Properties

Label 3150.2.a.j.1.1
Level 3150
Weight 2
Character 3150.1
Self dual yes
Analytic conductor 25.153
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.1528766367\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 350)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 3150.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{11} -6.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} -3.00000 q^{19} -5.00000 q^{22} +6.00000 q^{26} -1.00000 q^{28} +6.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} -1.00000 q^{34} +8.00000 q^{37} +3.00000 q^{38} -11.0000 q^{41} -8.00000 q^{43} +5.00000 q^{44} -2.00000 q^{47} +1.00000 q^{49} -6.00000 q^{52} -4.00000 q^{53} +1.00000 q^{56} -6.00000 q^{58} -4.00000 q^{59} -2.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +9.00000 q^{67} +1.00000 q^{68} +10.0000 q^{71} -7.00000 q^{73} -8.00000 q^{74} -3.00000 q^{76} -5.00000 q^{77} -2.00000 q^{79} +11.0000 q^{82} -11.0000 q^{83} +8.00000 q^{86} -5.00000 q^{88} +11.0000 q^{89} +6.00000 q^{91} +2.00000 q^{94} -10.0000 q^{97} -1.00000 q^{98} +O(q^{100})\)

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
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 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
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 0 0
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −5.00000 −1.06600
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 6.00000 1.17670
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −1.00000 −0.171499
\(35\) 0 0
\(36\) 0 0
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 3.00000 0.486664
\(39\) 0 0
\(40\) 0 0
\(41\) −11.0000 −1.71791 −0.858956 0.512050i \(-0.828886\pi\)
−0.858956 + 0.512050i \(0.828886\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 5.00000 0.753778
\(45\) 0 0
\(46\) 0 0
\(47\) −2.00000 −0.291730 −0.145865 0.989305i \(-0.546597\pi\)
−0.145865 + 0.989305i \(0.546597\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) −6.00000 −0.832050
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 9.00000 1.09952 0.549762 0.835321i \(-0.314718\pi\)
0.549762 + 0.835321i \(0.314718\pi\)
\(68\) 1.00000 0.121268
\(69\) 0 0
\(70\) 0 0
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 0 0
\(73\) −7.00000 −0.819288 −0.409644 0.912245i \(-0.634347\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −8.00000 −0.929981
\(75\) 0 0
\(76\) −3.00000 −0.344124
\(77\) −5.00000 −0.569803
\(78\) 0 0
\(79\) −2.00000 −0.225018 −0.112509 0.993651i \(-0.535889\pi\)
−0.112509 + 0.993651i \(0.535889\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 11.0000 1.21475
\(83\) −11.0000 −1.20741 −0.603703 0.797209i \(-0.706309\pi\)
−0.603703 + 0.797209i \(0.706309\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 8.00000 0.862662
\(87\) 0 0
\(88\) −5.00000 −0.533002
\(89\) 11.0000 1.16600 0.582999 0.812473i \(-0.301879\pi\)
0.582999 + 0.812473i \(0.301879\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) 0 0
\(93\) 0 0
\(94\) 2.00000 0.206284
\(95\) 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
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) −18.0000 −1.72409 −0.862044 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) 1.00000 0.0940721 0.0470360 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) 4.00000 0.368230
\(119\) −1.00000 −0.0916698
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 2.00000 0.181071
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) 0 0
\(126\) 0 0
\(127\) −14.0000 −1.24230 −0.621150 0.783692i \(-0.713334\pi\)
−0.621150 + 0.783692i \(0.713334\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 0 0
