Properties

Label 8003.2.a.b.1.4
Level 8003
Weight 2
Character 8003.1
Self dual yes
Analytic conductor 63.904
Analytic rank 1
Dimension 153
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.71996 q^{2} -3.40952 q^{3} +5.39818 q^{4} +0.859174 q^{5} +9.27375 q^{6} +3.37109 q^{7} -9.24292 q^{8} +8.62480 q^{9} +O(q^{10})\) \(q-2.71996 q^{2} -3.40952 q^{3} +5.39818 q^{4} +0.859174 q^{5} +9.27375 q^{6} +3.37109 q^{7} -9.24292 q^{8} +8.62480 q^{9} -2.33692 q^{10} +2.40541 q^{11} -18.4052 q^{12} -3.48432 q^{13} -9.16924 q^{14} -2.92937 q^{15} +14.3440 q^{16} +0.684330 q^{17} -23.4591 q^{18} -7.35748 q^{19} +4.63798 q^{20} -11.4938 q^{21} -6.54262 q^{22} -0.186673 q^{23} +31.5139 q^{24} -4.26182 q^{25} +9.47721 q^{26} -19.1778 q^{27} +18.1978 q^{28} +1.47872 q^{29} +7.96776 q^{30} +7.64661 q^{31} -20.5293 q^{32} -8.20128 q^{33} -1.86135 q^{34} +2.89636 q^{35} +46.5582 q^{36} +3.39270 q^{37} +20.0120 q^{38} +11.8798 q^{39} -7.94128 q^{40} +3.74770 q^{41} +31.2627 q^{42} +5.35095 q^{43} +12.9848 q^{44} +7.41020 q^{45} +0.507743 q^{46} +5.09621 q^{47} -48.9061 q^{48} +4.36428 q^{49} +11.5920 q^{50} -2.33323 q^{51} -18.8090 q^{52} -1.00000 q^{53} +52.1630 q^{54} +2.06666 q^{55} -31.1588 q^{56} +25.0854 q^{57} -4.02205 q^{58} -11.9157 q^{59} -15.8133 q^{60} -10.5630 q^{61} -20.7985 q^{62} +29.0750 q^{63} +27.1508 q^{64} -2.99363 q^{65} +22.3072 q^{66} -15.1682 q^{67} +3.69414 q^{68} +0.636464 q^{69} -7.87797 q^{70} +7.11200 q^{71} -79.7183 q^{72} -0.544635 q^{73} -9.22801 q^{74} +14.5307 q^{75} -39.7170 q^{76} +8.10886 q^{77} -32.3127 q^{78} +14.5016 q^{79} +12.3240 q^{80} +39.5128 q^{81} -10.1936 q^{82} +4.02419 q^{83} -62.0456 q^{84} +0.587959 q^{85} -14.5544 q^{86} -5.04170 q^{87} -22.2330 q^{88} +4.74919 q^{89} -20.1555 q^{90} -11.7460 q^{91} -1.00769 q^{92} -26.0712 q^{93} -13.8615 q^{94} -6.32135 q^{95} +69.9950 q^{96} -8.94108 q^{97} -11.8707 q^{98} +20.7462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71996 −1.92330 −0.961651 0.274276i \(-0.911562\pi\)
−0.961651 + 0.274276i \(0.911562\pi\)
\(3\) −3.40952 −1.96848 −0.984242 0.176824i \(-0.943418\pi\)
−0.984242 + 0.176824i \(0.943418\pi\)
\(4\) 5.39818 2.69909
\(5\) 0.859174 0.384234 0.192117 0.981372i \(-0.438465\pi\)
0.192117 + 0.981372i \(0.438465\pi\)
\(6\) 9.27375 3.78599
\(7\) 3.37109 1.27415 0.637077 0.770800i \(-0.280143\pi\)
0.637077 + 0.770800i \(0.280143\pi\)
\(8\) −9.24292 −3.26787
\(9\) 8.62480 2.87493
\(10\) −2.33692 −0.738998
\(11\) 2.40541 0.725258 0.362629 0.931934i \(-0.381879\pi\)
0.362629 + 0.931934i \(0.381879\pi\)
\(12\) −18.4052 −5.31312
\(13\) −3.48432 −0.966376 −0.483188 0.875517i \(-0.660521\pi\)
−0.483188 + 0.875517i \(0.660521\pi\)
\(14\) −9.16924 −2.45058
\(15\) −2.92937 −0.756359
\(16\) 14.3440 3.58600
\(17\) 0.684330 0.165974 0.0829872 0.996551i \(-0.473554\pi\)
0.0829872 + 0.996551i \(0.473554\pi\)
\(18\) −23.4591 −5.52937
\(19\) −7.35748 −1.68792 −0.843960 0.536406i \(-0.819782\pi\)
−0.843960 + 0.536406i \(0.819782\pi\)
\(20\) 4.63798 1.03708
\(21\) −11.4938 −2.50815
\(22\) −6.54262 −1.39489
\(23\) −0.186673 −0.0389240 −0.0194620 0.999811i \(-0.506195\pi\)
−0.0194620 + 0.999811i \(0.506195\pi\)
\(24\) 31.5139 6.43275
\(25\) −4.26182 −0.852364
\(26\) 9.47721 1.85863
\(27\) −19.1778 −3.69078
\(28\) 18.1978 3.43906
\(29\) 1.47872 0.274591 0.137295 0.990530i \(-0.456159\pi\)
0.137295 + 0.990530i \(0.456159\pi\)
\(30\) 7.96776 1.45471
\(31\) 7.64661 1.37337 0.686686 0.726954i \(-0.259065\pi\)
0.686686 + 0.726954i \(0.259065\pi\)
\(32\) −20.5293 −3.62910
\(33\) −8.20128 −1.42766
\(34\) −1.86135 −0.319219
\(35\) 2.89636 0.489574
\(36\) 46.5582 7.75971
\(37\) 3.39270 0.557757 0.278878 0.960326i \(-0.410037\pi\)
0.278878 + 0.960326i \(0.410037\pi\)
\(38\) 20.0120 3.24638
\(39\) 11.8798 1.90230
\(40\) −7.94128 −1.25563
\(41\) 3.74770 0.585293 0.292646 0.956221i \(-0.405464\pi\)
0.292646 + 0.956221i \(0.405464\pi\)
\(42\) 31.2627 4.82394
\(43\) 5.35095 0.816012 0.408006 0.912979i \(-0.366224\pi\)
0.408006 + 0.912979i \(0.366224\pi\)
\(44\) 12.9848 1.95754
\(45\) 7.41020 1.10465
\(46\) 0.507743 0.0748626
\(47\) 5.09621 0.743359 0.371680 0.928361i \(-0.378782\pi\)
0.371680 + 0.928361i \(0.378782\pi\)
\(48\) −48.9061 −7.05899
\(49\) 4.36428 0.623468
\(50\) 11.5920 1.63935
\(51\) −2.33323 −0.326718
\(52\) −18.8090 −2.60834
\(53\) −1.00000 −0.137361
\(54\) 52.1630 7.09848
\(55\) 2.06666 0.278669
\(56\) −31.1588 −4.16376
\(57\) 25.0854 3.32265
\(58\) −4.02205 −0.528121
\(59\) −11.9157 −1.55130 −0.775648 0.631165i \(-0.782577\pi\)
−0.775648 + 0.631165i \(0.782577\pi\)
\(60\) −15.8133 −2.04148
\(61\) −10.5630 −1.35246 −0.676228 0.736693i \(-0.736386\pi\)
−0.676228 + 0.736693i \(0.736386\pi\)
\(62\) −20.7985 −2.64141
\(63\) 29.0750 3.66311
\(64\) 27.1508 3.39386
\(65\) −2.99363 −0.371315
\(66\) 22.3072 2.74582
\(67\) −15.1682 −1.85309 −0.926545 0.376184i \(-0.877236\pi\)
−0.926545 + 0.376184i \(0.877236\pi\)
\(68\) 3.69414 0.447980
\(69\) 0.636464 0.0766213
\(70\) −7.87797 −0.941598
