Properties

Label 8007.2.a.f.1.22
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.22
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.240024 q^{2} -1.00000 q^{3} -1.94239 q^{4} -0.991325 q^{5} +0.240024 q^{6} +2.53606 q^{7} +0.946267 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.240024 q^{2} -1.00000 q^{3} -1.94239 q^{4} -0.991325 q^{5} +0.240024 q^{6} +2.53606 q^{7} +0.946267 q^{8} +1.00000 q^{9} +0.237941 q^{10} +0.968009 q^{11} +1.94239 q^{12} +2.48904 q^{13} -0.608715 q^{14} +0.991325 q^{15} +3.65765 q^{16} -1.00000 q^{17} -0.240024 q^{18} -5.03842 q^{19} +1.92554 q^{20} -2.53606 q^{21} -0.232345 q^{22} -1.80653 q^{23} -0.946267 q^{24} -4.01728 q^{25} -0.597429 q^{26} -1.00000 q^{27} -4.92602 q^{28} +5.21307 q^{29} -0.237941 q^{30} +6.87873 q^{31} -2.77046 q^{32} -0.968009 q^{33} +0.240024 q^{34} -2.51406 q^{35} -1.94239 q^{36} +2.49140 q^{37} +1.20934 q^{38} -2.48904 q^{39} -0.938057 q^{40} -1.02216 q^{41} +0.608715 q^{42} -9.96365 q^{43} -1.88025 q^{44} -0.991325 q^{45} +0.433611 q^{46} -3.98622 q^{47} -3.65765 q^{48} -0.568389 q^{49} +0.964241 q^{50} +1.00000 q^{51} -4.83469 q^{52} -5.76082 q^{53} +0.240024 q^{54} -0.959611 q^{55} +2.39979 q^{56} +5.03842 q^{57} -1.25126 q^{58} +0.764881 q^{59} -1.92554 q^{60} -6.15129 q^{61} -1.65106 q^{62} +2.53606 q^{63} -6.65033 q^{64} -2.46745 q^{65} +0.232345 q^{66} +0.538859 q^{67} +1.94239 q^{68} +1.80653 q^{69} +0.603434 q^{70} +9.03013 q^{71} +0.946267 q^{72} -2.45264 q^{73} -0.597996 q^{74} +4.01728 q^{75} +9.78657 q^{76} +2.45493 q^{77} +0.597429 q^{78} +7.60120 q^{79} -3.62592 q^{80} +1.00000 q^{81} +0.245344 q^{82} +2.86258 q^{83} +4.92602 q^{84} +0.991325 q^{85} +2.39151 q^{86} -5.21307 q^{87} +0.915995 q^{88} -0.260961 q^{89} +0.237941 q^{90} +6.31237 q^{91} +3.50899 q^{92} -6.87873 q^{93} +0.956787 q^{94} +4.99471 q^{95} +2.77046 q^{96} +11.8513 q^{97} +0.136427 q^{98} +0.968009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.240024 −0.169722 −0.0848612 0.996393i \(-0.527045\pi\)
−0.0848612 + 0.996393i \(0.527045\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.94239 −0.971194
\(5\) −0.991325 −0.443334 −0.221667 0.975122i \(-0.571150\pi\)
−0.221667 + 0.975122i \(0.571150\pi\)
\(6\) 0.240024 0.0979893
\(7\) 2.53606 0.958541 0.479271 0.877667i \(-0.340901\pi\)
0.479271 + 0.877667i \(0.340901\pi\)
\(8\) 0.946267 0.334556
\(9\) 1.00000 0.333333
\(10\) 0.237941 0.0752437
\(11\) 0.968009 0.291866 0.145933 0.989294i \(-0.453382\pi\)
0.145933 + 0.989294i \(0.453382\pi\)
\(12\) 1.94239 0.560719
\(13\) 2.48904 0.690336 0.345168 0.938541i \(-0.387822\pi\)
0.345168 + 0.938541i \(0.387822\pi\)
\(14\) −0.608715 −0.162686
\(15\) 0.991325 0.255959
\(16\) 3.65765 0.914413
\(17\) −1.00000 −0.242536
\(18\) −0.240024 −0.0565741
\(19\) −5.03842 −1.15589 −0.577946 0.816075i \(-0.696146\pi\)
−0.577946 + 0.816075i \(0.696146\pi\)
\(20\) 1.92554 0.430563
\(21\) −2.53606 −0.553414
\(22\) −0.232345 −0.0495361
\(23\) −1.80653 −0.376688 −0.188344 0.982103i \(-0.560312\pi\)
−0.188344 + 0.982103i \(0.560312\pi\)
\(24\) −0.946267 −0.193156
\(25\) −4.01728 −0.803455
\(26\) −0.597429 −0.117166
\(27\) −1.00000 −0.192450
\(28\) −4.92602 −0.930930
\(29\) 5.21307 0.968043 0.484022 0.875056i \(-0.339176\pi\)
0.484022 + 0.875056i \(0.339176\pi\)
\(30\) −0.237941 −0.0434420
\(31\) 6.87873 1.23546 0.617729 0.786391i \(-0.288053\pi\)
0.617729 + 0.786391i \(0.288053\pi\)
\(32\) −2.77046 −0.489752
\(33\) −0.968009 −0.168509
\(34\) 0.240024 0.0411637
\(35\) −2.51406 −0.424954
\(36\) −1.94239 −0.323731
\(37\) 2.49140 0.409584 0.204792 0.978805i \(-0.434348\pi\)
0.204792 + 0.978805i \(0.434348\pi\)
\(38\) 1.20934 0.196181
\(39\) −2.48904 −0.398566
\(40\) −0.938057 −0.148320
\(41\) −1.02216 −0.159635 −0.0798176 0.996809i \(-0.525434\pi\)
−0.0798176 + 0.996809i \(0.525434\pi\)
\(42\) 0.608715 0.0939268
\(43\) −9.96365 −1.51944 −0.759722 0.650249i \(-0.774665\pi\)
−0.759722 + 0.650249i \(0.774665\pi\)
\(44\) −1.88025 −0.283458
\(45\) −0.991325 −0.147778
\(46\) 0.433611 0.0639324
\(47\) −3.98622 −0.581450 −0.290725 0.956807i \(-0.593896\pi\)
−0.290725 + 0.956807i \(0.593896\pi\)
\(48\) −3.65765 −0.527936
\(49\) −0.568389 −0.0811984
\(50\) 0.964241 0.136364
\(51\) 1.00000 0.140028
\(52\) −4.83469 −0.670451
\(53\) −5.76082 −0.791309 −0.395654 0.918399i \(-0.629482\pi\)
−0.395654 + 0.918399i \(0.629482\pi\)
\(54\) 0.240024 0.0326631
\(55\) −0.959611 −0.129394
\(56\) 2.39979 0.320686
\(57\) 5.03842 0.667355
\(58\) −1.25126 −0.164299
\(59\) 0.764881 0.0995791 0.0497895 0.998760i \(-0.484145\pi\)
0.0497895 + 0.998760i \(0.484145\pi\)
\(60\) −1.92554 −0.248586
\(61\) −6.15129 −0.787592 −0.393796 0.919198i \(-0.628838\pi\)
−0.393796 + 0.919198i \(0.628838\pi\)
\(62\) −1.65106 −0.209685
\(63\) 2.53606 0.319514
\(64\) −6.65033 −0.831291
\(65\) −2.46745 −0.306049
\(66\) 0.232345 0.0285997
\(67\) 0.538859 0.0658321 0.0329160 0.999458i \(-0.489521\pi\)
0.0329160 + 0.999458i \(0.489521\pi\)
\(68\) 1.94239 0.235549
\(69\) 1.80653 0.217481
\(70\) 0.603434 0.0721242
\(71\) 9.03013 1.07168 0.535840 0.844320i \(-0.319995\pi\)
0.535840 + 0.844320i \(0.319995\pi\)
