Properties

Label 7350.2.a.bv.1.1
Level 7350
Weight 2
Character 7350.1
Self dual yes
Analytic conductor 58.690
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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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: \(0\)
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

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{12} -5.00000 q^{13} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} -7.00000 q^{19} +6.00000 q^{23} -1.00000 q^{24} -5.00000 q^{26} -1.00000 q^{27} +8.00000 q^{31} +1.00000 q^{32} +6.00000 q^{34} +1.00000 q^{36} +1.00000 q^{37} -7.00000 q^{38} +5.00000 q^{39} -8.00000 q^{43} +6.00000 q^{46} -6.00000 q^{47} -1.00000 q^{48} -6.00000 q^{51} -5.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} +7.00000 q^{57} -6.00000 q^{59} -1.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} +13.0000 q^{67} +6.00000 q^{68} -6.00000 q^{69} +12.0000 q^{71} +1.00000 q^{72} -5.00000 q^{73} +1.00000 q^{74} -7.00000 q^{76} +5.00000 q^{78} -7.00000 q^{79} +1.00000 q^{81} +18.0000 q^{83} -8.00000 q^{86} -6.00000 q^{89} +6.00000 q^{92} -8.00000 q^{93} -6.00000 q^{94} -1.00000 q^{96} +7.00000 q^{97} +O(q^{100})\)

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
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 1.00000 0.235702
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) −5.00000 −0.980581
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 1.00000 0.164399 0.0821995 0.996616i \(-0.473806\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) −7.00000 −1.13555
\(39\) 5.00000 0.800641
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 0 0
\(51\) −6.00000 −0.840168
\(52\) −5.00000 −0.693375
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) 7.00000 0.927173
\(58\) 0 0
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 0 0
\(61\) −1.00000 −0.128037 −0.0640184 0.997949i \(-0.520392\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 13.0000 1.58820 0.794101 0.607785i \(-0.207942\pi\)
0.794101 + 0.607785i \(0.207942\pi\)
\(68\) 6.00000 0.727607
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 1.00000 0.117851
\(73\) −5.00000 −0.585206 −0.292603 0.956234i \(-0.594521\pi\)
−0.292603 + 0.956234i \(0.594521\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) −7.00000 −0.802955
\(77\) 0 0
\(78\) 5.00000 0.566139
\(79\) −7.00000 −0.787562 −0.393781 0.919204i \(-0.628833\pi\)
−0.393781 + 0.919204i \(0.628833\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 18.0000 1.97576 0.987878 0.155230i \(-0.0496119\pi\)
0.987878 + 0.155230i \(0.0496119\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) −8.00000 −0.829561
\(94\) −6.00000 −0.618853
\(95\) 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
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −6.00000 −0.594089
\(103\) 13.0000 1.28093 0.640464 0.767988i \(-0.278742\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) −5.00000 −0.490290
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 18.0000 1.74013 0.870063 0.492941i \(-0.164078\pi\)
0.870063 + 0.492941i \(0.164078\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 0 0
\(111\) −1.00000 −0.0949158
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 7.00000 0.655610
\(115\) 0 0
\(116\) 0 0
\(117\) −5.00000 −0.462250
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −1.00000 −0.0905357
\(123\) 0 0
\(124\) 8.00000 0.718421
\(125\) 0 0
\(126\) 0 0
