Properties

Label 6001.2.a.d.1.8
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.51719 q^{2} +0.226046 q^{3} +4.33623 q^{4} -1.31460 q^{5} -0.569001 q^{6} -1.40872 q^{7} -5.88074 q^{8} -2.94890 q^{9} +O(q^{10})\) \(q-2.51719 q^{2} +0.226046 q^{3} +4.33623 q^{4} -1.31460 q^{5} -0.569001 q^{6} -1.40872 q^{7} -5.88074 q^{8} -2.94890 q^{9} +3.30910 q^{10} -1.02148 q^{11} +0.980189 q^{12} -5.01297 q^{13} +3.54602 q^{14} -0.297161 q^{15} +6.13046 q^{16} +1.00000 q^{17} +7.42294 q^{18} -0.951166 q^{19} -5.70043 q^{20} -0.318436 q^{21} +2.57126 q^{22} -1.09105 q^{23} -1.32932 q^{24} -3.27182 q^{25} +12.6186 q^{26} -1.34473 q^{27} -6.10856 q^{28} -6.92080 q^{29} +0.748010 q^{30} +1.56426 q^{31} -3.67004 q^{32} -0.230902 q^{33} -2.51719 q^{34} +1.85191 q^{35} -12.7871 q^{36} -4.13201 q^{37} +2.39426 q^{38} -1.13316 q^{39} +7.73085 q^{40} +5.99367 q^{41} +0.801564 q^{42} +2.31457 q^{43} -4.42939 q^{44} +3.87664 q^{45} +2.74639 q^{46} -3.40367 q^{47} +1.38577 q^{48} -5.01550 q^{49} +8.23578 q^{50} +0.226046 q^{51} -21.7374 q^{52} -7.12979 q^{53} +3.38493 q^{54} +1.34284 q^{55} +8.28434 q^{56} -0.215007 q^{57} +17.4209 q^{58} -8.87087 q^{59} -1.28856 q^{60} +5.70622 q^{61} -3.93753 q^{62} +4.15419 q^{63} -3.02274 q^{64} +6.59006 q^{65} +0.581224 q^{66} -4.65124 q^{67} +4.33623 q^{68} -0.246629 q^{69} -4.66161 q^{70} -7.50941 q^{71} +17.3417 q^{72} -16.3112 q^{73} +10.4010 q^{74} -0.739582 q^{75} -4.12448 q^{76} +1.43899 q^{77} +2.85238 q^{78} -12.2566 q^{79} -8.05913 q^{80} +8.54274 q^{81} -15.0872 q^{82} -0.783044 q^{83} -1.38082 q^{84} -1.31460 q^{85} -5.82621 q^{86} -1.56442 q^{87} +6.00707 q^{88} -6.64570 q^{89} -9.75823 q^{90} +7.06188 q^{91} -4.73107 q^{92} +0.353594 q^{93} +8.56767 q^{94} +1.25041 q^{95} -0.829599 q^{96} -1.92941 q^{97} +12.6250 q^{98} +3.01225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51719 −1.77992 −0.889960 0.456038i \(-0.849268\pi\)
−0.889960 + 0.456038i \(0.849268\pi\)
\(3\) 0.226046 0.130508 0.0652539 0.997869i \(-0.479214\pi\)
0.0652539 + 0.997869i \(0.479214\pi\)
\(4\) 4.33623 2.16812
\(5\) −1.31460 −0.587909 −0.293954 0.955819i \(-0.594971\pi\)
−0.293954 + 0.955819i \(0.594971\pi\)
\(6\) −0.569001 −0.232293
\(7\) −1.40872 −0.532447 −0.266224 0.963911i \(-0.585776\pi\)
−0.266224 + 0.963911i \(0.585776\pi\)
\(8\) −5.88074 −2.07916
\(9\) −2.94890 −0.982968
\(10\) 3.30910 1.04643
\(11\) −1.02148 −0.307988 −0.153994 0.988072i \(-0.549214\pi\)
−0.153994 + 0.988072i \(0.549214\pi\)
\(12\) 0.980189 0.282956
\(13\) −5.01297 −1.39035 −0.695173 0.718842i \(-0.744672\pi\)
−0.695173 + 0.718842i \(0.744672\pi\)
\(14\) 3.54602 0.947714
\(15\) −0.297161 −0.0767267
\(16\) 6.13046 1.53262
\(17\) 1.00000 0.242536
\(18\) 7.42294 1.74960
\(19\) −0.951166 −0.218212 −0.109106 0.994030i \(-0.534799\pi\)
−0.109106 + 0.994030i \(0.534799\pi\)
\(20\) −5.70043 −1.27466
\(21\) −0.318436 −0.0694885
\(22\) 2.57126 0.548195
\(23\) −1.09105 −0.227501 −0.113750 0.993509i \(-0.536286\pi\)
−0.113750 + 0.993509i \(0.536286\pi\)
\(24\) −1.32932 −0.271346
\(25\) −3.27182 −0.654363
\(26\) 12.6186 2.47471
\(27\) −1.34473 −0.258793
\(28\) −6.10856 −1.15441
\(29\) −6.92080 −1.28516 −0.642580 0.766219i \(-0.722136\pi\)
−0.642580 + 0.766219i \(0.722136\pi\)
\(30\) 0.748010 0.136567
\(31\) 1.56426 0.280949 0.140474 0.990084i \(-0.455137\pi\)
0.140474 + 0.990084i \(0.455137\pi\)
\(32\) −3.67004 −0.648778
\(33\) −0.230902 −0.0401949
\(34\) −2.51719 −0.431694
\(35\) 1.85191 0.313030
\(36\) −12.7871 −2.13119
\(37\) −4.13201 −0.679298 −0.339649 0.940552i \(-0.610308\pi\)
−0.339649 + 0.940552i \(0.610308\pi\)
\(38\) 2.39426 0.388401
\(39\) −1.13316 −0.181451
\(40\) 7.73085 1.22235
\(41\) 5.99367 0.936053 0.468027 0.883714i \(-0.344965\pi\)
0.468027 + 0.883714i \(0.344965\pi\)
\(42\) 0.801564 0.123684
\(43\) 2.31457 0.352969 0.176484 0.984303i \(-0.443528\pi\)
0.176484 + 0.984303i \(0.443528\pi\)
\(44\) −4.42939 −0.667755
\(45\) 3.87664 0.577895
\(46\) 2.74639 0.404933
\(47\) −3.40367 −0.496476 −0.248238 0.968699i \(-0.579851\pi\)
−0.248238 + 0.968699i \(0.579851\pi\)
\(48\) 1.38577 0.200018
\(49\) −5.01550 −0.716500
\(50\) 8.23578 1.16471
\(51\) 0.226046 0.0316528
\(52\) −21.7374 −3.01443
\(53\) −7.12979 −0.979352 −0.489676 0.871904i \(-0.662885\pi\)
−0.489676 + 0.871904i \(0.662885\pi\)
\(54\) 3.38493 0.460631
\(55\) 1.34284 0.181069
\(56\) 8.28434 1.10704
\(57\) −0.215007 −0.0284784
\(58\) 17.4209 2.28748
\(59\) −8.87087 −1.15489 −0.577444 0.816430i \(-0.695950\pi\)
−0.577444 + 0.816430i \(0.695950\pi\)
\(60\) −1.28856 −0.166352
\(61\) 5.70622 0.730606 0.365303 0.930889i \(-0.380965\pi\)
0.365303 + 0.930889i \(0.380965\pi\)
\(62\) −3.93753 −0.500067
\(63\) 4.15419 0.523379
\(64\) −3.02274 −0.377842
\(65\) 6.59006 0.817397
\(66\) 0.581224 0.0715437
\(67\) −4.65124 −0.568239 −0.284119 0.958789i \(-0.591701\pi\)
−0.284119 + 0.958789i \(0.591701\pi\)
\(68\) 4.33623 0.525846
\(69\) −0.246629 −0.0296906
\(70\) −4.66161 −0.557169
\(71\) −7.50941 −0.891203 −0.445601 0.895232i \(-0.647010\pi\)
−0.445601 + 0.895232i \(0.647010\pi\)
\(72\) 17.3417 2.04374
