Properties

Label 9450.2.a.w.1.1
Level 9450
Weight 2
Character 9450.1
Self dual yes
Analytic conductor 75.459
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9450.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(75.4586299101\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1890)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\) of \(x\)
Character \(\chi\) \(=\) 9450.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +4.00000 q^{11} -6.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.00000 q^{17} -4.00000 q^{22} -4.00000 q^{23} +6.00000 q^{26} -1.00000 q^{28} -3.00000 q^{29} +7.00000 q^{31} -1.00000 q^{32} +4.00000 q^{34} +1.00000 q^{37} +7.00000 q^{41} +10.0000 q^{43} +4.00000 q^{44} +4.00000 q^{46} +13.0000 q^{47} +1.00000 q^{49} -6.00000 q^{52} -6.00000 q^{53} +1.00000 q^{56} +3.00000 q^{58} +5.00000 q^{59} -7.00000 q^{61} -7.00000 q^{62} +1.00000 q^{64} -4.00000 q^{67} -4.00000 q^{68} +3.00000 q^{71} +7.00000 q^{73} -1.00000 q^{74} -4.00000 q^{77} +12.0000 q^{79} -7.00000 q^{82} +2.00000 q^{83} -10.0000 q^{86} -4.00000 q^{88} -14.0000 q^{89} +6.00000 q^{91} -4.00000 q^{92} -13.0000 q^{94} -10.0000 q^{97} -1.00000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 6.00000 1.17670
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 0 0
\(31\) 7.00000 1.25724 0.628619 0.777714i \(-0.283621\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 0 0
\(37\) 1.00000 0.164399 0.0821995 0.996616i \(-0.473806\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7.00000 1.09322 0.546608 0.837389i \(-0.315919\pi\)
0.546608 + 0.837389i \(0.315919\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 4.00000 0.603023
\(45\) 0 0
\(46\) 4.00000 0.589768
\(47\) 13.0000 1.89624 0.948122 0.317905i \(-0.102979\pi\)
0.948122 + 0.317905i \(0.102979\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) −6.00000 −0.832050
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) 3.00000 0.393919
\(59\) 5.00000 0.650945 0.325472 0.945552i \(-0.394477\pi\)
0.325472 + 0.945552i \(0.394477\pi\)
\(60\) 0 0
\(61\) −7.00000 −0.896258 −0.448129 0.893969i \(-0.647910\pi\)
−0.448129 + 0.893969i \(0.647910\pi\)
\(62\) −7.00000 −0.889001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −4.00000 −0.485071
\(69\) 0 0
\(70\) 0 0
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) 0 0
\(73\) 7.00000 0.819288 0.409644 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) −1.00000 −0.116248
\(75\) 0 0
\(76\) 0 0
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) 12.0000 1.35011 0.675053 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −7.00000 −0.773021
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −10.0000 −1.07833
\(87\) 0 0
\(88\) −4.00000 −0.426401
\(89\) −14.0000 −1.48400 −0.741999 0.670402i \(-0.766122\pi\)
−0.741999 + 0.670402i \(0.766122\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) −4.00000 −0.417029
\(93\) 0 0
\(94\) −13.0000 −1.34085
\(95\) 0 0
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −9.00000 −0.870063 −0.435031 0.900415i \(-0.643263\pi\)
−0.435031 + 0.900415i \(0.643263\pi\)
\(108\) 0 0
\(109\) −20.0000 −1.91565 −0.957826 0.287348i \(-0.907226\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) −3.00000 −0.282216 −0.141108 0.989994i \(-0.545067\pi\)
−0.141108 + 0.989994i \(0.545067\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −3.00000 −0.278543
\(117\) 0 0
\(118\) −5.00000 −0.460287
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 7.00000 0.633750
\(123\) 0 0
\(124\) 7.00000 0.628619
\(125\) 0 0
\(126\) 0 0