\(127\) −11.0000 −0.976092 −0.488046 0.872818i \(-0.662290\pi\)
−0.488046 + 0.872818i \(0.662290\pi\)
\(128\) 1.00000 0.0883883
\(129\) 8.00000 0.704361
\(130\) 0 0
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 13.0000 1.12303
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) −6.00000 −0.510754
\(139\) 11.0000 0.933008 0.466504 0.884519i \(-0.345513\pi\)
0.466504 + 0.884519i \(0.345513\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 12.0000 1.00702
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −5.00000 −0.413803
\(147\) 0 0
\(148\) 1.00000 0.0821995
\(149\) 12.0000 0.983078 0.491539 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788 −0.0406894 0.999172i \(-0.512955\pi\)
−0.0406894 + 0.999172i \(0.512955\pi\)
\(152\) −7.00000 −0.567775
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 5.00000 0.400320
\(157\) 1.00000 0.0798087 0.0399043 0.999204i \(-0.487295\pi\)
0.0399043 + 0.999204i \(0.487295\pi\)
\(158\) −7.00000 −0.556890
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 1.00000 0.0783260 0.0391630 0.999233i \(-0.487531\pi\)
0.0391630 + 0.999233i \(0.487531\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 18.0000 1.39707
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −7.00000 −0.535303
\(172\) −8.00000 −0.609994
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 6.00000 0.450988
\(178\) −6.00000 −0.449719
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 1.00000 0.0739221
\(184\) 6.00000 0.442326
\(185\) 0 0
\(186\) −8.00000 −0.586588
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) 24.0000 1.73658 0.868290 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 10.0000 0.719816 0.359908 0.932988i \(-0.382808\pi\)
0.359908 + 0.932988i \(0.382808\pi\)
\(194\) 7.00000 0.502571
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 11.0000 0.779769 0.389885 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) 0 0
\(201\) −13.0000 −0.916949
\(202\) 0 0
\(203\) 0 0
\(204\) −6.00000 −0.420084
\(205\) 0 0
\(206\) 13.0000 0.905753
\(207\) 6.00000 0.417029
\(208\) −5.00000 −0.346688
\(209\) 0 0
\(210\) 0 0
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 6.00000 0.412082
\(213\) −12.0000 −0.822226
\(214\) 18.0000 1.23045
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −7.00000 −0.474100
\(219\) 5.00000 0.337869
\(220\) 0 0
\(221\) −30.0000 −2.01802
\(222\) −1.00000 −0.0671156
\(223\) −17.0000 −1.13840 −0.569202 0.822198i \(-0.692748\pi\)
−0.569202 + 0.822198i \(0.692748\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 6.00000 0.399114
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) 7.00000 0.463586
\(229\) 5.00000 0.330409 0.165205 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −24.0000 −1.57229 −0.786146 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) −5.00000 −0.326860
\(235\) 0 0
\(236\) −6.00000 −0.390567
\(237\) 7.00000 0.454699
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) 5.00000 0.322078 0.161039 0.986948i \(-0.448515\pi\)
0.161039 + 0.986948i \(0.448515\pi\)
\(242\) −11.0000 −0.707107
\(243\) −1.00000 −0.0641500
\(244\) −1.00000 −0.0640184
\(245\) 0 0
\(246\) 0 0
\(247\) 35.0000 2.22700
\(248\) 8.00000 0.508001
\(249\) −18.0000 −1.14070
\(250\) 0 0
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −11.0000 −0.690201
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 24.0000 1.49708 0.748539 0.663090i \(-0.230755\pi\)
0.748539 + 0.663090i \(0.230755\pi\)
\(258\) 8.00000 0.498058
