Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(1,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.a (trivial) |
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: | yes |
Analytic conductor: | \(72.1727189158\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{4081}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1020 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(32.4414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −141.648 | −1.09261 | −0.546306 | − | 0.837586i | \(-0.683966\pi\) | ||||
−0.546306 | + | 0.837586i | \(0.683966\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −113.296 | −0.282315 | −0.141157 | − | 0.989987i | \(-0.545082\pi\) | ||||
−0.141157 | + | 0.989987i | \(0.545082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −61.7038 | −0.101264 | −0.0506318 | − | 0.998717i | \(-0.516123\pi\) | ||||
−0.0506318 | + | 0.998717i | \(0.516123\pi\) | |||||||
\(14\) | 566.592 | 0.772593 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1670.48 | −1.40191 | −0.700954 | − | 0.713207i | \(-0.747242\pi\) | ||||
−0.700954 | + | 0.713207i | \(0.747242\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −662.241 | −0.420854 | −0.210427 | − | 0.977610i | \(-0.567485\pi\) | ||||
−0.210427 | + | 0.977610i | \(0.567485\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 453.185 | 0.199627 | ||||||||
\(23\) | −86.4812 | −0.0340880 | −0.0170440 | − | 0.999855i | \(-0.505426\pi\) | ||||
−0.0170440 | + | 0.999855i | \(0.505426\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 246.815 | 0.0716042 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2266.37 | −0.546306 | ||||||||
\(29\) | 3233.30 | 0.713922 | 0.356961 | − | 0.934119i | \(-0.383813\pi\) | ||||
0.356961 | + | 0.934119i | \(0.383813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3812.24 | −0.712486 | −0.356243 | − | 0.934393i | \(-0.615942\pi\) | ||||
−0.356243 | + | 0.934393i | \(0.615942\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6681.92 | 0.991298 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10249.6 | −1.23084 | −0.615419 | − | 0.788200i | \(-0.711013\pi\) | ||||
−0.615419 | + | 0.788200i | \(0.711013\pi\) | |||||||
\(38\) | 2648.96 | 0.297589 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13459.4 | 1.25045 | 0.625227 | − | 0.780443i | \(-0.285007\pi\) | ||||
0.625227 | + | 0.780443i | \(0.285007\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4697.57 | 0.387438 | 0.193719 | − | 0.981057i | \(-0.437945\pi\) | ||||
0.193719 | + | 0.981057i | \(0.437945\pi\) | |||||||
\(44\) | −1812.74 | −0.141157 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 345.925 | 0.0241039 | ||||||||
\(47\) | 15264.8 | 1.00797 | 0.503984 | − | 0.863713i | \(-0.331867\pi\) | ||||
0.503984 | + | 0.863713i | \(0.331867\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3257.19 | 0.193800 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −987.260 | −0.0506318 | ||||||||
\(53\) | −498.632 | −0.0243832 | −0.0121916 | − | 0.999926i | \(-0.503881\pi\) | ||||
−0.0121916 | + | 0.999926i | \(0.503881\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9065.48 | 0.386296 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12933.2 | −0.504819 | ||||||||
\(59\) | 15294.3 | 0.572005 | 0.286002 | − | 0.958229i | \(-0.407673\pi\) | ||||
0.286002 | + | 0.958229i | \(0.407673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31811.3 | −1.09460 | −0.547302 | − | 0.836935i | \(-0.684345\pi\) | ||||
−0.547302 | + | 0.836935i | \(0.684345\pi\) | |||||||
\(62\) | 15249.0 | 0.503803 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −49274.9 | −1.34103 | −0.670516 | − | 0.741895i | \(-0.733927\pi\) | ||||
−0.670516 | + | 0.741895i | \(0.733927\pi\) | |||||||
\(68\) | −26727.7 | −0.700954 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −21057.7 | −0.495752 | −0.247876 | − | 0.968792i | \(-0.579733\pi\) | ||||
−0.247876 | + | 0.968792i | \(0.579733\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39447.8 | −0.866394 | −0.433197 | − | 0.901299i | \(-0.642615\pi\) | ||||
−0.433197 | + | 0.901299i | \(0.642615\pi\) | |||||||
\(74\) | 40998.2 | 0.870333 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10595.8 | −0.210427 | ||||||||
\(77\) | 16048.2 | 0.308460 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 72949.3 | 1.31508 | 0.657542 | − | 0.753418i | \(-0.271596\pi\) | ||||
0.657542 | + | 0.753418i | \(0.271596\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −53837.8 | −0.884204 | ||||||||
\(83\) | −100897. | −1.60762 | −0.803808 | − | 0.594889i | \(-0.797196\pi\) | ||||
−0.803808 | + | 0.594889i | \(0.797196\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −18790.3 | −0.273960 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7250.96 | 0.0998134 | ||||||||
\(89\) | 146714. | 1.96334 | 0.981671 | − | 0.190585i | \(-0.0610384\pi\) | ||||
0.981671 | + | 0.190585i | \(0.0610384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8740.22 | 0.110642 | ||||||||
\(92\) | −1383.70 | −0.0170440 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −61059.2 | −0.712741 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 43544.9 | 0.469903 | 0.234951 | − | 0.972007i | \(-0.424507\pi\) | ||||
0.234951 | + | 0.972007i | \(0.424507\pi\) | |||||||
\(98\) | −13028.8 | −0.137037 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 49966.3 | 0.487386 | 0.243693 | − | 0.969852i | \(-0.421641\pi\) | ||||
0.243693 | + | 0.969852i | \(0.421641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 50579.6 | 0.469766 | 0.234883 | − | 0.972024i | \(-0.424529\pi\) | ||||
0.234883 | + | 0.972024i | \(0.424529\pi\) | |||||||
\(104\) | 3949.04 | 0.0358021 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1994.53 | 0.0172415 | ||||||||
\(107\) | 191553. | 1.61744 | 0.808721 | − | 0.588193i | \(-0.200160\pi\) | ||||
0.808721 | + | 0.588193i | \(0.200160\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 71531.6 | 0.576676 | 0.288338 | − | 0.957529i | \(-0.406897\pi\) | ||||
0.288338 | + | 0.957529i | \(0.406897\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −36261.9 | −0.273153 | ||||||||
