Properties

Label 4029.2.a.l.1.15
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 32
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.249798 q^{2} -1.00000 q^{3} -1.93760 q^{4} +0.601573 q^{5} +0.249798 q^{6} -2.69175 q^{7} +0.983604 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.249798 q^{2} -1.00000 q^{3} -1.93760 q^{4} +0.601573 q^{5} +0.249798 q^{6} -2.69175 q^{7} +0.983604 q^{8} +1.00000 q^{9} -0.150272 q^{10} -4.01000 q^{11} +1.93760 q^{12} +6.29531 q^{13} +0.672392 q^{14} -0.601573 q^{15} +3.62950 q^{16} -1.00000 q^{17} -0.249798 q^{18} +7.87938 q^{19} -1.16561 q^{20} +2.69175 q^{21} +1.00169 q^{22} -0.0277886 q^{23} -0.983604 q^{24} -4.63811 q^{25} -1.57255 q^{26} -1.00000 q^{27} +5.21553 q^{28} -7.65335 q^{29} +0.150272 q^{30} +3.60362 q^{31} -2.87385 q^{32} +4.01000 q^{33} +0.249798 q^{34} -1.61928 q^{35} -1.93760 q^{36} -3.13719 q^{37} -1.96825 q^{38} -6.29531 q^{39} +0.591710 q^{40} -8.77814 q^{41} -0.672392 q^{42} -5.84403 q^{43} +7.76978 q^{44} +0.601573 q^{45} +0.00694153 q^{46} -6.01959 q^{47} -3.62950 q^{48} +0.245493 q^{49} +1.15859 q^{50} +1.00000 q^{51} -12.1978 q^{52} -10.8237 q^{53} +0.249798 q^{54} -2.41231 q^{55} -2.64761 q^{56} -7.87938 q^{57} +1.91179 q^{58} +11.2876 q^{59} +1.16561 q^{60} -0.767879 q^{61} -0.900177 q^{62} -2.69175 q^{63} -6.54112 q^{64} +3.78709 q^{65} -1.00169 q^{66} +11.3518 q^{67} +1.93760 q^{68} +0.0277886 q^{69} +0.404493 q^{70} +3.73870 q^{71} +0.983604 q^{72} +3.98797 q^{73} +0.783663 q^{74} +4.63811 q^{75} -15.2671 q^{76} +10.7939 q^{77} +1.57255 q^{78} +1.00000 q^{79} +2.18341 q^{80} +1.00000 q^{81} +2.19276 q^{82} +6.87292 q^{83} -5.21553 q^{84} -0.601573 q^{85} +1.45983 q^{86} +7.65335 q^{87} -3.94425 q^{88} -1.23369 q^{89} -0.150272 q^{90} -16.9454 q^{91} +0.0538432 q^{92} -3.60362 q^{93} +1.50368 q^{94} +4.74003 q^{95} +2.87385 q^{96} +12.6730 q^{97} -0.0613236 q^{98} -4.01000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.249798 −0.176634 −0.0883168 0.996092i \(-0.528149\pi\)
−0.0883168 + 0.996092i \(0.528149\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.93760 −0.968801
\(5\) 0.601573 0.269032 0.134516 0.990911i \(-0.457052\pi\)
0.134516 + 0.990911i \(0.457052\pi\)
\(6\) 0.249798 0.101980
\(7\) −2.69175 −1.01738 −0.508692 0.860949i \(-0.669871\pi\)
−0.508692 + 0.860949i \(0.669871\pi\)
\(8\) 0.983604 0.347756
\(9\) 1.00000 0.333333
\(10\) −0.150272 −0.0475201
\(11\) −4.01000 −1.20906 −0.604530 0.796582i \(-0.706639\pi\)
−0.604530 + 0.796582i \(0.706639\pi\)
\(12\) 1.93760 0.559337
\(13\) 6.29531 1.74600 0.873002 0.487716i \(-0.162170\pi\)
0.873002 + 0.487716i \(0.162170\pi\)
\(14\) 0.672392 0.179704
\(15\) −0.601573 −0.155326
\(16\) 3.62950 0.907375
\(17\) −1.00000 −0.242536
\(18\) −0.249798 −0.0588779
\(19\) 7.87938 1.80765 0.903827 0.427897i \(-0.140745\pi\)
0.903827 + 0.427897i \(0.140745\pi\)
\(20\) −1.16561 −0.260638
\(21\) 2.69175 0.587387
\(22\) 1.00169 0.213561
\(23\) −0.0277886 −0.00579432 −0.00289716 0.999996i \(-0.500922\pi\)
−0.00289716 + 0.999996i \(0.500922\pi\)
\(24\) −0.983604 −0.200777
\(25\) −4.63811 −0.927622
\(26\) −1.57255 −0.308403
\(27\) −1.00000 −0.192450
\(28\) 5.21553 0.985642
\(29\) −7.65335 −1.42119 −0.710595 0.703601i \(-0.751574\pi\)
−0.710595 + 0.703601i \(0.751574\pi\)
\(30\) 0.150272 0.0274357
\(31\) 3.60362 0.647230 0.323615 0.946189i \(-0.395102\pi\)
0.323615 + 0.946189i \(0.395102\pi\)
\(32\) −2.87385 −0.508029
\(33\) 4.01000 0.698051
\(34\) 0.249798 0.0428400
\(35\) −1.61928 −0.273709
\(36\) −1.93760 −0.322934
\(37\) −3.13719 −0.515751 −0.257876 0.966178i \(-0.583022\pi\)
−0.257876 + 0.966178i \(0.583022\pi\)
\(38\) −1.96825 −0.319293
\(39\) −6.29531 −1.00806
\(40\) 0.591710 0.0935576
\(41\) −8.77814 −1.37092 −0.685458 0.728112i \(-0.740398\pi\)
−0.685458 + 0.728112i \(0.740398\pi\)
\(42\) −0.672392 −0.103752
\(43\) −5.84403 −0.891206 −0.445603 0.895231i \(-0.647011\pi\)
−0.445603 + 0.895231i \(0.647011\pi\)
\(44\) 7.76978 1.17134
\(45\) 0.601573 0.0896773
\(46\) 0.00694153 0.00102347
\(47\) −6.01959 −0.878047 −0.439023 0.898476i \(-0.644675\pi\)
−0.439023 + 0.898476i \(0.644675\pi\)
\(48\) −3.62950 −0.523873
\(49\) 0.245493 0.0350704
\(50\) 1.15859 0.163849
\(51\) 1.00000 0.140028
\(52\) −12.1978 −1.69153
\(53\) −10.8237 −1.48674 −0.743372 0.668878i \(-0.766775\pi\)
−0.743372 + 0.668878i \(0.766775\pi\)
\(54\) 0.249798 0.0339932
\(55\) −2.41231 −0.325276
\(56\) −2.64761 −0.353802
\(57\) −7.87938 −1.04365
\(58\) 1.91179 0.251030
\(59\) 11.2876 1.46953 0.734763 0.678324i \(-0.237293\pi\)
0.734763 + 0.678324i \(0.237293\pi\)
\(60\) 1.16561 0.150480
\(61\) −0.767879 −0.0983169 −0.0491584 0.998791i \(-0.515654\pi\)
−0.0491584 + 0.998791i \(0.515654\pi\)
\(62\) −0.900177 −0.114323
\(63\) −2.69175 −0.339128
\(64\) −6.54112 −0.817640
\(65\) 3.78709 0.469731
\(66\) −1.00169 −0.123299
\(67\) 11.3518 1.38685 0.693424 0.720530i \(-0.256102\pi\)
0.693424 + 0.720530i \(0.256102\pi\)
\(68\) 1.93760 0.234969
\(69\) 0.0277886 0.00334535
\(70\) 0.404493 0.0483462
\(71\) 3.73870 0.443702 0.221851 0.975081i \(-0.428790\pi\)
0.221851 + 0.975081i \(0.428790\pi\)
