Properties

Label 7350.2.a.d.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: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{16} +5.00000 q^{17} -1.00000 q^{18} -6.00000 q^{19} +4.00000 q^{22} -5.00000 q^{23} +1.00000 q^{24} +1.00000 q^{26} -1.00000 q^{27} -3.00000 q^{29} -7.00000 q^{31} -1.00000 q^{32} +4.00000 q^{33} -5.00000 q^{34} +1.00000 q^{36} +4.00000 q^{37} +6.00000 q^{38} +1.00000 q^{39} +5.00000 q^{41} -1.00000 q^{43} -4.00000 q^{44} +5.00000 q^{46} -8.00000 q^{47} -1.00000 q^{48} -5.00000 q^{51} -1.00000 q^{52} +5.00000 q^{53} +1.00000 q^{54} +6.00000 q^{57} +3.00000 q^{58} -1.00000 q^{59} +1.00000 q^{61} +7.00000 q^{62} +1.00000 q^{64} -4.00000 q^{66} +4.00000 q^{67} +5.00000 q^{68} +5.00000 q^{69} -12.0000 q^{71} -1.00000 q^{72} +4.00000 q^{73} -4.00000 q^{74} -6.00000 q^{76} -1.00000 q^{78} -8.00000 q^{79} +1.00000 q^{81} -5.00000 q^{82} +13.0000 q^{83} +1.00000 q^{86} +3.00000 q^{87} +4.00000 q^{88} -2.00000 q^{89} -5.00000 q^{92} +7.00000 q^{93} +8.00000 q^{94} +1.00000 q^{96} +18.0000 q^{97} -4.00000 q^{99} +O(q^{100})\)

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
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 5.00000 1.21268 0.606339 0.795206i \(-0.292637\pi\)
0.606339 + 0.795206i \(0.292637\pi\)
\(18\) −1.00000 −0.235702
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) −5.00000 −1.04257 −0.521286 0.853382i \(-0.674548\pi\)
−0.521286 + 0.853382i \(0.674548\pi\)
\(24\) 1.00000 0.204124
\(25\) 0 0
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.00000 0.696311
\(34\) −5.00000 −0.857493
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 6.00000 0.973329
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 5.00000 0.737210
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 0 0
\(51\) −5.00000 −0.700140
\(52\) −1.00000 −0.138675
\(53\) 5.00000 0.686803 0.343401 0.939189i \(-0.388421\pi\)
0.343401 + 0.939189i \(0.388421\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) 6.00000 0.794719
\(58\) 3.00000 0.393919
\(59\) −1.00000 −0.130189 −0.0650945 0.997879i \(-0.520735\pi\)
−0.0650945 + 0.997879i \(0.520735\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037 0.0640184 0.997949i \(-0.479608\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 7.00000 0.889001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −4.00000 −0.492366
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 5.00000 0.606339
\(69\) 5.00000 0.601929
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) −1.00000 −0.117851
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) −4.00000 −0.464991
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) 0 0
\(78\) −1.00000 −0.113228
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −5.00000 −0.552158
\(83\) 13.0000 1.42694 0.713468 0.700688i \(-0.247124\pi\)
0.713468 + 0.700688i \(0.247124\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.00000 0.107833
\(87\) 3.00000 0.321634
\(88\) 4.00000 0.426401
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −5.00000 −0.521286
\(93\) 7.00000 0.725866
\(94\) 8.00000 0.825137
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 18.0000 1.82762 0.913812 0.406138i \(-0.133125\pi\)
0.913812 + 0.406138i \(0.133125\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 0 0
\(101\) −16.0000 −1.59206 −0.796030 0.605257i \(-0.793070\pi\)
−0.796030 + 0.605257i \(0.793070\pi\)
\(102\) 5.00000 0.495074
\(103\) 7.00000 0.689730 0.344865 0.938652i \(-0.387925\pi\)
0.344865 + 0.938652i \(0.387925\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −5.00000 −0.485643
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) −6.00000 −0.561951
\(115\) 0 0
\(116\) −3.00000 −0.278543
\(117\) −1.00000 −0.0924500
\(118\) 1.00000 0.0920575
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) −1.00000 −0.0905357
\(123\) −5.00000 −0.450835
\(124\) −7.00000 −0.628619
