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: | \(3\) |
Coefficient field: | 3.3.577880.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 98x - 232 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.53323\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.53323 | −0.801369 | −0.400685 | − | 0.916216i | \(-0.631228\pi\) | ||||
−0.400685 | + | 0.916216i | \(0.631228\pi\) | |||||||
\(3\) | 15.7249 | 1.00875 | 0.504377 | − | 0.863483i | \(-0.331722\pi\) | ||||
0.504377 | + | 0.863483i | \(0.331722\pi\) | |||||||
\(4\) | −11.4498 | −0.357808 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −71.2847 | −0.808384 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 196.968 | 1.08811 | ||||||||
\(9\) | 4.27317 | 0.0175851 | ||||||||
\(10\) | −113.331 | −0.358383 | ||||||||
\(11\) | 126.340 | 0.314818 | 0.157409 | − | 0.987533i | \(-0.449686\pi\) | ||||
0.157409 | + | 0.987533i | \(0.449686\pi\) | |||||||
\(12\) | −180.048 | −0.360940 | ||||||||
\(13\) | −833.688 | −1.36819 | −0.684093 | − | 0.729395i | \(-0.739802\pi\) | ||||
−0.684093 | + | 0.729395i | \(0.739802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 393.123 | 0.451129 | ||||||||
\(16\) | −526.506 | −0.514166 | ||||||||
\(17\) | −157.465 | −0.132148 | −0.0660742 | − | 0.997815i | \(-0.521047\pi\) | ||||
−0.0660742 | + | 0.997815i | \(0.521047\pi\) | |||||||
\(18\) | −19.3713 | −0.0140921 | ||||||||
\(19\) | 1005.50 | 0.638994 | 0.319497 | − | 0.947587i | \(-0.396486\pi\) | ||||
0.319497 | + | 0.947587i | \(0.396486\pi\) | |||||||
\(20\) | −286.246 | −0.160016 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −572.729 | −0.252286 | ||||||||
\(23\) | 73.5368 | 0.0289858 | 0.0144929 | − | 0.999895i | \(-0.495387\pi\) | ||||
0.0144929 | + | 0.999895i | \(0.495387\pi\) | |||||||
\(24\) | 3097.31 | 1.09763 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 3779.30 | 1.09642 | ||||||||
\(27\) | −3753.96 | −0.991015 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3691.42 | −0.815076 | −0.407538 | − | 0.913188i | \(-0.633613\pi\) | ||||
−0.407538 | + | 0.913188i | \(0.633613\pi\) | |||||||
\(30\) | −1782.12 | −0.361521 | ||||||||
\(31\) | −4804.05 | −0.897848 | −0.448924 | − | 0.893570i | \(-0.648193\pi\) | ||||
−0.448924 | + | 0.893570i | \(0.648193\pi\) | |||||||
\(32\) | −3916.21 | −0.676068 | ||||||||
\(33\) | 1986.69 | 0.317574 | ||||||||
\(34\) | 713.825 | 0.105900 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −48.9272 | −0.00629207 | ||||||||
\(37\) | 14269.4 | 1.71357 | 0.856784 | − | 0.515675i | \(-0.172459\pi\) | ||||
0.856784 | + | 0.515675i | \(0.172459\pi\) | |||||||
\(38\) | −4558.15 | −0.512070 | ||||||||
\(39\) | −13109.7 | −1.38016 | ||||||||
\(40\) | 4924.20 | 0.486615 | ||||||||
\(41\) | −18405.0 | −1.70992 | −0.854962 | − | 0.518691i | \(-0.826419\pi\) | ||||
−0.854962 | + | 0.518691i | \(0.826419\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16338.0 | 1.34750 | 0.673749 | − | 0.738960i | \(-0.264683\pi\) | ||||
0.673749 | + | 0.738960i | \(0.264683\pi\) | |||||||
\(44\) | −1446.58 | −0.112644 | ||||||||
\(45\) | 106.829 | 0.00786428 | ||||||||
\(46\) | −333.359 | −0.0232283 | ||||||||
\(47\) | 3364.00 | 0.222132 | 0.111066 | − | 0.993813i | \(-0.464574\pi\) | ||||
0.111066 | + | 0.993813i | \(0.464574\pi\) | |||||||
\(48\) | −8279.27 | −0.518667 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2833.27 | −0.160274 | ||||||||
\(51\) | −2476.12 | −0.133305 | ||||||||
\(52\) | 9545.60 | 0.489547 | ||||||||
\(53\) | −16706.5 | −0.816949 | −0.408475 | − | 0.912770i | \(-0.633939\pi\) | ||||
−0.408475 | + | 0.912770i | \(0.633939\pi\) | |||||||
\(54\) | 17017.6 | 0.794169 | ||||||||
\(55\) | 3158.51 | 0.140791 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15811.4 | 0.644588 | ||||||||
\(58\) | 16734.0 | 0.653177 | ||||||||
\(59\) | 17999.6 | 0.673184 | 0.336592 | − | 0.941651i | \(-0.390726\pi\) | ||||
0.336592 | + | 0.941651i | \(0.390726\pi\) | |||||||
\(60\) | −4501.20 | −0.161417 | ||||||||
\(61\) | −28042.0 | −0.964903 | −0.482452 | − | 0.875923i | \(-0.660254\pi\) | ||||
−0.482452 | + | 0.875923i | \(0.660254\pi\) | |||||||
\(62\) | 21777.8 | 0.719508 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 34601.2 | 1.05595 | ||||||||
\(65\) | −20842.2 | −0.611871 | ||||||||
\(66\) | −9006.12 | −0.254494 | ||||||||
\(67\) | −47357.0 | −1.28883 | −0.644417 | − | 0.764674i | \(-0.722900\pi\) | ||||
−0.644417 | + | 0.764674i | \(0.722900\pi\) | |||||||
\(68\) | 1802.95 | 0.0472837 | ||||||||
\(69\) | 1156.36 | 0.0292395 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −49174.1 | −1.15768 | −0.578842 | − | 0.815440i | \(-0.696495\pi\) | ||||
−0.578842 | + | 0.815440i | \(0.696495\pi\) | |||||||
\(72\) | 841.679 | 0.0191344 | ||||||||
\(73\) | −80842.8 | −1.77555 | −0.887777 | − | 0.460273i | \(-0.847751\pi\) | ||||
−0.887777 | + | 0.460273i | \(0.847751\pi\) | |||||||
\(74\) | −64686.5 | −1.37320 | ||||||||
\(75\) | 9828.08 | 0.201751 | ||||||||
\(76\) | −11512.8 | −0.228637 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 59429.2 | 1.10602 | ||||||||
\(79\) | −27299.5 | −0.492138 | −0.246069 | − | 0.969252i | \(-0.579139\pi\) | ||||
−0.246069 | + | 0.969252i | \(0.579139\pi\) | |||||||
\(80\) | −13162.7 | −0.229942 | ||||||||
\(81\) | −60069.1 | −1.01728 | ||||||||
\(82\) | 83434.1 | 1.37028 | ||||||||
\(83\) | 195.977 | 0.00312256 | 0.00156128 | − | 0.999999i | \(-0.499503\pi\) | ||||
0.00156128 | + | 0.999999i | \(0.499503\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3936.62 | −0.0590985 | ||||||||
\(86\) | −74063.9 | −1.07984 | ||||||||
\(87\) | −58047.3 | −0.822212 | ||||||||
\(88\) | 24885.0 | 0.342555 | ||||||||
\(89\) | −3602.48 | −0.0482088 | −0.0241044 | − | 0.999709i | \(-0.507673\pi\) | ||||
−0.0241044 | + | 0.999709i | \(0.507673\pi\) | |||||||
\(90\) | −484.282 | −0.00630219 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −841.985 | −0.0103713 | ||||||||
\(93\) | −75543.3 | −0.905708 | ||||||||
\(94\) | −15249.8 | −0.178010 | ||||||||
\(95\) | 25137.4 | 0.285767 | ||||||||
\(96\) | −61582.0 | −0.681987 | ||||||||
\(97\) | −158739. | −1.71299 | −0.856494 | − | 0.516157i | \(-0.827362\pi\) | ||||
−0.856494 | + | 0.516157i | \(0.827362\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 539.874 | 0.00553611 | ||||||||
\(100\) | −7156.15 | −0.0715615 | ||||||||
\(101\) | −159763. | −1.55838 | −0.779190 | − | 0.626787i | \(-0.784369\pi\) | ||||
−0.779190 | + | 0.626787i | \(0.784369\pi\) | |||||||
\(102\) | 11224.8 | 0.106827 | ||||||||
\(103\) | 53989.3 | 0.501435 | 0.250717 | − | 0.968060i | \(-0.419334\pi\) | ||||
0.250717 | + | 0.968060i | \(0.419334\pi\) | |||||||
\(104\) | −164210. | −1.48873 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 75734.2 | 0.654678 | ||||||||
\(107\) | 99584.5 | 0.840877 | 0.420438 | − | 0.907321i | \(-0.361876\pi\) | ||||
0.420438 | + | 0.907321i | \(0.361876\pi\) | |||||||
\(108\) | 42982.3 | 0.354593 | ||||||||
\(109\) | 120574. | 0.972044 | 0.486022 | − | 0.873947i | \(-0.338448\pi\) | ||||
0.486022 | + | 0.873947i | \(0.338448\pi\) | |||||||
\(110\) | −14318.2 | −0.112826 | ||||||||
