Properties

Label 4730.2.a.j.1.1
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
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
Root \(0\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +5.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +5.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} +5.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -2.00000 q^{18} +7.00000 q^{19} +1.00000 q^{20} +5.00000 q^{21} +1.00000 q^{22} +8.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -5.00000 q^{27} +5.00000 q^{28} -5.00000 q^{29} +1.00000 q^{30} -11.0000 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +5.00000 q^{35} -2.00000 q^{36} -7.00000 q^{37} +7.00000 q^{38} +4.00000 q^{39} +1.00000 q^{40} -12.0000 q^{41} +5.00000 q^{42} -1.00000 q^{43} +1.00000 q^{44} -2.00000 q^{45} +8.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} +18.0000 q^{49} +1.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} -13.0000 q^{53} -5.00000 q^{54} +1.00000 q^{55} +5.00000 q^{56} +7.00000 q^{57} -5.00000 q^{58} -8.00000 q^{59} +1.00000 q^{60} +5.00000 q^{61} -11.0000 q^{62} -10.0000 q^{63} +1.00000 q^{64} +4.00000 q^{65} +1.00000 q^{66} -12.0000 q^{67} +1.00000 q^{68} +8.00000 q^{69} +5.00000 q^{70} +1.00000 q^{71} -2.00000 q^{72} -10.0000 q^{73} -7.00000 q^{74} +1.00000 q^{75} +7.00000 q^{76} +5.00000 q^{77} +4.00000 q^{78} +8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -12.0000 q^{82} +4.00000 q^{83} +5.00000 q^{84} +1.00000 q^{85} -1.00000 q^{86} -5.00000 q^{87} +1.00000 q^{88} -9.00000 q^{89} -2.00000 q^{90} +20.0000 q^{91} +8.00000 q^{92} -11.0000 q^{93} +6.00000 q^{94} +7.00000 q^{95} +1.00000 q^{96} -8.00000 q^{97} +18.0000 q^{98} -2.00000 q^{99} +O(q^{100})\)

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 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.00000 0.408248
\(7\) 5.00000 1.88982 0.944911 0.327327i \(-0.106148\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) 1.00000 0.316228
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 5.00000 1.33631
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) −2.00000 −0.471405
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 1.00000 0.223607
\(21\) 5.00000 1.09109
\(22\) 1.00000 0.213201
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 4.00000 0.784465
\(27\) −5.00000 −0.962250
\(28\) 5.00000 0.944911
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 1.00000 0.182574
\(31\) −11.0000 −1.97566 −0.987829 0.155543i \(-0.950287\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) 1.00000 0.171499
\(35\) 5.00000 0.845154
\(36\) −2.00000 −0.333333
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) 7.00000 1.13555
\(39\) 4.00000 0.640513
\(40\) 1.00000 0.158114
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) 5.00000 0.771517
\(43\) −1.00000 −0.152499
\(44\) 1.00000 0.150756
\(45\) −2.00000 −0.298142
\(46\) 8.00000 1.17954
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 1.00000 0.144338
\(49\) 18.0000 2.57143
\(50\) 1.00000 0.141421
\(51\) 1.00000 0.140028
\(52\) 4.00000 0.554700
\(53\) −13.0000 −1.78569 −0.892844 0.450367i \(-0.851293\pi\)
−0.892844 + 0.450367i \(0.851293\pi\)
\(54\) −5.00000 −0.680414
\(55\) 1.00000 0.134840
\(56\) 5.00000 0.668153
\(57\) 7.00000 0.927173
\(58\) −5.00000 −0.656532
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 1.00000 0.129099
\(61\) 5.00000 0.640184 0.320092 0.947386i \(-0.396286\pi\)
0.320092 + 0.947386i \(0.396286\pi\)
\(62\) −11.0000 −1.39700
\(63\) −10.0000 −1.25988
\(64\) 1.00000 0.125000
\(65\) 4.00000 0.496139
\(66\) 1.00000 0.123091
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 1.00000 0.121268
\(69\) 8.00000 0.963087
\(70\) 5.00000 0.597614
\(71\) 1.00000 0.118678 0.0593391 0.998238i \(-0.481101\pi\)
0.0593391 + 0.998238i \(0.481101\pi\)
\(72\) −2.00000 −0.235702
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) −7.00000 −0.813733
\(75\) 1.00000 0.115470
\(76\) 7.00000 0.802955
\(77\) 5.00000 0.569803
\(78\) 4.00000 0.452911
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −12.0000 −1.32518
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 5.00000 0.545545
\(85\) 1.00000 0.108465
\(86\) −1.00000 −0.107833
\(87\) −5.00000 −0.536056
\(88\) 1.00000 0.106600
\(89\) −9.00000 −0.953998 −0.476999 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) −2.00000 −0.210819
\(91\) 20.0000 2.09657
\(92\) 8.00000 0.834058
\(93\) −11.0000 −1.14065
\(94\) 6.00000 0.618853
\(95\) 7.00000 0.718185
\(96\) 1.00000 0.102062
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 18.0000 1.81827
