Properties

Label 8007.2.a.f.1.12
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 1.12
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.54663 q^{2} -1.00000 q^{3} +0.392054 q^{4} +3.59105 q^{5} +1.54663 q^{6} -3.93711 q^{7} +2.48689 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.54663 q^{2} -1.00000 q^{3} +0.392054 q^{4} +3.59105 q^{5} +1.54663 q^{6} -3.93711 q^{7} +2.48689 q^{8} +1.00000 q^{9} -5.55401 q^{10} +3.85540 q^{11} -0.392054 q^{12} -1.41847 q^{13} +6.08924 q^{14} -3.59105 q^{15} -4.63040 q^{16} -1.00000 q^{17} -1.54663 q^{18} -0.145814 q^{19} +1.40789 q^{20} +3.93711 q^{21} -5.96287 q^{22} -0.400691 q^{23} -2.48689 q^{24} +7.89562 q^{25} +2.19385 q^{26} -1.00000 q^{27} -1.54356 q^{28} -4.77127 q^{29} +5.55401 q^{30} +9.59732 q^{31} +2.18772 q^{32} -3.85540 q^{33} +1.54663 q^{34} -14.1383 q^{35} +0.392054 q^{36} -8.11194 q^{37} +0.225520 q^{38} +1.41847 q^{39} +8.93055 q^{40} +2.99059 q^{41} -6.08924 q^{42} +3.02827 q^{43} +1.51153 q^{44} +3.59105 q^{45} +0.619719 q^{46} -8.05420 q^{47} +4.63040 q^{48} +8.50081 q^{49} -12.2116 q^{50} +1.00000 q^{51} -0.556118 q^{52} +4.69749 q^{53} +1.54663 q^{54} +13.8449 q^{55} -9.79116 q^{56} +0.145814 q^{57} +7.37938 q^{58} -8.98276 q^{59} -1.40789 q^{60} -11.7945 q^{61} -14.8435 q^{62} -3.93711 q^{63} +5.87722 q^{64} -5.09380 q^{65} +5.96287 q^{66} -5.49370 q^{67} -0.392054 q^{68} +0.400691 q^{69} +21.8667 q^{70} +12.1394 q^{71} +2.48689 q^{72} +6.38728 q^{73} +12.5461 q^{74} -7.89562 q^{75} -0.0571672 q^{76} -15.1791 q^{77} -2.19385 q^{78} +8.76482 q^{79} -16.6280 q^{80} +1.00000 q^{81} -4.62533 q^{82} -6.68788 q^{83} +1.54356 q^{84} -3.59105 q^{85} -4.68361 q^{86} +4.77127 q^{87} +9.58798 q^{88} -7.17883 q^{89} -5.55401 q^{90} +5.58468 q^{91} -0.157092 q^{92} -9.59732 q^{93} +12.4568 q^{94} -0.523626 q^{95} -2.18772 q^{96} -11.2410 q^{97} -13.1476 q^{98} +3.85540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.54663 −1.09363 −0.546815 0.837253i \(-0.684160\pi\)
−0.546815 + 0.837253i \(0.684160\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.392054 0.196027
\(5\) 3.59105 1.60596 0.802982 0.596003i \(-0.203245\pi\)
0.802982 + 0.596003i \(0.203245\pi\)
\(6\) 1.54663 0.631408
\(7\) −3.93711 −1.48809 −0.744043 0.668131i \(-0.767094\pi\)
−0.744043 + 0.668131i \(0.767094\pi\)
\(8\) 2.48689 0.879249
\(9\) 1.00000 0.333333
\(10\) −5.55401 −1.75633
\(11\) 3.85540 1.16245 0.581224 0.813744i \(-0.302574\pi\)
0.581224 + 0.813744i \(0.302574\pi\)
\(12\) −0.392054 −0.113176
\(13\) −1.41847 −0.393414 −0.196707 0.980462i \(-0.563025\pi\)
−0.196707 + 0.980462i \(0.563025\pi\)
\(14\) 6.08924 1.62742
\(15\) −3.59105 −0.927204
\(16\) −4.63040 −1.15760
\(17\) −1.00000 −0.242536
\(18\) −1.54663 −0.364543
\(19\) −0.145814 −0.0334521 −0.0167261 0.999860i \(-0.505324\pi\)
−0.0167261 + 0.999860i \(0.505324\pi\)
\(20\) 1.40789 0.314813
\(21\) 3.93711 0.859147
