Properties

Label 9200.2.a.cx.1.3
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $1$
Dimension $6$
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: \(6\)
Coefficient field: 6.6.143376304.1
Defining polynomial: \( x^{6} - 12x^{4} + 22x^{2} - 6x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 460)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.420790\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73961 q^{3} -3.32224 q^{7} +0.0262434 q^{9} +O(q^{10})\) \(q-1.73961 q^{3} -3.32224 q^{7} +0.0262434 q^{9} -5.77103 q^{11} +1.10197 q^{13} +0.893847 q^{17} -2.42839 q^{19} +5.77940 q^{21} -1.00000 q^{23} +5.17318 q^{27} +4.11268 q^{29} +9.54624 q^{31} +10.0393 q^{33} -7.69904 q^{37} -1.91700 q^{39} +0.00418347 q^{41} +9.97045 q^{43} -10.0079 q^{47} +4.03726 q^{49} -1.55495 q^{51} +6.25169 q^{53} +4.22445 q^{57} +10.7764 q^{59} +10.5929 q^{61} -0.0871868 q^{63} -10.9529 q^{67} +1.73961 q^{69} +12.9170 q^{71} +1.89943 q^{73} +19.1727 q^{77} +0.216085 q^{79} -9.07804 q^{81} +5.38967 q^{83} -7.15446 q^{87} +6.00657 q^{89} -3.66100 q^{91} -16.6067 q^{93} +2.08104 q^{97} -0.151451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 4 q^{3} - 9 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 4 q^{3} - 9 q^{7} + 10 q^{9} - 2 q^{11} + 8 q^{13} + 5 q^{17} - 4 q^{19} - 6 q^{23} - 22 q^{27} + 5 q^{29} - 9 q^{31} - 10 q^{33} + 21 q^{37} + 8 q^{39} - q^{41} - 16 q^{43} - 16 q^{47} + 19 q^{49} + 12 q^{51} - q^{53} + 12 q^{57} + 11 q^{59} - 4 q^{61} - 19 q^{63} - 25 q^{67} + 4 q^{69} + 17 q^{71} - 14 q^{73} + 20 q^{77} - 10 q^{79} + 14 q^{81} - 21 q^{83} - 64 q^{87} - 24 q^{89} + 4 q^{91} + 4 q^{97} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) −1.73961 −1.00436 −0.502182 0.864762i \(-0.667469\pi\)
−0.502182 + 0.864762i \(0.667469\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.32224 −1.25569 −0.627844 0.778339i \(-0.716062\pi\)
−0.627844 + 0.778339i \(0.716062\pi\)
\(8\) 0 0
\(9\) 0.0262434 0.00874780
\(10\) 0 0
\(11\) −5.77103 −1.74003 −0.870016 0.493024i \(-0.835891\pi\)
−0.870016 + 0.493024i \(0.835891\pi\)
\(12\) 0 0
\(13\) 1.10197 0.305631 0.152816 0.988255i \(-0.451166\pi\)
0.152816 + 0.988255i \(0.451166\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.893847 0.216790 0.108395 0.994108i \(-0.465429\pi\)
0.108395 + 0.994108i \(0.465429\pi\)
\(18\) 0 0
\(19\) −2.42839 −0.557111 −0.278555 0.960420i \(-0.589856\pi\)
−0.278555 + 0.960420i \(0.589856\pi\)
\(20\) 0 0
\(21\) 5.77940 1.26117
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.17318 0.995578
\(28\) 0 0
\(29\) 4.11268 0.763705 0.381853 0.924223i \(-0.375286\pi\)
0.381853 + 0.924223i \(0.375286\pi\)
\(30\) 0 0
\(31\) 9.54624 1.71456 0.857278 0.514854i \(-0.172154\pi\)
0.857278 + 0.514854i \(0.172154\pi\)
\(32\) 0 0
\(33\) 10.0393 1.74763
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7.69904 −1.26572 −0.632858 0.774268i \(-0.718118\pi\)
−0.632858 + 0.774268i \(0.718118\pi\)
\(38\) 0 0
\(39\) −1.91700 −0.306965
\(40\) 0 0
\(41\) 0.00418347 0.000653348 0 0.000326674 1.00000i \(-0.499896\pi\)
0.000326674 1.00000i \(0.499896\pi\)
\(42\) 0 0
\(43\) 9.97045 1.52048 0.760240 0.649643i \(-0.225081\pi\)
0.760240 + 0.649643i \(0.225081\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.0079 −1.45981 −0.729903 0.683551i \(-0.760435\pi\)
−0.729903 + 0.683551i \(0.760435\pi\)
\(48\) 0 0
\(49\) 4.03726 0.576751
\(50\) 0 0
\(51\) −1.55495 −0.217736
\(52\) 0 0
\(53\) 6.25169 0.858735 0.429368 0.903130i \(-0.358736\pi\)
0.429368 + 0.903130i \(0.358736\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.22445 0.559542
\(58\) 0 0
\(59\) 10.7764 1.40297 0.701486 0.712684i \(-0.252520\pi\)
0.701486 + 0.712684i \(0.252520\pi\)
\(60\) 0 0
\(61\) 10.5929 1.35628 0.678140 0.734932i \(-0.262786\pi\)
0.678140 + 0.734932i \(0.262786\pi\)
\(62\) 0 0
\(63\) −0.0871868 −0.0109845
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −10.9529 −1.33811 −0.669055 0.743213i \(-0.733301\pi\)
−0.669055 + 0.743213i \(0.733301\pi\)
\(68\) 0 0
\(69\) 1.73961 0.209424
\(70\) 0 0
\(71\) 12.9170 1.53296 0.766481 0.642267i \(-0.222006\pi\)
0.766481 + 0.642267i \(0.222006\pi\)