\(111\) | 224385. | 1.72857 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −259644. | −1.91285 | −0.956426 | − | 0.291975i | \(-0.905688\pi\) | ||||
−0.956426 | + | 0.291975i | \(0.905688\pi\) | |||||||
\(114\) | −71676.5 | −0.516553 | ||||||||
\(115\) | 1838.42 | 0.0129628 | ||||||||
\(116\) | 42266.2 | 0.291641 | ||||||||
\(117\) | −3562.49 | −0.0240597 | ||||||||
\(118\) | −81596.5 | −0.539469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 77432.7 | 0.490875 | ||||||||
\(121\) | −145089. | −0.900889 | ||||||||
\(122\) | 127121. | 0.773244 | ||||||||
\(123\) | −289417. | −1.72489 | ||||||||
\(124\) | 55005.6 | 0.321257 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −118169. | −0.650121 | −0.325061 | − | 0.945693i | \(-0.605385\pi\) | ||||
−0.325061 | + | 0.945693i | \(0.605385\pi\) | |||||||
\(128\) | −31536.8 | −0.170134 | ||||||||
\(129\) | 256914. | 1.35929 | ||||||||
\(130\) | 94482.4 | 0.490335 | ||||||||
\(131\) | −34613.9 | −0.176227 | −0.0881136 | − | 0.996110i | \(-0.528084\pi\) | ||||
−0.0881136 | + | 0.996110i | \(0.528084\pi\) | |||||||
\(132\) | −22747.3 | −0.113631 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 214680. | 1.03283 | ||||||||
\(135\) | −93849.0 | −0.443195 | ||||||||
\(136\) | −31015.6 | −0.143791 | ||||||||
\(137\) | 22671.4 | 0.103199 | 0.0515997 | − | 0.998668i | \(-0.483568\pi\) | ||||
0.0515997 | + | 0.998668i | \(0.483568\pi\) | |||||||
\(138\) | −5242.05 | −0.0234317 | ||||||||
\(139\) | −125034. | −0.548899 | −0.274449 | − | 0.961602i | \(-0.588496\pi\) | ||||
−0.274449 | + | 0.961602i | \(0.588496\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 52898.6 | 0.224077 | ||||||||
\(142\) | 222917. | 0.927732 | ||||||||
\(143\) | −105328. | −0.430730 | ||||||||
\(144\) | −2249.85 | −0.00904165 | ||||||||
\(145\) | −92285.5 | −0.364513 | ||||||||
\(146\) | 366479. | 1.42287 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −163382. | −0.613128 | ||||||||
\(149\) | 390090. | 1.43946 | 0.719729 | − | 0.694255i | \(-0.244266\pi\) | ||||
0.719729 | + | 0.694255i | \(0.244266\pi\) | |||||||
\(150\) | −44552.9 | −0.161677 | ||||||||
\(151\) | −71978.1 | −0.256896 | −0.128448 | − | 0.991716i | \(-0.541000\pi\) | ||||
−0.128448 | + | 0.991716i | \(0.541000\pi\) | |||||||
\(152\) | 198051. | 0.695293 | ||||||||
\(153\) | −672.875 | −0.00232384 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −120101. | −0.401530 | ||||||||
\(156\) | 150104. | 0.493833 | ||||||||
\(157\) | 88329.4 | 0.285994 | 0.142997 | − | 0.989723i | \(-0.454326\pi\) | ||||
0.142997 | + | 0.989723i | \(0.454326\pi\) | |||||||
\(158\) | 123755. | 0.394384 | ||||||||
\(159\) | −262708. | −0.824101 | ||||||||
\(160\) | −97905.1 | −0.302347 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 272307. | 0.815213 | ||||||||
\(163\) | 438774. | 1.29352 | 0.646758 | − | 0.762695i | \(-0.276124\pi\) | ||||
0.646758 | + | 0.762695i | \(0.276124\pi\) | |||||||
\(164\) | 210735. | 0.611824 | ||||||||
\(165\) | 49667.3 | 0.142024 | ||||||||
\(166\) | −888.410 | −0.00250232 | ||||||||
\(167\) | 391291. | 1.08570 | 0.542848 | − | 0.839831i | \(-0.317346\pi\) | ||||
0.542848 | + | 0.839831i | \(0.317346\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 323743. | 0.871933 | ||||||||
\(170\) | 17845.6 | 0.0473597 | ||||||||
\(171\) | 4296.66 | 0.0112368 | ||||||||
\(172\) | −187068. | −0.482145 | ||||||||
\(173\) | −387003. | −0.983103 | −0.491551 | − | 0.870849i | \(-0.663570\pi\) | ||||
−0.491551 | + | 0.870849i | \(0.663570\pi\) | |||||||
\(174\) | 263141. | 0.658895 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −66518.9 | −0.161869 | ||||||||
\(177\) | 283043. | 0.679077 | ||||||||
\(178\) | 16330.9 | 0.0386330 | ||||||||
\(179\) | 838441. | 1.95587 | 0.977935 | − | 0.208911i | \(-0.0669917\pi\) | ||||
0.977935 | + | 0.208911i | \(0.0669917\pi\) | |||||||
\(180\) | −1223.18 | −0.00281390 | ||||||||
\(181\) | 355885. | 0.807447 | 0.403723 | − | 0.914881i | \(-0.367716\pi\) | ||||
0.403723 | + | 0.914881i | \(0.367716\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −440958. | −0.973350 | ||||||||
\(184\) | 14484.4 | 0.0315396 | ||||||||
\(185\) | 356735. | 0.766331 | ||||||||
\(186\) | 342455. | 0.725807 | ||||||||
\(187\) | −19894.2 | −0.0416027 | ||||||||
\(188\) | −38517.3 | −0.0794805 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −113954. | −0.229005 | ||||||||
\(191\) | −176395. | −0.349866 | −0.174933 | − | 0.984580i | \(-0.555971\pi\) | ||||
−0.174933 | + | 0.984580i | \(0.555971\pi\) | |||||||
\(192\) | 544102. | 1.06519 | ||||||||
\(193\) | 697832. | 1.34852 | 0.674261 | − | 0.738493i | \(-0.264462\pi\) | ||||
0.674261 | + | 0.738493i | \(0.264462\pi\) | |||||||
\(194\) | 719600. | 1.37274 | ||||||||
\(195\) | −327742. | −0.617228 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 478810. | 0.879017 | 0.439509 | − | 0.898238i | \(-0.355153\pi\) | ||||
0.439509 | + | 0.898238i | \(0.355153\pi\) | |||||||
\(198\) | −2447.37 | −0.00443646 | ||||||||
\(199\) | 904995. | 1.61999 | 0.809997 | − | 0.586434i | \(-0.199469\pi\) | ||||
0.809997 | + | 0.586434i | \(0.199469\pi\) | |||||||
\(200\) | 123105. | 0.217621 | ||||||||
\(201\) | −744685. | −1.30012 | ||||||||
\(202\) | 724243. | 1.24884 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 28351.2 | 0.0476976 | ||||||||
\(205\) | −460125. | −0.764701 | ||||||||
\(206\) | −244746. | −0.401834 | ||||||||
\(207\) | 314.236 | 0.000509717 0 | ||||||||
\(208\) | 438942. | 0.703475 | ||||||||
\(209\) | 127035. | 0.201167 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −843592. | −1.30445 | −0.652223 | − | 0.758027i | \(-0.726164\pi\) | ||||
−0.652223 | + | 0.758027i | \(0.726164\pi\) | |||||||
\(212\) | 191286. | 0.292311 | ||||||||
\(213\) | −773258. | −1.16782 | ||||||||
\(214\) | −451439. | −0.673853 | ||||||||
\(215\) | 408450. | 0.602619 | ||||||||
\(216\) | −739410. | −1.07833 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −546587. | −0.778966 | ||||||||
\(219\) | −1.27125e6 | −1.79110 | ||||||||
\(220\) | −36164.4 | −0.0503761 | ||||||||
\(221\) | 131277. | 0.180803 | ||||||||
\(222\) | −1.01719e6 | −1.38522 | ||||||||
\(223\) | −584986. | −0.787741 | −0.393871 | − | 0.919166i | \(-0.628864\pi\) | ||||
−0.393871 | + | 0.919166i | \(0.628864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2670.73 | 0.00351701 | ||||||||
\(226\) | 1.17702e6 | 1.53290 | ||||||||
\(227\) | −849739. | −1.09451 | −0.547257 | − | 0.836965i | \(-0.684328\pi\) | ||||
−0.547257 | + | 0.836965i | \(0.684328\pi\) | |||||||
\(228\) | −181038. | −0.230639 | ||||||||
\(229\) | −193287. | −0.243564 | −0.121782 | − | 0.992557i | \(-0.538861\pi\) | ||||
−0.121782 | + | 0.992557i | \(0.538861\pi\) | |||||||
\(230\) | −8333.98 | −0.0103880 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −727091. | −0.886889 | ||||||||
\(233\) | −1.12669e6 | −1.35961 | −0.679803 | − | 0.733395i | \(-0.737935\pi\) | ||||
−0.679803 | + | 0.733395i | \(0.737935\pi\) | |||||||
\(234\) | 16149.6 | 0.0192807 | ||||||||
\(235\) | 84099.9 | 0.0993404 | ||||||||
\(236\) | −206093. | −0.240870 | ||||||||
\(237\) | −429283. | −0.496446 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −639017. | −0.723632 | −0.361816 | − | 0.932250i | \(-0.617843\pi\) | ||||