\(99\) −2.00000 −0.201008
\(100\) 1.00000 0.100000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 1.00000 0.0990148
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 4.00000 0.392232
\(105\) 5.00000 0.487950
\(106\) −13.0000 −1.26267
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) −5.00000 −0.481125
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 1.00000 0.0953463
\(111\) −7.00000 −0.664411
\(112\) 5.00000 0.472456
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 7.00000 0.655610
\(115\) 8.00000 0.746004
\(116\) −5.00000 −0.464238
\(117\) −8.00000 −0.739600
\(118\) −8.00000 −0.736460
\(119\) 5.00000 0.458349
\(120\) 1.00000 0.0912871
\(121\) 1.00000 0.0909091
\(122\) 5.00000 0.452679
\(123\) −12.0000 −1.08200
\(124\) −11.0000 −0.987829
\(125\) 1.00000 0.0894427
\(126\) −10.0000 −0.890871
\(127\) 12.0000 1.06483 0.532414 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.00000 −0.0880451
\(130\) 4.00000 0.350823
\(131\) 15.0000 1.31056 0.655278 0.755388i \(-0.272551\pi\)
0.655278 + 0.755388i \(0.272551\pi\)
\(132\) 1.00000 0.0870388
\(133\) 35.0000 3.03488
\(134\) −12.0000 −1.03664
\(135\) −5.00000 −0.430331
\(136\) 1.00000 0.0857493
\(137\) 10.0000 0.854358 0.427179 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 8.00000 0.681005
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 5.00000 0.422577
\(141\) 6.00000 0.505291
\(142\) 1.00000 0.0839181
\(143\) 4.00000 0.334497
\(144\) −2.00000 −0.166667
\(145\) −5.00000 −0.415227
\(146\) −10.0000 −0.827606
\(147\) 18.0000 1.48461
\(148\) −7.00000 −0.575396
\(149\) −3.00000 −0.245770 −0.122885 0.992421i \(-0.539215\pi\)
−0.122885 + 0.992421i \(0.539215\pi\)
\(150\) 1.00000 0.0816497
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) 7.00000 0.567775
\(153\) −2.00000 −0.161690
\(154\) 5.00000 0.402911
\(155\) −11.0000 −0.883541
\(156\) 4.00000 0.320256
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 8.00000 0.636446
\(159\) −13.0000 −1.03097
\(160\) 1.00000 0.0790569
\(161\) 40.0000 3.15244
\(162\) 1.00000 0.0785674
\(163\) 1.00000 0.0783260 0.0391630 0.999233i \(-0.487531\pi\)
0.0391630 + 0.999233i \(0.487531\pi\)
\(164\) −12.0000 −0.937043
\(165\) 1.00000 0.0778499
\(166\) 4.00000 0.310460
\(167\) 19.0000 1.47026 0.735132 0.677924i \(-0.237120\pi\)
0.735132 + 0.677924i \(0.237120\pi\)
\(168\) 5.00000 0.385758
\(169\) 3.00000 0.230769
\(170\) 1.00000 0.0766965
\(171\) −14.0000 −1.07061
\(172\) −1.00000 −0.0762493
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) −5.00000 −0.379049
\(175\) 5.00000 0.377964
\(176\) 1.00000 0.0753778
\(177\) −8.00000 −0.601317
\(178\) −9.00000 −0.674579
\(179\) −20.0000 −1.49487 −0.747435 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) −2.00000 −0.149071
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 20.0000 1.48250
\(183\) 5.00000 0.369611
\(184\) 8.00000 0.589768
\(185\) −7.00000 −0.514650
\(186\) −11.0000 −0.806559
\(187\) 1.00000 0.0731272
\(188\) 6.00000 0.437595
\(189\) −25.0000 −1.81848
\(190\) 7.00000 0.507833
\(191\) −4.00000 −0.289430 −0.144715 0.989473i \(-0.546227\pi\)
−0.144715 + 0.989473i \(0.546227\pi\)
\(192\) 1.00000 0.0721688
\(193\) 9.00000 0.647834 0.323917 0.946085i \(-0.395000\pi\)
0.323917 + 0.946085i \(0.395000\pi\)
\(194\) −8.00000 −0.574367
\(195\) 4.00000 0.286446
\(196\) 18.0000 1.28571
\(197\) −4.00000 −0.284988 −0.142494 0.989796i \(-0.545512\pi\)
−0.142494 + 0.989796i \(0.545512\pi\)
\(198\) −2.00000 −0.142134
\(199\) −7.00000 −0.496217 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) 1.00000 0.0707107
\(201\) −12.0000 −0.846415
\(202\) 6.00000 0.422159
\(203\) −25.0000 −1.75466
\(204\) 1.00000 0.0700140
\(205\) −12.0000 −0.838116
\(206\) 0 0
\(207\) −16.0000 −1.11208
\(208\) 4.00000 0.277350
\(209\) 7.00000 0.484200
\(210\) 5.00000 0.345033
\(211\) 23.0000 1.58339 0.791693 0.610920i \(-0.209200\pi\)
0.791693 + 0.610920i \(0.209200\pi\)
\(212\) −13.0000 −0.892844
\(213\) 1.00000 0.0685189
\(214\) 4.00000 0.273434
\(215\) −1.00000 −0.0681994
\(216\) −5.00000 −0.340207
\(217\) −55.0000 −3.73364
\(218\) −10.0000 −0.677285
\(219\) −10.0000 −0.675737
\(220\) 1.00000 0.0674200
\(221\) 4.00000 0.269069
\(222\) −7.00000 −0.469809
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 5.00000 0.334077
\(225\) −2.00000 −0.133333
\(226\) −12.0000 −0.798228
\(227\) 2.00000 0.132745 0.0663723 0.997795i \(-0.478857\pi\)
0.0663723 + 0.997795i \(0.478857\pi\)
\(228\) 7.00000 0.463586
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 8.00000 0.527504
\(231\) 5.00000 0.328976
