Properties

Label 4034.2.a.d.1.19
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.570351 q^{3} +1.00000 q^{4} -1.34990 q^{5} -0.570351 q^{6} -5.21632 q^{7} +1.00000 q^{8} -2.67470 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.570351 q^{3} +1.00000 q^{4} -1.34990 q^{5} -0.570351 q^{6} -5.21632 q^{7} +1.00000 q^{8} -2.67470 q^{9} -1.34990 q^{10} +4.89676 q^{11} -0.570351 q^{12} -1.50729 q^{13} -5.21632 q^{14} +0.769917 q^{15} +1.00000 q^{16} +0.322117 q^{17} -2.67470 q^{18} -4.66258 q^{19} -1.34990 q^{20} +2.97514 q^{21} +4.89676 q^{22} -9.15574 q^{23} -0.570351 q^{24} -3.17777 q^{25} -1.50729 q^{26} +3.23657 q^{27} -5.21632 q^{28} +2.96884 q^{29} +0.769917 q^{30} +5.76322 q^{31} +1.00000 q^{32} -2.79288 q^{33} +0.322117 q^{34} +7.04151 q^{35} -2.67470 q^{36} +8.51683 q^{37} -4.66258 q^{38} +0.859688 q^{39} -1.34990 q^{40} +6.87743 q^{41} +2.97514 q^{42} -1.22389 q^{43} +4.89676 q^{44} +3.61058 q^{45} -9.15574 q^{46} -4.13339 q^{47} -0.570351 q^{48} +20.2100 q^{49} -3.17777 q^{50} -0.183720 q^{51} -1.50729 q^{52} +11.4389 q^{53} +3.23657 q^{54} -6.61014 q^{55} -5.21632 q^{56} +2.65931 q^{57} +2.96884 q^{58} +11.2413 q^{59} +0.769917 q^{60} -11.6601 q^{61} +5.76322 q^{62} +13.9521 q^{63} +1.00000 q^{64} +2.03470 q^{65} -2.79288 q^{66} -8.42595 q^{67} +0.322117 q^{68} +5.22199 q^{69} +7.04151 q^{70} +6.79327 q^{71} -2.67470 q^{72} -11.4400 q^{73} +8.51683 q^{74} +1.81245 q^{75} -4.66258 q^{76} -25.5431 q^{77} +0.859688 q^{78} -7.18568 q^{79} -1.34990 q^{80} +6.17811 q^{81} +6.87743 q^{82} +0.615951 q^{83} +2.97514 q^{84} -0.434825 q^{85} -1.22389 q^{86} -1.69328 q^{87} +4.89676 q^{88} +17.3622 q^{89} +3.61058 q^{90} +7.86253 q^{91} -9.15574 q^{92} -3.28706 q^{93} -4.13339 q^{94} +6.29402 q^{95} -0.570351 q^{96} +11.3356 q^{97} +20.2100 q^{98} -13.0974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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
\(3\) −0.570351 −0.329293 −0.164646 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.34990 −0.603694 −0.301847 0.953356i \(-0.597603\pi\)
−0.301847 + 0.953356i \(0.597603\pi\)
\(6\) −0.570351 −0.232845
\(7\) −5.21632 −1.97158 −0.985792 0.167971i \(-0.946279\pi\)
−0.985792 + 0.167971i \(0.946279\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.67470 −0.891566
\(10\) −1.34990 −0.426876
\(11\) 4.89676 1.47643 0.738215 0.674566i \(-0.235669\pi\)
0.738215 + 0.674566i \(0.235669\pi\)
\(12\) −0.570351 −0.164646
\(13\) −1.50729 −0.418048 −0.209024 0.977910i \(-0.567029\pi\)
−0.209024 + 0.977910i \(0.567029\pi\)
\(14\) −5.21632 −1.39412
\(15\) 0.769917 0.198792
\(16\) 1.00000 0.250000
\(17\) 0.322117 0.0781247 0.0390624 0.999237i \(-0.487563\pi\)
0.0390624 + 0.999237i \(0.487563\pi\)
\(18\) −2.67470 −0.630433
\(19\) −4.66258 −1.06967 −0.534835 0.844956i \(-0.679626\pi\)
−0.534835 + 0.844956i \(0.679626\pi\)
\(20\) −1.34990 −0.301847
\(21\) 2.97514 0.649228
\(22\) 4.89676 1.04399
\(23\) −9.15574 −1.90910 −0.954551 0.298046i \(-0.903665\pi\)
−0.954551 + 0.298046i \(0.903665\pi\)
\(24\) −0.570351 −0.116422
\(25\) −3.17777 −0.635554
\(26\) −1.50729 −0.295605
\(27\) 3.23657 0.622879
\(28\) −5.21632 −0.985792
\(29\) 2.96884 0.551300 0.275650 0.961258i \(-0.411107\pi\)
0.275650 + 0.961258i \(0.411107\pi\)
\(30\) 0.769917 0.140567
\(31\) 5.76322 1.03510 0.517552 0.855651i \(-0.326843\pi\)
0.517552 + 0.855651i \(0.326843\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.79288 −0.486177
\(34\) 0.322117 0.0552425
\(35\) 7.04151 1.19023
\(36\) −2.67470 −0.445783
\(37\) 8.51683 1.40016 0.700079 0.714065i \(-0.253148\pi\)
0.700079 + 0.714065i \(0.253148\pi\)
\(38\) −4.66258 −0.756371
\(39\) 0.859688 0.137660
\(40\) −1.34990 −0.213438
\(41\) 6.87743 1.07407 0.537037 0.843559i \(-0.319544\pi\)
0.537037 + 0.843559i \(0.319544\pi\)
\(42\) 2.97514 0.459073
\(43\) −1.22389 −0.186641 −0.0933207 0.995636i \(-0.529748\pi\)
−0.0933207 + 0.995636i \(0.529748\pi\)
\(44\) 4.89676 0.738215
\(45\) 3.61058 0.538233
\(46\) −9.15574 −1.34994
\(47\) −4.13339 −0.602917 −0.301458 0.953479i \(-0.597473\pi\)
−0.301458 + 0.953479i \(0.597473\pi\)
\(48\) −0.570351 −0.0823231
\(49\) 20.2100 2.88714
\(50\) −3.17777 −0.449405
\(51\) −0.183720 −0.0257259
\(52\) −1.50729 −0.209024
\(53\) 11.4389 1.57126 0.785628 0.618699i \(-0.212340\pi\)
0.785628 + 0.618699i \(0.212340\pi\)
\(54\) 3.23657 0.440442
\(55\) −6.61014 −0.891311
\(56\) −5.21632 −0.697060
\(57\) 2.65931 0.352234
\(58\) 2.96884 0.389828
\(59\) 11.2413 1.46349 0.731747 0.681576i \(-0.238705\pi\)
0.731747 + 0.681576i \(0.238705\pi\)
\(60\) 0.769917 0.0993959
\(61\) −11.6601 −1.49293 −0.746463 0.665427i \(-0.768250\pi\)
−0.746463 + 0.665427i \(0.768250\pi\)
\(62\) 5.76322 0.731930
\(63\) 13.9521 1.75780
\(64\) 1.00000 0.125000
\(65\) 2.03470 0.252373
\(66\) −2.79288 −0.343779
\(67\) −8.42595 −1.02939 −0.514697 0.857372i \(-0.672096\pi\)
−0.514697 + 0.857372i \(0.672096\pi\)
\(68\) 0.322117 0.0390624
\(69\) 5.22199 0.628653
\(70\) 7.04151 0.841622
\(71\) 6.79327 0.806212 0.403106 0.915153i \(-0.367931\pi\)
0.403106 + 0.915153i \(0.367931\pi\)
\(72\) −2.67470 −0.315216
