Properties

Label 7350.2.a.bw.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

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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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{12} -3.00000 q^{13} +1.00000 q^{16} -3.00000 q^{17} +1.00000 q^{18} +2.00000 q^{19} -3.00000 q^{23} -1.00000 q^{24} -3.00000 q^{26} -1.00000 q^{27} +7.00000 q^{29} -1.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +1.00000 q^{36} -4.00000 q^{37} +2.00000 q^{38} +3.00000 q^{39} +5.00000 q^{41} +3.00000 q^{43} -3.00000 q^{46} -4.00000 q^{47} -1.00000 q^{48} +3.00000 q^{51} -3.00000 q^{52} -1.00000 q^{53} -1.00000 q^{54} -2.00000 q^{57} +7.00000 q^{58} -13.0000 q^{59} -13.0000 q^{61} -1.00000 q^{62} +1.00000 q^{64} +4.00000 q^{67} -3.00000 q^{68} +3.00000 q^{69} -4.00000 q^{71} +1.00000 q^{72} -4.00000 q^{74} +2.00000 q^{76} +3.00000 q^{78} +4.00000 q^{79} +1.00000 q^{81} +5.00000 q^{82} -7.00000 q^{83} +3.00000 q^{86} -7.00000 q^{87} +6.00000 q^{89} -3.00000 q^{92} +1.00000 q^{93} -4.00000 q^{94} -1.00000 q^{96} -14.0000 q^{97} +O(q^{100})\)

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
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) 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 \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) −3.00000 −0.588348
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 7.00000 1.29987 0.649934 0.759991i \(-0.274797\pi\)
0.649934 + 0.759991i \(0.274797\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605 −0.0898027 0.995960i \(-0.528624\pi\)
−0.0898027 + 0.995960i \(0.528624\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 2.00000 0.324443
\(39\) 3.00000 0.480384
\(40\) 0 0
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 0 0
\(43\) 3.00000 0.457496 0.228748 0.973486i \(-0.426537\pi\)
0.228748 + 0.973486i \(0.426537\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.00000 −0.442326
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 0 0
\(51\) 3.00000 0.420084
\(52\) −3.00000 −0.416025
\(53\) −1.00000 −0.137361 −0.0686803 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 7.00000 0.919145
\(59\) −13.0000 −1.69246 −0.846228 0.532821i \(-0.821132\pi\)
−0.846228 + 0.532821i \(0.821132\pi\)
\(60\) 0 0
\(61\) −13.0000 −1.66448 −0.832240 0.554416i \(-0.812942\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −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 \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −3.00000 −0.363803
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 1.00000 0.117851
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) −4.00000 −0.464991
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) 3.00000 0.339683
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 5.00000 0.552158
\(83\) −7.00000 −0.768350 −0.384175 0.923260i \(-0.625514\pi\)
−0.384175 + 0.923260i \(0.625514\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 3.00000 0.323498
\(87\) −7.00000 −0.750479
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.00000 −0.312772
\(93\) 1.00000 0.103695
\(94\) −4.00000 −0.412568
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.00000 0.398015 0.199007 0.979998i \(-0.436228\pi\)
0.199007 + 0.979998i \(0.436228\pi\)
\(102\) 3.00000 0.297044
\(103\) 9.00000 0.886796 0.443398 0.896325i \(-0.353773\pi\)
0.443398 + 0.896325i \(0.353773\pi\)
\(104\) −3.00000 −0.294174
\(105\) 0 0
\(106\) −1.00000 −0.0971286
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) −2.00000 −0.187317
\(115\) 0 0
\(116\) 7.00000 0.649934
\(117\) −3.00000 −0.277350
\(118\) −13.0000 −1.19675
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −13.0000 −1.17696
\(123\) −5.00000 −0.450835