\(72\) 0.983604 0.115919
\(73\) 3.98797 0.466756 0.233378 0.972386i \(-0.425022\pi\)
0.233378 + 0.972386i \(0.425022\pi\)
\(74\) 0.783663 0.0910990
\(75\) 4.63811 0.535563
\(76\) −15.2671 −1.75126
\(77\) 10.7939 1.23008
\(78\) 1.57255 0.178057
\(79\) 1.00000 0.112509
\(80\) 2.18341 0.244113
\(81\) 1.00000 0.111111
\(82\) 2.19276 0.242150
\(83\) 6.87292 0.754401 0.377201 0.926132i \(-0.376887\pi\)
0.377201 + 0.926132i \(0.376887\pi\)
\(84\) −5.21553 −0.569061
\(85\) −0.601573 −0.0652498
\(86\) 1.45983 0.157417
\(87\) 7.65335 0.820525
\(88\) −3.94425 −0.420459
\(89\) −1.23369 −0.130771 −0.0653854 0.997860i \(-0.520828\pi\)
−0.0653854 + 0.997860i \(0.520828\pi\)
\(90\) −0.150272 −0.0158400
\(91\) −16.9454 −1.77636
\(92\) 0.0538432 0.00561354
\(93\) −3.60362 −0.373678
\(94\) 1.50368 0.155093
\(95\) 4.74003 0.486317
\(96\) 2.87385 0.293311
\(97\) 12.6730 1.28675 0.643376 0.765550i \(-0.277533\pi\)
0.643376 + 0.765550i \(0.277533\pi\)
\(98\) −0.0613236 −0.00619462
\(99\) −4.01000 −0.403020
\(100\) 8.98681 0.898681
\(101\) −4.22605 −0.420508 −0.210254 0.977647i \(-0.567429\pi\)
−0.210254 + 0.977647i \(0.567429\pi\)
\(102\) −0.249798 −0.0247337
\(103\) −2.21463 −0.218214 −0.109107 0.994030i \(-0.534799\pi\)
−0.109107 + 0.994030i \(0.534799\pi\)
\(104\) 6.19209 0.607184
\(105\) 1.61928 0.158026
\(106\) 2.70373 0.262609
\(107\) 3.48114 0.336534 0.168267 0.985741i \(-0.446183\pi\)
0.168267 + 0.985741i \(0.446183\pi\)
\(108\) 1.93760 0.186446
\(109\) 9.80627 0.939270 0.469635 0.882861i \(-0.344385\pi\)
0.469635 + 0.882861i \(0.344385\pi\)
\(110\) 0.602589 0.0574547
\(111\) 3.13719 0.297769
\(112\) −9.76969 −0.923149
\(113\) 13.8424 1.30218 0.651091 0.759000i \(-0.274312\pi\)
0.651091 + 0.759000i \(0.274312\pi\)
\(114\) 1.96825 0.184344
\(115\) −0.0167169 −0.00155886
\(116\) 14.8291 1.37685
\(117\) 6.29531 0.582001
\(118\) −2.81963 −0.259568
\(119\) 2.69175 0.246752
\(120\) −0.591710 −0.0540155
\(121\) 5.08010 0.461827
\(122\) 0.191815 0.0173661
\(123\) 8.77814 0.791498
\(124\) −6.98239 −0.627037
\(125\) −5.79803 −0.518592
\(126\) 0.672392 0.0599014
\(127\) −3.04605 −0.270293 −0.135147 0.990826i \(-0.543151\pi\)
−0.135147 + 0.990826i \(0.543151\pi\)
\(128\) 7.38165 0.652452
\(129\) 5.84403 0.514538
\(130\) −0.946007 −0.0829703
\(131\) 3.57711 0.312533 0.156267 0.987715i \(-0.450054\pi\)
0.156267 + 0.987715i \(0.450054\pi\)
\(132\) −7.76978 −0.676273
\(133\) −21.2093 −1.83908
\(134\) −2.83566 −0.244964
\(135\) −0.601573 −0.0517752
\(136\) −0.983604 −0.0843433
\(137\) 3.12447 0.266941 0.133471 0.991053i \(-0.457388\pi\)
0.133471 + 0.991053i \(0.457388\pi\)
\(138\) −0.00694153 −0.000590902 0
\(139\) 2.85097 0.241816 0.120908 0.992664i \(-0.461419\pi\)
0.120908 + 0.992664i \(0.461419\pi\)
\(140\) 3.13752 0.265169
\(141\) 6.01959 0.506941
\(142\) −0.933919 −0.0783727
\(143\) −25.2442 −2.11102
\(144\) 3.62950 0.302458
\(145\) −4.60405 −0.382346
\(146\) −0.996185 −0.0824449
\(147\) −0.245493 −0.0202479
\(148\) 6.07862 0.499660
\(149\) 13.0077 1.06563 0.532816 0.846231i \(-0.321134\pi\)
0.532816 + 0.846231i \(0.321134\pi\)
\(150\) −1.15859 −0.0945984
\(151\) 4.01752 0.326941 0.163470 0.986548i \(-0.447731\pi\)
0.163470 + 0.986548i \(0.447731\pi\)
\(152\) 7.75019 0.628624
\(153\) −1.00000 −0.0808452
\(154\) −2.69629 −0.217273
\(155\) 2.16784 0.174125
\(156\) 12.1978 0.976605
\(157\) 16.2233 1.29476 0.647380 0.762167i \(-0.275865\pi\)
0.647380 + 0.762167i \(0.275865\pi\)
\(158\) −0.249798 −0.0198728
\(159\) 10.8237 0.858372
\(160\) −1.72883 −0.136676
\(161\) 0.0747998 0.00589505
\(162\) −0.249798 −0.0196260
\(163\) −15.2873 −1.19740 −0.598698 0.800975i \(-0.704315\pi\)
−0.598698 + 0.800975i \(0.704315\pi\)
\(164\) 17.0085 1.32814
\(165\) 2.41231 0.187798
\(166\) −1.71684 −0.133253
\(167\) 11.8122 0.914059 0.457030 0.889452i \(-0.348913\pi\)
0.457030 + 0.889452i \(0.348913\pi\)
\(168\) 2.64761 0.204268
\(169\) 26.6309 2.04853
\(170\) 0.150272 0.0115253
\(171\) 7.87938 0.602552
\(172\) 11.3234 0.863401
\(173\) −11.4073 −0.867283 −0.433641 0.901086i \(-0.642772\pi\)
−0.433641 + 0.901086i \(0.642772\pi\)
\(174\) −1.91179 −0.144932
\(175\) 12.4846 0.943748
\(176\) −14.5543 −1.09707
\(177\) −11.2876 −0.848431
\(178\) 0.308173 0.0230985
\(179\) 18.2483 1.36394 0.681972 0.731378i \(-0.261122\pi\)
0.681972 + 0.731378i \(0.261122\pi\)
\(180\) −1.16561 −0.0868794
\(181\) −20.9086 −1.55412 −0.777060 0.629426i \(-0.783290\pi\)
−0.777060 + 0.629426i \(0.783290\pi\)
\(182\) 4.23291 0.313764
\(183\) 0.767879 0.0567633
\(184\) −0.0273330 −0.00201501
\(185\) −1.88725 −0.138753
\(186\) 0.900177 0.0660042
\(187\) 4.01000 0.293240
\(188\) 11.6636 0.850652
\(189\) 2.69175 0.195796
\(190\) −1.18405 −0.0858999
\(191\) 11.5276 0.834107 0.417053 0.908882i \(-0.363063\pi\)
0.417053 + 0.908882i \(0.363063\pi\)
\(192\) 6.54112 0.472065
\(193\) 12.3391 0.888188 0.444094 0.895980i \(-0.353526\pi\)
0.444094 + 0.895980i \(0.353526\pi\)
\(194\) −3.16570 −0.227284
\(195\) −3.78709 −0.271199
\(196\) −0.475668 −0.0339763
\(197\) −18.5801 −1.32378 −0.661888 0.749602i \(-0.730245\pi\)
−0.661888 + 0.749602i \(0.730245\pi\)
\(198\) 1.00169 0.0711869