\(72\) 0.946267 0.111519
\(73\) −2.45264 −0.287060 −0.143530 0.989646i \(-0.545845\pi\)
−0.143530 + 0.989646i \(0.545845\pi\)
\(74\) −0.597996 −0.0695156
\(75\) 4.01728 0.463875
\(76\) 9.78657 1.12260
\(77\) 2.45493 0.279765
\(78\) 0.597429 0.0676456
\(79\) 7.60120 0.855202 0.427601 0.903968i \(-0.359359\pi\)
0.427601 + 0.903968i \(0.359359\pi\)
\(80\) −3.62592 −0.405390
\(81\) 1.00000 0.111111
\(82\) 0.245344 0.0270937
\(83\) 2.86258 0.314209 0.157105 0.987582i \(-0.449784\pi\)
0.157105 + 0.987582i \(0.449784\pi\)
\(84\) 4.92602 0.537473
\(85\) 0.991325 0.107524
\(86\) 2.39151 0.257884
\(87\) −5.21307 −0.558900
\(88\) 0.915995 0.0976454
\(89\) −0.260961 −0.0276618 −0.0138309 0.999904i \(-0.504403\pi\)
−0.0138309 + 0.999904i \(0.504403\pi\)
\(90\) 0.237941 0.0250812
\(91\) 6.31237 0.661716
\(92\) 3.50899 0.365837
\(93\) −6.87873 −0.713292
\(94\) 0.956787 0.0986851
\(95\) 4.99471 0.512446
\(96\) 2.77046 0.282759
\(97\) 11.8513 1.20332 0.601659 0.798753i \(-0.294507\pi\)
0.601659 + 0.798753i \(0.294507\pi\)
\(98\) 0.136427 0.0137812
\(99\) 0.968009 0.0972886
\(100\) 7.80311 0.780311
\(101\) −8.69500 −0.865185 −0.432592 0.901590i \(-0.642401\pi\)
−0.432592 + 0.901590i \(0.642401\pi\)
\(102\) −0.240024 −0.0237659
\(103\) −8.35617 −0.823358 −0.411679 0.911329i \(-0.635058\pi\)
−0.411679 + 0.911329i \(0.635058\pi\)
\(104\) 2.35530 0.230956
\(105\) 2.51406 0.245347
\(106\) 1.38273 0.134303
\(107\) 3.98996 0.385724 0.192862 0.981226i \(-0.438223\pi\)
0.192862 + 0.981226i \(0.438223\pi\)
\(108\) 1.94239 0.186906
\(109\) 12.8957 1.23519 0.617594 0.786497i \(-0.288107\pi\)
0.617594 + 0.786497i \(0.288107\pi\)
\(110\) 0.230329 0.0219610
\(111\) −2.49140 −0.236474
\(112\) 9.27603 0.876502
\(113\) −8.03772 −0.756125 −0.378062 0.925780i \(-0.623410\pi\)
−0.378062 + 0.925780i \(0.623410\pi\)
\(114\) −1.20934 −0.113265
\(115\) 1.79086 0.166999
\(116\) −10.1258 −0.940158
\(117\) 2.48904 0.230112
\(118\) −0.183590 −0.0169008
\(119\) −2.53606 −0.232480
\(120\) 0.938057 0.0856325
\(121\) −10.0630 −0.914814
\(122\) 1.47645 0.133672
\(123\) 1.02216 0.0921655
\(124\) −13.3612 −1.19987
\(125\) 8.93905 0.799533
\(126\) −0.608715 −0.0542286
\(127\) −22.2503 −1.97439 −0.987197 0.159505i \(-0.949010\pi\)
−0.987197 + 0.159505i \(0.949010\pi\)
\(128\) 7.13715 0.630841
\(129\) 9.96365 0.877251
\(130\) 0.592246 0.0519434
\(131\) 20.5053 1.79155 0.895777 0.444503i \(-0.146620\pi\)
0.895777 + 0.444503i \(0.146620\pi\)
\(132\) 1.88025 0.163655
\(133\) −12.7777 −1.10797
\(134\) −0.129339 −0.0111732
\(135\) 0.991325 0.0853196
\(136\) −0.946267 −0.0811417
\(137\) 7.65833 0.654295 0.327148 0.944973i \(-0.393913\pi\)
0.327148 + 0.944973i \(0.393913\pi\)
\(138\) −0.433611 −0.0369114
\(139\) −7.18251 −0.609212 −0.304606 0.952478i \(-0.598525\pi\)
−0.304606 + 0.952478i \(0.598525\pi\)
\(140\) 4.88328 0.412713
\(141\) 3.98622 0.335700
\(142\) −2.16745 −0.181888
\(143\) 2.40942 0.201486
\(144\) 3.65765 0.304804
\(145\) −5.16785 −0.429166
\(146\) 0.588692 0.0487205
\(147\) 0.568389 0.0468799
\(148\) −4.83927 −0.397786
\(149\) 15.5811 1.27645 0.638227 0.769848i \(-0.279668\pi\)
0.638227 + 0.769848i \(0.279668\pi\)
\(150\) −0.964241 −0.0787300
\(151\) −2.46873 −0.200902 −0.100451 0.994942i \(-0.532029\pi\)
−0.100451 + 0.994942i \(0.532029\pi\)
\(152\) −4.76769 −0.386711
\(153\) −1.00000 −0.0808452
\(154\) −0.589242 −0.0474824
\(155\) −6.81906 −0.547720
\(156\) 4.83469 0.387085
\(157\) −1.00000 −0.0798087
\(158\) −1.82447 −0.145147
\(159\) 5.76082 0.456862
\(160\) 2.74642 0.217124
\(161\) −4.58148 −0.361071
\(162\) −0.240024 −0.0188580
\(163\) −2.73288 −0.214056 −0.107028 0.994256i \(-0.534133\pi\)
−0.107028 + 0.994256i \(0.534133\pi\)
\(164\) 1.98544 0.155037
\(165\) 0.959611 0.0747056
\(166\) −0.687088 −0.0533283
\(167\) −3.20254 −0.247820 −0.123910 0.992293i \(-0.539543\pi\)
−0.123910 + 0.992293i \(0.539543\pi\)
\(168\) −2.39979 −0.185148
\(169\) −6.80466 −0.523436
\(170\) −0.237941 −0.0182493
\(171\) −5.03842 −0.385298
\(172\) 19.3533 1.47567
\(173\) −8.49128 −0.645580 −0.322790 0.946471i \(-0.604621\pi\)
−0.322790 + 0.946471i \(0.604621\pi\)
\(174\) 1.25126 0.0948579
\(175\) −10.1881 −0.770145
\(176\) 3.54064 0.266886
\(177\) −0.764881 −0.0574920
\(178\) 0.0626367 0.00469482
\(179\) 23.2801 1.74004 0.870019 0.493018i \(-0.164106\pi\)
0.870019 + 0.493018i \(0.164106\pi\)
\(180\) 1.92554 0.143521
\(181\) 8.46143 0.628933 0.314467 0.949269i \(-0.398174\pi\)
0.314467 + 0.949269i \(0.398174\pi\)
\(182\) −1.51512 −0.112308
\(183\) 6.15129 0.454716
\(184\) −1.70946 −0.126023
\(185\) −2.46979 −0.181583
\(186\) 1.65106 0.121062
\(187\) −0.968009 −0.0707878
\(188\) 7.74279 0.564701
\(189\) −2.53606 −0.184471
\(190\) −1.19885 −0.0869736
\(191\) −19.8888 −1.43911 −0.719553 0.694438i \(-0.755653\pi\)
−0.719553 + 0.694438i \(0.755653\pi\)
\(192\) 6.65033 0.479946
\(193\) 16.1007 1.15895 0.579476 0.814989i \(-0.303257\pi\)
0.579476 + 0.814989i \(0.303257\pi\)
\(194\) −2.84459 −0.204230
\(195\) 2.46745 0.176698
\(196\) 1.10403 0.0788594
\(197\) 3.62394 0.258195 0.129097 0.991632i \(-0.458792\pi\)
0.129097 + 0.991632i \(0.458792\pi\)