\(127\) 7.00000 0.621150 0.310575 0.950549i \(-0.399478\pi\)
0.310575 + 0.950549i \(0.399478\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −15.0000 −1.31056 −0.655278 0.755388i \(-0.727449\pi\)
−0.655278 + 0.755388i \(0.727449\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 4.00000 0.342997
\(137\) −15.0000 −1.28154 −0.640768 0.767734i \(-0.721384\pi\)
−0.640768 + 0.767734i \(0.721384\pi\)
\(138\) 0 0
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.00000 −0.251754
\(143\) −24.0000 −2.00698
\(144\) 0 0
\(145\) 0 0
\(146\) −7.00000 −0.579324
\(147\) 0 0
\(148\) 1.00000 0.0821995
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 0 0
\(151\) −14.0000 −1.13930 −0.569652 0.821886i \(-0.692922\pi\)
−0.569652 + 0.821886i \(0.692922\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 4.00000 0.322329
\(155\) 0 0
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −12.0000 −0.954669
\(159\) 0 0
\(160\) 0 0
\(161\) 4.00000 0.315244
\(162\) 0 0
\(163\) 14.0000 1.09656 0.548282 0.836293i \(-0.315282\pi\)
0.548282 + 0.836293i \(0.315282\pi\)
\(164\) 7.00000 0.546608
\(165\) 0 0
\(166\) −2.00000 −0.155230
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 0 0
\(172\) 10.0000 0.762493
\(173\) −17.0000 −1.29249 −0.646243 0.763132i \(-0.723661\pi\)
−0.646243 + 0.763132i \(0.723661\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) 14.0000 1.04934
\(179\) −16.0000 −1.19590 −0.597948 0.801535i \(-0.704017\pi\)
−0.597948 + 0.801535i \(0.704017\pi\)
\(180\) 0 0
\(181\) 23.0000 1.70958 0.854788 0.518977i \(-0.173687\pi\)
0.854788 + 0.518977i \(0.173687\pi\)
\(182\) −6.00000 −0.444750
\(183\) 0 0
\(184\) 4.00000 0.294884
\(185\) 0 0
\(186\) 0 0
\(187\) −16.0000 −1.17004
\(188\) 13.0000 0.948122
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) −2.00000 −0.143963 −0.0719816 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −8.00000 −0.569976 −0.284988 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) 0 0
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) 3.00000 0.210559
\(204\) 0 0
\(205\) 0 0
\(206\) −14.0000 −0.975426
\(207\) 0 0
\(208\) −6.00000 −0.416025
\(209\) 0 0
\(210\) 0 0
\(211\) −15.0000 −1.03264 −0.516321 0.856395i \(-0.672699\pi\)
−0.516321 + 0.856395i \(0.672699\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) 9.00000 0.615227
\(215\) 0 0
\(216\) 0 0
\(217\) −7.00000 −0.475191
\(218\) 20.0000 1.35457
\(219\) 0 0
\(220\) 0 0
\(221\) 24.0000 1.61441
\(222\) 0 0
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 3.00000 0.199557
\(227\) −16.0000 −1.06196 −0.530979 0.847385i \(-0.678176\pi\)
−0.530979 + 0.847385i \(0.678176\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 0.196960
\(233\) −11.0000 −0.720634 −0.360317 0.932830i \(-0.617331\pi\)
−0.360317 + 0.932830i \(0.617331\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 5.00000 0.325472
\(237\) 0 0
\(238\) −4.00000 −0.259281
\(239\) 13.0000 0.840900 0.420450 0.907316i \(-0.361872\pi\)
0.420450 + 0.907316i \(0.361872\pi\)
\(240\) 0 0
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0 0
\(244\) −7.00000 −0.448129
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −7.00000 −0.444500
\(249\) 0 0
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) −16.0000 −1.00591
\(254\) −7.00000 −0.439219
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 24.0000 1.49708 0.748539 0.663090i \(-0.230755\pi\)
0.748539 + 0.663090i \(0.230755\pi\)
\(258\) 0 0
\(259\) −1.00000 −0.0621370
\(260\) 0 0
\(261\) 0 0
\(262\) 15.0000 0.926703
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −4.00000 −0.244339