\(73\) −16.3112 −1.90908 −0.954541 0.298079i \(-0.903654\pi\)
−0.954541 + 0.298079i \(0.903654\pi\)
\(74\) 10.4010 1.20910
\(75\) −0.739582 −0.0853995
\(76\) −4.12448 −0.473110
\(77\) 1.43899 0.163988
\(78\) 2.85238 0.322968
\(79\) −12.2566 −1.37898 −0.689489 0.724296i \(-0.742165\pi\)
−0.689489 + 0.724296i \(0.742165\pi\)
\(80\) −8.05913 −0.901038
\(81\) 8.54274 0.949193
\(82\) −15.0872 −1.66610
\(83\) −0.783044 −0.0859503 −0.0429751 0.999076i \(-0.513684\pi\)
−0.0429751 + 0.999076i \(0.513684\pi\)
\(84\) −1.38082 −0.150659
\(85\) −1.31460 −0.142589
\(86\) −5.82621 −0.628256
\(87\) −1.56442 −0.167723
\(88\) 6.00707 0.640356
\(89\) −6.64570 −0.704443 −0.352221 0.935917i \(-0.614574\pi\)
−0.352221 + 0.935917i \(0.614574\pi\)
\(90\) −9.75823 −1.02861
\(91\) 7.06188 0.740286
\(92\) −4.73107 −0.493248
\(93\) 0.353594 0.0366660
\(94\) 8.56767 0.883687
\(95\) 1.25041 0.128289
\(96\) −0.829599 −0.0846706
\(97\) −1.92941 −0.195902 −0.0979510 0.995191i \(-0.531229\pi\)
−0.0979510 + 0.995191i \(0.531229\pi\)
\(98\) 12.6250 1.27531
\(99\) 3.01225 0.302743
\(100\) −14.1874 −1.41874
\(101\) −4.24603 −0.422495 −0.211248 0.977433i \(-0.567753\pi\)
−0.211248 + 0.977433i \(0.567753\pi\)
\(102\) −0.569001 −0.0563394
\(103\) −18.4570 −1.81862 −0.909311 0.416117i \(-0.863391\pi\)
−0.909311 + 0.416117i \(0.863391\pi\)
\(104\) 29.4800 2.89075
\(105\) 0.418618 0.0408529
\(106\) 17.9470 1.74317
\(107\) 5.69734 0.550783 0.275391 0.961332i \(-0.411193\pi\)
0.275391 + 0.961332i \(0.411193\pi\)
\(108\) −5.83105 −0.561093
\(109\) 2.42033 0.231826 0.115913 0.993259i \(-0.463021\pi\)
0.115913 + 0.993259i \(0.463021\pi\)
\(110\) −3.38019 −0.322289
\(111\) −0.934025 −0.0886537
\(112\) −8.63613 −0.816037
\(113\) 5.43135 0.510939 0.255469 0.966817i \(-0.417770\pi\)
0.255469 + 0.966817i \(0.417770\pi\)
\(114\) 0.541214 0.0506893
\(115\) 1.43430 0.133750
\(116\) −30.0102 −2.78638
\(117\) 14.7828 1.36667
\(118\) 22.3296 2.05561
\(119\) −1.40872 −0.129137
\(120\) 1.74753 0.159527
\(121\) −9.95657 −0.905143
\(122\) −14.3636 −1.30042
\(123\) 1.35485 0.122162
\(124\) 6.78299 0.609130
\(125\) 10.8742 0.972615
\(126\) −10.4569 −0.931572
\(127\) 7.45605 0.661617 0.330809 0.943698i \(-0.392679\pi\)
0.330809 + 0.943698i \(0.392679\pi\)
\(128\) 14.9489 1.32131
\(129\) 0.523200 0.0460652
\(130\) −16.5884 −1.45490
\(131\) −0.160797 −0.0140489 −0.00702445 0.999975i \(-0.502236\pi\)
−0.00702445 + 0.999975i \(0.502236\pi\)
\(132\) −1.00125 −0.0871472
\(133\) 1.33993 0.116187
\(134\) 11.7080 1.01142
\(135\) 1.76778 0.152146
\(136\) −5.88074 −0.504269
\(137\) −8.37661 −0.715662 −0.357831 0.933786i \(-0.616484\pi\)
−0.357831 + 0.933786i \(0.616484\pi\)
\(138\) 0.620810 0.0528469
\(139\) −15.5989 −1.32308 −0.661541 0.749909i \(-0.730097\pi\)
−0.661541 + 0.749909i \(0.730097\pi\)
\(140\) 8.03033 0.678687
\(141\) −0.769385 −0.0647939
\(142\) 18.9026 1.58627
\(143\) 5.12066 0.428211
\(144\) −18.0781 −1.50651
\(145\) 9.09811 0.755557
\(146\) 41.0584 3.39802
\(147\) −1.13373 −0.0935088
\(148\) −17.9174 −1.47280
\(149\) 13.5055 1.10641 0.553207 0.833044i \(-0.313404\pi\)
0.553207 + 0.833044i \(0.313404\pi\)
\(150\) 1.86167 0.152004
\(151\) 10.1311 0.824459 0.412229 0.911080i \(-0.364750\pi\)
0.412229 + 0.911080i \(0.364750\pi\)
\(152\) 5.59356 0.453698
\(153\) −2.94890 −0.238405
\(154\) −3.62220 −0.291885
\(155\) −2.05638 −0.165172
\(156\) −4.91365 −0.393407
\(157\) −1.25996 −0.100556 −0.0502778 0.998735i \(-0.516011\pi\)
−0.0502778 + 0.998735i \(0.516011\pi\)
\(158\) 30.8522 2.45447
\(159\) −1.61166 −0.127813
\(160\) 4.82465 0.381422
\(161\) 1.53699 0.121132
\(162\) −21.5037 −1.68949
\(163\) −11.5435 −0.904159 −0.452079 0.891978i \(-0.649318\pi\)
−0.452079 + 0.891978i \(0.649318\pi\)
\(164\) 25.9899 2.02947
\(165\) 0.303545 0.0236309
\(166\) 1.97107 0.152985
\(167\) −22.9962 −1.77950 −0.889750 0.456448i \(-0.849121\pi\)
−0.889750 + 0.456448i \(0.849121\pi\)
\(168\) 1.87264 0.144478
\(169\) 12.1298 0.933064
\(170\) 3.30910 0.253797
\(171\) 2.80490 0.214496
\(172\) 10.0365 0.765278
\(173\) 21.1518 1.60814 0.804071 0.594533i \(-0.202663\pi\)
0.804071 + 0.594533i \(0.202663\pi\)
\(174\) 3.93794 0.298534
\(175\) 4.60909 0.348414
\(176\) −6.26216 −0.472028
\(177\) −2.00523 −0.150722
\(178\) 16.7285 1.25385
\(179\) 22.2942 1.66635 0.833174 0.553011i \(-0.186521\pi\)
0.833174 + 0.553011i \(0.186521\pi\)
\(180\) 16.8100 1.25294
\(181\) 21.4779 1.59644 0.798220 0.602366i \(-0.205775\pi\)
0.798220 + 0.602366i \(0.205775\pi\)
\(182\) −17.7761 −1.31765
\(183\) 1.28987 0.0953498
\(184\) 6.41621 0.473009
\(185\) 5.43196 0.399365
\(186\) −0.890063 −0.0652626
\(187\) −1.02148 −0.0746982
\(188\) −14.7591 −1.07642
\(189\) 1.89435 0.137794
\(190\) −3.14751 −0.228344
\(191\) 15.4949 1.12117 0.560585 0.828097i \(-0.310576\pi\)
0.560585 + 0.828097i \(0.310576\pi\)
\(192\) −0.683278 −0.0493113
\(193\) −1.53595 −0.110560 −0.0552802 0.998471i \(-0.517605\pi\)
−0.0552802 + 0.998471i \(0.517605\pi\)
\(194\) 4.85669 0.348690
\(195\) 1.48966 0.106677
\(196\) −21.7484 −1.55346