\(71\) 7.11200 0.844039 0.422019 0.906587i \(-0.361321\pi\)
0.422019 + 0.906587i \(0.361321\pi\)
\(72\) −79.7183 −9.39490
\(73\) −0.544635 −0.0637448 −0.0318724 0.999492i \(-0.510147\pi\)
−0.0318724 + 0.999492i \(0.510147\pi\)
\(74\) −9.22801 −1.07273
\(75\) 14.5307 1.67787
\(76\) −39.7170 −4.55585
\(77\) 8.10886 0.924090
\(78\) −32.3127 −3.65869
\(79\) 14.5016 1.63155 0.815777 0.578366i \(-0.196309\pi\)
0.815777 + 0.578366i \(0.196309\pi\)
\(80\) 12.3240 1.37786
\(81\) 39.5128 4.39031
\(82\) −10.1936 −1.12569
\(83\) 4.02419 0.441712 0.220856 0.975306i \(-0.429115\pi\)
0.220856 + 0.975306i \(0.429115\pi\)
\(84\) −62.0456 −6.76973
\(85\) 0.587959 0.0637731
\(86\) −14.5544 −1.56944
\(87\) −5.04170 −0.540527
\(88\) −22.2330 −2.37005
\(89\) 4.74919 0.503413 0.251707 0.967804i \(-0.419008\pi\)
0.251707 + 0.967804i \(0.419008\pi\)
\(90\) −20.1555 −2.12457
\(91\) −11.7460 −1.23131
\(92\) −1.00769 −0.105059
\(93\) −26.0712 −2.70346
\(94\) −13.8615 −1.42970
\(95\) −6.32135 −0.648557
\(96\) 69.9950 7.14383
\(97\) −8.94108 −0.907829 −0.453915 0.891045i \(-0.649973\pi\)
−0.453915 + 0.891045i \(0.649973\pi\)
\(98\) −11.8707 −1.19912
\(99\) 20.7462 2.08507
\(100\) −23.0061 −2.30061
\(101\) 16.0576 1.59779 0.798895 0.601470i \(-0.205418\pi\)
0.798895 + 0.601470i \(0.205418\pi\)
\(102\) 6.34631 0.628378
\(103\) −12.7114 −1.25249 −0.626246 0.779625i \(-0.715410\pi\)
−0.626246 + 0.779625i \(0.715410\pi\)
\(104\) 32.2053 3.15799
\(105\) −9.87517 −0.963718
\(106\) 2.71996 0.264186
\(107\) −4.49200 −0.434258 −0.217129 0.976143i \(-0.569669\pi\)
−0.217129 + 0.976143i \(0.569669\pi\)
\(108\) −103.525 −9.96175
\(109\) −6.19932 −0.593787 −0.296894 0.954911i \(-0.595951\pi\)
−0.296894 + 0.954911i \(0.595951\pi\)
\(110\) −5.62124 −0.535965
\(111\) −11.5675 −1.09794
\(112\) 48.3550 4.56912
\(113\) 0.212688 0.0200080 0.0100040 0.999950i \(-0.496816\pi\)
0.0100040 + 0.999950i \(0.496816\pi\)
\(114\) −68.2314 −6.39045
\(115\) −0.160384 −0.0149559
\(116\) 7.98238 0.741145
\(117\) −30.0515 −2.77827
\(118\) 32.4103 2.98361
\(119\) 2.30694 0.211477
\(120\) 27.0759 2.47168
\(121\) −5.21401 −0.474001
\(122\) 28.7310 2.60118
\(123\) −12.7778 −1.15214
\(124\) 41.2778 3.70686
\(125\) −7.95751 −0.711742
\(126\) −79.0829 −7.04526
\(127\) −9.46172 −0.839591 −0.419796 0.907619i \(-0.637898\pi\)
−0.419796 + 0.907619i \(0.637898\pi\)
\(128\) −32.7906 −2.89831
\(129\) −18.2442 −1.60631
\(130\) 8.14257 0.714150
\(131\) 6.65768 0.581684 0.290842 0.956771i \(-0.406065\pi\)
0.290842 + 0.956771i \(0.406065\pi\)
\(132\) −44.2720 −3.85338
\(133\) −24.8027 −2.15067
\(134\) 41.2569 3.56405
\(135\) −16.4771 −1.41812
\(136\) −6.32521 −0.542382
\(137\) −8.51114 −0.727155 −0.363578 0.931564i \(-0.618445\pi\)
−0.363578 + 0.931564i \(0.618445\pi\)
\(138\) −1.73116 −0.147366
\(139\) 6.61698 0.561245 0.280622 0.959818i \(-0.409459\pi\)
0.280622 + 0.959818i \(0.409459\pi\)
\(140\) 15.6351 1.32140
\(141\) −17.3756 −1.46329
\(142\) −19.3443 −1.62334
\(143\) −8.38121 −0.700872
\(144\) 123.714 10.3095
\(145\) 1.27047 0.105507
\(146\) 1.48139 0.122600
\(147\) −14.8801 −1.22729
\(148\) 18.3144 1.50544
\(149\) −6.99588 −0.573125 −0.286562 0.958062i \(-0.592513\pi\)
−0.286562 + 0.958062i \(0.592513\pi\)
\(150\) −39.5230 −3.22704
\(151\) −1.00000 −0.0813788
\(152\) 68.0046 5.51590
\(153\) 5.90221 0.477165
\(154\) −22.0558 −1.77731
\(155\) 6.56977 0.527697
\(156\) 64.1295 5.13447
\(157\) 3.66105 0.292184 0.146092 0.989271i \(-0.453331\pi\)
0.146092 + 0.989271i \(0.453331\pi\)
\(158\) −39.4437 −3.13797
\(159\) 3.40952 0.270392
\(160\) −17.6382 −1.39442
\(161\) −0.629292 −0.0495951
\(162\) −107.473 −8.44389
\(163\) 5.11931 0.400975 0.200488 0.979696i \(-0.435747\pi\)
0.200488 + 0.979696i \(0.435747\pi\)
\(164\) 20.2308 1.57976
\(165\) −7.04632 −0.548556
\(166\) −10.9456 −0.849546
\(167\) −17.3096 −1.33946 −0.669729 0.742605i \(-0.733590\pi\)
−0.669729 + 0.742605i \(0.733590\pi\)
\(168\) 106.236 8.19631
\(169\) −0.859528 −0.0661175
\(170\) −1.59922 −0.122655
\(171\) −63.4568 −4.85266
\(172\) 28.8854 2.20249
\(173\) 23.0478 1.75229 0.876147 0.482044i \(-0.160106\pi\)
0.876147 + 0.482044i \(0.160106\pi\)
\(174\) 13.7132 1.03960
\(175\) −14.3670 −1.08604
\(176\) 34.5032 2.60078
\(177\) 40.6269 3.05370
\(178\) −12.9176 −0.968216
\(179\) 13.1705 0.984411 0.492206 0.870479i \(-0.336191\pi\)
0.492206 + 0.870479i \(0.336191\pi\)
\(180\) 40.0016 2.98154
\(181\) −10.6927 −0.794784 −0.397392 0.917649i \(-0.630085\pi\)
−0.397392 + 0.917649i \(0.630085\pi\)
\(182\) 31.9486 2.36818
\(183\) 36.0148 2.66229
\(184\) 1.72540 0.127198
\(185\) 2.91492 0.214309
\(186\) 70.9128 5.19958
\(187\) 1.64609 0.120374
\(188\) 27.5103 2.00639
\(189\) −64.6503 −4.70262
\(190\) 17.1938 1.24737
\(191\) 0.269105 0.0194718 0.00973588 0.999953i \(-0.496901\pi\)
0.00973588 + 0.999953i \(0.496901\pi\)
\(192\) −92.5712 −6.68075
\(193\) −2.96112 −0.213146 −0.106573 0.994305i \(-0.533988\pi\)
−0.106573 + 0.994305i \(0.533988\pi\)
\(194\) 24.3194 1.74603
\(195\) 10.2068 0.730927
\(196\) 23.5592 1.68280