\(73\) −11.4400 −1.33895 −0.669476 0.742834i \(-0.733481\pi\)
−0.669476 + 0.742834i \(0.733481\pi\)
\(74\) 8.51683 0.990062
\(75\) 1.81245 0.209283
\(76\) −4.66258 −0.534835
\(77\) −25.5431 −2.91091
\(78\) 0.859688 0.0973404
\(79\) −7.18568 −0.808452 −0.404226 0.914659i \(-0.632459\pi\)
−0.404226 + 0.914659i \(0.632459\pi\)
\(80\) −1.34990 −0.150923
\(81\) 6.17811 0.686457
\(82\) 6.87743 0.759485
\(83\) 0.615951 0.0676094 0.0338047 0.999428i \(-0.489238\pi\)
0.0338047 + 0.999428i \(0.489238\pi\)
\(84\) 2.97514 0.324614
\(85\) −0.434825 −0.0471634
\(86\) −1.22389 −0.131975
\(87\) −1.69328 −0.181539
\(88\) 4.89676 0.521997
\(89\) 17.3622 1.84039 0.920197 0.391456i \(-0.128028\pi\)
0.920197 + 0.391456i \(0.128028\pi\)
\(90\) 3.61058 0.380588
\(91\) 7.86253 0.824217
\(92\) −9.15574 −0.954551
\(93\) −3.28706 −0.340852
\(94\) −4.13339 −0.426326
\(95\) 6.29402 0.645753
\(96\) −0.570351 −0.0582112
\(97\) 11.3356 1.15096 0.575479 0.817817i \(-0.304816\pi\)
0.575479 + 0.817817i \(0.304816\pi\)
\(98\) 20.2100 2.04152
\(99\) −13.0974 −1.31634
\(100\) −3.17777 −0.317777
\(101\) −8.87668 −0.883263 −0.441631 0.897197i \(-0.645600\pi\)
−0.441631 + 0.897197i \(0.645600\pi\)
\(102\) −0.183720 −0.0181910
\(103\) 14.9086 1.46899 0.734496 0.678613i \(-0.237419\pi\)
0.734496 + 0.678613i \(0.237419\pi\)
\(104\) −1.50729 −0.147802
\(105\) −4.01614 −0.391935
\(106\) 11.4389 1.11105
\(107\) 4.02749 0.389352 0.194676 0.980868i \(-0.437634\pi\)
0.194676 + 0.980868i \(0.437634\pi\)
\(108\) 3.23657 0.311439
\(109\) −12.4478 −1.19228 −0.596139 0.802881i \(-0.703299\pi\)
−0.596139 + 0.802881i \(0.703299\pi\)
\(110\) −6.61014 −0.630252
\(111\) −4.85759 −0.461062
\(112\) −5.21632 −0.492896
\(113\) −12.5797 −1.18340 −0.591701 0.806157i \(-0.701543\pi\)
−0.591701 + 0.806157i \(0.701543\pi\)
\(114\) 2.65931 0.249067
\(115\) 12.3593 1.15251
\(116\) 2.96884 0.275650
\(117\) 4.03156 0.372718
\(118\) 11.2413 1.03485
\(119\) −1.68026 −0.154029
\(120\) 0.769917 0.0702835
\(121\) 12.9783 1.17985
\(122\) −11.6601 −1.05566
\(123\) −3.92255 −0.353684
\(124\) 5.76322 0.517552
\(125\) 11.0392 0.987374
\(126\) 13.9521 1.24295
\(127\) −17.8995 −1.58832 −0.794161 0.607708i \(-0.792089\pi\)
−0.794161 + 0.607708i \(0.792089\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0.698047 0.0614596
\(130\) 2.03470 0.178455
\(131\) 13.7807 1.20402 0.602012 0.798487i \(-0.294366\pi\)
0.602012 + 0.798487i \(0.294366\pi\)
\(132\) −2.79288 −0.243089
\(133\) 24.3215 2.10894
\(134\) −8.42595 −0.727892
\(135\) −4.36905 −0.376028
\(136\) 0.322117 0.0276213
\(137\) 19.1060 1.63234 0.816169 0.577814i \(-0.196094\pi\)
0.816169 + 0.577814i \(0.196094\pi\)
\(138\) 5.22199 0.444525
\(139\) 8.94678 0.758856 0.379428 0.925221i \(-0.376121\pi\)
0.379428 + 0.925221i \(0.376121\pi\)
\(140\) 7.04151 0.595116
\(141\) 2.35748 0.198536
\(142\) 6.79327 0.570078
\(143\) −7.38087 −0.617219
\(144\) −2.67470 −0.222892
\(145\) −4.00764 −0.332816
\(146\) −11.4400 −0.946782
\(147\) −11.5268 −0.950715
\(148\) 8.51683 0.700079
\(149\) 4.04808 0.331632 0.165816 0.986157i \(-0.446974\pi\)
0.165816 + 0.986157i \(0.446974\pi\)
\(150\) 1.81245 0.147986
\(151\) 6.54005 0.532221 0.266111 0.963942i \(-0.414261\pi\)
0.266111 + 0.963942i \(0.414261\pi\)
\(152\) −4.66258 −0.378186
\(153\) −0.861565 −0.0696534
\(154\) −25.5431 −2.05832
\(155\) −7.77977 −0.624886
\(156\) 0.859688 0.0688301
\(157\) −5.48019 −0.437367 −0.218684 0.975796i \(-0.570176\pi\)
−0.218684 + 0.975796i \(0.570176\pi\)
\(158\) −7.18568 −0.571662
\(159\) −6.52420 −0.517403
\(160\) −1.34990 −0.106719
\(161\) 47.7593 3.76396
\(162\) 6.17811 0.485399
\(163\) −1.13211 −0.0886733 −0.0443367 0.999017i \(-0.514117\pi\)
−0.0443367 + 0.999017i \(0.514117\pi\)
\(164\) 6.87743 0.537037
\(165\) 3.77010 0.293502
\(166\) 0.615951 0.0478071
\(167\) 5.63483 0.436036 0.218018 0.975945i \(-0.430041\pi\)
0.218018 + 0.975945i \(0.430041\pi\)
\(168\) 2.97514 0.229537
\(169\) −10.7281 −0.825236
\(170\) −0.434825 −0.0333496
\(171\) 12.4710 0.953682
\(172\) −1.22389 −0.0933207
\(173\) 8.86807 0.674227 0.337113 0.941464i \(-0.390549\pi\)
0.337113 + 0.941464i \(0.390549\pi\)
\(174\) −1.69328 −0.128367
\(175\) 16.5763 1.25305
\(176\) 4.89676 0.369107
\(177\) −6.41150 −0.481918
\(178\) 17.3622 1.30136
\(179\) −0.744506 −0.0556470 −0.0278235 0.999613i \(-0.508858\pi\)
−0.0278235 + 0.999613i \(0.508858\pi\)
\(180\) 3.61058 0.269117
\(181\) −9.27992 −0.689771 −0.344885 0.938645i \(-0.612082\pi\)
−0.344885 + 0.938645i \(0.612082\pi\)
\(182\) 7.86253 0.582810
\(183\) 6.65037 0.491609
\(184\) −9.15574 −0.674970
\(185\) −11.4969 −0.845267
\(186\) −3.28706 −0.241019
\(187\) 1.57733 0.115346
\(188\) −4.13339 −0.301458
\(189\) −16.8830 −1.22806
\(190\) 6.29402 0.456616
\(191\) 11.8110 0.854613 0.427307 0.904107i \(-0.359463\pi\)
0.427307 + 0.904107i \(0.359463\pi\)
\(192\) −0.570351 −0.0411616
\(193\) −1.38758 −0.0998804 −0.0499402 0.998752i \(-0.515903\pi\)
−0.0499402 + 0.998752i \(0.515903\pi\)
\(194\) 11.3356 0.813850
\(195\) −1.16049 −0.0831046
\(196\) 20.2100 1.44357
\(197\) −10.4728 −0.746156 −0.373078 0.927800i \(-0.621698\pi\)
