | ||||||||
\(191\) | − | 6762.97i | − | 0.185383i | −0.995695 | − | 0.0926916i | \(-0.970453\pi\) | ||
0.995695 | − | 0.0926916i | \(-0.0295471\pi\) | |||||||
\(192\) | 4717.95 | 0.127983 | ||||||||
\(193\) | 54646.4 | 1.46706 | 0.733528 | − | 0.679659i | \(-0.237872\pi\) | ||||
0.733528 | + | 0.679659i | \(0.237872\pi\) | |||||||
\(194\) | − | 15245.4i | − | 0.405075i | ||||||
\(195\) | 95.1076i | 0.00250119i | ||||||||
\(196\) | 417.540 | 0.0108689 | ||||||||
\(197\) | 34881.1 | 0.898789 | 0.449395 | − | 0.893333i | \(-0.351640\pi\) | ||||
0.449395 | + | 0.893333i | \(0.351640\pi\) | |||||||
\(198\) | 7568.48i | 0.193054i | ||||||||
\(199\) | 56991.5i | 1.43914i | 0.694418 | + | 0.719572i | \(0.255662\pi\) | ||||
−0.694418 | + | 0.719572i | \(0.744338\pi\) | |||||||
\(200\) | 27316.9 | 0.682922 | ||||||||
\(201\) | 3394.82i | 0.0840281i | ||||||||
\(202\) | −24888.8 | −0.609960 | ||||||||
\(203\) | − | 39464.5i | − | 0.957667i | ||||||
\(204\) | 27431.4i | 0.659154i | ||||||||
\(205\) | 13397.8i | 0.318806i | ||||||||
\(206\) | 31219.6i | 0.735688i | ||||||||
\(207\) | −3015.79 | − | 13961.0i | −0.0703818 | − | 0.325818i | ||||
\(208\) | 118.476 | 0.00273845 | ||||||||
\(209\) | −18996.7 | −0.434895 | ||||||||
\(210\) | −6144.54 | −0.139332 | ||||||||
\(211\) | 16055.7 | 0.360631 | 0.180316 | − | 0.983609i | \(-0.442288\pi\) | ||||
0.180316 | + | 0.983609i | \(0.442288\pi\) | |||||||
\(212\) | 14840.6i | 0.330201i | ||||||||
\(213\) | 8461.01 | 0.186493 | ||||||||
\(214\) | − | 17374.0i | − | 0.379379i | ||||||
\(215\) | −13629.1 | −0.294843 | ||||||||
\(216\) | 7912.74 | 0.169597 | ||||||||
\(217\) | 90455.3i | 1.92094i | ||||||||
\(218\) | − | 3867.33i | − | 0.0813764i | ||||||
\(219\) | −4317.63 | −0.0900237 | ||||||||
\(220\) | −19615.2 | −0.405272 | ||||||||
\(221\) | − | 683.551i | − | 0.0139954i | ||||||
\(222\) | − | 28136.8i | − | 0.570911i | ||||||
\(223\) | −49350.5 | −0.992389 | −0.496195 | − | 0.868211i | \(-0.665270\pi\) | ||||
−0.496195 | + | 0.868211i | \(0.665270\pi\) | |||||||
\(224\) | 52193.5i | 1.04021i | ||||||||
\(225\) | 13077.2 | 0.258314 | ||||||||
\(226\) | − | 17862.9i | − | 0.349731i | ||||||
\(227\) | − | 32093.6i | − | 0.622826i | −0.950275 | − | 0.311413i | \(-0.899198\pi\) | ||
0.950275 | − | 0.311413i | \(-0.100802\pi\) | |||||||
\(228\) | 8478.84i | 0.163105i | ||||||||
\(229\) | 98532.0i | 1.87891i | 0.342669 | + | 0.939456i | \(0.388669\pi\) | ||||
−0.342669 | + | 0.939456i | \(0.611331\pi\) | |||||||
\(230\) | −12388.5 | + | 2676.11i | −0.234187 | + | 0.0505880i | ||||
\(231\) | −35586.7 | −0.666905 | ||||||||
\(232\) | 45096.9 | 0.837858 | ||||||||
\(233\) | −82075.6 | −1.51183 | −0.755913 | − | 0.654672i | \(-0.772807\pi\) | ||||
−0.755913 | + | 0.654672i | \(0.772807\pi\) | |||||||
\(234\) | −84.1767 | −0.00153730 | ||||||||
\(235\) | − | 18382.9i | − | 0.332872i | ||||||
\(236\) | 3244.90 | 0.0582609 | ||||||||
\(237\) | 22654.5i | 0.403327i | ||||||||
\(238\) | 44161.7 | 0.779636 | ||||||||
\(239\) | 56560.3 | 0.990183 | 0.495092 | − | 0.868841i | \(-0.335134\pi\) | ||||
0.495092 | + | 0.868841i | \(0.335134\pi\) | |||||||
\(240\) | 4730.98i | 0.0821352i | ||||||||
\(241\) | 26464.4i | 0.455647i | 0.973702 | + | 0.227824i | \(0.0731610\pi\) | ||||
−0.973702 | + | 0.227824i | \(0.926839\pi\) | |||||||
\(242\) | 9319.61 | 0.159135 | ||||||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | 73575.6i | 1.23582i | ||||||||
\(245\) | − | 415.472i | − | 0.00692166i | ||||||
\(246\) | −11858.0 | −0.195948 | ||||||||
\(247\) | − | 211.281i | − | 0.00346311i | ||||||
\(248\) | −103365. | −1.68062 | ||||||||
\(249\) | − | 26918.3i | − | 0.434160i | ||||||
\(250\) | − | 26578.5i | − | 0.425256i | ||||||
\(251\) | 34816.3i | 0.552631i | 0.961067 | + | 0.276315i | \(0.0891135\pi\) | ||||
−0.961067 | + | 0.276315i | \(0.910887\pi\) | |||||||
\(252\) | 15883.5i | 0.250119i | ||||||||
\(253\) | −71749.2 | + | 15498.9i | −1.12092 | + | 0.242137i | ||||
\(254\) | 32497.1 | 0.503706 | ||||||||
\(255\) | 27295.5 | 0.419770 | ||||||||
\(256\) | −45002.4 | −0.686682 | ||||||||
\(257\) | 50347.6 | 0.762277 | 0.381138 | − | 0.924518i | \(-0.375532\pi\) | ||||
0.381138 | + | 0.924518i | \(0.375532\pi\) | |||||||
\(258\) | − | 12062.7i | − | 0.181220i | ||||||
\(259\) | 132298. | 1.97221 | ||||||||
\(260\) | − | 218.160i | − | 0.00322722i | ||||||
\(261\) | 21588.8 | 0.316919 | ||||||||
\(262\) | −19013.2 | −0.276982 | ||||||||
\(263\) | − | 91707.4i | − | 1.32584i | −0.748688 | − | 0.662922i | \(-0.769316\pi\) | ||
0.748688 | − | 0.662922i | \(-0.230684\pi\) | |||||||
\(264\) | − | 40665.6i | − | 0.583472i | ||||||
\(265\) | 14767.1 | 0.210282 | ||||||||
\(266\) | 13650.1 | 0.192917 | ||||||||
\(267\) | − | 24504.6i | − | 0.343736i | ||||||
\(268\) | − | 7787.11i | − | 0.108419i | ||||||
\(269\) | 104021. | 1.43753 | 0.718764 | − | 0.695254i | \(-0.244708\pi\) | ||||
0.718764 | + | 0.695254i | \(0.244708\pi\) | |||||||
\(270\) | − | 3361.34i | − | 0.0461089i | ||||||
\(271\) | −71982.7 | −0.980143 | −0.490072 | − | 0.871682i | \(-0.663029\pi\) | ||||
−0.490072 | + | 0.871682i | \(0.663029\pi\) | |||||||
\(272\) | − | 34002.2i | − | 0.459589i | ||||||
\(273\) | − | 395.795i | − | 0.00531062i | ||||||
\(274\) | 41627.3i | 0.554469i | ||||||||
\(275\) | − | 67207.0i | − | 0.888688i | ||||||
\(276\) | 6917.69 | + | 32024.0i | 0.0908119 | + | 0.420395i | ||||
\(277\) | −74174.4 | −0.966707 | −0.483353 | − | 0.875425i | \(-0.660581\pi\) | ||||
−0.483353 | + | 0.875425i | \(0.660581\pi\) | |||||||
\(278\) | 19153.6 | 0.247834 | ||||||||
\(279\) | −49483.0 | −0.635694 | ||||||||
\(280\) | 33014.8 | 0.421107 | ||||||||
\(281\) | − | 42936.8i | − | 0.543773i | −0.962329 | − | 0.271886i | \(-0.912353\pi\) | ||
0.962329 | − | 0.271886i | \(-0.0876475\pi\) | |||||||
\(282\) | 16270.1 | 0.204594 | ||||||||
\(283\) | − | 128674.i | − | 1.60664i | −0.595550 | − | 0.803318i | \(-0.703066\pi\) | ||
0.595550 | − | 0.803318i | \(-0.296934\pi\) | |||||||
\(284\) | −19408.1 | −0.240627 | ||||||||
\(285\) | 8436.85 | 0.103870 | ||||||||
\(286\) | 432.606i | 0.00528884i | ||||||||
