Newspace parameters
Level: | \( N \) | \(=\) | \( 207 = 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 207.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(33.1994507013\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
Defining polynomial: |
\( x^{5} - 113x^{3} - 257x^{2} + 1404x + 2197 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 69) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.40352\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 207.1 |
$q$-expansion
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.34908 | −1.65270 | −0.826350 | − | 0.563157i | \(-0.809586\pi\) | ||||
−0.826350 | + | 0.563157i | \(0.809586\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 55.4053 | 1.73141 | ||||||||
\(5\) | −70.5203 | −1.26151 | −0.630753 | − | 0.775984i | \(-0.717254\pi\) | ||||
−0.630753 | + | 0.775984i | \(0.717254\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −89.7132 | −0.692008 | −0.346004 | − | 0.938233i | \(-0.612462\pi\) | ||||
−0.346004 | + | 0.938233i | \(0.612462\pi\) | |||||||
\(8\) | −218.818 | −1.20881 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 659.300 | 2.08489 | ||||||||
\(11\) | 436.763 | 1.08834 | 0.544170 | − | 0.838975i | \(-0.316845\pi\) | ||||
0.544170 | + | 0.838975i | \(0.316845\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −258.865 | −0.424830 | −0.212415 | − | 0.977180i | \(-0.568133\pi\) | ||||
−0.212415 | + | 0.977180i | \(0.568133\pi\) | |||||||
\(14\) | 838.736 | 1.14368 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 272.775 | 0.266382 | ||||||||
\(17\) | −591.819 | −0.496669 | −0.248334 | − | 0.968674i | \(-0.579883\pi\) | ||||
−0.248334 | + | 0.968674i | \(0.579883\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1663.69 | 1.05727 | 0.528637 | − | 0.848848i | \(-0.322703\pi\) | ||||
0.528637 | + | 0.848848i | \(0.322703\pi\) | |||||||
\(20\) | −3907.20 | −2.18419 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4083.33 | −1.79870 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1848.12 | 0.591398 | ||||||||
\(26\) | 2420.15 | 0.702116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4970.58 | −1.19815 | ||||||||
\(29\) | 5121.48 | 1.13084 | 0.565419 | − | 0.824804i | \(-0.308714\pi\) | ||||
0.565419 | + | 0.824804i | \(0.308714\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1871.29 | 0.349733 | 0.174867 | − | 0.984592i | \(-0.444051\pi\) | ||||
0.174867 | + | 0.984592i | \(0.444051\pi\) | |||||||
\(32\) | 4451.97 | 0.768559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5532.96 | 0.820844 | ||||||||
\(35\) | 6326.60 | 0.872972 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 884.534 | 0.106221 | 0.0531105 | − | 0.998589i | \(-0.483086\pi\) | ||||
0.0531105 | + | 0.998589i | \(0.483086\pi\) | |||||||
\(38\) | −15554.0 | −1.74736 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 15431.1 | 1.52492 | ||||||||
\(41\) | 18410.5 | 1.71043 | 0.855216 | − | 0.518271i | \(-0.173424\pi\) | ||||
0.855216 | + | 0.518271i | \(0.173424\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12334.9 | 1.01734 | 0.508669 | − | 0.860962i | \(-0.330138\pi\) | ||||
0.508669 | + | 0.860962i | \(0.330138\pi\) | |||||||
\(44\) | 24199.0 | 1.88437 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4945.66 | −0.344612 | ||||||||
\(47\) | −23871.6 | −1.57629 | −0.788146 | − | 0.615489i | \(-0.788959\pi\) | ||||
−0.788146 | + | 0.615489i | \(0.788959\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8758.55 | −0.521125 | ||||||||
\(50\) | −17278.2 | −0.977403 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −14342.5 | −0.735556 | ||||||||
\(53\) | 14594.8 | 0.713690 | 0.356845 | − | 0.934164i | \(-0.383853\pi\) | ||||
0.356845 | + | 0.934164i | \(0.383853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −30800.7 | −1.37295 | ||||||||
\(56\) | 19630.8 | 0.836505 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −47881.1 | −1.86894 | ||||||||
\(59\) | −47739.1 | −1.78544 | −0.892718 | − | 0.450616i | \(-0.851205\pi\) | ||||
−0.892718 | + | 0.450616i | \(0.851205\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15351.5 | −0.528233 | −0.264116 | − | 0.964491i | \(-0.585080\pi\) | ||||
−0.264116 | + | 0.964491i | \(0.585080\pi\) | |||||||
\(62\) | −17494.8 | −0.578004 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −50350.6 | −1.53658 | ||||||||
\(65\) | 18255.2 | 0.535925 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −41174.4 | −1.12057 | −0.560287 | − | 0.828299i | \(-0.689309\pi\) | ||||
−0.560287 | + | 0.828299i | \(0.689309\pi\) | |||||||
\(68\) | −32789.9 | −0.859939 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −59147.9 | −1.44276 | ||||||||
\(71\) | 45608.3 | 1.07374 | 0.536869 | − | 0.843666i | \(-0.319607\pi\) | ||||
0.536869 | + | 0.843666i | \(0.319607\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7898.24 | −0.173470 | −0.0867348 | − | 0.996231i | \(-0.527643\pi\) | ||||
−0.0867348 | + | 0.996231i | \(0.527643\pi\) | |||||||
\(74\) | −8269.57 | −0.175551 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 92177.1 | 1.83058 | ||||||||
\(77\) | −39183.4 | −0.753140 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 71435.2 | 1.28779 | 0.643894 | − | 0.765115i | \(-0.277318\pi\) | ||||
0.643894 | + | 0.765115i | \(0.277318\pi\) | |||||||
\(80\) | −19236.2 | −0.336043 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −172121. | −2.82683 | ||||||||
\(83\) | −112580. | −1.79377 | −0.896885 | − | 0.442264i | \(-0.854175\pi\) | ||||
−0.896885 | + | 0.442264i | \(0.854175\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41735.3 | 0.626551 | ||||||||
\(86\) | −115320. | −1.68136 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −95571.5 | −1.31559 | ||||||||
\(89\) | −137845. | −1.84466 | −0.922330 | − | 0.386404i | \(-0.873717\pi\) | ||||
−0.922330 | + | 0.386404i | \(0.873717\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 23223.6 | 0.293985 | ||||||||
\(92\) | 29309.4 | 0.361025 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 223177. | 2.60514 | ||||||||
\(95\) | −117324. | −1.33376 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 41679.8 | 0.449776 | 0.224888 | − | 0.974385i | \(-0.427798\pi\) | ||||
0.224888 | + | 0.974385i | \(0.427798\pi\) | |||||||
\(98\) | 81884.3 | 0.861263 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 102395. | 1.02395 | ||||||||
\(101\) | −37100.3 | −0.361888 | −0.180944 | − | 0.983493i | \(-0.557915\pi\) | ||||
−0.180944 | + | 0.983493i | \(0.557915\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −123323. | −1.14538 | −0.572692 | − | 0.819771i | \(-0.694101\pi\) | ||||
−0.572692 | + | 0.819771i | \(0.694101\pi\) | |||||||
\(104\) | 56644.2 | 0.513538 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −136448. | −1.17951 | ||||||||
\(107\) | −107455. | −0.907338 | −0.453669 | − | 0.891170i | \(-0.649885\pi\) | ||||