\(133\) 3.00000 0.260133
\(134\) −9.00000 −0.777482
\(135\) 0 0
\(136\) −1.00000 −0.0857493
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 0 0
\(139\) −11.0000 −0.933008 −0.466504 0.884519i \(-0.654487\pi\)
−0.466504 + 0.884519i \(0.654487\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −10.0000 −0.839181
\(143\) −30.0000 −2.50873
\(144\) 0 0
\(145\) 0 0
\(146\) 7.00000 0.579324
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) −12.0000 −0.983078 −0.491539 0.870855i \(-0.663566\pi\)
−0.491539 + 0.870855i \(0.663566\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 3.00000 0.243332
\(153\) 0 0
\(154\) 5.00000 0.402911
\(155\) 0 0
\(156\) 0 0
\(157\) 4.00000 0.319235 0.159617 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) 2.00000 0.159111
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −19.0000 −1.48819 −0.744097 0.668071i \(-0.767120\pi\)
−0.744097 + 0.668071i \(0.767120\pi\)
\(164\) −11.0000 −0.858956
\(165\) 0 0
\(166\) 11.0000 0.853766
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 0 0
\(172\) −8.00000 −0.609994
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.00000 0.376889
\(177\) 0 0
\(178\) −11.0000 −0.824485
\(179\) −3.00000 −0.224231 −0.112115 0.993695i \(-0.535763\pi\)
−0.112115 + 0.993695i \(0.535763\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) −6.00000 −0.444750
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 5.00000 0.365636
\(188\) −2.00000 −0.145865
\(189\) 0 0
\(190\) 0 0
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 0 0
\(193\) −19.0000 −1.36765 −0.683825 0.729646i \(-0.739685\pi\)
−0.683825 + 0.729646i \(0.739685\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 0 0
\(199\) −10.0000 −0.708881 −0.354441 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −6.00000 −0.421117
\(204\) 0 0
\(205\) 0 0
\(206\) −4.00000 −0.278693
\(207\) 0 0
\(208\) −6.00000 −0.416025
\(209\) −15.0000 −1.03757
\(210\) 0 0
\(211\) 1.00000 0.0688428 0.0344214 0.999407i \(-0.489041\pi\)
0.0344214 + 0.999407i \(0.489041\pi\)
\(212\) −4.00000 −0.274721
\(213\) 0 0
\(214\) 3.00000 0.205076
\(215\) 0 0
\(216\) 0 0
\(217\) 4.00000 0.271538
\(218\) 18.0000 1.21911
\(219\) 0 0
\(220\) 0 0
\(221\) −6.00000 −0.403604
\(222\) 0 0
\(223\) 22.0000 1.47323 0.736614 0.676313i \(-0.236423\pi\)
0.736614 + 0.676313i \(0.236423\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −1.00000 −0.0665190
\(227\) 28.0000 1.85843 0.929213 0.369546i \(-0.120487\pi\)
0.929213 + 0.369546i \(0.120487\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −4.00000 −0.260378
\(237\) 0 0
\(238\) 1.00000 0.0648204
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 0 0
\(241\) −5.00000 −0.322078 −0.161039 0.986948i \(-0.551485\pi\)
−0.161039 + 0.986948i \(0.551485\pi\)
\(242\) −14.0000 −0.899954
\(243\) 0 0
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) 0 0
\(247\) 18.0000 1.14531
\(248\) 4.00000 0.254000
\(249\) 0 0
\(250\) 0 0
\(251\) −27.0000 −1.70422 −0.852112 0.523359i \(-0.824679\pi\)
−0.852112 + 0.523359i \(0.824679\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 14.0000 0.878438
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 0 0
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) 0 0
\(262\) 8.00000 0.494242
\(263\) 10.0000 0.616626 0.308313 0.951285i \(-0.400236\pi\)
0.308313 + 0.951285i \(0.400236\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −3.00000 −0.183942
\(267\) 0 0
\(268\) 9.00000 0.549762
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 0 0
\(271\) −6.00000 −0.364474 −0.182237 0.983255i \(-0.558334\pi\)