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) −11.0000 −0.668202 −0.334101 0.942537i \(-0.608433\pi\)
−0.334101 + 0.942537i \(0.608433\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) 15.0000 0.906183
\(275\) 0 0
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 14.0000 0.839664
\(279\) 0 0
\(280\) 0 0
\(281\) −24.0000 −1.43172 −0.715860 0.698244i \(-0.753965\pi\)
−0.715860 + 0.698244i \(0.753965\pi\)
\(282\) 0 0
\(283\) −7.00000 −0.416107 −0.208053 0.978117i \(-0.566713\pi\)
−0.208053 + 0.978117i \(0.566713\pi\)
\(284\) 3.00000 0.178017
\(285\) 0 0
\(286\) 24.0000 1.41915
\(287\) −7.00000 −0.413197
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 7.00000 0.409644
\(293\) −15.0000 −0.876309 −0.438155 0.898900i \(-0.644368\pi\)
−0.438155 + 0.898900i \(0.644368\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) 10.0000 0.579284
\(299\) 24.0000 1.38796
\(300\) 0 0
\(301\) −10.0000 −0.576390
\(302\) 14.0000 0.805609
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) −4.00000 −0.227921
\(309\) 0 0
\(310\) 0 0
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 0 0
\(313\) −26.0000 −1.46961 −0.734803 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 12.0000 0.675053
\(317\) 14.0000 0.786318 0.393159 0.919470i \(-0.371382\pi\)
0.393159 + 0.919470i \(0.371382\pi\)
\(318\) 0 0
\(319\) −12.0000 −0.671871
\(320\) 0 0
\(321\) 0 0
\(322\) −4.00000 −0.222911
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) −14.0000 −0.775388
\(327\) 0 0
\(328\) −7.00000 −0.386510
\(329\) −13.0000 −0.716713
\(330\) 0 0
\(331\) −35.0000 −1.92377 −0.961887 0.273447i \(-0.911836\pi\)
−0.961887 + 0.273447i \(0.911836\pi\)
\(332\) 2.00000 0.109764
\(333\) 0 0
\(334\) 3.00000 0.164153
\(335\) 0 0
\(336\) 0 0
\(337\) 16.0000 0.871576 0.435788 0.900049i \(-0.356470\pi\)
0.435788 + 0.900049i \(0.356470\pi\)
\(338\) −23.0000 −1.25104
\(339\) 0 0
\(340\) 0 0
\(341\) 28.0000 1.51629
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) 17.0000 0.913926
\(347\) −27.0000 −1.44944 −0.724718 0.689046i \(-0.758030\pi\)
−0.724718 + 0.689046i \(0.758030\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.00000 −0.213201
\(353\) −32.0000 −1.70319 −0.851594 0.524202i \(-0.824364\pi\)
−0.851594 + 0.524202i \(0.824364\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) 16.0000 0.845626
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) −23.0000 −1.20885
\(363\) 0 0
\(364\) 6.00000 0.314485
\(365\) 0 0
\(366\) 0 0
\(367\) −2.00000 −0.104399 −0.0521996 0.998637i \(-0.516623\pi\)
−0.0521996 + 0.998637i \(0.516623\pi\)
\(368\) −4.00000 −0.208514
\(369\) 0 0
\(370\) 0 0
\(371\) 6.00000 0.311504
\(372\) 0 0
\(373\) −3.00000 −0.155334 −0.0776671 0.996979i \(-0.524747\pi\)
−0.0776671 + 0.996979i \(0.524747\pi\)
\(374\) 16.0000 0.827340
\(375\) 0 0
\(376\) −13.0000 −0.670424
\(377\) 18.0000 0.927047
\(378\) 0 0
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8.00000 −0.408781 −0.204390 0.978889i \(-0.565521\pi\)
−0.204390 + 0.978889i \(0.565521\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.00000 0.101797
\(387\) 0 0
\(388\) −10.0000 −0.507673
\(389\) −23.0000 −1.16615 −0.583073 0.812420i \(-0.698150\pi\)
−0.583073 + 0.812420i \(0.698150\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) 8.00000 0.403034
\(395\) 0 0
\(396\) 0 0
\(397\) −14.0000 −0.702640 −0.351320 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 0 0
\(401\) −16.0000 −0.799002 −0.399501 0.916733i \(-0.630817\pi\)
−0.399501 + 0.916733i \(0.630817\pi\)
\(402\) 0 0
\(403\) −42.0000 −2.09217