\(124\) −1.00000 −0.0898027
\(125\) 0 0
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.00000 −0.264135
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 3.00000 0.255377
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 0 0
\(141\) 4.00000 0.336861
\(142\) −4.00000 −0.335673
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) 15.0000 1.22885 0.614424 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) 0 0
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 2.00000 0.162221
\(153\) −3.00000 −0.242536
\(154\) 0 0
\(155\) 0 0
\(156\) 3.00000 0.240192
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 4.00000 0.318223
\(159\) 1.00000 0.0793052
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 13.0000 1.01824 0.509119 0.860696i \(-0.329971\pi\)
0.509119 + 0.860696i \(0.329971\pi\)
\(164\) 5.00000 0.390434
\(165\) 0 0
\(166\) −7.00000 −0.543305
\(167\) −18.0000 −1.39288 −0.696441 0.717614i \(-0.745234\pi\)
−0.696441 + 0.717614i \(0.745234\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 2.00000 0.152944
\(172\) 3.00000 0.228748
\(173\) 18.0000 1.36851 0.684257 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) −7.00000 −0.530669
\(175\) 0 0
\(176\) 0 0
\(177\) 13.0000 0.977140
\(178\) 6.00000 0.449719
\(179\) 8.00000 0.597948 0.298974 0.954261i \(-0.403356\pi\)
0.298974 + 0.954261i \(0.403356\pi\)
\(180\) 0 0
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) 13.0000 0.960988
\(184\) −3.00000 −0.221163
\(185\) 0 0
\(186\) 1.00000 0.0733236
\(187\) 0 0
\(188\) −4.00000 −0.291730
\(189\) 0 0
\(190\) 0 0
\(191\) 7.00000 0.506502 0.253251 0.967401i \(-0.418500\pi\)
0.253251 + 0.967401i \(0.418500\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) 0 0
\(197\) −9.00000 −0.641223 −0.320612 0.947211i \(-0.603888\pi\)
−0.320612 + 0.947211i \(0.603888\pi\)
\(198\) 0 0
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 4.00000 0.281439
\(203\) 0 0
\(204\) 3.00000 0.210042
\(205\) 0 0
\(206\) 9.00000 0.627060
\(207\) −3.00000 −0.208514
\(208\) −3.00000 −0.208013
\(209\) 0 0
\(210\) 0 0
\(211\) 21.0000 1.44570 0.722850 0.691005i \(-0.242832\pi\)
0.722850 + 0.691005i \(0.242832\pi\)
\(212\) −1.00000 −0.0686803
\(213\) 4.00000 0.274075
\(214\) −10.0000 −0.683586
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −12.0000 −0.812743
\(219\) 0 0
\(220\) 0 0
\(221\) 9.00000 0.605406
\(222\) 4.00000 0.268462
\(223\) 5.00000 0.334825 0.167412 0.985887i \(-0.446459\pi\)
0.167412 + 0.985887i \(0.446459\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −29.0000 −1.92480 −0.962399 0.271640i \(-0.912434\pi\)
−0.962399 + 0.271640i \(0.912434\pi\)
\(228\) −2.00000 −0.132453
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 7.00000 0.459573
\(233\) −26.0000 −1.70332 −0.851658 0.524097i \(-0.824403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) −3.00000 −0.196116
\(235\) 0 0
\(236\) −13.0000 −0.846228
\(237\) −4.00000 −0.259828
\(238\) 0 0
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) −11.0000 −0.707107
\(243\) −1.00000 −0.0641500
\(244\) −13.0000 −0.832240
\(245\) 0 0
\(246\) −5.00000 −0.318788
\(247\) −6.00000 −0.381771
\(248\) −1.00000 −0.0635001
\(249\) 7.00000 0.443607
\(250\) 0 0
\(251\) 19.0000 1.19927 0.599635 0.800274i \(-0.295313\pi\)
0.599635 + 0.800274i \(0.295313\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 2.00000 0.125491
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 5.00000 0.311891 0.155946 0.987766i \(-0.450158\pi\)
0.155946 + 0.987766i \(0.450158\pi\)
\(258\) −3.00000 −0.186772
\(259\) 0 0
\(260\) 0 0
\(261\) 7.00000 0.433289
\(262\) −12.0000 −0.741362
\(263\) 5.00000 0.308313 0.154157 0.988046i \(-0.450734\pi\)