\(232\) −5.00000 −0.328266
\(233\) −25.0000 −1.63780 −0.818902 0.573933i \(-0.805417\pi\)
−0.818902 + 0.573933i \(0.805417\pi\)
\(234\) −8.00000 −0.522976
\(235\) 6.00000 0.391397
\(236\) −8.00000 −0.520756
\(237\) 8.00000 0.519656
\(238\) 5.00000 0.324102
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 1.00000 0.0645497
\(241\) 16.0000 1.03065 0.515325 0.856995i \(-0.327671\pi\)
0.515325 + 0.856995i \(0.327671\pi\)
\(242\) 1.00000 0.0642824
\(243\) 16.0000 1.02640
\(244\) 5.00000 0.320092
\(245\) 18.0000 1.14998
\(246\) −12.0000 −0.765092
\(247\) 28.0000 1.78160
\(248\) −11.0000 −0.698501
\(249\) 4.00000 0.253490
\(250\) 1.00000 0.0632456
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −10.0000 −0.629941
\(253\) 8.00000 0.502956
\(254\) 12.0000 0.752947
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) 14.0000 0.873296 0.436648 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(258\) −1.00000 −0.0622573
\(259\) −35.0000 −2.17479
\(260\) 4.00000 0.248069
\(261\) 10.0000 0.618984
\(262\) 15.0000 0.926703
\(263\) −5.00000 −0.308313 −0.154157 0.988046i \(-0.549266\pi\)
−0.154157 + 0.988046i \(0.549266\pi\)
\(264\) 1.00000 0.0615457
\(265\) −13.0000 −0.798584
\(266\) 35.0000 2.14599
\(267\) −9.00000 −0.550791
\(268\) −12.0000 −0.733017
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) −5.00000 −0.304290
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) 1.00000 0.0606339
\(273\) 20.0000 1.21046
\(274\) 10.0000 0.604122
\(275\) 1.00000 0.0603023
\(276\) 8.00000 0.481543
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 16.0000 0.959616
\(279\) 22.0000 1.31711
\(280\) 5.00000 0.298807
\(281\) 16.0000 0.954480 0.477240 0.878773i \(-0.341637\pi\)
0.477240 + 0.878773i \(0.341637\pi\)
\(282\) 6.00000 0.357295
\(283\) −18.0000 −1.06999 −0.534994 0.844856i \(-0.679686\pi\)
−0.534994 + 0.844856i \(0.679686\pi\)
\(284\) 1.00000 0.0593391
\(285\) 7.00000 0.414644
\(286\) 4.00000 0.236525
\(287\) −60.0000 −3.54169
\(288\) −2.00000 −0.117851
\(289\) −16.0000 −0.941176
\(290\) −5.00000 −0.293610
\(291\) −8.00000 −0.468968
\(292\) −10.0000 −0.585206
\(293\) 4.00000 0.233682 0.116841 0.993151i \(-0.462723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) 18.0000 1.04978
\(295\) −8.00000 −0.465778
\(296\) −7.00000 −0.406867
\(297\) −5.00000 −0.290129
\(298\) −3.00000 −0.173785
\(299\) 32.0000 1.85061
\(300\) 1.00000 0.0577350
\(301\) −5.00000 −0.288195
\(302\) 20.0000 1.15087
\(303\) 6.00000 0.344691
\(304\) 7.00000 0.401478
\(305\) 5.00000 0.286299
\(306\) −2.00000 −0.114332
\(307\) 10.0000 0.570730 0.285365 0.958419i \(-0.407885\pi\)
0.285365 + 0.958419i \(0.407885\pi\)
\(308\) 5.00000 0.284901
\(309\) 0 0
\(310\) −11.0000 −0.624758
\(311\) −35.0000 −1.98467 −0.992334 0.123585i \(-0.960561\pi\)
−0.992334 + 0.123585i \(0.960561\pi\)
\(312\) 4.00000 0.226455
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) −7.00000 −0.395033
\(315\) −10.0000 −0.563436
\(316\) 8.00000 0.450035
\(317\) −15.0000 −0.842484 −0.421242 0.906948i \(-0.638406\pi\)
−0.421242 + 0.906948i \(0.638406\pi\)
\(318\) −13.0000 −0.729004
\(319\) −5.00000 −0.279946
\(320\) 1.00000 0.0559017
\(321\) 4.00000 0.223258
\(322\) 40.0000 2.22911
\(323\) 7.00000 0.389490
\(324\) 1.00000 0.0555556
\(325\) 4.00000 0.221880
\(326\) 1.00000 0.0553849
\(327\) −10.0000 −0.553001
\(328\) −12.0000 −0.662589
\(329\) 30.0000 1.65395
\(330\) 1.00000 0.0550482
\(331\) 36.0000 1.97874 0.989369 0.145424i \(-0.0464545\pi\)
0.989369 + 0.145424i \(0.0464545\pi\)
\(332\) 4.00000 0.219529
\(333\) 14.0000 0.767195
\(334\) 19.0000 1.03963
\(335\) −12.0000 −0.655630
\(336\) 5.00000 0.272772
\(337\) 7.00000 0.381314 0.190657 0.981657i \(-0.438938\pi\)
0.190657 + 0.981657i \(0.438938\pi\)
\(338\) 3.00000 0.163178
\(339\) −12.0000 −0.651751
\(340\) 1.00000 0.0542326
\(341\) −11.0000 −0.595683
\(342\) −14.0000 −0.757033
\(343\) 55.0000 2.96972
\(344\) −1.00000 −0.0539164
\(345\) 8.00000 0.430706
\(346\) −2.00000 −0.107521
\(347\) −14.0000 −0.751559 −0.375780 0.926709i \(-0.622625\pi\)
−0.375780 + 0.926709i \(0.622625\pi\)
\(348\) −5.00000 −0.268028
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 5.00000 0.267261
\(351\) −20.0000 −1.06752
\(352\) 1.00000 0.0533002
\(353\) −28.0000 −1.49029 −0.745145 0.666903i \(-0.767620\pi\)
−0.745145 + 0.666903i \(0.767620\pi\)
\(354\) −8.00000 −0.425195
\(355\) 1.00000 0.0530745
\(356\) −9.00000 −0.476999
\(357\) 5.00000 0.264628
\(358\) −20.0000 −1.05703
\(359\) −4.00000 −0.211112 −0.105556 0.994413i \(-0.533662\pi\)
−0.105556 + 0.994413i \(0.533662\pi\)
\(360\) −2.00000 −0.105409
