Properties

Label 832.4.a.r.1.1
Level $832$
Weight $4$
Character 832.1
Self dual yes
Analytic conductor $49.090$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 832.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(49.0895891248\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 832.1

$q$-expansion

\(f(q)\) \(=\) \(q+7.00000 q^{3} +7.00000 q^{5} -13.0000 q^{7} +22.0000 q^{9} +O(q^{10})\) \(q+7.00000 q^{3} +7.00000 q^{5} -13.0000 q^{7} +22.0000 q^{9} +26.0000 q^{11} -13.0000 q^{13} +49.0000 q^{15} +77.0000 q^{17} +126.000 q^{19} -91.0000 q^{21} -96.0000 q^{23} -76.0000 q^{25} -35.0000 q^{27} +82.0000 q^{29} +196.000 q^{31} +182.000 q^{33} -91.0000 q^{35} +131.000 q^{37} -91.0000 q^{39} +336.000 q^{41} +201.000 q^{43} +154.000 q^{45} -105.000 q^{47} -174.000 q^{49} +539.000 q^{51} +432.000 q^{53} +182.000 q^{55} +882.000 q^{57} +294.000 q^{59} +56.0000 q^{61} -286.000 q^{63} -91.0000 q^{65} -478.000 q^{67} -672.000 q^{69} +9.00000 q^{71} +98.0000 q^{73} -532.000 q^{75} -338.000 q^{77} +1304.00 q^{79} -839.000 q^{81} +308.000 q^{83} +539.000 q^{85} +574.000 q^{87} -1190.00 q^{89} +169.000 q^{91} +1372.00 q^{93} +882.000 q^{95} +70.0000 q^{97} +572.000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 7.00000 1.34715 0.673575 0.739119i \(-0.264758\pi\)
0.673575 + 0.739119i \(0.264758\pi\)
\(4\) 0 0
\(5\) 7.00000 0.626099 0.313050 0.949737i \(-0.398649\pi\)
0.313050 + 0.949737i \(0.398649\pi\)
\(6\) 0 0
\(7\) −13.0000 −0.701934 −0.350967 0.936388i \(-0.614147\pi\)
−0.350967 + 0.936388i \(0.614147\pi\)
\(8\) 0 0
\(9\) 22.0000 0.814815
\(10\) 0 0
\(11\) 26.0000 0.712663 0.356332 0.934360i \(-0.384027\pi\)
0.356332 + 0.934360i \(0.384027\pi\)
\(12\) 0 0
\(13\) −13.0000 −0.277350
\(14\) 0 0
\(15\) 49.0000 0.843450
\(16\) 0 0
\(17\) 77.0000 1.09854 0.549272 0.835644i \(-0.314905\pi\)
0.549272 + 0.835644i \(0.314905\pi\)
\(18\) 0 0
\(19\) 126.000 1.52139 0.760694 0.649110i \(-0.224859\pi\)
0.760694 + 0.649110i \(0.224859\pi\)
\(20\) 0 0
\(21\) −91.0000 −0.945611
\(22\) 0 0
\(23\) −96.0000 −0.870321 −0.435161 0.900353i \(-0.643308\pi\)
−0.435161 + 0.900353i \(0.643308\pi\)
\(24\) 0 0
\(25\) −76.0000 −0.608000
\(26\) 0 0
\(27\) −35.0000 −0.249472
\(28\) 0 0
\(29\) 82.0000 0.525070 0.262535 0.964923i \(-0.415442\pi\)
0.262535 + 0.964923i \(0.415442\pi\)
\(30\) 0 0
\(31\) 196.000 1.13557 0.567785 0.823177i \(-0.307801\pi\)
0.567785 + 0.823177i \(0.307801\pi\)
\(32\) 0 0
\(33\) 182.000 0.960065
\(34\) 0 0
\(35\) −91.0000 −0.439480
\(36\) 0 0
\(37\) 131.000 0.582061 0.291031 0.956714i \(-0.406002\pi\)
0.291031 + 0.956714i \(0.406002\pi\)
\(38\) 0 0
\(39\) −91.0000 −0.373632
\(40\) 0 0
\(41\) 336.000 1.27986 0.639932 0.768432i \(-0.278963\pi\)
0.639932 + 0.768432i \(0.278963\pi\)
\(42\) 0 0
\(43\) 201.000 0.712842 0.356421 0.934325i \(-0.383997\pi\)
0.356421 + 0.934325i \(0.383997\pi\)
\(44\) 0 0
\(45\) 154.000 0.510155
\(46\) 0 0
\(47\) −105.000 −0.325869 −0.162934 0.986637i \(-0.552096\pi\)
−0.162934 + 0.986637i \(0.552096\pi\)
\(48\) 0 0
\(49\) −174.000 −0.507289
\(50\) 0 0
\(51\) 539.000 1.47990
\(52\) 0 0
\(53\) 432.000 1.11962 0.559809 0.828622i \(-0.310874\pi\)
0.559809 + 0.828622i \(0.310874\pi\)
\(54\) 0 0
\(55\) 182.000 0.446198
\(56\) 0 0
\(57\) 882.000 2.04954
\(58\) 0 0
\(59\) 294.000 0.648738 0.324369 0.945931i \(-0.394848\pi\)
0.324369 + 0.945931i \(0.394848\pi\)
\(60\) 0 0
\(61\) 56.0000 0.117542 0.0587710 0.998271i \(-0.481282\pi\)
0.0587710 + 0.998271i \(0.481282\pi\)
\(62\) 0 0
\(63\) −286.000 −0.571946
\(64\) 0 0
\(65\) −91.0000 −0.173649
\(66\) 0 0
\(67\) −478.000 −0.871597 −0.435798 0.900044i \(-0.643534\pi\)
−0.435798 + 0.900044i \(0.643534\pi\)
\(68\) 0 0
\(69\) −672.000 −1.17245
\(70\) 0 0
\(71\) 9.00000 0.0150437 0.00752186 0.999972i \(-0.497606\pi\)
0.00752186 + 0.999972i \(0.497606\pi\)
\(72\) 0 0
\(73\) 98.0000 0.157124 0.0785619 0.996909i \(-0.474967\pi\)
0.0785619 + 0.996909i \(0.474967\pi\)
\(74\) 0 0
\(75\) −532.000 −0.819068
\(76\) 0 0
\(77\) −338.000 −0.500243
\(78\) 0 0
\(79\) 1304.00 1.85711 0.928554 0.371198i \(-0.121053\pi\)
0.928554 + 0.371198i \(0.121053\pi\)
\(80\) 0 0
\(81\) −839.000 −1.15089
\(82\) 0 0
\(83\) 308.000 0.407318 0.203659 0.979042i \(-0.434717\pi\)
0.203659 + 0.979042i \(0.434717\pi\)