\(72\) 0 0
\(73\) 1.89943 0.222311 0.111156 0.993803i \(-0.464545\pi\)
0.111156 + 0.993803i \(0.464545\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 19.1727 2.18494
\(78\) 0 0
\(79\) 0.216085 0.0243114 0.0121557 0.999926i \(-0.496131\pi\)
0.0121557 + 0.999926i \(0.496131\pi\)
\(80\) 0 0
\(81\) −9.07804 −1.00867
\(82\) 0 0
\(83\) 5.38967 0.591593 0.295796 0.955251i \(-0.404415\pi\)
0.295796 + 0.955251i \(0.404415\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −7.15446 −0.767038
\(88\) 0 0
\(89\) 6.00657 0.636696 0.318348 0.947974i \(-0.396872\pi\)
0.318348 + 0.947974i \(0.396872\pi\)
\(90\) 0 0
\(91\) −3.66100 −0.383777
\(92\) 0 0
\(93\) −16.6067 −1.72204
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.08104 0.211297 0.105649 0.994404i \(-0.466308\pi\)
0.105649 + 0.994404i \(0.466308\pi\)
\(98\) 0 0
\(99\) −0.151451 −0.0152214
\(100\) 0 0
\(101\) −13.1576 −1.30923 −0.654617 0.755961i \(-0.727170\pi\)
−0.654617 + 0.755961i \(0.727170\pi\)
\(102\) 0 0
\(103\) −18.0956 −1.78301 −0.891507 0.453008i \(-0.850351\pi\)
−0.891507 + 0.453008i \(0.850351\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.97263 −0.674069 −0.337035 0.941492i \(-0.609424\pi\)
−0.337035 + 0.941492i \(0.609424\pi\)
\(108\) 0 0
\(109\) 10.2873 0.985344 0.492672 0.870215i \(-0.336020\pi\)
0.492672 + 0.870215i \(0.336020\pi\)
\(110\) 0 0
\(111\) 13.3933 1.27124
\(112\) 0 0
\(113\) −5.53454 −0.520646 −0.260323 0.965522i \(-0.583829\pi\)
−0.260323 + 0.965522i \(0.583829\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.0289194 0.00267360
\(118\) 0 0
\(119\) −2.96957 −0.272220
\(120\) 0 0
\(121\) 22.3048 2.02771
\(122\) 0 0
\(123\) −0.00727760 −0.000656199 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −11.1580 −0.990110 −0.495055 0.868862i \(-0.664852\pi\)
−0.495055 + 0.868862i \(0.664852\pi\)
\(128\) 0 0
\(129\) −17.3447 −1.52712
\(130\) 0 0
\(131\) 15.0421 1.31423 0.657117 0.753789i \(-0.271776\pi\)
0.657117 + 0.753789i \(0.271776\pi\)
\(132\) 0 0
\(133\) 8.06769 0.699557
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.21231 0.189010 0.0945050 0.995524i \(-0.469873\pi\)
0.0945050 + 0.995524i \(0.469873\pi\)
\(138\) 0 0
\(139\) 6.53729 0.554486 0.277243 0.960800i \(-0.410579\pi\)
0.277243 + 0.960800i \(0.410579\pi\)
\(140\) 0 0
\(141\) 17.4099 1.46618
\(142\) 0 0
\(143\) −6.35950 −0.531808
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −7.02326 −0.579269
\(148\) 0 0
\(149\) −11.1844 −0.916263 −0.458131 0.888884i \(-0.651481\pi\)
−0.458131 + 0.888884i \(0.651481\pi\)
\(150\) 0 0
\(151\) 1.29176 0.105122 0.0525610 0.998618i \(-0.483262\pi\)
0.0525610 + 0.998618i \(0.483262\pi\)
\(152\) 0 0
\(153\) 0.0234576 0.00189643
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 11.0465 0.881609 0.440805 0.897603i \(-0.354693\pi\)
0.440805 + 0.897603i \(0.354693\pi\)
\(158\) 0 0
\(159\) −10.8755 −0.862483
\(160\) 0 0
\(161\) 3.32224 0.261829
\(162\) 0 0
\(163\) −5.04265 −0.394971 −0.197485 0.980306i \(-0.563277\pi\)
−0.197485 + 0.980306i \(0.563277\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.20759 −0.0934465 −0.0467232 0.998908i \(-0.514878\pi\)
−0.0467232 + 0.998908i \(0.514878\pi\)
\(168\) 0 0
\(169\) −11.7857 −0.906590
\(170\) 0 0
\(171\) −0.0637292 −0.00487349
\(172\) 0 0
\(173\) −15.7392 −1.19663 −0.598313 0.801262i \(-0.704162\pi\)
−0.598313 + 0.801262i \(0.704162\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −18.7468 −1.40909
\(178\) 0 0
\(179\) −6.61963 −0.494774 −0.247387 0.968917i \(-0.579572\pi\)
−0.247387 + 0.968917i \(0.579572\pi\)
\(180\) 0 0
\(181\) −16.0433 −1.19249 −0.596245 0.802803i \(-0.703341\pi\)
−0.596245 + 0.802803i \(0.703341\pi\)
\(182\) 0 0
\(183\) −18.4275 −1.36220
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −5.15842 −0.377221
\(188\) 0 0
\(189\) −17.1865 −1.25014
\(190\) 0 0
\(191\) −0.295590 −0.0213881 −0.0106941 0.999943i \(-0.503404\pi\)
−0.0106941 + 0.999943i \(0.503404\pi\)
\(192\) 0 0
\(193\) −1.42564 −0.102620 −0.0513101 0.998683i \(-0.516340\pi\)
−0.0513101 + 0.998683i \(0.516340\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.60107 −0.612801 −0.306401 0.951903i \(-0.599125\pi\)
