Properties

Label 4027.2.a.c.1.20
Level 4027
Weight 2
Character 4027.1
Self dual yes
Analytic conductor 32.156
Analytic rank 0
Dimension 174
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1557568940\)
Analytic rank: \(0\)
Dimension: \(174\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.24334 q^{2} -2.49753 q^{3} +3.03259 q^{4} -3.94500 q^{5} +5.60282 q^{6} -4.10422 q^{7} -2.31645 q^{8} +3.23765 q^{9} +O(q^{10})\) \(q-2.24334 q^{2} -2.49753 q^{3} +3.03259 q^{4} -3.94500 q^{5} +5.60282 q^{6} -4.10422 q^{7} -2.31645 q^{8} +3.23765 q^{9} +8.85000 q^{10} -0.217569 q^{11} -7.57398 q^{12} +4.37046 q^{13} +9.20718 q^{14} +9.85276 q^{15} -0.868578 q^{16} +3.58887 q^{17} -7.26317 q^{18} -6.45241 q^{19} -11.9636 q^{20} +10.2504 q^{21} +0.488082 q^{22} -1.83067 q^{23} +5.78541 q^{24} +10.5630 q^{25} -9.80444 q^{26} -0.593547 q^{27} -12.4464 q^{28} +2.62301 q^{29} -22.1031 q^{30} +2.71082 q^{31} +6.58143 q^{32} +0.543385 q^{33} -8.05107 q^{34} +16.1912 q^{35} +9.81848 q^{36} -4.32785 q^{37} +14.4750 q^{38} -10.9154 q^{39} +9.13842 q^{40} -0.0643647 q^{41} -22.9952 q^{42} +4.26662 q^{43} -0.659798 q^{44} -12.7726 q^{45} +4.10683 q^{46} +1.29618 q^{47} +2.16930 q^{48} +9.84463 q^{49} -23.6965 q^{50} -8.96331 q^{51} +13.2538 q^{52} +11.9503 q^{53} +1.33153 q^{54} +0.858311 q^{55} +9.50724 q^{56} +16.1151 q^{57} -5.88431 q^{58} -7.97621 q^{59} +29.8794 q^{60} -7.88367 q^{61} -6.08131 q^{62} -13.2880 q^{63} -13.0272 q^{64} -17.2415 q^{65} -1.21900 q^{66} -7.62052 q^{67} +10.8836 q^{68} +4.57216 q^{69} -36.3223 q^{70} -14.7871 q^{71} -7.49988 q^{72} -13.1993 q^{73} +9.70885 q^{74} -26.3815 q^{75} -19.5675 q^{76} +0.892952 q^{77} +24.4869 q^{78} -7.20626 q^{79} +3.42654 q^{80} -8.23056 q^{81} +0.144392 q^{82} +3.03570 q^{83} +31.0853 q^{84} -14.1581 q^{85} -9.57148 q^{86} -6.55104 q^{87} +0.503989 q^{88} +14.1706 q^{89} +28.6532 q^{90} -17.9373 q^{91} -5.55168 q^{92} -6.77037 q^{93} -2.90778 q^{94} +25.4548 q^{95} -16.4373 q^{96} +5.81361 q^{97} -22.0849 q^{98} -0.704413 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24334 −1.58628 −0.793142 0.609037i \(-0.791556\pi\)
−0.793142 + 0.609037i \(0.791556\pi\)
\(3\) −2.49753 −1.44195 −0.720975 0.692961i \(-0.756306\pi\)
−0.720975 + 0.692961i \(0.756306\pi\)
\(4\) 3.03259 1.51629
\(5\) −3.94500 −1.76426 −0.882129 0.471007i \(-0.843891\pi\)
−0.882129 + 0.471007i \(0.843891\pi\)
\(6\) 5.60282 2.28734
\(7\) −4.10422 −1.55125 −0.775625 0.631194i \(-0.782565\pi\)
−0.775625 + 0.631194i \(0.782565\pi\)
\(8\) −2.31645 −0.818990
\(9\) 3.23765 1.07922
\(10\) 8.85000 2.79861
\(11\) −0.217569 −0.0655996 −0.0327998 0.999462i \(-0.510442\pi\)
−0.0327998 + 0.999462i \(0.510442\pi\)
\(12\) −7.57398 −2.18642
\(13\) 4.37046 1.21215 0.606074 0.795408i \(-0.292744\pi\)
0.606074 + 0.795408i \(0.292744\pi\)
\(14\) 9.20718 2.46072
\(15\) 9.85276 2.54397
\(16\) −0.868578 −0.217145
\(17\) 3.58887 0.870429 0.435214 0.900327i \(-0.356673\pi\)
0.435214 + 0.900327i \(0.356673\pi\)
\(18\) −7.26317 −1.71195
\(19\) −6.45241 −1.48028 −0.740142 0.672450i \(-0.765242\pi\)
−0.740142 + 0.672450i \(0.765242\pi\)
\(20\) −11.9636 −2.67514
\(21\) 10.2504 2.23682
\(22\) 0.488082 0.104059
\(23\) −1.83067 −0.381722 −0.190861 0.981617i \(-0.561128\pi\)
−0.190861 + 0.981617i \(0.561128\pi\)
\(24\) 5.78541 1.18094
\(25\) 10.5630 2.11261
\(26\) −9.80444 −1.92281
\(27\) −0.593547 −0.114228
\(28\) −12.4464 −2.35215
\(29\) 2.62301 0.487081 0.243540 0.969891i \(-0.421691\pi\)
0.243540 + 0.969891i \(0.421691\pi\)
\(30\) −22.1031 −4.03546
\(31\) 2.71082 0.486879 0.243439 0.969916i \(-0.421724\pi\)
0.243439 + 0.969916i \(0.421724\pi\)
\(32\) 6.58143 1.16344
\(33\) 0.543385 0.0945912
\(34\) −8.05107 −1.38075
\(35\) 16.1912 2.73681
\(36\) 9.81848 1.63641
\(37\) −4.32785 −0.711494 −0.355747 0.934582i \(-0.615773\pi\)
−0.355747 + 0.934582i \(0.615773\pi\)
\(38\) 14.4750 2.34815
\(39\) −10.9154 −1.74786
\(40\) 9.13842 1.44491
\(41\) −0.0643647 −0.0100521 −0.00502604 0.999987i \(-0.501600\pi\)
−0.00502604 + 0.999987i \(0.501600\pi\)
\(42\) −22.9952 −3.54824
\(43\) 4.26662 0.650653 0.325326 0.945602i \(-0.394526\pi\)
0.325326 + 0.945602i \(0.394526\pi\)
\(44\) −0.659798 −0.0994683
\(45\) −12.7726 −1.90402
\(46\) 4.10683 0.605519
\(47\) 1.29618 0.189067 0.0945336 0.995522i \(-0.469864\pi\)
0.0945336 + 0.995522i \(0.469864\pi\)
\(48\) 2.16930 0.313111
\(49\) 9.84463 1.40638
\(50\) −23.6965 −3.35120
\(51\) −8.96331 −1.25511
\(52\) 13.2538 1.83797
\(53\) 11.9503 1.64149 0.820747 0.571292i \(-0.193558\pi\)
0.820747 + 0.571292i \(0.193558\pi\)
\(54\) 1.33153 0.181198
\(55\) 0.858311 0.115735
\(56\) 9.50724 1.27046
\(57\) 16.1151 2.13450
\(58\) −5.88431 −0.772648
\(59\) −7.97621 −1.03841 −0.519207 0.854648i \(-0.673773\pi\)
−0.519207 + 0.854648i \(0.673773\pi\)
\(60\) 29.8794 3.85741
\(61\) −7.88367 −1.00940 −0.504700 0.863295i \(-0.668397\pi\)
−0.504700 + 0.863295i \(0.668397\pi\)
\(62\) −6.08131 −0.772327
\(63\) −13.2880 −1.67414
\(64\) −13.0272 −1.62841
\(65\) −17.2415 −2.13854
\(66\) −1.21900 −0.150048
\(67\) −7.62052 −0.930995 −0.465498 0.885049i \(-0.654125\pi\)
