Properties

Label 9200.2.a.cz.1.6
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(73.4623698596\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 7 x^{5} + 24 x^{4} + x^{3} - 35 x^{2} + 17 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.40334\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.40334 q^{3} -1.57117 q^{7} -1.03063 q^{9} +O(q^{10})\) \(q+1.40334 q^{3} -1.57117 q^{7} -1.03063 q^{9} -4.35401 q^{11} +0.964590 q^{13} -0.300242 q^{17} +8.62443 q^{19} -2.20489 q^{21} +1.00000 q^{23} -5.65635 q^{27} +4.76644 q^{29} +5.59148 q^{31} -6.11017 q^{33} -4.38462 q^{37} +1.35365 q^{39} -6.62014 q^{41} +1.72988 q^{43} +0.687333 q^{47} -4.53143 q^{49} -0.421342 q^{51} +8.05208 q^{53} +12.1030 q^{57} -5.74620 q^{59} -13.6547 q^{61} +1.61929 q^{63} -6.49053 q^{67} +1.40334 q^{69} -9.89977 q^{71} +6.35994 q^{73} +6.84088 q^{77} +6.95266 q^{79} -4.84592 q^{81} +0.185320 q^{83} +6.68895 q^{87} -1.64878 q^{89} -1.51553 q^{91} +7.84676 q^{93} -9.21689 q^{97} +4.48736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 3q^{3} - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 7q - 3q^{3} - 4q^{7} + 2q^{9} + 7q^{11} - 7q^{13} + 7q^{19} - 6q^{21} + 7q^{23} - 11q^{29} + 10q^{31} - 19q^{33} - 19q^{37} + 24q^{39} - 16q^{41} - 6q^{43} - 6q^{47} - 17q^{49} + 7q^{51} - 15q^{53} - 8q^{57} + 11q^{59} + 5q^{61} - 13q^{63} - 9q^{67} - 3q^{69} + 14q^{71} - 10q^{73} - 6q^{77} + 32q^{79} - 5q^{81} - q^{83} - 10q^{87} - 24q^{89} + 7q^{91} - 26q^{93} + 7q^{97} + 61q^{99} + O(q^{100}) \)

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
\(3\) 1.40334 0.810221 0.405110 0.914268i \(-0.367233\pi\)
0.405110 + 0.914268i \(0.367233\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.57117 −0.593846 −0.296923 0.954901i \(-0.595960\pi\)
−0.296923 + 0.954901i \(0.595960\pi\)
\(8\) 0 0
\(9\) −1.03063 −0.343543
\(10\) 0 0
\(11\) −4.35401 −1.31278 −0.656391 0.754421i \(-0.727918\pi\)
−0.656391 + 0.754421i \(0.727918\pi\)
\(12\) 0 0
\(13\) 0.964590 0.267529 0.133765 0.991013i \(-0.457293\pi\)
0.133765 + 0.991013i \(0.457293\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.300242 −0.0728193 −0.0364096 0.999337i \(-0.511592\pi\)
−0.0364096 + 0.999337i \(0.511592\pi\)
\(18\) 0 0
\(19\) 8.62443 1.97858 0.989290 0.145963i \(-0.0466280\pi\)
0.989290 + 0.145963i \(0.0466280\pi\)
\(20\) 0 0
\(21\) −2.20489 −0.481146
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −5.65635 −1.08857
\(28\) 0 0
\(29\) 4.76644 0.885106 0.442553 0.896742i \(-0.354073\pi\)
0.442553 + 0.896742i \(0.354073\pi\)
\(30\) 0 0
\(31\) 5.59148 1.00426 0.502129 0.864792i \(-0.332550\pi\)
0.502129 + 0.864792i \(0.332550\pi\)
\(32\) 0 0
\(33\) −6.11017 −1.06364
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.38462 −0.720827 −0.360413 0.932793i \(-0.617364\pi\)
−0.360413 + 0.932793i \(0.617364\pi\)
\(38\) 0 0
\(39\) 1.35365 0.216758
\(40\) 0 0
\(41\) −6.62014 −1.03389 −0.516946 0.856018i \(-0.672931\pi\)
−0.516946 + 0.856018i \(0.672931\pi\)
\(42\) 0 0
\(43\) 1.72988 0.263804 0.131902 0.991263i \(-0.457892\pi\)
0.131902 + 0.991263i \(0.457892\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.687333 0.100258 0.0501289 0.998743i \(-0.484037\pi\)
0.0501289 + 0.998743i \(0.484037\pi\)
\(48\) 0 0
\(49\) −4.53143 −0.647347
\(50\) 0 0
\(51\) −0.421342 −0.0589997
\(52\) 0 0
\(53\) 8.05208 1.10604 0.553019 0.833168i \(-0.313476\pi\)
0.553019 + 0.833168i \(0.313476\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 12.1030 1.60309
\(58\) 0 0
\(59\) −5.74620 −0.748091 −0.374046 0.927410i \(-0.622030\pi\)
−0.374046 + 0.927410i \(0.622030\pi\)
\(60\) 0 0
\(61\) −13.6547 −1.74831 −0.874153 0.485651i \(-0.838583\pi\)
−0.874153 + 0.485651i \(0.838583\pi\)
\(62\) 0 0
\(63\) 1.61929 0.204011
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.49053 −0.792945 −0.396472 0.918047i \(-0.629766\pi\)
−0.396472 + 0.918047i \(0.629766\pi\)
\(68\) 0 0
\(69\) 1.40334 0.168943
\(70\) 0 0
\(71\) −9.89977 −1.17489 −0.587443 0.809265i \(-0.699866\pi\)
−0.587443 + 0.809265i \(0.699866\pi\)
\(72\) 0 0
\(73\) 6.35994 0.744375 0.372187 0.928158i \(-0.378608\pi\)
