Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,6,Mod(1,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.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: | \(2.24537347738\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 14.1 |
$q$-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 | ||||||||
\(3\) | 10.0000 | 0.641500 | 0.320750 | − | 0.947164i | \(-0.396065\pi\) | ||||
0.320750 | + | 0.947164i | \(0.396065\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 84.0000 | 1.50264 | 0.751319 | − | 0.659939i | \(-0.229418\pi\) | ||||
0.751319 | + | 0.659939i | \(0.229418\pi\) | |||||||
\(6\) | −40.0000 | −0.453609 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | −143.000 | −0.588477 | ||||||||
\(10\) | −336.000 | −1.06253 | ||||||||
\(11\) | −336.000 | −0.837255 | −0.418627 | − | 0.908158i | \(-0.637489\pi\) | ||||
−0.418627 | + | 0.908158i | \(0.637489\pi\) | |||||||
\(12\) | 160.000 | 0.320750 | ||||||||
\(13\) | 584.000 | 0.958417 | 0.479208 | − | 0.877701i | \(-0.340924\pi\) | ||||
0.479208 | + | 0.877701i | \(0.340924\pi\) | |||||||
\(14\) | −196.000 | −0.267261 | ||||||||
\(15\) | 840.000 | 0.963943 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1458.00 | −1.22359 | −0.611794 | − | 0.791017i | \(-0.709552\pi\) | ||||
−0.611794 | + | 0.791017i | \(0.709552\pi\) | |||||||
\(18\) | 572.000 | 0.416116 | ||||||||
\(19\) | 470.000 | 0.298685 | 0.149343 | − | 0.988786i | \(-0.452284\pi\) | ||||
0.149343 | + | 0.988786i | \(0.452284\pi\) | |||||||
\(20\) | 1344.00 | 0.751319 | ||||||||
\(21\) | 490.000 | 0.242464 | ||||||||
\(22\) | 1344.00 | 0.592028 | ||||||||
\(23\) | −4200.00 | −1.65550 | −0.827751 | − | 0.561096i | \(-0.810380\pi\) | ||||
−0.827751 | + | 0.561096i | \(0.810380\pi\) | |||||||
\(24\) | −640.000 | −0.226805 | ||||||||
\(25\) | 3931.00 | 1.25792 | ||||||||
\(26\) | −2336.00 | −0.677703 | ||||||||
\(27\) | −3860.00 | −1.01901 | ||||||||
\(28\) | 784.000 | 0.188982 | ||||||||
\(29\) | 4866.00 | 1.07443 | 0.537214 | − | 0.843446i | \(-0.319477\pi\) | ||||
0.537214 | + | 0.843446i | \(0.319477\pi\) | |||||||
\(30\) | −3360.00 | −0.681610 | ||||||||
\(31\) | −7372.00 | −1.37778 | −0.688892 | − | 0.724864i | \(-0.741903\pi\) | ||||
−0.688892 | + | 0.724864i | \(0.741903\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −3360.00 | −0.537099 | ||||||||
\(34\) | 5832.00 | 0.865207 | ||||||||
\(35\) | 4116.00 | 0.567944 | ||||||||
\(36\) | −2288.00 | −0.294239 | ||||||||
\(37\) | 14330.0 | 1.72085 | 0.860423 | − | 0.509581i | \(-0.170200\pi\) | ||||
0.860423 | + | 0.509581i | \(0.170200\pi\) | |||||||
\(38\) | −1880.00 | −0.211202 | ||||||||
\(39\) | 5840.00 | 0.614825 | ||||||||
\(40\) | −5376.00 | −0.531263 | ||||||||
\(41\) | 6222.00 | 0.578057 | 0.289028 | − | 0.957321i | \(-0.406668\pi\) | ||||
0.289028 | + | 0.957321i | \(0.406668\pi\) | |||||||
\(42\) | −1960.00 | −0.171448 | ||||||||
\(43\) | 3704.00 | 0.305492 | 0.152746 | − | 0.988265i | \(-0.451188\pi\) | ||||
0.152746 | + | 0.988265i | \(0.451188\pi\) | |||||||
\(44\) | −5376.00 | −0.418627 | ||||||||
\(45\) | −12012.0 | −0.884268 | ||||||||
\(46\) | 16800.0 | 1.17062 | ||||||||
\(47\) | −1812.00 | −0.119650 | −0.0598251 | − | 0.998209i | \(-0.519054\pi\) | ||||
−0.0598251 | + | 0.998209i | \(0.519054\pi\) | |||||||
\(48\) | 2560.00 | 0.160375 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | −15724.0 | −0.889484 | ||||||||
\(51\) | −14580.0 | −0.784932 | ||||||||
\(52\) | 9344.00 | 0.479208 | ||||||||
\(53\) | −37242.0 | −1.82114 | −0.910570 | − | 0.413355i | \(-0.864357\pi\) | ||||
−0.910570 | + | 0.413355i | \(0.864357\pi\) | |||||||
\(54\) | 15440.0 | 0.720548 | ||||||||
\(55\) | −28224.0 | −1.25809 | ||||||||
\(56\) | −3136.00 | −0.133631 | ||||||||
\(57\) | 4700.00 | 0.191607 | ||||||||
\(58\) | −19464.0 | −0.759735 | ||||||||
\(59\) | 34302.0 | 1.28289 | 0.641445 | − | 0.767169i | \(-0.278335\pi\) | ||||
0.641445 | + | 0.767169i | \(0.278335\pi\) | |||||||
\(60\) | 13440.0 | 0.481971 | ||||||||
\(61\) | 24476.0 | 0.842201 | 0.421101 | − | 0.907014i | \(-0.361644\pi\) | ||||
0.421101 | + | 0.907014i | \(0.361644\pi\) | |||||||
\(62\) | 29488.0 | 0.974240 | ||||||||
\(63\) | −7007.00 | −0.222424 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 49056.0 | 1.44015 | ||||||||
\(66\) | 13440.0 | 0.379786 | ||||||||
\(67\) | −17452.0 | −0.474961 | −0.237481 | − | 0.971392i | \(-0.576322\pi\) | ||||
−0.237481 | + | 0.971392i | \(0.576322\pi\) | |||||||
\(68\) | −23328.0 | −0.611794 | ||||||||
\(69\) | −42000.0 | −1.06201 | ||||||||
\(70\) | −16464.0 | −0.401597 | ||||||||
\(71\) | 28224.0 | 0.664466 | 0.332233 | − | 0.943197i | \(-0.392198\pi\) | ||||
0.332233 | + | 0.943197i | \(0.392198\pi\) | |||||||
\(72\) | 9152.00 | 0.208058 | ||||||||
\(73\) | 3602.00 | 0.0791109 | 0.0395555 | − | 0.999217i | \(-0.487406\pi\) | ||||
0.0395555 | + | 0.999217i | \(0.487406\pi\) | |||||||
\(74\) | −57320.0 | −1.21682 | ||||||||
\(75\) | 39310.0 | 0.806956 | ||||||||
\(76\) | 7520.00 | 0.149343 | ||||||||
\(77\) | −16464.0 | −0.316453 | ||||||||
\(78\) | −23360.0 | −0.434747 | ||||||||
\(79\) | 42872.0 | 0.772869 | 0.386435 | − | 0.922317i | \(-0.373706\pi\) | ||||
0.386435 | + | 0.922317i | \(0.373706\pi\) | |||||||
\(80\) | 21504.0 | 0.375659 | ||||||||
\(81\) | −3851.00 | −0.0652170 | ||||||||
\(82\) | −24888.0 | −0.408748 | ||||||||
\(83\) | −35202.0 | −0.560883 | −0.280441 | − | 0.959871i | \(-0.590481\pi\) | ||||
−0.280441 | + | 0.959871i | \(0.590481\pi\) | |||||||
\(84\) | 7840.00 | 0.121232 | ||||||||
\(85\) | −122472. | −1.83861 | ||||||||
\(86\) | −14816.0 | −0.216015 | ||||||||
\(87\) | 48660.0 | 0.689246 | ||||||||
\(88\) | 21504.0 | 0.296014 | ||||||||
\(89\) | 26730.0 | 0.357704 | 0.178852 | − | 0.983876i | \(-0.442762\pi\) | ||||
0.178852 | + | 0.983876i | \(0.442762\pi\) | |||||||
\(90\) | 48048.0 | 0.625272 | ||||||||
\(91\) | 28616.0 | 0.362248 | ||||||||
\(92\) | −67200.0 | −0.827751 | ||||||||
\(93\) | −73720.0 | −0.883849 | ||||||||
\(94\) | 7248.00 | 0.0846055 | ||||||||
\(95\) | 39480.0 | 0.448816 | ||||||||
\(96\) | −10240.0 | −0.113402 | ||||||||
\(97\) | −16978.0 | −0.183213 | −0.0916067 | − | 0.995795i | \(-0.529200\pi\) | ||||
−0.0916067 | + | 0.995795i | \(0.529200\pi\) | |||||||
\(98\) | −9604.00 | −0.101015 | ||||||||
\(99\) | 48048.0 | 0.492705 | ||||||||
\(100\) | 62896.0 | 0.628960 | ||||||||
\(101\) | 99204.0 | 0.967667 | 0.483833 | − | 0.875160i | \(-0.339244\pi\) | ||||
0.483833 | + | 0.875160i | \(0.339244\pi\) | |||||||
\(102\) | 58320.0 | 0.555031 | ||||||||
\(103\) | −131644. | −1.22267 | −0.611333 | − | 0.791373i | \(-0.709366\pi\) | ||||
−0.611333 | + | 0.791373i | \(0.709366\pi\) | |||||||
\(104\) | −37376.0 | −0.338852 | ||||||||
\(105\) | 41160.0 | 0.364336 | ||||||||
\(106\) | 148968. | 1.28774 | ||||||||
\(107\) | 48852.0 | 0.412499 | 0.206250 | − | 0.978499i | \(-0.433874\pi\) | ||||
0.206250 | + | 0.978499i | \(0.433874\pi\) | |||||||
\(108\) | −61760.0 | −0.509504 | ||||||||
\(109\) | −56374.0 | −0.454478 | −0.227239 | − | 0.973839i | \(-0.572970\pi\) | ||||
−0.227239 | + | 0.973839i | \(0.572970\pi\) | |||||||
\(110\) | 112896. | 0.889604 | ||||||||
\(111\) | 143300. | 1.10392 | ||||||||
\(112\) | 12544.0 | 0.0944911 | ||||||||
\(113\) | 8742.00 | 0.0644043 | 0.0322021 | − | 0.999481i | \(-0.489748\pi\) | ||||
0.0322021 | + | 0.999481i | \(0.489748\pi\) | |||||||
\(114\) | −18800.0 | −0.135486 | ||||||||
\(115\) | −352800. | −2.48762 | ||||||||
