Properties

Label 7350.2.a.n.1.1
Level 7350
Weight 2
Character 7350.1
Self dual yes
Analytic conductor 58.690
Analytic rank 1
Dimension 1
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7350.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.6900454856\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1050)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7350.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{12} +4.00000 q^{13} +1.00000 q^{16} -3.00000 q^{17} -1.00000 q^{18} -2.00000 q^{19} +3.00000 q^{23} +1.00000 q^{24} -4.00000 q^{26} -1.00000 q^{27} +1.00000 q^{31} -1.00000 q^{32} +3.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} +2.00000 q^{38} -4.00000 q^{39} +9.00000 q^{41} -10.0000 q^{43} -3.00000 q^{46} +3.00000 q^{47} -1.00000 q^{48} +3.00000 q^{51} +4.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} +2.00000 q^{57} +6.00000 q^{59} -8.00000 q^{61} -1.00000 q^{62} +1.00000 q^{64} -4.00000 q^{67} -3.00000 q^{68} -3.00000 q^{69} +3.00000 q^{71} -1.00000 q^{72} -14.0000 q^{73} +10.0000 q^{74} -2.00000 q^{76} +4.00000 q^{78} +11.0000 q^{79} +1.00000 q^{81} -9.00000 q^{82} +10.0000 q^{86} +15.0000 q^{89} +3.00000 q^{92} -1.00000 q^{93} -3.00000 q^{94} +1.00000 q^{96} +7.00000 q^{97} +O(q^{100})\)

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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −1.00000 −0.288675
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 1.00000 0.204124
\(25\) 0 0
\(26\) −4.00000 −0.784465
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 1.00000 0.179605 0.0898027 0.995960i \(-0.471376\pi\)
0.0898027 + 0.995960i \(0.471376\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 2.00000 0.324443
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 0 0
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.00000 −0.442326
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 0 0
\(51\) 3.00000 0.420084
\(52\) 4.00000 0.554700
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 0 0
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) −1.00000 −0.127000
\(63\) 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 \(0.578571\pi\)
\(68\) −3.00000 −0.363803
\(69\) −3.00000 −0.361158
\(70\) 0 0
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) −1.00000 −0.117851
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 10.0000 1.16248
\(75\) 0 0
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 4.00000 0.452911
\(79\) 11.0000 1.23760 0.618798 0.785550i \(-0.287620\pi\)
0.618798 + 0.785550i \(0.287620\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −9.00000 −0.993884
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 10.0000 1.07833
\(87\) 0 0
\(88\) 0 0
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.00000 0.312772
\(93\) −1.00000 −0.103695
\(94\) −3.00000 −0.309426
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) −3.00000 −0.297044
\(103\) −5.00000 −0.492665 −0.246332 0.969185i \(-0.579225\pi\)
−0.246332 + 0.969185i \(0.579225\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −18.0000 −1.74013 −0.870063 0.492941i \(-0.835922\pi\)
−0.870063 + 0.492941i \(0.835922\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) 21.0000 1.97551 0.987757 0.156001i \(-0.0498603\pi\)
0.987757 + 0.156001i \(0.0498603\pi\)
\(114\) −2.00000 −0.187317
\(115\) 0 0
\(116\) 0 0
\(117\) 4.00000 0.369800
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 8.00000 0.724286
\(123\) −9.00000 −0.811503
\(124\) 1.00000 0.0898027
\(125\) 0 0
