Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(39.2940358542\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 246 x^{8} - 192 x^{7} + 20336 x^{6} + 25380 x^{5} - 639206 x^{4} - 722920 x^{3} + 7583055 x^{2} + 5935300 x - 22888100 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 7^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.63335\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.633352 | −0.111962 | −0.0559809 | − | 0.998432i | \(-0.517829\pi\) | ||||
−0.0559809 | + | 0.998432i | \(0.517829\pi\) | |||||||
\(3\) | −19.5171 | −1.25202 | −0.626012 | − | 0.779814i | \(-0.715314\pi\) | ||||
−0.626012 | + | 0.779814i | \(0.715314\pi\) | |||||||
\(4\) | −31.5989 | −0.987465 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 12.3612 | 0.140179 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 40.2804 | 0.222520 | ||||||||
\(9\) | 137.918 | 0.567563 | ||||||||
\(10\) | 15.8338 | 0.0500708 | ||||||||
\(11\) | 76.2344 | 0.189963 | 0.0949815 | − | 0.995479i | \(-0.469721\pi\) | ||||
0.0949815 | + | 0.995479i | \(0.469721\pi\) | |||||||
\(12\) | 616.719 | 1.23633 | ||||||||
\(13\) | −266.495 | −0.437352 | −0.218676 | − | 0.975798i | \(-0.570174\pi\) | ||||
−0.218676 | + | 0.975798i | \(0.570174\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 487.928 | 0.559922 | ||||||||
\(16\) | 985.652 | 0.962551 | ||||||||
\(17\) | −267.518 | −0.224508 | −0.112254 | − | 0.993680i | \(-0.535807\pi\) | ||||
−0.112254 | + | 0.993680i | \(0.535807\pi\) | |||||||
\(18\) | −87.3504 | −0.0635453 | ||||||||
\(19\) | 1763.32 | 1.12059 | 0.560296 | − | 0.828292i | \(-0.310687\pi\) | ||||
0.560296 | + | 0.828292i | \(0.310687\pi\) | |||||||
\(20\) | 789.972 | 0.441608 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −48.2831 | −0.0212686 | ||||||||
\(23\) | 4413.22 | 1.73954 | 0.869772 | − | 0.493453i | \(-0.164266\pi\) | ||||
0.869772 | + | 0.493453i | \(0.164266\pi\) | |||||||
\(24\) | −786.158 | −0.278600 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 168.785 | 0.0489667 | ||||||||
\(27\) | 2050.90 | 0.541422 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 129.019 | 0.0284879 | 0.0142439 | − | 0.999899i | \(-0.495466\pi\) | ||||
0.0142439 | + | 0.999899i | \(0.495466\pi\) | |||||||
\(30\) | −309.030 | −0.0626899 | ||||||||
\(31\) | −5981.45 | −1.11790 | −0.558949 | − | 0.829202i | \(-0.688795\pi\) | ||||
−0.558949 | + | 0.829202i | \(0.688795\pi\) | |||||||
\(32\) | −1913.24 | −0.330289 | ||||||||
\(33\) | −1487.87 | −0.237838 | ||||||||
\(34\) | 169.433 | 0.0251363 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4358.04 | −0.560448 | ||||||||
\(37\) | 8909.64 | 1.06993 | 0.534966 | − | 0.844874i | \(-0.320325\pi\) | ||||
0.534966 | + | 0.844874i | \(0.320325\pi\) | |||||||
\(38\) | −1116.80 | −0.125464 | ||||||||
\(39\) | 5201.22 | 0.547575 | ||||||||
\(40\) | −1007.01 | −0.0995140 | ||||||||
\(41\) | −9262.01 | −0.860490 | −0.430245 | − | 0.902712i | \(-0.641573\pi\) | ||||
−0.430245 | + | 0.902712i | \(0.641573\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6782.24 | −0.559374 | −0.279687 | − | 0.960091i | \(-0.590231\pi\) | ||||
−0.279687 | + | 0.960091i | \(0.590231\pi\) | |||||||
\(44\) | −2408.92 | −0.187582 | ||||||||
\(45\) | −3447.94 | −0.253822 | ||||||||
\(46\) | −2795.12 | −0.194763 | ||||||||
\(47\) | −25145.7 | −1.66042 | −0.830211 | − | 0.557450i | \(-0.811780\pi\) | ||||
−0.830211 | + | 0.557450i | \(0.811780\pi\) | |||||||
\(48\) | −19237.1 | −1.20514 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −395.845 | −0.0223924 | ||||||||
\(51\) | 5221.19 | 0.281089 | ||||||||
\(52\) | 8420.94 | 0.431869 | ||||||||
\(53\) | −3066.58 | −0.149956 | −0.0749782 | − | 0.997185i | \(-0.523889\pi\) | ||||
−0.0749782 | + | 0.997185i | \(0.523889\pi\) | |||||||
\(54\) | −1298.94 | −0.0606185 | ||||||||
\(55\) | −1905.86 | −0.0849540 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −34415.0 | −1.40301 | ||||||||
\(58\) | −81.7146 | −0.00318955 | ||||||||
\(59\) | 23669.3 | 0.885230 | 0.442615 | − | 0.896712i | \(-0.354051\pi\) | ||||
0.442615 | + | 0.896712i | \(0.354051\pi\) | |||||||
\(60\) | −15418.0 | −0.552903 | ||||||||
\(61\) | −32287.4 | −1.11099 | −0.555493 | − | 0.831521i | \(-0.687471\pi\) | ||||
−0.555493 | + | 0.831521i | \(0.687471\pi\) | |||||||
\(62\) | 3788.36 | 0.125162 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −30329.1 | −0.925571 | ||||||||
\(65\) | 6662.38 | 0.195590 | ||||||||
\(66\) | 942.348 | 0.0266288 | ||||||||
\(67\) | −31965.8 | −0.869960 | −0.434980 | − | 0.900440i | \(-0.643245\pi\) | ||||
−0.434980 | + | 0.900440i | \(0.643245\pi\) | |||||||
\(68\) | 8453.28 | 0.221693 | ||||||||
\(69\) | −86133.2 | −2.17795 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 59587.9 | 1.40285 | 0.701426 | − | 0.712742i | \(-0.252547\pi\) | ||||
0.701426 | + | 0.712742i | \(0.252547\pi\) | |||||||
\(72\) | 5555.39 | 0.126294 | ||||||||
\(73\) | 24102.7 | 0.529370 | 0.264685 | − | 0.964335i | \(-0.414732\pi\) | ||||
0.264685 | + | 0.964335i | \(0.414732\pi\) | |||||||
\(74\) | −5642.93 | −0.119791 | ||||||||
\(75\) | −12198.2 | −0.250405 | ||||||||
\(76\) | −55719.0 | −1.10655 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3294.20 | −0.0613074 | ||||||||
\(79\) | 107001. | 1.92895 | 0.964474 | − | 0.264178i | \(-0.0851007\pi\) | ||||
0.964474 | + | 0.264178i | \(0.0851007\pi\) | |||||||
\(80\) | −24641.3 | −0.430466 | ||||||||
\(81\) | −73541.7 | −1.24544 | ||||||||
\(82\) | 5866.11 | 0.0963420 | ||||||||
\(83\) | −5517.40 | −0.0879101 | −0.0439551 | − | 0.999034i | \(-0.513996\pi\) | ||||
−0.0439551 | + | 0.999034i | \(0.513996\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6687.96 | 0.100403 | ||||||||
\(86\) | 4295.54 | 0.0626285 | ||||||||
\(87\) | −2518.08 | −0.0356675 | ||||||||
\(88\) | 3070.75 | 0.0422706 | ||||||||
\(89\) | −39714.8 | −0.531469 | −0.265734 | − | 0.964046i | \(-0.585614\pi\) | ||||
−0.265734 | + | 0.964046i | \(0.585614\pi\) | |||||||
\(90\) | 2183.76 | 0.0284183 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −139453. | −1.71774 | ||||||||
\(93\) | 116741. | 1.39963 | ||||||||
\(94\) | 15926.0 | 0.185904 | ||||||||
\(95\) | −44083.0 | −0.501144 | ||||||||
\(96\) | 37340.9 | 0.413530 | ||||||||
\(97\) | 131282. | 1.41670 | 0.708348 | − | 0.705864i | \(-0.249441\pi\) | ||||
0.708348 | + | 0.705864i | \(0.249441\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10514.1 | 0.107816 | ||||||||
\(100\) | −19749.3 | −0.197493 | ||||||||
\(101\) | −170783. | −1.66587 | −0.832935 | − | 0.553371i | \(-0.813341\pi\) | ||||
−0.832935 | + | 0.553371i | \(0.813341\pi\) | |||||||
\(102\) | −3306.85 | −0.0314712 | ||||||||
\(103\) | −41960.6 | −0.389716 | −0.194858 | − | 0.980831i | \(-0.562425\pi\) | ||||
−0.194858 | + | 0.980831i | \(0.562425\pi\) | |||||||
\(104\) | −10734.5 | −0.0973196 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1942.22 | 0.0167894 | ||||||||
\(107\) | 126667. | 1.06956 | 0.534779 | − | 0.844992i | \(-0.320395\pi\) | ||||
0.534779 | + | 0.844992i | \(0.320395\pi\) | |||||||
\(108\) | −64806.2 | −0.534635 | ||||||||