\(116\) | 77856.0 | 0.537214 | ||||||||
\(117\) | −83512.0 | −0.564007 | ||||||||
\(118\) | −137208. | −0.907140 | ||||||||
\(119\) | −71442.0 | −0.462473 | ||||||||
\(120\) | −53760.0 | −0.340805 | ||||||||
\(121\) | −48155.0 | −0.299005 | ||||||||
\(122\) | −97904.0 | −0.595526 | ||||||||
\(123\) | 62220.0 | 0.370823 | ||||||||
\(124\) | −117952. | −0.688892 | ||||||||
\(125\) | 67704.0 | 0.387560 | ||||||||
\(126\) | 28028.0 | 0.157277 | ||||||||
\(127\) | 315992. | 1.73847 | 0.869234 | − | 0.494401i | \(-0.164612\pi\) | ||||
0.869234 | + | 0.494401i | \(0.164612\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 37040.0 | 0.195973 | ||||||||
\(130\) | −196224. | −1.01834 | ||||||||
\(131\) | −24666.0 | −0.125580 | −0.0627900 | − | 0.998027i | \(-0.520000\pi\) | ||||
−0.0627900 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(132\) | −53760.0 | −0.268550 | ||||||||
\(133\) | 23030.0 | 0.112892 | ||||||||
\(134\) | 69808.0 | 0.335848 | ||||||||
\(135\) | −324240. | −1.53120 | ||||||||
\(136\) | 93312.0 | 0.432604 | ||||||||
\(137\) | 303234. | 1.38031 | 0.690155 | − | 0.723662i | \(-0.257542\pi\) | ||||
0.690155 | + | 0.723662i | \(0.257542\pi\) | |||||||
\(138\) | 168000. | 0.750951 | ||||||||
\(139\) | 250586. | 1.10007 | 0.550034 | − | 0.835142i | \(-0.314615\pi\) | ||||
0.550034 | + | 0.835142i | \(0.314615\pi\) | |||||||
\(140\) | 65856.0 | 0.283972 | ||||||||
\(141\) | −18120.0 | −0.0767557 | ||||||||
\(142\) | −112896. | −0.469848 | ||||||||
\(143\) | −196224. | −0.802439 | ||||||||
\(144\) | −36608.0 | −0.147119 | ||||||||
\(145\) | 408744. | 1.61448 | ||||||||
\(146\) | −14408.0 | −0.0559399 | ||||||||
\(147\) | 24010.0 | 0.0916429 | ||||||||
\(148\) | 229280. | 0.860423 | ||||||||
\(149\) | −60594.0 | −0.223596 | −0.111798 | − | 0.993731i | \(-0.535661\pi\) | ||||
−0.111798 | + | 0.993731i | \(0.535661\pi\) | |||||||
\(150\) | −157240. | −0.570604 | ||||||||
\(151\) | 124448. | 0.444166 | 0.222083 | − | 0.975028i | \(-0.428714\pi\) | ||||
0.222083 | + | 0.975028i | \(0.428714\pi\) | |||||||
\(152\) | −30080.0 | −0.105601 | ||||||||
\(153\) | 208494. | 0.720054 | ||||||||
\(154\) | 65856.0 | 0.223766 | ||||||||
\(155\) | −619248. | −2.07031 | ||||||||
\(156\) | 93440.0 | 0.307412 | ||||||||
\(157\) | 76040.0 | 0.246203 | 0.123101 | − | 0.992394i | \(-0.460716\pi\) | ||||
0.123101 | + | 0.992394i | \(0.460716\pi\) | |||||||
\(158\) | −171488. | −0.546501 | ||||||||
\(159\) | −372420. | −1.16826 | ||||||||
\(160\) | −86016.0 | −0.265631 | ||||||||
\(161\) | −205800. | −0.625721 | ||||||||
\(162\) | 15404.0 | 0.0461154 | ||||||||
\(163\) | 124256. | 0.366310 | 0.183155 | − | 0.983084i | \(-0.441369\pi\) | ||||
0.183155 | + | 0.983084i | \(0.441369\pi\) | |||||||
\(164\) | 99552.0 | 0.289028 | ||||||||
\(165\) | −282240. | −0.807065 | ||||||||
\(166\) | 140808. | 0.396604 | ||||||||
\(167\) | −72420.0 | −0.200940 | −0.100470 | − | 0.994940i | \(-0.532035\pi\) | ||||
−0.100470 | + | 0.994940i | \(0.532035\pi\) | |||||||
\(168\) | −31360.0 | −0.0857241 | ||||||||
\(169\) | −30237.0 | −0.0814370 | ||||||||
\(170\) | 489888. | 1.30009 | ||||||||
\(171\) | −67210.0 | −0.175770 | ||||||||
\(172\) | 59264.0 | 0.152746 | ||||||||
\(173\) | −441552. | −1.12167 | −0.560837 | − | 0.827926i | \(-0.689521\pi\) | ||||
−0.560837 | + | 0.827926i | \(0.689521\pi\) | |||||||
\(174\) | −194640. | −0.487370 | ||||||||
\(175\) | 192619. | 0.475449 | ||||||||
\(176\) | −86016.0 | −0.209314 | ||||||||
\(177\) | 343020. | 0.822974 | ||||||||
\(178\) | −106920. | −0.252935 | ||||||||
\(179\) | −10692.0 | −0.0249417 | −0.0124709 | − | 0.999922i | \(-0.503970\pi\) | ||||
−0.0124709 | + | 0.999922i | \(0.503970\pi\) | |||||||
\(180\) | −192192. | −0.442134 | ||||||||
\(181\) | −546064. | −1.23893 | −0.619465 | − | 0.785024i | \(-0.712651\pi\) | ||||
−0.619465 | + | 0.785024i | \(0.712651\pi\) | |||||||
\(182\) | −114464. | −0.256148 | ||||||||
\(183\) | 244760. | 0.540272 | ||||||||
\(184\) | 268800. | 0.585308 | ||||||||
\(185\) | 1.20372e6 | 2.58581 | ||||||||
\(186\) | 294880. | 0.624975 | ||||||||
\(187\) | 489888. | 1.02445 | ||||||||
\(188\) | −28992.0 | −0.0598251 | ||||||||
\(189\) | −189140. | −0.385149 | ||||||||
\(190\) | −157920. | −0.317361 | ||||||||
\(191\) | −575976. | −1.14241 | −0.571204 | − | 0.820808i | \(-0.693523\pi\) | ||||
−0.571204 | + | 0.820808i | \(0.693523\pi\) | |||||||
\(192\) | 40960.0 | 0.0801875 | ||||||||
\(193\) | −413938. | −0.799912 | −0.399956 | − | 0.916534i | \(-0.630975\pi\) | ||||
−0.399956 | + | 0.916534i | \(0.630975\pi\) | |||||||
\(194\) | 67912.0 | 0.129551 | ||||||||
\(195\) | 490560. | 0.923859 | ||||||||
\(196\) | 38416.0 | 0.0714286 | ||||||||
\(197\) | −494946. | −0.908641 | −0.454320 | − | 0.890838i | \(-0.650118\pi\) | ||||
−0.454320 | + | 0.890838i | \(0.650118\pi\) | |||||||
\(198\) | −192192. | −0.348395 | ||||||||
\(199\) | 520364. | 0.931482 | 0.465741 | − | 0.884921i | \(-0.345788\pi\) | ||||
0.465741 | + | 0.884921i | \(0.345788\pi\) | |||||||
\(200\) | −251584. | −0.444742 | ||||||||
\(201\) | −174520. | −0.304688 | ||||||||
\(202\) | −396816. | −0.684244 | ||||||||
\(203\) | 238434. | 0.406095 | ||||||||
\(204\) | −233280. | −0.392466 | ||||||||
\(205\) | 522648. | 0.868610 | ||||||||
\(206\) | 526576. | 0.864556 | ||||||||
\(207\) | 600600. | 0.974225 | ||||||||
\(208\) | 149504. | 0.239604 | ||||||||
\(209\) | −157920. | −0.250076 | ||||||||
\(210\) | −164640. | −0.257624 | ||||||||
\(211\) | 183284. | 0.283412 | 0.141706 | − | 0.989909i | \(-0.454741\pi\) | ||||
0.141706 | + | 0.989909i | \(0.454741\pi\) | |||||||
\(212\) | −595872. | −0.910570 | ||||||||
\(213\) | 282240. | 0.426255 | ||||||||
\(214\) | −195408. | −0.291681 | ||||||||
\(215\) | 311136. | 0.459044 | ||||||||
\(216\) | 247040. | 0.360274 | ||||||||
\(217\) | −361228. | −0.520753 | ||||||||
\(218\) | 225496. | 0.321364 | ||||||||
\(219\) | 36020.0 | 0.0507497 | ||||||||
\(220\) | −451584. | −0.629045 | ||||||||
\(221\) | −851472. | −1.17271 | ||||||||
\(222\) | −573200. | −0.780591 | ||||||||
\(223\) | −1.27746e6 | −1.72023 | −0.860115 | − | 0.510100i | \(-0.829608\pi\) | ||||
−0.860115 | + | 0.510100i | \(0.829608\pi\) | |||||||
\(224\) | −50176.0 | −0.0668153 | ||||||||
\(225\) | −562133. | −0.740257 | ||||||||
\(226\) | −34968.0 | −0.0455407 | ||||||||
\(227\) | −1.28764e6 | −1.65856 | −0.829279 | − | 0.558835i | \(-0.811248\pi\) | ||||
−0.829279 | + | 0.558835i | \(0.811248\pi\) | |||||||
\(228\) | 75200.0 | 0.0958034 | ||||||||
\(229\) | 350936. | 0.442221 | 0.221110 | − | 0.975249i | \(-0.429032\pi\) | ||||
0.221110 | + | 0.975249i | \(0.429032\pi\) | |||||||
\(230\) | 1.41120e6 | 1.75901 | ||||||||
\(231\) | −164640. | −0.203004 | ||||||||
\(232\) | −311424. | −0.379867 | ||||||||
\(233\) | 836154. | 1.00901 | 0.504506 | − | 0.863408i | \(-0.331675\pi\) | ||||
0.504506 | + | 0.863408i | \(0.331675\pi\) | |||||||
\(234\) | 334048. | 0.398813 | ||||||||
\(235\) | −152208. | −0.179791 | ||||||||
\(236\) | 548832. | 0.641445 | ||||||||
\(237\) | 428720. | 0.495796 | ||||||||
\(238\) | 285768. | 0.327018 | ||||||||
\(239\) | 774336. | 0.876869 | 0.438434 | − | 0.898763i | \(-0.355533\pi\) | ||||
0.438434 | + | 0.898763i | \(0.355533\pi\) | |||||||
\(240\) | 215040. | 0.240986 | ||||||||
\(241\) | −1.15285e6 | −1.27859 | −0.639293 | − | 0.768963i | \(-0.720773\pi\) | ||||
−0.639293 | + | 0.768963i | \(0.720773\pi\) | |||||||
\(242\) | 192620. | 0.211428 | ||||||||