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 6.00000 0.370681
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 13.0000 0.794101
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) −6.00000 −0.361158
\(277\) 19.0000 1.14160 0.570800 0.821089i \(-0.306633\pi\)
0.570800 + 0.821089i \(0.306633\pi\)
\(278\) 11.0000 0.659736
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 6.00000 0.357295
\(283\) −5.00000 −0.297219 −0.148610 0.988896i \(-0.547480\pi\)
−0.148610 + 0.988896i \(0.547480\pi\)
\(284\) 12.0000 0.712069
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) −7.00000 −0.410347
\(292\) −5.00000 −0.292603
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 0.0581238
\(297\) 0 0
\(298\) 12.0000 0.695141
\(299\) −30.0000 −1.73494
\(300\) 0 0
\(301\) 0 0
\(302\) −1.00000 −0.0575435
\(303\) 0 0
\(304\) −7.00000 −0.401478
\(305\) 0 0
\(306\) 6.00000 0.342997
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) −13.0000 −0.739544
\(310\) 0 0
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 5.00000 0.283069
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) 1.00000 0.0564333
\(315\) 0 0
\(316\) −7.00000 −0.393781
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) −6.00000 −0.336463
\(319\) 0 0
\(320\) 0 0
\(321\) −18.0000 −1.00466
\(322\) 0 0
\(323\) −42.0000 −2.33694
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 1.00000 0.0553849
\(327\) 7.00000 0.387101
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −19.0000 −1.04433 −0.522167 0.852843i \(-0.674876\pi\)
−0.522167 + 0.852843i \(0.674876\pi\)
\(332\) 18.0000 0.987878
\(333\) 1.00000 0.0547997
\(334\) 6.00000 0.328305
\(335\) 0 0
\(336\) 0 0
\(337\) 34.0000 1.85210 0.926049 0.377403i \(-0.123183\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) 12.0000 0.652714
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) 0 0
\(342\) −7.00000 −0.378517
\(343\) 0 0
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) −18.0000 −0.967686
\(347\) −18.0000 −0.966291 −0.483145 0.875540i \(-0.660506\pi\)
−0.483145 + 0.875540i \(0.660506\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) 6.00000 0.318896
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 30.0000 1.58334 0.791670 0.610949i \(-0.209212\pi\)
0.791670 + 0.610949i \(0.209212\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) −10.0000 −0.525588
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 0 0
\(366\) 1.00000 0.0522708
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 6.00000 0.312772
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −8.00000 −0.414781
\(373\) 13.0000 0.673114 0.336557 0.941663i \(-0.390737\pi\)
0.336557 + 0.941663i \(0.390737\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −6.00000 −0.309426
\(377\) 0 0
\(378\) 0 0
\(379\) 11.0000 0.565032 0.282516 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(380\) 0 0
\(381\) 11.0000 0.563547
\(382\) 24.0000 1.22795
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) −8.00000 −0.406663
\(388\) 7.00000 0.355371
\(389\) −12.0000 −0.608424 −0.304212 0.952604i \(-0.598393\pi\)
−0.304212 + 0.952604i \(0.598393\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) 12.0000 0.604551
\(395\) 0 0
\(396\) 0 0
\(397\) −14.0000 −0.702640 −0.351320 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) 11.0000 0.551380
\(399\) 0 0
\(400\) 0 0
\(401\) −36.0000 −1.79775 −0.898877 0.438201i \(-0.855616\pi\)
−0.898877 + 0.438201i \(0.855616\pi\)