\(287\) | − | 55755.7i | − | 0.676902i | ||||||
\(288\) | −28552.2 | −0.344234 | ||||||||
\(289\) | −112656. | −1.34883 | ||||||||
\(290\) | − | 19157.2i | − | 0.227790i | ||||||
\(291\) | 39213.9i | 0.463078i | ||||||||
\(292\) | 9903.87 | 0.116155 | ||||||||
\(293\) | − | 55591.2i | − | 0.647546i | −0.946135 | − | 0.323773i | \(-0.895049\pi\) | ||
0.946135 | − | 0.323773i | \(-0.104951\pi\) | |||||||
\(294\) | 367.721 | 0.00425426 | ||||||||
\(295\) | − | 3228.83i | − | 0.0371023i | ||||||
\(296\) | 151180.i | 1.72548i | ||||||||
\(297\) | − | 19467.5i | − | 0.220697i | ||||||
\(298\) | − | 70388.8i | − | 0.792630i | ||||||
\(299\) | −172.379 | − | 797.994i | −0.00192816 | − | 0.00892601i | ||||
\(300\) | −29996.7 | −0.333297 | ||||||||
\(301\) | 56718.3 | 0.626023 | ||||||||
\(302\) | −39180.2 | −0.429588 | ||||||||
\(303\) | 64018.4 | 0.697300 | ||||||||
\(304\) | − | 10509.9i | − | 0.113723i | ||||||
\(305\) | 73211.3 | 0.787007 | ||||||||
\(306\) | 24158.4i | 0.258003i | ||||||||
\(307\) | 162102. | 1.71993 | 0.859967 | − | 0.510350i | \(-0.170484\pi\) | ||||
0.859967 | + | 0.510350i | \(0.170484\pi\) | |||||||
\(308\) | 81629.6 | 0.860491 | ||||||||
\(309\) | − | 80302.5i | − | 0.841031i | ||||||
\(310\) | 43909.5i | 0.456915i | ||||||||
\(311\) | −14298.7 | −0.147834 | −0.0739171 | − | 0.997264i | \(-0.523550\pi\) | ||||
−0.0739171 | + | 0.997264i | \(0.523550\pi\) | |||||||
\(312\) | 452.283 | 0.00464624 | ||||||||
\(313\) | − | 49552.0i | − | 0.505793i | −0.967493 | − | 0.252896i | \(-0.918617\pi\) | ||
0.967493 | − | 0.252896i | \(-0.0813831\pi\) | |||||||
\(314\) | − | 46253.5i | − | 0.469122i | ||||||
\(315\) | 15804.9 | 0.159283 | ||||||||
\(316\) | − | 51965.4i | − | 0.520403i | ||||||
\(317\) | −193612. | −1.92670 | −0.963349 | − | 0.268250i | \(-0.913555\pi\) | ||||
−0.963349 | + | 0.268250i | \(0.913555\pi\) | |||||||
\(318\) | 13069.9i | 0.129246i | ||||||||
\(319\) | − | 110951.i | − | 1.09031i | ||||||
\(320\) | 10768.5i | 0.105162i | ||||||||
\(321\) | 44689.1i | 0.433702i | ||||||||
\(322\) | 51555.4 | − | 11136.8i | 0.497236 | − | 0.107411i | ||||
\(323\) | −60636.8 | −0.581208 | ||||||||
\(324\) | −8688.99 | −0.0827712 | ||||||||
\(325\) | 747.476 | 0.00707670 | ||||||||
\(326\) | −69166.6 | −0.650820 | ||||||||
\(327\) | 9947.48i | 0.0930288i | ||||||||
\(328\) | 63713.2 | 0.592218 | ||||||||
\(329\) | 76501.4i | 0.706769i | ||||||||
\(330\) | −17274.8 | −0.158630 | ||||||||
\(331\) | 154717. | 1.41215 | 0.706075 | − | 0.708137i | \(-0.250464\pi\) | ||||
0.706075 | + | 0.708137i | \(0.250464\pi\) | |||||||
\(332\) | 61745.9i | 0.560186i | ||||||||
\(333\) | 72372.8i | 0.652660i | ||||||||
\(334\) | −90185.0 | −0.808428 | ||||||||
\(335\) | −7748.55 | −0.0690448 | ||||||||
\(336\) | − | 19688.3i | − | 0.174393i | ||||||
\(337\) | − | 123315.i | − | 1.08582i | −0.839791 | − | 0.542909i | \(-0.817323\pi\) | ||
0.839791 | − | 0.542909i | \(-0.182677\pi\) | |||||||
\(338\) | 57692.3 | 0.504992 | ||||||||
\(339\) | 45946.5i | 0.399809i | ||||||||
\(340\) | −62611.1 | −0.541618 | ||||||||
\(341\) | 254306.i | 2.18700i | ||||||||
\(342\) | 7467.19i | 0.0638417i | ||||||||
\(343\) | − | 116775.i | − | 0.992572i | ||||||
\(344\) | 64813.2i | 0.547705i | ||||||||
\(345\) | 31865.4 | − | 6883.43i | 0.267721 | − | 0.0578318i | ||||
\(346\) | −52767.9 | −0.440776 | ||||||||
\(347\) | −156697. | −1.30137 | −0.650685 | − | 0.759348i | \(-0.725518\pi\) | ||||
−0.650685 | + | 0.759348i | \(0.725518\pi\) | |||||||
\(348\) | −49520.9 | −0.408913 | ||||||||
\(349\) | −160116. | −1.31457 | −0.657287 | − | 0.753640i | \(-0.728296\pi\) | ||||
−0.657287 | + | 0.753640i | \(0.728296\pi\) | |||||||
\(350\) | 48291.6i | 0.394218i | ||||||||
\(351\) | 216.518 | 0.00175743 | ||||||||
\(352\) | 146737.i | 1.18428i | ||||||||
\(353\) | 216727. | 1.73925 | 0.869627 | − | 0.493709i | \(-0.164359\pi\) | ||||
0.869627 | + | 0.493709i | \(0.164359\pi\) | |||||||
\(354\) | 2857.73 | 0.0228042 | ||||||||
\(355\) | 19311.9i | 0.153239i | ||||||||
\(356\) | 56209.1i | 0.443513i | ||||||||
\(357\) | −113592. | −0.891273 | ||||||||
\(358\) | 37242.6 | 0.290586 | ||||||||
\(359\) | 158846.i | 1.23250i | 0.787550 | + | 0.616250i | \(0.211349\pi\) | ||||
−0.787550 | + | 0.616250i | \(0.788651\pi\) | |||||||
\(360\) | 18060.5i | 0.139356i | ||||||||
\(361\) | 111579. | 0.856183 | ||||||||
\(362\) | − | 40039.4i | − | 0.305541i | ||||||
\(363\) | −23971.7 | −0.181922 | ||||||||
\(364\) | 907.884i | 0.00685216i | ||||||||
\(365\) | − | 9854.83i | − | 0.0739713i | ||||||
\(366\) | 64797.0i | 0.483718i | ||||||||
\(367\) | − | 63218.6i | − | 0.469367i | −0.972072 | − | 0.234684i | \(-0.924595\pi\) | ||
0.972072 | − | 0.234684i | \(-0.0754054\pi\) | |||||||
\(368\) | −8574.74 | − | 39695.0i | −0.0633177 | − | 0.293117i | ||||
\(369\) | 30500.8 | 0.224006 | ||||||||
\(370\) | 64221.2 | 0.469110 | ||||||||
\(371\) | −61454.0 | −0.446480 | ||||||||
\(372\) | 113505. | 0.820220 | ||||||||
\(373\) | 35956.2i | 0.258438i | 0.991616 | + | 0.129219i | \(0.0412470\pi\) | ||||
−0.991616 | + | 0.129219i | \(0.958753\pi\) | |||||||
\(374\) | 124156. | 0.887617 | ||||||||
\(375\) | 68364.8i | 0.486149i | ||||||||
\(376\) | −87419.6 | −0.618348 | ||||||||
\(377\) | 1233.99 | 0.00868220 | ||||||||
\(378\) | 13988.4i | 0.0979003i | ||||||||
\(379\) | − | 92556.1i | − | 0.644357i | −0.946679 | − | 0.322179i | \(-0.895585\pi\) | ||
0.946679 | − | 0.322179i | \(-0.104415\pi\) | |||||||
\(380\) | −19352.6 | −0.134021 | ||||||||
\(381\) | −83588.5 | −0.575833 | ||||||||
\(382\) | 13662.1i | 0.0936248i | ||||||||
\(383\) | 94193.3i | 0.642129i | 0.947057 | + | 0.321065i | \(0.104041\pi\) | ||||
−0.947057 | + | 0.321065i | \(0.895959\pi\) | |||||||
\(384\) | 78387.0 | 0.531596 | ||||||||
\(385\) | − | 81225.4i | − | 0.547987i | ||||||
\(386\) | −110393. | −0.740913 | ||||||||
\(387\) | 31027.4i | 0.207169i | ||||||||
\(388\) | − | 89949.8i | − | 0.597498i | ||||||
\(389\) | − | 255864.i | − | 1.69087i | −0.534077 | − | 0.845436i | \(-0.679341\pi\) | ||
0.534077 | − | 0.845436i | \(-0.320659\pi\) | |||||||