−0.465498 + 0.885049i \(0.654125\pi\)
\(68\) 10.8836 1.31983
\(69\) 4.57216 0.550423
\(70\) −36.3223 −4.34135
\(71\) −14.7871 −1.75491 −0.877453 0.479662i \(-0.840759\pi\)
−0.877453 + 0.479662i \(0.840759\pi\)
\(72\) −7.49988 −0.883869
\(73\) −13.1993 −1.54486 −0.772429 0.635101i \(-0.780959\pi\)
−0.772429 + 0.635101i \(0.780959\pi\)
\(74\) 9.70885 1.12863
\(75\) −26.3815 −3.04628
\(76\) −19.5675 −2.24455
\(77\) 0.892952 0.101761
\(78\) 24.4869 2.77259
\(79\) −7.20626 −0.810768 −0.405384 0.914147i \(-0.632862\pi\)
−0.405384 + 0.914147i \(0.632862\pi\)
\(80\) 3.42654 0.383099
\(81\) −8.23056 −0.914507
\(82\) 0.144392 0.0159454
\(83\) 3.03570 0.333212 0.166606 0.986024i \(-0.446719\pi\)
0.166606 + 0.986024i \(0.446719\pi\)
\(84\) 31.0853 3.39168
\(85\) −14.1581 −1.53566
\(86\) −9.57148 −1.03212
\(87\) −6.55104 −0.702346
\(88\) 0.503989 0.0537254
\(89\) 14.1706 1.50208 0.751039 0.660258i \(-0.229553\pi\)
0.751039 + 0.660258i \(0.229553\pi\)
\(90\) 28.6532 3.02031
\(91\) −17.9373 −1.88034
\(92\) −5.55168 −0.578803
\(93\) −6.77037 −0.702054
\(94\) −2.90778 −0.299914
\(95\) 25.4548 2.61161
\(96\) −16.4373 −1.67763
\(97\) 5.81361 0.590283 0.295141 0.955454i \(-0.404633\pi\)
0.295141 + 0.955454i \(0.404633\pi\)
\(98\) −22.0849 −2.23091
\(99\) −0.704413 −0.0707962
\(100\) 32.0334 3.20334
\(101\) 7.09052 0.705533 0.352767 0.935711i \(-0.385241\pi\)
0.352767 + 0.935711i \(0.385241\pi\)
\(102\) 20.1078 1.99097
\(103\) −10.8468 −1.06877 −0.534384 0.845242i \(-0.679456\pi\)
−0.534384 + 0.845242i \(0.679456\pi\)
\(104\) −10.1240 −0.992737
\(105\) −40.4379 −3.94634
\(106\) −26.8085 −2.60387
\(107\) 16.8589 1.62981 0.814907 0.579592i \(-0.196788\pi\)
0.814907 + 0.579592i \(0.196788\pi\)
\(108\) −1.79999 −0.173204
\(109\) −4.42491 −0.423829 −0.211915 0.977288i \(-0.567970\pi\)
−0.211915 + 0.977288i \(0.567970\pi\)
\(110\) −1.92549 −0.183588
\(111\) 10.8089 1.02594
\(112\) 3.56484 0.336845
\(113\) −3.68215 −0.346387 −0.173194 0.984888i \(-0.555409\pi\)
−0.173194 + 0.984888i \(0.555409\pi\)
\(114\) −36.1517 −3.38591
\(115\) 7.22201 0.673456
\(116\) 7.95451 0.738558
\(117\) 14.1500 1.30817
\(118\) 17.8934 1.64722
\(119\) −14.7295 −1.35025
\(120\) −22.8235 −2.08349
\(121\) −10.9527 −0.995697
\(122\) 17.6858 1.60119
\(123\) 0.160753 0.0144946
\(124\) 8.22082 0.738251
\(125\) −21.9462 −1.96293
\(126\) 29.8097 2.65566
\(127\) 6.33120 0.561803 0.280902 0.959737i \(-0.409367\pi\)
0.280902 + 0.959737i \(0.409367\pi\)
\(128\) 16.0617 1.41967
\(129\) −10.6560 −0.938208
\(130\) 38.6786 3.39233
\(131\) −2.41466 −0.210970 −0.105485 0.994421i \(-0.533639\pi\)
−0.105485 + 0.994421i \(0.533639\pi\)
\(132\) 1.64786 0.143428
\(133\) 26.4821 2.29629
\(134\) 17.0955 1.47682
\(135\) 2.34155 0.201528
\(136\) −8.31345 −0.712873
\(137\) −5.64110 −0.481952 −0.240976 0.970531i \(-0.577468\pi\)
−0.240976 + 0.970531i \(0.577468\pi\)
\(138\) −10.2569 −0.873127
\(139\) −6.01783 −0.510425 −0.255213 0.966885i \(-0.582145\pi\)
−0.255213 + 0.966885i \(0.582145\pi\)
\(140\) 49.1012 4.14981
\(141\) −3.23725 −0.272625
\(142\) 33.1726 2.78378
\(143\) −0.950877 −0.0795163
\(144\) −2.81215 −0.234346
\(145\) −10.3478 −0.859336
\(146\) 29.6105 2.45058
\(147\) −24.5873 −2.02792
\(148\) −13.1246 −1.07883
\(149\) −14.6588 −1.20090 −0.600449 0.799663i \(-0.705011\pi\)
−0.600449 + 0.799663i \(0.705011\pi\)
\(150\) 59.1828 4.83226
\(151\) −3.99491 −0.325101 −0.162551 0.986700i \(-0.551972\pi\)
−0.162551 + 0.986700i \(0.551972\pi\)
\(152\) 14.9467 1.21234
\(153\) 11.6195 0.939382
\(154\) −2.00320 −0.161422
\(155\) −10.6942 −0.858980
\(156\) −33.1018 −2.65026
\(157\) 20.7605 1.65687 0.828434 0.560087i \(-0.189232\pi\)
0.828434 + 0.560087i \(0.189232\pi\)
\(158\) 16.1661 1.28611
\(159\) −29.8461 −2.36695
\(160\) −25.9637 −2.05261
\(161\) 7.51349 0.592146
\(162\) 18.4640 1.45067
\(163\) −21.9442 −1.71881 −0.859403 0.511299i \(-0.829164\pi\)
−0.859403 + 0.511299i \(0.829164\pi\)
\(164\) −0.195192 −0.0152419
\(165\) −2.14366 −0.166883
\(166\) −6.81013 −0.528568
\(167\) −24.2732 −1.87831 −0.939157 0.343489i \(-0.888391\pi\)
−0.939157 + 0.343489i \(0.888391\pi\)
\(168\) −23.7446 −1.83194
\(169\) 6.10093 0.469302
\(170\) 31.7615 2.43599
\(171\) −20.8907 −1.59755
\(172\) 12.9389 0.986582
\(173\) 2.96140 0.225151 0.112576 0.993643i \(-0.464090\pi\)
0.112576 + 0.993643i \(0.464090\pi\)
\(174\) 14.6962 1.11412
\(175\) −43.3531 −3.27718
\(176\) 0.188976 0.0142446
\(177\) 19.9208 1.49734
\(178\) −31.7895 −2.38272
\(179\) −19.9782 −1.49324 −0.746620 0.665251i \(-0.768324\pi\)
−0.746620 + 0.665251i \(0.768324\pi\)
\(180\) −38.7339 −2.88706
\(181\) 15.0690 1.12007 0.560036 0.828468i \(-0.310787\pi\)
0.560036 + 0.828468i \(0.310787\pi\)
\(182\) 40.2396 2.98276
\(183\) 19.6897 1.45550
\(184\) 4.24067 0.312626
\(185\) 17.0734 1.25526
\(186\) 15.1883 1.11366
\(187\) −0.780827 −0.0570997
\(188\) 3.93078 0.286682
\(189\) 2.43605 0.177197
\(190\) −57.1038 −4.14275
\(191\) −5.43991 −0.393618 −0.196809 0.980442i \(-0.563058\pi\)
−0.196809 + 0.980442i \(0.563058\pi\)
\(192\) 32.5359 2.34808