\(361\) 30.0000 1.57895
\(362\) −10.0000 −0.525588
\(363\) 1.00000 0.0524864
\(364\) 20.0000 1.04828
\(365\) −10.0000 −0.523424
\(366\) 5.00000 0.261354
\(367\) 18.0000 0.939592 0.469796 0.882775i \(-0.344327\pi\)
0.469796 + 0.882775i \(0.344327\pi\)
\(368\) 8.00000 0.417029
\(369\) 24.0000 1.24939
\(370\) −7.00000 −0.363913
\(371\) −65.0000 −3.37463
\(372\) −11.0000 −0.570323
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 1.00000 0.0517088
\(375\) 1.00000 0.0516398
\(376\) 6.00000 0.309426
\(377\) −20.0000 −1.03005
\(378\) −25.0000 −1.28586
\(379\) 24.0000 1.23280 0.616399 0.787434i \(-0.288591\pi\)
0.616399 + 0.787434i \(0.288591\pi\)
\(380\) 7.00000 0.359092
\(381\) 12.0000 0.614779
\(382\) −4.00000 −0.204658
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 1.00000 0.0510310
\(385\) 5.00000 0.254824
\(386\) 9.00000 0.458088
\(387\) 2.00000 0.101666
\(388\) −8.00000 −0.406138
\(389\) 4.00000 0.202808 0.101404 0.994845i \(-0.467667\pi\)
0.101404 + 0.994845i \(0.467667\pi\)
\(390\) 4.00000 0.202548
\(391\) 8.00000 0.404577
\(392\) 18.0000 0.909137
\(393\) 15.0000 0.756650
\(394\) −4.00000 −0.201517
\(395\) 8.00000 0.402524
\(396\) −2.00000 −0.100504
\(397\) −2.00000 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) −7.00000 −0.350878
\(399\) 35.0000 1.75219
\(400\) 1.00000 0.0500000
\(401\) −17.0000 −0.848939 −0.424470 0.905442i \(-0.639539\pi\)
−0.424470 + 0.905442i \(0.639539\pi\)
\(402\) −12.0000 −0.598506
\(403\) −44.0000 −2.19180
\(404\) 6.00000 0.298511
\(405\) 1.00000 0.0496904
\(406\) −25.0000 −1.24073
\(407\) −7.00000 −0.346977
\(408\) 1.00000 0.0495074
\(409\) −8.00000 −0.395575 −0.197787 0.980245i \(-0.563376\pi\)
−0.197787 + 0.980245i \(0.563376\pi\)
\(410\) −12.0000 −0.592638
\(411\) 10.0000 0.493264
\(412\) 0 0
\(413\) −40.0000 −1.96827
\(414\) −16.0000 −0.786357
\(415\) 4.00000 0.196352
\(416\) 4.00000 0.196116
\(417\) 16.0000 0.783523
\(418\) 7.00000 0.342381
\(419\) −6.00000 −0.293119 −0.146560 0.989202i \(-0.546820\pi\)
−0.146560 + 0.989202i \(0.546820\pi\)
\(420\) 5.00000 0.243975
\(421\) 28.0000 1.36464 0.682318 0.731055i \(-0.260972\pi\)
0.682318 + 0.731055i \(0.260972\pi\)
\(422\) 23.0000 1.11962
\(423\) −12.0000 −0.583460
\(424\) −13.0000 −0.631336
\(425\) 1.00000 0.0485071
\(426\) 1.00000 0.0484502
\(427\) 25.0000 1.20983
\(428\) 4.00000 0.193347
\(429\) 4.00000 0.193122
\(430\) −1.00000 −0.0482243
\(431\) −6.00000 −0.289010 −0.144505 0.989504i \(-0.546159\pi\)
−0.144505 + 0.989504i \(0.546159\pi\)
\(432\) −5.00000 −0.240563
\(433\) −20.0000 −0.961139 −0.480569 0.876957i \(-0.659570\pi\)
−0.480569 + 0.876957i \(0.659570\pi\)
\(434\) −55.0000 −2.64008
\(435\) −5.00000 −0.239732
\(436\) −10.0000 −0.478913
\(437\) 56.0000 2.67884
\(438\) −10.0000 −0.477818
\(439\) 22.0000 1.05000 0.525001 0.851101i \(-0.324065\pi\)
0.525001 + 0.851101i \(0.324065\pi\)
\(440\) 1.00000 0.0476731
\(441\) −36.0000 −1.71429
\(442\) 4.00000 0.190261
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) −7.00000 −0.332205
\(445\) −9.00000 −0.426641
\(446\) −16.0000 −0.757622
\(447\) −3.00000 −0.141895
\(448\) 5.00000 0.236228
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) −2.00000 −0.0942809
\(451\) −12.0000 −0.565058
\(452\) −12.0000 −0.564433
\(453\) 20.0000 0.939682
\(454\) 2.00000 0.0938647
\(455\) 20.0000 0.937614
\(456\) 7.00000 0.327805
\(457\) −3.00000 −0.140334 −0.0701670 0.997535i \(-0.522353\pi\)
−0.0701670 + 0.997535i \(0.522353\pi\)
\(458\) −14.0000 −0.654177
\(459\) −5.00000 −0.233380
\(460\) 8.00000 0.373002
\(461\) 35.0000 1.63011 0.815056 0.579382i \(-0.196706\pi\)
0.815056 + 0.579382i \(0.196706\pi\)
\(462\) 5.00000 0.232621
\(463\) 22.0000 1.02243 0.511213 0.859454i \(-0.329196\pi\)
0.511213 + 0.859454i \(0.329196\pi\)
\(464\) −5.00000 −0.232119
\(465\) −11.0000 −0.510113
\(466\) −25.0000 −1.15810
\(467\) 13.0000 0.601568 0.300784 0.953692i \(-0.402752\pi\)
0.300784 + 0.953692i \(0.402752\pi\)
\(468\) −8.00000 −0.369800
\(469\) −60.0000 −2.77054
\(470\) 6.00000 0.276759
\(471\) −7.00000 −0.322543
\(472\) −8.00000 −0.368230
\(473\) −1.00000 −0.0459800
\(474\) 8.00000 0.367452
\(475\) 7.00000 0.321182
\(476\) 5.00000 0.229175
\(477\) 26.0000 1.19046
\(478\) −6.00000 −0.274434
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 1.00000 0.0456435
\(481\) −28.0000 −1.27669
\(482\) 16.0000 0.728780
\(483\) 40.0000 1.82006
\(484\) 1.00000 0.0454545
\(485\) −8.00000 −0.363261
\(486\) 16.0000 0.725775
\(487\) −10.0000 −0.453143 −0.226572 0.973995i \(-0.572752\pi\)
−0.226572 + 0.973995i \(0.572752\pi\)
\(488\) 5.00000 0.226339
