Properties

Label 4730.2.a.bb.1.7
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 11
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: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.797340\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.797340 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.797340 q^{6} -1.54185 q^{7} -1.00000 q^{8} -2.36425 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.797340 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.797340 q^{6} -1.54185 q^{7} -1.00000 q^{8} -2.36425 q^{9} +1.00000 q^{10} -1.00000 q^{11} +0.797340 q^{12} -1.10794 q^{13} +1.54185 q^{14} -0.797340 q^{15} +1.00000 q^{16} -3.83917 q^{17} +2.36425 q^{18} +7.93463 q^{19} -1.00000 q^{20} -1.22938 q^{21} +1.00000 q^{22} -3.10794 q^{23} -0.797340 q^{24} +1.00000 q^{25} +1.10794 q^{26} -4.27713 q^{27} -1.54185 q^{28} -2.76882 q^{29} +0.797340 q^{30} +3.78854 q^{31} -1.00000 q^{32} -0.797340 q^{33} +3.83917 q^{34} +1.54185 q^{35} -2.36425 q^{36} +6.96120 q^{37} -7.93463 q^{38} -0.883404 q^{39} +1.00000 q^{40} -6.69318 q^{41} +1.22938 q^{42} +1.00000 q^{43} -1.00000 q^{44} +2.36425 q^{45} +3.10794 q^{46} -2.36057 q^{47} +0.797340 q^{48} -4.62269 q^{49} -1.00000 q^{50} -3.06113 q^{51} -1.10794 q^{52} +0.0407411 q^{53} +4.27713 q^{54} +1.00000 q^{55} +1.54185 q^{56} +6.32660 q^{57} +2.76882 q^{58} -14.7262 q^{59} -0.797340 q^{60} +11.6123 q^{61} -3.78854 q^{62} +3.64532 q^{63} +1.00000 q^{64} +1.10794 q^{65} +0.797340 q^{66} -9.13185 q^{67} -3.83917 q^{68} -2.47808 q^{69} -1.54185 q^{70} +15.6288 q^{71} +2.36425 q^{72} -0.994843 q^{73} -6.96120 q^{74} +0.797340 q^{75} +7.93463 q^{76} +1.54185 q^{77} +0.883404 q^{78} +2.35313 q^{79} -1.00000 q^{80} +3.68241 q^{81} +6.69318 q^{82} -15.6459 q^{83} -1.22938 q^{84} +3.83917 q^{85} -1.00000 q^{86} -2.20770 q^{87} +1.00000 q^{88} +7.56378 q^{89} -2.36425 q^{90} +1.70828 q^{91} -3.10794 q^{92} +3.02075 q^{93} +2.36057 q^{94} -7.93463 q^{95} -0.797340 q^{96} +6.65740 q^{97} +4.62269 q^{98} +2.36425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + O(q^{10}) \) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + 11q^{10} - 11q^{11} - q^{12} + 4q^{13} - 6q^{14} + q^{15} + 11q^{16} - 10q^{17} - 12q^{18} + 14q^{19} - 11q^{20} - 2q^{21} + 11q^{22} - 18q^{23} + q^{24} + 11q^{25} - 4q^{26} + 2q^{27} + 6q^{28} - 6q^{29} - q^{30} + 13q^{31} - 11q^{32} + q^{33} + 10q^{34} - 6q^{35} + 12q^{36} + q^{37} - 14q^{38} + 12q^{39} + 11q^{40} + 12q^{41} + 2q^{42} + 11q^{43} - 11q^{44} - 12q^{45} + 18q^{46} - 5q^{47} - q^{48} + 31q^{49} - 11q^{50} + q^{51} + 4q^{52} - 27q^{53} - 2q^{54} + 11q^{55} - 6q^{56} - 5q^{57} + 6q^{58} + 11q^{59} + q^{60} + 36q^{61} - 13q^{62} + 17q^{63} + 11q^{64} - 4q^{65} - q^{66} + 18q^{67} - 10q^{68} + 14q^{69} + 6q^{70} - 14q^{71} - 12q^{72} - 11q^{73} - q^{74} - q^{75} + 14q^{76} - 6q^{77} - 12q^{78} + 28q^{79} - 11q^{80} + 7q^{81} - 12q^{82} - 4q^{83} - 2q^{84} + 10q^{85} - 11q^{86} + 38q^{87} + 11q^{88} - 7q^{89} + 12q^{90} + 14q^{91} - 18q^{92} - 3q^{93} + 5q^{94} - 14q^{95} + q^{96} - q^{97} - 31q^{98} - 12q^{99} + O(q^{100}) \)

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
\(3\) 0.797340 0.460345 0.230172 0.973150i \(-0.426071\pi\)
0.230172 + 0.973150i \(0.426071\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −0.797340 −0.325513
\(7\) −1.54185 −0.582765 −0.291383 0.956607i \(-0.594115\pi\)
−0.291383 + 0.956607i \(0.594115\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.36425 −0.788083
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) 0.797340 0.230172
\(13\) −1.10794 −0.307287 −0.153643 0.988126i \(-0.549101\pi\)
−0.153643 + 0.988126i \(0.549101\pi\)
\(14\) 1.54185 0.412077
\(15\) −0.797340 −0.205872
\(16\) 1.00000 0.250000
\(17\) −3.83917 −0.931137 −0.465568 0.885012i \(-0.654150\pi\)
−0.465568 + 0.885012i \(0.654150\pi\)
\(18\) 2.36425 0.557259
\(19\) 7.93463 1.82033 0.910165 0.414247i \(-0.135955\pi\)
0.910165 + 0.414247i \(0.135955\pi\)
\(20\) −1.00000 −0.223607
\(21\) −1.22938 −0.268273
\(22\) 1.00000 0.213201
\(23\) −3.10794 −0.648050 −0.324025 0.946049i \(-0.605036\pi\)
−0.324025 + 0.946049i \(0.605036\pi\)
\(24\) −0.797340 −0.162756
\(25\) 1.00000 0.200000
\(26\) 1.10794 0.217285
\(27\) −4.27713 −0.823134
\(28\) −1.54185 −0.291383
\(29\) −2.76882 −0.514158 −0.257079 0.966390i \(-0.582760\pi\)
−0.257079 + 0.966390i \(0.582760\pi\)
\(30\) 0.797340 0.145574
\(31\) 3.78854 0.680441 0.340221 0.940346i \(-0.389498\pi\)
0.340221 + 0.940346i \(0.389498\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.797340 −0.138799
\(34\) 3.83917 0.658413
\(35\) 1.54185 0.260621
\(36\) −2.36425 −0.394041
\(37\) 6.96120 1.14441 0.572207 0.820109i \(-0.306087\pi\)
0.572207 + 0.820109i \(0.306087\pi\)
\(38\) −7.93463 −1.28717
\(39\) −0.883404 −0.141458
\(40\) 1.00000 0.158114
\(41\) −6.69318 −1.04530 −0.522650 0.852547i \(-0.675056\pi\)
−0.522650 + 0.852547i \(0.675056\pi\)
\(42\) 1.22938 0.189698
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) 2.36425 0.352441
\(46\) 3.10794 0.458240
\(47\) −2.36057 −0.344325 −0.172162 0.985069i \(-0.555075\pi\)
−0.172162 + 0.985069i \(0.555075\pi\)
\(48\) 0.797340 0.115086
\(49\) −4.62269 −0.660385
\(50\) −1.00000 −0.141421
\(51\) −3.06113 −0.428644
\(52\) −1.10794 −0.153643