−0.182237 + 0.983255i \(0.558334\pi\)
\(272\) 1.00000 0.0606339
\(273\) 0 0
\(274\) −3.00000 −0.181237
\(275\) 0 0
\(276\) 0 0
\(277\) −30.0000 −1.80253 −0.901263 0.433273i \(-0.857359\pi\)
−0.901263 + 0.433273i \(0.857359\pi\)
\(278\) 11.0000 0.659736
\(279\) 0 0
\(280\) 0 0
\(281\) −14.0000 −0.835170 −0.417585 0.908638i \(-0.637123\pi\)
−0.417585 + 0.908638i \(0.637123\pi\)
\(282\) 0 0
\(283\) −13.0000 −0.772770 −0.386385 0.922338i \(-0.626276\pi\)
−0.386385 + 0.922338i \(0.626276\pi\)
\(284\) 10.0000 0.593391
\(285\) 0 0
\(286\) 30.0000 1.77394
\(287\) 11.0000 0.649309
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) 0 0
\(292\) −7.00000 −0.409644
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −8.00000 −0.464991
\(297\) 0 0
\(298\) 12.0000 0.695141
\(299\) 0 0
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) −8.00000 −0.460348
\(303\) 0 0
\(304\) −3.00000 −0.172062
\(305\) 0 0
\(306\) 0 0
\(307\) 13.0000 0.741949 0.370975 0.928643i \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) −5.00000 −0.284901
\(309\) 0 0
\(310\) 0 0
\(311\) −6.00000 −0.340229 −0.170114 0.985424i \(-0.554414\pi\)
−0.170114 + 0.985424i \(0.554414\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −2.00000 −0.112509
\(317\) −4.00000 −0.224662 −0.112331 0.993671i \(-0.535832\pi\)
−0.112331 + 0.993671i \(0.535832\pi\)
\(318\) 0 0
\(319\) 30.0000 1.67968
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.00000 −0.166924
\(324\) 0 0
\(325\) 0 0
\(326\) 19.0000 1.05231
\(327\) 0 0
\(328\) 11.0000 0.607373
\(329\) 2.00000 0.110264
\(330\) 0 0
\(331\) −17.0000 −0.934405 −0.467202 0.884150i \(-0.654738\pi\)
−0.467202 + 0.884150i \(0.654738\pi\)
\(332\) −11.0000 −0.603703
\(333\) 0 0
\(334\) 12.0000 0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) −29.0000 −1.57973 −0.789865 0.613280i \(-0.789850\pi\)
−0.789865 + 0.613280i \(0.789850\pi\)
\(338\) −23.0000 −1.25104
\(339\) 0 0
\(340\) 0 0
\(341\) −20.0000 −1.08306
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) 2.00000 0.107521
\(347\) −19.0000 −1.01997 −0.509987 0.860182i \(-0.670350\pi\)
−0.509987 + 0.860182i \(0.670350\pi\)
\(348\) 0 0
\(349\) −8.00000 −0.428230 −0.214115 0.976808i \(-0.568687\pi\)
−0.214115 + 0.976808i \(0.568687\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5.00000 −0.266501
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 11.0000 0.582999
\(357\) 0 0
\(358\) 3.00000 0.158555
\(359\) −26.0000 −1.37223 −0.686114 0.727494i \(-0.740685\pi\)
−0.686114 + 0.727494i \(0.740685\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) −10.0000 −0.525588
\(363\) 0 0
\(364\) 6.00000 0.314485
\(365\) 0 0
\(366\) 0 0
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) −5.00000 −0.258544
\(375\) 0 0
\(376\) 2.00000 0.103142
\(377\) −36.0000 −1.85409
\(378\) 0 0
\(379\) 9.00000 0.462299 0.231149 0.972918i \(-0.425751\pi\)
0.231149 + 0.972918i \(0.425751\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −6.00000 −0.306987
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 19.0000 0.967075
\(387\) 0 0
\(388\) −10.0000 −0.507673
\(389\) −8.00000 −0.405616 −0.202808 0.979219i \(-0.565007\pi\)
−0.202808 + 0.979219i \(0.565007\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) −22.0000 −1.10834
\(395\) 0 0
\(396\) 0 0
\(397\) 10.0000 0.501886 0.250943 0.968002i \(-0.419259\pi\)
0.250943 + 0.968002i \(0.419259\pi\)
\(398\) 10.0000 0.501255
\(399\) 0 0
\(400\) 0 0
\(401\) −37.0000 −1.84769 −0.923846 0.382765i \(-0.874972\pi\)
−0.923846 + 0.382765i \(0.874972\pi\)
\(402\) 0 0
\(403\) 24.0000 1.19553
\(404\) 0 0
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) 40.0000 1.98273