−0.453669 | + | 0.891170i | \(0.649885\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 96652.7 | 0.779198 | 0.389599 | − | 0.920985i | \(-0.372614\pi\) | ||||
0.389599 | + | 0.920985i | \(0.372614\pi\) | |||||||
\(110\) | 287958. | 2.26907 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −24471.5 | −0.184338 | ||||||||
\(113\) | −55788.7 | −0.411008 | −0.205504 | − | 0.978656i | \(-0.565883\pi\) | ||||
−0.205504 | + | 0.978656i | \(0.565883\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −37305.3 | −0.263042 | ||||||||
\(116\) | 283757. | 1.95795 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 446317. | 2.95079 | ||||||||
\(119\) | 53094.0 | 0.343699 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 29711.1 | 0.184483 | ||||||||
\(122\) | 143522. | 0.873010 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 103679. | 0.605533 | ||||||||
\(125\) | 90046.2 | 0.515454 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 167839. | 0.923388 | 0.461694 | − | 0.887039i | \(-0.347242\pi\) | ||||
0.461694 | + | 0.887039i | \(0.347242\pi\) | |||||||
\(128\) | 328269. | 1.77094 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −170670. | −0.885723 | ||||||||
\(131\) | −129729. | −0.660476 | −0.330238 | − | 0.943898i | \(-0.607129\pi\) | ||||
−0.330238 | + | 0.943898i | \(0.607129\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −149255. | −0.731643 | ||||||||
\(134\) | 384943. | 1.85197 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 129501. | 0.600377 | ||||||||
\(137\) | 226702. | 1.03194 | 0.515970 | − | 0.856607i | \(-0.327432\pi\) | ||||
0.515970 | + | 0.856607i | \(0.327432\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −419175. | −1.84017 | −0.920086 | − | 0.391716i | \(-0.871882\pi\) | ||||
−0.920086 | + | 0.391716i | \(0.871882\pi\) | |||||||
\(140\) | 350527. | 1.51148 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −426396. | −1.77457 | ||||||||
\(143\) | −113063. | −0.462359 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −361169. | −1.42656 | ||||||||
\(146\) | 73841.3 | 0.286693 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 49007.8 | 0.183912 | ||||||||
\(149\) | −503270. | −1.85710 | −0.928551 | − | 0.371206i | \(-0.878945\pi\) | ||||
−0.928551 | + | 0.371206i | \(0.878945\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 517943. | 1.84858 | 0.924292 | − | 0.381685i | \(-0.124656\pi\) | ||||
0.924292 | + | 0.381685i | \(0.124656\pi\) | |||||||
\(152\) | −364044. | −1.27804 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 366329. | 1.24471 | ||||||||
\(155\) | −131964. | −0.441190 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −39747.9 | −0.128696 | −0.0643480 | − | 0.997928i | \(-0.520497\pi\) | ||||
−0.0643480 | + | 0.997928i | \(0.520497\pi\) | |||||||
\(158\) | −667853. | −2.12833 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −313954. | −0.969542 | ||||||||
\(161\) | −47458.3 | −0.144294 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −157828. | −0.465279 | −0.232640 | − | 0.972563i | \(-0.574736\pi\) | ||||
−0.232640 | + | 0.972563i | \(0.574736\pi\) | |||||||
\(164\) | 1.02004e6 | 2.96147 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.05252e6 | 2.96456 | ||||||||
\(167\) | 101000. | 0.280241 | 0.140120 | − | 0.990134i | \(-0.455251\pi\) | ||||
0.140120 | + | 0.990134i | \(0.455251\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −304282. | −0.819520 | ||||||||
\(170\) | −390187. | −1.03550 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 683420. | 1.76144 | ||||||||
\(173\) | −61568.5 | −0.156402 | −0.0782012 | − | 0.996938i | \(-0.524918\pi\) | ||||
−0.0782012 | + | 0.996938i | \(0.524918\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −165801. | −0.409252 | ||||||||
\(176\) | 119138. | 0.289914 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.28872e6 | 3.04867 | ||||||||
\(179\) | 610536. | 1.42423 | 0.712113 | − | 0.702065i | \(-0.247738\pi\) | ||||
0.712113 | + | 0.702065i | \(0.247738\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 121378. | 0.275387 | 0.137694 | − | 0.990475i | \(-0.456031\pi\) | ||||
0.137694 | + | 0.990475i | \(0.456031\pi\) | |||||||
\(182\) | −217119. | −0.485870 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −115755. | −0.252054 | ||||||||
\(185\) | −62377.6 | −0.133998 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −258485. | −0.540544 | ||||||||
\(188\) | −1.32261e6 | −2.72921 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.09687e6 | 2.20430 | ||||||||
\(191\) | 294581. | 0.584280 | 0.292140 | − | 0.956376i | \(-0.405633\pi\) | ||||
0.292140 | + | 0.956376i | \(0.405633\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8895.53 | −0.0171901 | −0.00859505 | − | 0.999963i | \(-0.502736\pi\) | ||||
−0.00859505 | + | 0.999963i | \(0.502736\pi\) | |||||||
\(194\) | −389668. | −0.743345 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −485270. | −0.902283 | ||||||||
\(197\) | 698113. | 1.28162 | 0.640811 | − | 0.767699i | \(-0.278598\pi\) | ||||
0.640811 | + | 0.767699i | \(0.278598\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −533271. | −0.954586 | −0.477293 | − | 0.878744i | \(-0.658382\pi\) | ||||
−0.477293 | + | 0.878744i | \(0.658382\pi\) | |||||||
\(200\) | −404401. | −0.714887 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 346854. | 0.598092 | ||||||||
\(203\) | −459464. | −0.782550 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.29831e6 | −2.15772 | ||||||||
\(206\) | 1.15296e6 | 1.89298 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −70611.9 | −0.113167 | ||||||||
\(209\) | 726638. | 1.15067 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −658407. | −1.01809 | −0.509047 | − | 0.860739i | \(-0.670002\pi\) | ||||
−0.509047 | + | 0.860739i | \(0.670002\pi\) | |||||||
\(212\) | 808630. | 1.23569 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.00461e6 | 1.49956 | ||||||||
\(215\) | −869864. | −1.28338 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −167879. | −0.242018 | ||||||||
\(218\) | −903614. | −1.28778 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.70652e6 | −2.37714 | ||||||||
\(221\) | 153201. | 0.211000 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 79895.6 | 0.107587 | 0.0537936 | − | 0.998552i | \(-0.482869\pi\) | ||||
0.0537936 | + | 0.998552i | \(0.482869\pi\) | |||||||
\(224\) | −399400. | −0.531849 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 521573. | 0.679273 | ||||||||
\(227\) | −716111. | −0.922393 | −0.461196 | − | 0.887298i | \(-0.652580\pi\) | ||||
−0.461196 | + | 0.887298i | \(0.652580\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −581299. | −0.732506 | −0.366253 | − | 0.930515i | \(-0.619360\pi\) | ||||
−0.366253 | + | 0.930515i | \(0.619360\pi\) | |||||||