\(390\) | − | 192.130i | − | 0.00126318i | ||||||
\(391\) | −229021. | + | 49472.2i | −1.49804 | + | 0.323599i | ||||
\(392\) | −1975.78 | −0.0128578 | ||||||||
\(393\) | 48905.3 | 0.316643 | ||||||||
\(394\) | −70464.6 | −0.453919 | ||||||||
\(395\) | −51708.1 | −0.331409 | ||||||||
\(396\) | 44655.0i | 0.284760i | ||||||||
\(397\) | 209181. | 1.32721 | 0.663607 | − | 0.748081i | \(-0.269025\pi\) | ||||
0.663607 | + | 0.748081i | \(0.269025\pi\) | |||||||
\(398\) | − | 115131.i | − | 0.726816i | ||||||
\(399\) | −35110.4 | −0.220541 | ||||||||
\(400\) | 37182.1 | 0.232388 | ||||||||
\(401\) | 130365.i | 0.810725i | 0.914156 | + | 0.405363i | \(0.132855\pi\) | ||||
−0.914156 | + | 0.405363i | \(0.867145\pi\) | |||||||
\(402\) | − | 6857.99i | − | 0.0424370i | ||||||
\(403\) | −2828.39 | −0.0174153 | ||||||||
\(404\) | −146847. | −0.899709 | ||||||||
\(405\) | 8645.96i | 0.0527112i | ||||||||
\(406\) | 79723.7i | 0.483654i | ||||||||
\(407\) | 371943. | 2.24537 | ||||||||
\(408\) | − | 129804.i | − | 0.779770i | ||||||
\(409\) | 41308.2 | 0.246939 | 0.123469 | − | 0.992348i | \(-0.460598\pi\) | ||||
0.123469 | + | 0.992348i | \(0.460598\pi\) | |||||||
\(410\) | − | 27065.4i | − | 0.161008i | ||||||
\(411\) | − | 107073.i | − | 0.633864i | ||||||
\(412\) | 184200.i | 1.08516i | ||||||||
\(413\) | 13437.0i | 0.0787772i | ||||||||
\(414\) | 6092.30 | + | 28203.1i | 0.0355452 | + | 0.164549i | ||||
\(415\) | 61440.2 | 0.356744 | ||||||||
\(416\) | −1632.01 | −0.00943053 | ||||||||
\(417\) | −49266.4 | −0.283321 | ||||||||
\(418\) | 38375.8 | 0.219637 | ||||||||
\(419\) | 81532.1i | 0.464409i | 0.972667 | + | 0.232204i | \(0.0745938\pi\) | ||||
−0.972667 | + | 0.232204i | \(0.925406\pi\) | |||||||
\(420\) | −36253.6 | −0.205519 | ||||||||
\(421\) | 190672.i | 1.07578i | 0.843016 | + | 0.537889i | \(0.180778\pi\) | ||||
−0.843016 | + | 0.537889i | \(0.819222\pi\) | |||||||
\(422\) | −32434.6 | −0.182131 | ||||||||
\(423\) | −41849.6 | −0.233890 | ||||||||
\(424\) | − | 70224.7i | − | 0.390623i | ||||||
\(425\) | − | 214523.i | − | 1.18767i | ||||||
\(426\) | −17092.4 | −0.0941854 | ||||||||
\(427\) | −304673. | −1.67101 | ||||||||
\(428\) | − | 102509.i | − | 0.559595i | ||||||
\(429\) | − | 1112.74i | − | 0.00604615i | ||||||
\(430\) | 27532.7 | 0.148906 | ||||||||
\(431\) | 329168.i | 1.77200i | 0.463685 | + | 0.886000i | \(0.346527\pi\) | ||||
−0.463685 | + | 0.886000i | \(0.653473\pi\) | |||||||
\(432\) | 10770.3 | 0.0577115 | ||||||||
\(433\) | − | 58185.4i | − | 0.310341i | −0.987888 | − | 0.155170i | \(-0.950407\pi\) | ||
0.987888 | − | 0.155170i | \(-0.0495926\pi\) | |||||||
\(434\) | − | 182732.i | − | 0.970141i | ||||||
\(435\) | 49275.7i | 0.260408i | ||||||||
\(436\) | − | 22817.7i | − | 0.120033i | ||||||
\(437\) | −70788.9 | + | 15291.5i | −0.370683 | + | 0.0800732i | ||||
\(438\) | 8722.20 | 0.0454650 | ||||||||
\(439\) | 196906. | 1.02172 | 0.510858 | − | 0.859665i | \(-0.329328\pi\) | ||||
0.510858 | + | 0.859665i | \(0.329328\pi\) | |||||||
\(440\) | 92817.9 | 0.479431 | ||||||||
\(441\) | −945.845 | −0.00486343 | ||||||||
\(442\) | 1380.87i | 0.00706817i | ||||||||
\(443\) | −6730.75 | −0.0342970 | −0.0171485 | − | 0.999853i | \(-0.505459\pi\) | ||||
−0.0171485 | + | 0.999853i | \(0.505459\pi\) | |||||||
\(444\) | − | 166010.i | − | 0.842111i | ||||||
\(445\) | 55930.8 | 0.282443 | ||||||||
\(446\) | 99694.8 | 0.501190 | ||||||||
\(447\) | 181053.i | 0.906128i | ||||||||
\(448\) | − | 44813.9i | − | 0.223284i | ||||||
\(449\) | −253160. | −1.25575 | −0.627874 | − | 0.778315i | \(-0.716075\pi\) | ||||
−0.627874 | + | 0.778315i | \(0.716075\pi\) | |||||||
\(450\) | −26417.7 | −0.130458 | ||||||||
\(451\) | − | 156752.i | − | 0.770654i | ||||||
\(452\) | − | 105393.i | − | 0.515864i | ||||||
\(453\) | 100778. | 0.491102 | ||||||||
\(454\) | 64833.5i | 0.314548i | ||||||||
\(455\) | 903.389 | 0.00436367 | ||||||||
\(456\) | − | 40121.4i | − | 0.192951i | ||||||
\(457\) | 386298.i | 1.84965i | 0.380388 | + | 0.924827i | \(0.375790\pi\) | ||||
−0.380388 | + | 0.924827i | \(0.624210\pi\) | |||||||
\(458\) | − | 199048.i | − | 0.948914i | ||||||
\(459\) | − | 62139.7i | − | 0.294947i | ||||||
\(460\) | −73093.7 | + | 15789.4i | −0.345433 | + | 0.0746189i | ||||
\(461\) | −215298. | −1.01307 | −0.506535 | − | 0.862220i | \(-0.669074\pi\) | ||||
−0.506535 | + | 0.862220i | \(0.669074\pi\) | |||||||
\(462\) | 71890.0 | 0.336810 | ||||||||
\(463\) | −58694.1 | −0.273800 | −0.136900 | − | 0.990585i | \(-0.543714\pi\) | ||||
−0.136900 | + | 0.990585i | \(0.543714\pi\) | |||||||
\(464\) | 61383.1 | 0.285110 | ||||||||
\(465\) | − | 112943.i | − | 0.522341i | ||||||
\(466\) | 165804. | 0.763524 | ||||||||
\(467\) | − | 201704.i | − | 0.924868i | −0.886654 | − | 0.462434i | \(-0.846976\pi\) | ||
0.886654 | − | 0.462434i | \(-0.153024\pi\) | |||||||
\(468\) | −496.653 | −0.00226757 | ||||||||
\(469\) | 32246.0 | 0.146599 | ||||||||
\(470\) | 37135.9i | 0.168112i | ||||||||
\(471\) | 118972.i | 0.536296i | ||||||||
\(472\) | −15354.7 | −0.0689218 | ||||||||
\(473\) | 159458. | 0.712729 | ||||||||
\(474\) | − | 45765.2i | − | 0.203694i | ||||||
\(475\) | − | 66307.5i | − | 0.293884i | ||||||
\(476\) | 260559. | 1.14999 | ||||||||
\(477\) | − | 33618.0i | − | 0.147753i | ||||||
\(478\) | −114259. | −0.500076 | ||||||||
\(479\) | − | 151028.i | − | 0.658242i | −0.944288 | − | 0.329121i | \(-0.893248\pi\) | ||
0.944288 | − | 0.329121i | \(-0.106752\pi\) | |||||||
\(480\) | − | 65169.3i | − | 0.282853i | ||||||
\(481\) | 4136.75i | 0.0178801i | ||||||||
\(482\) | − | 53461.8i | − | 0.230117i | ||||||
\(483\) | −132610. | + | 28645.8i | −0.568436 | + | 0.122791i | ||||
\(484\) | 54986.9 | 0.234730 | ||||||||
\(485\) | −89504.4 | −0.380505 | ||||||||
\(486\) | −7652.26 | −0.0323979 | ||||||||
\(487\) | −167922. | −0.708026 | −0.354013 | − | 0.935240i | \(-0.615183\pi\) | ||||
−0.354013 | + | 0.935240i | \(0.615183\pi\) | |||||||
\(488\) | − | 348156.i | − | 1.46195i | ||||||
\(489\) | 177909. | 0.744012 | ||||||||
\(490\) | 839.311i | 0.00349567i | ||||||||