\(197\) −18.3527 −1.30758 −0.653788 0.756678i \(-0.726821\pi\)
−0.653788 + 0.756678i \(0.726821\pi\)
\(198\) −56.4287 −4.01022
\(199\) 17.5054 1.24093 0.620463 0.784236i \(-0.286945\pi\)
0.620463 + 0.784236i \(0.286945\pi\)
\(200\) 39.3917 2.78541
\(201\) 51.7162 3.64778
\(202\) −43.6760 −3.07303
\(203\) 4.98489 0.349871
\(204\) −12.5952 −0.881842
\(205\) 3.21993 0.224889
\(206\) 34.5745 2.40892
\(207\) −1.61002 −0.111904
\(208\) −49.9791 −3.46543
\(209\) −17.6977 −1.22418
\(210\) 26.8601 1.85352
\(211\) −9.20183 −0.633480 −0.316740 0.948512i \(-0.602588\pi\)
−0.316740 + 0.948512i \(0.602588\pi\)
\(212\) −5.39818 −0.370749
\(213\) −24.2485 −1.66148
\(214\) 12.2181 0.835210
\(215\) 4.59740 0.313540
\(216\) 177.259 12.0610
\(217\) 25.7775 1.74989
\(218\) 16.8619 1.14203
\(219\) 1.85694 0.125481
\(220\) 11.1562 0.752153
\(221\) −2.38442 −0.160394
\(222\) 31.4631 2.11166
\(223\) 10.2206 0.684424 0.342212 0.939623i \(-0.388824\pi\)
0.342212 + 0.939623i \(0.388824\pi\)
\(224\) −69.2062 −4.62403
\(225\) −36.7573 −2.45049
\(226\) −0.578502 −0.0384814
\(227\) 12.0987 0.803019 0.401510 0.915855i \(-0.368486\pi\)
0.401510 + 0.915855i \(0.368486\pi\)
\(228\) 135.416 8.96813
\(229\) −15.7994 −1.04405 −0.522026 0.852930i \(-0.674824\pi\)
−0.522026 + 0.852930i \(0.674824\pi\)
\(230\) 0.436239 0.0287648
\(231\) −27.6473 −1.81906
\(232\) −13.6676 −0.897325
\(233\) −12.1921 −0.798733 −0.399367 0.916791i \(-0.630770\pi\)
−0.399367 + 0.916791i \(0.630770\pi\)
\(234\) 81.7390 5.34345
\(235\) 4.37853 0.285624
\(236\) −64.3233 −4.18709
\(237\) −49.4434 −3.21169
\(238\) −6.27479 −0.406734
\(239\) −22.7224 −1.46979 −0.734895 0.678181i \(-0.762769\pi\)
−0.734895 + 0.678181i \(0.762769\pi\)
\(240\) −42.0189 −2.71231
\(241\) −14.2838 −0.920099 −0.460050 0.887893i \(-0.652168\pi\)
−0.460050 + 0.887893i \(0.652168\pi\)
\(242\) 14.1819 0.911647
\(243\) −77.1859 −4.95148
\(244\) −57.0211 −3.65040
\(245\) 3.74967 0.239558
\(246\) 34.7552 2.21591
\(247\) 25.6358 1.63117
\(248\) −70.6770 −4.48800
\(249\) −13.7205 −0.869504
\(250\) 21.6441 1.36889
\(251\) 7.10158 0.448248 0.224124 0.974561i \(-0.428048\pi\)
0.224124 + 0.974561i \(0.428048\pi\)
\(252\) 156.952 9.88706
\(253\) −0.449024 −0.0282299
\(254\) 25.7355 1.61479
\(255\) −2.00465 −0.125536
\(256\) 34.8875 2.18047
\(257\) −10.3109 −0.643177 −0.321589 0.946879i \(-0.604217\pi\)
−0.321589 + 0.946879i \(0.604217\pi\)
\(258\) 49.6234 3.08942
\(259\) 11.4371 0.710668
\(260\) −16.1602 −1.00221
\(261\) 12.7536 0.789429
\(262\) −18.1086 −1.11875
\(263\) 12.5525 0.774020 0.387010 0.922075i \(-0.373508\pi\)
0.387010 + 0.922075i \(0.373508\pi\)
\(264\) 75.8038 4.66540
\(265\) −0.859174 −0.0527786
\(266\) 67.4625 4.13639
\(267\) −16.1924 −0.990961
\(268\) −81.8807 −5.00166
\(269\) 6.05135 0.368957 0.184479 0.982837i \(-0.440940\pi\)
0.184479 + 0.982837i \(0.440940\pi\)
\(270\) 44.8170 2.72748
\(271\) −30.1932 −1.83411 −0.917053 0.398766i \(-0.869439\pi\)
−0.917053 + 0.398766i \(0.869439\pi\)
\(272\) 9.81604 0.595185
\(273\) 40.0481 2.42382
\(274\) 23.1500 1.39854
\(275\) −10.2514 −0.618184
\(276\) 3.43575 0.206808
\(277\) 13.3790 0.803869 0.401934 0.915668i \(-0.368338\pi\)
0.401934 + 0.915668i \(0.368338\pi\)
\(278\) −17.9979 −1.07944
\(279\) 65.9505 3.94835
\(280\) −26.7708 −1.59986
\(281\) 7.17552 0.428055 0.214028 0.976828i \(-0.431342\pi\)
0.214028 + 0.976828i \(0.431342\pi\)
\(282\) 47.2610 2.81435
\(283\) −3.36337 −0.199932 −0.0999658 0.994991i \(-0.531873\pi\)
−0.0999658 + 0.994991i \(0.531873\pi\)
\(284\) 38.3919 2.27814
\(285\) 21.5527 1.27667
\(286\) 22.7966 1.34799
\(287\) 12.6339 0.745753
\(288\) −177.061 −10.4334
\(289\) −16.5317 −0.972452
\(290\) −3.45564 −0.202922
\(291\) 30.4848 1.78705
\(292\) −2.94004 −0.172053
\(293\) −19.7736 −1.15519 −0.577594 0.816325i \(-0.696008\pi\)
−0.577594 + 0.816325i \(0.696008\pi\)
\(294\) 40.4732 2.36045
\(295\) −10.2377 −0.596061
\(296\) −31.3585 −1.82267
\(297\) −46.1305 −2.67677
\(298\) 19.0285 1.10229
\(299\) 0.650427 0.0376152
\(300\) 78.4396 4.52871
\(301\) 18.0386 1.03973
\(302\) 2.71996 0.156516
\(303\) −54.7486 −3.14523
\(304\) −105.536 −6.05289
\(305\) −9.07546 −0.519660
\(306\) −16.0538 −0.917733
\(307\) 4.42509 0.252553 0.126277 0.991995i \(-0.459697\pi\)
0.126277 + 0.991995i \(0.459697\pi\)
\(308\) 43.7731 2.49420
\(309\) 43.3398 2.46551
\(310\) −17.8695 −1.01492
\(311\) −5.60454 −0.317804 −0.158902 0.987294i \(-0.550795\pi\)
−0.158902 + 0.987294i \(0.550795\pi\)
\(312\) −109.804 −6.21645
\(313\) 19.4179 1.09757 0.548783 0.835965i \(-0.315091\pi\)
0.548783 + 0.835965i \(0.315091\pi\)
\(314\) −9.95791 −0.561957
\(315\) 24.9805 1.40749
\(316\) 78.2822 4.40372
\(317\) −17.4569 −0.980476 −0.490238 0.871589i \(-0.663090\pi\)
−0.490238 + 0.871589i \(0.663090\pi\)
\(318\) −9.27375 −0.520046
\(319\) 3.55691 0.199149
\(320\) 23.3273 1.30404
\(321\) 15.3156 0.854831
\(322\) 1.71165 0.0953864
\(323\) −5.03494 −0.280152
\(324\) 213.297 11.8498
\(325\) 14.8495 0.823704
\(326\) −13.9243 −0.771197
\(327\) 21.1367 1.16886
\(328\) −34.6397 −1.91266