\(22\) −5.96287 −1.27129
\(23\) −0.400691 −0.0835498 −0.0417749 0.999127i \(-0.513301\pi\)
−0.0417749 + 0.999127i \(0.513301\pi\)
\(24\) −2.48689 −0.507635
\(25\) 7.89562 1.57912
\(26\) 2.19385 0.430249
\(27\) −1.00000 −0.192450
\(28\) −1.54356 −0.291705
\(29\) −4.77127 −0.886003 −0.443002 0.896521i \(-0.646086\pi\)
−0.443002 + 0.896521i \(0.646086\pi\)
\(30\) 5.55401 1.01402
\(31\) 9.59732 1.72373 0.861865 0.507138i \(-0.169297\pi\)
0.861865 + 0.507138i \(0.169297\pi\)
\(32\) 2.18772 0.386738
\(33\) −3.85540 −0.671140
\(34\) 1.54663 0.265244
\(35\) −14.1383 −2.38981
\(36\) 0.392054 0.0653424
\(37\) −8.11194 −1.33360 −0.666798 0.745239i \(-0.732335\pi\)
−0.666798 + 0.745239i \(0.732335\pi\)
\(38\) 0.225520 0.0365842
\(39\) 1.41847 0.227137
\(40\) 8.93055 1.41204
\(41\) 2.99059 0.467052 0.233526 0.972351i \(-0.424974\pi\)
0.233526 + 0.972351i \(0.424974\pi\)
\(42\) −6.08924 −0.939589
\(43\) 3.02827 0.461807 0.230904 0.972977i \(-0.425832\pi\)
0.230904 + 0.972977i \(0.425832\pi\)
\(44\) 1.51153 0.227871
\(45\) 3.59105 0.535322
\(46\) 0.619719 0.0913725
\(47\) −8.05420 −1.17483 −0.587413 0.809287i \(-0.699854\pi\)
−0.587413 + 0.809287i \(0.699854\pi\)
\(48\) 4.63040 0.668341
\(49\) 8.50081 1.21440
\(50\) −12.2116 −1.72698
\(51\) 1.00000 0.140028
\(52\) −0.556118 −0.0771197
\(53\) 4.69749 0.645250 0.322625 0.946527i \(-0.395435\pi\)
0.322625 + 0.946527i \(0.395435\pi\)
\(54\) 1.54663 0.210469
\(55\) 13.8449 1.86685
\(56\) −9.79116 −1.30840
\(57\) 0.145814 0.0193136
\(58\) 7.37938 0.968960
\(59\) −8.98276 −1.16946 −0.584728 0.811230i \(-0.698799\pi\)
−0.584728 + 0.811230i \(0.698799\pi\)
\(60\) −1.40789 −0.181757
\(61\) −11.7945 −1.51014 −0.755068 0.655647i \(-0.772396\pi\)
−0.755068 + 0.655647i \(0.772396\pi\)
\(62\) −14.8435 −1.88512
\(63\) −3.93711 −0.496029
\(64\) 5.87722 0.734652
\(65\) −5.09380 −0.631808
\(66\) 5.96287 0.733979
\(67\) −5.49370 −0.671162 −0.335581 0.942011i \(-0.608933\pi\)
−0.335581 + 0.942011i \(0.608933\pi\)
\(68\) −0.392054 −0.0475436
\(69\) 0.400691 0.0482375
\(70\) 21.8667 2.61357
\(71\) 12.1394 1.44068 0.720341 0.693620i \(-0.243985\pi\)
0.720341 + 0.693620i \(0.243985\pi\)
\(72\) 2.48689 0.293083
\(73\) 6.38728 0.747575 0.373787 0.927514i \(-0.378059\pi\)
0.373787 + 0.927514i \(0.378059\pi\)
\(74\) 12.5461 1.45846
\(75\) −7.89562 −0.911707
\(76\) −0.0571672 −0.00655752
\(77\) −15.1791 −1.72982
\(78\) −2.19385 −0.248404
\(79\) 8.76482 0.986119 0.493059 0.869996i \(-0.335879\pi\)
0.493059 + 0.869996i \(0.335879\pi\)
\(80\) −16.6280 −1.85907
\(81\) 1.00000 0.111111
\(82\) −4.62533 −0.510783
\(83\) −6.68788 −0.734091 −0.367045 0.930203i \(-0.619631\pi\)
−0.367045 + 0.930203i \(0.619631\pi\)
\(84\) 1.54356 0.168416
\(85\) −3.59105 −0.389504
\(86\) −4.68361 −0.505046
\(87\) 4.77127 0.511534
\(88\) 9.58798 1.02208
\(89\) −7.17883 −0.760954 −0.380477 0.924790i \(-0.624240\pi\)
−0.380477 + 0.924790i \(0.624240\pi\)