−0.373078 + 0.927800i \(0.621698\pi\)
\(198\) −13.0974 −0.930790
\(199\) 14.8353 1.05164 0.525822 0.850594i \(-0.323758\pi\)
0.525822 + 0.850594i \(0.323758\pi\)
\(200\) −3.17777 −0.224702
\(201\) 4.80575 0.338972
\(202\) −8.87668 −0.624561
\(203\) −15.4864 −1.08693
\(204\) −0.183720 −0.0128629
\(205\) −9.28384 −0.648411
\(206\) 14.9086 1.03873
\(207\) 24.4888 1.70209
\(208\) −1.50729 −0.104512
\(209\) −22.8316 −1.57929
\(210\) −4.01614 −0.277140
\(211\) 26.9035 1.85211 0.926057 0.377384i \(-0.123176\pi\)
0.926057 + 0.377384i \(0.123176\pi\)
\(212\) 11.4389 0.785628
\(213\) −3.87455 −0.265480
\(214\) 4.02749 0.275314
\(215\) 1.65213 0.112674
\(216\) 3.23657 0.220221
\(217\) −30.0628 −2.04080
\(218\) −12.4478 −0.843068
\(219\) 6.52482 0.440907
\(220\) −6.61014 −0.445656
\(221\) −0.485525 −0.0326599
\(222\) −4.85759 −0.326020
\(223\) 5.37965 0.360248 0.180124 0.983644i \(-0.442350\pi\)
0.180124 + 0.983644i \(0.442350\pi\)
\(224\) −5.21632 −0.348530
\(225\) 8.49958 0.566639
\(226\) −12.5797 −0.836792
\(227\) 17.7145 1.17576 0.587878 0.808950i \(-0.299964\pi\)
0.587878 + 0.808950i \(0.299964\pi\)
\(228\) 2.65931 0.176117
\(229\) 15.0714 0.995947 0.497974 0.867192i \(-0.334078\pi\)
0.497974 + 0.867192i \(0.334078\pi\)
\(230\) 12.3593 0.814950
\(231\) 14.5685 0.958539
\(232\) 2.96884 0.194914
\(233\) 2.85531 0.187057 0.0935287 0.995617i \(-0.470185\pi\)
0.0935287 + 0.995617i \(0.470185\pi\)
\(234\) 4.03156 0.263551
\(235\) 5.57966 0.363977
\(236\) 11.2413 0.731747
\(237\) 4.09836 0.266217
\(238\) −1.68026 −0.108915
\(239\) 1.54106 0.0996831 0.0498415 0.998757i \(-0.484128\pi\)
0.0498415 + 0.998757i \(0.484128\pi\)
\(240\) 0.769917 0.0496979
\(241\) 2.05203 0.132183 0.0660914 0.997814i \(-0.478947\pi\)
0.0660914 + 0.997814i \(0.478947\pi\)
\(242\) 12.9783 0.834277
\(243\) −13.2334 −0.848924
\(244\) −11.6601 −0.746463
\(245\) −27.2815 −1.74295
\(246\) −3.92255 −0.250093
\(247\) 7.02789 0.447174
\(248\) 5.76322 0.365965
\(249\) −0.351308 −0.0222633
\(250\) 11.0392 0.698179
\(251\) −21.3125 −1.34523 −0.672616 0.739992i \(-0.734829\pi\)
−0.672616 + 0.739992i \(0.734829\pi\)
\(252\) 13.9521 0.878899
\(253\) −44.8335 −2.81866
\(254\) −17.8995 −1.12311
\(255\) 0.248003 0.0155306
\(256\) 1.00000 0.0625000
\(257\) 1.74967 0.109142 0.0545708 0.998510i \(-0.482621\pi\)
0.0545708 + 0.998510i \(0.482621\pi\)
\(258\) 0.698047 0.0434585
\(259\) −44.4265 −2.76053
\(260\) 2.03470 0.126187
\(261\) −7.94075 −0.491520
\(262\) 13.7807 0.851374
\(263\) −12.0852 −0.745204 −0.372602 0.927991i \(-0.621534\pi\)
−0.372602 + 0.927991i \(0.621534\pi\)
\(264\) −2.79288 −0.171890
\(265\) −15.4414 −0.948557
\(266\) 24.3215 1.49125
\(267\) −9.90258 −0.606028
\(268\) −8.42595 −0.514697
\(269\) 16.6643 1.01604 0.508020 0.861345i \(-0.330377\pi\)
0.508020 + 0.861345i \(0.330377\pi\)
\(270\) −4.36905 −0.265892
\(271\) −14.5424 −0.883387 −0.441694 0.897166i \(-0.645622\pi\)
−0.441694 + 0.897166i \(0.645622\pi\)
\(272\) 0.322117 0.0195312
\(273\) −4.48441 −0.271409
\(274\) 19.1060 1.15424
\(275\) −15.5608 −0.938351
\(276\) 5.22199 0.314327
\(277\) −4.14787 −0.249221 −0.124611 0.992206i \(-0.539768\pi\)
−0.124611 + 0.992206i \(0.539768\pi\)
\(278\) 8.94678 0.536592
\(279\) −15.4149 −0.922865
\(280\) 7.04151 0.420811
\(281\) 17.6806 1.05474 0.527368 0.849637i \(-0.323179\pi\)
0.527368 + 0.849637i \(0.323179\pi\)
\(282\) 2.35748 0.140386
\(283\) −20.8410 −1.23887 −0.619436 0.785048i \(-0.712638\pi\)
−0.619436 + 0.785048i \(0.712638\pi\)
\(284\) 6.79327 0.403106
\(285\) −3.58980 −0.212642
\(286\) −7.38087 −0.436440
\(287\) −35.8749 −2.11763
\(288\) −2.67470 −0.157608
\(289\) −16.8962 −0.993897
\(290\) −4.00764 −0.235336
\(291\) −6.46528 −0.379002
\(292\) −11.4400 −0.669476
\(293\) 11.4157 0.666911 0.333455 0.942766i \(-0.391785\pi\)
0.333455 + 0.942766i \(0.391785\pi\)
\(294\) −11.5268 −0.672257
\(295\) −15.1747 −0.883503
\(296\) 8.51683 0.495031
\(297\) 15.8487 0.919637
\(298\) 4.04808 0.234499
\(299\) 13.8004 0.798097
\(300\) 1.81245 0.104642
\(301\) 6.38420 0.367979
\(302\) 6.54005 0.376337
\(303\) 5.06283 0.290852
\(304\) −4.66258 −0.267418
\(305\) 15.7400 0.901270
\(306\) −0.861565 −0.0492524
\(307\) −1.95560 −0.111612 −0.0558059 0.998442i \(-0.517773\pi\)
−0.0558059 + 0.998442i \(0.517773\pi\)
\(308\) −25.5431 −1.45545
\(309\) −8.50316 −0.483728
\(310\) −7.77977 −0.441861
\(311\) 20.7951 1.17918 0.589591 0.807702i \(-0.299289\pi\)
0.589591 + 0.807702i \(0.299289\pi\)
\(312\) 0.859688 0.0486702
\(313\) 9.78998 0.553363 0.276681 0.960962i \(-0.410765\pi\)
0.276681 + 0.960962i \(0.410765\pi\)
\(314\) −5.48019 −0.309265
\(315\) −18.8339 −1.06117
\(316\) −7.18568 −0.404226
\(317\) 21.4136 1.20271 0.601355 0.798982i \(-0.294628\pi\)
0.601355 + 0.798982i \(0.294628\pi\)
\(318\) −6.52420 −0.365859
\(319\) 14.5377 0.813955
\(320\) −1.34990 −0.0754617
\(321\) −2.29709 −0.128211
\(322\) 47.7593 2.66152
\(323\) −1.50190 −0.0835677
\(324\) 6.17811 0.343229
\(325\) 4.78984 0.265692
\(326\) −1.13211 −0.0627015
\(327\) 7.09959 0.392608
\(328\) 6.87743 0.379742