\(329\) 17.1798 0.947154
\(330\) 19.1657 1.05504
\(331\) 18.2570 1.00349 0.501746 0.865015i \(-0.332691\pi\)
0.501746 + 0.865015i \(0.332691\pi\)
\(332\) 21.7233 1.19222
\(333\) 29.2614 1.60351
\(334\) 47.0815 2.57618
\(335\) −13.0321 −0.712020
\(336\) −164.867 −8.99424
\(337\) 34.6957 1.89000 0.944999 0.327075i \(-0.106063\pi\)
0.944999 + 0.327075i \(0.106063\pi\)
\(338\) 2.33788 0.127164
\(339\) −0.725162 −0.0393854
\(340\) 3.17391 0.172129
\(341\) 18.3932 0.996049
\(342\) 172.600 9.33313
\(343\) −8.88527 −0.479759
\(344\) −49.4584 −2.66662
\(345\) 0.546833 0.0294405
\(346\) −62.6892 −3.37019
\(347\) −16.4013 −0.880469 −0.440235 0.897883i \(-0.645105\pi\)
−0.440235 + 0.897883i \(0.645105\pi\)
\(348\) −27.2160 −1.45893
\(349\) −10.9435 −0.585794 −0.292897 0.956144i \(-0.594619\pi\)
−0.292897 + 0.956144i \(0.594619\pi\)
\(350\) 39.0777 2.08879
\(351\) 66.8217 3.56668
\(352\) −49.3813 −2.63203
\(353\) −28.0567 −1.49331 −0.746655 0.665212i \(-0.768341\pi\)
−0.746655 + 0.665212i \(0.768341\pi\)
\(354\) −110.504 −5.87320
\(355\) 6.11044 0.324309
\(356\) 25.6370 1.35876
\(357\) −7.86555 −0.416289
\(358\) −35.8233 −1.89332
\(359\) 35.0882 1.85188 0.925942 0.377666i \(-0.123273\pi\)
0.925942 + 0.377666i \(0.123273\pi\)
\(360\) −68.4919 −3.60984
\(361\) 35.1324 1.84908
\(362\) 29.0838 1.52861
\(363\) 17.7772 0.933063
\(364\) −63.4069 −3.32342
\(365\) −0.467936 −0.0244929
\(366\) −97.9587 −5.12038
\(367\) −24.1359 −1.25989 −0.629943 0.776641i \(-0.716922\pi\)
−0.629943 + 0.776641i \(0.716922\pi\)
\(368\) −2.67764 −0.139581
\(369\) 32.3232 1.68268
\(370\) −7.92846 −0.412181
\(371\) −3.37109 −0.175019
\(372\) −140.737 −7.29689
\(373\) −17.9290 −0.928327 −0.464163 0.885750i \(-0.653645\pi\)
−0.464163 + 0.885750i \(0.653645\pi\)
\(374\) −4.47731 −0.231516
\(375\) 27.1313 1.40105
\(376\) −47.1039 −2.42920
\(377\) −5.15231 −0.265358
\(378\) 175.846 9.04456
\(379\) 0.880119 0.0452087 0.0226043 0.999744i \(-0.492804\pi\)
0.0226043 + 0.999744i \(0.492804\pi\)
\(380\) −34.1238 −1.75051
\(381\) 32.2599 1.65272
\(382\) −0.731955 −0.0374501
\(383\) 36.2049 1.84998 0.924992 0.379986i \(-0.124071\pi\)
0.924992 + 0.379986i \(0.124071\pi\)
\(384\) 111.800 5.70528
\(385\) 6.96692 0.355067
\(386\) 8.05412 0.409944
\(387\) 46.1509 2.34598
\(388\) −48.2656 −2.45031
\(389\) 11.4485 0.580462 0.290231 0.956957i \(-0.406268\pi\)
0.290231 + 0.956957i \(0.406268\pi\)
\(390\) −27.7622 −1.40579
\(391\) −0.127746 −0.00646038
\(392\) −40.3387 −2.03741
\(393\) −22.6995 −1.14504
\(394\) 49.9186 2.51486
\(395\) 12.4594 0.626899
\(396\) 111.992 5.62779
\(397\) −34.6323 −1.73815 −0.869073 0.494684i \(-0.835284\pi\)
−0.869073 + 0.494684i \(0.835284\pi\)
\(398\) −47.6140 −2.38668
\(399\) 84.5654 4.23356
\(400\) −61.1316 −3.05658
\(401\) 7.81705 0.390365 0.195182 0.980767i \(-0.437470\pi\)
0.195182 + 0.980767i \(0.437470\pi\)
\(402\) −140.666 −7.01578
\(403\) −26.6432 −1.32719
\(404\) 86.6818 4.31258
\(405\) 33.9483 1.68691
\(406\) −13.5587 −0.672907
\(407\) 8.16083 0.404517
\(408\) 21.5659 1.06767
\(409\) 0.422897 0.0209109 0.0104555 0.999945i \(-0.496672\pi\)
0.0104555 + 0.999945i \(0.496672\pi\)
\(410\) −8.75807 −0.432530
\(411\) 29.0189 1.43139
\(412\) −68.6185 −3.38059
\(413\) −40.1691 −1.97659
\(414\) 4.37918 0.215225
\(415\) 3.45748 0.169721
\(416\) 71.5306 3.50708
\(417\) −22.5607 −1.10480
\(418\) 48.1371 2.35446
\(419\) 1.67102 0.0816349 0.0408174 0.999167i \(-0.487004\pi\)
0.0408174 + 0.999167i \(0.487004\pi\)
\(420\) −53.3080 −2.60116
\(421\) −9.20988 −0.448862 −0.224431 0.974490i \(-0.572052\pi\)
−0.224431 + 0.974490i \(0.572052\pi\)
\(422\) 25.0286 1.21837
\(423\) 43.9538 2.13711
\(424\) 9.24292 0.448876
\(425\) −2.91649 −0.141471
\(426\) 65.9549 3.19552
\(427\) −35.6089 −1.72324
\(428\) −24.2486 −1.17210
\(429\) 28.5759 1.37966
\(430\) −12.5047 −0.603032
\(431\) 36.4356 1.75504 0.877521 0.479537i \(-0.159196\pi\)
0.877521 + 0.479537i \(0.159196\pi\)
\(432\) −275.087 −13.2351
\(433\) −8.50000 −0.408484 −0.204242 0.978920i \(-0.565473\pi\)
−0.204242 + 0.978920i \(0.565473\pi\)
\(434\) −70.1136 −3.36556
\(435\) −4.33170 −0.207689
\(436\) −33.4651 −1.60269
\(437\) 1.37344 0.0657006
\(438\) −5.05081 −0.241337
\(439\) −22.9377 −1.09476 −0.547379 0.836885i \(-0.684374\pi\)
−0.547379 + 0.836885i \(0.684374\pi\)
\(440\) −19.1020 −0.910653
\(441\) 37.6410 1.79243
\(442\) 6.48554 0.308486
\(443\) −4.54266 −0.215829 −0.107914 0.994160i \(-0.534417\pi\)
−0.107914 + 0.994160i \(0.534417\pi\)
\(444\) −62.4433 −2.96343
\(445\) 4.08038 0.193429
\(446\) −27.7997 −1.31635
\(447\) 23.8526 1.12819
\(448\) 91.5281 4.32429
\(449\) 28.7987 1.35909 0.679547 0.733632i \(-0.262176\pi\)
0.679547 + 0.733632i \(0.262176\pi\)
\(450\) 99.9785 4.71303
\(451\) 9.01475 0.424488
\(452\) 1.14813 0.0540034
\(453\) 3.40952 0.160193
\(454\) −32.9080 −1.54445
\(455\) −10.0918 −0.473112
\(456\) −231.863 −10.8580
\(457\) 22.8788 1.07023 0.535113 0.844780i \(-0.320269\pi\)
0.535113 + 0.844780i \(0.320269\pi\)
\(458\) 42.9737 2.00803
\(459\) −13.1240 −0.612575