\(197\) −13.3486 −0.951051 −0.475525 0.879702i \(-0.657742\pi\)
−0.475525 + 0.879702i \(0.657742\pi\)
\(198\) −7.58240 −0.538858
\(199\) −15.4734 −1.09688 −0.548439 0.836190i \(-0.684778\pi\)
−0.548439 + 0.836190i \(0.684778\pi\)
\(200\) 19.2407 1.36052
\(201\) −1.05139 −0.0741596
\(202\) 10.6880 0.752008
\(203\) 9.74949 0.684280
\(204\) 0.980189 0.0686270
\(205\) −7.87930 −0.550314
\(206\) 46.4597 3.23700
\(207\) 3.21741 0.223626
\(208\) −30.7318 −2.13087
\(209\) 0.971599 0.0672069
\(210\) −1.05374 −0.0727149
\(211\) −11.1948 −0.770684 −0.385342 0.922774i \(-0.625917\pi\)
−0.385342 + 0.922774i \(0.625917\pi\)
\(212\) −30.9165 −2.12335
\(213\) −1.69747 −0.116309
\(214\) −14.3413 −0.980350
\(215\) −3.04274 −0.207513
\(216\) 7.90799 0.538071
\(217\) −2.20361 −0.149591
\(218\) −6.09243 −0.412632
\(219\) −3.68709 −0.249150
\(220\) 5.82289 0.392579
\(221\) −5.01297 −0.337209
\(222\) 2.35112 0.157797
\(223\) −4.05908 −0.271816 −0.135908 0.990721i \(-0.543395\pi\)
−0.135908 + 0.990721i \(0.543395\pi\)
\(224\) 5.17008 0.345440
\(225\) 9.64827 0.643218
\(226\) −13.6717 −0.909430
\(227\) −16.0124 −1.06278 −0.531390 0.847127i \(-0.678330\pi\)
−0.531390 + 0.847127i \(0.678330\pi\)
\(228\) −0.932323 −0.0617446
\(229\) 11.8656 0.784099 0.392050 0.919944i \(-0.371766\pi\)
0.392050 + 0.919944i \(0.371766\pi\)
\(230\) −3.61041 −0.238064
\(231\) 0.325277 0.0214017
\(232\) 40.6994 2.67205
\(233\) 12.3850 0.811369 0.405685 0.914013i \(-0.367033\pi\)
0.405685 + 0.914013i \(0.367033\pi\)
\(234\) −37.2110 −2.43256
\(235\) 4.47447 0.291882
\(236\) −38.4662 −2.50393
\(237\) −2.77056 −0.179967
\(238\) 3.54602 0.229854
\(239\) 7.73043 0.500040 0.250020 0.968241i \(-0.419563\pi\)
0.250020 + 0.968241i \(0.419563\pi\)
\(240\) −1.82174 −0.117592
\(241\) −7.99939 −0.515286 −0.257643 0.966240i \(-0.582946\pi\)
−0.257643 + 0.966240i \(0.582946\pi\)
\(242\) 25.0626 1.61108
\(243\) 5.96523 0.382670
\(244\) 24.7435 1.58404
\(245\) 6.59339 0.421236
\(246\) −3.41040 −0.217439
\(247\) 4.76816 0.303391
\(248\) −9.19900 −0.584137
\(249\) −0.177004 −0.0112172
\(250\) −27.3723 −1.73118
\(251\) 12.2332 0.772154 0.386077 0.922467i \(-0.373830\pi\)
0.386077 + 0.922467i \(0.373830\pi\)
\(252\) 18.0135 1.13475
\(253\) 1.11449 0.0700675
\(254\) −18.7683 −1.17763
\(255\) −0.297161 −0.0186089
\(256\) −31.5837 −1.97398
\(257\) 4.04582 0.252371 0.126186 0.992007i \(-0.459727\pi\)
0.126186 + 0.992007i \(0.459727\pi\)
\(258\) −1.31699 −0.0819923
\(259\) 5.82086 0.361691
\(260\) 28.5761 1.77221
\(261\) 20.4088 1.26327
\(262\) 0.404756 0.0250059
\(263\) −8.36439 −0.515770 −0.257885 0.966176i \(-0.583026\pi\)
−0.257885 + 0.966176i \(0.583026\pi\)
\(264\) 1.35788 0.0835715
\(265\) 9.37285 0.575770
\(266\) −3.37286 −0.206803
\(267\) −1.50223 −0.0919352
\(268\) −20.1689 −1.23201
\(269\) −7.96237 −0.485474 −0.242737 0.970092i \(-0.578045\pi\)
−0.242737 + 0.970092i \(0.578045\pi\)
\(270\) −4.44984 −0.270809
\(271\) 13.6117 0.826851 0.413426 0.910538i \(-0.364332\pi\)
0.413426 + 0.910538i \(0.364332\pi\)
\(272\) 6.13046 0.371714
\(273\) 1.59631 0.0966131
\(274\) 21.0855 1.27382
\(275\) 3.34210 0.201536
\(276\) −1.06944 −0.0643727
\(277\) −32.6275 −1.96039 −0.980197 0.198023i \(-0.936548\pi\)
−0.980197 + 0.198023i \(0.936548\pi\)
\(278\) 39.2654 2.35498
\(279\) −4.61284 −0.276164
\(280\) −10.8906 −0.650839
\(281\) 6.39414 0.381442 0.190721 0.981644i \(-0.438917\pi\)
0.190721 + 0.981644i \(0.438917\pi\)
\(282\) 1.93669 0.115328
\(283\) −14.4517 −0.859062 −0.429531 0.903052i \(-0.641321\pi\)
−0.429531 + 0.903052i \(0.641321\pi\)
\(284\) −32.5626 −1.93223
\(285\) 0.282650 0.0167427
\(286\) −12.8897 −0.762181
\(287\) −8.44342 −0.498399
\(288\) 10.8226 0.637728
\(289\) 1.00000 0.0588235
\(290\) −22.9016 −1.34483
\(291\) −0.436136 −0.0255667
\(292\) −70.7292 −4.13912
\(293\) 31.1633 1.82058 0.910290 0.413971i \(-0.135858\pi\)
0.910290 + 0.413971i \(0.135858\pi\)
\(294\) 2.85382 0.166438
\(295\) 11.6617 0.678969
\(296\) 24.2993 1.41237
\(297\) 1.37361 0.0797052
\(298\) −33.9959 −1.96933
\(299\) 5.46942 0.316305
\(300\) −3.20700 −0.185156
\(301\) −3.26059 −0.187937
\(302\) −25.5019 −1.46747
\(303\) −0.959798 −0.0551389
\(304\) −5.83109 −0.334436
\(305\) −7.50141 −0.429530
\(306\) 7.42294 0.424341
\(307\) 9.06668 0.517463 0.258731 0.965949i \(-0.416696\pi\)
0.258731 + 0.965949i \(0.416696\pi\)
\(308\) 6.23978 0.355544
\(309\) −4.17213 −0.237344
\(310\) 5.17629 0.293994
\(311\) 2.45790 0.139375 0.0696874 0.997569i \(-0.477800\pi\)
0.0696874 + 0.997569i \(0.477800\pi\)
\(312\) 6.66383 0.377265
\(313\) −13.7705 −0.778355 −0.389178 0.921163i \(-0.627241\pi\)
−0.389178 + 0.921163i \(0.627241\pi\)
\(314\) 3.17155 0.178981
\(315\) −5.46111 −0.307699
\(316\) −53.1476 −2.98979
\(317\) −12.0510 −0.676851 −0.338425 0.940993i \(-0.609894\pi\)
−0.338425 + 0.940993i \(0.609894\pi\)
\(318\) 4.05686 0.227497
\(319\) 7.06947 0.395814
\(320\) 3.97370 0.222137
\(321\) 1.28786 0.0718814
\(322\) −3.86890 −0.215605
\(323\) −0.951166 −0.0529243
\(324\) 37.0433 2.05796
\(325\) 16.4015 0.909792
\(326\) 29.0572 1.60933
\(327\) 0.547107 0.0302551