0.372187 + 0.928158i \(0.378608\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.84088 0.779591
\(78\) 0 0
\(79\) 6.95266 0.782236 0.391118 0.920341i \(-0.372088\pi\)
0.391118 + 0.920341i \(0.372088\pi\)
\(80\) 0 0
\(81\) −4.84592 −0.538436
\(82\) 0 0
\(83\) 0.185320 0.0203415 0.0101707 0.999948i \(-0.496762\pi\)
0.0101707 + 0.999948i \(0.496762\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 6.68895 0.717131
\(88\) 0 0
\(89\) −1.64878 −0.174770 −0.0873852 0.996175i \(-0.527851\pi\)
−0.0873852 + 0.996175i \(0.527851\pi\)
\(90\) 0 0
\(91\) −1.51553 −0.158871
\(92\) 0 0
\(93\) 7.84676 0.813671
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −9.21689 −0.935834 −0.467917 0.883773i \(-0.654995\pi\)
−0.467917 + 0.883773i \(0.654995\pi\)
\(98\) 0 0
\(99\) 4.48736 0.450997
\(100\) 0 0
\(101\) −0.719780 −0.0716208 −0.0358104 0.999359i \(-0.511401\pi\)
−0.0358104 + 0.999359i \(0.511401\pi\)
\(102\) 0 0
\(103\) −9.16137 −0.902696 −0.451348 0.892348i \(-0.649057\pi\)
−0.451348 + 0.892348i \(0.649057\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.7486 1.23245 0.616226 0.787570i \(-0.288661\pi\)
0.616226 + 0.787570i \(0.288661\pi\)
\(108\) 0 0
\(109\) −3.38019 −0.323763 −0.161882 0.986810i \(-0.551756\pi\)
−0.161882 + 0.986810i \(0.551756\pi\)
\(110\) 0 0
\(111\) −6.15312 −0.584029
\(112\) 0 0
\(113\) −15.8547 −1.49148 −0.745741 0.666237i \(-0.767904\pi\)
−0.745741 + 0.666237i \(0.767904\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.994133 −0.0919076
\(118\) 0 0
\(119\) 0.471730 0.0432434
\(120\) 0 0
\(121\) 7.95739 0.723399
\(122\) 0 0
\(123\) −9.29032 −0.837680
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −15.2222 −1.35075 −0.675377 0.737473i \(-0.736019\pi\)
−0.675377 + 0.737473i \(0.736019\pi\)
\(128\) 0 0
\(129\) 2.42762 0.213740
\(130\) 0 0
\(131\) 12.8695 1.12441 0.562207 0.826997i \(-0.309953\pi\)
0.562207 + 0.826997i \(0.309953\pi\)
\(132\) 0 0
\(133\) −13.5504 −1.17497
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 16.7433 1.43048 0.715238 0.698881i \(-0.246318\pi\)
0.715238 + 0.698881i \(0.246318\pi\)
\(138\) 0 0
\(139\) 11.8293 1.00335 0.501676 0.865056i \(-0.332717\pi\)
0.501676 + 0.865056i \(0.332717\pi\)
\(140\) 0 0
\(141\) 0.964565 0.0812310
\(142\) 0 0
\(143\) −4.19983 −0.351208
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −6.35915 −0.524494
\(148\) 0 0
\(149\) 1.46021 0.119625 0.0598125 0.998210i \(-0.480950\pi\)
0.0598125 + 0.998210i \(0.480950\pi\)
\(150\) 0 0
\(151\) −17.7897 −1.44771 −0.723854 0.689953i \(-0.757631\pi\)
−0.723854 + 0.689953i \(0.757631\pi\)
\(152\) 0 0
\(153\) 0.309437 0.0250165
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −20.0359 −1.59904 −0.799518 0.600642i \(-0.794912\pi\)
−0.799518 + 0.600642i \(0.794912\pi\)
\(158\) 0 0
\(159\) 11.2998 0.896135
\(160\) 0 0
\(161\) −1.57117 −0.123825
\(162\) 0 0
\(163\) −22.9076 −1.79426 −0.897130 0.441766i \(-0.854352\pi\)
−0.897130 + 0.441766i \(0.854352\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.826887 0.0639864 0.0319932 0.999488i \(-0.489815\pi\)
0.0319932 + 0.999488i \(0.489815\pi\)
\(168\) 0 0
\(169\) −12.0696 −0.928428
\(170\) 0 0
\(171\) −8.88858 −0.679727
\(172\) 0 0
\(173\) −8.03904 −0.611197 −0.305599 0.952160i \(-0.598857\pi\)
−0.305599 + 0.952160i \(0.598857\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −8.06389 −0.606119
\(178\) 0 0
\(179\) 21.6941 1.62149 0.810747 0.585397i \(-0.199061\pi\)
0.810747 + 0.585397i \(0.199061\pi\)
\(180\) 0 0
\(181\) −14.9499 −1.11122 −0.555609 0.831444i \(-0.687515\pi\)
−0.555609 + 0.831444i \(0.687515\pi\)
\(182\) 0 0
\(183\) −19.1622 −1.41651
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.30725 0.0955959
\(188\) 0 0
\(189\) 8.88709 0.646441
\(190\) 0 0
\(191\) 7.86406 0.569024 0.284512 0.958673i \(-0.408169\pi\)
0.284512 + 0.958673i \(0.408169\pi\)
\(192\) 0 0
\(193\) 15.1864 1.09314 0.546571 0.837413i \(-0.315933\pi\)
0.546571 + 0.837413i \(0.315933\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −12.2911 −0.875707 −0.437853 0.899046i \(-0.644261\pi\)
−0.437853 + 0.899046i \(0.644261\pi\)