\(402\) −13.0000 −0.648381
\(403\) −40.0000 −1.99254
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −6.00000 −0.297044
\(409\) 5.00000 0.247234 0.123617 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(410\) 0 0
\(411\) −18.0000 −0.887875
\(412\) 13.0000 0.640464
\(413\) 0 0
\(414\) 6.00000 0.294884
\(415\) 0 0
\(416\) −5.00000 −0.245145
\(417\) −11.0000 −0.538672
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 5.00000 0.243685 0.121843 0.992549i \(-0.461120\pi\)
0.121843 + 0.992549i \(0.461120\pi\)
\(422\) −13.0000 −0.632830
\(423\) −6.00000 −0.291730
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) 0 0
\(428\) 18.0000 0.870063
\(429\) 0 0
\(430\) 0 0
\(431\) −18.0000 −0.867029 −0.433515 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 34.0000 1.63394 0.816968 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −7.00000 −0.335239
\(437\) −42.0000 −2.00913
\(438\) 5.00000 0.238909
\(439\) 5.00000 0.238637 0.119318 0.992856i \(-0.461929\pi\)
0.119318 + 0.992856i \(0.461929\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −30.0000 −1.42695
\(443\) 42.0000 1.99548 0.997740 0.0671913i \(-0.0214038\pi\)
0.997740 + 0.0671913i \(0.0214038\pi\)
\(444\) −1.00000 −0.0474579
\(445\) 0 0
\(446\) −17.0000 −0.804973
\(447\) −12.0000 −0.567581
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) 1.00000 0.0469841
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) 7.00000 0.327805
\(457\) −29.0000 −1.35656 −0.678281 0.734802i \(-0.737275\pi\)
−0.678281 + 0.734802i \(0.737275\pi\)
\(458\) 5.00000 0.233635
\(459\) −6.00000 −0.280056
\(460\) 0 0
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) 31.0000 1.44069 0.720346 0.693615i \(-0.243983\pi\)
0.720346 + 0.693615i \(0.243983\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −24.0000 −1.11178
\(467\) −30.0000 −1.38823 −0.694117 0.719862i \(-0.744205\pi\)
−0.694117 + 0.719862i \(0.744205\pi\)
\(468\) −5.00000 −0.231125
\(469\) 0 0
\(470\) 0 0
\(471\) −1.00000 −0.0460776
\(472\) −6.00000 −0.276172
\(473\) 0 0
\(474\) 7.00000 0.321521
\(475\) 0 0
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) −12.0000 −0.548867
\(479\) 18.0000 0.822441 0.411220 0.911536i \(-0.365103\pi\)
0.411220 + 0.911536i \(0.365103\pi\)
\(480\) 0 0
\(481\) −5.00000 −0.227980
\(482\) 5.00000 0.227744
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 40.0000 1.81257 0.906287 0.422664i \(-0.138905\pi\)
0.906287 + 0.422664i \(0.138905\pi\)
\(488\) −1.00000 −0.0452679
\(489\) −1.00000 −0.0452216
\(490\) 0 0
\(491\) −6.00000 −0.270776 −0.135388 0.990793i \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 35.0000 1.57472
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) −18.0000 −0.806599
\(499\) 5.00000 0.223831 0.111915 0.993718i \(-0.464301\pi\)
0.111915 + 0.993718i \(0.464301\pi\)
\(500\) 0 0
\(501\) −6.00000 −0.268060
\(502\) −24.0000 −1.07117
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −12.0000 −0.532939
\(508\) −11.0000 −0.488046
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 7.00000 0.309058
\(514\) 24.0000 1.05859
\(515\) 0 0
\(516\) 8.00000 0.352180
\(517\) 0 0
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 0 0
\(523\) −32.0000 −1.39926 −0.699631 0.714504i \(-0.746652\pi\)
−0.699631 + 0.714504i \(0.746652\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) 0 0
\(527\) 48.0000 2.09091
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 0 0
\(533\) 0 0
\(534\) 6.00000 0.259645