\(460\) −0.865784 −0.0403674
\(461\) 26.4983 1.23415 0.617074 0.786905i \(-0.288318\pi\)
0.617074 + 0.786905i \(0.288318\pi\)
\(462\) 75.1995 3.49860
\(463\) 7.85173 0.364901 0.182450 0.983215i \(-0.441597\pi\)
0.182450 + 0.983215i \(0.441597\pi\)
\(464\) 21.2107 0.984682
\(465\) −22.3997 −1.03876
\(466\) 33.1621 1.53621
\(467\) −8.15815 −0.377514 −0.188757 0.982024i \(-0.560446\pi\)
−0.188757 + 0.982024i \(0.560446\pi\)
\(468\) −162.224 −7.49879
\(469\) −51.1334 −2.36112
\(470\) −11.9094 −0.549341
\(471\) −12.4824 −0.575159
\(472\) 110.136 5.06943
\(473\) 12.8712 0.591820
\(474\) 134.484 6.17705
\(475\) 31.3562 1.43872
\(476\) 12.4533 0.570796
\(477\) −8.62480 −0.394902
\(478\) 61.8040 2.82685
\(479\) 5.83104 0.266427 0.133214 0.991087i \(-0.457470\pi\)
0.133214 + 0.991087i \(0.457470\pi\)
\(480\) 60.1378 2.74490
\(481\) −11.8212 −0.539003
\(482\) 38.8513 1.76963
\(483\) 2.14558 0.0976273
\(484\) −28.1462 −1.27937
\(485\) −7.68194 −0.348819
\(486\) 209.942 9.52318
\(487\) 9.97499 0.452010 0.226005 0.974126i \(-0.427433\pi\)
0.226005 + 0.974126i \(0.427433\pi\)
\(488\) 97.6331 4.41964
\(489\) −17.4544 −0.789314
\(490\) −10.1990 −0.460742
\(491\) −13.0671 −0.589712 −0.294856 0.955542i \(-0.595272\pi\)
−0.294856 + 0.955542i \(0.595272\pi\)
\(492\) −68.9771 −3.10973
\(493\) 1.01193 0.0455750
\(494\) −69.7283 −3.13723
\(495\) 17.8246 0.801154
\(496\) 109.683 4.92492
\(497\) 23.9752 1.07544
\(498\) 37.3193 1.67232
\(499\) −41.2518 −1.84668 −0.923341 0.383981i \(-0.874553\pi\)
−0.923341 + 0.383981i \(0.874553\pi\)
\(500\) −42.9561 −1.92106
\(501\) 59.0174 2.63670
\(502\) −19.3160 −0.862116
\(503\) 38.9778 1.73793 0.868967 0.494871i \(-0.164785\pi\)
0.868967 + 0.494871i \(0.164785\pi\)
\(504\) −268.738 −11.9705
\(505\) 13.7963 0.613926
\(506\) 1.22133 0.0542947
\(507\) 2.93057 0.130151
\(508\) −51.0761 −2.26613
\(509\) −38.5306 −1.70784 −0.853920 0.520404i \(-0.825781\pi\)
−0.853920 + 0.520404i \(0.825781\pi\)
\(510\) 5.45258 0.241444
\(511\) −1.83602 −0.0812206
\(512\) −29.3113 −1.29539
\(513\) 141.101 6.22974
\(514\) 28.0453 1.23702
\(515\) −10.9213 −0.481251
\(516\) −98.4853 −4.33557
\(517\) 12.2585 0.539127
\(518\) −31.1085 −1.36683
\(519\) −78.5819 −3.44936
\(520\) 27.6699 1.21341
\(521\) 35.3738 1.54975 0.774877 0.632112i \(-0.217812\pi\)
0.774877 + 0.632112i \(0.217812\pi\)
\(522\) −34.6893 −1.51831
\(523\) 28.4591 1.24443 0.622215 0.782847i \(-0.286233\pi\)
0.622215 + 0.782847i \(0.286233\pi\)
\(524\) 35.9394 1.57002
\(525\) 48.9845 2.13786
\(526\) −34.1423 −1.48868
\(527\) 5.23281 0.227945
\(528\) −117.639 −5.11959
\(529\) −22.9652 −0.998485
\(530\) 2.33692 0.101509
\(531\) −102.771 −4.45987
\(532\) −133.890 −5.80486
\(533\) −13.0582 −0.565613
\(534\) 44.0428 1.90592
\(535\) −3.85941 −0.166857
\(536\) 140.198 6.05565
\(537\) −44.9051 −1.93780
\(538\) −16.4594 −0.709616
\(539\) 10.4979 0.452175
\(540\) −88.9464 −3.82764
\(541\) −27.6006 −1.18664 −0.593321 0.804966i \(-0.702184\pi\)
−0.593321 + 0.804966i \(0.702184\pi\)
\(542\) 82.1243 3.52754
\(543\) 36.4570 1.56452
\(544\) −14.0488 −0.602338
\(545\) −5.32629 −0.228153
\(546\) −108.929 −4.66174
\(547\) 9.98261 0.426826 0.213413 0.976962i \(-0.431542\pi\)
0.213413 + 0.976962i \(0.431542\pi\)
\(548\) −45.9447 −1.96266
\(549\) −91.1039 −3.88822
\(550\) 27.8835 1.18895
\(551\) −10.8796 −0.463487
\(552\) −5.88279 −0.250388
\(553\) 48.8862 2.07885
\(554\) −36.3905 −1.54608
\(555\) −9.93846 −0.421864
\(556\) 35.7197 1.51485
\(557\) 38.2056 1.61882 0.809411 0.587243i \(-0.199787\pi\)
0.809411 + 0.587243i \(0.199787\pi\)
\(558\) −179.383 −7.59388
\(559\) −18.6444 −0.788575
\(560\) 41.5454 1.75561
\(561\) −5.61238 −0.236955
\(562\) −19.5171 −0.823280
\(563\) −33.7961 −1.42434 −0.712168 0.702009i \(-0.752287\pi\)
−0.712168 + 0.702009i \(0.752287\pi\)
\(564\) −93.7968 −3.94956
\(565\) 0.182736 0.00768775
\(566\) 9.14823 0.384529
\(567\) 133.201 5.59393
\(568\) −65.7356 −2.75821
\(569\) −28.9499 −1.21364 −0.606822 0.794838i \(-0.707556\pi\)
−0.606822 + 0.794838i \(0.707556\pi\)
\(570\) −58.6226 −2.45543
\(571\) −24.8670 −1.04065 −0.520326 0.853967i \(-0.674190\pi\)
−0.520326 + 0.853967i \(0.674190\pi\)
\(572\) −45.2433 −1.89172
\(573\) −0.917518 −0.0383299
\(574\) −34.3636 −1.43431
\(575\) 0.795566 0.0331774
\(576\) 234.171 9.75711
\(577\) −36.2956 −1.51101 −0.755503 0.655145i \(-0.772608\pi\)
−0.755503 + 0.655145i \(0.772608\pi\)
\(578\) 44.9655 1.87032
\(579\) 10.0960 0.419575
\(580\) 6.85825 0.284773
\(581\) 13.5659 0.562810
\(582\) −82.9173 −3.43703
\(583\) −2.40541 −0.0996218
\(584\) 5.03402 0.208309
\(585\) −25.8195 −1.06750
\(586\) 53.7835 2.22177
\(587\) −32.4294 −1.33850 −0.669252 0.743035i \(-0.733385\pi\)
−0.669252 + 0.743035i \(0.733385\pi\)
\(588\) −80.3254 −3.31256
\(589\) −56.2598 −2.31814
\(590\) 27.8461 1.14641
\(591\) 62.5738 2.57394
\(592\) 48.6649 2.00012
\(593\) −47.8197 −1.96372 −0.981859 0.189612i \(-0.939277\pi\)
−0.981859 + 0.189612i \(0.939277\pi\)
\(594\) 125.473 5.14823
\(595\) 1.98206 0.0812567
