Properties

Label 4029.2.a.k.1.17
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
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: \(31\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.308270 q^{2} +1.00000 q^{3} -1.90497 q^{4} +2.48291 q^{5} +0.308270 q^{6} +3.17570 q^{7} -1.20379 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.308270 q^{2} +1.00000 q^{3} -1.90497 q^{4} +2.48291 q^{5} +0.308270 q^{6} +3.17570 q^{7} -1.20379 q^{8} +1.00000 q^{9} +0.765408 q^{10} -2.66964 q^{11} -1.90497 q^{12} +6.37503 q^{13} +0.978975 q^{14} +2.48291 q^{15} +3.43885 q^{16} +1.00000 q^{17} +0.308270 q^{18} +8.52916 q^{19} -4.72988 q^{20} +3.17570 q^{21} -0.822969 q^{22} +6.90544 q^{23} -1.20379 q^{24} +1.16486 q^{25} +1.96523 q^{26} +1.00000 q^{27} -6.04962 q^{28} -2.52889 q^{29} +0.765408 q^{30} -10.7183 q^{31} +3.46767 q^{32} -2.66964 q^{33} +0.308270 q^{34} +7.88500 q^{35} -1.90497 q^{36} -10.4005 q^{37} +2.62929 q^{38} +6.37503 q^{39} -2.98890 q^{40} -1.66405 q^{41} +0.978975 q^{42} -1.09029 q^{43} +5.08558 q^{44} +2.48291 q^{45} +2.12874 q^{46} +3.69443 q^{47} +3.43885 q^{48} +3.08509 q^{49} +0.359092 q^{50} +1.00000 q^{51} -12.1442 q^{52} -0.219567 q^{53} +0.308270 q^{54} -6.62848 q^{55} -3.82287 q^{56} +8.52916 q^{57} -0.779582 q^{58} +10.6739 q^{59} -4.72988 q^{60} -4.77746 q^{61} -3.30412 q^{62} +3.17570 q^{63} -5.80872 q^{64} +15.8287 q^{65} -0.822969 q^{66} -11.3088 q^{67} -1.90497 q^{68} +6.90544 q^{69} +2.43071 q^{70} -10.3718 q^{71} -1.20379 q^{72} +11.2993 q^{73} -3.20616 q^{74} +1.16486 q^{75} -16.2478 q^{76} -8.47797 q^{77} +1.96523 q^{78} +1.00000 q^{79} +8.53836 q^{80} +1.00000 q^{81} -0.512977 q^{82} -10.9627 q^{83} -6.04962 q^{84} +2.48291 q^{85} -0.336105 q^{86} -2.52889 q^{87} +3.21367 q^{88} +14.0122 q^{89} +0.765408 q^{90} +20.2452 q^{91} -13.1547 q^{92} -10.7183 q^{93} +1.13888 q^{94} +21.1772 q^{95} +3.46767 q^{96} +6.68616 q^{97} +0.951042 q^{98} -2.66964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.308270 0.217980 0.108990 0.994043i \(-0.465238\pi\)
0.108990 + 0.994043i \(0.465238\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.90497 −0.952485
\(5\) 2.48291 1.11039 0.555196 0.831719i \(-0.312643\pi\)
0.555196 + 0.831719i \(0.312643\pi\)
\(6\) 0.308270 0.125851
\(7\) 3.17570 1.20030 0.600152 0.799886i \(-0.295107\pi\)
0.600152 + 0.799886i \(0.295107\pi\)
\(8\) −1.20379 −0.425603
\(9\) 1.00000 0.333333
\(10\) 0.765408 0.242043
\(11\) −2.66964 −0.804926 −0.402463 0.915436i \(-0.631846\pi\)
−0.402463 + 0.915436i \(0.631846\pi\)
\(12\) −1.90497 −0.549917
\(13\) 6.37503 1.76812 0.884058 0.467378i \(-0.154801\pi\)
0.884058 + 0.467378i \(0.154801\pi\)
\(14\) 0.978975 0.261642
\(15\) 2.48291 0.641086
\(16\) 3.43885 0.859712
\(17\) 1.00000 0.242536
\(18\) 0.308270 0.0726600
\(19\) 8.52916 1.95672 0.978362 0.206903i \(-0.0663384\pi\)
0.978362 + 0.206903i \(0.0663384\pi\)
\(20\) −4.72988 −1.05763
\(21\) 3.17570 0.692995
\(22\) −0.822969 −0.175458
\(23\) 6.90544 1.43988 0.719942 0.694034i \(-0.244168\pi\)
0.719942 + 0.694034i \(0.244168\pi\)
\(24\) −1.20379 −0.245722
\(25\) 1.16486 0.232973
\(26\) 1.96523 0.385414
\(27\) 1.00000 0.192450
\(28\) −6.04962 −1.14327
\(29\) −2.52889 −0.469604 −0.234802 0.972043i \(-0.575444\pi\)
−0.234802 + 0.972043i \(0.575444\pi\)
\(30\) 0.765408 0.139744
\(31\) −10.7183 −1.92506 −0.962529 0.271178i \(-0.912587\pi\)
−0.962529 + 0.271178i \(0.912587\pi\)
\(32\) 3.46767 0.613002
\(33\) −2.66964 −0.464724
\(34\) 0.308270 0.0528679
\(35\) 7.88500 1.33281
\(36\) −1.90497 −0.317495
\(37\) −10.4005 −1.70983 −0.854916 0.518767i \(-0.826391\pi\)
−0.854916 + 0.518767i \(0.826391\pi\)
\(38\) 2.62929 0.426526
\(39\) 6.37503 1.02082
\(40\) −2.98890 −0.472586
\(41\) −1.66405 −0.259881 −0.129940 0.991522i \(-0.541479\pi\)
−0.129940 + 0.991522i \(0.541479\pi\)
\(42\) 0.978975 0.151059
\(43\) −1.09029 −0.166268 −0.0831340 0.996538i \(-0.526493\pi\)
−0.0831340 + 0.996538i \(0.526493\pi\)
\(44\) 5.08558 0.766680
\(45\) 2.48291 0.370131
\(46\) 2.12874 0.313866
\(47\) 3.69443 0.538887 0.269444 0.963016i \(-0.413160\pi\)
0.269444 + 0.963016i \(0.413160\pi\)
\(48\) 3.43885 0.496355
\(49\) 3.08509 0.440727
\(50\) 0.359092 0.0507833
\(51\) 1.00000 0.140028
\(52\) −12.1442 −1.68410
\(53\) −0.219567 −0.0301598 −0.0150799 0.999886i \(-0.504800\pi\)
−0.0150799 + 0.999886i \(0.504800\pi\)
\(54\) 0.308270 0.0419503
\(55\) −6.62848 −0.893784
\(56\) −3.82287 −0.510852
\(57\) 8.52916 1.12971
\(58\) −0.779582 −0.102364
\(59\) 10.6739 1.38963 0.694815 0.719189i \(-0.255486\pi\)
0.694815 + 0.719189i \(0.255486\pi\)
\(60\) −4.72988 −0.610624
\(61\) −4.77746 −0.611691 −0.305845 0.952081i \(-0.598939\pi\)
−0.305845 + 0.952081i \(0.598939\pi\)
\(62\) −3.30412 −0.419624
\(63\) 3.17570 0.400101
\(64\) −5.80872 −0.726090
\(65\) 15.8287 1.96330
\(66\) −0.822969 −0.101301
\(67\) −11.3088 −1.38159 −0.690797 0.723049i \(-0.742740\pi\)
−0.690797 + 0.723049i \(0.742740\pi\)
\(68\) −1.90497 −0.231011
\(69\) 6.90544 0.831318
\(70\) 2.43071 0.290525
\(71\) −10.3718 −1.23091 −0.615453 0.788173i \(-0.711027\pi\)