\(125\) 0 0
\(126\) 0 0
\(127\) −6.00000 −0.532414 −0.266207 0.963916i \(-0.585770\pi\)
−0.266207 + 0.963916i \(0.585770\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.00000 0.0880451
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) −5.00000 −0.428746
\(137\) −10.0000 −0.854358 −0.427179 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) −5.00000 −0.425628
\(139\) 22.0000 1.86602 0.933008 0.359856i \(-0.117174\pi\)
0.933008 + 0.359856i \(0.117174\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 12.0000 1.00702
\(143\) 4.00000 0.334497
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) 5.00000 0.409616 0.204808 0.978802i \(-0.434343\pi\)
0.204808 + 0.978802i \(0.434343\pi\)
\(150\) 0 0
\(151\) 12.0000 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) 6.00000 0.486664
\(153\) 5.00000 0.404226
\(154\) 0 0
\(155\) 0 0
\(156\) 1.00000 0.0800641
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 8.00000 0.636446
\(159\) −5.00000 −0.396526
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −23.0000 −1.80150 −0.900750 0.434339i \(-0.856982\pi\)
−0.900750 + 0.434339i \(0.856982\pi\)
\(164\) 5.00000 0.390434
\(165\) 0 0
\(166\) −13.0000 −1.00900
\(167\) 18.0000 1.39288 0.696441 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −6.00000 −0.458831
\(172\) −1.00000 −0.0762493
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −3.00000 −0.227429
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 1.00000 0.0751646
\(178\) 2.00000 0.149906
\(179\) −8.00000 −0.597948 −0.298974 0.954261i \(-0.596644\pi\)
−0.298974 + 0.954261i \(0.596644\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) −1.00000 −0.0739221
\(184\) 5.00000 0.368605
\(185\) 0 0
\(186\) −7.00000 −0.513265
\(187\) −20.0000 −1.46254
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) 0 0
\(191\) −15.0000 −1.08536 −0.542681 0.839939i \(-0.682591\pi\)
−0.542681 + 0.839939i \(0.682591\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −18.0000 −1.29567 −0.647834 0.761781i \(-0.724325\pi\)
−0.647834 + 0.761781i \(0.724325\pi\)
\(194\) −18.0000 −1.29232
\(195\) 0 0
\(196\) 0 0
\(197\) 21.0000 1.49619 0.748094 0.663593i \(-0.230969\pi\)
0.748094 + 0.663593i \(0.230969\pi\)
\(198\) 4.00000 0.284268
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 16.0000 1.12576
\(203\) 0 0
\(204\) −5.00000 −0.350070
\(205\) 0 0
\(206\) −7.00000 −0.487713
\(207\) −5.00000 −0.347524
\(208\) −1.00000 −0.0693375
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) 17.0000 1.17033 0.585164 0.810915i \(-0.301030\pi\)
0.585164 + 0.810915i \(0.301030\pi\)
\(212\) 5.00000 0.343401
\(213\) 12.0000 0.822226
\(214\) 6.00000 0.410152
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) −16.0000 −1.08366
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) −5.00000 −0.336336
\(222\) 4.00000 0.268462
\(223\) 19.0000 1.27233 0.636167 0.771551i \(-0.280519\pi\)
0.636167 + 0.771551i \(0.280519\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 4.00000 0.266076
\(227\) 15.0000 0.995585 0.497792 0.867296i \(-0.334144\pi\)
0.497792 + 0.867296i \(0.334144\pi\)
\(228\) 6.00000 0.397360
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 0.196960
\(233\) −10.0000 −0.655122 −0.327561 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) 1.00000 0.0653720
\(235\) 0 0
\(236\) −1.00000 −0.0650945
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) −5.00000 −0.321412
\(243\) −1.00000 −0.0641500
\(244\) 1.00000 0.0640184
\(245\) 0 0
\(246\) 5.00000 0.318788
\(247\) 6.00000 0.381771
\(248\) 7.00000 0.444500
\(249\) −13.0000 −0.823842
\(250\) 0 0
\(251\) −25.0000 −1.57799 −0.788993 0.614402i \(-0.789397\pi\)
−0.788993 + 0.614402i \(0.789397\pi\)
\(252\) 0 0
\(253\) 20.0000 1.25739
\(254\) 6.00000 0.376473
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −27.0000 −1.68421 −0.842107 0.539311i \(-0.818685\pi\)