\(198\) 0 0
\(199\) 4.37123 0.309869 0.154934 0.987925i \(-0.450483\pi\)
0.154934 + 0.987925i \(0.450483\pi\)
\(200\) 0 0
\(201\) −9.10845 −0.642460
\(202\) 0 0
\(203\) −7.48888 −0.525617
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.03063 −0.0716336
\(208\) 0 0
\(209\) −37.5508 −2.59745
\(210\) 0 0
\(211\) 8.93960 0.615427 0.307714 0.951479i \(-0.400436\pi\)
0.307714 + 0.951479i \(0.400436\pi\)
\(212\) 0 0
\(213\) −13.8928 −0.951917
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −8.78516 −0.596375
\(218\) 0 0
\(219\) 8.92518 0.603108
\(220\) 0 0
\(221\) −0.289610 −0.0194813
\(222\) 0 0
\(223\) −11.9586 −0.800806 −0.400403 0.916339i \(-0.631130\pi\)
−0.400403 + 0.916339i \(0.631130\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.85445 0.123084 0.0615419 0.998104i \(-0.480398\pi\)
0.0615419 + 0.998104i \(0.480398\pi\)
\(228\) 0 0
\(229\) −16.5190 −1.09161 −0.545804 0.837913i \(-0.683776\pi\)
−0.545804 + 0.837913i \(0.683776\pi\)
\(230\) 0 0
\(231\) 9.60011 0.631641
\(232\) 0 0
\(233\) −24.5906 −1.61099 −0.805493 0.592606i \(-0.798099\pi\)
−0.805493 + 0.592606i \(0.798099\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 9.75697 0.633783
\(238\) 0 0
\(239\) −27.1169 −1.75405 −0.877025 0.480446i \(-0.840475\pi\)
−0.877025 + 0.480446i \(0.840475\pi\)
\(240\) 0 0
\(241\) −12.8855 −0.830030 −0.415015 0.909815i \(-0.636224\pi\)
−0.415015 + 0.909815i \(0.636224\pi\)
\(242\) 0 0
\(243\) 10.1686 0.652314
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 8.31904 0.529328
\(248\) 0 0
\(249\) 0.260067 0.0164811
\(250\) 0 0
\(251\) 12.4610 0.786533 0.393267 0.919424i \(-0.371345\pi\)
0.393267 + 0.919424i \(0.371345\pi\)
\(252\) 0 0
\(253\) −4.35401 −0.273734
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −13.5073 −0.842564 −0.421282 0.906930i \(-0.638420\pi\)
−0.421282 + 0.906930i \(0.638420\pi\)
\(258\) 0 0
\(259\) 6.88898 0.428060
\(260\) 0 0
\(261\) −4.91243 −0.304072
\(262\) 0 0
\(263\) 27.2579 1.68080 0.840399 0.541969i \(-0.182321\pi\)
0.840399 + 0.541969i \(0.182321\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −2.31380 −0.141603
\(268\) 0 0
\(269\) −17.8409 −1.08778 −0.543889 0.839157i \(-0.683049\pi\)
−0.543889 + 0.839157i \(0.683049\pi\)
\(270\) 0 0
\(271\) −2.31906 −0.140873 −0.0704364 0.997516i \(-0.522439\pi\)
−0.0704364 + 0.997516i \(0.522439\pi\)
\(272\) 0 0
\(273\) −2.12681 −0.128721
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −32.0762 −1.92727 −0.963637 0.267215i \(-0.913897\pi\)
−0.963637 + 0.267215i \(0.913897\pi\)
\(278\) 0 0
\(279\) −5.76273 −0.345006
\(280\) 0 0
\(281\) 12.9448 0.772221 0.386110 0.922453i \(-0.373818\pi\)
0.386110 + 0.922453i \(0.373818\pi\)
\(282\) 0 0
\(283\) −22.6070 −1.34385 −0.671923 0.740621i \(-0.734532\pi\)
−0.671923 + 0.740621i \(0.734532\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.4014 0.613972
\(288\) 0 0
\(289\) −16.9099 −0.994697
\(290\) 0 0
\(291\) −12.9345 −0.758232
\(292\) 0 0
\(293\) −5.61612 −0.328097 −0.164049 0.986452i \(-0.552455\pi\)
−0.164049 + 0.986452i \(0.552455\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 24.6278 1.42905
\(298\) 0 0
\(299\) 0.964590 0.0557837
\(300\) 0 0
\(301\) −2.71794 −0.156659
\(302\) 0 0
\(303\) −1.01010 −0.0580286
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.42467 0.138383 0.0691915 0.997603i \(-0.477958\pi\)
0.0691915 + 0.997603i \(0.477958\pi\)
\(308\) 0 0
\(309\) −12.8565 −0.731383
\(310\) 0 0
\(311\) −3.57886 −0.202938 −0.101469 0.994839i \(-0.532354\pi\)
−0.101469 + 0.994839i \(0.532354\pi\)
\(312\) 0 0
\(313\) 5.51000 0.311443 0.155722 0.987801i \(-0.450230\pi\)
0.155722 + 0.987801i \(0.450230\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.88368 −0.330461 −0.165230 0.986255i \(-0.552837\pi\)
−0.165230 + 0.986255i \(0.552837\pi\)
\(318\) 0 0
\(319\) −20.7531 −1.16195
\(320\) 0 0
\(321\) 17.8906 0.998558
\(322\) 0 0
\(323\) −2.58941 −0.144079
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −4.74356 −0.262320
\(328\) 0 0
\(329\) −1.07992 −0.0595377
\(330\) 0 0
\(331\) 18.6138 1.02311 0.511553 0.859252i \(-0.329070\pi\)