\(113\) | −163395. | −1.20377 | −0.601885 | − | 0.798583i | \(-0.705583\pi\) | ||||
−0.601885 | + | 0.798583i | \(0.705583\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 51732.7 | 0.356961 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −61177.2 | −0.404468 | ||||||||
\(119\) | 236621. | 1.53174 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −148215. | −0.920298 | ||||||||
\(122\) | 127245. | 0.774002 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −60995.8 | −0.356243 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 34350.7 | 0.188984 | 0.0944922 | − | 0.995526i | \(-0.469877\pi\) | ||||
0.0944922 | + | 0.995526i | \(0.469877\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 349293. | 1.77833 | 0.889164 | − | 0.457588i | \(-0.151287\pi\) | ||||
0.889164 | + | 0.457588i | \(0.151287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 93805.1 | 0.459830 | ||||||||
\(134\) | 197100. | 0.948253 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 106911. | 0.495649 | ||||||||
\(137\) | 274334. | 1.24876 | 0.624379 | − | 0.781122i | \(-0.285352\pi\) | ||||
0.624379 | + | 0.781122i | \(0.285352\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −47842.2 | −0.210027 | −0.105013 | − | 0.994471i | \(-0.533489\pi\) | ||||
−0.105013 | + | 0.994471i | \(0.533489\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 84230.6 | 0.350549 | ||||||||
\(143\) | 6990.80 | 0.0285882 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 157791. | 0.612633 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −163993. | −0.615419 | ||||||||
\(149\) | 335645. | 1.23855 | 0.619276 | − | 0.785174i | \(-0.287426\pi\) | ||||
0.619276 | + | 0.785174i | \(0.287426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 336370. | 1.20054 | 0.600268 | − | 0.799799i | \(-0.295061\pi\) | ||||
0.600268 | + | 0.799799i | \(0.295061\pi\) | |||||||
\(152\) | 42383.4 | 0.148794 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −64192.8 | −0.218114 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 381573. | 1.23546 | 0.617729 | − | 0.786391i | \(-0.288053\pi\) | ||||
0.617729 | + | 0.786391i | \(0.288053\pi\) | |||||||
\(158\) | −291797. | −0.929905 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12249.9 | 0.0372450 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 579006. | 1.70692 | 0.853462 | − | 0.521155i | \(-0.174499\pi\) | ||||
0.853462 | + | 0.521155i | \(0.174499\pi\) | |||||||
\(164\) | 215351. | 0.625227 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 403587. | 1.13676 | ||||||||
\(167\) | −128108. | −0.355455 | −0.177728 | − | 0.984080i | \(-0.556875\pi\) | ||||
−0.177728 | + | 0.984080i | \(0.556875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −367486. | −0.989746 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 75161.2 | 0.193719 | ||||||||
\(173\) | −487187. | −1.23760 | −0.618800 | − | 0.785548i | \(-0.712381\pi\) | ||||
−0.618800 | + | 0.785548i | \(0.712381\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −29003.8 | −0.0705787 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −586855. | −1.38829 | ||||||||
\(179\) | 848235. | 1.97872 | 0.989359 | − | 0.145497i | \(-0.0464781\pi\) | ||||
0.989359 | + | 0.145497i | \(0.0464781\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −575423. | −1.30554 | −0.652771 | − | 0.757555i | \(-0.726394\pi\) | ||||
−0.652771 | + | 0.757555i | \(0.726394\pi\) | |||||||
\(182\) | −34960.9 | −0.0782355 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5534.79 | 0.0120519 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 189259. | 0.395779 | ||||||||
\(188\) | 244237. | 0.503984 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18362.7 | −0.0364211 | −0.0182105 | − | 0.999834i | \(-0.505797\pi\) | ||||
−0.0182105 | + | 0.999834i | \(0.505797\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 349513. | 0.675414 | 0.337707 | − | 0.941251i | \(-0.390349\pi\) | ||||
0.337707 | + | 0.941251i | \(0.390349\pi\) | |||||||
\(194\) | −174180. | −0.332272 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 52115.0 | 0.0968998 | ||||||||
\(197\) | 371791. | 0.682547 | 0.341274 | − | 0.939964i | \(-0.389142\pi\) | ||||
0.341274 | + | 0.939964i | \(0.389142\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 300569. | 0.538036 | 0.269018 | − | 0.963135i | \(-0.413301\pi\) | ||||
0.269018 | + | 0.963135i | \(0.413301\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −199865. | −0.344634 | ||||||||
\(203\) | −457990. | −0.780039 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −202318. | −0.332175 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15796.2 | −0.0253159 | ||||||||
\(209\) | 75029.4 | 0.118813 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 59499.2 | 0.0920036 | 0.0460018 | − | 0.998941i | \(-0.485352\pi\) | ||||
0.0460018 | + | 0.998941i | \(0.485352\pi\) | |||||||
\(212\) | −7978.11 | −0.0121916 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −766210. | −1.14370 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 539997. | 0.778470 | ||||||||
\(218\) | −286127. | −0.407772 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 103075. | 0.141962 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 866124. | 1.16632 | 0.583160 | − | 0.812357i | \(-0.301816\pi\) | ||||
0.583160 | + | 0.812357i | \(0.301816\pi\) | |||||||
\(224\) | 145048. | 0.193148 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 653581. | 0.851194 | ||||||||
\(227\) | 737058. | 0.949374 | 0.474687 | − | 0.880155i | \(-0.342561\pi\) | ||||
0.474687 | + | 0.880155i | \(0.342561\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 846501. | 1.06669 | 0.533346 | − | 0.845897i | \(-0.320935\pi\) | ||||
0.533346 | + | 0.845897i | \(0.320935\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −206931. | −0.252409 | ||||||||
\(233\) | 590760. | 0.712888 | 0.356444 | − | 0.934317i | \(-0.383989\pi\) | ||||
0.356444 | + | 0.934317i | \(0.383989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 244709. | 0.286002 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −946482. | −1.08310 | ||||||||