\(199\) 8.55614 0.606529 0.303264 0.952906i \(-0.401923\pi\)
0.303264 + 0.952906i \(0.401923\pi\)
\(200\) −4.56206 −0.322587
\(201\) −11.3518 −0.800697
\(202\) 1.05566 0.0742758
\(203\) 20.6009 1.44590
\(204\) −1.93760 −0.135659
\(205\) −5.28070 −0.368820
\(206\) 0.553210 0.0385440
\(207\) −0.0277886 −0.00193144
\(208\) 22.8488 1.58428
\(209\) −31.5963 −2.18556
\(210\) −0.404493 −0.0279127
\(211\) −2.28730 −0.157464 −0.0787321 0.996896i \(-0.525087\pi\)
−0.0787321 + 0.996896i \(0.525087\pi\)
\(212\) 20.9719 1.44036
\(213\) −3.73870 −0.256171
\(214\) −0.869580 −0.0594433
\(215\) −3.51561 −0.239763
\(216\) −0.983604 −0.0669258
\(217\) −9.70004 −0.658482
\(218\) −2.44958 −0.165907
\(219\) −3.98797 −0.269482
\(220\) 4.67409 0.315127
\(221\) −6.29531 −0.423468
\(222\) −0.783663 −0.0525960
\(223\) −17.4110 −1.16593 −0.582964 0.812498i \(-0.698107\pi\)
−0.582964 + 0.812498i \(0.698107\pi\)
\(224\) 7.73567 0.516861
\(225\) −4.63811 −0.309207
\(226\) −3.45780 −0.230009
\(227\) −14.3574 −0.952934 −0.476467 0.879192i \(-0.658083\pi\)
−0.476467 + 0.879192i \(0.658083\pi\)
\(228\) 15.2671 1.01109
\(229\) −19.8645 −1.31268 −0.656340 0.754465i \(-0.727896\pi\)
−0.656340 + 0.754465i \(0.727896\pi\)
\(230\) 0.00417584 0.000275347 0
\(231\) −10.7939 −0.710186
\(232\) −7.52786 −0.494228
\(233\) −1.19241 −0.0781175 −0.0390587 0.999237i \(-0.512436\pi\)
−0.0390587 + 0.999237i \(0.512436\pi\)
\(234\) −1.57255 −0.102801
\(235\) −3.62122 −0.236223
\(236\) −21.8710 −1.42368
\(237\) −1.00000 −0.0649570
\(238\) −0.672392 −0.0435847
\(239\) 9.86106 0.637859 0.318930 0.947778i \(-0.396677\pi\)
0.318930 + 0.947778i \(0.396677\pi\)
\(240\) −2.18341 −0.140939
\(241\) 11.7090 0.754246 0.377123 0.926163i \(-0.376913\pi\)
0.377123 + 0.926163i \(0.376913\pi\)
\(242\) −1.26900 −0.0815742
\(243\) −1.00000 −0.0641500
\(244\) 1.48784 0.0952494
\(245\) 0.147682 0.00943506
\(246\) −2.19276 −0.139805
\(247\) 49.6032 3.15617
\(248\) 3.54454 0.225078
\(249\) −6.87292 −0.435554
\(250\) 1.44834 0.0916008
\(251\) −10.6286 −0.670869 −0.335435 0.942064i \(-0.608883\pi\)
−0.335435 + 0.942064i \(0.608883\pi\)
\(252\) 5.21553 0.328547
\(253\) 0.111432 0.00700569
\(254\) 0.760897 0.0477429
\(255\) 0.601573 0.0376720
\(256\) 11.2383 0.702395
\(257\) 14.1092 0.880107 0.440053 0.897972i \(-0.354960\pi\)
0.440053 + 0.897972i \(0.354960\pi\)
\(258\) −1.45983 −0.0908848
\(259\) 8.44452 0.524717
\(260\) −7.33787 −0.455075
\(261\) −7.65335 −0.473730
\(262\) −0.893553 −0.0552039
\(263\) 8.07927 0.498189 0.249095 0.968479i \(-0.419867\pi\)
0.249095 + 0.968479i \(0.419867\pi\)
\(264\) 3.94425 0.242752
\(265\) −6.51123 −0.399982
\(266\) 5.29803 0.324843
\(267\) 1.23369 0.0755005
\(268\) −21.9953 −1.34358
\(269\) 20.5467 1.25275 0.626377 0.779520i \(-0.284537\pi\)
0.626377 + 0.779520i \(0.284537\pi\)
\(270\) 0.150272 0.00914524
\(271\) 21.9411 1.33283 0.666415 0.745581i \(-0.267828\pi\)
0.666415 + 0.745581i \(0.267828\pi\)
\(272\) −3.62950 −0.220071
\(273\) 16.9454 1.02558
\(274\) −0.780485 −0.0471508
\(275\) 18.5988 1.12155
\(276\) −0.0538432 −0.00324098
\(277\) −22.0171 −1.32288 −0.661438 0.750000i \(-0.730054\pi\)
−0.661438 + 0.750000i \(0.730054\pi\)
\(278\) −0.712165 −0.0427128
\(279\) 3.60362 0.215743
\(280\) −1.59273 −0.0951840
\(281\) −12.9901 −0.774924 −0.387462 0.921886i \(-0.626648\pi\)
−0.387462 + 0.921886i \(0.626648\pi\)
\(282\) −1.50368 −0.0895428
\(283\) 25.5826 1.52073 0.760365 0.649496i \(-0.225020\pi\)
0.760365 + 0.649496i \(0.225020\pi\)
\(284\) −7.24411 −0.429859
\(285\) −4.74003 −0.280775
\(286\) 6.30594 0.372878
\(287\) 23.6285 1.39475
\(288\) −2.87385 −0.169343
\(289\) 1.00000 0.0588235
\(290\) 1.15008 0.0675351
\(291\) −12.6730 −0.742907
\(292\) −7.72709 −0.452194
\(293\) −4.43391 −0.259032 −0.129516 0.991577i \(-0.541342\pi\)
−0.129516 + 0.991577i \(0.541342\pi\)
\(294\) 0.0613236 0.00357647
\(295\) 6.79035 0.395349
\(296\) −3.08575 −0.179356
\(297\) 4.01000 0.232684
\(298\) −3.24929 −0.188226
\(299\) −0.174938 −0.0101169
\(300\) −8.98681 −0.518853
\(301\) 15.7306 0.906699
\(302\) −1.00357 −0.0577488
\(303\) 4.22605 0.242780
\(304\) 28.5982 1.64022
\(305\) −0.461936 −0.0264504
\(306\) 0.249798 0.0142800
\(307\) 16.4764 0.940358 0.470179 0.882571i \(-0.344189\pi\)
0.470179 + 0.882571i \(0.344189\pi\)
\(308\) −20.9143 −1.19170
\(309\) 2.21463 0.125986
\(310\) −0.541523 −0.0307564
\(311\) −23.7040 −1.34413 −0.672066 0.740491i \(-0.734593\pi\)
−0.672066 + 0.740491i \(0.734593\pi\)
\(312\) −6.19209 −0.350558
\(313\) −14.7103 −0.831473 −0.415736 0.909485i \(-0.636476\pi\)
−0.415736 + 0.909485i \(0.636476\pi\)
\(314\) −4.05254 −0.228698
\(315\) −1.61928 −0.0912362
\(316\) −1.93760 −0.108999
\(317\) 13.4989 0.758174 0.379087 0.925361i \(-0.376238\pi\)
0.379087 + 0.925361i \(0.376238\pi\)
\(318\) −2.70373 −0.151617
\(319\) 30.6899 1.71831
\(320\) −3.93496 −0.219971
\(321\) −3.48114 −0.194298
\(322\) −0.0186848 −0.00104126
\(323\) −7.87938 −0.438421
\(324\) −1.93760 −0.107645
\(325\) −29.1983 −1.61963
\(326\) 3.81874 0.211500
\(327\) −9.80627 −0.542288
\(328\) −8.63421 −0.476745
\(329\) 16.2032 0.893311
\(330\) −0.602589 −0.0331715