\(109\) | 149620. | 1.20621 | 0.603107 | − | 0.797661i | \(-0.293929\pi\) | ||||
0.603107 | + | 0.797661i | \(0.293929\pi\) | |||||||
\(110\) | 1207.08 | 0.00951161 | ||||||||
\(111\) | −173890. | −1.33958 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 84809.5 | 0.624810 | 0.312405 | − | 0.949949i | \(-0.398865\pi\) | ||||
0.312405 | + | 0.949949i | \(0.398865\pi\) | |||||||
\(114\) | 21796.8 | 0.157083 | ||||||||
\(115\) | −110330. | −0.777948 | ||||||||
\(116\) | −4076.86 | −0.0281307 | ||||||||
\(117\) | −36754.4 | −0.248225 | ||||||||
\(118\) | −14991.0 | −0.0991120 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 19653.9 | 0.124594 | ||||||||
\(121\) | −155239. | −0.963914 | ||||||||
\(122\) | 20449.3 | 0.124388 | ||||||||
\(123\) | 180768. | 1.07735 | ||||||||
\(124\) | 189007. | 1.10388 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −248125. | −1.36509 | −0.682545 | − | 0.730844i | \(-0.739127\pi\) | ||||
−0.682545 | + | 0.730844i | \(0.739127\pi\) | |||||||
\(128\) | 80432.6 | 0.433918 | ||||||||
\(129\) | 132370. | 0.700349 | ||||||||
\(130\) | −4219.63 | −0.0218986 | ||||||||
\(131\) | −261050. | −1.32906 | −0.664532 | − | 0.747260i | \(-0.731369\pi\) | ||||
−0.664532 | + | 0.747260i | \(0.731369\pi\) | |||||||
\(132\) | 47015.1 | 0.234857 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 20245.6 | 0.0974022 | ||||||||
\(135\) | −51272.6 | −0.242131 | ||||||||
\(136\) | −10775.8 | −0.0499575 | ||||||||
\(137\) | −16931.3 | −0.0770706 | −0.0385353 | − | 0.999257i | \(-0.512269\pi\) | ||||
−0.0385353 | + | 0.999257i | \(0.512269\pi\) | |||||||
\(138\) | 54552.6 | 0.243847 | ||||||||
\(139\) | 179252. | 0.786914 | 0.393457 | − | 0.919343i | \(-0.371279\pi\) | ||||
0.393457 | + | 0.919343i | \(0.371279\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 490771. | 2.07889 | ||||||||
\(142\) | −37740.1 | −0.157066 | ||||||||
\(143\) | −20316.1 | −0.0830806 | ||||||||
\(144\) | 135939. | 0.546308 | ||||||||
\(145\) | −3225.48 | −0.0127402 | ||||||||
\(146\) | −15265.5 | −0.0592692 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −281535. | −1.05652 | ||||||||
\(149\) | −376763. | −1.39028 | −0.695140 | − | 0.718875i | \(-0.744658\pi\) | ||||
−0.695140 | + | 0.718875i | \(0.744658\pi\) | |||||||
\(150\) | 7725.75 | 0.0280358 | ||||||||
\(151\) | −355503. | −1.26882 | −0.634412 | − | 0.772995i | \(-0.718758\pi\) | ||||
−0.634412 | + | 0.772995i | \(0.718758\pi\) | |||||||
\(152\) | 71027.4 | 0.249354 | ||||||||
\(153\) | −36895.5 | −0.127422 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 149536. | 0.499939 | ||||||||
\(156\) | −164353. | −0.540711 | ||||||||
\(157\) | 491459. | 1.59125 | 0.795624 | − | 0.605791i | \(-0.207143\pi\) | ||||
0.795624 | + | 0.605791i | \(0.207143\pi\) | |||||||
\(158\) | −67769.3 | −0.215968 | ||||||||
\(159\) | 59850.8 | 0.187749 | ||||||||
\(160\) | 47831.0 | 0.147710 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 46577.8 | 0.139441 | ||||||||
\(163\) | −143009. | −0.421593 | −0.210796 | − | 0.977530i | \(-0.567606\pi\) | ||||
−0.210796 | + | 0.977530i | \(0.567606\pi\) | |||||||
\(164\) | 292669. | 0.849703 | ||||||||
\(165\) | 37196.9 | 0.106364 | ||||||||
\(166\) | 3494.45 | 0.00984258 | ||||||||
\(167\) | 313947. | 0.871094 | 0.435547 | − | 0.900166i | \(-0.356555\pi\) | ||||
0.435547 | + | 0.900166i | \(0.356555\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −300273. | −0.808723 | ||||||||
\(170\) | −4235.83 | −0.0112413 | ||||||||
\(171\) | 243193. | 0.636006 | ||||||||
\(172\) | 214311. | 0.552362 | ||||||||
\(173\) | 437124. | 1.11043 | 0.555213 | − | 0.831708i | \(-0.312637\pi\) | ||||
0.555213 | + | 0.831708i | \(0.312637\pi\) | |||||||
\(174\) | 1594.83 | 0.00399339 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 75140.5 | 0.182849 | ||||||||
\(177\) | −461957. | −1.10833 | ||||||||
\(178\) | 25153.5 | 0.0595042 | ||||||||
\(179\) | −391475. | −0.913211 | −0.456605 | − | 0.889669i | \(-0.650935\pi\) | ||||
−0.456605 | + | 0.889669i | \(0.650935\pi\) | |||||||
\(180\) | 108951. | 0.250640 | ||||||||
\(181\) | 82459.5 | 0.187087 | 0.0935437 | − | 0.995615i | \(-0.470181\pi\) | ||||
0.0935437 | + | 0.995615i | \(0.470181\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 630157. | 1.39098 | ||||||||
\(184\) | 177766. | 0.387084 | ||||||||
\(185\) | −222741. | −0.478488 | ||||||||
\(186\) | −73937.9 | −0.156706 | ||||||||
\(187\) | −20394.1 | −0.0426482 | ||||||||
\(188\) | 794574. | 1.63961 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 27920.1 | 0.0561090 | ||||||||
\(191\) | −849381. | −1.68469 | −0.842343 | − | 0.538942i | \(-0.818824\pi\) | ||||
−0.842343 | + | 0.538942i | \(0.818824\pi\) | |||||||
\(192\) | 591937. | 1.15884 | ||||||||
\(193\) | 284540. | 0.549857 | 0.274928 | − | 0.961465i | \(-0.411346\pi\) | ||||
0.274928 | + | 0.961465i | \(0.411346\pi\) | |||||||
\(194\) | −83147.8 | −0.158616 | ||||||||
\(195\) | −130030. | −0.244883 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 554266. | 1.01754 | 0.508772 | − | 0.860902i | \(-0.330100\pi\) | ||||
0.508772 | + | 0.860902i | \(0.330100\pi\) | |||||||
\(198\) | −6659.10 | −0.0120713 | ||||||||
\(199\) | −635373. | −1.13735 | −0.568677 | − | 0.822561i | \(-0.692545\pi\) | ||||
−0.568677 | + | 0.822561i | \(0.692545\pi\) | |||||||
\(200\) | 25175.3 | 0.0445040 | ||||||||
\(201\) | 623881. | 1.08921 | ||||||||
\(202\) | 108166. | 0.186514 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −164984. | −0.277565 | ||||||||
\(205\) | 231550. | 0.384823 | ||||||||
\(206\) | 26575.8 | 0.0436333 | ||||||||
\(207\) | 608661. | 0.987301 | ||||||||
\(208\) | −262671. | −0.420973 | ||||||||
\(209\) | 134426. | 0.212871 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −280331. | −0.433476 | −0.216738 | − | 0.976230i | \(-0.569542\pi\) | ||||
−0.216738 | + | 0.976230i | \(0.569542\pi\) | |||||||
\(212\) | 96900.5 | 0.148077 | ||||||||
\(213\) | −1.16298e6 | −1.75640 | ||||||||
\(214\) | −80224.8 | −0.119750 | ||||||||
\(215\) | 169556. | 0.250160 | ||||||||
\(216\) | 82611.3 | 0.120477 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −94762.2 | −0.135050 | ||||||||
\(219\) | −470416. | −0.662783 | ||||||||
\(220\) | 60223.0 | 0.0838891 | ||||||||
\(221\) | 71292.3 | 0.0981888 | ||||||||
\(222\) | 110134. | 0.149982 | ||||||||
\(223\) | 970109. | 1.30635 | 0.653173 | − | 0.757208i | \(-0.273437\pi\) | ||||
0.653173 | + | 0.757208i | \(0.273437\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 86198.6 | 0.113513 | ||||||||
\(226\) | −53714.2 | −0.0699549 | ||||||||
\(227\) | −569413. | −0.733437 | −0.366719 | − | 0.930332i | \(-0.619519\pi\) | ||||
−0.366719 | + | 0.930332i | \(0.619519\pi\) | |||||||
\(228\) | 1.08747e6 | 1.38542 | ||||||||
\(229\) | −77988.6 | −0.0982748 | −0.0491374 | − | 0.998792i | \(-0.515647\pi\) | ||||
−0.0491374 | + | 0.998792i | \(0.515647\pi\) | |||||||
\(230\) | 69877.9 | 0.0871005 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5196.95 | 0.00633912 | ||||||||
\(233\) | 829373. | 1.00083 | 0.500415 | − | 0.865786i | \(-0.333181\pi\) | ||||
0.500415 | + | 0.865786i | \(0.333181\pi\) | |||||||
\(234\) | 23278.5 | 0.0277917 | ||||||||
