Properties

Label 4029.2.a.k.1.14
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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: \(31\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.103363 q^{2} +1.00000 q^{3} -1.98932 q^{4} -2.25663 q^{5} -0.103363 q^{6} +4.11147 q^{7} +0.412347 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.103363 q^{2} +1.00000 q^{3} -1.98932 q^{4} -2.25663 q^{5} -0.103363 q^{6} +4.11147 q^{7} +0.412347 q^{8} +1.00000 q^{9} +0.233252 q^{10} +3.41549 q^{11} -1.98932 q^{12} +3.88047 q^{13} -0.424973 q^{14} -2.25663 q^{15} +3.93601 q^{16} +1.00000 q^{17} -0.103363 q^{18} -2.55629 q^{19} +4.48916 q^{20} +4.11147 q^{21} -0.353034 q^{22} +2.82500 q^{23} +0.412347 q^{24} +0.0923998 q^{25} -0.401096 q^{26} +1.00000 q^{27} -8.17901 q^{28} +9.03694 q^{29} +0.233252 q^{30} +2.07562 q^{31} -1.23153 q^{32} +3.41549 q^{33} -0.103363 q^{34} -9.27808 q^{35} -1.98932 q^{36} +0.222616 q^{37} +0.264225 q^{38} +3.88047 q^{39} -0.930516 q^{40} -9.66686 q^{41} -0.424973 q^{42} -11.3497 q^{43} -6.79448 q^{44} -2.25663 q^{45} -0.291999 q^{46} +0.936384 q^{47} +3.93601 q^{48} +9.90418 q^{49} -0.00955069 q^{50} +1.00000 q^{51} -7.71948 q^{52} -1.47935 q^{53} -0.103363 q^{54} -7.70751 q^{55} +1.69535 q^{56} -2.55629 q^{57} -0.934083 q^{58} +8.03969 q^{59} +4.48916 q^{60} +1.23827 q^{61} -0.214542 q^{62} +4.11147 q^{63} -7.74473 q^{64} -8.75680 q^{65} -0.353034 q^{66} -5.75544 q^{67} -1.98932 q^{68} +2.82500 q^{69} +0.959008 q^{70} +14.6544 q^{71} +0.412347 q^{72} -9.54271 q^{73} -0.0230102 q^{74} +0.0923998 q^{75} +5.08527 q^{76} +14.0427 q^{77} -0.401096 q^{78} +1.00000 q^{79} -8.88214 q^{80} +1.00000 q^{81} +0.999194 q^{82} +7.96281 q^{83} -8.17901 q^{84} -2.25663 q^{85} +1.17313 q^{86} +9.03694 q^{87} +1.40836 q^{88} +0.331886 q^{89} +0.233252 q^{90} +15.9544 q^{91} -5.61981 q^{92} +2.07562 q^{93} -0.0967872 q^{94} +5.76862 q^{95} -1.23153 q^{96} -13.1352 q^{97} -1.02372 q^{98} +3.41549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.103363 −0.0730885 −0.0365443 0.999332i \(-0.511635\pi\)
−0.0365443 + 0.999332i \(0.511635\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.98932 −0.994658
\(5\) −2.25663 −1.00920 −0.504599 0.863354i \(-0.668360\pi\)
−0.504599 + 0.863354i \(0.668360\pi\)
\(6\) −0.103363 −0.0421977
\(7\) 4.11147 1.55399 0.776995 0.629507i \(-0.216743\pi\)
0.776995 + 0.629507i \(0.216743\pi\)
\(8\) 0.412347 0.145787
\(9\) 1.00000 0.333333
\(10\) 0.233252 0.0737608
\(11\) 3.41549 1.02981 0.514904 0.857248i \(-0.327828\pi\)
0.514904 + 0.857248i \(0.327828\pi\)
\(12\) −1.98932 −0.574266
\(13\) 3.88047 1.07625 0.538124 0.842865i \(-0.319133\pi\)
0.538124 + 0.842865i \(0.319133\pi\)
\(14\) −0.424973 −0.113579
\(15\) −2.25663 −0.582661
\(16\) 3.93601 0.984003
\(17\) 1.00000 0.242536
\(18\) −0.103363 −0.0243628
\(19\) −2.55629 −0.586454 −0.293227 0.956043i \(-0.594729\pi\)
−0.293227 + 0.956043i \(0.594729\pi\)
\(20\) 4.48916 1.00381
\(21\) 4.11147 0.897196
\(22\) −0.353034 −0.0752671
\(23\) 2.82500 0.589052 0.294526 0.955643i \(-0.404838\pi\)
0.294526 + 0.955643i \(0.404838\pi\)
\(24\) 0.412347 0.0841699
\(25\) 0.0923998 0.0184800
\(26\) −0.401096 −0.0786614
\(27\) 1.00000 0.192450
\(28\) −8.17901 −1.54569
\(29\) 9.03694 1.67812 0.839059 0.544041i \(-0.183106\pi\)
0.839059 + 0.544041i \(0.183106\pi\)
\(30\) 0.233252 0.0425858
\(31\) 2.07562 0.372792 0.186396 0.982475i \(-0.440319\pi\)
0.186396 + 0.982475i \(0.440319\pi\)
\(32\) −1.23153 −0.217706
\(33\) 3.41549 0.594560
\(34\) −0.103363 −0.0177266
\(35\) −9.27808 −1.56828
\(36\) −1.98932 −0.331553
\(37\) 0.222616 0.0365978 0.0182989 0.999833i \(-0.494175\pi\)
0.0182989 + 0.999833i \(0.494175\pi\)
\(38\) 0.264225 0.0428630
\(39\) 3.88047 0.621372
\(40\) −0.930516 −0.147127
\(41\) −9.66686 −1.50971 −0.754855 0.655891i \(-0.772293\pi\)
−0.754855 + 0.655891i \(0.772293\pi\)
\(42\) −0.424973 −0.0655747
\(43\) −11.3497 −1.73081 −0.865405 0.501073i \(-0.832939\pi\)
−0.865405 + 0.501073i \(0.832939\pi\)
\(44\) −6.79448 −1.02431
\(45\) −2.25663 −0.336399
\(46\) −0.291999 −0.0430530
\(47\) 0.936384 0.136586 0.0682928 0.997665i \(-0.478245\pi\)
0.0682928 + 0.997665i \(0.478245\pi\)
\(48\) 3.93601 0.568114
\(49\) 9.90418 1.41488
\(50\) −0.00955069 −0.00135067
\(51\) 1.00000 0.140028
\(52\) −7.71948 −1.07050
\(53\) −1.47935 −0.203204 −0.101602 0.994825i \(-0.532397\pi\)
−0.101602 + 0.994825i \(0.532397\pi\)
\(54\) −0.103363 −0.0140659
\(55\) −7.70751 −1.03928
\(56\) 1.69535 0.226551
\(57\) −2.55629 −0.338589
\(58\) −0.934083 −0.122651
\(59\) 8.03969 1.04668 0.523339 0.852125i \(-0.324686\pi\)
0.523339 + 0.852125i \(0.324686\pi\)
\(60\) 4.48916 0.579548
\(61\) 1.23827 0.158544 0.0792719 0.996853i \(-0.474740\pi\)
0.0792719 + 0.996853i \(0.474740\pi\)
\(62\) −0.214542 −0.0272468
\(63\) 4.11147 0.517996
\(64\) −7.74473 −0.968091
\(65\) −8.75680 −1.08615
\(66\) −0.353034 −0.0434555
\(67\) −5.75544 −0.703139 −0.351570 0.936162i \(-0.614352\pi\)
−0.351570 + 0.936162i \(0.614352\pi\)
\(68\) −1.98932 −0.241240
\(69\) 2.82500 0.340090
\(70\) 0.959008 0.114623
\(71\) 14.6544 1.73916 0.869579 0.493794i \(-0.164390\pi\)