\(239\) | −1.60375e6 | −1.81611 | −0.908054 | − | 0.418853i | \(-0.862432\pi\) | ||||
−0.908054 | + | 0.418853i | \(0.862432\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −347071. | −0.384925 | −0.192463 | − | 0.981304i | \(-0.561647\pi\) | ||||
−0.192463 | + | 0.981304i | \(0.561647\pi\) | |||||||
\(242\) | 592860. | 0.650749 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −508981. | −0.547302 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 40862.7 | 0.0426172 | ||||||||
\(248\) | 243983. | 0.251902 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −536438. | −0.537446 | −0.268723 | − | 0.963217i | \(-0.586602\pi\) | ||||
−0.268723 | + | 0.963217i | \(0.586602\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9797.99 | 0.00962356 | ||||||||
\(254\) | −137403. | −0.133632 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −763565. | −0.721130 | −0.360565 | − | 0.932734i | \(-0.617416\pi\) | ||||
−0.360565 | + | 0.932734i | \(0.617416\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.45183e6 | 1.34483 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.39717e6 | −1.25747 | ||||||||
\(263\) | 341099. | 0.304082 | 0.152041 | − | 0.988374i | \(-0.451415\pi\) | ||||
0.152041 | + | 0.988374i | \(0.451415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −375221. | −0.325149 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −788399. | −0.670516 | ||||||||
\(269\) | −750163. | −0.632084 | −0.316042 | − | 0.948745i | \(-0.602354\pi\) | ||||
−0.316042 | + | 0.948745i | \(0.602354\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.64462e6 | −1.36033 | −0.680163 | − | 0.733061i | \(-0.738091\pi\) | ||||
−0.680163 | + | 0.733061i | \(0.738091\pi\) | |||||||
\(272\) | −427643. | −0.350477 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.09734e6 | −0.883005 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.04631e6 | −0.819337 | −0.409668 | − | 0.912235i | \(-0.634356\pi\) | ||||
−0.409668 | + | 0.912235i | \(0.634356\pi\) | |||||||
\(278\) | 191369. | 0.148511 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 54503.6 | 0.0411774 | 0.0205887 | − | 0.999788i | \(-0.493446\pi\) | ||||
0.0205887 | + | 0.999788i | \(0.493446\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −150130. | −0.111429 | −0.0557147 | − | 0.998447i | \(-0.517744\pi\) | ||||
−0.0557147 | + | 0.998447i | \(0.517744\pi\) | |||||||
\(284\) | −336923. | −0.247876 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −27963.2 | −0.0202149 | ||||||||
\(287\) | −1.90650e6 | −1.36626 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.37065e6 | 0.965344 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −631164. | −0.433197 | ||||||||
\(293\) | 1.54001e6 | 1.04799 | 0.523993 | − | 0.851723i | \(-0.324442\pi\) | ||||
0.523993 | + | 0.851723i | \(0.324442\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 655972. | 0.435167 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.34258e6 | −0.875788 | ||||||||
\(299\) | 5336.21 | 0.00345188 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −665402. | −0.423319 | ||||||||
\(302\) | −1.34548e6 | −0.848907 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −169534. | −0.105214 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 914773. | 0.553946 | 0.276973 | − | 0.960878i | \(-0.410669\pi\) | ||||
0.276973 | + | 0.960878i | \(0.410669\pi\) | |||||||
\(308\) | 256771. | 0.154230 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.59808e6 | −0.936910 | −0.468455 | − | 0.883487i | \(-0.655189\pi\) | ||||
−0.468455 | + | 0.883487i | \(0.655189\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.38412e6 | 1.37552 | 0.687760 | − | 0.725938i | \(-0.258594\pi\) | ||||
0.687760 | + | 0.725938i | \(0.258594\pi\) | |||||||
\(314\) | −1.52629e6 | −0.873601 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.16719e6 | 0.657542 | ||||||||
\(317\) | −2.00013e6 | −1.11792 | −0.558960 | − | 0.829194i | \(-0.688800\pi\) | ||||
−0.558960 | + | 0.829194i | \(0.688800\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −366320. | −0.201551 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −48999.6 | −0.0263362 | ||||||||
\(323\) | 1.10626e6 | 0.589999 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.31602e6 | −1.20698 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −861404. | −0.442102 | ||||||||
\(329\) | −2.16223e6 | −1.10132 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.48362e6 | −0.744306 | −0.372153 | − | 0.928171i | \(-0.621380\pi\) | ||||
−0.372153 | + | 0.928171i | \(0.621380\pi\) | |||||||
\(332\) | −1.61435e6 | −0.803808 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 512432. | 0.251345 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.42490e6 | −1.16311 | −0.581553 | − | 0.813508i | \(-0.697555\pi\) | ||||
−0.581553 | + | 0.813508i | \(0.697555\pi\) | |||||||
\(338\) | 1.46994e6 | 0.699856 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 431912. | 0.201145 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.91931e6 | 0.880864 | ||||||||
\(344\) | −300645. | −0.136980 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.94875e6 | 0.875116 | ||||||||
\(347\) | −1.26681e6 | −0.564793 | −0.282397 | − | 0.959298i | \(-0.591129\pi\) | ||||
−0.282397 | + | 0.959298i | \(0.591129\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.54257e6 | 1.11740 | 0.558701 | − | 0.829369i | \(-0.311300\pi\) | ||||
0.558701 | + | 0.829369i | \(0.311300\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 116015. | 0.0499067 | ||||||||
\(353\) | 1.28509e6 | 0.548906 | 0.274453 | − | 0.961601i | \(-0.411503\pi\) | ||||
0.274453 | + | 0.961601i | \(0.411503\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.34742e6 | 0.981671 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.39294e6 | −1.39916 | ||||||||
\(359\) | −4.16251e6 | −1.70459 | −0.852294 | − | 0.523063i | \(-0.824789\pi\) | ||||
−0.852294 | + | 0.523063i | \(0.824789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.03754e6 | −0.822882 | ||||||||
\(362\) | 2.30169e6 | 0.923158 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 139844. | 0.0553209 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.13066e6 | 0.438195 | 0.219098 | − | 0.975703i | \(-0.429689\pi\) | ||||