−0.615453 + 0.788173i \(0.711027\pi\)
\(72\) −1.20379 −0.141868
\(73\) 11.2993 1.32248 0.661241 0.750173i \(-0.270030\pi\)
0.661241 + 0.750173i \(0.270030\pi\)
\(74\) −3.20616 −0.372709
\(75\) 1.16486 0.134507
\(76\) −16.2478 −1.86375
\(77\) −8.47797 −0.966155
\(78\) 1.96523 0.222519
\(79\) 1.00000 0.112509
\(80\) 8.53836 0.954618
\(81\) 1.00000 0.111111
\(82\) −0.512977 −0.0566488
\(83\) −10.9627 −1.20331 −0.601655 0.798756i \(-0.705492\pi\)
−0.601655 + 0.798756i \(0.705492\pi\)
\(84\) −6.04962 −0.660067
\(85\) 2.48291 0.269310
\(86\) −0.336105 −0.0362431
\(87\) −2.52889 −0.271126
\(88\) 3.21367 0.342578
\(89\) 14.0122 1.48529 0.742643 0.669687i \(-0.233572\pi\)
0.742643 + 0.669687i \(0.233572\pi\)
\(90\) 0.765408 0.0806811
\(91\) 20.2452 2.12227
\(92\) −13.1547 −1.37147
\(93\) −10.7183 −1.11143
\(94\) 1.13888 0.117467
\(95\) 21.1772 2.17273
\(96\) 3.46767 0.353917
\(97\) 6.68616 0.678877 0.339438 0.940628i \(-0.389763\pi\)
0.339438 + 0.940628i \(0.389763\pi\)
\(98\) 0.951042 0.0960698
\(99\) −2.66964 −0.268309
\(100\) −2.21903 −0.221903
\(101\) 3.44515 0.342805 0.171403 0.985201i \(-0.445170\pi\)
0.171403 + 0.985201i \(0.445170\pi\)
\(102\) 0.308270 0.0305233
\(103\) −3.22307 −0.317578 −0.158789 0.987313i \(-0.550759\pi\)
−0.158789 + 0.987313i \(0.550759\pi\)
\(104\) −7.67417 −0.752514
\(105\) 7.88500 0.769497
\(106\) −0.0676858 −0.00657423
\(107\) 17.3765 1.67985 0.839925 0.542702i \(-0.182599\pi\)
0.839925 + 0.542702i \(0.182599\pi\)
\(108\) −1.90497 −0.183306
\(109\) −7.64031 −0.731809 −0.365905 0.930652i \(-0.619240\pi\)
−0.365905 + 0.930652i \(0.619240\pi\)
\(110\) −2.04336 −0.194827
\(111\) −10.4005 −0.987172
\(112\) 10.9208 1.03191
\(113\) 4.47356 0.420837 0.210419 0.977611i \(-0.432517\pi\)
0.210419 + 0.977611i \(0.432517\pi\)
\(114\) 2.62929 0.246255
\(115\) 17.1456 1.59884
\(116\) 4.81746 0.447290
\(117\) 6.37503 0.589372
\(118\) 3.29046 0.302911
\(119\) 3.17570 0.291116
\(120\) −2.98890 −0.272848
\(121\) −3.87304 −0.352094
\(122\) −1.47275 −0.133336
\(123\) −1.66405 −0.150042
\(124\) 20.4180 1.83359
\(125\) −9.52232 −0.851702
\(126\) 0.978975 0.0872140
\(127\) −3.47704 −0.308538 −0.154269 0.988029i \(-0.549302\pi\)
−0.154269 + 0.988029i \(0.549302\pi\)
\(128\) −8.72599 −0.771275
\(129\) −1.09029 −0.0959949
\(130\) 4.87950 0.427961
\(131\) 8.52888 0.745172 0.372586 0.927998i \(-0.378471\pi\)
0.372586 + 0.927998i \(0.378471\pi\)
\(132\) 5.08558 0.442643
\(133\) 27.0861 2.34866
\(134\) −3.48618 −0.301160
\(135\) 2.48291 0.213695
\(136\) −1.20379 −0.103224
\(137\) 14.7316 1.25860 0.629301 0.777162i \(-0.283341\pi\)
0.629301 + 0.777162i \(0.283341\pi\)
\(138\) 2.12874 0.181211
\(139\) 8.75975 0.742992 0.371496 0.928435i \(-0.378845\pi\)
0.371496 + 0.928435i \(0.378845\pi\)
\(140\) −15.0207 −1.26948
\(141\) 3.69443 0.311127
\(142\) −3.19732 −0.268313
\(143\) −17.0190 −1.42320
\(144\) 3.43885 0.286571
\(145\) −6.27903 −0.521445
\(146\) 3.48324 0.288275
\(147\) 3.08509 0.254454
\(148\) 19.8126 1.62859
\(149\) −0.927884 −0.0760152 −0.0380076 0.999277i \(-0.512101\pi\)
−0.0380076 + 0.999277i \(0.512101\pi\)
\(150\) 0.359092 0.0293198
\(151\) −7.69312 −0.626057 −0.313028 0.949744i \(-0.601344\pi\)
−0.313028 + 0.949744i \(0.601344\pi\)
\(152\) −10.2673 −0.832786
\(153\) 1.00000 0.0808452
\(154\) −2.61351 −0.210602
\(155\) −26.6125 −2.13757
\(156\) −12.1442 −0.972317
\(157\) −22.5272 −1.79786 −0.898932 0.438087i \(-0.855656\pi\)
−0.898932 + 0.438087i \(0.855656\pi\)
\(158\) 0.308270 0.0245247
\(159\) −0.219567 −0.0174128
\(160\) 8.60992 0.680674
\(161\) 21.9296 1.72830
\(162\) 0.308270 0.0242200
\(163\) 5.28450 0.413914 0.206957 0.978350i \(-0.433644\pi\)
0.206957 + 0.978350i \(0.433644\pi\)
\(164\) 3.16996 0.247532
\(165\) −6.62848 −0.516026
\(166\) −3.37947 −0.262298
\(167\) −14.9243 −1.15488 −0.577438 0.816435i \(-0.695947\pi\)
−0.577438 + 0.816435i \(0.695947\pi\)
\(168\) −3.82287 −0.294941
\(169\) 27.6410 2.12623
\(170\) 0.765408 0.0587041
\(171\) 8.52916 0.652241
\(172\) 2.07697 0.158368
\(173\) 20.1069 1.52870 0.764350 0.644802i \(-0.223060\pi\)
0.764350 + 0.644802i \(0.223060\pi\)
\(174\) −0.779582 −0.0591000
\(175\) 3.69926 0.279638
\(176\) −9.18047 −0.692004
\(177\) 10.6739 0.802303
\(178\) 4.31953 0.323763
\(179\) −17.3799 −1.29903 −0.649517 0.760347i \(-0.725029\pi\)
−0.649517 + 0.760347i \(0.725029\pi\)
\(180\) −4.72988 −0.352544
\(181\) 16.7714 1.24661 0.623304 0.781980i \(-0.285790\pi\)
0.623304 + 0.781980i \(0.285790\pi\)
\(182\) 6.24099 0.462613
\(183\) −4.77746 −0.353160
\(184\) −8.31267 −0.612818
\(185\) −25.8235 −1.89858
\(186\) −3.30412 −0.242270
\(187\) −2.66964 −0.195223
\(188\) −7.03777 −0.513282
\(189\) 3.17570 0.230998
\(190\) 6.52829 0.473612
\(191\) −15.8317 −1.14554 −0.572772 0.819715i \(-0.694132\pi\)
−0.572772 + 0.819715i \(0.694132\pi\)
\(192\) −5.80872 −0.419208
\(193\) −16.7147 −1.20315 −0.601575 0.798817i \(-0.705460\pi\)
−0.601575 + 0.798817i \(0.705460\pi\)
\(194\) 2.06114 0.147982
\(195\) 15.8287 1.13351
\(196\) −5.87701 −0.419786
\(197\) 2.20508 0.157105 0.0785527 0.996910i \(-0.474970\pi\)
0.0785527 + 0.996910i \(0.474970\pi\)