\(84\) 0 0
\(85\) 539.000 0.687797
\(86\) 0 0
\(87\) 574.000 0.707348
\(88\) 0 0
\(89\) −1190.00 −1.41730 −0.708650 0.705560i \(-0.750696\pi\)
−0.708650 + 0.705560i \(0.750696\pi\)
\(90\) 0 0
\(91\) 169.000 0.194681
\(92\) 0 0
\(93\) 1372.00 1.52978
\(94\) 0 0
\(95\) 882.000 0.952540
\(96\) 0 0
\(97\) 70.0000 0.0732724 0.0366362 0.999329i \(-0.488336\pi\)
0.0366362 + 0.999329i \(0.488336\pi\)
\(98\) 0 0
\(99\) 572.000 0.580689
\(100\) 0 0
\(101\) −420.000 −0.413778 −0.206889 0.978364i \(-0.566334\pi\)
−0.206889 + 0.978364i \(0.566334\pi\)
\(102\) 0 0
\(103\) 588.000 0.562499 0.281249 0.959635i \(-0.409251\pi\)
0.281249 + 0.959635i \(0.409251\pi\)
\(104\) 0 0
\(105\) −637.000 −0.592046
\(106\) 0 0
\(107\) 684.000 0.617989 0.308994 0.951064i \(-0.400008\pi\)
0.308994 + 0.951064i \(0.400008\pi\)
\(108\) 0 0
\(109\) −373.000 −0.327770 −0.163885 0.986479i \(-0.552403\pi\)
−0.163885 + 0.986479i \(0.552403\pi\)
\(110\) 0 0
\(111\) 917.000 0.784124
\(112\) 0 0
\(113\) −1734.00 −1.44355 −0.721774 0.692128i \(-0.756673\pi\)
−0.721774 + 0.692128i \(0.756673\pi\)
\(114\) 0 0
\(115\) −672.000 −0.544907
\(116\) 0 0
\(117\) −286.000 −0.225989
\(118\) 0 0
\(119\) −1001.00 −0.771105
\(120\) 0 0
\(121\) −655.000 −0.492111
\(122\) 0 0
\(123\) 2352.00 1.72417
\(124\) 0 0
\(125\) −1407.00 −1.00677
\(126\) 0 0
\(127\) 1892.00 1.32195 0.660976 0.750407i \(-0.270143\pi\)
0.660976 + 0.750407i \(0.270143\pi\)
\(128\) 0 0
\(129\) 1407.00 0.960306
\(130\) 0 0
\(131\) −1435.00 −0.957073 −0.478536 0.878068i \(-0.658833\pi\)
−0.478536 + 0.878068i \(0.658833\pi\)
\(132\) 0 0
\(133\) −1638.00 −1.06791
\(134\) 0 0
\(135\) −245.000 −0.156194
\(136\) 0 0
\(137\) −1776.00 −1.10755 −0.553773 0.832667i \(-0.686813\pi\)
−0.553773 + 0.832667i \(0.686813\pi\)
\(138\) 0 0
\(139\) 1869.00 1.14048 0.570239 0.821479i \(-0.306850\pi\)
0.570239 + 0.821479i \(0.306850\pi\)
\(140\) 0 0
\(141\) −735.000 −0.438994
\(142\) 0 0
\(143\) −338.000 −0.197657
\(144\) 0 0
\(145\) 574.000 0.328746
\(146\) 0 0
\(147\) −1218.00 −0.683394
\(148\) 0 0
\(149\) −2466.00 −1.35586 −0.677928 0.735128i \(-0.737122\pi\)
−0.677928 + 0.735128i \(0.737122\pi\)
\(150\) 0 0
\(151\) −3323.00 −1.79087 −0.895437 0.445189i \(-0.853137\pi\)
−0.895437 + 0.445189i \(0.853137\pi\)
\(152\) 0 0
\(153\) 1694.00 0.895110
\(154\) 0 0
\(155\) 1372.00 0.710979
\(156\) 0 0
\(157\) 2730.00 1.38776 0.693878 0.720092i \(-0.255901\pi\)
0.693878 + 0.720092i \(0.255901\pi\)
\(158\) 0 0
\(159\) 3024.00 1.50829
\(160\) 0 0
\(161\) 1248.00 0.610908
\(162\) 0 0
\(163\) 544.000 0.261407 0.130704 0.991421i \(-0.458276\pi\)
0.130704 + 0.991421i \(0.458276\pi\)
\(164\) 0 0
\(165\) 1274.00 0.601096
\(166\) 0 0
\(167\) 1624.00 0.752508 0.376254 0.926516i \(-0.377212\pi\)
0.376254 + 0.926516i \(0.377212\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 0 0
\(171\) 2772.00 1.23965
\(172\) 0 0
\(173\) 336.000 0.147662 0.0738312 0.997271i \(-0.476477\pi\)
0.0738312 + 0.997271i \(0.476477\pi\)
\(174\) 0 0
\(175\) 988.000 0.426776
\(176\) 0 0
\(177\) 2058.00 0.873948
\(178\) 0 0
\(179\) 3029.00 1.26479 0.632397 0.774645i \(-0.282071\pi\)
0.632397 + 0.774645i \(0.282071\pi\)
\(180\) 0 0
\(181\) 28.0000 0.0114985 0.00574924 0.999983i \(-0.498170\pi\)
0.00574924 + 0.999983i \(0.498170\pi\)
\(182\) 0 0
\(183\) 392.000 0.158347
\(184\) 0 0
\(185\) 917.000 0.364428
\(186\) 0 0
\(187\) 2002.00 0.782892
\(188\) 0 0
\(189\) 455.000 0.175113
\(190\) 0 0
\(191\) 422.000 0.159868 0.0799342 0.996800i \(-0.474529\pi\)
0.0799342 + 0.996800i \(0.474529\pi\)
\(192\) 0 0
\(193\) 492.000 0.183497 0.0917485 0.995782i \(-0.470754\pi\)
0.0917485 + 0.995782i \(0.470754\pi\)
\(194\) 0 0
\(195\) −637.000 −0.233931
\(196\) 0 0
\(197\) −2991.00 −1.08173 −0.540863 0.841111i \(-0.681902\pi\)
−0.540863 + 0.841111i \(0.681902\pi\)
\(198\) 0 0
\(199\) −70.0000 −0.0249355 −0.0124678 0.999922i \(-0.503969\pi\)
−0.0124678 + 0.999922i \(0.503969\pi\)
\(200\) 0 0
\(201\) −3346.00 −1.17417
\(202\) 0 0
\(203\) −1066.00 −0.368564
\(204\) 0 0
\(205\) 2352.00 0.801321
\(206\) 0 0
\(207\) −2112.00 −0.709150
\(208\) 0 0
\(209\) 3276.00 1.08424
\(210\) 0 0
\(211\) −2851.00 −0.930194 −0.465097 0.885260i \(-0.653981\pi\)
−0.465097 + 0.885260i \(0.653981\pi\)
\(212\) 0 0
\(213\) 63.0000 0.0202661
\(214\) 0 0