\(408\) 0 0
\(409\) −21.0000 −1.03838 −0.519192 0.854658i \(-0.673767\pi\)
−0.519192 + 0.854658i \(0.673767\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 4.00000 0.197066
\(413\) 4.00000 0.196827
\(414\) 0 0
\(415\) 0 0
\(416\) 6.00000 0.294174
\(417\) 0 0
\(418\) 15.0000 0.733674
\(419\) 39.0000 1.90527 0.952637 0.304109i \(-0.0983586\pi\)
0.952637 + 0.304109i \(0.0983586\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 0 0
\(424\) 4.00000 0.194257
\(425\) 0 0
\(426\) 0 0
\(427\) 2.00000 0.0967868
\(428\) −3.00000 −0.145010
\(429\) 0 0
\(430\) 0 0
\(431\) 36.0000 1.73406 0.867029 0.498257i \(-0.166026\pi\)
0.867029 + 0.498257i \(0.166026\pi\)
\(432\) 0 0
\(433\) −1.00000 −0.0480569 −0.0240285 0.999711i \(-0.507649\pi\)
−0.0240285 + 0.999711i \(0.507649\pi\)
\(434\) −4.00000 −0.192006
\(435\) 0 0
\(436\) −18.0000 −0.862044
\(437\) 0 0
\(438\) 0 0
\(439\) 28.0000 1.33637 0.668184 0.743996i \(-0.267072\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 6.00000 0.285391
\(443\) −37.0000 −1.75792 −0.878962 0.476893i \(-0.841763\pi\)
−0.878962 + 0.476893i \(0.841763\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −22.0000 −1.04173
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) −33.0000 −1.55737 −0.778683 0.627417i \(-0.784112\pi\)
−0.778683 + 0.627417i \(0.784112\pi\)
\(450\) 0 0
\(451\) −55.0000 −2.58985
\(452\) 1.00000 0.0470360
\(453\) 0 0
\(454\) −28.0000 −1.31411
\(455\) 0 0
\(456\) 0 0
\(457\) 25.0000 1.16945 0.584725 0.811231i \(-0.301202\pi\)
0.584725 + 0.811231i \(0.301202\pi\)
\(458\) 14.0000 0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) 38.0000 1.76984 0.884918 0.465746i \(-0.154214\pi\)
0.884918 + 0.465746i \(0.154214\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) 4.00000 0.185098 0.0925490 0.995708i \(-0.470499\pi\)
0.0925490 + 0.995708i \(0.470499\pi\)
\(468\) 0 0
\(469\) −9.00000 −0.415581
\(470\) 0 0
\(471\) 0 0
\(472\) 4.00000 0.184115
\(473\) −40.0000 −1.83920
\(474\) 0 0
\(475\) 0 0
\(476\) −1.00000 −0.0458349
\(477\) 0 0
\(478\) 4.00000 0.182956
\(479\) 6.00000 0.274147 0.137073 0.990561i \(-0.456230\pi\)
0.137073 + 0.990561i \(0.456230\pi\)
\(480\) 0 0
\(481\) −48.0000 −2.18861
\(482\) 5.00000 0.227744
\(483\) 0 0
\(484\) 14.0000 0.636364
\(485\) 0 0
\(486\) 0 0
\(487\) −34.0000 −1.54069 −0.770344 0.637629i \(-0.779915\pi\)
−0.770344 + 0.637629i \(0.779915\pi\)
\(488\) 2.00000 0.0905357
\(489\) 0 0
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) 6.00000 0.270226
\(494\) −18.0000 −0.809858
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) −10.0000 −0.448561
\(498\) 0 0
\(499\) 36.0000 1.61158 0.805791 0.592200i \(-0.201741\pi\)
0.805791 + 0.592200i \(0.201741\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 27.0000 1.20507
\(503\) 30.0000 1.33763 0.668817 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −14.0000 −0.621150
\(509\) 14.0000 0.620539 0.310270 0.950649i \(-0.399581\pi\)
0.310270 + 0.950649i \(0.399581\pi\)
\(510\) 0 0
\(511\) 7.00000 0.309662
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 2.00000 0.0882162
\(515\) 0 0
\(516\) 0 0
\(517\) −10.0000 −0.439799
\(518\) 8.00000 0.351500
\(519\) 0 0
\(520\) 0 0
\(521\) −11.0000 −0.481919 −0.240959 0.970535i \(-0.577462\pi\)
−0.240959 + 0.970535i \(0.577462\pi\)
\(522\) 0 0
\(523\) 13.0000 0.568450 0.284225 0.958758i \(-0.408264\pi\)
0.284225 + 0.958758i \(0.408264\pi\)
\(524\) −8.00000 −0.349482
\(525\) 0 0
\(526\) −10.0000 −0.436021
\(527\) −4.00000 −0.174243
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 3.00000 0.130066
\(533\) 66.0000 2.85878
\(534\) 0 0