−0.306401 + 0.951903i \(0.599125\pi\)
\(198\) 0 0
\(199\) −3.81515 −0.270449 −0.135224 0.990815i \(-0.543176\pi\)
−0.135224 + 0.990815i \(0.543176\pi\)
\(200\) 0 0
\(201\) 19.0538 1.34395
\(202\) 0 0
\(203\) −13.6633 −0.958975
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.0262434 −0.00182404
\(208\) 0 0
\(209\) 14.0143 0.969390
\(210\) 0 0
\(211\) −1.32370 −0.0911273 −0.0455637 0.998961i \(-0.514508\pi\)
−0.0455637 + 0.998961i \(0.514508\pi\)
\(212\) 0 0
\(213\) −22.4705 −1.53965
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −31.7149 −2.15295
\(218\) 0 0
\(219\) −3.30427 −0.223282
\(220\) 0 0
\(221\) 0.984992 0.0662577
\(222\) 0 0
\(223\) −25.1286 −1.68274 −0.841368 0.540462i \(-0.818249\pi\)
−0.841368 + 0.540462i \(0.818249\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 23.8021 1.57980 0.789900 0.613236i \(-0.210133\pi\)
0.789900 + 0.613236i \(0.210133\pi\)
\(228\) 0 0
\(229\) −0.789351 −0.0521618 −0.0260809 0.999660i \(-0.508303\pi\)
−0.0260809 + 0.999660i \(0.508303\pi\)
\(230\) 0 0
\(231\) −33.3531 −2.19447
\(232\) 0 0
\(233\) −20.8101 −1.36331 −0.681656 0.731672i \(-0.738740\pi\)
−0.681656 + 0.731672i \(0.738740\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −0.375903 −0.0244175
\(238\) 0 0
\(239\) 25.2398 1.63262 0.816312 0.577611i \(-0.196015\pi\)
0.816312 + 0.577611i \(0.196015\pi\)
\(240\) 0 0
\(241\) 5.27710 0.339928 0.169964 0.985450i \(-0.445635\pi\)
0.169964 + 0.985450i \(0.445635\pi\)
\(242\) 0 0
\(243\) 0.272722 0.0174951
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.67601 −0.170270
\(248\) 0 0
\(249\) −9.37592 −0.594175
\(250\) 0 0
\(251\) 10.8439 0.684461 0.342230 0.939616i \(-0.388818\pi\)
0.342230 + 0.939616i \(0.388818\pi\)
\(252\) 0 0
\(253\) 5.77103 0.362822
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.6238 1.16172 0.580859 0.814004i \(-0.302717\pi\)
0.580859 + 0.814004i \(0.302717\pi\)
\(258\) 0 0
\(259\) 25.5781 1.58934
\(260\) 0 0
\(261\) 0.107931 0.00668074
\(262\) 0 0
\(263\) 19.4370 1.19854 0.599269 0.800548i \(-0.295458\pi\)
0.599269 + 0.800548i \(0.295458\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −10.4491 −0.639474
\(268\) 0 0
\(269\) −3.80493 −0.231991 −0.115995 0.993250i \(-0.537006\pi\)
−0.115995 + 0.993250i \(0.537006\pi\)
\(270\) 0 0
\(271\) 18.2100 1.10618 0.553089 0.833122i \(-0.313449\pi\)
0.553089 + 0.833122i \(0.313449\pi\)
\(272\) 0 0
\(273\) 6.36872 0.385452
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 14.7624 0.886988 0.443494 0.896277i \(-0.353739\pi\)
0.443494 + 0.896277i \(0.353739\pi\)
\(278\) 0 0
\(279\) 0.250526 0.0149986
\(280\) 0 0
\(281\) −6.29738 −0.375670 −0.187835 0.982201i \(-0.560147\pi\)
−0.187835 + 0.982201i \(0.560147\pi\)
\(282\) 0 0
\(283\) −28.4443 −1.69084 −0.845418 0.534105i \(-0.820649\pi\)
−0.845418 + 0.534105i \(0.820649\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.0138985 −0.000820401 0
\(288\) 0 0
\(289\) −16.2010 −0.953002
\(290\) 0 0
\(291\) −3.62020 −0.212220
\(292\) 0 0
\(293\) 14.4907 0.846556 0.423278 0.906000i \(-0.360879\pi\)
0.423278 + 0.906000i \(0.360879\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −29.8546 −1.73234
\(298\) 0 0
\(299\) −1.10197 −0.0637285
\(300\) 0 0
\(301\) −33.1242 −1.90925
\(302\) 0 0
\(303\) 22.8892 1.31495
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 30.4707 1.73905 0.869527 0.493885i \(-0.164424\pi\)
0.869527 + 0.493885i \(0.164424\pi\)
\(308\) 0 0
\(309\) 31.4793 1.79080
\(310\) 0 0
\(311\) −20.9031 −1.18531 −0.592654 0.805457i \(-0.701920\pi\)
−0.592654 + 0.805457i \(0.701920\pi\)
\(312\) 0 0
\(313\) 14.3614 0.811757 0.405878 0.913927i \(-0.366966\pi\)
0.405878 + 0.913927i \(0.366966\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 33.6939 1.89244 0.946220 0.323525i \(-0.104868\pi\)
0.946220 + 0.323525i \(0.104868\pi\)
\(318\) 0 0
\(319\) −23.7344 −1.32887
\(320\) 0 0
\(321\) 12.1297 0.677011
\(322\) 0 0
\(323\) −2.17061 −0.120776
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −17.8959 −0.989644
\(328\) 0 0
\(329\) 33.2487 1.83306
\(330\) 0 0
\(331\) −9.82292 −0.539917 −0.269958 0.962872i \(-0.587010\pi\)