0.154157 + 0.988046i \(0.450734\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −6.00000 −0.367194
\(268\) 4.00000 0.244339
\(269\) −20.0000 −1.21942 −0.609711 0.792624i \(-0.708714\pi\)
−0.609711 + 0.792624i \(0.708714\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 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
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 4.00000 0.238197
\(283\) −10.0000 −0.594438 −0.297219 0.954809i \(-0.596059\pi\)
−0.297219 + 0.954809i \(0.596059\pi\)
\(284\) −4.00000 −0.237356
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 14.0000 0.820695
\(292\) 0 0
\(293\) −4.00000 −0.233682 −0.116841 0.993151i \(-0.537277\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 0 0
\(298\) 15.0000 0.868927
\(299\) 9.00000 0.520483
\(300\) 0 0
\(301\) 0 0
\(302\) −20.0000 −1.15087
\(303\) −4.00000 −0.229794
\(304\) 2.00000 0.114708
\(305\) 0 0
\(306\) −3.00000 −0.171499
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) −9.00000 −0.511992
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 3.00000 0.169842
\(313\) 16.0000 0.904373 0.452187 0.891923i \(-0.350644\pi\)
0.452187 + 0.891923i \(0.350644\pi\)
\(314\) −22.0000 −1.24153
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 11.0000 0.617822 0.308911 0.951091i \(-0.400036\pi\)
0.308911 + 0.951091i \(0.400036\pi\)
\(318\) 1.00000 0.0560772
\(319\) 0 0
\(320\) 0 0
\(321\) 10.0000 0.558146
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 13.0000 0.720003
\(327\) 12.0000 0.663602
\(328\) 5.00000 0.276079
\(329\) 0 0
\(330\) 0 0
\(331\) −17.0000 −0.934405 −0.467202 0.884150i \(-0.654738\pi\)
−0.467202 + 0.884150i \(0.654738\pi\)
\(332\) −7.00000 −0.384175
\(333\) −4.00000 −0.219199
\(334\) −18.0000 −0.984916
\(335\) 0 0
\(336\) 0 0
\(337\) 17.0000 0.926049 0.463025 0.886345i \(-0.346764\pi\)
0.463025 + 0.886345i \(0.346764\pi\)
\(338\) −4.00000 −0.217571
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 2.00000 0.108148
\(343\) 0 0
\(344\) 3.00000 0.161749
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) 22.0000 1.18102 0.590511 0.807030i \(-0.298926\pi\)
0.590511 + 0.807030i \(0.298926\pi\)
\(348\) −7.00000 −0.375239
\(349\) 5.00000 0.267644 0.133822 0.991005i \(-0.457275\pi\)
0.133822 + 0.991005i \(0.457275\pi\)
\(350\) 0 0
\(351\) 3.00000 0.160128
\(352\) 0 0
\(353\) −34.0000 −1.80964 −0.904819 0.425797i \(-0.859994\pi\)
−0.904819 + 0.425797i \(0.859994\pi\)
\(354\) 13.0000 0.690942
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 8.00000 0.422813
\(359\) −9.00000 −0.475002 −0.237501 0.971387i \(-0.576328\pi\)
−0.237501 + 0.971387i \(0.576328\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 22.0000 1.15629
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 0 0
\(366\) 13.0000 0.679521
\(367\) −29.0000 −1.51379 −0.756894 0.653538i \(-0.773284\pi\)
−0.756894 + 0.653538i \(0.773284\pi\)
\(368\) −3.00000 −0.156386
\(369\) 5.00000 0.260290
\(370\) 0 0
\(371\) 0 0
\(372\) 1.00000 0.0518476
\(373\) 32.0000 1.65690 0.828449 0.560065i \(-0.189224\pi\)
0.828449 + 0.560065i \(0.189224\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −4.00000 −0.206284
\(377\) −21.0000 −1.08156
\(378\) 0 0
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) 0 0
\(381\) −2.00000 −0.102463
\(382\) 7.00000 0.358151
\(383\) 14.0000 0.715367 0.357683 0.933843i \(-0.383567\pi\)
0.357683 + 0.933843i \(0.383567\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 3.00000 0.152499
\(388\) −14.0000 −0.710742
\(389\) 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
\(394\) −9.00000 −0.453413
\(395\) 0 0
\(396\) 0 0
\(397\) −13.0000 −0.652451 −0.326226 0.945292i \(-0.605777\pi\)
−0.326226 + 0.945292i \(0.605777\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 0 0