\(193\) −17.7693 −1.27906 −0.639531 0.768765i \(-0.720871\pi\)
−0.639531 + 0.768765i \(0.720871\pi\)
\(194\) −13.0419 −0.936356
\(195\) 43.0611 3.08367
\(196\) 29.8547 2.13248
\(197\) −5.54189 −0.394843 −0.197422 0.980319i \(-0.563257\pi\)
−0.197422 + 0.980319i \(0.563257\pi\)
\(198\) 1.58024 0.112303
\(199\) 14.3453 1.01691 0.508456 0.861088i \(-0.330217\pi\)
0.508456 + 0.861088i \(0.330217\pi\)
\(200\) −24.4688 −1.73021
\(201\) 19.0325 1.34245
\(202\) −15.9065 −1.11918
\(203\) −10.7654 −0.755584
\(204\) −27.1820 −1.90312
\(205\) 0.253919 0.0177345
\(206\) 24.3331 1.69537
\(207\) −5.92708 −0.411961
\(208\) −3.79609 −0.263211
\(209\) 1.40385 0.0971060
\(210\) 90.7161 6.26001
\(211\) 9.67793 0.666256 0.333128 0.942882i \(-0.391896\pi\)
0.333128 + 0.942882i \(0.391896\pi\)
\(212\) 36.2402 2.48899
\(213\) 36.9312 2.53049
\(214\) −37.8203 −2.58535
\(215\) −16.8318 −1.14792
\(216\) 1.37493 0.0935518
\(217\) −11.1258 −0.755270
\(218\) 9.92659 0.672313
\(219\) 32.9656 2.22761
\(220\) 2.60290 0.175488
\(221\) 15.6850 1.05509
\(222\) −24.2481 −1.62743
\(223\) 2.81404 0.188442 0.0942209 0.995551i \(-0.469964\pi\)
0.0942209 + 0.995551i \(0.469964\pi\)
\(224\) −27.0116 −1.80479
\(225\) 34.1995 2.27997
\(226\) 8.26033 0.549469
\(227\) 28.8944 1.91779 0.958896 0.283759i \(-0.0915816\pi\)
0.958896 + 0.283759i \(0.0915816\pi\)
\(228\) 48.8705 3.23652
\(229\) −19.9203 −1.31637 −0.658184 0.752857i \(-0.728675\pi\)
−0.658184 + 0.752857i \(0.728675\pi\)
\(230\) −16.2014 −1.06829
\(231\) −2.23017 −0.146735
\(232\) −6.07608 −0.398914
\(233\) 18.4574 1.20919 0.604593 0.796535i \(-0.293336\pi\)
0.604593 + 0.796535i \(0.293336\pi\)
\(234\) −31.7434 −2.07513
\(235\) −5.11343 −0.333564
\(236\) −24.1886 −1.57454
\(237\) 17.9978 1.16909
\(238\) 33.0434 2.14188
\(239\) 2.26363 0.146422 0.0732111 0.997316i \(-0.476675\pi\)
0.0732111 + 0.997316i \(0.476675\pi\)
\(240\) −8.55789 −0.552410
\(241\) −16.8340 −1.08437 −0.542186 0.840259i \(-0.682403\pi\)
−0.542186 + 0.840259i \(0.682403\pi\)
\(242\) 24.5706 1.57946
\(243\) 22.3367 1.43290
\(244\) −23.9079 −1.53055
\(245\) −38.8371 −2.48121
\(246\) −0.360624 −0.0229925
\(247\) −28.2000 −1.79432
\(248\) −6.27950 −0.398749
\(249\) −7.58176 −0.480475
\(250\) 49.2329 3.11376
\(251\) −4.45960 −0.281487 −0.140744 0.990046i \(-0.544949\pi\)
−0.140744 + 0.990046i \(0.544949\pi\)
\(252\) −40.2972 −2.53848
\(253\) 0.398298 0.0250408
\(254\) −14.2031 −0.891179
\(255\) 35.3603 2.21435
\(256\) −9.97749 −0.623593
\(257\) 7.52441 0.469360 0.234680 0.972073i \(-0.424596\pi\)
0.234680 + 0.972073i \(0.424596\pi\)
\(258\) 23.9051 1.48826
\(259\) 17.7624 1.10370
\(260\) −52.2863 −3.24266
\(261\) 8.49240 0.525666
\(262\) 5.41690 0.334657
\(263\) −15.4403 −0.952089 −0.476044 0.879421i \(-0.657930\pi\)
−0.476044 + 0.879421i \(0.657930\pi\)
\(264\) −1.25873 −0.0774693
\(265\) −47.1438 −2.89602
\(266\) −59.4085 −3.64257
\(267\) −35.3914 −2.16592
\(268\) −23.1099 −1.41166
\(269\) −3.00899 −0.183461 −0.0917306 0.995784i \(-0.529240\pi\)
−0.0917306 + 0.995784i \(0.529240\pi\)
\(270\) −5.25289 −0.319681
\(271\) 8.08179 0.490933 0.245467 0.969405i \(-0.421059\pi\)
0.245467 + 0.969405i \(0.421059\pi\)
\(272\) −3.11721 −0.189009
\(273\) 44.7990 2.71136
\(274\) 12.6549 0.764513
\(275\) −2.29819 −0.138586
\(276\) 13.8655 0.834604
\(277\) 9.27397 0.557219 0.278609 0.960404i \(-0.410127\pi\)
0.278609 + 0.960404i \(0.410127\pi\)
\(278\) 13.5001 0.809679
\(279\) 8.77671 0.525448
\(280\) −37.5061 −2.24142
\(281\) −9.25705 −0.552229 −0.276115 0.961125i \(-0.589047\pi\)
−0.276115 + 0.961125i \(0.589047\pi\)
\(282\) 7.26226 0.432461
\(283\) −6.96901 −0.414265 −0.207132 0.978313i \(-0.566413\pi\)
−0.207132 + 0.978313i \(0.566413\pi\)
\(284\) −44.8432 −2.66096
\(285\) −63.5741 −3.76580
\(286\) 2.13314 0.126135
\(287\) 0.264167 0.0155933
\(288\) 21.3084 1.25561
\(289\) −4.12002 −0.242354
\(290\) 23.2136 1.36315
\(291\) −14.5197 −0.851158
\(292\) −40.0280 −2.34246
\(293\) 24.4728 1.42972 0.714859 0.699269i \(-0.246491\pi\)
0.714859 + 0.699269i \(0.246491\pi\)
\(294\) 55.1577 3.21686
\(295\) 31.4662 1.83203
\(296\) 10.0253 0.582706
\(297\) 0.129138 0.00749332
\(298\) 32.8848 1.90496
\(299\) −8.00088 −0.462703
\(300\) −80.0043 −4.61905
\(301\) −17.5111 −1.00932
\(302\) 8.96196 0.515703
\(303\) −17.7088 −1.01734
\(304\) 5.60442 0.321436
\(305\) 31.1011 1.78084
\(306\) −26.0666 −1.49013
\(307\) 24.4598 1.39600 0.697998 0.716100i \(-0.254075\pi\)
0.697998 + 0.716100i \(0.254075\pi\)
\(308\) 2.70796 0.154300
\(309\) 27.0902 1.54111
\(310\) 23.9908 1.36259
\(311\) −2.24474 −0.127287 −0.0636437 0.997973i \(-0.520272\pi\)
−0.0636437 + 0.997973i \(0.520272\pi\)
\(312\) 25.2849 1.43148
\(313\) −22.3634 −1.26406 −0.632028 0.774945i \(-0.717777\pi\)
−0.632028 + 0.774945i \(0.717777\pi\)
\(314\) −46.5729 −2.62826
\(315\) 52.4214 2.95361
\(316\) −21.8536 −1.22936
\(317\) 17.8888 1.00473 0.502367 0.864655i \(-0.332463\pi\)
0.502367 + 0.864655i \(0.332463\pi\)
\(318\) 66.9551 3.75465
\(319\) −0.570686 −0.0319523
\(320\) 51.3925 2.87293
\(321\) −42.1057 −2.35011
\(322\) −16.8553 −0.939311