\(230\) | 348770. | 0.434730 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.12067e6 | −1.36697 | ||||||||
\(233\) | −122734. | −0.148107 | −0.0740534 | − | 0.997254i | \(-0.523594\pi\) | ||||
−0.0740534 | + | 0.997254i | \(0.523594\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.68343e6 | 1.98850 | ||||||||
\(236\) | −2.64500e6 | −3.09133 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −496380. | −0.568031 | ||||||||
\(239\) | −210076. | −0.237893 | −0.118946 | − | 0.992901i | \(-0.537952\pi\) | ||||
−0.118946 | + | 0.992901i | \(0.537952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.23224e6 | 1.36664 | 0.683319 | − | 0.730120i | \(-0.260536\pi\) | ||||
0.683319 | + | 0.730120i | \(0.260536\pi\) | |||||||
\(242\) | −277772. | −0.304894 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −850553. | −0.914590 | ||||||||
\(245\) | 617656. | 0.657402 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −430670. | −0.449162 | ||||||||
\(248\) | −409471. | −0.422760 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −841849. | −0.851891 | ||||||||
\(251\) | 545986. | 0.547012 | 0.273506 | − | 0.961870i | \(-0.411817\pi\) | ||||
0.273506 | + | 0.961870i | \(0.411817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 231048. | 0.226934 | ||||||||
\(254\) | −1.56914e6 | −1.52608 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.45779e6 | −1.39026 | ||||||||
\(257\) | −556705. | −0.525765 | −0.262883 | − | 0.964828i | \(-0.584673\pi\) | ||||
−0.262883 | + | 0.964828i | \(0.584673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −79354.3 | −0.0735057 | ||||||||
\(260\) | 1.01144e6 | 0.927909 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.21284e6 | 1.09157 | ||||||||
\(263\) | −1.65392e6 | −1.47443 | −0.737217 | − | 0.675656i | \(-0.763860\pi\) | ||||
−0.737217 | + | 0.675656i | \(0.763860\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.02923e6 | −0.900324 | ||||||||
\(266\) | 1.39539e6 | 1.20919 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.28128e6 | −1.94018 | ||||||||
\(269\) | 2.06545e6 | 1.74034 | 0.870168 | − | 0.492755i | \(-0.164010\pi\) | ||||
0.870168 | + | 0.492755i | \(0.164010\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 708326. | 0.585881 | 0.292941 | − | 0.956131i | \(-0.405366\pi\) | ||||
0.292941 | + | 0.956131i | \(0.405366\pi\) | |||||||
\(272\) | −161434. | −0.132304 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.11946e6 | −1.70549 | ||||||||
\(275\) | 807190. | 0.643641 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17729.4 | −0.0138833 | −0.00694167 | − | 0.999976i | \(-0.502210\pi\) | ||||
−0.00694167 | + | 0.999976i | \(0.502210\pi\) | |||||||
\(278\) | 3.91890e6 | 3.04125 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.38437e6 | −1.05526 | ||||||||
\(281\) | −754660. | −0.570145 | −0.285073 | − | 0.958506i | \(-0.592018\pi\) | ||||
−0.285073 | + | 0.958506i | \(0.592018\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −417633. | −0.309976 | −0.154988 | − | 0.987916i | \(-0.549534\pi\) | ||||
−0.154988 | + | 0.987916i | \(0.549534\pi\) | |||||||
\(284\) | 2.52694e6 | 1.85909 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.05703e6 | 0.764140 | ||||||||
\(287\) | −1.65166e6 | −1.18363 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.06961e6 | −0.753320 | ||||||||
\(290\) | 3.37659e6 | 2.35767 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −437604. | −0.300348 | ||||||||
\(293\) | 2.68010e6 | 1.82382 | 0.911908 | − | 0.410394i | \(-0.134609\pi\) | ||||
0.911908 | + | 0.410394i | \(0.134609\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.36658e6 | 2.25234 | ||||||||
\(296\) | −193552. | −0.128401 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.70511e6 | 3.06923 | ||||||||
\(299\) | −136940. | −0.0885831 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.10661e6 | −0.704007 | ||||||||
\(302\) | −4.84229e6 | −3.05515 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 453813. | 0.281639 | ||||||||
\(305\) | 1.08259e6 | 0.666369 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.42927e6 | −1.47106 | −0.735528 | − | 0.677494i | \(-0.763066\pi\) | ||||
−0.735528 | + | 0.677494i | \(0.763066\pi\) | |||||||
\(308\) | −2.17097e6 | −1.30400 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.23374e6 | 0.729155 | ||||||||
\(311\) | −1.71783e6 | −1.00712 | −0.503559 | − | 0.863961i | \(-0.667976\pi\) | ||||
−0.503559 | + | 0.863961i | \(0.667976\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.56583e6 | 0.903406 | 0.451703 | − | 0.892168i | \(-0.350817\pi\) | ||||
0.451703 | + | 0.892168i | \(0.350817\pi\) | |||||||
\(314\) | 371606. | 0.212696 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.95789e6 | 2.22970 | ||||||||
\(317\) | −673750. | −0.376574 | −0.188287 | − | 0.982114i | \(-0.560294\pi\) | ||||
−0.188287 | + | 0.982114i | \(0.560294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.23688e6 | 1.23074 | ||||||||
\(320\) | 3.55074e6 | 1.93840 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 443691. | 0.238474 | ||||||||
\(323\) | −984603. | −0.525115 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −478413. | −0.251243 | ||||||||
\(326\) | 1.47554e6 | 0.768967 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.02854e6 | −2.06759 | ||||||||
\(329\) | 2.14159e6 | 1.09081 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.69768e6 | 0.851699 | 0.425850 | − | 0.904794i | \(-0.359975\pi\) | ||||
0.425850 | + | 0.904794i | \(0.359975\pi\) | |||||||
\(332\) | −6.23754e6 | −3.10576 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −944259. | −0.463153 | ||||||||
\(335\) | 2.90363e6 | 1.41361 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.37281e6 | −1.13812 | −0.569061 | − | 0.822295i | \(-0.692693\pi\) | ||||
−0.569061 | + | 0.822295i | \(0.692693\pi\) | |||||||
\(338\) | 2.84476e6 | 1.35442 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.31236e6 | 1.08482 | ||||||||
\(341\) | 817310. | 0.380628 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.29357e6 | 1.05263 | ||||||||
\(344\) | −2.69910e6 | −1.22977 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 575609. | 0.258486 | ||||||||
\(347\) | −3.98316e6 | −1.77584 | −0.887921 | − | 0.459996i | \(-0.847851\pi\) | ||||
−0.887921 | + | 0.459996i | \(0.847851\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.10463e6 | −0.924935 | −0.462468 | − | 0.886636i | \(-0.653036\pi\) | ||||
−0.462468 | + | 0.886636i | \(0.653036\pi\) | |||||||
\(350\) | 1.55008e6 | 0.676370 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.94446e6 | 0.836453 | ||||||||
\(353\) | −3.41107e6 | −1.45698 | −0.728490 | − | 0.685056i | \(-0.759778\pi\) | ||||
−0.728490 | + | 0.685056i | \(0.759778\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.21631e6 | −1.35453 | ||||||||