\(535\) 0 0
\(536\) 13.0000 0.561514
\(537\) −12.0000 −0.517838
\(538\) −24.0000 −1.03471
\(539\) 0 0
\(540\) 0 0
\(541\) −43.0000 −1.84871 −0.924357 0.381528i \(-0.875398\pi\)
−0.924357 + 0.381528i \(0.875398\pi\)
\(542\) 20.0000 0.859074
\(543\) 10.0000 0.429141
\(544\) 6.00000 0.257248
\(545\) 0 0
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 18.0000 0.768922
\(549\) −1.00000 −0.0426790
\(550\) 0 0
\(551\) 0 0
\(552\) −6.00000 −0.255377
\(553\) 0 0
\(554\) 19.0000 0.807233
\(555\) 0 0
\(556\) 11.0000 0.466504
\(557\) 12.0000 0.508456 0.254228 0.967144i \(-0.418179\pi\)
0.254228 + 0.967144i \(0.418179\pi\)
\(558\) 8.00000 0.338667
\(559\) 40.0000 1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) −18.0000 −0.759284
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 6.00000 0.252646
\(565\) 0 0
\(566\) −5.00000 −0.210166
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) −36.0000 −1.50920 −0.754599 0.656186i \(-0.772169\pi\)
−0.754599 + 0.656186i \(0.772169\pi\)
\(570\) 0 0
\(571\) 5.00000 0.209243 0.104622 0.994512i \(-0.466637\pi\)
0.104622 + 0.994512i \(0.466637\pi\)
\(572\) 0 0
\(573\) −24.0000 −1.00261
\(574\) 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 \(0.594126\pi\)
\(578\) 19.0000 0.790296
\(579\) −10.0000 −0.415586
\(580\) 0 0
\(581\) 0 0
\(582\) −7.00000 −0.290159
\(583\) 0 0
\(584\) −5.00000 −0.206901
\(585\) 0 0
\(586\) 24.0000 0.991431
\(587\) 30.0000 1.23823 0.619116 0.785299i \(-0.287491\pi\)
0.619116 + 0.785299i \(0.287491\pi\)
\(588\) 0 0
\(589\) −56.0000 −2.30744
\(590\) 0 0
\(591\) −12.0000 −0.493614
\(592\) 1.00000 0.0410997
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12.0000 0.491539
\(597\) −11.0000 −0.450200
\(598\) −30.0000 −1.22679
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) 35.0000 1.42768 0.713840 0.700309i \(-0.246954\pi\)
0.713840 + 0.700309i \(0.246954\pi\)
\(602\) 0 0
\(603\) 13.0000 0.529401
\(604\) −1.00000 −0.0406894
\(605\) 0 0
\(606\) 0 0
\(607\) 43.0000 1.74532 0.872658 0.488332i \(-0.162394\pi\)
0.872658 + 0.488332i \(0.162394\pi\)
\(608\) −7.00000 −0.283887
\(609\) 0 0
\(610\) 0 0
\(611\) 30.0000 1.21367
\(612\) 6.00000 0.242536
\(613\) −38.0000 −1.53481 −0.767403 0.641165i \(-0.778451\pi\)
−0.767403 + 0.641165i \(0.778451\pi\)
\(614\) 28.0000 1.12999
\(615\) 0 0
\(616\) 0 0
\(617\) −48.0000 −1.93241 −0.966204 0.257780i \(-0.917009\pi\)
−0.966204 + 0.257780i \(0.917009\pi\)
\(618\) −13.0000 −0.522937
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) −6.00000 −0.240772
\(622\) 18.0000 0.721734
\(623\) 0 0
\(624\) 5.00000 0.200160
\(625\) 0 0
\(626\) −14.0000 −0.559553
\(627\) 0 0
\(628\) 1.00000 0.0399043
\(629\) 6.00000 0.239236
\(630\) 0 0
\(631\) −19.0000 −0.756378 −0.378189 0.925728i \(-0.623453\pi\)
−0.378189 + 0.925728i \(0.623453\pi\)
\(632\) −7.00000 −0.278445
\(633\) 13.0000 0.516704
\(634\) 18.0000 0.714871
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) −24.0000 −0.947943 −0.473972 0.880540i \(-0.657180\pi\)
−0.473972 + 0.880540i \(0.657180\pi\)
\(642\) −18.0000 −0.710403
\(643\) −11.0000 −0.433798 −0.216899 0.976194i \(-0.569594\pi\)
−0.216899 + 0.976194i \(0.569594\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −42.0000 −1.65247
\(647\) 12.0000 0.471769 0.235884 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 1.00000 0.0391630
\(653\) 36.0000 1.40879 0.704394 0.709809i \(-0.251219\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(654\) 7.00000 0.273722