\(535\) 0 0
\(536\) −9.00000 −0.388741
\(537\) 0 0
\(538\) 18.0000 0.776035
\(539\) 5.00000 0.215365
\(540\) 0 0
\(541\) −42.0000 −1.80572 −0.902861 0.429934i \(-0.858537\pi\)
−0.902861 + 0.429934i \(0.858537\pi\)
\(542\) 6.00000 0.257722
\(543\) 0 0
\(544\) −1.00000 −0.0428746
\(545\) 0 0
\(546\) 0 0
\(547\) 27.0000 1.15444 0.577218 0.816590i \(-0.304138\pi\)
0.577218 + 0.816590i \(0.304138\pi\)
\(548\) 3.00000 0.128154
\(549\) 0 0
\(550\) 0 0
\(551\) −18.0000 −0.766826
\(552\) 0 0
\(553\) 2.00000 0.0850487
\(554\) 30.0000 1.27458
\(555\) 0 0
\(556\) −11.0000 −0.466504
\(557\) −4.00000 −0.169485 −0.0847427 0.996403i \(-0.527007\pi\)
−0.0847427 + 0.996403i \(0.527007\pi\)
\(558\) 0 0
\(559\) 48.0000 2.03018
\(560\) 0 0
\(561\) 0 0
\(562\) 14.0000 0.590554
\(563\) −20.0000 −0.842900 −0.421450 0.906852i \(-0.638479\pi\)
−0.421450 + 0.906852i \(0.638479\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 13.0000 0.546431
\(567\) 0 0
\(568\) −10.0000 −0.419591
\(569\) −21.0000 −0.880366 −0.440183 0.897908i \(-0.645086\pi\)
−0.440183 + 0.897908i \(0.645086\pi\)
\(570\) 0 0
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) −30.0000 −1.25436
\(573\) 0 0
\(574\) −11.0000 −0.459131
\(575\) 0 0
\(576\) 0 0
\(577\) 13.0000 0.541197 0.270599 0.962692i \(-0.412778\pi\)
0.270599 + 0.962692i \(0.412778\pi\)
\(578\) 16.0000 0.665512
\(579\) 0 0
\(580\) 0 0
\(581\) 11.0000 0.456357
\(582\) 0 0
\(583\) −20.0000 −0.828315
\(584\) 7.00000 0.289662
\(585\) 0 0
\(586\) −14.0000 −0.578335
\(587\) 13.0000 0.536567 0.268284 0.963340i \(-0.413544\pi\)
0.268284 + 0.963340i \(0.413544\pi\)
\(588\) 0 0
\(589\) 12.0000 0.494451
\(590\) 0 0
\(591\) 0 0
\(592\) 8.00000 0.328798
\(593\) 39.0000 1.60154 0.800769 0.598973i \(-0.204424\pi\)
0.800769 + 0.598973i \(0.204424\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −12.0000 −0.491539
\(597\) 0 0
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) 21.0000 0.856608 0.428304 0.903635i \(-0.359111\pi\)
0.428304 + 0.903635i \(0.359111\pi\)
\(602\) −8.00000 −0.326056
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 0 0
\(606\) 0 0
\(607\) 28.0000 1.13648 0.568242 0.822861i \(-0.307624\pi\)
0.568242 + 0.822861i \(0.307624\pi\)
\(608\) 3.00000 0.121666
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) 0 0
\(613\) 18.0000 0.727013 0.363507 0.931592i \(-0.381579\pi\)
0.363507 + 0.931592i \(0.381579\pi\)
\(614\) −13.0000 −0.524637
\(615\) 0 0
\(616\) 5.00000 0.201456
\(617\) −14.0000 −0.563619 −0.281809 0.959470i \(-0.590935\pi\)
−0.281809 + 0.959470i \(0.590935\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 6.00000 0.240578
\(623\) −11.0000 −0.440706
\(624\) 0 0
\(625\) 0 0
\(626\) 10.0000 0.399680
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 2.00000 0.0795557
\(633\) 0 0
\(634\) 4.00000 0.158860
\(635\) 0 0
\(636\) 0 0
\(637\) −6.00000 −0.237729
\(638\) −30.0000 −1.18771
\(639\) 0 0
\(640\) 0 0
\(641\) −2.00000 −0.0789953 −0.0394976 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 0 0
\(643\) 16.0000 0.630978 0.315489 0.948929i \(-0.397831\pi\)
0.315489 + 0.948929i \(0.397831\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 3.00000 0.118033
\(647\) 8.00000 0.314512 0.157256 0.987558i \(-0.449735\pi\)
0.157256 + 0.987558i \(0.449735\pi\)
\(648\) 0 0
\(649\) −20.0000 −0.785069
\(650\) 0 0
\(651\) 0 0
\(652\) −19.0000 −0.744097
\(653\) 28.0000 1.09572 0.547862 0.836569i \(-0.315442\pi\)
0.547862 + 0.836569i \(0.315442\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −11.0000 −0.429478
\(657\) 0 0
\(658\) −2.00000 −0.0779681
\(659\) −1.00000 −0.0389545 −0.0194772 0.999810i \(-0.506200\pi\)