0.511553 + 0.859252i \(0.329070\pi\)
\(332\) 0 0
\(333\) 4.51891 0.247635
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −29.9571 −1.63187 −0.815933 0.578146i \(-0.803776\pi\)
−0.815933 + 0.578146i \(0.803776\pi\)
\(338\) 0 0
\(339\) −22.2495 −1.20843
\(340\) 0 0
\(341\) −24.3453 −1.31837
\(342\) 0 0
\(343\) 18.1178 0.978270
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −26.7363 −1.43528 −0.717640 0.696415i \(-0.754778\pi\)
−0.717640 + 0.696415i \(0.754778\pi\)
\(348\) 0 0
\(349\) 28.7392 1.53837 0.769186 0.639025i \(-0.220662\pi\)
0.769186 + 0.639025i \(0.220662\pi\)
\(350\) 0 0
\(351\) −5.45606 −0.291223
\(352\) 0 0
\(353\) 0.662874 0.0352812 0.0176406 0.999844i \(-0.494385\pi\)
0.0176406 + 0.999844i \(0.494385\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0.661999 0.0350367
\(358\) 0 0
\(359\) 16.0576 0.847485 0.423743 0.905783i \(-0.360716\pi\)
0.423743 + 0.905783i \(0.360716\pi\)
\(360\) 0 0
\(361\) 55.3808 2.91478
\(362\) 0 0
\(363\) 11.1669 0.586113
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −27.5855 −1.43995 −0.719976 0.693999i \(-0.755847\pi\)
−0.719976 + 0.693999i \(0.755847\pi\)
\(368\) 0 0
\(369\) 6.82290 0.355186
\(370\) 0 0
\(371\) −12.6512 −0.656817
\(372\) 0 0
\(373\) −33.1014 −1.71393 −0.856964 0.515376i \(-0.827652\pi\)
−0.856964 + 0.515376i \(0.827652\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.59766 0.236791
\(378\) 0 0
\(379\) −2.17121 −0.111527 −0.0557637 0.998444i \(-0.517759\pi\)
−0.0557637 + 0.998444i \(0.517759\pi\)
\(380\) 0 0
\(381\) −21.3620 −1.09441
\(382\) 0 0
\(383\) 5.52673 0.282403 0.141201 0.989981i \(-0.454903\pi\)
0.141201 + 0.989981i \(0.454903\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.78286 −0.0906281
\(388\) 0 0
\(389\) 17.1036 0.867185 0.433593 0.901109i \(-0.357246\pi\)
0.433593 + 0.901109i \(0.357246\pi\)
\(390\) 0 0
\(391\) −0.300242 −0.0151839
\(392\) 0 0
\(393\) 18.0603 0.911023
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 12.7419 0.639497 0.319748 0.947503i \(-0.396402\pi\)
0.319748 + 0.947503i \(0.396402\pi\)
\(398\) 0 0
\(399\) −19.0159 −0.951987
\(400\) 0 0
\(401\) 14.1997 0.709098 0.354549 0.935038i \(-0.384634\pi\)
0.354549 + 0.935038i \(0.384634\pi\)
\(402\) 0 0
\(403\) 5.39348 0.268668
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 19.0907 0.946289
\(408\) 0 0
\(409\) −0.0235143 −0.00116271 −0.000581354 1.00000i \(-0.500185\pi\)
−0.000581354 1.00000i \(0.500185\pi\)
\(410\) 0 0
\(411\) 23.4966 1.15900
\(412\) 0 0
\(413\) 9.02825 0.444251
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 16.6006 0.812936
\(418\) 0 0
\(419\) 20.2763 0.990562 0.495281 0.868733i \(-0.335065\pi\)
0.495281 + 0.868733i \(0.335065\pi\)
\(420\) 0 0
\(421\) 12.5320 0.610771 0.305386 0.952229i \(-0.401215\pi\)
0.305386 + 0.952229i \(0.401215\pi\)
\(422\) 0 0
\(423\) −0.708385 −0.0344429
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 21.4539 1.03822
\(428\) 0 0
\(429\) −5.89380 −0.284556
\(430\) 0 0
\(431\) 22.8635 1.10130 0.550648 0.834737i \(-0.314381\pi\)
0.550648 + 0.834737i \(0.314381\pi\)
\(432\) 0 0
\(433\) −23.7997 −1.14374 −0.571871 0.820343i \(-0.693782\pi\)
−0.571871 + 0.820343i \(0.693782\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.62443 0.412562
\(438\) 0 0
\(439\) −4.66686 −0.222737 −0.111368 0.993779i \(-0.535523\pi\)
−0.111368 + 0.993779i \(0.535523\pi\)
\(440\) 0 0
\(441\) 4.67022 0.222391
\(442\) 0 0
\(443\) 13.6616 0.649082 0.324541 0.945872i \(-0.394790\pi\)
0.324541 + 0.945872i \(0.394790\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 2.04917 0.0969226
\(448\) 0 0
\(449\) −25.8921 −1.22192 −0.610961 0.791661i \(-0.709217\pi\)
−0.610961 + 0.791661i \(0.709217\pi\)
\(450\) 0 0
\(451\) 28.8241 1.35727
\(452\) 0 0
\(453\) −24.9651 −1.17296
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 12.6856 0.593405 0.296703 0.954970i \(-0.404113\pi\)
0.296703 + 0.954970i \(0.404113\pi\)
\(458\) 0 0
\(459\) 1.69827 0.0792686
\(460\) 0 0
\(461\) 26.5769 1.23781 0.618904 0.785466i \(-0.287577\pi\)
0.618904 + 0.785466i \(0.287577\pi\)
\(462\) 0 0