\(655\) 0 0
\(656\) 0 0
\(657\) −5.00000 −0.195069
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 35.0000 1.36134 0.680671 0.732589i \(-0.261688\pi\)
0.680671 + 0.732589i \(0.261688\pi\)
\(662\) −19.0000 −0.738456
\(663\) 30.0000 1.16510
\(664\) 18.0000 0.698535
\(665\) 0 0
\(666\) 1.00000 0.0387492
\(667\) 0 0
\(668\) 6.00000 0.232147
\(669\) 17.0000 0.657258
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.00000 0.0385472 0.0192736 0.999814i \(-0.493865\pi\)
0.0192736 + 0.999814i \(0.493865\pi\)
\(674\) 34.0000 1.30963
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) −6.00000 −0.230429
\(679\) 0 0
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) −7.00000 −0.267652
\(685\) 0 0
\(686\) 0 0
\(687\) −5.00000 −0.190762
\(688\) −8.00000 −0.304997
\(689\) −30.0000 −1.14291
\(690\) 0 0
\(691\) −7.00000 −0.266293 −0.133146 0.991096i \(-0.542508\pi\)
−0.133146 + 0.991096i \(0.542508\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) −18.0000 −0.683271
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 26.0000 0.984115
\(699\) 24.0000 0.907763
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 5.00000 0.188713
\(703\) −7.00000 −0.264010
\(704\) 0 0
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) 6.00000 0.225494
\(709\) −7.00000 −0.262891 −0.131445 0.991323i \(-0.541962\pi\)
−0.131445 + 0.991323i \(0.541962\pi\)
\(710\) 0 0
\(711\) −7.00000 −0.262521
\(712\) −6.00000 −0.224860
\(713\) 48.0000 1.79761
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 12.0000 0.448148
\(718\) 30.0000 1.11959
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 30.0000 1.11648
\(723\) −5.00000 −0.185952
\(724\) −10.0000 −0.371647
\(725\) 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
\(731\) −48.0000 −1.77534
\(732\) 1.00000 0.0369611
\(733\) −41.0000 −1.51437 −0.757185 0.653201i \(-0.773426\pi\)
−0.757185 + 0.653201i \(0.773426\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) 0 0
\(739\) −25.0000 −0.919640 −0.459820 0.888012i \(-0.652086\pi\)
−0.459820 + 0.888012i \(0.652086\pi\)
\(740\) 0 0
\(741\) −35.0000 −1.28576
\(742\) 0 0
\(743\) −30.0000 −1.10059 −0.550297 0.834969i \(-0.685485\pi\)
−0.550297 + 0.834969i \(0.685485\pi\)
\(744\) −8.00000 −0.293294
\(745\) 0 0
\(746\) 13.0000 0.475964
\(747\) 18.0000 0.658586
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −25.0000 −0.912263 −0.456131 0.889912i \(-0.650765\pi\)
−0.456131 + 0.889912i \(0.650765\pi\)
\(752\) −6.00000 −0.218797
\(753\) 24.0000 0.874609
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −29.0000 −1.05402 −0.527011 0.849858i \(-0.676688\pi\)
−0.527011 + 0.849858i \(0.676688\pi\)
\(758\) 11.0000 0.399538
\(759\) 0 0
\(760\) 0 0
\(761\) 18.0000 0.652499 0.326250 0.945284i \(-0.394215\pi\)
0.326250 + 0.945284i \(0.394215\pi\)
\(762\) 11.0000 0.398488
\(763\) 0 0
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) 6.00000 0.216789
\(767\) 30.0000 1.08324
\(768\) −1.00000 −0.0360844
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) −24.0000 −0.864339
\(772\) 10.0000 0.359908
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) −8.00000 −0.287554
\(775\) 0 0
\(776\) 7.00000 0.251285
\(777\) 0 0
\(778\) −12.0000 −0.430221
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 36.0000 1.28736
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) −6.00000 −0.214013
\(787\) −23.0000 −0.819861 −0.409931 0.912117i \(-0.634447\pi\)
−0.409931 + 0.912117i \(0.634447\pi\)