−0.842107 + 0.539311i \(0.818685\pi\)
\(258\) −1.00000 −0.0622573
\(259\) 0 0
\(260\) 0 0
\(261\) −3.00000 −0.185695
\(262\) 12.0000 0.741362
\(263\) 3.00000 0.184988 0.0924940 0.995713i \(-0.470516\pi\)
0.0924940 + 0.995713i \(0.470516\pi\)
\(264\) −4.00000 −0.246183
\(265\) 0 0
\(266\) 0 0
\(267\) 2.00000 0.122398
\(268\) 4.00000 0.244339
\(269\) 28.0000 1.70719 0.853595 0.520937i \(-0.174417\pi\)
0.853595 + 0.520937i \(0.174417\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 5.00000 0.303170
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) 0 0
\(276\) 5.00000 0.300965
\(277\) −8.00000 −0.480673 −0.240337 0.970690i \(-0.577258\pi\)
−0.240337 + 0.970690i \(0.577258\pi\)
\(278\) −22.0000 −1.31947
\(279\) −7.00000 −0.419079
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) −8.00000 −0.476393
\(283\) 22.0000 1.30776 0.653882 0.756596i \(-0.273139\pi\)
0.653882 + 0.756596i \(0.273139\pi\)
\(284\) −12.0000 −0.712069
\(285\) 0 0
\(286\) −4.00000 −0.236525
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) −18.0000 −1.05518
\(292\) 4.00000 0.234082
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 4.00000 0.232104
\(298\) −5.00000 −0.289642
\(299\) 5.00000 0.289157
\(300\) 0 0
\(301\) 0 0
\(302\) −12.0000 −0.690522
\(303\) 16.0000 0.919176
\(304\) −6.00000 −0.344124
\(305\) 0 0
\(306\) −5.00000 −0.285831
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) −7.00000 −0.398216
\(310\) 0 0
\(311\) −28.0000 −1.58773 −0.793867 0.608091i \(-0.791935\pi\)
−0.793867 + 0.608091i \(0.791935\pi\)
\(312\) −1.00000 −0.0566139
\(313\) 4.00000 0.226093 0.113047 0.993590i \(-0.463939\pi\)
0.113047 + 0.993590i \(0.463939\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −15.0000 −0.842484 −0.421242 0.906948i \(-0.638406\pi\)
−0.421242 + 0.906948i \(0.638406\pi\)
\(318\) 5.00000 0.280386
\(319\) 12.0000 0.671871
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) −30.0000 −1.66924
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 23.0000 1.27385
\(327\) −16.0000 −0.884802
\(328\) −5.00000 −0.276079
\(329\) 0 0
\(330\) 0 0
\(331\) 35.0000 1.92377 0.961887 0.273447i \(-0.0881639\pi\)
0.961887 + 0.273447i \(0.0881639\pi\)
\(332\) 13.0000 0.713468
\(333\) 4.00000 0.219199
\(334\) −18.0000 −0.984916
\(335\) 0 0
\(336\) 0 0
\(337\) −31.0000 −1.68868 −0.844339 0.535810i \(-0.820006\pi\)
−0.844339 + 0.535810i \(0.820006\pi\)
\(338\) 12.0000 0.652714
\(339\) 4.00000 0.217250
\(340\) 0 0
\(341\) 28.0000 1.51629
\(342\) 6.00000 0.324443
\(343\) 0 0
\(344\) 1.00000 0.0539164
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) 22.0000 1.18102 0.590511 0.807030i \(-0.298926\pi\)
0.590511 + 0.807030i \(0.298926\pi\)
\(348\) 3.00000 0.160817
\(349\) 23.0000 1.23116 0.615581 0.788074i \(-0.288921\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 4.00000 0.213201
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) −1.00000 −0.0531494
\(355\) 0 0
\(356\) −2.00000 −0.106000
\(357\) 0 0
\(358\) 8.00000 0.422813
\(359\) 1.00000 0.0527780 0.0263890 0.999652i \(-0.491599\pi\)
0.0263890 + 0.999652i \(0.491599\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) −10.0000 −0.525588
\(363\) −5.00000 −0.262432
\(364\) 0 0
\(365\) 0 0
\(366\) 1.00000 0.0522708
\(367\) 29.0000 1.51379 0.756894 0.653538i \(-0.226716\pi\)
0.756894 + 0.653538i \(0.226716\pi\)
\(368\) −5.00000 −0.260643
\(369\) 5.00000 0.260290
\(370\) 0 0
\(371\) 0 0
\(372\) 7.00000 0.362933
\(373\) 12.0000 0.621336 0.310668 0.950518i \(-0.399447\pi\)
0.310668 + 0.950518i \(0.399447\pi\)
\(374\) 20.0000 1.03418
\(375\) 0 0
\(376\) 8.00000 0.412568
\(377\) 3.00000 0.154508
\(378\) 0 0
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) 0 0
\(381\) 6.00000 0.307389
\(382\) 15.0000 0.767467
\(383\) 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
\(386\) 18.0000 0.916176
\(387\) −1.00000 −0.0508329