−0.361816 | + | 0.932250i | \(0.617843\pi\) | |||||||
\(240\) | −206982. | −0.231955 | ||||||||
\(241\) | 256273. | 0.284224 | 0.142112 | − | 0.989851i | \(-0.454611\pi\) | ||||
0.142112 | + | 0.989851i | \(0.454611\pi\) | |||||||
\(242\) | 657722. | 0.721945 | ||||||||
\(243\) | −32369.8 | −0.0351661 | ||||||||
\(244\) | 321076. | 0.345250 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.31200e6 | 1.38228 | ||||||||
\(247\) | −838271. | −0.874263 | ||||||||
\(248\) | −946244. | −0.976953 | ||||||||
\(249\) | 3081.73 | 0.00314989 | ||||||||
\(250\) | −70831.7 | −0.0716766 | ||||||||
\(251\) | 1.70726e6 | 1.71047 | 0.855236 | − | 0.518239i | \(-0.173412\pi\) | ||||
0.855236 | + | 0.518239i | \(0.173412\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9290.66 | 0.00912526 | ||||||||
\(254\) | 535687. | 0.520987 | ||||||||
\(255\) | −61903.1 | −0.0596159 | ||||||||
\(256\) | −964277. | −0.919606 | ||||||||
\(257\) | −1.45103e6 | −1.37039 | −0.685193 | − | 0.728362i | \(-0.740282\pi\) | ||||
−0.685193 | + | 0.728362i | \(0.740282\pi\) | |||||||
\(258\) | −1.16465e6 | −1.08930 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 238640. | 0.218932 | ||||||||
\(261\) | −15774.1 | −0.0143332 | ||||||||
\(262\) | 156913. | 0.141223 | ||||||||
\(263\) | 1.64253e6 | 1.46428 | 0.732142 | − | 0.681152i | \(-0.238521\pi\) | ||||
0.732142 | + | 0.681152i | \(0.238521\pi\) | |||||||
\(264\) | 391315. | 0.345554 | ||||||||
\(265\) | −417662. | −0.365351 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −56648.7 | −0.0486308 | ||||||||
\(268\) | 542230. | 0.461155 | ||||||||
\(269\) | 608608. | 0.512811 | 0.256405 | − | 0.966569i | \(-0.417462\pi\) | ||||
0.256405 | + | 0.966569i | \(0.417462\pi\) | |||||||
\(270\) | 425439. | 0.355163 | ||||||||
\(271\) | 804294. | 0.665260 | 0.332630 | − | 0.943057i | \(-0.392064\pi\) | ||||
0.332630 | + | 0.943057i | \(0.392064\pi\) | |||||||
\(272\) | 82906.3 | 0.0679462 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −102775. | −0.0827008 | ||||||||
\(275\) | 78962.7 | 0.0629637 | ||||||||
\(276\) | −13240.2 | −0.0104621 | ||||||||
\(277\) | −820333. | −0.642378 | −0.321189 | − | 0.947015i | \(-0.604082\pi\) | ||||
−0.321189 | + | 0.947015i | \(0.604082\pi\) | |||||||
\(278\) | 566809. | 0.439870 | ||||||||
\(279\) | −20528.5 | −0.0157887 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.17132e6 | 0.884934 | 0.442467 | − | 0.896785i | \(-0.354103\pi\) | ||||
0.442467 | + | 0.896785i | \(0.354103\pi\) | |||||||
\(282\) | −239801. | −0.179568 | ||||||||
\(283\) | −1.99761e6 | −1.48267 | −0.741335 | − | 0.671136i | \(-0.765807\pi\) | ||||
−0.741335 | + | 0.671136i | \(0.765807\pi\) | |||||||
\(284\) | 563035. | 0.414228 | ||||||||
\(285\) | 395284. | 0.288269 | ||||||||
\(286\) | 477477. | 0.345174 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16734.6 | −0.0118887 | ||||||||
\(289\) | −1.39506e6 | −0.982537 | ||||||||
\(290\) | 418351. | 0.292110 | ||||||||
\(291\) | −2.49616e6 | −1.72798 | ||||||||
\(292\) | 925637. | 0.635307 | ||||||||
\(293\) | −174337. | −0.118637 | −0.0593184 | − | 0.998239i | \(-0.518893\pi\) | ||||
−0.0593184 | + | 0.998239i | \(0.518893\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 449991. | 0.301057 | ||||||||
\(296\) | 2.81062e6 | 1.86454 | ||||||||
\(297\) | −474276. | −0.311990 | ||||||||
\(298\) | −1.76837e6 | −1.15354 | ||||||||
\(299\) | −61306.8 | −0.0396580 | ||||||||
\(300\) | −112530. | −0.0721880 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 326293. | 0.205869 | ||||||||
\(303\) | −2.51227e6 | −1.57202 | ||||||||
\(304\) | −529400. | −0.328549 | ||||||||
\(305\) | −701049. | −0.431518 | ||||||||
\(306\) | 3050.30 | 0.00186225 | ||||||||
\(307\) | 987671. | 0.598089 | 0.299045 | − | 0.954239i | \(-0.403332\pi\) | ||||
0.299045 | + | 0.954239i | \(0.403332\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 848977. | 0.505825 | ||||||||
\(310\) | 544446. | 0.321774 | ||||||||
\(311\) | 2.40496e6 | 1.40996 | 0.704981 | − | 0.709226i | \(-0.250956\pi\) | ||||
0.704981 | + | 0.709226i | \(0.250956\pi\) | |||||||
\(312\) | −2.58219e6 | −1.50176 | ||||||||
\(313\) | 1.89499e6 | 1.09332 | 0.546658 | − | 0.837356i | \(-0.315900\pi\) | ||||
0.546658 | + | 0.837356i | \(0.315900\pi\) | |||||||
\(314\) | −400417. | −0.229186 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 312575. | 0.176091 | ||||||||
\(317\) | −737403. | −0.412151 | −0.206076 | − | 0.978536i | \(-0.566069\pi\) | ||||
−0.206076 | + | 0.978536i | \(0.566069\pi\) | |||||||
\(318\) | 1.19092e6 | 0.660409 | ||||||||
\(319\) | −466375. | −0.256601 | ||||||||
\(320\) | 865031. | 0.472234 | ||||||||
\(321\) | 1.56596e6 | 0.848238 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −158331. | −0.0844420 | ||||||||
\(324\) | 687782. | 0.363989 | ||||||||
\(325\) | −521055. | −0.273637 | ||||||||
\(326\) | −1.98906e6 | −1.03658 | ||||||||
\(327\) | 1.89601e6 | 0.980553 | ||||||||
\(328\) | −3.62520e6 | −1.86058 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −225153. | −0.113813 | ||||||||
\(331\) | 3.68290e6 | 1.84765 | 0.923826 | − | 0.382813i | \(-0.125045\pi\) | ||||
0.923826 | + | 0.382813i | \(0.125045\pi\) | |||||||
\(332\) | −2243.91 | −0.00111727 | ||||||||
\(333\) | 60975.6 | 0.0301332 | ||||||||
\(334\) | −1.77381e6 | −0.870044 | ||||||||
\(335\) | −1.18392e6 | −0.576384 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 564674. | 0.270846 | 0.135423 | − | 0.990788i | \(-0.456761\pi\) | ||||
0.135423 | + | 0.990788i | \(0.456761\pi\) | |||||||
\(338\) | −1.46760e6 | −0.698740 | ||||||||
\(339\) | −4.08287e6 | −1.92960 | ||||||||
\(340\) | 45073.7 | 0.0211459 | ||||||||
\(341\) | −606945. | −0.282659 | ||||||||
\(342\) | −19477.8 | −0.00900479 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.21807e6 | 1.46622 | ||||||||
\(345\) | 28909.0 | 0.0130763 | ||||||||
\(346\) | 1.75437e6 | 0.787828 | ||||||||
\(347\) | 1.74360e6 | 0.777361 | 0.388681 | − | 0.921373i | \(-0.372931\pi\) | ||||
0.388681 | + | 0.921373i | \(0.372931\pi\) | |||||||
\(348\) | 664632. | 0.294194 | ||||||||
\(349\) | −1.75374e6 | −0.770727 | −0.385363 | − | 0.922765i | \(-0.625924\pi\) | ||||
−0.385363 | + | 0.922765i | \(0.625924\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.12963e6 | 1.35589 | ||||||||
\(352\) | −494774. | −0.212839 | ||||||||
\(353\) | 823880. | 0.351906 | 0.175953 | − | 0.984399i | \(-0.443699\pi\) | ||||
0.175953 | + | 0.984399i | \(0.443699\pi\) | |||||||
\(354\) | −1.28310e6 | −0.544192 | ||||||||
\(355\) | −1.22935e6 | −0.517732 | ||||||||
\(356\) | 41247.8 | 0.0172495 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.80084e6 | −1.56737 | ||||||||
\(359\) | 3.56016e6 | 1.45792 | 0.728959 | − | 0.684557i | \(-0.240004\pi\) | ||||
0.728959 | + | 0.684557i | \(0.240004\pi\) | |||||||
\(360\) | 21042.0 | 0.00855717 | ||||||||
\(361\) | −1.46507e6 | −0.591686 | ||||||||
\(362\) | −1.61331e6 | −0.647063 | ||||||||
\(363\) | −2.28152e6 | −0.908776 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.02107e6 | −0.794052 | ||||||||
\(366\) | 1.99896e6 | 0.780013 | ||||||||