\(53\) 0.0407411 0.00559622 0.00279811 0.999996i \(-0.499109\pi\)
0.00279811 + 0.999996i \(0.499109\pi\)
\(54\) 4.27713 0.582044
\(55\) 1.00000 0.134840
\(56\) 1.54185 0.206039
\(57\) 6.32660 0.837979
\(58\) 2.76882 0.363565
\(59\) −14.7262 −1.91719 −0.958593 0.284779i \(-0.908080\pi\)
−0.958593 + 0.284779i \(0.908080\pi\)
\(60\) −0.797340 −0.102936
\(61\) 11.6123 1.48680 0.743402 0.668844i \(-0.233211\pi\)
0.743402 + 0.668844i \(0.233211\pi\)
\(62\) −3.78854 −0.481144
\(63\) 3.64532 0.459267
\(64\) 1.00000 0.125000
\(65\) 1.10794 0.137423
\(66\) 0.797340 0.0981458
\(67\) −9.13185 −1.11563 −0.557816 0.829964i \(-0.688361\pi\)
−0.557816 + 0.829964i \(0.688361\pi\)
\(68\) −3.83917 −0.465568
\(69\) −2.47808 −0.298326
\(70\) −1.54185 −0.184287
\(71\) 15.6288 1.85480 0.927399 0.374073i \(-0.122039\pi\)
0.927399 + 0.374073i \(0.122039\pi\)
\(72\) 2.36425 0.278629
\(73\) −0.994843 −0.116438 −0.0582188 0.998304i \(-0.518542\pi\)
−0.0582188 + 0.998304i \(0.518542\pi\)
\(74\) −6.96120 −0.809224
\(75\) 0.797340 0.0920689
\(76\) 7.93463 0.910165
\(77\) 1.54185 0.175710
\(78\) 0.883404 0.100026
\(79\) 2.35313 0.264748 0.132374 0.991200i \(-0.457740\pi\)
0.132374 + 0.991200i \(0.457740\pi\)
\(80\) −1.00000 −0.111803
\(81\) 3.68241 0.409157
\(82\) 6.69318 0.739138
\(83\) −15.6459 −1.71736 −0.858682 0.512509i \(-0.828716\pi\)
−0.858682 + 0.512509i \(0.828716\pi\)
\(84\) −1.22938 −0.134136
\(85\) 3.83917 0.416417
\(86\) −1.00000 −0.107833
\(87\) −2.20770 −0.236690
\(88\) 1.00000 0.106600
\(89\) 7.56378 0.801759 0.400879 0.916131i \(-0.368705\pi\)
0.400879 + 0.916131i \(0.368705\pi\)
\(90\) −2.36425 −0.249214
\(91\) 1.70828 0.179076
\(92\) −3.10794 −0.324025
\(93\) 3.02075 0.313237
\(94\) 2.36057 0.243474
\(95\) −7.93463 −0.814076
\(96\) −0.797340 −0.0813782
\(97\) 6.65740 0.675957 0.337978 0.941154i \(-0.390257\pi\)
0.337978 + 0.941154i \(0.390257\pi\)
\(98\) 4.62269 0.466963
\(99\) 2.36425 0.237616
\(100\) 1.00000 0.100000
\(101\) −1.58227 −0.157442 −0.0787208 0.996897i \(-0.525084\pi\)
−0.0787208 + 0.996897i \(0.525084\pi\)
\(102\) 3.06113 0.303097
\(103\) −10.4974 −1.03434 −0.517169 0.855883i \(-0.673014\pi\)
−0.517169 + 0.855883i \(0.673014\pi\)
\(104\) 1.10794 0.108642
\(105\) 1.22938 0.119975
\(106\) −0.0407411 −0.00395712
\(107\) 12.2521 1.18446 0.592229 0.805770i \(-0.298248\pi\)
0.592229 + 0.805770i \(0.298248\pi\)
\(108\) −4.27713 −0.411567
\(109\) 10.4965 1.00538 0.502691 0.864466i \(-0.332343\pi\)
0.502691 + 0.864466i \(0.332343\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 5.55045 0.526825
\(112\) −1.54185 −0.145691
\(113\) 14.0084 1.31780 0.658900 0.752231i \(-0.271022\pi\)
0.658900 + 0.752231i \(0.271022\pi\)
\(114\) −6.32660 −0.592541
\(115\) 3.10794 0.289817
\(116\) −2.76882 −0.257079
\(117\) 2.61944 0.242167
\(118\) 14.7262 1.35566
\(119\) 5.91944 0.542634
\(120\) 0.797340 0.0727869
\(121\) 1.00000 0.0909091
\(122\) −11.6123 −1.05133
\(123\) −5.33675 −0.481198
\(124\) 3.78854 0.340221
\(125\) −1.00000 −0.0894427
\(126\) −3.64532 −0.324751
\(127\) 8.58390 0.761698 0.380849 0.924637i \(-0.375632\pi\)
0.380849 + 0.924637i \(0.375632\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.797340 0.0702019
\(130\) −1.10794 −0.0971726
\(131\) 20.0738 1.75385 0.876926 0.480625i \(-0.159590\pi\)
0.876926 + 0.480625i \(0.159590\pi\)
\(132\) −0.797340 −0.0693996
\(133\) −12.2340 −1.06082
\(134\) 9.13185 0.788871
\(135\) 4.27713 0.368117
\(136\) 3.83917 0.329207
\(137\) 6.88382 0.588125 0.294062 0.955786i \(-0.404993\pi\)
0.294062 + 0.955786i \(0.404993\pi\)
\(138\) 2.47808 0.210949
\(139\) −8.31893 −0.705602 −0.352801 0.935698i \(-0.614771\pi\)
−0.352801 + 0.935698i \(0.614771\pi\)
\(140\) 1.54185 0.130310
\(141\) −1.88218 −0.158508
\(142\) −15.6288 −1.31154
\(143\) 1.10794 0.0926505
\(144\) −2.36425 −0.197021
\(145\) 2.76882 0.229938
\(146\) 0.994843 0.0823338
\(147\) −3.68586 −0.304005
\(148\) 6.96120 0.572207
\(149\) 14.2155 1.16458 0.582290 0.812981i \(-0.302157\pi\)
0.582290 + 0.812981i \(0.302157\pi\)
\(150\) −0.797340 −0.0651026
\(151\) 2.20290 0.179269 0.0896347 0.995975i \(-0.471430\pi\)
0.0896347 + 0.995975i \(0.471430\pi\)
\(152\) −7.93463 −0.643583
\(153\) 9.07676 0.733813
\(154\) −1.54185 −0.124246
\(155\) −3.78854 −0.304302
\(156\) −0.883404 −0.0707289
\(157\) 11.4383 0.912879 0.456439 0.889755i \(-0.349125\pi\)
0.456439 + 0.889755i \(0.349125\pi\)
\(158\) −2.35313 −0.187205
\(159\) 0.0324845 0.00257619
\(160\) 1.00000 0.0790569
\(161\) 4.79198 0.377661
\(162\) −3.68241 −0.289318
\(163\) 9.28190 0.727015 0.363507 0.931591i \(-0.381579\pi\)
0.363507 + 0.931591i \(0.381579\pi\)
\(164\) −6.69318 −0.522650
\(165\) 0.797340 0.0620729
\(166\) 15.6459 1.21436
\(167\) −7.93432 −0.613976 −0.306988 0.951713i \(-0.599321\pi\)
−0.306988 + 0.951713i \(0.599321\pi\)
\(168\) 1.22938 0.0948488
\(169\) −11.7725 −0.905575
\(170\) −3.83917 −0.294451
\(171\) −18.7594 −1.43457
\(172\) 1.00000 0.0762493
\(173\) 21.9293 1.66725 0.833627 0.552327i \(-0.186260\pi\)
0.833627 + 0.552327i \(0.186260\pi\)
\(174\) 2.20770 0.167365
\(175\) −1.54185 −0.116553
\(176\) −1.00000 −0.0753778
\(177\) −11.7418 −0.882567
\(178\) −7.56378 −0.566929
\(179\) 17.9201 1.33941 0.669706 0.742626i \(-0.266420\pi\)
0.669706 + 0.742626i \(0.266420\pi\)