\(90\) −5.55401 −0.585444
\(91\) 5.58468 0.585433
\(92\) −0.157092 −0.0163780
\(93\) −9.59732 −0.995196
\(94\) 12.4568 1.28483
\(95\) −0.523626 −0.0537229
\(96\) −2.18772 −0.223283
\(97\) −11.2410 −1.14135 −0.570675 0.821176i \(-0.693318\pi\)
−0.570675 + 0.821176i \(0.693318\pi\)
\(98\) −13.1476 −1.32811
\(99\) 3.85540 0.387483
\(100\) 3.09551 0.309551
\(101\) 1.25851 0.125227 0.0626135 0.998038i \(-0.480056\pi\)
0.0626135 + 0.998038i \(0.480056\pi\)
\(102\) −1.54663 −0.153139
\(103\) −10.7296 −1.05722 −0.528610 0.848865i \(-0.677287\pi\)
−0.528610 + 0.848865i \(0.677287\pi\)
\(104\) −3.52759 −0.345908
\(105\) 14.1383 1.37976
\(106\) −7.26527 −0.705665
\(107\) −12.5171 −1.21007 −0.605035 0.796199i \(-0.706841\pi\)
−0.605035 + 0.796199i \(0.706841\pi\)
\(108\) −0.392054 −0.0377254
\(109\) 4.19169 0.401491 0.200745 0.979643i \(-0.435664\pi\)
0.200745 + 0.979643i \(0.435664\pi\)
\(110\) −21.4130 −2.04164
\(111\) 8.11194 0.769952
\(112\) 18.2304 1.72261
\(113\) 3.05047 0.286964 0.143482 0.989653i \(-0.454170\pi\)
0.143482 + 0.989653i \(0.454170\pi\)
\(114\) −0.225520 −0.0211219
\(115\) −1.43890 −0.134178
\(116\) −1.87060 −0.173681
\(117\) −1.41847 −0.131138
\(118\) 13.8930 1.27895
\(119\) 3.93711 0.360914
\(120\) −8.93055 −0.815243
\(121\) 3.86415 0.351286
\(122\) 18.2417 1.65153
\(123\) −2.99059 −0.269653
\(124\) 3.76267 0.337898
\(125\) 10.3983 0.930052
\(126\) 6.08924 0.542472
\(127\) 8.27405 0.734203 0.367102 0.930181i \(-0.380350\pi\)
0.367102 + 0.930181i \(0.380350\pi\)
\(128\) −13.4653 −1.19018
\(129\) −3.02827 −0.266625
\(130\) 7.87821 0.690965
\(131\) 3.42735 0.299449 0.149724 0.988728i \(-0.452161\pi\)
0.149724 + 0.988728i \(0.452161\pi\)
\(132\) −1.51153 −0.131562
\(133\) 0.574087 0.0497796
\(134\) 8.49670 0.734003
\(135\) −3.59105 −0.309068
\(136\) −2.48689 −0.213249
\(137\) −22.2343 −1.89960 −0.949802 0.312852i \(-0.898716\pi\)
−0.949802 + 0.312852i \(0.898716\pi\)
\(138\) −0.619719 −0.0527540
\(139\) 8.46971 0.718392 0.359196 0.933262i \(-0.383051\pi\)
0.359196 + 0.933262i \(0.383051\pi\)
\(140\) −5.54299 −0.468469
\(141\) 8.05420 0.678286
\(142\) −18.7751 −1.57557
\(143\) −5.46879 −0.457323
\(144\) −4.63040 −0.385867
\(145\) −17.1339 −1.42289
\(146\) −9.87874 −0.817570
\(147\) −8.50081 −0.701135
\(148\) −3.18032 −0.261421
\(149\) 3.96393 0.324738 0.162369 0.986730i \(-0.448087\pi\)
0.162369 + 0.986730i \(0.448087\pi\)
\(150\) 12.2116 0.997071
\(151\) −9.32731 −0.759046 −0.379523 0.925182i \(-0.623912\pi\)
−0.379523 + 0.925182i \(0.623912\pi\)
\(152\) −0.362625 −0.0294127
\(153\) −1.00000 −0.0808452
\(154\) 23.4765 1.89179
\(155\) 34.4644 2.76825
\(156\) 0.556118 0.0445251
\(157\) −1.00000 −0.0798087
\(158\) −13.5559 −1.07845
\(159\) −4.69749 −0.372535
\(160\) 7.85620 0.621087
\(161\) 1.57756 0.124329
\(162\) −1.54663 −0.121514
\(163\) 13.7238 1.07493 0.537465 0.843286i \(-0.319382\pi\)