0.219098 | + | 0.975703i | \(0.429689\pi\) | |||||||
\(368\) | −22139.2 | −0.00852201 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 70630.3 | 0.0266413 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 312371. | 0.116251 | 0.0581257 | − | 0.998309i | \(-0.481488\pi\) | ||||
0.0581257 | + | 0.998309i | \(0.481488\pi\) | |||||||
\(374\) | −757037. | −0.279858 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −976948. | −0.356371 | ||||||||
\(377\) | −199507. | −0.0722943 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.19990e6 | −0.786692 | −0.393346 | − | 0.919390i | \(-0.628683\pi\) | ||||
−0.393346 | + | 0.919390i | \(0.628683\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 73450.8 | 0.0257536 | ||||||||
\(383\) | 3.93331e6 | 1.37013 | 0.685065 | − | 0.728482i | \(-0.259774\pi\) | ||||
0.685065 | + | 0.728482i | \(0.259774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.39805e6 | −0.477590 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 696719. | 0.234951 | ||||||||
\(389\) | −4.20593e6 | −1.40925 | −0.704625 | − | 0.709580i | \(-0.748885\pi\) | ||||
−0.704625 | + | 0.709580i | \(0.748885\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 144465. | 0.0477883 | ||||||||
\(392\) | −208460. | −0.0685185 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.48716e6 | −0.482634 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.39484e6 | 0.762606 | 0.381303 | − | 0.924450i | \(-0.375475\pi\) | ||||
0.381303 | + | 0.924450i | \(0.375475\pi\) | |||||||
\(398\) | −1.20228e6 | −0.380449 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.42161e6 | −1.37315 | −0.686577 | − | 0.727057i | \(-0.740888\pi\) | ||||
−0.686577 | + | 0.727057i | \(0.740888\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 235230. | 0.0721488 | ||||||||
\(404\) | 799460. | 0.243693 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.83196e6 | 0.551571 | ||||||||
\(407\) | 1.16124e6 | 0.347484 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.61075e6 | −0.771717 | −0.385858 | − | 0.922558i | \(-0.626095\pi\) | ||||
−0.385858 | + | 0.922558i | \(0.626095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 809273. | 0.234883 | ||||||||
\(413\) | −2.16641e6 | −0.624979 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 63184.7 | 0.0179010 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −300117. | −0.0840138 | ||||||||
\(419\) | −1.01624e6 | −0.282789 | −0.141395 | − | 0.989953i | \(-0.545159\pi\) | ||||
−0.141395 | + | 0.989953i | \(0.545159\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.96915e6 | 1.64137 | 0.820687 | − | 0.571379i | \(-0.193591\pi\) | ||||
0.820687 | + | 0.571379i | \(0.193591\pi\) | |||||||
\(422\) | −237997. | −0.0650564 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 31912.4 | 0.00862076 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.50601e6 | 1.19598 | ||||||||
\(428\) | 3.06484e6 | 0.808721 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.97145e6 | 0.770504 | 0.385252 | − | 0.922811i | \(-0.374115\pi\) | ||||
0.385252 | + | 0.922811i | \(0.374115\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.95237e6 | 1.26938 | 0.634692 | − | 0.772765i | \(-0.281127\pi\) | ||||
0.634692 | + | 0.772765i | \(0.281127\pi\) | |||||||
\(434\) | −2.15999e6 | −0.550461 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.14451e6 | 0.288338 | ||||||||
\(437\) | 57271.3 | 0.0143461 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.12115e6 | −0.277652 | −0.138826 | − | 0.990317i | \(-0.544333\pi\) | ||||
−0.138826 | + | 0.990317i | \(0.544333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −412300. | −0.100382 | ||||||||
\(443\) | −2.66233e6 | −0.644544 | −0.322272 | − | 0.946647i | \(-0.604447\pi\) | ||||
−0.322272 | + | 0.946647i | \(0.604447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.46449e6 | −0.824713 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −580191. | −0.136576 | ||||||||
\(449\) | 3.88781e6 | 0.910101 | 0.455050 | − | 0.890466i | \(-0.349621\pi\) | ||||
0.455050 | + | 0.890466i | \(0.349621\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.52490e6 | −0.353022 | ||||||||
\(452\) | −2.61432e6 | −0.601885 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.94823e6 | −0.671309 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.52630e6 | −0.565841 | −0.282920 | − | 0.959143i | \(-0.591303\pi\) | ||||
−0.282920 | + | 0.959143i | \(0.591303\pi\) | |||||||
\(458\) | −3.38600e6 | −0.754265 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.63589e6 | −1.01597 | −0.507985 | − | 0.861366i | \(-0.669610\pi\) | ||||
−0.507985 | + | 0.861366i | \(0.669610\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.62380e6 | −0.785619 | −0.392810 | − | 0.919620i | \(-0.628497\pi\) | ||||
−0.392810 | + | 0.919620i | \(0.628497\pi\) | |||||||
\(464\) | 827724. | 0.178480 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.36304e6 | −0.504088 | ||||||||
\(467\) | −3.72757e6 | −0.790922 | −0.395461 | − | 0.918483i | \(-0.629415\pi\) | ||||
−0.395461 | + | 0.918483i | \(0.629415\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.97970e6 | 1.46523 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −978835. | −0.202234 | ||||||||
\(473\) | −532217. | −0.109380 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.78593e6 | 0.765870 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.41500e6 | 1.28418 | ||||||||
\(479\) | 6.88374e6 | 1.37084 | 0.685418 | − | 0.728150i | \(-0.259619\pi\) | ||||
0.685418 | + | 0.728150i | \(0.259619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 632436. | 0.124639 | ||||||||
\(482\) | 1.38829e6 | 0.272183 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.37144e6 | −0.460149 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.58990e6 | 1.64122 | 0.820608 | − | 0.571492i | \(-0.193635\pi\) | ||||
0.820608 | + | 0.571492i | \(0.193635\pi\) | |||||||
\(488\) | 2.03593e6 | 0.387001 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.46999e6 | 0.275176 | 0.137588 | − | 0.990490i | \(-0.456065\pi\) | ||||