\(180\) 2.36425 0.176221
\(181\) −0.396161 −0.0294464 −0.0147232 0.999892i \(-0.504687\pi\)
−0.0147232 + 0.999892i \(0.504687\pi\)
\(182\) −1.70828 −0.126626
\(183\) 9.25897 0.684443
\(184\) 3.10794 0.229120
\(185\) −6.96120 −0.511798
\(186\) −3.02075 −0.221492
\(187\) 3.83917 0.280748
\(188\) −2.36057 −0.172162
\(189\) 6.59470 0.479694
\(190\) 7.93463 0.575639
\(191\) 10.3449 0.748532 0.374266 0.927321i \(-0.377895\pi\)
0.374266 + 0.927321i \(0.377895\pi\)
\(192\) 0.797340 0.0575431
\(193\) 26.9533 1.94014 0.970069 0.242830i \(-0.0780756\pi\)
0.970069 + 0.242830i \(0.0780756\pi\)
\(194\) −6.65740 −0.477974
\(195\) 0.883404 0.0632619
\(196\) −4.62269 −0.330192
\(197\) −15.0400 −1.07155 −0.535776 0.844360i \(-0.679981\pi\)
−0.535776 + 0.844360i \(0.679981\pi\)
\(198\) −2.36425 −0.168020
\(199\) −2.22430 −0.157677 −0.0788383 0.996887i \(-0.525121\pi\)
−0.0788383 + 0.996887i \(0.525121\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −7.28119 −0.513576
\(202\) 1.58227 0.111328
\(203\) 4.26912 0.299633
\(204\) −3.06113 −0.214322
\(205\) 6.69318 0.467472
\(206\) 10.4974 0.731388
\(207\) 7.34794 0.510717
\(208\) −1.10794 −0.0768217
\(209\) −7.93463 −0.548850
\(210\) −1.22938 −0.0848353
\(211\) 9.34608 0.643411 0.321705 0.946840i \(-0.395744\pi\)
0.321705 + 0.946840i \(0.395744\pi\)
\(212\) 0.0407411 0.00279811
\(213\) 12.4615 0.853847
\(214\) −12.2521 −0.837538
\(215\) −1.00000 −0.0681994
\(216\) 4.27713 0.291022
\(217\) −5.84136 −0.396537
\(218\) −10.4965 −0.710912
\(219\) −0.793229 −0.0536014
\(220\) 1.00000 0.0674200
\(221\) 4.25357 0.286126
\(222\) −5.55045 −0.372522
\(223\) −16.6826 −1.11715 −0.558576 0.829453i \(-0.688652\pi\)
−0.558576 + 0.829453i \(0.688652\pi\)
\(224\) 1.54185 0.103019
\(225\) −2.36425 −0.157617
\(226\) −14.0084 −0.931825
\(227\) 0.426720 0.0283224 0.0141612 0.999900i \(-0.495492\pi\)
0.0141612 + 0.999900i \(0.495492\pi\)
\(228\) 6.32660 0.418989
\(229\) 2.08701 0.137914 0.0689569 0.997620i \(-0.478033\pi\)
0.0689569 + 0.997620i \(0.478033\pi\)
\(230\) −3.10794 −0.204931
\(231\) 1.22938 0.0808873
\(232\) 2.76882 0.181782
\(233\) 14.5553 0.953551 0.476775 0.879025i \(-0.341806\pi\)
0.476775 + 0.879025i \(0.341806\pi\)
\(234\) −2.61944 −0.171238
\(235\) 2.36057 0.153987
\(236\) −14.7262 −0.958593
\(237\) 1.87625 0.121875
\(238\) −5.91944 −0.383700
\(239\) 17.9401 1.16045 0.580224 0.814457i \(-0.302965\pi\)
0.580224 + 0.814457i \(0.302965\pi\)
\(240\) −0.797340 −0.0514681
\(241\) −6.28095 −0.404592 −0.202296 0.979324i \(-0.564840\pi\)
−0.202296 + 0.979324i \(0.564840\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 15.7675 1.01149
\(244\) 11.6123 0.743402
\(245\) 4.62269 0.295333
\(246\) 5.33675 0.340258
\(247\) −8.79108 −0.559363
\(248\) −3.78854 −0.240572
\(249\) −12.4751 −0.790579
\(250\) 1.00000 0.0632456
\(251\) −7.46854 −0.471410 −0.235705 0.971825i \(-0.575740\pi\)
−0.235705 + 0.971825i \(0.575740\pi\)
\(252\) 3.64532 0.229634
\(253\) 3.10794 0.195394
\(254\) −8.58390 −0.538602
\(255\) 3.06113 0.191695
\(256\) 1.00000 0.0625000
\(257\) 0.905186 0.0564639 0.0282320 0.999601i \(-0.491012\pi\)
0.0282320 + 0.999601i \(0.491012\pi\)
\(258\) −0.797340 −0.0496402
\(259\) −10.7331 −0.666925
\(260\) 1.10794 0.0687114
\(261\) 6.54619 0.405199
\(262\) −20.0738 −1.24016
\(263\) −17.3546 −1.07013 −0.535065 0.844811i \(-0.679713\pi\)
−0.535065 + 0.844811i \(0.679713\pi\)
\(264\) 0.797340 0.0490729
\(265\) −0.0407411 −0.00250270
\(266\) 12.2340 0.750116
\(267\) 6.03091 0.369086
\(268\) −9.13185 −0.557816
\(269\) −16.3542 −0.997132 −0.498566 0.866852i \(-0.666140\pi\)
−0.498566 + 0.866852i \(0.666140\pi\)
\(270\) −4.27713 −0.260298
\(271\) 3.86001 0.234479 0.117239 0.993104i \(-0.462596\pi\)
0.117239 + 0.993104i \(0.462596\pi\)
\(272\) −3.83917 −0.232784
\(273\) 1.36208 0.0824367
\(274\) −6.88382 −0.415867
\(275\) −1.00000 −0.0603023
\(276\) −2.47808 −0.149163
\(277\) −22.0709 −1.32611 −0.663056 0.748569i \(-0.730741\pi\)
−0.663056 + 0.748569i \(0.730741\pi\)
\(278\) 8.31893 0.498936
\(279\) −8.95704 −0.536244
\(280\) −1.54185 −0.0921433
\(281\) −3.04874 −0.181872 −0.0909362 0.995857i \(-0.528986\pi\)
−0.0909362 + 0.995857i \(0.528986\pi\)
\(282\) 1.88218 0.112082
\(283\) 26.6122 1.58193 0.790967 0.611859i \(-0.209578\pi\)
0.790967 + 0.611859i \(0.209578\pi\)
\(284\) 15.6288 0.927399
\(285\) −6.32660 −0.374756
\(286\) −1.10794 −0.0655138
\(287\) 10.3199 0.609164
\(288\) 2.36425 0.139315
\(289\) −2.26074 −0.132985
\(290\) −2.76882 −0.162591
\(291\) 5.30822 0.311173
\(292\) −0.994843 −0.0582188
\(293\) −3.66988 −0.214397 −0.107198 0.994238i \(-0.534188\pi\)
−0.107198 + 0.994238i \(0.534188\pi\)
\(294\) 3.68586 0.214964
\(295\) 14.7262 0.857392
\(296\) −6.96120 −0.404612
\(297\) 4.27713 0.248184
\(298\) −14.2155 −0.823483
\(299\) 3.44340 0.199137
\(300\) 0.797340 0.0460345
\(301\) −1.54185 −0.0888709
\(302\) −2.20290 −0.126763
\(303\) −1.26161 −0.0724774
\(304\) 7.93463 0.455082
\(305\) −11.6123 −0.664919
\(306\) −9.07676 −0.518884
\(307\) 25.2657 1.44199 0.720996 0.692940i \(-0.243685\pi\)
0.720996 + 0.692940i \(0.243685\pi\)
\(308\) 1.54185 0.0878552
\(309\) −8.37000 −0.476152
\(310\) 3.78854 0.215174
\(311\) 2.33109 0.132184 0.0660921 0.997814i \(-0.478947\pi\)
0.0660921 + 0.997814i \(0.478947\pi\)