0.537465 + 0.843286i \(0.319382\pi\)
\(164\) 1.17247 0.0915549
\(165\) −13.8449 −1.07783
\(166\) 10.3437 0.802824
\(167\) 5.47079 0.423342 0.211671 0.977341i \(-0.432109\pi\)
0.211671 + 0.977341i \(0.432109\pi\)
\(168\) 9.79116 0.755404
\(169\) −10.9879 −0.845226
\(170\) 5.55401 0.425973
\(171\) −0.145814 −0.0111507
\(172\) 1.18725 0.0905268
\(173\) −9.34451 −0.710450 −0.355225 0.934781i \(-0.615596\pi\)
−0.355225 + 0.934781i \(0.615596\pi\)
\(174\) −7.37938 −0.559429
\(175\) −31.0859 −2.34987
\(176\) −17.8521 −1.34565
\(177\) 8.98276 0.675185
\(178\) 11.1030 0.832202
\(179\) 3.01972 0.225704 0.112852 0.993612i \(-0.464001\pi\)
0.112852 + 0.993612i \(0.464001\pi\)
\(180\) 1.40789 0.104938
\(181\) 1.97516 0.146813 0.0734063 0.997302i \(-0.476613\pi\)
0.0734063 + 0.997302i \(0.476613\pi\)
\(182\) −8.63741 −0.640248
\(183\) 11.7945 0.871877
\(184\) −0.996474 −0.0734610
\(185\) −29.1304 −2.14171
\(186\) 14.8435 1.08838
\(187\) −3.85540 −0.281935
\(188\) −3.15768 −0.230298
\(189\) 3.93711 0.286382
\(190\) 0.809854 0.0587530
\(191\) −18.7075 −1.35363 −0.676815 0.736153i \(-0.736640\pi\)
−0.676815 + 0.736153i \(0.736640\pi\)
\(192\) −5.87722 −0.424152
\(193\) −5.35036 −0.385127 −0.192564 0.981284i \(-0.561680\pi\)
−0.192564 + 0.981284i \(0.561680\pi\)
\(194\) 17.3856 1.24821
\(195\) 5.09380 0.364775
\(196\) 3.33278 0.238056
\(197\) −4.07175 −0.290100 −0.145050 0.989424i \(-0.546334\pi\)
−0.145050 + 0.989424i \(0.546334\pi\)
\(198\) −5.96287 −0.423763
\(199\) 2.43646 0.172716 0.0863581 0.996264i \(-0.472477\pi\)
0.0863581 + 0.996264i \(0.472477\pi\)
\(200\) 19.6355 1.38844
\(201\) 5.49370 0.387495
\(202\) −1.94645 −0.136952
\(203\) 18.7850 1.31845
\(204\) 0.392054 0.0274493
\(205\) 10.7394 0.750070
\(206\) 16.5947 1.15621
\(207\) −0.400691 −0.0278499
\(208\) 6.56810 0.455416
\(209\) −0.562174 −0.0388864
\(210\) −21.8667 −1.50895
\(211\) −6.39005 −0.439909 −0.219955 0.975510i \(-0.570591\pi\)
−0.219955 + 0.975510i \(0.570591\pi\)
\(212\) 1.84167 0.126486
\(213\) −12.1394 −0.831778
\(214\) 19.3592 1.32337
\(215\) 10.8747 0.741646
\(216\) −2.48689 −0.169212
\(217\) −37.7857 −2.56506
\(218\) −6.48297 −0.439082
\(219\) −6.38728 −0.431612
\(220\) 5.42797 0.365953
\(221\) 1.41847 0.0954168
\(222\) −12.5461 −0.842042
\(223\) 15.7994 1.05801 0.529004 0.848619i \(-0.322566\pi\)
0.529004 + 0.848619i \(0.322566\pi\)
\(224\) −8.61329 −0.575499
\(225\) 7.89562 0.526374
\(226\) −4.71793 −0.313832
\(227\) 22.3025 1.48027 0.740133 0.672460i \(-0.234762\pi\)
0.740133 + 0.672460i \(0.234762\pi\)
\(228\) 0.0571672 0.00378599
\(229\) 8.60868 0.568878 0.284439 0.958694i \(-0.408193\pi\)
0.284439 + 0.958694i \(0.408193\pi\)
\(230\) 2.22544 0.146741
\(231\) 15.1791 0.998714
\(232\) −11.8656 −0.779018
\(233\) 16.5862 1.08660 0.543299 0.839539i \(-0.317175\pi\)
0.543299 + 0.839539i \(0.317175\pi\)
\(234\) 2.19385 0.143416
\(235\) −28.9230 −1.88673