0.137588 | + | 0.990490i | \(0.456065\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.40116e6 | −1.00085 | ||||||||
\(494\) | −163451. | −0.0301349 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −975934. | −0.178121 | ||||||||
\(497\) | 2.98278e6 | 0.541664 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.13043e6 | −0.562798 | −0.281399 | − | 0.959591i | \(-0.590798\pi\) | ||||
−0.281399 | + | 0.959591i | \(0.590798\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.14575e6 | 0.380032 | ||||||||
\(503\) | −2.29993e6 | −0.405317 | −0.202658 | − | 0.979249i | \(-0.564958\pi\) | ||||
−0.202658 | + | 0.979249i | \(0.564958\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −39192.0 | −0.00680488 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 549611. | 0.0944922 | ||||||||
\(509\) | 5.16574e6 | 0.883767 | 0.441884 | − | 0.897072i | \(-0.354310\pi\) | ||||
0.441884 | + | 0.897072i | \(0.354310\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.58770e6 | 0.946632 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.05426e6 | 0.509916 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.72945e6 | −0.284564 | ||||||||
\(518\) | −5.80732e6 | −0.950936 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.12853e7 | 1.82146 | 0.910729 | − | 0.413004i | \(-0.135520\pi\) | ||||
0.910729 | + | 0.413004i | \(0.135520\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.86022e6 | 0.776966 | 0.388483 | − | 0.921456i | \(-0.372999\pi\) | ||||
0.388483 | + | 0.921456i | \(0.372999\pi\) | |||||||
\(524\) | 5.58869e6 | 0.889164 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.36440e6 | −0.215019 | ||||||||
\(527\) | 6.36828e6 | 0.998839 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.42886e6 | −0.998838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.50088e6 | 0.229915 | ||||||||
\(533\) | −830498. | −0.126625 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.15360e6 | 0.474126 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.00065e6 | 0.446951 | ||||||||
\(539\) | −369027. | −0.0547125 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.23864e6 | −0.769530 | −0.384765 | − | 0.923015i | \(-0.625717\pi\) | ||||
−0.384765 | + | 0.923015i | \(0.625717\pi\) | |||||||
\(542\) | 6.57849e6 | 0.961896 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.71057e6 | 0.247825 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.88586e6 | −0.412389 | −0.206194 | − | 0.978511i | \(-0.566108\pi\) | ||||
−0.206194 | + | 0.978511i | \(0.566108\pi\) | |||||||
\(548\) | 4.38934e6 | 0.624379 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.14122e6 | −0.300457 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.03331e7 | −1.43688 | ||||||||
\(554\) | 4.18525e6 | 0.579359 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −765476. | −0.105013 | ||||||||
\(557\) | 3.27936e6 | 0.447869 | 0.223935 | − | 0.974604i | \(-0.428110\pi\) | ||||
0.223935 | + | 0.974604i | \(0.428110\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −289858. | −0.0392334 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −218014. | −0.0291168 | ||||||||
\(563\) | −664023. | −0.0882901 | −0.0441451 | − | 0.999025i | \(-0.514056\pi\) | ||||
−0.0441451 | + | 0.999025i | \(0.514056\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 600518. | 0.0787925 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.34769e6 | 0.175275 | ||||||||
\(569\) | 3.00851e6 | 0.389557 | 0.194778 | − | 0.980847i | \(-0.437601\pi\) | ||||
0.194778 | + | 0.980847i | \(0.437601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.07571e7 | 1.38072 | 0.690359 | − | 0.723467i | \(-0.257453\pi\) | ||||
0.690359 | + | 0.723467i | \(0.257453\pi\) | |||||||
\(572\) | 111853. | 0.0142941 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.62602e6 | 0.966091 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.53859e7 | −1.92390 | −0.961952 | − | 0.273220i | \(-0.911911\pi\) | ||||
−0.961952 | + | 0.273220i | \(0.911911\pi\) | |||||||
\(578\) | −5.48260e6 | −0.682601 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.42918e7 | 1.75650 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 56493.1 | 0.00688374 | ||||||||
\(584\) | 2.52466e6 | 0.306316 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.16005e6 | −0.741038 | ||||||||
\(587\) | 1.16896e7 | 1.40025 | 0.700125 | − | 0.714020i | \(-0.253128\pi\) | ||||
0.700125 | + | 0.714020i | \(0.253128\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.52462e6 | 0.299853 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.62389e6 | −0.307709 | ||||||||
\(593\) | −2.29301e6 | −0.267774 | −0.133887 | − | 0.990997i | \(-0.542746\pi\) | ||||
−0.133887 | + | 0.990997i | \(0.542746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.37031e6 | 0.619276 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −21344.9 | −0.00244084 | ||||||||
\(599\) | 1.58740e7 | 1.80767 | 0.903834 | − | 0.427884i | \(-0.140741\pi\) | ||||
0.903834 | + | 0.427884i | \(0.140741\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.16506e7 | −1.31571 | −0.657855 | − | 0.753144i | \(-0.728536\pi\) | ||||
−0.657855 | + | 0.753144i | \(0.728536\pi\) | |||||||
\(602\) | 2.66161e6 | 0.299332 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.38193e6 | 0.600268 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.40797e6 | −1.03639 | −0.518196 | − | 0.855262i | \(-0.673396\pi\) | ||||
−0.518196 | + | 0.855262i | \(0.673396\pi\) | |||||||
\(608\) | 678134. | 0.0743972 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −941896. | −0.102070 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.30509e6 | −1.00016 | −0.500080 | − | 0.865979i | \(-0.666696\pi\) | ||||
−0.500080 | + | 0.865979i | \(0.666696\pi\) | |||||||
\(614\) | −3.65909e6 | −0.391699 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.02708e6 | −0.109057 | ||||||||
\(617\) | −268346. | −0.0283780 | −0.0141890 | − | 0.999899i | \(-0.504517\pi\) | ||||
−0.0141890 | + | 0.999899i | \(0.504517\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.97678e6 | −0.836760 | −0.418380 | − | 0.908272i | \(-0.637402\pi\) | ||||