0.869579 + 0.493794i \(0.164390\pi\)
\(72\) 0.412347 0.0485955
\(73\) −9.54271 −1.11689 −0.558445 0.829541i \(-0.688602\pi\)
−0.558445 + 0.829541i \(0.688602\pi\)
\(74\) −0.0230102 −0.00267488
\(75\) 0.0923998 0.0106694
\(76\) 5.08527 0.583321
\(77\) 14.0427 1.60031
\(78\) −0.401096 −0.0454152
\(79\) 1.00000 0.112509
\(80\) −8.88214 −0.993053
\(81\) 1.00000 0.111111
\(82\) 0.999194 0.110342
\(83\) 7.96281 0.874031 0.437016 0.899454i \(-0.356035\pi\)
0.437016 + 0.899454i \(0.356035\pi\)
\(84\) −8.17901 −0.892403
\(85\) −2.25663 −0.244766
\(86\) 1.17313 0.126502
\(87\) 9.03694 0.968862
\(88\) 1.40836 0.150132
\(89\) 0.331886 0.0351799 0.0175899 0.999845i \(-0.494401\pi\)
0.0175899 + 0.999845i \(0.494401\pi\)
\(90\) 0.233252 0.0245869
\(91\) 15.9544 1.67248
\(92\) −5.61981 −0.585906
\(93\) 2.07562 0.215232
\(94\) −0.0967872 −0.00998284
\(95\) 5.76862 0.591848
\(96\) −1.23153 −0.125693
\(97\) −13.1352 −1.33368 −0.666838 0.745203i \(-0.732353\pi\)
−0.666838 + 0.745203i \(0.732353\pi\)
\(98\) −1.02372 −0.103412
\(99\) 3.41549 0.343269
\(100\) −0.183812 −0.0183812
\(101\) 13.8201 1.37515 0.687573 0.726115i \(-0.258676\pi\)
0.687573 + 0.726115i \(0.258676\pi\)
\(102\) −0.103363 −0.0102344
\(103\) 7.92873 0.781241 0.390621 0.920552i \(-0.372260\pi\)
0.390621 + 0.920552i \(0.372260\pi\)
\(104\) 1.60010 0.156903
\(105\) −9.27808 −0.905448
\(106\) 0.152910 0.0148519
\(107\) −7.91500 −0.765172 −0.382586 0.923920i \(-0.624966\pi\)
−0.382586 + 0.923920i \(0.624966\pi\)
\(108\) −1.98932 −0.191422
\(109\) −1.10428 −0.105771 −0.0528853 0.998601i \(-0.516842\pi\)
−0.0528853 + 0.998601i \(0.516842\pi\)
\(110\) 0.796669 0.0759594
\(111\) 0.222616 0.0211298
\(112\) 16.1828 1.52913
\(113\) 4.66181 0.438546 0.219273 0.975664i \(-0.429631\pi\)
0.219273 + 0.975664i \(0.429631\pi\)
\(114\) 0.264225 0.0247470
\(115\) −6.37498 −0.594470
\(116\) −17.9773 −1.66915
\(117\) 3.88047 0.358750
\(118\) −0.831004 −0.0765002
\(119\) 4.11147 0.376898
\(120\) −0.930516 −0.0849441
\(121\) 0.665550 0.0605046
\(122\) −0.127991 −0.0115877
\(123\) −9.66686 −0.871632
\(124\) −4.12906 −0.370801
\(125\) 11.0747 0.990548
\(126\) −0.424973 −0.0378596
\(127\) 13.9060 1.23396 0.616978 0.786980i \(-0.288357\pi\)
0.616978 + 0.786980i \(0.288357\pi\)
\(128\) 3.26358 0.288462
\(129\) −11.3497 −0.999284
\(130\) 0.905127 0.0793849
\(131\) −2.67978 −0.234134 −0.117067 0.993124i \(-0.537349\pi\)
−0.117067 + 0.993124i \(0.537349\pi\)
\(132\) −6.79448 −0.591384
\(133\) −10.5101 −0.911343
\(134\) 0.594899 0.0513914
\(135\) −2.25663 −0.194220
\(136\) 0.412347 0.0353584
\(137\) 12.1779 1.04042 0.520212 0.854037i \(-0.325853\pi\)
0.520212 + 0.854037i \(0.325853\pi\)
\(138\) −0.291999 −0.0248566
\(139\) 21.5354 1.82661 0.913303 0.407282i \(-0.133523\pi\)
0.913303 + 0.407282i \(0.133523\pi\)
\(140\) 18.4570 1.55990
\(141\) 0.936384 0.0788577
\(142\) −1.51472 −0.127112
\(143\) 13.2537 1.10833
\(144\) 3.93601 0.328001
\(145\) −20.3931 −1.69355
\(146\) 0.986361 0.0816318
\(147\) 9.90418 0.816883
\(148\) −0.442853 −0.0364023
\(149\) 14.9571 1.22533 0.612665 0.790342i \(-0.290097\pi\)
0.612665 + 0.790342i \(0.290097\pi\)
\(150\) −0.00955069 −0.000779811 0
\(151\) −7.46476 −0.607474 −0.303737 0.952756i \(-0.598234\pi\)
−0.303737 + 0.952756i \(0.598234\pi\)
\(152\) −1.05408 −0.0854971
\(153\) 1.00000 0.0808452
\(154\) −1.45149 −0.116964
\(155\) −4.68391 −0.376221
\(156\) −7.71948 −0.618053
\(157\) −4.39671 −0.350896 −0.175448 0.984489i \(-0.556137\pi\)
−0.175448 + 0.984489i \(0.556137\pi\)
\(158\) −0.103363 −0.00822310
\(159\) −1.47935 −0.117320
\(160\) 2.77911 0.219708
\(161\) 11.6149 0.915381
\(162\) −0.103363 −0.00812095
\(163\) −22.5135 −1.76340 −0.881698 0.471815i \(-0.843599\pi\)
−0.881698 + 0.471815i \(0.843599\pi\)
\(164\) 19.2304 1.50165
\(165\) −7.70751 −0.600029
\(166\) −0.823058 −0.0638817
\(167\) −2.64140 −0.204398 −0.102199 0.994764i \(-0.532588\pi\)
−0.102199 + 0.994764i \(0.532588\pi\)
\(168\) 1.69535 0.130799
\(169\) 2.05804 0.158311
\(170\) 0.233252 0.0178896
\(171\) −2.55629 −0.195485
\(172\) 22.5781 1.72156
\(173\) −22.4015 −1.70315 −0.851577 0.524229i \(-0.824353\pi\)
−0.851577 + 0.524229i \(0.824353\pi\)
\(174\) −0.934083 −0.0708127
\(175\) 0.379899 0.0287176
\(176\) 13.4434 1.01333
\(177\) 8.03969 0.604300
\(178\) −0.0343047 −0.00257124
\(179\) −15.5245 −1.16035 −0.580176 0.814491i \(-0.697016\pi\)
−0.580176 + 0.814491i \(0.697016\pi\)
\(180\) 4.48916 0.334602
\(181\) −7.46336 −0.554747 −0.277373 0.960762i \(-0.589464\pi\)
−0.277373 + 0.960762i \(0.589464\pi\)
\(182\) −1.64909 −0.122239
\(183\) 1.23827 0.0915353
\(184\) 1.16488 0.0858759
\(185\) −0.502362 −0.0369344
\(186\) −0.214542 −0.0157310
\(187\) 3.41549 0.249765
\(188\) −1.86276 −0.135856
\(189\) 4.11147 0.299065
\(190\) −0.596260 −0.0432573
\(191\) 16.0425 1.16079 0.580396 0.814334i \(-0.302898\pi\)
0.580396 + 0.814334i \(0.302898\pi\)
\(192\) −7.74473 −0.558928
\(193\) −6.59109 −0.474437 −0.237219 0.971456i \(-0.576236\pi\)
−0.237219 + 0.971456i \(0.576236\pi\)
\(194\) 1.35769 0.0974763
\(195\) −8.75680 −0.627088
\(196\) −19.7025 −1.40732
\(197\) 13.5393 0.964634 0.482317 0.875997i \(-0.339795\pi\)