\(243\) | 899470. | 0.977172 | ||||||||
\(244\) | 391616. | 0.421101 | ||||||||
\(245\) | 201684. | 0.214663 | ||||||||
\(246\) | −248880. | −0.262212 | ||||||||
\(247\) | 274480. | 0.286265 | ||||||||
\(248\) | 471808. | 0.487120 | ||||||||
\(249\) | −352020. | −0.359806 | ||||||||
\(250\) | −270816. | −0.274047 | ||||||||
\(251\) | 1.35801e6 | 1.36056 | 0.680282 | − | 0.732951i | \(-0.261858\pi\) | ||||
0.680282 | + | 0.732951i | \(0.261858\pi\) | |||||||
\(252\) | −112112. | −0.111212 | ||||||||
\(253\) | 1.41120e6 | 1.38608 | ||||||||
\(254\) | −1.26397e6 | −1.22928 | ||||||||
\(255\) | −1.22472e6 | −1.17947 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −317742. | −0.300083 | −0.150042 | − | 0.988680i | \(-0.547941\pi\) | ||||
−0.150042 | + | 0.988680i | \(0.547941\pi\) | |||||||
\(258\) | −148160. | −0.138574 | ||||||||
\(259\) | 702170. | 0.650418 | ||||||||
\(260\) | 784896. | 0.720077 | ||||||||
\(261\) | −695838. | −0.632276 | ||||||||
\(262\) | 98664.0 | 0.0887985 | ||||||||
\(263\) | 1.05101e6 | 0.936951 | 0.468475 | − | 0.883477i | \(-0.344804\pi\) | ||||
0.468475 | + | 0.883477i | \(0.344804\pi\) | |||||||
\(264\) | 215040. | 0.189893 | ||||||||
\(265\) | −3.12833e6 | −2.73651 | ||||||||
\(266\) | −92120.0 | −0.0798270 | ||||||||
\(267\) | 267300. | 0.229467 | ||||||||
\(268\) | −279232. | −0.237481 | ||||||||
\(269\) | 1.18958e6 | 1.00234 | 0.501169 | − | 0.865349i | \(-0.332903\pi\) | ||||
0.501169 | + | 0.865349i | \(0.332903\pi\) | |||||||
\(270\) | 1.29696e6 | 1.08272 | ||||||||
\(271\) | −1.43008e6 | −1.18287 | −0.591435 | − | 0.806353i | \(-0.701438\pi\) | ||||
−0.591435 | + | 0.806353i | \(0.701438\pi\) | |||||||
\(272\) | −373248. | −0.305897 | ||||||||
\(273\) | 286160. | 0.232382 | ||||||||
\(274\) | −1.21294e6 | −0.976026 | ||||||||
\(275\) | −1.32082e6 | −1.05320 | ||||||||
\(276\) | −672000. | −0.531003 | ||||||||
\(277\) | 63302.0 | 0.0495699 | 0.0247849 | − | 0.999693i | \(-0.492110\pi\) | ||||
0.0247849 | + | 0.999693i | \(0.492110\pi\) | |||||||
\(278\) | −1.00234e6 | −0.777866 | ||||||||
\(279\) | 1.05420e6 | 0.810795 | ||||||||
\(280\) | −263424. | −0.200798 | ||||||||
\(281\) | −496614. | −0.375192 | −0.187596 | − | 0.982246i | \(-0.560070\pi\) | ||||
−0.187596 | + | 0.982246i | \(0.560070\pi\) | |||||||
\(282\) | 72480.0 | 0.0542744 | ||||||||
\(283\) | −1.15842e6 | −0.859803 | −0.429902 | − | 0.902876i | \(-0.641452\pi\) | ||||
−0.429902 | + | 0.902876i | \(0.641452\pi\) | |||||||
\(284\) | 451584. | 0.332233 | ||||||||
\(285\) | 394800. | 0.287915 | ||||||||
\(286\) | 784896. | 0.567410 | ||||||||
\(287\) | 304878. | 0.218485 | ||||||||
\(288\) | 146432. | 0.104029 | ||||||||
\(289\) | 705907. | 0.497168 | ||||||||
\(290\) | −1.63498e6 | −1.14161 | ||||||||
\(291\) | −169780. | −0.117531 | ||||||||
\(292\) | 57632.0 | 0.0395555 | ||||||||
\(293\) | 1.43886e6 | 0.979151 | 0.489575 | − | 0.871961i | \(-0.337152\pi\) | ||||
0.489575 | + | 0.871961i | \(0.337152\pi\) | |||||||
\(294\) | −96040.0 | −0.0648013 | ||||||||
\(295\) | 2.88137e6 | 1.92772 | ||||||||
\(296\) | −917120. | −0.608411 | ||||||||
\(297\) | 1.29696e6 | 0.853170 | ||||||||
\(298\) | 242376. | 0.158106 | ||||||||
\(299\) | −2.45280e6 | −1.58666 | ||||||||
\(300\) | 628960. | 0.403478 | ||||||||
\(301\) | 181496. | 0.115465 | ||||||||
\(302\) | −497792. | −0.314073 | ||||||||
\(303\) | 992040. | 0.620758 | ||||||||
\(304\) | 120320. | 0.0746713 | ||||||||
\(305\) | 2.05598e6 | 1.26552 | ||||||||
\(306\) | −833976. | −0.509155 | ||||||||
\(307\) | −989098. | −0.598954 | −0.299477 | − | 0.954104i | \(-0.596812\pi\) | ||||
−0.299477 | + | 0.954104i | \(0.596812\pi\) | |||||||
\(308\) | −263424. | −0.158226 | ||||||||
\(309\) | −1.31644e6 | −0.784341 | ||||||||
\(310\) | 2.47699e6 | 1.46393 | ||||||||
\(311\) | −2.22050e6 | −1.30182 | −0.650909 | − | 0.759155i | \(-0.725612\pi\) | ||||
−0.650909 | + | 0.759155i | \(0.725612\pi\) | |||||||
\(312\) | −373760. | −0.217373 | ||||||||
\(313\) | 2.33008e6 | 1.34434 | 0.672171 | − | 0.740396i | \(-0.265362\pi\) | ||||
0.672171 | + | 0.740396i | \(0.265362\pi\) | |||||||
\(314\) | −304160. | −0.174092 | ||||||||
\(315\) | −588588. | −0.334222 | ||||||||
\(316\) | 685952. | 0.386435 | ||||||||
\(317\) | 427542. | 0.238963 | 0.119481 | − | 0.992836i | \(-0.461877\pi\) | ||||
0.119481 | + | 0.992836i | \(0.461877\pi\) | |||||||
\(318\) | 1.48968e6 | 0.826086 | ||||||||
\(319\) | −1.63498e6 | −0.899569 | ||||||||
\(320\) | 344064. | 0.187830 | ||||||||
\(321\) | 488520. | 0.264618 | ||||||||
\(322\) | 823200. | 0.442452 | ||||||||
\(323\) | −685260. | −0.365468 | ||||||||
\(324\) | −61616.0 | −0.0326085 | ||||||||
\(325\) | 2.29570e6 | 1.20561 | ||||||||
\(326\) | −497024. | −0.259020 | ||||||||
\(327\) | −563740. | −0.291548 | ||||||||
\(328\) | −398208. | −0.204374 | ||||||||
\(329\) | −88788.0 | −0.0452235 | ||||||||
\(330\) | 1.12896e6 | 0.570681 | ||||||||
\(331\) | −396616. | −0.198976 | −0.0994879 | − | 0.995039i | \(-0.531720\pi\) | ||||
−0.0994879 | + | 0.995039i | \(0.531720\pi\) | |||||||
\(332\) | −563232. | −0.280441 | ||||||||
\(333\) | −2.04919e6 | −1.01268 | ||||||||
\(334\) | 289680. | 0.142086 | ||||||||
\(335\) | −1.46597e6 | −0.713695 | ||||||||
\(336\) | 125440. | 0.0606161 | ||||||||
\(337\) | −3.21819e6 | −1.54361 | −0.771805 | − | 0.635860i | \(-0.780646\pi\) | ||||
−0.771805 | + | 0.635860i | \(0.780646\pi\) | |||||||
\(338\) | 120948. | 0.0575847 | ||||||||
\(339\) | 87420.0 | 0.0413154 | ||||||||
\(340\) | −1.95955e6 | −0.919305 | ||||||||
\(341\) | 2.47699e6 | 1.15356 | ||||||||
\(342\) | 268840. | 0.124288 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | −237056. | −0.108008 | ||||||||
\(345\) | −3.52800e6 | −1.59581 | ||||||||
\(346\) | 1.76621e6 | 0.793143 | ||||||||
\(347\) | 2.78018e6 | 1.23951 | 0.619755 | − | 0.784796i | \(-0.287232\pi\) | ||||
0.619755 | + | 0.784796i | \(0.287232\pi\) | |||||||
\(348\) | 778560. | 0.344623 | ||||||||
\(349\) | −338800. | −0.148895 | −0.0744475 | − | 0.997225i | \(-0.523719\pi\) | ||||
−0.0744475 | + | 0.997225i | \(0.523719\pi\) | |||||||
\(350\) | −770476. | −0.336193 | ||||||||
\(351\) | −2.25424e6 | −0.976635 | ||||||||
\(352\) | 344064. | 0.148007 | ||||||||
\(353\) | −362046. | −0.154642 | −0.0773209 | − | 0.997006i | \(-0.524637\pi\) | ||||
−0.0773209 | + | 0.997006i | \(0.524637\pi\) | |||||||
\(354\) | −1.37208e6 | −0.581931 | ||||||||
\(355\) | 2.37082e6 | 0.998451 | ||||||||
\(356\) | 427680. | 0.178852 | ||||||||
\(357\) | −714420. | −0.296676 | ||||||||
\(358\) | 42768.0 | 0.0176365 | ||||||||
\(359\) | 876528. | 0.358946 | 0.179473 | − | 0.983763i | \(-0.442561\pi\) | ||||
0.179473 | + | 0.983763i | \(0.442561\pi\) | |||||||
\(360\) | 768768. | 0.312636 | ||||||||
\(361\) | −2.25520e6 | −0.910787 | ||||||||
\(362\) | 2.18426e6 | 0.876056 | ||||||||
\(363\) | −481550. | −0.191812 | ||||||||
\(364\) | 457856. | 0.181124 | ||||||||
\(365\) | 302568. | 0.118875 | ||||||||
\(366\) | −979040. | −0.382030 | ||||||||
\(367\) | 2.98062e6 | 1.15516 | 0.577578 | − | 0.816335i | \(-0.303998\pi\) | ||||
0.577578 | + | 0.816335i | \(0.303998\pi\) | |||||||
\(368\) | −1.07520e6 | −0.413875 | ||||||||
\(369\) | −889746. | −0.340173 | ||||||||
\(370\) | −4.81488e6 | −1.82844 | ||||||||
\(371\) | −1.82486e6 | −0.688326 | ||||||||
\(372\) | −1.17952e6 | −0.441924 | ||||||||
\(373\) | 3.91441e6 | 1.45678 | 0.728391 | − | 0.685162i | \(-0.240268\pi\) | ||||
0.728391 | + | 0.685162i | \(0.240268\pi\) | |||||||