\(367\) | −3.14208e6 | −1.21773 | −0.608867 | − | 0.793272i | \(-0.708376\pi\) | ||||
−0.608867 | + | 0.793272i | \(0.708376\pi\) | |||||||
\(368\) | −38717.6 | −0.0149035 | ||||||||
\(369\) | −78647.8 | −0.0300691 | ||||||||
\(370\) | −1.61716e6 | −0.614114 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 864959. | 0.324069 | ||||||||
\(373\) | −2.64076e6 | −0.982782 | −0.491391 | − | 0.870939i | \(-0.663511\pi\) | ||||
−0.491391 | + | 0.870939i | \(0.663511\pi\) | |||||||
\(374\) | 90184.8 | 0.0333391 | ||||||||
\(375\) | 245702. | 0.0902257 | ||||||||
\(376\) | 662600. | 0.241703 | ||||||||
\(377\) | 3.07749e6 | 1.11518 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.62170e6 | −0.937531 | −0.468766 | − | 0.883323i | \(-0.655301\pi\) | ||||
−0.468766 | + | 0.883323i | \(0.655301\pi\) | |||||||
\(380\) | −287820. | −0.102250 | ||||||||
\(381\) | −1.85820e6 | −0.655813 | ||||||||
\(382\) | 799637. | 0.280372 | ||||||||
\(383\) | 2.15463e6 | 0.750543 | 0.375272 | − | 0.926915i | \(-0.377549\pi\) | ||||
0.375272 | + | 0.926915i | \(0.377549\pi\) | |||||||
\(384\) | −495913. | −0.171624 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.16343e6 | −1.08066 | ||||||||
\(387\) | 69815.2 | 0.0236958 | ||||||||
\(388\) | 1.81754e6 | 0.612920 | ||||||||
\(389\) | −551834. | −0.184899 | −0.0924495 | − | 0.995717i | \(-0.529470\pi\) | ||||
−0.0924495 | + | 0.995717i | \(0.529470\pi\) | |||||||
\(390\) | 1.48573e6 | 0.494627 | ||||||||
\(391\) | −11579.5 | −0.00383042 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −544301. | −0.177770 | ||||||||
\(394\) | −2.17055e6 | −0.704417 | ||||||||
\(395\) | −682488. | −0.220091 | ||||||||
\(396\) | −6181.47 | −0.00198086 | ||||||||
\(397\) | −721152. | −0.229642 | −0.114821 | − | 0.993386i | \(-0.536629\pi\) | ||||
−0.114821 | + | 0.993386i | \(0.536629\pi\) | |||||||
\(398\) | −4.10255e6 | −1.29821 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −329066. | −0.102833 | ||||||||
\(401\) | −5.40555e6 | −1.67872 | −0.839361 | − | 0.543575i | \(-0.817070\pi\) | ||||
−0.839361 | + | 0.543575i | \(0.817070\pi\) | |||||||
\(402\) | 3.37583e6 | 1.04187 | ||||||||
\(403\) | 4.00508e6 | 1.22842 | ||||||||
\(404\) | 1.82926e6 | 0.557601 | ||||||||
\(405\) | −1.50173e6 | −0.454940 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.80280e6 | 0.539463 | ||||||||
\(408\) | −487717. | −0.145050 | ||||||||
\(409\) | 756615. | 0.223649 | 0.111824 | − | 0.993728i | \(-0.464331\pi\) | ||||
0.111824 | + | 0.993728i | \(0.464331\pi\) | |||||||
\(410\) | 2.08585e6 | 0.612808 | ||||||||
\(411\) | 356506. | 0.104103 | ||||||||
\(412\) | −618169. | −0.179417 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1424.50 | −0.000408472 0 | ||||||||
\(415\) | 4899.43 | 0.00139645 | ||||||||
\(416\) | 3.26489e6 | 0.924987 | ||||||||
\(417\) | −1.96615e6 | −0.553704 | ||||||||
\(418\) | −575878. | −0.161209 | ||||||||
\(419\) | 4.63489e6 | 1.28975 | 0.644873 | − | 0.764290i | \(-0.276910\pi\) | ||||
0.644873 | + | 0.764290i | \(0.276910\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.13555e6 | 1.68713 | 0.843564 | − | 0.537028i | \(-0.180453\pi\) | ||||
0.843564 | + | 0.537028i | \(0.180453\pi\) | |||||||
\(422\) | 3.82419e6 | 1.04534 | ||||||||
\(423\) | 14374.9 | 0.00390621 | ||||||||
\(424\) | −3.29064e6 | −0.888927 | ||||||||
\(425\) | −98415.6 | −0.0264297 | ||||||||
\(426\) | 3.50536e6 | 0.935854 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.14023e6 | −0.300872 | ||||||||
\(429\) | −1.65628e6 | −0.434501 | ||||||||
\(430\) | −1.85160e6 | −0.482920 | ||||||||
\(431\) | 2.11928e6 | 0.549534 | 0.274767 | − | 0.961511i | \(-0.411399\pi\) | ||||
0.274767 | + | 0.961511i | \(0.411399\pi\) | |||||||
\(432\) | 1.97648e6 | 0.509546 | ||||||||
\(433\) | −4.34108e6 | −1.11270 | −0.556350 | − | 0.830948i | \(-0.687799\pi\) | ||||
−0.556350 | + | 0.830948i | \(0.687799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.45118e6 | −0.367704 | ||||||||
\(436\) | −1.38055e6 | −0.347805 | ||||||||
\(437\) | 73941.1 | 0.0185218 | ||||||||
\(438\) | 5.76285e6 | 1.43533 | ||||||||
\(439\) | −6.74539e6 | −1.67050 | −0.835248 | − | 0.549873i | \(-0.814676\pi\) | ||||
−0.835248 | + | 0.549873i | \(0.814676\pi\) | |||||||
\(440\) | 622125. | 0.153195 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −595107. | −0.144890 | ||||||||
\(443\) | −4.42765e6 | −1.07192 | −0.535962 | − | 0.844242i | \(-0.680051\pi\) | ||||
−0.535962 | + | 0.844242i | \(0.680051\pi\) | |||||||
\(444\) | −2.56918e6 | −0.618495 | ||||||||
\(445\) | −90062.0 | −0.0215596 | ||||||||
\(446\) | 2.65188e6 | 0.631272 | ||||||||
\(447\) | 6.13413e6 | 1.45206 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.84556e6 | −1.36839 | −0.684196 | − | 0.729299i | \(-0.739847\pi\) | ||||
−0.684196 | + | 0.729299i | \(0.739847\pi\) | |||||||
\(450\) | −12107.0 | −0.00281843 | ||||||||
\(451\) | −2.32529e6 | −0.538315 | ||||||||
\(452\) | 2.97288e6 | 0.684433 | ||||||||
\(453\) | −1.13185e6 | −0.259145 | ||||||||
\(454\) | 3.85206e6 | 0.877109 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.11433e6 | 0.701380 | ||||||||
\(457\) | 3.33675e6 | 0.747366 | 0.373683 | − | 0.927556i | \(-0.378095\pi\) | ||||
0.373683 | + | 0.927556i | \(0.378095\pi\) | |||||||
\(458\) | 876213. | 0.195185 | ||||||||
\(459\) | 591117. | 0.130961 | ||||||||
\(460\) | −21049.6 | −0.00463820 | ||||||||
\(461\) | 7.61305e6 | 1.66842 | 0.834212 | − | 0.551444i | \(-0.185923\pi\) | ||||
0.834212 | + | 0.551444i | \(0.185923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.82147e6 | −0.611679 | −0.305839 | − | 0.952083i | \(-0.598937\pi\) | ||||
−0.305839 | + | 0.952083i | \(0.598937\pi\) | |||||||
\(464\) | 1.94355e6 | 0.419085 | ||||||||
\(465\) | −1.88858e6 | −0.405045 | ||||||||
\(466\) | 5.10753e6 | 1.08955 | ||||||||
\(467\) | −2.61119e6 | −0.554046 | −0.277023 | − | 0.960863i | \(-0.589348\pi\) | ||||
−0.277023 | + | 0.960863i | \(0.589348\pi\) | |||||||
\(468\) | 40790.0 | 0.00860873 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −381244. | −0.0796084 | ||||||||
\(471\) | 1.38897e6 | 0.288497 | ||||||||
\(472\) | 3.54535e6 | 0.732495 | ||||||||
\(473\) | 2.06415e6 | 0.424217 | ||||||||
\(474\) | 1.94604e6 | 0.397837 | ||||||||
\(475\) | 628436. | 0.127799 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −71389.6 | −0.0143661 | ||||||||
\(478\) | 2.89681e6 | 0.579896 | ||||||||
\(479\) | −817014. | −0.162701 | −0.0813506 | − | 0.996686i | \(-0.525923\pi\) | ||||
−0.0813506 | + | 0.996686i | \(0.525923\pi\) | |||||||
\(480\) | −1.53955e6 | −0.304994 | ||||||||
\(481\) | −1.18962e7 | −2.34448 | ||||||||
\(482\) | −1.16174e6 | −0.227768 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.66125e6 | 0.322345 | ||||||||
\(485\) | −3.96848e6 | −0.766072 | ||||||||
\(486\) | 146740. | 0.0281810 | ||||||||
\(487\) | −2.11091e6 | −0.403317 | −0.201659 | − | 0.979456i | \(-0.564633\pi\) | ||||
−0.201659 | + | 0.979456i | \(0.564633\pi\) | |||||||
\(488\) | −5.52337e6 | −1.04992 | ||||||||
\(489\) | 6.89968e6 | 1.30484 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.71666e6 | 0.321352 | 0.160676 | − | 0.987007i | \(-0.448633\pi\) | ||||
0.160676 | + | 0.987007i | \(0.448633\pi\) | |||||||