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.0000 0.880451
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 3.00000 0.257248
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) 3.00000 0.255377
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) −3.00000 −0.251754
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 14.0000 1.15865
\(147\) 0 0
\(148\) −10.0000 −0.821995
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 2.00000 0.162221
\(153\) −3.00000 −0.242536
\(154\) 0 0
\(155\) 0 0
\(156\) −4.00000 −0.320256
\(157\) −8.00000 −0.638470 −0.319235 0.947676i \(-0.603426\pi\)
−0.319235 + 0.947676i \(0.603426\pi\)
\(158\) −11.0000 −0.875113
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 8.00000 0.626608 0.313304 0.949653i \(-0.398564\pi\)
0.313304 + 0.949653i \(0.398564\pi\)
\(164\) 9.00000 0.702782
\(165\) 0 0
\(166\) 0 0
\(167\) 24.0000 1.85718 0.928588 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −2.00000 −0.152944
\(172\) −10.0000 −0.762493
\(173\) 18.0000 1.36851 0.684257 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) −15.0000 −1.12430
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) −3.00000 −0.221163
\(185\) 0 0
\(186\) 1.00000 0.0733236
\(187\) 0 0
\(188\) 3.00000 0.218797
\(189\) 0 0
\(190\) 0 0
\(191\) −21.0000 −1.51951 −0.759753 0.650211i \(-0.774680\pi\)
−0.759753 + 0.650211i \(0.774680\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 17.0000 1.22369 0.611843 0.790979i \(-0.290428\pi\)
0.611843 + 0.790979i \(0.290428\pi\)
\(194\) −7.00000 −0.502571
\(195\) 0 0
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) −11.0000 −0.779769 −0.389885 0.920864i \(-0.627485\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) 18.0000 1.26648
\(203\) 0 0
\(204\) 3.00000 0.210042
\(205\) 0 0
\(206\) 5.00000 0.348367
\(207\) 3.00000 0.208514
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) −6.00000 −0.412082
\(213\) −3.00000 −0.205557
\(214\) 18.0000 1.23045
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) 14.0000 0.946032
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) −10.0000 −0.671156
\(223\) 19.0000 1.27233 0.636167 0.771551i \(-0.280519\pi\)
0.636167 + 0.771551i \(0.280519\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −21.0000 −1.39690
\(227\) 6.00000 0.398234 0.199117 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(228\) 2.00000 0.132453
\(229\) 4.00000 0.264327 0.132164 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −30.0000 −1.96537 −0.982683 0.185296i \(-0.940675\pi\)
−0.982683 + 0.185296i \(0.940675\pi\)
\(234\) −4.00000 −0.261488
\(235\) 0 0
\(236\) 6.00000 0.390567
\(237\) −11.0000 −0.714527
\(238\) 0 0
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) 0 0
\(241\) −14.0000 −0.901819 −0.450910 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 11.0000 0.707107
\(243\) −1.00000 −0.0641500
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) 9.00000 0.573819
\(247\) −8.00000 −0.509028
\(248\) −1.00000 −0.0635001
\(249\) 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
\(253\) 0 0
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −30.0000 −1.87135 −0.935674 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) −10.0000 −0.622573
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −12.0000 −0.741362
\(263\) 9.00000 0.554964 0.277482 0.960731i \(-0.410500\pi\)
0.277482 + 0.960731i \(0.410500\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −15.0000 −0.917985
\(268\) −4.00000 −0.244339