\(198\) −0.232345 −0.0165120
\(199\) 20.1136 1.42582 0.712908 0.701257i \(-0.247378\pi\)
0.712908 + 0.701257i \(0.247378\pi\)
\(200\) −3.80141 −0.268801
\(201\) −0.538859 −0.0380082
\(202\) 2.08701 0.146841
\(203\) 13.2207 0.927910
\(204\) −1.94239 −0.135994
\(205\) 1.01330 0.0707717
\(206\) 2.00568 0.139742
\(207\) −1.80653 −0.125563
\(208\) 9.10405 0.631252
\(209\) −4.87723 −0.337365
\(210\) −0.603434 −0.0416409
\(211\) −25.9012 −1.78311 −0.891555 0.452913i \(-0.850385\pi\)
−0.891555 + 0.452913i \(0.850385\pi\)
\(212\) 11.1897 0.768515
\(213\) −9.03013 −0.618734
\(214\) −0.957685 −0.0654660
\(215\) 9.87722 0.673621
\(216\) −0.946267 −0.0643853
\(217\) 17.4449 1.18424
\(218\) −3.09529 −0.209639
\(219\) 2.45264 0.165734
\(220\) 1.86394 0.125667
\(221\) −2.48904 −0.167431
\(222\) 0.597996 0.0401349
\(223\) −5.20612 −0.348628 −0.174314 0.984690i \(-0.555771\pi\)
−0.174314 + 0.984690i \(0.555771\pi\)
\(224\) −7.02605 −0.469448
\(225\) −4.01728 −0.267818
\(226\) 1.92924 0.128331
\(227\) 10.0078 0.664241 0.332120 0.943237i \(-0.392236\pi\)
0.332120 + 0.943237i \(0.392236\pi\)
\(228\) −9.78657 −0.648131
\(229\) −12.7031 −0.839446 −0.419723 0.907652i \(-0.637873\pi\)
−0.419723 + 0.907652i \(0.637873\pi\)
\(230\) −0.429849 −0.0283434
\(231\) −2.45493 −0.161523
\(232\) 4.93296 0.323865
\(233\) −7.43985 −0.487401 −0.243700 0.969851i \(-0.578361\pi\)
−0.243700 + 0.969851i \(0.578361\pi\)
\(234\) −0.597429 −0.0390552
\(235\) 3.95164 0.257776
\(236\) −1.48570 −0.0967106
\(237\) −7.60120 −0.493751
\(238\) 0.608715 0.0394571
\(239\) 21.9317 1.41864 0.709320 0.704886i \(-0.249002\pi\)
0.709320 + 0.704886i \(0.249002\pi\)
\(240\) 3.62592 0.234052
\(241\) −0.669110 −0.0431012 −0.0215506 0.999768i \(-0.506860\pi\)
−0.0215506 + 0.999768i \(0.506860\pi\)
\(242\) 2.41535 0.155264
\(243\) −1.00000 −0.0641500
\(244\) 11.9482 0.764905
\(245\) 0.563458 0.0359980
\(246\) −0.245344 −0.0156425
\(247\) −12.5408 −0.797955
\(248\) 6.50912 0.413329
\(249\) −2.86258 −0.181409
\(250\) −2.14558 −0.135699
\(251\) −20.6937 −1.30617 −0.653087 0.757283i \(-0.726527\pi\)
−0.653087 + 0.757283i \(0.726527\pi\)
\(252\) −4.92602 −0.310310
\(253\) −1.74874 −0.109942
\(254\) 5.34060 0.335099
\(255\) −0.991325 −0.0620792
\(256\) 11.5876 0.724223
\(257\) −1.50443 −0.0938436 −0.0469218 0.998899i \(-0.514941\pi\)
−0.0469218 + 0.998899i \(0.514941\pi\)
\(258\) −2.39151 −0.148889
\(259\) 6.31835 0.392603
\(260\) 4.79275 0.297234
\(261\) 5.21307 0.322681
\(262\) −4.92175 −0.304067
\(263\) −28.9952 −1.78792 −0.893960 0.448146i \(-0.852084\pi\)
−0.893960 + 0.448146i \(0.852084\pi\)
\(264\) −0.915995 −0.0563756
\(265\) 5.71084 0.350814
\(266\) 3.06696 0.188047
\(267\) 0.260961 0.0159705
\(268\) −1.04667 −0.0639358
\(269\) 5.53574 0.337520 0.168760 0.985657i \(-0.446024\pi\)
0.168760 + 0.985657i \(0.446024\pi\)
\(270\) −0.237941 −0.0144807
\(271\) 19.9638 1.21272 0.606358 0.795192i \(-0.292630\pi\)
0.606358 + 0.795192i \(0.292630\pi\)
\(272\) −3.65765 −0.221778
\(273\) −6.31237 −0.382042
\(274\) −1.83818 −0.111049
\(275\) −3.88876 −0.234501
\(276\) −3.50899 −0.211216
\(277\) 16.8330 1.01140 0.505700 0.862710i \(-0.331234\pi\)
0.505700 + 0.862710i \(0.331234\pi\)
\(278\) 1.72397 0.103397
\(279\) 6.87873 0.411819
\(280\) −2.37897 −0.142171
\(281\) −16.0062 −0.954851 −0.477425 0.878672i \(-0.658430\pi\)
−0.477425 + 0.878672i \(0.658430\pi\)
\(282\) −0.956787 −0.0569759
\(283\) −14.3986 −0.855907 −0.427954 0.903801i \(-0.640765\pi\)
−0.427954 + 0.903801i \(0.640765\pi\)
\(284\) −17.5400 −1.04081
\(285\) −4.99471 −0.295861
\(286\) −0.578317 −0.0341966
\(287\) −2.59227 −0.153017
\(288\) −2.77046 −0.163251
\(289\) 1.00000 0.0588235
\(290\) 1.24041 0.0728391
\(291\) −11.8513 −0.694736
\(292\) 4.76398 0.278791
\(293\) −21.0986 −1.23260 −0.616298 0.787513i \(-0.711368\pi\)
−0.616298 + 0.787513i \(0.711368\pi\)
\(294\) −0.136427 −0.00795657
\(295\) −0.758246 −0.0441468
\(296\) 2.35753 0.137029
\(297\) −0.968009 −0.0561696
\(298\) −3.73983 −0.216643
\(299\) −4.49654 −0.260042
\(300\) −7.80311 −0.450513
\(301\) −25.2684 −1.45645
\(302\) 0.592554 0.0340977
\(303\) 8.69500 0.499515
\(304\) −18.4288 −1.05696
\(305\) 6.09792 0.349166
\(306\) 0.240024 0.0137212
\(307\) −22.6024 −1.28999 −0.644994 0.764187i \(-0.723140\pi\)
−0.644994 + 0.764187i \(0.723140\pi\)
\(308\) −4.76843 −0.271707
\(309\) 8.35617 0.475366
\(310\) 1.63674 0.0929603
\(311\) 7.89681 0.447787 0.223893 0.974614i \(-0.428123\pi\)
0.223893 + 0.974614i \(0.428123\pi\)
\(312\) −2.35530 −0.133343
\(313\) −3.90937 −0.220970 −0.110485 0.993878i \(-0.535240\pi\)
−0.110485 + 0.993878i \(0.535240\pi\)
\(314\) 0.240024 0.0135453
\(315\) −2.51406 −0.141651
\(316\) −14.7645 −0.830567
\(317\) −16.1235 −0.905586 −0.452793 0.891616i \(-0.649572\pi\)
−0.452793 + 0.891616i \(0.649572\pi\)
\(318\) −1.38273 −0.0775398
\(319\) 5.04630 0.282539
\(320\) 6.59263 0.368539
\(321\) −3.98996 −0.222698
\(322\) 1.09966 0.0612819
\(323\) 5.03842 0.280345
\(324\) −1.94239 −0.107910
\(325\) −9.99917 −0.554654
\(326\) 0.655956 0.0363300
\(327\) −12.8957 −0.713137
\(328\) −0.967240 −0.0534069
\(329\) −10.1093 −0.557344