\(596\) −37.7650 −1.54692
\(597\) −59.6850 −2.44274
\(598\) −1.76914 −0.0723454
\(599\) 3.77767 0.154352 0.0771758 0.997018i \(-0.475410\pi\)
0.0771758 + 0.997018i \(0.475410\pi\)
\(600\) −134.307 −5.48304
\(601\) −45.0536 −1.83778 −0.918888 0.394519i \(-0.870911\pi\)
−0.918888 + 0.394519i \(0.870911\pi\)
\(602\) −49.0642 −1.99971
\(603\) −130.823 −5.32751
\(604\) −5.39818 −0.219649
\(605\) −4.47974 −0.182127
\(606\) 148.914 6.04922
\(607\) −15.5546 −0.631340 −0.315670 0.948869i \(-0.602229\pi\)
−0.315670 + 0.948869i \(0.602229\pi\)
\(608\) 151.044 6.12563
\(609\) −16.9961 −0.688715
\(610\) 24.6849 0.999462
\(611\) −17.7568 −0.718364
\(612\) 31.8612 1.28791
\(613\) 45.7279 1.84693 0.923467 0.383679i \(-0.125343\pi\)
0.923467 + 0.383679i \(0.125343\pi\)
\(614\) −12.0361 −0.485736
\(615\) −10.9784 −0.442691
\(616\) −74.9496 −3.01980
\(617\) 8.23058 0.331351 0.165675 0.986180i \(-0.447020\pi\)
0.165675 + 0.986180i \(0.447020\pi\)
\(618\) −117.882 −4.74193
\(619\) 9.06005 0.364154 0.182077 0.983284i \(-0.441718\pi\)
0.182077 + 0.983284i \(0.441718\pi\)
\(620\) 35.4648 1.42430
\(621\) 3.57998 0.143660
\(622\) 15.2441 0.611233
\(623\) 16.0100 0.641426
\(624\) 170.405 6.82164
\(625\) 14.4722 0.578889
\(626\) −52.8159 −2.11095
\(627\) 60.3407 2.40978
\(628\) 19.7630 0.788630
\(629\) 2.32173 0.0925733
\(630\) −67.9459 −2.70703
\(631\) −34.3981 −1.36937 −0.684683 0.728841i \(-0.740059\pi\)
−0.684683 + 0.728841i \(0.740059\pi\)
\(632\) −134.037 −5.33170
\(633\) 31.3738 1.24700
\(634\) 47.4820 1.88575
\(635\) −8.12926 −0.322600
\(636\) 18.4052 0.729813
\(637\) −15.2065 −0.602505
\(638\) −9.67467 −0.383024
\(639\) 61.3395 2.42655
\(640\) −28.1728 −1.11363
\(641\) −20.0849 −0.793305 −0.396652 0.917969i \(-0.629828\pi\)
−0.396652 + 0.917969i \(0.629828\pi\)
\(642\) −41.6577 −1.64410
\(643\) 6.79226 0.267861 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(644\) −3.39703 −0.133862
\(645\) −15.6749 −0.617198
\(646\) 13.6948 0.538816
\(647\) 14.8431 0.583541 0.291770 0.956488i \(-0.405756\pi\)
0.291770 + 0.956488i \(0.405756\pi\)
\(648\) −365.213 −14.3469
\(649\) −28.6622 −1.12509
\(650\) −40.3902 −1.58423
\(651\) −87.8886 −3.44463
\(652\) 27.6350 1.08227
\(653\) 5.33362 0.208721 0.104360 0.994540i \(-0.466720\pi\)
0.104360 + 0.994540i \(0.466720\pi\)
\(654\) −57.4909 −2.24807
\(655\) 5.72010 0.223503
\(656\) 53.7571 2.09886
\(657\) −4.69737 −0.183262
\(658\) −46.7284 −1.82166
\(659\) −37.1744 −1.44811 −0.724054 0.689743i \(-0.757724\pi\)
−0.724054 + 0.689743i \(0.757724\pi\)
\(660\) −38.0373 −1.48060
\(661\) 14.7625 0.574197 0.287098 0.957901i \(-0.407309\pi\)
0.287098 + 0.957901i \(0.407309\pi\)
\(662\) −49.6582 −1.93002
\(663\) 8.12973 0.315733
\(664\) −37.1953 −1.44346
\(665\) −21.3099 −0.826361
\(666\) −79.5897 −3.08404
\(667\) −0.276036 −0.0106882
\(668\) −93.4405 −3.61532
\(669\) −34.8474 −1.34728
\(670\) 35.4468 1.36943
\(671\) −25.4084 −0.980879
\(672\) 235.960 9.10234
\(673\) −6.19593 −0.238835 −0.119418 0.992844i \(-0.538103\pi\)
−0.119418 + 0.992844i \(0.538103\pi\)
\(674\) −94.3710 −3.63504
\(675\) 81.7325 3.14589
\(676\) −4.63989 −0.178457
\(677\) −29.8898 −1.14876 −0.574379 0.818590i \(-0.694756\pi\)
−0.574379 + 0.818590i \(0.694756\pi\)
\(678\) 1.97241 0.0757500
\(679\) −30.1412 −1.15671
\(680\) −5.43445 −0.208402
\(681\) −41.2507 −1.58073
\(682\) −50.0288 −1.91570
\(683\) −5.88873 −0.225326 −0.112663 0.993633i \(-0.535938\pi\)
−0.112663 + 0.993633i \(0.535938\pi\)
\(684\) −342.551 −13.0978
\(685\) −7.31255 −0.279398
\(686\) 24.1676 0.922722
\(687\) 53.8682 2.05520
\(688\) 76.7541 2.92622
\(689\) 3.48432 0.132742
\(690\) −1.48736 −0.0566230
\(691\) 21.0106 0.799280 0.399640 0.916672i \(-0.369135\pi\)
0.399640 + 0.916672i \(0.369135\pi\)
\(692\) 124.416 4.72960
\(693\) 69.9373 2.65670
\(694\) 44.6109 1.69341
\(695\) 5.68513 0.215649
\(696\) 46.6001 1.76637
\(697\) 2.56466 0.0971436
\(698\) 29.7660 1.12666
\(699\) 41.5693 1.57229
\(700\) −77.5557 −2.93133
\(701\) −28.6485 −1.08204 −0.541020 0.841010i \(-0.681961\pi\)
−0.541020 + 0.841010i \(0.681961\pi\)
\(702\) −181.752 −6.85980
\(703\) −24.9617 −0.941449
\(704\) 65.3089 2.46142
\(705\) −14.9287 −0.562247
\(706\) 76.3132 2.87209
\(707\) 54.1317 2.03583
\(708\) 219.311 8.24223
\(709\) 42.2511 1.58677 0.793387 0.608717i \(-0.208316\pi\)
0.793387 + 0.608717i \(0.208316\pi\)
\(710\) −16.6202 −0.623743
\(711\) 125.073 4.69061
\(712\) −43.8964 −1.64509
\(713\) −1.42741 −0.0534571
\(714\) 21.3940 0.800650
\(715\) −7.20091 −0.269299
\(716\) 71.0969 2.65702
\(717\) 77.4724 2.89326
\(718\) −95.4385 −3.56173
\(719\) 34.0378 1.26940 0.634698 0.772760i \(-0.281124\pi\)
0.634698 + 0.772760i \(0.281124\pi\)
\(720\) 106.292 3.96127
\(721\) −42.8514 −1.59587
\(722\) −95.5589 −3.55633
\(723\) 48.7008 1.81120
\(724\) −57.7213 −2.14520
\(725\) −6.30202 −0.234051
\(726\) −48.3534 −1.79456
\(727\) −3.52713 −0.130814 −0.0654069 0.997859i \(-0.520835\pi\)
−0.0654069 + 0.997859i \(0.520835\pi\)
\(728\) 108.567 4.02376
\(729\) 144.628 5.35660
\(730\) 1.27277 0.0471073