\(328\) −35.2472 −1.94620
\(329\) 4.79482 0.264347
\(330\) −0.764079 −0.0420612
\(331\) −28.7869 −1.58227 −0.791135 0.611642i \(-0.790509\pi\)
−0.791135 + 0.611642i \(0.790509\pi\)
\(332\) −3.39546 −0.186350
\(333\) 12.1849 0.667728
\(334\) 57.8858 3.16737
\(335\) 6.11453 0.334073
\(336\) −1.95216 −0.106499
\(337\) 3.11784 0.169840 0.0849199 0.996388i \(-0.472937\pi\)
0.0849199 + 0.996388i \(0.472937\pi\)
\(338\) −30.5331 −1.66078
\(339\) 1.22774 0.0666815
\(340\) −5.70043 −0.309149
\(341\) −1.59786 −0.0865290
\(342\) −7.06045 −0.381786
\(343\) 16.9265 0.913946
\(344\) −13.6114 −0.733877
\(345\) 0.324219 0.0174554
\(346\) −53.2431 −2.86237
\(347\) −8.66605 −0.465218 −0.232609 0.972570i \(-0.574726\pi\)
−0.232609 + 0.972570i \(0.574726\pi\)
\(348\) −6.78369 −0.363644
\(349\) 15.1240 0.809568 0.404784 0.914412i \(-0.367347\pi\)
0.404784 + 0.914412i \(0.367347\pi\)
\(350\) −11.6019 −0.620149
\(351\) 6.74107 0.359812
\(352\) 3.74888 0.199816
\(353\) −1.00000 −0.0532246
\(354\) 5.04753 0.268273
\(355\) 9.87189 0.523946
\(356\) −28.8173 −1.52731
\(357\) −0.318436 −0.0168534
\(358\) −56.1187 −2.96597
\(359\) 14.4053 0.760285 0.380142 0.924928i \(-0.375875\pi\)
0.380142 + 0.924928i \(0.375875\pi\)
\(360\) −22.7975 −1.20153
\(361\) −18.0953 −0.952383
\(362\) −54.0639 −2.84154
\(363\) −2.25064 −0.118128
\(364\) 30.6220 1.60503
\(365\) 21.4428 1.12237
\(366\) −3.24684 −0.169715
\(367\) 18.8529 0.984112 0.492056 0.870563i \(-0.336245\pi\)
0.492056 + 0.870563i \(0.336245\pi\)
\(368\) −6.68867 −0.348671
\(369\) −17.6747 −0.920110
\(370\) −13.6733 −0.710839
\(371\) 10.0439 0.521454
\(372\) 1.53327 0.0794963
\(373\) −29.4885 −1.52685 −0.763427 0.645894i \(-0.776485\pi\)
−0.763427 + 0.645894i \(0.776485\pi\)
\(374\) 2.57126 0.132957
\(375\) 2.45806 0.126934
\(376\) 20.0161 1.03225
\(377\) 34.6937 1.78682
\(378\) −4.76843 −0.245261
\(379\) −7.47070 −0.383744 −0.191872 0.981420i \(-0.561456\pi\)
−0.191872 + 0.981420i \(0.561456\pi\)
\(380\) 5.42206 0.278146
\(381\) 1.68541 0.0863462
\(382\) −39.0035 −1.99559
\(383\) −9.42889 −0.481794 −0.240897 0.970551i \(-0.577442\pi\)
−0.240897 + 0.970551i \(0.577442\pi\)
\(384\) 3.37914 0.172441
\(385\) −1.89170 −0.0964097
\(386\) 3.86628 0.196789
\(387\) −6.82544 −0.346957
\(388\) −8.36638 −0.424739
\(389\) −25.6280 −1.29939 −0.649696 0.760194i \(-0.725104\pi\)
−0.649696 + 0.760194i \(0.725104\pi\)
\(390\) −3.74975 −0.189876
\(391\) −1.09105 −0.0551770
\(392\) 29.4949 1.48972
\(393\) −0.0363475 −0.00183349
\(394\) 33.6010 1.69279
\(395\) 16.1126 0.810713
\(396\) 13.0618 0.656382
\(397\) 5.64709 0.283419 0.141710 0.989908i \(-0.454740\pi\)
0.141710 + 0.989908i \(0.454740\pi\)
\(398\) 38.9494 1.95236
\(399\) 0.302886 0.0151633
\(400\) −20.0578 −1.00289
\(401\) 16.0817 0.803084 0.401542 0.915841i \(-0.368474\pi\)
0.401542 + 0.915841i \(0.368474\pi\)
\(402\) 2.64656 0.131998
\(403\) −7.84157 −0.390616
\(404\) −18.4118 −0.916020
\(405\) −11.2303 −0.558039
\(406\) −24.5413 −1.21796
\(407\) 4.22077 0.209216
\(408\) −1.32932 −0.0658111
\(409\) −25.8404 −1.27773 −0.638864 0.769320i \(-0.720595\pi\)
−0.638864 + 0.769320i \(0.720595\pi\)
\(410\) 19.8337 0.979515
\(411\) −1.89350 −0.0933995
\(412\) −80.0339 −3.94299
\(413\) 12.4966 0.614917
\(414\) −8.09883 −0.398036
\(415\) 1.02939 0.0505309
\(416\) 18.3978 0.902027
\(417\) −3.52607 −0.172673
\(418\) −2.44570 −0.119623
\(419\) 15.6134 0.762764 0.381382 0.924418i \(-0.375448\pi\)
0.381382 + 0.924418i \(0.375448\pi\)
\(420\) 1.81522 0.0885739
\(421\) 27.8087 1.35531 0.677657 0.735378i \(-0.262996\pi\)
0.677657 + 0.735378i \(0.262996\pi\)
\(422\) 28.1795 1.37176
\(423\) 10.0371 0.488020
\(424\) 41.9285 2.03623
\(425\) −3.27182 −0.158706
\(426\) 4.27286 0.207021
\(427\) −8.03848 −0.389009
\(428\) 24.7050 1.19416
\(429\) 1.15750 0.0558848
\(430\) 7.65916 0.369357
\(431\) 10.1001 0.486503 0.243251 0.969963i \(-0.421786\pi\)
0.243251 + 0.969963i \(0.421786\pi\)
\(432\) −8.24380 −0.396630
\(433\) 9.55758 0.459308 0.229654 0.973272i \(-0.426241\pi\)
0.229654 + 0.973272i \(0.426241\pi\)
\(434\) 5.54689 0.266259
\(435\) 2.05659 0.0986060
\(436\) 10.4951 0.502626
\(437\) 1.03777 0.0496435
\(438\) 9.28109 0.443467
\(439\) −35.8363 −1.71037 −0.855186 0.518321i \(-0.826557\pi\)
−0.855186 + 0.518321i \(0.826557\pi\)
\(440\) −7.89692 −0.376471
\(441\) 14.7902 0.704296
\(442\) 12.6186 0.600205
\(443\) −18.8100 −0.893689 −0.446844 0.894612i \(-0.647452\pi\)
−0.446844 + 0.894612i \(0.647452\pi\)
\(444\) −4.05015 −0.192212
\(445\) 8.73646 0.414148
\(446\) 10.2175 0.483811
\(447\) 3.05286 0.144396
\(448\) 4.25820 0.201181
\(449\) 6.28119 0.296428 0.148214 0.988955i \(-0.452648\pi\)
0.148214 + 0.988955i \(0.452648\pi\)
\(450\) −24.2865 −1.14488
\(451\) −6.12242 −0.288294
\(452\) 23.5516 1.10778
\(453\) 2.29010 0.107598
\(454\) 40.3062 1.89167
\(455\) −9.28358 −0.435221
\(456\) 1.26440 0.0592111
\(457\) −2.01982 −0.0944831 −0.0472415 0.998883i \(-0.515043\pi\)
−0.0472415 + 0.998883i \(0.515043\pi\)
\(458\) −29.8679 −1.39563
\(459\) −1.34473 −0.0627665
\(460\) 6.21948 0.289985