\(492\) | 3.31378e6 | 0.617180 | ||||||||
\(493\) | 581269. | 0.107711 | ||||||||
\(494\) | 3.80007e6 | 0.700607 | ||||||||
\(495\) | 13496.8 | 0.00247582 | ||||||||
\(496\) | 2.52936e6 | 0.461643 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −13970.2 | −0.00252423 | ||||||||
\(499\) | 7.64091e6 | 1.37371 | 0.686853 | − | 0.726797i | \(-0.258992\pi\) | ||||
0.686853 | + | 0.726797i | \(0.258992\pi\) | |||||||
\(500\) | −178904. | −0.0320033 | ||||||||
\(501\) | 6.15302e6 | 1.09520 | ||||||||
\(502\) | −7.73941e6 | −1.37072 | ||||||||
\(503\) | −2.90660e6 | −0.512231 | −0.256115 | − | 0.966646i | \(-0.582443\pi\) | ||||
−0.256115 | + | 0.966646i | \(0.582443\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.99408e6 | −0.696929 | ||||||||
\(506\) | −42116.7 | −0.00731270 | ||||||||
\(507\) | 5.09083e6 | 0.879566 | ||||||||
\(508\) | 1.35302e6 | 0.232618 | ||||||||
\(509\) | −602745. | −0.103119 | −0.0515595 | − | 0.998670i | \(-0.516419\pi\) | ||||
−0.0515595 | + | 0.998670i | \(0.516419\pi\) | |||||||
\(510\) | 280621. | 0.0477743 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.38046e6 | 0.907078 | ||||||||
\(513\) | −3.77460e6 | −0.633253 | ||||||||
\(514\) | 6.57784e6 | 1.09818 | ||||||||
\(515\) | 1.34973e6 | 0.224248 | ||||||||
\(516\) | −2.94162e6 | −0.486366 | ||||||||
\(517\) | 425008. | 0.0699312 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.08559e6 | −0.991709 | ||||||||
\(520\) | −4.10525e6 | −0.665780 | ||||||||
\(521\) | 611890. | 0.0987595 | 0.0493797 | − | 0.998780i | \(-0.484276\pi\) | ||||
0.0493797 | + | 0.998780i | \(0.484276\pi\) | |||||||
\(522\) | 71507.5 | 0.0114862 | ||||||||
\(523\) | 9.02368e6 | 1.44255 | 0.721273 | − | 0.692651i | \(-0.243557\pi\) | ||||
0.721273 | + | 0.692651i | \(0.243557\pi\) | |||||||
\(524\) | 396324. | 0.0630554 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.44598e6 | −1.17343 | ||||||||
\(527\) | 756469. | 0.118649 | ||||||||
\(528\) | −1.04600e6 | −0.163286 | ||||||||
\(529\) | −6.43094e6 | −0.999160 | ||||||||
\(530\) | 1.89336e6 | 0.292781 | ||||||||
\(531\) | 76915.6 | 0.0118380 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.53440e7 | 2.33949 | ||||||||
\(534\) | 256801. | 0.0389712 | ||||||||
\(535\) | 2.48961e6 | 0.376052 | ||||||||
\(536\) | −9.32781e6 | −1.40239 | ||||||||
\(537\) | 1.31844e7 | 1.97299 | ||||||||
\(538\) | −2.75896e6 | −0.410951 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.07456e6 | 0.158579 | ||||||||
\(541\) | 2.23016e6 | 0.327600 | 0.163800 | − | 0.986494i | \(-0.447625\pi\) | ||||
0.163800 | + | 0.986494i | \(0.447625\pi\) | |||||||
\(542\) | −3.64605e6 | −0.533119 | ||||||||
\(543\) | 5.59627e6 | 0.814515 | ||||||||
\(544\) | 616665. | 0.0893413 | ||||||||
\(545\) | 3.01434e6 | 0.434711 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.20299e7 | −1.71907 | −0.859535 | − | 0.511077i | \(-0.829247\pi\) | ||||
−0.859535 | + | 0.511077i | \(0.829247\pi\) | |||||||
\(548\) | −259584. | −0.0369255 | ||||||||
\(549\) | −119828. | −0.0169679 | ||||||||
\(550\) | −357956. | −0.0504571 | ||||||||
\(551\) | −3.71171e6 | −0.520829 | ||||||||
\(552\) | 227766. | 0.0318157 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.71876e6 | 0.514782 | ||||||||
\(555\) | 5.60963e6 | 0.773040 | ||||||||
\(556\) | 1.43162e6 | 0.196400 | ||||||||
\(557\) | 4.42512e6 | 0.604348 | 0.302174 | − | 0.953253i | \(-0.402288\pi\) | ||||
0.302174 | + | 0.953253i | \(0.402288\pi\) | |||||||
\(558\) | 93060.5 | 0.0126526 | ||||||||
\(559\) | −1.36208e7 | −1.84363 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −312834. | −0.0419669 | ||||||||
\(562\) | −5.30987e6 | −0.709159 | ||||||||
\(563\) | 7.64181e6 | 1.01607 | 0.508037 | − | 0.861335i | \(-0.330371\pi\) | ||||
0.508037 | + | 0.861335i | \(0.330371\pi\) | |||||||
\(564\) | −605681. | −0.0801763 | ||||||||
\(565\) | −6.49109e6 | −0.855453 | ||||||||
\(566\) | 9.05561e6 | 1.18817 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.68572e6 | −1.25968 | ||||||||
\(569\) | 1.63458e6 | 0.211653 | 0.105826 | − | 0.994385i | \(-0.466251\pi\) | ||||
0.105826 | + | 0.994385i | \(0.466251\pi\) | |||||||
\(570\) | −1.79191e6 | −0.231010 | ||||||||
\(571\) | −4.20562e6 | −0.539809 | −0.269905 | − | 0.962887i | \(-0.586992\pi\) | ||||
−0.269905 | + | 0.962887i | \(0.586992\pi\) | |||||||
\(572\) | 1.20599e6 | 0.154119 | ||||||||
\(573\) | −2.77379e6 | −0.352929 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 45960.5 | 0.00579716 | ||||||||
\(576\) | 147857. | 0.0185689 | ||||||||
\(577\) | 9.07317e6 | 1.13454 | 0.567270 | − | 0.823532i | \(-0.308000\pi\) | ||||
0.567270 | + | 0.823532i | \(0.308000\pi\) | |||||||
\(578\) | 6.32413e6 | 0.787375 | ||||||||
\(579\) | 1.09734e7 | 1.36033 | ||||||||
\(580\) | 1.05665e6 | 0.130426 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.13157e7 | 1.38475 | ||||||||
\(583\) | −2.11070e6 | −0.257191 | ||||||||
\(584\) | −1.59234e7 | −1.93199 | ||||||||
\(585\) | −89062.3 | −0.0107598 | ||||||||
\(586\) | 790308. | 0.0950719 | ||||||||
\(587\) | −8.91120e6 | −1.06743 | −0.533717 | − | 0.845663i | \(-0.679205\pi\) | ||||
−0.533717 | + | 0.845663i | \(0.679205\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.83046e6 | −0.573720 | ||||||||
\(590\) | −2.03991e6 | −0.241258 | ||||||||
\(591\) | 7.52924e6 | 0.886712 | ||||||||
\(592\) | −7.51293e6 | −0.881059 | ||||||||
\(593\) | 9.36933e6 | 1.09414 | 0.547069 | − | 0.837088i | \(-0.315744\pi\) | ||||
0.547069 | + | 0.837088i | \(0.315744\pi\) | |||||||
\(594\) | 2.15000e6 | 0.250019 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.46647e6 | −0.515049 | ||||||||
\(597\) | 1.42310e7 | 1.63418 | ||||||||
\(598\) | 277918. | 0.0317807 | ||||||||
\(599\) | 3.91658e6 | 0.446005 | 0.223003 | − | 0.974818i | \(-0.428414\pi\) | ||||
0.223003 | + | 0.974818i | \(0.428414\pi\) | |||||||
\(600\) | 1.93582e6 | 0.219526 | ||||||||
\(601\) | −9.01467e6 | −1.01804 | −0.509019 | − | 0.860755i | \(-0.669992\pi\) | ||||
−0.509019 | + | 0.860755i | \(0.669992\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −202365. | −0.0226642 | ||||||||
\(604\) | 824138. | 0.0919195 | ||||||||
\(605\) | −3.62723e6 | −0.402890 | ||||||||
\(606\) | 1.13887e7 | 1.25977 | ||||||||
\(607\) | 1.47500e6 | 0.162488 | 0.0812439 | − | 0.996694i | \(-0.474111\pi\) | ||||
0.0812439 | + | 0.996694i | \(0.474111\pi\) | |||||||
\(608\) | −3.93773e6 | −0.432004 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.17801e6 | 0.345805 | ||||||||
\(611\) | −2.80452e6 | −0.303918 | ||||||||
\(612\) | 7704.31 | 0.000831487 0 | ||||||||
\(613\) | −4.14590e6 | −0.445623 | −0.222811 | − | 0.974862i | \(-0.571523\pi\) | ||||
−0.222811 | + | 0.974862i | \(0.571523\pi\) | |||||||
\(614\) | −4.47734e6 | −0.479290 | ||||||||
\(615\) | −7.23544e6 | −0.771395 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.99859e6 | 0.317105 | 0.158553 | − | 0.987351i | \(-0.449317\pi\) | ||||
0.158553 | + | 0.987351i | \(0.449317\pi\) | |||||||
\(618\) | −3.84861e6 | −0.405352 | ||||||||
\(619\) | 9.80100e6 | 1.02812 | 0.514060 | − | 0.857754i | \(-0.328141\pi\) | ||||
0.514060 | + | 0.857754i | \(0.328141\pi\) | |||||||