\(356\) | −7.63734e6 | −3.19387 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.70795e6 | −2.35382 | ||||||||
\(359\) | 1.86760e6 | 0.764800 | 0.382400 | − | 0.923997i | \(-0.375098\pi\) | ||||
0.382400 | + | 0.923997i | \(0.375098\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 291759. | 0.117830 | ||||||||
\(362\) | −1.13477e6 | −0.455132 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.28671e6 | 0.509011 | ||||||||
\(365\) | 556987. | 0.218833 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −437210. | −0.169444 | −0.0847218 | − | 0.996405i | \(-0.527000\pi\) | ||||
−0.0847218 | + | 0.996405i | \(0.527000\pi\) | |||||||
\(368\) | 144298. | 0.0555445 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 583173. | 0.221459 | ||||||||
\(371\) | −1.30935e6 | −0.493879 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −921734. | −0.343031 | −0.171516 | − | 0.985181i | \(-0.554866\pi\) | ||||
−0.171516 | + | 0.985181i | \(0.554866\pi\) | |||||||
\(374\) | 2.41660e6 | 0.893357 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.22352e6 | 1.90543 | ||||||||
\(377\) | −1.32577e6 | −0.480414 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.80141e6 | −1.35940 | −0.679699 | − | 0.733491i | \(-0.737889\pi\) | ||||
−0.679699 | + | 0.733491i | \(0.737889\pi\) | |||||||
\(380\) | −6.50036e6 | −2.30929 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.75406e6 | −0.965639 | ||||||||
\(383\) | 4.52311e6 | 1.57558 | 0.787790 | − | 0.615944i | \(-0.211225\pi\) | ||||
0.787790 | + | 0.615944i | \(0.211225\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.76323e6 | 0.950090 | ||||||||
\(386\) | 83165.0 | 0.0284101 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.30928e6 | 0.778749 | ||||||||
\(389\) | −4.48168e6 | −1.50164 | −0.750822 | − | 0.660505i | \(-0.770342\pi\) | ||||
−0.750822 | + | 0.660505i | \(0.770342\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −313072. | −0.103563 | ||||||||
\(392\) | 1.91652e6 | 0.629940 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.52671e6 | −2.11814 | ||||||||
\(395\) | −5.03763e6 | −1.62455 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.76656e6 | 0.562539 | 0.281269 | − | 0.959629i | \(-0.409245\pi\) | ||||
0.281269 | + | 0.959629i | \(0.409245\pi\) | |||||||
\(398\) | 4.98559e6 | 1.57764 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 504121. | 0.157538 | ||||||||
\(401\) | 522373. | 0.162226 | 0.0811128 | − | 0.996705i | \(-0.474153\pi\) | ||||
0.0811128 | + | 0.996705i | \(0.474153\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −484411. | −0.148577 | ||||||||
\(404\) | −2.05555e6 | −0.626579 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.29557e6 | 1.29332 | ||||||||
\(407\) | 386332. | 0.115604 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.60642e6 | −0.474845 | −0.237422 | − | 0.971407i | \(-0.576303\pi\) | ||||
−0.237422 | + | 0.971407i | \(0.576303\pi\) | |||||||
\(410\) | 1.21380e7 | 3.56606 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.83275e6 | −1.98314 | ||||||||
\(413\) | 4.28283e6 | 1.23554 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.93919e6 | 2.26285 | ||||||||
\(416\) | −1.15246e6 | −0.326507 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.79339e6 | −1.90172 | ||||||||
\(419\) | 5.30658e6 | 1.47666 | 0.738329 | − | 0.674441i | \(-0.235615\pi\) | ||||
0.738329 | + | 0.674441i | \(0.235615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.30575e6 | −0.634025 | −0.317012 | − | 0.948421i | \(-0.602680\pi\) | ||||
−0.317012 | + | 0.948421i | \(0.602680\pi\) | |||||||
\(422\) | 6.15549e6 | 1.68260 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.19361e6 | −0.862714 | ||||||||
\(425\) | −1.09375e6 | −0.293729 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.37723e6 | 0.365541 | ||||||||
\(428\) | −5.95360e6 | −1.57098 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.13242e6 | 2.12104 | ||||||||
\(431\) | 1.27091e6 | 0.329549 | 0.164775 | − | 0.986331i | \(-0.447310\pi\) | ||||
0.164775 | + | 0.986331i | \(0.447310\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.71880e6 | −0.953199 | −0.476599 | − | 0.879121i | \(-0.658131\pi\) | ||||
−0.476599 | + | 0.879121i | \(0.658131\pi\) | |||||||
\(434\) | 1.56952e6 | 0.399983 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.35507e6 | 1.34911 | ||||||||
\(437\) | 880091. | 0.220457 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.51069e6 | −0.869423 | −0.434711 | − | 0.900570i | \(-0.643150\pi\) | ||||
−0.434711 | + | 0.900570i | \(0.643150\pi\) | |||||||
\(440\) | 6.73974e6 | 1.65963 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.43229e6 | −0.348719 | ||||||||
\(443\) | −2.67040e6 | −0.646497 | −0.323248 | − | 0.946314i | \(-0.604775\pi\) | ||||
−0.323248 | + | 0.946314i | \(0.604775\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.72088e6 | 2.32705 | ||||||||
\(446\) | −746950. | −0.177809 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.51711e6 | 1.06332 | ||||||||
\(449\) | −808771. | −0.189326 | −0.0946628 | − | 0.995509i | \(-0.530177\pi\) | ||||
−0.0946628 | + | 0.995509i | \(0.530177\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.04103e6 | 1.86153 | ||||||||
\(452\) | −3.09099e6 | −0.711625 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.69498e6 | 1.52444 | ||||||||
\(455\) | −1.63774e6 | −0.370864 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.03865e6 | −1.35254 | −0.676269 | − | 0.736655i | \(-0.736404\pi\) | ||||
−0.676269 | + | 0.736655i | \(0.736404\pi\) | |||||||
\(458\) | 5.43461e6 | 1.21061 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.06691e6 | −0.455435 | ||||||||
\(461\) | 6.06334e6 | 1.32880 | 0.664399 | − | 0.747378i | \(-0.268687\pi\) | ||||
0.664399 | + | 0.747378i | \(0.268687\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −987185. | −0.214016 | −0.107008 | − | 0.994258i | \(-0.534127\pi\) | ||||
−0.107008 | + | 0.994258i | \(0.534127\pi\) | |||||||
\(464\) | 1.39701e6 | 0.301235 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.14745e6 | 0.244776 | ||||||||
\(467\) | 2.75869e6 | 0.585344 | 0.292672 | − | 0.956213i | \(-0.405456\pi\) | ||||
0.292672 | + | 0.956213i | \(0.405456\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.69389e6 | 0.775446 | ||||||||
\(470\) | −1.57385e7 | −3.28639 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.04462e7 | 2.15825 | ||||||||
\(473\) | 5.38745e6 | 1.10721 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.07469e6 | 0.625270 | ||||||||
\(476\) | 2.94169e6 | 0.595085 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.96402e6 | 0.393165 | ||||||||
\(479\) | 1.43871e6 | 0.286507 | 0.143254 | − | 0.989686i | \(-0.454244\pi\) | ||||
0.143254 | + | 0.989686i | \(0.454244\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −228975. | −0.0451258 | ||||||||
\(482\) | −1.15203e7 | −2.25864 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.64615e6 | 0.319416 | ||||||||