\(323\) −23.1569 −1.28848
\(324\) −24.9599 −1.38666
\(325\) 46.1654 2.56079
\(326\) 49.2285 2.72651
\(327\) 11.0513 0.611140
\(328\) 0.149098 0.00823255
\(329\) −5.31981 −0.293291
\(330\) 4.80896 0.264724
\(331\) 8.87253 0.487678 0.243839 0.969816i \(-0.421593\pi\)
0.243839 + 0.969816i \(0.421593\pi\)
\(332\) 9.20605 0.505247
\(333\) −14.0121 −0.767857
\(334\) 54.4530 2.97954
\(335\) 30.0630 1.64252
\(336\) −8.90328 −0.485714
\(337\) −27.0914 −1.47576 −0.737881 0.674931i \(-0.764173\pi\)
−0.737881 + 0.674931i \(0.764173\pi\)
\(338\) −13.6865 −0.744446
\(339\) 9.19628 0.499473
\(340\) −42.9357 −2.32852
\(341\) −0.589792 −0.0319390
\(342\) 46.8650 2.53417
\(343\) −11.6750 −0.630390
\(344\) −9.88342 −0.532878
\(345\) −18.0372 −0.971089
\(346\) −6.64344 −0.357154
\(347\) −1.34021 −0.0719465 −0.0359732 0.999353i \(-0.511453\pi\)
−0.0359732 + 0.999353i \(0.511453\pi\)
\(348\) −19.8666 −1.06496
\(349\) 3.80454 0.203652 0.101826 0.994802i \(-0.467531\pi\)
0.101826 + 0.994802i \(0.467531\pi\)
\(350\) 97.2558 5.19854
\(351\) −2.59408 −0.138462
\(352\) −1.43192 −0.0763213
\(353\) −19.4985 −1.03780 −0.518899 0.854835i \(-0.673658\pi\)
−0.518899 + 0.854835i \(0.673658\pi\)
\(354\) −44.6893 −2.37521
\(355\) 58.3352 3.09611
\(356\) 42.9735 2.27759
\(357\) 36.7874 1.94700
\(358\) 44.8179 2.36870
\(359\) −8.43354 −0.445105 −0.222553 0.974921i \(-0.571439\pi\)
−0.222553 + 0.974921i \(0.571439\pi\)
\(360\) 29.5870 1.55937
\(361\) 22.6336 1.19124
\(362\) −33.8050 −1.77675
\(363\) 27.3546 1.43574
\(364\) −54.3966 −2.85116
\(365\) 52.0712 2.72553
\(366\) −44.1707 −2.30884
\(367\) 9.63677 0.503035 0.251518 0.967853i \(-0.419070\pi\)
0.251518 + 0.967853i \(0.419070\pi\)
\(368\) 1.59008 0.0828888
\(369\) −0.208391 −0.0108484
\(370\) −38.3014 −1.99120
\(371\) −49.0465 −2.54637
\(372\) −20.5317 −1.06452
\(373\) −30.8966 −1.59977 −0.799883 0.600156i \(-0.795105\pi\)
−0.799883 + 0.600156i \(0.795105\pi\)
\(374\) 1.75166 0.0905764
\(375\) 54.8114 2.83045
\(376\) −3.00254 −0.154844
\(377\) 11.4638 0.590414
\(378\) −5.46490 −0.281084
\(379\) −18.4952 −0.950034 −0.475017 0.879977i \(-0.657558\pi\)
−0.475017 + 0.879977i \(0.657558\pi\)
\(380\) 77.1939 3.95996
\(381\) −15.8124 −0.810092
\(382\) 12.2036 0.624390
\(383\) 37.2166 1.90168 0.950840 0.309683i \(-0.100223\pi\)
0.950840 + 0.309683i \(0.100223\pi\)
\(384\) −40.1146 −2.04709
\(385\) −3.52270 −0.179533
\(386\) 39.8626 2.02895
\(387\) 13.8138 0.702196
\(388\) 17.6303 0.895043
\(389\) 26.6153 1.34945 0.674725 0.738070i \(-0.264262\pi\)
0.674725 + 0.738070i \(0.264262\pi\)
\(390\) −96.6008 −4.89157
\(391\) −6.57005 −0.332262
\(392\) −22.8046 −1.15181
\(393\) 6.03068 0.304207
\(394\) 12.4324 0.626333
\(395\) 28.4287 1.43040
\(396\) −2.13620 −0.107348
\(397\) −23.9554 −1.20229 −0.601144 0.799140i \(-0.705288\pi\)
−0.601144 + 0.799140i \(0.705288\pi\)
\(398\) −32.1814 −1.61311
\(399\) −66.1399 −3.31114
\(400\) −9.17483 −0.458742
\(401\) 26.8213 1.33939 0.669697 0.742634i \(-0.266424\pi\)
0.669697 + 0.742634i \(0.266424\pi\)
\(402\) −42.6964 −2.12950
\(403\) 11.8476 0.590169
\(404\) 21.5026 1.06980
\(405\) 32.4696 1.61343
\(406\) 24.1505 1.19857
\(407\) 0.941606 0.0466737
\(408\) 20.7631 1.02793
\(409\) 5.53512 0.273694 0.136847 0.990592i \(-0.456303\pi\)
0.136847 + 0.990592i \(0.456303\pi\)
\(410\) −0.569628 −0.0281319
\(411\) 14.0888 0.694950
\(412\) −32.8939 −1.62057
\(413\) 32.7361 1.61084
\(414\) 13.2965 0.653487
\(415\) −11.9759 −0.587872
\(416\) 28.7639 1.41026
\(417\) 15.0297 0.736008
\(418\) −3.14931 −0.154038
\(419\) −36.4214 −1.77930 −0.889652 0.456639i \(-0.849053\pi\)
−0.889652 + 0.456639i \(0.849053\pi\)
\(420\) −122.632 −5.98381
\(421\) 15.9599 0.777837 0.388919 0.921272i \(-0.372849\pi\)
0.388919 + 0.921272i \(0.372849\pi\)
\(422\) −21.7109 −1.05687
\(423\) 4.19658 0.204045
\(424\) −27.6822 −1.34437
\(425\) 37.9094 1.83888
\(426\) −82.8494 −4.01407
\(427\) 32.3563 1.56583
\(428\) 51.1262 2.47128
\(429\) 2.37484 0.114659
\(430\) 37.7595 1.82093
\(431\) −22.6199 −1.08956 −0.544782 0.838578i \(-0.683387\pi\)
−0.544782 + 0.838578i \(0.683387\pi\)
\(432\) 0.515542 0.0248040
\(433\) −32.1318 −1.54415 −0.772077 0.635529i \(-0.780782\pi\)
−0.772077 + 0.635529i \(0.780782\pi\)
\(434\) 24.9590 1.19807
\(435\) 25.8439 1.23912
\(436\) −13.4189 −0.642650
\(437\) 11.8123 0.565057
\(438\) −73.9531 −3.53362
\(439\) 29.8089 1.42270 0.711351 0.702837i \(-0.248084\pi\)
0.711351 + 0.702837i \(0.248084\pi\)
\(440\) −1.98824 −0.0947855
\(441\) 31.8735 1.51779
\(442\) −35.1869 −1.67367
\(443\) −19.0668 −0.905893 −0.452947 0.891538i \(-0.649627\pi\)
−0.452947 + 0.891538i \(0.649627\pi\)
\(444\) 32.7790 1.55562
\(445\) −55.9030 −2.65005
\(446\) −6.31285 −0.298922
\(447\) 36.6108 1.73163
\(448\) 53.4667 2.52606
\(449\) 1.13547 0.0535862 0.0267931 0.999641i \(-0.491470\pi\)
0.0267931 + 0.999641i \(0.491470\pi\)
\(450\) −76.7212 −3.61667
\(451\) 0.0140038 0.000659412 0
\(452\) −11.1664 −0.525226
\(453\) 9.97741 0.468780
\(454\) −64.8201 −3.04216
\(455\) 70.7628 3.31741
\(456\) −37.3299 −1.74813
\(457\) −24.0864 −1.12672 −0.563358 0.826213i \(-0.690491\pi\)