\(198\) −0.822969 −0.0584859
\(199\) −6.40547 −0.454072 −0.227036 0.973886i \(-0.572903\pi\)
−0.227036 + 0.973886i \(0.572903\pi\)
\(200\) −1.40225 −0.0991537
\(201\) −11.3088 −0.797664
\(202\) 1.06204 0.0747246
\(203\) −8.03102 −0.563667
\(204\) −1.90497 −0.133375
\(205\) −4.13169 −0.288570
\(206\) −0.993575 −0.0692256
\(207\) 6.90544 0.479961
\(208\) 21.9228 1.52007
\(209\) −22.7698 −1.57502
\(210\) 2.43071 0.167735
\(211\) 1.83566 0.126372 0.0631859 0.998002i \(-0.479874\pi\)
0.0631859 + 0.998002i \(0.479874\pi\)
\(212\) 0.418268 0.0287267
\(213\) −10.3718 −0.710664
\(214\) 5.35666 0.366174
\(215\) −2.70710 −0.184623
\(216\) −1.20379 −0.0819072
\(217\) −34.0380 −2.31065
\(218\) −2.35528 −0.159520
\(219\) 11.2993 0.763535
\(220\) 12.6271 0.851316
\(221\) 6.37503 0.428831
\(222\) −3.20616 −0.215184
\(223\) 6.27182 0.419992 0.209996 0.977702i \(-0.432655\pi\)
0.209996 + 0.977702i \(0.432655\pi\)
\(224\) 11.0123 0.735789
\(225\) 1.16486 0.0776575
\(226\) 1.37907 0.0917341
\(227\) 25.3970 1.68566 0.842829 0.538182i \(-0.180889\pi\)
0.842829 + 0.538182i \(0.180889\pi\)
\(228\) −16.2478 −1.07604
\(229\) −4.87536 −0.322173 −0.161087 0.986940i \(-0.551500\pi\)
−0.161087 + 0.986940i \(0.551500\pi\)
\(230\) 5.28548 0.348514
\(231\) −8.47797 −0.557810
\(232\) 3.04425 0.199865
\(233\) 7.18402 0.470641 0.235320 0.971918i \(-0.424386\pi\)
0.235320 + 0.971918i \(0.424386\pi\)
\(234\) 1.96523 0.128471
\(235\) 9.17294 0.598377
\(236\) −20.3335 −1.32360
\(237\) 1.00000 0.0649570
\(238\) 0.978975 0.0634575
\(239\) −1.15315 −0.0745913 −0.0372956 0.999304i \(-0.511874\pi\)
−0.0372956 + 0.999304i \(0.511874\pi\)
\(240\) 8.53836 0.551149
\(241\) −10.8434 −0.698486 −0.349243 0.937032i \(-0.613561\pi\)
−0.349243 + 0.937032i \(0.613561\pi\)
\(242\) −1.19394 −0.0767495
\(243\) 1.00000 0.0641500
\(244\) 9.10091 0.582626
\(245\) 7.66002 0.489381
\(246\) −0.512977 −0.0327062
\(247\) 54.3736 3.45971
\(248\) 12.9025 0.819310
\(249\) −10.9627 −0.694732
\(250\) −2.93545 −0.185654
\(251\) 15.8366 0.999600 0.499800 0.866141i \(-0.333407\pi\)
0.499800 + 0.866141i \(0.333407\pi\)
\(252\) −6.04962 −0.381090
\(253\) −18.4350 −1.15900
\(254\) −1.07187 −0.0672550
\(255\) 2.48291 0.155486
\(256\) 8.92747 0.557967
\(257\) 8.89323 0.554745 0.277372 0.960763i \(-0.410536\pi\)
0.277372 + 0.960763i \(0.410536\pi\)
\(258\) −0.336105 −0.0209250
\(259\) −33.0289 −2.05232
\(260\) −30.1531 −1.87002
\(261\) −2.52889 −0.156535
\(262\) 2.62920 0.162432
\(263\) −1.67803 −0.103472 −0.0517358 0.998661i \(-0.516475\pi\)
−0.0517358 + 0.998661i \(0.516475\pi\)
\(264\) 3.21367 0.197788
\(265\) −0.545165 −0.0334892
\(266\) 8.34983 0.511961
\(267\) 14.0122 0.857531
\(268\) 21.5430 1.31595
\(269\) −13.9950 −0.853291 −0.426645 0.904419i \(-0.640305\pi\)
−0.426645 + 0.904419i \(0.640305\pi\)
\(270\) 0.765408 0.0465813
\(271\) −28.1446 −1.70966 −0.854831 0.518906i \(-0.826339\pi\)
−0.854831 + 0.518906i \(0.826339\pi\)
\(272\) 3.43885 0.208511
\(273\) 20.2452 1.22530
\(274\) 4.54130 0.274350
\(275\) −3.10976 −0.187526
\(276\) −13.1547 −0.791817
\(277\) 9.08819 0.546057 0.273028 0.962006i \(-0.411975\pi\)
0.273028 + 0.962006i \(0.411975\pi\)
\(278\) 2.70037 0.161957
\(279\) −10.7183 −0.641686
\(280\) −9.49185 −0.567246
\(281\) −18.0375 −1.07603 −0.538014 0.842936i \(-0.680825\pi\)
−0.538014 + 0.842936i \(0.680825\pi\)
\(282\) 1.13888 0.0678194
\(283\) −7.22656 −0.429575 −0.214787 0.976661i \(-0.568906\pi\)
−0.214787 + 0.976661i \(0.568906\pi\)
\(284\) 19.7580 1.17242
\(285\) 21.1772 1.25443
\(286\) −5.24646 −0.310229
\(287\) −5.28453 −0.311936
\(288\) 3.46767 0.204334
\(289\) 1.00000 0.0588235
\(290\) −1.93564 −0.113664
\(291\) 6.68616 0.391950
\(292\) −21.5248 −1.25964
\(293\) 2.41975 0.141363 0.0706817 0.997499i \(-0.477483\pi\)
0.0706817 + 0.997499i \(0.477483\pi\)
\(294\) 0.951042 0.0554659
\(295\) 26.5025 1.54304
\(296\) 12.5200 0.727709
\(297\) −2.66964 −0.154908
\(298\) −0.286039 −0.0165698
\(299\) 44.0224 2.54588
\(300\) −2.21903 −0.128116
\(301\) −3.46245 −0.199572
\(302\) −2.37156 −0.136468
\(303\) 3.44515 0.197919
\(304\) 29.3305 1.68222
\(305\) −11.8620 −0.679217
\(306\) 0.308270 0.0176226
\(307\) 16.2282 0.926194 0.463097 0.886308i \(-0.346738\pi\)
0.463097 + 0.886308i \(0.346738\pi\)
\(308\) 16.1503 0.920248
\(309\) −3.22307 −0.183354
\(310\) −8.20386 −0.465948
\(311\) 17.8581 1.01264 0.506321 0.862345i \(-0.331005\pi\)
0.506321 + 0.862345i \(0.331005\pi\)
\(312\) −7.67417 −0.434464
\(313\) −1.70694 −0.0964821 −0.0482411 0.998836i \(-0.515362\pi\)
−0.0482411 + 0.998836i \(0.515362\pi\)
\(314\) −6.94446 −0.391898
\(315\) 7.88500 0.444269
\(316\) −1.90497 −0.107163
\(317\) 15.3198 0.860447 0.430223 0.902723i \(-0.358435\pi\)
0.430223 + 0.902723i \(0.358435\pi\)
\(318\) −0.0676858 −0.00379563
\(319\) 6.75123 0.377996
\(320\) −14.4225 −0.806245
\(321\) 17.3765 0.969862
\(322\) 6.76025 0.376734
\(323\) 8.52916 0.474575
\(324\) −1.90497 −0.105832
\(325\) 7.42603 0.411922
\(326\) 1.62906 0.0902250
\(327\) −7.64031 −0.422510
\(328\) 2.00316 0.110606
\(329\) 11.7324 0.646828