\(215\) 1407.00 0.446310
\(216\) 0 0
\(217\) −2548.00 −0.797095
\(218\) 0 0
\(219\) 686.000 0.211669
\(220\) 0 0
\(221\) −1001.00 −0.304681
\(222\) 0 0
\(223\) 217.000 0.0651632 0.0325816 0.999469i \(-0.489627\pi\)
0.0325816 + 0.999469i \(0.489627\pi\)
\(224\) 0 0
\(225\) −1672.00 −0.495407
\(226\) 0 0
\(227\) 2576.00 0.753194 0.376597 0.926377i \(-0.377094\pi\)
0.376597 + 0.926377i \(0.377094\pi\)
\(228\) 0 0
\(229\) −455.000 −0.131298 −0.0656490 0.997843i \(-0.520912\pi\)
−0.0656490 + 0.997843i \(0.520912\pi\)
\(230\) 0 0
\(231\) −2366.00 −0.673902
\(232\) 0 0
\(233\) 3061.00 0.860656 0.430328 0.902673i \(-0.358398\pi\)
0.430328 + 0.902673i \(0.358398\pi\)
\(234\) 0 0
\(235\) −735.000 −0.204026
\(236\) 0 0
\(237\) 9128.00 2.50180
\(238\) 0 0
\(239\) −3477.00 −0.941039 −0.470520 0.882389i \(-0.655934\pi\)
−0.470520 + 0.882389i \(0.655934\pi\)
\(240\) 0 0
\(241\) −1610.00 −0.430329 −0.215164 0.976578i \(-0.569029\pi\)
−0.215164 + 0.976578i \(0.569029\pi\)
\(242\) 0 0
\(243\) −4928.00 −1.30095
\(244\) 0 0
\(245\) −1218.00 −0.317613
\(246\) 0 0
\(247\) −1638.00 −0.421957
\(248\) 0 0
\(249\) 2156.00 0.548719
\(250\) 0 0
\(251\) −1008.00 −0.253484 −0.126742 0.991936i \(-0.540452\pi\)
−0.126742 + 0.991936i \(0.540452\pi\)
\(252\) 0 0
\(253\) −2496.00 −0.620246
\(254\) 0 0
\(255\) 3773.00 0.926566
\(256\) 0 0
\(257\) 6041.00 1.46625 0.733127 0.680092i \(-0.238060\pi\)
0.733127 + 0.680092i \(0.238060\pi\)
\(258\) 0 0
\(259\) −1703.00 −0.408569
\(260\) 0 0
\(261\) 1804.00 0.427834
\(262\) 0 0
\(263\) −3708.00 −0.869373 −0.434686 0.900582i \(-0.643141\pi\)
−0.434686 + 0.900582i \(0.643141\pi\)
\(264\) 0 0
\(265\) 3024.00 0.700992
\(266\) 0 0
\(267\) −8330.00 −1.90932
\(268\) 0 0
\(269\) −8344.00 −1.89124 −0.945618 0.325278i \(-0.894542\pi\)
−0.945618 + 0.325278i \(0.894542\pi\)
\(270\) 0 0
\(271\) −1617.00 −0.362457 −0.181228 0.983441i \(-0.558007\pi\)
−0.181228 + 0.983441i \(0.558007\pi\)
\(272\) 0 0
\(273\) 1183.00 0.262265
\(274\) 0 0
\(275\) −1976.00 −0.433299
\(276\) 0 0
\(277\) 3820.00 0.828598 0.414299 0.910141i \(-0.364027\pi\)
0.414299 + 0.910141i \(0.364027\pi\)
\(278\) 0 0
\(279\) 4312.00 0.925278
\(280\) 0 0
\(281\) −6214.00 −1.31920 −0.659602 0.751615i \(-0.729275\pi\)
−0.659602 + 0.751615i \(0.729275\pi\)
\(282\) 0 0
\(283\) 5292.00 1.11158 0.555789 0.831323i \(-0.312416\pi\)
0.555789 + 0.831323i \(0.312416\pi\)
\(284\) 0 0
\(285\) 6174.00 1.28321
\(286\) 0 0
\(287\) −4368.00 −0.898379
\(288\) 0 0
\(289\) 1016.00 0.206798
\(290\) 0 0
\(291\) 490.000 0.0987090
\(292\) 0 0
\(293\) 903.000 0.180047 0.0900236 0.995940i \(-0.471306\pi\)
0.0900236 + 0.995940i \(0.471306\pi\)
\(294\) 0 0
\(295\) 2058.00 0.406174
\(296\) 0 0
\(297\) −910.000 −0.177790
\(298\) 0 0
\(299\) 1248.00 0.241384
\(300\) 0 0
\(301\) −2613.00 −0.500368
\(302\) 0 0
\(303\) −2940.00 −0.557421
\(304\) 0 0
\(305\) 392.000 0.0735930
\(306\) 0 0
\(307\) −2114.00 −0.393004 −0.196502 0.980503i \(-0.562958\pi\)
−0.196502 + 0.980503i \(0.562958\pi\)
\(308\) 0 0
\(309\) 4116.00 0.757770
\(310\) 0 0
\(311\) 3402.00 0.620288 0.310144 0.950690i \(-0.399623\pi\)
0.310144 + 0.950690i \(0.399623\pi\)
\(312\) 0 0
\(313\) −10689.0 −1.93028 −0.965141 0.261732i \(-0.915706\pi\)
−0.965141 + 0.261732i \(0.915706\pi\)
\(314\) 0 0
\(315\) −2002.00 −0.358095
\(316\) 0 0
\(317\) 7054.00 1.24982 0.624909 0.780698i \(-0.285136\pi\)
0.624909 + 0.780698i \(0.285136\pi\)
\(318\) 0 0
\(319\) 2132.00 0.374198
\(320\) 0 0
\(321\) 4788.00 0.832524
\(322\) 0 0
\(323\) 9702.00 1.67131
\(324\) 0 0
\(325\) 988.000 0.168629
\(326\) 0 0
\(327\) −2611.00 −0.441555
\(328\) 0 0
\(329\) 1365.00 0.228738
\(330\) 0 0
\(331\) −9704.00 −1.61142 −0.805710 0.592310i \(-0.798216\pi\)
−0.805710 + 0.592310i \(0.798216\pi\)
\(332\) 0 0
\(333\) 2882.00 0.474272
\(334\) 0 0
\(335\) −3346.00 −0.545706
\(336\) 0 0
\(337\) −10449.0 −1.68900 −0.844500 0.535555i \(-0.820103\pi\)
−0.844500 + 0.535555i \(0.820103\pi\)
\(338\) 0 0
\(339\) −12138.0 −1.94468
\(340\) 0 0
\(341\) 5096.00 0.809278
\(342\) 0 0
\(343\) 6721.00 1.05802
\(344\) 0 0
\(345\) −4704.00 −0.734072
\(346\) 0 0
\(347\) 621.000 0.0960721 0.0480361 0.998846i \(-0.484704\pi\)
0.0480361 + 0.998846i \(0.484704\pi\)
\(348\) 0 0
\(349\) −12481.0 −1.91431 −0.957153 0.289584i \(-0.906483\pi\)