\(236\) −3.52173 −0.229245
\(237\) −8.76482 −0.569336
\(238\) −6.08924 −0.394706
\(239\) −20.8882 −1.35115 −0.675574 0.737292i \(-0.736104\pi\)
−0.675574 + 0.737292i \(0.736104\pi\)
\(240\) 16.6280 1.07333
\(241\) −14.4173 −0.928699 −0.464349 0.885652i \(-0.653712\pi\)
−0.464349 + 0.885652i \(0.653712\pi\)
\(242\) −5.97639 −0.384177
\(243\) −1.00000 −0.0641500
\(244\) −4.62410 −0.296027
\(245\) 30.5268 1.95029
\(246\) 4.62533 0.294900
\(247\) 0.206834 0.0131605
\(248\) 23.8675 1.51559
\(249\) 6.68788 0.423827
\(250\) −16.0823 −1.01713
\(251\) 23.9164 1.50959 0.754794 0.655962i \(-0.227737\pi\)
0.754794 + 0.655962i \(0.227737\pi\)
\(252\) −1.54356 −0.0972351
\(253\) −1.54482 −0.0971223
\(254\) −12.7969 −0.802947
\(255\) 3.59105 0.224880
\(256\) 9.07136 0.566960
\(257\) 4.37343 0.272807 0.136404 0.990653i \(-0.456446\pi\)
0.136404 + 0.990653i \(0.456446\pi\)
\(258\) 4.68361 0.291589
\(259\) 31.9376 1.98451
\(260\) −1.99705 −0.123852
\(261\) −4.77127 −0.295334
\(262\) −5.30083 −0.327486
\(263\) −5.15870 −0.318099 −0.159050 0.987271i \(-0.550843\pi\)
−0.159050 + 0.987271i \(0.550843\pi\)
\(264\) −9.58798 −0.590099
\(265\) 16.8689 1.03625
\(266\) −0.887898 −0.0544405
\(267\) 7.17883 0.439337
\(268\) −2.15383 −0.131566
\(269\) −23.3617 −1.42439 −0.712193 0.701984i \(-0.752298\pi\)
−0.712193 + 0.701984i \(0.752298\pi\)
\(270\) 5.55401 0.338006
\(271\) 11.8120 0.717528 0.358764 0.933428i \(-0.383198\pi\)
0.358764 + 0.933428i \(0.383198\pi\)
\(272\) 4.63040 0.280759
\(273\) −5.58468 −0.338000
\(274\) 34.3882 2.07746
\(275\) 30.4408 1.83565
\(276\) 0.157092 0.00945585
\(277\) 12.8652 0.772992 0.386496 0.922291i \(-0.373685\pi\)
0.386496 + 0.922291i \(0.373685\pi\)
\(278\) −13.0995 −0.785655
\(279\) 9.59732 0.574577
\(280\) −35.1605 −2.10124
\(281\) 22.4357 1.33840 0.669201 0.743082i \(-0.266637\pi\)
0.669201 + 0.743082i \(0.266637\pi\)
\(282\) −12.4568 −0.741794
\(283\) 1.03185 0.0613370 0.0306685 0.999530i \(-0.490236\pi\)
0.0306685 + 0.999530i \(0.490236\pi\)
\(284\) 4.75930 0.282413
\(285\) 0.523626 0.0310169
\(286\) 8.45817 0.500142
\(287\) −11.7743 −0.695014
\(288\) 2.18772 0.128913
\(289\) 1.00000 0.0588235
\(290\) 26.4997 1.55612
\(291\) 11.2410 0.658958
\(292\) 2.50416 0.146545
\(293\) 14.6591 0.856394 0.428197 0.903685i \(-0.359149\pi\)
0.428197 + 0.903685i \(0.359149\pi\)
\(294\) 13.1476 0.766783
\(295\) −32.2575 −1.87810
\(296\) −20.1735 −1.17256
\(297\) −3.85540 −0.223713
\(298\) −6.13072 −0.355143
\(299\) 0.568369 0.0328696
\(300\) −3.09551 −0.178719
\(301\) −11.9226 −0.687209
\(302\) 14.4259 0.830115
\(303\) −1.25851 −0.0722998
\(304\) 0.675179 0.0387242
\(305\) −42.3547 −2.42522
\(306\) 1.54663 0.0884148
\(307\) 20.9980 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(308\) −5.95105 −0.339092
\(309\) 10.7296 0.610386
\(310\) −53.3036 −3.02744
\(311\) 5.09870 0.289121 0.144560 0.989496i \(-0.453823\pi\)