\(330\) −2.04336 −0.112483
\(331\) 8.91869 0.490216 0.245108 0.969496i \(-0.421177\pi\)
0.245108 + 0.969496i \(0.421177\pi\)
\(332\) 20.8836 1.14613
\(333\) −10.4005 −0.569944
\(334\) −4.60071 −0.251740
\(335\) −28.0789 −1.53411
\(336\) 10.9208 0.595776
\(337\) −33.3454 −1.81644 −0.908220 0.418494i \(-0.862558\pi\)
−0.908220 + 0.418494i \(0.862558\pi\)
\(338\) 8.52090 0.463476
\(339\) 4.47356 0.242971
\(340\) −4.72988 −0.256514
\(341\) 28.6139 1.54953
\(342\) 2.62929 0.142175
\(343\) −12.4326 −0.671297
\(344\) 1.31248 0.0707641
\(345\) 17.1456 0.923089
\(346\) 6.19836 0.333226
\(347\) −12.4751 −0.669697 −0.334848 0.942272i \(-0.608685\pi\)
−0.334848 + 0.942272i \(0.608685\pi\)
\(348\) 4.81746 0.258243
\(349\) −22.4032 −1.19922 −0.599608 0.800294i \(-0.704677\pi\)
−0.599608 + 0.800294i \(0.704677\pi\)
\(350\) 1.14037 0.0609554
\(351\) 6.37503 0.340274
\(352\) −9.25741 −0.493422
\(353\) 0.970716 0.0516660 0.0258330 0.999666i \(-0.491776\pi\)
0.0258330 + 0.999666i \(0.491776\pi\)
\(354\) 3.29046 0.174886
\(355\) −25.7523 −1.36679
\(356\) −26.6927 −1.41471
\(357\) 3.17570 0.168076
\(358\) −5.35770 −0.283163
\(359\) −24.2927 −1.28212 −0.641061 0.767490i \(-0.721505\pi\)
−0.641061 + 0.767490i \(0.721505\pi\)
\(360\) −2.98890 −0.157529
\(361\) 53.7465 2.82876
\(362\) 5.17012 0.271736
\(363\) −3.87304 −0.203282
\(364\) −38.5665 −2.02143
\(365\) 28.0552 1.46847
\(366\) −1.47275 −0.0769818
\(367\) 30.6216 1.59843 0.799216 0.601043i \(-0.205248\pi\)
0.799216 + 0.601043i \(0.205248\pi\)
\(368\) 23.7468 1.23789
\(369\) −1.66405 −0.0866269
\(370\) −7.96063 −0.413853
\(371\) −0.697278 −0.0362009
\(372\) 20.4180 1.05862
\(373\) −22.7812 −1.17956 −0.589782 0.807563i \(-0.700786\pi\)
−0.589782 + 0.807563i \(0.700786\pi\)
\(374\) −0.822969 −0.0425547
\(375\) −9.52232 −0.491730
\(376\) −4.44730 −0.229352
\(377\) −16.1218 −0.830313
\(378\) 0.978975 0.0503530
\(379\) −10.4079 −0.534619 −0.267309 0.963611i \(-0.586135\pi\)
−0.267309 + 0.963611i \(0.586135\pi\)
\(380\) −40.3419 −2.06949
\(381\) −3.47704 −0.178134
\(382\) −4.88045 −0.249705
\(383\) 21.1881 1.08266 0.541332 0.840809i \(-0.317920\pi\)
0.541332 + 0.840809i \(0.317920\pi\)
\(384\) −8.72599 −0.445296
\(385\) −21.0501 −1.07281
\(386\) −5.15264 −0.262262
\(387\) −1.09029 −0.0554227
\(388\) −12.7369 −0.646620
\(389\) −18.7504 −0.950685 −0.475343 0.879801i \(-0.657676\pi\)
−0.475343 + 0.879801i \(0.657676\pi\)
\(390\) 4.87950 0.247083
\(391\) 6.90544 0.349223
\(392\) −3.71379 −0.187575
\(393\) 8.52888 0.430225
\(394\) 0.679760 0.0342458
\(395\) 2.48291 0.124929
\(396\) 5.08558 0.255560
\(397\) 0.491395 0.0246624 0.0123312 0.999924i \(-0.496075\pi\)
0.0123312 + 0.999924i \(0.496075\pi\)
\(398\) −1.97461 −0.0989785
\(399\) 27.0861 1.35600
\(400\) 4.00579 0.200289
\(401\) 17.5979 0.878796 0.439398 0.898293i \(-0.355192\pi\)
0.439398 + 0.898293i \(0.355192\pi\)
\(402\) −3.48618 −0.173875
\(403\) −68.3293 −3.40372
\(404\) −6.56290 −0.326517
\(405\) 2.48291 0.123377
\(406\) −2.47572 −0.122868
\(407\) 27.7656 1.37629
\(408\) −1.20379 −0.0595963
\(409\) 21.3567 1.05602 0.528009 0.849239i \(-0.322939\pi\)
0.528009 + 0.849239i \(0.322939\pi\)
\(410\) −1.27368 −0.0629024
\(411\) 14.7316 0.726654
\(412\) 6.13984 0.302488
\(413\) 33.8973 1.66798
\(414\) 2.12874 0.104622
\(415\) −27.2194 −1.33615
\(416\) 22.1065 1.08386
\(417\) 8.75975 0.428967
\(418\) −7.01924 −0.343322
\(419\) 15.3366 0.749242 0.374621 0.927178i \(-0.377773\pi\)
0.374621 + 0.927178i \(0.377773\pi\)
\(420\) −15.0207 −0.732934
\(421\) 3.12005 0.152062 0.0760309 0.997105i \(-0.475775\pi\)
0.0760309 + 0.997105i \(0.475775\pi\)
\(422\) 0.565878 0.0275465
\(423\) 3.69443 0.179629
\(424\) 0.264311 0.0128361
\(425\) 1.16486 0.0565041
\(426\) −3.19732 −0.154911
\(427\) −15.1718 −0.734214
\(428\) −33.1017 −1.60003
\(429\) −17.0190 −0.821686
\(430\) −0.834519 −0.0402441
\(431\) 17.0120 0.819439 0.409720 0.912212i \(-0.365627\pi\)
0.409720 + 0.912212i \(0.365627\pi\)
\(432\) 3.43885 0.165452
\(433\) −14.5796 −0.700649 −0.350325 0.936628i \(-0.613929\pi\)
−0.350325 + 0.936628i \(0.613929\pi\)
\(434\) −10.4929 −0.503676
\(435\) −6.27903 −0.301056
\(436\) 14.5546 0.697037
\(437\) 58.8976 2.81745
\(438\) 3.48324 0.166435
\(439\) 10.9217 0.521264 0.260632 0.965438i \(-0.416069\pi\)
0.260632 + 0.965438i \(0.416069\pi\)
\(440\) 7.97927 0.380397
\(441\) 3.08509 0.146909
\(442\) 1.96523 0.0934765
\(443\) 8.27778 0.393289 0.196645 0.980475i \(-0.436996\pi\)
0.196645 + 0.980475i \(0.436996\pi\)
\(444\) 19.8126 0.940266
\(445\) 34.7910 1.64925
\(446\) 1.93341 0.0915498
\(447\) −0.927884 −0.0438874
\(448\) −18.4468 −0.871528
\(449\) −30.0245 −1.41694 −0.708472 0.705739i \(-0.750615\pi\)
−0.708472 + 0.705739i \(0.750615\pi\)
\(450\) 0.359092 0.0169278
\(451\) 4.44241 0.209185
\(452\) −8.52200 −0.400841
\(453\) −7.69312 −0.361454
\(454\) 7.82914 0.367440
\(455\) 50.2671 2.35656
\(456\) −10.2673 −0.480809
\(457\) 10.6431 0.497861 0.248930 0.968521i \(-0.419921\pi\)
0.248930 + 0.968521i \(0.419921\pi\)
\(458\) −1.50293 −0.0702273
\(459\) 1.00000 0.0466760
\(460\) −32.6619 −1.52287