\(620\) | 1.37514e6 | 0.143671 | ||||||||
\(621\) | −276054. | −0.0287254 | ||||||||
\(622\) | −1.09022e7 | −1.12990 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.90232e6 | 0.709633 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −8.59041e6 | −0.876149 | ||||||||
\(627\) | 1.99761e6 | 0.202928 | ||||||||
\(628\) | −1.01136e6 | −0.102331 | ||||||||
\(629\) | −2.24693e6 | −0.226445 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 465144. | 0.0465065 | 0.0232533 | − | 0.999730i | \(-0.492598\pi\) | ||||
0.0232533 | + | 0.999730i | \(0.492598\pi\) | |||||||
\(632\) | −5.37713e6 | −0.535498 | ||||||||
\(633\) | −1.32654e7 | −1.31587 | ||||||||
\(634\) | 3.34281e6 | 0.330285 | ||||||||
\(635\) | −2.95423e6 | −0.290743 | ||||||||
\(636\) | 3.00797e6 | 0.294870 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.11418e6 | 0.205632 | ||||||||
\(639\) | −210129. | −0.0203580 | ||||||||
\(640\) | −788419. | −0.0760864 | ||||||||
\(641\) | −1.42324e7 | −1.36815 | −0.684075 | − | 0.729412i | \(-0.739794\pi\) | ||||
−0.684075 | + | 0.729412i | \(0.739794\pi\) | |||||||
\(642\) | −7.09885e6 | −0.679752 | ||||||||
\(643\) | 7.46870e6 | 0.712390 | 0.356195 | − | 0.934412i | \(-0.384074\pi\) | ||||
0.356195 | + | 0.934412i | \(0.384074\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.42285e6 | 0.607895 | ||||||||
\(646\) | 717749. | 0.0676692 | ||||||||
\(647\) | −1.00619e7 | −0.944972 | −0.472486 | − | 0.881338i | \(-0.656643\pi\) | ||||
−0.472486 | + | 0.881338i | \(0.656643\pi\) | |||||||
\(648\) | −1.18317e7 | −1.10690 | ||||||||
\(649\) | 2.27408e6 | 0.211931 | ||||||||
\(650\) | 2.36206e6 | 0.219284 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.02389e6 | −0.462830 | ||||||||
\(653\) | 1.14074e7 | 1.04690 | 0.523450 | − | 0.852056i | \(-0.324645\pi\) | ||||
0.523450 | + | 0.852056i | \(0.324645\pi\) | |||||||
\(654\) | −8.59504e6 | −0.785785 | ||||||||
\(655\) | −865348. | −0.0788112 | ||||||||
\(656\) | 9.69035e6 | 0.879184 | ||||||||
\(657\) | −345455. | −0.0312233 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.91403e6 | 0.889276 | 0.444638 | − | 0.895710i | \(-0.353332\pi\) | ||||
0.444638 | + | 0.895710i | \(0.353332\pi\) | |||||||
\(660\) | −568683. | −0.0508171 | ||||||||
\(661\) | −151734. | −0.0135076 | −0.00675382 | − | 0.999977i | \(-0.502150\pi\) | ||||
−0.00675382 | + | 0.999977i | \(0.502150\pi\) | |||||||
\(662\) | −1.66954e7 | −1.48065 | ||||||||
\(663\) | 2.06431e6 | 0.182386 | ||||||||
\(664\) | 38601.3 | 0.00339767 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −276416. | −0.0241478 | ||||||||
\(667\) | −271455. | −0.0236256 | ||||||||
\(668\) | −4.48022e6 | −0.388471 | ||||||||
\(669\) | −9.19887e6 | −0.794637 | ||||||||
\(670\) | 5.36700e6 | 0.461896 | ||||||||
\(671\) | −3.54283e6 | −0.303769 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.84679e6 | −0.412493 | −0.206247 | − | 0.978500i | \(-0.566125\pi\) | ||||
−0.206247 | + | 0.978500i | \(0.566125\pi\) | |||||||
\(674\) | −2.55980e6 | −0.217048 | ||||||||
\(675\) | −2.34623e6 | −0.198203 | ||||||||
\(676\) | −3.70680e6 | −0.311984 | ||||||||
\(677\) | −4.35480e6 | −0.365172 | −0.182586 | − | 0.983190i | \(-0.558447\pi\) | ||||
−0.182586 | + | 0.983190i | \(0.558447\pi\) | |||||||
\(678\) | 1.85086e7 | 1.54632 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −775389. | −0.0643054 | ||||||||
\(681\) | −1.33621e7 | −1.10410 | ||||||||
\(682\) | 2.75142e6 | 0.226514 | ||||||||
\(683\) | −2.22591e7 | −1.82581 | −0.912904 | − | 0.408174i | \(-0.866166\pi\) | ||||
−0.912904 | + | 0.408174i | \(0.866166\pi\) | |||||||
\(684\) | −49196.1 | −0.00402060 | ||||||||
\(685\) | 566785. | 0.0461522 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.03942e6 | −0.245696 | ||||||||
\(688\) | −8.60206e6 | −0.692838 | ||||||||
\(689\) | 1.39280e7 | 1.11774 | ||||||||
\(690\) | −131051. | −0.0104790 | ||||||||
\(691\) | −148279. | −0.0118137 | −0.00590685 | − | 0.999983i | \(-0.501880\pi\) | ||||
−0.00590685 | + | 0.999983i | \(0.501880\pi\) | |||||||
\(692\) | 4.43112e6 | 0.351762 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.90413e6 | −0.622953 | ||||||||
\(695\) | −3.12586e6 | −0.245475 | ||||||||
\(696\) | −1.14335e7 | −0.894653 | ||||||||
\(697\) | 2.89815e6 | 0.225963 | ||||||||
\(698\) | 7.95008e6 | 0.617637 | ||||||||
\(699\) | −1.77171e7 | −1.37151 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.93655e7 | 1.48845 | 0.744223 | − | 0.667931i | \(-0.232820\pi\) | ||||
0.744223 | + | 0.667931i | \(0.232820\pi\) | |||||||
\(702\) | −1.41873e7 | −1.08657 | ||||||||
\(703\) | 1.43478e7 | 1.09496 | ||||||||
\(704\) | 4.37153e6 | 0.332431 | ||||||||
\(705\) | 1.32247e6 | 0.100210 | ||||||||
\(706\) | −3.73484e6 | −0.282007 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.24080e6 | −0.242979 | ||||||||
\(709\) | 8.30106e6 | 0.620180 | 0.310090 | − | 0.950707i | \(-0.399641\pi\) | ||||
0.310090 | + | 0.950707i | \(0.399641\pi\) | |||||||
\(710\) | 5.57293e6 | 0.414895 | ||||||||
\(711\) | −116656. | −0.00865429 | ||||||||
\(712\) | −709573. | −0.0524562 | ||||||||
\(713\) | −353274. | −0.0260249 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.63321e6 | −0.192628 | ||||||||
\(716\) | −9.60002e6 | −0.699825 | ||||||||
\(717\) | −1.00485e7 | −0.729967 | ||||||||
\(718\) | −1.61390e7 | −1.16833 | ||||||||
\(719\) | −7.65756e6 | −0.552418 | −0.276209 | − | 0.961098i | \(-0.589078\pi\) | ||||
−0.276209 | + | 0.961098i | \(0.589078\pi\) | |||||||
\(720\) | −56246.3 | −0.00404355 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.64151e6 | 0.474159 | ||||||||
\(723\) | 4.02987e6 | 0.286712 | ||||||||
\(724\) | −4.07483e6 | −0.288911 | ||||||||
\(725\) | −2.30714e6 | −0.163015 | ||||||||
\(726\) | 1.03426e7 | 0.728265 | ||||||||
\(727\) | 1.09211e7 | 0.766353 | 0.383177 | − | 0.923675i | \(-0.374830\pi\) | ||||
0.383177 | + | 0.923675i | \(0.374830\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.40878e7 | 0.981802 | ||||||||
\(730\) | 9.16197e6 | 0.636329 | ||||||||
\(731\) | −2.57266e6 | −0.178070 | ||||||||
\(732\) | 5.04890e6 | 0.348272 | ||||||||
\(733\) | −2.23972e7 | −1.53969 | −0.769847 | − | 0.638229i | \(-0.779667\pi\) | ||||
−0.769847 | + | 0.638229i | \(0.779667\pi\) | |||||||
\(734\) | 1.42438e7 | 0.975854 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −287985. | −0.0195964 | ||||||||
\(737\) | −5.98310e6 | −0.405749 | ||||||||
\(738\) | 356529. | 0.0240965 | ||||||||
\(739\) | 5.17870e6 | 0.348827 | 0.174413 | − | 0.984673i | \(-0.444197\pi\) | ||||
0.174413 | + | 0.984673i | \(0.444197\pi\) | |||||||
\(740\) | −4.08456e6 | −0.274199 | ||||||||
\(741\) | −1.31817e7 | −0.881916 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.99391e6 | −0.198961 | −0.0994804 | − | 0.995040i | \(-0.531718\pi\) | ||||
−0.0994804 | + | 0.995040i | \(0.531718\pi\) | |||||||
\(744\) | −1.48796e7 | −0.985506 | ||||||||
\(745\) | 9.75225e6 | 0.643745 | ||||||||
\(746\) | 1.19712e7 | 0.787571 | ||||||||
\(747\) | 837.445 | 5.49104e−5 0 | ||||||||
\(748\) | 227785. | 0.0148858 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.11382e6 | −0.0723041 | ||||||||