\(374\) | −1.95955e6 | −0.724399 | ||||||||
\(375\) | 677040. | 0.248620 | ||||||||
\(376\) | 115968. | 0.0423027 | ||||||||
\(377\) | 2.84174e6 | 1.02975 | ||||||||
\(378\) | 756560. | 0.272342 | ||||||||
\(379\) | 3.60661e6 | 1.28974 | 0.644868 | − | 0.764294i | \(-0.276912\pi\) | ||||
0.644868 | + | 0.764294i | \(0.276912\pi\) | |||||||
\(380\) | 631680. | 0.224408 | ||||||||
\(381\) | 3.15992e6 | 1.11523 | ||||||||
\(382\) | 2.30390e6 | 0.807804 | ||||||||
\(383\) | −2.66644e6 | −0.928826 | −0.464413 | − | 0.885619i | \(-0.653735\pi\) | ||||
−0.464413 | + | 0.885619i | \(0.653735\pi\) | |||||||
\(384\) | −163840. | −0.0567012 | ||||||||
\(385\) | −1.38298e6 | −0.475513 | ||||||||
\(386\) | 1.65575e6 | 0.565623 | ||||||||
\(387\) | −529672. | −0.179775 | ||||||||
\(388\) | −271648. | −0.0916067 | ||||||||
\(389\) | −213366. | −0.0714910 | −0.0357455 | − | 0.999361i | \(-0.511381\pi\) | ||||
−0.0357455 | + | 0.999361i | \(0.511381\pi\) | |||||||
\(390\) | −1.96224e6 | −0.653267 | ||||||||
\(391\) | 6.12360e6 | 2.02565 | ||||||||
\(392\) | −153664. | −0.0505076 | ||||||||
\(393\) | −246660. | −0.0805596 | ||||||||
\(394\) | 1.97978e6 | 0.642506 | ||||||||
\(395\) | 3.60125e6 | 1.16134 | ||||||||
\(396\) | 768768. | 0.246353 | ||||||||
\(397\) | −4.09408e6 | −1.30371 | −0.651854 | − | 0.758345i | \(-0.726008\pi\) | ||||
−0.651854 | + | 0.758345i | \(0.726008\pi\) | |||||||
\(398\) | −2.08146e6 | −0.658657 | ||||||||
\(399\) | 230300. | 0.0724205 | ||||||||
\(400\) | 1.00634e6 | 0.314480 | ||||||||
\(401\) | 942366. | 0.292657 | 0.146328 | − | 0.989236i | \(-0.453254\pi\) | ||||
0.146328 | + | 0.989236i | \(0.453254\pi\) | |||||||
\(402\) | 698080. | 0.215447 | ||||||||
\(403\) | −4.30525e6 | −1.32049 | ||||||||
\(404\) | 1.58726e6 | 0.483833 | ||||||||
\(405\) | −323484. | −0.0979976 | ||||||||
\(406\) | −953736. | −0.287153 | ||||||||
\(407\) | −4.81488e6 | −1.44079 | ||||||||
\(408\) | 933120. | 0.277515 | ||||||||
\(409\) | −4.84561e6 | −1.43232 | −0.716160 | − | 0.697936i | \(-0.754102\pi\) | ||||
−0.716160 | + | 0.697936i | \(0.754102\pi\) | |||||||
\(410\) | −2.09059e6 | −0.614200 | ||||||||
\(411\) | 3.03234e6 | 0.885469 | ||||||||
\(412\) | −2.10630e6 | −0.611333 | ||||||||
\(413\) | 1.68080e6 | 0.484887 | ||||||||
\(414\) | −2.40240e6 | −0.688881 | ||||||||
\(415\) | −2.95697e6 | −0.842804 | ||||||||
\(416\) | −598016. | −0.169426 | ||||||||
\(417\) | 2.50586e6 | 0.705694 | ||||||||
\(418\) | 631680. | 0.176830 | ||||||||
\(419\) | −1.73485e6 | −0.482754 | −0.241377 | − | 0.970431i | \(-0.577599\pi\) | ||||
−0.241377 | + | 0.970431i | \(0.577599\pi\) | |||||||
\(420\) | 658560. | 0.182168 | ||||||||
\(421\) | −1.65145e6 | −0.454109 | −0.227055 | − | 0.973882i | \(-0.572910\pi\) | ||||
−0.227055 | + | 0.973882i | \(0.572910\pi\) | |||||||
\(422\) | −733136. | −0.200403 | ||||||||
\(423\) | 259116. | 0.0704115 | ||||||||
\(424\) | 2.38349e6 | 0.643870 | ||||||||
\(425\) | −5.73140e6 | −1.53918 | ||||||||
\(426\) | −1.12896e6 | −0.301408 | ||||||||
\(427\) | 1.19932e6 | 0.318322 | ||||||||
\(428\) | 781632. | 0.206250 | ||||||||
\(429\) | −1.96224e6 | −0.514765 | ||||||||
\(430\) | −1.24454e6 | −0.324593 | ||||||||
\(431\) | 4.14360e6 | 1.07445 | 0.537223 | − | 0.843440i | \(-0.319473\pi\) | ||||
0.537223 | + | 0.843440i | \(0.319473\pi\) | |||||||
\(432\) | −988160. | −0.254752 | ||||||||
\(433\) | −3.03966e6 | −0.779121 | −0.389561 | − | 0.921001i | \(-0.627373\pi\) | ||||
−0.389561 | + | 0.921001i | \(0.627373\pi\) | |||||||
\(434\) | 1.44491e6 | 0.368228 | ||||||||
\(435\) | 4.08744e6 | 1.03569 | ||||||||
\(436\) | −901984. | −0.227239 | ||||||||
\(437\) | −1.97400e6 | −0.494474 | ||||||||
\(438\) | −144080. | −0.0358855 | ||||||||
\(439\) | 2.54271e6 | 0.629703 | 0.314852 | − | 0.949141i | \(-0.398045\pi\) | ||||
0.314852 | + | 0.949141i | \(0.398045\pi\) | |||||||
\(440\) | 1.80634e6 | 0.444802 | ||||||||
\(441\) | −343343. | −0.0840682 | ||||||||
\(442\) | 3.40589e6 | 0.829229 | ||||||||
\(443\) | −2.43210e6 | −0.588806 | −0.294403 | − | 0.955681i | \(-0.595121\pi\) | ||||
−0.294403 | + | 0.955681i | \(0.595121\pi\) | |||||||
\(444\) | 2.29280e6 | 0.551961 | ||||||||
\(445\) | 2.24532e6 | 0.537500 | ||||||||
\(446\) | 5.10986e6 | 1.21639 | ||||||||
\(447\) | −605940. | −0.143437 | ||||||||
\(448\) | 200704. | 0.0472456 | ||||||||
\(449\) | 1.82853e6 | 0.428042 | 0.214021 | − | 0.976829i | \(-0.431344\pi\) | ||||
0.214021 | + | 0.976829i | \(0.431344\pi\) | |||||||
\(450\) | 2.24853e6 | 0.523441 | ||||||||
\(451\) | −2.09059e6 | −0.483981 | ||||||||
\(452\) | 139872. | 0.0322021 | ||||||||
\(453\) | 1.24448e6 | 0.284933 | ||||||||
\(454\) | 5.15057e6 | 1.17278 | ||||||||
\(455\) | 2.40374e6 | 0.544327 | ||||||||
\(456\) | −300800. | −0.0677432 | ||||||||
\(457\) | 1.58063e6 | 0.354030 | 0.177015 | − | 0.984208i | \(-0.443356\pi\) | ||||
0.177015 | + | 0.984208i | \(0.443356\pi\) | |||||||
\(458\) | −1.40374e6 | −0.312697 | ||||||||
\(459\) | 5.62788e6 | 1.24685 | ||||||||
\(460\) | −5.64480e6 | −1.24381 | ||||||||
\(461\) | 5.09604e6 | 1.11681 | 0.558407 | − | 0.829567i | \(-0.311413\pi\) | ||||
0.558407 | + | 0.829567i | \(0.311413\pi\) | |||||||
\(462\) | 658560. | 0.143546 | ||||||||
\(463\) | −7.02338e6 | −1.52263 | −0.761313 | − | 0.648384i | \(-0.775445\pi\) | ||||
−0.761313 | + | 0.648384i | \(0.775445\pi\) | |||||||
\(464\) | 1.24570e6 | 0.268607 | ||||||||
\(465\) | −6.19248e6 | −1.32810 | ||||||||
\(466\) | −3.34462e6 | −0.713479 | ||||||||
\(467\) | −4.24845e6 | −0.901443 | −0.450722 | − | 0.892665i | \(-0.648833\pi\) | ||||
−0.450722 | + | 0.892665i | \(0.648833\pi\) | |||||||
\(468\) | −1.33619e6 | −0.282003 | ||||||||
\(469\) | −855148. | −0.179518 | ||||||||
\(470\) | 608832. | 0.127131 | ||||||||
\(471\) | 760400. | 0.157939 | ||||||||
\(472\) | −2.19533e6 | −0.453570 | ||||||||
\(473\) | −1.24454e6 | −0.255775 | ||||||||
\(474\) | −1.71488e6 | −0.350581 | ||||||||
\(475\) | 1.84757e6 | 0.375722 | ||||||||
\(476\) | −1.14307e6 | −0.231236 | ||||||||
\(477\) | 5.32561e6 | 1.07170 | ||||||||
\(478\) | −3.09734e6 | −0.620040 | ||||||||
\(479\) | 559284. | 0.111377 | 0.0556883 | − | 0.998448i | \(-0.482265\pi\) | ||||
0.0556883 | + | 0.998448i | \(0.482265\pi\) | |||||||
\(480\) | −860160. | −0.170403 | ||||||||
\(481\) | 8.36872e6 | 1.64929 | ||||||||
\(482\) | 4.61140e6 | 0.904097 | ||||||||
\(483\) | −2.05800e6 | −0.401400 | ||||||||
\(484\) | −770480. | −0.149502 | ||||||||
\(485\) | −1.42615e6 | −0.275303 | ||||||||
\(486\) | −3.59788e6 | −0.690965 | ||||||||
\(487\) | −1.32057e6 | −0.252312 | −0.126156 | − | 0.992010i | \(-0.540264\pi\) | ||||
−0.126156 | + | 0.992010i | \(0.540264\pi\) | |||||||
\(488\) | −1.56646e6 | −0.297763 | ||||||||
\(489\) | 1.24256e6 | 0.234988 | ||||||||
\(490\) | −806736. | −0.151789 | ||||||||
\(491\) | 6.27193e6 | 1.17408 | 0.587040 | − | 0.809558i | \(-0.300293\pi\) | ||||
0.587040 | + | 0.809558i | \(0.300293\pi\) | |||||||
\(492\) | 995520. | 0.185412 | ||||||||
\(493\) | −7.09463e6 | −1.31466 | ||||||||
\(494\) | −1.09792e6 | −0.202420 | ||||||||
\(495\) | 4.03603e6 | 0.740358 | ||||||||
\(496\) | −1.88723e6 | −0.344446 | ||||||||
\(497\) | 1.38298e6 | 0.251144 | ||||||||
\(498\) | 1.40808e6 | 0.254422 | ||||||||
\(499\) | −3.93785e6 | −0.707959 | −0.353979 | − | 0.935253i | \(-0.615172\pi\) | ||||
−0.353979 | + | 0.935253i | \(0.615172\pi\) | |||||||
\(500\) | 1.08326e6 | 0.193780 | ||||||||
\(501\) | −724200. | −0.128903 | ||||||||