\(461\) −25.3204 −1.17929 −0.589645 0.807663i \(-0.700732\pi\)
−0.589645 + 0.807663i \(0.700732\pi\)
\(462\) −2.61351 −0.121591
\(463\) −11.3424 −0.527128 −0.263564 0.964642i \(-0.584898\pi\)
−0.263564 + 0.964642i \(0.584898\pi\)
\(464\) −8.69648 −0.403724
\(465\) −26.6125 −1.23413
\(466\) 2.21462 0.102590
\(467\) 36.8602 1.70569 0.852844 0.522166i \(-0.174876\pi\)
0.852844 + 0.522166i \(0.174876\pi\)
\(468\) −12.1442 −0.561368
\(469\) −35.9135 −1.65833
\(470\) 2.82774 0.130434
\(471\) −22.5272 −1.03800
\(472\) −12.8491 −0.591430
\(473\) 2.91068 0.133833
\(474\) 0.308270 0.0141593
\(475\) 9.93530 0.455863
\(476\) −6.04962 −0.277284
\(477\) −0.219567 −0.0100533
\(478\) −0.355483 −0.0162594
\(479\) 16.4430 0.751300 0.375650 0.926762i \(-0.377419\pi\)
0.375650 + 0.926762i \(0.377419\pi\)
\(480\) 8.60992 0.392987
\(481\) −66.3035 −3.02318
\(482\) −3.34270 −0.152256
\(483\) 21.9296 0.997833
\(484\) 7.37802 0.335365
\(485\) 16.6012 0.753820
\(486\) 0.308270 0.0139834
\(487\) 33.0200 1.49628 0.748139 0.663542i \(-0.230947\pi\)
0.748139 + 0.663542i \(0.230947\pi\)
\(488\) 5.75104 0.260337
\(489\) 5.28450 0.238974
\(490\) 2.36136 0.106675
\(491\) −5.58343 −0.251977 −0.125988 0.992032i \(-0.540210\pi\)
−0.125988 + 0.992032i \(0.540210\pi\)
\(492\) 3.16996 0.142913
\(493\) −2.52889 −0.113896
\(494\) 16.7618 0.754148
\(495\) −6.62848 −0.297928
\(496\) −36.8585 −1.65500
\(497\) −32.9378 −1.47746
\(498\) −3.37947 −0.151438
\(499\) −20.1760 −0.903203 −0.451601 0.892220i \(-0.649147\pi\)
−0.451601 + 0.892220i \(0.649147\pi\)
\(500\) 18.1397 0.811233
\(501\) −14.9243 −0.666768
\(502\) 4.88197 0.217893
\(503\) 16.5401 0.737485 0.368742 0.929532i \(-0.379788\pi\)
0.368742 + 0.929532i \(0.379788\pi\)
\(504\) −3.82287 −0.170284
\(505\) 8.55401 0.380648
\(506\) −5.68297 −0.252639
\(507\) 27.6410 1.22758
\(508\) 6.62366 0.293877
\(509\) −34.0855 −1.51081 −0.755407 0.655256i \(-0.772561\pi\)
−0.755407 + 0.655256i \(0.772561\pi\)
\(510\) 0.765408 0.0338929
\(511\) 35.8832 1.58738
\(512\) 20.2040 0.892901
\(513\) 8.52916 0.376572
\(514\) 2.74152 0.120923
\(515\) −8.00259 −0.352636
\(516\) 2.07697 0.0914337
\(517\) −9.86277 −0.433764
\(518\) −10.1818 −0.447364
\(519\) 20.1069 0.882595
\(520\) −19.0543 −0.835587
\(521\) −6.96670 −0.305217 −0.152608 0.988287i \(-0.548767\pi\)
−0.152608 + 0.988287i \(0.548767\pi\)
\(522\) −0.779582 −0.0341214
\(523\) −40.5036 −1.77110 −0.885549 0.464547i \(-0.846217\pi\)
−0.885549 + 0.464547i \(0.846217\pi\)
\(524\) −16.2473 −0.709765
\(525\) 3.69926 0.161449
\(526\) −0.517286 −0.0225547
\(527\) −10.7183 −0.466895
\(528\) −9.18047 −0.399529
\(529\) 24.6851 1.07327
\(530\) −0.168058 −0.00729998
\(531\) 10.6739 0.463210
\(532\) −51.5981 −2.23706
\(533\) −10.6084 −0.459499
\(534\) 4.31953 0.186924
\(535\) 43.1444 1.86529
\(536\) 13.6134 0.588010
\(537\) −17.3799 −0.749998
\(538\) −4.31425 −0.186000
\(539\) −8.23608 −0.354753
\(540\) −4.72988 −0.203541
\(541\) 21.6771 0.931973 0.465987 0.884792i \(-0.345699\pi\)
0.465987 + 0.884792i \(0.345699\pi\)
\(542\) −8.67614 −0.372672
\(543\) 16.7714 0.719729
\(544\) 3.46767 0.148675
\(545\) −18.9702 −0.812596
\(546\) 6.24099 0.267090
\(547\) 11.6608 0.498581 0.249291 0.968429i \(-0.419803\pi\)
0.249291 + 0.968429i \(0.419803\pi\)
\(548\) −28.0632 −1.19880
\(549\) −4.77746 −0.203897
\(550\) −0.958646 −0.0408768
\(551\) −21.5693 −0.918884
\(552\) −8.31267 −0.353811
\(553\) 3.17570 0.135045
\(554\) 2.80162 0.119029
\(555\) −25.8235 −1.09615
\(556\) −16.6870 −0.707689
\(557\) −31.8534 −1.34967 −0.674837 0.737967i \(-0.735786\pi\)
−0.674837 + 0.737967i \(0.735786\pi\)
\(558\) −3.30412 −0.139875
\(559\) −6.95065 −0.293981
\(560\) 27.1153 1.14583
\(561\) −2.66964 −0.112712
\(562\) −5.56043 −0.234553
\(563\) 2.28644 0.0963619 0.0481810 0.998839i \(-0.484658\pi\)
0.0481810 + 0.998839i \(0.484658\pi\)
\(564\) −7.03777 −0.296343
\(565\) 11.1075 0.467295
\(566\) −2.22773 −0.0936387
\(567\) 3.17570 0.133367
\(568\) 12.4854 0.523877
\(569\) −34.0593 −1.42784 −0.713919 0.700228i \(-0.753082\pi\)
−0.713919 + 0.700228i \(0.753082\pi\)
\(570\) 6.52829 0.273440
\(571\) −1.12238 −0.0469701 −0.0234850 0.999724i \(-0.507476\pi\)
−0.0234850 + 0.999724i \(0.507476\pi\)
\(572\) 32.4207 1.35558
\(573\) −15.8317 −0.661380
\(574\) −1.62906 −0.0679957
\(575\) 8.04389 0.335453
\(576\) −5.80872 −0.242030
\(577\) 8.44834 0.351709 0.175854 0.984416i \(-0.443731\pi\)
0.175854 + 0.984416i \(0.443731\pi\)
\(578\) 0.308270 0.0128224
\(579\) −16.7147 −0.694639
\(580\) 11.9614 0.496668
\(581\) −34.8142 −1.44434
\(582\) 2.06114 0.0854372
\(583\) 0.586163 0.0242764
\(584\) −13.6019 −0.562852
\(585\) 15.8287 0.654434
\(586\) 0.745937 0.0308144
\(587\) −33.0442 −1.36388 −0.681940 0.731408i \(-0.738863\pi\)
−0.681940 + 0.731408i \(0.738863\pi\)
\(588\) −5.87701 −0.242364
\(589\) −91.4178 −3.76681
\(590\) 8.16993 0.336351
\(591\) 2.20508 0.0907049
\(592\) −35.7657 −1.46996
\(593\) −25.9449 −1.06543 −0.532715 0.846295i \(-0.678828\pi\)
−0.532715 + 0.846295i \(0.678828\pi\)
\(594\) −0.822969 −0.0337668
\(595\) 7.88500 0.323253
\(596\) 1.76759 0.0724033