\(751\) | 1.32983e7 | 0.860391 | 0.430195 | − | 0.902736i | \(-0.358445\pi\) | ||||
0.430195 | + | 0.902736i | \(0.358445\pi\) | |||||||
\(752\) | −1.77117e6 | −0.114213 | ||||||||
\(753\) | 2.68466e7 | 1.72545 | ||||||||
\(754\) | −1.39510e7 | −0.893667 | ||||||||
\(755\) | −1.79945e6 | −0.114888 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.09742e6 | −0.196454 | −0.0982269 | − | 0.995164i | \(-0.531317\pi\) | ||||
−0.0982269 | + | 0.995164i | \(0.531317\pi\) | |||||||
\(758\) | 1.18848e7 | 0.751308 | ||||||||
\(759\) | 146095. | 0.00920515 | ||||||||
\(760\) | 4.95127e6 | 0.310944 | ||||||||
\(761\) | 2.52491e7 | 1.58046 | 0.790231 | − | 0.612809i | \(-0.209961\pi\) | ||||
0.790231 | + | 0.612809i | \(0.209961\pi\) | |||||||
\(762\) | 8.42364e6 | 0.525548 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.01969e6 | 0.125185 | ||||||||
\(765\) | −16821.9 | −0.00103925 | ||||||||
\(766\) | −9.76743e6 | −0.601462 | ||||||||
\(767\) | −1.50061e7 | −0.921041 | ||||||||
\(768\) | −1.51632e7 | −0.927656 | ||||||||
\(769\) | −807096. | −0.0492164 | −0.0246082 | − | 0.999697i | \(-0.507834\pi\) | ||||
−0.0246082 | + | 0.999697i | \(0.507834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.28173e7 | −1.38238 | ||||||||
\(772\) | −7.99007e6 | −0.482511 | ||||||||
\(773\) | −1.97132e7 | −1.18661 | −0.593306 | − | 0.804977i | \(-0.702178\pi\) | ||||
−0.593306 | + | 0.804977i | \(0.702178\pi\) | |||||||
\(774\) | −316488. | −0.0189891 | ||||||||
\(775\) | −3.00253e6 | −0.179570 | ||||||||
\(776\) | −3.12665e7 | −1.86391 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.50159e6 | 0.148172 | ||||||||
\(779\) | −1.85062e7 | −1.09263 | ||||||||
\(780\) | 3.75259e6 | 0.220849 | ||||||||
\(781\) | −6.21266e6 | −0.364460 | ||||||||
\(782\) | 52492.4 | 0.00306958 | ||||||||
\(783\) | 1.38574e7 | 0.807753 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.20824e6 | 0.127900 | ||||||||
\(786\) | 2.46744e6 | 0.142459 | ||||||||
\(787\) | −6.51938e6 | −0.375206 | −0.187603 | − | 0.982245i | \(-0.560072\pi\) | ||||
−0.187603 | + | 0.982245i | \(0.560072\pi\) | |||||||
\(788\) | −5.48230e6 | −0.314519 | ||||||||
\(789\) | 2.58287e7 | 1.47710 | ||||||||
\(790\) | 3.09387e6 | 0.176374 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 106338. | 0.00602386 | ||||||||
\(793\) | 2.33782e7 | 1.32017 | ||||||||
\(794\) | 3.26915e6 | 0.184028 | ||||||||
\(795\) | −6.56770e6 | −0.368549 | ||||||||
\(796\) | −1.03621e7 | −0.579646 | ||||||||
\(797\) | 1.71577e7 | 0.956780 | 0.478390 | − | 0.878147i | \(-0.341220\pi\) | ||||
0.478390 | + | 0.878147i | \(0.341220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −529712. | −0.0293544 | ||||||||
\(800\) | −2.44763e6 | −0.135214 | ||||||||
\(801\) | −15394.0 | −0.000847755 0 | ||||||||
\(802\) | 2.45046e7 | 1.34528 | ||||||||
\(803\) | −1.02137e7 | −0.558977 | ||||||||
\(804\) | 8.52653e6 | 0.465192 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.81559e7 | −0.984421 | ||||||||
\(807\) | 9.57032e6 | 0.517300 | ||||||||
\(808\) | −3.14683e7 | −1.69568 | ||||||||
\(809\) | 9.99850e6 | 0.537111 | 0.268555 | − | 0.963264i | \(-0.413454\pi\) | ||||
0.268555 | + | 0.963264i | \(0.413454\pi\) | |||||||
\(810\) | 6.80768e6 | 0.364575 | ||||||||
\(811\) | −6.02515e6 | −0.321674 | −0.160837 | − | 0.986981i | \(-0.551419\pi\) | ||||
−0.160837 | + | 0.986981i | \(0.551419\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.26475e7 | 0.671084 | ||||||||
\(814\) | −8.17251e6 | −0.432309 | ||||||||
\(815\) | 1.09693e7 | 0.578478 | ||||||||
\(816\) | 1.30369e6 | 0.0685410 | ||||||||
\(817\) | 1.64278e7 | 0.861043 | ||||||||
\(818\) | −3.42991e6 | −0.179225 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.26836e6 | 0.273616 | ||||||||
\(821\) | 1.01366e7 | 0.524848 | 0.262424 | − | 0.964953i | \(-0.415478\pi\) | ||||
0.262424 | + | 0.964953i | \(0.415478\pi\) | |||||||
\(822\) | −1.61612e6 | −0.0834248 | ||||||||
\(823\) | −3.17893e7 | −1.63599 | −0.817995 | − | 0.575225i | \(-0.804915\pi\) | ||||
−0.817995 | + | 0.575225i | \(0.804915\pi\) | |||||||
\(824\) | 1.06342e7 | 0.545614 | ||||||||
\(825\) | 1.24168e6 | 0.0635149 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.48323e7 | −0.754125 | −0.377062 | − | 0.926188i | \(-0.623066\pi\) | ||||
−0.377062 | + | 0.926188i | \(0.623066\pi\) | |||||||
\(828\) | −3597.95 | −0.000182381 0 | ||||||||
\(829\) | 2.25871e7 | 1.14149 | 0.570747 | − | 0.821126i | \(-0.306654\pi\) | ||||
0.570747 | + | 0.821126i | \(0.306654\pi\) | |||||||
\(830\) | −22210.2 | −0.00111907 | ||||||||
\(831\) | −1.28997e7 | −0.648002 | ||||||||
\(832\) | −2.88466e7 | −1.44473 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.91303e6 | 0.443721 | ||||||||
\(835\) | 9.78227e6 | 0.485538 | ||||||||
\(836\) | −1.45453e6 | −0.0719791 | ||||||||
\(837\) | 1.80342e7 | 0.889781 | ||||||||
\(838\) | −2.10110e7 | −1.03356 | ||||||||
\(839\) | −9.13225e6 | −0.447891 | −0.223946 | − | 0.974602i | \(-0.571894\pi\) | ||||
−0.223946 | + | 0.974602i | \(0.571894\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.88458e6 | −0.335651 | ||||||||
\(842\) | −2.78138e7 | −1.35201 | ||||||||
\(843\) | 1.84190e7 | 0.892681 | ||||||||
\(844\) | 9.65900e6 | 0.466741 | ||||||||
\(845\) | 8.09356e6 | 0.389940 | ||||||||
\(846\) | −65164.9 | −0.00313031 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.79606e6 | 0.420048 | ||||||||
\(849\) | −3.14122e7 | −1.49565 | ||||||||
\(850\) | 446140. | 0.0211799 | ||||||||
\(851\) | 1.04933e6 | 0.0496692 | ||||||||
\(852\) | 8.85369e6 | 0.417855 | ||||||||
\(853\) | 7.84791e6 | 0.369302 | 0.184651 | − | 0.982804i | \(-0.440885\pi\) | ||||
0.184651 | + | 0.982804i | \(0.440885\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 107417. | 0.00502523 | ||||||||
\(856\) | 1.96150e7 | 0.914962 | ||||||||
\(857\) | −3.07813e7 | −1.43164 | −0.715822 | − | 0.698283i | \(-0.753948\pi\) | ||||
−0.715822 | + | 0.698283i | \(0.753948\pi\) | |||||||
\(858\) | 7.50830e6 | 0.348196 | ||||||||
\(859\) | −962472. | −0.0445046 | −0.0222523 | − | 0.999752i | \(-0.507084\pi\) | ||||
−0.0222523 | + | 0.999752i | \(0.507084\pi\) | |||||||
\(860\) | −4.67669e6 | −0.215622 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.60717e6 | −0.440380 | ||||||||
\(863\) | 8.60992e6 | 0.393525 | 0.196762 | − | 0.980451i | \(-0.436957\pi\) | ||||
0.196762 | + | 0.980451i | \(0.436957\pi\) | |||||||
\(864\) | 1.47013e7 | 0.669994 | ||||||||
\(865\) | −9.67507e6 | −0.439657 | ||||||||
\(866\) | 1.96791e7 | 0.891684 | ||||||||
\(867\) | −2.19372e7 | −0.991138 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.44903e6 | −0.154934 | ||||||||
\(870\) | 6.57854e6 | 0.294667 | ||||||||
\(871\) | 3.94809e7 | 1.76336 | ||||||||
\(872\) | 2.37491e7 | 1.05769 | ||||||||
\(873\) | −678319. | −0.0301230 | ||||||||
\(874\) | −335192. | −0.0148428 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.45556e7 | 0.640869 | ||||||||
\(877\) | −7.93397e6 | −0.348331 | −0.174165 | − | 0.984716i | \(-0.555723\pi\) | ||||
−0.174165 | + | 0.984716i | \(0.555723\pi\) | |||||||
\(878\) | 3.05784e7 | 1.33868 | ||||||||
\(879\) | −2.74143e6 | −0.119675 | ||||||||
\(880\) | −1.66297e6 | −0.0723900 | ||||||||