\(235\) | 628641. | 0.742563 | ||||||||
\(236\) | −747924. | −0.874133 | ||||||||
\(237\) | −2.08835e6 | −2.41509 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 252273. | 0.285678 | 0.142839 | − | 0.989746i | \(-0.454377\pi\) | ||||
0.142839 | + | 0.989746i | \(0.454377\pi\) | |||||||
\(240\) | 480927. | 0.538953 | ||||||||
\(241\) | 535968. | 0.594424 | 0.297212 | − | 0.954812i | \(-0.403943\pi\) | ||||
0.297212 | + | 0.954812i | \(0.403943\pi\) | |||||||
\(242\) | 98321.1 | 0.107922 | ||||||||
\(243\) | 936953. | 1.01789 | ||||||||
\(244\) | 1.02025e6 | 1.09706 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −114490. | −0.120622 | ||||||||
\(247\) | −469917. | −0.490093 | ||||||||
\(248\) | −240935. | −0.248755 | ||||||||
\(249\) | 107684. | 0.110066 | ||||||||
\(250\) | 9896.12 | 0.0100142 | ||||||||
\(251\) | 52953.6 | 0.0530531 | 0.0265266 | − | 0.999648i | \(-0.491555\pi\) | ||||
0.0265266 | + | 0.999648i | \(0.491555\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 336439. | 0.330449 | ||||||||
\(254\) | 157150. | 0.152838 | ||||||||
\(255\) | −130530. | −0.125707 | ||||||||
\(256\) | 919589. | 0.876989 | ||||||||
\(257\) | 527109. | 0.497814 | 0.248907 | − | 0.968527i | \(-0.419929\pi\) | ||||
0.248907 | + | 0.968527i | \(0.419929\pi\) | |||||||
\(258\) | −83836.6 | −0.0784123 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −210524. | −0.193138 | ||||||||
\(261\) | 17794.1 | 0.0161686 | ||||||||
\(262\) | 165337. | 0.148804 | ||||||||
\(263\) | −1.26966e6 | −1.13187 | −0.565935 | − | 0.824450i | \(-0.691485\pi\) | ||||
−0.565935 | + | 0.824450i | \(0.691485\pi\) | |||||||
\(264\) | −59932.2 | −0.0529238 | ||||||||
\(265\) | 76664.6 | 0.0670625 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 775119. | 0.665412 | ||||||||
\(268\) | 1.01008e6 | 0.859054 | ||||||||
\(269\) | −863268. | −0.727386 | −0.363693 | − | 0.931519i | \(-0.618484\pi\) | ||||
−0.363693 | + | 0.931519i | \(0.618484\pi\) | |||||||
\(270\) | 32473.6 | 0.0271094 | ||||||||
\(271\) | −1.82397e6 | −1.50867 | −0.754335 | − | 0.656490i | \(-0.772040\pi\) | ||||
−0.754335 | + | 0.656490i | \(0.772040\pi\) | |||||||
\(272\) | −263680. | −0.216100 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10723.5 | 0.00862896 | ||||||||
\(275\) | 47646.5 | 0.0379926 | ||||||||
\(276\) | 2.72171e6 | 2.15065 | ||||||||
\(277\) | −2.09940e6 | −1.64398 | −0.821990 | − | 0.569503i | \(-0.807136\pi\) | ||||
−0.821990 | + | 0.569503i | \(0.807136\pi\) | |||||||
\(278\) | −113530. | −0.0881042 | ||||||||
\(279\) | −824948. | −0.634477 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.72140e6 | −1.30052 | −0.650260 | − | 0.759712i | \(-0.725340\pi\) | ||||
−0.650260 | + | 0.759712i | \(0.725340\pi\) | |||||||
\(282\) | −310830. | −0.232756 | ||||||||
\(283\) | −2.53726e6 | −1.88321 | −0.941606 | − | 0.336716i | \(-0.890684\pi\) | ||||
−0.941606 | + | 0.336716i | \(0.890684\pi\) | |||||||
\(284\) | −1.88291e6 | −1.38527 | ||||||||
\(285\) | 860374. | 0.627444 | ||||||||
\(286\) | 12867.2 | 0.00930186 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −263869. | −0.187460 | ||||||||
\(289\) | −1.34829e6 | −0.949596 | ||||||||
\(290\) | 2042.86 | 0.00142641 | ||||||||
\(291\) | −2.56225e6 | −1.77374 | ||||||||
\(292\) | −761619. | −0.522734 | ||||||||
\(293\) | −1.14064e6 | −0.776213 | −0.388106 | − | 0.921615i | \(-0.626871\pi\) | ||||
−0.388106 | + | 0.921615i | \(0.626871\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −591734. | −0.395887 | ||||||||
\(296\) | 358884. | 0.238081 | ||||||||
\(297\) | 156349. | 0.102850 | ||||||||
\(298\) | 238623. | 0.155658 | ||||||||
\(299\) | −1.17610e6 | −0.760793 | ||||||||
\(300\) | 385449. | 0.247266 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 225158. | 0.142060 | ||||||||
\(303\) | 3.33319e6 | 2.08571 | ||||||||
\(304\) | 1.73802e6 | 1.07863 | ||||||||
\(305\) | 807186. | 0.496848 | ||||||||
\(306\) | 23367.8 | 0.0142664 | ||||||||
\(307\) | −1.50913e6 | −0.913861 | −0.456931 | − | 0.889502i | \(-0.651051\pi\) | ||||
−0.456931 | + | 0.889502i | \(0.651051\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 818950. | 0.487934 | ||||||||
\(310\) | −94709.0 | −0.0559741 | ||||||||
\(311\) | 3.37087e6 | 1.97625 | 0.988124 | − | 0.153660i | \(-0.0491059\pi\) | ||||
0.988124 | + | 0.153660i | \(0.0491059\pi\) | |||||||
\(312\) | 209507. | 0.121846 | ||||||||
\(313\) | 427067. | 0.246397 | 0.123198 | − | 0.992382i | \(-0.460685\pi\) | ||||
0.123198 | + | 0.992382i | \(0.460685\pi\) | |||||||
\(314\) | −311266. | −0.178159 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.38111e6 | −1.90477 | ||||||||
\(317\) | −868486. | −0.485417 | −0.242708 | − | 0.970099i | \(-0.578036\pi\) | ||||
−0.242708 | + | 0.970099i | \(0.578036\pi\) | |||||||
\(318\) | −37906.6 | −0.0210207 | ||||||||
\(319\) | 9835.70 | 0.00541164 | ||||||||
\(320\) | 758228. | 0.413928 | ||||||||
\(321\) | −2.47218e6 | −1.33911 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −471721. | −0.251582 | ||||||||
\(324\) | 2.32383e6 | 1.22982 | ||||||||
\(325\) | −166559. | −0.0874703 | ||||||||
\(326\) | 90574.7 | 0.0472023 | ||||||||
\(327\) | −2.92016e6 | −1.51021 | ||||||||
\(328\) | −373078. | −0.191476 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −23558.7 | −0.0119088 | ||||||||
\(331\) | −1.48917e6 | −0.747092 | −0.373546 | − | 0.927612i | \(-0.621858\pi\) | ||||
−0.373546 | + | 0.927612i | \(0.621858\pi\) | |||||||
\(332\) | 174343. | 0.0868082 | ||||||||
\(333\) | 1.22880e6 | 0.607253 | ||||||||
\(334\) | −198839. | −0.0975293 | ||||||||
\(335\) | 799146. | 0.389058 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.73365e6 | 0.831547 | 0.415773 | − | 0.909468i | \(-0.363511\pi\) | ||||
0.415773 | + | 0.909468i | \(0.363511\pi\) | |||||||
\(338\) | 190179. | 0.0905461 | ||||||||
\(339\) | −1.65524e6 | −0.782277 | ||||||||
\(340\) | −211332. | −0.0991443 | ||||||||
\(341\) | −455992. | −0.212359 | ||||||||
\(342\) | −154027. | −0.0712084 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −273192. | −0.124472 | ||||||||
\(345\) | 2.15333e6 | 0.974009 | ||||||||
\(346\) | −276853. | −0.124325 | ||||||||
\(347\) | −3.26650e6 | −1.45633 | −0.728164 | − | 0.685403i | \(-0.759626\pi\) | ||||
−0.728164 | + | 0.685403i | \(0.759626\pi\) | |||||||
\(348\) | 79568.6 | 0.0352204 | ||||||||
\(349\) | −4.01741e6 | −1.76556 | −0.882779 | − | 0.469788i | \(-0.844330\pi\) | ||||
−0.882779 | + | 0.469788i | \(0.844330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −546555. | −0.236792 | ||||||||
\(352\) | −145854. | −0.0627427 | ||||||||
\(353\) | −2.44907e6 | −1.04608 | −0.523040 | − | 0.852308i | \(-0.675202\pi\) | ||||
−0.523040 | + | 0.852308i | \(0.675202\pi\) | |||||||
\(354\) | 292581. | 0.124090 | ||||||||
\(355\) | −1.48970e6 | −0.627375 | ||||||||
\(356\) | 1.25494e6 | 0.524807 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 247941. | 0.102245 | ||||||||
\(359\) | −177274. | −0.0725954 | −0.0362977 | − | 0.999341i | \(-0.511556\pi\) | ||||
−0.0362977 | + | 0.999341i | \(0.511556\pi\) | |||||||
\(360\) | −138885. | −0.0564804 | ||||||||