\(597\) −6.40547 −0.262158
\(598\) 13.5708 0.554951
\(599\) −33.1246 −1.35343 −0.676716 0.736244i \(-0.736598\pi\)
−0.676716 + 0.736244i \(0.736598\pi\)
\(600\) −1.40225 −0.0572464
\(601\) −23.4938 −0.958330 −0.479165 0.877725i \(-0.659061\pi\)
−0.479165 + 0.877725i \(0.659061\pi\)
\(602\) −1.06737 −0.0435027
\(603\) −11.3088 −0.460531
\(604\) 14.6552 0.596310
\(605\) −9.61642 −0.390963
\(606\) 1.06204 0.0431423
\(607\) 32.2185 1.30771 0.653854 0.756621i \(-0.273151\pi\)
0.653854 + 0.756621i \(0.273151\pi\)
\(608\) 29.5763 1.19948
\(609\) −8.03102 −0.325433
\(610\) −3.65671 −0.148056
\(611\) 23.5521 0.952815
\(612\) −1.90497 −0.0770038
\(613\) 24.4103 0.985921 0.492961 0.870052i \(-0.335915\pi\)
0.492961 + 0.870052i \(0.335915\pi\)
\(614\) 5.00268 0.201892
\(615\) −4.13169 −0.166606
\(616\) 10.2057 0.411198
\(617\) 13.2441 0.533186 0.266593 0.963809i \(-0.414102\pi\)
0.266593 + 0.963809i \(0.414102\pi\)
\(618\) −0.993575 −0.0399674
\(619\) −20.0734 −0.806816 −0.403408 0.915020i \(-0.632175\pi\)
−0.403408 + 0.915020i \(0.632175\pi\)
\(620\) 50.6961 2.03600
\(621\) 6.90544 0.277106
\(622\) 5.50513 0.220736
\(623\) 44.4985 1.78279
\(624\) 21.9228 0.877613
\(625\) −29.4674 −1.17870
\(626\) −0.526200 −0.0210312
\(627\) −22.7698 −0.909336
\(628\) 42.9136 1.71244
\(629\) −10.4005 −0.414695
\(630\) 2.43071 0.0968418
\(631\) 7.18197 0.285910 0.142955 0.989729i \(-0.454340\pi\)
0.142955 + 0.989729i \(0.454340\pi\)
\(632\) −1.20379 −0.0478840
\(633\) 1.83566 0.0729608
\(634\) 4.72264 0.187560
\(635\) −8.63320 −0.342598
\(636\) 0.418268 0.0165854
\(637\) 19.6676 0.779257
\(638\) 2.08120 0.0823956
\(639\) −10.3718 −0.410302
\(640\) −21.6659 −0.856419
\(641\) 7.88544 0.311456 0.155728 0.987800i \(-0.450228\pi\)
0.155728 + 0.987800i \(0.450228\pi\)
\(642\) 5.35666 0.211410
\(643\) −6.17922 −0.243685 −0.121842 0.992549i \(-0.538880\pi\)
−0.121842 + 0.992549i \(0.538880\pi\)
\(644\) −41.7753 −1.64618
\(645\) −2.70710 −0.106592
\(646\) 2.62929 0.103448
\(647\) −40.8799 −1.60715 −0.803577 0.595201i \(-0.797072\pi\)
−0.803577 + 0.595201i \(0.797072\pi\)
\(648\) −1.20379 −0.0472892
\(649\) −28.4956 −1.11855
\(650\) 2.28923 0.0897908
\(651\) −34.0380 −1.33406
\(652\) −10.0668 −0.394247
\(653\) −43.0718 −1.68553 −0.842764 0.538282i \(-0.819073\pi\)
−0.842764 + 0.538282i \(0.819073\pi\)
\(654\) −2.35528 −0.0920988
\(655\) 21.1765 0.827433
\(656\) −5.72241 −0.223423
\(657\) 11.2993 0.440827
\(658\) 3.61675 0.140996
\(659\) 30.7760 1.19886 0.599432 0.800426i \(-0.295393\pi\)
0.599432 + 0.800426i \(0.295393\pi\)
\(660\) 12.6271 0.491507
\(661\) −44.9574 −1.74864 −0.874321 0.485348i \(-0.838693\pi\)
−0.874321 + 0.485348i \(0.838693\pi\)
\(662\) 2.74937 0.106857
\(663\) 6.37503 0.247586
\(664\) 13.1967 0.512132
\(665\) 67.2524 2.60794
\(666\) −3.20616 −0.124236
\(667\) −17.4631 −0.676175
\(668\) 28.4303 1.10000
\(669\) 6.27182 0.242482
\(670\) −8.65588 −0.334406
\(671\) 12.7541 0.492366
\(672\) 11.0123 0.424808
\(673\) 8.36670 0.322513 0.161256 0.986913i \(-0.448445\pi\)
0.161256 + 0.986913i \(0.448445\pi\)
\(674\) −10.2794 −0.395947
\(675\) 1.16486 0.0448356
\(676\) −52.6553 −2.02520
\(677\) −19.6219 −0.754131 −0.377065 0.926187i \(-0.623067\pi\)
−0.377065 + 0.926187i \(0.623067\pi\)
\(678\) 1.37907 0.0529627
\(679\) 21.2333 0.814858
\(680\) −2.98890 −0.114619
\(681\) 25.3970 0.973215
\(682\) 8.82081 0.337766
\(683\) 46.7556 1.78905 0.894526 0.447016i \(-0.147513\pi\)
0.894526 + 0.447016i \(0.147513\pi\)
\(684\) −16.2478 −0.621250
\(685\) 36.5772 1.39754
\(686\) −3.83260 −0.146329
\(687\) −4.87536 −0.186007
\(688\) −3.74935 −0.142943
\(689\) −1.39974 −0.0533260
\(690\) 5.28548 0.201215
\(691\) −22.1127 −0.841206 −0.420603 0.907245i \(-0.638181\pi\)
−0.420603 + 0.907245i \(0.638181\pi\)
\(692\) −38.3030 −1.45606
\(693\) −8.47797 −0.322052
\(694\) −3.84569 −0.145980
\(695\) 21.7497 0.825013
\(696\) 3.04425 0.115392
\(697\) −1.66405 −0.0630303
\(698\) −6.90624 −0.261405
\(699\) 7.18402 0.271725
\(700\) −7.04697 −0.266351
\(701\) −10.3861 −0.392278 −0.196139 0.980576i \(-0.562840\pi\)
−0.196139 + 0.980576i \(0.562840\pi\)
\(702\) 1.96523 0.0741729
\(703\) −88.7075 −3.34567
\(704\) 15.5072 0.584448
\(705\) 9.17294 0.345473
\(706\) 0.299243 0.0112622
\(707\) 10.9408 0.411470
\(708\) −20.3335 −0.764181
\(709\) −38.4299 −1.44327 −0.721633 0.692276i \(-0.756608\pi\)
−0.721633 + 0.692276i \(0.756608\pi\)
\(710\) −7.93867 −0.297933
\(711\) 1.00000 0.0375029
\(712\) −16.8676 −0.632142
\(713\) −74.0144 −2.77186
\(714\) 0.978975 0.0366372
\(715\) −42.2568 −1.58031
\(716\) 33.1082 1.23731
\(717\) −1.15315 −0.0430653
\(718\) −7.48873 −0.279477
\(719\) −41.9706 −1.56524 −0.782621 0.622499i \(-0.786117\pi\)
−0.782621 + 0.622499i \(0.786117\pi\)
\(720\) 8.53836 0.318206
\(721\) −10.2355 −0.381190
\(722\) 16.5685 0.616614
\(723\) −10.8434 −0.403271
\(724\) −31.9490 −1.18737
\(725\) −2.94581 −0.109405
\(726\) −1.19394 −0.0443114
\(727\) −15.2135 −0.564239 −0.282119 0.959379i \(-0.591037\pi\)
−0.282119 + 0.959379i \(0.591037\pi\)
\(728\) −24.3709 −0.903245
\(729\) 1.00000 0.0370370