\(331\) 32.2146 1.77068 0.885338 0.464948i \(-0.153927\pi\)
0.885338 + 0.464948i \(0.153927\pi\)
\(332\) −13.3170 −0.730864
\(333\) −3.13719 −0.171917
\(334\) −2.95067 −0.161454
\(335\) 6.82896 0.373106
\(336\) 9.76969 0.532980
\(337\) −6.53365 −0.355911 −0.177955 0.984039i \(-0.556948\pi\)
−0.177955 + 0.984039i \(0.556948\pi\)
\(338\) −6.65234 −0.361840
\(339\) −13.8424 −0.751815
\(340\) 1.16561 0.0632140
\(341\) −14.4505 −0.782540
\(342\) −1.96825 −0.106431
\(343\) 18.1814 0.981704
\(344\) −5.74821 −0.309923
\(345\) 0.0167169 0.000900007 0
\(346\) 2.84952 0.153191
\(347\) 27.4956 1.47604 0.738021 0.674778i \(-0.235761\pi\)
0.738021 + 0.674778i \(0.235761\pi\)
\(348\) −14.8291 −0.794925
\(349\) 1.02891 0.0550765 0.0275383 0.999621i \(-0.491233\pi\)
0.0275383 + 0.999621i \(0.491233\pi\)
\(350\) −3.11863 −0.166698
\(351\) −6.29531 −0.336019
\(352\) 11.5241 0.614238
\(353\) 22.5864 1.20215 0.601076 0.799192i \(-0.294739\pi\)
0.601076 + 0.799192i \(0.294739\pi\)
\(354\) 2.81963 0.149862
\(355\) 2.24910 0.119370
\(356\) 2.39040 0.126691
\(357\) −2.69175 −0.142462
\(358\) −4.55839 −0.240919
\(359\) 7.69373 0.406059 0.203030 0.979173i \(-0.434921\pi\)
0.203030 + 0.979173i \(0.434921\pi\)
\(360\) 0.591710 0.0311859
\(361\) 43.0847 2.26762
\(362\) 5.22291 0.274510
\(363\) −5.08010 −0.266636
\(364\) 32.8334 1.72094
\(365\) 2.39906 0.125572
\(366\) −0.191815 −0.0100263
\(367\) 18.2696 0.953665 0.476832 0.878994i \(-0.341785\pi\)
0.476832 + 0.878994i \(0.341785\pi\)
\(368\) −0.100859 −0.00525762
\(369\) −8.77814 −0.456972
\(370\) 0.471431 0.0245085
\(371\) 29.1345 1.51259
\(372\) 6.98239 0.362020
\(373\) 9.68397 0.501417 0.250709 0.968063i \(-0.419336\pi\)
0.250709 + 0.968063i \(0.419336\pi\)
\(374\) −1.00169 −0.0517961
\(375\) 5.79803 0.299409
\(376\) −5.92089 −0.305346
\(377\) −48.1802 −2.48140
\(378\) −0.672392 −0.0345841
\(379\) −2.60077 −0.133593 −0.0667964 0.997767i \(-0.521278\pi\)
−0.0667964 + 0.997767i \(0.521278\pi\)
\(380\) −9.18428 −0.471144
\(381\) 3.04605 0.156054
\(382\) −2.87957 −0.147331
\(383\) −22.3068 −1.13982 −0.569912 0.821706i \(-0.693023\pi\)
−0.569912 + 0.821706i \(0.693023\pi\)
\(384\) −7.38165 −0.376693
\(385\) 6.49332 0.330930
\(386\) −3.08228 −0.156884
\(387\) −5.84403 −0.297069
\(388\) −24.5553 −1.24661
\(389\) −14.7227 −0.746472 −0.373236 0.927736i \(-0.621752\pi\)
−0.373236 + 0.927736i \(0.621752\pi\)
\(390\) 0.946007 0.0479029
\(391\) 0.0277886 0.00140533
\(392\) 0.241468 0.0121960
\(393\) −3.57711 −0.180441
\(394\) 4.64127 0.233824
\(395\) 0.601573 0.0302684
\(396\) 7.76978 0.390446
\(397\) 22.2911 1.11876 0.559378 0.828913i \(-0.311040\pi\)
0.559378 + 0.828913i \(0.311040\pi\)
\(398\) −2.13731 −0.107133
\(399\) 21.2093 1.06179
\(400\) −16.8340 −0.841701
\(401\) −19.8299 −0.990259 −0.495129 0.868819i \(-0.664879\pi\)
−0.495129 + 0.868819i \(0.664879\pi\)
\(402\) 2.83566 0.141430
\(403\) 22.6859 1.13007
\(404\) 8.18840 0.407388
\(405\) 0.601573 0.0298924
\(406\) −5.14605 −0.255394
\(407\) 12.5801 0.623574
\(408\) 0.983604 0.0486956
\(409\) −16.4773 −0.814749 −0.407375 0.913261i \(-0.633556\pi\)
−0.407375 + 0.913261i \(0.633556\pi\)
\(410\) 1.31911 0.0651460
\(411\) −3.12447 −0.154119
\(412\) 4.29107 0.211406
\(413\) −30.3835 −1.49507
\(414\) 0.00694153 0.000341158 0
\(415\) 4.13457 0.202958
\(416\) −18.0918 −0.887022
\(417\) −2.85097 −0.139613
\(418\) 7.89269 0.386044
\(419\) −19.9343 −0.973856 −0.486928 0.873442i \(-0.661883\pi\)
−0.486928 + 0.873442i \(0.661883\pi\)
\(420\) −3.13752 −0.153095
\(421\) 27.9251 1.36099 0.680494 0.732754i \(-0.261765\pi\)
0.680494 + 0.732754i \(0.261765\pi\)
\(422\) 0.571362 0.0278135
\(423\) −6.01959 −0.292682
\(424\) −10.6462 −0.517025
\(425\) 4.63811 0.224981
\(426\) 0.933919 0.0452485
\(427\) 2.06694 0.100026
\(428\) −6.74506 −0.326035
\(429\) 25.2442 1.21880
\(430\) 0.878192 0.0423502
\(431\) 37.9667 1.82879 0.914397 0.404819i \(-0.132666\pi\)
0.914397 + 0.404819i \(0.132666\pi\)
\(432\) −3.62950 −0.174624
\(433\) −2.28993 −0.110047 −0.0550234 0.998485i \(-0.517523\pi\)
−0.0550234 + 0.998485i \(0.517523\pi\)
\(434\) 2.42305 0.116310
\(435\) 4.60405 0.220747
\(436\) −19.0006 −0.909966
\(437\) −0.218957 −0.0104741
\(438\) 0.996185 0.0475996
\(439\) −2.44673 −0.116776 −0.0583880 0.998294i \(-0.518596\pi\)
−0.0583880 + 0.998294i \(0.518596\pi\)
\(440\) −2.37276 −0.113117
\(441\) 0.245493 0.0116901
\(442\) 1.57255 0.0747988
\(443\) 8.23273 0.391149 0.195574 0.980689i \(-0.437343\pi\)
0.195574 + 0.980689i \(0.437343\pi\)
\(444\) −6.07862 −0.288479
\(445\) −0.742154 −0.0351815
\(446\) 4.34924 0.205942
\(447\) −13.0077 −0.615243
\(448\) 17.6070 0.831854
\(449\) −0.490723 −0.0231587 −0.0115793 0.999933i \(-0.503686\pi\)
−0.0115793 + 0.999933i \(0.503686\pi\)
\(450\) 1.15859 0.0546164
\(451\) 35.2003 1.65752
\(452\) −26.8210 −1.26155
\(453\) −4.01752 −0.188759
\(454\) 3.58645 0.168320
\(455\) −10.1939 −0.477897
\(456\) −7.75019 −0.362936
\(457\) 30.1693 1.41126 0.705631 0.708580i \(-0.250664\pi\)
0.705631 + 0.708580i \(0.250664\pi\)
\(458\) 4.96210 0.231864
\(459\) 1.00000 0.0466760
\(460\) 0.0323906 0.00151022