\(463\) −14.6461 −0.680664 −0.340332 0.940305i \(-0.610539\pi\)
−0.340332 + 0.940305i \(0.610539\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12.7601 −0.590467 −0.295233 0.955425i \(-0.595397\pi\)
−0.295233 + 0.955425i \(0.595397\pi\)
\(468\) 0 0
\(469\) 10.1977 0.470887
\(470\) 0 0
\(471\) −28.1172 −1.29557
\(472\) 0 0
\(473\) −7.53192 −0.346318
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −8.29870 −0.379971
\(478\) 0 0
\(479\) −10.2315 −0.467488 −0.233744 0.972298i \(-0.575098\pi\)
−0.233744 + 0.972298i \(0.575098\pi\)
\(480\) 0 0
\(481\) −4.22936 −0.192842
\(482\) 0 0
\(483\) −2.20489 −0.100326
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 21.8299 0.989207 0.494603 0.869119i \(-0.335313\pi\)
0.494603 + 0.869119i \(0.335313\pi\)
\(488\) 0 0
\(489\) −32.1472 −1.45375
\(490\) 0 0
\(491\) 38.1315 1.72085 0.860426 0.509575i \(-0.170198\pi\)
0.860426 + 0.509575i \(0.170198\pi\)
\(492\) 0 0
\(493\) −1.43108 −0.0644527
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 15.5542 0.697702
\(498\) 0 0
\(499\) −6.36523 −0.284947 −0.142474 0.989799i \(-0.545506\pi\)
−0.142474 + 0.989799i \(0.545506\pi\)
\(500\) 0 0
\(501\) 1.16041 0.0518431
\(502\) 0 0
\(503\) 21.3160 0.950433 0.475217 0.879869i \(-0.342370\pi\)
0.475217 + 0.879869i \(0.342370\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −16.9377 −0.752232
\(508\) 0 0
\(509\) −25.5122 −1.13081 −0.565405 0.824814i \(-0.691280\pi\)
−0.565405 + 0.824814i \(0.691280\pi\)
\(510\) 0 0
\(511\) −9.99254 −0.442044
\(512\) 0 0
\(513\) −48.7828 −2.15381
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −2.99266 −0.131617
\(518\) 0 0
\(519\) −11.2815 −0.495205
\(520\) 0 0
\(521\) −40.7247 −1.78418 −0.892091 0.451856i \(-0.850762\pi\)
−0.892091 + 0.451856i \(0.850762\pi\)
\(522\) 0 0
\(523\) −23.3437 −1.02075 −0.510374 0.859953i \(-0.670493\pi\)
−0.510374 + 0.859953i \(0.670493\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.67879 −0.0731294
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 5.92219 0.257001
\(532\) 0 0
\(533\) −6.38571 −0.276596
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 30.4443 1.31377
\(538\) 0 0
\(539\) 19.7299 0.849826
\(540\) 0 0
\(541\) 1.23303 0.0530123 0.0265061 0.999649i \(-0.491562\pi\)
0.0265061 + 0.999649i \(0.491562\pi\)
\(542\) 0 0
\(543\) −20.9798 −0.900331
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.56470 0.0669018 0.0334509 0.999440i \(-0.489350\pi\)
0.0334509 + 0.999440i \(0.489350\pi\)
\(548\) 0 0
\(549\) 14.0729 0.600618
\(550\) 0 0
\(551\) 41.1078 1.75125
\(552\) 0 0
\(553\) −10.9238 −0.464528
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.4857 0.952749 0.476375 0.879242i \(-0.341951\pi\)
0.476375 + 0.879242i \(0.341951\pi\)
\(558\) 0 0
\(559\) 1.66863 0.0705753
\(560\) 0 0
\(561\) 1.83453 0.0774537
\(562\) 0 0
\(563\) −7.68774 −0.324000 −0.162000 0.986791i \(-0.551794\pi\)
−0.162000 + 0.986791i \(0.551794\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 7.61376 0.319748
\(568\) 0 0
\(569\) 28.1828 1.18149 0.590743 0.806860i \(-0.298835\pi\)
0.590743 + 0.806860i \(0.298835\pi\)
\(570\) 0 0
\(571\) −31.1444 −1.30335 −0.651676 0.758497i \(-0.725934\pi\)
−0.651676 + 0.758497i \(0.725934\pi\)
\(572\) 0 0
\(573\) 11.0360 0.461035
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.20837 −0.0503051 −0.0251525 0.999684i \(-0.508007\pi\)
−0.0251525 + 0.999684i \(0.508007\pi\)
\(578\) 0 0
\(579\) 21.3118 0.885687
\(580\) 0 0
\(581\) −0.291168 −0.0120797
\(582\) 0 0
\(583\) −35.0588 −1.45199
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 13.4162 0.553746 0.276873 0.960906i \(-0.410702\pi\)
0.276873 + 0.960906i \(0.410702\pi\)
\(588\) 0 0
\(589\) 48.2233 1.98701
\(590\) 0 0
\(591\) −17.2487 −0.709516
\(592\) 0 0
\(593\) −5.37465 −0.220711 −0.110355 0.993892i \(-0.535199\pi\)
−0.110355 + 0.993892i \(0.535199\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.13434 0.251062
\(598\) 0 0
\(599\) 18.7001 0.764064 0.382032 0.924149i \(-0.375224\pi\)
0.382032 + 0.924149i \(0.375224\pi\)
\(600\) 0 0
\(601\) 18.4418 0.752255 0.376128 0.926568i \(-0.377255\pi\)
0.376128 + 0.926568i \(0.377255\pi\)