\(485\) | −2.93927e6 | −0.567395 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.54793e6 | −1.82426 | −0.912130 | − | 0.409901i | \(-0.865563\pi\) | ||||
−0.912130 | + | 0.409901i | \(0.865563\pi\) | |||||||
\(488\) | 3.35917e6 | 0.638532 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.77451e6 | −1.08649 | ||||||||
\(491\) | −8.94131e6 | −1.67378 | −0.836889 | − | 0.547373i | \(-0.815628\pi\) | ||||
−0.836889 | + | 0.547373i | \(0.815628\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.03099e6 | −0.561652 | ||||||||
\(494\) | 4.02637e6 | 0.742329 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 510441. | 0.0931626 | ||||||||
\(497\) | −4.09167e6 | −0.743035 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.34135e6 | 0.420934 | 0.210467 | − | 0.977601i | \(-0.432501\pi\) | ||||
0.210467 | + | 0.977601i | \(0.432501\pi\) | |||||||
\(500\) | 4.98903e6 | 0.892465 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.10446e6 | −0.904046 | ||||||||
\(503\) | −41307.7 | −0.00727966 | −0.00363983 | − | 0.999993i | \(-0.501159\pi\) | ||||
−0.00363983 | + | 0.999993i | \(0.501159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.61633e6 | 0.456524 | ||||||||
\(506\) | −2.16008e6 | −0.375054 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.29918e6 | 1.59877 | ||||||||
\(509\) | −3.09166e6 | −0.528929 | −0.264464 | − | 0.964395i | \(-0.585195\pi\) | ||||
−0.264464 | + | 0.964395i | \(0.585195\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 708576. | 0.120042 | ||||||||
\(512\) | 3.12440e6 | 0.526735 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.20467e6 | 0.868932 | ||||||||
\(515\) | 8.69678e6 | 1.44491 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.04262e7 | −1.71554 | ||||||||
\(518\) | 741890. | 0.121483 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.99457e6 | −0.647831 | ||||||||
\(521\) | −6.02002e6 | −0.971635 | −0.485818 | − | 0.874060i | \(-0.661478\pi\) | ||||
−0.485818 | + | 0.874060i | \(0.661478\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.39458e6 | −1.02225 | −0.511125 | − | 0.859506i | \(-0.670771\pi\) | ||||
−0.511125 | + | 0.859506i | \(0.670771\pi\) | |||||||
\(524\) | −7.18764e6 | −1.14356 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.54626e7 | 2.43679 | ||||||||
\(527\) | −1.10746e6 | −0.173701 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 9.62237e6 | 1.48796 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.26950e6 | −1.26678 | ||||||||
\(533\) | −4.76583e6 | −0.726642 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.57779e6 | 1.14461 | ||||||||
\(536\) | 9.00969e6 | 1.35456 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.93100e7 | −2.87625 | ||||||||
\(539\) | −3.82541e6 | −0.567161 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.24248e6 | −0.476304 | −0.238152 | − | 0.971228i | \(-0.576542\pi\) | ||||
−0.238152 | + | 0.971228i | \(0.576542\pi\) | |||||||
\(542\) | −6.62219e6 | −0.968286 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.63476e6 | −0.381719 | ||||||||
\(545\) | −6.81598e6 | −0.982963 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.39508e6 | 1.34255 | 0.671277 | − | 0.741206i | \(-0.265746\pi\) | ||||
0.671277 | + | 0.741206i | \(0.265746\pi\) | |||||||
\(548\) | 1.25605e7 | 1.78671 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.54648e6 | −1.06375 | ||||||||
\(551\) | 8.52055e6 | 1.19561 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.40868e6 | −0.891160 | ||||||||
\(554\) | 165753. | 0.0229450 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.32245e7 | −3.18610 | ||||||||
\(557\) | −2.95696e6 | −0.403839 | −0.201919 | − | 0.979402i | \(-0.564718\pi\) | ||||
−0.201919 | + | 0.979402i | \(0.564718\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.19308e6 | −0.432196 | ||||||||
\(560\) | 1.72574e6 | 0.232544 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.05538e6 | 0.942279 | ||||||||
\(563\) | 1.35314e7 | 1.79917 | 0.899584 | − | 0.436747i | \(-0.143870\pi\) | ||||
0.899584 | + | 0.436747i | \(0.143870\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.93424e6 | 0.518489 | ||||||||
\(566\) | 3.90448e6 | 0.512297 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.97991e6 | −1.29794 | ||||||||
\(569\) | −1.32776e7 | −1.71924 | −0.859622 | − | 0.510931i | \(-0.829301\pi\) | ||||
−0.859622 | + | 0.510931i | \(0.829301\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.74960e6 | 0.994693 | 0.497346 | − | 0.867552i | \(-0.334308\pi\) | ||||
0.497346 | + | 0.867552i | \(0.334308\pi\) | |||||||
\(572\) | −6.26427e6 | −0.800535 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.54415e7 | 1.95619 | ||||||||
\(575\) | 977654. | 0.123315 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.83479e6 | −0.604558 | −0.302279 | − | 0.953220i | \(-0.597747\pi\) | ||||
−0.302279 | + | 0.953220i | \(0.597747\pi\) | |||||||
\(578\) | 9.99984e6 | 1.24501 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.00106e7 | −2.46997 | ||||||||
\(581\) | 1.00999e7 | 1.24130 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.37448e6 | 0.776736 | ||||||||
\(584\) | 1.72827e6 | 0.209691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.50564e7 | −3.01422 | ||||||||
\(587\) | −5.13380e6 | −0.614955 | −0.307478 | − | 0.951555i | \(-0.599485\pi\) | ||||
−0.307478 | + | 0.951555i | \(0.599485\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.11324e6 | 0.369764 | ||||||||
\(590\) | −3.14744e7 | −3.72244 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 241279. | 0.0282953 | ||||||||
\(593\) | −1.29134e7 | −1.50801 | −0.754003 | − | 0.656871i | \(-0.771879\pi\) | ||||
−0.754003 | + | 0.656871i | \(0.771879\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.74421e6 | −0.433578 | ||||||||
\(596\) | −2.78838e7 | −3.21541 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.28026e6 | 0.146401 | ||||||||
\(599\) | 5.79980e6 | 0.660460 | 0.330230 | − | 0.943901i | \(-0.392874\pi\) | ||||
0.330230 | + | 0.943901i | \(0.392874\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.06993e7 | 1.20829 | 0.604144 | − | 0.796875i | \(-0.293515\pi\) | ||||
0.604144 | + | 0.796875i | \(0.293515\pi\) | |||||||
\(602\) | 1.03457e7 | 1.16351 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.86968e7 | 3.20067 | ||||||||
\(605\) | −2.09524e6 | −0.232726 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.48509e7 | −1.63600 | −0.817998 | − | 0.575221i | \(-0.804916\pi\) | ||||
−0.817998 | + | 0.575221i | \(0.804916\pi\) | |||||||
\(608\) | 7.40669e6 | 0.812578 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.01212e7 | −1.10131 | ||||||||
\(611\) | 6.17951e6 | 0.669655 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.64415e6 | −0.821633 | −0.410816 | − | 0.911718i | \(-0.634756\pi\) | ||||