\(330\) −0.230329 −0.0126792
\(331\) 19.4464 1.06887 0.534436 0.845209i \(-0.320524\pi\)
0.534436 + 0.845209i \(0.320524\pi\)
\(332\) −5.56025 −0.305158
\(333\) 2.49140 0.136528
\(334\) 0.768686 0.0420606
\(335\) −0.534184 −0.0291856
\(336\) −9.27603 −0.506049
\(337\) −35.7471 −1.94727 −0.973635 0.228109i \(-0.926746\pi\)
−0.973635 + 0.228109i \(0.926746\pi\)
\(338\) 1.63328 0.0888387
\(339\) 8.03772 0.436549
\(340\) −1.92554 −0.104427
\(341\) 6.65868 0.360588
\(342\) 1.20934 0.0653936
\(343\) −19.1939 −1.03637
\(344\) −9.42827 −0.508338
\(345\) −1.79086 −0.0964167
\(346\) 2.03811 0.109569
\(347\) −14.9314 −0.801559 −0.400780 0.916174i \(-0.631261\pi\)
−0.400780 + 0.916174i \(0.631261\pi\)
\(348\) 10.1258 0.542801
\(349\) −25.4274 −1.36110 −0.680550 0.732702i \(-0.738259\pi\)
−0.680550 + 0.732702i \(0.738259\pi\)
\(350\) 2.44538 0.130711
\(351\) −2.48904 −0.132855
\(352\) −2.68183 −0.142942
\(353\) 13.7431 0.731470 0.365735 0.930719i \(-0.380818\pi\)
0.365735 + 0.930719i \(0.380818\pi\)
\(354\) 0.183590 0.00975768
\(355\) −8.95179 −0.475112
\(356\) 0.506887 0.0268650
\(357\) 2.53606 0.134223
\(358\) −5.58778 −0.295323
\(359\) 11.5161 0.607798 0.303899 0.952704i \(-0.401711\pi\)
0.303899 + 0.952704i \(0.401711\pi\)
\(360\) −0.938057 −0.0494400
\(361\) 6.38566 0.336088
\(362\) −2.03094 −0.106744
\(363\) 10.0630 0.528168
\(364\) −12.2611 −0.642655
\(365\) 2.43136 0.127263
\(366\) −1.47645 −0.0771755
\(367\) 14.6221 0.763265 0.381633 0.924314i \(-0.375362\pi\)
0.381633 + 0.924314i \(0.375362\pi\)
\(368\) −6.60767 −0.344448
\(369\) −1.02216 −0.0532118
\(370\) 0.592808 0.0308186
\(371\) −14.6098 −0.758502
\(372\) 13.3612 0.692745
\(373\) −27.4428 −1.42093 −0.710467 0.703731i \(-0.751516\pi\)
−0.710467 + 0.703731i \(0.751516\pi\)
\(374\) 0.232345 0.0120143
\(375\) −8.93905 −0.461610
\(376\) −3.77203 −0.194527
\(377\) 12.9756 0.668276
\(378\) 0.608715 0.0313089
\(379\) −11.9824 −0.615492 −0.307746 0.951469i \(-0.599575\pi\)
−0.307746 + 0.951469i \(0.599575\pi\)
\(380\) −9.70166 −0.497685
\(381\) 22.2503 1.13992
\(382\) 4.77379 0.244248
\(383\) −24.6762 −1.26089 −0.630446 0.776233i \(-0.717128\pi\)
−0.630446 + 0.776233i \(0.717128\pi\)
\(384\) −7.13715 −0.364216
\(385\) −2.43363 −0.124029
\(386\) −3.86455 −0.196700
\(387\) −9.96365 −0.506481
\(388\) −23.0198 −1.16865
\(389\) 28.9910 1.46990 0.734950 0.678121i \(-0.237206\pi\)
0.734950 + 0.678121i \(0.237206\pi\)
\(390\) −0.592246 −0.0299896
\(391\) 1.80653 0.0913603
\(392\) −0.537847 −0.0271654
\(393\) −20.5053 −1.03435
\(394\) −0.869830 −0.0438214
\(395\) −7.53526 −0.379140
\(396\) −1.88025 −0.0944861
\(397\) −24.1759 −1.21335 −0.606677 0.794948i \(-0.707498\pi\)
−0.606677 + 0.794948i \(0.707498\pi\)
\(398\) −4.82774 −0.241993
\(399\) 12.7777 0.639687
\(400\) −14.6938 −0.734690
\(401\) −27.0335 −1.34999 −0.674995 0.737822i \(-0.735854\pi\)
−0.674995 + 0.737822i \(0.735854\pi\)
\(402\) 0.129339 0.00645084
\(403\) 17.1215 0.852881
\(404\) 16.8891 0.840262
\(405\) −0.991325 −0.0492593
\(406\) −3.17328 −0.157487
\(407\) 2.41170 0.119544
\(408\) 0.946267 0.0468472
\(409\) −6.84701 −0.338563 −0.169281 0.985568i \(-0.554145\pi\)
−0.169281 + 0.985568i \(0.554145\pi\)
\(410\) −0.243215 −0.0120115
\(411\) −7.65833 −0.377758
\(412\) 16.2309 0.799641
\(413\) 1.93979 0.0954506
\(414\) 0.433611 0.0213108
\(415\) −2.83775 −0.139300
\(416\) −6.89579 −0.338094
\(417\) 7.18251 0.351729
\(418\) 1.17065 0.0572585
\(419\) −13.1885 −0.644299 −0.322149 0.946689i \(-0.604405\pi\)
−0.322149 + 0.946689i \(0.604405\pi\)
\(420\) −4.88328 −0.238280
\(421\) −30.3604 −1.47968 −0.739838 0.672785i \(-0.765098\pi\)
−0.739838 + 0.672785i \(0.765098\pi\)
\(422\) 6.21689 0.302634
\(423\) −3.98622 −0.193817
\(424\) −5.45127 −0.264737
\(425\) 4.01728 0.194866
\(426\) 2.16745 0.105013
\(427\) −15.6000 −0.754939
\(428\) −7.75006 −0.374613
\(429\) −2.40942 −0.116328
\(430\) −2.37077 −0.114328
\(431\) −12.8162 −0.617334 −0.308667 0.951170i \(-0.599883\pi\)
−0.308667 + 0.951170i \(0.599883\pi\)
\(432\) −3.65765 −0.175979
\(433\) 24.2000 1.16298 0.581490 0.813554i \(-0.302470\pi\)
0.581490 + 0.813554i \(0.302470\pi\)
\(434\) −4.18719 −0.200991
\(435\) 5.16785 0.247779
\(436\) −25.0486 −1.19961
\(437\) 9.10207 0.435411
\(438\) −0.588692 −0.0281288
\(439\) −0.594555 −0.0283766 −0.0141883 0.999899i \(-0.504516\pi\)
−0.0141883 + 0.999899i \(0.504516\pi\)
\(440\) −0.908048 −0.0432895
\(441\) −0.568389 −0.0270661
\(442\) 0.597429 0.0284168
\(443\) 20.0073 0.950578 0.475289 0.879830i \(-0.342344\pi\)
0.475289 + 0.879830i \(0.342344\pi\)
\(444\) 4.83927 0.229662
\(445\) 0.258697 0.0122634
\(446\) 1.24959 0.0591699
\(447\) −15.5811 −0.736961
\(448\) −16.8656 −0.796827
\(449\) −30.4016 −1.43474 −0.717371 0.696691i \(-0.754655\pi\)
−0.717371 + 0.696691i \(0.754655\pi\)
\(450\) 0.964241 0.0454548
\(451\) −0.989465 −0.0465921
\(452\) 15.6124 0.734344
\(453\) 2.46873 0.115991
\(454\) −2.40211 −0.112737
\(455\) −6.25761 −0.293361
\(456\) 4.76769 0.223267
\(457\) −18.1442 −0.848750 −0.424375 0.905487i \(-0.639506\pi\)
−0.424375 + 0.905487i \(0.639506\pi\)
\(458\) 3.04905 0.142473
\(459\) 1.00000 0.0466760