−0.957153 + 0.289584i \(0.906483\pi\)
\(350\) 0 0
\(351\) 455.000 0.0691912
\(352\) 0 0
\(353\) −1400.00 −0.211089 −0.105545 0.994415i \(-0.533659\pi\)
−0.105545 + 0.994415i \(0.533659\pi\)
\(354\) 0 0
\(355\) 63.0000 0.00941885
\(356\) 0 0
\(357\) −7007.00 −1.03879
\(358\) 0 0
\(359\) −4968.00 −0.730365 −0.365182 0.930936i \(-0.618993\pi\)
−0.365182 + 0.930936i \(0.618993\pi\)
\(360\) 0 0
\(361\) 9017.00 1.31462
\(362\) 0 0
\(363\) −4585.00 −0.662948
\(364\) 0 0
\(365\) 686.000 0.0983750
\(366\) 0 0
\(367\) 8722.00 1.24056 0.620279 0.784381i \(-0.287019\pi\)
0.620279 + 0.784381i \(0.287019\pi\)
\(368\) 0 0
\(369\) 7392.00 1.04285
\(370\) 0 0
\(371\) −5616.00 −0.785898
\(372\) 0 0
\(373\) −10012.0 −1.38982 −0.694908 0.719098i \(-0.744555\pi\)
−0.694908 + 0.719098i \(0.744555\pi\)
\(374\) 0 0
\(375\) −9849.00 −1.35627
\(376\) 0 0
\(377\) −1066.00 −0.145628
\(378\) 0 0
\(379\) 3372.00 0.457013 0.228507 0.973542i \(-0.426616\pi\)
0.228507 + 0.973542i \(0.426616\pi\)
\(380\) 0 0
\(381\) 13244.0 1.78087
\(382\) 0 0
\(383\) −847.000 −0.113002 −0.0565009 0.998403i \(-0.517994\pi\)
−0.0565009 + 0.998403i \(0.517994\pi\)
\(384\) 0 0
\(385\) −2366.00 −0.313201
\(386\) 0 0
\(387\) 4422.00 0.580834
\(388\) 0 0
\(389\) −11314.0 −1.47466 −0.737330 0.675533i \(-0.763914\pi\)
−0.737330 + 0.675533i \(0.763914\pi\)
\(390\) 0 0
\(391\) −7392.00 −0.956086
\(392\) 0 0
\(393\) −10045.0 −1.28932
\(394\) 0 0
\(395\) 9128.00 1.16273
\(396\) 0 0
\(397\) −1862.00 −0.235393 −0.117697 0.993050i \(-0.537551\pi\)
−0.117697 + 0.993050i \(0.537551\pi\)
\(398\) 0 0
\(399\) −11466.0 −1.43864
\(400\) 0 0
\(401\) 6820.00 0.849313 0.424657 0.905355i \(-0.360395\pi\)
0.424657 + 0.905355i \(0.360395\pi\)
\(402\) 0 0
\(403\) −2548.00 −0.314950
\(404\) 0 0
\(405\) −5873.00 −0.720572
\(406\) 0 0
\(407\) 3406.00 0.414814
\(408\) 0 0
\(409\) −12992.0 −1.57069 −0.785346 0.619057i \(-0.787515\pi\)
−0.785346 + 0.619057i \(0.787515\pi\)
\(410\) 0 0
\(411\) −12432.0 −1.49203
\(412\) 0 0
\(413\) −3822.00 −0.455371
\(414\) 0 0
\(415\) 2156.00 0.255021
\(416\) 0 0
\(417\) 13083.0 1.53640
\(418\) 0 0
\(419\) 7343.00 0.856155 0.428078 0.903742i \(-0.359191\pi\)
0.428078 + 0.903742i \(0.359191\pi\)
\(420\) 0 0
\(421\) 5059.00 0.585655 0.292827 0.956165i \(-0.405404\pi\)
0.292827 + 0.956165i \(0.405404\pi\)
\(422\) 0 0
\(423\) −2310.00 −0.265523
\(424\) 0 0
\(425\) −5852.00 −0.667915
\(426\) 0 0
\(427\) −728.000 −0.0825068
\(428\) 0 0
\(429\) −2366.00 −0.266274
\(430\) 0 0
\(431\) 3243.00 0.362436 0.181218 0.983443i \(-0.441996\pi\)
0.181218 + 0.983443i \(0.441996\pi\)
\(432\) 0 0
\(433\) 11599.0 1.28733 0.643663 0.765309i \(-0.277414\pi\)
0.643663 + 0.765309i \(0.277414\pi\)
\(434\) 0 0
\(435\) 4018.00 0.442870
\(436\) 0 0
\(437\) −12096.0 −1.32410
\(438\) 0 0
\(439\) −17374.0 −1.88887 −0.944437 0.328692i \(-0.893392\pi\)
−0.944437 + 0.328692i \(0.893392\pi\)
\(440\) 0 0
\(441\) −3828.00 −0.413346
\(442\) 0 0
\(443\) −989.000 −0.106070 −0.0530348 0.998593i \(-0.516889\pi\)
−0.0530348 + 0.998593i \(0.516889\pi\)
\(444\) 0 0
\(445\) −8330.00 −0.887370
\(446\) 0 0
\(447\) −17262.0 −1.82654
\(448\) 0 0
\(449\) −14474.0 −1.52131 −0.760657 0.649154i \(-0.775123\pi\)
−0.760657 + 0.649154i \(0.775123\pi\)
\(450\) 0 0
\(451\) 8736.00 0.912111
\(452\) 0 0
\(453\) −23261.0 −2.41258
\(454\) 0 0
\(455\) 1183.00 0.121890
\(456\) 0 0
\(457\) −1594.00 −0.163160 −0.0815801 0.996667i \(-0.525997\pi\)
−0.0815801 + 0.996667i \(0.525997\pi\)
\(458\) 0 0
\(459\) −2695.00 −0.274056
\(460\) 0 0
\(461\) 5915.00 0.597590 0.298795 0.954317i \(-0.403415\pi\)
0.298795 + 0.954317i \(0.403415\pi\)
\(462\) 0 0
\(463\) −11072.0 −1.11136 −0.555680 0.831396i \(-0.687542\pi\)
−0.555680 + 0.831396i \(0.687542\pi\)
\(464\) 0 0
\(465\) 9604.00 0.957795
\(466\) 0 0
\(467\) −1260.00 −0.124852 −0.0624260 0.998050i \(-0.519884\pi\)
−0.0624260 + 0.998050i \(0.519884\pi\)
\(468\) 0 0
\(469\) 6214.00 0.611804
\(470\) 0 0
\(471\) 19110.0 1.86952
\(472\) 0 0
\(473\) 5226.00 0.508016
\(474\) 0 0
\(475\) −9576.00 −0.925004
\(476\) 0 0
\(477\) 9504.00 0.912281
\(478\) 0 0
\(479\) −12033.0 −1.14781 −0.573906 0.818921i \(-0.694572\pi\)
−0.573906 + 0.818921i \(0.694572\pi\)
\(480\) 0 0
\(481\) −1703.00 −0.161435
\(482\) 0 0