\(404\) −10.0000 −0.497519
\(405\) 0 0
\(406\) −3.00000 −0.148888
\(407\) 4.00000 0.198273
\(408\) 0 0
\(409\) 20.0000 0.988936 0.494468 0.869196i \(-0.335363\pi\)
0.494468 + 0.869196i \(0.335363\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 14.0000 0.689730
\(413\) −5.00000 −0.246034
\(414\) 0 0
\(415\) 0 0
\(416\) 6.00000 0.294174
\(417\) 0 0
\(418\) 0 0
\(419\) 25.0000 1.22133 0.610665 0.791889i \(-0.290902\pi\)
0.610665 + 0.791889i \(0.290902\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 15.0000 0.730189
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) 7.00000 0.338754
\(428\) −9.00000 −0.435031
\(429\) 0 0
\(430\) 0 0
\(431\) −11.0000 −0.529851 −0.264926 0.964269i \(-0.585347\pi\)
−0.264926 + 0.964269i \(0.585347\pi\)
\(432\) 0 0
\(433\) −29.0000 −1.39365 −0.696826 0.717241i \(-0.745405\pi\)
−0.696826 + 0.717241i \(0.745405\pi\)
\(434\) 7.00000 0.336011
\(435\) 0 0
\(436\) −20.0000 −0.957826
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −24.0000 −1.14156
\(443\) −9.00000 −0.427603 −0.213801 0.976877i \(-0.568585\pi\)
−0.213801 + 0.976877i \(0.568585\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −4.00000 −0.189405
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) −36.0000 −1.69895 −0.849473 0.527633i \(-0.823080\pi\)
−0.849473 + 0.527633i \(0.823080\pi\)
\(450\) 0 0
\(451\) 28.0000 1.31847
\(452\) −3.00000 −0.141108
\(453\) 0 0
\(454\) 16.0000 0.750917
\(455\) 0 0
\(456\) 0 0
\(457\) −8.00000 −0.374224 −0.187112 0.982339i \(-0.559913\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) −14.0000 −0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) 36.0000 1.67669 0.838344 0.545142i \(-0.183524\pi\)
0.838344 + 0.545142i \(0.183524\pi\)
\(462\) 0 0
\(463\) 33.0000 1.53364 0.766820 0.641862i \(-0.221838\pi\)
0.766820 + 0.641862i \(0.221838\pi\)
\(464\) −3.00000 −0.139272
\(465\) 0 0
\(466\) 11.0000 0.509565
\(467\) 18.0000 0.832941 0.416470 0.909149i \(-0.363267\pi\)
0.416470 + 0.909149i \(0.363267\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) 0 0
\(472\) −5.00000 −0.230144
\(473\) 40.0000 1.83920
\(474\) 0 0
\(475\) 0 0
\(476\) 4.00000 0.183340
\(477\) 0 0
\(478\) −13.0000 −0.594606
\(479\) 4.00000 0.182765 0.0913823 0.995816i \(-0.470871\pi\)
0.0913823 + 0.995816i \(0.470871\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 2.00000 0.0910975
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) 0 0
\(487\) 21.0000 0.951601 0.475800 0.879553i \(-0.342158\pi\)
0.475800 + 0.879553i \(0.342158\pi\)
\(488\) 7.00000 0.316875
\(489\) 0 0
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) 12.0000 0.540453
\(494\) 0 0
\(495\) 0 0
\(496\) 7.00000 0.314309
\(497\) −3.00000 −0.134568
\(498\) 0 0
\(499\) 9.00000 0.402895 0.201448 0.979499i \(-0.435435\pi\)
0.201448 + 0.979499i \(0.435435\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 12.0000 0.535586
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 16.0000 0.711287
\(507\) 0 0
\(508\) 7.00000 0.310575
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) −7.00000 −0.309662
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −24.0000 −1.05859
\(515\) 0 0
\(516\) 0 0
\(517\) 52.0000 2.28696
\(518\) 1.00000 0.0439375
\(519\) 0 0
\(520\) 0 0
\(521\) 38.0000 1.66481 0.832405 0.554168i \(-0.186963\pi\)
0.832405 + 0.554168i \(0.186963\pi\)
\(522\) 0 0
\(523\) −28.0000 −1.22435 −0.612177 0.790721i \(-0.709706\pi\)
−0.612177 + 0.790721i \(0.709706\pi\)
\(524\) −15.0000 −0.655278
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) −28.0000 −1.21970