\(329\) 21.5611 1.18870
\(330\) 3.77010 0.207537
\(331\) 20.0123 1.09997 0.549986 0.835174i \(-0.314633\pi\)
0.549986 + 0.835174i \(0.314633\pi\)
\(332\) 0.615951 0.0338047
\(333\) −22.7800 −1.24833
\(334\) 5.63483 0.308324
\(335\) 11.3742 0.621439
\(336\) 2.97514 0.162307
\(337\) 12.9771 0.706906 0.353453 0.935452i \(-0.385007\pi\)
0.353453 + 0.935452i \(0.385007\pi\)
\(338\) −10.7281 −0.583530
\(339\) 7.17487 0.389685
\(340\) −0.434825 −0.0235817
\(341\) 28.2211 1.52826
\(342\) 12.4710 0.674355
\(343\) −68.9076 −3.72066
\(344\) −1.22389 −0.0659877
\(345\) −7.04916 −0.379514
\(346\) 8.86807 0.476750
\(347\) −31.8177 −1.70806 −0.854031 0.520221i \(-0.825849\pi\)
−0.854031 + 0.520221i \(0.825849\pi\)
\(348\) −1.69328 −0.0907694
\(349\) −29.6834 −1.58892 −0.794459 0.607318i \(-0.792245\pi\)
−0.794459 + 0.607318i \(0.792245\pi\)
\(350\) 16.5763 0.886039
\(351\) −4.87847 −0.260393
\(352\) 4.89676 0.260998
\(353\) 21.3908 1.13852 0.569258 0.822159i \(-0.307231\pi\)
0.569258 + 0.822159i \(0.307231\pi\)
\(354\) −6.41150 −0.340767
\(355\) −9.17023 −0.486705
\(356\) 17.3622 0.920197
\(357\) 0.958341 0.0507208
\(358\) −0.744506 −0.0393483
\(359\) −33.2527 −1.75501 −0.877504 0.479568i \(-0.840793\pi\)
−0.877504 + 0.479568i \(0.840793\pi\)
\(360\) 3.61058 0.190294
\(361\) 2.73969 0.144194
\(362\) −9.27992 −0.487742
\(363\) −7.40219 −0.388514
\(364\) 7.86253 0.412109
\(365\) 15.4429 0.808317
\(366\) 6.65037 0.347620
\(367\) −9.57219 −0.499664 −0.249832 0.968289i \(-0.580375\pi\)
−0.249832 + 0.968289i \(0.580375\pi\)
\(368\) −9.15574 −0.477276
\(369\) −18.3950 −0.957608
\(370\) −11.4969 −0.597694
\(371\) −59.6691 −3.09786
\(372\) −3.28706 −0.170426
\(373\) −21.7305 −1.12516 −0.562582 0.826742i \(-0.690192\pi\)
−0.562582 + 0.826742i \(0.690192\pi\)
\(374\) 1.57733 0.0815617
\(375\) −6.29621 −0.325135
\(376\) −4.13339 −0.213163
\(377\) −4.47492 −0.230470
\(378\) −16.8830 −0.868368
\(379\) −31.9976 −1.64361 −0.821803 0.569771i \(-0.807032\pi\)
−0.821803 + 0.569771i \(0.807032\pi\)
\(380\) 6.29402 0.322877
\(381\) 10.2090 0.523022
\(382\) 11.8110 0.604303
\(383\) 16.0904 0.822183 0.411091 0.911594i \(-0.365148\pi\)
0.411091 + 0.911594i \(0.365148\pi\)
\(384\) −0.570351 −0.0291056
\(385\) 34.4806 1.75730
\(386\) −1.38758 −0.0706261
\(387\) 3.27354 0.166403
\(388\) 11.3356 0.575479
\(389\) 12.6861 0.643213 0.321607 0.946873i \(-0.395777\pi\)
0.321607 + 0.946873i \(0.395777\pi\)
\(390\) −1.16049 −0.0587638
\(391\) −2.94921 −0.149148
\(392\) 20.2100 1.02076
\(393\) −7.85983 −0.396476
\(394\) −10.4728 −0.527612
\(395\) 9.69995 0.488057
\(396\) −13.0974 −0.658168
\(397\) −0.346410 −0.0173858 −0.00869291 0.999962i \(-0.502767\pi\)
−0.00869291 + 0.999962i \(0.502767\pi\)
\(398\) 14.8353 0.743625
\(399\) −13.8718 −0.694460
\(400\) −3.17777 −0.158888
\(401\) 23.8455 1.19079 0.595394 0.803434i \(-0.296996\pi\)
0.595394 + 0.803434i \(0.296996\pi\)
\(402\) 4.80575 0.239689
\(403\) −8.68687 −0.432724
\(404\) −8.87668 −0.441631
\(405\) −8.33984 −0.414410
\(406\) −15.4864 −0.768578
\(407\) 41.7049 2.06724
\(408\) −0.183720 −0.00909548
\(409\) −1.11996 −0.0553783 −0.0276891 0.999617i \(-0.508815\pi\)
−0.0276891 + 0.999617i \(0.508815\pi\)
\(410\) −9.28384 −0.458496
\(411\) −10.8971 −0.537516
\(412\) 14.9086 0.734496
\(413\) −58.6383 −2.88540
\(414\) 24.4888 1.20356
\(415\) −0.831472 −0.0408154
\(416\) −1.50729 −0.0739012
\(417\) −5.10281 −0.249885
\(418\) −22.8316 −1.11673
\(419\) −37.9806 −1.85547 −0.927737 0.373235i \(-0.878249\pi\)
−0.927737 + 0.373235i \(0.878249\pi\)
\(420\) −4.01614 −0.195967
\(421\) −3.97835 −0.193893 −0.0969464 0.995290i \(-0.530908\pi\)
−0.0969464 + 0.995290i \(0.530908\pi\)
\(422\) 26.9035 1.30964
\(423\) 11.0556 0.537540
\(424\) 11.4389 0.555523
\(425\) −1.02361 −0.0496525
\(426\) −3.87455 −0.187722
\(427\) 60.8230 2.94343
\(428\) 4.02749 0.194676
\(429\) 4.20969 0.203246
\(430\) 1.65213 0.0796727
\(431\) 20.1325 0.969748 0.484874 0.874584i \(-0.338865\pi\)
0.484874 + 0.874584i \(0.338865\pi\)
\(432\) 3.23657 0.155720
\(433\) 36.4879 1.75350 0.876748 0.480949i \(-0.159708\pi\)
0.876748 + 0.480949i \(0.159708\pi\)
\(434\) −30.0628 −1.44306
\(435\) 2.28576 0.109594
\(436\) −12.4478 −0.596139
\(437\) 42.6894 2.04211
\(438\) 6.52482 0.311768
\(439\) −22.6093 −1.07908 −0.539541 0.841959i \(-0.681402\pi\)
−0.539541 + 0.841959i \(0.681402\pi\)
\(440\) −6.61014 −0.315126
\(441\) −54.0557 −2.57408
\(442\) −0.485525 −0.0230940
\(443\) −20.8098 −0.988705 −0.494352 0.869262i \(-0.664595\pi\)
−0.494352 + 0.869262i \(0.664595\pi\)
\(444\) −4.85759 −0.230531
\(445\) −23.4373 −1.11103
\(446\) 5.37965 0.254734
\(447\) −2.30883 −0.109204
\(448\) −5.21632 −0.246448
\(449\) −38.4084 −1.81260 −0.906302 0.422630i \(-0.861107\pi\)
−0.906302 + 0.422630i \(0.861107\pi\)
\(450\) 8.49958 0.400674
\(451\) 33.6771 1.58579
\(452\) −12.5797 −0.591701
\(453\) −3.73012 −0.175257
\(454\) 17.7145 0.831385
\(455\) −10.6136 −0.497575
\(456\) 2.65931 0.124534
\(457\) 22.2360 1.04016 0.520079 0.854118i \(-0.325903\pi\)
0.520079 + 0.854118i \(0.325903\pi\)
\(458\) 15.0714 0.704241
\(459\) 1.04255 0.0486622