−0.0194772 + 0.999810i \(0.506200\pi\)
\(660\) 0 0
\(661\) −50.0000 −1.94477 −0.972387 0.233373i \(-0.925024\pi\)
−0.972387 + 0.233373i \(0.925024\pi\)
\(662\) 17.0000 0.660724
\(663\) 0 0
\(664\) 11.0000 0.426883
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −12.0000 −0.464294
\(669\) 0 0
\(670\) 0 0
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 29.0000 1.11704
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) 48.0000 1.84479 0.922395 0.386248i \(-0.126229\pi\)
0.922395 + 0.386248i \(0.126229\pi\)
\(678\) 0 0
\(679\) 10.0000 0.383765
\(680\) 0 0
\(681\) 0 0
\(682\) 20.0000 0.765840
\(683\) 13.0000 0.497431 0.248716 0.968577i \(-0.419992\pi\)
0.248716 + 0.968577i \(0.419992\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) −8.00000 −0.304997
\(689\) 24.0000 0.914327
\(690\) 0 0
\(691\) 49.0000 1.86405 0.932024 0.362397i \(-0.118041\pi\)
0.932024 + 0.362397i \(0.118041\pi\)
\(692\) −2.00000 −0.0760286
\(693\) 0 0
\(694\) 19.0000 0.721230
\(695\) 0 0
\(696\) 0 0
\(697\) −11.0000 −0.416655
\(698\) 8.00000 0.302804
\(699\) 0 0
\(700\) 0 0
\(701\) 32.0000 1.20862 0.604312 0.796748i \(-0.293448\pi\)
0.604312 + 0.796748i \(0.293448\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) 5.00000 0.188445
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) 0 0
\(708\) 0 0
\(709\) 4.00000 0.150223 0.0751116 0.997175i \(-0.476069\pi\)
0.0751116 + 0.997175i \(0.476069\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −11.0000 −0.412242
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −3.00000 −0.112115
\(717\) 0 0
\(718\) 26.0000 0.970311
\(719\) 48.0000 1.79010 0.895049 0.445968i \(-0.147140\pi\)
0.895049 + 0.445968i \(0.147140\pi\)
\(720\) 0 0
\(721\) −4.00000 −0.148968
\(722\) 10.0000 0.372161
\(723\) 0 0
\(724\) 10.0000 0.371647
\(725\) 0 0
\(726\) 0 0
\(727\) 6.00000 0.222528 0.111264 0.993791i \(-0.464510\pi\)
0.111264 + 0.993791i \(0.464510\pi\)
\(728\) −6.00000 −0.222375
\(729\) 0 0
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 0 0
\(733\) 40.0000 1.47743 0.738717 0.674016i \(-0.235432\pi\)
0.738717 + 0.674016i \(0.235432\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) 0 0
\(737\) 45.0000 1.65760
\(738\) 0 0
\(739\) 4.00000 0.147142 0.0735712 0.997290i \(-0.476560\pi\)
0.0735712 + 0.997290i \(0.476560\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −4.00000 −0.146845
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 4.00000 0.146450
\(747\) 0 0
\(748\) 5.00000 0.182818
\(749\) 3.00000 0.109618
\(750\) 0 0
\(751\) 50.0000 1.82453 0.912263 0.409605i \(-0.134333\pi\)
0.912263 + 0.409605i \(0.134333\pi\)
\(752\) −2.00000 −0.0729325
\(753\) 0 0
\(754\) 36.0000 1.31104
\(755\) 0 0
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −9.00000 −0.326895
\(759\) 0 0
\(760\) 0 0
\(761\) −27.0000 −0.978749 −0.489375 0.872074i \(-0.662775\pi\)
−0.489375 + 0.872074i \(0.662775\pi\)
\(762\) 0 0
\(763\) 18.0000 0.651644
\(764\) 6.00000 0.217072
\(765\) 0 0
\(766\) −6.00000 −0.216789
\(767\) 24.0000 0.866590
\(768\) 0 0
\(769\) 19.0000 0.685158 0.342579 0.939489i \(-0.388700\pi\)
0.342579 + 0.939489i \(0.388700\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −19.0000 −0.683825
\(773\) −36.0000 −1.29483 −0.647415 0.762138i \(-0.724150\pi\)
−0.647415 + 0.762138i \(0.724150\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) 8.00000 0.286814
\(779\) 33.0000 1.18235
\(780\) 0 0
\(781\) 50.0000 1.78914
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) 52.0000 1.85360 0.926800 0.375555i \(-0.122548\pi\)
0.926800 + 0.375555i \(0.122548\pi\)
\(788\) 22.0000 0.783718