\(388\) 18.0000 0.913812
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) −25.0000 −1.26430
\(392\) 0 0
\(393\) 12.0000 0.605320
\(394\) −21.0000 −1.05796
\(395\) 0 0
\(396\) −4.00000 −0.201008
\(397\) −31.0000 −1.55585 −0.777923 0.628360i \(-0.783727\pi\)
−0.777923 + 0.628360i \(0.783727\pi\)
\(398\) −8.00000 −0.401004
\(399\) 0 0
\(400\) 0 0
\(401\) −38.0000 −1.89763 −0.948815 0.315833i \(-0.897716\pi\)
−0.948815 + 0.315833i \(0.897716\pi\)
\(402\) 4.00000 0.199502
\(403\) 7.00000 0.348695
\(404\) −16.0000 −0.796030
\(405\) 0 0
\(406\) 0 0
\(407\) −16.0000 −0.793091
\(408\) 5.00000 0.247537
\(409\) −4.00000 −0.197787 −0.0988936 0.995098i \(-0.531530\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) 0 0
\(411\) 10.0000 0.493264
\(412\) 7.00000 0.344865
\(413\) 0 0
\(414\) 5.00000 0.245737
\(415\) 0 0
\(416\) 1.00000 0.0490290
\(417\) −22.0000 −1.07734
\(418\) −24.0000 −1.17388
\(419\) 33.0000 1.61216 0.806078 0.591810i \(-0.201586\pi\)
0.806078 + 0.591810i \(0.201586\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) −17.0000 −0.827547
\(423\) −8.00000 −0.388973
\(424\) −5.00000 −0.242821
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) 0 0
\(428\) −6.00000 −0.290021
\(429\) −4.00000 −0.193122
\(430\) 0 0
\(431\) −15.0000 −0.722525 −0.361262 0.932464i \(-0.617654\pi\)
−0.361262 + 0.932464i \(0.617654\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 16.0000 0.766261
\(437\) 30.0000 1.43509
\(438\) 4.00000 0.191127
\(439\) 5.00000 0.238637 0.119318 0.992856i \(-0.461929\pi\)
0.119318 + 0.992856i \(0.461929\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 5.00000 0.237826
\(443\) 8.00000 0.380091 0.190046 0.981775i \(-0.439136\pi\)
0.190046 + 0.981775i \(0.439136\pi\)
\(444\) −4.00000 −0.189832
\(445\) 0 0
\(446\) −19.0000 −0.899676
\(447\) −5.00000 −0.236492
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) −20.0000 −0.941763
\(452\) −4.00000 −0.188144
\(453\) −12.0000 −0.563809
\(454\) −15.0000 −0.703985
\(455\) 0 0
\(456\) −6.00000 −0.280976
\(457\) 33.0000 1.54367 0.771837 0.635820i \(-0.219338\pi\)
0.771837 + 0.635820i \(0.219338\pi\)
\(458\) −14.0000 −0.654177
\(459\) −5.00000 −0.233380
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 38.0000 1.76601 0.883005 0.469364i \(-0.155517\pi\)
0.883005 + 0.469364i \(0.155517\pi\)
\(464\) −3.00000 −0.139272
\(465\) 0 0
\(466\) 10.0000 0.463241
\(467\) 5.00000 0.231372 0.115686 0.993286i \(-0.463093\pi\)
0.115686 + 0.993286i \(0.463093\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 0 0
\(470\) 0 0
\(471\) −14.0000 −0.645086
\(472\) 1.00000 0.0460287
\(473\) 4.00000 0.183920
\(474\) −8.00000 −0.367452
\(475\) 0 0
\(476\) 0 0
\(477\) 5.00000 0.228934
\(478\) −16.0000 −0.731823
\(479\) −34.0000 −1.55350 −0.776750 0.629809i \(-0.783133\pi\)
−0.776750 + 0.629809i \(0.783133\pi\)
\(480\) 0 0
\(481\) −4.00000 −0.182384
\(482\) 22.0000 1.00207
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) −1.00000 −0.0452679
\(489\) 23.0000 1.04010
\(490\) 0 0
\(491\) 18.0000 0.812329 0.406164 0.913800i \(-0.366866\pi\)
0.406164 + 0.913800i \(0.366866\pi\)
\(492\) −5.00000 −0.225417
\(493\) −15.0000 −0.675566
\(494\) −6.00000 −0.269953
\(495\) 0 0
\(496\) −7.00000 −0.314309
\(497\) 0 0
\(498\) 13.0000 0.582544
\(499\) 43.0000 1.92494 0.962472 0.271380i \(-0.0874801\pi\)
0.962472 + 0.271380i \(0.0874801\pi\)
\(500\) 0 0
\(501\) −18.0000 −0.804181
\(502\) 25.0000 1.11580
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −20.0000 −0.889108
\(507\) 12.0000 0.532939
\(508\) −6.00000 −0.266207
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 6.00000 0.264906
\(514\) 27.0000 1.19092
\(515\) 0 0
\(516\) 1.00000 0.0440225
\(517\) 32.0000 1.40736
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 27.0000 1.18289 0.591446 0.806345i \(-0.298557\pi\)
0.591446 + 0.806345i \(0.298557\pi\)