\(502\) | −5.43204e6 | −0.962063 | ||||||||
\(503\) | −7.59830e6 | −1.33905 | −0.669525 | − | 0.742790i | \(-0.733502\pi\) | ||||
−0.669525 | + | 0.742790i | \(0.733502\pi\) | |||||||
\(504\) | 448448. | 0.0786386 | ||||||||
\(505\) | 8.33314e6 | 1.45405 | ||||||||
\(506\) | −5.64480e6 | −0.980104 | ||||||||
\(507\) | −302370. | −0.0522419 | ||||||||
\(508\) | 5.05587e6 | 0.869234 | ||||||||
\(509\) | −7.82664e6 | −1.33900 | −0.669501 | − | 0.742812i | \(-0.733492\pi\) | ||||
−0.669501 | + | 0.742812i | \(0.733492\pi\) | |||||||
\(510\) | 4.89888e6 | 0.834010 | ||||||||
\(511\) | 176498. | 0.0299011 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −1.81420e6 | −0.304363 | ||||||||
\(514\) | 1.27097e6 | 0.212191 | ||||||||
\(515\) | −1.10581e7 | −1.83722 | ||||||||
\(516\) | 592640. | 0.0979866 | ||||||||
\(517\) | 608832. | 0.100178 | ||||||||
\(518\) | −2.80868e6 | −0.459915 | ||||||||
\(519\) | −4.41552e6 | −0.719554 | ||||||||
\(520\) | −3.13958e6 | −0.509171 | ||||||||
\(521\) | 8.94454e6 | 1.44366 | 0.721828 | − | 0.692072i | \(-0.243302\pi\) | ||||
0.721828 | + | 0.692072i | \(0.243302\pi\) | |||||||
\(522\) | 2.78335e6 | 0.447087 | ||||||||
\(523\) | 4.07481e6 | 0.651407 | 0.325704 | − | 0.945472i | \(-0.394399\pi\) | ||||
0.325704 | + | 0.945472i | \(0.394399\pi\) | |||||||
\(524\) | −394656. | −0.0627900 | ||||||||
\(525\) | 1.92619e6 | 0.305001 | ||||||||
\(526\) | −4.20403e6 | −0.662524 | ||||||||
\(527\) | 1.07484e7 | 1.68584 | ||||||||
\(528\) | −860160. | −0.134275 | ||||||||
\(529\) | 1.12037e7 | 1.74069 | ||||||||
\(530\) | 1.25133e7 | 1.93501 | ||||||||
\(531\) | −4.90519e6 | −0.754952 | ||||||||
\(532\) | 368480. | 0.0564462 | ||||||||
\(533\) | 3.63365e6 | 0.554019 | ||||||||
\(534\) | −1.06920e6 | −0.162258 | ||||||||
\(535\) | 4.10357e6 | 0.619837 | ||||||||
\(536\) | 1.11693e6 | 0.167924 | ||||||||
\(537\) | −106920. | −0.0160001 | ||||||||
\(538\) | −4.75834e6 | −0.708760 | ||||||||
\(539\) | −806736. | −0.119608 | ||||||||
\(540\) | −5.18784e6 | −0.765600 | ||||||||
\(541\) | −1.18676e7 | −1.74329 | −0.871644 | − | 0.490140i | \(-0.836946\pi\) | ||||
−0.871644 | + | 0.490140i | \(0.836946\pi\) | |||||||
\(542\) | 5.72032e6 | 0.836416 | ||||||||
\(543\) | −5.46064e6 | −0.794775 | ||||||||
\(544\) | 1.49299e6 | 0.216302 | ||||||||
\(545\) | −4.73542e6 | −0.682915 | ||||||||
\(546\) | −1.14464e6 | −0.164319 | ||||||||
\(547\) | −5.37801e6 | −0.768516 | −0.384258 | − | 0.923226i | \(-0.625543\pi\) | ||||
−0.384258 | + | 0.923226i | \(0.625543\pi\) | |||||||
\(548\) | 4.85174e6 | 0.690155 | ||||||||
\(549\) | −3.50007e6 | −0.495616 | ||||||||
\(550\) | 5.28326e6 | 0.744724 | ||||||||
\(551\) | 2.28702e6 | 0.320916 | ||||||||
\(552\) | 2.68800e6 | 0.375475 | ||||||||
\(553\) | 2.10073e6 | 0.292117 | ||||||||
\(554\) | −253208. | −0.0350512 | ||||||||
\(555\) | 1.20372e7 | 1.65880 | ||||||||
\(556\) | 4.00938e6 | 0.550034 | ||||||||
\(557\) | −5.64878e6 | −0.771466 | −0.385733 | − | 0.922611i | \(-0.626051\pi\) | ||||
−0.385733 | + | 0.922611i | \(0.626051\pi\) | |||||||
\(558\) | −4.21678e6 | −0.573318 | ||||||||
\(559\) | 2.16314e6 | 0.292789 | ||||||||
\(560\) | 1.05370e6 | 0.141986 | ||||||||
\(561\) | 4.89888e6 | 0.657188 | ||||||||
\(562\) | 1.98646e6 | 0.265301 | ||||||||
\(563\) | 4.56407e6 | 0.606850 | 0.303425 | − | 0.952855i | \(-0.401870\pi\) | ||||
0.303425 | + | 0.952855i | \(0.401870\pi\) | |||||||
\(564\) | −289920. | −0.0383778 | ||||||||
\(565\) | 734328. | 0.0967763 | ||||||||
\(566\) | 4.63367e6 | 0.607973 | ||||||||
\(567\) | −188699. | −0.0246497 | ||||||||
\(568\) | −1.80634e6 | −0.234924 | ||||||||
\(569\) | 8.00165e6 | 1.03609 | 0.518047 | − | 0.855352i | \(-0.326659\pi\) | ||||
0.518047 | + | 0.855352i | \(0.326659\pi\) | |||||||
\(570\) | −1.57920e6 | −0.203587 | ||||||||
\(571\) | −1.37164e7 | −1.76055 | −0.880275 | − | 0.474464i | \(-0.842642\pi\) | ||||
−0.880275 | + | 0.474464i | \(0.842642\pi\) | |||||||
\(572\) | −3.13958e6 | −0.401220 | ||||||||
\(573\) | −5.75976e6 | −0.732855 | ||||||||
\(574\) | −1.21951e6 | −0.154492 | ||||||||
\(575\) | −1.65102e7 | −2.08249 | ||||||||
\(576\) | −585728. | −0.0735597 | ||||||||
\(577\) | 6.09797e6 | 0.762510 | 0.381255 | − | 0.924470i | \(-0.375492\pi\) | ||||
0.381255 | + | 0.924470i | \(0.375492\pi\) | |||||||
\(578\) | −2.82363e6 | −0.351551 | ||||||||
\(579\) | −4.13938e6 | −0.513144 | ||||||||
\(580\) | 6.53990e6 | 0.807238 | ||||||||
\(581\) | −1.72490e6 | −0.211994 | ||||||||
\(582\) | 679120. | 0.0831073 | ||||||||
\(583\) | 1.25133e7 | 1.52476 | ||||||||
\(584\) | −230528. | −0.0279699 | ||||||||
\(585\) | −7.01501e6 | −0.847498 | ||||||||
\(586\) | −5.75544e6 | −0.692364 | ||||||||
\(587\) | −8.08462e6 | −0.968422 | −0.484211 | − | 0.874951i | \(-0.660893\pi\) | ||||
−0.484211 | + | 0.874951i | \(0.660893\pi\) | |||||||
\(588\) | 384160. | 0.0458214 | ||||||||
\(589\) | −3.46484e6 | −0.411524 | ||||||||
\(590\) | −1.15255e7 | −1.36310 | ||||||||
\(591\) | −4.94946e6 | −0.582893 | ||||||||
\(592\) | 3.66848e6 | 0.430211 | ||||||||
\(593\) | 1.41575e6 | 0.165330 | 0.0826649 | − | 0.996577i | \(-0.473657\pi\) | ||||
0.0826649 | + | 0.996577i | \(0.473657\pi\) | |||||||
\(594\) | −5.18784e6 | −0.603282 | ||||||||
\(595\) | −6.00113e6 | −0.694929 | ||||||||
\(596\) | −969504. | −0.111798 | ||||||||
\(597\) | 5.20364e6 | 0.597546 | ||||||||
\(598\) | 9.81120e6 | 1.12194 | ||||||||
\(599\) | 8.75460e6 | 0.996941 | 0.498470 | − | 0.866907i | \(-0.333895\pi\) | ||||
0.498470 | + | 0.866907i | \(0.333895\pi\) | |||||||
\(600\) | −2.51584e6 | −0.285302 | ||||||||
\(601\) | 8.70276e6 | 0.982813 | 0.491407 | − | 0.870930i | \(-0.336483\pi\) | ||||
0.491407 | + | 0.870930i | \(0.336483\pi\) | |||||||
\(602\) | −725984. | −0.0816462 | ||||||||
\(603\) | 2.49564e6 | 0.279504 | ||||||||
\(604\) | 1.99117e6 | 0.222083 | ||||||||
\(605\) | −4.04502e6 | −0.449296 | ||||||||
\(606\) | −3.96816e6 | −0.438942 | ||||||||
\(607\) | −1.69578e7 | −1.86809 | −0.934045 | − | 0.357157i | \(-0.883746\pi\) | ||||
−0.934045 | + | 0.357157i | \(0.883746\pi\) | |||||||
\(608\) | −481280. | −0.0528006 | ||||||||
\(609\) | 2.38434e6 | 0.260510 | ||||||||
\(610\) | −8.22394e6 | −0.894860 | ||||||||
\(611\) | −1.05821e6 | −0.114675 | ||||||||
\(612\) | 3.33590e6 | 0.360027 | ||||||||
\(613\) | 1.76743e7 | 1.89973 | 0.949866 | − | 0.312658i | \(-0.101220\pi\) | ||||
0.949866 | + | 0.312658i | \(0.101220\pi\) | |||||||
\(614\) | 3.95639e6 | 0.423524 | ||||||||
\(615\) | 5.22648e6 | 0.557213 | ||||||||
\(616\) | 1.05370e6 | 0.111883 | ||||||||
\(617\) | −9.70636e6 | −1.02646 | −0.513232 | − | 0.858250i | \(-0.671552\pi\) | ||||
−0.513232 | + | 0.858250i | \(0.671552\pi\) | |||||||
\(618\) | 5.26576e6 | 0.554613 | ||||||||
\(619\) | 1.48739e7 | 1.56027 | 0.780133 | − | 0.625613i | \(-0.215151\pi\) | ||||
0.780133 | + | 0.625613i | \(0.215151\pi\) | |||||||
\(620\) | −9.90797e6 | −1.03515 | ||||||||
\(621\) | 1.62120e7 | 1.68697 | ||||||||
\(622\) | 8.88202e6 | 0.920525 | ||||||||
\(623\) | 1.30977e6 | 0.135199 | ||||||||
\(624\) | 1.49504e6 | 0.153706 | ||||||||
\(625\) | −6.59724e6 | −0.675557 | ||||||||
\(626\) | −9.32031e6 | −0.950593 | ||||||||
\(627\) | −1.57920e6 | −0.160424 | ||||||||
\(628\) | 1.21664e6 | 0.123101 | ||||||||
\(629\) | −2.08931e7 | −2.10561 | ||||||||
\(630\) | 2.35435e6 | 0.236331 | ||||||||
\(631\) | 1.26353e7 | 1.26331 | 0.631656 | − | 0.775248i | \(-0.282375\pi\) | ||||
0.631656 | + | 0.775248i | \(0.282375\pi\) | |||||||