−0.418380 | + | 0.908272i | \(0.637402\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.39233e6 | 0.662496 | ||||||||
\(623\) | −2.07817e7 | −2.14517 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.53647e6 | −0.972640 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.10516e6 | 0.617729 | ||||||||
\(629\) | 1.71217e7 | 1.72552 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.94679e6 | 0.294629 | 0.147314 | − | 0.989090i | \(-0.452937\pi\) | ||||
0.147314 | + | 0.989090i | \(0.452937\pi\) | |||||||
\(632\) | −4.66876e6 | −0.464952 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.00053e6 | 0.790489 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −200981. | −0.0196248 | ||||||||
\(638\) | 1.46528e6 | 0.142518 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.28989e7 | −1.23996 | −0.619981 | − | 0.784617i | \(-0.712860\pi\) | ||||
−0.619981 | + | 0.784617i | \(0.712860\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.20262e6 | −0.877777 | −0.438889 | − | 0.898542i | \(-0.644628\pi\) | ||||
−0.438889 | + | 0.898542i | \(0.644628\pi\) | |||||||
\(644\) | 195998. | 0.0186225 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.42504e6 | −0.417192 | ||||||||
\(647\) | 177907. | 0.0167083 | 0.00835417 | − | 0.999965i | \(-0.497341\pi\) | ||||
0.00835417 | + | 0.999965i | \(0.497341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.73279e6 | −0.161485 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.26410e6 | 0.853462 | ||||||||
\(653\) | −1.11867e7 | −1.02664 | −0.513321 | − | 0.858197i | \(-0.671585\pi\) | ||||
−0.513321 | + | 0.858197i | \(0.671585\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.44562e6 | 0.312613 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.64893e6 | 0.778749 | ||||||||
\(659\) | −2.34591e6 | −0.210425 | −0.105213 | − | 0.994450i | \(-0.533552\pi\) | ||||
−0.105213 | + | 0.994450i | \(0.533552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.73844e6 | −0.332803 | −0.166401 | − | 0.986058i | \(-0.553215\pi\) | ||||
−0.166401 | + | 0.986058i | \(0.553215\pi\) | |||||||
\(662\) | 5.93446e6 | 0.526304 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.45740e6 | 0.568378 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −279619. | −0.0243362 | ||||||||
\(668\) | −2.04973e6 | −0.177728 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.60410e6 | 0.309023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.11773e6 | −0.520658 | −0.260329 | − | 0.965520i | \(-0.583831\pi\) | ||||
−0.260329 | + | 0.965520i | \(0.583831\pi\) | |||||||
\(674\) | 9.69961e6 | 0.822440 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.87977e6 | −0.494873 | ||||||||
\(677\) | 6.50221e6 | 0.545242 | 0.272621 | − | 0.962121i | \(-0.412109\pi\) | ||||
0.272621 | + | 0.962121i | \(0.412109\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.16805e6 | −0.513421 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.72765e6 | −0.142231 | ||||||||
\(683\) | 1.37285e7 | 1.12609 | 0.563044 | − | 0.826427i | \(-0.309630\pi\) | ||||
0.563044 | + | 0.826427i | \(0.309630\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.67722e6 | −0.622865 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.20258e6 | 0.0968595 | ||||||||
\(689\) | 30767.5 | 0.00246913 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.36316e7 | 1.08606 | 0.543028 | − | 0.839715i | \(-0.317278\pi\) | ||||
0.543028 | + | 0.839715i | \(0.317278\pi\) | |||||||
\(692\) | −7.79499e6 | −0.618800 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.06726e6 | 0.399369 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.24837e7 | −1.75302 | ||||||||
\(698\) | −1.01703e7 | −0.790123 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.08567e6 | −0.160306 | −0.0801531 | − | 0.996783i | \(-0.525541\pi\) | ||||
−0.0801531 | + | 0.996783i | \(0.525541\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.78767e6 | 0.518003 | ||||||||
\(704\) | −464061. | −0.0352894 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.14037e6 | −0.388135 | ||||||||
\(707\) | −7.07763e6 | −0.532524 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.23349e7 | 0.921554 | 0.460777 | − | 0.887516i | \(-0.347571\pi\) | ||||
0.460777 | + | 0.887516i | \(0.347571\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.38968e6 | −0.694146 | ||||||||
\(713\) | 329687. | 0.0242872 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.35718e7 | 0.989359 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.66500e7 | 1.20533 | ||||||||
\(719\) | 2.83517e6 | 0.204530 | 0.102265 | − | 0.994757i | \(-0.467391\pi\) | ||||
0.102265 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.16450e6 | −0.513272 | ||||||||
\(722\) | 8.15015e6 | 0.581865 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.20677e6 | −0.652771 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.19423e7 | 0.838017 | 0.419009 | − | 0.907982i | \(-0.362378\pi\) | ||||
0.419009 | + | 0.907982i | \(0.362378\pi\) | |||||||
\(728\) | −559374. | −0.0391178 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.84721e6 | −0.543152 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.50999e7 | −1.72549 | −0.862744 | − | 0.505642i | \(-0.831256\pi\) | ||||
−0.862744 | + | 0.505642i | \(0.831256\pi\) | |||||||
\(734\) | −4.52265e6 | −0.309851 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 88556.7 | 0.00602597 | ||||||||
\(737\) | 5.58267e6 | 0.378593 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.66189e6 | −0.111942 | −0.0559708 | − | 0.998432i | \(-0.517825\pi\) | ||||
−0.0559708 | + | 0.998432i | \(0.517825\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −282521. | −0.0188383 | ||||||||
\(743\) | −988158. | −0.0656681 | −0.0328340 | − | 0.999461i | \(-0.510453\pi\) | ||||
−0.0328340 | + | 0.999461i | \(0.510453\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.24948e6 | −0.0822022 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.02815e6 | 0.197890 | ||||||||
\(749\) | −2.71331e7 | −1.76724 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.42260e7 | 1.56741 | 0.783704 | − | 0.621135i | \(-0.213328\pi\) | ||||
0.783704 | + | 0.621135i | \(0.213328\pi\) | |||||||