\(489\) 1.00000 0.0452216
\(490\) 18.0000 0.813157
\(491\) 27.0000 1.21849 0.609246 0.792981i \(-0.291472\pi\)
0.609246 + 0.792981i \(0.291472\pi\)
\(492\) −12.0000 −0.541002
\(493\) −5.00000 −0.225189
\(494\) 28.0000 1.25978
\(495\) −2.00000 −0.0898933
\(496\) −11.0000 −0.493915
\(497\) 5.00000 0.224281
\(498\) 4.00000 0.179244
\(499\) 6.00000 0.268597 0.134298 0.990941i \(-0.457122\pi\)
0.134298 + 0.990941i \(0.457122\pi\)
\(500\) 1.00000 0.0447214
\(501\) 19.0000 0.848857
\(502\) 12.0000 0.535586
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) −10.0000 −0.445435
\(505\) 6.00000 0.266996
\(506\) 8.00000 0.355643
\(507\) 3.00000 0.133235
\(508\) 12.0000 0.532414
\(509\) −12.0000 −0.531891 −0.265945 0.963988i \(-0.585684\pi\)
−0.265945 + 0.963988i \(0.585684\pi\)
\(510\) 1.00000 0.0442807
\(511\) −50.0000 −2.21187
\(512\) 1.00000 0.0441942
\(513\) −35.0000 −1.54529
\(514\) 14.0000 0.617514
\(515\) 0 0
\(516\) −1.00000 −0.0440225
\(517\) 6.00000 0.263880
\(518\) −35.0000 −1.53781
\(519\) −2.00000 −0.0877903
\(520\) 4.00000 0.175412
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 10.0000 0.437688
\(523\) 30.0000 1.31181 0.655904 0.754844i \(-0.272288\pi\)
0.655904 + 0.754844i \(0.272288\pi\)
\(524\) 15.0000 0.655278
\(525\) 5.00000 0.218218
\(526\) −5.00000 −0.218010
\(527\) −11.0000 −0.479168
\(528\) 1.00000 0.0435194
\(529\) 41.0000 1.78261
\(530\) −13.0000 −0.564684
\(531\) 16.0000 0.694341
\(532\) 35.0000 1.51744
\(533\) −48.0000 −2.07911
\(534\) −9.00000 −0.389468
\(535\) 4.00000 0.172935
\(536\) −12.0000 −0.518321
\(537\) −20.0000 −0.863064
\(538\) −18.0000 −0.776035
\(539\) 18.0000 0.775315
\(540\) −5.00000 −0.215166
\(541\) −39.0000 −1.67674 −0.838370 0.545101i \(-0.816491\pi\)
−0.838370 + 0.545101i \(0.816491\pi\)
\(542\) 22.0000 0.944981
\(543\) −10.0000 −0.429141
\(544\) 1.00000 0.0428746
\(545\) −10.0000 −0.428353
\(546\) 20.0000 0.855921
\(547\) 44.0000 1.88130 0.940652 0.339372i \(-0.110215\pi\)
0.940652 + 0.339372i \(0.110215\pi\)
\(548\) 10.0000 0.427179
\(549\) −10.0000 −0.426790
\(550\) 1.00000 0.0426401
\(551\) −35.0000 −1.49105
\(552\) 8.00000 0.340503
\(553\) 40.0000 1.70097
\(554\) −22.0000 −0.934690
\(555\) −7.00000 −0.297133
\(556\) 16.0000 0.678551
\(557\) −38.0000 −1.61011 −0.805056 0.593199i \(-0.797865\pi\)
−0.805056 + 0.593199i \(0.797865\pi\)
\(558\) 22.0000 0.931334
\(559\) −4.00000 −0.169182
\(560\) 5.00000 0.211289
\(561\) 1.00000 0.0422200
\(562\) 16.0000 0.674919
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 6.00000 0.252646
\(565\) −12.0000 −0.504844
\(566\) −18.0000 −0.756596
\(567\) 5.00000 0.209980
\(568\) 1.00000 0.0419591
\(569\) −34.0000 −1.42535 −0.712677 0.701492i \(-0.752517\pi\)
−0.712677 + 0.701492i \(0.752517\pi\)
\(570\) 7.00000 0.293198
\(571\) −39.0000 −1.63210 −0.816050 0.577982i \(-0.803840\pi\)
−0.816050 + 0.577982i \(0.803840\pi\)
\(572\) 4.00000 0.167248
\(573\) −4.00000 −0.167102
\(574\) −60.0000 −2.50435
\(575\) 8.00000 0.333623
\(576\) −2.00000 −0.0833333
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −16.0000 −0.665512
\(579\) 9.00000 0.374027
\(580\) −5.00000 −0.207614
\(581\) 20.0000 0.829740
\(582\) −8.00000 −0.331611
\(583\) −13.0000 −0.538405
\(584\) −10.0000 −0.413803
\(585\) −8.00000 −0.330759
\(586\) 4.00000 0.165238
\(587\) −33.0000 −1.36206 −0.681028 0.732257i \(-0.738467\pi\)
−0.681028 + 0.732257i \(0.738467\pi\)
\(588\) 18.0000 0.742307
\(589\) −77.0000 −3.17273
\(590\) −8.00000 −0.329355
\(591\) −4.00000 −0.164538
\(592\) −7.00000 −0.287698
\(593\) 42.0000 1.72473 0.862367 0.506284i \(-0.168981\pi\)
0.862367 + 0.506284i \(0.168981\pi\)
\(594\) −5.00000 −0.205152
\(595\) 5.00000 0.204980
\(596\) −3.00000 −0.122885
\(597\) −7.00000 −0.286491
\(598\) 32.0000 1.30858
\(599\) 17.0000 0.694601 0.347301 0.937754i \(-0.387098\pi\)
0.347301 + 0.937754i \(0.387098\pi\)
\(600\) 1.00000 0.0408248
\(601\) 20.0000 0.815817 0.407909 0.913023i \(-0.366258\pi\)
0.407909 + 0.913023i \(0.366258\pi\)
\(602\) −5.00000 −0.203785
\(603\) 24.0000 0.977356
\(604\) 20.0000 0.813788
\(605\) 1.00000 0.0406558
\(606\) 6.00000 0.243733
\(607\) −1.00000 −0.0405887 −0.0202944 0.999794i \(-0.506460\pi\)
−0.0202944 + 0.999794i \(0.506460\pi\)
\(608\) 7.00000 0.283887
\(609\) −25.0000 −1.01305
\(610\) 5.00000 0.202444
\(611\) 24.0000 0.970936
\(612\) −2.00000 −0.0808452
\(613\) −20.0000 −0.807792 −0.403896 0.914805i \(-0.632344\pi\)
−0.403896 + 0.914805i \(0.632344\pi\)
\(614\) 10.0000 0.403567
\(615\) −12.0000 −0.483887
\(616\) 5.00000 0.201456