\(632\) | −2.74381e6 | −0.273251 | ||||||||
\(633\) | 1.83284e6 | 0.181809 | ||||||||
\(634\) | −1.71017e6 | −0.168972 | ||||||||
\(635\) | 2.65433e7 | 2.61229 | ||||||||
\(636\) | −5.95872e6 | −0.584131 | ||||||||
\(637\) | 1.40218e6 | 0.136917 | ||||||||
\(638\) | 6.53990e6 | 0.636092 | ||||||||
\(639\) | −4.03603e6 | −0.391023 | ||||||||
\(640\) | −1.37626e6 | −0.132816 | ||||||||
\(641\) | 6.23398e6 | 0.599267 | 0.299634 | − | 0.954054i | \(-0.403136\pi\) | ||||
0.299634 | + | 0.954054i | \(0.403136\pi\) | |||||||
\(642\) | −1.95408e6 | −0.187113 | ||||||||
\(643\) | 1.06874e7 | 1.01940 | 0.509701 | − | 0.860352i | \(-0.329756\pi\) | ||||
0.509701 | + | 0.860352i | \(0.329756\pi\) | |||||||
\(644\) | −3.29280e6 | −0.312860 | ||||||||
\(645\) | 3.11136e6 | 0.294477 | ||||||||
\(646\) | 2.74104e6 | 0.258425 | ||||||||
\(647\) | 1.83258e7 | 1.72109 | 0.860544 | − | 0.509376i | \(-0.170124\pi\) | ||||
0.860544 | + | 0.509376i | \(0.170124\pi\) | |||||||
\(648\) | 246464. | 0.0230577 | ||||||||
\(649\) | −1.15255e7 | −1.07411 | ||||||||
\(650\) | −9.18282e6 | −0.852496 | ||||||||
\(651\) | −3.61228e6 | −0.334063 | ||||||||
\(652\) | 1.98810e6 | 0.183155 | ||||||||
\(653\) | −7.28857e6 | −0.668897 | −0.334448 | − | 0.942414i | \(-0.608550\pi\) | ||||
−0.334448 | + | 0.942414i | \(0.608550\pi\) | |||||||
\(654\) | 2.25496e6 | 0.206155 | ||||||||
\(655\) | −2.07194e6 | −0.188701 | ||||||||
\(656\) | 1.59283e6 | 0.144514 | ||||||||
\(657\) | −515086. | −0.0465550 | ||||||||
\(658\) | 355152. | 0.0319779 | ||||||||
\(659\) | 4.54337e6 | 0.407534 | 0.203767 | − | 0.979019i | \(-0.434681\pi\) | ||||
0.203767 | + | 0.979019i | \(0.434681\pi\) | |||||||
\(660\) | −4.51584e6 | −0.403533 | ||||||||
\(661\) | −2.10021e7 | −1.86964 | −0.934821 | − | 0.355120i | \(-0.884440\pi\) | ||||
−0.934821 | + | 0.355120i | \(0.884440\pi\) | |||||||
\(662\) | 1.58646e6 | 0.140697 | ||||||||
\(663\) | −8.51472e6 | −0.752292 | ||||||||
\(664\) | 2.25293e6 | 0.198302 | ||||||||
\(665\) | 1.93452e6 | 0.169636 | ||||||||
\(666\) | 8.19676e6 | 0.716072 | ||||||||
\(667\) | −2.04372e7 | −1.77872 | ||||||||
\(668\) | −1.15872e6 | −0.100470 | ||||||||
\(669\) | −1.27746e7 | −1.10353 | ||||||||
\(670\) | 5.86387e6 | 0.504658 | ||||||||
\(671\) | −8.22394e6 | −0.705137 | ||||||||
\(672\) | −501760. | −0.0428620 | ||||||||
\(673\) | 3.46923e6 | 0.295253 | 0.147627 | − | 0.989043i | \(-0.452837\pi\) | ||||
0.147627 | + | 0.989043i | \(0.452837\pi\) | |||||||
\(674\) | 1.28728e7 | 1.09150 | ||||||||
\(675\) | −1.51737e7 | −1.28183 | ||||||||
\(676\) | −483792. | −0.0407185 | ||||||||
\(677\) | −1.80916e7 | −1.51707 | −0.758536 | − | 0.651631i | \(-0.774085\pi\) | ||||
−0.758536 | + | 0.651631i | \(0.774085\pi\) | |||||||
\(678\) | −349680. | −0.0292144 | ||||||||
\(679\) | −831922. | −0.0692481 | ||||||||
\(680\) | 7.83821e6 | 0.650047 | ||||||||
\(681\) | −1.28764e7 | −1.06397 | ||||||||
\(682\) | −9.90797e6 | −0.815687 | ||||||||
\(683\) | 4.67752e6 | 0.383675 | 0.191838 | − | 0.981427i | \(-0.438555\pi\) | ||||
0.191838 | + | 0.981427i | \(0.438555\pi\) | |||||||
\(684\) | −1.07536e6 | −0.0878848 | ||||||||
\(685\) | 2.54717e7 | 2.07411 | ||||||||
\(686\) | −470596. | −0.0381802 | ||||||||
\(687\) | 3.50936e6 | 0.283685 | ||||||||
\(688\) | 948224. | 0.0763730 | ||||||||
\(689\) | −2.17493e7 | −1.74541 | ||||||||
\(690\) | 1.41120e7 | 1.12841 | ||||||||
\(691\) | 1.68960e7 | 1.34614 | 0.673069 | − | 0.739579i | \(-0.264976\pi\) | ||||
0.673069 | + | 0.739579i | \(0.264976\pi\) | |||||||
\(692\) | −7.06483e6 | −0.560837 | ||||||||
\(693\) | 2.35435e6 | 0.186225 | ||||||||
\(694\) | −1.11207e7 | −0.876466 | ||||||||
\(695\) | 2.10492e7 | 1.65300 | ||||||||
\(696\) | −3.11424e6 | −0.243685 | ||||||||
\(697\) | −9.07168e6 | −0.707303 | ||||||||
\(698\) | 1.35520e6 | 0.105285 | ||||||||
\(699\) | 8.36154e6 | 0.647282 | ||||||||
\(700\) | 3.08190e6 | 0.237725 | ||||||||
\(701\) | 2.40964e6 | 0.185207 | 0.0926035 | − | 0.995703i | \(-0.470481\pi\) | ||||
0.0926035 | + | 0.995703i | \(0.470481\pi\) | |||||||
\(702\) | 9.01696e6 | 0.690585 | ||||||||
\(703\) | 6.73510e6 | 0.513991 | ||||||||
\(704\) | −1.37626e6 | −0.104657 | ||||||||
\(705\) | −1.52208e6 | −0.115336 | ||||||||
\(706\) | 1.44818e6 | 0.109348 | ||||||||
\(707\) | 4.86100e6 | 0.365744 | ||||||||
\(708\) | 5.48832e6 | 0.411487 | ||||||||
\(709\) | −5.77010e6 | −0.431090 | −0.215545 | − | 0.976494i | \(-0.569153\pi\) | ||||
−0.215545 | + | 0.976494i | \(0.569153\pi\) | |||||||
\(710\) | −9.48326e6 | −0.706012 | ||||||||
\(711\) | −6.13070e6 | −0.454816 | ||||||||
\(712\) | −1.71072e6 | −0.126468 | ||||||||
\(713\) | 3.09624e7 | 2.28092 | ||||||||
\(714\) | 2.85768e6 | 0.209782 | ||||||||
\(715\) | −1.64828e7 | −1.20578 | ||||||||
\(716\) | −171072. | −0.0124709 | ||||||||
\(717\) | 7.74336e6 | 0.562512 | ||||||||
\(718\) | −3.50611e6 | −0.253813 | ||||||||
\(719\) | −1.43716e7 | −1.03677 | −0.518385 | − | 0.855147i | \(-0.673467\pi\) | ||||
−0.518385 | + | 0.855147i | \(0.673467\pi\) | |||||||
\(720\) | −3.07507e6 | −0.221067 | ||||||||
\(721\) | −6.45056e6 | −0.462124 | ||||||||
\(722\) | 9.02080e6 | 0.644024 | ||||||||
\(723\) | −1.15285e7 | −0.820214 | ||||||||
\(724\) | −8.73702e6 | −0.619465 | ||||||||
\(725\) | 1.91282e7 | 1.35154 | ||||||||
\(726\) | 1.92620e6 | 0.135631 | ||||||||
\(727\) | −1.40705e7 | −0.987353 | −0.493676 | − | 0.869646i | \(-0.664347\pi\) | ||||
−0.493676 | + | 0.869646i | \(0.664347\pi\) | |||||||
\(728\) | −1.83142e6 | −0.128074 | ||||||||
\(729\) | 9.93049e6 | 0.692073 | ||||||||
\(730\) | −1.21027e6 | −0.0840574 | ||||||||
\(731\) | −5.40043e6 | −0.373796 | ||||||||
\(732\) | 3.91616e6 | 0.270136 | ||||||||
\(733\) | −3.75000e6 | −0.257793 | −0.128897 | − | 0.991658i | \(-0.541144\pi\) | ||||
−0.128897 | + | 0.991658i | \(0.541144\pi\) | |||||||
\(734\) | −1.19225e7 | −0.816819 | ||||||||
\(735\) | 2.01684e6 | 0.137706 | ||||||||
\(736\) | 4.30080e6 | 0.292654 | ||||||||
\(737\) | 5.86387e6 | 0.397664 | ||||||||
\(738\) | 3.55898e6 | 0.240539 | ||||||||
\(739\) | 2.61318e7 | 1.76019 | 0.880093 | − | 0.474802i | \(-0.157480\pi\) | ||||
0.880093 | + | 0.474802i | \(0.157480\pi\) | |||||||
\(740\) | 1.92595e7 | 1.29290 | ||||||||
\(741\) | 2.74480e6 | 0.183639 | ||||||||
\(742\) | 7.29943e6 | 0.486720 | ||||||||
\(743\) | −159072. | −0.0105711 | −0.00528557 | − | 0.999986i | \(-0.501682\pi\) | ||||
−0.00528557 | + | 0.999986i | \(0.501682\pi\) | |||||||
\(744\) | 4.71808e6 | 0.312488 | ||||||||
\(745\) | −5.08990e6 | −0.335984 | ||||||||
\(746\) | −1.56577e7 | −1.03010 | ||||||||
\(747\) | 5.03389e6 | 0.330067 | ||||||||
\(748\) | 7.83821e6 | 0.512227 | ||||||||
\(749\) | 2.39375e6 | 0.155910 | ||||||||
\(750\) | −2.70816e6 | −0.175801 | ||||||||
\(751\) | −2.65311e7 | −1.71654 | −0.858272 | − | 0.513196i | \(-0.828461\pi\) | ||||
−0.858272 | + | 0.513196i | \(0.828461\pi\) | |||||||
\(752\) | −463872. | −0.0299126 | ||||||||
\(753\) | 1.35801e7 | 0.872802 | ||||||||
\(754\) | −1.13670e7 | −0.728143 | ||||||||
\(755\) | 1.04536e7 | 0.667421 | ||||||||
\(756\) | −3.02624e6 | −0.192575 | ||||||||
\(757\) | −1.52032e7 | −0.964260 | −0.482130 | − | 0.876100i | \(-0.660137\pi\) | ||||
−0.482130 | + | 0.876100i | \(0.660137\pi\) | |||||||
\(758\) | −1.44264e7 | −0.911981 | ||||||||
\(759\) | 1.41120e7 | 0.889169 | ||||||||
\(760\) | −2.52672e6 | −0.158680 | ||||||||
\(761\) | 4.71380e6 | 0.295059 | 0.147530 | − | 0.989058i | \(-0.452868\pi\) | ||||