\(361\) | 633205. | 0.255727 | ||||||||
\(362\) | −52225.9 | −0.0209466 | ||||||||
\(363\) | 3.02982e6 | 1.20684 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −602568. | −0.236741 | ||||||||
\(366\) | −399111. | −0.155737 | ||||||||
\(367\) | −3.26871e6 | −1.26681 | −0.633405 | − | 0.773820i | \(-0.718343\pi\) | ||||
−0.633405 | + | 0.773820i | \(0.718343\pi\) | |||||||
\(368\) | 4.34990e6 | 1.67440 | ||||||||
\(369\) | −1.27740e6 | −0.488382 | ||||||||
\(370\) | 141073. | 0.0535724 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.68887e6 | −1.38209 | ||||||||
\(373\) | 3.59046e6 | 1.33622 | 0.668110 | − | 0.744062i | \(-0.267104\pi\) | ||||
0.668110 | + | 0.744062i | \(0.267104\pi\) | |||||||
\(374\) | 12916.6 | 0.00477496 | ||||||||
\(375\) | 304955. | 0.111984 | ||||||||
\(376\) | −1.01288e6 | −0.369477 | ||||||||
\(377\) | −34383.0 | −0.0124592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −444241. | −0.158862 | −0.0794312 | − | 0.996840i | \(-0.525310\pi\) | ||||
−0.0794312 | + | 0.996840i | \(0.525310\pi\) | |||||||
\(380\) | 1.39297e6 | 0.494862 | ||||||||
\(381\) | 4.84268e6 | 1.70912 | ||||||||
\(382\) | 537957. | 0.188621 | ||||||||
\(383\) | 4.56035e6 | 1.58855 | 0.794275 | − | 0.607558i | \(-0.207851\pi\) | ||||
0.794275 | + | 0.607558i | \(0.207851\pi\) | |||||||
\(384\) | −1.56981e6 | −0.543275 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −180214. | −0.0615629 | ||||||||
\(387\) | −935391. | −0.317480 | ||||||||
\(388\) | −4.14837e6 | −1.39894 | ||||||||
\(389\) | 2.50465e6 | 0.839215 | 0.419608 | − | 0.907706i | \(-0.362168\pi\) | ||||
0.419608 | + | 0.907706i | \(0.362168\pi\) | |||||||
\(390\) | 82354.9 | 0.0274175 | ||||||||
\(391\) | −1.18062e6 | −0.390541 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.09495e6 | 1.66402 | ||||||||
\(394\) | −351045. | −0.113926 | ||||||||
\(395\) | −2.67503e6 | −0.862652 | ||||||||
\(396\) | −332233. | −0.106464 | ||||||||
\(397\) | −2.38913e6 | −0.760787 | −0.380394 | − | 0.924825i | \(-0.624211\pi\) | ||||
−0.380394 | + | 0.924825i | \(0.624211\pi\) | |||||||
\(398\) | 402414. | 0.127340 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 616033. | 0.192510 | ||||||||
\(401\) | 62929.2 | 0.0195430 | 0.00977150 | − | 0.999952i | \(-0.496890\pi\) | ||||
0.00977150 | + | 0.999952i | \(0.496890\pi\) | |||||||
\(402\) | −395136. | −0.121950 | ||||||||
\(403\) | 1.59403e6 | 0.488915 | ||||||||
\(404\) | 5.39655e6 | 1.64499 | ||||||||
\(405\) | 1.83854e6 | 0.556976 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 679221. | 0.203247 | ||||||||
\(408\) | 210312. | 0.0625479 | ||||||||
\(409\) | −404988. | −0.119711 | −0.0598555 | − | 0.998207i | \(-0.519064\pi\) | ||||
−0.0598555 | + | 0.998207i | \(0.519064\pi\) | |||||||
\(410\) | −146653. | −0.0430855 | ||||||||
\(411\) | 330450. | 0.0964942 | ||||||||
\(412\) | 1.32591e6 | 0.384831 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −385496. | −0.110540 | ||||||||
\(415\) | 137935. | 0.0393146 | ||||||||
\(416\) | 509869. | 0.144452 | ||||||||
\(417\) | −3.49848e6 | −0.985234 | ||||||||
\(418\) | −85138.7 | −0.0238334 | ||||||||
\(419\) | 1.73727e6 | 0.483429 | 0.241714 | − | 0.970347i | \(-0.422290\pi\) | ||||
0.241714 | + | 0.970347i | \(0.422290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.09244e6 | 0.850347 | 0.425174 | − | 0.905112i | \(-0.360213\pi\) | ||||
0.425174 | + | 0.905112i | \(0.360213\pi\) | |||||||
\(422\) | 177548. | 0.0485328 | ||||||||
\(423\) | −3.46803e6 | −0.942393 | ||||||||
\(424\) | −123523. | −0.0333683 | ||||||||
\(425\) | −167199. | −0.0449015 | ||||||||
\(426\) | 736577. | 0.196650 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.00254e6 | −1.05615 | ||||||||
\(429\) | 396511. | 0.104019 | ||||||||
\(430\) | −107389. | −0.0280083 | ||||||||
\(431\) | −3.04862e6 | −0.790515 | −0.395258 | − | 0.918570i | \(-0.629345\pi\) | ||||
−0.395258 | + | 0.918570i | \(0.629345\pi\) | |||||||
\(432\) | 2.02148e6 | 0.521146 | ||||||||
\(433\) | 986108. | 0.252758 | 0.126379 | − | 0.991982i | \(-0.459664\pi\) | ||||
0.126379 | + | 0.991982i | \(0.459664\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 62952.1 | 0.0159510 | ||||||||
\(436\) | −4.72783e6 | −1.19109 | ||||||||
\(437\) | 7.78192e6 | 1.94932 | ||||||||
\(438\) | 297939. | 0.0742064 | ||||||||
\(439\) | −3.69313e6 | −0.914603 | −0.457302 | − | 0.889312i | \(-0.651184\pi\) | ||||
−0.457302 | + | 0.889312i | \(0.651184\pi\) | |||||||
\(440\) | −76768.8 | −0.0189040 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −45153.1 | −0.0109934 | ||||||||
\(443\) | 1.92890e6 | 0.466983 | 0.233492 | − | 0.972359i | \(-0.424985\pi\) | ||||
0.233492 | + | 0.972359i | \(0.424985\pi\) | |||||||
\(444\) | 5.49474e6 | 1.32279 | ||||||||
\(445\) | 992871. | 0.237680 | ||||||||
\(446\) | −614420. | −0.146261 | ||||||||
\(447\) | 7.35332e6 | 1.74066 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.12359e6 | 0.965295 | 0.482647 | − | 0.875815i | \(-0.339675\pi\) | ||||
0.482647 | + | 0.875815i | \(0.339675\pi\) | |||||||
\(450\) | −54594.0 | −0.0127091 | ||||||||
\(451\) | −706084. | −0.163461 | ||||||||
\(452\) | −2.67988e6 | −0.616978 | ||||||||
\(453\) | 6.93840e6 | 1.58860 | ||||||||
\(454\) | 360639. | 0.0821170 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.38625e6 | −0.312197 | ||||||||
\(457\) | −3.96950e6 | −0.889089 | −0.444544 | − | 0.895757i | \(-0.646634\pi\) | ||||
−0.444544 | + | 0.895757i | \(0.646634\pi\) | |||||||
\(458\) | 49394.2 | 0.0110030 | ||||||||
\(459\) | −548654. | −0.121553 | ||||||||
\(460\) | 3.48632e6 | 0.768196 | ||||||||
\(461\) | −3.39581e6 | −0.744202 | −0.372101 | − | 0.928192i | \(-0.621362\pi\) | ||||
−0.372101 | + | 0.928192i | \(0.621362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.05461e6 | 0.228633 | 0.114317 | − | 0.993444i | \(-0.463532\pi\) | ||||
0.114317 | + | 0.993444i | \(0.463532\pi\) | |||||||
\(464\) | 127168. | 0.0274210 | ||||||||
\(465\) | −2.91852e6 | −0.625936 | ||||||||
\(466\) | −525285. | −0.112055 | ||||||||
\(467\) | −984239. | −0.208837 | −0.104419 | − | 0.994533i | \(-0.533298\pi\) | ||||
−0.104419 | + | 0.994533i | \(0.533298\pi\) | |||||||
\(468\) | 1.16140e6 | 0.245113 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −398151. | −0.0831387 | ||||||||
\(471\) | −9.59186e6 | −1.99228 | ||||||||
\(472\) | 953412. | 0.196982 | ||||||||
\(473\) | −517040. | −0.106260 | ||||||||
\(474\) | 1.32266e6 | 0.270398 | ||||||||
\(475\) | 1.10208e6 | 0.224118 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −422936. | −0.0851097 | ||||||||
\(478\) | −159778. | −0.0319850 | ||||||||
\(479\) | 5.10476e6 | 1.01657 | 0.508284 | − | 0.861189i | \(-0.330280\pi\) | ||||
0.508284 | + | 0.861189i | \(0.330280\pi\) | |||||||
\(480\) | −933522. | −0.184936 | ||||||||
\(481\) | −2.37438e6 | −0.467936 | ||||||||
\(482\) | −339456. | −0.0665527 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.90539e6 | 0.951831 | ||||||||
\(485\) | −3.28206e6 | −0.633566 | ||||||||
\(486\) | −593420. | −0.113965 | ||||||||
\(487\) | 6.71429e6 | 1.28286 | 0.641428 | − | 0.767184i | \(-0.278342\pi\) | ||||