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) 7.00000 0.425220 0.212610 0.977137i \(-0.431804\pi\)
0.212610 + 0.977137i \(0.431804\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) 9.00000 0.543710
\(275\) 0 0
\(276\) −3.00000 −0.180579
\(277\) −28.0000 −1.68236 −0.841178 0.540758i \(-0.818138\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 2.00000 0.119952
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 3.00000 0.178647
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 3.00000 0.178017
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −7.00000 −0.410347
\(292\) −14.0000 −0.819288
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 10.0000 0.581238
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 12.0000 0.693978
\(300\) 0 0
\(301\) 0 0
\(302\) −8.00000 −0.460348
\(303\) 18.0000 1.03407
\(304\) −2.00000 −0.114708
\(305\) 0 0
\(306\) 3.00000 0.171499
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 5.00000 0.284440
\(310\) 0 0
\(311\) −9.00000 −0.510343 −0.255172 0.966896i \(-0.582132\pi\)
−0.255172 + 0.966896i \(0.582132\pi\)
\(312\) 4.00000 0.226455
\(313\) −5.00000 −0.282617 −0.141308 0.989966i \(-0.545131\pi\)
−0.141308 + 0.989966i \(0.545131\pi\)
\(314\) 8.00000 0.451466
\(315\) 0 0
\(316\) 11.0000 0.618798
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) −6.00000 −0.336463
\(319\) 0 0
\(320\) 0 0
\(321\) 18.0000 1.00466
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −8.00000 −0.443079
\(327\) −2.00000 −0.110600
\(328\) −9.00000 −0.496942
\(329\) 0 0
\(330\) 0 0
\(331\) −10.0000 −0.549650 −0.274825 0.961494i \(-0.588620\pi\)
−0.274825 + 0.961494i \(0.588620\pi\)
\(332\) 0 0
\(333\) −10.0000 −0.547997
\(334\) −24.0000 −1.31322
\(335\) 0 0
\(336\) 0 0
\(337\) 11.0000 0.599208 0.299604 0.954064i \(-0.403145\pi\)
0.299604 + 0.954064i \(0.403145\pi\)
\(338\) −3.00000 −0.163178
\(339\) −21.0000 −1.14056
\(340\) 0 0
\(341\) 0 0
\(342\) 2.00000 0.108148
\(343\) 0 0
\(344\) 10.0000 0.539164
\(345\) 0 0
\(346\) −18.0000 −0.967686
\(347\) −36.0000 −1.93258 −0.966291 0.257454i \(-0.917117\pi\)
−0.966291 + 0.257454i \(0.917117\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) 15.0000 0.798369 0.399185 0.916871i \(-0.369293\pi\)
0.399185 + 0.916871i \(0.369293\pi\)
\(354\) 6.00000 0.318896
\(355\) 0 0
\(356\) 15.0000 0.794998
\(357\) 0 0
\(358\) 6.00000 0.317110
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 8.00000 0.420471
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 0 0
\(366\) −8.00000 −0.418167
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 3.00000 0.156386
\(369\) 9.00000 0.468521
\(370\) 0 0
\(371\) 0 0
\(372\) −1.00000 −0.0518476
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 −0.154713
\(377\) 0 0
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 16.0000 0.819705
\(382\) 21.0000 1.07445
\(383\) −21.0000 −1.07305 −0.536525 0.843884i \(-0.680263\pi\)
−0.536525 + 0.843884i \(0.680263\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −17.0000 −0.865277
\(387\) −10.0000 −0.508329
\(388\) 7.00000 0.355371
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 0 0
\(393\) −12.0000 −0.605320
\(394\) 12.0000 0.604551
\(395\) 0 0
\(396\) 0 0
\(397\) 22.0000 1.10415 0.552074 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 11.0000 0.551380
\(399\) 0 0
\(400\) 0 0
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) −4.00000 −0.199502
\(403\) 4.00000 0.199254
\(404\) −18.0000 −0.895533
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −3.00000 −0.148522