\(491\) | 143884. | 0.596827 | 0.298414 | − | 0.954437i | \(-0.403543\pi\) | ||||
0.298414 | + | 0.954437i | \(0.403543\pi\) | |||||||
\(492\) | −69963.5 | −0.289029 | ||||||||
\(493\) | − | 354151.i | − | 1.45712i | ||||||
\(494\) | 426.816i | 0.00174899i | ||||||||
\(495\) | 44433.9 | 0.181344 | ||||||||
\(496\) | −140694. | −0.571891 | ||||||||
\(497\) | − | 80367.7i | − | 0.325364i | ||||||
\(498\) | 54378.7i | 0.219265i | ||||||||
\(499\) | 101117. | 0.406089 | 0.203045 | − | 0.979169i | \(-0.434916\pi\) | ||||
0.203045 | + | 0.979169i | \(0.434916\pi\) | |||||||
\(500\) | − | 156817.i | − | 0.627266i | ||||||
\(501\) | 231972. | 0.924188 | ||||||||
\(502\) | − | 70333.6i | − | 0.279097i | ||||||
\(503\) | 240661.i | 0.951195i | 0.879663 | + | 0.475597i | \(0.157768\pi\) | ||||
−0.879663 | + | 0.475597i | \(0.842232\pi\) | |||||||
\(504\) | − | 75159.9i | − | 0.295887i | ||||||
\(505\) | 146120.i | 0.572963i | ||||||||
\(506\) | 144943. | − | 31309.9i | 0.566104 | − | 0.122287i | ||||
\(507\) | −148395. | −0.577302 | ||||||||
\(508\) | 191737. | 0.742983 | ||||||||
\(509\) | −59313.3 | −0.228937 | −0.114469 | − | 0.993427i | \(-0.536517\pi\) | ||||
−0.114469 | + | 0.993427i | \(0.536517\pi\) | |||||||
\(510\) | −55140.6 | −0.211998 | ||||||||
\(511\) | 41011.4i | 0.157059i | ||||||||
\(512\) | −150458. | −0.573953 | ||||||||
\(513\) | − | 19206.9i | − | 0.0729833i | ||||||
\(514\) | −101709. | −0.384976 | ||||||||
\(515\) | 183288. | 0.691065 | ||||||||
\(516\) | − | 71171.4i | − | 0.267305i | ||||||
\(517\) | 215076.i | 0.804658i | ||||||||
\(518\) | −267260. | −0.996034 | ||||||||
\(519\) | 135729. | 0.503891 | ||||||||
\(520\) | 1032.32i | 0.00381775i | ||||||||
\(521\) | − | 90521.5i | − | 0.333485i | −0.986000 | − | 0.166742i | \(-0.946675\pi\) | ||
0.986000 | − | 0.166742i | \(-0.0533248\pi\) | |||||||
\(522\) | −43612.4 | −0.160055 | ||||||||
\(523\) | 198379.i | 0.725258i | 0.931934 | + | 0.362629i | \(0.118121\pi\) | ||||
−0.931934 | + | 0.362629i | \(0.881879\pi\) | |||||||
\(524\) | −112180. | −0.408557 | ||||||||
\(525\) | − | 124215.i | − | 0.450666i | ||||||
\(526\) | 185261.i | 0.669597i | ||||||||
\(527\) | 811739.i | 2.92277i | ||||||||
\(528\) | − | 55351.6i | − | 0.198547i | ||||||
\(529\) | −254889. | + | 115510.i | −0.910835 | + | 0.412770i | ||||
\(530\) | −29831.5 | −0.106200 | ||||||||
\(531\) | −7350.60 | −0.0260696 | ||||||||
\(532\) | 80537.1 | 0.284559 | ||||||||
\(533\) | 1743.39 | 0.00613679 | ||||||||
\(534\) | 49502.5i | 0.173598i | ||||||||
\(535\) | −102001. | −0.356368 | ||||||||
\(536\) | 36848.2i | 0.128259i | ||||||||
\(537\) | −95794.8 | −0.332195 | ||||||||
\(538\) | −210137. | −0.726001 | ||||||||
\(539\) | 4860.95i | 0.0167318i | ||||||||
\(540\) | − | 19832.3i | − | 0.0680120i | ||||||
\(541\) | −104556. | −0.357234 | −0.178617 | − | 0.983919i | \(-0.557162\pi\) | ||||
−0.178617 | + | 0.983919i | \(0.557162\pi\) | |||||||
\(542\) | 145415. | 0.495006 | ||||||||
\(543\) | 102988.i | 0.349292i | ||||||||
\(544\) | 468381.i | 1.58271i | ||||||||
\(545\) | −22704.8 | −0.0764405 | ||||||||
\(546\) | 799.560i | 0.00268204i | ||||||||
\(547\) | 77964.8 | 0.260570 | 0.130285 | − | 0.991477i | \(-0.458411\pi\) | ||||
0.130285 | + | 0.991477i | \(0.458411\pi\) | |||||||
\(548\) | 245606.i | 0.817859i | ||||||||
\(549\) | − | 166669.i | − | 0.552982i | ||||||
\(550\) | 135767.i | 0.448817i | ||||||||
\(551\) | − | 109466.i | − | 0.360558i | ||||||
\(552\) | −32734.1 | − | 151536.i | −0.107429 | − | 0.497321i | ||||
\(553\) | 215186. | 0.703661 | ||||||||
\(554\) | 149842. | 0.488220 | ||||||||
\(555\) | −165188. | −0.536282 | ||||||||
\(556\) | 113008. | 0.365562 | ||||||||
\(557\) | 336204.i | 1.08366i | 0.840488 | + | 0.541830i | \(0.182268\pi\) | ||||
−0.840488 | + | 0.541830i | \(0.817732\pi\) | |||||||
\(558\) | 99962.4 | 0.321047 | ||||||||
\(559\) | 1773.49i | 0.00567552i | ||||||||
\(560\) | 44937.7 | 0.143296 | ||||||||
\(561\) | −319352. | −1.01472 | ||||||||
\(562\) | 86738.2i | 0.274624i | ||||||||
\(563\) | 168359.i | 0.531153i | 0.964090 | + | 0.265576i | \(0.0855622\pi\) | ||||
−0.964090 | + | 0.265576i | \(0.914438\pi\) | |||||||
\(564\) | 95995.6 | 0.301782 | ||||||||
\(565\) | −104871. | −0.328518 | ||||||||
\(566\) | 259939.i | 0.811406i | ||||||||
\(567\) | − | 35980.6i | − | 0.111919i | ||||||
\(568\) | 91837.8 | 0.284659 | ||||||||
\(569\) | − | 165559.i | − | 0.511361i | −0.966761 | − | 0.255681i | \(-0.917700\pi\) | ||
0.966761 | − | 0.255681i | \(-0.0822996\pi\) | |||||||
\(570\) | −17043.6 | −0.0524579 | ||||||||
\(571\) | − | 41362.8i | − | 0.126864i | −0.997986 | − | 0.0634318i | \(-0.979795\pi\) | ||
0.997986 | − | 0.0634318i | \(-0.0202045\pi\) | |||||||
\(572\) | 2552.43i | 0.00780120i | ||||||||
\(573\) | − | 35141.4i | − | 0.107031i | ||||||
\(574\) | 112634.i | 0.341858i | ||||||||
\(575\) | −54098.8 | − | 250439.i | −0.163626 | − | 0.757472i | ||||
\(576\) | 24515.2 | 0.0738908 | ||||||||
\(577\) | 302679. | 0.909139 | 0.454569 | − | 0.890711i | \(-0.349793\pi\) | ||||
0.454569 | + | 0.890711i | \(0.349793\pi\) | |||||||
\(578\) | 227580. | 0.681205 | ||||||||
\(579\) | 283951. | 0.847005 | ||||||||
\(580\) | − | 113030.i | − | 0.335998i | ||||||
\(581\) | −255687. | −0.757453 | ||||||||
\(582\) | − | 79217.4i | − | 0.233870i | ||||||
\(583\) | −172772. | −0.508318 | ||||||||
\(584\) | −46864.6 | −0.137410 | ||||||||
\(585\) | 494.193i | 0.00144406i | ||||||||
\(586\) | 112302.i | 0.327033i | ||||||||
\(587\) | 75857.9 | 0.220153 | 0.110076 | − | 0.993923i | \(-0.464890\pi\) | ||||
0.110076 | + | 0.993923i | \(0.464890\pi\) | |||||||
\(588\) | 2169.60 | 0.00627517 | ||||||||
\(589\) | 250903.i | 0.723227i | ||||||||
\(590\) | 6522.67i | 0.0187379i | ||||||||
\(591\) | 181248. | 0.518916 | ||||||||
\(592\) | 205777.i | 0.587154i | ||||||||
\(593\) | −204326. | −0.581050 | −0.290525 | − | 0.956867i | \(-0.593830\pi\) | ||||
−0.290525 | + | 0.956867i | \(0.593830\pi\) | |||||||
\(594\) | 39327.0i | 0.111460i | ||||||||
\(595\) | − | 259269.i | − | 0.732347i | ||||||