0.641428 | + | 0.767184i | \(0.278342\pi\) | |||||||
\(488\) | −1.30055e6 | −0.247217 | ||||||||
\(489\) | 2.79111e6 | 0.527844 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.62514e6 | 1.61459 | 0.807295 | − | 0.590148i | \(-0.200931\pi\) | ||||
0.807295 | + | 0.590148i | \(0.200931\pi\) | |||||||
\(492\) | −5.71206e6 | −1.06385 | ||||||||
\(493\) | −34515.0 | −0.00639574 | ||||||||
\(494\) | 297622. | 0.0548717 | ||||||||
\(495\) | −262852. | −0.0482167 | ||||||||
\(496\) | −5.89563e6 | −1.07603 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −68201.6 | −0.0123231 | ||||||||
\(499\) | −9.39508e6 | −1.68908 | −0.844538 | − | 0.535496i | \(-0.820125\pi\) | ||||
−0.844538 | + | 0.535496i | \(0.820125\pi\) | |||||||
\(500\) | 493732. | 0.0883215 | ||||||||
\(501\) | −6.12734e6 | −1.09063 | ||||||||
\(502\) | −33538.2 | −0.00593993 | ||||||||
\(503\) | 429394. | 0.0756722 | 0.0378361 | − | 0.999284i | \(-0.487954\pi\) | ||||
0.0378361 | + | 0.999284i | \(0.487954\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.26957e6 | 0.745000 | ||||||||
\(506\) | −213084. | −0.0369977 | ||||||||
\(507\) | 5.86047e6 | 1.01254 | ||||||||
\(508\) | 7.84047e6 | 1.34798 | ||||||||
\(509\) | 248510. | 0.0425157 | 0.0212579 | − | 0.999774i | \(-0.493233\pi\) | ||||
0.0212579 | + | 0.999774i | \(0.493233\pi\) | |||||||
\(510\) | 82671.2 | 0.0140744 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.15627e6 | −0.532107 | ||||||||
\(513\) | 3.61640e6 | 0.606713 | ||||||||
\(514\) | −333845. | −0.0557362 | ||||||||
\(515\) | 1.04901e6 | 0.174286 | ||||||||
\(516\) | −4.18273e6 | −0.691570 | ||||||||
\(517\) | −1.91696e6 | −0.315419 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.53140e6 | −1.39028 | ||||||||
\(520\) | 268364. | 0.0435226 | ||||||||
\(521\) | 4.77060e6 | 0.769979 | 0.384990 | − | 0.922921i | \(-0.374205\pi\) | ||||
0.384990 | + | 0.922921i | \(0.374205\pi\) | |||||||
\(522\) | −11269.9 | −0.00181027 | ||||||||
\(523\) | −2.70325e6 | −0.432148 | −0.216074 | − | 0.976377i | \(-0.569325\pi\) | ||||
−0.216074 | + | 0.976377i | \(0.569325\pi\) | |||||||
\(524\) | 8.24889e6 | 1.31240 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 804139. | 0.126726 | ||||||||
\(527\) | 1.60015e6 | 0.250977 | ||||||||
\(528\) | −1.46653e6 | −0.228931 | ||||||||
\(529\) | 1.30401e7 | 2.02602 | ||||||||
\(530\) | −48555.6 | −0.00750844 | ||||||||
\(531\) | 3.26442e6 | 0.502424 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.46828e6 | 0.376337 | ||||||||
\(534\) | −490923. | −0.0745007 | ||||||||
\(535\) | −3.16668e6 | −0.478321 | ||||||||
\(536\) | −1.28760e6 | −0.193584 | ||||||||
\(537\) | 7.64046e6 | 1.14336 | ||||||||
\(538\) | 546752. | 0.0814395 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.62015e6 | 0.239096 | ||||||||
\(541\) | −5.93736e6 | −0.872168 | −0.436084 | − | 0.899906i | \(-0.643635\pi\) | ||||
−0.436084 | + | 0.899906i | \(0.643635\pi\) | |||||||
\(542\) | 1.15521e6 | 0.168913 | ||||||||
\(543\) | −1.60937e6 | −0.234238 | ||||||||
\(544\) | 511826. | 0.0741524 | ||||||||
\(545\) | −3.74051e6 | −0.539435 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.27658e7 | −1.82422 | −0.912112 | − | 0.409941i | \(-0.865549\pi\) | ||||
−0.912112 | + | 0.409941i | \(0.865549\pi\) | |||||||
\(548\) | 535010. | 0.0761045 | ||||||||
\(549\) | −4.45301e6 | −0.630555 | ||||||||
\(550\) | −30177.0 | −0.00425372 | ||||||||
\(551\) | 227503. | 0.0319233 | ||||||||
\(552\) | −3.46948e6 | −0.484638 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.32966e6 | 0.184063 | ||||||||
\(555\) | 4.34726e6 | 0.599078 | ||||||||
\(556\) | −5.66416e6 | −0.777049 | ||||||||
\(557\) | 7.25744e6 | 0.991163 | 0.495582 | − | 0.868561i | \(-0.334955\pi\) | ||||
0.495582 | + | 0.868561i | \(0.334955\pi\) | |||||||
\(558\) | 522482. | 0.0710372 | ||||||||
\(559\) | 1.80743e6 | 0.244643 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 398034. | 0.0533965 | ||||||||
\(562\) | 1.09025e6 | 0.145609 | ||||||||
\(563\) | −6.52782e6 | −0.867955 | −0.433977 | − | 0.900924i | \(-0.642890\pi\) | ||||
−0.433977 | + | 0.900924i | \(0.642890\pi\) | |||||||
\(564\) | −1.55078e7 | −2.05283 | ||||||||
\(565\) | −2.12024e6 | −0.279424 | ||||||||
\(566\) | 1.60698e6 | 0.210848 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.40023e6 | 0.312163 | ||||||||
\(569\) | 3.51551e6 | 0.455206 | 0.227603 | − | 0.973754i | \(-0.426911\pi\) | ||||
0.227603 | + | 0.973754i | \(0.426911\pi\) | |||||||
\(570\) | −544919. | −0.0702498 | ||||||||
\(571\) | −41320.8 | −0.00530370 | −0.00265185 | − | 0.999996i | \(-0.500844\pi\) | ||||
−0.00265185 | + | 0.999996i | \(0.500844\pi\) | |||||||
\(572\) | 641965. | 0.0820392 | ||||||||
\(573\) | 1.65775e7 | 2.10927 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.75826e6 | 0.347909 | ||||||||
\(576\) | −4.18292e6 | −0.525320 | ||||||||
\(577\) | 919163. | 0.114935 | 0.0574676 | − | 0.998347i | \(-0.481697\pi\) | ||||
0.0574676 | + | 0.998347i | \(0.481697\pi\) | |||||||
\(578\) | 853942. | 0.106319 | ||||||||
\(579\) | −5.55339e6 | −0.688434 | ||||||||
\(580\) | 101922. | 0.0125805 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.62280e6 | 0.198591 | ||||||||
\(583\) | −233779. | −0.0284862 | ||||||||
\(584\) | 970869. | 0.117795 | ||||||||
\(585\) | 918860. | 0.111009 | ||||||||
\(586\) | 722428. | 0.0869062 | ||||||||
\(587\) | 182482. | 0.0218587 | 0.0109294 | − | 0.999940i | \(-0.496521\pi\) | ||||
0.0109294 | + | 0.999940i | \(0.496521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.05472e7 | −1.25271 | ||||||||
\(590\) | 374775. | 0.0443242 | ||||||||
\(591\) | −1.08177e7 | −1.27399 | ||||||||
\(592\) | 8.78181e6 | 1.02986 | ||||||||
\(593\) | 1.59052e7 | 1.85739 | 0.928695 | − | 0.370846i | \(-0.120932\pi\) | ||||
0.928695 | + | 0.370846i | \(0.120932\pi\) | |||||||
\(594\) | −99024.0 | −0.0115153 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.19053e7 | 1.37285 | ||||||||
\(597\) | 1.24006e7 | 1.42399 | ||||||||
\(598\) | 744885. | 0.0851797 | ||||||||
\(599\) | 935648. | 0.106548 | 0.0532740 | − | 0.998580i | \(-0.483034\pi\) | ||||
0.0532740 | + | 0.998580i | \(0.483034\pi\) | |||||||
\(600\) | −491349. | −0.0557201 | ||||||||
\(601\) | −6.79914e6 | −0.767835 | −0.383917 | − | 0.923367i | \(-0.625425\pi\) | ||||
−0.383917 | + | 0.923367i | \(0.625425\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.40866e6 | −0.493757 | ||||||||
\(604\) | 1.12335e7 | 1.25292 | ||||||||
\(605\) | 3.88098e6 | 0.431075 | ||||||||
\(606\) | −2.11108e6 | −0.233520 | ||||||||
\(607\) | −3.15831e6 | −0.347923 | −0.173962 | − | 0.984752i | \(-0.555657\pi\) | ||||
−0.173962 | + | 0.984752i | \(0.555657\pi\) | |||||||
\(608\) | −3.37366e6 | −0.370119 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −511232. | −0.0556280 | ||||||||
\(611\) | 6.70119e6 | 0.726188 | ||||||||
\(612\) | 1.16586e6 | 0.125825 | ||||||||
\(613\) | −2.50952e6 | −0.269736 | −0.134868 | − | 0.990864i | \(-0.543061\pi\) | ||||
−0.134868 | + | 0.990864i | \(0.543061\pi\) | |||||||
\(614\) | 955809. | 0.102318 | ||||||||
\(615\) | −4.51919e6 | −0.481807 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.18777e7 | 1.25608 | 0.628042 | − | 0.778179i | \(-0.283857\pi\) | ||||