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) 14.0000 0.562708 0.281354 0.959604i \(-0.409217\pi\)
0.281354 + 0.959604i \(0.409217\pi\)
\(620\) −11.0000 −0.441771
\(621\) −40.0000 −1.60514
\(622\) −35.0000 −1.40337
\(623\) −45.0000 −1.80289
\(624\) 4.00000 0.160128
\(625\) 1.00000 0.0400000
\(626\) 26.0000 1.03917
\(627\) 7.00000 0.279553
\(628\) −7.00000 −0.279330
\(629\) −7.00000 −0.279108
\(630\) −10.0000 −0.398410
\(631\) 17.0000 0.676759 0.338380 0.941010i \(-0.390121\pi\)
0.338380 + 0.941010i \(0.390121\pi\)
\(632\) 8.00000 0.318223
\(633\) 23.0000 0.914168
\(634\) −15.0000 −0.595726
\(635\) 12.0000 0.476205
\(636\) −13.0000 −0.515484
\(637\) 72.0000 2.85274
\(638\) −5.00000 −0.197952
\(639\) −2.00000 −0.0791188
\(640\) 1.00000 0.0395285
\(641\) 9.00000 0.355479 0.177739 0.984078i \(-0.443122\pi\)
0.177739 + 0.984078i \(0.443122\pi\)
\(642\) 4.00000 0.157867
\(643\) 35.0000 1.38027 0.690133 0.723683i \(-0.257552\pi\)
0.690133 + 0.723683i \(0.257552\pi\)
\(644\) 40.0000 1.57622
\(645\) −1.00000 −0.0393750
\(646\) 7.00000 0.275411
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.00000 0.0392837
\(649\) −8.00000 −0.314027
\(650\) 4.00000 0.156893
\(651\) −55.0000 −2.15562
\(652\) 1.00000 0.0391630
\(653\) 39.0000 1.52619 0.763094 0.646288i \(-0.223679\pi\)
0.763094 + 0.646288i \(0.223679\pi\)
\(654\) −10.0000 −0.391031
\(655\) 15.0000 0.586098
\(656\) −12.0000 −0.468521
\(657\) 20.0000 0.780274
\(658\) 30.0000 1.16952
\(659\) −41.0000 −1.59713 −0.798567 0.601906i \(-0.794408\pi\)
−0.798567 + 0.601906i \(0.794408\pi\)
\(660\) 1.00000 0.0389249
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) 36.0000 1.39918
\(663\) 4.00000 0.155347
\(664\) 4.00000 0.155230
\(665\) 35.0000 1.35724
\(666\) 14.0000 0.542489
\(667\) −40.0000 −1.54881
\(668\) 19.0000 0.735132
\(669\) −16.0000 −0.618596
\(670\) −12.0000 −0.463600
\(671\) 5.00000 0.193023
\(672\) 5.00000 0.192879
\(673\) −37.0000 −1.42625 −0.713123 0.701039i \(-0.752720\pi\)
−0.713123 + 0.701039i \(0.752720\pi\)
\(674\) 7.00000 0.269630
\(675\) −5.00000 −0.192450
\(676\) 3.00000 0.115385
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −12.0000 −0.460857
\(679\) −40.0000 −1.53506
\(680\) 1.00000 0.0383482
\(681\) 2.00000 0.0766402
\(682\) −11.0000 −0.421212
\(683\) 21.0000 0.803543 0.401771 0.915740i \(-0.368395\pi\)
0.401771 + 0.915740i \(0.368395\pi\)
\(684\) −14.0000 −0.535303
\(685\) 10.0000 0.382080
\(686\) 55.0000 2.09991
\(687\) −14.0000 −0.534133
\(688\) −1.00000 −0.0381246
\(689\) −52.0000 −1.98104
\(690\) 8.00000 0.304555
\(691\) −40.0000 −1.52167 −0.760836 0.648944i \(-0.775211\pi\)
−0.760836 + 0.648944i \(0.775211\pi\)
\(692\) −2.00000 −0.0760286
\(693\) −10.0000 −0.379869
\(694\) −14.0000 −0.531433
\(695\) 16.0000 0.606915
\(696\) −5.00000 −0.189525
\(697\) −12.0000 −0.454532
\(698\) 10.0000 0.378506
\(699\) −25.0000 −0.945587
\(700\) 5.00000 0.188982
\(701\) 23.0000 0.868698 0.434349 0.900745i \(-0.356978\pi\)
0.434349 + 0.900745i \(0.356978\pi\)
\(702\) −20.0000 −0.754851
\(703\) −49.0000 −1.84807
\(704\) 1.00000 0.0376889
\(705\) 6.00000 0.225973
\(706\) −28.0000 −1.05379
\(707\) 30.0000 1.12827
\(708\) −8.00000 −0.300658
\(709\) −12.0000 −0.450669 −0.225335 0.974281i \(-0.572348\pi\)
−0.225335 + 0.974281i \(0.572348\pi\)
\(710\) 1.00000 0.0375293
\(711\) −16.0000 −0.600047
\(712\) −9.00000 −0.337289
\(713\) −88.0000 −3.29563
\(714\) 5.00000 0.187120
\(715\) 4.00000 0.149592
\(716\) −20.0000 −0.747435
\(717\) −6.00000 −0.224074
\(718\) −4.00000 −0.149279
\(719\) 13.0000 0.484818 0.242409 0.970174i \(-0.422062\pi\)
0.242409 + 0.970174i \(0.422062\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 0 0
\(722\) 30.0000 1.11648
\(723\) 16.0000 0.595046
\(724\) −10.0000 −0.371647
\(725\) −5.00000 −0.185695
\(726\) 1.00000 0.0371135
\(727\) 18.0000 0.667583 0.333792 0.942647i \(-0.391672\pi\)
0.333792 + 0.942647i \(0.391672\pi\)
\(728\) 20.0000 0.741249
\(729\) 13.0000 0.481481
\(730\) −10.0000 −0.370117
\(731\) −1.00000 −0.0369863
\(732\) 5.00000 0.184805
\(733\) −2.00000 −0.0738717 −0.0369358 0.999318i \(-0.511760\pi\)
−0.0369358 + 0.999318i \(0.511760\pi\)
\(734\) 18.0000 0.664392
\(735\) 18.0000 0.663940
\(736\) 8.00000 0.294884
\(737\) −12.0000 −0.442026
\(738\) 24.0000 0.883452
\(739\) 8.00000 0.294285 0.147142 0.989115i \(-0.452992\pi\)
0.147142 + 0.989115i \(0.452992\pi\)
\(740\) −7.00000 −0.257325
\(741\) 28.0000 1.02861
\(742\) −65.0000 −2.38623
\(743\) −31.0000 −1.13728 −0.568640 0.822587i \(-0.692530\pi\)
−0.568640 + 0.822587i \(0.692530\pi\)
\(744\) −11.0000 −0.403280
\(745\) −3.00000 −0.109911
\(746\) 0 0