\(409\) −5.00000 −0.247234 −0.123617 0.992330i \(-0.539449\pi\)
−0.123617 + 0.992330i \(0.539449\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) −5.00000 −0.246332
\(413\) 0 0
\(414\) −3.00000 −0.147442
\(415\) 0 0
\(416\) −4.00000 −0.196116
\(417\) 2.00000 0.0979404
\(418\) 0 0
\(419\) −18.0000 −0.879358 −0.439679 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(420\) 0 0
\(421\) −40.0000 −1.94948 −0.974740 0.223341i \(-0.928304\pi\)
−0.974740 + 0.223341i \(0.928304\pi\)
\(422\) −14.0000 −0.681509
\(423\) 3.00000 0.145865
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 3.00000 0.145350
\(427\) 0 0
\(428\) −18.0000 −0.870063
\(429\) 0 0
\(430\) 0 0
\(431\) −27.0000 −1.30054 −0.650272 0.759701i \(-0.725345\pi\)
−0.650272 + 0.759701i \(0.725345\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −29.0000 −1.39365 −0.696826 0.717241i \(-0.745405\pi\)
−0.696826 + 0.717241i \(0.745405\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) −6.00000 −0.287019
\(438\) −14.0000 −0.668946
\(439\) −5.00000 −0.238637 −0.119318 0.992856i \(-0.538071\pi\)
−0.119318 + 0.992856i \(0.538071\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 10.0000 0.474579
\(445\) 0 0
\(446\) −19.0000 −0.899676
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) −21.0000 −0.991051 −0.495526 0.868593i \(-0.665025\pi\)
−0.495526 + 0.868593i \(0.665025\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 21.0000 0.987757
\(453\) −8.00000 −0.375873
\(454\) −6.00000 −0.281594
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 2.00000 0.0935561 0.0467780 0.998905i \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) −4.00000 −0.186908
\(459\) 3.00000 0.140028
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 5.00000 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 30.0000 1.38972
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 4.00000 0.184900
\(469\) 0 0
\(470\) 0 0
\(471\) 8.00000 0.368621
\(472\) −6.00000 −0.276172
\(473\) 0 0
\(474\) 11.0000 0.505247
\(475\) 0 0
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) −15.0000 −0.686084
\(479\) 27.0000 1.23366 0.616831 0.787096i \(-0.288416\pi\)
0.616831 + 0.787096i \(0.288416\pi\)
\(480\) 0 0
\(481\) −40.0000 −1.82384
\(482\) 14.0000 0.637683
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −31.0000 −1.40474 −0.702372 0.711810i \(-0.747876\pi\)
−0.702372 + 0.711810i \(0.747876\pi\)
\(488\) 8.00000 0.362143
\(489\) −8.00000 −0.361773
\(490\) 0 0
\(491\) −6.00000 −0.270776 −0.135388 0.990793i \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) −9.00000 −0.405751
\(493\) 0 0
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) 1.00000 0.0449013
\(497\) 0 0
\(498\) 0 0
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 0 0
\(501\) −24.0000 −1.07224
\(502\) 12.0000 0.535586
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −3.00000 −0.133235
\(508\) −16.0000 −0.709885
\(509\) 36.0000 1.59567 0.797836 0.602875i \(-0.205978\pi\)
0.797836 + 0.602875i \(0.205978\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 0.0883022
\(514\) 30.0000 1.32324
\(515\) 0 0
\(516\) 10.0000 0.440225
\(517\) 0 0
\(518\) 0 0
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) −15.0000 −0.657162 −0.328581 0.944476i \(-0.606570\pi\)
−0.328581 + 0.944476i \(0.606570\pi\)
\(522\) 0 0
\(523\) −32.0000 −1.39926 −0.699631 0.714504i \(-0.746652\pi\)
−0.699631 + 0.714504i \(0.746652\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) −9.00000 −0.392419