\(460\) 12.3593 0.576257
\(461\) 8.26591 0.384982 0.192491 0.981299i \(-0.438343\pi\)
0.192491 + 0.981299i \(0.438343\pi\)
\(462\) 14.5685 0.677790
\(463\) −27.2271 −1.26535 −0.632675 0.774417i \(-0.718043\pi\)
−0.632675 + 0.774417i \(0.718043\pi\)
\(464\) 2.96884 0.137825
\(465\) 4.43720 0.205770
\(466\) 2.85531 0.132270
\(467\) −5.58987 −0.258668 −0.129334 0.991601i \(-0.541284\pi\)
−0.129334 + 0.991601i \(0.541284\pi\)
\(468\) 4.03156 0.186359
\(469\) 43.9525 2.02954
\(470\) 5.57966 0.257371
\(471\) 3.12564 0.144022
\(472\) 11.2413 0.517424
\(473\) −5.99310 −0.275563
\(474\) 4.09836 0.188244
\(475\) 14.8166 0.679833
\(476\) −1.68026 −0.0770147
\(477\) −30.5957 −1.40088
\(478\) 1.54106 0.0704866
\(479\) 2.67407 0.122182 0.0610908 0.998132i \(-0.480542\pi\)
0.0610908 + 0.998132i \(0.480542\pi\)
\(480\) 0.769917 0.0351418
\(481\) −12.8374 −0.585334
\(482\) 2.05203 0.0934673
\(483\) −27.2396 −1.23944
\(484\) 12.9783 0.589923
\(485\) −15.3019 −0.694826
\(486\) −13.2334 −0.600280
\(487\) 40.4979 1.83513 0.917567 0.397581i \(-0.130150\pi\)
0.917567 + 0.397581i \(0.130150\pi\)
\(488\) −11.6601 −0.527829
\(489\) 0.645698 0.0291995
\(490\) −27.2815 −1.23245
\(491\) 18.4772 0.833865 0.416932 0.908938i \(-0.363105\pi\)
0.416932 + 0.908938i \(0.363105\pi\)
\(492\) −3.92255 −0.176842
\(493\) 0.956312 0.0430701
\(494\) 7.02789 0.316200
\(495\) 17.6801 0.794663
\(496\) 5.76322 0.258776
\(497\) −35.4359 −1.58952
\(498\) −0.351308 −0.0157425
\(499\) −29.2974 −1.31153 −0.655766 0.754964i \(-0.727654\pi\)
−0.655766 + 0.754964i \(0.727654\pi\)
\(500\) 11.0392 0.493687
\(501\) −3.21383 −0.143583
\(502\) −21.3125 −0.951222
\(503\) −0.315857 −0.0140834 −0.00704169 0.999975i \(-0.502241\pi\)
−0.00704169 + 0.999975i \(0.502241\pi\)
\(504\) 13.9521 0.621475
\(505\) 11.9826 0.533220
\(506\) −44.8335 −1.99309
\(507\) 6.11877 0.271744
\(508\) −17.8995 −0.794161
\(509\) 42.7339 1.89415 0.947074 0.321016i \(-0.104024\pi\)
0.947074 + 0.321016i \(0.104024\pi\)
\(510\) 0.248003 0.0109818
\(511\) 59.6747 2.63986
\(512\) 1.00000 0.0441942
\(513\) −15.0908 −0.666275
\(514\) 1.74967 0.0771748
\(515\) −20.1252 −0.886821
\(516\) 0.698047 0.0307298
\(517\) −20.2402 −0.890164
\(518\) −44.4265 −1.95199
\(519\) −5.05792 −0.222018
\(520\) 2.03470 0.0892274
\(521\) 7.72520 0.338447 0.169224 0.985578i \(-0.445874\pi\)
0.169224 + 0.985578i \(0.445874\pi\)
\(522\) −7.94075 −0.347557
\(523\) −4.49738 −0.196657 −0.0983283 0.995154i \(-0.531350\pi\)
−0.0983283 + 0.995154i \(0.531350\pi\)
\(524\) 13.7807 0.602012
\(525\) −9.45430 −0.412619
\(526\) −12.0852 −0.526939
\(527\) 1.85643 0.0808673
\(528\) −2.79288 −0.121544
\(529\) 60.8275 2.64467
\(530\) −15.4414 −0.670731
\(531\) −30.0671 −1.30480
\(532\) 24.3215 1.05447
\(533\) −10.3663 −0.449015
\(534\) −9.90258 −0.428526
\(535\) −5.43671 −0.235050
\(536\) −8.42595 −0.363946
\(537\) 0.424630 0.0183241
\(538\) 16.6643 0.718449
\(539\) 98.9636 4.26267
\(540\) −4.36905 −0.188014
\(541\) −23.9482 −1.02962 −0.514808 0.857306i \(-0.672137\pi\)
−0.514808 + 0.857306i \(0.672137\pi\)
\(542\) −14.5424 −0.624649
\(543\) 5.29281 0.227136
\(544\) 0.322117 0.0138106
\(545\) 16.8032 0.719771
\(546\) −4.48441 −0.191915
\(547\) −28.8409 −1.23315 −0.616573 0.787298i \(-0.711480\pi\)
−0.616573 + 0.787298i \(0.711480\pi\)
\(548\) 19.1060 0.816169
\(549\) 31.1873 1.33104
\(550\) −15.5608 −0.663514
\(551\) −13.8425 −0.589709
\(552\) 5.22199 0.222262
\(553\) 37.4828 1.59393
\(554\) −4.14787 −0.176226
\(555\) 6.55726 0.278340
\(556\) 8.94678 0.379428
\(557\) −29.5672 −1.25280 −0.626402 0.779500i \(-0.715473\pi\)
−0.626402 + 0.779500i \(0.715473\pi\)
\(558\) −15.4149 −0.652564
\(559\) 1.84476 0.0780251
\(560\) 7.04151 0.297558
\(561\) −0.899632 −0.0379825
\(562\) 17.6806 0.745811
\(563\) −25.6045 −1.07910 −0.539551 0.841953i \(-0.681406\pi\)
−0.539551 + 0.841953i \(0.681406\pi\)
\(564\) 2.35748 0.0992679
\(565\) 16.9814 0.714412
\(566\) −20.8410 −0.876014
\(567\) −32.2270 −1.35341
\(568\) 6.79327 0.285039
\(569\) 29.7372 1.24665 0.623325 0.781963i \(-0.285782\pi\)
0.623325 + 0.781963i \(0.285782\pi\)
\(570\) −3.58980 −0.150360
\(571\) 28.3577 1.18673 0.593367 0.804932i \(-0.297798\pi\)
0.593367 + 0.804932i \(0.297798\pi\)
\(572\) −7.38087 −0.308610
\(573\) −6.73641 −0.281418
\(574\) −35.8749 −1.49739
\(575\) 29.0948 1.21334
\(576\) −2.67470 −0.111446
\(577\) 37.8697 1.57653 0.788267 0.615333i \(-0.210978\pi\)
0.788267 + 0.615333i \(0.210978\pi\)
\(578\) −16.8962 −0.702791
\(579\) 0.791410 0.0328899
\(580\) −4.00764 −0.166408
\(581\) −3.21300 −0.133298
\(582\) −6.46528 −0.267995
\(583\) 56.0137 2.31985
\(584\) −11.4400 −0.473391
\(585\) −5.44220 −0.225007
\(586\) 11.4157 0.471577
\(587\) −15.5658 −0.642470 −0.321235 0.947000i \(-0.604098\pi\)
−0.321235 + 0.947000i \(0.604098\pi\)
\(588\) −11.5268 −0.475357
\(589\) −26.8715 −1.10722
\(590\) −15.1747 −0.624731
\(591\) 5.97318 0.245704
\(592\) 8.51683 0.350040
\(593\) 33.2364 1.36486 0.682428 0.730953i \(-0.260924\pi\)
0.682428 + 0.730953i \(0.260924\pi\)
\(594\) 15.8487 0.650281
\(595\) 2.26819 0.0929866