0.482317 + 0.875997i \(0.339795\pi\)
\(198\) −0.353034 −0.0250890
\(199\) 27.5511 1.95305 0.976523 0.215412i \(-0.0691093\pi\)
0.976523 + 0.215412i \(0.0691093\pi\)
\(200\) 0.0381007 0.00269413
\(201\) −5.75544 −0.405958
\(202\) −1.42848 −0.100507
\(203\) 37.1551 2.60778
\(204\) −1.98932 −0.139280
\(205\) 21.8146 1.52360
\(206\) −0.819536 −0.0570998
\(207\) 2.82500 0.196351
\(208\) 15.2736 1.05903
\(209\) −8.73098 −0.603935
\(210\) 0.959008 0.0661779
\(211\) 24.3779 1.67825 0.839123 0.543942i \(-0.183069\pi\)
0.839123 + 0.543942i \(0.183069\pi\)
\(212\) 2.94290 0.202119
\(213\) 14.6544 1.00410
\(214\) 0.818116 0.0559253
\(215\) 25.6121 1.74673
\(216\) 0.412347 0.0280566
\(217\) 8.53384 0.579315
\(218\) 0.114141 0.00773062
\(219\) −9.54271 −0.644837
\(220\) 15.3327 1.03373
\(221\) 3.88047 0.261029
\(222\) −0.0230102 −0.00154434
\(223\) −15.1922 −1.01735 −0.508673 0.860960i \(-0.669864\pi\)
−0.508673 + 0.860960i \(0.669864\pi\)
\(224\) −5.06340 −0.338313
\(225\) 0.0923998 0.00615998
\(226\) −0.481858 −0.0320527
\(227\) −21.5081 −1.42755 −0.713773 0.700377i \(-0.753015\pi\)
−0.713773 + 0.700377i \(0.753015\pi\)
\(228\) 5.08527 0.336780
\(229\) 12.9452 0.855442 0.427721 0.903911i \(-0.359317\pi\)
0.427721 + 0.903911i \(0.359317\pi\)
\(230\) 0.658936 0.0434490
\(231\) 14.0427 0.923940
\(232\) 3.72635 0.244647
\(233\) 7.29501 0.477912 0.238956 0.971030i \(-0.423195\pi\)
0.238956 + 0.971030i \(0.423195\pi\)
\(234\) −0.401096 −0.0262205
\(235\) −2.11308 −0.137842
\(236\) −15.9935 −1.04109
\(237\) 1.00000 0.0649570
\(238\) −0.424973 −0.0275469
\(239\) −24.1130 −1.55974 −0.779869 0.625942i \(-0.784715\pi\)
−0.779869 + 0.625942i \(0.784715\pi\)
\(240\) −8.88214 −0.573340
\(241\) 13.5990 0.875992 0.437996 0.898977i \(-0.355688\pi\)
0.437996 + 0.898977i \(0.355688\pi\)
\(242\) −0.0687931 −0.00442219
\(243\) 1.00000 0.0641500
\(244\) −2.46330 −0.157697
\(245\) −22.3501 −1.42790
\(246\) 0.999194 0.0637063
\(247\) −9.91961 −0.631170
\(248\) 0.855874 0.0543481
\(249\) 7.96281 0.504622
\(250\) −1.14471 −0.0723977
\(251\) −8.69606 −0.548890 −0.274445 0.961603i \(-0.588494\pi\)
−0.274445 + 0.961603i \(0.588494\pi\)
\(252\) −8.17901 −0.515229
\(253\) 9.64874 0.606611
\(254\) −1.43736 −0.0901881
\(255\) −2.25663 −0.141316
\(256\) 15.1521 0.947008
\(257\) 26.4319 1.64878 0.824388 0.566025i \(-0.191520\pi\)
0.824388 + 0.566025i \(0.191520\pi\)
\(258\) 1.17313 0.0730362
\(259\) 0.915278 0.0568726
\(260\) 17.4200 1.08035
\(261\) 9.03694 0.559373
\(262\) 0.276990 0.0171125
\(263\) −9.73137 −0.600062 −0.300031 0.953930i \(-0.596997\pi\)
−0.300031 + 0.953930i \(0.596997\pi\)
\(264\) 1.40836 0.0866789
\(265\) 3.33835 0.205073
\(266\) 1.08635 0.0666087
\(267\) 0.331886 0.0203111
\(268\) 11.4494 0.699383
\(269\) 8.36111 0.509786 0.254893 0.966969i \(-0.417960\pi\)
0.254893 + 0.966969i \(0.417960\pi\)
\(270\) 0.233252 0.0141953
\(271\) 24.9853 1.51775 0.758873 0.651239i \(-0.225750\pi\)
0.758873 + 0.651239i \(0.225750\pi\)
\(272\) 3.93601 0.238656
\(273\) 15.9544 0.965606
\(274\) −1.25874 −0.0760431
\(275\) 0.315590 0.0190308
\(276\) −5.61981 −0.338273
\(277\) 4.74679 0.285207 0.142604 0.989780i \(-0.454453\pi\)
0.142604 + 0.989780i \(0.454453\pi\)
\(278\) −2.22595 −0.133504
\(279\) 2.07562 0.124264
\(280\) −3.82579 −0.228635
\(281\) 20.0142 1.19395 0.596973 0.802261i \(-0.296370\pi\)
0.596973 + 0.802261i \(0.296370\pi\)
\(282\) −0.0967872 −0.00576359
\(283\) 0.611321 0.0363393 0.0181696 0.999835i \(-0.494216\pi\)
0.0181696 + 0.999835i \(0.494216\pi\)
\(284\) −29.1522 −1.72987
\(285\) 5.76862 0.341703
\(286\) −1.36994 −0.0810062
\(287\) −39.7450 −2.34607
\(288\) −1.23153 −0.0725686
\(289\) 1.00000 0.0588235
\(290\) 2.10788 0.123779
\(291\) −13.1352 −0.769998
\(292\) 18.9835 1.11092
\(293\) −7.19357 −0.420253 −0.210127 0.977674i \(-0.567388\pi\)
−0.210127 + 0.977674i \(0.567388\pi\)
\(294\) −1.02372 −0.0597048
\(295\) −18.1426 −1.05631
\(296\) 0.0917949 0.00533547
\(297\) 3.41549 0.198187
\(298\) −1.54600 −0.0895576
\(299\) 10.9623 0.633967
\(300\) −0.183812 −0.0106124
\(301\) −46.6639 −2.68966
\(302\) 0.771579 0.0443994
\(303\) 13.8201 0.793941
\(304\) −10.0616 −0.577072
\(305\) −2.79432 −0.160002
\(306\) −0.103363 −0.00590886
\(307\) 23.8255 1.35980 0.679898 0.733307i \(-0.262024\pi\)
0.679898 + 0.733307i \(0.262024\pi\)
\(308\) −27.9353 −1.59176
\(309\) 7.92873 0.451050
\(310\) 0.484142 0.0274974
\(311\) 1.82437 0.103451 0.0517253 0.998661i \(-0.483528\pi\)
0.0517253 + 0.998661i \(0.483528\pi\)
\(312\) 1.60010 0.0905878
\(313\) −28.2597 −1.59733 −0.798667 0.601773i \(-0.794461\pi\)
−0.798667 + 0.601773i \(0.794461\pi\)
\(314\) 0.454456 0.0256465
\(315\) −9.27808 −0.522761
\(316\) −1.98932 −0.111908
\(317\) 22.8240 1.28192 0.640961 0.767574i \(-0.278536\pi\)
0.640961 + 0.767574i \(0.278536\pi\)
\(318\) 0.152910 0.00857476
\(319\) 30.8655 1.72814
\(320\) 17.4770 0.976995
\(321\) −7.91500 −0.441772
\(322\) −1.20055 −0.0669039
\(323\) −2.55629 −0.142236
\(324\) −1.98932 −0.110518
\(325\) 0.358554 0.0198890
\(326\) 2.32706 0.128884
\(327\) −1.10428 −0.0610667
\(328\) −3.98610 −0.220096
\(329\) 3.84991 0.212253
\(330\) 0.796669 0.0438552