\(401\) −10.0000 −0.499376 −0.249688 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) −4.00000 −0.199502
\(403\) 3.00000 0.149441
\(404\) 4.00000 0.199007
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 3.00000 0.148522
\(409\) −16.0000 −0.791149 −0.395575 0.918434i \(-0.629455\pi\)
−0.395575 + 0.918434i \(0.629455\pi\)
\(410\) 0 0
\(411\) −2.00000 −0.0986527
\(412\) 9.00000 0.443398
\(413\) 0 0
\(414\) −3.00000 −0.147442
\(415\) 0 0
\(416\) −3.00000 −0.147087
\(417\) −2.00000 −0.0979404
\(418\) 0 0
\(419\) −3.00000 −0.146560 −0.0732798 0.997311i \(-0.523347\pi\)
−0.0732798 + 0.997311i \(0.523347\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 21.0000 1.02226
\(423\) −4.00000 −0.194487
\(424\) −1.00000 −0.0485643
\(425\) 0 0
\(426\) 4.00000 0.193801
\(427\) 0 0
\(428\) −10.0000 −0.483368
\(429\) 0 0
\(430\) 0 0
\(431\) 15.0000 0.722525 0.361262 0.932464i \(-0.382346\pi\)
0.361262 + 0.932464i \(0.382346\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 6.00000 0.288342 0.144171 0.989553i \(-0.453949\pi\)
0.144171 + 0.989553i \(0.453949\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −12.0000 −0.574696
\(437\) −6.00000 −0.287019
\(438\) 0 0
\(439\) 19.0000 0.906821 0.453410 0.891302i \(-0.350207\pi\)
0.453410 + 0.891302i \(0.350207\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 9.00000 0.428086
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 4.00000 0.189832
\(445\) 0 0
\(446\) 5.00000 0.236757
\(447\) −15.0000 −0.709476
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 20.0000 0.939682
\(454\) −29.0000 −1.36104
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) −23.0000 −1.07589 −0.537947 0.842978i \(-0.680800\pi\)
−0.537947 + 0.842978i \(0.680800\pi\)
\(458\) 10.0000 0.467269
\(459\) 3.00000 0.140028
\(460\) 0 0
\(461\) 16.0000 0.745194 0.372597 0.927993i \(-0.378467\pi\)
0.372597 + 0.927993i \(0.378467\pi\)
\(462\) 0 0
\(463\) −26.0000 −1.20832 −0.604161 0.796862i \(-0.706492\pi\)
−0.604161 + 0.796862i \(0.706492\pi\)
\(464\) 7.00000 0.324967
\(465\) 0 0
\(466\) −26.0000 −1.20443
\(467\) 9.00000 0.416470 0.208235 0.978079i \(-0.433228\pi\)
0.208235 + 0.978079i \(0.433228\pi\)
\(468\) −3.00000 −0.138675
\(469\) 0 0
\(470\) 0 0
\(471\) 22.0000 1.01371
\(472\) −13.0000 −0.598374
\(473\) 0 0
\(474\) −4.00000 −0.183726
\(475\) 0 0
\(476\) 0 0
\(477\) −1.00000 −0.0457869
\(478\) 8.00000 0.365911
\(479\) −6.00000 −0.274147 −0.137073 0.990561i \(-0.543770\pi\)
−0.137073 + 0.990561i \(0.543770\pi\)
\(480\) 0 0
\(481\) 12.0000 0.547153
\(482\) 14.0000 0.637683
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −18.0000 −0.815658 −0.407829 0.913058i \(-0.633714\pi\)
−0.407829 + 0.913058i \(0.633714\pi\)
\(488\) −13.0000 −0.588482
\(489\) −13.0000 −0.587880
\(490\) 0 0
\(491\) −34.0000 −1.53440 −0.767199 0.641409i \(-0.778350\pi\)
−0.767199 + 0.641409i \(0.778350\pi\)
\(492\) −5.00000 −0.225417
\(493\) −21.0000 −0.945792
\(494\) −6.00000 −0.269953
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) 0 0
\(498\) 7.00000 0.313678
\(499\) −17.0000 −0.761025 −0.380512 0.924776i \(-0.624252\pi\)
−0.380512 + 0.924776i \(0.624252\pi\)
\(500\) 0 0
\(501\) 18.0000 0.804181
\(502\) 19.0000 0.848012
\(503\) 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
\(507\) 4.00000 0.177646
\(508\) 2.00000 0.0887357
\(509\) 34.0000 1.50702 0.753512 0.657434i \(-0.228358\pi\)
0.753512 + 0.657434i \(0.228358\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −2.00000 −0.0883022
\(514\) 5.00000 0.220541
\(515\) 0 0
\(516\) −3.00000 −0.132068
\(517\) 0 0
\(518\) 0 0
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 43.0000 1.88386 0.941932 0.335803i \(-0.109008\pi\)
0.941932 + 0.335803i \(0.109008\pi\)