\(596\) 4.04808 0.165816
\(597\) −8.46132 −0.346299
\(598\) 13.8004 0.564340
\(599\) −34.2324 −1.39870 −0.699349 0.714781i \(-0.746527\pi\)
−0.699349 + 0.714781i \(0.746527\pi\)
\(600\) 1.81245 0.0739928
\(601\) −0.459329 −0.0187364 −0.00936821 0.999956i \(-0.502982\pi\)
−0.00936821 + 0.999956i \(0.502982\pi\)
\(602\) 6.38420 0.260201
\(603\) 22.5369 0.917773
\(604\) 6.54005 0.266111
\(605\) −17.5194 −0.712265
\(606\) 5.06283 0.205663
\(607\) −39.7664 −1.61407 −0.807034 0.590506i \(-0.798928\pi\)
−0.807034 + 0.590506i \(0.798928\pi\)
\(608\) −4.66258 −0.189093
\(609\) 8.83270 0.357919
\(610\) 15.7400 0.637294
\(611\) 6.23023 0.252048
\(612\) −0.861565 −0.0348267
\(613\) −24.6191 −0.994358 −0.497179 0.867648i \(-0.665631\pi\)
−0.497179 + 0.867648i \(0.665631\pi\)
\(614\) −1.95560 −0.0789215
\(615\) 5.29505 0.213517
\(616\) −25.5431 −1.02916
\(617\) 34.4311 1.38614 0.693071 0.720869i \(-0.256257\pi\)
0.693071 + 0.720869i \(0.256257\pi\)
\(618\) −8.50316 −0.342047
\(619\) 10.0546 0.404128 0.202064 0.979372i \(-0.435235\pi\)
0.202064 + 0.979372i \(0.435235\pi\)
\(620\) −7.77977 −0.312443
\(621\) −29.6332 −1.18914
\(622\) 20.7951 0.833808
\(623\) −90.5670 −3.62849
\(624\) 0.859688 0.0344150
\(625\) 0.987070 0.0394828
\(626\) 9.78998 0.391286
\(627\) 13.0220 0.520049
\(628\) −5.48019 −0.218684
\(629\) 2.74341 0.109387
\(630\) −18.8339 −0.750362
\(631\) 11.3772 0.452920 0.226460 0.974020i \(-0.427285\pi\)
0.226460 + 0.974020i \(0.427285\pi\)
\(632\) −7.18568 −0.285831
\(633\) −15.3444 −0.609887
\(634\) 21.4136 0.850444
\(635\) 24.1625 0.958859
\(636\) −6.52420 −0.258701
\(637\) −30.4624 −1.20697
\(638\) 14.5377 0.575553
\(639\) −18.1699 −0.718792
\(640\) −1.34990 −0.0533595
\(641\) 45.9301 1.81413 0.907065 0.420991i \(-0.138318\pi\)
0.907065 + 0.420991i \(0.138318\pi\)
\(642\) −2.29709 −0.0906587
\(643\) 23.6098 0.931079 0.465540 0.885027i \(-0.345860\pi\)
0.465540 + 0.885027i \(0.345860\pi\)
\(644\) 47.7593 1.88198
\(645\) −0.942293 −0.0371028
\(646\) −1.50190 −0.0590913
\(647\) 14.5105 0.570468 0.285234 0.958458i \(-0.407929\pi\)
0.285234 + 0.958458i \(0.407929\pi\)
\(648\) 6.17811 0.242699
\(649\) 55.0461 2.16075
\(650\) 4.78984 0.187873
\(651\) 17.1464 0.672019
\(652\) −1.13211 −0.0443367
\(653\) 32.5732 1.27469 0.637344 0.770579i \(-0.280033\pi\)
0.637344 + 0.770579i \(0.280033\pi\)
\(654\) 7.09959 0.277616
\(655\) −18.6026 −0.726862
\(656\) 6.87743 0.268518
\(657\) 30.5986 1.19376
\(658\) 21.5611 0.840538
\(659\) −9.88742 −0.385159 −0.192580 0.981281i \(-0.561685\pi\)
−0.192580 + 0.981281i \(0.561685\pi\)
\(660\) 3.77010 0.146751
\(661\) 35.1654 1.36777 0.683887 0.729588i \(-0.260288\pi\)
0.683887 + 0.729588i \(0.260288\pi\)
\(662\) 20.0123 0.777798
\(663\) 0.276920 0.0107547
\(664\) 0.615951 0.0239035
\(665\) −32.8316 −1.27316
\(666\) −22.7800 −0.882706
\(667\) −27.1819 −1.05249
\(668\) 5.63483 0.218018
\(669\) −3.06829 −0.118627
\(670\) 11.3742 0.439424
\(671\) −57.0969 −2.20420
\(672\) 2.97514 0.114768
\(673\) −23.4595 −0.904296 −0.452148 0.891943i \(-0.649342\pi\)
−0.452148 + 0.891943i \(0.649342\pi\)
\(674\) 12.9771 0.499858
\(675\) −10.2851 −0.395873
\(676\) −10.7281 −0.412618
\(677\) 22.5313 0.865947 0.432974 0.901407i \(-0.357464\pi\)
0.432974 + 0.901407i \(0.357464\pi\)
\(678\) 7.17487 0.275549
\(679\) −59.1302 −2.26921
\(680\) −0.434825 −0.0166748
\(681\) −10.1035 −0.387167
\(682\) 28.2211 1.08064
\(683\) 35.8628 1.37225 0.686127 0.727482i \(-0.259310\pi\)
0.686127 + 0.727482i \(0.259310\pi\)
\(684\) 12.4710 0.476841
\(685\) −25.7912 −0.985432
\(686\) −68.9076 −2.63091
\(687\) −8.59600 −0.327958
\(688\) −1.22389 −0.0466603
\(689\) −17.2418 −0.656861
\(690\) −7.04916 −0.268357
\(691\) −26.4427 −1.00593 −0.502964 0.864308i \(-0.667757\pi\)
−0.502964 + 0.864308i \(0.667757\pi\)
\(692\) 8.86807 0.337113
\(693\) 68.3201 2.59527
\(694\) −31.8177 −1.20778
\(695\) −12.0773 −0.458116
\(696\) −1.69328 −0.0641837
\(697\) 2.21533 0.0839117
\(698\) −29.6834 −1.12353
\(699\) −1.62853 −0.0615966
\(700\) 16.5763 0.626524
\(701\) 1.80863 0.0683109 0.0341555 0.999417i \(-0.489126\pi\)
0.0341555 + 0.999417i \(0.489126\pi\)
\(702\) −4.87847 −0.184126
\(703\) −39.7105 −1.49771
\(704\) 4.89676 0.184554
\(705\) −3.18237 −0.119855
\(706\) 21.3908 0.805052
\(707\) 46.3036 1.74143
\(708\) −6.41150 −0.240959
\(709\) 12.8308 0.481869 0.240935 0.970541i \(-0.422546\pi\)
0.240935 + 0.970541i \(0.422546\pi\)
\(710\) −9.17023 −0.344153
\(711\) 19.2195 0.720789
\(712\) 17.3622 0.650678
\(713\) −52.7665 −1.97612
\(714\) 0.958341 0.0358650
\(715\) 9.96343 0.372611
\(716\) −0.744506 −0.0278235
\(717\) −0.878947 −0.0328249
\(718\) −33.2527 −1.24098
\(719\) 15.9441 0.594616 0.297308 0.954782i \(-0.403911\pi\)
0.297308 + 0.954782i \(0.403911\pi\)
\(720\) 3.61058 0.134558
\(721\) −77.7683 −2.89624
\(722\) 2.73969 0.101961
\(723\) −1.17038 −0.0435268
\(724\) −9.27992 −0.344885
\(725\) −9.43429 −0.350381
\(726\) −7.40219 −0.274721
\(727\) −42.8669 −1.58985 −0.794923 0.606710i \(-0.792489\pi\)
−0.794923 + 0.606710i \(0.792489\pi\)
\(728\) 7.86253 0.291405
\(729\) −10.9866 −0.406913