\(331\) −20.8797 −1.14765 −0.573827 0.818977i \(-0.694542\pi\)
−0.573827 + 0.818977i \(0.694542\pi\)
\(332\) −15.8405 −0.869362
\(333\) 0.222616 0.0121993
\(334\) 0.273023 0.0149391
\(335\) 12.9879 0.709607
\(336\) 16.1828 0.882843
\(337\) 11.7891 0.642195 0.321098 0.947046i \(-0.395948\pi\)
0.321098 + 0.947046i \(0.395948\pi\)
\(338\) −0.212725 −0.0115707
\(339\) 4.66181 0.253195
\(340\) 4.48916 0.243459
\(341\) 7.08925 0.383904
\(342\) 0.264225 0.0142877
\(343\) 11.9404 0.644723
\(344\) −4.68001 −0.252329
\(345\) −6.37498 −0.343218
\(346\) 2.31548 0.124481
\(347\) 1.22964 0.0660106 0.0330053 0.999455i \(-0.489492\pi\)
0.0330053 + 0.999455i \(0.489492\pi\)
\(348\) −17.9773 −0.963686
\(349\) 28.7056 1.53658 0.768289 0.640103i \(-0.221108\pi\)
0.768289 + 0.640103i \(0.221108\pi\)
\(350\) −0.0392674 −0.00209893
\(351\) 3.88047 0.207124
\(352\) −4.20628 −0.224195
\(353\) −2.01481 −0.107238 −0.0536188 0.998561i \(-0.517076\pi\)
−0.0536188 + 0.998561i \(0.517076\pi\)
\(354\) −0.831004 −0.0441674
\(355\) −33.0696 −1.75515
\(356\) −0.660227 −0.0349919
\(357\) 4.11147 0.217602
\(358\) 1.60465 0.0848085
\(359\) −23.8578 −1.25917 −0.629583 0.776934i \(-0.716774\pi\)
−0.629583 + 0.776934i \(0.716774\pi\)
\(360\) −0.930516 −0.0490425
\(361\) −12.4654 −0.656072
\(362\) 0.771433 0.0405456
\(363\) 0.665550 0.0349323
\(364\) −31.7384 −1.66354
\(365\) 21.5344 1.12716
\(366\) −0.127991 −0.00669018
\(367\) −0.797399 −0.0416239 −0.0208120 0.999783i \(-0.506625\pi\)
−0.0208120 + 0.999783i \(0.506625\pi\)
\(368\) 11.1192 0.579629
\(369\) −9.66686 −0.503237
\(370\) 0.0519256 0.00269948
\(371\) −6.08231 −0.315778
\(372\) −4.12906 −0.214082
\(373\) 14.2509 0.737884 0.368942 0.929452i \(-0.379720\pi\)
0.368942 + 0.929452i \(0.379720\pi\)
\(374\) −0.353034 −0.0182550
\(375\) 11.0747 0.571893
\(376\) 0.386115 0.0199123
\(377\) 35.0676 1.80607
\(378\) −0.424973 −0.0218582
\(379\) −30.7021 −1.57706 −0.788530 0.614997i \(-0.789157\pi\)
−0.788530 + 0.614997i \(0.789157\pi\)
\(380\) −11.4756 −0.588686
\(381\) 13.9060 0.712425
\(382\) −1.65819 −0.0848406
\(383\) 13.8220 0.706273 0.353136 0.935572i \(-0.385115\pi\)
0.353136 + 0.935572i \(0.385115\pi\)
\(384\) 3.26358 0.166544
\(385\) −31.6892 −1.61503
\(386\) 0.681273 0.0346759
\(387\) −11.3497 −0.576937
\(388\) 26.1300 1.32655
\(389\) −31.6403 −1.60423 −0.802114 0.597171i \(-0.796292\pi\)
−0.802114 + 0.597171i \(0.796292\pi\)
\(390\) 0.905127 0.0458329
\(391\) 2.82500 0.142866
\(392\) 4.08396 0.206271
\(393\) −2.67978 −0.135177
\(394\) −1.39946 −0.0705036
\(395\) −2.25663 −0.113544
\(396\) −6.79448 −0.341436
\(397\) −15.0934 −0.757514 −0.378757 0.925496i \(-0.623648\pi\)
−0.378757 + 0.925496i \(0.623648\pi\)
\(398\) −2.84776 −0.142745
\(399\) −10.5101 −0.526164
\(400\) 0.363686 0.0181843
\(401\) 15.7747 0.787750 0.393875 0.919164i \(-0.371134\pi\)
0.393875 + 0.919164i \(0.371134\pi\)
\(402\) 0.594899 0.0296708
\(403\) 8.05437 0.401217
\(404\) −27.4925 −1.36780
\(405\) −2.25663 −0.112133
\(406\) −3.84045 −0.190599
\(407\) 0.760341 0.0376887
\(408\) 0.412347 0.0204142
\(409\) 27.4829 1.35894 0.679471 0.733702i \(-0.262209\pi\)
0.679471 + 0.733702i \(0.262209\pi\)
\(410\) −2.25482 −0.111357
\(411\) 12.1779 0.600689
\(412\) −15.7728 −0.777068
\(413\) 33.0549 1.62653
\(414\) −0.291999 −0.0143510
\(415\) −17.9691 −0.882070
\(416\) −4.77892 −0.234306
\(417\) 21.5354 1.05459
\(418\) 0.902459 0.0441407
\(419\) −0.342752 −0.0167446 −0.00837228 0.999965i \(-0.502665\pi\)
−0.00837228 + 0.999965i \(0.502665\pi\)
\(420\) 18.4570 0.900611
\(421\) 19.8389 0.966889 0.483445 0.875375i \(-0.339385\pi\)
0.483445 + 0.875375i \(0.339385\pi\)
\(422\) −2.51977 −0.122661
\(423\) 0.936384 0.0455285
\(424\) −0.610006 −0.0296245
\(425\) 0.0923998 0.00448205
\(426\) −1.51472 −0.0733884
\(427\) 5.09110 0.246375
\(428\) 15.7454 0.761084
\(429\) 13.2537 0.639894
\(430\) −2.64734 −0.127666
\(431\) −27.0817 −1.30448 −0.652239 0.758013i \(-0.726170\pi\)
−0.652239 + 0.758013i \(0.726170\pi\)
\(432\) 3.93601 0.189371
\(433\) −35.0547 −1.68462 −0.842310 0.538993i \(-0.818805\pi\)
−0.842310 + 0.538993i \(0.818805\pi\)
\(434\) −0.882081 −0.0423413
\(435\) −20.3931 −0.977773
\(436\) 2.19676 0.105206
\(437\) −7.22152 −0.345452
\(438\) 0.986361 0.0471302
\(439\) −22.1696 −1.05810 −0.529049 0.848591i \(-0.677451\pi\)
−0.529049 + 0.848591i \(0.677451\pi\)
\(440\) −3.17817 −0.151513
\(441\) 9.90418 0.471628
\(442\) −0.401096 −0.0190782
\(443\) −1.58164 −0.0751462 −0.0375731 0.999294i \(-0.511963\pi\)
−0.0375731 + 0.999294i \(0.511963\pi\)
\(444\) −0.442853 −0.0210169
\(445\) −0.748946 −0.0355034
\(446\) 1.57031 0.0743563
\(447\) 14.9571 0.707445
\(448\) −31.8422 −1.50440
\(449\) −4.16269 −0.196449 −0.0982247 0.995164i \(-0.531316\pi\)
−0.0982247 + 0.995164i \(0.531316\pi\)
\(450\) −0.00955069 −0.000450224 0
\(451\) −33.0170 −1.55471
\(452\) −9.27381 −0.436204
\(453\) −7.46476 −0.350725
\(454\) 2.22314 0.104337
\(455\) −36.0033 −1.68786
\(456\) −1.05408 −0.0493618
\(457\) −26.7430 −1.25099 −0.625493 0.780230i \(-0.715102\pi\)
−0.625493 + 0.780230i \(0.715102\pi\)
\(458\) −1.33805 −0.0625230
\(459\) 1.00000 0.0466760