−0.410816 | + | 0.911718i | \(0.634756\pi\) | |||||||
\(614\) | 2.27114e7 | 2.43121 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.57402e6 | 0.910401 | ||||||||
\(617\) | 8.02025e6 | 0.848155 | 0.424077 | − | 0.905626i | \(-0.360598\pi\) | ||||
0.424077 | + | 0.905626i | \(0.360598\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.46459e6 | 0.992831 | 0.496416 | − | 0.868085i | \(-0.334649\pi\) | ||||
0.496416 | + | 0.868085i | \(0.334649\pi\) | |||||||
\(620\) | −7.31150e6 | −0.763883 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.60602e7 | 1.66446 | ||||||||
\(623\) | 1.23665e7 | 1.27652 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.21255e7 | −1.24165 | ||||||||
\(626\) | −1.46390e7 | −1.49306 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.20224e6 | −0.222826 | ||||||||
\(629\) | −523484. | −0.0527566 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.76525e6 | 0.876377 | 0.438189 | − | 0.898883i | \(-0.355620\pi\) | ||||
0.438189 | + | 0.898883i | \(0.355620\pi\) | |||||||
\(632\) | −1.56313e7 | −1.55669 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.29894e6 | 0.622364 | ||||||||
\(635\) | −1.18361e7 | −1.16486 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.26728e6 | 0.221389 | ||||||||
\(638\) | −2.09127e7 | −2.03404 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.31496e7 | −2.23406 | ||||||||
\(641\) | 8.04677e6 | 0.773529 | 0.386764 | − | 0.922179i | \(-0.373593\pi\) | ||||
0.386764 | + | 0.922179i | \(0.373593\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.81157e7 | 1.72794 | 0.863970 | − | 0.503543i | \(-0.167970\pi\) | ||||
0.863970 | + | 0.503543i | \(0.167970\pi\) | |||||||
\(644\) | −2.62944e6 | −0.249832 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.20513e6 | 0.867858 | ||||||||
\(647\) | −6.09047e6 | −0.571992 | −0.285996 | − | 0.958231i | \(-0.592324\pi\) | ||||
−0.285996 | + | 0.958231i | \(0.592324\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.08507e7 | −1.94316 | ||||||||
\(650\) | 4.47272e6 | 0.415230 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.74448e6 | −0.805591 | ||||||||
\(653\) | −1.73408e7 | −1.59142 | −0.795712 | − | 0.605675i | \(-0.792903\pi\) | ||||
−0.795712 | + | 0.605675i | \(0.792903\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.14850e6 | 0.833195 | ||||||||
\(656\) | 5.02193e6 | 0.455629 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.00219e7 | −1.80277 | ||||||||
\(659\) | −1.27618e7 | −1.14471 | −0.572357 | − | 0.820004i | \(-0.693971\pi\) | ||||
−0.572357 | + | 0.820004i | \(0.693971\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.44195e6 | −0.573474 | −0.286737 | − | 0.958009i | \(-0.592571\pi\) | ||||
−0.286737 | + | 0.958009i | \(0.592571\pi\) | |||||||
\(662\) | −1.58718e7 | −1.40760 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.46345e7 | 2.16832 | ||||||||
\(665\) | 1.05255e7 | 0.922972 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.70926e6 | 0.235796 | ||||||||
\(668\) | 5.59594e6 | 0.485213 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.71463e7 | −2.33627 | ||||||||
\(671\) | −6.70496e6 | −0.574897 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.64864e6 | 0.736055 | 0.368028 | − | 0.929815i | \(-0.380033\pi\) | ||||
0.368028 | + | 0.929815i | \(0.380033\pi\) | |||||||
\(674\) | 2.21836e7 | 1.88097 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.68588e7 | −1.41893 | ||||||||
\(677\) | 1.22020e7 | 1.02320 | 0.511600 | − | 0.859223i | \(-0.329053\pi\) | ||||
0.511600 | + | 0.859223i | \(0.329053\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.73923e6 | −0.311249 | ||||||||
\(680\) | −9.13242e6 | −0.757380 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.64110e6 | −0.629064 | ||||||||
\(683\) | 1.10784e7 | 0.908708 | 0.454354 | − | 0.890821i | \(-0.349870\pi\) | ||||
0.454354 | + | 0.890821i | \(0.349870\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.59871e7 | −1.30180 | ||||||||
\(686\) | −2.14427e7 | −1.73968 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.36466e6 | 0.271001 | ||||||||
\(689\) | −3.77809e6 | −0.303196 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.24814e7 | −0.994415 | −0.497207 | − | 0.867632i | \(-0.665641\pi\) | ||||
−0.497207 | + | 0.867632i | \(0.665641\pi\) | |||||||
\(692\) | −3.41122e6 | −0.270797 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.72389e7 | 2.93493 | ||||||||
\(695\) | 2.95604e7 | 2.32139 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.08957e7 | −0.849518 | ||||||||
\(698\) | 1.96763e7 | 1.52864 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.18622e6 | −0.708585 | ||||||||
\(701\) | 4.71570e6 | 0.362452 | 0.181226 | − | 0.983441i | \(-0.441993\pi\) | ||||
0.181226 | + | 0.983441i | \(0.441993\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.47159e6 | 0.112305 | ||||||||
\(704\) | −2.19913e7 | −1.67232 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.18903e7 | 2.40795 | ||||||||
\(707\) | 3.32839e6 | 0.250430 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.05958e7 | 0.791620 | 0.395810 | − | 0.918332i | \(-0.370464\pi\) | ||||
0.395810 | + | 0.918332i | \(0.370464\pi\) | |||||||
\(710\) | 3.00696e7 | 2.23863 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.01629e7 | 2.22984 | ||||||||
\(713\) | 989912. | 0.0729244 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.97322e6 | 0.583268 | ||||||||
\(716\) | 3.38269e7 | 2.46593 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.74603e7 | −1.26398 | ||||||||
\(719\) | −2.95783e6 | −0.213379 | −0.106689 | − | 0.994292i | \(-0.534025\pi\) | ||||
−0.106689 | + | 0.994292i | \(0.534025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.10637e7 | 0.792615 | ||||||||
\(722\) | −2.72768e6 | −0.194738 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.72499e6 | 0.476810 | ||||||||
\(725\) | 9.46510e6 | 0.668776 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.30768e7 | −0.917625 | −0.458813 | − | 0.888533i | \(-0.651725\pi\) | ||||
−0.458813 | + | 0.888533i | \(0.651725\pi\) | |||||||
\(728\) | −5.08173e6 | −0.355372 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.20731e6 | −0.361665 | ||||||||
\(731\) | −7.30005e6 | −0.505280 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.06819e6 | 0.348412 | 0.174206 | − | 0.984709i | \(-0.444264\pi\) | ||||
0.174206 | + | 0.984709i | \(0.444264\pi\) | |||||||
\(734\) | 4.08751e6 | 0.280039 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.35509e6 | 0.160256 | ||||||||
\(737\) | −1.79835e7 | −1.21956 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.39832e6 | 0.363620 | 0.181810 | − | 0.983334i | \(-0.441804\pi\) | ||||
0.181810 | + | 0.983334i | \(0.441804\pi\) | |||||||
\(740\) | −3.45605e6 | −0.232007 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.22412e7 | 0.816233 | ||||||||