\(461\) 32.9453 1.53442 0.767208 0.641399i \(-0.221646\pi\)
0.767208 + 0.641399i \(0.221646\pi\)
\(462\) 2.69629 0.125443
\(463\) 1.25815 0.0584712 0.0292356 0.999573i \(-0.490693\pi\)
0.0292356 + 0.999573i \(0.490693\pi\)
\(464\) −27.7778 −1.28955
\(465\) −2.16784 −0.100531
\(466\) 0.297862 0.0137982
\(467\) −30.5249 −1.41252 −0.706261 0.707951i \(-0.749620\pi\)
−0.706261 + 0.707951i \(0.749620\pi\)
\(468\) −12.1978 −0.563843
\(469\) −30.5562 −1.41096
\(470\) 0.904573 0.0417249
\(471\) −16.2233 −0.747530
\(472\) 11.1026 0.511037
\(473\) 23.4346 1.07752
\(474\) 0.249798 0.0114736
\(475\) −36.5454 −1.67682
\(476\) −5.21553 −0.239053
\(477\) −10.8237 −0.495582
\(478\) −2.46327 −0.112667
\(479\) 22.4564 1.02606 0.513030 0.858371i \(-0.328523\pi\)
0.513030 + 0.858371i \(0.328523\pi\)
\(480\) 1.72883 0.0789100
\(481\) −19.7496 −0.900503
\(482\) −2.92489 −0.133225
\(483\) −0.0747998 −0.00340351
\(484\) −9.84320 −0.447418
\(485\) 7.62377 0.346177
\(486\) 0.249798 0.0113311
\(487\) 28.4735 1.29026 0.645129 0.764074i \(-0.276804\pi\)
0.645129 + 0.764074i \(0.276804\pi\)
\(488\) −0.755289 −0.0341903
\(489\) 15.2873 0.691317
\(490\) −0.0368907 −0.00166655
\(491\) −22.3317 −1.00782 −0.503909 0.863757i \(-0.668105\pi\)
−0.503909 + 0.863757i \(0.668105\pi\)
\(492\) −17.0085 −0.766804
\(493\) 7.65335 0.344689
\(494\) −12.3908 −0.557486
\(495\) −2.41231 −0.108425
\(496\) 13.0794 0.587280
\(497\) −10.0636 −0.451415
\(498\) 1.71684 0.0769335
\(499\) −14.2687 −0.638753 −0.319377 0.947628i \(-0.603474\pi\)
−0.319377 + 0.947628i \(0.603474\pi\)
\(500\) 11.2343 0.502412
\(501\) −11.8122 −0.527732
\(502\) 2.65499 0.118498
\(503\) −2.91169 −0.129826 −0.0649129 0.997891i \(-0.520677\pi\)
−0.0649129 + 0.997891i \(0.520677\pi\)
\(504\) −2.64761 −0.117934
\(505\) −2.54228 −0.113130
\(506\) −0.0278355 −0.00123744
\(507\) −26.6309 −1.18272
\(508\) 5.90203 0.261860
\(509\) −24.1866 −1.07205 −0.536026 0.844201i \(-0.680075\pi\)
−0.536026 + 0.844201i \(0.680075\pi\)
\(510\) −0.150272 −0.00665414
\(511\) −10.7346 −0.474871
\(512\) −17.5706 −0.776519
\(513\) −7.87938 −0.347883
\(514\) −3.52444 −0.155456
\(515\) −1.33226 −0.0587066
\(516\) −11.3234 −0.498485
\(517\) 24.1385 1.06161
\(518\) −2.10942 −0.0926827
\(519\) 11.4073 0.500726
\(520\) 3.72500 0.163352
\(521\) 16.3236 0.715151 0.357576 0.933884i \(-0.383603\pi\)
0.357576 + 0.933884i \(0.383603\pi\)
\(522\) 1.91179 0.0836767
\(523\) 40.2601 1.76045 0.880225 0.474556i \(-0.157391\pi\)
0.880225 + 0.474556i \(0.157391\pi\)
\(524\) −6.93101 −0.302782
\(525\) −12.4846 −0.544873
\(526\) −2.01818 −0.0879970
\(527\) −3.60362 −0.156976
\(528\) 14.5543 0.633394
\(529\) −22.9992 −0.999966
\(530\) 1.62649 0.0706502
\(531\) 11.2876 0.489842
\(532\) 41.0952 1.78170
\(533\) −55.2611 −2.39362
\(534\) −0.308173 −0.0133359
\(535\) 2.09416 0.0905384
\(536\) 11.1657 0.482285
\(537\) −18.2483 −0.787474
\(538\) −5.13252 −0.221279
\(539\) −0.984427 −0.0424023
\(540\) 1.16561 0.0501598
\(541\) 8.33378 0.358297 0.179149 0.983822i \(-0.442666\pi\)
0.179149 + 0.983822i \(0.442666\pi\)
\(542\) −5.48085 −0.235423
\(543\) 20.9086 0.897272
\(544\) 2.87385 0.123215
\(545\) 5.89919 0.252694
\(546\) −4.23291 −0.181152
\(547\) 4.12593 0.176412 0.0882060 0.996102i \(-0.471887\pi\)
0.0882060 + 0.996102i \(0.471887\pi\)
\(548\) −6.05398 −0.258613
\(549\) −0.767879 −0.0327723
\(550\) −4.64594 −0.198104
\(551\) −60.3037 −2.56902
\(552\) 0.0273330 0.00116337
\(553\) −2.69175 −0.114465
\(554\) 5.49981 0.233665
\(555\) 1.88725 0.0801093
\(556\) −5.52404 −0.234271
\(557\) −35.2923 −1.49538 −0.747691 0.664047i \(-0.768838\pi\)
−0.747691 + 0.664047i \(0.768838\pi\)
\(558\) −0.900177 −0.0381075
\(559\) −36.7900 −1.55605
\(560\) −5.87719 −0.248356
\(561\) −4.01000 −0.169302
\(562\) 3.24490 0.136878
\(563\) −20.9611 −0.883404 −0.441702 0.897162i \(-0.645625\pi\)
−0.441702 + 0.897162i \(0.645625\pi\)
\(564\) −11.6636 −0.491124
\(565\) 8.32721 0.350328
\(566\) −6.39049 −0.268612
\(567\) −2.69175 −0.113043
\(568\) 3.67740 0.154300
\(569\) 39.8443 1.67036 0.835179 0.549978i \(-0.185364\pi\)
0.835179 + 0.549978i \(0.185364\pi\)
\(570\) 1.18405 0.0495943
\(571\) −25.0859 −1.04981 −0.524907 0.851160i \(-0.675900\pi\)
−0.524907 + 0.851160i \(0.675900\pi\)
\(572\) 48.9132 2.04516
\(573\) −11.5276 −0.481572
\(574\) −5.90235 −0.246359
\(575\) 0.128887 0.00537494
\(576\) −6.54112 −0.272547
\(577\) 21.3996 0.890877 0.445438 0.895313i \(-0.353048\pi\)
0.445438 + 0.895313i \(0.353048\pi\)
\(578\) −0.249798 −0.0103902
\(579\) −12.3391 −0.512796
\(580\) 8.92081 0.370417
\(581\) −18.5002 −0.767516
\(582\) 3.16570 0.131222
\(583\) 43.4029 1.79756
\(584\) 3.92258 0.162318
\(585\) 3.78709 0.156577
\(586\) 1.10758 0.0457538
\(587\) −1.65094 −0.0681417 −0.0340708 0.999419i \(-0.510847\pi\)
−0.0340708 + 0.999419i \(0.510847\pi\)
\(588\) 0.475668 0.0196162
\(589\) 28.3943 1.16997
\(590\) −1.69621 −0.0698320
\(591\) 18.5801 0.764283
\(592\) −11.3864 −0.467980
\(593\) −16.2107 −0.665695 −0.332848 0.942981i \(-0.608010\pi\)
−0.332848 + 0.942981i \(0.608010\pi\)
\(594\) −1.00169 −0.0410998
\(595\) 1.61928 0.0663841
\(596\) −25.2037 −1.03238