\(460\) −3.47855 −0.162188
\(461\) −14.3459 −0.668153 −0.334077 0.942546i \(-0.608424\pi\)
−0.334077 + 0.942546i \(0.608424\pi\)
\(462\) 0.589242 0.0274140
\(463\) −13.9429 −0.647981 −0.323990 0.946060i \(-0.605025\pi\)
−0.323990 + 0.946060i \(0.605025\pi\)
\(464\) 19.0676 0.885191
\(465\) 6.81906 0.316226
\(466\) 1.78574 0.0827228
\(467\) 5.68107 0.262888 0.131444 0.991324i \(-0.458039\pi\)
0.131444 + 0.991324i \(0.458039\pi\)
\(468\) −4.83469 −0.223484
\(469\) 1.36658 0.0631028
\(470\) −0.948487 −0.0437504
\(471\) 1.00000 0.0460776
\(472\) 0.723782 0.0333147
\(473\) −9.64491 −0.443473
\(474\) 1.82447 0.0838006
\(475\) 20.2407 0.928708
\(476\) 4.92602 0.225784
\(477\) −5.76082 −0.263770
\(478\) −5.26412 −0.240775
\(479\) −30.6261 −1.39934 −0.699672 0.714464i \(-0.746671\pi\)
−0.699672 + 0.714464i \(0.746671\pi\)
\(480\) −2.74642 −0.125356
\(481\) 6.20121 0.282751
\(482\) 0.160602 0.00731524
\(483\) 4.58148 0.208465
\(484\) 19.5462 0.888463
\(485\) −11.7485 −0.533471
\(486\) 0.240024 0.0108877
\(487\) 21.1475 0.958285 0.479143 0.877737i \(-0.340948\pi\)
0.479143 + 0.877737i \(0.340948\pi\)
\(488\) −5.82076 −0.263493
\(489\) 2.73288 0.123585
\(490\) −0.135243 −0.00610966
\(491\) 8.48807 0.383061 0.191531 0.981487i \(-0.438655\pi\)
0.191531 + 0.981487i \(0.438655\pi\)
\(492\) −1.98544 −0.0895106
\(493\) −5.21307 −0.234785
\(494\) 3.01010 0.135431
\(495\) −0.959611 −0.0431313
\(496\) 25.1600 1.12972
\(497\) 22.9010 1.02725
\(498\) 0.687088 0.0307891
\(499\) 1.38700 0.0620906 0.0310453 0.999518i \(-0.490116\pi\)
0.0310453 + 0.999518i \(0.490116\pi\)
\(500\) −17.3631 −0.776502
\(501\) 3.20254 0.143079
\(502\) 4.96698 0.221687
\(503\) 12.6444 0.563785 0.281893 0.959446i \(-0.409038\pi\)
0.281893 + 0.959446i \(0.409038\pi\)
\(504\) 2.39979 0.106895
\(505\) 8.61957 0.383566
\(506\) 0.419739 0.0186597
\(507\) 6.80466 0.302206
\(508\) 43.2187 1.91752
\(509\) 6.76191 0.299716 0.149858 0.988708i \(-0.452118\pi\)
0.149858 + 0.988708i \(0.452118\pi\)
\(510\) 0.237941 0.0105362
\(511\) −6.22005 −0.275159
\(512\) −17.0556 −0.753758
\(513\) 5.03842 0.222452
\(514\) 0.361098 0.0159274
\(515\) 8.28368 0.365023
\(516\) −19.3533 −0.851981
\(517\) −3.85870 −0.169705
\(518\) −1.51655 −0.0666336
\(519\) 8.49128 0.372726
\(520\) −2.33487 −0.102391
\(521\) −36.0732 −1.58040 −0.790198 0.612852i \(-0.790022\pi\)
−0.790198 + 0.612852i \(0.790022\pi\)
\(522\) −1.25126 −0.0547662
\(523\) −1.59381 −0.0696926 −0.0348463 0.999393i \(-0.511094\pi\)
−0.0348463 + 0.999393i \(0.511094\pi\)
\(524\) −39.8292 −1.73995
\(525\) 10.1881 0.444643
\(526\) 6.95954 0.303450
\(527\) −6.87873 −0.299642
\(528\) −3.54064 −0.154087
\(529\) −19.7364 −0.858106
\(530\) −1.37074 −0.0595410
\(531\) 0.764881 0.0331930
\(532\) 24.8193 1.07605
\(533\) −2.54421 −0.110202
\(534\) −0.0626367 −0.00271056
\(535\) −3.95535 −0.171005
\(536\) 0.509904 0.0220245
\(537\) −23.2801 −1.00461
\(538\) −1.32871 −0.0572847
\(539\) −0.550205 −0.0236990
\(540\) −1.92554 −0.0828619
\(541\) 6.57918 0.282861 0.141431 0.989948i \(-0.454830\pi\)
0.141431 + 0.989948i \(0.454830\pi\)
\(542\) −4.79179 −0.205825
\(543\) −8.46143 −0.363115
\(544\) 2.77046 0.118782
\(545\) −12.7839 −0.547601
\(546\) 1.51512 0.0648411
\(547\) 13.8876 0.593791 0.296896 0.954910i \(-0.404049\pi\)
0.296896 + 0.954910i \(0.404049\pi\)
\(548\) −14.8755 −0.635448
\(549\) −6.15129 −0.262531
\(550\) 0.933394 0.0398001
\(551\) −26.2656 −1.11895
\(552\) 1.70946 0.0727595
\(553\) 19.2771 0.819747
\(554\) −4.04033 −0.171657
\(555\) 2.46979 0.104837
\(556\) 13.9512 0.591664
\(557\) −14.2308 −0.602979 −0.301489 0.953470i \(-0.597484\pi\)
−0.301489 + 0.953470i \(0.597484\pi\)
\(558\) −1.65106 −0.0698949
\(559\) −24.8000 −1.04893
\(560\) −9.19556 −0.388583
\(561\) 0.968009 0.0408694
\(562\) 3.84187 0.162060
\(563\) 17.6032 0.741887 0.370943 0.928656i \(-0.379034\pi\)
0.370943 + 0.928656i \(0.379034\pi\)
\(564\) −7.74279 −0.326030
\(565\) 7.96799 0.335216
\(566\) 3.45600 0.145267
\(567\) 2.53606 0.106505
\(568\) 8.54491 0.358537
\(569\) 25.1751 1.05540 0.527698 0.849432i \(-0.323055\pi\)
0.527698 + 0.849432i \(0.323055\pi\)
\(570\) 1.19885 0.0502142
\(571\) 24.7789 1.03697 0.518483 0.855088i \(-0.326497\pi\)
0.518483 + 0.855088i \(0.326497\pi\)
\(572\) −4.68002 −0.195682
\(573\) 19.8888 0.830868
\(574\) 0.622207 0.0259704
\(575\) 7.25734 0.302652
\(576\) −6.65033 −0.277097
\(577\) 3.99043 0.166124 0.0830620 0.996544i \(-0.473530\pi\)
0.0830620 + 0.996544i \(0.473530\pi\)
\(578\) −0.240024 −0.00998367
\(579\) −16.1007 −0.669122
\(580\) 10.0380 0.416804
\(581\) 7.25969 0.301183
\(582\) 2.84459 0.117912
\(583\) −5.57652 −0.230956
\(584\) −2.32085 −0.0960376
\(585\) −2.46745 −0.102016
\(586\) 5.06417 0.209199
\(587\) −1.46024 −0.0602705 −0.0301352 0.999546i \(-0.509594\pi\)
−0.0301352 + 0.999546i \(0.509594\pi\)
\(588\) −1.10403 −0.0455295
\(589\) −34.6579 −1.42806
\(590\) 0.181997 0.00749269
\(591\) −3.62394 −0.149069
\(592\) 9.11268 0.374529
\(593\) −4.74474 −0.194843 −0.0974216 0.995243i \(-0.531060\pi\)
−0.0974216 + 0.995243i \(0.531060\pi\)
\(594\) 0.232345 0.00953324
\(595\) 2.51406 0.103066