\(596\) | − | 415302.i | − | 1.16915i | ||||||
\(597\) | 296137.i | 0.830890i | ||||||||
\(598\) | 348.229 | + | 1612.06i | 0.000973784 | + | 0.00450794i | ||||
\(599\) | −485028. | −1.35180 | −0.675901 | − | 0.736992i | \(-0.736245\pi\) | ||||
−0.675901 | + | 0.736992i | \(0.736245\pi\) | |||||||
\(600\) | 141943. | 0.394285 | ||||||||
\(601\) | 172356. | 0.477175 | 0.238588 | − | 0.971121i | \(-0.423316\pi\) | ||||
0.238588 | + | 0.971121i | \(0.423316\pi\) | |||||||
\(602\) | −114579. | −0.316163 | ||||||||
\(603\) | 17640.0i | 0.0485136i | ||||||||
\(604\) | −231168. | −0.633656 | ||||||||
\(605\) | − | 54714.6i | − | 0.149483i | ||||||
\(606\) | −129326. | −0.352160 | ||||||||
\(607\) | 182994. | 0.496660 | 0.248330 | − | 0.968675i | \(-0.420118\pi\) | ||||
0.248330 | + | 0.968675i | \(0.420118\pi\) | |||||||
\(608\) | 144773.i | 0.391634i | ||||||||
\(609\) | − | 205064.i | − | 0.552909i | ||||||
\(610\) | −147897. | −0.397465 | ||||||||
\(611\) | −2392.08 | −0.00640756 | ||||||||
\(612\) | 142538.i | 0.380563i | ||||||||
\(613\) | − | 556006.i | − | 1.47965i | −0.672800 | − | 0.739824i | \(-0.734909\pi\) | ||
0.672800 | − | 0.739824i | \(-0.265091\pi\) | |||||||
\(614\) | −327468. | −0.868625 | ||||||||
\(615\) | 69617.1i | 0.184063i | ||||||||
\(616\) | −386267. | −1.01795 | ||||||||
\(617\) | − | 648584.i | − | 1.70371i | −0.523776 | − | 0.851856i | \(-0.675477\pi\) | ||
0.523776 | − | 0.851856i | \(-0.324523\pi\) | |||||||
\(618\) | 162222.i | 0.424749i | ||||||||
\(619\) | − | 565911.i | − | 1.47695i | −0.674279 | − | 0.738477i | \(-0.735545\pi\) | ||
0.674279 | − | 0.738477i | \(-0.264455\pi\) | |||||||
\(620\) | 259072.i | 0.673964i | ||||||||
\(621\) | −15670.5 | − | 72543.4i | −0.0406349 | − | 0.188111i | ||||
\(622\) | 28885.2 | 0.0746612 | ||||||||
\(623\) | −232759. | −0.599695 | ||||||||
\(624\) | 615.621 | 0.00158104 | ||||||||
\(625\) | 146672. | 0.375481 | ||||||||
\(626\) | 100102.i | 0.255442i | ||||||||
\(627\) | −98709.5 | −0.251087 | ||||||||
\(628\) | − | 272901.i | − | 0.691969i | ||||||
\(629\) | 1.18723e6 | 3.00078 | ||||||||
\(630\) | −31928.0 | −0.0804434 | ||||||||
\(631\) | − | 126414.i | − | 0.317494i | −0.987319 | − | 0.158747i | \(-0.949255\pi\) | ||
0.987319 | − | 0.158747i | \(-0.0507455\pi\) | |||||||
\(632\) | 245897.i | 0.615630i | ||||||||
\(633\) | 83427.7 | 0.208211 | ||||||||
\(634\) | 391123. | 0.973048 | ||||||||
\(635\) | − | 190788.i | − | 0.473154i | ||||||
\(636\) | 77113.8i | 0.190642i | ||||||||
\(637\) | −54.0635 | −0.000133237 | ||||||||
\(638\) | 224135.i | 0.550642i | ||||||||
\(639\) | 43964.7 | 0.107672 | ||||||||
\(640\) | 178915.i | 0.436805i | ||||||||
\(641\) | − | 321370.i | − | 0.782148i | −0.920359 | − | 0.391074i | \(-0.872104\pi\) | ||
0.920359 | − | 0.391074i | \(-0.127896\pi\) | |||||||
\(642\) | − | 90278.1i | − | 0.219034i | ||||||
\(643\) | − | 417589.i | − | 1.01001i | −0.863115 | − | 0.505007i | \(-0.831490\pi\) | ||
0.863115 | − | 0.505007i | \(-0.168510\pi\) | |||||||
\(644\) | 304183. | − | 65708.3i | 0.733439 | − | 0.158434i | ||||
\(645\) | −70819.0 | −0.170228 | ||||||||
\(646\) | 122495. | 0.293530 | ||||||||
\(647\) | 558983. | 1.33534 | 0.667668 | − | 0.744460i | \(-0.267293\pi\) | ||||
0.667668 | + | 0.744460i | \(0.267293\pi\) | |||||||
\(648\) | 41115.8 | 0.0979171 | ||||||||
\(649\) | 37776.7i | 0.0896880i | ||||||||
\(650\) | −1510.00 | −0.00357397 | ||||||||
\(651\) | 470019.i | 1.10906i | ||||||||
\(652\) | −408091. | −0.959980 | ||||||||
\(653\) | 481380. | 1.12892 | 0.564458 | − | 0.825462i | \(-0.309085\pi\) | ||||
0.564458 | + | 0.825462i | \(0.309085\pi\) | |||||||
\(654\) | − | 20095.2i | − | 0.0469827i | ||||||
\(655\) | 111624.i | 0.260182i | ||||||||
\(656\) | 86722.5 | 0.201523 | ||||||||
\(657\) | −22435.1 | −0.0519752 | ||||||||
\(658\) | − | 154543.i | − | 0.356942i | ||||||
\(659\) | 622949.i | 1.43444i | 0.696848 | + | 0.717218i | \(0.254585\pi\) | ||||
−0.696848 | + | 0.717218i | \(0.745415\pi\) | |||||||
\(660\) | −101923. | −0.233984 | ||||||||
\(661\) | − | 529511.i | − | 1.21191i | −0.795497 | − | 0.605957i | \(-0.792790\pi\) | ||
0.795497 | − | 0.605957i | \(-0.207210\pi\) | |||||||
\(662\) | −312549. | −0.713184 | ||||||||
\(663\) | − | 3551.84i | − | 0.00808027i | ||||||
\(664\) | − | 292178.i | − | 0.662692i | ||||||
\(665\) | − | 80138.3i | − | 0.181216i | ||||||
\(666\) | − | 146203.i | − | 0.329616i | ||||||
\(667\) | −89310.5 | − | 413445.i | −0.200748 | − | 0.929321i | ||||
\(668\) | −532103. | −1.19246 | ||||||||
\(669\) | −256433. | −0.572956 | ||||||||
\(670\) | 15653.1 | 0.0348700 | ||||||||
\(671\) | −856558. | −1.90244 | ||||||||
\(672\) | 271206.i | 0.600565i | ||||||||
\(673\) | −506899. | −1.11916 | −0.559579 | − | 0.828777i | \(-0.689037\pi\) | ||||
−0.559579 | + | 0.828777i | \(0.689037\pi\) | |||||||
\(674\) | 249114.i | 0.548375i | ||||||||
\(675\) | 67951.0 | 0.149138 | ||||||||
\(676\) | 340392. | 0.744879 | ||||||||
\(677\) | − | 547712.i | − | 1.19502i | −0.801862 | − | 0.597510i | \(-0.796157\pi\) | ||
0.801862 | − | 0.597510i | \(-0.203843\pi\) | |||||||
\(678\) | − | 92818.1i | − | 0.201917i | ||||||
\(679\) | 372477. | 0.807905 | ||||||||
\(680\) | 296272. | 0.640727 | ||||||||
\(681\) | − | 166763.i | − | 0.359589i | ||||||
\(682\) | − | 513733.i | − | 1.10451i | ||||||
\(683\) | −368670. | −0.790308 | −0.395154 | − | 0.918615i | \(-0.629309\pi\) | ||||
−0.395154 | + | 0.918615i | \(0.629309\pi\) | |||||||
\(684\) | 44057.3i | 0.0941686i | ||||||||
\(685\) | 244390. | 0.520838 | ||||||||
\(686\) | 235902.i | 0.501283i | ||||||||
\(687\) | 511988.i | 1.08479i | ||||||||
\(688\) | 88219.8i | 0.186376i | ||||||||
\(689\) | − | 1921.57i | − | 0.00404778i | ||||||
\(690\) | −64372.5 | + | 13905.5i | −0.135208 | + | 0.0292070i | ||||
\(691\) | 744240. | 1.55868 | 0.779340 | − | 0.626601i | \(-0.215555\pi\) | ||||
0.779340 | + | 0.626601i | \(0.215555\pi\) | |||||||
\(692\) | −311337. | −0.650158 | ||||||||
\(693\) | −184914. | −0.385038 | ||||||||
\(694\) | 316549. | 0.657236 | ||||||||
\(695\) | − | 112449.i | − | 0.232801i | ||||||