−0.269958 + 0.962872i \(0.587010\pi\)
\(332\) 0 0
\(333\) −0.202049 −0.0110722
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −13.2410 −0.721286 −0.360643 0.932704i \(-0.617443\pi\)
−0.360643 + 0.932704i \(0.617443\pi\)
\(338\) 0 0
\(339\) 9.62795 0.522918
\(340\) 0 0
\(341\) −55.0917 −2.98338
\(342\) 0 0
\(343\) 9.84292 0.531468
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9.15627 0.491534 0.245767 0.969329i \(-0.420960\pi\)
0.245767 + 0.969329i \(0.420960\pi\)
\(348\) 0 0
\(349\) 25.7744 1.37967 0.689836 0.723966i \(-0.257683\pi\)
0.689836 + 0.723966i \(0.257683\pi\)
\(350\) 0 0
\(351\) 5.70068 0.304280
\(352\) 0 0
\(353\) −2.40654 −0.128087 −0.0640436 0.997947i \(-0.520400\pi\)
−0.0640436 + 0.997947i \(0.520400\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 5.16590 0.273408
\(358\) 0 0
\(359\) −21.5236 −1.13597 −0.567985 0.823039i \(-0.692277\pi\)
−0.567985 + 0.823039i \(0.692277\pi\)
\(360\) 0 0
\(361\) −13.1029 −0.689628
\(362\) 0 0
\(363\) −38.8016 −2.03656
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 6.47203 0.337837 0.168919 0.985630i \(-0.445972\pi\)
0.168919 + 0.985630i \(0.445972\pi\)
\(368\) 0 0
\(369\) 0.000109788 0 5.71536e−6 0
\(370\) 0 0
\(371\) −20.7696 −1.07830
\(372\) 0 0
\(373\) −27.7866 −1.43874 −0.719368 0.694629i \(-0.755569\pi\)
−0.719368 + 0.694629i \(0.755569\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.53204 0.233412
\(378\) 0 0
\(379\) −7.63904 −0.392391 −0.196196 0.980565i \(-0.562859\pi\)
−0.196196 + 0.980565i \(0.562859\pi\)
\(380\) 0 0
\(381\) 19.4105 0.994432
\(382\) 0 0
\(383\) 19.4206 0.992348 0.496174 0.868223i \(-0.334738\pi\)
0.496174 + 0.868223i \(0.334738\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.261659 0.0133009
\(388\) 0 0
\(389\) −26.1255 −1.32461 −0.662306 0.749233i \(-0.730422\pi\)
−0.662306 + 0.749233i \(0.730422\pi\)
\(390\) 0 0
\(391\) −0.893847 −0.0452038
\(392\) 0 0
\(393\) −26.1674 −1.31997
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −11.5388 −0.579117 −0.289558 0.957160i \(-0.593508\pi\)
−0.289558 + 0.957160i \(0.593508\pi\)
\(398\) 0 0
\(399\) −14.0346 −0.702610
\(400\) 0 0
\(401\) −0.188549 −0.00941568 −0.00470784 0.999989i \(-0.501499\pi\)
−0.00470784 + 0.999989i \(0.501499\pi\)
\(402\) 0 0
\(403\) 10.5197 0.524022
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 44.4314 2.20238
\(408\) 0 0
\(409\) −8.48327 −0.419471 −0.209735 0.977758i \(-0.567260\pi\)
−0.209735 + 0.977758i \(0.567260\pi\)
\(410\) 0 0
\(411\) −3.84855 −0.189835
\(412\) 0 0
\(413\) −35.8018 −1.76169
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −11.3723 −0.556906
\(418\) 0 0
\(419\) 2.15604 0.105329 0.0526647 0.998612i \(-0.483229\pi\)
0.0526647 + 0.998612i \(0.483229\pi\)
\(420\) 0 0
\(421\) 8.01842 0.390794 0.195397 0.980724i \(-0.437400\pi\)
0.195397 + 0.980724i \(0.437400\pi\)
\(422\) 0 0
\(423\) −0.262642 −0.0127701
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −35.1921 −1.70307
\(428\) 0 0
\(429\) 11.0630 0.534129
\(430\) 0 0
\(431\) 15.3343 0.738629 0.369315 0.929304i \(-0.379592\pi\)
0.369315 + 0.929304i \(0.379592\pi\)
\(432\) 0 0
\(433\) 16.3093 0.783777 0.391888 0.920013i \(-0.371822\pi\)
0.391888 + 0.920013i \(0.371822\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.42839 0.116166
\(438\) 0 0
\(439\) 23.9534 1.14323 0.571617 0.820520i \(-0.306316\pi\)
0.571617 + 0.820520i \(0.306316\pi\)
\(440\) 0 0
\(441\) 0.105951 0.00504531
\(442\) 0 0
\(443\) 29.2360 1.38905 0.694523 0.719471i \(-0.255616\pi\)
0.694523 + 0.719471i \(0.255616\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 19.4565 0.920262
\(448\) 0 0
\(449\) −21.2244 −1.00164 −0.500822 0.865550i \(-0.666969\pi\)
−0.500822 + 0.865550i \(0.666969\pi\)
\(450\) 0 0
\(451\) −0.0241429 −0.00113685
\(452\) 0 0
\(453\) −2.24716 −0.105581
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −31.5959 −1.47799 −0.738996 0.673710i \(-0.764700\pi\)
−0.738996 + 0.673710i \(0.764700\pi\)
\(458\) 0 0
\(459\) 4.62403 0.215831
\(460\) 0 0
\(461\) 16.4858 0.767820 0.383910 0.923370i \(-0.374577\pi\)
0.383910 + 0.923370i \(0.374577\pi\)
\(462\) 0 0