\(596\) −30.2646 −1.23968
\(597\) −20.1136 −0.823196
\(598\) 1.07928 0.0441349
\(599\) −2.37282 −0.0969510 −0.0484755 0.998824i \(-0.515436\pi\)
−0.0484755 + 0.998824i \(0.515436\pi\)
\(600\) 3.80141 0.155192
\(601\) −15.4996 −0.632244 −0.316122 0.948719i \(-0.602381\pi\)
−0.316122 + 0.948719i \(0.602381\pi\)
\(602\) 6.06503 0.247192
\(603\) 0.538859 0.0219440
\(604\) 4.79524 0.195115
\(605\) 9.97566 0.405568
\(606\) −2.08701 −0.0847788
\(607\) 21.3333 0.865893 0.432946 0.901420i \(-0.357474\pi\)
0.432946 + 0.901420i \(0.357474\pi\)
\(608\) 13.9587 0.566101
\(609\) −13.2207 −0.535729
\(610\) −1.46365 −0.0592613
\(611\) −9.92188 −0.401396
\(612\) 1.94239 0.0785164
\(613\) −27.8282 −1.12397 −0.561985 0.827148i \(-0.689962\pi\)
−0.561985 + 0.827148i \(0.689962\pi\)
\(614\) 5.42512 0.218940
\(615\) −1.01330 −0.0408601
\(616\) 2.32302 0.0935971
\(617\) 13.8149 0.556168 0.278084 0.960557i \(-0.410301\pi\)
0.278084 + 0.960557i \(0.410301\pi\)
\(618\) −2.00568 −0.0806803
\(619\) −23.3186 −0.937253 −0.468626 0.883396i \(-0.655251\pi\)
−0.468626 + 0.883396i \(0.655251\pi\)
\(620\) 13.2453 0.531942
\(621\) 1.80653 0.0724937
\(622\) −1.89542 −0.0759995
\(623\) −0.661812 −0.0265150
\(624\) −9.10405 −0.364454
\(625\) 11.2249 0.448995
\(626\) 0.938340 0.0375036
\(627\) 4.87723 0.194778
\(628\) 1.94239 0.0775097
\(629\) −2.49140 −0.0993388
\(630\) 0.603434 0.0240414
\(631\) −45.2232 −1.80031 −0.900154 0.435572i \(-0.856546\pi\)
−0.900154 + 0.435572i \(0.856546\pi\)
\(632\) 7.19276 0.286113
\(633\) 25.9012 1.02948
\(634\) 3.87002 0.153698
\(635\) 22.0573 0.875316
\(636\) −11.1897 −0.443702
\(637\) −1.41474 −0.0560542
\(638\) −1.21123 −0.0479531
\(639\) 9.03013 0.357226
\(640\) −7.07523 −0.279673
\(641\) 45.6453 1.80288 0.901440 0.432904i \(-0.142511\pi\)
0.901440 + 0.432904i \(0.142511\pi\)
\(642\) 0.957685 0.0377968
\(643\) −29.8558 −1.17740 −0.588700 0.808352i \(-0.700360\pi\)
−0.588700 + 0.808352i \(0.700360\pi\)
\(644\) 8.89901 0.350670
\(645\) −9.87722 −0.388915
\(646\) −1.20934 −0.0475808
\(647\) −18.3694 −0.722177 −0.361088 0.932532i \(-0.617595\pi\)
−0.361088 + 0.932532i \(0.617595\pi\)
\(648\) 0.946267 0.0371729
\(649\) 0.740412 0.0290637
\(650\) 2.40004 0.0941373
\(651\) −17.4449 −0.683719
\(652\) 5.30831 0.207890
\(653\) 6.73493 0.263558 0.131779 0.991279i \(-0.457931\pi\)
0.131779 + 0.991279i \(0.457931\pi\)
\(654\) 3.09529 0.121035
\(655\) −20.3274 −0.794257
\(656\) −3.73872 −0.145973
\(657\) −2.45264 −0.0956866
\(658\) 2.42647 0.0945937
\(659\) −1.03915 −0.0404796 −0.0202398 0.999795i \(-0.506443\pi\)
−0.0202398 + 0.999795i \(0.506443\pi\)
\(660\) −1.86394 −0.0725537
\(661\) −17.2076 −0.669298 −0.334649 0.942343i \(-0.608618\pi\)
−0.334649 + 0.942343i \(0.608618\pi\)
\(662\) −4.66761 −0.181412
\(663\) 2.48904 0.0966664
\(664\) 2.70877 0.105121
\(665\) 12.6669 0.491201
\(666\) −0.597996 −0.0231719
\(667\) −9.41759 −0.364650
\(668\) 6.22058 0.240682
\(669\) 5.20612 0.201280
\(670\) 0.128217 0.00495345
\(671\) −5.95450 −0.229871
\(672\) 7.02605 0.271036
\(673\) −0.609968 −0.0235125 −0.0117563 0.999931i \(-0.503742\pi\)
−0.0117563 + 0.999931i \(0.503742\pi\)
\(674\) 8.58016 0.330495
\(675\) 4.01728 0.154625
\(676\) 13.2173 0.508358
\(677\) 49.1829 1.89025 0.945126 0.326707i \(-0.105939\pi\)
0.945126 + 0.326707i \(0.105939\pi\)
\(678\) −1.92924 −0.0740921
\(679\) 30.0556 1.15343
\(680\) 0.938057 0.0359729
\(681\) −10.0078 −0.383500
\(682\) −1.59824 −0.0611998
\(683\) 1.15275 0.0441089 0.0220545 0.999757i \(-0.492979\pi\)
0.0220545 + 0.999757i \(0.492979\pi\)
\(684\) 9.78657 0.374199
\(685\) −7.59189 −0.290071
\(686\) 4.60699 0.175896
\(687\) 12.7031 0.484654
\(688\) −36.4436 −1.38940
\(689\) −14.3389 −0.546269
\(690\) 0.429849 0.0163641
\(691\) 16.4839 0.627076 0.313538 0.949576i \(-0.398486\pi\)
0.313538 + 0.949576i \(0.398486\pi\)
\(692\) 16.4934 0.626984
\(693\) 2.45493 0.0932551
\(694\) 3.58389 0.136043
\(695\) 7.12020 0.270084
\(696\) −4.93296 −0.186983
\(697\) 1.02216 0.0387172
\(698\) 6.10319 0.231009
\(699\) 7.43985 0.281401
\(700\) 19.7892 0.747960
\(701\) −4.92799 −0.186128 −0.0930639 0.995660i \(-0.529666\pi\)
−0.0930639 + 0.995660i \(0.529666\pi\)
\(702\) 0.597429 0.0225485
\(703\) −12.5527 −0.473435
\(704\) −6.43758 −0.242625
\(705\) −3.95164 −0.148827
\(706\) −3.29866 −0.124147
\(707\) −22.0511 −0.829315
\(708\) 1.48570 0.0558359
\(709\) −26.2907 −0.987368 −0.493684 0.869641i \(-0.664350\pi\)
−0.493684 + 0.869641i \(0.664350\pi\)
\(710\) 2.14864 0.0806371
\(711\) 7.60120 0.285067
\(712\) −0.246938 −0.00925441
\(713\) −12.4267 −0.465382
\(714\) −0.608715 −0.0227806
\(715\) −2.38851 −0.0893254
\(716\) −45.2191 −1.68992
\(717\) −21.9317 −0.819053
\(718\) −2.76415 −0.103157
\(719\) 29.1849 1.08841 0.544206 0.838952i \(-0.316831\pi\)
0.544206 + 0.838952i \(0.316831\pi\)
\(720\) −3.62592 −0.135130
\(721\) −21.1918 −0.789223
\(722\) −1.53271 −0.0570416
\(723\) 0.669110 0.0248845
\(724\) −16.4354 −0.610816
\(725\) −20.9424 −0.777779
\(726\) −2.41535 −0.0896420
\(727\) −42.1030 −1.56151 −0.780756 0.624836i \(-0.785166\pi\)
−0.780756 + 0.624836i \(0.785166\pi\)
\(728\) 5.97318 0.221381