\(696\) | 234330. | 0.483738 | ||||||||
\(697\) | − | 500348.i | − | 1.02993i | ||||||
\(698\) | 323457. | 0.663905 | ||||||||
\(699\) | −426477. | −0.872854 | ||||||||
\(700\) | 284927.i | 0.581483i | ||||||||
\(701\) | − | 523105.i | − | 1.06452i | −0.846582 | − | 0.532258i | \(-0.821343\pi\) | ||
0.846582 | − | 0.532258i | \(-0.178657\pi\) | |||||||
\(702\) | −437.395 | −0.000887563 | ||||||||
\(703\) | 366965. | 0.742530 | ||||||||
\(704\) | − | 125990.i | − | 0.254209i | ||||||
\(705\) | − | 95520.3i | − | 0.192184i | ||||||
\(706\) | −437817. | −0.878383 | ||||||||
\(707\) | − | 608086.i | − | 1.21654i | ||||||
\(708\) | 16861.0 | 0.0336369 | ||||||||
\(709\) | 344738.i | 0.685798i | 0.939372 | + | 0.342899i | \(0.111409\pi\) | ||||
−0.939372 | + | 0.342899i | \(0.888591\pi\) | |||||||
\(710\) | − | 39012.7i | − | 0.0773909i | ||||||
\(711\) | 117716.i | 0.232861i | ||||||||
\(712\) | − | 265978.i | − | 0.524670i | ||||||
\(713\) | 204706. | + | 947643.i | 0.402671 | + | 1.86409i | ||||
\(714\) | 229471. | 0.450123 | ||||||||
\(715\) | 2539.79 | 0.00496805 | ||||||||
\(716\) | 219736. | 0.428623 | ||||||||
\(717\) | 293896. | 0.571683 | ||||||||
\(718\) | − | 320890.i | − | 0.622455i | ||||||
\(719\) | −811269. | −1.56930 | −0.784652 | − | 0.619937i | \(-0.787158\pi\) | ||||
−0.784652 | + | 0.619937i | \(0.787158\pi\) | |||||||
\(720\) | 24582.9i | 0.0474208i | ||||||||
\(721\) | −762761. | −1.46730 | ||||||||
\(722\) | −225404. | −0.432401 | ||||||||
\(723\) | 137513.i | 0.263068i | ||||||||
\(724\) | − | 236237.i | − | 0.450683i | ||||||
\(725\) | 387271. | 0.736783 | ||||||||
\(726\) | 48426.1 | 0.0918769 | ||||||||
\(727\) | 339414.i | 0.642186i | 0.947048 | + | 0.321093i | \(0.104050\pi\) | ||||
−0.947048 | + | 0.321093i | \(0.895950\pi\) | |||||||
\(728\) | − | 4296.06i | − | 0.00810601i | ||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 19908.1i | 0.0373580i | ||||||||
\(731\) | 508986. | 0.952513 | ||||||||
\(732\) | 382310.i | 0.713500i | ||||||||
\(733\) | 372296.i | 0.692917i | 0.938065 | + | 0.346458i | \(0.112616\pi\) | ||||
−0.938065 | + | 0.346458i | \(0.887384\pi\) | |||||||
\(734\) | 127710.i | 0.237046i | ||||||||
\(735\) | − | 2158.86i | − | 0.00399622i | ||||||
\(736\) | 118117. | + | 546799.i | 0.218050 | + | 1.00942i | ||||
\(737\) | 90656.6 | 0.166903 | ||||||||
\(738\) | −61615.8 | −0.113130 | ||||||||
\(739\) | −641928. | −1.17543 | −0.587716 | − | 0.809067i | \(-0.699973\pi\) | ||||
−0.587716 | + | 0.809067i | \(0.699973\pi\) | |||||||
\(740\) | 378913. | 0.691952 | ||||||||
\(741\) | − | 1097.85i | − | 0.00199943i | ||||||
\(742\) | 124145. | 0.225488 | ||||||||
\(743\) | 866593.i | 1.56978i | 0.619638 | + | 0.784888i | \(0.287279\pi\) | ||||
−0.619638 | + | 0.784888i | \(0.712721\pi\) | |||||||
\(744\) | −537101. | −0.970308 | ||||||||
\(745\) | −413246. | −0.744554 | ||||||||
\(746\) | − | 72636.4i | − | 0.130520i | ||||||
\(747\) | − | 139872.i | − | 0.250662i | ||||||
\(748\) | 732538. | 1.30926 | ||||||||
\(749\) | 424484. | 0.756655 | ||||||||
\(750\) | − | 138106.i | − | 0.245522i | ||||||
\(751\) | 516803.i | 0.916316i | 0.888871 | + | 0.458158i | \(0.151491\pi\) | ||||
−0.888871 | + | 0.458158i | \(0.848509\pi\) | |||||||
\(752\) | −118990. | −0.210415 | ||||||||
\(753\) | 180911.i | 0.319062i | ||||||||
\(754\) | −2492.83 | −0.00438481 | ||||||||
\(755\) | 230023.i | 0.403532i | ||||||||
\(756\) | 82533.2i | 0.144406i | ||||||||
\(757\) | 520664.i | 0.908586i | 0.890852 | + | 0.454293i | \(0.150108\pi\) | ||||
−0.890852 | + | 0.454293i | \(0.849892\pi\) | |||||||
\(758\) | 186976.i | 0.325422i | ||||||||
\(759\) | −372820. | + | 80534.8i | −0.647165 | + | 0.139798i | ||||
\(760\) | 91575.6 | 0.158545 | ||||||||
\(761\) | −700906. | −1.21029 | −0.605146 | − | 0.796114i | \(-0.706885\pi\) | ||||
−0.605146 | + | 0.796114i | \(0.706885\pi\) | |||||||
\(762\) | 168860. | 0.290815 | ||||||||
\(763\) | 94487.1 | 0.162302 | ||||||||
\(764\) | 80608.2i | 0.138100i | ||||||||
\(765\) | 141832. | 0.242354 | ||||||||
\(766\) | − | 190283.i | − | 0.324297i | ||||||
\(767\) | −420.152 | −0.000714194 | ||||||||
\(768\) | −233839. | −0.396456 | ||||||||
\(769\) | 1.03699e6i | 1.75357i | 0.480886 | + | 0.876783i | \(0.340315\pi\) | ||||
−0.480886 | + | 0.876783i | \(0.659685\pi\) | |||||||
\(770\) | 164086.i | 0.276752i | ||||||||
\(771\) | 261614. | 0.440101 | ||||||||
\(772\) | −651333. | −1.09287 | ||||||||
\(773\) | − | 90854.6i | − | 0.152050i | −0.997106 | − | 0.0760252i | \(-0.975777\pi\) | ||
0.997106 | − | 0.0760252i | \(-0.0242230\pi\) | |||||||
\(774\) | − | 62679.6i | − | 0.104627i | ||||||
\(775\) | −887652. | −1.47788 | ||||||||
\(776\) | 425637.i | 0.706832i | ||||||||
\(777\) | 687441. | 1.13866 | ||||||||
\(778\) | 516881.i | 0.853948i | ||||||||
\(779\) | − | 154654.i | − | 0.254851i | ||||||
\(780\) | − | 1133.59i | − | 0.00186323i | ||||||
\(781\) | − | 225946.i | − | 0.370427i | ||||||
\(782\) | 462654. | − | 99940.5i | 0.756559 | − | 0.163429i | ||||
\(783\) | 112179. | 0.182973 | ||||||||
\(784\) | −2689.31 | −0.00437530 | ||||||||
\(785\) | −271550. | −0.440667 | ||||||||
\(786\) | −98795.3 | −0.159916 | ||||||||
\(787\) | − | 672862.i | − | 1.08637i | −0.839614 | − | 0.543183i | \(-0.817219\pi\) | ||
0.839614 | − | 0.543183i | \(-0.182781\pi\) | |||||||
\(788\) | −415750. | −0.669545 | ||||||||
\(789\) | − | 476525.i | − | 0.765477i | ||||||
\(790\) | 104457. | 0.167373 | ||||||||
\(791\) | 436427. | 0.697524 | ||||||||
\(792\) | − | 211305.i | − | 0.336868i | ||||||
\(793\) | − | 9526.64i | − | 0.0151493i | ||||||
\(794\) | −422574. | −0.670288 | ||||||||
\(795\) | 76731.9 | 0.121406 | ||||||||
\(796\) | − | 679285.i | − | 1.07208i | ||||||
\(797\) | − | 505332.i | − | 0.795537i | −0.917486 | − | 0.397769i | \(-0.869785\pi\) | ||
0.917486 | − | 0.397769i | \(-0.130215\pi\) | |||||||
\(798\) | 70927.8 | 0.111381 | ||||||||
\(799\) | 686517.i | 1.07537i | ||||||||
\(800\) | −512183. | −0.800286 | ||||||||
\(801\) | − | 127329.i | − | 0.198456i | ||||||
\(802\) | − | 263356.i | − | 0.409444i | ||||||