\(527\) −3.00000 −0.130682
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) 6.00000 0.260378
\(532\) 0 0
\(533\) 36.0000 1.55933
\(534\) 15.0000 0.649113
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) 6.00000 0.258919
\(538\) −6.00000 −0.258678
\(539\) 0 0
\(540\) 0 0
\(541\) −16.0000 −0.687894 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(542\) −7.00000 −0.300676
\(543\) 8.00000 0.343313
\(544\) 3.00000 0.128624
\(545\) 0 0
\(546\) 0 0
\(547\) 26.0000 1.11168 0.555840 0.831289i \(-0.312397\pi\)
0.555840 + 0.831289i \(0.312397\pi\)
\(548\) −9.00000 −0.384461
\(549\) −8.00000 −0.341432
\(550\) 0 0
\(551\) 0 0
\(552\) 3.00000 0.127688
\(553\) 0 0
\(554\) 28.0000 1.18961
\(555\) 0 0
\(556\) −2.00000 −0.0848189
\(557\) 6.00000 0.254228 0.127114 0.991888i \(-0.459429\pi\)
0.127114 + 0.991888i \(0.459429\pi\)
\(558\) −1.00000 −0.0423334
\(559\) −40.0000 −1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) −9.00000 −0.379642
\(563\) 30.0000 1.26435 0.632175 0.774826i \(-0.282163\pi\)
0.632175 + 0.774826i \(0.282163\pi\)
\(564\) −3.00000 −0.126323
\(565\) 0 0
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) −3.00000 −0.125877
\(569\) 27.0000 1.13190 0.565949 0.824440i \(-0.308510\pi\)
0.565949 + 0.824440i \(0.308510\pi\)
\(570\) 0 0
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 0 0
\(573\) 21.0000 0.877288
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) 8.00000 0.332756
\(579\) −17.0000 −0.706496
\(580\) 0 0
\(581\) 0 0
\(582\) 7.00000 0.290159
\(583\) 0 0
\(584\) 14.0000 0.579324
\(585\) 0 0
\(586\) −24.0000 −0.991431
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 0 0
\(589\) −2.00000 −0.0824086
\(590\) 0 0
\(591\) 12.0000 0.493614
\(592\) −10.0000 −0.410997
\(593\) −21.0000 −0.862367 −0.431183 0.902264i \(-0.641904\pi\)
−0.431183 + 0.902264i \(0.641904\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 11.0000 0.450200
\(598\) −12.0000 −0.490716
\(599\) −3.00000 −0.122577 −0.0612883 0.998120i \(-0.519521\pi\)
−0.0612883 + 0.998120i \(0.519521\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 8.00000 0.325515
\(605\) 0 0
\(606\) −18.0000 −0.731200
\(607\) 7.00000 0.284121 0.142061 0.989858i \(-0.454627\pi\)
0.142061 + 0.989858i \(0.454627\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) −3.00000 −0.121268
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) −28.0000 −1.12999
\(615\) 0 0
\(616\) 0 0
\(617\) −15.0000 −0.603877 −0.301939 0.953327i \(-0.597634\pi\)
−0.301939 + 0.953327i \(0.597634\pi\)
\(618\) −5.00000 −0.201129
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 0 0
\(621\) −3.00000 −0.120386
\(622\) 9.00000 0.360867
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 0 0
\(626\) 5.00000 0.199840
\(627\) 0 0
\(628\) −8.00000 −0.319235
\(629\) 30.0000 1.19618
\(630\) 0 0
\(631\) −37.0000 −1.47295 −0.736473 0.676467i \(-0.763510\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(632\) −11.0000 −0.437557
\(633\) −14.0000 −0.556450
\(634\) 18.0000 0.714871
\(635\) 0 0
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 3.00000 0.118678
\(640\) 0 0
\(641\) −33.0000 −1.30342 −0.651711 0.758468i \(-0.725948\pi\)
−0.651711 + 0.758468i \(0.725948\pi\)
\(642\) −18.0000 −0.710403
\(643\) −38.0000 −1.49857 −0.749287 0.662246i \(-0.769604\pi\)
−0.749287 + 0.662246i \(0.769604\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.00000 −0.236067
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 8.00000 0.313304
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 2.00000 0.0782062