\(461\) 12.4472 0.579725 0.289862 0.957068i \(-0.406390\pi\)
0.289862 + 0.957068i \(0.406390\pi\)
\(462\) −0.818784 −0.0380933
\(463\) 26.2053 1.21786 0.608931 0.793223i \(-0.291598\pi\)
0.608931 + 0.793223i \(0.291598\pi\)
\(464\) −42.4277 −1.96966
\(465\) −0.464836 −0.0215563
\(466\) −31.1754 −1.44417
\(467\) −17.0538 −0.789156 −0.394578 0.918862i \(-0.629109\pi\)
−0.394578 + 0.918862i \(0.629109\pi\)
\(468\) 64.1015 2.96309
\(469\) 6.55231 0.302557
\(470\) −11.2631 −0.519527
\(471\) −0.284809 −0.0131233
\(472\) 52.1673 2.40119
\(473\) −2.36429 −0.108710
\(474\) 6.97403 0.320328
\(475\) 3.11204 0.142790
\(476\) −6.10856 −0.279985
\(477\) 21.0251 0.962672
\(478\) −19.4590 −0.890032
\(479\) 6.48745 0.296419 0.148210 0.988956i \(-0.452649\pi\)
0.148210 + 0.988956i \(0.452649\pi\)
\(480\) 1.09059 0.0497786
\(481\) 20.7136 0.944460
\(482\) 20.1360 0.917168
\(483\) 0.347431 0.0158087
\(484\) −43.1740 −1.96246
\(485\) 2.53641 0.115173
\(486\) −15.0156 −0.681122
\(487\) 10.4743 0.474634 0.237317 0.971432i \(-0.423732\pi\)
0.237317 + 0.971432i \(0.423732\pi\)
\(488\) −33.5568 −1.51904
\(489\) −2.60937 −0.118000
\(490\) −16.5968 −0.749767
\(491\) −33.8748 −1.52875 −0.764375 0.644772i \(-0.776952\pi\)
−0.764375 + 0.644772i \(0.776952\pi\)
\(492\) 5.87493 0.264862
\(493\) −6.92080 −0.311697
\(494\) −12.0024 −0.540012
\(495\) −3.95992 −0.177985
\(496\) 9.58963 0.430587
\(497\) 10.5787 0.474519
\(498\) 0.445553 0.0199657
\(499\) 15.7015 0.702896 0.351448 0.936207i \(-0.385689\pi\)
0.351448 + 0.936207i \(0.385689\pi\)
\(500\) 47.1529 2.10874
\(501\) −5.19820 −0.232239
\(502\) −30.7933 −1.37437
\(503\) 3.86430 0.172300 0.0861502 0.996282i \(-0.472543\pi\)
0.0861502 + 0.996282i \(0.472543\pi\)
\(504\) −24.4297 −1.08819
\(505\) 5.58184 0.248389
\(506\) −2.80539 −0.124715
\(507\) 2.74190 0.121772
\(508\) 32.3312 1.43446
\(509\) 34.2055 1.51613 0.758065 0.652179i \(-0.226145\pi\)
0.758065 + 0.652179i \(0.226145\pi\)
\(510\) 0.748010 0.0331224
\(511\) 22.9780 1.01649
\(512\) 49.6043 2.19222
\(513\) 1.27906 0.0564718
\(514\) −10.1841 −0.449201
\(515\) 24.2636 1.06918
\(516\) 2.26872 0.0998747
\(517\) 3.47678 0.152909
\(518\) −14.6522 −0.643780
\(519\) 4.78129 0.209875
\(520\) −38.7545 −1.69950
\(521\) 33.6971 1.47629 0.738147 0.674640i \(-0.235701\pi\)
0.738147 + 0.674640i \(0.235701\pi\)
\(522\) −51.3727 −2.24852
\(523\) −25.8606 −1.13080 −0.565402 0.824815i \(-0.691279\pi\)
−0.565402 + 0.824815i \(0.691279\pi\)
\(524\) −0.697253 −0.0304597
\(525\) 1.04187 0.0454707
\(526\) 21.0547 0.918030
\(527\) 1.56426 0.0681401
\(528\) −1.41554 −0.0616033
\(529\) −21.8096 −0.948244
\(530\) −23.5932 −1.02482
\(531\) 26.1593 1.13522
\(532\) 5.81025 0.251906
\(533\) −30.0460 −1.30144
\(534\) 3.78141 0.163637
\(535\) −7.48975 −0.323810
\(536\) 27.3527 1.18146
\(537\) 5.03952 0.217471
\(538\) 20.0428 0.864105
\(539\) 5.12324 0.220674
\(540\) 7.66552 0.329871
\(541\) −3.66888 −0.157737 −0.0788686 0.996885i \(-0.525131\pi\)
−0.0788686 + 0.996885i \(0.525131\pi\)
\(542\) −34.2632 −1.47173
\(543\) 4.85500 0.208348
\(544\) −3.67004 −0.157352
\(545\) −3.18178 −0.136292
\(546\) −4.01821 −0.171964
\(547\) −23.6004 −1.00908 −0.504539 0.863389i \(-0.668338\pi\)
−0.504539 + 0.863389i \(0.668338\pi\)
\(548\) −36.3230 −1.55164
\(549\) −16.8271 −0.718162
\(550\) −8.41270 −0.358719
\(551\) 6.58283 0.280438
\(552\) 1.45036 0.0617314
\(553\) 17.2662 0.734233
\(554\) 82.1295 3.48935
\(555\) 1.22787 0.0521203
\(556\) −67.6405 −2.86860
\(557\) −43.4823 −1.84241 −0.921203 0.389083i \(-0.872792\pi\)
−0.921203 + 0.389083i \(0.872792\pi\)
\(558\) 11.6114 0.491550
\(559\) −11.6029 −0.490749
\(560\) 11.3531 0.479755
\(561\) −0.230902 −0.00974869
\(562\) −16.0953 −0.678937
\(563\) −9.00718 −0.379607 −0.189804 0.981822i \(-0.560785\pi\)
−0.189804 + 0.981822i \(0.560785\pi\)
\(564\) −3.33624 −0.140481
\(565\) −7.14008 −0.300385
\(566\) 36.3776 1.52906
\(567\) −12.0344 −0.505395
\(568\) 44.1609 1.85295
\(569\) −0.164297 −0.00688770 −0.00344385 0.999994i \(-0.501096\pi\)
−0.00344385 + 0.999994i \(0.501096\pi\)
\(570\) −0.711482 −0.0298007
\(571\) 19.3848 0.811227 0.405614 0.914045i \(-0.367058\pi\)
0.405614 + 0.914045i \(0.367058\pi\)
\(572\) 22.2044 0.928411
\(573\) 3.50256 0.146321
\(574\) 21.2537 0.887111
\(575\) 3.56973 0.148868
\(576\) 8.91376 0.371407
\(577\) 6.27380 0.261182 0.130591 0.991436i \(-0.458313\pi\)
0.130591 + 0.991436i \(0.458313\pi\)
\(578\) −2.51719 −0.104701
\(579\) −0.347196 −0.0144290
\(580\) 39.4515 1.63814
\(581\) 1.10309 0.0457640
\(582\) 1.09784 0.0455068
\(583\) 7.28295 0.301629
\(584\) 95.9220 3.96928
\(585\) −19.4335 −0.803475
\(586\) −78.4439 −3.24049
\(587\) 11.9381 0.492738 0.246369 0.969176i \(-0.420762\pi\)
0.246369 + 0.969176i \(0.420762\pi\)
\(588\) −4.91614 −0.202738
\(589\) −1.48787 −0.0613066
\(590\) −29.3546 −1.20851
\(591\) −3.01741 −0.124120
\(592\) −25.3311 −1.04110
\(593\) −8.12303 −0.333573 −0.166786 0.985993i \(-0.553339\pi\)
−0.166786 + 0.985993i \(0.553339\pi\)
\(594\) −3.45764 −0.141869
\(595\) 1.85191 0.0759210
\(596\) 58.5630 2.39883
\(597\) −3.49770 −0.143151