\(483\) 8736.00 0.822985
\(484\) 0 0
\(485\) 490.000 0.0458758
\(486\) 0 0
\(487\) −2280.00 −0.212149 −0.106075 0.994358i \(-0.533828\pi\)
−0.106075 + 0.994358i \(0.533828\pi\)
\(488\) 0 0
\(489\) 3808.00 0.352155
\(490\) 0 0
\(491\) −16767.0 −1.54111 −0.770554 0.637375i \(-0.780020\pi\)
−0.770554 + 0.637375i \(0.780020\pi\)
\(492\) 0 0
\(493\) 6314.00 0.576812
\(494\) 0 0
\(495\) 4004.00 0.363569
\(496\) 0 0
\(497\) −117.000 −0.0105597
\(498\) 0 0
\(499\) −12840.0 −1.15190 −0.575949 0.817485i \(-0.695367\pi\)
−0.575949 + 0.817485i \(0.695367\pi\)
\(500\) 0 0
\(501\) 11368.0 1.01374
\(502\) 0 0
\(503\) −2198.00 −0.194839 −0.0974195 0.995243i \(-0.531059\pi\)
−0.0974195 + 0.995243i \(0.531059\pi\)
\(504\) 0 0
\(505\) −2940.00 −0.259066
\(506\) 0 0
\(507\) 1183.00 0.103627
\(508\) 0 0
\(509\) 17066.0 1.48612 0.743062 0.669223i \(-0.233373\pi\)
0.743062 + 0.669223i \(0.233373\pi\)
\(510\) 0 0
\(511\) −1274.00 −0.110290
\(512\) 0 0
\(513\) −4410.00 −0.379544
\(514\) 0 0
\(515\) 4116.00 0.352180
\(516\) 0 0
\(517\) −2730.00 −0.232235
\(518\) 0 0
\(519\) 2352.00 0.198924
\(520\) 0 0
\(521\) 2583.00 0.217204 0.108602 0.994085i \(-0.465363\pi\)
0.108602 + 0.994085i \(0.465363\pi\)
\(522\) 0 0
\(523\) −18620.0 −1.55678 −0.778390 0.627781i \(-0.783963\pi\)
−0.778390 + 0.627781i \(0.783963\pi\)
\(524\) 0 0
\(525\) 6916.00 0.574931
\(526\) 0 0
\(527\) 15092.0 1.24747
\(528\) 0 0
\(529\) −2951.00 −0.242541
\(530\) 0 0
\(531\) 6468.00 0.528601
\(532\) 0 0
\(533\) −4368.00 −0.354970
\(534\) 0 0
\(535\) 4788.00 0.386922
\(536\) 0 0
\(537\) 21203.0 1.70387
\(538\) 0 0
\(539\) −4524.00 −0.361526
\(540\) 0 0
\(541\) 16833.0 1.33772 0.668861 0.743388i \(-0.266782\pi\)
0.668861 + 0.743388i \(0.266782\pi\)
\(542\) 0 0
\(543\) 196.000 0.0154902
\(544\) 0 0
\(545\) −2611.00 −0.205216
\(546\) 0 0
\(547\) 8615.00 0.673402 0.336701 0.941612i \(-0.390689\pi\)
0.336701 + 0.941612i \(0.390689\pi\)
\(548\) 0 0
\(549\) 1232.00 0.0957750
\(550\) 0 0
\(551\) 10332.0 0.798835
\(552\) 0 0
\(553\) −16952.0 −1.30357
\(554\) 0 0
\(555\) 6419.00 0.490939
\(556\) 0 0
\(557\) −8535.00 −0.649263 −0.324632 0.945841i \(-0.605240\pi\)
−0.324632 + 0.945841i \(0.605240\pi\)
\(558\) 0 0
\(559\) −2613.00 −0.197707
\(560\) 0 0
\(561\) 14014.0 1.05467
\(562\) 0 0
\(563\) 4641.00 0.347415 0.173708 0.984797i \(-0.444425\pi\)
0.173708 + 0.984797i \(0.444425\pi\)
\(564\) 0 0
\(565\) −12138.0 −0.903804
\(566\) 0 0
\(567\) 10907.0 0.807850
\(568\) 0 0
\(569\) −4793.00 −0.353134 −0.176567 0.984289i \(-0.556499\pi\)
−0.176567 + 0.984289i \(0.556499\pi\)
\(570\) 0 0
\(571\) 5563.00 0.407713 0.203857 0.979001i \(-0.434652\pi\)
0.203857 + 0.979001i \(0.434652\pi\)
\(572\) 0 0
\(573\) 2954.00 0.215367
\(574\) 0 0
\(575\) 7296.00 0.529155
\(576\) 0 0
\(577\) 24038.0 1.73434 0.867171 0.498011i \(-0.165936\pi\)
0.867171 + 0.498011i \(0.165936\pi\)
\(578\) 0 0
\(579\) 3444.00 0.247198
\(580\) 0 0
\(581\) −4004.00 −0.285910
\(582\) 0 0
\(583\) 11232.0 0.797911
\(584\) 0 0
\(585\) −2002.00 −0.141491
\(586\) 0 0
\(587\) 21224.0 1.49235 0.746174 0.665751i \(-0.231889\pi\)
0.746174 + 0.665751i \(0.231889\pi\)
\(588\) 0 0
\(589\) 24696.0 1.72764
\(590\) 0 0
\(591\) −20937.0 −1.45725
\(592\) 0 0
\(593\) 4354.00 0.301513 0.150757 0.988571i \(-0.451829\pi\)
0.150757 + 0.988571i \(0.451829\pi\)
\(594\) 0 0
\(595\) −7007.00 −0.482788
\(596\) 0 0
\(597\) −490.000 −0.0335919
\(598\) 0 0
\(599\) 7310.00 0.498629 0.249314 0.968423i \(-0.419795\pi\)
0.249314 + 0.968423i \(0.419795\pi\)
\(600\) 0 0
\(601\) −7595.00 −0.515485 −0.257743 0.966214i \(-0.582979\pi\)
−0.257743 + 0.966214i \(0.582979\pi\)
\(602\) 0 0
\(603\) −10516.0 −0.710190
\(604\) 0 0
\(605\) −4585.00 −0.308110
\(606\) 0 0
\(607\) −826.000 −0.0552328 −0.0276164 0.999619i \(-0.508792\pi\)
−0.0276164 + 0.999619i \(0.508792\pi\)
\(608\) 0 0
\(609\) −7462.00 −0.496511
\(610\) 0 0
\(611\) 1365.00 0.0903797
\(612\) 0 0
\(613\) −14590.0 −0.961312 −0.480656 0.876909i \(-0.659602\pi\)
−0.480656 + 0.876909i \(0.659602\pi\)
\(614\) 0 0
\(615\) 16464.0 1.07950
\(616\) 0 0
\(617\) 4888.00 0.318936 0.159468 0.987203i \(-0.449022\pi\)
0.159468 + 0.987203i \(0.449022\pi\)
\(618\) 0 0
\(619\) 11004.0 0.714520 0.357260 0.934005i \(-0.383711\pi\)
0.357260 + 0.934005i \(0.383711\pi\)
\(620\) 0 0