\(747\) −8.00000 −0.292705
\(748\) 1.00000 0.0365636
\(749\) 20.0000 0.730784
\(750\) 1.00000 0.0365148
\(751\) −25.0000 −0.912263 −0.456131 0.889912i \(-0.650765\pi\)
−0.456131 + 0.889912i \(0.650765\pi\)
\(752\) 6.00000 0.218797
\(753\) 12.0000 0.437304
\(754\) −20.0000 −0.728357
\(755\) 20.0000 0.727875
\(756\) −25.0000 −0.909241
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 24.0000 0.871719
\(759\) 8.00000 0.290382
\(760\) 7.00000 0.253917
\(761\) 32.0000 1.16000 0.580000 0.814617i \(-0.303053\pi\)
0.580000 + 0.814617i \(0.303053\pi\)
\(762\) 12.0000 0.434714
\(763\) −50.0000 −1.81012
\(764\) −4.00000 −0.144715
\(765\) −2.00000 −0.0723102
\(766\) −24.0000 −0.867155
\(767\) −32.0000 −1.15545
\(768\) 1.00000 0.0360844
\(769\) 6.00000 0.216366 0.108183 0.994131i \(-0.465497\pi\)
0.108183 + 0.994131i \(0.465497\pi\)
\(770\) 5.00000 0.180187
\(771\) 14.0000 0.504198
\(772\) 9.00000 0.323917
\(773\) −11.0000 −0.395643 −0.197821 0.980238i \(-0.563387\pi\)
−0.197821 + 0.980238i \(0.563387\pi\)
\(774\) 2.00000 0.0718885
\(775\) −11.0000 −0.395132
\(776\) −8.00000 −0.287183
\(777\) −35.0000 −1.25562
\(778\) 4.00000 0.143407
\(779\) −84.0000 −3.00961
\(780\) 4.00000 0.143223
\(781\) 1.00000 0.0357828
\(782\) 8.00000 0.286079
\(783\) 25.0000 0.893427
\(784\) 18.0000 0.642857
\(785\) −7.00000 −0.249841
\(786\) 15.0000 0.535032
\(787\) 8.00000 0.285169 0.142585 0.989783i \(-0.454459\pi\)
0.142585 + 0.989783i \(0.454459\pi\)
\(788\) −4.00000 −0.142494
\(789\) −5.00000 −0.178005
\(790\) 8.00000 0.284627
\(791\) −60.0000 −2.13335
\(792\) −2.00000 −0.0710669
\(793\) 20.0000 0.710221
\(794\) −2.00000 −0.0709773
\(795\) −13.0000 −0.461062
\(796\) −7.00000 −0.248108
\(797\) 22.0000 0.779280 0.389640 0.920967i \(-0.372599\pi\)
0.389640 + 0.920967i \(0.372599\pi\)
\(798\) 35.0000 1.23899
\(799\) 6.00000 0.212265
\(800\) 1.00000 0.0353553
\(801\) 18.0000 0.635999
\(802\) −17.0000 −0.600291
\(803\) −10.0000 −0.352892
\(804\) −12.0000 −0.423207
\(805\) 40.0000 1.40981
\(806\) −44.0000 −1.54983
\(807\) −18.0000 −0.633630
\(808\) 6.00000 0.211079
\(809\) −36.0000 −1.26569 −0.632846 0.774277i \(-0.718114\pi\)
−0.632846 + 0.774277i \(0.718114\pi\)
\(810\) 1.00000 0.0351364
\(811\) −23.0000 −0.807639 −0.403820 0.914839i \(-0.632318\pi\)
−0.403820 + 0.914839i \(0.632318\pi\)
\(812\) −25.0000 −0.877328
\(813\) 22.0000 0.771574
\(814\) −7.00000 −0.245350
\(815\) 1.00000 0.0350285
\(816\) 1.00000 0.0350070
\(817\) −7.00000 −0.244899
\(818\) −8.00000 −0.279713
\(819\) −40.0000 −1.39771
\(820\) −12.0000 −0.419058
\(821\) 30.0000 1.04701 0.523504 0.852023i \(-0.324625\pi\)
0.523504 + 0.852023i \(0.324625\pi\)
\(822\) 10.0000 0.348790
\(823\) −22.0000 −0.766872 −0.383436 0.923567i \(-0.625259\pi\)
−0.383436 + 0.923567i \(0.625259\pi\)
\(824\) 0 0
\(825\) 1.00000 0.0348155
\(826\) −40.0000 −1.39178
\(827\) 20.0000 0.695468 0.347734 0.937593i \(-0.386951\pi\)
0.347734 + 0.937593i \(0.386951\pi\)
\(828\) −16.0000 −0.556038
\(829\) −38.0000 −1.31979 −0.659897 0.751356i \(-0.729400\pi\)
−0.659897 + 0.751356i \(0.729400\pi\)
\(830\) 4.00000 0.138842
\(831\) −22.0000 −0.763172
\(832\) 4.00000 0.138675
\(833\) 18.0000 0.623663
\(834\) 16.0000 0.554035
\(835\) 19.0000 0.657522
\(836\) 7.00000 0.242100
\(837\) 55.0000 1.90108
\(838\) −6.00000 −0.207267
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 5.00000 0.172516
\(841\) −4.00000 −0.137931
\(842\) 28.0000 0.964944
\(843\) 16.0000 0.551069
\(844\) 23.0000 0.791693
\(845\) 3.00000 0.103203
\(846\) −12.0000 −0.412568
\(847\) 5.00000 0.171802
\(848\) −13.0000 −0.446422
\(849\) −18.0000 −0.617758
\(850\) 1.00000 0.0342997
\(851\) −56.0000 −1.91966
\(852\) 1.00000 0.0342594
\(853\) 4.00000 0.136957 0.0684787 0.997653i \(-0.478185\pi\)
0.0684787 + 0.997653i \(0.478185\pi\)
\(854\) 25.0000 0.855482
\(855\) −14.0000 −0.478790
\(856\) 4.00000 0.136717
\(857\) −27.0000 −0.922302 −0.461151 0.887322i \(-0.652563\pi\)
−0.461151 + 0.887322i \(0.652563\pi\)
\(858\) 4.00000 0.136558
\(859\) −30.0000 −1.02359 −0.511793 0.859109i \(-0.671019\pi\)
−0.511793 + 0.859109i \(0.671019\pi\)
\(860\) −1.00000 −0.0340997
\(861\) −60.0000 −2.04479
\(862\) −6.00000 −0.204361
\(863\) −14.0000 −0.476566 −0.238283 0.971196i \(-0.576585\pi\)
−0.238283 + 0.971196i \(0.576585\pi\)
\(864\) −5.00000 −0.170103
\(865\) −2.00000 −0.0680020
\(866\) −20.0000 −0.679628
\(867\) −16.0000 −0.543388
\(868\) −55.0000 −1.86682
\(869\) 8.00000 0.271381
\(870\) −5.00000 −0.169516
\(871\) −48.0000 −1.62642
\(872\) −10.0000 −0.338643
\(873\) 16.0000 0.541518
\(874\) 56.0000 1.89423