\(788\) 12.0000 0.427482
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 5.00000 0.177555
\(794\) −14.0000 −0.496841
\(795\) 0 0
\(796\) 11.0000 0.389885
\(797\) −54.0000 −1.91278 −0.956389 0.292096i \(-0.905647\pi\)
−0.956389 + 0.292096i \(0.905647\pi\)
\(798\) 0 0
\(799\) −36.0000 −1.27359
\(800\) 0 0
\(801\) −6.00000 −0.212000
\(802\) −36.0000 −1.27120
\(803\) 0 0
\(804\) −13.0000 −0.458475
\(805\) 0 0
\(806\) −40.0000 −1.40894
\(807\) 24.0000 0.844840
\(808\) 0 0
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 0 0
\(811\) 11.0000 0.386262 0.193131 0.981173i \(-0.438136\pi\)
0.193131 + 0.981173i \(0.438136\pi\)
\(812\) 0 0
\(813\) −20.0000 −0.701431
\(814\) 0 0
\(815\) 0 0
\(816\) −6.00000 −0.210042
\(817\) 56.0000 1.95919
\(818\) 5.00000 0.174821
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) −18.0000 −0.627822
\(823\) −5.00000 −0.174289 −0.0871445 0.996196i \(-0.527774\pi\)
−0.0871445 + 0.996196i \(0.527774\pi\)
\(824\) 13.0000 0.452876
\(825\) 0 0
\(826\) 0 0
\(827\) 24.0000 0.834562 0.417281 0.908778i \(-0.362983\pi\)
0.417281 + 0.908778i \(0.362983\pi\)
\(828\) 6.00000 0.208514
\(829\) −7.00000 −0.243120 −0.121560 0.992584i \(-0.538790\pi\)
−0.121560 + 0.992584i \(0.538790\pi\)
\(830\) 0 0
\(831\) −19.0000 −0.659103
\(832\) −5.00000 −0.173344
\(833\) 0 0
\(834\) −11.0000 −0.380899
\(835\) 0 0
\(836\) 0 0
\(837\) −8.00000 −0.276520
\(838\) 0 0
\(839\) −18.0000 −0.621429 −0.310715 0.950503i \(-0.600568\pi\)
−0.310715 + 0.950503i \(0.600568\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 5.00000 0.172311
\(843\) 18.0000 0.619953
\(844\) −13.0000 −0.447478
\(845\) 0 0
\(846\) −6.00000 −0.206284
\(847\) 0 0
\(848\) 6.00000 0.206041
\(849\) 5.00000 0.171600
\(850\) 0 0
\(851\) 6.00000 0.205677
\(852\) −12.0000 −0.411113
\(853\) −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
\(857\) −18.0000 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 0 0
\(859\) −4.00000 −0.136478 −0.0682391 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −18.0000 −0.613082
\(863\) −30.0000 −1.02121 −0.510606 0.859815i \(-0.670579\pi\)
−0.510606 + 0.859815i \(0.670579\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) 34.0000 1.15537
\(867\) −19.0000 −0.645274
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −65.0000 −2.20244
\(872\) −7.00000 −0.237050
\(873\) 7.00000 0.236914
\(874\) −42.0000 −1.42067
\(875\) 0 0
\(876\) 5.00000 0.168934
\(877\) −47.0000 −1.58708 −0.793539 0.608520i \(-0.791764\pi\)
−0.793539 + 0.608520i \(0.791764\pi\)
\(878\) 5.00000 0.168742
\(879\) −24.0000 −0.809500
\(880\) 0 0
\(881\) −12.0000 −0.404290 −0.202145 0.979356i \(-0.564791\pi\)
−0.202145 + 0.979356i \(0.564791\pi\)
\(882\) 0 0
\(883\) 25.0000 0.841317 0.420658 0.907219i \(-0.361799\pi\)
0.420658 + 0.907219i \(0.361799\pi\)
\(884\) −30.0000 −1.00901
\(885\) 0 0
\(886\) 42.0000 1.41102
\(887\) 6.00000 0.201460 0.100730 0.994914i \(-0.467882\pi\)
0.100730 + 0.994914i \(0.467882\pi\)
\(888\) −1.00000 −0.0335578
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) −17.0000 −0.569202
\(893\) 42.0000 1.40548
\(894\) −12.0000 −0.401340
\(895\) 0 0
\(896\) 0 0
\(897\) 30.0000 1.00167
\(898\) 6.00000 0.200223
\(899\) 0 0
\(900\) 0 0
\(901\) 36.0000 1.19933
\(902\) 0 0
\(903\) 0 0
\(904\) 6.00000 0.199557
\(905\) 0 0
\(906\) 1.00000 0.0332228
\(907\) 7.00000 0.232431 0.116216 0.993224i \(-0.462924\pi\)
0.116216 + 0.993224i \(0.462924\pi\)
\(908\) −12.0000 −0.398234