\(522\) 7.00000 0.306382
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 5.00000 0.218010
\(527\) 3.00000 0.130682
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) −13.0000 −0.564152
\(532\) 0 0
\(533\) −15.0000 −0.649722
\(534\) −6.00000 −0.259645
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) −8.00000 −0.345225
\(538\) −20.0000 −0.862261
\(539\) 0 0
\(540\) 0 0
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) 0 0
\(543\) −22.0000 −0.944110
\(544\) −3.00000 −0.128624
\(545\) 0 0
\(546\) 0 0
\(547\) 9.00000 0.384812 0.192406 0.981315i \(-0.438371\pi\)
0.192406 + 0.981315i \(0.438371\pi\)
\(548\) 2.00000 0.0854358
\(549\) −13.0000 −0.554826
\(550\) 0 0
\(551\) 14.0000 0.596420
\(552\) 3.00000 0.127688
\(553\) 0 0
\(554\) −28.0000 −1.18961
\(555\) 0 0
\(556\) 2.00000 0.0848189
\(557\) 22.0000 0.932170 0.466085 0.884740i \(-0.345664\pi\)
0.466085 + 0.884740i \(0.345664\pi\)
\(558\) −1.00000 −0.0423334
\(559\) −9.00000 −0.380659
\(560\) 0 0
\(561\) 0 0
\(562\) −12.0000 −0.506189
\(563\) 9.00000 0.379305 0.189652 0.981851i \(-0.439264\pi\)
0.189652 + 0.981851i \(0.439264\pi\)
\(564\) 4.00000 0.168430
\(565\) 0 0
\(566\) −10.0000 −0.420331
\(567\) 0 0
\(568\) −4.00000 −0.167836
\(569\) 20.0000 0.838444 0.419222 0.907884i \(-0.362303\pi\)
0.419222 + 0.907884i \(0.362303\pi\)
\(570\) 0 0
\(571\) −31.0000 −1.29731 −0.648655 0.761083i \(-0.724668\pi\)
−0.648655 + 0.761083i \(0.724668\pi\)
\(572\) 0 0
\(573\) −7.00000 −0.292429
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) −8.00000 −0.332756
\(579\) 10.0000 0.415586
\(580\) 0 0
\(581\) 0 0
\(582\) 14.0000 0.580319
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −4.00000 −0.165238
\(587\) −35.0000 −1.44460 −0.722302 0.691577i \(-0.756916\pi\)
−0.722302 + 0.691577i \(0.756916\pi\)
\(588\) 0 0
\(589\) −2.00000 −0.0824086
\(590\) 0 0
\(591\) 9.00000 0.370211
\(592\) −4.00000 −0.164399
\(593\) −14.0000 −0.574911 −0.287456 0.957794i \(-0.592809\pi\)
−0.287456 + 0.957794i \(0.592809\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.0000 0.614424
\(597\) 24.0000 0.982255
\(598\) 9.00000 0.368037
\(599\) 11.0000 0.449448 0.224724 0.974422i \(-0.427852\pi\)
0.224724 + 0.974422i \(0.427852\pi\)
\(600\) 0 0
\(601\) 18.0000 0.734235 0.367118 0.930175i \(-0.380345\pi\)
0.367118 + 0.930175i \(0.380345\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) −20.0000 −0.813788
\(605\) 0 0
\(606\) −4.00000 −0.162489
\(607\) 28.0000 1.13648 0.568242 0.822861i \(-0.307624\pi\)
0.568242 + 0.822861i \(0.307624\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) −3.00000 −0.121268
\(613\) 30.0000 1.21169 0.605844 0.795583i \(-0.292835\pi\)
0.605844 + 0.795583i \(0.292835\pi\)
\(614\) −28.0000 −1.12999
\(615\) 0 0
\(616\) 0 0
\(617\) 36.0000 1.44931 0.724653 0.689114i \(-0.242000\pi\)
0.724653 + 0.689114i \(0.242000\pi\)
\(618\) −9.00000 −0.362033
\(619\) −22.0000 −0.884255 −0.442127 0.896952i \(-0.645776\pi\)
−0.442127 + 0.896952i \(0.645776\pi\)
\(620\) 0 0
\(621\) 3.00000 0.120386
\(622\) −12.0000 −0.481156
\(623\) 0 0
\(624\) 3.00000 0.120096
\(625\) 0 0
\(626\) 16.0000 0.639489
\(627\) 0 0
\(628\) −22.0000 −0.877896
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 26.0000 1.03504 0.517522 0.855670i \(-0.326855\pi\)
0.517522 + 0.855670i \(0.326855\pi\)
\(632\) 4.00000 0.159111
\(633\) −21.0000 −0.834675
\(634\) 11.0000 0.436866
\(635\) 0 0
\(636\) 1.00000 0.0396526
\(637\) 0 0
\(638\) 0 0
\(639\) −4.00000 −0.158238
\(640\) 0 0
\(641\) −12.0000 −0.473972 −0.236986 0.971513i \(-0.576159\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(642\) 10.0000 0.394669
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.00000 −0.236067