−0.563358 + 0.826213i \(0.690491\pi\)
\(458\) 44.6880 2.08813
\(459\) −2.13016 −0.0994276
\(460\) 21.9014 1.02116
\(461\) 20.6878 0.963525 0.481762 0.876302i \(-0.339997\pi\)
0.481762 + 0.876302i \(0.339997\pi\)
\(462\) 5.00304 0.232763
\(463\) 35.3155 1.64125 0.820624 0.571468i \(-0.193626\pi\)
0.820624 + 0.571468i \(0.193626\pi\)
\(464\) −2.27829 −0.105767
\(465\) 26.7091 1.23861
\(466\) −41.4063 −1.91811
\(467\) 10.0664 0.465815 0.232908 0.972499i \(-0.425176\pi\)
0.232908 + 0.972499i \(0.425176\pi\)
\(468\) 42.9113 1.98357
\(469\) 31.2763 1.44421
\(470\) 11.4712 0.529126
\(471\) −51.8499 −2.38912
\(472\) 18.4765 0.850451
\(473\) −0.928284 −0.0426825
\(474\) −40.3753 −1.85450
\(475\) −68.1571 −3.12726
\(476\) −44.6686 −2.04738
\(477\) 38.6908 1.77153
\(478\) −5.07810 −0.232267
\(479\) 17.2022 0.785988 0.392994 0.919541i \(-0.371439\pi\)
0.392994 + 0.919541i \(0.371439\pi\)
\(480\) 64.8452 2.95977
\(481\) −18.9147 −0.862435
\(482\) 37.7644 1.72012
\(483\) −18.7652 −0.853844
\(484\) −33.2149 −1.50977
\(485\) −22.9347 −1.04141
\(486\) −50.1089 −2.27299
\(487\) 13.3144 0.603331 0.301665 0.953414i \(-0.402457\pi\)
0.301665 + 0.953414i \(0.402457\pi\)
\(488\) 18.2622 0.826689
\(489\) 54.8064 2.47843
\(490\) 87.1249 3.93590
\(491\) 12.8657 0.580623 0.290311 0.956932i \(-0.406241\pi\)
0.290311 + 0.956932i \(0.406241\pi\)
\(492\) 0.487497 0.0219781
\(493\) 9.41364 0.423969
\(494\) 63.2623 2.84631
\(495\) 2.77891 0.124903
\(496\) −2.35456 −0.105723
\(497\) 60.6896 2.72230
\(498\) 17.0085 0.762169
\(499\) 29.8390 1.33578 0.667888 0.744262i \(-0.267199\pi\)
0.667888 + 0.744262i \(0.267199\pi\)
\(500\) −66.5539 −2.97638
\(501\) 60.6229 2.70843
\(502\) 10.0044 0.446519
\(503\) −35.8234 −1.59729 −0.798643 0.601806i \(-0.794448\pi\)
−0.798643 + 0.601806i \(0.794448\pi\)
\(504\) 30.7811 1.37110
\(505\) −27.9721 −1.24474
\(506\) −0.893519 −0.0397218
\(507\) −15.2372 −0.676710
\(508\) 19.1999 0.851860
\(509\) 30.3538 1.34541 0.672704 0.739912i \(-0.265133\pi\)
0.672704 + 0.739912i \(0.265133\pi\)
\(510\) −79.3252 −3.51258
\(511\) 54.1728 2.39646
\(512\) −9.74052 −0.430474
\(513\) 3.82981 0.169090
\(514\) −16.8798 −0.744538
\(515\) 42.7907 1.88558
\(516\) −32.3153 −1.42260
\(517\) −0.282009 −0.0124027
\(518\) −39.8472 −1.75079
\(519\) −7.39619 −0.324657
\(520\) 39.9391 1.75145
\(521\) −16.8857 −0.739778 −0.369889 0.929076i \(-0.620604\pi\)
−0.369889 + 0.929076i \(0.620604\pi\)
\(522\) −19.0514 −0.833855
\(523\) −14.6739 −0.641644 −0.320822 0.947140i \(-0.603959\pi\)
−0.320822 + 0.947140i \(0.603959\pi\)
\(524\) −7.32266 −0.319892
\(525\) 108.276 4.72553
\(526\) 34.6379 1.51028
\(527\) 9.72880 0.423793
\(528\) −0.471972 −0.0205400
\(529\) −19.6486 −0.854289
\(530\) 105.760 4.59391
\(531\) −25.8242 −1.12068
\(532\) 80.3094 3.48185
\(533\) −0.281303 −0.0121846
\(534\) 79.3951 3.43576
\(535\) −66.5085 −2.87541
\(536\) 17.6526 0.762476
\(537\) 49.8961 2.15318
\(538\) 6.75020 0.291022
\(539\) −2.14189 −0.0922576
\(540\) 7.10095 0.305576
\(541\) −19.3417 −0.831565 −0.415782 0.909464i \(-0.636492\pi\)
−0.415782 + 0.909464i \(0.636492\pi\)
\(542\) −18.1302 −0.778760
\(543\) −37.6354 −1.61509
\(544\) 23.6199 1.01269
\(545\) 17.4563 0.747745
\(546\) −100.500 −4.30099
\(547\) −9.67779 −0.413793 −0.206896 0.978363i \(-0.566336\pi\)
−0.206896 + 0.978363i \(0.566336\pi\)
\(548\) −17.1072 −0.730781
\(549\) −25.5246 −1.08936
\(550\) 5.15564 0.219837
\(551\) −16.9247 −0.721018
\(552\) −10.5912 −0.450791
\(553\) 29.5761 1.25770
\(554\) −20.8047 −0.883907
\(555\) −42.6412 −1.81002
\(556\) −18.2496 −0.773955
\(557\) −15.9441 −0.675573 −0.337786 0.941223i \(-0.609678\pi\)
−0.337786 + 0.941223i \(0.609678\pi\)
\(558\) −19.6892 −0.833509
\(559\) 18.6471 0.788687
\(560\) −14.0633 −0.594282
\(561\) 1.95014 0.0823349
\(562\) 20.7667 0.875992
\(563\) 0.201349 0.00848584 0.00424292 0.999991i \(-0.498649\pi\)
0.00424292 + 0.999991i \(0.498649\pi\)
\(564\) −9.81725 −0.413381
\(565\) 14.5261 0.611117
\(566\) 15.6339 0.657141
\(567\) 33.7800 1.41863
\(568\) 34.2537 1.43725
\(569\) 19.8581 0.832497 0.416248 0.909251i \(-0.363345\pi\)
0.416248 + 0.909251i \(0.363345\pi\)
\(570\) 142.618 5.97363
\(571\) −20.0192 −0.837776 −0.418888 0.908038i \(-0.637580\pi\)
−0.418888 + 0.908038i \(0.637580\pi\)
\(572\) −2.88362 −0.120570
\(573\) 13.5863 0.567578
\(574\) −0.592617 −0.0247354
\(575\) −19.3375 −0.806429
\(576\) −42.1777 −1.75740
\(577\) −3.12079 −0.129920 −0.0649601 0.997888i \(-0.520692\pi\)
−0.0649601 + 0.997888i \(0.520692\pi\)
\(578\) 9.24261 0.384442
\(579\) 44.3793 1.84434
\(580\) −31.3806 −1.30301
\(581\) −12.4592 −0.516895
\(582\) 32.5726 1.35018
\(583\) −2.60001 −0.107681
\(584\) 30.5755 1.26522
\(585\) −55.8219 −2.30795
\(586\) −54.9010 −2.26794
\(587\) −4.82351 −0.199088 −0.0995438 0.995033i \(-0.531738\pi\)
−0.0995438 + 0.995033i \(0.531738\pi\)
\(588\) −74.5631 −3.07493
\(589\) −17.4914 −0.720719
\(590\) −70.5895 −2.90612
\(591\) 13.8410 0.569344
\(592\) 3.75907 0.154497
\(593\) −26.8403 −1.10220 −0.551100 0.834439i \(-0.685792\pi\)