\(621\) 3360.00 0.217121
\(622\) 0 0
\(623\) 15470.0 0.994851
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) 0 0
\(627\) 22932.0 1.46063
\(628\) 0 0
\(629\) 10087.0 0.639420
\(630\) 0 0
\(631\) −4975.00 −0.313869 −0.156935 0.987609i \(-0.550161\pi\)
−0.156935 + 0.987609i \(0.550161\pi\)
\(632\) 0 0
\(633\) −19957.0 −1.25311
\(634\) 0 0
\(635\) 13244.0 0.827673
\(636\) 0 0
\(637\) 2262.00 0.140697
\(638\) 0 0
\(639\) 198.000 0.0122578
\(640\) 0 0
\(641\) 3950.00 0.243394 0.121697 0.992567i \(-0.461166\pi\)
0.121697 + 0.992567i \(0.461166\pi\)
\(642\) 0 0
\(643\) 3682.00 0.225823 0.112911 0.993605i \(-0.463982\pi\)
0.112911 + 0.993605i \(0.463982\pi\)
\(644\) 0 0
\(645\) 9849.00 0.601247
\(646\) 0 0
\(647\) 10402.0 0.632063 0.316032 0.948749i \(-0.397649\pi\)
0.316032 + 0.948749i \(0.397649\pi\)
\(648\) 0 0
\(649\) 7644.00 0.462332
\(650\) 0 0
\(651\) −17836.0 −1.07381
\(652\) 0 0
\(653\) 31680.0 1.89852 0.949260 0.314491i \(-0.101834\pi\)
0.949260 + 0.314491i \(0.101834\pi\)
\(654\) 0 0
\(655\) −10045.0 −0.599222
\(656\) 0 0
\(657\) 2156.00 0.128027
\(658\) 0 0
\(659\) −21940.0 −1.29691 −0.648453 0.761255i \(-0.724584\pi\)
−0.648453 + 0.761255i \(0.724584\pi\)
\(660\) 0 0
\(661\) 31374.0 1.84615 0.923077 0.384616i \(-0.125666\pi\)
0.923077 + 0.384616i \(0.125666\pi\)
\(662\) 0 0
\(663\) −7007.00 −0.410451
\(664\) 0 0
\(665\) −11466.0 −0.668620
\(666\) 0 0
\(667\) −7872.00 −0.456979
\(668\) 0 0
\(669\) 1519.00 0.0877847
\(670\) 0 0
\(671\) 1456.00 0.0837679
\(672\) 0 0
\(673\) 18013.0 1.03172 0.515862 0.856672i \(-0.327472\pi\)
0.515862 + 0.856672i \(0.327472\pi\)
\(674\) 0 0
\(675\) 2660.00 0.151679
\(676\) 0 0
\(677\) 10640.0 0.604030 0.302015 0.953303i \(-0.402341\pi\)
0.302015 + 0.953303i \(0.402341\pi\)
\(678\) 0 0
\(679\) −910.000 −0.0514324
\(680\) 0 0
\(681\) 18032.0 1.01467
\(682\) 0 0
\(683\) 9336.00 0.523034 0.261517 0.965199i \(-0.415777\pi\)
0.261517 + 0.965199i \(0.415777\pi\)
\(684\) 0 0
\(685\) −12432.0 −0.693434
\(686\) 0 0
\(687\) −3185.00 −0.176878
\(688\) 0 0
\(689\) −5616.00 −0.310526
\(690\) 0 0
\(691\) −4200.00 −0.231224 −0.115612 0.993294i \(-0.536883\pi\)
−0.115612 + 0.993294i \(0.536883\pi\)
\(692\) 0 0
\(693\) −7436.00 −0.407605
\(694\) 0 0
\(695\) 13083.0 0.714052
\(696\) 0 0
\(697\) 25872.0 1.40599
\(698\) 0 0
\(699\) 21427.0 1.15943
\(700\) 0 0
\(701\) −9872.00 −0.531898 −0.265949 0.963987i \(-0.585685\pi\)
−0.265949 + 0.963987i \(0.585685\pi\)
\(702\) 0 0
\(703\) 16506.0 0.885541
\(704\) 0 0
\(705\) −5145.00 −0.274854
\(706\) 0 0
\(707\) 5460.00 0.290445
\(708\) 0 0
\(709\) −28450.0 −1.50700 −0.753499 0.657449i \(-0.771636\pi\)
−0.753499 + 0.657449i \(0.771636\pi\)
\(710\) 0 0
\(711\) 28688.0 1.51320
\(712\) 0 0
\(713\) −18816.0 −0.988310
\(714\) 0 0
\(715\) −2366.00 −0.123753
\(716\) 0 0
\(717\) −24339.0 −1.26772
\(718\) 0 0
\(719\) 32718.0 1.69705 0.848523 0.529159i \(-0.177493\pi\)
0.848523 + 0.529159i \(0.177493\pi\)
\(720\) 0 0
\(721\) −7644.00 −0.394837
\(722\) 0 0
\(723\) −11270.0 −0.579718
\(724\) 0 0
\(725\) −6232.00 −0.319242
\(726\) 0 0
\(727\) −22834.0 −1.16488 −0.582439 0.812874i \(-0.697901\pi\)
−0.582439 + 0.812874i \(0.697901\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) 0 0
\(731\) 15477.0 0.783088
\(732\) 0 0
\(733\) −7875.00 −0.396821 −0.198410 0.980119i \(-0.563578\pi\)
−0.198410 + 0.980119i \(0.563578\pi\)
\(734\) 0 0
\(735\) −8526.00 −0.427872
\(736\) 0 0
\(737\) −12428.0 −0.621155
\(738\) 0 0
\(739\) 2140.00 0.106524 0.0532620 0.998581i \(-0.483038\pi\)
0.0532620 + 0.998581i \(0.483038\pi\)
\(740\) 0 0
\(741\) −11466.0 −0.568440
\(742\) 0 0
\(743\) 31971.0 1.57860 0.789302 0.614006i \(-0.210443\pi\)
0.789302 + 0.614006i \(0.210443\pi\)
\(744\) 0 0
\(745\) −17262.0 −0.848900
\(746\) 0 0
\(747\) 6776.00 0.331889
\(748\) 0 0
\(749\) −8892.00 −0.433787
\(750\) 0 0
\(751\) −7432.00 −0.361115 −0.180558 0.983564i \(-0.557790\pi\)
−0.180558 + 0.983564i \(0.557790\pi\)
\(752\) 0 0
\(753\) −7056.00 −0.341481
\(754\) 0 0
\(755\) −23261.0 −1.12126
\(756\) 0 0
\(757\) −20176.0 −0.968704 −0.484352 0.874873i \(-0.660945\pi\)
−0.484352 + 0.874873i \(0.660945\pi\)
\(758\) 0 0
\(759\) −17472.0 −0.835564
\(760\) 0 0
\(761\) −9478.00 −0.451481 −0.225741 0.974187i \(-0.572480\pi\)