\(522\) 3.00000 0.131306
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) −3.00000 −0.130806
\(527\) −35.0000 −1.52462
\(528\) 4.00000 0.174078
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) −1.00000 −0.0433963
\(532\) 0 0
\(533\) −5.00000 −0.216574
\(534\) −2.00000 −0.0865485
\(535\) 0 0
\(536\) −4.00000 −0.172774
\(537\) 8.00000 0.345225
\(538\) −28.0000 −1.20717
\(539\) 0 0
\(540\) 0 0
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −8.00000 −0.343629
\(543\) −10.0000 −0.429141
\(544\) −5.00000 −0.214373
\(545\) 0 0
\(546\) 0 0
\(547\) 5.00000 0.213785 0.106892 0.994271i \(-0.465910\pi\)
0.106892 + 0.994271i \(0.465910\pi\)
\(548\) −10.0000 −0.427179
\(549\) 1.00000 0.0426790
\(550\) 0 0
\(551\) 18.0000 0.766826
\(552\) −5.00000 −0.212814
\(553\) 0 0
\(554\) 8.00000 0.339887
\(555\) 0 0
\(556\) 22.0000 0.933008
\(557\) 42.0000 1.77960 0.889799 0.456354i \(-0.150845\pi\)
0.889799 + 0.456354i \(0.150845\pi\)
\(558\) 7.00000 0.296334
\(559\) 1.00000 0.0422955
\(560\) 0 0
\(561\) 20.0000 0.844401
\(562\) 4.00000 0.168730
\(563\) 21.0000 0.885044 0.442522 0.896758i \(-0.354084\pi\)
0.442522 + 0.896758i \(0.354084\pi\)
\(564\) 8.00000 0.336861
\(565\) 0 0
\(566\) −22.0000 −0.924729
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) 16.0000 0.670755 0.335377 0.942084i \(-0.391136\pi\)
0.335377 + 0.942084i \(0.391136\pi\)
\(570\) 0 0
\(571\) 21.0000 0.878823 0.439411 0.898286i \(-0.355187\pi\)
0.439411 + 0.898286i \(0.355187\pi\)
\(572\) 4.00000 0.167248
\(573\) 15.0000 0.626634
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 34.0000 1.41544 0.707719 0.706494i \(-0.249724\pi\)
0.707719 + 0.706494i \(0.249724\pi\)
\(578\) −8.00000 −0.332756
\(579\) 18.0000 0.748054
\(580\) 0 0
\(581\) 0 0
\(582\) 18.0000 0.746124
\(583\) −20.0000 −0.828315
\(584\) −4.00000 −0.165521
\(585\) 0 0
\(586\) 12.0000 0.495715
\(587\) −7.00000 −0.288921 −0.144460 0.989511i \(-0.546145\pi\)
−0.144460 + 0.989511i \(0.546145\pi\)
\(588\) 0 0
\(589\) 42.0000 1.73058
\(590\) 0 0
\(591\) −21.0000 −0.863825
\(592\) 4.00000 0.164399
\(593\) −14.0000 −0.574911 −0.287456 0.957794i \(-0.592809\pi\)
−0.287456 + 0.957794i \(0.592809\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) 5.00000 0.204808
\(597\) −8.00000 −0.327418
\(598\) −5.00000 −0.204465
\(599\) 29.0000 1.18491 0.592454 0.805604i \(-0.298159\pi\)
0.592454 + 0.805604i \(0.298159\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 12.0000 0.488273
\(605\) 0 0
\(606\) −16.0000 −0.649956
\(607\) 20.0000 0.811775 0.405887 0.913923i \(-0.366962\pi\)
0.405887 + 0.913923i \(0.366962\pi\)
\(608\) 6.00000 0.243332
\(609\) 0 0
\(610\) 0 0
\(611\) 8.00000 0.323645
\(612\) 5.00000 0.202113
\(613\) −34.0000 −1.37325 −0.686624 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 20.0000 0.807134
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000 0.483102 0.241551 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) 7.00000 0.281581
\(619\) 30.0000 1.20580 0.602901 0.797816i \(-0.294011\pi\)
0.602901 + 0.797816i \(0.294011\pi\)
\(620\) 0 0
\(621\) 5.00000 0.200643
\(622\) 28.0000 1.12270
\(623\) 0 0
\(624\) 1.00000 0.0400320
\(625\) 0 0
\(626\) −4.00000 −0.159872
\(627\) −24.0000 −0.958468
\(628\) 14.0000 0.558661
\(629\) 20.0000 0.797452
\(630\) 0 0
\(631\) 10.0000 0.398094 0.199047 0.979990i \(-0.436215\pi\)
0.199047 + 0.979990i \(0.436215\pi\)
\(632\) 8.00000 0.318223
\(633\) −17.0000 −0.675689
\(634\) 15.0000 0.595726
\(635\) 0 0
\(636\) −5.00000 −0.198263
\(637\) 0 0
\(638\) −12.0000 −0.475085
\(639\) −12.0000 −0.474713
\(640\) 0 0
\(641\) −12.0000 −0.473972 −0.236986 0.971513i \(-0.576159\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(642\) −6.00000 −0.236801
\(643\) 24.0000 0.946468 0.473234 0.880937i \(-0.343087\pi\)
0.473234 + 0.880937i \(0.343087\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 30.0000 1.18033