\(729\) 1.00000 0.0370370
\(730\) −0.583585 −0.0215994
\(731\) 9.96365 0.368519
\(732\) −11.9482 −0.441618
\(733\) 27.8306 1.02794 0.513972 0.857807i \(-0.328173\pi\)
0.513972 + 0.857807i \(0.328173\pi\)
\(734\) −3.50964 −0.129543
\(735\) −0.563458 −0.0207834
\(736\) 5.00492 0.184484
\(737\) 0.521620 0.0192141
\(738\) 0.245344 0.00903123
\(739\) 11.3089 0.416004 0.208002 0.978128i \(-0.433304\pi\)
0.208002 + 0.978128i \(0.433304\pi\)
\(740\) 4.79729 0.176352
\(741\) 12.5408 0.460699
\(742\) 3.50669 0.128735
\(743\) −36.1091 −1.32471 −0.662357 0.749188i \(-0.730444\pi\)
−0.662357 + 0.749188i \(0.730444\pi\)
\(744\) −6.50912 −0.238636
\(745\) −15.4459 −0.565895
\(746\) 6.58692 0.241164
\(747\) 2.86258 0.104736
\(748\) 1.88025 0.0687487
\(749\) 10.1188 0.369733
\(750\) 2.14558 0.0783456
\(751\) −38.0646 −1.38900 −0.694498 0.719494i \(-0.744374\pi\)
−0.694498 + 0.719494i \(0.744374\pi\)
\(752\) −14.5802 −0.531685
\(753\) 20.6937 0.754120
\(754\) −3.11444 −0.113421
\(755\) 2.44731 0.0890669
\(756\) 4.92602 0.179158
\(757\) 32.7274 1.18950 0.594749 0.803912i \(-0.297251\pi\)
0.594749 + 0.803912i \(0.297251\pi\)
\(758\) 2.87605 0.104463
\(759\) 1.74874 0.0634752
\(760\) 4.72633 0.171442
\(761\) 2.74772 0.0996046 0.0498023 0.998759i \(-0.484141\pi\)
0.0498023 + 0.998759i \(0.484141\pi\)
\(762\) −5.34060 −0.193469
\(763\) 32.7044 1.18398
\(764\) 38.6319 1.39765
\(765\) 0.991325 0.0358414
\(766\) 5.92286 0.214002
\(767\) 1.90382 0.0687430
\(768\) −11.5876 −0.418130
\(769\) −47.6072 −1.71676 −0.858379 0.513016i \(-0.828528\pi\)
−0.858379 + 0.513016i \(0.828528\pi\)
\(770\) 0.584130 0.0210506
\(771\) 1.50443 0.0541806
\(772\) −31.2738 −1.12557
\(773\) 0.0699166 0.00251473 0.00125736 0.999999i \(-0.499600\pi\)
0.00125736 + 0.999999i \(0.499600\pi\)
\(774\) 2.39151 0.0859612
\(775\) −27.6338 −0.992634
\(776\) 11.2145 0.402577
\(777\) −6.31835 −0.226670
\(778\) −6.95852 −0.249475
\(779\) 5.15009 0.184521
\(780\) −4.79275 −0.171608
\(781\) 8.74125 0.312786
\(782\) −0.433611 −0.0155059
\(783\) −5.21307 −0.186300
\(784\) −2.07897 −0.0742488
\(785\) 0.991325 0.0353819
\(786\) 4.92175 0.175553
\(787\) 9.29281 0.331253 0.165626 0.986189i \(-0.447035\pi\)
0.165626 + 0.986189i \(0.447035\pi\)
\(788\) −7.03909 −0.250757
\(789\) 28.9952 1.03226
\(790\) 1.80864 0.0643485
\(791\) −20.3842 −0.724777
\(792\) 0.915995 0.0325485
\(793\) −15.3108 −0.543703
\(794\) 5.80279 0.205933
\(795\) −5.71084 −0.202543
\(796\) −39.0685 −1.38474
\(797\) −8.05133 −0.285193 −0.142596 0.989781i \(-0.545545\pi\)
−0.142596 + 0.989781i \(0.545545\pi\)
\(798\) −3.06696 −0.108569
\(799\) 3.98622 0.141022
\(800\) 11.1297 0.393494
\(801\) −0.260961 −0.00922059
\(802\) 6.48869 0.229124
\(803\) −2.37418 −0.0837830
\(804\) 1.04667 0.0369133
\(805\) 4.54173 0.160075
\(806\) −4.10956 −0.144753
\(807\) −5.53574 −0.194867
\(808\) −8.22779 −0.289453
\(809\) −15.4751 −0.544076 −0.272038 0.962286i \(-0.587698\pi\)
−0.272038 + 0.962286i \(0.587698\pi\)
\(810\) 0.237941 0.00836041
\(811\) 16.3627 0.574573 0.287286 0.957845i \(-0.407247\pi\)
0.287286 + 0.957845i \(0.407247\pi\)
\(812\) −25.6797 −0.901181
\(813\) −19.9638 −0.700162
\(814\) −0.578865 −0.0202892
\(815\) 2.70917 0.0948981
\(816\) 3.65765 0.128043
\(817\) 50.2011 1.75631
\(818\) 1.64344 0.0574617
\(819\) 6.31237 0.220572
\(820\) −1.96822 −0.0687331
\(821\) 37.9202 1.32342 0.661711 0.749759i \(-0.269830\pi\)
0.661711 + 0.749759i \(0.269830\pi\)
\(822\) 1.83818 0.0641139
\(823\) −37.4816 −1.30653 −0.653263 0.757131i \(-0.726600\pi\)
−0.653263 + 0.757131i \(0.726600\pi\)
\(824\) −7.90717 −0.275459
\(825\) 3.88876 0.135389
\(826\) −0.465595 −0.0162001
\(827\) 0.707432 0.0245998 0.0122999 0.999924i \(-0.496085\pi\)
0.0122999 + 0.999924i \(0.496085\pi\)
\(828\) 3.50899 0.121946
\(829\) −26.3553 −0.915359 −0.457679 0.889117i \(-0.651319\pi\)
−0.457679 + 0.889117i \(0.651319\pi\)
\(830\) 0.681127 0.0236423
\(831\) −16.8330 −0.583932
\(832\) −16.5530 −0.573870
\(833\) 0.568389 0.0196935
\(834\) −1.72397 −0.0596963
\(835\) 3.17476 0.109867
\(836\) 9.47349 0.327647
\(837\) −6.87873 −0.237764
\(838\) 3.16554 0.109352
\(839\) −43.2798 −1.49419 −0.747093 0.664720i \(-0.768551\pi\)
−0.747093 + 0.664720i \(0.768551\pi\)
\(840\) 2.37897 0.0820823
\(841\) −1.82387 −0.0628920
\(842\) 7.28722 0.251134
\(843\) 16.0062 0.551283
\(844\) 50.3101 1.73175
\(845\) 6.74563 0.232057
\(846\) 0.956787 0.0328950
\(847\) −25.5203 −0.876887
\(848\) −21.0711 −0.723583
\(849\) 14.3986 0.494158
\(850\) −0.964241 −0.0330732
\(851\) −4.50080 −0.154286
\(852\) 17.5400 0.600911
\(853\) 33.4424 1.14505 0.572523 0.819889i \(-0.305965\pi\)
0.572523 + 0.819889i \(0.305965\pi\)
\(854\) 3.74438 0.128130
\(855\) 4.99471 0.170815
\(856\) 3.77557 0.129046
\(857\) −37.6711 −1.28682 −0.643410 0.765521i \(-0.722481\pi\)
−0.643410 + 0.765521i \(0.722481\pi\)
\(858\) 0.578317 0.0197434
\(859\) 28.5567 0.974343 0.487172 0.873306i \(-0.338029\pi\)
0.487172 + 0.873306i \(0.338029\pi\)
\(860\) −19.1854 −0.654216
\(861\) 2.59227 0.0883444
\(862\) 3.07619 0.104775
\(863\) 1.18690 0.0404027 0.0202013 0.999796i \(-0.493569\pi\)
0.0202013 + 0.999796i \(0.493569\pi\)