\(647\) 4.00000 0.157256 0.0786281 0.996904i \(-0.474946\pi\)
0.0786281 + 0.996904i \(0.474946\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 13.0000 0.509119
\(653\) −14.0000 −0.547862 −0.273931 0.961749i \(-0.588324\pi\)
−0.273931 + 0.961749i \(0.588324\pi\)
\(654\) 12.0000 0.469237
\(655\) 0 0
\(656\) 5.00000 0.195217
\(657\) 0 0
\(658\) 0 0
\(659\) 6.00000 0.233727 0.116863 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) 0 0
\(661\) 18.0000 0.700119 0.350059 0.936727i \(-0.386161\pi\)
0.350059 + 0.936727i \(0.386161\pi\)
\(662\) −17.0000 −0.660724
\(663\) −9.00000 −0.349531
\(664\) −7.00000 −0.271653
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) −21.0000 −0.813123
\(668\) −18.0000 −0.696441
\(669\) −5.00000 −0.193311
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 5.00000 0.192736 0.0963679 0.995346i \(-0.469277\pi\)
0.0963679 + 0.995346i \(0.469277\pi\)
\(674\) 17.0000 0.654816
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) −2.00000 −0.0768662 −0.0384331 0.999261i \(-0.512237\pi\)
−0.0384331 + 0.999261i \(0.512237\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 29.0000 1.11128
\(682\) 0 0
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 2.00000 0.0764719
\(685\) 0 0
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) 3.00000 0.114374
\(689\) 3.00000 0.114291
\(690\) 0 0
\(691\) 34.0000 1.29342 0.646710 0.762736i \(-0.276144\pi\)
0.646710 + 0.762736i \(0.276144\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) 22.0000 0.835109
\(695\) 0 0
\(696\) −7.00000 −0.265334
\(697\) −15.0000 −0.568166
\(698\) 5.00000 0.189253
\(699\) 26.0000 0.983410
\(700\) 0 0
\(701\) −33.0000 −1.24639 −0.623196 0.782065i \(-0.714166\pi\)
−0.623196 + 0.782065i \(0.714166\pi\)
\(702\) 3.00000 0.113228
\(703\) −8.00000 −0.301726
\(704\) 0 0
\(705\) 0 0
\(706\) −34.0000 −1.27961
\(707\) 0 0
\(708\) 13.0000 0.488570
\(709\) −34.0000 −1.27690 −0.638448 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) 0 0
\(711\) 4.00000 0.150012
\(712\) 6.00000 0.224860
\(713\) 3.00000 0.112351
\(714\) 0 0
\(715\) 0 0
\(716\) 8.00000 0.298974
\(717\) −8.00000 −0.298765
\(718\) −9.00000 −0.335877
\(719\) 8.00000 0.298350 0.149175 0.988811i \(-0.452338\pi\)
0.149175 + 0.988811i \(0.452338\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15.0000 −0.558242
\(723\) −14.0000 −0.520666
\(724\) 22.0000 0.817624
\(725\) 0 0
\(726\) 11.0000 0.408248
\(727\) −19.0000 −0.704671 −0.352335 0.935874i \(-0.614612\pi\)
−0.352335 + 0.935874i \(0.614612\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −9.00000 −0.332877
\(732\) 13.0000 0.480494
\(733\) 7.00000 0.258551 0.129275 0.991609i \(-0.458735\pi\)
0.129275 + 0.991609i \(0.458735\pi\)
\(734\) −29.0000 −1.07041
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 0 0
\(738\) 5.00000 0.184053
\(739\) −19.0000 −0.698926 −0.349463 0.936950i \(-0.613636\pi\)
−0.349463 + 0.936950i \(0.613636\pi\)
\(740\) 0 0
\(741\) 6.00000 0.220416
\(742\) 0 0
\(743\) −33.0000 −1.21065 −0.605326 0.795977i \(-0.706957\pi\)
−0.605326 + 0.795977i \(0.706957\pi\)
\(744\) 1.00000 0.0366618
\(745\) 0 0
\(746\) 32.0000 1.17160
\(747\) −7.00000 −0.256117
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −44.0000 −1.60558 −0.802791 0.596260i \(-0.796653\pi\)
−0.802791 + 0.596260i \(0.796653\pi\)
\(752\) −4.00000 −0.145865
\(753\) −19.0000 −0.692398
\(754\) −21.0000 −0.764775
\(755\) 0 0
\(756\) 0 0
\(757\) 16.0000 0.581530 0.290765 0.956795i \(-0.406090\pi\)
0.290765 + 0.956795i \(0.406090\pi\)
\(758\) −23.0000 −0.835398
\(759\) 0 0
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) −2.00000 −0.0724524
\(763\) 0 0
\(764\) 7.00000 0.253251
\(765\) 0 0
\(766\) 14.0000 0.505841
\(767\) 39.0000 1.40821