−0.225741 + 0.974187i \(0.572480\pi\)
\(762\) 0 0
\(763\) 4849.00 0.230073
\(764\) 0 0
\(765\) 11858.0 0.560427
\(766\) 0 0
\(767\) −3822.00 −0.179928
\(768\) 0 0
\(769\) −12096.0 −0.567221 −0.283610 0.958940i \(-0.591532\pi\)
−0.283610 + 0.958940i \(0.591532\pi\)
\(770\) 0 0
\(771\) 42287.0 1.97526
\(772\) 0 0
\(773\) −17941.0 −0.834790 −0.417395 0.908725i \(-0.637057\pi\)
−0.417395 + 0.908725i \(0.637057\pi\)
\(774\) 0 0
\(775\) −14896.0 −0.690426
\(776\) 0 0
\(777\) −11921.0 −0.550403
\(778\) 0 0
\(779\) 42336.0 1.94717
\(780\) 0 0
\(781\) 234.000 0.0107211
\(782\) 0 0
\(783\) −2870.00 −0.130990
\(784\) 0 0
\(785\) 19110.0 0.868873
\(786\) 0 0
\(787\) −6664.00 −0.301837 −0.150919 0.988546i \(-0.548223\pi\)
−0.150919 + 0.988546i \(0.548223\pi\)
\(788\) 0 0
\(789\) −25956.0 −1.17118
\(790\) 0 0
\(791\) 22542.0 1.01328
\(792\) 0 0
\(793\) −728.000 −0.0326003
\(794\) 0 0
\(795\) 21168.0 0.944342
\(796\) 0 0
\(797\) 1442.00 0.0640882 0.0320441 0.999486i \(-0.489798\pi\)
0.0320441 + 0.999486i \(0.489798\pi\)
\(798\) 0 0
\(799\) −8085.00 −0.357981
\(800\) 0 0
\(801\) −26180.0 −1.15484
\(802\) 0 0
\(803\) 2548.00 0.111976
\(804\) 0 0
\(805\) 8736.00 0.382489
\(806\) 0 0
\(807\) −58408.0 −2.54778
\(808\) 0 0
\(809\) 30207.0 1.31276 0.656379 0.754431i \(-0.272087\pi\)
0.656379 + 0.754431i \(0.272087\pi\)
\(810\) 0 0
\(811\) −21140.0 −0.915322 −0.457661 0.889127i \(-0.651313\pi\)
−0.457661 + 0.889127i \(0.651313\pi\)
\(812\) 0 0
\(813\) −11319.0 −0.488284
\(814\) 0 0
\(815\) 3808.00 0.163667
\(816\) 0 0
\(817\) 25326.0 1.08451
\(818\) 0 0
\(819\) 3718.00 0.158629
\(820\) 0 0
\(821\) −569.000 −0.0241879 −0.0120939 0.999927i \(-0.503850\pi\)
−0.0120939 + 0.999927i \(0.503850\pi\)
\(822\) 0 0
\(823\) −8538.00 −0.361623 −0.180812 0.983518i \(-0.557872\pi\)
−0.180812 + 0.983518i \(0.557872\pi\)
\(824\) 0 0
\(825\) −13832.0 −0.583719
\(826\) 0 0
\(827\) 32702.0 1.37504 0.687521 0.726164i \(-0.258699\pi\)
0.687521 + 0.726164i \(0.258699\pi\)
\(828\) 0 0
\(829\) 21154.0 0.886259 0.443130 0.896458i \(-0.353868\pi\)
0.443130 + 0.896458i \(0.353868\pi\)
\(830\) 0 0
\(831\) 26740.0 1.11625
\(832\) 0 0
\(833\) −13398.0 −0.557279
\(834\) 0 0
\(835\) 11368.0 0.471145
\(836\) 0 0
\(837\) −6860.00 −0.283293
\(838\) 0 0
\(839\) −2184.00 −0.0898690 −0.0449345 0.998990i \(-0.514308\pi\)
−0.0449345 + 0.998990i \(0.514308\pi\)
\(840\) 0 0
\(841\) −17665.0 −0.724302
\(842\) 0 0
\(843\) −43498.0 −1.77717
\(844\) 0 0
\(845\) 1183.00 0.0481615
\(846\) 0 0
\(847\) 8515.00 0.345430
\(848\) 0 0
\(849\) 37044.0 1.49746
\(850\) 0 0
\(851\) −12576.0 −0.506580
\(852\) 0 0
\(853\) −36687.0 −1.47261 −0.736307 0.676648i \(-0.763432\pi\)
−0.736307 + 0.676648i \(0.763432\pi\)
\(854\) 0 0
\(855\) 19404.0 0.776144
\(856\) 0 0
\(857\) 36806.0 1.46706 0.733529 0.679658i \(-0.237872\pi\)
0.733529 + 0.679658i \(0.237872\pi\)
\(858\) 0 0
\(859\) −4900.00 −0.194628 −0.0973142 0.995254i \(-0.531025\pi\)
−0.0973142 + 0.995254i \(0.531025\pi\)
\(860\) 0 0
\(861\) −30576.0 −1.21025
\(862\) 0 0
\(863\) −13697.0 −0.540268 −0.270134 0.962823i \(-0.587068\pi\)
−0.270134 + 0.962823i \(0.587068\pi\)
\(864\) 0 0
\(865\) 2352.00 0.0924513
\(866\) 0 0
\(867\) 7112.00 0.278588
\(868\) 0 0
\(869\) 33904.0 1.32349
\(870\) 0 0
\(871\) 6214.00 0.241737
\(872\) 0 0
\(873\) 1540.00 0.0597034
\(874\) 0 0
\(875\) 18291.0 0.706684
\(876\) 0 0
\(877\) −6239.00 −0.240224 −0.120112 0.992760i \(-0.538325\pi\)
−0.120112 + 0.992760i \(0.538325\pi\)
\(878\) 0 0
\(879\) 6321.00 0.242551
\(880\) 0 0
\(881\) 133.000 0.00508613 0.00254307 0.999997i \(-0.499191\pi\)
0.00254307 + 0.999997i \(0.499191\pi\)
\(882\) 0 0
\(883\) 26003.0 0.991020 0.495510 0.868602i \(-0.334981\pi\)
0.495510 + 0.868602i \(0.334981\pi\)
\(884\) 0 0
\(885\) 14406.0 0.547178
\(886\) 0 0
\(887\) −31248.0 −1.18287 −0.591435 0.806353i \(-0.701438\pi\)
−0.591435 + 0.806353i \(0.701438\pi\)
\(888\) 0 0
\(889\) −24596.0 −0.927923
\(890\) 0 0
\(891\) −21814.0 −0.820198
\(892\) 0 0
\(893\) −13230.0 −0.495773
\(894\) 0 0
\(895\) 21203.0 0.791886
\(896\) 0 0
\(897\) 8736.00 0.325180
\(898\) 0 0
\(899\) 16072.0 0.596253
\(900\) 0 0
\(901\) 33264.0 1.22995
\(902\) 0 0
\(903\) −18291.0 −0.674071
\(904\) 0 0
\(905\) 196.000 0.00719918
\(906\) 0 0
\(907\) 38253.0 1.40041 0.700204 0.713943i \(-0.253092\pi\)