\(460\) 12.6819 0.591295
\(461\) −27.5308 −1.28224 −0.641118 0.767442i \(-0.721529\pi\)
−0.641118 + 0.767442i \(0.721529\pi\)
\(462\) −1.45149 −0.0675294
\(463\) −40.1196 −1.86452 −0.932258 0.361795i \(-0.882164\pi\)
−0.932258 + 0.361795i \(0.882164\pi\)
\(464\) 35.5695 1.65127
\(465\) −4.68391 −0.217211
\(466\) −0.754033 −0.0349299
\(467\) 5.85171 0.270785 0.135392 0.990792i \(-0.456771\pi\)
0.135392 + 0.990792i \(0.456771\pi\)
\(468\) −7.71948 −0.356833
\(469\) −23.6633 −1.09267
\(470\) 0.218413 0.0100747
\(471\) −4.39671 −0.202590
\(472\) 3.31514 0.152592
\(473\) −38.7647 −1.78240
\(474\) −0.103363 −0.00474761
\(475\) −0.236201 −0.0108376
\(476\) −8.17901 −0.374884
\(477\) −1.47935 −0.0677348
\(478\) 2.49238 0.113999
\(479\) −25.8669 −1.18189 −0.590944 0.806713i \(-0.701245\pi\)
−0.590944 + 0.806713i \(0.701245\pi\)
\(480\) 2.77911 0.126849
\(481\) 0.863854 0.0393883
\(482\) −1.40564 −0.0640249
\(483\) 11.6149 0.528496
\(484\) −1.32399 −0.0601814
\(485\) 29.6413 1.34594
\(486\) −0.103363 −0.00468863
\(487\) 14.7433 0.668081 0.334040 0.942559i \(-0.391588\pi\)
0.334040 + 0.942559i \(0.391588\pi\)
\(488\) 0.510595 0.0231136
\(489\) −22.5135 −1.01810
\(490\) 2.31017 0.104363
\(491\) 16.8884 0.762162 0.381081 0.924542i \(-0.375552\pi\)
0.381081 + 0.924542i \(0.375552\pi\)
\(492\) 19.2304 0.866975
\(493\) 9.03694 0.407003
\(494\) 1.02532 0.0461313
\(495\) −7.70751 −0.346427
\(496\) 8.16966 0.366828
\(497\) 60.2511 2.70263
\(498\) −0.823058 −0.0368821
\(499\) −18.3125 −0.819779 −0.409890 0.912135i \(-0.634433\pi\)
−0.409890 + 0.912135i \(0.634433\pi\)
\(500\) −22.0310 −0.985256
\(501\) −2.64140 −0.118009
\(502\) 0.898849 0.0401176
\(503\) 13.6167 0.607140 0.303570 0.952809i \(-0.401821\pi\)
0.303570 + 0.952809i \(0.401821\pi\)
\(504\) 1.69535 0.0755169
\(505\) −31.1868 −1.38779
\(506\) −0.997320 −0.0443363
\(507\) 2.05804 0.0914009
\(508\) −27.6634 −1.22737
\(509\) 13.2859 0.588888 0.294444 0.955669i \(-0.404865\pi\)
0.294444 + 0.955669i \(0.404865\pi\)
\(510\) 0.233252 0.0103286
\(511\) −39.2346 −1.73564
\(512\) −8.09332 −0.357678
\(513\) −2.55629 −0.112863
\(514\) −2.73207 −0.120507
\(515\) −17.8923 −0.788427
\(516\) 22.5781 0.993946
\(517\) 3.19821 0.140657
\(518\) −0.0946057 −0.00415673
\(519\) −22.4015 −0.983317
\(520\) −3.61084 −0.158346
\(521\) 41.0750 1.79953 0.899765 0.436375i \(-0.143738\pi\)
0.899765 + 0.436375i \(0.143738\pi\)
\(522\) −0.934083 −0.0408837
\(523\) −0.662665 −0.0289763 −0.0144882 0.999895i \(-0.504612\pi\)
−0.0144882 + 0.999895i \(0.504612\pi\)
\(524\) 5.33094 0.232883
\(525\) 0.379899 0.0165801
\(526\) 1.00586 0.0438576
\(527\) 2.07562 0.0904154
\(528\) 13.4434 0.585049
\(529\) −15.0194 −0.653017
\(530\) −0.345062 −0.0149885
\(531\) 8.03969 0.348893
\(532\) 20.9079 0.906474
\(533\) −37.5120 −1.62482
\(534\) −0.0343047 −0.00148451
\(535\) 17.8613 0.772210
\(536\) −2.37324 −0.102508
\(537\) −15.5245 −0.669930
\(538\) −0.864228 −0.0372595
\(539\) 33.8276 1.45706
\(540\) 4.48916 0.193183
\(541\) 20.7675 0.892866 0.446433 0.894817i \(-0.352694\pi\)
0.446433 + 0.894817i \(0.352694\pi\)
\(542\) −2.58254 −0.110930
\(543\) −7.46336 −0.320283
\(544\) −1.23153 −0.0528014
\(545\) 2.49195 0.106743
\(546\) −1.64909 −0.0705747
\(547\) 11.2688 0.481818 0.240909 0.970548i \(-0.422554\pi\)
0.240909 + 0.970548i \(0.422554\pi\)
\(548\) −24.2256 −1.03487
\(549\) 1.23827 0.0528479
\(550\) −0.0326203 −0.00139093
\(551\) −23.1011 −0.984138
\(552\) 1.16488 0.0495805
\(553\) 4.11147 0.174837
\(554\) −0.490641 −0.0208454
\(555\) −0.502362 −0.0213241
\(556\) −42.8406 −1.81685
\(557\) 1.38234 0.0585716 0.0292858 0.999571i \(-0.490677\pi\)
0.0292858 + 0.999571i \(0.490677\pi\)
\(558\) −0.214542 −0.00908227
\(559\) −44.0421 −1.86278
\(560\) −36.5186 −1.54319
\(561\) 3.41549 0.144202
\(562\) −2.06872 −0.0872638
\(563\) 16.2735 0.685844 0.342922 0.939364i \(-0.388583\pi\)
0.342922 + 0.939364i \(0.388583\pi\)
\(564\) −1.86276 −0.0784365
\(565\) −10.5200 −0.442580
\(566\) −0.0631879 −0.00265598
\(567\) 4.11147 0.172665
\(568\) 6.04270 0.253546
\(569\) 30.0681 1.26052 0.630260 0.776384i \(-0.282948\pi\)
0.630260 + 0.776384i \(0.282948\pi\)
\(570\) −0.596260 −0.0249746
\(571\) 18.3594 0.768315 0.384158 0.923267i \(-0.374492\pi\)
0.384158 + 0.923267i \(0.374492\pi\)
\(572\) −26.3658 −1.10241
\(573\) 16.0425 0.670184
\(574\) 4.10815 0.171471
\(575\) 0.261029 0.0108857
\(576\) −7.74473 −0.322697
\(577\) 45.5266 1.89530 0.947648 0.319317i \(-0.103454\pi\)
0.947648 + 0.319317i \(0.103454\pi\)
\(578\) −0.103363 −0.00429932
\(579\) −6.59109 −0.273916
\(580\) 40.5683 1.68451
\(581\) 32.7388 1.35824
\(582\) 1.35769 0.0562780
\(583\) −5.05270 −0.209262
\(584\) −3.93491 −0.162828
\(585\) −8.75680 −0.362049
\(586\) 0.743548 0.0307157
\(587\) 21.5288 0.888587 0.444294 0.895881i \(-0.353455\pi\)
0.444294 + 0.895881i \(0.353455\pi\)
\(588\) −19.7025 −0.812519
\(589\) −5.30589 −0.218625
\(590\) 1.87527 0.0772038
\(591\) 13.5393 0.556931
\(592\) 0.876218 0.0360123
\(593\) −18.5086 −0.760058 −0.380029 0.924974i \(-0.624086\pi\)
−0.380029 + 0.924974i \(0.624086\pi\)
\(594\) −0.353034 −0.0144852
\(595\) −9.27808 −0.380364