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −42.0000 −1.81922
\(534\) 0 0
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) 0 0
\(538\) 0 0
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −32.0000 −1.37579 −0.687894 0.725811i \(-0.741464\pi\)
−0.687894 + 0.725811i \(0.741464\pi\)
\(542\) 11.0000 0.472490
\(543\) 0 0
\(544\) 4.00000 0.171499
\(545\) 0 0
\(546\) 0 0
\(547\) −32.0000 −1.36822 −0.684111 0.729378i \(-0.739809\pi\)
−0.684111 + 0.729378i \(0.739809\pi\)
\(548\) −15.0000 −0.640768
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −12.0000 −0.510292
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) −14.0000 −0.593732
\(557\) −12.0000 −0.508456 −0.254228 0.967144i \(-0.581821\pi\)
−0.254228 + 0.967144i \(0.581821\pi\)
\(558\) 0 0
\(559\) −60.0000 −2.53773
\(560\) 0 0
\(561\) 0 0
\(562\) 24.0000 1.01238
\(563\) 10.0000 0.421450 0.210725 0.977545i \(-0.432418\pi\)
0.210725 + 0.977545i \(0.432418\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 7.00000 0.294232
\(567\) 0 0
\(568\) −3.00000 −0.125877
\(569\) −20.0000 −0.838444 −0.419222 0.907884i \(-0.637697\pi\)
−0.419222 + 0.907884i \(0.637697\pi\)
\(570\) 0 0
\(571\) 19.0000 0.795125 0.397563 0.917575i \(-0.369856\pi\)
0.397563 + 0.917575i \(0.369856\pi\)
\(572\) −24.0000 −1.00349
\(573\) 0 0
\(574\) 7.00000 0.292174
\(575\) 0 0
\(576\) 0 0
\(577\) −11.0000 −0.457936 −0.228968 0.973434i \(-0.573535\pi\)
−0.228968 + 0.973434i \(0.573535\pi\)
\(578\) 1.00000 0.0415945
\(579\) 0 0
\(580\) 0 0
\(581\) −2.00000 −0.0829740
\(582\) 0 0
\(583\) −24.0000 −0.993978
\(584\) −7.00000 −0.289662
\(585\) 0 0
\(586\) 15.0000 0.619644
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.00000 0.0410997
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) 0 0
\(598\) −24.0000 −0.981433
\(599\) 15.0000 0.612883 0.306442 0.951889i \(-0.400862\pi\)
0.306442 + 0.951889i \(0.400862\pi\)
\(600\) 0 0
\(601\) 44.0000 1.79480 0.897399 0.441221i \(-0.145454\pi\)
0.897399 + 0.441221i \(0.145454\pi\)
\(602\) 10.0000 0.407570
\(603\) 0 0
\(604\) −14.0000 −0.569652
\(605\) 0 0
\(606\) 0 0
\(607\) 14.0000 0.568242 0.284121 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −78.0000 −3.15554
\(612\) 0 0
\(613\) 22.0000 0.888572 0.444286 0.895885i \(-0.353457\pi\)
0.444286 + 0.895885i \(0.353457\pi\)
\(614\) −12.0000 −0.484281
\(615\) 0 0
\(616\) 4.00000 0.161165
\(617\) −31.0000 −1.24801 −0.624007 0.781419i \(-0.714496\pi\)
−0.624007 + 0.781419i \(0.714496\pi\)
\(618\) 0 0
\(619\) −40.0000 −1.60774 −0.803868 0.594808i \(-0.797228\pi\)
−0.803868 + 0.594808i \(0.797228\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −30.0000 −1.20289
\(623\) 14.0000 0.560898
\(624\) 0 0
\(625\) 0 0
\(626\) 26.0000 1.03917
\(627\) 0 0
\(628\) 14.0000 0.558661
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) −12.0000 −0.477334
\(633\) 0 0
\(634\) −14.0000 −0.556011
\(635\) 0 0
\(636\) 0 0
\(637\) −6.00000 −0.237729
\(638\) 12.0000 0.475085
\(639\) 0 0
\(640\) 0 0
\(641\) −26.0000 −1.02694 −0.513469 0.858108i \(-0.671640\pi\)
−0.513469 + 0.858108i \(0.671640\pi\)
\(642\) 0 0
\(643\) −39.0000 −1.53801 −0.769005 0.639243i \(-0.779248\pi\)
−0.769005 + 0.639243i \(0.779248\pi\)
\(644\) 4.00000 0.157622
\(645\) 0 0
\(646\) 0 0
\(647\) 33.0000 1.29736 0.648682 0.761060i \(-0.275321\pi\)
0.648682 + 0.761060i \(0.275321\pi\)
\(648\) 0 0
\(649\) 20.0000 0.785069
\(650\) 0 0
\(651\) 0 0
\(652\) 14.0000 0.548282
\(653\) 14.0000 0.547862 0.273931 0.961749i \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 7.00000 0.273304
\(657\) 0 0
\(658\) 13.0000 0.506793