\(647\) 16.0000 0.629025 0.314512 0.949253i \(-0.398159\pi\)
0.314512 + 0.949253i \(0.398159\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 4.00000 0.157014
\(650\) 0 0
\(651\) 0 0
\(652\) −23.0000 −0.900750
\(653\) −26.0000 −1.01746 −0.508729 0.860927i \(-0.669885\pi\)
−0.508729 + 0.860927i \(0.669885\pi\)
\(654\) 16.0000 0.625650
\(655\) 0 0
\(656\) 5.00000 0.195217
\(657\) 4.00000 0.156055
\(658\) 0 0
\(659\) 14.0000 0.545363 0.272681 0.962104i \(-0.412090\pi\)
0.272681 + 0.962104i \(0.412090\pi\)
\(660\) 0 0
\(661\) 38.0000 1.47803 0.739014 0.673690i \(-0.235292\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) −35.0000 −1.36031
\(663\) 5.00000 0.194184
\(664\) −13.0000 −0.504498
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) 15.0000 0.580802
\(668\) 18.0000 0.696441
\(669\) −19.0000 −0.734582
\(670\) 0 0
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) 31.0000 1.19408
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 2.00000 0.0768662 0.0384331 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) −4.00000 −0.153619
\(679\) 0 0
\(680\) 0 0
\(681\) −15.0000 −0.574801
\(682\) −28.0000 −1.07218
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) −6.00000 −0.229416
\(685\) 0 0
\(686\) 0 0
\(687\) −14.0000 −0.534133
\(688\) −1.00000 −0.0381246
\(689\) −5.00000 −0.190485
\(690\) 0 0
\(691\) 10.0000 0.380418 0.190209 0.981744i \(-0.439083\pi\)
0.190209 + 0.981744i \(0.439083\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −22.0000 −0.835109
\(695\) 0 0
\(696\) −3.00000 −0.113715
\(697\) 25.0000 0.946943
\(698\) −23.0000 −0.870563
\(699\) 10.0000 0.378235
\(700\) 0 0
\(701\) −11.0000 −0.415464 −0.207732 0.978186i \(-0.566608\pi\)
−0.207732 + 0.978186i \(0.566608\pi\)
\(702\) −1.00000 −0.0377426
\(703\) −24.0000 −0.905177
\(704\) −4.00000 −0.150756
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 0 0
\(708\) 1.00000 0.0375823
\(709\) −18.0000 −0.676004 −0.338002 0.941145i \(-0.609751\pi\)
−0.338002 + 0.941145i \(0.609751\pi\)
\(710\) 0 0
\(711\) −8.00000 −0.300023
\(712\) 2.00000 0.0749532
\(713\) 35.0000 1.31076
\(714\) 0 0
\(715\) 0 0
\(716\) −8.00000 −0.298974
\(717\) −16.0000 −0.597531
\(718\) −1.00000 −0.0373197
\(719\) 36.0000 1.34257 0.671287 0.741198i \(-0.265742\pi\)
0.671287 + 0.741198i \(0.265742\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −17.0000 −0.632674
\(723\) 22.0000 0.818189
\(724\) 10.0000 0.371647
\(725\) 0 0
\(726\) 5.00000 0.185567
\(727\) −13.0000 −0.482143 −0.241072 0.970507i \(-0.577499\pi\)
−0.241072 + 0.970507i \(0.577499\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −5.00000 −0.184932
\(732\) −1.00000 −0.0369611
\(733\) 21.0000 0.775653 0.387826 0.921732i \(-0.373226\pi\)
0.387826 + 0.921732i \(0.373226\pi\)
\(734\) −29.0000 −1.07041
\(735\) 0 0
\(736\) 5.00000 0.184302
\(737\) −16.0000 −0.589368
\(738\) −5.00000 −0.184053
\(739\) −15.0000 −0.551784 −0.275892 0.961189i \(-0.588973\pi\)
−0.275892 + 0.961189i \(0.588973\pi\)
\(740\) 0 0
\(741\) −6.00000 −0.220416
\(742\) 0 0
\(743\) −15.0000 −0.550297 −0.275148 0.961402i \(-0.588727\pi\)
−0.275148 + 0.961402i \(0.588727\pi\)
\(744\) −7.00000 −0.256632
\(745\) 0 0
\(746\) −12.0000 −0.439351
\(747\) 13.0000 0.475645
\(748\) −20.0000 −0.731272
\(749\) 0 0
\(750\) 0 0
\(751\) 40.0000 1.45962 0.729810 0.683650i \(-0.239608\pi\)
0.729810 + 0.683650i \(0.239608\pi\)
\(752\) −8.00000 −0.291730
\(753\) 25.0000 0.911051
\(754\) −3.00000 −0.109254
\(755\) 0 0
\(756\) 0 0
\(757\) 20.0000 0.726912 0.363456 0.931611i \(-0.381597\pi\)
0.363456 + 0.931611i \(0.381597\pi\)
\(758\) 19.0000 0.690111
\(759\) −20.0000 −0.725954
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) −6.00000 −0.217357
\(763\) 0 0
\(764\) −15.0000 −0.542681
\(765\) 0 0
\(766\) −14.0000 −0.505841
\(767\) 1.00000 0.0361079
\(768\) −1.00000 −0.0360844