\(596\) −29.7543 −1.21878
\(597\) 27.5511 1.12759
\(598\) −1.13309 −0.0463357
\(599\) −38.7741 −1.58427 −0.792134 0.610347i \(-0.791030\pi\)
−0.792134 + 0.610347i \(0.791030\pi\)
\(600\) 0.0381007 0.00155546
\(601\) −9.51671 −0.388195 −0.194097 0.980982i \(-0.562178\pi\)
−0.194097 + 0.980982i \(0.562178\pi\)
\(602\) 4.82331 0.196583
\(603\) −5.75544 −0.234380
\(604\) 14.8498 0.604229
\(605\) −1.50190 −0.0610611
\(606\) −1.42848 −0.0580280
\(607\) −37.6589 −1.52853 −0.764263 0.644905i \(-0.776897\pi\)
−0.764263 + 0.644905i \(0.776897\pi\)
\(608\) 3.14815 0.127674
\(609\) 37.1551 1.50560
\(610\) 0.288828 0.0116943
\(611\) 3.63361 0.147000
\(612\) −1.98932 −0.0804133
\(613\) −17.7438 −0.716665 −0.358333 0.933594i \(-0.616655\pi\)
−0.358333 + 0.933594i \(0.616655\pi\)
\(614\) −2.46267 −0.0993855
\(615\) 21.8146 0.879649
\(616\) 5.79045 0.233304
\(617\) 7.26489 0.292473 0.146237 0.989250i \(-0.453284\pi\)
0.146237 + 0.989250i \(0.453284\pi\)
\(618\) −0.819536 −0.0329666
\(619\) 3.82609 0.153784 0.0768919 0.997039i \(-0.475500\pi\)
0.0768919 + 0.997039i \(0.475500\pi\)
\(620\) 9.31778 0.374211
\(621\) 2.82500 0.113363
\(622\) −0.188572 −0.00756105
\(623\) 1.36454 0.0546691
\(624\) 15.2736 0.611432
\(625\) −25.4535 −1.01814
\(626\) 2.92100 0.116747
\(627\) −8.73098 −0.348682
\(628\) 8.74645 0.349021
\(629\) 0.222616 0.00887627
\(630\) 0.959008 0.0382078
\(631\) 8.87289 0.353224 0.176612 0.984281i \(-0.443486\pi\)
0.176612 + 0.984281i \(0.443486\pi\)
\(632\) 0.412347 0.0164023
\(633\) 24.3779 0.968936
\(634\) −2.35915 −0.0936937
\(635\) −31.3807 −1.24531
\(636\) 2.94290 0.116693
\(637\) 38.4329 1.52277
\(638\) −3.19035 −0.126307
\(639\) 14.6544 0.579719
\(640\) −7.36470 −0.291115
\(641\) −9.93501 −0.392409 −0.196205 0.980563i \(-0.562862\pi\)
−0.196205 + 0.980563i \(0.562862\pi\)
\(642\) 0.818116 0.0322885
\(643\) −23.7309 −0.935854 −0.467927 0.883767i \(-0.654999\pi\)
−0.467927 + 0.883767i \(0.654999\pi\)
\(644\) −23.1057 −0.910491
\(645\) 25.6121 1.00847
\(646\) 0.264225 0.0103958
\(647\) 37.2200 1.46327 0.731634 0.681698i \(-0.238758\pi\)
0.731634 + 0.681698i \(0.238758\pi\)
\(648\) 0.412347 0.0161985
\(649\) 27.4594 1.07788
\(650\) −0.0370612 −0.00145366
\(651\) 8.53384 0.334468
\(652\) 44.7865 1.75398
\(653\) −36.4939 −1.42812 −0.714058 0.700087i \(-0.753145\pi\)
−0.714058 + 0.700087i \(0.753145\pi\)
\(654\) 0.114141 0.00446328
\(655\) 6.04729 0.236287
\(656\) −38.0489 −1.48556
\(657\) −9.54271 −0.372297
\(658\) −0.397938 −0.0155132
\(659\) 12.0293 0.468595 0.234297 0.972165i \(-0.424721\pi\)
0.234297 + 0.972165i \(0.424721\pi\)
\(660\) 15.3327 0.596823
\(661\) −5.99406 −0.233142 −0.116571 0.993182i \(-0.537190\pi\)
−0.116571 + 0.993182i \(0.537190\pi\)
\(662\) 2.15819 0.0838803
\(663\) 3.88047 0.150705
\(664\) 3.28344 0.127422
\(665\) 23.7175 0.919725
\(666\) −0.0230102 −0.000891627 0
\(667\) 25.5293 0.988499
\(668\) 5.25459 0.203306
\(669\) −15.1922 −0.587365
\(670\) −1.34247 −0.0518641
\(671\) 4.22928 0.163270
\(672\) −5.06340 −0.195325
\(673\) −19.0368 −0.733814 −0.366907 0.930258i \(-0.619583\pi\)
−0.366907 + 0.930258i \(0.619583\pi\)
\(674\) −1.21856 −0.0469371
\(675\) 0.0923998 0.00355647
\(676\) −4.09410 −0.157465
\(677\) −22.7123 −0.872906 −0.436453 0.899727i \(-0.643766\pi\)
−0.436453 + 0.899727i \(0.643766\pi\)
\(678\) −0.481858 −0.0185056
\(679\) −54.0049 −2.07252
\(680\) −0.930516 −0.0356837
\(681\) −21.5081 −0.824194
\(682\) −0.732764 −0.0280590
\(683\) −48.9665 −1.87365 −0.936826 0.349796i \(-0.886251\pi\)
−0.936826 + 0.349796i \(0.886251\pi\)
\(684\) 5.08527 0.194440
\(685\) −27.4810 −1.04999
\(686\) −1.23420 −0.0471219
\(687\) 12.9452 0.493889
\(688\) −44.6725 −1.70312
\(689\) −5.74058 −0.218699
\(690\) 0.658936 0.0250853
\(691\) 10.3956 0.395469 0.197734 0.980256i \(-0.436642\pi\)
0.197734 + 0.980256i \(0.436642\pi\)
\(692\) 44.5637 1.69406
\(693\) 14.0427 0.533437
\(694\) −0.127099 −0.00482461
\(695\) −48.5974 −1.84341
\(696\) 3.72635 0.141247
\(697\) −9.66686 −0.366159
\(698\) −2.96709 −0.112306
\(699\) 7.29501 0.275923
\(700\) −0.755739 −0.0285642
\(701\) 28.3636 1.07128 0.535640 0.844447i \(-0.320071\pi\)
0.535640 + 0.844447i \(0.320071\pi\)
\(702\) −0.401096 −0.0151384
\(703\) −0.569071 −0.0214629
\(704\) −26.4520 −0.996948
\(705\) −2.11308 −0.0795830
\(706\) 0.208257 0.00783784
\(707\) 56.8207 2.13696
\(708\) −15.9935 −0.601072
\(709\) −4.85767 −0.182434 −0.0912169 0.995831i \(-0.529076\pi\)
−0.0912169 + 0.995831i \(0.529076\pi\)
\(710\) 3.41817 0.128282
\(711\) 1.00000 0.0375029
\(712\) 0.136852 0.00512875
\(713\) 5.86361 0.219594
\(714\) −0.424973 −0.0159042
\(715\) −29.9087 −1.11852
\(716\) 30.8831 1.15415
\(717\) −24.1130 −0.900516
\(718\) 2.46601 0.0920305
\(719\) 14.7157 0.548804 0.274402 0.961615i \(-0.411520\pi\)
0.274402 + 0.961615i \(0.411520\pi\)
\(720\) −8.88214 −0.331018
\(721\) 32.5987 1.21404
\(722\) 1.28846 0.0479513
\(723\) 13.5990 0.505754
\(724\) 14.8470 0.551783
\(725\) 0.835011 0.0310115
\(726\) −0.0687931 −0.00255315
\(727\) 45.5142 1.68803 0.844015 0.536320i \(-0.180186\pi\)
0.844015 + 0.536320i \(0.180186\pi\)
\(728\) 6.57876 0.243825
\(729\) 1.00000 0.0370370