\(768\) −1.00000 −0.0360844
\(769\) 40.0000 1.44244 0.721218 0.692708i \(-0.243582\pi\)
0.721218 + 0.692708i \(0.243582\pi\)
\(770\) 0 0
\(771\) −5.00000 −0.180071
\(772\) −10.0000 −0.359908
\(773\) −4.00000 −0.143870 −0.0719350 0.997409i \(-0.522917\pi\)
−0.0719350 + 0.997409i \(0.522917\pi\)
\(774\) 3.00000 0.107833
\(775\) 0 0
\(776\) −14.0000 −0.502571
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) 10.0000 0.358287
\(780\) 0 0
\(781\) 0 0
\(782\) 9.00000 0.321839
\(783\) −7.00000 −0.250160
\(784\) 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 \(0.371746\pi\)
\(788\) −9.00000 −0.320612
\(789\) −5.00000 −0.178005
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 39.0000 1.38493
\(794\) −13.0000 −0.461353
\(795\) 0 0
\(796\) −24.0000 −0.850657
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 12.0000 0.424529
\(800\) 0 0
\(801\) 6.00000 0.212000
\(802\) −10.0000 −0.353112
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) 3.00000 0.105670
\(807\) 20.0000 0.704033
\(808\) 4.00000 0.140720
\(809\) 48.0000 1.68759 0.843795 0.536666i \(-0.180316\pi\)
0.843795 + 0.536666i \(0.180316\pi\)
\(810\) 0 0
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 3.00000 0.105021
\(817\) 6.00000 0.209913
\(818\) −16.0000 −0.559427
\(819\) 0 0
\(820\) 0 0
\(821\) 30.0000 1.04701 0.523504 0.852023i \(-0.324625\pi\)
0.523504 + 0.852023i \(0.324625\pi\)
\(822\) −2.00000 −0.0697580
\(823\) 24.0000 0.836587 0.418294 0.908312i \(-0.362628\pi\)
0.418294 + 0.908312i \(0.362628\pi\)
\(824\) 9.00000 0.313530
\(825\) 0 0
\(826\) 0 0
\(827\) −48.0000 −1.66912 −0.834562 0.550914i \(-0.814279\pi\)
−0.834562 + 0.550914i \(0.814279\pi\)
\(828\) −3.00000 −0.104257
\(829\) 37.0000 1.28506 0.642532 0.766259i \(-0.277884\pi\)
0.642532 + 0.766259i \(0.277884\pi\)
\(830\) 0 0
\(831\) 28.0000 0.971309
\(832\) −3.00000 −0.104006
\(833\) 0 0
\(834\) −2.00000 −0.0692543
\(835\) 0 0
\(836\) 0 0
\(837\) 1.00000 0.0345651
\(838\) −3.00000 −0.103633
\(839\) 34.0000 1.17381 0.586905 0.809656i \(-0.300346\pi\)
0.586905 + 0.809656i \(0.300346\pi\)
\(840\) 0 0
\(841\) 20.0000 0.689655
\(842\) 2.00000 0.0689246
\(843\) 12.0000 0.413302
\(844\) 21.0000 0.722850
\(845\) 0 0
\(846\) −4.00000 −0.137523
\(847\) 0 0
\(848\) −1.00000 −0.0343401
\(849\) 10.0000 0.343199
\(850\) 0 0
\(851\) 12.0000 0.411355
\(852\) 4.00000 0.137038
\(853\) −5.00000 −0.171197 −0.0855984 0.996330i \(-0.527280\pi\)
−0.0855984 + 0.996330i \(0.527280\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −10.0000 −0.341793
\(857\) 30.0000 1.02478 0.512390 0.858753i \(-0.328760\pi\)
0.512390 + 0.858753i \(0.328760\pi\)
\(858\) 0 0
\(859\) 52.0000 1.77422 0.887109 0.461561i \(-0.152710\pi\)
0.887109 + 0.461561i \(0.152710\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 15.0000 0.510902
\(863\) 8.00000 0.272323 0.136162 0.990687i \(-0.456523\pi\)
0.136162 + 0.990687i \(0.456523\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) 6.00000 0.203888
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −12.0000 −0.406604
\(872\) −12.0000 −0.406371
\(873\) −14.0000 −0.473828
\(874\) −6.00000 −0.202953
\(875\) 0 0
\(876\) 0 0
\(877\) 32.0000 1.08056 0.540282 0.841484i \(-0.318318\pi\)
0.540282 + 0.841484i \(0.318318\pi\)
\(878\) 19.0000 0.641219
\(879\) 4.00000 0.134917
\(880\) 0 0
\(881\) −3.00000 −0.101073 −0.0505363 0.998722i \(-0.516093\pi\)
−0.0505363 + 0.998722i \(0.516093\pi\)
\(882\) 0 0
\(883\) 25.0000 0.841317 0.420658 0.907219i \(-0.361799\pi\)
0.420658 + 0.907219i \(0.361799\pi\)
\(884\) 9.00000 0.302703
\(885\) 0 0
\(886\) −36.0000 −1.20944
\(887\) −20.0000 −0.671534 −0.335767 0.941945i \(-0.608996\pi\)
−0.335767 + 0.941945i \(0.608996\pi\)
\(888\) 4.00000 0.134231