\(909\) 0 0
\(910\) 0 0
\(911\) 30.0000 0.993944 0.496972 0.867766i \(-0.334445\pi\)
0.496972 + 0.867766i \(0.334445\pi\)
\(912\) 7.00000 0.231793
\(913\) 0 0
\(914\) −29.0000 −0.959235
\(915\) 0 0
\(916\) 5.00000 0.165205
\(917\) 0 0
\(918\) −6.00000 −0.198030
\(919\) 8.00000 0.263896 0.131948 0.991257i \(-0.457877\pi\)
0.131948 + 0.991257i \(0.457877\pi\)
\(920\) 0 0
\(921\) −28.0000 −0.922631
\(922\) 6.00000 0.197599
\(923\) −60.0000 −1.97492
\(924\) 0 0
\(925\) 0 0
\(926\) 31.0000 1.01872
\(927\) 13.0000 0.426976
\(928\) 0 0
\(929\) −36.0000 −1.18112 −0.590561 0.806993i \(-0.701093\pi\)
−0.590561 + 0.806993i \(0.701093\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −24.0000 −0.786146
\(933\) −18.0000 −0.589294
\(934\) −30.0000 −0.981630
\(935\) 0 0
\(936\) −5.00000 −0.163430
\(937\) 10.0000 0.326686 0.163343 0.986569i \(-0.447772\pi\)
0.163343 + 0.986569i \(0.447772\pi\)
\(938\) 0 0
\(939\) 14.0000 0.456873
\(940\) 0 0
\(941\) −6.00000 −0.195594 −0.0977972 0.995206i \(-0.531180\pi\)
−0.0977972 + 0.995206i \(0.531180\pi\)
\(942\) −1.00000 −0.0325818
\(943\) 0 0
\(944\) −6.00000 −0.195283
\(945\) 0 0
\(946\) 0 0
\(947\) −42.0000 −1.36482 −0.682408 0.730971i \(-0.739067\pi\)
−0.682408 + 0.730971i \(0.739067\pi\)
\(948\) 7.00000 0.227349
\(949\) 25.0000 0.811534
\(950\) 0 0
\(951\) −18.0000 −0.583690
\(952\) 0 0
\(953\) 12.0000 0.388718 0.194359 0.980930i \(-0.437737\pi\)
0.194359 + 0.980930i \(0.437737\pi\)
\(954\) 6.00000 0.194257
\(955\) 0 0
\(956\) −12.0000 −0.388108
\(957\) 0 0
\(958\) 18.0000 0.581554
\(959\) 0 0
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) −5.00000 −0.161206
\(963\) 18.0000 0.580042
\(964\) 5.00000 0.161039
\(965\) 0 0
\(966\) 0 0
\(967\) −41.0000 −1.31847 −0.659236 0.751936i \(-0.729120\pi\)
−0.659236 + 0.751936i \(0.729120\pi\)
\(968\) −11.0000 −0.353553
\(969\) 42.0000 1.34923
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) 40.0000 1.28168
\(975\) 0 0
\(976\) −1.00000 −0.0320092
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) −1.00000 −0.0319765
\(979\) 0 0
\(980\) 0 0
\(981\) −7.00000 −0.223493
\(982\) −6.00000 −0.191468
\(983\) 30.0000 0.956851 0.478426 0.878128i \(-0.341208\pi\)
0.478426 + 0.878128i \(0.341208\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 35.0000 1.11350
\(989\) −48.0000 −1.52631
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) 8.00000 0.254000
\(993\) 19.0000 0.602947
\(994\) 0 0
\(995\) 0 0
\(996\) −18.0000 −0.570352
\(997\) 13.0000 0.411714 0.205857 0.978582i \(-0.434002\pi\)
0.205857 + 0.978582i \(0.434002\pi\)
\(998\) 5.00000 0.158272
\(999\) −1.00000 −0.0316386
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.bv.1.1 1
5.4 even 2 7350.2.a.bf.1.1 1
7.2 even 3 1050.2.i.g.151.1 2
7.4 even 3 1050.2.i.g.751.1 yes 2
7.6 odd 2 7350.2.a.cv.1.1 1
35.2 odd 12 1050.2.o.d.949.2 4
35.4 even 6 1050.2.i.n.751.1 yes 2
35.9 even 6 1050.2.i.n.151.1 yes 2
35.18 odd 12 1050.2.o.d.499.2 4
35.23 odd 12 1050.2.o.d.949.1 4
35.32 odd 12 1050.2.o.d.499.1 4
35.34 odd 2 7350.2.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.i.g.151.1 2 7.2 even 3
1050.2.i.g.751.1 yes 2 7.4 even 3
1050.2.i.n.151.1 yes 2 35.9 even 6
1050.2.i.n.751.1 yes 2 35.4 even 6
1050.2.o.d.499.1 4 35.32 odd 12
1050.2.o.d.499.2 4 35.18 odd 12
1050.2.o.d.949.1 4 35.23 odd 12
1050.2.o.d.949.2 4 35.2 odd 12
7350.2.a.k.1.1 1 35.34 odd 2
7350.2.a.bf.1.1 1 5.4 even 2
7350.2.a.bv.1.1 1 1.1 even 1 trivial
7350.2.a.cv.1.1 1 7.6 odd 2