0.700204 + 0.713943i \(0.253092\pi\)
\(908\) 0 0
\(909\) −9240.00 −0.337152
\(910\) 0 0
\(911\) 36374.0 1.32286 0.661429 0.750007i \(-0.269950\pi\)
0.661429 + 0.750007i \(0.269950\pi\)
\(912\) 0 0
\(913\) 8008.00 0.290281
\(914\) 0 0
\(915\) 2744.00 0.0991408
\(916\) 0 0
\(917\) 18655.0 0.671802
\(918\) 0 0
\(919\) −27648.0 −0.992408 −0.496204 0.868206i \(-0.665273\pi\)
−0.496204 + 0.868206i \(0.665273\pi\)
\(920\) 0 0
\(921\) −14798.0 −0.529436
\(922\) 0 0
\(923\) −117.000 −0.00417237
\(924\) 0 0
\(925\) −9956.00 −0.353893
\(926\) 0 0
\(927\) 12936.0 0.458332
\(928\) 0 0
\(929\) 756.000 0.0266992 0.0133496 0.999911i \(-0.495751\pi\)
0.0133496 + 0.999911i \(0.495751\pi\)
\(930\) 0 0
\(931\) −21924.0 −0.771783
\(932\) 0 0
\(933\) 23814.0 0.835622
\(934\) 0 0
\(935\) 14014.0 0.490168
\(936\) 0 0
\(937\) 20846.0 0.726797 0.363399 0.931634i \(-0.381616\pi\)
0.363399 + 0.931634i \(0.381616\pi\)
\(938\) 0 0
\(939\) −74823.0 −2.60038
\(940\) 0 0
\(941\) 41321.0 1.43148 0.715742 0.698365i \(-0.246089\pi\)
0.715742 + 0.698365i \(0.246089\pi\)
\(942\) 0 0
\(943\) −32256.0 −1.11389
\(944\) 0 0
\(945\) 3185.00 0.109638
\(946\) 0 0
\(947\) −54966.0 −1.88612 −0.943060 0.332624i \(-0.892066\pi\)
−0.943060 + 0.332624i \(0.892066\pi\)
\(948\) 0 0
\(949\) −1274.00 −0.0435783
\(950\) 0 0
\(951\) 49378.0 1.68369
\(952\) 0 0
\(953\) −44553.0 −1.51439 −0.757195 0.653189i \(-0.773431\pi\)
−0.757195 + 0.653189i \(0.773431\pi\)
\(954\) 0 0
\(955\) 2954.00 0.100093
\(956\) 0 0
\(957\) 14924.0 0.504101
\(958\) 0 0
\(959\) 23088.0 0.777425
\(960\) 0 0
\(961\) 8625.00 0.289517
\(962\) 0 0
\(963\) 15048.0 0.503546
\(964\) 0 0
\(965\) 3444.00 0.114887
\(966\) 0 0
\(967\) −27907.0 −0.928054 −0.464027 0.885821i \(-0.653596\pi\)
−0.464027 + 0.885821i \(0.653596\pi\)
\(968\) 0 0
\(969\) 67914.0 2.25151
\(970\) 0 0
\(971\) 16443.0 0.543441 0.271720 0.962376i \(-0.412407\pi\)
0.271720 + 0.962376i \(0.412407\pi\)
\(972\) 0 0
\(973\) −24297.0 −0.800541
\(974\) 0 0
\(975\) 6916.00 0.227168
\(976\) 0 0
\(977\) −45414.0 −1.48713 −0.743563 0.668666i \(-0.766866\pi\)
−0.743563 + 0.668666i \(0.766866\pi\)
\(978\) 0 0
\(979\) −30940.0 −1.01006
\(980\) 0 0
\(981\) −8206.00 −0.267072
\(982\) 0 0
\(983\) −8981.00 −0.291403 −0.145702 0.989329i \(-0.546544\pi\)
−0.145702 + 0.989329i \(0.546544\pi\)
\(984\) 0 0
\(985\) −20937.0 −0.677267
\(986\) 0 0
\(987\) 9555.00 0.308145
\(988\) 0 0
\(989\) −19296.0 −0.620402
\(990\) 0 0
\(991\) −17414.0 −0.558198 −0.279099 0.960262i \(-0.590036\pi\)
−0.279099 + 0.960262i \(0.590036\pi\)
\(992\) 0 0
\(993\) −67928.0 −2.17083
\(994\) 0 0
\(995\) −490.000 −0.0156121
\(996\) 0 0
\(997\) 23702.0 0.752909 0.376454 0.926435i \(-0.377143\pi\)
0.376454 + 0.926435i \(0.377143\pi\)
\(998\) 0 0
\(999\) −4585.00 −0.145208
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 832.4.a.r.1.1 1
4.3 odd 2 832.4.a.a.1.1 1
8.3 odd 2 208.4.a.g.1.1 1
8.5 even 2 13.4.a.a.1.1 1
24.5 odd 2 117.4.a.b.1.1 1
24.11 even 2 1872.4.a.k.1.1 1
40.13 odd 4 325.4.b.b.274.2 2
40.29 even 2 325.4.a.d.1.1 1
40.37 odd 4 325.4.b.b.274.1 2
56.13 odd 2 637.4.a.a.1.1 1
88.21 odd 2 1573.4.a.a.1.1 1
104.5 odd 4 169.4.b.a.168.2 2
104.21 odd 4 169.4.b.a.168.1 2
104.29 even 6 169.4.c.e.22.1 2
104.37 odd 12 169.4.e.e.147.2 4
104.45 odd 12 169.4.e.e.23.2 4
104.61 even 6 169.4.c.e.146.1 2
104.69 even 6 169.4.c.a.146.1 2
104.77 even 2 169.4.a.e.1.1 1
104.85 odd 12 169.4.e.e.23.1 4
104.93 odd 12 169.4.e.e.147.1 4
104.101 even 6 169.4.c.a.22.1 2
312.77 odd 2 1521.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.4.a.a.1.1 1 8.5 even 2
117.4.a.b.1.1 1 24.5 odd 2
169.4.a.e.1.1 1 104.77 even 2
169.4.b.a.168.1 2 104.21 odd 4
169.4.b.a.168.2 2 104.5 odd 4
169.4.c.a.22.1 2 104.101 even 6
169.4.c.a.146.1 2 104.69 even 6
169.4.c.e.22.1 2 104.29 even 6
169.4.c.e.146.1 2 104.61 even 6
169.4.e.e.23.1 4 104.85 odd 12
169.4.e.e.23.2 4 104.45 odd 12
169.4.e.e.147.1 4 104.93 odd 12
169.4.e.e.147.2 4 104.37 odd 12
208.4.a.g.1.1 1 8.3 odd 2
325.4.a.d.1.1 1 40.29 even 2
325.4.b.b.274.1 2 40.37 odd 4
325.4.b.b.274.2 2 40.13 odd 4
637.4.a.a.1.1 1 56.13 odd 2
832.4.a.a.1.1 1 4.3 odd 2
832.4.a.r.1.1 1 1.1 even 1 trivial
1521.4.a.a.1.1 1 312.77 odd 2
1573.4.a.a.1.1 1 88.21 odd 2
1872.4.a.k.1.1 1 24.11 even 2