\(769\) 20.0000 0.721218 0.360609 0.932717i \(-0.382569\pi\)
0.360609 + 0.932717i \(0.382569\pi\)
\(770\) 0 0
\(771\) 27.0000 0.972381
\(772\) −18.0000 −0.647834
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 1.00000 0.0359443
\(775\) 0 0
\(776\) −18.0000 −0.646162
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) −30.0000 −1.07486
\(780\) 0 0
\(781\) 48.0000 1.71758
\(782\) 25.0000 0.893998
\(783\) 3.00000 0.107211
\(784\) 0 0
\(785\) 0 0
\(786\) −12.0000 −0.428026
\(787\) −30.0000 −1.06938 −0.534692 0.845047i \(-0.679572\pi\)
−0.534692 + 0.845047i \(0.679572\pi\)
\(788\) 21.0000 0.748094
\(789\) −3.00000 −0.106803
\(790\) 0 0
\(791\) 0 0
\(792\) 4.00000 0.142134
\(793\) −1.00000 −0.0355110
\(794\) 31.0000 1.10015
\(795\) 0 0
\(796\) 8.00000 0.283552
\(797\) −28.0000 −0.991811 −0.495905 0.868377i \(-0.665164\pi\)
−0.495905 + 0.868377i \(0.665164\pi\)
\(798\) 0 0
\(799\) −40.0000 −1.41510
\(800\) 0 0
\(801\) −2.00000 −0.0706665
\(802\) 38.0000 1.34183
\(803\) −16.0000 −0.564628
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) −7.00000 −0.246564
\(807\) −28.0000 −0.985647
\(808\) 16.0000 0.562878
\(809\) −28.0000 −0.984428 −0.492214 0.870474i \(-0.663812\pi\)
−0.492214 + 0.870474i \(0.663812\pi\)
\(810\) 0 0
\(811\) 16.0000 0.561836 0.280918 0.959732i \(-0.409361\pi\)
0.280918 + 0.959732i \(0.409361\pi\)
\(812\) 0 0
\(813\) −8.00000 −0.280572
\(814\) 16.0000 0.560800
\(815\) 0 0
\(816\) −5.00000 −0.175035
\(817\) 6.00000 0.209913
\(818\) 4.00000 0.139857
\(819\) 0 0
\(820\) 0 0
\(821\) −30.0000 −1.04701 −0.523504 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) −10.0000 −0.348790
\(823\) −44.0000 −1.53374 −0.766872 0.641800i \(-0.778188\pi\)
−0.766872 + 0.641800i \(0.778188\pi\)
\(824\) −7.00000 −0.243857
\(825\) 0 0
\(826\) 0 0
\(827\) 16.0000 0.556375 0.278187 0.960527i \(-0.410266\pi\)
0.278187 + 0.960527i \(0.410266\pi\)
\(828\) −5.00000 −0.173762
\(829\) −17.0000 −0.590434 −0.295217 0.955430i \(-0.595392\pi\)
−0.295217 + 0.955430i \(0.595392\pi\)
\(830\) 0 0
\(831\) 8.00000 0.277517
\(832\) −1.00000 −0.0346688
\(833\) 0 0
\(834\) 22.0000 0.761798
\(835\) 0 0
\(836\) 24.0000 0.830057
\(837\) 7.00000 0.241955
\(838\) −33.0000 −1.13997
\(839\) −6.00000 −0.207143 −0.103572 0.994622i \(-0.533027\pi\)
−0.103572 + 0.994622i \(0.533027\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) 34.0000 1.17172
\(843\) 4.00000 0.137767
\(844\) 17.0000 0.585164
\(845\) 0 0
\(846\) 8.00000 0.275046
\(847\) 0 0
\(848\) 5.00000 0.171701
\(849\) −22.0000 −0.755038
\(850\) 0 0
\(851\) −20.0000 −0.685591
\(852\) 12.0000 0.411113
\(853\) 17.0000 0.582069 0.291034 0.956713i \(-0.406001\pi\)
0.291034 + 0.956713i \(0.406001\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 6.00000 0.205076
\(857\) 30.0000 1.02478 0.512390 0.858753i \(-0.328760\pi\)
0.512390 + 0.858753i \(0.328760\pi\)
\(858\) 4.00000 0.136558
\(859\) 4.00000 0.136478 0.0682391 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 15.0000 0.510902
\(863\) 48.0000 1.63394 0.816970 0.576681i \(-0.195652\pi\)
0.816970 + 0.576681i \(0.195652\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) −2.00000 −0.0679628
\(867\) −8.00000 −0.271694
\(868\) 0 0
\(869\) 32.0000 1.08553
\(870\) 0 0
\(871\) −4.00000 −0.135535
\(872\) −16.0000 −0.541828
\(873\) 18.0000 0.609208
\(874\) −30.0000 −1.01477
\(875\) 0 0
\(876\) −4.00000 −0.135147
\(877\) 48.0000 1.62084 0.810422 0.585846i \(-0.199238\pi\)
0.810422 + 0.585846i \(0.199238\pi\)
\(878\) −5.00000 −0.168742
\(879\) 12.0000 0.404750
\(880\) 0 0
\(881\) 37.0000 1.24656 0.623281 0.781998i \(-0.285799\pi\)
0.623281 + 0.781998i \(0.285799\pi\)
\(882\) 0 0
\(883\) 29.0000 0.975928 0.487964 0.872864i \(-0.337740\pi\)
0.487964 + 0.872864i \(0.337740\pi\)
\(884\) −5.00000 −0.168168
\(885\) 0 0
\(886\) −8.00000 −0.268765
\(887\) 4.00000 0.134307 0.0671534 0.997743i \(-0.478608\pi\)