\(730\) −2.22586 −0.0823827
\(731\) −11.3497 −0.419783
\(732\) −2.46330 −0.0910463
\(733\) −26.9213 −0.994362 −0.497181 0.867647i \(-0.665631\pi\)
−0.497181 + 0.867647i \(0.665631\pi\)
\(734\) 0.0824214 0.00304223
\(735\) −22.3501 −0.824396
\(736\) −3.47907 −0.128240
\(737\) −19.6576 −0.724099
\(738\) 0.999194 0.0367808
\(739\) −13.5725 −0.499272 −0.249636 0.968340i \(-0.580311\pi\)
−0.249636 + 0.968340i \(0.580311\pi\)
\(740\) 0.999358 0.0367371
\(741\) −9.91961 −0.364406
\(742\) 0.628684 0.0230797
\(743\) 45.7597 1.67876 0.839380 0.543545i \(-0.182918\pi\)
0.839380 + 0.543545i \(0.182918\pi\)
\(744\) 0.855874 0.0313779
\(745\) −33.7526 −1.23660
\(746\) −1.47301 −0.0539308
\(747\) 7.96281 0.291344
\(748\) −6.79448 −0.248431
\(749\) −32.5423 −1.18907
\(750\) −1.14471 −0.0417988
\(751\) −29.6084 −1.08043 −0.540213 0.841528i \(-0.681656\pi\)
−0.540213 + 0.841528i \(0.681656\pi\)
\(752\) 3.68562 0.134401
\(753\) −8.69606 −0.316902
\(754\) −3.62468 −0.132003
\(755\) 16.8452 0.613061
\(756\) −8.17901 −0.297468
\(757\) 25.2492 0.917698 0.458849 0.888514i \(-0.348262\pi\)
0.458849 + 0.888514i \(0.348262\pi\)
\(758\) 3.17345 0.115265
\(759\) 9.64874 0.350227
\(760\) 2.37867 0.0862835
\(761\) −24.0148 −0.870537 −0.435268 0.900301i \(-0.643347\pi\)
−0.435268 + 0.900301i \(0.643347\pi\)
\(762\) −1.43736 −0.0520701
\(763\) −4.54020 −0.164366
\(764\) −31.9135 −1.15459
\(765\) −2.25663 −0.0815888
\(766\) −1.42868 −0.0516204
\(767\) 31.1978 1.12649
\(768\) 15.1521 0.546755
\(769\) −18.4740 −0.666188 −0.333094 0.942894i \(-0.608093\pi\)
−0.333094 + 0.942894i \(0.608093\pi\)
\(770\) 3.27548 0.118040
\(771\) 26.4319 0.951921
\(772\) 13.1118 0.471903
\(773\) 19.4386 0.699157 0.349579 0.936907i \(-0.386325\pi\)
0.349579 + 0.936907i \(0.386325\pi\)
\(774\) 1.17313 0.0421675
\(775\) 0.191787 0.00688918
\(776\) −5.41625 −0.194432
\(777\) 0.915278 0.0328354
\(778\) 3.27043 0.117251
\(779\) 24.7113 0.885375
\(780\) 17.4200 0.623738
\(781\) 50.0519 1.79100
\(782\) −0.291999 −0.0104419
\(783\) 9.03694 0.322954
\(784\) 38.9830 1.39225
\(785\) 9.92177 0.354123
\(786\) 0.276990 0.00987990
\(787\) 20.0273 0.713895 0.356947 0.934124i \(-0.383818\pi\)
0.356947 + 0.934124i \(0.383818\pi\)
\(788\) −26.9339 −0.959481
\(789\) −9.73137 −0.346446
\(790\) 0.233252 0.00829873
\(791\) 19.1669 0.681496
\(792\) 1.40836 0.0500441
\(793\) 4.80506 0.170633
\(794\) 1.56009 0.0553656
\(795\) 3.33835 0.118399
\(796\) −54.8079 −1.94261
\(797\) 13.8042 0.488970 0.244485 0.969653i \(-0.421381\pi\)
0.244485 + 0.969653i \(0.421381\pi\)
\(798\) 1.08635 0.0384565
\(799\) 0.936384 0.0331269
\(800\) −0.113793 −0.00402319
\(801\) 0.331886 0.0117266
\(802\) −1.63051 −0.0575754
\(803\) −32.5930 −1.15018
\(804\) 11.4494 0.403789
\(805\) −26.2106 −0.923801
\(806\) −0.832522 −0.0293243
\(807\) 8.36111 0.294325
\(808\) 5.69865 0.200478
\(809\) 24.0426 0.845293 0.422647 0.906295i \(-0.361101\pi\)
0.422647 + 0.906295i \(0.361101\pi\)
\(810\) 0.233252 0.00819564
\(811\) −14.1894 −0.498256 −0.249128 0.968471i \(-0.580144\pi\)
−0.249128 + 0.968471i \(0.580144\pi\)
\(812\) −73.9132 −2.59385
\(813\) 24.9853 0.876271
\(814\) −0.0785910 −0.00275461
\(815\) 50.8048 1.77961
\(816\) 3.93601 0.137788
\(817\) 29.0131 1.01504
\(818\) −2.84071 −0.0993230
\(819\) 15.9544 0.557493
\(820\) −43.3961 −1.51546
\(821\) −25.4942 −0.889753 −0.444877 0.895592i \(-0.646752\pi\)
−0.444877 + 0.895592i \(0.646752\pi\)
\(822\) −1.25874 −0.0439035
\(823\) −25.5858 −0.891866 −0.445933 0.895066i \(-0.647128\pi\)
−0.445933 + 0.895066i \(0.647128\pi\)
\(824\) 3.26939 0.113895
\(825\) 0.315590 0.0109874
\(826\) −3.41665 −0.118880
\(827\) −20.1308 −0.700015 −0.350007 0.936747i \(-0.613821\pi\)
−0.350007 + 0.936747i \(0.613821\pi\)
\(828\) −5.61981 −0.195302
\(829\) −5.42513 −0.188422 −0.0942112 0.995552i \(-0.530033\pi\)
−0.0942112 + 0.995552i \(0.530033\pi\)
\(830\) 1.85734 0.0644692
\(831\) 4.74679 0.164664
\(832\) −30.0532 −1.04191
\(833\) 9.90418 0.343159
\(834\) −2.22595 −0.0770785
\(835\) 5.96068 0.206278
\(836\) 17.3687 0.600709
\(837\) 2.07562 0.0717439
\(838\) 0.0354278 0.00122383
\(839\) 28.9248 0.998596 0.499298 0.866430i \(-0.333591\pi\)
0.499298 + 0.866430i \(0.333591\pi\)
\(840\) −3.82579 −0.132002
\(841\) 52.6663 1.81608
\(842\) −2.05061 −0.0706685
\(843\) 20.0142 0.689325
\(844\) −48.4954 −1.66928
\(845\) −4.64425 −0.159767
\(846\) −0.0967872 −0.00332761
\(847\) 2.73639 0.0940235
\(848\) −5.82274 −0.199954
\(849\) 0.611321 0.0209805
\(850\) −0.00955069 −0.000327586 0
\(851\) 0.628889 0.0215580
\(852\) −29.1522 −0.998740
\(853\) 29.9618 1.02587 0.512936 0.858427i \(-0.328558\pi\)
0.512936 + 0.858427i \(0.328558\pi\)
\(854\) −0.526230 −0.0180072
\(855\) 5.76862 0.197283
\(856\) −3.26372 −0.111552
\(857\) 8.18399 0.279560 0.139780 0.990183i \(-0.455360\pi\)
0.139780 + 0.990183i \(0.455360\pi\)
\(858\) −1.36994 −0.0467689
\(859\) 19.6111 0.669123 0.334561 0.942374i \(-0.391412\pi\)
0.334561 + 0.942374i \(0.391412\pi\)
\(860\) −50.9505 −1.73740
\(861\) −39.7450 −1.35451
\(862\) 2.79924 0.0953424
\(863\) 21.1317 0.719333 0.359666 0.933081i \(-0.382890\pi\)
0.359666 + 0.933081i \(0.382890\pi\)