\(602\) 0 0
\(603\) 6.68932 0.272410
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 15.6501 0.635218 0.317609 0.948222i \(-0.397120\pi\)
0.317609 + 0.948222i \(0.397120\pi\)
\(608\) 0 0
\(609\) −10.5095 −0.425865
\(610\) 0 0
\(611\) 0.662995 0.0268219
\(612\) 0 0
\(613\) 2.18552 0.0882725 0.0441363 0.999026i \(-0.485946\pi\)
0.0441363 + 0.999026i \(0.485946\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.07539 0.164069 0.0820346 0.996629i \(-0.473858\pi\)
0.0820346 + 0.996629i \(0.473858\pi\)
\(618\) 0 0
\(619\) 0.0289543 0.00116377 0.000581885 1.00000i \(-0.499815\pi\)
0.000581885 1.00000i \(0.499815\pi\)
\(620\) 0 0
\(621\) −5.65635 −0.226982
\(622\) 0 0
\(623\) 2.59051 0.103787
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −52.6967 −2.10450
\(628\) 0 0
\(629\) 1.31644 0.0524901
\(630\) 0 0
\(631\) −33.3679 −1.32836 −0.664178 0.747575i \(-0.731218\pi\)
−0.664178 + 0.747575i \(0.731218\pi\)
\(632\) 0 0
\(633\) 12.5453 0.498632
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −4.37097 −0.173184
\(638\) 0 0
\(639\) 10.2030 0.403624
\(640\) 0 0
\(641\) 1.56295 0.0617327 0.0308663 0.999524i \(-0.490173\pi\)
0.0308663 + 0.999524i \(0.490173\pi\)
\(642\) 0 0
\(643\) 33.3037 1.31337 0.656684 0.754166i \(-0.271958\pi\)
0.656684 + 0.754166i \(0.271958\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.54230 −0.0606343 −0.0303171 0.999540i \(-0.509652\pi\)
−0.0303171 + 0.999540i \(0.509652\pi\)
\(648\) 0 0
\(649\) 25.0190 0.982081
\(650\) 0 0
\(651\) −12.3286 −0.483195
\(652\) 0 0
\(653\) −13.1195 −0.513407 −0.256703 0.966490i \(-0.582636\pi\)
−0.256703 + 0.966490i \(0.582636\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −6.55473 −0.255724
\(658\) 0 0
\(659\) −7.38016 −0.287490 −0.143745 0.989615i \(-0.545915\pi\)
−0.143745 + 0.989615i \(0.545915\pi\)
\(660\) 0 0
\(661\) −25.0266 −0.973421 −0.486710 0.873563i \(-0.661803\pi\)
−0.486710 + 0.873563i \(0.661803\pi\)
\(662\) 0 0
\(663\) −0.406422 −0.0157841
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 4.76644 0.184557
\(668\) 0 0
\(669\) −16.7820 −0.648830
\(670\) 0 0
\(671\) 59.4527 2.29515
\(672\) 0 0
\(673\) 35.2500 1.35879 0.679395 0.733773i \(-0.262243\pi\)
0.679395 + 0.733773i \(0.262243\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.04850 −0.232463 −0.116231 0.993222i \(-0.537081\pi\)
−0.116231 + 0.993222i \(0.537081\pi\)
\(678\) 0 0
\(679\) 14.4813 0.555741
\(680\) 0 0
\(681\) 2.60242 0.0997251
\(682\) 0 0
\(683\) −32.9347 −1.26021 −0.630105 0.776510i \(-0.716988\pi\)
−0.630105 + 0.776510i \(0.716988\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −23.1819 −0.884443
\(688\) 0 0
\(689\) 7.76696 0.295897
\(690\) 0 0
\(691\) −11.7152 −0.445668 −0.222834 0.974856i \(-0.571531\pi\)
−0.222834 + 0.974856i \(0.571531\pi\)
\(692\) 0 0
\(693\) −7.05040 −0.267823
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1.98764 0.0752872
\(698\) 0 0
\(699\) −34.5091 −1.30525
\(700\) 0 0
\(701\) 43.8861 1.65756 0.828779 0.559577i \(-0.189036\pi\)
0.828779 + 0.559577i \(0.189036\pi\)
\(702\) 0 0
\(703\) −37.8148 −1.42621
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.13090 0.0425317
\(708\) 0 0
\(709\) 30.2394 1.13567 0.567833 0.823144i \(-0.307782\pi\)
0.567833 + 0.823144i \(0.307782\pi\)
\(710\) 0 0
\(711\) −7.16561 −0.268731
\(712\) 0 0
\(713\) 5.59148 0.209402
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −38.0544 −1.42117
\(718\) 0 0
\(719\) −27.5338 −1.02684 −0.513419 0.858138i \(-0.671621\pi\)
−0.513419 + 0.858138i \(0.671621\pi\)
\(720\) 0 0
\(721\) 14.3941 0.536063
\(722\) 0 0
\(723\) −18.0828 −0.672507
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −33.7995 −1.25356 −0.626778 0.779198i \(-0.715627\pi\)
−0.626778 + 0.779198i \(0.715627\pi\)
\(728\) 0 0
\(729\) 28.8078 1.06695
\(730\) 0 0
\(731\) −0.519382 −0.0192100
\(732\) 0 0
\(733\) 48.3133 1.78449 0.892246 0.451550i \(-0.149129\pi\)
0.892246 + 0.451550i \(0.149129\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 28.2598 1.04096
\(738\) 0 0
\(739\) 22.7004 0.835048 0.417524 0.908666i \(-0.362898\pi\)