\(598\) −13.7676 −0.562997
\(599\) −5.04744 −0.206233 −0.103116 0.994669i \(-0.532881\pi\)
−0.103116 + 0.994669i \(0.532881\pi\)
\(600\) 4.34929 0.177559
\(601\) −5.72672 −0.233598 −0.116799 0.993156i \(-0.537263\pi\)
−0.116799 + 0.993156i \(0.537263\pi\)
\(602\) 8.20752 0.334513
\(603\) 13.7160 0.558561
\(604\) 43.9309 1.78752
\(605\) 13.0889 0.532141
\(606\) 2.41599 0.0981429
\(607\) 24.9072 1.01095 0.505476 0.862841i \(-0.331317\pi\)
0.505476 + 0.862841i \(0.331317\pi\)
\(608\) 3.49082 0.141572
\(609\) 2.20383 0.0893039
\(610\) 18.8825 0.764529
\(611\) 17.0625 0.690273
\(612\) −12.7871 −0.516889
\(613\) −7.54483 −0.304733 −0.152366 0.988324i \(-0.548689\pi\)
−0.152366 + 0.988324i \(0.548689\pi\)
\(614\) −22.8225 −0.921042
\(615\) −1.78108 −0.0718202
\(616\) −8.46230 −0.340956
\(617\) 19.3009 0.777024 0.388512 0.921444i \(-0.372989\pi\)
0.388512 + 0.921444i \(0.372989\pi\)
\(618\) 10.5020 0.422454
\(619\) 29.1962 1.17350 0.586748 0.809770i \(-0.300408\pi\)
0.586748 + 0.809770i \(0.300408\pi\)
\(620\) −8.91694 −0.358113
\(621\) 1.46717 0.0588755
\(622\) −6.18700 −0.248076
\(623\) 9.36195 0.375079
\(624\) −6.94681 −0.278095
\(625\) 2.06387 0.0825549
\(626\) 34.6630 1.38541
\(627\) 0.219626 0.00877103
\(628\) −5.46348 −0.218016
\(629\) −4.13201 −0.164754
\(630\) 13.7466 0.547679
\(631\) 30.3443 1.20799 0.603993 0.796990i \(-0.293575\pi\)
0.603993 + 0.796990i \(0.293575\pi\)
\(632\) 72.0781 2.86711
\(633\) −2.53055 −0.100580
\(634\) 30.3346 1.20474
\(635\) −9.80175 −0.388970
\(636\) −6.98854 −0.277114
\(637\) 25.1425 0.996183
\(638\) −17.7952 −0.704518
\(639\) 22.1445 0.876023
\(640\) −19.6519 −0.776808
\(641\) 4.53817 0.179247 0.0896235 0.995976i \(-0.471434\pi\)
0.0896235 + 0.995976i \(0.471434\pi\)
\(642\) −3.24179 −0.127943
\(643\) −41.7656 −1.64707 −0.823536 0.567263i \(-0.808002\pi\)
−0.823536 + 0.567263i \(0.808002\pi\)
\(644\) 6.66477 0.262629
\(645\) −0.687800 −0.0270821
\(646\) 2.39426 0.0942010
\(647\) 45.1787 1.77616 0.888079 0.459692i \(-0.152040\pi\)
0.888079 + 0.459692i \(0.152040\pi\)
\(648\) −50.2376 −1.97352
\(649\) 9.06143 0.355692
\(650\) −41.2857 −1.61936
\(651\) −0.498117 −0.0195227
\(652\) −50.0554 −1.96032
\(653\) 2.04722 0.0801138 0.0400569 0.999197i \(-0.487246\pi\)
0.0400569 + 0.999197i \(0.487246\pi\)
\(654\) −1.37717 −0.0538516
\(655\) 0.211384 0.00825947
\(656\) 36.7440 1.43461
\(657\) 48.1002 1.87657
\(658\) −12.0695 −0.470517
\(659\) 27.6716 1.07793 0.538966 0.842328i \(-0.318815\pi\)
0.538966 + 0.842328i \(0.318815\pi\)
\(660\) 1.31624 0.0512346
\(661\) −19.2316 −0.748022 −0.374011 0.927424i \(-0.622018\pi\)
−0.374011 + 0.927424i \(0.622018\pi\)
\(662\) 72.4620 2.81631
\(663\) −1.13316 −0.0440083
\(664\) 4.60488 0.178704
\(665\) −1.76148 −0.0683071
\(666\) −30.6717 −1.18850
\(667\) 7.55097 0.292375
\(668\) −99.7169 −3.85816
\(669\) −0.917539 −0.0354741
\(670\) −15.3914 −0.594623
\(671\) −5.82880 −0.225018
\(672\) 1.16868 0.0450826
\(673\) 2.10297 0.0810635 0.0405317 0.999178i \(-0.487095\pi\)
0.0405317 + 0.999178i \(0.487095\pi\)
\(674\) −7.84820 −0.302301
\(675\) 4.39970 0.169344
\(676\) 52.5978 2.02299
\(677\) −5.72501 −0.220030 −0.110015 0.993930i \(-0.535090\pi\)
−0.110015 + 0.993930i \(0.535090\pi\)
\(678\) −3.09044 −0.118688
\(679\) 2.71801 0.104308
\(680\) 7.73085 0.296464
\(681\) −3.61954 −0.138701
\(682\) 4.02212 0.154015
\(683\) 20.2773 0.775891 0.387945 0.921682i \(-0.373185\pi\)
0.387945 + 0.921682i \(0.373185\pi\)
\(684\) 12.1627 0.465052
\(685\) 11.0119 0.420744
\(686\) −42.6072 −1.62675
\(687\) 2.68217 0.102331
\(688\) 14.1894 0.540965
\(689\) 35.7414 1.36164
\(690\) −0.816120 −0.0310691
\(691\) 12.8820 0.490053 0.245027 0.969516i \(-0.421203\pi\)
0.245027 + 0.969516i \(0.421203\pi\)
\(692\) 91.7193 3.48664
\(693\) −4.24343 −0.161195
\(694\) 21.8141 0.828051
\(695\) 20.5064 0.777852
\(696\) 9.19995 0.348723
\(697\) 5.99367 0.227026
\(698\) −38.0699 −1.44097
\(699\) 2.79958 0.105890
\(700\) 19.9861 0.755403
\(701\) 4.33328 0.163666 0.0818328 0.996646i \(-0.473923\pi\)
0.0818328 + 0.996646i \(0.473923\pi\)
\(702\) −16.9685 −0.640436
\(703\) 3.93023 0.148231
\(704\) 3.08767 0.116371
\(705\) 1.01144 0.0380929
\(706\) 2.51719 0.0947356
\(707\) 5.98148 0.224957
\(708\) −8.69513 −0.326783
\(709\) 15.3229 0.575465 0.287733 0.957711i \(-0.407099\pi\)
0.287733 + 0.957711i \(0.407099\pi\)
\(710\) −24.8494 −0.932582
\(711\) 36.1436 1.35549
\(712\) 39.0816 1.46465
\(713\) −1.70669 −0.0639160
\(714\) 0.801564 0.0299978
\(715\) −6.73163 −0.251749
\(716\) 96.6729 3.61284
\(717\) 1.74743 0.0652591
\(718\) −36.2610 −1.35325
\(719\) −42.0079 −1.56663 −0.783316 0.621624i \(-0.786473\pi\)
−0.783316 + 0.621624i \(0.786473\pi\)
\(720\) 23.7656 0.885691
\(721\) 26.0008 0.968320
\(722\) 45.5492 1.69517
\(723\) −1.80823 −0.0672488
\(724\) 93.1332 3.46127
\(725\) 22.6436 0.840962
\(726\) 5.66530 0.210259
\(727\) 17.7469 0.658197 0.329099 0.944296i \(-0.393255\pi\)
0.329099 + 0.944296i \(0.393255\pi\)
\(728\) −41.5291 −1.53917
\(729\) −24.2798 −0.899252
\(730\) −53.9755 −1.99772
\(731\) 2.31457 0.0856075