\(463\) −30.1555 −1.40144 −0.700722 0.713435i \(-0.747139\pi\)
−0.700722 + 0.713435i \(0.747139\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.89645 0.365404 0.182702 0.983168i \(-0.441516\pi\)
0.182702 + 0.983168i \(0.441516\pi\)
\(468\) 0 0
\(469\) 36.3882 1.68025
\(470\) 0 0
\(471\) −19.2167 −0.885457
\(472\) 0 0
\(473\) −57.5398 −2.64568
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.164066 0.00751205
\(478\) 0 0
\(479\) −39.5234 −1.80587 −0.902935 0.429778i \(-0.858592\pi\)
−0.902935 + 0.429778i \(0.858592\pi\)
\(480\) 0 0
\(481\) −8.48411 −0.386842
\(482\) 0 0
\(483\) −5.77940 −0.262972
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −3.20444 −0.145207 −0.0726035 0.997361i \(-0.523131\pi\)
−0.0726035 + 0.997361i \(0.523131\pi\)
\(488\) 0 0
\(489\) 8.77224 0.396695
\(490\) 0 0
\(491\) −34.8865 −1.57441 −0.787203 0.616694i \(-0.788472\pi\)
−0.787203 + 0.616694i \(0.788472\pi\)
\(492\) 0 0
\(493\) 3.67611 0.165564
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −42.9132 −1.92492
\(498\) 0 0
\(499\) −33.1594 −1.48442 −0.742210 0.670167i \(-0.766222\pi\)
−0.742210 + 0.670167i \(0.766222\pi\)
\(500\) 0 0
\(501\) 2.10074 0.0938543
\(502\) 0 0
\(503\) −7.05945 −0.314765 −0.157383 0.987538i \(-0.550306\pi\)
−0.157383 + 0.987538i \(0.550306\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 20.5025 0.910546
\(508\) 0 0
\(509\) 16.6812 0.739382 0.369691 0.929155i \(-0.379464\pi\)
0.369691 + 0.929155i \(0.379464\pi\)
\(510\) 0 0
\(511\) −6.31035 −0.279154
\(512\) 0 0
\(513\) −12.5625 −0.554648
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 57.7560 2.54011
\(518\) 0 0
\(519\) 27.3800 1.20185
\(520\) 0 0
\(521\) −24.9941 −1.09501 −0.547507 0.836801i \(-0.684423\pi\)
−0.547507 + 0.836801i \(0.684423\pi\)
\(522\) 0 0
\(523\) 14.3283 0.626535 0.313267 0.949665i \(-0.398576\pi\)
0.313267 + 0.949665i \(0.398576\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.53289 0.371698
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0.282810 0.0122729
\(532\) 0 0
\(533\) 0.00461005 0.000199683 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 11.5156 0.496934
\(538\) 0 0
\(539\) −23.2992 −1.00357
\(540\) 0 0
\(541\) 22.0323 0.947244 0.473622 0.880728i \(-0.342946\pi\)
0.473622 + 0.880728i \(0.342946\pi\)
\(542\) 0 0
\(543\) 27.9091 1.19769
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −21.5194 −0.920104 −0.460052 0.887892i \(-0.652169\pi\)
−0.460052 + 0.887892i \(0.652169\pi\)
\(548\) 0 0
\(549\) 0.277993 0.0118645
\(550\) 0 0
\(551\) −9.98719 −0.425468
\(552\) 0 0
\(553\) −0.717884 −0.0305276
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −21.1923 −0.897945 −0.448972 0.893546i \(-0.648210\pi\)
−0.448972 + 0.893546i \(0.648210\pi\)
\(558\) 0 0
\(559\) 10.9871 0.464706
\(560\) 0 0
\(561\) 8.97364 0.378867
\(562\) 0 0
\(563\) −23.6292 −0.995851 −0.497925 0.867220i \(-0.665905\pi\)
−0.497925 + 0.867220i \(0.665905\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 30.1594 1.26658
\(568\) 0 0
\(569\) −33.7490 −1.41483 −0.707415 0.706798i \(-0.750139\pi\)
−0.707415 + 0.706798i \(0.750139\pi\)
\(570\) 0 0
\(571\) 25.4667 1.06575 0.532874 0.846194i \(-0.321112\pi\)
0.532874 + 0.846194i \(0.321112\pi\)
\(572\) 0 0
\(573\) 0.514211 0.0214815
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −22.7293 −0.946234 −0.473117 0.881000i \(-0.656871\pi\)
−0.473117 + 0.881000i \(0.656871\pi\)
\(578\) 0 0
\(579\) 2.48006 0.103068
\(580\) 0 0
\(581\) −17.9057 −0.742856
\(582\) 0 0
\(583\) −36.0787 −1.49423
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 35.6609 1.47188 0.735941 0.677045i \(-0.236740\pi\)
0.735941 + 0.677045i \(0.236740\pi\)
\(588\) 0 0
\(589\) −23.1820 −0.955198
\(590\) 0 0
\(591\) 14.9625 0.615476
\(592\) 0 0
\(593\) 20.8412 0.855845 0.427922 0.903815i \(-0.359246\pi\)
0.427922 + 0.903815i \(0.359246\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.63687 0.271629
\(598\) 0 0
\(599\) 10.9952 0.449252 0.224626 0.974445i \(-0.427884\pi\)
0.224626 + 0.974445i \(0.427884\pi\)
\(600\) 0 0
\(601\) 2.35032 0.0958714 0.0479357 0.998850i \(-0.484736\pi\)
0.0479357 + 0.998850i \(0.484736\pi\)
\(602\) 0 0