\(803\) | 115300.i | 0.178812i | ||||||||
\(804\) | − | 40463.0i | − | 0.0625959i | ||||||
\(805\) | −65382.9 | − | 302677.i | −0.100896 | − | 0.467076i | ||||
\(806\) | 5713.74 | 0.00879529 | ||||||||
\(807\) | 540509. | 0.829958 | ||||||||
\(808\) | 694871. | 1.06434 | ||||||||
\(809\) | −9994.35 | −0.0152707 | −0.00763533 | − | 0.999971i | \(-0.502430\pi\) | ||||
−0.00763533 | + | 0.999971i | \(0.502430\pi\) | |||||||
\(810\) | − | 17466.0i | − | 0.0266210i | ||||||
\(811\) | 682250. | 1.03729 | 0.518647 | − | 0.854988i | \(-0.326436\pi\) | ||||
0.518647 | + | 0.854988i | \(0.326436\pi\) | |||||||
\(812\) | 470380.i | 0.713405i | ||||||||
\(813\) | −374033. | −0.565886 | ||||||||
\(814\) | −751375. | −1.13399 | ||||||||
\(815\) | 406071.i | 0.611345i | ||||||||
\(816\) | − | 176681.i | − | 0.265344i | ||||||
\(817\) | 157324. | 0.235695 | ||||||||
\(818\) | −83448.1 | −0.124712 | ||||||||
\(819\) | − | 2056.61i | − | 0.00306609i | ||||||
\(820\) | − | 159689.i | − | 0.237491i | ||||||
\(821\) | −514646. | −0.763523 | −0.381762 | − | 0.924261i | \(-0.624682\pi\) | ||||
−0.381762 | + | 0.924261i | \(0.624682\pi\) | |||||||
\(822\) | 216302.i | 0.320123i | ||||||||
\(823\) | 992478. | 1.46528 | 0.732641 | − | 0.680615i | \(-0.238287\pi\) | ||||
0.732641 | + | 0.680615i | \(0.238287\pi\) | |||||||
\(824\) | − | 871623.i | − | 1.28373i | ||||||
\(825\) | − | 349218.i | − | 0.513084i | ||||||
\(826\) | − | 27144.5i | − | 0.0397852i | ||||||
\(827\) | 68379.1i | 0.0999798i | 0.998750 | + | 0.0499899i | \(0.0159189\pi\) | ||||
−0.998750 | + | 0.0499899i | \(0.984081\pi\) | |||||||
\(828\) | 35945.3 | + | 166402.i | 0.0524303 | + | 0.242715i | ||||
\(829\) | 548249. | 0.797754 | 0.398877 | − | 0.917004i | \(-0.369400\pi\) | ||||
0.398877 | + | 0.917004i | \(0.369400\pi\) | |||||||
\(830\) | −124117. | −0.180168 | ||||||||
\(831\) | −385422. | −0.558128 | ||||||||
\(832\) | 1401.26 | 0.00202429 | ||||||||
\(833\) | 15516.0i | 0.0223609i | ||||||||
\(834\) | 99524.9 | 0.143087 | ||||||||
\(835\) | 529468.i | 0.759393i | ||||||||
\(836\) | 226422. | 0.323971 | ||||||||
\(837\) | −257121. | −0.367018 | ||||||||
\(838\) | − | 164706.i | − | 0.234542i | ||||||
\(839\) | 404909.i | 0.575220i | 0.957748 | + | 0.287610i | \(0.0928607\pi\) | ||||
−0.957748 | + | 0.287610i | \(0.907139\pi\) | |||||||
\(840\) | 171550. | 0.243126 | ||||||||
\(841\) | −67942.9 | −0.0960621 | ||||||||
\(842\) | − | 385183.i | − | 0.543304i | ||||||
\(843\) | − | 223106.i | − | 0.313947i | ||||||
\(844\) | −191368. | −0.268649 | ||||||||
\(845\) | − | 338706.i | − | 0.474362i | ||||||
\(846\) | 84541.9 | 0.118122 | ||||||||
\(847\) | 227698.i | 0.317389i | ||||||||
\(848\) | − | 95585.6i | − | 0.132923i | ||||||
\(849\) | − | 668609.i | − | 0.927592i | ||||||
\(850\) | 433365.i | 0.599814i | ||||||||
\(851\) | 1.38600e6 | − | 299398.i | 1.91384 | − | 0.413419i | ||||
\(852\) | −100847. | −0.138926 | ||||||||
\(853\) | −662146. | −0.910030 | −0.455015 | − | 0.890484i | \(-0.650366\pi\) | ||||
−0.455015 | + | 0.890484i | \(0.650366\pi\) | |||||||
\(854\) | 615480. | 0.843915 | ||||||||
\(855\) | 43839.2 | 0.0599694 | ||||||||
\(856\) | 485066.i | 0.661993i | ||||||||
\(857\) | −644207. | −0.877130 | −0.438565 | − | 0.898700i | \(-0.644513\pi\) | ||||
−0.438565 | + | 0.898700i | \(0.644513\pi\) | |||||||
\(858\) | 2247.89i | 0.00305351i | ||||||||
\(859\) | −439207. | −0.595228 | −0.297614 | − | 0.954686i | \(-0.596191\pi\) | ||||
−0.297614 | + | 0.954686i | \(0.596191\pi\) | |||||||
\(860\) | 162446. | 0.219641 | ||||||||
\(861\) | − | 289715.i | − | 0.390810i | ||||||
\(862\) | − | 664965.i | − | 0.894920i | ||||||
\(863\) | −523440. | −0.702823 | −0.351411 | − | 0.936221i | \(-0.614298\pi\) | ||||
−0.351411 | + | 0.936221i | \(0.614298\pi\) | |||||||
\(864\) | −148361. | −0.198744 | ||||||||
\(865\) | 309796.i | 0.414041i | ||||||||
\(866\) | 117542.i | 0.156733i | ||||||||
\(867\) | −585376. | −0.778748 | ||||||||
\(868\) | − | 1.07814e6i | − | 1.43099i | ||||||
\(869\) | 604975. | 0.801120 | ||||||||
\(870\) | − | 99543.6i | − | 0.131515i | ||||||
\(871\) | 1008.28i | 0.00132906i | ||||||||
\(872\) | 107972.i | 0.141997i | ||||||||
\(873\) | 203762.i | 0.267358i | ||||||||
\(874\) | 143003. | − | 30890.9i | 0.187207 | − | 0.0404397i | ||||
\(875\) | 649369. | 0.848156 | ||||||||
\(876\) | 51462.0 | 0.0670624 | ||||||||
\(877\) | −328707. | −0.427376 | −0.213688 | − | 0.976902i | \(-0.568548\pi\) | ||||
−0.213688 | + | 0.976902i | \(0.568548\pi\) | |||||||
\(878\) | −397777. | −0.516001 | ||||||||
\(879\) | − | 288860.i | − | 0.373861i | ||||||
\(880\) | 126338. | 0.163143 | ||||||||
\(881\) | − | 1.45433e6i | − | 1.87375i | −0.349663 | − | 0.936875i | \(-0.613704\pi\) | ||
0.349663 | − | 0.936875i | \(-0.386296\pi\) | |||||||
\(882\) | 1910.74 | 0.00245620 | ||||||||
\(883\) | −342671. | −0.439497 | −0.219748 | − | 0.975557i | \(-0.570524\pi\) | ||||
−0.219748 | + | 0.975557i | \(0.570524\pi\) | |||||||
\(884\) | 8147.28i | 0.0104258i | ||||||||
\(885\) | − | 16777.5i | − | 0.0214210i | ||||||
\(886\) | 13597.0 | 0.0173211 | ||||||||
\(887\) | 819987. | 1.04222 | 0.521111 | − | 0.853489i | \(-0.325518\pi\) | ||||
0.521111 | + | 0.853489i | \(0.325518\pi\) | |||||||
\(888\) | 785552.i | 0.996206i | ||||||||
\(889\) | 793973.i | 1.00462i | ||||||||
\(890\) | −112988. | −0.142643 | ||||||||
\(891\) | − | 101156.i | − | 0.127420i | ||||||
\(892\) | 588211. | 0.739271 | ||||||||
\(893\) | 212198.i | 0.266096i | ||||||||
\(894\) | − | 365751.i | − | 0.457625i | ||||||
\(895\) | − | 218648.i | − | 0.272960i | ||||||
\(896\) | − | 744566.i | − | 0.927443i | ||||||
\(897\) | −895.708 | − | 4146.50i | −0.00111322 | − | 0.00515343i | ||||
\(898\) | 511417. | 0.634195 | ||||||||
\(899\) | −1.46541e6 | −1.81317 | ||||||||
\(900\) | −155867. | −0.192429 | ||||||||
\(901\) | −551483. | −0.679333 | ||||||||
\(902\) | 316660.i | 0.389206i | ||||||||
\(903\) | 294717. | 0.361435 | ||||||||
\(904\) | 498714.i | 0.610260i | ||||||||
\(905\) | −235068. | −0.287009 | ||||||||
\(906\) | −203586. | −0.248023 | ||||||||