\(875\) 5.00000 0.169031
\(876\) −10.0000 −0.337869
\(877\) −14.0000 −0.472746 −0.236373 0.971662i \(-0.575959\pi\)
−0.236373 + 0.971662i \(0.575959\pi\)
\(878\) 22.0000 0.742464
\(879\) 4.00000 0.134917
\(880\) 1.00000 0.0337100
\(881\) −42.0000 −1.41502 −0.707508 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) −36.0000 −1.21218
\(883\) 29.0000 0.975928 0.487964 0.872864i \(-0.337740\pi\)
0.487964 + 0.872864i \(0.337740\pi\)
\(884\) 4.00000 0.134535
\(885\) −8.00000 −0.268917
\(886\) 12.0000 0.403148
\(887\) −8.00000 −0.268614 −0.134307 0.990940i \(-0.542881\pi\)
−0.134307 + 0.990940i \(0.542881\pi\)
\(888\) −7.00000 −0.234905
\(889\) 60.0000 2.01234
\(890\) −9.00000 −0.301681
\(891\) 1.00000 0.0335013
\(892\) −16.0000 −0.535720
\(893\) 42.0000 1.40548
\(894\) −3.00000 −0.100335
\(895\) −20.0000 −0.668526
\(896\) 5.00000 0.167038
\(897\) 32.0000 1.06845
\(898\) 18.0000 0.600668
\(899\) 55.0000 1.83435
\(900\) −2.00000 −0.0666667
\(901\) −13.0000 −0.433093
\(902\) −12.0000 −0.399556
\(903\) −5.00000 −0.166390
\(904\) −12.0000 −0.399114
\(905\) −10.0000 −0.332411
\(906\) 20.0000 0.664455
\(907\) −9.00000 −0.298840 −0.149420 0.988774i \(-0.547741\pi\)
−0.149420 + 0.988774i \(0.547741\pi\)
\(908\) 2.00000 0.0663723
\(909\) −12.0000 −0.398015
\(910\) 20.0000 0.662994
\(911\) −15.0000 −0.496972 −0.248486 0.968635i \(-0.579933\pi\)
−0.248486 + 0.968635i \(0.579933\pi\)
\(912\) 7.00000 0.231793
\(913\) 4.00000 0.132381
\(914\) −3.00000 −0.0992312
\(915\) 5.00000 0.165295
\(916\) −14.0000 −0.462573
\(917\) 75.0000 2.47672
\(918\) −5.00000 −0.165025
\(919\) −20.0000 −0.659739 −0.329870 0.944027i \(-0.607005\pi\)
−0.329870 + 0.944027i \(0.607005\pi\)
\(920\) 8.00000 0.263752
\(921\) 10.0000 0.329511
\(922\) 35.0000 1.15266
\(923\) 4.00000 0.131662
\(924\) 5.00000 0.164488
\(925\) −7.00000 −0.230159
\(926\) 22.0000 0.722965
\(927\) 0 0
\(928\) −5.00000 −0.164133
\(929\) 13.0000 0.426516 0.213258 0.976996i \(-0.431592\pi\)
0.213258 + 0.976996i \(0.431592\pi\)
\(930\) −11.0000 −0.360704
\(931\) 126.000 4.12948
\(932\) −25.0000 −0.818902
\(933\) −35.0000 −1.14585
\(934\) 13.0000 0.425373
\(935\) 1.00000 0.0327035
\(936\) −8.00000 −0.261488
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) −60.0000 −1.95907
\(939\) 26.0000 0.848478
\(940\) 6.00000 0.195698
\(941\) 33.0000 1.07577 0.537885 0.843018i \(-0.319224\pi\)
0.537885 + 0.843018i \(0.319224\pi\)
\(942\) −7.00000 −0.228072
\(943\) −96.0000 −3.12619
\(944\) −8.00000 −0.260378
\(945\) −25.0000 −0.813250
\(946\) −1.00000 −0.0325128
\(947\) −39.0000 −1.26733 −0.633665 0.773608i \(-0.718450\pi\)
−0.633665 + 0.773608i \(0.718450\pi\)
\(948\) 8.00000 0.259828
\(949\) −40.0000 −1.29845
\(950\) 7.00000 0.227110
\(951\) −15.0000 −0.486408
\(952\) 5.00000 0.162051
\(953\) −11.0000 −0.356325 −0.178162 0.984001i \(-0.557015\pi\)
−0.178162 + 0.984001i \(0.557015\pi\)
\(954\) 26.0000 0.841781
\(955\) −4.00000 −0.129437
\(956\) −6.00000 −0.194054
\(957\) −5.00000 −0.161627
\(958\) 0 0
\(959\) 50.0000 1.61458
\(960\) 1.00000 0.0322749
\(961\) 90.0000 2.90323
\(962\) −28.0000 −0.902756
\(963\) −8.00000 −0.257796
\(964\) 16.0000 0.515325
\(965\) 9.00000 0.289720
\(966\) 40.0000 1.28698
\(967\) −19.0000 −0.610999 −0.305499 0.952192i \(-0.598823\pi\)
−0.305499 + 0.952192i \(0.598823\pi\)
\(968\) 1.00000 0.0321412
\(969\) 7.00000 0.224872
\(970\) −8.00000 −0.256865
\(971\) −12.0000 −0.385098 −0.192549 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) 16.0000 0.513200
\(973\) 80.0000 2.56468
\(974\) −10.0000 −0.320421
\(975\) 4.00000 0.128103
\(976\) 5.00000 0.160046
\(977\) −36.0000 −1.15174 −0.575871 0.817541i \(-0.695337\pi\)
−0.575871 + 0.817541i \(0.695337\pi\)
\(978\) 1.00000 0.0319765
\(979\) −9.00000 −0.287641
\(980\) 18.0000 0.574989
\(981\) 20.0000 0.638551
\(982\) 27.0000 0.861605
\(983\) −4.00000 −0.127580 −0.0637901 0.997963i \(-0.520319\pi\)
−0.0637901 + 0.997963i \(0.520319\pi\)
\(984\) −12.0000 −0.382546
\(985\) −4.00000 −0.127451
\(986\) −5.00000 −0.159232
\(987\) 30.0000 0.954911
\(988\) 28.0000 0.890799
\(989\) −8.00000 −0.254385
\(990\) −2.00000 −0.0635642
\(991\) 40.0000 1.27064 0.635321 0.772248i \(-0.280868\pi\)
0.635321 + 0.772248i \(0.280868\pi\)
\(992\) −11.0000 −0.349250
\(993\) 36.0000 1.14243
\(994\) 5.00000 0.158590
\(995\) −7.00000 −0.221915
\(996\) 4.00000 0.126745
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 6.00000 0.189927
\(999\) 35.0000 1.10735
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 4730.2.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.j.1.1 1 1.1 even 1 trivial