0.628042 | + | 0.778179i | \(0.283857\pi\) | |||||||
\(618\) | −518683. | −0.0546300 | ||||||||
\(619\) | −6.97529e6 | −0.731705 | −0.365852 | − | 0.930673i | \(-0.619222\pi\) | ||||
−0.365852 | + | 0.930673i | \(0.619222\pi\) | |||||||
\(620\) | −4.72518e6 | −0.493672 | ||||||||
\(621\) | 9.05108e6 | 0.941827 | ||||||||
\(622\) | −2.13495e6 | −0.221264 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.12659e6 | 0.527068 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −270484. | −0.0275870 | ||||||||
\(627\) | −2.62360e6 | −0.266520 | ||||||||
\(628\) | −1.55295e7 | −1.57130 | ||||||||
\(629\) | −2.38349e6 | −0.240208 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.05579e7 | −1.05561 | −0.527807 | − | 0.849364i | \(-0.676986\pi\) | ||||
−0.527807 | + | 0.849364i | \(0.676986\pi\) | |||||||
\(632\) | 4.31005e6 | 0.429230 | ||||||||
\(633\) | 5.47126e6 | 0.542723 | ||||||||
\(634\) | 550057. | 0.0543481 | ||||||||
\(635\) | 6.20313e6 | 0.610487 | ||||||||
\(636\) | −1.89122e6 | −0.185395 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6229.46 | −0.000605897 0 | ||||||||
\(639\) | 8.21822e6 | 0.796207 | ||||||||
\(640\) | −2.01082e6 | −0.194054 | ||||||||
\(641\) | −1.01477e7 | −0.975488 | −0.487744 | − | 0.872987i | \(-0.662180\pi\) | ||||
−0.487744 | + | 0.872987i | \(0.662180\pi\) | |||||||
\(642\) | 1.56576e6 | 0.149929 | ||||||||
\(643\) | −9.41430e6 | −0.897968 | −0.448984 | − | 0.893540i | \(-0.648214\pi\) | ||||
−0.448984 | + | 0.893540i | \(0.648214\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.30924e6 | −0.313206 | ||||||||
\(646\) | 298765. | 0.0281675 | ||||||||
\(647\) | 1.08548e7 | 1.01943 | 0.509717 | − | 0.860342i | \(-0.329750\pi\) | ||||
0.509717 | + | 0.860342i | \(0.329750\pi\) | |||||||
\(648\) | −2.96229e6 | −0.277134 | ||||||||
\(649\) | 1.80442e6 | 0.168161 | ||||||||
\(650\) | 105491. | 0.00979334 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.51891e6 | 0.416308 | ||||||||
\(653\) | 7.47330e6 | 0.685850 | 0.342925 | − | 0.939363i | \(-0.388582\pi\) | ||||
0.342925 | + | 0.939363i | \(0.388582\pi\) | |||||||
\(654\) | 1.84948e6 | 0.169086 | ||||||||
\(655\) | 6.52626e6 | 0.594376 | ||||||||
\(656\) | −9.12912e6 | −0.828265 | ||||||||
\(657\) | 3.32419e6 | 0.300451 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.62806e7 | −1.46035 | −0.730176 | − | 0.683259i | \(-0.760562\pi\) | ||||
−0.730176 | + | 0.683259i | \(0.760562\pi\) | |||||||
\(660\) | −1.17538e6 | −0.105031 | ||||||||
\(661\) | 5.36073e6 | 0.477222 | 0.238611 | − | 0.971115i | \(-0.423308\pi\) | ||||
0.238611 | + | 0.971115i | \(0.423308\pi\) | |||||||
\(662\) | 943168. | 0.0836458 | ||||||||
\(663\) | −1.39142e6 | −0.122935 | ||||||||
\(664\) | −222243. | −0.0195618 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −778261. | −0.0679891 | ||||||||
\(667\) | 569390. | 0.0495559 | ||||||||
\(668\) | −9.92037e6 | −0.860175 | ||||||||
\(669\) | −1.89337e7 | −1.63558 | ||||||||
\(670\) | −506140. | −0.0435596 | ||||||||
\(671\) | −2.46141e6 | −0.211046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.77331e7 | −1.50920 | −0.754602 | − | 0.656183i | \(-0.772170\pi\) | ||||
−0.754602 | + | 0.656183i | \(0.772170\pi\) | |||||||
\(674\) | −1.09801e6 | −0.0931015 | ||||||||
\(675\) | 1.28181e6 | 0.108284 | ||||||||
\(676\) | 9.48830e6 | 0.798586 | ||||||||
\(677\) | −5.82373e6 | −0.488348 | −0.244174 | − | 0.969731i | \(-0.578517\pi\) | ||||
−0.244174 | + | 0.969731i | \(0.578517\pi\) | |||||||
\(678\) | 1.04835e6 | 0.0875852 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 269394. | 0.0223417 | ||||||||
\(681\) | 1.11133e7 | 0.918281 | ||||||||
\(682\) | 288803. | 0.0237761 | ||||||||
\(683\) | −1.56080e7 | −1.28025 | −0.640126 | − | 0.768270i | \(-0.721118\pi\) | ||||
−0.640126 | + | 0.768270i | \(0.721118\pi\) | |||||||
\(684\) | −7.68463e6 | −0.628034 | ||||||||
\(685\) | 423282. | 0.0344670 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.52211e6 | 0.123042 | ||||||||
\(688\) | −6.68493e6 | −0.538426 | ||||||||
\(689\) | 817229. | 0.0655837 | ||||||||
\(690\) | −1.36382e6 | −0.109052 | ||||||||
\(691\) | −8.52021e6 | −0.678821 | −0.339410 | − | 0.940638i | \(-0.610228\pi\) | ||||
−0.339410 | + | 0.940638i | \(0.610228\pi\) | |||||||
\(692\) | −1.38126e7 | −1.09651 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.06884e6 | 0.163053 | ||||||||
\(695\) | −4.48130e6 | −0.351918 | ||||||||
\(696\) | −101430. | −0.00793673 | ||||||||
\(697\) | 2.47776e6 | 0.193187 | ||||||||
\(698\) | 2.54443e6 | 0.197675 | ||||||||
\(699\) | −1.61870e7 | −1.25306 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.48253e6 | −0.421392 | −0.210696 | − | 0.977552i | \(-0.567573\pi\) | ||||
−0.210696 | + | 0.977552i | \(0.567573\pi\) | |||||||
\(702\) | 346162. | 0.0265116 | ||||||||
\(703\) | 1.57106e7 | 1.19896 | ||||||||
\(704\) | −2.31212e6 | −0.175824 | ||||||||
\(705\) | −1.22693e7 | −0.929706 | ||||||||
\(706\) | 1.55112e6 | 0.117121 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.45973e7 | 1.09444 | ||||||||
\(709\) | −1.75446e7 | −1.31078 | −0.655388 | − | 0.755292i | \(-0.727495\pi\) | ||||
−0.655388 | + | 0.755292i | \(0.727495\pi\) | |||||||
\(710\) | 943502. | 0.0702420 | ||||||||
\(711\) | 1.47573e7 | 1.09480 | ||||||||
\(712\) | −1.59973e6 | −0.118263 | ||||||||
\(713\) | −2.63974e7 | −1.94463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 507902. | 0.0371548 | ||||||||
\(716\) | 1.23702e7 | 0.901763 | ||||||||
\(717\) | −4.92365e6 | −0.357675 | ||||||||
\(718\) | 112277. | 0.00812791 | ||||||||
\(719\) | −2.90492e6 | −0.209562 | −0.104781 | − | 0.994495i | \(-0.533414\pi\) | ||||
−0.104781 | + | 0.994495i | \(0.533414\pi\) | |||||||
\(720\) | −3.39847e6 | −0.244316 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −401042. | −0.0286317 | ||||||||
\(723\) | −1.04605e7 | −0.744232 | ||||||||
\(724\) | −2.60563e6 | −0.184742 | ||||||||
\(725\) | 80637.1 | 0.00569757 | ||||||||
\(726\) | −1.91894e6 | −0.135120 | ||||||||
\(727\) | −1.58709e7 | −1.11369 | −0.556846 | − | 0.830616i | \(-0.687988\pi\) | ||||
−0.556846 | + | 0.830616i | \(0.687988\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −415975. | −0.0289900 | ||||||||
\(730\) | 381638. | 0.0265060 | ||||||||
\(731\) | 1.81437e6 | 0.125584 | ||||||||
\(732\) | −1.99123e7 | −1.37354 | ||||||||
\(733\) | −2.22308e7 | −1.52825 | −0.764127 | − | 0.645065i | \(-0.776830\pi\) | ||||
−0.764127 | + | 0.645065i | \(0.776830\pi\) | |||||||
\(734\) | 2.07025e6 | 0.141834 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.44353e6 | −0.574552 | ||||||||
\(737\) | −2.43690e6 | −0.165260 | ||||||||
\(738\) | 809041. | 0.0546801 | ||||||||
\(739\) | 2.25210e7 | 1.51697 | 0.758484 | − | 0.651691i | \(-0.225940\pi\) | ||||
0.758484 | + | 0.651691i | \(0.225940\pi\) | |||||||
\(740\) | 7.03836e6 | 0.472490 | ||||||||
\(741\) | 9.17142e6 | 0.613608 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.71099e7 | −1.13704 | −0.568521 | − | 0.822669i | \(-0.692484\pi\) | ||||
−0.568521 | + | 0.822669i | \(0.692484\pi\) | |||||||