\(743\) | −3.71690e6 | −0.247007 | −0.123503 | − | 0.992344i | \(-0.539413\pi\) | ||||
−0.123503 | + | 0.992344i | \(0.539413\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.54908e7 | 2.34274 | ||||||||
\(746\) | 8.61736e6 | 0.566927 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.43214e7 | −0.935906 | ||||||||
\(749\) | 9.64017e6 | 0.627885 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00711e7 | 0.651594 | 0.325797 | − | 0.945440i | \(-0.394367\pi\) | ||||
0.325797 | + | 0.945440i | \(0.394367\pi\) | |||||||
\(752\) | −6.51157e6 | −0.419896 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.23947e7 | 0.793979 | ||||||||
\(755\) | −3.65255e7 | −2.33200 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.49996e6 | −0.539110 | −0.269555 | − | 0.962985i | \(-0.586877\pi\) | ||||
−0.269555 | + | 0.962985i | \(0.586877\pi\) | |||||||
\(758\) | 3.55397e7 | 2.24667 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.56725e7 | 1.61226 | ||||||||
\(761\) | −2.62780e7 | −1.64487 | −0.822434 | − | 0.568861i | \(-0.807384\pi\) | ||||
−0.822434 | + | 0.568861i | \(0.807384\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.67102e6 | −0.539211 | ||||||||
\(764\) | 1.63213e7 | 1.01163 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.22869e7 | −2.60396 | ||||||||
\(767\) | 1.23580e7 | 0.758506 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 899889. | 0.0548748 | 0.0274374 | − | 0.999624i | \(-0.491265\pi\) | ||||
0.0274374 | + | 0.999624i | \(0.491265\pi\) | |||||||
\(770\) | −2.58336e7 | −1.57021 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −492859. | −0.0297632 | ||||||||
\(773\) | 1.33758e7 | 0.805140 | 0.402570 | − | 0.915389i | \(-0.368117\pi\) | ||||
0.402570 | + | 0.915389i | \(0.368117\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.45836e6 | 0.206831 | ||||||||
\(776\) | −9.12028e6 | −0.543693 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.18996e7 | 2.48177 | ||||||||
\(779\) | 3.06293e7 | 1.80840 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.99200e7 | 1.16859 | ||||||||
\(782\) | 2.92694e6 | 0.171158 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.38911e6 | −0.138818 | ||||||||
\(785\) | 2.80304e6 | 0.162351 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.67690e7 | 0.965098 | 0.482549 | − | 0.875869i | \(-0.339711\pi\) | ||||
0.482549 | + | 0.875869i | \(0.339711\pi\) | |||||||
\(788\) | 3.86791e7 | 2.21902 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.70972e7 | 2.68490 | ||||||||
\(791\) | 5.00498e6 | 0.284421 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.97396e6 | 0.224409 | ||||||||
\(794\) | −1.65157e7 | −0.929707 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.95460e7 | −1.65278 | ||||||||
\(797\) | −2.78280e7 | −1.55180 | −0.775902 | − | 0.630854i | \(-0.782705\pi\) | ||||
−0.775902 | + | 0.630854i | \(0.782705\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.41277e7 | 0.782894 | ||||||||
\(800\) | 8.22776e6 | 0.454524 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.88370e6 | −0.268110 | ||||||||
\(803\) | −3.44966e6 | −0.188794 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.34677e6 | 0.182027 | ||||||||
\(806\) | 4.52880e6 | 0.245553 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.11821e6 | 0.437454 | ||||||||
\(809\) | 1.98606e7 | 1.06689 | 0.533447 | − | 0.845834i | \(-0.320897\pi\) | ||||
0.533447 | + | 0.845834i | \(0.320897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.95245e7 | 1.04238 | 0.521192 | − | 0.853439i | \(-0.325488\pi\) | ||||
0.521192 | + | 0.853439i | \(0.325488\pi\) | |||||||
\(812\) | −2.54568e7 | −1.35492 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.61185e6 | −0.191059 | ||||||||
\(815\) | 1.11301e7 | 0.586953 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.05215e7 | 1.07561 | ||||||||
\(818\) | 1.50186e7 | 0.784775 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.19335e7 | −3.73591 | ||||||||
\(821\) | 2.39444e7 | 1.23978 | 0.619891 | − | 0.784688i | \(-0.287177\pi\) | ||||
0.619891 | + | 0.784688i | \(0.287177\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.78310e7 | −1.43229 | −0.716143 | − | 0.697953i | \(-0.754094\pi\) | ||||
−0.716143 | + | 0.697953i | \(0.754094\pi\) | |||||||
\(824\) | 2.69853e7 | 1.38455 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.00405e7 | −2.04197 | ||||||||
\(827\) | 1.94204e7 | 0.987405 | 0.493703 | − | 0.869631i | \(-0.335643\pi\) | ||||
0.493703 | + | 0.869631i | \(0.335643\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.66039e7 | 1.34449 | 0.672247 | − | 0.740327i | \(-0.265329\pi\) | ||||
0.672247 | + | 0.740327i | \(0.265329\pi\) | |||||||
\(830\) | −7.42241e7 | −3.73981 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.30340e7 | 0.652784 | ||||||||
\(833\) | 5.18348e6 | 0.258826 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.12257e6 | −0.353525 | ||||||||
\(836\) | 4.02596e7 | 1.99229 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.96117e7 | −2.44047 | ||||||||
\(839\) | 1.41085e7 | 0.691954 | 0.345977 | − | 0.938243i | \(-0.387547\pi\) | ||||
0.345977 | + | 0.938243i | \(0.387547\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.71843e6 | 0.278796 | ||||||||
\(842\) | 2.15566e7 | 1.04785 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.64792e7 | −1.76274 | ||||||||
\(845\) | 2.14581e7 | 1.03383 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.66548e6 | −0.127664 | ||||||||
\(848\) | 3.98111e6 | 0.190114 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.02256e7 | 0.485445 | ||||||||
\(851\) | 467918. | 0.0221486 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.87882e7 | −0.884122 | −0.442061 | − | 0.896985i | \(-0.645752\pi\) | ||||
−0.442061 | + | 0.896985i | \(0.645752\pi\) | |||||||
\(854\) | −1.28758e7 | −0.604130 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.35131e7 | 1.09680 | ||||||||
\(857\) | −3.67369e7 | −1.70864 | −0.854320 | − | 0.519748i | \(-0.826026\pi\) | ||||
−0.854320 | + | 0.519748i | \(0.826026\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.03228e6 | 0.0939723 | 0.0469861 | − | 0.998896i | \(-0.485038\pi\) | ||||
0.0469861 | + | 0.998896i | \(0.485038\pi\) | |||||||
\(860\) | −4.81950e7 | −2.22206 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.18818e7 | −0.544646 | ||||||||
\(863\) | 1.21735e7 | 0.556400 | 0.278200 | − | 0.960523i | \(-0.410262\pi\) | ||||
0.278200 | + | 0.960523i | \(0.410262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.34183e6 | 0.197303 | ||||||||
\(866\) | 3.47674e7 | 1.57535 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.30140e6 | −0.419034 | ||||||||
\(869\) | 3.12003e7 | 1.40155 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.06586e7 | 0.476053 | ||||||||
\(872\) | −2.11493e7 | −0.941901 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.22804e6 | −0.364349 | ||||||||