−0.551100 + 0.834439i \(0.685792\pi\)
\(594\) −0.289700 −0.0118865
\(595\) 58.1080 2.38219
\(596\) −44.4542 −1.82091
\(597\) −35.8278 −1.46634
\(598\) 17.9487 0.733978
\(599\) −38.7869 −1.58479 −0.792394 0.610010i \(-0.791166\pi\)
−0.792394 + 0.610010i \(0.791166\pi\)
\(600\) 61.1116 2.49487
\(601\) 16.8284 0.686444 0.343222 0.939254i \(-0.388482\pi\)
0.343222 + 0.939254i \(0.388482\pi\)
\(602\) 39.2835 1.60108
\(603\) −24.6726 −1.00475
\(604\) −12.1149 −0.492950
\(605\) 43.2083 1.75667
\(606\) 39.7269 1.61379
\(607\) −17.7468 −0.720320 −0.360160 0.932891i \(-0.617278\pi\)
−0.360160 + 0.932891i \(0.617278\pi\)
\(608\) −42.4661 −1.72223
\(609\) 26.8869 1.08951
\(610\) −69.7704 −2.82492
\(611\) 5.66490 0.229177
\(612\) 35.2372 1.42438
\(613\) −3.15716 −0.127517 −0.0637583 0.997965i \(-0.520309\pi\)
−0.0637583 + 0.997965i \(0.520309\pi\)
\(614\) −54.8718 −2.21444
\(615\) −0.634170 −0.0255722
\(616\) −2.06848 −0.0833415
\(617\) −8.88355 −0.357638 −0.178819 0.983882i \(-0.557228\pi\)
−0.178819 + 0.983882i \(0.557228\pi\)
\(618\) −60.7727 −2.44464
\(619\) −24.4870 −0.984218 −0.492109 0.870534i \(-0.663774\pi\)
−0.492109 + 0.870534i \(0.663774\pi\)
\(620\) −32.4312 −1.30247
\(621\) 1.08659 0.0436034
\(622\) 5.03571 0.201914
\(623\) −58.1592 −2.33010
\(624\) 9.48084 0.379537
\(625\) 33.7627 1.35051
\(626\) 50.1689 2.00515
\(627\) −3.50615 −0.140022
\(628\) 62.9581 2.51230
\(629\) −15.5321 −0.619304
\(630\) −117.599 −4.68526
\(631\) 7.41375 0.295137 0.147568 0.989052i \(-0.452855\pi\)
0.147568 + 0.989052i \(0.452855\pi\)
\(632\) 16.6930 0.664011
\(633\) −24.1709 −0.960708
\(634\) −40.1307 −1.59379
\(635\) −24.9766 −0.991167
\(636\) −90.5110 −3.58900
\(637\) 43.0256 1.70474
\(638\) 1.28024 0.0506854
\(639\) −47.8755 −1.89393
\(640\) −63.3636 −2.50467
\(641\) −19.5533 −0.772310 −0.386155 0.922434i \(-0.626197\pi\)
−0.386155 + 0.922434i \(0.626197\pi\)
\(642\) 94.4574 3.72794
\(643\) −46.4522 −1.83189 −0.915947 0.401299i \(-0.868559\pi\)
−0.915947 + 0.401299i \(0.868559\pi\)
\(644\) 22.7853 0.897867
\(645\) 42.0379 1.65524
\(646\) 51.9488 2.04390
\(647\) 38.6524 1.51958 0.759791 0.650168i \(-0.225301\pi\)
0.759791 + 0.650168i \(0.225301\pi\)
\(648\) 19.0657 0.748972
\(649\) 1.73538 0.0681195
\(650\) −103.565 −4.06215
\(651\) 27.7871 1.08906
\(652\) −66.5479 −2.60622
\(653\) −43.6034 −1.70633 −0.853167 0.521637i \(-0.825321\pi\)
−0.853167 + 0.521637i \(0.825321\pi\)
\(654\) −24.7919 −0.969442
\(655\) 9.52583 0.372205
\(656\) 0.0559058 0.00218275
\(657\) −42.7347 −1.66724
\(658\) 11.9342 0.465242
\(659\) 17.4086 0.678142 0.339071 0.940761i \(-0.389887\pi\)
0.339071 + 0.940761i \(0.389887\pi\)
\(660\) −6.50083 −0.253044
\(661\) −39.8828 −1.55126 −0.775631 0.631187i \(-0.782568\pi\)
−0.775631 + 0.631187i \(0.782568\pi\)
\(662\) −19.9041 −0.773596
\(663\) −39.1738 −1.52138
\(664\) −7.03207 −0.272897
\(665\) −104.472 −4.05125
\(666\) 31.4339 1.21804
\(667\) −4.80187 −0.185929
\(668\) −73.6105 −2.84808
\(669\) −7.02814 −0.271724
\(670\) −67.4416 −2.60550
\(671\) 1.71524 0.0662162
\(672\) 67.4623 2.60242
\(673\) 15.7869 0.608539 0.304269 0.952586i \(-0.401588\pi\)
0.304269 + 0.952586i \(0.401588\pi\)
\(674\) 60.7753 2.34098
\(675\) −6.26967 −0.241320
\(676\) 18.5016 0.711600
\(677\) 31.3896 1.20640 0.603200 0.797590i \(-0.293892\pi\)
0.603200 + 0.797590i \(0.293892\pi\)
\(678\) −20.6304 −0.792306
\(679\) −23.8604 −0.915676
\(680\) 32.7966 1.25769
\(681\) −72.1647 −2.76536
\(682\) 1.32311 0.0506643
\(683\) 15.9637 0.610835 0.305418 0.952218i \(-0.401204\pi\)
0.305418 + 0.952218i \(0.401204\pi\)
\(684\) −63.3528 −2.42236
\(685\) 22.2542 0.850288
\(686\) 26.1910 0.999978
\(687\) 49.7514 1.89814
\(688\) −3.70589 −0.141286
\(689\) 52.2281 1.98973
\(690\) 40.4636 1.54042
\(691\) −19.6577 −0.747812 −0.373906 0.927467i \(-0.621982\pi\)
−0.373906 + 0.927467i \(0.621982\pi\)
\(692\) 8.98072 0.341396
\(693\) 2.89107 0.109823
\(694\) 3.00656 0.114127
\(695\) 23.7403 0.900522
\(696\) 15.1752 0.575214
\(697\) −0.230997 −0.00874962
\(698\) −8.53489 −0.323050
\(699\) −46.0979 −1.74358
\(700\) −131.472 −4.96918
\(701\) −15.1876 −0.573629 −0.286815 0.957986i \(-0.592596\pi\)
−0.286815 + 0.957986i \(0.592596\pi\)
\(702\) 5.81940 0.219639
\(703\) 27.9250 1.05321
\(704\) 2.83433 0.106823
\(705\) 12.7710 0.480982
\(706\) 43.7417 1.64624
\(707\) −29.1011 −1.09446
\(708\) 60.4117 2.27041
\(709\) 46.4836 1.74573 0.872864 0.487964i \(-0.162260\pi\)
0.872864 + 0.487964i \(0.162260\pi\)
\(710\) −130.866 −4.91131
\(711\) −23.3314 −0.874995
\(712\) −32.8255 −1.23019
\(713\) −4.96263 −0.185852
\(714\) −82.5268 −3.08849
\(715\) 3.75121 0.140287
\(716\) −60.5856 −2.26419
\(717\) −5.65349 −0.211133
\(718\) 18.9193 0.706063
\(719\) −13.3143 −0.496540 −0.248270 0.968691i \(-0.579862\pi\)
−0.248270 + 0.968691i \(0.579862\pi\)
\(720\) 11.0940 0.413447
\(721\) 44.5177 1.65793
\(722\) −50.7750 −1.88965
\(723\) 42.0434 1.56361
\(724\) 45.6982 1.69836
\(725\) 27.7070 1.02901
\(726\) −61.3658 −2.27750
\(727\) 18.1740 0.674035 0.337018 0.941498i \(-0.390582\pi\)
0.337018 + 0.941498i \(0.390582\pi\)