\(744\) | 4.70236e6 | 0.311447 | ||||||||
\(745\) | 9.41907e6 | 0.621752 | ||||||||
\(746\) | −2.27402e6 | −0.149606 | ||||||||
\(747\) | −760947. | −0.0498945 | ||||||||
\(748\) | 644430. | 0.0421135 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −193144. | −0.0125380 | ||||||||
\(751\) | 1.52459e7 | 0.986401 | 0.493201 | − | 0.869916i | \(-0.335827\pi\) | ||||
0.493201 | + | 0.869916i | \(0.335827\pi\) | |||||||
\(752\) | −2.47849e7 | −1.59824 | ||||||||
\(753\) | −1.03350e6 | −0.0664238 | ||||||||
\(754\) | 21776.5 | 0.00139496 | ||||||||
\(755\) | 8.88758e6 | 0.567435 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.18251e7 | −0.750004 | −0.375002 | − | 0.927024i | \(-0.622358\pi\) | ||||
−0.375002 | + | 0.927024i | \(0.622358\pi\) | |||||||
\(758\) | 281361. | 0.0177865 | ||||||||
\(759\) | −6.56631e6 | −0.413730 | ||||||||
\(760\) | −1.77568e6 | −0.111515 | ||||||||
\(761\) | 4.31523e6 | 0.270111 | 0.135056 | − | 0.990838i | \(-0.456879\pi\) | ||||
0.135056 | + | 0.990838i | \(0.456879\pi\) | |||||||
\(762\) | −3.06712e6 | −0.191357 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.68395e7 | 1.66357 | ||||||||
\(765\) | 922388. | 0.0569849 | ||||||||
\(766\) | −2.88830e6 | −0.177857 | ||||||||
\(767\) | −6.30776e6 | −0.387157 | ||||||||
\(768\) | −1.79477e7 | −1.09801 | ||||||||
\(769\) | 1.74124e7 | 1.06180 | 0.530900 | − | 0.847434i | \(-0.321854\pi\) | ||||
0.530900 | + | 0.847434i | \(0.321854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.02876e7 | −0.623275 | ||||||||
\(772\) | −8.99113e6 | −0.542964 | ||||||||
\(773\) | 2.39416e7 | 1.44113 | 0.720566 | − | 0.693386i | \(-0.243882\pi\) | ||||
0.720566 | + | 0.693386i | \(0.243882\pi\) | |||||||
\(774\) | 592431. | 0.0355456 | ||||||||
\(775\) | −3.73841e6 | −0.223580 | ||||||||
\(776\) | 5.28811e6 | 0.315243 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.58632e6 | −0.0939600 | ||||||||
\(779\) | −1.63319e7 | −0.964258 | ||||||||
\(780\) | 4.10881e6 | 0.241813 | ||||||||
\(781\) | 4.54264e6 | 0.266490 | ||||||||
\(782\) | 747745. | 0.0437257 | ||||||||
\(783\) | 264606. | 0.0154239 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.22865e7 | −0.711628 | ||||||||
\(786\) | −3.22689e6 | −0.186307 | ||||||||
\(787\) | −3.01391e7 | −1.73458 | −0.867288 | − | 0.497807i | \(-0.834139\pi\) | ||||
−0.867288 | + | 0.497807i | \(0.834139\pi\) | |||||||
\(788\) | −1.75142e7 | −1.00479 | ||||||||
\(789\) | 2.47800e7 | 1.41713 | ||||||||
\(790\) | 1.69423e6 | 0.0965840 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 423511. | 0.0239912 | ||||||||
\(793\) | 8.60444e6 | 0.485892 | ||||||||
\(794\) | 1.51316e6 | 0.0851791 | ||||||||
\(795\) | −1.49627e6 | −0.0839639 | ||||||||
\(796\) | 2.00771e7 | 1.12310 | ||||||||
\(797\) | 2.19395e7 | 1.22344 | 0.611718 | − | 0.791076i | \(-0.290479\pi\) | ||||
0.611718 | + | 0.791076i | \(0.290479\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.72692e6 | 0.372777 | ||||||||
\(800\) | −1.19577e6 | −0.0660578 | ||||||||
\(801\) | −5.47738e6 | −0.301642 | ||||||||
\(802\) | −39856.3 | −0.00218807 | ||||||||
\(803\) | 1.83746e6 | 0.100561 | ||||||||
\(804\) | −1.97139e7 | −1.07556 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.00958e6 | −0.0547398 | ||||||||
\(807\) | 1.68485e7 | 0.910705 | ||||||||
\(808\) | −6.87921e6 | −0.370690 | ||||||||
\(809\) | −1.09650e7 | −0.589029 | −0.294514 | − | 0.955647i | \(-0.595158\pi\) | ||||
−0.294514 | + | 0.955647i | \(0.595158\pi\) | |||||||
\(810\) | −1.16444e6 | −0.0623600 | ||||||||
\(811\) | 1.80078e7 | 0.961409 | 0.480705 | − | 0.876883i | \(-0.340381\pi\) | ||||
0.480705 | + | 0.876883i | \(0.340381\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.55986e7 | 1.88889 | ||||||||
\(814\) | −430185. | −0.0227559 | ||||||||
\(815\) | 3.57521e6 | 0.188542 | ||||||||
\(816\) | 5.14627e6 | 0.270562 | ||||||||
\(817\) | −1.19593e7 | −0.626830 | ||||||||
\(818\) | 256500. | 0.0134030 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.31673e6 | −0.379999 | ||||||||
\(821\) | 3.23751e7 | 1.67630 | 0.838152 | − | 0.545437i | \(-0.183636\pi\) | ||||
0.838152 | + | 0.545437i | \(0.183636\pi\) | |||||||
\(822\) | −209291. | −0.0108037 | ||||||||
\(823\) | 3.24695e7 | 1.67100 | 0.835500 | − | 0.549491i | \(-0.185178\pi\) | ||||
0.835500 | + | 0.549491i | \(0.185178\pi\) | |||||||
\(824\) | −1.69019e6 | −0.0867197 | ||||||||
\(825\) | −929922. | −0.0475676 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.10708e7 | 1.57975 | 0.789876 | − | 0.613267i | \(-0.210145\pi\) | ||||
0.789876 | + | 0.613267i | \(0.210145\pi\) | |||||||
\(828\) | −1.92330e7 | −0.974924 | ||||||||
\(829\) | −2.82139e6 | −0.142586 | −0.0712931 | − | 0.997455i | \(-0.522713\pi\) | ||||
−0.0712931 | + | 0.997455i | \(0.522713\pi\) | |||||||
\(830\) | −87361.3 | −0.00440173 | ||||||||
\(831\) | 4.09743e7 | 2.05830 | ||||||||
\(832\) | 8.08256e6 | 0.404800 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.21577e6 | 0.110309 | ||||||||
\(835\) | −7.84867e6 | −0.389565 | ||||||||
\(836\) | −4.24770e6 | −0.210203 | ||||||||
\(837\) | −1.22674e7 | −0.605254 | ||||||||
\(838\) | −1.10030e6 | −0.0541255 | ||||||||
\(839\) | −2.48604e6 | −0.121928 | −0.0609639 | − | 0.998140i | \(-0.519417\pi\) | ||||
−0.0609639 | + | 0.998140i | \(0.519417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.04945e7 | −0.999188 | ||||||||
\(842\) | −1.95860e6 | −0.0952064 | ||||||||
\(843\) | 3.35968e7 | 1.62828 | ||||||||
\(844\) | 8.85815e6 | 0.428043 | ||||||||
\(845\) | 7.50683e6 | 0.361672 | ||||||||
\(846\) | 2.19648e6 | 0.105512 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.02258e6 | −0.144341 | ||||||||
\(849\) | 4.95201e7 | 2.35783 | ||||||||
\(850\) | 105896. | 0.00502726 | ||||||||
\(851\) | 3.93202e7 | 1.86119 | ||||||||
\(852\) | 3.67489e7 | 1.73439 | ||||||||
\(853\) | 2.80284e6 | 0.131894 | 0.0659472 | − | 0.997823i | \(-0.478993\pi\) | ||||
0.0659472 | + | 0.997823i | \(0.478993\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.07983e6 | −0.284431 | ||||||||
\(856\) | 5.10220e6 | 0.237998 | ||||||||
\(857\) | −8.57829e6 | −0.398978 | −0.199489 | − | 0.979900i | \(-0.563928\pi\) | ||||
−0.199489 | + | 0.979900i | \(0.563928\pi\) | |||||||
\(858\) | −251131. | −0.0116461 | ||||||||
\(859\) | −7.92542e6 | −0.366471 | −0.183235 | − | 0.983069i | \(-0.558657\pi\) | ||||
−0.183235 | + | 0.983069i | \(0.558657\pi\) | |||||||
\(860\) | −5.35778e6 | −0.247024 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.93085e6 | 0.0885075 | ||||||||
\(863\) | −3.64157e7 | −1.66441 | −0.832207 | − | 0.554466i | \(-0.812923\pi\) | ||||
−0.832207 | + | 0.554466i | \(0.812923\pi\) | |||||||
\(864\) | −3.92387e6 | −0.178826 | ||||||||
\(865\) | −1.09281e7 | −0.496598 | ||||||||
\(866\) | −624553. | −0.0282992 | ||||||||
\(867\) | 2.63147e7 | 1.18892 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.15716e6 | 0.366429 | ||||||||
\(870\) | −39870.8 | −0.00178590 | ||||||||
\(871\) | 8.51874e6 | 0.380478 | ||||||||
\(872\) | 6.02677e6 | 0.268407 | ||||||||
\(873\) | 1.81061e7 | 0.804064 | ||||||||
\(874\) | −4.92869e6 | −0.218249 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.48646e7 | 0.654475 | ||||||||