\(659\) 26.0000 1.01282 0.506408 0.862294i \(-0.330973\pi\)
0.506408 + 0.862294i \(0.330973\pi\)
\(660\) 0 0
\(661\) −19.0000 −0.739014 −0.369507 0.929228i \(-0.620473\pi\)
−0.369507 + 0.929228i \(0.620473\pi\)
\(662\) 35.0000 1.36031
\(663\) 0 0
\(664\) −2.00000 −0.0776151
\(665\) 0 0
\(666\) 0 0
\(667\) 12.0000 0.464642
\(668\) −3.00000 −0.116073
\(669\) 0 0
\(670\) 0 0
\(671\) −28.0000 −1.08093
\(672\) 0 0
\(673\) 36.0000 1.38770 0.693849 0.720121i \(-0.255914\pi\)
0.693849 + 0.720121i \(0.255914\pi\)
\(674\) −16.0000 −0.616297
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) 29.0000 1.11456 0.557280 0.830324i \(-0.311845\pi\)
0.557280 + 0.830324i \(0.311845\pi\)
\(678\) 0 0
\(679\) 10.0000 0.383765
\(680\) 0 0
\(681\) 0 0
\(682\) −28.0000 −1.07218
\(683\) −1.00000 −0.0382639 −0.0191320 0.999817i \(-0.506090\pi\)
−0.0191320 + 0.999817i \(0.506090\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) 10.0000 0.381246
\(689\) 36.0000 1.37149
\(690\) 0 0
\(691\) −38.0000 −1.44559 −0.722794 0.691063i \(-0.757142\pi\)
−0.722794 + 0.691063i \(0.757142\pi\)
\(692\) −17.0000 −0.646243
\(693\) 0 0
\(694\) 27.0000 1.02491
\(695\) 0 0
\(696\) 0 0
\(697\) −28.0000 −1.06058
\(698\) 2.00000 0.0757011
\(699\) 0 0
\(700\) 0 0
\(701\) −35.0000 −1.32193 −0.660966 0.750416i \(-0.729853\pi\)
−0.660966 + 0.750416i \(0.729853\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 4.00000 0.150756
\(705\) 0 0
\(706\) 32.0000 1.20434
\(707\) 10.0000 0.376089
\(708\) 0 0
\(709\) 48.0000 1.80268 0.901339 0.433114i \(-0.142585\pi\)
0.901339 + 0.433114i \(0.142585\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 14.0000 0.524672
\(713\) −28.0000 −1.04861
\(714\) 0 0
\(715\) 0 0
\(716\) −16.0000 −0.597948
\(717\) 0 0
\(718\) −12.0000 −0.447836
\(719\) −2.00000 −0.0745874 −0.0372937 0.999304i \(-0.511874\pi\)
−0.0372937 + 0.999304i \(0.511874\pi\)
\(720\) 0 0
\(721\) −14.0000 −0.521387
\(722\) 19.0000 0.707107
\(723\) 0 0
\(724\) 23.0000 0.854788
\(725\) 0 0
\(726\) 0 0
\(727\) −6.00000 −0.222528 −0.111264 0.993791i \(-0.535490\pi\)
−0.111264 + 0.993791i \(0.535490\pi\)
\(728\) −6.00000 −0.222375
\(729\) 0 0
\(730\) 0 0
\(731\) −40.0000 −1.47945
\(732\) 0 0
\(733\) 44.0000 1.62518 0.812589 0.582838i \(-0.198058\pi\)
0.812589 + 0.582838i \(0.198058\pi\)
\(734\) 2.00000 0.0738213
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) −16.0000 −0.589368
\(738\) 0 0
\(739\) 13.0000 0.478213 0.239106 0.970993i \(-0.423146\pi\)
0.239106 + 0.970993i \(0.423146\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −6.00000 −0.220267
\(743\) −18.0000 −0.660356 −0.330178 0.943919i \(-0.607109\pi\)
−0.330178 + 0.943919i \(0.607109\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 3.00000 0.109838
\(747\) 0 0
\(748\) −16.0000 −0.585018
\(749\) 9.00000 0.328853
\(750\) 0 0
\(751\) −22.0000 −0.802791 −0.401396 0.915905i \(-0.631475\pi\)
−0.401396 + 0.915905i \(0.631475\pi\)
\(752\) 13.0000 0.474061
\(753\) 0 0
\(754\) −18.0000 −0.655521
\(755\) 0 0
\(756\) 0 0
\(757\) 19.0000 0.690567 0.345283 0.938498i \(-0.387783\pi\)
0.345283 + 0.938498i \(0.387783\pi\)
\(758\) 1.00000 0.0363216
\(759\) 0 0
\(760\) 0 0
\(761\) −3.00000 −0.108750 −0.0543750 0.998521i \(-0.517317\pi\)
−0.0543750 + 0.998521i \(0.517317\pi\)
\(762\) 0 0
\(763\) 20.0000 0.724049
\(764\) 0 0
\(765\) 0 0
\(766\) 8.00000 0.289052
\(767\) −30.0000 −1.08324
\(768\) 0 0
\(769\) −12.0000 −0.432731 −0.216366 0.976312i \(-0.569420\pi\)
−0.216366 + 0.976312i \(0.569420\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.00000 −0.0719816