\(597\) −8.55614 −0.350180
\(598\) 0.0436991 0.00178699
\(599\) 42.1829 1.72355 0.861774 0.507293i \(-0.169354\pi\)
0.861774 + 0.507293i \(0.169354\pi\)
\(600\) 4.56206 0.186245
\(601\) −32.4009 −1.32166 −0.660830 0.750536i \(-0.729795\pi\)
−0.660830 + 0.750536i \(0.729795\pi\)
\(602\) −3.92948 −0.160154
\(603\) 11.3518 0.462282
\(604\) −7.78434 −0.316740
\(605\) 3.05605 0.124246
\(606\) −1.05566 −0.0428832
\(607\) 26.4988 1.07555 0.537776 0.843087i \(-0.319264\pi\)
0.537776 + 0.843087i \(0.319264\pi\)
\(608\) −22.6442 −0.918342
\(609\) −20.6009 −0.834789
\(610\) 0.115391 0.00467203
\(611\) −37.8951 −1.53307
\(612\) 1.93760 0.0783229
\(613\) 26.9517 1.08857 0.544284 0.838901i \(-0.316801\pi\)
0.544284 + 0.838901i \(0.316801\pi\)
\(614\) −4.11577 −0.166099
\(615\) 5.28070 0.212938
\(616\) 10.6169 0.427768
\(617\) −12.1534 −0.489276 −0.244638 0.969615i \(-0.578669\pi\)
−0.244638 + 0.969615i \(0.578669\pi\)
\(618\) −0.553210 −0.0222534
\(619\) −48.8721 −1.96434 −0.982168 0.188005i \(-0.939798\pi\)
−0.982168 + 0.188005i \(0.939798\pi\)
\(620\) −4.20042 −0.168693
\(621\) 0.0277886 0.00111512
\(622\) 5.92122 0.237419
\(623\) 3.32078 0.133044
\(624\) −22.8488 −0.914685
\(625\) 19.7026 0.788104
\(626\) 3.67459 0.146866
\(627\) 31.5963 1.26184
\(628\) −31.4343 −1.25436
\(629\) 3.13719 0.125088
\(630\) 0.404493 0.0161154
\(631\) 0.205425 0.00817784 0.00408892 0.999992i \(-0.498698\pi\)
0.00408892 + 0.999992i \(0.498698\pi\)
\(632\) 0.983604 0.0391257
\(633\) 2.28730 0.0909120
\(634\) −3.37199 −0.133919
\(635\) −1.83242 −0.0727175
\(636\) −20.9719 −0.831592
\(637\) 1.54545 0.0612331
\(638\) −7.66627 −0.303511
\(639\) 3.73870 0.147901
\(640\) 4.44061 0.175530
\(641\) 26.9007 1.06251 0.531257 0.847211i \(-0.321720\pi\)
0.531257 + 0.847211i \(0.321720\pi\)
\(642\) 0.869580 0.0343196
\(643\) 43.9322 1.73252 0.866259 0.499596i \(-0.166518\pi\)
0.866259 + 0.499596i \(0.166518\pi\)
\(644\) −0.144932 −0.00571113
\(645\) 3.51561 0.138427
\(646\) 1.96825 0.0774399
\(647\) −11.9167 −0.468493 −0.234247 0.972177i \(-0.575262\pi\)
−0.234247 + 0.972177i \(0.575262\pi\)
\(648\) 0.983604 0.0386396
\(649\) −45.2635 −1.77675
\(650\) 7.29368 0.286082
\(651\) 9.70004 0.380175
\(652\) 29.6207 1.16004
\(653\) −0.908436 −0.0355499 −0.0177749 0.999842i \(-0.505658\pi\)
−0.0177749 + 0.999842i \(0.505658\pi\)
\(654\) 2.44958 0.0957863
\(655\) 2.15189 0.0840814
\(656\) −31.8603 −1.24393
\(657\) 3.98797 0.155585
\(658\) −4.04752 −0.157789
\(659\) 50.3795 1.96251 0.981253 0.192724i \(-0.0617323\pi\)
0.981253 + 0.192724i \(0.0617323\pi\)
\(660\) −4.67409 −0.181939
\(661\) 27.3573 1.06408 0.532039 0.846720i \(-0.321426\pi\)
0.532039 + 0.846720i \(0.321426\pi\)
\(662\) −8.04714 −0.312761
\(663\) 6.29531 0.244489
\(664\) 6.76023 0.262348
\(665\) −12.7590 −0.494771
\(666\) 0.783663 0.0303663
\(667\) 0.212676 0.00823484
\(668\) −22.8874 −0.885541
\(669\) 17.4110 0.673149
\(670\) −1.70586 −0.0659031
\(671\) 3.07920 0.118871
\(672\) −7.73567 −0.298410
\(673\) −17.0332 −0.656582 −0.328291 0.944577i \(-0.606473\pi\)
−0.328291 + 0.944577i \(0.606473\pi\)
\(674\) 1.63209 0.0628658
\(675\) 4.63811 0.178521
\(676\) −51.6001 −1.98462
\(677\) 5.34461 0.205410 0.102705 0.994712i \(-0.467250\pi\)
0.102705 + 0.994712i \(0.467250\pi\)
\(678\) 3.45780 0.132796
\(679\) −34.1126 −1.30912
\(680\) −0.591710 −0.0226910
\(681\) 14.3574 0.550177
\(682\) 3.60971 0.138223
\(683\) 1.88682 0.0721971 0.0360985 0.999348i \(-0.488507\pi\)
0.0360985 + 0.999348i \(0.488507\pi\)
\(684\) −15.2671 −0.583752
\(685\) 1.87960 0.0718157
\(686\) −4.54168 −0.173402
\(687\) 19.8645 0.757876
\(688\) −21.2109 −0.808658
\(689\) −68.1383 −2.59586
\(690\) −0.00417584 −0.000158971 0
\(691\) 49.8882 1.89784 0.948918 0.315522i \(-0.102179\pi\)
0.948918 + 0.315522i \(0.102179\pi\)
\(692\) 22.1028 0.840224
\(693\) 10.7939 0.410026
\(694\) −6.86834 −0.260719
\(695\) 1.71507 0.0650562
\(696\) 7.52786 0.285343
\(697\) 8.77814 0.332496
\(698\) −0.257020 −0.00972837
\(699\) 1.19241 0.0451011
\(700\) −24.1902 −0.914303
\(701\) −14.5824 −0.550769 −0.275385 0.961334i \(-0.588805\pi\)
−0.275385 + 0.961334i \(0.588805\pi\)
\(702\) 1.57255 0.0593522
\(703\) −24.7191 −0.932300
\(704\) 26.2299 0.988576
\(705\) 3.62122 0.136383
\(706\) −5.64203 −0.212341
\(707\) 11.3754 0.427818
\(708\) 21.8710 0.821961
\(709\) −36.9391 −1.38728 −0.693639 0.720323i \(-0.743994\pi\)
−0.693639 + 0.720323i \(0.743994\pi\)
\(710\) −0.561821 −0.0210848
\(711\) 1.00000 0.0375029
\(712\) −1.21346 −0.0454764
\(713\) −0.100140 −0.00375026
\(714\) 0.672392 0.0251636
\(715\) −15.1862 −0.567933
\(716\) −35.3580 −1.32139
\(717\) −9.86106 −0.368268
\(718\) −1.92188 −0.0717238
\(719\) 11.9176 0.444451 0.222225 0.974995i \(-0.428668\pi\)
0.222225 + 0.974995i \(0.428668\pi\)
\(720\) 2.18341 0.0813709
\(721\) 5.96123 0.222008
\(722\) −10.7625 −0.400537
\(723\) −11.7090 −0.435464
\(724\) 40.5124 1.50563
\(725\) 35.4971 1.31833
\(726\) 1.26900 0.0470969
\(727\) −23.1710 −0.859363 −0.429682 0.902980i \(-0.641374\pi\)
−0.429682 + 0.902980i \(0.641374\pi\)
\(728\) −16.6675 −0.617740
\(729\) 1.00000 0.0370370