0.144560 + 0.989496i \(0.453823\pi\)
\(312\) 3.52759 0.199710
\(313\) −26.1297 −1.47694 −0.738468 0.674289i \(-0.764450\pi\)
−0.738468 + 0.674289i \(0.764450\pi\)
\(314\) 1.54663 0.0872812
\(315\) −14.1383 −0.796605
\(316\) 3.43628 0.193306
\(317\) −19.6132 −1.10159 −0.550794 0.834641i \(-0.685675\pi\)
−0.550794 + 0.834641i \(0.685675\pi\)
\(318\) 7.26527 0.407416
\(319\) −18.3952 −1.02993
\(320\) 21.1054 1.17983
\(321\) 12.5171 0.698635
\(322\) −2.43990 −0.135970
\(323\) 0.145814 0.00811333
\(324\) 0.392054 0.0217808
\(325\) −11.1997 −0.621248
\(326\) −21.2256 −1.17558
\(327\) −4.19169 −0.231801
\(328\) 7.43728 0.410655
\(329\) 31.7103 1.74824
\(330\) 21.4130 1.17874
\(331\) −18.1817 −0.999357 −0.499679 0.866211i \(-0.666549\pi\)
−0.499679 + 0.866211i \(0.666549\pi\)
\(332\) −2.62201 −0.143902
\(333\) −8.11194 −0.444532
\(334\) −8.46127 −0.462980
\(335\) −19.7281 −1.07786
\(336\) −18.2304 −0.994549
\(337\) −32.1581 −1.75176 −0.875882 0.482525i \(-0.839720\pi\)
−0.875882 + 0.482525i \(0.839720\pi\)
\(338\) 16.9942 0.924364
\(339\) −3.05047 −0.165679
\(340\) −1.40789 −0.0763533
\(341\) 37.0016 2.00375
\(342\) 0.225520 0.0121947
\(343\) −5.90886 −0.319049
\(344\) 7.53099 0.406044
\(345\) 1.43890 0.0774677
\(346\) 14.4525 0.776970
\(347\) −4.85588 −0.260677 −0.130339 0.991470i \(-0.541606\pi\)
−0.130339 + 0.991470i \(0.541606\pi\)
\(348\) 1.87060 0.100275
\(349\) −1.73178 −0.0927002 −0.0463501 0.998925i \(-0.514759\pi\)
−0.0463501 + 0.998925i \(0.514759\pi\)
\(350\) 48.0783 2.56989
\(351\) 1.41847 0.0757125
\(352\) 8.43454 0.449563
\(353\) −11.0390 −0.587545 −0.293773 0.955875i \(-0.594911\pi\)
−0.293773 + 0.955875i \(0.594911\pi\)
\(354\) −13.8930 −0.738403
\(355\) 43.5931 2.31368
\(356\) −2.81449 −0.149168
\(357\) −3.93711 −0.208374
\(358\) −4.67037 −0.246837
\(359\) 31.7766 1.67710 0.838552 0.544821i \(-0.183403\pi\)
0.838552 + 0.544821i \(0.183403\pi\)
\(360\) 8.93055 0.470681
\(361\) −18.9787 −0.998881
\(362\) −3.05484 −0.160559
\(363\) −3.86415 −0.202815
\(364\) 2.18950 0.114761
\(365\) 22.9370 1.20058
\(366\) −18.2417 −0.953511
\(367\) −2.61589 −0.136548 −0.0682742 0.997667i \(-0.521749\pi\)
−0.0682742 + 0.997667i \(0.521749\pi\)
\(368\) 1.85536 0.0967172
\(369\) 2.99059 0.155684
\(370\) 45.0538 2.34224
\(371\) −18.4945 −0.960188
\(372\) −3.76267 −0.195085
\(373\) 12.3696 0.640472 0.320236 0.947338i \(-0.396238\pi\)
0.320236 + 0.947338i \(0.396238\pi\)
\(374\) 5.96287 0.308333
\(375\) −10.3983 −0.536966
\(376\) −20.0299 −1.03296
\(377\) 6.76792 0.348566
\(378\) −6.08924 −0.313196
\(379\) −9.19981 −0.472563 −0.236281 0.971685i \(-0.575929\pi\)
−0.236281 + 0.971685i \(0.575929\pi\)
\(380\) −0.205290 −0.0105312
\(381\) −8.27405 −0.423893
\(382\) 28.9336 1.48037
\(383\) −34.5042 −1.76308 −0.881542 0.472105i \(-0.843494\pi\)
−0.881542 + 0.472105i \(0.843494\pi\)
\(384\) 13.4653 0.687148
\(385\) −54.5090 −2.77804
\(386\) 8.27501 0.421187