\(877\) | −1.69244e7 | −0.743045 | −0.371523 | − | 0.928424i | \(-0.621164\pi\) | ||||
−0.371523 | + | 0.928424i | \(0.621164\pi\) | |||||||
\(878\) | 2.33905e6 | 0.102401 | ||||||||
\(879\) | 2.22621e7 | 0.971837 | ||||||||
\(880\) | −1.87851e6 | −0.0817726 | ||||||||
\(881\) | 4.18273e7 | 1.81560 | 0.907799 | − | 0.419405i | \(-0.137761\pi\) | ||||
0.907799 | + | 0.419405i | \(0.137761\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.08396e7 | 0.467857 | 0.233928 | − | 0.972254i | \(-0.424842\pi\) | ||||
0.233928 | + | 0.972254i | \(0.424842\pi\) | |||||||
\(884\) | −2.25276e6 | −0.0969580 | ||||||||
\(885\) | 1.15489e7 | 0.495660 | ||||||||
\(886\) | −1.22167e6 | −0.0522843 | ||||||||
\(887\) | −1.10623e7 | −0.472104 | −0.236052 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236052 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(888\) | −7.00438e6 | −0.298083 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −628836. | −0.0266111 | ||||||||
\(891\) | −5.60640e6 | −0.236587 | ||||||||
\(892\) | −3.06544e7 | −1.28997 | ||||||||
\(893\) | −4.43399e7 | −1.86066 | ||||||||
\(894\) | −4.65724e6 | −0.194888 | ||||||||
\(895\) | 9.78687e6 | 0.408400 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.29541e7 | 0.952530 | ||||||||
\(898\) | −2.61168e6 | −0.108076 | ||||||||
\(899\) | −771723. | −0.0318465 | ||||||||
\(900\) | −2.72378e6 | −0.112090 | ||||||||
\(901\) | 820367. | 0.0336664 | ||||||||
\(902\) | 447199. | 0.0183014 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.41616e6 | 0.139033 | ||||||||
\(905\) | −2.06149e6 | −0.0836680 | ||||||||
\(906\) | −4.39444e6 | −0.177862 | ||||||||
\(907\) | 9.50001e6 | 0.383447 | 0.191724 | − | 0.981449i | \(-0.438592\pi\) | ||||
0.191724 | + | 0.981449i | \(0.438592\pi\) | |||||||
\(908\) | 1.79928e7 | 0.724243 | ||||||||
\(909\) | −2.35540e7 | −0.945486 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.64397e7 | 0.656295 | 0.328147 | − | 0.944627i | \(-0.393576\pi\) | ||||
0.328147 | + | 0.944627i | \(0.393576\pi\) | |||||||
\(912\) | −3.39212e7 | −1.35047 | ||||||||
\(913\) | −420615. | −0.0166997 | ||||||||
\(914\) | 2.51409e6 | 0.0995440 | ||||||||
\(915\) | −1.57539e7 | −0.622066 | ||||||||
\(916\) | 2.46435e6 | 0.0970429 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 347491. | 0.0136093 | ||||||||
\(919\) | −3.69090e7 | −1.44160 | −0.720799 | − | 0.693144i | \(-0.756225\pi\) | ||||
−0.720799 | + | 0.693144i | \(0.756225\pi\) | |||||||
\(920\) | −4.44416e6 | −0.173109 | ||||||||
\(921\) | 2.94538e7 | 1.14418 | ||||||||
\(922\) | 2.15074e6 | 0.0833222 | ||||||||
\(923\) | −1.58799e7 | −0.613540 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.56853e6 | 0.213986 | ||||||||
\(926\) | −667939. | −0.0255982 | ||||||||
\(927\) | −5.78711e6 | −0.221188 | ||||||||
\(928\) | −246845. | −0.00940922 | ||||||||
\(929\) | 3.53275e7 | 1.34299 | 0.671497 | − | 0.741007i | \(-0.265652\pi\) | ||||
0.671497 | + | 0.741007i | \(0.265652\pi\) | |||||||
\(930\) | 1.84845e6 | 0.0700809 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.62073e7 | −0.988284 | ||||||||
\(933\) | −6.57897e7 | −2.47431 | ||||||||
\(934\) | 623369. | 0.0233818 | ||||||||
\(935\) | 509852. | 0.0190728 | ||||||||
\(936\) | −1.48048e6 | −0.0552349 | ||||||||
\(937\) | 4.24339e7 | 1.57893 | 0.789467 | − | 0.613793i | \(-0.210357\pi\) | ||||
0.789467 | + | 0.613793i | \(0.210357\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.33512e6 | −0.308495 | ||||||||
\(940\) | −1.98644e7 | −0.733255 | ||||||||
\(941\) | 3.71877e6 | 0.136907 | 0.0684534 | − | 0.997654i | \(-0.478194\pi\) | ||||
0.0684534 | + | 0.997654i | \(0.478194\pi\) | |||||||
\(942\) | 6.07502e6 | 0.223059 | ||||||||
\(943\) | −4.08753e7 | −1.49686 | ||||||||
\(944\) | 2.33297e7 | 0.852079 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 327468. | 0.0118971 | ||||||||
\(947\) | 3.42458e7 | 1.24089 | 0.620444 | − | 0.784250i | \(-0.286952\pi\) | ||||
0.620444 | + | 0.784250i | \(0.286952\pi\) | |||||||
\(948\) | 6.59896e7 | 2.38481 | ||||||||
\(949\) | −6.42326e6 | −0.231521 | ||||||||
\(950\) | −698002. | −0.0250927 | ||||||||
\(951\) | 1.69503e7 | 0.607753 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.77379e7 | −1.70267 | −0.851336 | − | 0.524621i | \(-0.824207\pi\) | ||||
−0.851336 | + | 0.524621i | \(0.824207\pi\) | |||||||
\(954\) | 267867. | 0.00952903 | ||||||||
\(955\) | 2.12345e7 | 0.753415 | ||||||||
\(956\) | −7.97155e6 | −0.282097 | ||||||||
\(957\) | −191965. | −0.00677550 | ||||||||
\(958\) | −3.23311e6 | −0.113817 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.47984e7 | −0.518248 | ||||||||
\(961\) | 7.14860e6 | 0.249696 | ||||||||
\(962\) | 1.50381e6 | 0.0523910 | ||||||||
\(963\) | 1.74696e7 | 0.607041 | ||||||||
\(964\) | −1.69360e7 | −0.586972 | ||||||||
\(965\) | −7.11349e6 | −0.245903 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.11582e6 | 0.141543 | 0.0707717 | − | 0.997493i | \(-0.477454\pi\) | ||||
0.0707717 | + | 0.997493i | \(0.477454\pi\) | |||||||
\(968\) | −6.25311e6 | −0.214490 | ||||||||
\(969\) | 9.20663e6 | 0.314986 | ||||||||
\(970\) | 2.07869e6 | 0.0709351 | ||||||||
\(971\) | −3.11715e7 | −1.06099 | −0.530493 | − | 0.847689i | \(-0.677993\pi\) | ||||
−0.530493 | + | 0.847689i | \(0.677993\pi\) | |||||||
\(972\) | −2.96066e7 | −1.00513 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.25251e6 | −0.143631 | ||||||||
\(975\) | 3.25076e6 | 0.109515 | ||||||||
\(976\) | −3.18242e7 | −1.06938 | ||||||||
\(977\) | −1.40483e7 | −0.470857 | −0.235428 | − | 0.971892i | \(-0.575649\pi\) | ||||
−0.235428 | + | 0.971892i | \(0.575649\pi\) | |||||||
\(978\) | −1.76776e6 | −0.0590984 | ||||||||
\(979\) | −3.02764e6 | −0.100959 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.06353e7 | 0.684602 | ||||||||
\(982\) | −5.46274e6 | −0.180772 | ||||||||
\(983\) | 4.87717e6 | 0.160985 | 0.0804923 | − | 0.996755i | \(-0.474351\pi\) | ||||
0.0804923 | + | 0.996755i | \(0.474351\pi\) | |||||||
\(984\) | 7.28141e6 | 0.239733 | ||||||||
\(985\) | −1.38567e7 | −0.455059 | ||||||||
\(986\) | 21860.1 | 0.000716079 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.48488e7 | 0.483949 | ||||||||
\(989\) | −2.99315e7 | −0.973056 | ||||||||
\(990\) | 166478. | 0.00539843 | ||||||||
\(991\) | 2.73913e7 | 0.885990 | 0.442995 | − | 0.896524i | \(-0.353916\pi\) | ||||
0.442995 | + | 0.896524i | \(0.353916\pi\) | |||||||
\(992\) | 1.14439e7 | 0.369230 | ||||||||
\(993\) | 2.90643e7 | 0.935377 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.58843e7 | 0.508641 | ||||||||
\(996\) | −3.40268e6 | −0.108686 | ||||||||
\(997\) | 3.59221e7 | 1.14452 | 0.572261 | − | 0.820072i | \(-0.306067\pi\) | ||||
0.572261 | + | 0.820072i | \(0.306067\pi\) | |||||||
\(998\) | 5.95039e6 | 0.189112 | ||||||||
\(999\) | 1.82728e7 | 0.579284 |
(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 | 245.6.a.l.1.5 | ✓ | 10 | |
7.6 | odd | 2 | 245.6.a.m.1.5 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.6.a.l.1.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
245.6.a.m.1.5 | yes | 10 | 7.6 | odd | 2 |