\(907\) | − | 645547.i | − | 0.784718i | −0.919812 | − | 0.392359i | \(-0.871659\pi\) | ||
0.919812 | − | 0.392359i | \(-0.128341\pi\) | |||||||
\(908\) | 382525.i | 0.463969i | ||||||||
\(909\) | 332650. | 0.402587 | ||||||||
\(910\) | −1824.97 | −0.00220380 | ||||||||
\(911\) | 594043.i | 0.715782i | 0.933763 | + | 0.357891i | \(0.116504\pi\) | ||||
−0.933763 | + | 0.357891i | \(0.883496\pi\) | |||||||
\(912\) | − | 54610.8i | − | 0.0656582i | ||||||
\(913\) | −718838. | −0.862362 | ||||||||
\(914\) | − | 780375.i | − | 0.934138i | ||||||
\(915\) | 380417. | 0.454378 | ||||||||
\(916\) | − | 1.17441e6i | − | 1.39968i | ||||||
\(917\) | − | 464531.i | − | 0.552429i | ||||||
\(918\) | 125531.i | 0.148958i | ||||||||
\(919\) | 1.36511e6i | 1.61636i | 0.588938 | + | 0.808178i | \(0.299546\pi\) | ||||
−0.588938 | + | 0.808178i | \(0.700454\pi\) | |||||||
\(920\) | 345875. | − | 74714.4i | 0.408643 | − | 0.0882731i | ||||
\(921\) | 842307. | 0.993004 | ||||||||
\(922\) | 434932. | 0.511634 | ||||||||
\(923\) | 2512.97 | 0.00294974 | ||||||||
\(924\) | 424160. | 0.496805 | ||||||||
\(925\) | 1.29826e6i | 1.51732i | ||||||||
\(926\) | 118570. | 0.138278 | ||||||||
\(927\) | − | 417264.i | − | 0.485570i | ||||||
\(928\) | −845552. | −0.981849 | ||||||||
\(929\) | 1.05613e6 | 1.22374 | 0.611868 | − | 0.790960i | \(-0.290418\pi\) | ||||
0.611868 | + | 0.790960i | \(0.290418\pi\) | |||||||
\(930\) | 228161.i | 0.263800i | ||||||||
\(931\) | 4795.89i | 0.00553312i | ||||||||
\(932\) | 978263. | 1.12622 | ||||||||
\(933\) | −74298.0 | −0.0853521 | ||||||||
\(934\) | 407469.i | 0.467090i | ||||||||
\(935\) | − | 728910.i | − | 0.833779i | ||||||
\(936\) | 2350.13 | 0.00268251 | ||||||||
\(937\) | 683295.i | 0.778268i | 0.921181 | + | 0.389134i | \(0.127226\pi\) | ||||
−0.921181 | + | 0.389134i | \(0.872774\pi\) | |||||||
\(938\) | −65141.3 | −0.0740374 | ||||||||
\(939\) | − | 257480.i | − | 0.292019i | ||||||
\(940\) | 219107.i | 0.247970i | ||||||||
\(941\) | 110797.i | 0.125126i | 0.998041 | + | 0.0625631i | \(0.0199275\pi\) | ||||
−0.998041 | + | 0.0625631i | \(0.980073\pi\) | |||||||
\(942\) | − | 240340.i | − | 0.270847i | ||||||
\(943\) | −126178. | − | 584118.i | −0.141893 | − | 0.656866i | ||||
\(944\) | −20899.8 | −0.0234530 | ||||||||
\(945\) | 82124.5 | 0.0919622 | ||||||||
\(946\) | −322127. | −0.359952 | ||||||||
\(947\) | −1.07809e6 | −1.20214 | −0.601071 | − | 0.799195i | \(-0.705259\pi\) | ||||
−0.601071 | + | 0.799195i | \(0.705259\pi\) | |||||||
\(948\) | − | 270020.i | − | 0.300455i | ||||||
\(949\) | −1282.36 | −0.00142390 | ||||||||
\(950\) | 133950.i | 0.148421i | ||||||||
\(951\) | −1.00604e6 | −1.11238 | ||||||||
\(952\) | −1.23295e6 | −1.36042 | ||||||||
\(953\) | − | 828193.i | − | 0.911897i | −0.890006 | − | 0.455948i | \(-0.849300\pi\) | ||
0.890006 | − | 0.455948i | \(-0.150700\pi\) | |||||||
\(954\) | 67913.0i | 0.0746201i | ||||||||
\(955\) | 80209.0 | 0.0879461 | ||||||||
\(956\) | −674145. | −0.737628 | ||||||||
\(957\) | − | 576516.i | − | 0.629489i | ||||||
\(958\) | 305096.i | 0.332434i | ||||||||
\(959\) | −1.01704e6 | −1.10586 | ||||||||
\(960\) | 55955.0i | 0.0607151i | ||||||||
\(961\) | 2.43529e6 | 2.63696 | ||||||||
\(962\) | − | 8356.80i | − | 0.00903004i | ||||||
\(963\) | 232211.i | 0.250398i | ||||||||
\(964\) | − | 315431.i | − | 0.339430i | ||||||
\(965\) | 648108.i | 0.695973i | ||||||||
\(966\) | 267890. | − | 57868.3i | 0.287079 | − | 0.0620136i | ||||
\(967\) | 464748. | 0.497010 | 0.248505 | − | 0.968631i | \(-0.420061\pi\) | ||||
0.248505 | + | 0.968631i | \(0.420061\pi\) | |||||||
\(968\) | −260195. | −0.277682 | ||||||||
\(969\) | −315078. | −0.335560 | ||||||||
\(970\) | 180811. | 0.192168 | ||||||||
\(971\) | − | 1.21507e6i | − | 1.28873i | −0.764719 | − | 0.644364i | \(-0.777122\pi\) | ||
0.764719 | − | 0.644364i | \(-0.222878\pi\) | |||||||
\(972\) | −45149.3 | −0.0477880 | ||||||||
\(973\) | 467962.i | 0.494294i | ||||||||
\(974\) | 339225. | 0.357577 | ||||||||
\(975\) | 3884.00 | 0.00408573 | ||||||||
\(976\) | − | 473888.i | − | 0.497481i | ||||||
\(977\) | 565350.i | 0.592282i | 0.955144 | + | 0.296141i | \(0.0956997\pi\) | ||||
−0.955144 | + | 0.296141i | \(0.904300\pi\) | |||||||
\(978\) | −359400. | −0.375751 | ||||||||
\(979\) | −654379. | −0.682754 | ||||||||
\(980\) | 4952.04i | 0.00515622i | ||||||||
\(981\) | 51688.6i | 0.0537102i | ||||||||
\(982\) | −290665. | −0.301418 | ||||||||
\(983\) | 977831.i | 1.01195i | 0.862550 | + | 0.505973i | \(0.168866\pi\) | ||||
−0.862550 | + | 0.505973i | \(0.831134\pi\) | |||||||
\(984\) | 331063. | 0.341917 | ||||||||
\(985\) | 413691.i | 0.426387i | ||||||||
\(986\) | 715434.i | 0.735895i | ||||||||
\(987\) | 397513.i | 0.408053i | ||||||||
\(988\) | 2518.27i | 0.00257981i | ||||||||
\(989\) | 594202. | − | 128357.i | 0.607494 | − | 0.131228i | ||||
\(990\) | −89762.4 | −0.0915850 | ||||||||
\(991\) | −204101. | −0.207825 | −0.103913 | − | 0.994586i | \(-0.533136\pi\) | ||||
−0.103913 | + | 0.994586i | \(0.533136\pi\) | |||||||
\(992\) | 1.93806e6 | 1.96945 | ||||||||
\(993\) | 803931. | 0.815306 | ||||||||
\(994\) | 162354.i | 0.164320i | ||||||||
\(995\) | −675921. | −0.682731 | ||||||||
\(996\) | 320841.i | 0.323423i | ||||||||
\(997\) | −171468. | −0.172502 | −0.0862508 | − | 0.996273i | \(-0.527489\pi\) | ||||
−0.0862508 | + | 0.996273i | \(0.527489\pi\) | |||||||
\(998\) | −204269. | −0.205089 | ||||||||
\(999\) | 376060.i | 0.376814i |
(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 | 69.5.d.a.22.6 | yes | 16 | |
3.2 | odd | 2 | 207.5.d.c.91.11 | 16 | |||
4.3 | odd | 2 | 1104.5.c.c.1057.5 | 16 | |||
23.22 | odd | 2 | inner | 69.5.d.a.22.5 | ✓ | 16 | |
69.68 | even | 2 | 207.5.d.c.91.12 | 16 | |||
92.91 | even | 2 | 1104.5.c.c.1057.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.5.d.a.22.5 | ✓ | 16 | 23.22 | odd | 2 | inner | |
69.5.d.a.22.6 | yes | 16 | 1.1 | even | 1 | trivial | |
207.5.d.c.91.11 | 16 | 3.2 | odd | 2 | |||
207.5.d.c.91.12 | 16 | 69.68 | even | 2 | |||
1104.5.c.c.1057.4 | 16 | 92.91 | even | 2 | |||
1104.5.c.c.1057.5 | 16 | 4.3 | odd | 2 |