\(731\) 3.66182 0.135437
\(732\) 194.414 7.18576
\(733\) 12.6933 0.468839 0.234419 0.972136i \(-0.424681\pi\)
0.234419 + 0.972136i \(0.424681\pi\)
\(734\) 65.6488 2.42314
\(735\) −12.7846 −0.471566
\(736\) 3.83226 0.141259
\(737\) −36.4857 −1.34397
\(738\) −87.9177 −3.23630
\(739\) −40.4664 −1.48858 −0.744290 0.667857i \(-0.767212\pi\)
−0.744290 + 0.667857i \(0.767212\pi\)
\(740\) 15.7353 0.578440
\(741\) −87.4056 −3.21093
\(742\) 9.16924 0.336613
\(743\) 1.48947 0.0546434 0.0273217 0.999627i \(-0.491302\pi\)
0.0273217 + 0.999627i \(0.491302\pi\)
\(744\) 240.974 8.83455
\(745\) −6.01067 −0.220214
\(746\) 48.7661 1.78545
\(747\) 34.7078 1.26989
\(748\) 8.88591 0.324901
\(749\) −15.1430 −0.553312
\(750\) −73.7960 −2.69465
\(751\) 31.4438 1.14740 0.573701 0.819065i \(-0.305507\pi\)
0.573701 + 0.819065i \(0.305507\pi\)
\(752\) 73.1001 2.66569
\(753\) −24.2129 −0.882369
\(754\) 14.0141 0.510363
\(755\) −0.859174 −0.0312685
\(756\) −348.994 −12.6928
\(757\) 40.0089 1.45415 0.727073 0.686560i \(-0.240880\pi\)
0.727073 + 0.686560i \(0.240880\pi\)
\(758\) −2.39389 −0.0869499
\(759\) 1.53096 0.0555702
\(760\) 58.4277 2.11940
\(761\) −3.03210 −0.109914 −0.0549569 0.998489i \(-0.517502\pi\)
−0.0549569 + 0.998489i \(0.517502\pi\)
\(762\) −87.7456 −3.17869
\(763\) −20.8985 −0.756576
\(764\) 1.45268 0.0525561
\(765\) 5.07102 0.183343
\(766\) −98.4759 −3.55808
\(767\) 41.5182 1.49914
\(768\) −118.949 −4.29222
\(769\) −12.6658 −0.456739 −0.228369 0.973575i \(-0.573339\pi\)
−0.228369 + 0.973575i \(0.573339\pi\)
\(770\) −18.9497 −0.682901
\(771\) 35.1552 1.26609
\(772\) −15.9847 −0.575300
\(773\) 30.7892 1.10741 0.553705 0.832713i \(-0.313213\pi\)
0.553705 + 0.832713i \(0.313213\pi\)
\(774\) −125.529 −4.51203
\(775\) −32.5885 −1.17061
\(776\) 82.6417 2.96666
\(777\) −38.9950 −1.39894
\(778\) −31.1394 −1.11640
\(779\) −27.5736 −0.987927
\(780\) 55.0984 1.97284
\(781\) 17.1073 0.612146
\(782\) 0.347464 0.0124253
\(783\) −28.3586 −1.01345
\(784\) 62.6013 2.23576
\(785\) 3.14548 0.112267
\(786\) 61.7416 2.20225
\(787\) −22.6530 −0.807493 −0.403747 0.914871i \(-0.632292\pi\)
−0.403747 + 0.914871i \(0.632292\pi\)
\(788\) −99.0712 −3.52927
\(789\) −42.7980 −1.52365
\(790\) −33.8890 −1.20572
\(791\) 0.716990 0.0254932
\(792\) −191.755 −6.81372
\(793\) 36.8049 1.30698
\(794\) 94.1985 3.34298
\(795\) 2.92937 0.103894
\(796\) 94.4975 3.34937
\(797\) −35.9331 −1.27281 −0.636407 0.771353i \(-0.719580\pi\)
−0.636407 + 0.771353i \(0.719580\pi\)
\(798\) −230.014 −8.14242
\(799\) 3.48749 0.123379
\(800\) 87.4922 3.09332
\(801\) 40.9608 1.44728
\(802\) −21.2621 −0.750789
\(803\) −1.31007 −0.0462314
\(804\) 279.173 9.84569
\(805\) −0.540671 −0.0190561
\(806\) 72.4685 2.55259
\(807\) −20.6322 −0.726286
\(808\) −148.419 −5.22136
\(809\) 23.6332 0.830901 0.415450 0.909616i \(-0.363624\pi\)
0.415450 + 0.909616i \(0.363624\pi\)
\(810\) −92.3381 −3.24443
\(811\) 30.6084 1.07481 0.537403 0.843325i \(-0.319405\pi\)
0.537403 + 0.843325i \(0.319405\pi\)
\(812\) 26.9093 0.944333
\(813\) 102.944 3.61041
\(814\) −22.1971 −0.778009
\(815\) 4.39838 0.154068
\(816\) −33.4679 −1.17161
\(817\) −39.3695 −1.37736
\(818\) −1.15026 −0.0402180
\(819\) −101.307 −3.53994
\(820\) 17.3817 0.606997
\(821\) 19.0320 0.664221 0.332111 0.943240i \(-0.392239\pi\)
0.332111 + 0.943240i \(0.392239\pi\)
\(822\) −78.9301 −2.75300
\(823\) −26.1676 −0.912146 −0.456073 0.889942i \(-0.650744\pi\)
−0.456073 + 0.889942i \(0.650744\pi\)
\(824\) 117.491 4.09298
\(825\) 34.9524 1.21689
\(826\) 109.258 3.80158
\(827\) 34.4580 1.19822 0.599111 0.800666i \(-0.295521\pi\)
0.599111 + 0.800666i \(0.295521\pi\)
\(828\) −8.69116 −0.302039
\(829\) −37.9197 −1.31701 −0.658503 0.752578i \(-0.728810\pi\)
−0.658503 + 0.752578i \(0.728810\pi\)
\(830\) −9.40420 −0.326425
\(831\) −45.6161 −1.58240
\(832\) −94.6022 −3.27974
\(833\) 2.98661 0.103480
\(834\) 61.3642 2.12487
\(835\) −14.8720 −0.514666
\(836\) −95.5356 −3.30417
\(837\) −146.646 −5.06881
\(838\) −4.54512 −0.157009
\(839\) −29.9289 −1.03326 −0.516631 0.856208i \(-0.672814\pi\)
−0.516631 + 0.856208i \(0.672814\pi\)
\(840\) 91.2754 3.14930
\(841\) −26.8134 −0.924600
\(842\) 25.0505 0.863297
\(843\) −24.4650 −0.842621
\(844\) −49.6731 −1.70982
\(845\) −0.738484 −0.0254046
\(846\) −119.553 −4.11030
\(847\) −17.5769 −0.603950
\(848\) −14.3440 −0.492575
\(849\) 11.4675 0.393562
\(850\) 7.93274 0.272091
\(851\) −0.633325 −0.0217101
\(852\) −130.898 −4.48448
\(853\) 0.637030 0.0218115 0.0109058 0.999941i \(-0.496529\pi\)
0.0109058 + 0.999941i \(0.496529\pi\)
\(854\) 96.8548 3.31430
\(855\) −54.5204 −1.86456
\(856\) 41.5192 1.41910
\(857\) −35.2063 −1.20262 −0.601312 0.799014i \(-0.705355\pi\)
−0.601312 + 0.799014i \(0.705355\pi\)
\(858\) −77.7252 −2.65349
\(859\) 9.86511 0.336593 0.168297 0.985736i \(-0.446173\pi\)
0.168297 + 0.985736i \(0.446173\pi\)
\(860\) 24.8176 0.846273
\(861\) −43.0753 −1.46800
\(862\) −99.1035 −3.37548
\(863\) 11.5832 0.394296 0.197148 0.980374i \(-0.436832\pi\)
0.197148 + 0.980374i \(0.436832\pi\)