\(728\) 41.5510 1.53998
\(729\) −31.0949 −1.15166
\(730\) −116.814 −4.32346
\(731\) 15.3123 0.566347
\(732\) 59.7108 2.20697
\(733\) 19.5452 0.721920 0.360960 0.932581i \(-0.382449\pi\)
0.360960 + 0.932581i \(0.382449\pi\)
\(734\) −21.6186 −0.797957
\(735\) 96.9968 3.57778
\(736\) −12.0484 −0.444111
\(737\) 1.65799 0.0610729
\(738\) 0.467492 0.0172086
\(739\) −25.0554 −0.921677 −0.460838 0.887484i \(-0.652451\pi\)
−0.460838 + 0.887484i \(0.652451\pi\)
\(740\) 51.7765 1.90334
\(741\) 70.4304 2.58732
\(742\) 110.028 4.03926
\(743\) 29.9220 1.09773 0.548865 0.835911i \(-0.315060\pi\)
0.548865 + 0.835911i \(0.315060\pi\)
\(744\) 15.6832 0.574975
\(745\) 57.8291 2.11869
\(746\) 69.3117 2.53768
\(747\) 9.82856 0.359608
\(748\) −2.36793 −0.0865800
\(749\) −69.1927 −2.52825
\(750\) −122.961 −4.48989
\(751\) −4.28158 −0.156237 −0.0781186 0.996944i \(-0.524891\pi\)
−0.0781186 + 0.996944i \(0.524891\pi\)
\(752\) −1.12583 −0.0410549
\(753\) 11.1380 0.405890
\(754\) −25.7171 −0.936563
\(755\) 15.7599 0.573563
\(756\) 7.38754 0.268682
\(757\) 49.2188 1.78889 0.894444 0.447179i \(-0.147571\pi\)
0.894444 + 0.447179i \(0.147571\pi\)
\(758\) 41.4911 1.50702
\(759\) −0.994761 −0.0361075
\(760\) −58.9648 −2.13888
\(761\) −7.52454 −0.272764 −0.136382 0.990656i \(-0.543547\pi\)
−0.136382 + 0.990656i \(0.543547\pi\)
\(762\) 35.4726 1.28504
\(763\) 18.1608 0.657465
\(764\) −16.4970 −0.596841
\(765\) −45.8390 −1.65731
\(766\) −83.4896 −3.01660
\(767\) −34.8597 −1.25871
\(768\) 24.9191 0.899190
\(769\) 0.374850 0.0135174 0.00675871 0.999977i \(-0.497849\pi\)
0.00675871 + 0.999977i \(0.497849\pi\)
\(770\) 7.90262 0.284791
\(771\) −18.7924 −0.676793
\(772\) −53.8870 −1.93943
\(773\) −11.4720 −0.412621 −0.206310 0.978487i \(-0.566146\pi\)
−0.206310 + 0.978487i \(0.566146\pi\)
\(774\) −30.9892 −1.11388
\(775\) 28.6346 1.02858
\(776\) −13.4670 −0.483436
\(777\) −44.3622 −1.59149
\(778\) −59.7073 −2.14061
\(779\) 0.415308 0.0148799
\(780\) 130.587 4.67575
\(781\) 3.21722 0.115121
\(782\) 14.7389 0.527061
\(783\) −1.55688 −0.0556384
\(784\) −8.55083 −0.305387
\(785\) −81.9002 −2.92314
\(786\) −13.5289 −0.482559
\(787\) 18.4569 0.657918 0.328959 0.944344i \(-0.393302\pi\)
0.328959 + 0.944344i \(0.393302\pi\)
\(788\) −16.8063 −0.598699
\(789\) 38.5626 1.37286
\(790\) −63.7754 −2.26903
\(791\) 15.1124 0.537333
\(792\) 1.63174 0.0579814
\(793\) −34.4553 −1.22354
\(794\) 53.7403 1.90717
\(795\) 117.743 4.17591
\(796\) 43.5034 1.54194
\(797\) −32.4634 −1.14991 −0.574957 0.818184i \(-0.694981\pi\)
−0.574957 + 0.818184i \(0.694981\pi\)
\(798\) 148.374 5.25240
\(799\) 4.65182 0.164570
\(800\) 69.5199 2.45790
\(801\) 45.8794 1.62107
\(802\) −60.1695 −2.12466
\(803\) 2.87176 0.101342
\(804\) 57.7177 2.03555
\(805\) −29.6407 −1.04470
\(806\) −26.5781 −0.936175
\(807\) 7.51504 0.264542
\(808\) −16.4249 −0.577825
\(809\) −55.3352 −1.94548 −0.972741 0.231896i \(-0.925507\pi\)
−0.972741 + 0.231896i \(0.925507\pi\)
\(810\) −72.8404 −2.55935
\(811\) 10.8280 0.380223 0.190112 0.981763i \(-0.439115\pi\)
0.190112 + 0.981763i \(0.439115\pi\)
\(812\) −32.6471 −1.14569
\(813\) −20.1845 −0.707901
\(814\) −2.11234 −0.0740376
\(815\) 86.5701 3.03242
\(816\) 7.78533 0.272541
\(817\) −27.5300 −0.963151
\(818\) −12.4172 −0.434157
\(819\) −58.0749 −2.02930
\(820\) 0.770032 0.0268907
\(821\) −30.5709 −1.06693 −0.533466 0.845822i \(-0.679111\pi\)
−0.533466 + 0.845822i \(0.679111\pi\)
\(822\) −31.6061 −1.10239
\(823\) 8.63633 0.301043 0.150522 0.988607i \(-0.451905\pi\)
0.150522 + 0.988607i \(0.451905\pi\)
\(824\) 25.1261 0.875310
\(825\) 5.73980 0.199834
\(826\) −73.4384 −2.55525
\(827\) 50.5086 1.75636 0.878178 0.478334i \(-0.158759\pi\)
0.878178 + 0.478334i \(0.158759\pi\)
\(828\) −17.9744 −0.624654
\(829\) 26.4181 0.917538 0.458769 0.888556i \(-0.348291\pi\)
0.458769 + 0.888556i \(0.348291\pi\)
\(830\) 26.8660 0.932531
\(831\) −23.1620 −0.803481
\(832\) −56.9351 −1.97387
\(833\) 35.3311 1.22415
\(834\) −33.7168 −1.16752
\(835\) 95.7577 3.31383
\(836\) 4.25729 0.147241
\(837\) −1.60900 −0.0556153
\(838\) 81.7058 2.82248
\(839\) −4.39345 −0.151679 −0.0758393 0.997120i \(-0.524164\pi\)
−0.0758393 + 0.997120i \(0.524164\pi\)
\(840\) 93.6726 3.23201
\(841\) −22.1198 −0.762753
\(842\) −35.8035 −1.23387
\(843\) 23.1197 0.796286
\(844\) 29.3492 1.01024
\(845\) −24.0682 −0.827970
\(846\) −9.41438 −0.323673
\(847\) 44.9522 1.54457
\(848\) −10.3797 −0.356441
\(849\) 17.4053 0.597349
\(850\) −85.0438 −2.91698
\(851\) 7.92287 0.271592
\(852\) 111.997 3.83696
\(853\) 24.2441 0.830103 0.415051 0.909798i \(-0.363764\pi\)
0.415051 + 0.909798i \(0.363764\pi\)
\(854\) −72.5863 −2.48385
\(855\) 82.4138 2.81849
\(856\) −39.0529 −1.33480
\(857\) −3.71754 −0.126989 −0.0634943 0.997982i \(-0.520224\pi\)
−0.0634943 + 0.997982i \(0.520224\pi\)
\(858\) −5.32759 −0.181881
\(859\) 17.3165 0.590830 0.295415 0.955369i \(-0.404542\pi\)
0.295415 + 0.955369i \(0.404542\pi\)
\(860\) −51.0440 −1.74059
\(861\) −0.659765 −0.0224847
\(862\) 50.7442 1.72836
\(863\) 9.98843 0.340010 0.170005 0.985443i \(-0.445622\pi\)