\(730\) 8.64857 0.320098
\(731\) −1.09029 −0.0403259
\(732\) 9.10091 0.336379
\(733\) 13.0377 0.481559 0.240780 0.970580i \(-0.422597\pi\)
0.240780 + 0.970580i \(0.422597\pi\)
\(734\) 9.43972 0.348426
\(735\) 7.66002 0.282544
\(736\) 23.9458 0.882653
\(737\) 30.1905 1.11208
\(738\) −0.512977 −0.0188829
\(739\) −24.7703 −0.911191 −0.455596 0.890187i \(-0.650574\pi\)
−0.455596 + 0.890187i \(0.650574\pi\)
\(740\) 49.1931 1.80837
\(741\) 54.3736 1.99747
\(742\) −0.214950 −0.00789107
\(743\) −0.886641 −0.0325277 −0.0162638 0.999868i \(-0.505177\pi\)
−0.0162638 + 0.999868i \(0.505177\pi\)
\(744\) 12.9025 0.473029
\(745\) −2.30386 −0.0844068
\(746\) −7.02275 −0.257121
\(747\) −10.9627 −0.401104
\(748\) 5.08558 0.185947
\(749\) 55.1826 2.01633
\(750\) −2.93545 −0.107187
\(751\) 34.0442 1.24229 0.621146 0.783695i \(-0.286668\pi\)
0.621146 + 0.783695i \(0.286668\pi\)
\(752\) 12.7046 0.463288
\(753\) 15.8366 0.577120
\(754\) −4.96986 −0.180992
\(755\) −19.1013 −0.695169
\(756\) −6.04962 −0.220022
\(757\) 9.99230 0.363176 0.181588 0.983375i \(-0.441876\pi\)
0.181588 + 0.983375i \(0.441876\pi\)
\(758\) −3.20845 −0.116536
\(759\) −18.4350 −0.669149
\(760\) −25.4928 −0.924720
\(761\) −46.9128 −1.70059 −0.850294 0.526308i \(-0.823576\pi\)
−0.850294 + 0.526308i \(0.823576\pi\)
\(762\) −1.07187 −0.0388297
\(763\) −24.2634 −0.878393
\(764\) 30.1589 1.09111
\(765\) 2.48291 0.0897700
\(766\) 6.53167 0.235999
\(767\) 68.0467 2.45703
\(768\) 8.92747 0.322142
\(769\) −7.06792 −0.254876 −0.127438 0.991847i \(-0.540675\pi\)
−0.127438 + 0.991847i \(0.540675\pi\)
\(770\) −6.48911 −0.233851
\(771\) 8.89323 0.320282
\(772\) 31.8410 1.14598
\(773\) 44.8961 1.61480 0.807400 0.590005i \(-0.200874\pi\)
0.807400 + 0.590005i \(0.200874\pi\)
\(774\) −0.336105 −0.0120810
\(775\) −12.4853 −0.448486
\(776\) −8.04870 −0.288932
\(777\) −33.0289 −1.18491
\(778\) −5.78020 −0.207230
\(779\) −14.1929 −0.508515
\(780\) −30.1531 −1.07965
\(781\) 27.6889 0.990788
\(782\) 2.12874 0.0761237
\(783\) −2.52889 −0.0903753
\(784\) 10.6092 0.378899
\(785\) −55.9331 −1.99634
\(786\) 2.62920 0.0937804
\(787\) 1.18545 0.0422566 0.0211283 0.999777i \(-0.493274\pi\)
0.0211283 + 0.999777i \(0.493274\pi\)
\(788\) −4.20061 −0.149641
\(789\) −1.67803 −0.0597393
\(790\) 0.765408 0.0272320
\(791\) 14.2067 0.505132
\(792\) 3.21367 0.114193
\(793\) −30.4564 −1.08154
\(794\) 0.151482 0.00537591
\(795\) −0.545165 −0.0193350
\(796\) 12.2022 0.432496
\(797\) 27.3862 0.970071 0.485035 0.874495i \(-0.338807\pi\)
0.485035 + 0.874495i \(0.338807\pi\)
\(798\) 8.34983 0.295581
\(799\) 3.69443 0.130699
\(800\) 4.03935 0.142813
\(801\) 14.0122 0.495096
\(802\) 5.42490 0.191560
\(803\) −30.1650 −1.06450
\(804\) 21.5430 0.759763
\(805\) 54.4494 1.91909
\(806\) −21.0639 −0.741944
\(807\) −13.9950 −0.492648
\(808\) −4.14722 −0.145899
\(809\) 44.8128 1.57554 0.787768 0.615972i \(-0.211237\pi\)
0.787768 + 0.615972i \(0.211237\pi\)
\(810\) 0.765408 0.0268937
\(811\) 12.8672 0.451830 0.225915 0.974147i \(-0.427463\pi\)
0.225915 + 0.974147i \(0.427463\pi\)
\(812\) 15.2988 0.536884
\(813\) −28.1446 −0.987074
\(814\) 8.55929 0.300003
\(815\) 13.1210 0.459608
\(816\) 3.43885 0.120384
\(817\) −9.29928 −0.325340
\(818\) 6.58362 0.230191
\(819\) 20.2452 0.707425
\(820\) 7.87074 0.274858
\(821\) −43.1356 −1.50544 −0.752722 0.658338i \(-0.771260\pi\)
−0.752722 + 0.658338i \(0.771260\pi\)
\(822\) 4.54130 0.158396
\(823\) 39.6752 1.38299 0.691495 0.722382i \(-0.256953\pi\)
0.691495 + 0.722382i \(0.256953\pi\)
\(824\) 3.87988 0.135162
\(825\) −3.10976 −0.108268
\(826\) 10.4495 0.363585
\(827\) 27.5850 0.959226 0.479613 0.877480i \(-0.340777\pi\)
0.479613 + 0.877480i \(0.340777\pi\)
\(828\) −13.1547 −0.457156
\(829\) 2.66595 0.0925924 0.0462962 0.998928i \(-0.485258\pi\)
0.0462962 + 0.998928i \(0.485258\pi\)
\(830\) −8.39093 −0.291253
\(831\) 9.08819 0.315266
\(832\) −37.0307 −1.28381
\(833\) 3.08509 0.106892
\(834\) 2.70037 0.0935061
\(835\) −37.0557 −1.28237
\(836\) 43.3757 1.50018
\(837\) −10.7183 −0.370478
\(838\) 4.72782 0.163320
\(839\) −12.2946 −0.424457 −0.212229 0.977220i \(-0.568072\pi\)
−0.212229 + 0.977220i \(0.568072\pi\)
\(840\) −9.49185 −0.327500
\(841\) −22.6047 −0.779472
\(842\) 0.961818 0.0331464
\(843\) −18.0375 −0.621245
\(844\) −3.49687 −0.120367
\(845\) 68.6302 2.36095
\(846\) 1.13888 0.0391555
\(847\) −12.2996 −0.422620
\(848\) −0.755056 −0.0259287
\(849\) −7.22656 −0.248015
\(850\) 0.359092 0.0123168
\(851\) −71.8200 −2.46196
\(852\) 19.7580 0.676897
\(853\) −25.6995 −0.879936 −0.439968 0.898014i \(-0.645010\pi\)
−0.439968 + 0.898014i \(0.645010\pi\)
\(854\) −4.67701 −0.160044
\(855\) 21.1772 0.724244
\(856\) −20.9176 −0.714948
\(857\) 20.3237 0.694246 0.347123 0.937820i \(-0.387159\pi\)
0.347123 + 0.937820i \(0.387159\pi\)
\(858\) −5.24646 −0.179111
\(859\) 4.72667 0.161272 0.0806360 0.996744i \(-0.474305\pi\)
0.0806360 + 0.996744i \(0.474305\pi\)
\(860\) 5.15695 0.175850
\(861\) −5.28453 −0.180096
\(862\) 5.24429 0.178621
\(863\) 14.2759 0.485958 0.242979 0.970031i \(-0.421875\pi\)
0.242979 + 0.970031i \(0.421875\pi\)