\(655\) 0 0
\(656\) 9.00000 0.351391
\(657\) −14.0000 −0.546192
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) 10.0000 0.388661
\(663\) 12.0000 0.466041
\(664\) 0 0
\(665\) 0 0
\(666\) 10.0000 0.387492
\(667\) 0 0
\(668\) 24.0000 0.928588
\(669\) −19.0000 −0.734582
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) −11.0000 −0.423704
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 12.0000 0.461197 0.230599 0.973049i \(-0.425932\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(678\) 21.0000 0.806500
\(679\) 0 0
\(680\) 0 0
\(681\) −6.00000 −0.229920
\(682\) 0 0
\(683\) 6.00000 0.229584 0.114792 0.993390i \(-0.463380\pi\)
0.114792 + 0.993390i \(0.463380\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 0 0
\(686\) 0 0
\(687\) −4.00000 −0.152610
\(688\) −10.0000 −0.381246
\(689\) −24.0000 −0.914327
\(690\) 0 0
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) 36.0000 1.36654
\(695\) 0 0
\(696\) 0 0
\(697\) −27.0000 −1.02270
\(698\) 26.0000 0.984115
\(699\) 30.0000 1.13470
\(700\) 0 0
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 4.00000 0.150970
\(703\) 20.0000 0.754314
\(704\) 0 0
\(705\) 0 0
\(706\) −15.0000 −0.564532
\(707\) 0 0
\(708\) −6.00000 −0.225494
\(709\) −34.0000 −1.27690 −0.638448 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) 0 0
\(711\) 11.0000 0.412532
\(712\) −15.0000 −0.562149
\(713\) 3.00000 0.112351
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 −0.224231
\(717\) −15.0000 −0.560185
\(718\) −12.0000 −0.447836
\(719\) 27.0000 1.00693 0.503465 0.864016i \(-0.332058\pi\)
0.503465 + 0.864016i \(0.332058\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.0000 0.558242
\(723\) 14.0000 0.520666
\(724\) −8.00000 −0.297318
\(725\) 0 0
\(726\) −11.0000 −0.408248
\(727\) 37.0000 1.37225 0.686127 0.727482i \(-0.259309\pi\)
0.686127 + 0.727482i \(0.259309\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 30.0000 1.10959
\(732\) 8.00000 0.295689
\(733\) −14.0000 −0.517102 −0.258551 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 0 0
\(738\) −9.00000 −0.331295
\(739\) 2.00000 0.0735712 0.0367856 0.999323i \(-0.488288\pi\)
0.0367856 + 0.999323i \(0.488288\pi\)
\(740\) 0 0
\(741\) 8.00000 0.293887
\(742\) 0 0
\(743\) −51.0000 −1.87101 −0.935504 0.353315i \(-0.885054\pi\)
−0.935504 + 0.353315i \(0.885054\pi\)
\(744\) 1.00000 0.0366618
\(745\) 0 0
\(746\) 4.00000 0.146450
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) 3.00000 0.109399
\(753\) 12.0000 0.437304
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −16.0000 −0.581530 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) 16.0000 0.581146
\(759\) 0 0
\(760\) 0 0
\(761\) −27.0000 −0.978749 −0.489375 0.872074i \(-0.662775\pi\)
−0.489375 + 0.872074i \(0.662775\pi\)
\(762\) −16.0000 −0.579619
\(763\) 0 0
\(764\) −21.0000 −0.759753
\(765\) 0 0
\(766\) 21.0000 0.758761
\(767\) 24.0000 0.866590
\(768\) −1.00000 −0.0360844
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 0 0
\(771\) 30.0000 1.08042
\(772\) 17.0000 0.611843
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 10.0000 0.359443
\(775\) 0 0
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) −18.0000 −0.644917
\(780\) 0 0
\(781\) 0 0
\(782\) 9.00000 0.321839
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 12.0000 0.428026
\(787\) 22.0000 0.784215 0.392108 0.919919i \(-0.371746\pi\)
0.392108 + 0.919919i \(0.371746\pi\)
\(788\) −12.0000 −0.427482
\(789\) −9.00000 −0.320408