\(312\) 0.883404 0.0500129
\(313\) −1.74866 −0.0988399 −0.0494200 0.998778i \(-0.515737\pi\)
−0.0494200 + 0.998778i \(0.515737\pi\)
\(314\) −11.4383 −0.645503
\(315\) −3.64532 −0.205391
\(316\) 2.35313 0.132374
\(317\) −15.3541 −0.862374 −0.431187 0.902262i \(-0.641905\pi\)
−0.431187 + 0.902262i \(0.641905\pi\)
\(318\) −0.0324845 −0.00182164
\(319\) 2.76882 0.155024
\(320\) −1.00000 −0.0559017
\(321\) 9.76912 0.545259
\(322\) −4.79198 −0.267047
\(323\) −30.4624 −1.69497
\(324\) 3.68241 0.204579
\(325\) −1.10794 −0.0614574
\(326\) −9.28190 −0.514077
\(327\) 8.36928 0.462822
\(328\) 6.69318 0.369569
\(329\) 3.63965 0.200660
\(330\) −0.797340 −0.0438921
\(331\) −27.6659 −1.52066 −0.760329 0.649538i \(-0.774962\pi\)
−0.760329 + 0.649538i \(0.774962\pi\)
\(332\) −15.6459 −0.858682
\(333\) −16.4580 −0.901894
\(334\) 7.93432 0.434147
\(335\) 9.13185 0.498926
\(336\) −1.22938 −0.0670682
\(337\) 27.7248 1.51027 0.755133 0.655572i \(-0.227572\pi\)
0.755133 + 0.655572i \(0.227572\pi\)
\(338\) 11.7725 0.640338
\(339\) 11.1695 0.606642
\(340\) 3.83917 0.208208
\(341\) −3.78854 −0.205161
\(342\) 18.7594 1.01439
\(343\) 17.9205 0.967614
\(344\) −1.00000 −0.0539164
\(345\) 2.47808 0.133416
\(346\) −21.9293 −1.17893
\(347\) −0.889018 −0.0477250 −0.0238625 0.999715i \(-0.507596\pi\)
−0.0238625 + 0.999715i \(0.507596\pi\)
\(348\) −2.20770 −0.118345
\(349\) −18.5117 −0.990908 −0.495454 0.868634i \(-0.664998\pi\)
−0.495454 + 0.868634i \(0.664998\pi\)
\(350\) 1.54185 0.0824154
\(351\) 4.73880 0.252938
\(352\) 1.00000 0.0533002
\(353\) 1.26480 0.0673183 0.0336592 0.999433i \(-0.489284\pi\)
0.0336592 + 0.999433i \(0.489284\pi\)
\(354\) 11.7418 0.624069
\(355\) −15.6288 −0.829491
\(356\) 7.56378 0.400879
\(357\) 4.71981 0.249799
\(358\) −17.9201 −0.947107
\(359\) 15.1777 0.801049 0.400524 0.916286i \(-0.368828\pi\)
0.400524 + 0.916286i \(0.368828\pi\)
\(360\) −2.36425 −0.124607
\(361\) 43.9584 2.31360
\(362\) 0.396161 0.0208217
\(363\) 0.797340 0.0418495
\(364\) 1.70828 0.0895380
\(365\) 0.994843 0.0520725
\(366\) −9.25897 −0.483974
\(367\) 22.5445 1.17681 0.588407 0.808565i \(-0.299755\pi\)
0.588407 + 0.808565i \(0.299755\pi\)
\(368\) −3.10794 −0.162012
\(369\) 15.8243 0.823783
\(370\) 6.96120 0.361896
\(371\) −0.0628167 −0.00326128
\(372\) 3.02075 0.156619
\(373\) −32.3140 −1.67316 −0.836578 0.547847i \(-0.815447\pi\)
−0.836578 + 0.547847i \(0.815447\pi\)
\(374\) −3.83917 −0.198519
\(375\) −0.797340 −0.0411745
\(376\) 2.36057 0.121737
\(377\) 3.06769 0.157994
\(378\) −6.59470 −0.339195
\(379\) −11.6097 −0.596350 −0.298175 0.954511i \(-0.596378\pi\)
−0.298175 + 0.954511i \(0.596378\pi\)
\(380\) −7.93463 −0.407038
\(381\) 6.84429 0.350644
\(382\) −10.3449 −0.529292
\(383\) −12.2737 −0.627158 −0.313579 0.949562i \(-0.601528\pi\)
−0.313579 + 0.949562i \(0.601528\pi\)
\(384\) −0.797340 −0.0406891
\(385\) −1.54185 −0.0785800
\(386\) −26.9533 −1.37188
\(387\) −2.36425 −0.120181
\(388\) 6.65740 0.337978
\(389\) −16.1198 −0.817306 −0.408653 0.912690i \(-0.634001\pi\)
−0.408653 + 0.912690i \(0.634001\pi\)
\(390\) −0.883404 −0.0447329
\(391\) 11.9319 0.603423
\(392\) 4.62269 0.233481
\(393\) 16.0056 0.807377
\(394\) 15.0400 0.757702
\(395\) −2.35313 −0.118399
\(396\) 2.36425 0.118808
\(397\) −23.7055 −1.18974 −0.594872 0.803821i \(-0.702797\pi\)
−0.594872 + 0.803821i \(0.702797\pi\)
\(398\) 2.22430 0.111494
\(399\) −9.75468 −0.488345
\(400\) 1.00000 0.0500000
\(401\) 38.1181 1.90353 0.951765 0.306829i \(-0.0992679\pi\)
0.951765 + 0.306829i \(0.0992679\pi\)
\(402\) 7.28119 0.363153
\(403\) −4.19746 −0.209091
\(404\) −1.58227 −0.0787208
\(405\) −3.68241 −0.182981
\(406\) −4.26912 −0.211873
\(407\) −6.96120 −0.345054
\(408\) 3.06113 0.151548
\(409\) −3.03368 −0.150006 −0.0750030 0.997183i \(-0.523897\pi\)
−0.0750030 + 0.997183i \(0.523897\pi\)
\(410\) −6.69318 −0.330553
\(411\) 5.48875 0.270740
\(412\) −10.4974 −0.517169
\(413\) 22.7056 1.11727
\(414\) −7.34794 −0.361131
\(415\) 15.6459 0.768028
\(416\) 1.10794 0.0543211
\(417\) −6.63302 −0.324820
\(418\) 7.93463 0.388095
\(419\) 7.12381 0.348021 0.174010 0.984744i \(-0.444327\pi\)
0.174010 + 0.984744i \(0.444327\pi\)
\(420\) 1.22938 0.0599876
\(421\) 26.4911 1.29109 0.645547 0.763720i \(-0.276629\pi\)
0.645547 + 0.763720i \(0.276629\pi\)
\(422\) −9.34608 −0.454960
\(423\) 5.58097 0.271356
\(424\) −0.0407411 −0.00197856
\(425\) −3.83917 −0.186227
\(426\) −12.4615 −0.603761
\(427\) −17.9045 −0.866458
\(428\) 12.2521 0.592229
\(429\) 0.883404 0.0426511
\(430\) 1.00000 0.0482243
\(431\) 25.5980 1.23301 0.616507 0.787350i \(-0.288547\pi\)
0.616507 + 0.787350i \(0.288547\pi\)
\(432\) −4.27713 −0.205784
\(433\) 23.3971 1.12439 0.562196 0.827004i \(-0.309956\pi\)
0.562196 + 0.827004i \(0.309956\pi\)
\(434\) 5.84136 0.280394
\(435\) 2.20770 0.105851
\(436\) 10.4965 0.502691
\(437\) −24.6603 −1.17966
\(438\) 0.793229 0.0379019
\(439\) 29.5628 1.41095 0.705477 0.708733i \(-0.250733\pi\)
0.705477 + 0.708733i \(0.250733\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 10.9292 0.520438
\(442\) −4.25357 −0.202322
\(443\) 3.80670 0.180862 0.0904308 0.995903i \(-0.471176\pi\)
0.0904308 + 0.995903i \(0.471176\pi\)
\(444\) 5.55045 0.263413
\(445\) −7.56378 −0.358558
\(446\) 16.6826 0.789946