\(864\) 3.46767 0.117972
\(865\) 49.9237 1.69746
\(866\) −4.49445 −0.152727
\(867\) 1.00000 0.0339618
\(868\) 64.8414 2.20086
\(869\) −2.66964 −0.0905612
\(870\) −1.93564 −0.0656242
\(871\) −72.0942 −2.44282
\(872\) 9.19730 0.311460
\(873\) 6.68616 0.226292
\(874\) 18.1564 0.614149
\(875\) −30.2401 −1.02230
\(876\) −21.5248 −0.727256
\(877\) 14.5218 0.490368 0.245184 0.969477i \(-0.421152\pi\)
0.245184 + 0.969477i \(0.421152\pi\)
\(878\) 3.36683 0.113625
\(879\) 2.41975 0.0816162
\(880\) −22.7943 −0.768397
\(881\) 27.4767 0.925712 0.462856 0.886433i \(-0.346825\pi\)
0.462856 + 0.886433i \(0.346825\pi\)
\(882\) 0.951042 0.0320233
\(883\) −18.6394 −0.627265 −0.313632 0.949544i \(-0.601546\pi\)
−0.313632 + 0.949544i \(0.601546\pi\)
\(884\) −12.1442 −0.408455
\(885\) 26.5025 0.890872
\(886\) 2.55179 0.0857291
\(887\) −8.22724 −0.276244 −0.138122 0.990415i \(-0.544107\pi\)
−0.138122 + 0.990415i \(0.544107\pi\)
\(888\) 12.5200 0.420143
\(889\) −11.0421 −0.370339
\(890\) 10.7250 0.359504
\(891\) −2.66964 −0.0894362
\(892\) −11.9476 −0.400036
\(893\) 31.5103 1.05445
\(894\) −0.286039 −0.00956658
\(895\) −43.1528 −1.44244
\(896\) −27.7111 −0.925764
\(897\) 44.0224 1.46987
\(898\) −9.25567 −0.308866
\(899\) 27.1054 0.904015
\(900\) −2.21903 −0.0739676
\(901\) −0.219567 −0.00731482
\(902\) 1.36946 0.0455981
\(903\) −3.46245 −0.115223
\(904\) −5.38521 −0.179109
\(905\) 41.6419 1.38422
\(906\) −2.37156 −0.0787898
\(907\) −16.5562 −0.549740 −0.274870 0.961481i \(-0.588635\pi\)
−0.274870 + 0.961481i \(0.588635\pi\)
\(908\) −48.3805 −1.60556
\(909\) 3.44515 0.114268
\(910\) 15.4959 0.513682
\(911\) 34.4530 1.14148 0.570740 0.821131i \(-0.306656\pi\)
0.570740 + 0.821131i \(0.306656\pi\)
\(912\) 29.3305 0.971229
\(913\) 29.2664 0.968576
\(914\) 3.28094 0.108524
\(915\) −11.8620 −0.392146
\(916\) 9.28742 0.306865
\(917\) 27.0852 0.894432
\(918\) 0.308270 0.0101744
\(919\) 39.8674 1.31510 0.657552 0.753409i \(-0.271592\pi\)
0.657552 + 0.753409i \(0.271592\pi\)
\(920\) −20.6397 −0.680469
\(921\) 16.2282 0.534738
\(922\) −7.80553 −0.257062
\(923\) −66.1206 −2.17638
\(924\) 16.1503 0.531305
\(925\) −12.1152 −0.398344
\(926\) −3.49654 −0.114903
\(927\) −3.22307 −0.105859
\(928\) −8.76936 −0.287868
\(929\) 7.12093 0.233630 0.116815 0.993154i \(-0.462732\pi\)
0.116815 + 0.993154i \(0.462732\pi\)
\(930\) −8.20386 −0.269015
\(931\) 26.3132 0.862382
\(932\) −13.6853 −0.448278
\(933\) 17.8581 0.584649
\(934\) 11.3629 0.371806
\(935\) −6.62848 −0.216774
\(936\) −7.67417 −0.250838
\(937\) −42.9110 −1.40184 −0.700921 0.713239i \(-0.747227\pi\)
−0.700921 + 0.713239i \(0.747227\pi\)
\(938\) −11.0711 −0.361483
\(939\) −1.70694 −0.0557040
\(940\) −17.4742 −0.569945
\(941\) −18.9403 −0.617438 −0.308719 0.951153i \(-0.599900\pi\)
−0.308719 + 0.951153i \(0.599900\pi\)
\(942\) −6.94446 −0.226263
\(943\) −11.4910 −0.374198
\(944\) 36.7061 1.19468
\(945\) 7.88500 0.256499
\(946\) 0.897277 0.0291730
\(947\) 51.2717 1.66610 0.833052 0.553194i \(-0.186591\pi\)
0.833052 + 0.553194i \(0.186591\pi\)
\(948\) −1.90497 −0.0618705
\(949\) 72.0333 2.33830
\(950\) 3.06276 0.0993689
\(951\) 15.3198 0.496779
\(952\) −3.82287 −0.123900
\(953\) 0.0503342 0.00163048 0.000815242 1.00000i \(-0.499741\pi\)
0.000815242 1.00000i \(0.499741\pi\)
\(954\) −0.0676858 −0.00219141
\(955\) −39.3088 −1.27200
\(956\) 2.19672 0.0710470
\(957\) 6.75123 0.218236
\(958\) 5.06889 0.163768
\(959\) 46.7831 1.51070
\(960\) −14.4225 −0.465486
\(961\) 83.8813 2.70585
\(962\) −20.4394 −0.658992
\(963\) 17.3765 0.559950
\(964\) 20.6564 0.665298
\(965\) −41.5011 −1.33597
\(966\) 6.76025 0.217508
\(967\) 8.92585 0.287036 0.143518 0.989648i \(-0.454159\pi\)
0.143518 + 0.989648i \(0.454159\pi\)
\(968\) 4.66231 0.149852
\(969\) 8.52916 0.273996
\(970\) 5.11764 0.164318
\(971\) 9.84156 0.315831 0.157915 0.987453i \(-0.449523\pi\)
0.157915 + 0.987453i \(0.449523\pi\)
\(972\) −1.90497 −0.0611019
\(973\) 27.8184 0.891816
\(974\) 10.1791 0.326159
\(975\) 7.42603 0.237823
\(976\) −16.4290 −0.525878
\(977\) −49.4226 −1.58117 −0.790584 0.612354i \(-0.790223\pi\)
−0.790584 + 0.612354i \(0.790223\pi\)
\(978\) 1.62906 0.0520914
\(979\) −37.4074 −1.19555
\(980\) −14.5921 −0.466128
\(981\) −7.64031 −0.243936
\(982\) −1.72121 −0.0549259
\(983\) −7.22029 −0.230291 −0.115146 0.993349i \(-0.536733\pi\)
−0.115146 + 0.993349i \(0.536733\pi\)
\(984\) 2.00316 0.0638584
\(985\) 5.47502 0.174449
\(986\) −0.779582 −0.0248270
\(987\) 11.7324 0.373446
\(988\) −103.580 −3.29532
\(989\) −7.52895 −0.239407
\(990\) −2.04336 −0.0649423
\(991\) −53.4752 −1.69870 −0.849349 0.527832i \(-0.823005\pi\)
−0.849349 + 0.527832i \(0.823005\pi\)
\(992\) −37.1674 −1.18007
\(993\) 8.91869 0.283026
\(994\) −10.1537 −0.322057
\(995\) −15.9042 −0.504198
\(996\) 20.8836 0.661721
\(997\) 39.2086 1.24175 0.620875 0.783910i \(-0.286778\pi\)
0.620875 + 0.783910i \(0.286778\pi\)
\(998\) −6.21967 −0.196880
\(999\) −10.4005 −0.329057
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.1.17 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.17 31 1.1 even 1 trivial