0.170005 + 0.985443i \(0.445622\pi\)
\(864\) −3.90639 −0.132898
\(865\) −11.6827 −0.397225
\(866\) 72.0826 2.44947
\(867\) 10.2899 0.349462
\(868\) −33.7401 −1.14521
\(869\) 1.56786 0.0531860
\(870\) −57.9767 −1.96559
\(871\) −33.3052 −1.12850
\(872\) 10.2501 0.347112
\(873\) 18.8225 0.637044
\(874\) −26.4989 −0.896340
\(875\) 90.0722 3.04500
\(876\) 99.9711 3.37771
\(877\) 5.81447 0.196341 0.0981703 0.995170i \(-0.468701\pi\)
0.0981703 + 0.995170i \(0.468701\pi\)
\(878\) −66.8717 −2.25681
\(879\) −61.1216 −2.06158
\(880\) −0.745510 −0.0251311
\(881\) −1.24996 −0.0421122 −0.0210561 0.999778i \(-0.506703\pi\)
−0.0210561 + 0.999778i \(0.506703\pi\)
\(882\) −71.5032 −2.40764
\(883\) −9.29759 −0.312889 −0.156444 0.987687i \(-0.550003\pi\)
−0.156444 + 0.987687i \(0.550003\pi\)
\(884\) 47.5662 1.59982
\(885\) −78.5877 −2.64170
\(886\) 42.7735 1.43700
\(887\) −44.9923 −1.51069 −0.755347 0.655324i \(-0.772532\pi\)
−0.755347 + 0.655324i \(0.772532\pi\)
\(888\) −25.0384 −0.840233
\(889\) −25.9847 −0.871497
\(890\) 125.410 4.20374
\(891\) 1.79072 0.0599912
\(892\) 8.53382 0.285733
\(893\) −8.36349 −0.279873
\(894\) −82.1307 −2.74686
\(895\) 78.8140 2.63446
\(896\) −65.9209 −2.20226
\(897\) 19.9824 0.667194
\(898\) −2.54725 −0.0850030
\(899\) 7.11052 0.237149
\(900\) 103.713 3.45710
\(901\) 42.8879 1.42880
\(902\) −0.0314153 −0.00104601
\(903\) 43.7346 1.45540
\(904\) 8.52953 0.283688
\(905\) −59.4474 −1.97610
\(906\) −22.3828 −0.743618
\(907\) 1.46191 0.0485418 0.0242709 0.999705i \(-0.492274\pi\)
0.0242709 + 0.999705i \(0.492274\pi\)
\(908\) 87.6250 2.90794
\(909\) 22.9567 0.761424
\(910\) −158.745 −5.26236
\(911\) −28.2872 −0.937195 −0.468598 0.883412i \(-0.655241\pi\)
−0.468598 + 0.883412i \(0.655241\pi\)
\(912\) −13.9972 −0.463494
\(913\) −0.660475 −0.0218585
\(914\) 54.0341 1.78729
\(915\) −77.6759 −2.56789
\(916\) −60.4100 −1.99600
\(917\) 9.91029 0.327266
\(918\) 4.77869 0.157720
\(919\) −37.4941 −1.23682 −0.618408 0.785857i \(-0.712222\pi\)
−0.618408 + 0.785857i \(0.712222\pi\)
\(920\) −16.7295 −0.551554
\(921\) −61.0891 −2.01295
\(922\) −46.4097 −1.52842
\(923\) −64.6265 −2.12721
\(924\) −6.76320 −0.222493
\(925\) −45.7152 −1.50311
\(926\) −79.2247 −2.60349
\(927\) −35.1182 −1.15343
\(928\) 17.2631 0.566690
\(929\) 50.0552 1.64226 0.821129 0.570742i \(-0.193345\pi\)
0.821129 + 0.570742i \(0.193345\pi\)
\(930\) −59.9177 −1.96478
\(931\) −63.5216 −2.08184
\(932\) 55.9738 1.83348
\(933\) 5.60630 0.183542
\(934\) −22.5823 −0.738915
\(935\) 3.08037 0.100739
\(936\) −32.7779 −1.07138
\(937\) −3.71842 −0.121476 −0.0607378 0.998154i \(-0.519345\pi\)
−0.0607378 + 0.998154i \(0.519345\pi\)
\(938\) −70.1635 −2.29092
\(939\) 55.8533 1.82271
\(940\) −15.5069 −0.505781
\(941\) −31.5735 −1.02927 −0.514634 0.857410i \(-0.672072\pi\)
−0.514634 + 0.857410i \(0.672072\pi\)
\(942\) 116.317 3.78982
\(943\) 0.117831 0.00383710
\(944\) 6.92796 0.225486
\(945\) −9.61022 −0.312621
\(946\) 2.08246 0.0677066
\(947\) 5.42150 0.176175 0.0880875 0.996113i \(-0.471924\pi\)
0.0880875 + 0.996113i \(0.471924\pi\)
\(948\) 54.5801 1.77268
\(949\) −57.6869 −1.87260
\(950\) 152.900 4.96073
\(951\) −44.6777 −1.44877
\(952\) 34.1202 1.10584
\(953\) 38.3285 1.24158 0.620790 0.783977i \(-0.286812\pi\)
0.620790 + 0.783977i \(0.286812\pi\)
\(954\) −86.7967 −2.81015
\(955\) 21.4605 0.694445
\(956\) 6.86467 0.222019
\(957\) 1.42530 0.0460736
\(958\) −38.5904 −1.24680
\(959\) 23.1523 0.747628
\(960\) −128.354 −4.14262
\(961\) −23.6514 −0.762949
\(962\) 42.4321 1.36807
\(963\) 54.5833 1.75892
\(964\) −51.0505 −1.64423
\(965\) 70.0999 2.25660
\(966\) 42.0967 1.35444
\(967\) −52.5425 −1.68965 −0.844827 0.535040i \(-0.820297\pi\)
−0.844827 + 0.535040i \(0.820297\pi\)
\(968\) 25.3713 0.815466
\(969\) 57.8349 1.85793
\(970\) 51.4505 1.65197
\(971\) −14.7274 −0.472624 −0.236312 0.971677i \(-0.575939\pi\)
−0.236312 + 0.971677i \(0.575939\pi\)
\(972\) 67.7381 2.17270
\(973\) 24.6985 0.791797
\(974\) −29.8687 −0.957054
\(975\) −115.299 −3.69254
\(976\) 6.84758 0.219186
\(977\) 46.0163 1.47219 0.736097 0.676876i \(-0.236667\pi\)
0.736097 + 0.676876i \(0.236667\pi\)
\(978\) −122.950 −3.93149
\(979\) −3.08308 −0.0985356
\(980\) −117.777 −3.76225
\(981\) −14.3263 −0.457404
\(982\) −28.8623 −0.921032
\(983\) −6.11824 −0.195142 −0.0975708 0.995229i \(-0.531107\pi\)
−0.0975708 + 0.995229i \(0.531107\pi\)
\(984\) −0.372376 −0.0118709
\(985\) 21.8628 0.696605
\(986\) −21.1180 −0.672535
\(987\) 13.2864 0.422910
\(988\) −85.5191 −2.72072
\(989\) −7.81078 −0.248368
\(990\) −6.23406 −0.198131
\(991\) 6.03667 0.191761 0.0958806 0.995393i \(-0.469433\pi\)
0.0958806 + 0.995393i \(0.469433\pi\)
\(992\) 17.8411 0.566455
\(993\) −22.1594 −0.703207
\(994\) −136.148 −4.31834
\(995\) −56.5923 −1.79410
\(996\) −22.9924 −0.728541
\(997\) −40.5370 −1.28382 −0.641910 0.766780i \(-0.721858\pi\)
−0.641910 + 0.766780i \(0.721858\pi\)
\(998\) −66.9391 −2.11892
\(999\) 2.56878 0.0812727
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 4027.2.a.c.1.20 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.20 174 1.1 even 1 trivial