\(730\) −0.599279 −0.0221803
\(731\) 5.84403 0.216149
\(732\) −1.48784 −0.0549923
\(733\) −19.0576 −0.703910 −0.351955 0.936017i \(-0.614483\pi\)
−0.351955 + 0.936017i \(0.614483\pi\)
\(734\) −4.56370 −0.168449
\(735\) −0.147682 −0.00544734
\(736\) 0.0798602 0.00294369
\(737\) −45.5208 −1.67678
\(738\) 2.19276 0.0807166
\(739\) 10.0997 0.371525 0.185763 0.982595i \(-0.440524\pi\)
0.185763 + 0.982595i \(0.440524\pi\)
\(740\) 3.65674 0.134424
\(741\) −49.6032 −1.82222
\(742\) −7.27774 −0.267174
\(743\) 36.1643 1.32674 0.663369 0.748292i \(-0.269126\pi\)
0.663369 + 0.748292i \(0.269126\pi\)
\(744\) −3.54454 −0.129949
\(745\) 7.82508 0.286689
\(746\) −2.41904 −0.0885672
\(747\) 6.87292 0.251467
\(748\) −7.76978 −0.284091
\(749\) −9.37034 −0.342385
\(750\) −1.44834 −0.0528857
\(751\) −38.1877 −1.39349 −0.696745 0.717319i \(-0.745369\pi\)
−0.696745 + 0.717319i \(0.745369\pi\)
\(752\) −21.8481 −0.796718
\(753\) 10.6286 0.387326
\(754\) 12.0353 0.438300
\(755\) 2.41683 0.0879575
\(756\) −5.21553 −0.189687
\(757\) −5.71912 −0.207865 −0.103932 0.994584i \(-0.533143\pi\)
−0.103932 + 0.994584i \(0.533143\pi\)
\(758\) 0.649667 0.0235970
\(759\) −0.111432 −0.00404474
\(760\) 4.66231 0.169120
\(761\) 12.2142 0.442766 0.221383 0.975187i \(-0.428943\pi\)
0.221383 + 0.975187i \(0.428943\pi\)
\(762\) −0.760897 −0.0275644
\(763\) −26.3960 −0.955599
\(764\) −22.3359 −0.808083
\(765\) −0.601573 −0.0217499
\(766\) 5.57219 0.201331
\(767\) 71.0592 2.56580
\(768\) −11.2383 −0.405528
\(769\) −48.5415 −1.75045 −0.875226 0.483714i \(-0.839288\pi\)
−0.875226 + 0.483714i \(0.839288\pi\)
\(770\) −1.62202 −0.0584535
\(771\) −14.1092 −0.508130
\(772\) −23.9083 −0.860477
\(773\) 35.5001 1.27685 0.638425 0.769684i \(-0.279586\pi\)
0.638425 + 0.769684i \(0.279586\pi\)
\(774\) 1.45983 0.0524723
\(775\) −16.7140 −0.600385
\(776\) 12.4653 0.447477
\(777\) −8.44452 −0.302945
\(778\) 3.67770 0.131852
\(779\) −69.1664 −2.47814
\(780\) 7.33787 0.262738
\(781\) −14.9922 −0.536463
\(782\) −0.00694153 −0.000248229 0
\(783\) 7.65335 0.273508
\(784\) 0.891017 0.0318220
\(785\) 9.75951 0.348332
\(786\) 0.893553 0.0318720
\(787\) −38.3312 −1.36636 −0.683180 0.730250i \(-0.739403\pi\)
−0.683180 + 0.730250i \(0.739403\pi\)
\(788\) 36.0008 1.28248
\(789\) −8.07927 −0.287630
\(790\) −0.150272 −0.00534643
\(791\) −37.2602 −1.32482
\(792\) −3.94425 −0.140153
\(793\) −4.83404 −0.171662
\(794\) −5.56826 −0.197610
\(795\) 6.51123 0.230930
\(796\) −16.5784 −0.587606
\(797\) 12.9802 0.459782 0.229891 0.973216i \(-0.426163\pi\)
0.229891 + 0.973216i \(0.426163\pi\)
\(798\) −5.29803 −0.187548
\(799\) 6.01959 0.212958
\(800\) 13.3292 0.471259
\(801\) −1.23369 −0.0435902
\(802\) 4.95347 0.174913
\(803\) −15.9918 −0.564337
\(804\) 21.9953 0.775715
\(805\) 0.0449976 0.00158596
\(806\) −5.66689 −0.199608
\(807\) −20.5467 −0.723278
\(808\) −4.15676 −0.146234
\(809\) 13.6188 0.478811 0.239405 0.970920i \(-0.423047\pi\)
0.239405 + 0.970920i \(0.423047\pi\)
\(810\) −0.150272 −0.00528001
\(811\) 29.2445 1.02691 0.513457 0.858115i \(-0.328365\pi\)
0.513457 + 0.858115i \(0.328365\pi\)
\(812\) −39.9162 −1.40079
\(813\) −21.9411 −0.769509
\(814\) −3.14249 −0.110144
\(815\) −9.19645 −0.322138
\(816\) 3.62950 0.127058
\(817\) −46.0474 −1.61099
\(818\) 4.11599 0.143912
\(819\) −16.9454 −0.592119
\(820\) 10.2319 0.357313
\(821\) −31.0045 −1.08207 −0.541033 0.841002i \(-0.681966\pi\)
−0.541033 + 0.841002i \(0.681966\pi\)
\(822\) 0.780485 0.0272226
\(823\) −47.6571 −1.66122 −0.830610 0.556854i \(-0.812008\pi\)
−0.830610 + 0.556854i \(0.812008\pi\)
\(824\) −2.17832 −0.0758854
\(825\) −18.5988 −0.647528
\(826\) 7.58972 0.264080
\(827\) 19.9323 0.693113 0.346557 0.938029i \(-0.387351\pi\)
0.346557 + 0.938029i \(0.387351\pi\)
\(828\) 0.0538432 0.00187118
\(829\) 13.9548 0.484670 0.242335 0.970193i \(-0.422087\pi\)
0.242335 + 0.970193i \(0.422087\pi\)
\(830\) −1.03281 −0.0358492
\(831\) 22.0171 0.763763
\(832\) −41.1784 −1.42760
\(833\) −0.245493 −0.00850583
\(834\) 0.712165 0.0246603
\(835\) 7.10593 0.245911
\(836\) 61.2211 2.11738
\(837\) −3.60362 −0.124559
\(838\) 4.97955 0.172016
\(839\) 23.3920 0.807582 0.403791 0.914851i \(-0.367692\pi\)
0.403791 + 0.914851i \(0.367692\pi\)
\(840\) 1.59273 0.0549545
\(841\) 29.5737 1.01978
\(842\) −6.97564 −0.240396
\(843\) 12.9901 0.447403
\(844\) 4.43187 0.152551
\(845\) 16.0204 0.551120
\(846\) 1.50368 0.0516975
\(847\) −13.6743 −0.469856
\(848\) −39.2845 −1.34903
\(849\) −25.5826 −0.877994
\(850\) −1.15859 −0.0397393
\(851\) 0.0871781 0.00298843
\(852\) 7.24411 0.248179
\(853\) 31.5811 1.08132 0.540659 0.841242i \(-0.318175\pi\)
0.540659 + 0.841242i \(0.318175\pi\)
\(854\) −0.516316 −0.0176680
\(855\) 4.74003 0.162106
\(856\) 3.42406 0.117032
\(857\) −12.8744 −0.439780 −0.219890 0.975525i \(-0.570570\pi\)
−0.219890 + 0.975525i \(0.570570\pi\)
\(858\) −6.30594 −0.215281
\(859\) 50.1112 1.70977 0.854886 0.518817i \(-0.173627\pi\)
0.854886 + 0.518817i \(0.173627\pi\)
\(860\) 6.81186 0.232282
\(861\) −23.6285 −0.805258
\(862\) −9.48400 −0.323026
\(863\) 3.75594 0.127854 0.0639269 0.997955i \(-0.479638\pi\)
0.0639269 + 0.997955i \(0.479638\pi\)