\(875\) | −8.07833e6 | −0.356698 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.13453e7 | 1.81521 | 0.907605 | − | 0.419825i | \(-0.137909\pi\) | ||||
0.907605 | + | 0.419825i | \(0.137909\pi\) | |||||||
\(878\) | 3.28217e7 | 1.43689 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.40166e6 | −0.365728 | ||||||||
\(881\) | −1.92417e7 | −0.835227 | −0.417613 | − | 0.908625i | \(-0.637133\pi\) | ||||
−0.417613 | + | 0.908625i | \(0.637133\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.59010e6 | 0.198117 | 0.0990583 | − | 0.995082i | \(-0.468417\pi\) | ||||
0.0990583 | + | 0.995082i | \(0.468417\pi\) | |||||||
\(884\) | 8.48815e6 | 0.365328 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.49657e7 | 1.06846 | ||||||||
\(887\) | 1.34822e7 | 0.575374 | 0.287687 | − | 0.957724i | \(-0.407114\pi\) | ||||
0.287687 | + | 0.957724i | \(0.407114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.50574e7 | −0.638992 | ||||||||
\(890\) | −9.08813e7 | −3.84591 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.42663e6 | 0.186278 | ||||||||
\(893\) | −3.97149e7 | −1.66657 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.30552e7 | −1.79667 | ||||||||
\(896\) | −2.94500e7 | −1.22551 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.56126e6 | 0.312898 | ||||||||
\(899\) | 9.58377e6 | 0.395492 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.63750e6 | −0.354467 | ||||||||
\(902\) | −7.51762e7 | −3.07655 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.22076e7 | 0.496830 | ||||||||
\(905\) | −8.55962e6 | −0.347403 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.13039e6 | 0.207077 | 0.103539 | − | 0.994625i | \(-0.466983\pi\) | ||||
0.103539 | + | 0.994625i | \(0.466983\pi\) | |||||||
\(908\) | −3.96763e7 | −1.59704 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.53113e7 | 0.612927 | ||||||||
\(911\) | −3.88471e7 | −1.55082 | −0.775411 | − | 0.631456i | \(-0.782457\pi\) | ||||
−0.775411 | + | 0.631456i | \(0.782457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.91709e7 | −1.95223 | ||||||||
\(914\) | 5.64558e7 | 2.23534 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.22071e7 | −1.26827 | ||||||||
\(917\) | 1.16384e7 | 0.457055 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.43482e7 | 0.950993 | 0.475496 | − | 0.879718i | \(-0.342268\pi\) | ||||
0.475496 | + | 0.879718i | \(0.342268\pi\) | |||||||
\(920\) | 8.16305e6 | 0.317968 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.66866e7 | −2.19610 | ||||||||
\(923\) | −1.18064e7 | −0.456156 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.63472e6 | 0.0628188 | ||||||||
\(926\) | 9.22927e6 | 0.353704 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.28007e7 | 0.869116 | ||||||||
\(929\) | −2.17027e7 | −0.825040 | −0.412520 | − | 0.910948i | \(-0.635351\pi\) | ||||
−0.412520 | + | 0.910948i | \(0.635351\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.45715e7 | −0.550972 | ||||||||
\(932\) | −6.80010e6 | −0.256434 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.57912e7 | −0.967397 | ||||||||
\(935\) | 1.82284e7 | 0.681900 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.01218e6 | −0.0748718 | −0.0374359 | − | 0.999299i | \(-0.511919\pi\) | ||||
−0.0374359 | + | 0.999299i | \(0.511919\pi\) | |||||||
\(938\) | −3.45344e7 | −1.28158 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.32710e7 | 3.44292 | ||||||||
\(941\) | 1.17136e7 | 0.431237 | 0.215618 | − | 0.976478i | \(-0.430823\pi\) | ||||
0.215618 | + | 0.976478i | \(0.430823\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.73916e6 | 0.356650 | ||||||||
\(944\) | −1.30220e7 | −0.475608 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.03676e7 | −1.82989 | ||||||||
\(947\) | −571455. | −0.0207065 | −0.0103533 | − | 0.999946i | \(-0.503296\pi\) | ||||
−0.0103533 | + | 0.999946i | \(0.503296\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.04458e6 | 0.0736950 | ||||||||
\(950\) | −2.87455e7 | −1.03338 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.16179e7 | −0.415466 | ||||||||
\(953\) | −2.03678e7 | −0.726461 | −0.363231 | − | 0.931699i | \(-0.618326\pi\) | ||||
−0.363231 | + | 0.931699i | \(0.618326\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.07739e7 | −0.737073 | ||||||||
\(956\) | −1.16393e7 | −0.411891 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.34506e7 | −0.473510 | ||||||||
\(959\) | −2.03382e7 | −0.714110 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.51274e7 | −0.877687 | ||||||||
\(962\) | 2.14070e6 | 0.0745794 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.82727e7 | 2.36622 | ||||||||
\(965\) | 627316. | 0.0216854 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.93183e7 | −1.35216 | −0.676081 | − | 0.736827i | \(-0.736323\pi\) | ||||
−0.676081 | + | 0.736827i | \(0.736323\pi\) | |||||||
\(968\) | −6.50132e6 | −0.223004 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.74795e7 | 0.937734 | ||||||||
\(971\) | −4.86930e7 | −1.65736 | −0.828682 | − | 0.559719i | \(-0.810909\pi\) | ||||
−0.828682 | + | 0.559719i | \(0.810909\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.76055e7 | 1.27341 | ||||||||
\(974\) | 8.92643e7 | 3.01495 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.18750e6 | −0.140712 | ||||||||
\(977\) | 1.11758e7 | 0.374577 | 0.187288 | − | 0.982305i | \(-0.440030\pi\) | ||||
0.187288 | + | 0.982305i | \(0.440030\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.02056e7 | −2.00762 | ||||||||
\(980\) | 3.42214e7 | 1.13824 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.35930e7 | 2.76625 | ||||||||
\(983\) | −2.09439e7 | −0.691310 | −0.345655 | − | 0.938362i | \(-0.612343\pi\) | ||||
−0.345655 | + | 0.938362i | \(0.612343\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.92311e7 | −1.61677 | ||||||||
\(986\) | 2.83370e7 | 0.928242 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.38614e7 | −0.777685 | ||||||||
\(989\) | 6.52518e6 | 0.212130 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.95125e7 | −0.631144 | −0.315572 | − | 0.948902i | \(-0.602196\pi\) | ||||
−0.315572 | + | 0.948902i | \(0.602196\pi\) | |||||||
\(992\) | 8.33092e6 | 0.268790 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.82533e7 | 1.22801 | ||||||||
\(995\) | 3.76064e7 | 1.20422 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.32696e7 | 0.422786 | 0.211393 | − | 0.977401i | \(-0.432200\pi\) | ||||
0.211393 | + | 0.977401i | \(0.432200\pi\) | |||||||
\(998\) | −2.18894e7 | −0.695678 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 207.6.a.f.1.1 | 5 | ||
3.2 | odd | 2 | 69.6.a.e.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 1104.6.a.r.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.a.e.1.5 | ✓ | 5 | 3.2 | odd | 2 | ||
207.6.a.f.1.1 | 5 | 1.1 | even | 1 | trivial | ||
1104.6.a.r.1.4 | 5 | 12.11 | even | 2 |