\(447\) 11.3346 0.536109
\(448\) −1.54185 −0.0728456
\(449\) 9.97857 0.470918 0.235459 0.971884i \(-0.424341\pi\)
0.235459 + 0.971884i \(0.424341\pi\)
\(450\) 2.36425 0.111452
\(451\) 6.69318 0.315170
\(452\) 14.0084 0.658900
\(453\) 1.75646 0.0825258
\(454\) −0.426720 −0.0200270
\(455\) −1.70828 −0.0800852
\(456\) −6.32660 −0.296270
\(457\) −8.52399 −0.398735 −0.199368 0.979925i \(-0.563889\pi\)
−0.199368 + 0.979925i \(0.563889\pi\)
\(458\) −2.08701 −0.0975198
\(459\) 16.4207 0.766451
\(460\) 3.10794 0.144908
\(461\) −35.0606 −1.63294 −0.816468 0.577391i \(-0.804071\pi\)
−0.816468 + 0.577391i \(0.804071\pi\)
\(462\) −1.22938 −0.0571960
\(463\) −4.68102 −0.217545 −0.108773 0.994067i \(-0.534692\pi\)
−0.108773 + 0.994067i \(0.534692\pi\)
\(464\) −2.76882 −0.128539
\(465\) −3.02075 −0.140084
\(466\) −14.5553 −0.674262
\(467\) −36.4304 −1.68580 −0.842899 0.538071i \(-0.819153\pi\)
−0.842899 + 0.538071i \(0.819153\pi\)
\(468\) 2.61944 0.121084
\(469\) 14.0800 0.650152
\(470\) −2.36057 −0.108885
\(471\) 9.12025 0.420239
\(472\) 14.7262 0.677828
\(473\) −1.00000 −0.0459800
\(474\) −1.87625 −0.0861789
\(475\) 7.93463 0.364066
\(476\) 5.91944 0.271317
\(477\) −0.0963220 −0.00441028
\(478\) −17.9401 −0.820560
\(479\) 28.1107 1.28441 0.642206 0.766532i \(-0.278020\pi\)
0.642206 + 0.766532i \(0.278020\pi\)
\(480\) 0.797340 0.0363934
\(481\) −7.71258 −0.351664
\(482\) 6.28095 0.286090
\(483\) 3.82084 0.173854
\(484\) 1.00000 0.0454545
\(485\) −6.65740 −0.302297
\(486\) −15.7675 −0.715230
\(487\) −40.7399 −1.84610 −0.923049 0.384681i \(-0.874311\pi\)
−0.923049 + 0.384681i \(0.874311\pi\)
\(488\) −11.6123 −0.525665
\(489\) 7.40084 0.334677
\(490\) −4.62269 −0.208832
\(491\) 22.4611 1.01366 0.506829 0.862047i \(-0.330818\pi\)
0.506829 + 0.862047i \(0.330818\pi\)
\(492\) −5.33675 −0.240599
\(493\) 10.6300 0.478751
\(494\) 8.79108 0.395529
\(495\) −2.36425 −0.106265
\(496\) 3.78854 0.170110
\(497\) −24.0973 −1.08091
\(498\) 12.4751 0.559024
\(499\) −22.3880 −1.00222 −0.501111 0.865383i \(-0.667075\pi\)
−0.501111 + 0.865383i \(0.667075\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −6.32635 −0.282641
\(502\) 7.46854 0.333337
\(503\) −33.3956 −1.48904 −0.744518 0.667603i \(-0.767320\pi\)
−0.744518 + 0.667603i \(0.767320\pi\)
\(504\) −3.64532 −0.162375
\(505\) 1.58227 0.0704100
\(506\) −3.10794 −0.138165
\(507\) −9.38667 −0.416877
\(508\) 8.58390 0.380849
\(509\) −1.62579 −0.0720617 −0.0360309 0.999351i \(-0.511471\pi\)
−0.0360309 + 0.999351i \(0.511471\pi\)
\(510\) −3.06113 −0.135549
\(511\) 1.53390 0.0678558
\(512\) −1.00000 −0.0441942
\(513\) −33.9375 −1.49838
\(514\) −0.905186 −0.0399260
\(515\) 10.4974 0.462570
\(516\) 0.797340 0.0351010
\(517\) 2.36057 0.103818
\(518\) 10.7331 0.471587
\(519\) 17.4851 0.767512
\(520\) −1.10794 −0.0485863
\(521\) 39.1274 1.71420 0.857101 0.515149i \(-0.172263\pi\)
0.857101 + 0.515149i \(0.172263\pi\)
\(522\) −6.54619 −0.286519
\(523\) 3.34218 0.146143 0.0730717 0.997327i \(-0.476720\pi\)
0.0730717 + 0.997327i \(0.476720\pi\)
\(524\) 20.0738 0.876926
\(525\) −1.22938 −0.0536546
\(526\) 17.3546 0.756696
\(527\) −14.5448 −0.633584
\(528\) −0.797340 −0.0346998
\(529\) −13.3407 −0.580031
\(530\) 0.0407411 0.00176968
\(531\) 34.8164 1.51090
\(532\) −12.2340 −0.530412
\(533\) 7.41563 0.321207
\(534\) −6.03091 −0.260983
\(535\) −12.2521 −0.529706
\(536\) 9.13185 0.394436
\(537\) 14.2884 0.616591
\(538\) 16.3542 0.705079
\(539\) 4.62269 0.199113
\(540\) 4.27713 0.184058
\(541\) 0.335401 0.0144200 0.00721001 0.999974i \(-0.497705\pi\)
0.00721001 + 0.999974i \(0.497705\pi\)
\(542\) −3.86001 −0.165802
\(543\) −0.315875 −0.0135555
\(544\) 3.83917 0.164603
\(545\) −10.4965 −0.449620
\(546\) −1.36208 −0.0582916
\(547\) 3.32579 0.142201 0.0711003 0.997469i \(-0.477349\pi\)
0.0711003 + 0.997469i \(0.477349\pi\)
\(548\) 6.88382 0.294062
\(549\) −27.4544 −1.17173
\(550\) 1.00000 0.0426401
\(551\) −21.9696 −0.935937
\(552\) 2.47808 0.105474
\(553\) −3.62818 −0.154286
\(554\) 22.0709 0.937703
\(555\) −5.55045 −0.235603
\(556\) −8.31893 −0.352801
\(557\) −9.00032 −0.381356 −0.190678 0.981653i \(-0.561069\pi\)
−0.190678 + 0.981653i \(0.561069\pi\)
\(558\) 8.95704 0.379182
\(559\) −1.10794 −0.0468608
\(560\) 1.54185 0.0651551
\(561\) 3.06113 0.129241
\(562\) 3.04874 0.128603
\(563\) 7.90272 0.333060 0.166530 0.986036i \(-0.446744\pi\)
0.166530 + 0.986036i \(0.446744\pi\)
\(564\) −1.88218 −0.0792540
\(565\) −14.0084 −0.589338
\(566\) −26.6122 −1.11860
\(567\) −5.67774 −0.238443
\(568\) −15.6288 −0.655770
\(569\) −43.8015 −1.83625 −0.918127 0.396286i \(-0.870299\pi\)
−0.918127 + 0.396286i \(0.870299\pi\)
\(570\) 6.32660 0.264992
\(571\) 29.5061 1.23479 0.617396 0.786652i \(-0.288188\pi\)
0.617396 + 0.786652i \(0.288188\pi\)
\(572\) 1.10794 0.0463252
\(573\) 8.24842 0.344583
\(574\) −10.3199 −0.430744
\(575\) −3.10794 −0.129610
\(576\) −2.36425 −0.0985103
\(577\) −25.2189 −1.04988 −0.524938 0.851140i \(-0.675912\pi\)
−0.524938 + 0.851140i \(0.675912\pi\)
\(578\) 2.26074 0.0940343
\(579\) 21.4909 0.893132
\(580\) 2.76882 0.114969
\(581\) 24.1237 1.00082
\(582\) −5.30822 −0.220033
\(583\) −0.0407411 −0.00168732
\(584\) 0.994843 0.0411669
\(585\) −2.61944 −0.108301
\(586\) 3.66988 0.151601