\(732\) 5.59317 0.206730
\(733\) 5.27157 0.194710 0.0973549 0.995250i \(-0.468962\pi\)
0.0973549 + 0.995250i \(0.468962\pi\)
\(734\) −47.4562 −1.75164
\(735\) 1.49041 0.0549746
\(736\) 4.00422 0.147597
\(737\) 4.75115 0.175011
\(738\) 44.4906 1.63772
\(739\) −10.9566 −0.403044 −0.201522 0.979484i \(-0.564589\pi\)
−0.201522 + 0.979484i \(0.564589\pi\)
\(740\) 23.5542 0.865871
\(741\) 1.07782 0.0395949
\(742\) −25.2824 −0.928146
\(743\) −18.5926 −0.682097 −0.341049 0.940046i \(-0.610782\pi\)
−0.341049 + 0.940046i \(0.610782\pi\)
\(744\) −2.07940 −0.0762344
\(745\) −17.7544 −0.650470
\(746\) 74.2280 2.71768
\(747\) 2.30912 0.0844863
\(748\) −4.42939 −0.161954
\(749\) −8.02598 −0.293263
\(750\) −6.18740 −0.225932
\(751\) −4.73229 −0.172684 −0.0863418 0.996266i \(-0.527518\pi\)
−0.0863418 + 0.996266i \(0.527518\pi\)
\(752\) −20.8660 −0.760907
\(753\) 2.76527 0.100772
\(754\) −87.3306 −3.18039
\(755\) −13.3184 −0.484706
\(756\) 8.21434 0.298753
\(757\) 17.0694 0.620400 0.310200 0.950671i \(-0.399604\pi\)
0.310200 + 0.950671i \(0.399604\pi\)
\(758\) 18.8051 0.683034
\(759\) 0.251927 0.00914436
\(760\) −7.35332 −0.266733
\(761\) 16.6592 0.603896 0.301948 0.953324i \(-0.402363\pi\)
0.301948 + 0.953324i \(0.402363\pi\)
\(762\) −4.24249 −0.153689
\(763\) −3.40958 −0.123435
\(764\) 67.1894 2.43083
\(765\) 3.87664 0.140160
\(766\) 23.7343 0.857555
\(767\) 44.4694 1.60570
\(768\) −7.13937 −0.257620
\(769\) 1.59039 0.0573508 0.0286754 0.999589i \(-0.490871\pi\)
0.0286754 + 0.999589i \(0.490871\pi\)
\(770\) 4.76175 0.171602
\(771\) 0.914541 0.0329364
\(772\) −6.66026 −0.239708
\(773\) −25.4927 −0.916907 −0.458454 0.888718i \(-0.651596\pi\)
−0.458454 + 0.888718i \(0.651596\pi\)
\(774\) 17.1809 0.617556
\(775\) −5.11797 −0.183843
\(776\) 11.3464 0.407311
\(777\) 1.31578 0.0472034
\(778\) 64.5105 2.31281
\(779\) −5.70097 −0.204259
\(780\) 6.45951 0.231288
\(781\) 7.67073 0.274480
\(782\) 2.74639 0.0982107
\(783\) 9.30658 0.332590
\(784\) −30.7473 −1.09812
\(785\) 1.65635 0.0591175
\(786\) 0.0914936 0.00326347
\(787\) −22.2458 −0.792979 −0.396489 0.918039i \(-0.629772\pi\)
−0.396489 + 0.918039i \(0.629772\pi\)
\(788\) −57.8828 −2.06199
\(789\) −1.89074 −0.0673121
\(790\) −40.5585 −1.44301
\(791\) −7.65127 −0.272048
\(792\) −17.7143 −0.629449
\(793\) −28.6051 −1.01580
\(794\) −14.2148 −0.504464
\(795\) 2.11870 0.0751424
\(796\) −67.0962 −2.37816
\(797\) 19.2321 0.681237 0.340618 0.940202i \(-0.389364\pi\)
0.340618 + 0.940202i \(0.389364\pi\)
\(798\) −0.762421 −0.0269894
\(799\) −3.40367 −0.120413
\(800\) 12.0077 0.424537
\(801\) 19.5975 0.692444
\(802\) −40.4808 −1.42943
\(803\) 16.6616 0.587975
\(804\) −4.55909 −0.160787
\(805\) −2.02054 −0.0712146
\(806\) 19.7387 0.695266
\(807\) −1.79986 −0.0633582
\(808\) 24.9698 0.878434
\(809\) −3.99308 −0.140389 −0.0701946 0.997533i \(-0.522362\pi\)
−0.0701946 + 0.997533i \(0.522362\pi\)
\(810\) 28.2688 0.993265
\(811\) −7.55121 −0.265159 −0.132579 0.991172i \(-0.542326\pi\)
−0.132579 + 0.991172i \(0.542326\pi\)
\(812\) 42.2761 1.48360
\(813\) 3.07687 0.107911
\(814\) −10.6245 −0.372388
\(815\) 15.1752 0.531563
\(816\) 1.38577 0.0485116
\(817\) −2.20154 −0.0770222
\(818\) 65.0452 2.27425
\(819\) −20.8248 −0.727678
\(820\) −34.1665 −1.19315
\(821\) −32.7376 −1.14255 −0.571275 0.820759i \(-0.693551\pi\)
−0.571275 + 0.820759i \(0.693551\pi\)
\(822\) 4.76630 0.166244
\(823\) 28.0235 0.976837 0.488419 0.872609i \(-0.337574\pi\)
0.488419 + 0.872609i \(0.337574\pi\)
\(824\) 108.541 3.78120
\(825\) 0.755469 0.0263021
\(826\) −31.4563 −1.09450
\(827\) −8.65602 −0.300999 −0.150500 0.988610i \(-0.548088\pi\)
−0.150500 + 0.988610i \(0.548088\pi\)
\(828\) 13.9515 0.484847
\(829\) 10.5150 0.365201 0.182600 0.983187i \(-0.441549\pi\)
0.182600 + 0.983187i \(0.441549\pi\)
\(830\) −2.59118 −0.0899410
\(831\) −7.37531 −0.255847
\(832\) 15.1529 0.525331
\(833\) −5.01550 −0.173777
\(834\) 8.87579 0.307343
\(835\) 30.2309 1.04618
\(836\) 4.21308 0.145712
\(837\) −2.10350 −0.0727076
\(838\) −39.3018 −1.35766
\(839\) 25.7370 0.888538 0.444269 0.895893i \(-0.353463\pi\)
0.444269 + 0.895893i \(0.353463\pi\)
\(840\) −2.46178 −0.0849396
\(841\) 18.8974 0.651636
\(842\) −69.9997 −2.41235
\(843\) 1.44537 0.0497812
\(844\) −48.5435 −1.67093
\(845\) −15.9459 −0.548556
\(846\) −25.2652 −0.868636
\(847\) 14.0261 0.481941
\(848\) −43.7089 −1.50097
\(849\) −3.26674 −0.112114
\(850\) 8.23578 0.282485
\(851\) 4.50825 0.154541
\(852\) −7.36064 −0.252171
\(853\) −25.9860 −0.889744 −0.444872 0.895594i \(-0.646751\pi\)
−0.444872 + 0.895594i \(0.646751\pi\)
\(854\) 20.2344 0.692406
\(855\) −3.68733 −0.126104
\(856\) −33.5046 −1.14516
\(857\) 36.3072 1.24023 0.620114 0.784511i \(-0.287086\pi\)
0.620114 + 0.784511i \(0.287086\pi\)
\(858\) −2.91366 −0.0994706
\(859\) −44.1007 −1.50470 −0.752349 0.658765i \(-0.771079\pi\)
−0.752349 + 0.658765i \(0.771079\pi\)
\(860\) −13.1940 −0.449913
\(861\) −1.90860 −0.0650450
\(862\) −25.4238 −0.865937
\(863\) −9.87300 −0.336081 −0.168040 0.985780i \(-0.553744\pi\)
−0.168040 + 0.985780i \(0.553744\pi\)