\(752\) | 3.90779e6 | 0.251992 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 798026. | 0.0511198 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.03239e6 | 0.509454 | 0.254727 | − | 0.967013i | \(-0.418014\pi\) | ||||
0.254727 | + | 0.967013i | \(0.418014\pi\) | |||||||
\(758\) | 8.79960e6 | 0.556275 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.44956e6 | 0.528899 | 0.264449 | − | 0.964400i | \(-0.414810\pi\) | ||||
0.264449 | + | 0.964400i | \(0.414810\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.01323e7 | −0.630083 | ||||||||
\(764\) | −293803. | −0.0182105 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.57333e7 | −0.968828 | ||||||||
\(767\) | −943716. | −0.0579232 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.68674e7 | −1.02857 | −0.514285 | − | 0.857620i | \(-0.671943\pi\) | ||||
−0.514285 | + | 0.857620i | \(0.671943\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.59220e6 | 0.337707 | ||||||||
\(773\) | 2.37205e7 | 1.42782 | 0.713912 | − | 0.700236i | \(-0.246922\pi\) | ||||
0.713912 | + | 0.700236i | \(0.246922\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.78687e6 | −0.166136 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.68237e7 | 0.996490 | ||||||||
\(779\) | −8.91339e6 | −0.526259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.38575e6 | 0.139958 | ||||||||
\(782\) | −577861. | −0.0337914 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 833840. | 0.0484499 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.21145e7 | 1.27274 | 0.636370 | − | 0.771384i | \(-0.280435\pi\) | ||||
0.636370 | + | 0.771384i | \(0.280435\pi\) | |||||||
\(788\) | 5.94865e6 | 0.341274 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.31446e7 | 1.31525 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.96288e6 | 0.110844 | ||||||||
\(794\) | −9.57936e6 | −0.539244 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.80910e6 | 0.269018 | ||||||||
\(797\) | −1.86780e6 | −0.104156 | −0.0520779 | − | 0.998643i | \(-0.516584\pi\) | ||||
−0.0520779 | + | 0.998643i | \(0.516584\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.54996e7 | −1.41308 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.76864e7 | 0.970967 | ||||||||
\(803\) | 4.46928e6 | 0.244596 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −940918. | −0.0510169 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.19784e6 | −0.172317 | ||||||||
\(809\) | 203197. | 0.0109156 | 0.00545778 | − | 0.999985i | \(-0.498263\pi\) | ||||
0.00545778 | + | 0.999985i | \(0.498263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.27341e7 | 1.21374 | 0.606870 | − | 0.794801i | \(-0.292425\pi\) | ||||
0.606870 | + | 0.794801i | \(0.292425\pi\) | |||||||
\(812\) | −7.32785e6 | −0.390019 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.64494e6 | −0.245708 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.11092e6 | −0.163055 | ||||||||
\(818\) | 1.04430e7 | 0.545686 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.56056e7 | −1.32579 | −0.662897 | − | 0.748710i | \(-0.730673\pi\) | ||||
−0.662897 | + | 0.748710i | \(0.730673\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.10878e6 | 0.365844 | 0.182922 | − | 0.983127i | \(-0.441444\pi\) | ||||
0.182922 | + | 0.983127i | \(0.441444\pi\) | |||||||
\(824\) | −3.23709e6 | −0.166087 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.66563e6 | 0.441927 | ||||||||
\(827\) | −2.69334e7 | −1.36939 | −0.684695 | − | 0.728830i | \(-0.740065\pi\) | ||||
−0.684695 | + | 0.728830i | \(0.740065\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.89570e7 | 1.46341 | 0.731707 | − | 0.681619i | \(-0.238724\pi\) | ||||
0.731707 | + | 0.681619i | \(0.238724\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −252739. | −0.0126579 | ||||||||
\(833\) | −5.44107e6 | −0.271689 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.20047e6 | 0.0594067 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.06498e6 | 0.199962 | ||||||||
\(839\) | −1.95591e7 | −0.959279 | −0.479639 | − | 0.877466i | \(-0.659233\pi\) | ||||
−0.479639 | + | 0.877466i | \(0.659233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00569e7 | −0.490316 | ||||||||
\(842\) | −2.38766e7 | −1.16063 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 951987. | 0.0460018 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.09944e7 | 1.00553 | ||||||||
\(848\) | −127650. | −0.00609580 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 886393. | 0.0419568 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.74251e7 | −0.819981 | −0.409990 | − | 0.912090i | \(-0.634468\pi\) | ||||
−0.409990 | + | 0.912090i | \(0.634468\pi\) | |||||||
\(854\) | −1.80241e7 | −0.845684 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.22594e7 | −0.571852 | ||||||||
\(857\) | −2.03324e7 | −0.945663 | −0.472831 | − | 0.881153i | \(-0.656768\pi\) | ||||
−0.472831 | + | 0.881153i | \(0.656768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.19607e7 | −0.553061 | −0.276530 | − | 0.961005i | \(-0.589185\pi\) | ||||
−0.276530 | + | 0.961005i | \(0.589185\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.18858e7 | −0.544829 | ||||||||
\(863\) | 3.87101e7 | 1.76928 | 0.884640 | − | 0.466274i | \(-0.154404\pi\) | ||||
0.884640 | + | 0.466274i | \(0.154404\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.98095e7 | −0.897590 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.63995e6 | 0.389235 | ||||||||
\(869\) | −8.26488e6 | −0.371268 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.04045e6 | 0.135798 | ||||||||
\(872\) | −4.57802e6 | −0.203886 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −229085. | −0.0101442 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.76410e7 | −1.65258 | −0.826289 | − | 0.563247i | \(-0.809552\pi\) | ||||
−0.826289 | + | 0.563247i | \(0.809552\pi\) | |||||||
\(878\) | 4.48459e6 | 0.196330 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.92452e6 | −0.126945 | −0.0634723 | − | 0.997984i | \(-0.520217\pi\) | ||||
−0.0634723 | + | 0.997984i | \(0.520217\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.90249e7 | 1.68438 | 0.842190 | − | 0.539181i | \(-0.181266\pi\) | ||||