\(587\) −19.9248 −0.822385 −0.411192 0.911549i \(-0.634888\pi\)
−0.411192 + 0.911549i \(0.634888\pi\)
\(588\) −3.68586 −0.152002
\(589\) 30.0606 1.23863
\(590\) −14.7262 −0.606268
\(591\) −11.9920 −0.493284
\(592\) 6.96120 0.286104
\(593\) 45.6001 1.87257 0.936286 0.351239i \(-0.114239\pi\)
0.936286 + 0.351239i \(0.114239\pi\)
\(594\) −4.27713 −0.175493
\(595\) −5.91944 −0.242673
\(596\) 14.2155 0.582290
\(597\) −1.77353 −0.0725856
\(598\) −3.44340 −0.140811
\(599\) −22.2320 −0.908375 −0.454188 0.890906i \(-0.650070\pi\)
−0.454188 + 0.890906i \(0.650070\pi\)
\(600\) −0.797340 −0.0325513
\(601\) 6.91402 0.282029 0.141014 0.990008i \(-0.454964\pi\)
0.141014 + 0.990008i \(0.454964\pi\)
\(602\) 1.54185 0.0628412
\(603\) 21.5900 0.879211
\(604\) 2.20290 0.0896347
\(605\) −1.00000 −0.0406558
\(606\) 1.26161 0.0512493
\(607\) −21.9576 −0.891233 −0.445617 0.895224i \(-0.647016\pi\)
−0.445617 + 0.895224i \(0.647016\pi\)
\(608\) −7.93463 −0.321792
\(609\) 3.40394 0.137935
\(610\) 11.6123 0.470169
\(611\) 2.61537 0.105806
\(612\) 9.07676 0.366906
\(613\) 29.5738 1.19447 0.597237 0.802064i \(-0.296265\pi\)
0.597237 + 0.802064i \(0.296265\pi\)
\(614\) −25.2657 −1.01964
\(615\) 5.33675 0.215198
\(616\) −1.54185 −0.0621230
\(617\) −30.8554 −1.24219 −0.621095 0.783735i \(-0.713312\pi\)
−0.621095 + 0.783735i \(0.713312\pi\)
\(618\) 8.37000 0.336691
\(619\) 41.7274 1.67717 0.838584 0.544773i \(-0.183384\pi\)
0.838584 + 0.544773i \(0.183384\pi\)
\(620\) −3.78854 −0.152151
\(621\) 13.2931 0.533432
\(622\) −2.33109 −0.0934684
\(623\) −11.6622 −0.467237
\(624\) −0.883404 −0.0353645
\(625\) 1.00000 0.0400000
\(626\) 1.74866 0.0698904
\(627\) −6.32660 −0.252660
\(628\) 11.4383 0.456439
\(629\) −26.7253 −1.06561
\(630\) 3.64532 0.145233
\(631\) 12.5749 0.500599 0.250300 0.968168i \(-0.419471\pi\)
0.250300 + 0.968168i \(0.419471\pi\)
\(632\) −2.35313 −0.0936026
\(633\) 7.45201 0.296191
\(634\) 15.3541 0.609791
\(635\) −8.58390 −0.340642
\(636\) 0.0324845 0.00128809
\(637\) 5.12166 0.202927
\(638\) −2.76882 −0.109619
\(639\) −36.9504 −1.46173
\(640\) 1.00000 0.0395285
\(641\) 38.1618 1.50730 0.753651 0.657275i \(-0.228291\pi\)
0.753651 + 0.657275i \(0.228291\pi\)
\(642\) −9.76912 −0.385556
\(643\) 20.0564 0.790947 0.395473 0.918477i \(-0.370581\pi\)
0.395473 + 0.918477i \(0.370581\pi\)
\(644\) 4.79198 0.188830
\(645\) −0.797340 −0.0313952
\(646\) 30.4624 1.19853
\(647\) 37.6532 1.48030 0.740149 0.672443i \(-0.234755\pi\)
0.740149 + 0.672443i \(0.234755\pi\)
\(648\) −3.68241 −0.144659
\(649\) 14.7262 0.578053
\(650\) 1.10794 0.0434569
\(651\) −4.65755 −0.182544
\(652\) 9.28190 0.363507
\(653\) −42.4118 −1.65970 −0.829850 0.557986i \(-0.811574\pi\)
−0.829850 + 0.557986i \(0.811574\pi\)
\(654\) −8.36928 −0.327265
\(655\) −20.0738 −0.784346
\(656\) −6.69318 −0.261325
\(657\) 2.35206 0.0917625
\(658\) −3.63965 −0.141888
\(659\) 45.9687 1.79069 0.895343 0.445377i \(-0.146930\pi\)
0.895343 + 0.445377i \(0.146930\pi\)
\(660\) 0.797340 0.0310364
\(661\) −3.82044 −0.148598 −0.0742989 0.997236i \(-0.523672\pi\)
−0.0742989 + 0.997236i \(0.523672\pi\)
\(662\) 27.6659 1.07527
\(663\) 3.39154 0.131717
\(664\) 15.6459 0.607180
\(665\) 12.2340 0.474415
\(666\) 16.4580 0.637735
\(667\) 8.60534 0.333200
\(668\) −7.93432 −0.306988
\(669\) −13.3017 −0.514275
\(670\) −9.13185 −0.352794
\(671\) −11.6123 −0.448289
\(672\) 1.22938 0.0474244
\(673\) 0.352240 0.0135779 0.00678894 0.999977i \(-0.497839\pi\)
0.00678894 + 0.999977i \(0.497839\pi\)
\(674\) −27.7248 −1.06792
\(675\) −4.27713 −0.164627
\(676\) −11.7725 −0.452787
\(677\) −3.16612 −0.121684 −0.0608419 0.998147i \(-0.519379\pi\)
−0.0608419 + 0.998147i \(0.519379\pi\)
\(678\) −11.1695 −0.428961
\(679\) −10.2647 −0.393924
\(680\) −3.83917 −0.147226
\(681\) 0.340241 0.0130381
\(682\) 3.78854 0.145071
\(683\) 6.41970 0.245643 0.122821 0.992429i \(-0.460806\pi\)
0.122821 + 0.992429i \(0.460806\pi\)
\(684\) −18.7594 −0.717285
\(685\) −6.88382 −0.263017
\(686\) −17.9205 −0.684207
\(687\) 1.66406 0.0634879
\(688\) 1.00000 0.0381246
\(689\) −0.0451386 −0.00171964
\(690\) −2.47808 −0.0943391
\(691\) 40.2445 1.53097 0.765486 0.643453i \(-0.222499\pi\)
0.765486 + 0.643453i \(0.222499\pi\)
\(692\) 21.9293 0.833627
\(693\) −3.64532 −0.138474
\(694\) 0.889018 0.0337467
\(695\) 8.31893 0.315555
\(696\) 2.20770 0.0836825
\(697\) 25.6963 0.973317
\(698\) 18.5117 0.700678
\(699\) 11.6055 0.438962
\(700\) −1.54185 −0.0582765
\(701\) −21.6765 −0.818712 −0.409356 0.912375i \(-0.634247\pi\)
−0.409356 + 0.912375i \(0.634247\pi\)
\(702\) −4.73880 −0.178854
\(703\) 55.2346 2.08321
\(704\) −1.00000 −0.0376889
\(705\) 1.88218 0.0708869
\(706\) −1.26480 −0.0476012
\(707\) 2.43962 0.0917515
\(708\) −11.7418 −0.441283
\(709\) 23.8119 0.894274 0.447137 0.894465i \(-0.352444\pi\)
0.447137 + 0.894465i \(0.352444\pi\)
\(710\) 15.6288 0.586539
\(711\) −5.56339 −0.208643
\(712\) −7.56378 −0.283465
\(713\) −11.7745 −0.440960
\(714\) −4.71981 −0.176634
\(715\) −1.10794 −0.0414345
\(716\) 17.9201 0.669706
\(717\) 14.3043 0.534206
\(718\) −15.1777 −0.566427
\(719\) −35.9884 −1.34214 −0.671071 0.741393i \(-0.734165\pi\)
−0.671071 + 0.741393i \(0.734165\pi\)
\(720\) 2.36425 0.0881103
\(721\) 16.1854 0.602777
\(722\) −43.9584 −1.63596
\(723\) −5.00806 −0.186252