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 5.00000 0.167412
\(893\) −8.00000 −0.267710
\(894\) −15.0000 −0.501675
\(895\) 0 0
\(896\) 0 0
\(897\) −9.00000 −0.300501
\(898\) 14.0000 0.467186
\(899\) −7.00000 −0.233463
\(900\) 0 0
\(901\) 3.00000 0.0999445
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 20.0000 0.664455
\(907\) −47.0000 −1.56061 −0.780305 0.625400i \(-0.784936\pi\)
−0.780305 + 0.625400i \(0.784936\pi\)
\(908\) −29.0000 −0.962399
\(909\) 4.00000 0.132672
\(910\) 0 0
\(911\) −3.00000 −0.0993944 −0.0496972 0.998764i \(-0.515826\pi\)
−0.0496972 + 0.998764i \(0.515826\pi\)
\(912\) −2.00000 −0.0662266
\(913\) 0 0
\(914\) −23.0000 −0.760772
\(915\) 0 0
\(916\) 10.0000 0.330409
\(917\) 0 0
\(918\) 3.00000 0.0990148
\(919\) −26.0000 −0.857661 −0.428830 0.903385i \(-0.641074\pi\)
−0.428830 + 0.903385i \(0.641074\pi\)
\(920\) 0 0
\(921\) 28.0000 0.922631
\(922\) 16.0000 0.526932
\(923\) 12.0000 0.394985
\(924\) 0 0
\(925\) 0 0
\(926\) −26.0000 −0.854413
\(927\) 9.00000 0.295599
\(928\) 7.00000 0.229786
\(929\) −3.00000 −0.0984268 −0.0492134 0.998788i \(-0.515671\pi\)
−0.0492134 + 0.998788i \(0.515671\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −26.0000 −0.851658
\(933\) 12.0000 0.392862
\(934\) 9.00000 0.294489
\(935\) 0 0
\(936\) −3.00000 −0.0980581
\(937\) −12.0000 −0.392023 −0.196011 0.980602i \(-0.562799\pi\)
−0.196011 + 0.980602i \(0.562799\pi\)
\(938\) 0 0
\(939\) −16.0000 −0.522140
\(940\) 0 0
\(941\) 44.0000 1.43436 0.717180 0.696888i \(-0.245433\pi\)
0.717180 + 0.696888i \(0.245433\pi\)
\(942\) 22.0000 0.716799
\(943\) −15.0000 −0.488467
\(944\) −13.0000 −0.423114
\(945\) 0 0
\(946\) 0 0
\(947\) 6.00000 0.194974 0.0974869 0.995237i \(-0.468920\pi\)
0.0974869 + 0.995237i \(0.468920\pi\)
\(948\) −4.00000 −0.129914
\(949\) 0 0
\(950\) 0 0
\(951\) −11.0000 −0.356699
\(952\) 0 0
\(953\) 36.0000 1.16615 0.583077 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(954\) −1.00000 −0.0323762
\(955\) 0 0
\(956\) 8.00000 0.258738
\(957\) 0 0
\(958\) −6.00000 −0.193851
\(959\) 0 0
\(960\) 0 0
\(961\) −30.0000 −0.967742
\(962\) 12.0000 0.386896
\(963\) −10.0000 −0.322245
\(964\) 14.0000 0.450910
\(965\) 0 0
\(966\) 0 0
\(967\) −42.0000 −1.35063 −0.675314 0.737530i \(-0.735992\pi\)
−0.675314 + 0.737530i \(0.735992\pi\)
\(968\) −11.0000 −0.353553
\(969\) 6.00000 0.192748
\(970\) 0 0
\(971\) 20.0000 0.641831 0.320915 0.947108i \(-0.396010\pi\)
0.320915 + 0.947108i \(0.396010\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −18.0000 −0.576757
\(975\) 0 0
\(976\) −13.0000 −0.416120
\(977\) 36.0000 1.15174 0.575871 0.817541i \(-0.304663\pi\)
0.575871 + 0.817541i \(0.304663\pi\)
\(978\) −13.0000 −0.415694
\(979\) 0 0
\(980\) 0 0
\(981\) −12.0000 −0.383131
\(982\) −34.0000 −1.08498
\(983\) 12.0000 0.382741 0.191370 0.981518i \(-0.438707\pi\)
0.191370 + 0.981518i \(0.438707\pi\)
\(984\) −5.00000 −0.159394
\(985\) 0 0
\(986\) −21.0000 −0.668776
\(987\) 0 0
\(988\) −6.00000 −0.190885
\(989\) −9.00000 −0.286183
\(990\) 0 0
\(991\) −4.00000 −0.127064 −0.0635321 0.997980i \(-0.520237\pi\)
−0.0635321 + 0.997980i \(0.520237\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 17.0000 0.539479
\(994\) 0 0
\(995\) 0 0
\(996\) 7.00000 0.221803
\(997\) 54.0000 1.71020 0.855099 0.518465i \(-0.173497\pi\)
0.855099 + 0.518465i \(0.173497\pi\)
\(998\) −17.0000 −0.538126
\(999\) 4.00000 0.126554
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.bw.1.1 yes 1
5.4 even 2 7350.2.a.be.1.1 yes 1
7.6 odd 2 7350.2.a.cu.1.1 yes 1
35.34 odd 2 7350.2.a.l.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7350.2.a.l.1.1 1 35.34 odd 2
7350.2.a.be.1.1 yes 1 5.4 even 2
7350.2.a.bw.1.1 yes 1 1.1 even 1 trivial
7350.2.a.cu.1.1 yes 1 7.6 odd 2