\(864\) 2.77046 0.0942528
\(865\) 8.41762 0.286208
\(866\) −5.80858 −0.197384
\(867\) −1.00000 −0.0339618
\(868\) −33.8848 −1.15012
\(869\) 7.35803 0.249604
\(870\) −1.24041 −0.0420537
\(871\) 1.34124 0.0454463
\(872\) 12.2028 0.413240
\(873\) 11.8513 0.401106
\(874\) −2.18471 −0.0738990
\(875\) 22.6700 0.766385
\(876\) −4.76398 −0.160960
\(877\) 29.7271 1.00381 0.501907 0.864922i \(-0.332632\pi\)
0.501907 + 0.864922i \(0.332632\pi\)
\(878\) 0.142707 0.00481614
\(879\) 21.0986 0.711639
\(880\) −3.50992 −0.118319
\(881\) 41.8281 1.40922 0.704612 0.709593i \(-0.251121\pi\)
0.704612 + 0.709593i \(0.251121\pi\)
\(882\) 0.136427 0.00459373
\(883\) 6.76538 0.227673 0.113837 0.993499i \(-0.463686\pi\)
0.113837 + 0.993499i \(0.463686\pi\)
\(884\) 4.83469 0.162608
\(885\) 0.758246 0.0254881
\(886\) −4.80224 −0.161334
\(887\) −7.59763 −0.255104 −0.127552 0.991832i \(-0.540712\pi\)
−0.127552 + 0.991832i \(0.540712\pi\)
\(888\) −2.35753 −0.0791136
\(889\) −56.4281 −1.89254
\(890\) −0.0620933 −0.00208137
\(891\) 0.968009 0.0324295
\(892\) 10.1123 0.338585
\(893\) 20.0842 0.672094
\(894\) 3.73983 0.125079
\(895\) −23.0782 −0.771418
\(896\) 18.1003 0.604687
\(897\) 4.49654 0.150135
\(898\) 7.29711 0.243508
\(899\) 35.8593 1.19598
\(900\) 7.80311 0.260104
\(901\) 5.76082 0.191921
\(902\) 0.237495 0.00790772
\(903\) 25.2684 0.840881
\(904\) −7.60582 −0.252966
\(905\) −8.38802 −0.278827
\(906\) −0.592554 −0.0196863
\(907\) 5.19380 0.172457 0.0862286 0.996275i \(-0.472518\pi\)
0.0862286 + 0.996275i \(0.472518\pi\)
\(908\) −19.4390 −0.645107
\(909\) −8.69500 −0.288395
\(910\) 1.50197 0.0497899
\(911\) 35.0858 1.16244 0.581222 0.813745i \(-0.302575\pi\)
0.581222 + 0.813745i \(0.302575\pi\)
\(912\) 18.4288 0.610238
\(913\) 2.77101 0.0917069
\(914\) 4.35504 0.144052
\(915\) −6.09792 −0.201591
\(916\) 24.6744 0.815265
\(917\) 52.0027 1.71728
\(918\) −0.240024 −0.00792196
\(919\) −10.8085 −0.356539 −0.178270 0.983982i \(-0.557050\pi\)
−0.178270 + 0.983982i \(0.557050\pi\)
\(920\) 1.69463 0.0558703
\(921\) 22.6024 0.744775
\(922\) 3.44335 0.113401
\(923\) 22.4764 0.739819
\(924\) 4.76843 0.156870
\(925\) −10.0087 −0.329083
\(926\) 3.34662 0.109977
\(927\) −8.35617 −0.274453
\(928\) −14.4426 −0.474101
\(929\) 12.8050 0.420117 0.210059 0.977689i \(-0.432635\pi\)
0.210059 + 0.977689i \(0.432635\pi\)
\(930\) −1.63674 −0.0536707
\(931\) 2.86378 0.0938566
\(932\) 14.4511 0.473361
\(933\) −7.89681 −0.258530
\(934\) −1.36359 −0.0446180
\(935\) 0.959611 0.0313826
\(936\) 2.35530 0.0769854
\(937\) 51.6603 1.68767 0.843834 0.536604i \(-0.180293\pi\)
0.843834 + 0.536604i \(0.180293\pi\)
\(938\) −0.328012 −0.0107100
\(939\) 3.90937 0.127577
\(940\) −7.67562 −0.250351
\(941\) −33.8917 −1.10484 −0.552418 0.833567i \(-0.686295\pi\)
−0.552418 + 0.833567i \(0.686295\pi\)
\(942\) −0.240024 −0.00782039
\(943\) 1.84657 0.0601327
\(944\) 2.79767 0.0910564
\(945\) 2.51406 0.0817824
\(946\) 2.31501 0.0752674
\(947\) −4.92203 −0.159945 −0.0799723 0.996797i \(-0.525483\pi\)
−0.0799723 + 0.996797i \(0.525483\pi\)
\(948\) 14.7645 0.479528
\(949\) −6.10473 −0.198168
\(950\) −4.85825 −0.157622
\(951\) 16.1235 0.522840
\(952\) −2.39979 −0.0777777
\(953\) 49.6887 1.60957 0.804787 0.593564i \(-0.202279\pi\)
0.804787 + 0.593564i \(0.202279\pi\)
\(954\) 1.38273 0.0447676
\(955\) 19.7163 0.638004
\(956\) −42.5998 −1.37778
\(957\) −5.04630 −0.163124
\(958\) 7.35100 0.237500
\(959\) 19.4220 0.627169
\(960\) −6.59263 −0.212776
\(961\) 16.3170 0.526354
\(962\) −1.48844 −0.0479892
\(963\) 3.98996 0.128575
\(964\) 1.29967 0.0418596
\(965\) −15.9610 −0.513803
\(966\) −1.09966 −0.0353811
\(967\) −28.6202 −0.920364 −0.460182 0.887825i \(-0.652216\pi\)
−0.460182 + 0.887825i \(0.652216\pi\)
\(968\) −9.52224 −0.306056
\(969\) −5.03842 −0.161857
\(970\) 2.81991 0.0905420
\(971\) 6.93039 0.222407 0.111203 0.993798i \(-0.464529\pi\)
0.111203 + 0.993798i \(0.464529\pi\)
\(972\) 1.94239 0.0623021
\(973\) −18.2153 −0.583955
\(974\) −5.07590 −0.162642
\(975\) 9.99917 0.320230
\(976\) −22.4993 −0.720184
\(977\) 22.6649 0.725113 0.362557 0.931962i \(-0.381904\pi\)
0.362557 + 0.931962i \(0.381904\pi\)
\(978\) −0.655956 −0.0209751
\(979\) −0.252612 −0.00807352
\(980\) −1.09445 −0.0349610
\(981\) 12.8957 0.411730
\(982\) −2.03734 −0.0650140
\(983\) 46.2607 1.47549 0.737743 0.675081i \(-0.235892\pi\)
0.737743 + 0.675081i \(0.235892\pi\)
\(984\) 0.967240 0.0308345
\(985\) −3.59250 −0.114466
\(986\) 1.25126 0.0398483
\(987\) 10.1093 0.321783
\(988\) 24.3592 0.774969
\(989\) 17.9997 0.572356
\(990\) 0.230329 0.00732035
\(991\) −29.5112 −0.937455 −0.468728 0.883343i \(-0.655287\pi\)
−0.468728 + 0.883343i \(0.655287\pi\)
\(992\) −19.0572 −0.605068
\(993\) −19.4464 −0.617114
\(994\) −5.49678 −0.174347
\(995\) −19.9391 −0.632113
\(996\) 5.56025 0.176183
\(997\) −19.4844 −0.617079 −0.308539 0.951212i \(-0.599840\pi\)
−0.308539 + 0.951212i \(0.599840\pi\)
\(998\) −0.332913 −0.0105382
\(999\) −2.49140 −0.0788245
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 8007.2.a.f.1.22 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.22 48 1.1 even 1 trivial