\(603\) −0.287442 −0.0117055
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −31.8412 −1.29239 −0.646197 0.763170i \(-0.723642\pi\)
−0.646197 + 0.763170i \(0.723642\pi\)
\(608\) 0 0
\(609\) 23.7688 0.963160
\(610\) 0 0
\(611\) −11.0284 −0.446162
\(612\) 0 0
\(613\) 29.0597 1.17371 0.586856 0.809692i \(-0.300366\pi\)
0.586856 + 0.809692i \(0.300366\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −29.9851 −1.20715 −0.603577 0.797304i \(-0.706259\pi\)
−0.603577 + 0.797304i \(0.706259\pi\)
\(618\) 0 0
\(619\) 16.9204 0.680089 0.340045 0.940409i \(-0.389558\pi\)
0.340045 + 0.940409i \(0.389558\pi\)
\(620\) 0 0
\(621\) −5.17318 −0.207592
\(622\) 0 0
\(623\) −19.9553 −0.799491
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −24.3794 −0.973621
\(628\) 0 0
\(629\) −6.88177 −0.274394
\(630\) 0 0
\(631\) 20.4522 0.814188 0.407094 0.913386i \(-0.366542\pi\)
0.407094 + 0.913386i \(0.366542\pi\)
\(632\) 0 0
\(633\) 2.30272 0.0915250
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 4.44894 0.176273
\(638\) 0 0
\(639\) 0.338985 0.0134100
\(640\) 0 0
\(641\) −8.27686 −0.326916 −0.163458 0.986550i \(-0.552265\pi\)
−0.163458 + 0.986550i \(0.552265\pi\)
\(642\) 0 0
\(643\) −0.627685 −0.0247535 −0.0123767 0.999923i \(-0.503940\pi\)
−0.0123767 + 0.999923i \(0.503940\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −12.3508 −0.485561 −0.242781 0.970081i \(-0.578060\pi\)
−0.242781 + 0.970081i \(0.578060\pi\)
\(648\) 0 0
\(649\) −62.1911 −2.44121
\(650\) 0 0
\(651\) 55.1715 2.16234
\(652\) 0 0
\(653\) −18.3211 −0.716959 −0.358480 0.933538i \(-0.616705\pi\)
−0.358480 + 0.933538i \(0.616705\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0.0498475 0.00194473
\(658\) 0 0
\(659\) 39.1896 1.52661 0.763306 0.646038i \(-0.223575\pi\)
0.763306 + 0.646038i \(0.223575\pi\)
\(660\) 0 0
\(661\) 9.38565 0.365060 0.182530 0.983200i \(-0.441571\pi\)
0.182530 + 0.983200i \(0.441571\pi\)
\(662\) 0 0
\(663\) −1.71350 −0.0665469
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.11268 −0.159244
\(668\) 0 0
\(669\) 43.7140 1.69008
\(670\) 0 0
\(671\) −61.1319 −2.35997
\(672\) 0 0
\(673\) 8.05600 0.310536 0.155268 0.987872i \(-0.450376\pi\)
0.155268 + 0.987872i \(0.450376\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.9461 −0.651293 −0.325647 0.945492i \(-0.605582\pi\)
−0.325647 + 0.945492i \(0.605582\pi\)
\(678\) 0 0
\(679\) −6.91370 −0.265324
\(680\) 0 0
\(681\) −41.4063 −1.58669
\(682\) 0 0
\(683\) 0.111363 0.00426119 0.00213059 0.999998i \(-0.499322\pi\)
0.00213059 + 0.999998i \(0.499322\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 1.37316 0.0523894
\(688\) 0 0
\(689\) 6.88917 0.262456
\(690\) 0 0
\(691\) 38.1718 1.45212 0.726062 0.687629i \(-0.241348\pi\)
0.726062 + 0.687629i \(0.241348\pi\)
\(692\) 0 0
\(693\) 0.503158 0.0191134
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0.00373938 0.000141639 0
\(698\) 0 0
\(699\) 36.2014 1.36926
\(700\) 0 0
\(701\) 38.7698 1.46431 0.732157 0.681136i \(-0.238514\pi\)
0.732157 + 0.681136i \(0.238514\pi\)
\(702\) 0 0
\(703\) 18.6963 0.705144
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 43.7128 1.64399
\(708\) 0 0
\(709\) −47.4028 −1.78025 −0.890126 0.455715i \(-0.849383\pi\)
−0.890126 + 0.455715i \(0.849383\pi\)
\(710\) 0 0
\(711\) 0.00567080 0.000212671 0
\(712\) 0 0
\(713\) −9.54624 −0.357510
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −43.9073 −1.63975
\(718\) 0 0
\(719\) 17.7370 0.661479 0.330740 0.943722i \(-0.392702\pi\)
0.330740 + 0.943722i \(0.392702\pi\)
\(720\) 0 0
\(721\) 60.1179 2.23891
\(722\) 0 0
\(723\) −9.18010 −0.341412
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 50.7341 1.88163 0.940813 0.338927i \(-0.110064\pi\)
0.940813 + 0.338927i \(0.110064\pi\)
\(728\) 0 0
\(729\) 26.7597 0.991100
\(730\) 0 0
\(731\) 8.91206 0.329625
\(732\) 0 0
\(733\) −18.9970 −0.701670 −0.350835 0.936437i \(-0.614102\pi\)
−0.350835 + 0.936437i \(0.614102\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 63.2096 2.32835
\(738\) 0 0
\(739\) 44.6999 1.64431 0.822156 0.569263i \(-0.192771\pi\)
0.822156 + 0.569263i \(0.192771\pi\)
\(740\) 0 0
\(741\) 4.65522 0.171014
\(742\) 0 0