\(864\) 4.93521 0.167899
\(865\) −27.8063 −0.945441
\(866\) −24.0582 −0.817532
\(867\) 0.226046 0.00767693
\(868\) −9.55535 −0.324330
\(869\) 12.5199 0.424709
\(870\) −5.17683 −0.175511
\(871\) 23.3165 0.790049
\(872\) −14.2334 −0.482002
\(873\) 5.68965 0.192565
\(874\) −2.61227 −0.0883614
\(875\) −15.3187 −0.517866
\(876\) −15.9881 −0.540187
\(877\) 47.9676 1.61975 0.809875 0.586603i \(-0.199535\pi\)
0.809875 + 0.586603i \(0.199535\pi\)
\(878\) 90.2067 3.04433
\(879\) 7.04435 0.237600
\(880\) 8.23226 0.277509
\(881\) 17.3149 0.583353 0.291677 0.956517i \(-0.405787\pi\)
0.291677 + 0.956517i \(0.405787\pi\)
\(882\) −37.2298 −1.25359
\(883\) 37.5856 1.26486 0.632428 0.774619i \(-0.282058\pi\)
0.632428 + 0.774619i \(0.282058\pi\)
\(884\) −21.7374 −0.731108
\(885\) 2.63608 0.0886107
\(886\) 47.3482 1.59069
\(887\) −37.8419 −1.27061 −0.635303 0.772263i \(-0.719125\pi\)
−0.635303 + 0.772263i \(0.719125\pi\)
\(888\) 5.49276 0.184325
\(889\) −10.5035 −0.352276
\(890\) −21.9913 −0.737150
\(891\) −8.72626 −0.292341
\(892\) −17.6011 −0.589329
\(893\) 3.23745 0.108337
\(894\) −7.68463 −0.257013
\(895\) −29.3080 −0.979660
\(896\) −21.0588 −0.703527
\(897\) 1.23634 0.0412802
\(898\) −15.8109 −0.527618
\(899\) −10.8259 −0.361064
\(900\) 41.8372 1.39457
\(901\) −7.12979 −0.237528
\(902\) 15.4113 0.513140
\(903\) −0.737044 −0.0245273
\(904\) −31.9404 −1.06232
\(905\) −28.2349 −0.938561
\(906\) −5.76461 −0.191516
\(907\) 24.0021 0.796977 0.398488 0.917173i \(-0.369535\pi\)
0.398488 + 0.917173i \(0.369535\pi\)
\(908\) −69.4336 −2.30423
\(909\) 12.5211 0.415299
\(910\) 23.3685 0.774658
\(911\) 45.7637 1.51622 0.758110 0.652127i \(-0.226123\pi\)
0.758110 + 0.652127i \(0.226123\pi\)
\(912\) −1.31810 −0.0436465
\(913\) 0.799866 0.0264717
\(914\) 5.08426 0.168172
\(915\) −1.69567 −0.0560570
\(916\) 51.4519 1.70002
\(917\) 0.226518 0.00748030
\(918\) 3.38493 0.111719
\(919\) 57.9941 1.91305 0.956524 0.291654i \(-0.0942054\pi\)
0.956524 + 0.291654i \(0.0942054\pi\)
\(920\) −8.43477 −0.278086
\(921\) 2.04949 0.0675329
\(922\) −31.3320 −1.03186
\(923\) 37.6444 1.23908
\(924\) 1.41048 0.0464013
\(925\) 13.5192 0.444508
\(926\) −65.9636 −2.16770
\(927\) 54.4279 1.78765
\(928\) 25.3996 0.833784
\(929\) −37.6625 −1.23567 −0.617833 0.786309i \(-0.711989\pi\)
−0.617833 + 0.786309i \(0.711989\pi\)
\(930\) 1.17008 0.0383685
\(931\) 4.77057 0.156349
\(932\) 53.7043 1.75914
\(933\) 0.555599 0.0181895
\(934\) 42.9276 1.40464
\(935\) 1.34284 0.0439157
\(936\) −86.9336 −2.84151
\(937\) −28.4965 −0.930940 −0.465470 0.885064i \(-0.654115\pi\)
−0.465470 + 0.885064i \(0.654115\pi\)
\(938\) −16.4934 −0.538528
\(939\) −3.11277 −0.101581
\(940\) 19.4024 0.632835
\(941\) −7.13056 −0.232450 −0.116225 0.993223i \(-0.537079\pi\)
−0.116225 + 0.993223i \(0.537079\pi\)
\(942\) 0.716917 0.0233584
\(943\) −6.53942 −0.212953
\(944\) −54.3825 −1.77000
\(945\) −2.49032 −0.0810100
\(946\) 5.95137 0.193496
\(947\) −25.2752 −0.821333 −0.410667 0.911786i \(-0.634704\pi\)
−0.410667 + 0.911786i \(0.634704\pi\)
\(948\) −12.0138 −0.390190
\(949\) 81.7675 2.65429
\(950\) −7.83359 −0.254155
\(951\) −2.72408 −0.0883343
\(952\) 8.28434 0.268497
\(953\) −54.8068 −1.77537 −0.887684 0.460454i \(-0.847687\pi\)
−0.887684 + 0.460454i \(0.847687\pi\)
\(954\) −52.9240 −1.71348
\(955\) −20.3696 −0.659145
\(956\) 33.5210 1.08415
\(957\) 1.59803 0.0516569
\(958\) −16.3301 −0.527602
\(959\) 11.8003 0.381053
\(960\) 0.898239 0.0289906
\(961\) −28.5531 −0.921068
\(962\) −52.1401 −1.68106
\(963\) −16.8009 −0.541402
\(964\) −34.6872 −1.11720
\(965\) 2.01917 0.0649994
\(966\) −0.874550 −0.0281382
\(967\) 14.3275 0.460743 0.230371 0.973103i \(-0.426006\pi\)
0.230371 + 0.973103i \(0.426006\pi\)
\(968\) 58.5520 1.88193
\(969\) −0.215007 −0.00690703
\(970\) −6.38463 −0.204998
\(971\) −45.7927 −1.46956 −0.734779 0.678306i \(-0.762714\pi\)
−0.734779 + 0.678306i \(0.762714\pi\)
\(972\) 25.8666 0.829673
\(973\) 21.9746 0.704472
\(974\) −26.3657 −0.844811
\(975\) 3.70750 0.118735
\(976\) 34.9817 1.11974
\(977\) 46.5848 1.49038 0.745190 0.666852i \(-0.232359\pi\)
0.745190 + 0.666852i \(0.232359\pi\)
\(978\) 6.56827 0.210030
\(979\) 6.78846 0.216960
\(980\) 28.5905 0.913290
\(981\) −7.13733 −0.227877
\(982\) 85.2693 2.72105
\(983\) −5.91694 −0.188721 −0.0943605 0.995538i \(-0.530081\pi\)
−0.0943605 + 0.995538i \(0.530081\pi\)
\(984\) −7.96749 −0.253994
\(985\) 17.5482 0.559131
\(986\) 17.4209 0.554796
\(987\) 1.08385 0.0344994
\(988\) 20.6759 0.657787
\(989\) −2.52532 −0.0803006
\(990\) 9.96786 0.316799
\(991\) 62.2444 1.97726 0.988630 0.150369i \(-0.0480463\pi\)
0.988630 + 0.150369i \(0.0480463\pi\)
\(992\) −5.74090 −0.182274
\(993\) −6.50716 −0.206499
\(994\) −26.6285 −0.844605
\(995\) 20.3414 0.644865
\(996\) −0.767531 −0.0243202
\(997\) −44.5025 −1.40941 −0.704704 0.709501i \(-0.748920\pi\)
−0.704704 + 0.709501i \(0.748920\pi\)
\(998\) −39.5236 −1.25110
\(999\) 5.55642 0.175797
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 6001.2.a.d.1.8 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.8 121 1.1 even 1 trivial