\(864\) 2.87385 0.0977703
\(865\) −6.86234 −0.233327
\(866\) 0.572018 0.0194380
\(867\) −1.00000 −0.0339618
\(868\) 18.7948 0.637937
\(869\) −4.01000 −0.136030
\(870\) −1.15008 −0.0389914
\(871\) 71.4633 2.42144
\(872\) 9.64548 0.326637
\(873\) 12.6730 0.428918
\(874\) 0.0546950 0.00185009
\(875\) 15.6068 0.527607
\(876\) 7.72709 0.261074
\(877\) 0.789518 0.0266601 0.0133301 0.999911i \(-0.495757\pi\)
0.0133301 + 0.999911i \(0.495757\pi\)
\(878\) 0.611187 0.0206266
\(879\) 4.43391 0.149552
\(880\) −8.75548 −0.295147
\(881\) 28.0249 0.944182 0.472091 0.881550i \(-0.343499\pi\)
0.472091 + 0.881550i \(0.343499\pi\)
\(882\) −0.0613236 −0.00206487
\(883\) 0.0211698 0.000712420 0 0.000356210 1.00000i \(-0.499887\pi\)
0.000356210 1.00000i \(0.499887\pi\)
\(884\) 12.1978 0.410256
\(885\) −6.79035 −0.228255
\(886\) −2.05652 −0.0690900
\(887\) −32.9697 −1.10701 −0.553507 0.832845i \(-0.686711\pi\)
−0.553507 + 0.832845i \(0.686711\pi\)
\(888\) 3.08575 0.103551
\(889\) 8.19920 0.274992
\(890\) 0.185388 0.00621424
\(891\) −4.01000 −0.134340
\(892\) 33.7356 1.12955
\(893\) −47.4306 −1.58721
\(894\) 3.24929 0.108673
\(895\) 10.9777 0.366945
\(896\) −19.8695 −0.663795
\(897\) 0.174938 0.00584100
\(898\) 0.122582 0.00409060
\(899\) −27.5798 −0.919837
\(900\) 8.98681 0.299560
\(901\) 10.8237 0.360589
\(902\) −8.79297 −0.292774
\(903\) −15.7306 −0.523483
\(904\) 13.6154 0.452842
\(905\) −12.5780 −0.418108
\(906\) 1.00357 0.0333413
\(907\) −45.0629 −1.49629 −0.748145 0.663536i \(-0.769055\pi\)
−0.748145 + 0.663536i \(0.769055\pi\)
\(908\) 27.8189 0.923203
\(909\) −4.22605 −0.140169
\(910\) 2.54641 0.0844126
\(911\) 3.35577 0.111181 0.0555907 0.998454i \(-0.482296\pi\)
0.0555907 + 0.998454i \(0.482296\pi\)
\(912\) −28.5982 −0.946982
\(913\) −27.5604 −0.912117
\(914\) −7.53623 −0.249276
\(915\) 0.461936 0.0152711
\(916\) 38.4894 1.27173
\(917\) −9.62866 −0.317966
\(918\) −0.249798 −0.00824455
\(919\) −29.8453 −0.984507 −0.492253 0.870452i \(-0.663827\pi\)
−0.492253 + 0.870452i \(0.663827\pi\)
\(920\) −0.0164428 −0.000542103 0
\(921\) −16.4764 −0.542916
\(922\) −8.22966 −0.271029
\(923\) 23.5363 0.774706
\(924\) 20.9143 0.688029
\(925\) 14.5506 0.478422
\(926\) −0.314283 −0.0103280
\(927\) −2.21463 −0.0727381
\(928\) 21.9946 0.722007
\(929\) 58.6973 1.92580 0.962898 0.269865i \(-0.0869792\pi\)
0.962898 + 0.269865i \(0.0869792\pi\)
\(930\) 0.541523 0.0177572
\(931\) 1.93433 0.0633952
\(932\) 2.31042 0.0756802
\(933\) 23.7040 0.776035
\(934\) 7.62504 0.249499
\(935\) 2.41231 0.0788910
\(936\) 6.19209 0.202395
\(937\) −2.20885 −0.0721599 −0.0360799 0.999349i \(-0.511487\pi\)
−0.0360799 + 0.999349i \(0.511487\pi\)
\(938\) 7.63288 0.249222
\(939\) 14.7103 0.480051
\(940\) 7.01649 0.228853
\(941\) 57.5794 1.87704 0.938518 0.345230i \(-0.112199\pi\)
0.938518 + 0.345230i \(0.112199\pi\)
\(942\) 4.05254 0.132039
\(943\) 0.243932 0.00794353
\(944\) 40.9685 1.33341
\(945\) 1.61928 0.0526753
\(946\) −5.85390 −0.190327
\(947\) 46.2003 1.50131 0.750654 0.660696i \(-0.229739\pi\)
0.750654 + 0.660696i \(0.229739\pi\)
\(948\) 1.93760 0.0629304
\(949\) 25.1055 0.814959
\(950\) 9.12897 0.296183
\(951\) −13.4989 −0.437732
\(952\) 2.64761 0.0858096
\(953\) −30.7402 −0.995772 −0.497886 0.867242i \(-0.665890\pi\)
−0.497886 + 0.867242i \(0.665890\pi\)
\(954\) 2.70373 0.0875364
\(955\) 6.93469 0.224401
\(956\) −19.1068 −0.617958
\(957\) −30.6899 −0.992064
\(958\) −5.60956 −0.181237
\(959\) −8.41028 −0.271582
\(960\) 3.93496 0.127000
\(961\) −18.0139 −0.581093
\(962\) 4.93340 0.159059
\(963\) 3.48114 0.112178
\(964\) −22.6875 −0.730714
\(965\) 7.42288 0.238951
\(966\) 0.0186848 0.000601174 0
\(967\) 23.5600 0.757638 0.378819 0.925471i \(-0.376330\pi\)
0.378819 + 0.925471i \(0.376330\pi\)
\(968\) 4.99680 0.160603
\(969\) 7.87938 0.253122
\(970\) −1.90440 −0.0611466
\(971\) −9.69426 −0.311103 −0.155552 0.987828i \(-0.549716\pi\)
−0.155552 + 0.987828i \(0.549716\pi\)
\(972\) 1.93760 0.0621486
\(973\) −7.67408 −0.246020
\(974\) −7.11262 −0.227903
\(975\) 29.1983 0.935095
\(976\) −2.78702 −0.0892103
\(977\) 37.8674 1.21149 0.605743 0.795660i \(-0.292876\pi\)
0.605743 + 0.795660i \(0.292876\pi\)
\(978\) −3.81874 −0.122110
\(979\) 4.94709 0.158110
\(980\) −0.286149 −0.00914070
\(981\) 9.80627 0.313090
\(982\) 5.57842 0.178015
\(983\) 6.38505 0.203652 0.101826 0.994802i \(-0.467532\pi\)
0.101826 + 0.994802i \(0.467532\pi\)
\(984\) 8.63421 0.275249
\(985\) −11.1773 −0.356138
\(986\) −1.91179 −0.0608837
\(987\) −16.2032 −0.515753
\(988\) −96.1111 −3.05770
\(989\) 0.162397 0.00516394
\(990\) 0.602589 0.0191516
\(991\) 7.00641 0.222566 0.111283 0.993789i \(-0.464504\pi\)
0.111283 + 0.993789i \(0.464504\pi\)
\(992\) −10.3563 −0.328812
\(993\) −32.2146 −1.02230
\(994\) 2.51387 0.0797352
\(995\) 5.14715 0.163176
\(996\) 13.3170 0.421965
\(997\) −22.2470 −0.704569 −0.352284 0.935893i \(-0.614595\pi\)
−0.352284 + 0.935893i \(0.614595\pi\)
\(998\) 3.56428 0.112825
\(999\) 3.13719 0.0992563
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 4029.2.a.l.1.15 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.15 32 1.1 even 1 trivial