\(789\) 0 0
\(790\) 0 0
\(791\) −1.00000 −0.0355559
\(792\) 0 0
\(793\) 12.0000 0.426132
\(794\) −10.0000 −0.354887
\(795\) 0 0
\(796\) −10.0000 −0.354441
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) −2.00000 −0.0707549
\(800\) 0 0
\(801\) 0 0
\(802\) 37.0000 1.30652
\(803\) −35.0000 −1.23512
\(804\) 0 0
\(805\) 0 0
\(806\) −24.0000 −0.845364
\(807\) 0 0
\(808\) 0 0
\(809\) −6.00000 −0.210949 −0.105474 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) 0 0
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) −6.00000 −0.210559
\(813\) 0 0
\(814\) −40.0000 −1.40200
\(815\) 0 0
\(816\) 0 0
\(817\) 24.0000 0.839654
\(818\) 21.0000 0.734248
\(819\) 0 0
\(820\) 0 0
\(821\) 24.0000 0.837606 0.418803 0.908077i \(-0.362450\pi\)
0.418803 + 0.908077i \(0.362450\pi\)
\(822\) 0 0
\(823\) 10.0000 0.348578 0.174289 0.984695i \(-0.444237\pi\)
0.174289 + 0.984695i \(0.444237\pi\)
\(824\) −4.00000 −0.139347
\(825\) 0 0
\(826\) −4.00000 −0.139178
\(827\) −41.0000 −1.42571 −0.712855 0.701312i \(-0.752598\pi\)
−0.712855 + 0.701312i \(0.752598\pi\)
\(828\) 0 0
\(829\) −4.00000 −0.138926 −0.0694629 0.997585i \(-0.522129\pi\)
−0.0694629 + 0.997585i \(0.522129\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −6.00000 −0.208013
\(833\) 1.00000 0.0346479
\(834\) 0 0
\(835\) 0 0
\(836\) −15.0000 −0.518786
\(837\) 0 0
\(838\) −39.0000 −1.34723
\(839\) −2.00000 −0.0690477 −0.0345238 0.999404i \(-0.510991\pi\)
−0.0345238 + 0.999404i \(0.510991\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −20.0000 −0.689246
\(843\) 0 0
\(844\) 1.00000 0.0344214
\(845\) 0 0
\(846\) 0 0
\(847\) −14.0000 −0.481046
\(848\) −4.00000 −0.137361
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −34.0000 −1.16414 −0.582069 0.813139i \(-0.697757\pi\)
−0.582069 + 0.813139i \(0.697757\pi\)
\(854\) −2.00000 −0.0684386
\(855\) 0 0
\(856\) 3.00000 0.102538
\(857\) −3.00000 −0.102478 −0.0512390 0.998686i \(-0.516317\pi\)
−0.0512390 + 0.998686i \(0.516317\pi\)
\(858\) 0 0
\(859\) −51.0000 −1.74010 −0.870049 0.492966i \(-0.835913\pi\)
−0.870049 + 0.492966i \(0.835913\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −36.0000 −1.22616
\(863\) −4.00000 −0.136162 −0.0680808 0.997680i \(-0.521688\pi\)
−0.0680808 + 0.997680i \(0.521688\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 1.00000 0.0339814
\(867\) 0 0
\(868\) 4.00000 0.135769
\(869\) −10.0000 −0.339227
\(870\) 0 0
\(871\) −54.0000 −1.82972
\(872\) 18.0000 0.609557
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 32.0000 1.08056 0.540282 0.841484i \(-0.318318\pi\)
0.540282 + 0.841484i \(0.318318\pi\)
\(878\) −28.0000 −0.944954
\(879\) 0 0
\(880\) 0 0
\(881\) −26.0000 −0.875962 −0.437981 0.898984i \(-0.644306\pi\)
−0.437981 + 0.898984i \(0.644306\pi\)
\(882\) 0 0
\(883\) 15.0000 0.504790 0.252395 0.967624i \(-0.418782\pi\)
0.252395 + 0.967624i \(0.418782\pi\)
\(884\) −6.00000 −0.201802
\(885\) 0 0
\(886\) 37.0000 1.24304
\(887\) 34.0000 1.14161 0.570804 0.821086i \(-0.306632\pi\)
0.570804 + 0.821086i \(0.306632\pi\)
\(888\) 0 0
\(889\) 14.0000 0.469545
\(890\) 0 0
\(891\) 0 0
\(892\) 22.0000 0.736614
\(893\) 6.00000 0.200782
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 33.0000 1.10122
\(899\) −24.0000 −0.800445
\(900\) 0 0
\(901\) −4.00000 −0.133259
\(902\) 55.0000 1.83130
\(903\) 0 0
\(904\) −1.00000 −0.0332595
\(905\) 0 0
\(906\) 0 0
\(907\) −4.00000 −0.132818 −0.0664089 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) 28.0000 0.929213
\(909\) 0 0
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 0 0
\(913\) −55.0000 −1.82023
\(914\) −25.0000 −0.826927
\(915\) 0 0