\(743\) −38.9841 −1.43019 −0.715094 0.699029i \(-0.753616\pi\)
−0.715094 + 0.699029i \(0.753616\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.141443 0.00517513
\(748\) 0 0
\(749\) 23.1647 0.846421
\(750\) 0 0
\(751\) −3.97027 −0.144877 −0.0724386 0.997373i \(-0.523078\pi\)
−0.0724386 + 0.997373i \(0.523078\pi\)
\(752\) 0 0
\(753\) −18.8641 −0.687448
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −23.2885 −0.846436 −0.423218 0.906028i \(-0.639100\pi\)
−0.423218 + 0.906028i \(0.639100\pi\)
\(758\) 0 0
\(759\) −10.0393 −0.364405
\(760\) 0 0
\(761\) 5.62214 0.203802 0.101901 0.994795i \(-0.467507\pi\)
0.101901 + 0.994795i \(0.467507\pi\)
\(762\) 0 0
\(763\) −34.1768 −1.23728
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 11.8753 0.428792
\(768\) 0 0
\(769\) −33.0457 −1.19166 −0.595828 0.803112i \(-0.703176\pi\)
−0.595828 + 0.803112i \(0.703176\pi\)
\(770\) 0 0
\(771\) −32.3981 −1.16679
\(772\) 0 0
\(773\) −46.8196 −1.68398 −0.841991 0.539491i \(-0.818617\pi\)
−0.841991 + 0.539491i \(0.818617\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −44.4958 −1.59628
\(778\) 0 0
\(779\) −0.0101591 −0.000363987 0
\(780\) 0 0
\(781\) −74.5442 −2.66740
\(782\) 0 0
\(783\) 21.2756 0.760328
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −35.1470 −1.25286 −0.626428 0.779479i \(-0.715484\pi\)
−0.626428 + 0.779479i \(0.715484\pi\)
\(788\) 0 0
\(789\) −33.8128 −1.20377
\(790\) 0 0
\(791\) 18.3871 0.653769
\(792\) 0 0
\(793\) 11.6730 0.414522
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 21.8566 0.774200 0.387100 0.922038i \(-0.373477\pi\)
0.387100 + 0.922038i \(0.373477\pi\)
\(798\) 0 0
\(799\) −8.94556 −0.316471
\(800\) 0 0
\(801\) 0.157633 0.00556969
\(802\) 0 0
\(803\) −10.9617 −0.386829
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 6.61909 0.233003
\(808\) 0 0
\(809\) −2.24801 −0.0790357 −0.0395178 0.999219i \(-0.512582\pi\)
−0.0395178 + 0.999219i \(0.512582\pi\)
\(810\) 0 0
\(811\) −29.5155 −1.03643 −0.518215 0.855250i \(-0.673403\pi\)
−0.518215 + 0.855250i \(0.673403\pi\)
\(812\) 0 0
\(813\) −31.6783 −1.11101
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −24.2121 −0.847076
\(818\) 0 0
\(819\) −0.0960772 −0.00335721
\(820\) 0 0
\(821\) −29.1470 −1.01724 −0.508618 0.860992i \(-0.669843\pi\)
−0.508618 + 0.860992i \(0.669843\pi\)
\(822\) 0 0
\(823\) 13.1354 0.457873 0.228936 0.973441i \(-0.426475\pi\)
0.228936 + 0.973441i \(0.426475\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −54.7619 −1.90426 −0.952129 0.305698i \(-0.901110\pi\)
−0.952129 + 0.305698i \(0.901110\pi\)
\(828\) 0 0
\(829\) −41.3545 −1.43630 −0.718151 0.695887i \(-0.755011\pi\)
−0.718151 + 0.695887i \(0.755011\pi\)
\(830\) 0 0
\(831\) −25.6809 −0.890859
\(832\) 0 0
\(833\) 3.60869 0.125034
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 49.3844 1.70698
\(838\) 0 0
\(839\) −8.60909 −0.297219 −0.148609 0.988896i \(-0.547480\pi\)
−0.148609 + 0.988896i \(0.547480\pi\)
\(840\) 0 0
\(841\) −12.0859 −0.416755
\(842\) 0 0
\(843\) 10.9550 0.377310
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −74.1018 −2.54617
\(848\) 0 0
\(849\) 49.4819 1.69822
\(850\) 0 0
\(851\) 7.69904 0.263920
\(852\) 0 0
\(853\) 53.2697 1.82392 0.911960 0.410280i \(-0.134569\pi\)
0.911960 + 0.410280i \(0.134569\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 13.3201 0.455005 0.227502 0.973778i \(-0.426944\pi\)
0.227502 + 0.973778i \(0.426944\pi\)
\(858\) 0 0
\(859\) −23.3425 −0.796434 −0.398217 0.917291i \(-0.630371\pi\)
−0.398217 + 0.917291i \(0.630371\pi\)
\(860\) 0 0
\(861\) 0.0241779 0.000823981 0
\(862\) 0 0
\(863\) −21.8395 −0.743426 −0.371713 0.928348i \(-0.621229\pi\)
−0.371713 + 0.928348i \(0.621229\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 28.1835 0.957161
\(868\) 0 0
\(869\) −1.24703 −0.0423026
\(870\) 0 0
\(871\) −12.0698 −0.408968
\(872\) 0 0
\(873\) 0.0546135 0.00184839
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −29.0903 −0.982309 −0.491155 0.871072i \(-0.663425\pi\)
−0.491155 + 0.871072i \(0.663425\pi\)
\(878\) 0 0
\(879\) −25.2082 −0.850251
\(880\) 0 0
\(881\) −44.7215 −1.50671 −0.753353 0.657616i \(-0.771565\pi\)