0.147530 | + | 0.989058i | \(0.452868\pi\) | |||||||
\(762\) | −1.26397e7 | −0.788585 | ||||||||
\(763\) | −2.76233e6 | −0.171776 | ||||||||
\(764\) | −9.21562e6 | −0.571204 | ||||||||
\(765\) | 1.75135e7 | 1.08198 | ||||||||
\(766\) | 1.06657e7 | 0.656779 | ||||||||
\(767\) | 2.00324e7 | 1.22954 | ||||||||
\(768\) | 655360. | 0.0400938 | ||||||||
\(769\) | −1.58977e6 | −0.0969434 | −0.0484717 | − | 0.998825i | \(-0.515435\pi\) | ||||
−0.0484717 | + | 0.998825i | \(0.515435\pi\) | |||||||
\(770\) | 5.53190e6 | 0.336239 | ||||||||
\(771\) | −3.17742e6 | −0.192504 | ||||||||
\(772\) | −6.62301e6 | −0.399956 | ||||||||
\(773\) | −9.69095e6 | −0.583334 | −0.291667 | − | 0.956520i | \(-0.594210\pi\) | ||||
−0.291667 | + | 0.956520i | \(0.594210\pi\) | |||||||
\(774\) | 2.11869e6 | 0.127120 | ||||||||
\(775\) | −2.89793e7 | −1.73314 | ||||||||
\(776\) | 1.08659e6 | 0.0647757 | ||||||||
\(777\) | 7.02170e6 | 0.417244 | ||||||||
\(778\) | 853464. | 0.0505518 | ||||||||
\(779\) | 2.92434e6 | 0.172657 | ||||||||
\(780\) | 7.84896e6 | 0.461929 | ||||||||
\(781\) | −9.48326e6 | −0.556327 | ||||||||
\(782\) | −2.44944e7 | −1.43235 | ||||||||
\(783\) | −1.87828e7 | −1.09485 | ||||||||
\(784\) | 614656. | 0.0357143 | ||||||||
\(785\) | 6.38736e6 | 0.369954 | ||||||||
\(786\) | 986640. | 0.0569642 | ||||||||
\(787\) | −1.57170e6 | −0.0904549 | −0.0452275 | − | 0.998977i | \(-0.514401\pi\) | ||||
−0.0452275 | + | 0.998977i | \(0.514401\pi\) | |||||||
\(788\) | −7.91914e6 | −0.454320 | ||||||||
\(789\) | 1.05101e7 | 0.601054 | ||||||||
\(790\) | −1.44050e7 | −0.821193 | ||||||||
\(791\) | 428358. | 0.0243425 | ||||||||
\(792\) | −3.07507e6 | −0.174198 | ||||||||
\(793\) | 1.42940e7 | 0.807180 | ||||||||
\(794\) | 1.63763e7 | 0.921860 | ||||||||
\(795\) | −3.12833e7 | −1.75547 | ||||||||
\(796\) | 8.32582e6 | 0.465741 | ||||||||
\(797\) | −2.25298e6 | −0.125635 | −0.0628175 | − | 0.998025i | \(-0.520009\pi\) | ||||
−0.0628175 | + | 0.998025i | \(0.520009\pi\) | |||||||
\(798\) | −921200. | −0.0512090 | ||||||||
\(799\) | 2.64190e6 | 0.146403 | ||||||||
\(800\) | −4.02534e6 | −0.222371 | ||||||||
\(801\) | −3.82239e6 | −0.210501 | ||||||||
\(802\) | −3.76946e6 | −0.206940 | ||||||||
\(803\) | −1.21027e6 | −0.0662360 | ||||||||
\(804\) | −2.79232e6 | −0.152344 | ||||||||
\(805\) | −1.72872e7 | −0.940232 | ||||||||
\(806\) | 1.72210e7 | 0.933728 | ||||||||
\(807\) | 1.18958e7 | 0.643000 | ||||||||
\(808\) | −6.34906e6 | −0.342122 | ||||||||
\(809\) | −2.37938e7 | −1.27818 | −0.639090 | − | 0.769132i | \(-0.720689\pi\) | ||||
−0.639090 | + | 0.769132i | \(0.720689\pi\) | |||||||
\(810\) | 1.29394e6 | 0.0692947 | ||||||||
\(811\) | 5.32300e6 | 0.284187 | 0.142093 | − | 0.989853i | \(-0.454617\pi\) | ||||
0.142093 | + | 0.989853i | \(0.454617\pi\) | |||||||
\(812\) | 3.81494e6 | 0.203048 | ||||||||
\(813\) | −1.43008e7 | −0.758812 | ||||||||
\(814\) | 1.92595e7 | 1.01879 | ||||||||
\(815\) | 1.04375e7 | 0.550431 | ||||||||
\(816\) | −3.73248e6 | −0.196233 | ||||||||
\(817\) | 1.74088e6 | 0.0912460 | ||||||||
\(818\) | 1.93824e7 | 1.01280 | ||||||||
\(819\) | −4.09209e6 | −0.213174 | ||||||||
\(820\) | 8.36237e6 | 0.434305 | ||||||||
\(821\) | 1.48802e7 | 0.770464 | 0.385232 | − | 0.922820i | \(-0.374121\pi\) | ||||
0.385232 | + | 0.922820i | \(0.374121\pi\) | |||||||
\(822\) | −1.21294e7 | −0.626121 | ||||||||
\(823\) | 2.00601e7 | 1.03236 | 0.516182 | − | 0.856479i | \(-0.327353\pi\) | ||||
0.516182 | + | 0.856479i | \(0.327353\pi\) | |||||||
\(824\) | 8.42522e6 | 0.432278 | ||||||||
\(825\) | −1.32082e7 | −0.675628 | ||||||||
\(826\) | −6.72319e6 | −0.342867 | ||||||||
\(827\) | 1.21539e7 | 0.617949 | 0.308975 | − | 0.951070i | \(-0.400014\pi\) | ||||
0.308975 | + | 0.951070i | \(0.400014\pi\) | |||||||
\(828\) | 9.60960e6 | 0.487113 | ||||||||
\(829\) | 3.21197e7 | 1.62325 | 0.811625 | − | 0.584179i | \(-0.198583\pi\) | ||||
0.811625 | + | 0.584179i | \(0.198583\pi\) | |||||||
\(830\) | 1.18279e7 | 0.595952 | ||||||||
\(831\) | 633020. | 0.0317991 | ||||||||
\(832\) | 2.39206e6 | 0.119802 | ||||||||
\(833\) | −3.50066e6 | −0.174798 | ||||||||
\(834\) | −1.00234e7 | −0.499001 | ||||||||
\(835\) | −6.08328e6 | −0.301941 | ||||||||
\(836\) | −2.52672e6 | −0.125038 | ||||||||
\(837\) | 2.84559e7 | 1.40397 | ||||||||
\(838\) | 6.93938e6 | 0.341359 | ||||||||
\(839\) | −1.01320e6 | −0.0496922 | −0.0248461 | − | 0.999691i | \(-0.507910\pi\) | ||||
−0.0248461 | + | 0.999691i | \(0.507910\pi\) | |||||||
\(840\) | −2.63424e6 | −0.128812 | ||||||||
\(841\) | 3.16681e6 | 0.154394 | ||||||||
\(842\) | 6.60580e6 | 0.321104 | ||||||||
\(843\) | −4.96614e6 | −0.240686 | ||||||||
\(844\) | 2.93254e6 | 0.141706 | ||||||||
\(845\) | −2.53991e6 | −0.122370 | ||||||||
\(846\) | −1.03646e6 | −0.0497884 | ||||||||
\(847\) | −2.35960e6 | −0.113013 | ||||||||
\(848\) | −9.53395e6 | −0.455285 | ||||||||
\(849\) | −1.15842e7 | −0.551564 | ||||||||
\(850\) | 2.29256e7 | 1.08836 | ||||||||
\(851\) | −6.01860e7 | −2.84886 | ||||||||
\(852\) | 4.51584e6 | 0.213128 | ||||||||
\(853\) | 234824. | 0.0110502 | 0.00552510 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552510 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(854\) | −4.79730e6 | −0.225088 | ||||||||
\(855\) | −5.64564e6 | −0.264118 | ||||||||
\(856\) | −3.12653e6 | −0.145840 | ||||||||
\(857\) | 2.83802e7 | 1.31997 | 0.659985 | − | 0.751279i | \(-0.270563\pi\) | ||||
0.659985 | + | 0.751279i | \(0.270563\pi\) | |||||||
\(858\) | 7.84896e6 | 0.363994 | ||||||||
\(859\) | 4.00081e7 | 1.84997 | 0.924986 | − | 0.380001i | \(-0.124076\pi\) | ||||
0.924986 | + | 0.380001i | \(0.124076\pi\) | |||||||
\(860\) | 4.97818e6 | 0.229522 | ||||||||
\(861\) | 3.04878e6 | 0.140158 | ||||||||
\(862\) | −1.65744e7 | −0.759748 | ||||||||
\(863\) | −2.08030e7 | −0.950823 | −0.475411 | − | 0.879764i | \(-0.657701\pi\) | ||||
−0.475411 | + | 0.879764i | \(0.657701\pi\) | |||||||
\(864\) | 3.95264e6 | 0.180137 | ||||||||
\(865\) | −3.70904e7 | −1.68547 | ||||||||
\(866\) | 1.21586e7 | 0.550922 | ||||||||
\(867\) | 7.05907e6 | 0.318933 | ||||||||
\(868\) | −5.77965e6 | −0.260377 | ||||||||
\(869\) | −1.44050e7 | −0.647088 | ||||||||
\(870\) | −1.63498e7 | −0.732341 | ||||||||
\(871\) | −1.01920e7 | −0.455211 | ||||||||
\(872\) | 3.60794e6 | 0.160682 | ||||||||
\(873\) | 2.42785e6 | 0.107817 | ||||||||
\(874\) | 7.89600e6 | 0.349646 | ||||||||
\(875\) | 3.31750e6 | 0.146484 | ||||||||
\(876\) | 576320. | 0.0253748 | ||||||||
\(877\) | 3.03559e7 | 1.33273 | 0.666367 | − | 0.745624i | \(-0.267848\pi\) | ||||
0.666367 | + | 0.745624i | \(0.267848\pi\) | |||||||
\(878\) | −1.01708e7 | −0.445267 | ||||||||
\(879\) | 1.43886e7 | 0.628125 | ||||||||
\(880\) | −7.22534e6 | −0.314523 | ||||||||
\(881\) | −2.58936e7 | −1.12396 | −0.561981 | − | 0.827150i | \(-0.689961\pi\) | ||||
−0.561981 | + | 0.827150i | \(0.689961\pi\) | |||||||
\(882\) | 1.37337e6 | 0.0594452 | ||||||||
\(883\) | −1.88813e7 | −0.814950 | −0.407475 | − | 0.913216i | \(-0.633591\pi\) | ||||
−0.407475 | + | 0.913216i | \(0.633591\pi\) | |||||||
\(884\) | −1.36236e7 | −0.586354 | ||||||||
\(885\) | 2.88137e7 | 1.23663 | ||||||||
\(886\) | 9.72840e6 | 0.416349 | ||||||||
\(887\) | −2.34431e7 | −1.00048 | −0.500238 | − | 0.865888i | \(-0.666754\pi\) | ||||
−0.500238 | + | 0.865888i | \(0.666754\pi\) | |||||||
\(888\) | −9.17120e6 | −0.390296 | ||||||||
\(889\) | 1.54836e7 | 0.657079 | ||||||||
\(890\) | −8.98128e6 | −0.380070 | ||||||||