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −32.0000 −1.13635
\(794\) −22.0000 −0.780751
\(795\) 0 0
\(796\) −11.0000 −0.389885
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) −9.00000 −0.318397
\(800\) 0 0
\(801\) 15.0000 0.529999
\(802\) −18.0000 −0.635602
\(803\) 0 0
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) −6.00000 −0.211210
\(808\) 18.0000 0.633238
\(809\) 6.00000 0.210949 0.105474 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 0 0
\(811\) −56.0000 −1.96643 −0.983213 0.182462i \(-0.941593\pi\)
−0.983213 + 0.182462i \(0.941593\pi\)
\(812\) 0 0
\(813\) −7.00000 −0.245501
\(814\) 0 0
\(815\) 0 0
\(816\) 3.00000 0.105021
\(817\) 20.0000 0.699711
\(818\) 5.00000 0.174821
\(819\) 0 0
\(820\) 0 0
\(821\) −54.0000 −1.88461 −0.942306 0.334751i \(-0.891348\pi\)
−0.942306 + 0.334751i \(0.891348\pi\)
\(822\) −9.00000 −0.313911
\(823\) 32.0000 1.11545 0.557725 0.830026i \(-0.311674\pi\)
0.557725 + 0.830026i \(0.311674\pi\)
\(824\) 5.00000 0.174183
\(825\) 0 0
\(826\) 0 0
\(827\) 48.0000 1.66912 0.834562 0.550914i \(-0.185721\pi\)
0.834562 + 0.550914i \(0.185721\pi\)
\(828\) 3.00000 0.104257
\(829\) −2.00000 −0.0694629 −0.0347314 0.999397i \(-0.511058\pi\)
−0.0347314 + 0.999397i \(0.511058\pi\)
\(830\) 0 0
\(831\) 28.0000 0.971309
\(832\) 4.00000 0.138675
\(833\) 0 0
\(834\) −2.00000 −0.0692543
\(835\) 0 0
\(836\) 0 0
\(837\) −1.00000 −0.0345651
\(838\) 18.0000 0.621800
\(839\) −27.0000 −0.932144 −0.466072 0.884747i \(-0.654331\pi\)
−0.466072 + 0.884747i \(0.654331\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 40.0000 1.37849
\(843\) −9.00000 −0.309976
\(844\) 14.0000 0.481900
\(845\) 0 0
\(846\) −3.00000 −0.103142
\(847\) 0 0
\(848\) −6.00000 −0.206041
\(849\) −4.00000 −0.137280
\(850\) 0 0
\(851\) −30.0000 −1.02839
\(852\) −3.00000 −0.102778
\(853\) −26.0000 −0.890223 −0.445112 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 18.0000 0.615227
\(857\) −54.0000 −1.84460 −0.922302 0.386469i \(-0.873695\pi\)
−0.922302 + 0.386469i \(0.873695\pi\)
\(858\) 0 0
\(859\) 4.00000 0.136478 0.0682391 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 27.0000 0.919624
\(863\) −15.0000 −0.510606 −0.255303 0.966861i \(-0.582175\pi\)
−0.255303 + 0.966861i \(0.582175\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) 29.0000 0.985460
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −16.0000 −0.542139
\(872\) −2.00000 −0.0677285
\(873\) 7.00000 0.236914
\(874\) 6.00000 0.202953
\(875\) 0 0
\(876\) 14.0000 0.473016
\(877\) 38.0000 1.28317 0.641584 0.767052i \(-0.278277\pi\)
0.641584 + 0.767052i \(0.278277\pi\)
\(878\) 5.00000 0.168742
\(879\) −24.0000 −0.809500
\(880\) 0 0
\(881\) 3.00000 0.101073 0.0505363 0.998722i \(-0.483907\pi\)
0.0505363 + 0.998722i \(0.483907\pi\)
\(882\) 0 0
\(883\) 38.0000 1.27880 0.639401 0.768874i \(-0.279182\pi\)
0.639401 + 0.768874i \(0.279182\pi\)
\(884\) −12.0000 −0.403604
\(885\) 0 0
\(886\) 6.00000 0.201574
\(887\) −48.0000 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) −10.0000 −0.335578
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 19.0000 0.636167
\(893\) −6.00000 −0.200782
\(894\) −6.00000 −0.200670
\(895\) 0 0
\(896\) 0 0
\(897\) −12.0000 −0.400668
\(898\) 21.0000 0.700779
\(899\) 0 0
\(900\) 0 0
\(901\) 18.0000 0.599667
\(902\) 0 0
\(903\) 0 0
\(904\) −21.0000 −0.698450
\(905\) 0 0
\(906\) 8.00000 0.265782
\(907\) −16.0000 −0.531271 −0.265636 0.964073i \(-0.585582\pi\)
−0.265636 + 0.964073i \(0.585582\pi\)
\(908\) 6.00000 0.199117
\(909\) −18.0000 −0.597022