\(387\) 3.02827 0.153936
\(388\) −4.40708 −0.223735
\(389\) −13.3264 −0.675678 −0.337839 0.941204i \(-0.609696\pi\)
−0.337839 + 0.941204i \(0.609696\pi\)
\(390\) −7.87821 −0.398929
\(391\) 0.400691 0.0202638
\(392\) 21.1406 1.06776
\(393\) −3.42735 −0.172887
\(394\) 6.29748 0.317262
\(395\) 31.4749 1.58367
\(396\) 1.51153 0.0759571
\(397\) −4.13738 −0.207649 −0.103825 0.994596i \(-0.533108\pi\)
−0.103825 + 0.994596i \(0.533108\pi\)
\(398\) −3.76830 −0.188888
\(399\) −0.574087 −0.0287403
\(400\) −36.5599 −1.82799
\(401\) 20.6376 1.03059 0.515295 0.857013i \(-0.327682\pi\)
0.515295 + 0.857013i \(0.327682\pi\)
\(402\) −8.49670 −0.423777
\(403\) −13.6135 −0.678139
\(404\) 0.493406 0.0245479
\(405\) 3.59105 0.178441
\(406\) −29.0534 −1.44190
\(407\) −31.2748 −1.55024
\(408\) 2.48689 0.123119
\(409\) 27.3417 1.35196 0.675981 0.736919i \(-0.263720\pi\)
0.675981 + 0.736919i \(0.263720\pi\)
\(410\) −16.6098 −0.820299
\(411\) 22.2343 1.09674
\(412\) −4.20659 −0.207244
\(413\) 35.3661 1.74025
\(414\) 0.619719 0.0304575
\(415\) −24.0165 −1.17892
\(416\) −3.10322 −0.152148
\(417\) −8.46971 −0.414764
\(418\) 0.869473 0.0425273
\(419\) −27.5130 −1.34410 −0.672049 0.740506i \(-0.734586\pi\)
−0.672049 + 0.740506i \(0.734586\pi\)
\(420\) 5.54299 0.270470
\(421\) −25.6647 −1.25082 −0.625410 0.780297i \(-0.715068\pi\)
−0.625410 + 0.780297i \(0.715068\pi\)
\(422\) 9.88303 0.481098
\(423\) −8.05420 −0.391609
\(424\) 11.6822 0.567335
\(425\) −7.89562 −0.382994
\(426\) 18.7751 0.909657
\(427\) 46.4363 2.24721
\(428\) −4.90737 −0.237207
\(429\) 5.46879 0.264035
\(430\) −16.8191 −0.811087
\(431\) 10.4757 0.504595 0.252298 0.967650i \(-0.418814\pi\)
0.252298 + 0.967650i \(0.418814\pi\)
\(432\) 4.63040 0.222780
\(433\) −26.0663 −1.25267 −0.626334 0.779555i \(-0.715445\pi\)
−0.626334 + 0.779555i \(0.715445\pi\)
\(434\) 58.4403 2.80523
\(435\) 17.1339 0.821506
\(436\) 1.64337 0.0787031
\(437\) 0.0584265 0.00279492
\(438\) 9.87874 0.472024
\(439\) −5.14461 −0.245539 −0.122769 0.992435i \(-0.539178\pi\)
−0.122769 + 0.992435i \(0.539178\pi\)
\(440\) 34.4309 1.64143
\(441\) 8.50081 0.404801
\(442\) −2.19385 −0.104351
\(443\) 30.7733 1.46208 0.731041 0.682334i \(-0.239035\pi\)
0.731041 + 0.682334i \(0.239035\pi\)
\(444\) 3.18032 0.150931
\(445\) −25.7795 −1.22207
\(446\) −24.4358 −1.15707
\(447\) −3.96393 −0.187487
\(448\) −23.1392 −1.09323
\(449\) 20.7647 0.979948 0.489974 0.871737i \(-0.337006\pi\)
0.489974 + 0.871737i \(0.337006\pi\)
\(450\) −12.2116 −0.575659
\(451\) 11.5299 0.542924
\(452\) 1.19595 0.0562527
\(453\) 9.32731 0.438235
\(454\) −34.4936 −1.61886
\(455\) 20.0548 0.940186
\(456\) 0.362625 0.0169815
\(457\) −11.0585 −0.517293 −0.258647 0.965972i \(-0.583277\pi\)
−0.258647 + 0.965972i \(0.583277\pi\)
\(458\) −13.3144 −0.622142
\(459\) 1.00000 0.0466760
\(460\) −0.564126 −0.0263025
\(461\) −24.8112 −1.15557 −0.577787 0.816188i \(-0.696083\pi\)