0.842190 | + | 0.539181i | \(0.181266\pi\) | |||||||
\(884\) | 1.64920e6 | 0.0709811 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.06493e7 | 0.455761 | ||||||||
\(887\) | −1.16063e7 | −0.495318 | −0.247659 | − | 0.968847i | \(-0.579661\pi\) | ||||
−0.247659 | + | 0.968847i | \(0.579661\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.86571e6 | −0.206487 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.38580e7 | 0.583160 | ||||||||
\(893\) | −1.01090e7 | −0.424208 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.32076e6 | 0.0965741 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.55513e7 | −0.643538 | ||||||||
\(899\) | −1.23261e7 | −0.508659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 832955. | 0.0341830 | ||||||||
\(902\) | 6.09962e6 | 0.249624 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.04573e7 | 0.425597 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.80327e7 | 1.53511 | 0.767554 | − | 0.640984i | \(-0.221473\pi\) | ||||
0.767554 | + | 0.640984i | \(0.221473\pi\) | |||||||
\(908\) | 1.17929e7 | 0.474687 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.76995e7 | −1.90422 | −0.952112 | − | 0.305748i | \(-0.901093\pi\) | ||||
−0.952112 | + | 0.305748i | \(0.901093\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.14312e7 | 0.453854 | ||||||||
\(914\) | 1.01052e7 | 0.400110 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.35440e7 | 0.533346 | ||||||||
\(917\) | −4.94767e7 | −1.94302 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.06445e7 | −1.19692 | −0.598459 | − | 0.801154i | \(-0.704220\pi\) | ||||
−0.598459 | + | 0.801154i | \(0.704220\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.85436e7 | 0.718400 | ||||||||
\(923\) | 1.29934e6 | 0.0502016 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.44952e7 | 0.555517 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.31090e6 | −0.126205 | ||||||||
\(929\) | −4.20442e7 | −1.59833 | −0.799165 | − | 0.601112i | \(-0.794725\pi\) | ||||
−0.799165 | + | 0.601112i | \(0.794725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.15704e6 | −0.0815614 | ||||||||
\(932\) | 9.45216e6 | 0.356444 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.49103e7 | 0.559267 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.09921e7 | −0.781101 | −0.390551 | − | 0.920582i | \(-0.627715\pi\) | ||||
−0.390551 | + | 0.920582i | \(0.627715\pi\) | |||||||
\(938\) | −2.79188e7 | −1.03607 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.06080e7 | −0.390536 | −0.195268 | − | 0.980750i | \(-0.562558\pi\) | ||||
−0.195268 | + | 0.980750i | \(0.562558\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.16399e6 | −0.0426255 | ||||||||
\(944\) | 3.91534e6 | 0.143001 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.12887e6 | 0.0773430 | ||||||||
\(947\) | 2.66948e7 | 0.967280 | 0.483640 | − | 0.875267i | \(-0.339314\pi\) | ||||
0.483640 | + | 0.875267i | \(0.339314\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.43408e6 | 0.0877341 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.51437e7 | −0.541552 | ||||||||
\(953\) | 2.68015e7 | 0.955932 | 0.477966 | − | 0.878378i | \(-0.341374\pi\) | ||||
0.477966 | + | 0.878378i | \(0.341374\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.56600e7 | −0.908054 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.75350e7 | −0.969328 | ||||||||
\(959\) | −3.88589e7 | −1.36441 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.40960e7 | −0.492364 | ||||||||
\(962\) | −2.52974e6 | −0.0881331 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.55314e6 | −0.192463 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.43270e7 | 1.18051 | 0.590255 | − | 0.807217i | \(-0.299027\pi\) | ||||
0.590255 | + | 0.807217i | \(0.299027\pi\) | |||||||
\(968\) | 9.48576e6 | 0.325375 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.43606e7 | 0.488791 | 0.244396 | − | 0.969676i | \(-0.421410\pi\) | ||||
0.244396 | + | 0.969676i | \(0.421410\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.77676e6 | 0.229477 | ||||||||
\(974\) | −3.43596e7 | −1.16051 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.14370e6 | −0.273651 | ||||||||
\(977\) | 1.16248e7 | 0.389627 | 0.194813 | − | 0.980840i | \(-0.437590\pi\) | ||||
0.194813 | + | 0.980840i | \(0.437590\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.66221e7 | −0.554280 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.87996e6 | −0.194579 | ||||||||
\(983\) | 3.11250e6 | 0.102737 | 0.0513683 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513683 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.16046e7 | 0.707709 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 653804. | 0.0213086 | ||||||||
\(989\) | −406251. | −0.0132070 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.33325e7 | −0.754704 | −0.377352 | − | 0.926070i | \(-0.623165\pi\) | ||||
−0.377352 | + | 0.926070i | \(0.623165\pi\) | |||||||
\(992\) | 3.90373e6 | 0.125951 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.19311e7 | −0.383014 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.35497e7 | −1.70616 | −0.853079 | − | 0.521782i | \(-0.825267\pi\) | ||||
−0.853079 | + | 0.521782i | \(0.825267\pi\) | |||||||
\(998\) | 1.25217e7 | 0.397958 | ||||||||
\(999\) | 0 | 0 |
(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 | 450.6.a.ba.1.1 | yes | 2 | |
3.2 | odd | 2 | 450.6.a.bf.1.1 | yes | 2 | ||
5.2 | odd | 4 | 450.6.c.q.199.1 | 4 | |||
5.3 | odd | 4 | 450.6.c.q.199.4 | 4 | |||
5.4 | even | 2 | 450.6.a.bd.1.2 | yes | 2 | ||
15.2 | even | 4 | 450.6.c.p.199.3 | 4 | |||
15.8 | even | 4 | 450.6.c.p.199.2 | 4 | |||
15.14 | odd | 2 | 450.6.a.y.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.6.a.y.1.2 | ✓ | 2 | 15.14 | odd | 2 | ||
450.6.a.ba.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
450.6.a.bd.1.2 | yes | 2 | 5.4 | even | 2 | ||
450.6.a.bf.1.1 | yes | 2 | 3.2 | odd | 2 | ||
450.6.c.p.199.2 | 4 | 15.8 | even | 4 | |||
450.6.c.p.199.3 | 4 | 15.2 | even | 4 | |||
450.6.c.q.199.1 | 4 | 5.2 | odd | 4 | |||
450.6.c.q.199.4 | 4 | 5.3 | odd | 4 |