0.0671534 + 0.997743i \(0.478608\pi\)
\(888\) 4.00000 0.134231
\(889\) 0 0
\(890\) 0 0
\(891\) −4.00000 −0.134005
\(892\) 19.0000 0.636167
\(893\) 48.0000 1.60626
\(894\) 5.00000 0.167225
\(895\) 0 0
\(896\) 0 0
\(897\) −5.00000 −0.166945
\(898\) −30.0000 −1.00111
\(899\) 21.0000 0.700389
\(900\) 0 0
\(901\) 25.0000 0.832871
\(902\) 20.0000 0.665927
\(903\) 0 0
\(904\) 4.00000 0.133038
\(905\) 0 0
\(906\) 12.0000 0.398673
\(907\) 5.00000 0.166022 0.0830111 0.996549i \(-0.473546\pi\)
0.0830111 + 0.996549i \(0.473546\pi\)
\(908\) 15.0000 0.497792
\(909\) −16.0000 −0.530687
\(910\) 0 0
\(911\) −53.0000 −1.75597 −0.877984 0.478690i \(-0.841112\pi\)
−0.877984 + 0.478690i \(0.841112\pi\)
\(912\) 6.00000 0.198680
\(913\) −52.0000 −1.72095
\(914\) −33.0000 −1.09154
\(915\) 0 0
\(916\) 14.0000 0.462573
\(917\) 0 0
\(918\) 5.00000 0.165025
\(919\) 2.00000 0.0659739 0.0329870 0.999456i \(-0.489498\pi\)
0.0329870 + 0.999456i \(0.489498\pi\)
\(920\) 0 0
\(921\) 20.0000 0.659022
\(922\) −12.0000 −0.395199
\(923\) 12.0000 0.394985
\(924\) 0 0
\(925\) 0 0
\(926\) −38.0000 −1.24876
\(927\) 7.00000 0.229910
\(928\) 3.00000 0.0984798
\(929\) −27.0000 −0.885841 −0.442921 0.896561i \(-0.646058\pi\)
−0.442921 + 0.896561i \(0.646058\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −10.0000 −0.327561
\(933\) 28.0000 0.916679
\(934\) −5.00000 −0.163605
\(935\) 0 0
\(936\) 1.00000 0.0326860
\(937\) −60.0000 −1.96011 −0.980057 0.198715i \(-0.936323\pi\)
−0.980057 + 0.198715i \(0.936323\pi\)
\(938\) 0 0
\(939\) −4.00000 −0.130535
\(940\) 0 0
\(941\) 28.0000 0.912774 0.456387 0.889781i \(-0.349143\pi\)
0.456387 + 0.889781i \(0.349143\pi\)
\(942\) 14.0000 0.456145
\(943\) −25.0000 −0.814112
\(944\) −1.00000 −0.0325472
\(945\) 0 0
\(946\) −4.00000 −0.130051
\(947\) −18.0000 −0.584921 −0.292461 0.956278i \(-0.594474\pi\)
−0.292461 + 0.956278i \(0.594474\pi\)
\(948\) 8.00000 0.259828
\(949\) −4.00000 −0.129845
\(950\) 0 0
\(951\) 15.0000 0.486408
\(952\) 0 0
\(953\) 4.00000 0.129573 0.0647864 0.997899i \(-0.479363\pi\)
0.0647864 + 0.997899i \(0.479363\pi\)
\(954\) −5.00000 −0.161881
\(955\) 0 0
\(956\) 16.0000 0.517477
\(957\) −12.0000 −0.387905
\(958\) 34.0000 1.09849
\(959\) 0 0
\(960\) 0 0
\(961\) 18.0000 0.580645
\(962\) 4.00000 0.128965
\(963\) −6.00000 −0.193347
\(964\) −22.0000 −0.708572
\(965\) 0 0
\(966\) 0 0
\(967\) −38.0000 −1.22200 −0.610999 0.791632i \(-0.709232\pi\)
−0.610999 + 0.791632i \(0.709232\pi\)
\(968\) −5.00000 −0.160706
\(969\) 30.0000 0.963739
\(970\) 0 0
\(971\) 44.0000 1.41203 0.706014 0.708198i \(-0.250492\pi\)
0.706014 + 0.708198i \(0.250492\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −2.00000 −0.0640841
\(975\) 0 0
\(976\) 1.00000 0.0320092
\(977\) −36.0000 −1.15174 −0.575871 0.817541i \(-0.695337\pi\)
−0.575871 + 0.817541i \(0.695337\pi\)
\(978\) −23.0000 −0.735459
\(979\) 8.00000 0.255681
\(980\) 0 0
\(981\) 16.0000 0.510841
\(982\) −18.0000 −0.574403
\(983\) −28.0000 −0.893061 −0.446531 0.894768i \(-0.647341\pi\)
−0.446531 + 0.894768i \(0.647341\pi\)
\(984\) 5.00000 0.159394
\(985\) 0 0
\(986\) 15.0000 0.477697
\(987\) 0 0
\(988\) 6.00000 0.190885
\(989\) 5.00000 0.158991
\(990\) 0 0
\(991\) 48.0000 1.52477 0.762385 0.647124i \(-0.224028\pi\)
0.762385 + 0.647124i \(0.224028\pi\)
\(992\) 7.00000 0.222250
\(993\) −35.0000 −1.11069
\(994\) 0 0
\(995\) 0 0
\(996\) −13.0000 −0.411921
\(997\) 18.0000 0.570066 0.285033 0.958518i \(-0.407995\pi\)
0.285033 + 0.958518i \(0.407995\pi\)
\(998\) −43.0000 −1.36114
\(999\) −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.d.1.1 1
5.4 even 2 7350.2.a.ck.1.1 yes 1
7.6 odd 2 7350.2.a.x.1.1 yes 1
35.34 odd 2 7350.2.a.bq.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7350.2.a.d.1.1 1 1.1 even 1 trivial
7350.2.a.x.1.1 yes 1 7.6 odd 2
7350.2.a.bq.1.1 yes 1 35.34 odd 2
7350.2.a.ck.1.1 yes 1 5.4 even 2