0.417524 + 0.908666i \(0.362898\pi\)
\(740\) 0 0
\(741\) 11.6745 0.428872
\(742\) 0 0
\(743\) −20.9953 −0.770242 −0.385121 0.922866i \(-0.625840\pi\)
−0.385121 + 0.922866i \(0.625840\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.190995 −0.00698816
\(748\) 0 0
\(749\) −20.0302 −0.731887
\(750\) 0 0
\(751\) 21.3909 0.780565 0.390283 0.920695i \(-0.372377\pi\)
0.390283 + 0.920695i \(0.372377\pi\)
\(752\) 0 0
\(753\) 17.4871 0.637266
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −54.7364 −1.98943 −0.994715 0.102676i \(-0.967260\pi\)
−0.994715 + 0.102676i \(0.967260\pi\)
\(758\) 0 0
\(759\) −6.11017 −0.221785
\(760\) 0 0
\(761\) 7.87321 0.285404 0.142702 0.989766i \(-0.454421\pi\)
0.142702 + 0.989766i \(0.454421\pi\)
\(762\) 0 0
\(763\) 5.31084 0.192265
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.54272 −0.200136
\(768\) 0 0
\(769\) 32.7134 1.17968 0.589838 0.807522i \(-0.299192\pi\)
0.589838 + 0.807522i \(0.299192\pi\)
\(770\) 0 0
\(771\) −18.9554 −0.682663
\(772\) 0 0
\(773\) 2.88974 0.103937 0.0519684 0.998649i \(-0.483450\pi\)
0.0519684 + 0.998649i \(0.483450\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 9.66760 0.346823
\(778\) 0 0
\(779\) −57.0949 −2.04564
\(780\) 0 0
\(781\) 43.1037 1.54237
\(782\) 0 0
\(783\) −26.9607 −0.963496
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 46.4472 1.65566 0.827832 0.560976i \(-0.189574\pi\)
0.827832 + 0.560976i \(0.189574\pi\)
\(788\) 0 0
\(789\) 38.2523 1.36182
\(790\) 0 0
\(791\) 24.9104 0.885710
\(792\) 0 0
\(793\) −13.1712 −0.467723
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −45.6713 −1.61776 −0.808880 0.587974i \(-0.799926\pi\)
−0.808880 + 0.587974i \(0.799926\pi\)
\(798\) 0 0
\(799\) −0.206366 −0.00730070
\(800\) 0 0
\(801\) 1.69928 0.0600411
\(802\) 0 0
\(803\) −27.6912 −0.977202
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −25.0369 −0.881340
\(808\) 0 0
\(809\) 37.7080 1.32574 0.662872 0.748733i \(-0.269337\pi\)
0.662872 + 0.748733i \(0.269337\pi\)
\(810\) 0 0
\(811\) −9.02541 −0.316925 −0.158462 0.987365i \(-0.550654\pi\)
−0.158462 + 0.987365i \(0.550654\pi\)
\(812\) 0 0
\(813\) −3.25444 −0.114138
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 14.9192 0.521958
\(818\) 0 0
\(819\) 1.56195 0.0545790
\(820\) 0 0
\(821\) −34.2481 −1.19527 −0.597634 0.801769i \(-0.703892\pi\)
−0.597634 + 0.801769i \(0.703892\pi\)
\(822\) 0 0
\(823\) 10.1842 0.354999 0.177499 0.984121i \(-0.443199\pi\)
0.177499 + 0.984121i \(0.443199\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 34.0710 1.18477 0.592383 0.805656i \(-0.298187\pi\)
0.592383 + 0.805656i \(0.298187\pi\)
\(828\) 0 0
\(829\) −24.5131 −0.851376 −0.425688 0.904870i \(-0.639968\pi\)
−0.425688 + 0.904870i \(0.639968\pi\)
\(830\) 0 0
\(831\) −45.0140 −1.56152
\(832\) 0 0
\(833\) 1.36052 0.0471393
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −31.6274 −1.09320
\(838\) 0 0
\(839\) −19.2362 −0.664107 −0.332053 0.943261i \(-0.607741\pi\)
−0.332053 + 0.943261i \(0.607741\pi\)
\(840\) 0 0
\(841\) −6.28105 −0.216588
\(842\) 0 0
\(843\) 18.1660 0.625669
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −12.5024 −0.429588
\(848\) 0 0
\(849\) −31.7254 −1.08881
\(850\) 0 0
\(851\) −4.38462 −0.150303
\(852\) 0 0
\(853\) −34.8964 −1.19483 −0.597415 0.801932i \(-0.703805\pi\)
−0.597415 + 0.801932i \(0.703805\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −41.9040 −1.43141 −0.715706 0.698401i \(-0.753895\pi\)
−0.715706 + 0.698401i \(0.753895\pi\)
\(858\) 0 0
\(859\) 19.1286 0.652658 0.326329 0.945256i \(-0.394188\pi\)
0.326329 + 0.945256i \(0.394188\pi\)
\(860\) 0 0
\(861\) 14.5967 0.497453
\(862\) 0 0
\(863\) −0.509621 −0.0173477 −0.00867385 0.999962i \(-0.502761\pi\)
−0.00867385 + 0.999962i \(0.502761\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −23.7303 −0.805924
\(868\) 0 0
\(869\) −30.2719 −1.02691
\(870\) 0 0
\(871\) −6.26070 −0.212136
\(872\) 0 0
\(873\) 9.49919 0.321499
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −15.6710 −0.529171 −0.264586 0.964362i \(-0.585235\pi\)
−0.264586 + 0.964362i \(0.585235\pi\)
\(878\) 0 0
\(879\) −7.88135 −0.265831