\(910\) 0 0
\(911\) 39.0000 1.29213 0.646064 0.763283i \(-0.276414\pi\)
0.646064 + 0.763283i \(0.276414\pi\)
\(912\) 2.00000 0.0662266
\(913\) 0 0
\(914\) −2.00000 −0.0661541
\(915\) 0 0
\(916\) 4.00000 0.132164
\(917\) 0 0
\(918\) −3.00000 −0.0990148
\(919\) −19.0000 −0.626752 −0.313376 0.949629i \(-0.601460\pi\)
−0.313376 + 0.949629i \(0.601460\pi\)
\(920\) 0 0
\(921\) −28.0000 −0.922631
\(922\) −12.0000 −0.395199
\(923\) 12.0000 0.394985
\(924\) 0 0
\(925\) 0 0
\(926\) −5.00000 −0.164310
\(927\) −5.00000 −0.164222
\(928\) 0 0
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −30.0000 −0.982683
\(933\) 9.00000 0.294647
\(934\) 12.0000 0.392652
\(935\) 0 0
\(936\) −4.00000 −0.130744
\(937\) −26.0000 −0.849383 −0.424691 0.905338i \(-0.639617\pi\)
−0.424691 + 0.905338i \(0.639617\pi\)
\(938\) 0 0
\(939\) 5.00000 0.163169
\(940\) 0 0
\(941\) −30.0000 −0.977972 −0.488986 0.872292i \(-0.662633\pi\)
−0.488986 + 0.872292i \(0.662633\pi\)
\(942\) −8.00000 −0.260654
\(943\) 27.0000 0.879241
\(944\) 6.00000 0.195283
\(945\) 0 0
\(946\) 0 0
\(947\) −48.0000 −1.55979 −0.779895 0.625910i \(-0.784728\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(948\) −11.0000 −0.357263
\(949\) −56.0000 −1.81784
\(950\) 0 0
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 6.00000 0.194257
\(955\) 0 0
\(956\) 15.0000 0.485135
\(957\) 0 0
\(958\) −27.0000 −0.872330
\(959\) 0 0
\(960\) 0 0
\(961\) −30.0000 −0.967742
\(962\) 40.0000 1.28965
\(963\) −18.0000 −0.580042
\(964\) −14.0000 −0.450910
\(965\) 0 0
\(966\) 0 0
\(967\) −49.0000 −1.57573 −0.787867 0.615846i \(-0.788815\pi\)
−0.787867 + 0.615846i \(0.788815\pi\)
\(968\) 11.0000 0.353553
\(969\) −6.00000 −0.192748
\(970\) 0 0
\(971\) 36.0000 1.15529 0.577647 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) 31.0000 0.993304
\(975\) 0 0
\(976\) −8.00000 −0.256074
\(977\) 27.0000 0.863807 0.431903 0.901920i \(-0.357842\pi\)
0.431903 + 0.901920i \(0.357842\pi\)
\(978\) 8.00000 0.255812
\(979\) 0 0
\(980\) 0 0
\(981\) 2.00000 0.0638551
\(982\) 6.00000 0.191468
\(983\) 12.0000 0.382741 0.191370 0.981518i \(-0.438707\pi\)
0.191370 + 0.981518i \(0.438707\pi\)
\(984\) 9.00000 0.286910
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −8.00000 −0.254514
\(989\) −30.0000 −0.953945
\(990\) 0 0
\(991\) 59.0000 1.87420 0.937098 0.349065i \(-0.113501\pi\)
0.937098 + 0.349065i \(0.113501\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 10.0000 0.317340
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 40.0000 1.26681 0.633406 0.773819i \(-0.281656\pi\)
0.633406 + 0.773819i \(0.281656\pi\)
\(998\) −32.0000 −1.01294
\(999\) 10.0000 0.316386
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 7350.2.a.n.1.1 1
5.4 even 2 7350.2.a.cq.1.1 1
7.3 odd 6 1050.2.i.m.751.1 yes 2
7.5 odd 6 1050.2.i.m.151.1 yes 2
7.6 odd 2 7350.2.a.bb.1.1 1
35.3 even 12 1050.2.o.e.499.1 4
35.12 even 12 1050.2.o.e.949.1 4
35.17 even 12 1050.2.o.e.499.2 4
35.19 odd 6 1050.2.i.h.151.1 2
35.24 odd 6 1050.2.i.h.751.1 yes 2
35.33 even 12 1050.2.o.e.949.2 4
35.34 odd 2 7350.2.a.by.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.i.h.151.1 2 35.19 odd 6
1050.2.i.h.751.1 yes 2 35.24 odd 6
1050.2.i.m.151.1 yes 2 7.5 odd 6
1050.2.i.m.751.1 yes 2 7.3 odd 6
1050.2.o.e.499.1 4 35.3 even 12
1050.2.o.e.499.2 4 35.17 even 12
1050.2.o.e.949.1 4 35.12 even 12
1050.2.o.e.949.2 4 35.33 even 12
7350.2.a.n.1.1 1 1.1 even 1 trivial
7350.2.a.bb.1.1 1 7.6 odd 2
7350.2.a.by.1.1 1 35.34 odd 2
7350.2.a.cq.1.1 1 5.4 even 2