−0.753353 + 0.657616i \(0.771565\pi\)
\(882\) 0 0
\(883\) −19.4889 −0.655855 −0.327927 0.944703i \(-0.606350\pi\)
−0.327927 + 0.944703i \(0.606350\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 24.0317 0.806906 0.403453 0.915000i \(-0.367810\pi\)
0.403453 + 0.915000i \(0.367810\pi\)
\(888\) 0 0
\(889\) 37.0694 1.24327
\(890\) 0 0
\(891\) 52.3897 1.75512
\(892\) 0 0
\(893\) 24.3031 0.813274
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 1.91700 0.0640067
\(898\) 0 0
\(899\) 39.2606 1.30942
\(900\) 0 0
\(901\) 5.58806 0.186165
\(902\) 0 0
\(903\) 57.6232 1.91758
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −16.2777 −0.540491 −0.270245 0.962792i \(-0.587105\pi\)
−0.270245 + 0.962792i \(0.587105\pi\)
\(908\) 0 0
\(909\) −0.345301 −0.0114529
\(910\) 0 0
\(911\) −23.8128 −0.788952 −0.394476 0.918906i \(-0.629074\pi\)
−0.394476 + 0.918906i \(0.629074\pi\)
\(912\) 0 0
\(913\) −31.1039 −1.02939
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −49.9734 −1.65027
\(918\) 0 0
\(919\) −22.0433 −0.727141 −0.363571 0.931567i \(-0.618442\pi\)
−0.363571 + 0.931567i \(0.618442\pi\)
\(920\) 0 0
\(921\) −53.0071 −1.74664
\(922\) 0 0
\(923\) 14.2341 0.468521
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −0.474890 −0.0155974
\(928\) 0 0
\(929\) −5.19696 −0.170507 −0.0852534 0.996359i \(-0.527170\pi\)
−0.0852534 + 0.996359i \(0.527170\pi\)
\(930\) 0 0
\(931\) −9.80404 −0.321315
\(932\) 0 0
\(933\) 36.3633 1.19048
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −29.0029 −0.947482 −0.473741 0.880664i \(-0.657097\pi\)
−0.473741 + 0.880664i \(0.657097\pi\)
\(938\) 0 0
\(939\) −24.9833 −0.815300
\(940\) 0 0
\(941\) 50.2138 1.63692 0.818461 0.574562i \(-0.194827\pi\)
0.818461 + 0.574562i \(0.194827\pi\)
\(942\) 0 0
\(943\) −0.00418347 −0.000136232 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18.3661 −0.596817 −0.298408 0.954438i \(-0.596456\pi\)
−0.298408 + 0.954438i \(0.596456\pi\)
\(948\) 0 0
\(949\) 2.09311 0.0679453
\(950\) 0 0
\(951\) −58.6143 −1.90070
\(952\) 0 0
\(953\) 34.9542 1.13228 0.566139 0.824310i \(-0.308437\pi\)
0.566139 + 0.824310i \(0.308437\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 41.2886 1.33467
\(958\) 0 0
\(959\) −7.34980 −0.237338
\(960\) 0 0
\(961\) 60.1308 1.93970
\(962\) 0 0
\(963\) −0.182985 −0.00589662
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −48.3107 −1.55357 −0.776784 0.629767i \(-0.783150\pi\)
−0.776784 + 0.629767i \(0.783150\pi\)
\(968\) 0 0
\(969\) 3.77602 0.121303
\(970\) 0 0
\(971\) 14.8815 0.477570 0.238785 0.971072i \(-0.423251\pi\)
0.238785 + 0.971072i \(0.423251\pi\)
\(972\) 0 0
\(973\) −21.7184 −0.696261
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 18.6833 0.597730 0.298865 0.954295i \(-0.403392\pi\)
0.298865 + 0.954295i \(0.403392\pi\)
\(978\) 0 0
\(979\) −34.6641 −1.10787
\(980\) 0 0
\(981\) 0.269974 0.00861959
\(982\) 0 0
\(983\) −28.4191 −0.906428 −0.453214 0.891402i \(-0.649723\pi\)
−0.453214 + 0.891402i \(0.649723\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −57.8398 −1.84106
\(988\) 0 0
\(989\) −9.97045 −0.317042
\(990\) 0 0
\(991\) 28.4942 0.905148 0.452574 0.891727i \(-0.350506\pi\)
0.452574 + 0.891727i \(0.350506\pi\)
\(992\) 0 0
\(993\) 17.0881 0.542273
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 26.5435 0.840642 0.420321 0.907375i \(-0.361917\pi\)
0.420321 + 0.907375i \(0.361917\pi\)
\(998\) 0 0
\(999\) −39.8285 −1.26012
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.cx.1.3 6
4.3 odd 2 2300.2.a.o.1.4 6
5.2 odd 4 1840.2.e.f.369.9 12
5.3 odd 4 1840.2.e.f.369.4 12
5.4 even 2 9200.2.a.cy.1.4 6
20.3 even 4 460.2.c.a.369.9 yes 12
20.7 even 4 460.2.c.a.369.4 12
20.19 odd 2 2300.2.a.n.1.3 6
60.23 odd 4 4140.2.f.b.829.1 12
60.47 odd 4 4140.2.f.b.829.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.c.a.369.4 12 20.7 even 4
460.2.c.a.369.9 yes 12 20.3 even 4
1840.2.e.f.369.4 12 5.3 odd 4
1840.2.e.f.369.9 12 5.2 odd 4
2300.2.a.n.1.3 6 20.19 odd 2
2300.2.a.o.1.4 6 4.3 odd 2
4140.2.f.b.829.1 12 60.23 odd 4
4140.2.f.b.829.2 12 60.47 odd 4
9200.2.a.cx.1.3 6 1.1 even 1 trivial
9200.2.a.cy.1.4 6 5.4 even 2