\(880\) 0 0
\(881\) −2.00846 −0.0676667 −0.0338333 0.999427i \(-0.510772\pi\)
−0.0338333 + 0.999427i \(0.510772\pi\)
\(882\) 0 0
\(883\) 16.7848 0.564854 0.282427 0.959289i \(-0.408861\pi\)
0.282427 + 0.959289i \(0.408861\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −51.7294 −1.73690 −0.868452 0.495774i \(-0.834884\pi\)
−0.868452 + 0.495774i \(0.834884\pi\)
\(888\) 0 0
\(889\) 23.9167 0.802140
\(890\) 0 0
\(891\) 21.0992 0.706849
\(892\) 0 0
\(893\) 5.92786 0.198368
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 1.35365 0.0451971
\(898\) 0 0
\(899\) 26.6514 0.888875
\(900\) 0 0
\(901\) −2.41757 −0.0805409
\(902\) 0 0
\(903\) −3.81420 −0.126929
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 29.0849 0.965747 0.482874 0.875690i \(-0.339593\pi\)
0.482874 + 0.875690i \(0.339593\pi\)
\(908\) 0 0
\(909\) 0.741825 0.0246048
\(910\) 0 0
\(911\) −26.3517 −0.873070 −0.436535 0.899687i \(-0.643795\pi\)
−0.436535 + 0.899687i \(0.643795\pi\)
\(912\) 0 0
\(913\) −0.806883 −0.0267039
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −20.2202 −0.667728
\(918\) 0 0
\(919\) 46.0148 1.51789 0.758945 0.651155i \(-0.225715\pi\)
0.758945 + 0.651155i \(0.225715\pi\)
\(920\) 0 0
\(921\) 3.40264 0.112121
\(922\) 0 0
\(923\) −9.54922 −0.314316
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 9.44196 0.310115
\(928\) 0 0
\(929\) 26.1770 0.858838 0.429419 0.903105i \(-0.358718\pi\)
0.429419 + 0.903105i \(0.358718\pi\)
\(930\) 0 0
\(931\) −39.0810 −1.28083
\(932\) 0 0
\(933\) −5.02237 −0.164425
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 44.4429 1.45189 0.725944 0.687754i \(-0.241403\pi\)
0.725944 + 0.687754i \(0.241403\pi\)
\(938\) 0 0
\(939\) 7.73242 0.252338
\(940\) 0 0
\(941\) 7.07346 0.230588 0.115294 0.993331i \(-0.463219\pi\)
0.115294 + 0.993331i \(0.463219\pi\)
\(942\) 0 0
\(943\) −6.62014 −0.215581
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −14.4533 −0.469670 −0.234835 0.972035i \(-0.575455\pi\)
−0.234835 + 0.972035i \(0.575455\pi\)
\(948\) 0 0
\(949\) 6.13473 0.199142
\(950\) 0 0
\(951\) −8.25683 −0.267746
\(952\) 0 0
\(953\) 32.3773 1.04880 0.524402 0.851471i \(-0.324289\pi\)
0.524402 + 0.851471i \(0.324289\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −29.1237 −0.941437
\(958\) 0 0
\(959\) −26.3065 −0.849482
\(960\) 0 0
\(961\) 0.264608 0.00853575
\(962\) 0 0
\(963\) −13.1390 −0.423400
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −25.8993 −0.832865 −0.416433 0.909167i \(-0.636720\pi\)
−0.416433 + 0.909167i \(0.636720\pi\)
\(968\) 0 0
\(969\) −3.63383 −0.116736
\(970\) 0 0
\(971\) 25.2153 0.809197 0.404599 0.914494i \(-0.367411\pi\)
0.404599 + 0.914494i \(0.367411\pi\)
\(972\) 0 0
\(973\) −18.5859 −0.595837
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 5.64235 0.180515 0.0902573 0.995918i \(-0.471231\pi\)
0.0902573 + 0.995918i \(0.471231\pi\)
\(978\) 0 0
\(979\) 7.17880 0.229436
\(980\) 0 0
\(981\) 3.48371 0.111226
\(982\) 0 0
\(983\) −37.0322 −1.18114 −0.590571 0.806986i \(-0.701097\pi\)
−0.590571 + 0.806986i \(0.701097\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −1.51549 −0.0482387
\(988\) 0 0
\(989\) 1.72988 0.0550070
\(990\) 0 0
\(991\) −7.14822 −0.227071 −0.113535 0.993534i \(-0.536218\pi\)
−0.113535 + 0.993534i \(0.536218\pi\)
\(992\) 0 0
\(993\) 26.1215 0.828942
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −4.96521 −0.157250 −0.0786249 0.996904i \(-0.525053\pi\)
−0.0786249 + 0.996904i \(0.525053\pi\)
\(998\) 0 0
\(999\) 24.8010 0.784667
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 9200.2.a.cz.1.6 7
4.3 odd 2 4600.2.a.bi.1.2 7
5.2 odd 4 1840.2.e.g.369.5 14
5.3 odd 4 1840.2.e.g.369.10 14
5.4 even 2 9200.2.a.dc.1.2 7
20.3 even 4 920.2.e.b.369.5 14
20.7 even 4 920.2.e.b.369.10 yes 14
20.19 odd 2 4600.2.a.bh.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.e.b.369.5 14 20.3 even 4
920.2.e.b.369.10 yes 14 20.7 even 4
1840.2.e.g.369.5 14 5.2 odd 4
1840.2.e.g.369.10 14 5.3 odd 4
4600.2.a.bh.1.6 7 20.19 odd 2
4600.2.a.bi.1.2 7 4.3 odd 2
9200.2.a.cz.1.6 7 1.1 even 1 trivial
9200.2.a.dc.1.2 7 5.4 even 2