\(864\) −1.23153 −0.0418975
\(865\) 50.5520 1.71882
\(866\) 3.62335 0.123126
\(867\) 1.00000 0.0339618
\(868\) −16.9765 −0.576220
\(869\) 3.41549 0.115862
\(870\) 2.10788 0.0714640
\(871\) −22.3338 −0.756753
\(872\) −0.455345 −0.0154199
\(873\) −13.1352 −0.444558
\(874\) 0.746436 0.0252486
\(875\) 45.5331 1.53930
\(876\) 18.9835 0.641392
\(877\) −17.4488 −0.589203 −0.294601 0.955620i \(-0.595187\pi\)
−0.294601 + 0.955620i \(0.595187\pi\)
\(878\) 2.29151 0.0773349
\(879\) −7.19357 −0.242633
\(880\) −30.3368 −1.02265
\(881\) −6.42031 −0.216306 −0.108153 0.994134i \(-0.534494\pi\)
−0.108153 + 0.994134i \(0.534494\pi\)
\(882\) −1.02372 −0.0344706
\(883\) 32.2212 1.08433 0.542164 0.840272i \(-0.317605\pi\)
0.542164 + 0.840272i \(0.317605\pi\)
\(884\) −7.71948 −0.259634
\(885\) −18.1426 −0.609858
\(886\) 0.163483 0.00549232
\(887\) −43.8386 −1.47196 −0.735979 0.677005i \(-0.763278\pi\)
−0.735979 + 0.677005i \(0.763278\pi\)
\(888\) 0.0917949 0.00308044
\(889\) 57.1740 1.91756
\(890\) 0.0774131 0.00259489
\(891\) 3.41549 0.114423
\(892\) 30.2221 1.01191
\(893\) −2.39367 −0.0801011
\(894\) −1.54600 −0.0517061
\(895\) 35.0330 1.17103
\(896\) 13.4181 0.448267
\(897\) 10.9623 0.366021
\(898\) 0.430267 0.0143582
\(899\) 18.7572 0.625589
\(900\) −0.183812 −0.00612708
\(901\) −1.47935 −0.0492843
\(902\) 3.41273 0.113632
\(903\) −46.6639 −1.55288
\(904\) 1.92228 0.0639342
\(905\) 16.8421 0.559849
\(906\) 0.771579 0.0256340
\(907\) 43.9748 1.46016 0.730080 0.683361i \(-0.239483\pi\)
0.730080 + 0.683361i \(0.239483\pi\)
\(908\) 42.7865 1.41992
\(909\) 13.8201 0.458382
\(910\) 3.72140 0.123363
\(911\) 38.5233 1.27633 0.638167 0.769898i \(-0.279693\pi\)
0.638167 + 0.769898i \(0.279693\pi\)
\(912\) −10.0616 −0.333173
\(913\) 27.1969 0.900085
\(914\) 2.76423 0.0914327
\(915\) −2.79432 −0.0923772
\(916\) −25.7521 −0.850872
\(917\) −11.0178 −0.363841
\(918\) −0.103363 −0.00341148
\(919\) −18.6949 −0.616687 −0.308343 0.951275i \(-0.599775\pi\)
−0.308343 + 0.951275i \(0.599775\pi\)
\(920\) −2.62870 −0.0866658
\(921\) 23.8255 0.785078
\(922\) 2.84566 0.0937167
\(923\) 56.8660 1.87177
\(924\) −27.9353 −0.919004
\(925\) 0.0205696 0.000676326 0
\(926\) 4.14687 0.136275
\(927\) 7.92873 0.260414
\(928\) −11.1293 −0.365336
\(929\) −41.5483 −1.36315 −0.681577 0.731746i \(-0.738706\pi\)
−0.681577 + 0.731746i \(0.738706\pi\)
\(930\) 0.484142 0.0158756
\(931\) −25.3180 −0.829763
\(932\) −14.5121 −0.475359
\(933\) 1.82437 0.0597273
\(934\) −0.604849 −0.0197913
\(935\) −7.70751 −0.252062
\(936\) 1.60010 0.0523009
\(937\) −50.2457 −1.64146 −0.820729 0.571318i \(-0.806432\pi\)
−0.820729 + 0.571318i \(0.806432\pi\)
\(938\) 2.44591 0.0798617
\(939\) −28.2597 −0.922221
\(940\) 4.20358 0.137106
\(941\) 55.5146 1.80972 0.904862 0.425706i \(-0.139974\pi\)
0.904862 + 0.425706i \(0.139974\pi\)
\(942\) 0.454456 0.0148070
\(943\) −27.3089 −0.889299
\(944\) 31.6443 1.02993
\(945\) −9.27808 −0.301816
\(946\) 4.00683 0.130273
\(947\) −30.7473 −0.999152 −0.499576 0.866270i \(-0.666511\pi\)
−0.499576 + 0.866270i \(0.666511\pi\)
\(948\) −1.98932 −0.0646100
\(949\) −37.0302 −1.20205
\(950\) 0.0244144 0.000792107 0
\(951\) 22.8240 0.740118
\(952\) 1.69535 0.0549466
\(953\) 32.6368 1.05721 0.528605 0.848868i \(-0.322715\pi\)
0.528605 + 0.848868i \(0.322715\pi\)
\(954\) 0.152910 0.00495064
\(955\) −36.2020 −1.17147
\(956\) 47.9683 1.55141
\(957\) 30.8655 0.997741
\(958\) 2.67367 0.0863825
\(959\) 50.0689 1.61681
\(960\) 17.4770 0.564068
\(961\) −26.6918 −0.861026
\(962\) −0.0892903 −0.00287884
\(963\) −7.91500 −0.255057
\(964\) −27.0528 −0.871312
\(965\) 14.8737 0.478801
\(966\) −1.20055 −0.0386270
\(967\) −46.0847 −1.48198 −0.740992 0.671514i \(-0.765644\pi\)
−0.740992 + 0.671514i \(0.765644\pi\)
\(968\) 0.274437 0.00882076
\(969\) −2.55629 −0.0821199
\(970\) −3.06381 −0.0983729
\(971\) −21.4748 −0.689159 −0.344579 0.938757i \(-0.611978\pi\)
−0.344579 + 0.938757i \(0.611978\pi\)
\(972\) −1.98932 −0.0638073
\(973\) 88.5420 2.83852
\(974\) −1.52390 −0.0488290
\(975\) 0.358554 0.0114829
\(976\) 4.87383 0.156008
\(977\) −34.2612 −1.09611 −0.548057 0.836441i \(-0.684632\pi\)
−0.548057 + 0.836441i \(0.684632\pi\)
\(978\) 2.32706 0.0744112
\(979\) 1.13355 0.0362285
\(980\) 44.4614 1.42027
\(981\) −1.10428 −0.0352569
\(982\) −1.74563 −0.0557053
\(983\) −18.8464 −0.601106 −0.300553 0.953765i \(-0.597171\pi\)
−0.300553 + 0.953765i \(0.597171\pi\)
\(984\) −3.98610 −0.127072
\(985\) −30.5532 −0.973506
\(986\) −0.934083 −0.0297473
\(987\) 3.84991 0.122544
\(988\) 19.7332 0.627798
\(989\) −32.0628 −1.01954
\(990\) 0.796669 0.0253198
\(991\) −56.1745 −1.78444 −0.892221 0.451599i \(-0.850854\pi\)
−0.892221 + 0.451599i \(0.850854\pi\)
\(992\) −2.55619 −0.0811590
\(993\) −20.8797 −0.662598
\(994\) −6.22772 −0.197531
\(995\) −62.1728 −1.97101
\(996\) −15.8405 −0.501927
\(997\) −11.6470 −0.368865 −0.184432 0.982845i \(-0.559045\pi\)
−0.184432 + 0.982845i \(0.559045\pi\)
\(998\) 1.89283 0.0599164
\(999\) 0.222616 0.00704325
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.k.1.14 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.14 31 1.1 even 1 trivial