\(864\) 393.708 13.3942
\(865\) 19.8021 0.673291
\(866\) 23.1197 0.785638
\(867\) 56.3651 1.91426
\(868\) 139.151 4.72311
\(869\) 34.8822 1.18330
\(870\) 11.7820 0.399449
\(871\) 52.8508 1.79078
\(872\) 57.2998 1.94042
\(873\) −77.1150 −2.60995
\(874\) −3.73570 −0.126362
\(875\) −26.8255 −0.906868
\(876\) 10.0241 0.338684
\(877\) −28.9186 −0.976511 −0.488255 0.872701i \(-0.662367\pi\)
−0.488255 + 0.872701i \(0.662367\pi\)
\(878\) 62.3897 2.10555
\(879\) 67.4185 2.27397
\(880\) 29.6443 0.999307
\(881\) −22.1792 −0.747237 −0.373619 0.927582i \(-0.621883\pi\)
−0.373619 + 0.927582i \(0.621883\pi\)
\(882\) −102.382 −3.44738
\(883\) 54.9090 1.84784 0.923918 0.382591i \(-0.124968\pi\)
0.923918 + 0.382591i \(0.124968\pi\)
\(884\) −12.8716 −0.432917
\(885\) 34.9056 1.17334
\(886\) 12.3559 0.415103
\(887\) 34.2062 1.14853 0.574265 0.818669i \(-0.305288\pi\)
0.574265 + 0.818669i \(0.305288\pi\)
\(888\) 106.917 3.58791
\(889\) −31.8963 −1.06977
\(890\) −11.0985 −0.372022
\(891\) 95.0443 3.18411
\(892\) 55.1728 1.84732
\(893\) −37.4953 −1.25473
\(894\) −64.8780 −2.16984
\(895\) 11.3158 0.378244
\(896\) −110.540 −3.69289
\(897\) −2.21764 −0.0740449
\(898\) −78.3313 −2.61395
\(899\) 11.3072 0.377115
\(900\) −198.423 −6.61410
\(901\) −0.684330 −0.0227983
\(902\) −24.5198 −0.816419
\(903\) −61.5028 −2.04668
\(904\) −1.96586 −0.0653834
\(905\) −9.18691 −0.305383
\(906\) −9.27375 −0.308100
\(907\) −57.3282 −1.90355 −0.951776 0.306795i \(-0.900744\pi\)
−0.951776 + 0.306795i \(0.900744\pi\)
\(908\) 65.3110 2.16742
\(909\) 138.494 4.59354
\(910\) 27.4494 0.909937
\(911\) 16.3948 0.543185 0.271592 0.962412i \(-0.412450\pi\)
0.271592 + 0.962412i \(0.412450\pi\)
\(912\) 359.826 11.9150
\(913\) 9.67982 0.320355
\(914\) −62.2295 −2.05837
\(915\) 30.9429 1.02294
\(916\) −85.2879 −2.81799
\(917\) 22.4437 0.741155
\(918\) 35.6967 1.17817
\(919\) 50.1888 1.65558 0.827788 0.561040i \(-0.189599\pi\)
0.827788 + 0.561040i \(0.189599\pi\)
\(920\) 1.48242 0.0488739
\(921\) −15.0874 −0.497147
\(922\) −72.0742 −2.37364
\(923\) −24.7805 −0.815659
\(924\) −149.245 −4.90980
\(925\) −14.4591 −0.475412
\(926\) −21.3564 −0.701815
\(927\) −109.633 −3.60083
\(928\) −30.3570 −0.996517
\(929\) −38.1403 −1.25134 −0.625671 0.780087i \(-0.715175\pi\)
−0.625671 + 0.780087i \(0.715175\pi\)
\(930\) 60.9264 1.99785
\(931\) −32.1101 −1.05237
\(932\) −65.8154 −2.15585
\(933\) 19.1088 0.625593
\(934\) 22.1898 0.726074
\(935\) 1.41428 0.0462519
\(936\) 277.764 9.07900
\(937\) −1.77357 −0.0579399 −0.0289699 0.999580i \(-0.509223\pi\)
−0.0289699 + 0.999580i \(0.509223\pi\)
\(938\) 139.081 4.54115
\(939\) −66.2057 −2.16054
\(940\) 23.6361 0.770925
\(941\) −20.5078 −0.668536 −0.334268 0.942478i \(-0.608489\pi\)
−0.334268 + 0.942478i \(0.608489\pi\)
\(942\) 33.9517 1.10620
\(943\) −0.699594 −0.0227819
\(944\) −170.919 −5.56295
\(945\) −55.5459 −1.80691
\(946\) −35.0092 −1.13825
\(947\) 25.6908 0.834838 0.417419 0.908714i \(-0.362935\pi\)
0.417419 + 0.908714i \(0.362935\pi\)
\(948\) −266.904 −8.66865
\(949\) 1.89768 0.0616014
\(950\) −85.2877 −2.76710
\(951\) 59.5195 1.93005
\(952\) −21.3229 −0.691079
\(953\) 13.2486 0.429165 0.214583 0.976706i \(-0.431161\pi\)
0.214583 + 0.976706i \(0.431161\pi\)
\(954\) 23.4591 0.759517
\(955\) 0.231208 0.00748172
\(956\) −122.660 −3.96710
\(957\) −12.1274 −0.392022
\(958\) −15.8602 −0.512420
\(959\) −28.6918 −0.926508
\(960\) −79.5348 −2.56697
\(961\) 27.4707 0.886151
\(962\) 32.1533 1.03666
\(963\) −38.7426 −1.24846
\(964\) −77.1065 −2.48343
\(965\) −2.54411 −0.0818979
\(966\) −5.83589 −0.187767
\(967\) 37.8743 1.21796 0.608978 0.793187i \(-0.291580\pi\)
0.608978 + 0.793187i \(0.291580\pi\)
\(968\) 48.1927 1.54897
\(969\) 17.1667 0.551474
\(970\) 20.8946 0.670884
\(971\) 7.53642 0.241855 0.120928 0.992661i \(-0.461413\pi\)
0.120928 + 0.992661i \(0.461413\pi\)
\(972\) −416.663 −13.3645
\(973\) 22.3065 0.715112
\(974\) −27.1316 −0.869352
\(975\) −50.6297 −1.62145
\(976\) −151.516 −4.84991
\(977\) −42.7960 −1.36917 −0.684583 0.728934i \(-0.740016\pi\)
−0.684583 + 0.728934i \(0.740016\pi\)
\(978\) 47.4752 1.51809
\(979\) 11.4237 0.365104
\(980\) 20.2414 0.646589
\(981\) −53.4679 −1.70710
\(982\) 35.5421 1.13419
\(983\) 51.1788 1.63235 0.816176 0.577804i \(-0.196090\pi\)
0.816176 + 0.577804i \(0.196090\pi\)
\(984\) 118.105 3.76504
\(985\) −15.7682 −0.502415
\(986\) −2.75241 −0.0876545
\(987\) −58.5749 −1.86446
\(988\) 138.387 4.40267
\(989\) −0.998877 −0.0317624
\(990\) −48.4821 −1.54086
\(991\) −53.5386 −1.70071 −0.850354 0.526210i \(-0.823612\pi\)
−0.850354 + 0.526210i \(0.823612\pi\)
\(992\) −156.980 −4.98411
\(993\) −62.2474 −1.97536
\(994\) −65.2116 −2.06839
\(995\) 15.0402 0.476806
\(996\) −74.0660 −2.34687
\(997\) −34.8352 −1.10324 −0.551621 0.834095i \(-0.685991\pi\)
−0.551621 + 0.834095i \(0.685991\pi\)
\(998\) 112.203 3.55173
\(999\) −65.0647 −2.05856
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 8003.2.a.b.1.4 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.4 153 1.1 even 1 trivial