\(724\) −0.396161 −0.0147232
\(725\) −2.76882 −0.102832
\(726\) −0.797340 −0.0295921
\(727\) 1.77159 0.0657046 0.0328523 0.999460i \(-0.489541\pi\)
0.0328523 + 0.999460i \(0.489541\pi\)
\(728\) −1.70828 −0.0633129
\(729\) 1.52485 0.0564759
\(730\) −0.994843 −0.0368208
\(731\) −3.83917 −0.141997
\(732\) 9.25897 0.342221
\(733\) −34.4755 −1.27338 −0.636691 0.771119i \(-0.719697\pi\)
−0.636691 + 0.771119i \(0.719697\pi\)
\(734\) −22.5445 −0.832133
\(735\) 3.68586 0.135955
\(736\) 3.10794 0.114560
\(737\) 9.13185 0.336376
\(738\) −15.8243 −0.582502
\(739\) 37.1542 1.36674 0.683370 0.730072i \(-0.260513\pi\)
0.683370 + 0.730072i \(0.260513\pi\)
\(740\) −6.96120 −0.255899
\(741\) −7.00948 −0.257500
\(742\) 0.0628167 0.00230607
\(743\) −19.8144 −0.726919 −0.363460 0.931610i \(-0.618405\pi\)
−0.363460 + 0.931610i \(0.618405\pi\)
\(744\) −3.02075 −0.110746
\(745\) −14.2155 −0.520816
\(746\) 32.3140 1.18310
\(747\) 36.9909 1.35342
\(748\) 3.83917 0.140374
\(749\) −18.8910 −0.690261
\(750\) 0.797340 0.0291148
\(751\) −6.87619 −0.250916 −0.125458 0.992099i \(-0.540040\pi\)
−0.125458 + 0.992099i \(0.540040\pi\)
\(752\) −2.36057 −0.0860811
\(753\) −5.95497 −0.217011
\(754\) −3.06769 −0.111719
\(755\) −2.20290 −0.0801718
\(756\) 6.59470 0.239847
\(757\) 14.6193 0.531346 0.265673 0.964063i \(-0.414406\pi\)
0.265673 + 0.964063i \(0.414406\pi\)
\(758\) 11.6097 0.421683
\(759\) 2.47808 0.0899488
\(760\) 7.93463 0.287819
\(761\) 16.9298 0.613707 0.306853 0.951757i \(-0.400724\pi\)
0.306853 + 0.951757i \(0.400724\pi\)
\(762\) −6.84429 −0.247943
\(763\) −16.1840 −0.585901
\(764\) 10.3449 0.374266
\(765\) −9.07676 −0.328171
\(766\) 12.2737 0.443468
\(767\) 16.3157 0.589126
\(768\) 0.797340 0.0287715
\(769\) 32.5040 1.17212 0.586061 0.810267i \(-0.300678\pi\)
0.586061 + 0.810267i \(0.300678\pi\)
\(770\) 1.54185 0.0555645
\(771\) 0.721741 0.0259929
\(772\) 26.9533 0.970069
\(773\) 0.0944775 0.00339812 0.00169906 0.999999i \(-0.499459\pi\)
0.00169906 + 0.999999i \(0.499459\pi\)
\(774\) 2.36425 0.0849811
\(775\) 3.78854 0.136088
\(776\) −6.65740 −0.238987
\(777\) −8.55797 −0.307015
\(778\) 16.1198 0.577923
\(779\) −53.1079 −1.90279
\(780\) 0.883404 0.0316309
\(781\) −15.6288 −0.559243
\(782\) −11.9319 −0.426685
\(783\) 11.8426 0.423221
\(784\) −4.62269 −0.165096
\(785\) −11.4383 −0.408252
\(786\) −16.0056 −0.570901
\(787\) 17.6027 0.627467 0.313733 0.949511i \(-0.398420\pi\)
0.313733 + 0.949511i \(0.398420\pi\)
\(788\) −15.0400 −0.535776
\(789\) −13.8375 −0.492628
\(790\) 2.35313 0.0837207
\(791\) −21.5989 −0.767968
\(792\) −2.36425 −0.0840099
\(793\) −12.8657 −0.456875
\(794\) 23.7055 0.841276
\(795\) −0.0324845 −0.00115211
\(796\) −2.22430 −0.0788383
\(797\) −27.3366 −0.968311 −0.484156 0.874982i \(-0.660873\pi\)
−0.484156 + 0.874982i \(0.660873\pi\)
\(798\) 9.75468 0.345312
\(799\) 9.06264 0.320613
\(800\) −1.00000 −0.0353553
\(801\) −17.8827 −0.631852
\(802\) −38.1181 −1.34600
\(803\) 0.994843 0.0351073
\(804\) −7.28119 −0.256788
\(805\) −4.79198 −0.168895
\(806\) 4.19746 0.147849
\(807\) −13.0399 −0.459025
\(808\) 1.58227 0.0556640
\(809\) 24.5666 0.863714 0.431857 0.901942i \(-0.357858\pi\)
0.431857 + 0.901942i \(0.357858\pi\)
\(810\) 3.68241 0.129387
\(811\) 9.74512 0.342197 0.171099 0.985254i \(-0.445268\pi\)
0.171099 + 0.985254i \(0.445268\pi\)
\(812\) 4.26912 0.149817
\(813\) 3.07774 0.107941
\(814\) 6.96120 0.243990
\(815\) −9.28190 −0.325131
\(816\) −3.06113 −0.107161
\(817\) 7.93463 0.277598
\(818\) 3.03368 0.106070
\(819\) −4.03879 −0.141127
\(820\) 6.69318 0.233736
\(821\) 46.5085 1.62316 0.811579 0.584243i \(-0.198608\pi\)
0.811579 + 0.584243i \(0.198608\pi\)
\(822\) −5.48875 −0.191442
\(823\) −33.6425 −1.17270 −0.586351 0.810057i \(-0.699436\pi\)
−0.586351 + 0.810057i \(0.699436\pi\)
\(824\) 10.4974 0.365694
\(825\) −0.797340 −0.0277598
\(826\) −22.7056 −0.790029
\(827\) 14.4250 0.501606 0.250803 0.968038i \(-0.419305\pi\)
0.250803 + 0.968038i \(0.419305\pi\)
\(828\) 7.34794 0.255358
\(829\) −23.6766 −0.822322 −0.411161 0.911563i \(-0.634877\pi\)
−0.411161 + 0.911563i \(0.634877\pi\)
\(830\) −15.6459 −0.543078
\(831\) −17.5980 −0.610469
\(832\) −1.10794 −0.0384108
\(833\) 17.7473 0.614908
\(834\) 6.63302 0.229683
\(835\) 7.93432 0.274578
\(836\) −7.93463 −0.274425
\(837\) −16.2041 −0.560094
\(838\) −7.12381 −0.246088
\(839\) 47.5625 1.64204 0.821020 0.570899i \(-0.193405\pi\)
0.821020 + 0.570899i \(0.193405\pi\)
\(840\) −1.22938 −0.0424177
\(841\) −21.3336 −0.735642
\(842\) −26.4911 −0.912942
\(843\) −2.43088 −0.0837240
\(844\) 9.34608 0.321705
\(845\) 11.7725 0.404985
\(846\) −5.58097 −0.191878
\(847\) −1.54185 −0.0529787
\(848\) 0.0407411 0.00139905
\(849\) 21.2190 0.728235
\(850\) 3.83917 0.131683
\(851\) −21.6350 −0.741638
\(852\) 12.4615 0.426923
\(853\) 7.72737 0.264580 0.132290 0.991211i \(-0.457767\pi\)
0.132290 + 0.991211i \(0.457767\pi\)
\(854\) 17.9045 0.612678
\(855\) 18.7594 0.641559
\(856\) −12.2521 −0.418769
\(857\) −30.0118 −1.02518 −0.512591 0.858633i \(-0.671314\pi\)
−0.512591 + 0.858633i \(0.671314\pi\)
\(858\) −0.883404 −0.0301589
\(859\) 1.29093 0.0440460 0.0220230 0.999757i \(-0.492989\pi\)
0.0220230 + 0.999757i \(0.492989\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 8.22847 0.280426
\(862\) −25.5980 −0.871872