\(773\) 27.0000 0.971123 0.485561 0.874203i \(-0.338615\pi\)
0.485561 + 0.874203i \(0.338615\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) 23.0000 0.824590
\(779\) 0 0
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) −16.0000 −0.572159
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) 7.00000 0.249523 0.124762 0.992187i \(-0.460183\pi\)
0.124762 + 0.992187i \(0.460183\pi\)
\(788\) −8.00000 −0.284988
\(789\) 0 0
\(790\) 0 0
\(791\) 3.00000 0.106668
\(792\) 0 0
\(793\) 42.0000 1.49146
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) 24.0000 0.850657
\(797\) −37.0000 −1.31061 −0.655304 0.755366i \(-0.727459\pi\)
−0.655304 + 0.755366i \(0.727459\pi\)
\(798\) 0 0
\(799\) −52.0000 −1.83963
\(800\) 0 0
\(801\) 0 0
\(802\) 16.0000 0.564980
\(803\) 28.0000 0.988099
\(804\) 0 0
\(805\) 0 0
\(806\) 42.0000 1.47939
\(807\) 0 0
\(808\) 10.0000 0.351799
\(809\) −18.0000 −0.632846 −0.316423 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) 0 0
\(811\) −14.0000 −0.491606 −0.245803 0.969320i \(-0.579052\pi\)
−0.245803 + 0.969320i \(0.579052\pi\)
\(812\) 3.00000 0.105279
\(813\) 0 0
\(814\) −4.00000 −0.140200
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −20.0000 −0.699284
\(819\) 0 0
\(820\) 0 0
\(821\) 2.00000 0.0698005 0.0349002 0.999391i \(-0.488889\pi\)
0.0349002 + 0.999391i \(0.488889\pi\)
\(822\) 0 0
\(823\) 51.0000 1.77775 0.888874 0.458151i \(-0.151488\pi\)
0.888874 + 0.458151i \(0.151488\pi\)
\(824\) −14.0000 −0.487713
\(825\) 0 0
\(826\) 5.00000 0.173972
\(827\) −25.0000 −0.869335 −0.434668 0.900591i \(-0.643134\pi\)
−0.434668 + 0.900591i \(0.643134\pi\)
\(828\) 0 0
\(829\) 6.00000 0.208389 0.104194 0.994557i \(-0.466774\pi\)
0.104194 + 0.994557i \(0.466774\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −6.00000 −0.208013
\(833\) −4.00000 −0.138592
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) −25.0000 −0.863611
\(839\) −4.00000 −0.138095 −0.0690477 0.997613i \(-0.521996\pi\)
−0.0690477 + 0.997613i \(0.521996\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) 20.0000 0.689246
\(843\) 0 0
\(844\) −15.0000 −0.516321
\(845\) 0 0
\(846\) 0 0
\(847\) −5.00000 −0.171802
\(848\) −6.00000 −0.206041
\(849\) 0 0
\(850\) 0 0
\(851\) −4.00000 −0.137118
\(852\) 0 0
\(853\) −16.0000 −0.547830 −0.273915 0.961754i \(-0.588319\pi\)
−0.273915 + 0.961754i \(0.588319\pi\)
\(854\) −7.00000 −0.239535
\(855\) 0 0
\(856\) 9.00000 0.307614
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) −40.0000 −1.36478 −0.682391 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 11.0000 0.374661
\(863\) −6.00000 −0.204242 −0.102121 0.994772i \(-0.532563\pi\)
−0.102121 + 0.994772i \(0.532563\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 29.0000 0.985460
\(867\) 0 0
\(868\) −7.00000 −0.237595
\(869\) 48.0000 1.62829
\(870\) 0 0
\(871\) 24.0000 0.813209
\(872\) 20.0000 0.677285
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −49.0000 −1.65461 −0.827306 0.561751i \(-0.810128\pi\)
−0.827306 + 0.561751i \(0.810128\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −33.0000 −1.11180 −0.555899 0.831250i \(-0.687626\pi\)
−0.555899 + 0.831250i \(0.687626\pi\)
\(882\) 0 0
\(883\) 54.0000 1.81724 0.908622 0.417619i \(-0.137135\pi\)
0.908622 + 0.417619i \(0.137135\pi\)
\(884\) 24.0000 0.807207
\(885\) 0 0
\(886\) 9.00000 0.302361
\(887\) −39.0000 −1.30949 −0.654746 0.755849i \(-0.727224\pi\)
−0.654746 + 0.755849i \(0.727224\pi\)
\(888\) 0 0
\(889\) −7.00000 −0.234772
\(890\) 0 0
\(891\) 0 0
\(892\) 4.00000 0.133930
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 36.0000 1.20134