\(881\) | −1.44812e7 | −0.628586 | −0.314293 | − | 0.949326i | \(-0.601767\pi\) | ||||
−0.314293 | + | 0.949326i | \(0.601767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.51794e6 | −0.151840 | −0.0759200 | − | 0.997114i | \(-0.524189\pi\) | ||||
−0.0759200 | + | 0.997114i | \(0.524189\pi\) | |||||||
\(884\) | −1.50310e6 | −0.0646929 | ||||||||
\(885\) | 7.07608e6 | 0.303693 | ||||||||
\(886\) | 2.00716e7 | 0.859007 | ||||||||
\(887\) | −2.82971e6 | −0.120763 | −0.0603814 | − | 0.998175i | \(-0.519232\pi\) | ||||
−0.0603814 | + | 0.998175i | \(0.519232\pi\) | |||||||
\(888\) | 4.41967e7 | 1.88087 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 408271. | 0.0172772 | ||||||||
\(891\) | −7.58915e6 | −0.320257 | ||||||||
\(892\) | 6.69800e6 | 0.281860 | ||||||||
\(893\) | 3.38249e6 | 0.141941 | ||||||||
\(894\) | −2.78074e7 | −1.16364 | ||||||||
\(895\) | 2.09610e7 | 0.874691 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −964044. | −0.0400051 | ||||||||
\(898\) | 2.64993e7 | 1.09659 | ||||||||
\(899\) | 1.77337e7 | 0.731815 | ||||||||
\(900\) | −30579.5 | −0.00125841 | ||||||||
\(901\) | 2.63068e6 | 0.107958 | ||||||||
\(902\) | 1.05411e7 | 0.431389 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.11415e7 | −2.08138 | ||||||||
\(905\) | 8.89714e6 | 0.361101 | ||||||||
\(906\) | 5.13094e6 | 0.207671 | ||||||||
\(907\) | 1.46684e7 | 0.592059 | 0.296030 | − | 0.955179i | \(-0.404337\pi\) | ||||
0.296030 | + | 0.955179i | \(0.404337\pi\) | |||||||
\(908\) | 9.72938e6 | 0.391625 | ||||||||
\(909\) | −682696. | −0.0274042 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −87366.6 | −0.00348778 | −0.00174389 | − | 0.999998i | \(-0.500555\pi\) | ||||
−0.00174389 | + | 0.999998i | \(0.500555\pi\) | |||||||
\(912\) | −8.32478e6 | −0.331425 | ||||||||
\(913\) | 24759.8 | 0.000983039 0 | ||||||||
\(914\) | −1.51263e7 | −0.598916 | ||||||||
\(915\) | −1.10239e7 | −0.435295 | ||||||||
\(916\) | 2.21310e6 | 0.0871491 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.67967e6 | −0.104948 | ||||||||
\(919\) | 2.94662e7 | 1.15090 | 0.575448 | − | 0.817838i | \(-0.304828\pi\) | ||||
0.575448 | + | 0.817838i | \(0.304828\pi\) | |||||||
\(920\) | 362110. | 0.0141049 | ||||||||
\(921\) | 1.55310e7 | 0.603325 | ||||||||
\(922\) | −3.45117e7 | −1.33702 | ||||||||
\(923\) | 4.09958e7 | 1.58393 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.91838e6 | 0.342714 | ||||||||
\(926\) | 1.27904e7 | 0.490180 | ||||||||
\(927\) | 230706. | 0.00881777 | ||||||||
\(928\) | 1.44564e7 | 0.551047 | ||||||||
\(929\) | 3.07331e7 | 1.16834 | 0.584168 | − | 0.811633i | \(-0.301421\pi\) | ||||
0.584168 | + | 0.811633i | \(0.301421\pi\) | |||||||
\(930\) | 8.56137e6 | 0.324591 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.29004e7 | 0.486478 | ||||||||
\(933\) | 3.78179e7 | 1.42231 | ||||||||
\(934\) | 1.18371e7 | 0.443996 | ||||||||
\(935\) | −497354. | −0.0186053 | ||||||||
\(936\) | −701697. | −0.0261794 | ||||||||
\(937\) | −1.87911e7 | −0.699203 | −0.349602 | − | 0.936898i | \(-0.613683\pi\) | ||||
−0.349602 | + | 0.936898i | \(0.613683\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.97985e7 | 1.10289 | ||||||||
\(940\) | −962931. | −0.0355448 | ||||||||
\(941\) | −3.59306e7 | −1.32279 | −0.661394 | − | 0.750039i | \(-0.730035\pi\) | ||||
−0.661394 | + | 0.750039i | \(0.730035\pi\) | |||||||
\(942\) | −6.29653e6 | −0.231193 | ||||||||
\(943\) | −1.35345e6 | −0.0495635 | ||||||||
\(944\) | −9.47692e6 | −0.346128 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.35726e6 | −0.339954 | ||||||||
\(947\) | 4.56598e7 | 1.65447 | 0.827235 | − | 0.561856i | \(-0.189912\pi\) | ||||
0.827235 | + | 0.561856i | \(0.189912\pi\) | |||||||
\(948\) | 4.91522e6 | 0.177632 | ||||||||
\(949\) | 6.73976e7 | 2.42929 | ||||||||
\(950\) | −2.84884e6 | −0.102414 | ||||||||
\(951\) | −1.15956e7 | −0.415759 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.96804e7 | 1.05861 | 0.529307 | − | 0.848430i | \(-0.322452\pi\) | ||||
0.529307 | + | 0.848430i | \(0.322452\pi\) | |||||||
\(954\) | 323626. | 0.0115126 | ||||||||
\(955\) | −4.40987e6 | −0.156465 | ||||||||
\(956\) | 7.31665e6 | 0.258921 | ||||||||
\(957\) | −7.33371e6 | −0.258847 | ||||||||
\(958\) | 3.70371e6 | 0.130384 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.36025e7 | 0.476368 | ||||||||
\(961\) | −5.55028e6 | −0.193868 | ||||||||
\(962\) | 5.39283e7 | 1.87879 | ||||||||
\(963\) | 425542. | 0.0147869 | ||||||||
\(964\) | −2.93429e6 | −0.101697 | ||||||||
\(965\) | 1.74458e7 | 0.603077 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.33565e7 | −1.83494 | −0.917468 | − | 0.397810i | \(-0.869770\pi\) | ||||
−0.917468 | + | 0.397810i | \(0.869770\pi\) | |||||||
\(968\) | −2.85779e7 | −0.980262 | ||||||||
\(969\) | −2.48974e6 | −0.0851812 | ||||||||
\(970\) | 1.79900e7 | 0.613906 | ||||||||
\(971\) | −3.10322e7 | −1.05624 | −0.528122 | − | 0.849169i | \(-0.677104\pi\) | ||||
−0.528122 | + | 0.849169i | \(0.677104\pi\) | |||||||
\(972\) | 370629. | 0.0125827 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.56922e6 | 0.323206 | ||||||||
\(975\) | −8.19355e6 | −0.276033 | ||||||||
\(976\) | 1.47643e7 | 0.496120 | ||||||||
\(977\) | −328987. | −0.0110266 | −0.00551330 | − | 0.999985i | \(-0.501755\pi\) | ||||
−0.00551330 | + | 0.999985i | \(0.501755\pi\) | |||||||
\(978\) | −3.12778e7 | −1.04566 | ||||||||
\(979\) | −455138. | −0.0151770 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 515232. | 0.0170935 | ||||||||
\(982\) | −7.78202e6 | −0.257522 | ||||||||
\(983\) | −2.90474e7 | −0.958790 | −0.479395 | − | 0.877599i | \(-0.659144\pi\) | ||||
−0.479395 | + | 0.877599i | \(0.659144\pi\) | |||||||
\(984\) | −5.70060e7 | −1.87686 | ||||||||
\(985\) | 1.19702e7 | 0.393108 | ||||||||
\(986\) | −2.63503e6 | −0.0863162 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.59807e6 | 0.312818 | ||||||||
\(989\) | 1.20145e6 | 0.0390583 | ||||||||
\(990\) | −61184.3 | −0.00198405 | ||||||||
\(991\) | −2.77388e7 | −0.897230 | −0.448615 | − | 0.893725i | \(-0.648083\pi\) | ||||
−0.448615 | + | 0.893725i | \(0.648083\pi\) | |||||||
\(992\) | 1.88136e7 | 0.607007 | ||||||||
\(993\) | 5.79133e7 | 1.86383 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.26249e7 | 0.724483 | ||||||||
\(996\) | −35285.3 | −0.00112706 | ||||||||
\(997\) | −4.43451e7 | −1.41289 | −0.706444 | − | 0.707769i | \(-0.749702\pi\) | ||||
−0.706444 | + | 0.707769i | \(0.749702\pi\) | |||||||
\(998\) | −3.46380e7 | −1.10085 | ||||||||
\(999\) | −5.35668e7 | −1.69817 |
(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.d.1.2 | 3 | ||
7.6 | odd | 2 | 35.6.a.c.1.2 | ✓ | 3 | ||
21.20 | even | 2 | 315.6.a.i.1.2 | 3 | |||
28.27 | even | 2 | 560.6.a.q.1.3 | 3 | |||
35.13 | even | 4 | 175.6.b.e.99.4 | 6 | |||
35.27 | even | 4 | 175.6.b.e.99.3 | 6 | |||
35.34 | odd | 2 | 175.6.a.e.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.a.c.1.2 | ✓ | 3 | 7.6 | odd | 2 | ||
175.6.a.e.1.2 | 3 | 35.34 | odd | 2 | |||
175.6.b.e.99.3 | 6 | 35.27 | even | 4 | |||
175.6.b.e.99.4 | 6 | 35.13 | even | 4 | |||
245.6.a.d.1.2 | 3 | 1.1 | even | 1 | trivial | ||
315.6.a.i.1.2 | 3 | 21.20 | even | 2 | |||
560.6.a.q.1.3 | 3 | 28.27 | even | 2 |