\(863\) −1.94837 −0.0663233 −0.0331616 0.999450i \(-0.510558\pi\)
−0.0331616 + 0.999450i \(0.510558\pi\)
\(864\) 4.27713 0.145511
\(865\) −21.9293 −0.745619
\(866\) −23.3971 −0.795066
\(867\) −1.80258 −0.0612188
\(868\) −5.84136 −0.198269
\(869\) −2.35313 −0.0798246
\(870\) −2.20770 −0.0748479
\(871\) 10.1175 0.342819
\(872\) −10.4965 −0.355456
\(873\) −15.7398 −0.532710
\(874\) 24.6603 0.834148
\(875\) 1.54185 0.0521241
\(876\) −0.793229 −0.0268007
\(877\) −1.92327 −0.0649443 −0.0324722 0.999473i \(-0.510338\pi\)
−0.0324722 + 0.999473i \(0.510338\pi\)
\(878\) −29.5628 −0.997695
\(879\) −2.92614 −0.0986964
\(880\) 1.00000 0.0337100
\(881\) 19.6557 0.662216 0.331108 0.943593i \(-0.392578\pi\)
0.331108 + 0.943593i \(0.392578\pi\)
\(882\) −10.9292 −0.368005
\(883\) 6.59115 0.221810 0.110905 0.993831i \(-0.464625\pi\)
0.110905 + 0.993831i \(0.464625\pi\)
\(884\) 4.25357 0.143063
\(885\) 11.7418 0.394696
\(886\) −3.80670 −0.127888
\(887\) 0.548999 0.0184336 0.00921680 0.999958i \(-0.497066\pi\)
0.00921680 + 0.999958i \(0.497066\pi\)
\(888\) −5.55045 −0.186261
\(889\) −13.2351 −0.443891
\(890\) 7.56378 0.253538
\(891\) −3.68241 −0.123366
\(892\) −16.6826 −0.558576
\(893\) −18.7302 −0.626784
\(894\) −11.3346 −0.379086
\(895\) −17.9201 −0.599003
\(896\) 1.54185 0.0515097
\(897\) 2.74556 0.0916717
\(898\) −9.97857 −0.332989
\(899\) −10.4898 −0.349854
\(900\) −2.36425 −0.0788083
\(901\) −0.156412 −0.00521084
\(902\) −6.69318 −0.222859
\(903\) −1.22938 −0.0409112
\(904\) −14.0084 −0.465912
\(905\) 0.396161 0.0131688
\(906\) −1.75646 −0.0583545
\(907\) −43.7416 −1.45241 −0.726207 0.687476i \(-0.758719\pi\)
−0.726207 + 0.687476i \(0.758719\pi\)
\(908\) 0.426720 0.0141612
\(909\) 3.74088 0.124077
\(910\) 1.70828 0.0566288
\(911\) −13.9346 −0.461675 −0.230837 0.972992i \(-0.574147\pi\)
−0.230837 + 0.972992i \(0.574147\pi\)
\(912\) 6.32660 0.209495
\(913\) 15.6459 0.517805
\(914\) 8.52399 0.281948
\(915\) −9.25897 −0.306092
\(916\) 2.08701 0.0689569
\(917\) −30.9508 −1.02208
\(918\) −16.4207 −0.541962
\(919\) −22.8133 −0.752540 −0.376270 0.926510i \(-0.622794\pi\)
−0.376270 + 0.926510i \(0.622794\pi\)
\(920\) −3.10794 −0.102466
\(921\) 20.1454 0.663813
\(922\) 35.0606 1.15466
\(923\) −17.3158 −0.569955
\(924\) 1.22938 0.0404437
\(925\) 6.96120 0.228883
\(926\) 4.68102 0.153828
\(927\) 24.8184 0.815145
\(928\) 2.76882 0.0908911
\(929\) −14.1156 −0.463119 −0.231559 0.972821i \(-0.574383\pi\)
−0.231559 + 0.972821i \(0.574383\pi\)
\(930\) 3.02075 0.0990544
\(931\) −36.6794 −1.20212
\(932\) 14.5553 0.476775
\(933\) 1.85868 0.0608503
\(934\) 36.4304 1.19204
\(935\) −3.83917 −0.125554
\(936\) −2.61944 −0.0856191
\(937\) 15.2763 0.499055 0.249528 0.968368i \(-0.419725\pi\)
0.249528 + 0.968368i \(0.419725\pi\)
\(938\) −14.0800 −0.459727
\(939\) −1.39428 −0.0455004
\(940\) 2.36057 0.0769933
\(941\) −8.03056 −0.261789 −0.130894 0.991396i \(-0.541785\pi\)
−0.130894 + 0.991396i \(0.541785\pi\)
\(942\) −9.12025 −0.297154
\(943\) 20.8020 0.677406
\(944\) −14.7262 −0.479297
\(945\) −6.59470 −0.214526
\(946\) 1.00000 0.0325128
\(947\) −33.0870 −1.07518 −0.537591 0.843205i \(-0.680666\pi\)
−0.537591 + 0.843205i \(0.680666\pi\)
\(948\) 1.87625 0.0609377
\(949\) 1.10222 0.0357797
\(950\) −7.93463 −0.257433
\(951\) −12.2425 −0.396990
\(952\) −5.91944 −0.191850
\(953\) 28.7463 0.931183 0.465591 0.885000i \(-0.345842\pi\)
0.465591 + 0.885000i \(0.345842\pi\)
\(954\) 0.0963220 0.00311854
\(955\) −10.3449 −0.334754
\(956\) 17.9401 0.580224
\(957\) 2.20770 0.0713647
\(958\) −28.1107 −0.908216
\(959\) −10.6138 −0.342739
\(960\) −0.797340 −0.0257341
\(961\) −16.6470 −0.537000
\(962\) 7.71258 0.248664
\(963\) −28.9671 −0.933451
\(964\) −6.28095 −0.202296
\(965\) −26.9533 −0.867656
\(966\) −3.82084 −0.122933
\(967\) −45.0894 −1.44998 −0.724988 0.688761i \(-0.758155\pi\)
−0.724988 + 0.688761i \(0.758155\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −24.2889 −0.780273
\(970\) 6.65740 0.213756
\(971\) −46.8478 −1.50342 −0.751709 0.659495i \(-0.770770\pi\)
−0.751709 + 0.659495i \(0.770770\pi\)
\(972\) 15.7675 0.505744
\(973\) 12.8266 0.411200
\(974\) 40.7399 1.30539
\(975\) −0.883404 −0.0282916
\(976\) 11.6123 0.371701
\(977\) −52.7059 −1.68621 −0.843105 0.537749i \(-0.819275\pi\)
−0.843105 + 0.537749i \(0.819275\pi\)
\(978\) −7.40084 −0.236653
\(979\) −7.56378 −0.241739
\(980\) 4.62269 0.147667
\(981\) −24.8163 −0.792324
\(982\) −22.4611 −0.716764
\(983\) 40.4769 1.29101 0.645507 0.763755i \(-0.276646\pi\)
0.645507 + 0.763755i \(0.276646\pi\)
\(984\) 5.33675 0.170129
\(985\) 15.0400 0.479213
\(986\) −10.6300 −0.338528
\(987\) 2.90204 0.0923729
\(988\) −8.79108 −0.279682
\(989\) −3.10794 −0.0988267
\(990\) 2.36425 0.0751407
\(991\) −30.3799 −0.965050 −0.482525 0.875882i \(-0.660280\pi\)
−0.482525 + 0.875882i \(0.660280\pi\)
\(992\) −3.78854 −0.120286
\(993\) −22.0592 −0.700027
\(994\) 24.0973 0.764320
\(995\) 2.22430 0.0705151
\(996\) −12.4751 −0.395290
\(997\) 51.8876 1.64330 0.821649 0.569994i \(-0.193054\pi\)
0.821649 + 0.569994i \(0.193054\pi\)
\(998\) 22.3880 0.708678
\(999\) −29.7740 −0.942007
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.bb.1.7 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.bb.1.7 11 1.1 even 1 trivial