\(899\) −21.0000 −0.700389
\(900\) 0 0
\(901\) 24.0000 0.799556
\(902\) −28.0000 −0.932298
\(903\) 0 0
\(904\) 3.00000 0.0997785
\(905\) 0 0
\(906\) 0 0
\(907\) 24.0000 0.796907 0.398453 0.917189i \(-0.369547\pi\)
0.398453 + 0.917189i \(0.369547\pi\)
\(908\) −16.0000 −0.530979
\(909\) 0 0
\(910\) 0 0
\(911\) −9.00000 −0.298183 −0.149092 0.988823i \(-0.547635\pi\)
−0.149092 + 0.988823i \(0.547635\pi\)
\(912\) 0 0
\(913\) 8.00000 0.264761
\(914\) 8.00000 0.264616
\(915\) 0 0
\(916\) 14.0000 0.462573
\(917\) 15.0000 0.495344
\(918\) 0 0
\(919\) 18.0000 0.593765 0.296883 0.954914i \(-0.404053\pi\)
0.296883 + 0.954914i \(0.404053\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −36.0000 −1.18560
\(923\) −18.0000 −0.592477
\(924\) 0 0
\(925\) 0 0
\(926\) −33.0000 −1.08445
\(927\) 0 0
\(928\) 3.00000 0.0984798
\(929\) 42.0000 1.37798 0.688988 0.724773i \(-0.258055\pi\)
0.688988 + 0.724773i \(0.258055\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −11.0000 −0.360317
\(933\) 0 0
\(934\) −18.0000 −0.588978
\(935\) 0 0
\(936\) 0 0
\(937\) 23.0000 0.751377 0.375689 0.926746i \(-0.377406\pi\)
0.375689 + 0.926746i \(0.377406\pi\)
\(938\) −4.00000 −0.130605
\(939\) 0 0
\(940\) 0 0
\(941\) 40.0000 1.30396 0.651981 0.758235i \(-0.273938\pi\)
0.651981 + 0.758235i \(0.273938\pi\)
\(942\) 0 0
\(943\) −28.0000 −0.911805
\(944\) 5.00000 0.162736
\(945\) 0 0
\(946\) −40.0000 −1.30051
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) 0 0
\(949\) −42.0000 −1.36338
\(950\) 0 0
\(951\) 0 0
\(952\) −4.00000 −0.129641
\(953\) −38.0000 −1.23094 −0.615470 0.788160i \(-0.711034\pi\)
−0.615470 + 0.788160i \(0.711034\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 13.0000 0.420450
\(957\) 0 0
\(958\) −4.00000 −0.129234
\(959\) 15.0000 0.484375
\(960\) 0 0
\(961\) 18.0000 0.580645
\(962\) 6.00000 0.193448
\(963\) 0 0
\(964\) −2.00000 −0.0644157
\(965\) 0 0
\(966\) 0 0
\(967\) 29.0000 0.932577 0.466289 0.884633i \(-0.345591\pi\)
0.466289 + 0.884633i \(0.345591\pi\)
\(968\) −5.00000 −0.160706
\(969\) 0 0
\(970\) 0 0
\(971\) −33.0000 −1.05902 −0.529510 0.848304i \(-0.677624\pi\)
−0.529510 + 0.848304i \(0.677624\pi\)
\(972\) 0 0
\(973\) 14.0000 0.448819
\(974\) −21.0000 −0.672883
\(975\) 0 0
\(976\) −7.00000 −0.224065
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 0 0
\(979\) −56.0000 −1.78977
\(980\) 0 0
\(981\) 0 0
\(982\) −30.0000 −0.957338
\(983\) 52.0000 1.65854 0.829271 0.558846i \(-0.188756\pi\)
0.829271 + 0.558846i \(0.188756\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −12.0000 −0.382158
\(987\) 0 0
\(988\) 0 0
\(989\) −40.0000 −1.27193
\(990\) 0 0
\(991\) −2.00000 −0.0635321 −0.0317660 0.999495i \(-0.510113\pi\)
−0.0317660 + 0.999495i \(0.510113\pi\)
\(992\) −7.00000 −0.222250
\(993\) 0 0
\(994\) 3.00000 0.0951542
\(995\) 0 0
\(996\) 0 0
\(997\) 12.0000 0.380044 0.190022 0.981780i \(-0.439144\pi\)
0.190022 + 0.981780i \(0.439144\pi\)
\(998\) −9.00000 −0.284890
\(999\) 0 0
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 9450.2.a.w.1.1 1
3.2 odd 2 9450.2.a.cc.1.1 1
5.2 odd 4 1890.2.g.k.379.1 yes 2
5.3 odd 4 1890.2.g.k.379.2 yes 2
5.4 even 2 9450.2.a.dx.1.1 1
15.2 even 4 1890.2.g.a.379.2 yes 2
15.8 even 4 1890.2.g.a.379.1 2
15.14 odd 2 9450.2.a.be.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1890.2.g.a.379.1 2 15.8 even 4
1890.2.g.a.379.2 yes 2 15.2 even 4
1890.2.g.k.379.1 yes 2 5.2 odd 4
1890.2.g.k.379.2 yes 2 5.3 odd 4
9450.2.a.w.1.1 1 1.1 even 1 trivial
9450.2.a.be.1.1 1 15.14 odd 2
9450.2.a.cc.1.1 1 3.2 odd 2
9450.2.a.dx.1.1 1 5.4 even 2