\(891\) | 1.29394e6 | 0.0546033 | ||||||||
\(892\) | −2.04394e7 | −0.860115 | ||||||||
\(893\) | −851640. | −0.0357378 | ||||||||
\(894\) | 2.42376e6 | 0.101425 | ||||||||
\(895\) | −898128. | −0.0374784 | ||||||||
\(896\) | −802816. | −0.0334077 | ||||||||
\(897\) | −2.45280e7 | −1.01784 | ||||||||
\(898\) | −7.31412e6 | −0.302671 | ||||||||
\(899\) | −3.58722e7 | −1.48033 | ||||||||
\(900\) | −8.99413e6 | −0.370129 | ||||||||
\(901\) | 5.42988e7 | 2.22833 | ||||||||
\(902\) | 8.36237e6 | 0.342226 | ||||||||
\(903\) | 1.81496e6 | 0.0740709 | ||||||||
\(904\) | −559488. | −0.0227703 | ||||||||
\(905\) | −4.58694e7 | −1.86166 | ||||||||
\(906\) | −4.97792e6 | −0.201478 | ||||||||
\(907\) | −5.60873e6 | −0.226384 | −0.113192 | − | 0.993573i | \(-0.536108\pi\) | ||||
−0.113192 | + | 0.993573i | \(0.536108\pi\) | |||||||
\(908\) | −2.06023e7 | −0.829279 | ||||||||
\(909\) | −1.41862e7 | −0.569450 | ||||||||
\(910\) | −9.61498e6 | −0.384897 | ||||||||
\(911\) | 2.16215e7 | 0.863156 | 0.431578 | − | 0.902076i | \(-0.357957\pi\) | ||||
0.431578 | + | 0.902076i | \(0.357957\pi\) | |||||||
\(912\) | 1.20320e6 | 0.0479017 | ||||||||
\(913\) | 1.18279e7 | 0.469602 | ||||||||
\(914\) | −6.32252e6 | −0.250337 | ||||||||
\(915\) | 2.05598e7 | 0.811834 | ||||||||
\(916\) | 5.61498e6 | 0.221110 | ||||||||
\(917\) | −1.20863e6 | −0.0474648 | ||||||||
\(918\) | −2.25115e7 | −0.881654 | ||||||||
\(919\) | 4.51695e7 | 1.76424 | 0.882119 | − | 0.471028i | \(-0.156117\pi\) | ||||
0.882119 | + | 0.471028i | \(0.156117\pi\) | |||||||
\(920\) | 2.25792e7 | 0.879506 | ||||||||
\(921\) | −9.89098e6 | −0.384229 | ||||||||
\(922\) | −2.03842e7 | −0.789706 | ||||||||
\(923\) | 1.64828e7 | 0.636835 | ||||||||
\(924\) | −2.63424e6 | −0.101502 | ||||||||
\(925\) | 5.63312e7 | 2.16469 | ||||||||
\(926\) | 2.80935e7 | 1.07666 | ||||||||
\(927\) | 1.88251e7 | 0.719512 | ||||||||
\(928\) | −4.98278e6 | −0.189934 | ||||||||
\(929\) | −2.28729e7 | −0.869524 | −0.434762 | − | 0.900545i | \(-0.643168\pi\) | ||||
−0.434762 | + | 0.900545i | \(0.643168\pi\) | |||||||
\(930\) | 2.47699e7 | 0.939112 | ||||||||
\(931\) | 1.12847e6 | 0.0426693 | ||||||||
\(932\) | 1.33785e7 | 0.504506 | ||||||||
\(933\) | −2.22050e7 | −0.835117 | ||||||||
\(934\) | 1.69938e7 | 0.637417 | ||||||||
\(935\) | 4.11506e7 | 1.53938 | ||||||||
\(936\) | 5.34477e6 | 0.199406 | ||||||||
\(937\) | −1.79616e7 | −0.668336 | −0.334168 | − | 0.942514i | \(-0.608455\pi\) | ||||
−0.334168 | + | 0.942514i | \(0.608455\pi\) | |||||||
\(938\) | 3.42059e6 | 0.126939 | ||||||||
\(939\) | 2.33008e7 | 0.862395 | ||||||||
\(940\) | −2.43533e6 | −0.0898955 | ||||||||
\(941\) | −1.79697e7 | −0.661558 | −0.330779 | − | 0.943708i | \(-0.607311\pi\) | ||||
−0.330779 | + | 0.943708i | \(0.607311\pi\) | |||||||
\(942\) | −3.04160e6 | −0.111680 | ||||||||
\(943\) | −2.61324e7 | −0.956974 | ||||||||
\(944\) | 8.78131e6 | 0.320722 | ||||||||
\(945\) | −1.58878e7 | −0.578740 | ||||||||
\(946\) | 4.97818e6 | 0.180860 | ||||||||
\(947\) | 4.32115e7 | 1.56576 | 0.782879 | − | 0.622174i | \(-0.213750\pi\) | ||||
0.782879 | + | 0.622174i | \(0.213750\pi\) | |||||||
\(948\) | 6.85952e6 | 0.247898 | ||||||||
\(949\) | 2.10357e6 | 0.0758213 | ||||||||
\(950\) | −7.39028e6 | −0.265676 | ||||||||
\(951\) | 4.27542e6 | 0.153295 | ||||||||
\(952\) | 4.57229e6 | 0.163509 | ||||||||
\(953\) | −7.50965e6 | −0.267848 | −0.133924 | − | 0.990992i | \(-0.542758\pi\) | ||||
−0.133924 | + | 0.990992i | \(0.542758\pi\) | |||||||
\(954\) | −2.13024e7 | −0.757806 | ||||||||
\(955\) | −4.83820e7 | −1.71662 | ||||||||
\(956\) | 1.23894e7 | 0.438434 | ||||||||
\(957\) | −1.63498e7 | −0.577074 | ||||||||
\(958\) | −2.23714e6 | −0.0787551 | ||||||||
\(959\) | 1.48585e7 | 0.521708 | ||||||||
\(960\) | 3.44064e6 | 0.120493 | ||||||||
\(961\) | 2.57172e7 | 0.898288 | ||||||||
\(962\) | −3.34749e7 | −1.16622 | ||||||||
\(963\) | −6.98584e6 | −0.242746 | ||||||||
\(964\) | −1.84456e7 | −0.639293 | ||||||||
\(965\) | −3.47708e7 | −1.20198 | ||||||||
\(966\) | 8.23200e6 | 0.283833 | ||||||||
\(967\) | −1.69305e7 | −0.582242 | −0.291121 | − | 0.956686i | \(-0.594028\pi\) | ||||
−0.291121 | + | 0.956686i | \(0.594028\pi\) | |||||||
\(968\) | 3.08192e6 | 0.105714 | ||||||||
\(969\) | −6.85260e6 | −0.234448 | ||||||||
\(970\) | 5.70461e6 | 0.194669 | ||||||||
\(971\) | 2.86144e7 | 0.973949 | 0.486974 | − | 0.873416i | \(-0.338101\pi\) | ||||
0.486974 | + | 0.873416i | \(0.338101\pi\) | |||||||
\(972\) | 1.43915e7 | 0.488586 | ||||||||
\(973\) | 1.22787e7 | 0.415787 | ||||||||
\(974\) | 5.28227e6 | 0.178412 | ||||||||
\(975\) | 2.29570e7 | 0.773400 | ||||||||
\(976\) | 6.26586e6 | 0.210550 | ||||||||
\(977\) | 3.69445e7 | 1.23826 | 0.619132 | − | 0.785287i | \(-0.287485\pi\) | ||||
0.619132 | + | 0.785287i | \(0.287485\pi\) | |||||||
\(978\) | −4.97024e6 | −0.166161 | ||||||||
\(979\) | −8.98128e6 | −0.299489 | ||||||||
\(980\) | 3.22694e6 | 0.107331 | ||||||||
\(981\) | 8.06148e6 | 0.267450 | ||||||||
\(982\) | −2.50877e7 | −0.830200 | ||||||||
\(983\) | −3.88787e7 | −1.28330 | −0.641650 | − | 0.766998i | \(-0.721750\pi\) | ||||
−0.641650 | + | 0.766998i | \(0.721750\pi\) | |||||||
\(984\) | −3.98208e6 | −0.131106 | ||||||||
\(985\) | −4.15755e7 | −1.36536 | ||||||||
\(986\) | 2.83785e7 | 0.929603 | ||||||||
\(987\) | −887880. | −0.0290109 | ||||||||
\(988\) | 4.39168e6 | 0.143133 | ||||||||
\(989\) | −1.55568e7 | −0.505743 | ||||||||
\(990\) | −1.61441e7 | −0.523512 | ||||||||
\(991\) | 2.49212e7 | 0.806092 | 0.403046 | − | 0.915180i | \(-0.367951\pi\) | ||||
0.403046 | + | 0.915180i | \(0.367951\pi\) | |||||||
\(992\) | 7.54893e6 | 0.243560 | ||||||||
\(993\) | −3.96616e6 | −0.127643 | ||||||||
\(994\) | −5.53190e6 | −0.177586 | ||||||||
\(995\) | 4.37106e7 | 1.39968 | ||||||||
\(996\) | −5.63232e6 | −0.179903 | ||||||||
\(997\) | 1.01956e7 | 0.324845 | 0.162422 | − | 0.986721i | \(-0.448069\pi\) | ||||
0.162422 | + | 0.986721i | \(0.448069\pi\) | |||||||
\(998\) | 1.57514e7 | 0.500603 | ||||||||
\(999\) | −5.53138e7 | −1.75356 |
(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 | 14.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 126.6.a.f.1.1 | 1 | |||
4.3 | odd | 2 | 112.6.a.c.1.1 | 1 | |||
5.2 | odd | 4 | 350.6.c.d.99.1 | 2 | |||
5.3 | odd | 4 | 350.6.c.d.99.2 | 2 | |||
5.4 | even | 2 | 350.6.a.i.1.1 | 1 | |||
7.2 | even | 3 | 98.6.c.c.67.1 | 2 | |||
7.3 | odd | 6 | 98.6.c.d.79.1 | 2 | |||
7.4 | even | 3 | 98.6.c.c.79.1 | 2 | |||
7.5 | odd | 6 | 98.6.c.d.67.1 | 2 | |||
7.6 | odd | 2 | 98.6.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 448.6.a.l.1.1 | 1 | |||
8.5 | even | 2 | 448.6.a.e.1.1 | 1 | |||
12.11 | even | 2 | 1008.6.a.b.1.1 | 1 | |||
21.20 | even | 2 | 882.6.a.x.1.1 | 1 | |||
28.27 | even | 2 | 784.6.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
98.6.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
98.6.c.c.67.1 | 2 | 7.2 | even | 3 | |||
98.6.c.c.79.1 | 2 | 7.4 | even | 3 | |||
98.6.c.d.67.1 | 2 | 7.5 | odd | 6 | |||
98.6.c.d.79.1 | 2 | 7.3 | odd | 6 | |||
112.6.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
126.6.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
350.6.a.i.1.1 | 1 | 5.4 | even | 2 | |||
350.6.c.d.99.1 | 2 | 5.2 | odd | 4 | |||
350.6.c.d.99.2 | 2 | 5.3 | odd | 4 | |||
448.6.a.e.1.1 | 1 | 8.5 | even | 2 | |||
448.6.a.l.1.1 | 1 | 8.3 | odd | 2 | |||
784.6.a.i.1.1 | 1 | 28.27 | even | 2 | |||
882.6.a.x.1.1 | 1 | 21.20 | even | 2 | |||
1008.6.a.b.1.1 | 1 | 12.11 | even | 2 |