\(916\) −14.0000 −0.462573
\(917\) 8.00000 0.264183
\(918\) 0 0
\(919\) −34.0000 −1.12156 −0.560778 0.827966i \(-0.689498\pi\)
−0.560778 + 0.827966i \(0.689498\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −38.0000 −1.25146
\(923\) −60.0000 −1.97492
\(924\) 0 0
\(925\) 0 0
\(926\) −8.00000 −0.262896
\(927\) 0 0
\(928\) −6.00000 −0.196960
\(929\) −46.0000 −1.50921 −0.754606 0.656179i \(-0.772172\pi\)
−0.754606 + 0.656179i \(0.772172\pi\)
\(930\) 0 0
\(931\) −3.00000 −0.0983210
\(932\) −6.00000 −0.196537
\(933\) 0 0
\(934\) −4.00000 −0.130884
\(935\) 0 0
\(936\) 0 0
\(937\) −7.00000 −0.228680 −0.114340 0.993442i \(-0.536475\pi\)
−0.114340 + 0.993442i \(0.536475\pi\)
\(938\) 9.00000 0.293860
\(939\) 0 0
\(940\) 0 0
\(941\) −56.0000 −1.82555 −0.912774 0.408465i \(-0.866064\pi\)
−0.912774 + 0.408465i \(0.866064\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) 40.0000 1.30051
\(947\) 4.00000 0.129983 0.0649913 0.997886i \(-0.479298\pi\)
0.0649913 + 0.997886i \(0.479298\pi\)
\(948\) 0 0
\(949\) 42.0000 1.36338
\(950\) 0 0
\(951\) 0 0
\(952\) 1.00000 0.0324102
\(953\) −9.00000 −0.291539 −0.145769 0.989319i \(-0.546566\pi\)
−0.145769 + 0.989319i \(0.546566\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −4.00000 −0.129369
\(957\) 0 0
\(958\) −6.00000 −0.193851
\(959\) −3.00000 −0.0968751
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 48.0000 1.54758
\(963\) 0 0
\(964\) −5.00000 −0.161039
\(965\) 0 0
\(966\) 0 0
\(967\) −2.00000 −0.0643157 −0.0321578 0.999483i \(-0.510238\pi\)
−0.0321578 + 0.999483i \(0.510238\pi\)
\(968\) −14.0000 −0.449977
\(969\) 0 0
\(970\) 0 0
\(971\) 51.0000 1.63667 0.818334 0.574743i \(-0.194898\pi\)
0.818334 + 0.574743i \(0.194898\pi\)
\(972\) 0 0
\(973\) 11.0000 0.352644
\(974\) 34.0000 1.08943
\(975\) 0 0
\(976\) −2.00000 −0.0640184
\(977\) −21.0000 −0.671850 −0.335925 0.941889i \(-0.609049\pi\)
−0.335925 + 0.941889i \(0.609049\pi\)
\(978\) 0 0
\(979\) 55.0000 1.75781
\(980\) 0 0
\(981\) 0 0
\(982\) −12.0000 −0.382935
\(983\) 4.00000 0.127580 0.0637901 0.997963i \(-0.479681\pi\)
0.0637901 + 0.997963i \(0.479681\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −6.00000 −0.191079
\(987\) 0 0
\(988\) 18.0000 0.572656
\(989\) 0 0
\(990\) 0 0
\(991\) 4.00000 0.127064 0.0635321 0.997980i \(-0.479763\pi\)
0.0635321 + 0.997980i \(0.479763\pi\)
\(992\) 4.00000 0.127000
\(993\) 0 0
\(994\) 10.0000 0.317181
\(995\) 0 0
\(996\) 0 0
\(997\) −58.0000 −1.83688 −0.918439 0.395562i \(-0.870550\pi\)
−0.918439 + 0.395562i \(0.870550\pi\)
\(998\) −36.0000 −1.13956
\(999\) 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 3150.2.a.j.1.1 1
3.2 odd 2 350.2.a.d.1.1 yes 1
5.2 odd 4 3150.2.g.v.2899.1 2
5.3 odd 4 3150.2.g.v.2899.2 2
5.4 even 2 3150.2.a.bq.1.1 1
12.11 even 2 2800.2.a.bg.1.1 1
15.2 even 4 350.2.c.a.99.2 2
15.8 even 4 350.2.c.a.99.1 2
15.14 odd 2 350.2.a.c.1.1 1
21.20 even 2 2450.2.a.bg.1.1 1
60.23 odd 4 2800.2.g.a.449.2 2
60.47 odd 4 2800.2.g.a.449.1 2
60.59 even 2 2800.2.a.b.1.1 1
105.62 odd 4 2450.2.c.r.99.2 2
105.83 odd 4 2450.2.c.r.99.1 2
105.104 even 2 2450.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.a.c.1.1 1 15.14 odd 2
350.2.a.d.1.1 yes 1 3.2 odd 2
350.2.c.a.99.1 2 15.8 even 4
350.2.c.a.99.2 2 15.2 even 4
2450.2.a.a.1.1 1 105.104 even 2
2450.2.a.bg.1.1 1 21.20 even 2
2450.2.c.r.99.1 2 105.83 odd 4
2450.2.c.r.99.2 2 105.62 odd 4
2800.2.a.b.1.1 1 60.59 even 2
2800.2.a.bg.1.1 1 12.11 even 2
2800.2.g.a.449.1 2 60.47 odd 4
2800.2.g.a.449.2 2 60.23 odd 4
3150.2.a.j.1.1 1 1.1 even 1 trivial
3150.2.a.bq.1.1 1 5.4 even 2
3150.2.g.v.2899.1 2 5.2 odd 4
3150.2.g.v.2899.2 2 5.3 odd 4