\(730\) 15.4429 0.571566
\(731\) −0.394235 −0.0145813
\(732\) 6.65037 0.245805
\(733\) 18.1886 0.671810 0.335905 0.941896i \(-0.390958\pi\)
0.335905 + 0.941896i \(0.390958\pi\)
\(734\) −9.57219 −0.353316
\(735\) 15.5600 0.573940
\(736\) −9.15574 −0.337485
\(737\) −41.2599 −1.51983
\(738\) −18.3950 −0.677131
\(739\) −28.1395 −1.03513 −0.517565 0.855644i \(-0.673161\pi\)
−0.517565 + 0.855644i \(0.673161\pi\)
\(740\) −11.4969 −0.422633
\(741\) −4.00837 −0.147251
\(742\) −59.6691 −2.19052
\(743\) 24.1449 0.885791 0.442895 0.896573i \(-0.353951\pi\)
0.442895 + 0.896573i \(0.353951\pi\)
\(744\) −3.28706 −0.120509
\(745\) −5.46451 −0.200204
\(746\) −21.7305 −0.795611
\(747\) −1.64748 −0.0602783
\(748\) 1.57733 0.0576729
\(749\) −21.0087 −0.767641
\(750\) −6.29621 −0.229905
\(751\) −4.34927 −0.158707 −0.0793536 0.996847i \(-0.525286\pi\)
−0.0793536 + 0.996847i \(0.525286\pi\)
\(752\) −4.13339 −0.150729
\(753\) 12.1556 0.442975
\(754\) −4.47492 −0.162967
\(755\) −8.82841 −0.321299
\(756\) −16.8830 −0.614029
\(757\) −29.4399 −1.07001 −0.535005 0.844849i \(-0.679690\pi\)
−0.535005 + 0.844849i \(0.679690\pi\)
\(758\) −31.9976 −1.16221
\(759\) 25.5708 0.928163
\(760\) 6.29402 0.228308
\(761\) −4.73746 −0.171733 −0.0858665 0.996307i \(-0.527366\pi\)
−0.0858665 + 0.996307i \(0.527366\pi\)
\(762\) 10.2090 0.369833
\(763\) 64.9315 2.35068
\(764\) 11.8110 0.427307
\(765\) 1.16303 0.0420493
\(766\) 16.0904 0.581371
\(767\) −16.9440 −0.611812
\(768\) −0.570351 −0.0205808
\(769\) 7.09119 0.255715 0.127857 0.991793i \(-0.459190\pi\)
0.127857 + 0.991793i \(0.459190\pi\)
\(770\) 34.4806 1.24260
\(771\) −0.997929 −0.0359395
\(772\) −1.38758 −0.0499402
\(773\) −48.2015 −1.73369 −0.866844 0.498579i \(-0.833856\pi\)
−0.866844 + 0.498579i \(0.833856\pi\)
\(774\) 3.27354 0.117665
\(775\) −18.3142 −0.657865
\(776\) 11.3356 0.406925
\(777\) 25.3387 0.909022
\(778\) 12.6861 0.454820
\(779\) −32.0666 −1.14890
\(780\) −1.16049 −0.0415523
\(781\) 33.2650 1.19032
\(782\) −2.94921 −0.105464
\(783\) 9.60886 0.343393
\(784\) 20.2100 0.721786
\(785\) 7.39772 0.264036
\(786\) −7.85983 −0.280351
\(787\) 42.7134 1.52257 0.761284 0.648419i \(-0.224569\pi\)
0.761284 + 0.648419i \(0.224569\pi\)
\(788\) −10.4728 −0.373078
\(789\) 6.89280 0.245390
\(790\) 9.69995 0.345109
\(791\) 65.6199 2.33318
\(792\) −13.0974 −0.465395
\(793\) 17.5752 0.624115
\(794\) −0.346410 −0.0122936
\(795\) 8.80702 0.312353
\(796\) 14.8353 0.525822
\(797\) 33.1497 1.17422 0.587111 0.809506i \(-0.300265\pi\)
0.587111 + 0.809506i \(0.300265\pi\)
\(798\) −13.8718 −0.491057
\(799\) −1.33143 −0.0471027
\(800\) −3.17777 −0.112351
\(801\) −46.4388 −1.64083
\(802\) 23.8455 0.842015
\(803\) −56.0190 −1.97687
\(804\) 4.80575 0.169486
\(805\) −64.4702 −2.27228
\(806\) −8.68687 −0.305982
\(807\) −9.50451 −0.334575
\(808\) −8.87668 −0.312280
\(809\) −35.0877 −1.23362 −0.616810 0.787112i \(-0.711575\pi\)
−0.616810 + 0.787112i \(0.711575\pi\)
\(810\) −8.33984 −0.293032
\(811\) 7.14130 0.250765 0.125382 0.992108i \(-0.459984\pi\)
0.125382 + 0.992108i \(0.459984\pi\)
\(812\) −15.4864 −0.543467
\(813\) 8.29427 0.290893
\(814\) 41.7049 1.46176
\(815\) 1.52823 0.0535315
\(816\) −0.183720 −0.00643147
\(817\) 5.70649 0.199645
\(818\) −1.11996 −0.0391583
\(819\) −21.0299 −0.734845
\(820\) −9.28384 −0.324206
\(821\) −12.4706 −0.435226 −0.217613 0.976035i \(-0.569827\pi\)
−0.217613 + 0.976035i \(0.569827\pi\)
\(822\) −10.8971 −0.380082
\(823\) 7.16190 0.249648 0.124824 0.992179i \(-0.460163\pi\)
0.124824 + 0.992179i \(0.460163\pi\)
\(824\) 14.9086 0.519367
\(825\) 8.87512 0.308992
\(826\) −58.6383 −2.04029
\(827\) −51.1621 −1.77908 −0.889541 0.456856i \(-0.848976\pi\)
−0.889541 + 0.456856i \(0.848976\pi\)
\(828\) 24.4888 0.851046
\(829\) 40.4277 1.40411 0.702056 0.712122i \(-0.252266\pi\)
0.702056 + 0.712122i \(0.252266\pi\)
\(830\) −0.831472 −0.0288608
\(831\) 2.36574 0.0820667
\(832\) −1.50729 −0.0522560
\(833\) 6.50998 0.225557
\(834\) −5.10281 −0.176696
\(835\) −7.60646 −0.263232
\(836\) −22.8316 −0.789647
\(837\) 18.6531 0.644745
\(838\) −37.9806 −1.31202
\(839\) −32.1188 −1.10887 −0.554433 0.832229i \(-0.687065\pi\)
−0.554433 + 0.832229i \(0.687065\pi\)
\(840\) −4.01614 −0.138570
\(841\) −20.1860 −0.696069
\(842\) −3.97835 −0.137103
\(843\) −10.0842 −0.347317
\(844\) 26.9035 0.926057
\(845\) 14.4818 0.498190
\(846\) 11.0556 0.380098
\(847\) −67.6990 −2.32616
\(848\) 11.4389 0.392814
\(849\) 11.8867 0.407951
\(850\) −1.02361 −0.0351096
\(851\) −77.9779 −2.67305
\(852\) −3.87455 −0.132740
\(853\) 29.8726 1.02282 0.511409 0.859337i \(-0.329124\pi\)
0.511409 + 0.859337i \(0.329124\pi\)
\(854\) 60.8230 2.08132
\(855\) −16.8346 −0.575732
\(856\) 4.02749 0.137657
\(857\) −36.3366 −1.24124 −0.620618 0.784113i \(-0.713118\pi\)
−0.620618 + 0.784113i \(0.713118\pi\)
\(858\) 4.20969 0.143716
\(859\) 16.2362 0.553973 0.276986 0.960874i \(-0.410664\pi\)
0.276986 + 0.960874i \(0.410664\pi\)
\(860\) 1.65213 0.0563371
\(861\) 20.4613 0.697318
\(862\) 20.1325 0.685715
\(863\) 21.2757 0.724233 0.362117 0.932133i \(-0.382054\pi\)
0.362117 + 0.932133i \(0.382054\pi\)
\(864\) 3.23657 0.110110
\(865\) −11.9710 −0.407026
\(866\) 36.4879 1.23991
\(867\) 9.63679 0.327283
\(868\) −30.0628 −1.02040
\(869\) −35.1866 −1.19362
\(870\) 2.28576 0.0774945
\(871\) 12.7004 0.430336
\(872\) −12.4478 −0.421534
\(873\) −30.3194 −1.02615
\(874\) 42.6894 1.44399
\(875\) −57.5839 −1.94669
\(876\) 6.52482 0.220453
\(877\) 34.6583 1.17033 0.585164 0.810915i \(-0.301030\pi\)
0.585164 + 0.810915i \(0.301030\pi\)
\(878\) −22.6093 −0.763026
\(879\) −6.51094 −0.219609
\(880\) −6.61014 −0.222828
\(881\) −35.0066 −1.17940 −0.589701 0.807622i \(-0.700754\pi\)
−0.589701 + 0.807622i \(0.700754\pi\)
\(882\) −54.0557 −1.82015
\(883\) 23.4321 0.788553 0.394277 0.918992i \(-0.370995\pi\)
0.394277 + 0.918992i \(0.370995\pi\)
\(884\) −0.485525 −0.0163300
\(885\) 8.65488 0.290931
\(886\) −20.8098 −0.699120
\(887\) −53.8044 −1.80658 −0.903288 0.429035i \(-0.858854\pi\)
−0.903288 + 0.429035i \(0.858854\pi\)
\(888\) −4.85759 −0.163010
\(889\) 93.3694 3.13151
\(890\) −23.4373 −0.785620
\(891\) 30.2528 1.01351
\(892\) 5.37965 0.180124
\(893\) 19.2723 0.644922
\(894\) −2.30883 −0.0772188
\(895\) 1.00501 0.0335937
\(896\) −5.21632 −0.174265
\(897\) −7.87107 −0.262807
\(898\) −38.4084 −1.28170
\(899\) 17.1101 0.570653
\(900\) 8.49958 0.283319
\(901\) 3.68466 0.122754
\(902\) 33.6771 1.12133
\(903\) −3.64124 −0.121173
\(904\) −12.5797 −0.418396
\(905\) 12.5270 0.416410
\(906\) −3.73012 −0.123925
\(907\) 13.1054 0.435157 0.217578 0.976043i \(-0.430184\pi\)
0.217578 + 0.976043i \(0.430184\pi\)
\(908\) 17.7145 0.587878
\(909\) 23.7424 0.787487
\(910\) −10.6136 −0.351839
\(911\) −4.35027 −0.144131 −0.0720654 0.997400i \(-0.522959\pi\)
−0.0720654 + 0.997400i \(0.522959\pi\)
\(912\) 2.65931 0.0880586
\(913\) 3.01617 0.0998205
\(914\) 22.2360 0.735503
\(915\) −8.97733 −0.296781
\(916\) 15.0714 0.497974
\(917\) −71.8845 −2.37384
\(918\) 1.04255 0.0344094
\(919\) 51.8873 1.71160 0.855802 0.517303i \(-0.173064\pi\)
0.855802 + 0.517303i \(0.173064\pi\)
\(920\) 12.3593 0.407475
\(921\) 1.11538 0.0367529
\(922\) 8.26591 0.272223
\(923\) −10.2395 −0.337036
\(924\) 14.5685 0.479270
\(925\) −27.0645 −0.889876
\(926\) −27.2271 −0.894738
\(927\) −39.8761 −1.30970
\(928\) 2.96884 0.0974569
\(929\) 31.6185 1.03737 0.518684 0.854966i \(-0.326422\pi\)
0.518684 + 0.854966i \(0.326422\pi\)
\(930\) 4.43720 0.145502
\(931\) −94.2309 −3.08829
\(932\) 2.85531 0.0935287
\(933\) −11.8605 −0.388296
\(934\) −5.58987 −0.182906
\(935\) −2.12924 −0.0696335
\(936\) 4.03156 0.131776
\(937\) 29.0006 0.947407 0.473704 0.880684i \(-0.342917\pi\)
0.473704 + 0.880684i \(0.342917\pi\)
\(938\) 43.9525 1.43510
\(939\) −5.58373 −0.182218
\(940\) 5.57966 0.181988
\(941\) −1.22096 −0.0398021 −0.0199011 0.999802i \(-0.506335\pi\)
−0.0199011 + 0.999802i \(0.506335\pi\)
\(942\) 3.12564 0.101839
\(943\) −62.9679 −2.05052
\(944\) 11.2413 0.365874
\(945\) 22.7904 0.741371
\(946\) −5.99310 −0.194852
\(947\) 45.0609 1.46428 0.732141 0.681154i \(-0.238521\pi\)
0.732141 + 0.681154i \(0.238521\pi\)
\(948\) 4.09836 0.133109
\(949\) 17.2435 0.559746
\(950\) 14.8166 0.480715
\(951\) −12.2133 −0.396043
\(952\) −1.68026 −0.0544576
\(953\) −19.2424 −0.623323 −0.311661 0.950193i \(-0.600885\pi\)
−0.311661 + 0.950193i \(0.600885\pi\)
\(954\) −30.5957 −0.990571
\(955\) −15.9437 −0.515925
\(956\) 1.54106 0.0498415
\(957\) −8.29160 −0.268029
\(958\) 2.67407 0.0863954
\(959\) −99.6631 −3.21829
\(960\) 0.769917 0.0248490
\(961\) 2.21470 0.0714421
\(962\) −12.8374 −0.413894
\(963\) −10.7723 −0.347133
\(964\) 2.05203 0.0660914
\(965\) 1.87310 0.0602972
\(966\) −27.2396 −0.876418
\(967\) −5.11420 −0.164462 −0.0822309 0.996613i \(-0.526204\pi\)
−0.0822309 + 0.996613i \(0.526204\pi\)
\(968\) 12.9783 0.417138
\(969\) 0.856608 0.0275182
\(970\) −15.3019 −0.491316
\(971\) 51.4507 1.65113 0.825566 0.564306i \(-0.190856\pi\)
0.825566 + 0.564306i \(0.190856\pi\)
\(972\) −13.2334 −0.424462
\(973\) −46.6693 −1.49615
\(974\) 40.4979 1.29764
\(975\) −2.73189 −0.0874905
\(976\) −11.6601 −0.373232
\(977\) −16.9760 −0.543110 −0.271555 0.962423i \(-0.587538\pi\)
−0.271555 + 0.962423i \(0.587538\pi\)
\(978\) 0.645698 0.0206471
\(979\) 85.0188 2.71721
\(980\) −27.2815 −0.871475
\(981\) 33.2940 1.06300
\(982\) 18.4772 0.589631
\(983\) −0.922623 −0.0294271 −0.0147135 0.999892i \(-0.504684\pi\)
−0.0147135 + 0.999892i \(0.504684\pi\)
\(984\) −3.92255 −0.125046
\(985\) 14.1372 0.450450
\(986\) 0.956312 0.0304552
\(987\) −12.2974 −0.391430
\(988\) 7.02789 0.223587
\(989\) 11.2056 0.356318
\(990\) 17.6801 0.561912
\(991\) 26.2547 0.834008 0.417004 0.908905i \(-0.363080\pi\)
0.417004 + 0.908905i \(0.363080\pi\)
\(992\) 5.76322 0.182982
\(993\) −11.4140 −0.362213
\(994\) −35.4359 −1.12396
\(995\) −20.0261 −0.634871
\(996\) −0.351308 −0.0111316
\(997\) 29.4017 0.931160 0.465580 0.885006i \(-0.345846\pi\)
0.465580 + 0.885006i \(0.345846\pi\)
\(998\) −29.2974 −0.927393
\(999\) 27.5653 0.872129
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 4034.2.a.d.1.19 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.19 52 1.1 even 1 trivial