−0.577787 + 0.816188i \(0.696083\pi\)
\(462\) −23.4765 −1.09222
\(463\) 4.78200 0.222239 0.111119 0.993807i \(-0.464556\pi\)
0.111119 + 0.993807i \(0.464556\pi\)
\(464\) 22.0929 1.02564
\(465\) −34.4644 −1.59825
\(466\) −25.6527 −1.18834
\(467\) −15.7466 −0.728667 −0.364333 0.931269i \(-0.618703\pi\)
−0.364333 + 0.931269i \(0.618703\pi\)
\(468\) −0.556118 −0.0257066
\(469\) 21.6293 0.998747
\(470\) 44.7331 2.06338
\(471\) 1.00000 0.0460776
\(472\) −22.3391 −1.02824
\(473\) 11.6752 0.536827
\(474\) 13.5559 0.622643
\(475\) −1.15129 −0.0528250
\(476\) 1.54356 0.0707489
\(477\) 4.69749 0.215083
\(478\) 32.3063 1.47766
\(479\) 10.3222 0.471635 0.235817 0.971797i \(-0.424223\pi\)
0.235817 + 0.971797i \(0.424223\pi\)
\(480\) −7.85620 −0.358585
\(481\) 11.5066 0.524654
\(482\) 22.2982 1.01565
\(483\) −1.57756 −0.0717815
\(484\) 1.51495 0.0688616
\(485\) −40.3669 −1.83297
\(486\) 1.54663 0.0701564
\(487\) 25.0533 1.13527 0.567636 0.823280i \(-0.307858\pi\)
0.567636 + 0.823280i \(0.307858\pi\)
\(488\) −29.3317 −1.32779
\(489\) −13.7238 −0.620611
\(490\) −47.2136 −2.13289
\(491\) −41.1123 −1.85537 −0.927685 0.373363i \(-0.878204\pi\)
−0.927685 + 0.373363i \(0.878204\pi\)
\(492\) −1.17247 −0.0528593
\(493\) 4.77127 0.214887
\(494\) −0.319895 −0.0143927
\(495\) 13.8449 0.622284
\(496\) −44.4394 −1.99539
\(497\) −47.7941 −2.14386
\(498\) −10.3437 −0.463510
\(499\) 33.2480 1.48838 0.744192 0.667966i \(-0.232835\pi\)
0.744192 + 0.667966i \(0.232835\pi\)
\(500\) 4.07670 0.182315
\(501\) −5.47079 −0.244417
\(502\) −36.9897 −1.65093
\(503\) 11.1986 0.499323 0.249661 0.968333i \(-0.419681\pi\)
0.249661 + 0.968333i \(0.419681\pi\)
\(504\) −9.79116 −0.436133
\(505\) 4.51939 0.201110
\(506\) 2.38927 0.106216
\(507\) 10.9879 0.487991
\(508\) 3.24388 0.143924
\(509\) −8.34251 −0.369775 −0.184888 0.982760i \(-0.559192\pi\)
−0.184888 + 0.982760i \(0.559192\pi\)
\(510\) −5.55401 −0.245936
\(511\) −25.1474 −1.11246
\(512\) 12.9006 0.570131
\(513\) 0.145814 0.00643786
\(514\) −6.76406 −0.298350
\(515\) −38.5305 −1.69786
\(516\) −1.18725 −0.0522657
\(517\) −31.0522 −1.36567
\(518\) −49.3955 −2.17032
\(519\) 9.34451 0.410179
\(520\) −12.6677 −0.555517
\(521\) 25.9794 1.13818 0.569090 0.822275i \(-0.307296\pi\)
0.569090 + 0.822275i \(0.307296\pi\)
\(522\) 7.37938 0.322987
\(523\) 3.60811 0.157772 0.0788859 0.996884i \(-0.474864\pi\)
0.0788859 + 0.996884i \(0.474864\pi\)
\(524\) 1.34371 0.0587001
\(525\) 31.0859 1.35670
\(526\) 7.97859 0.347883
\(527\) −9.59732 −0.418066
\(528\) 17.8521 0.776912
\(529\) −22.8394 −0.993019
\(530\) −26.0899 −1.13327
\(531\) −8.98276 −0.389819
\(532\) 0.225073 0.00975816
\(533\) −4.24208 −0.183745
\(534\) −11.1030 −0.480472
\(535\) −44.9494 −1.94333
\(536\) −13.6622 −0.590118
\(537\) −3.01972 −0.130310
\(538\) 36.1318 1.55775
\(539\) 32.7741 1.41168
\(540\) −1.40789 −0.0605857
\(541\) −21.7946 −0.937025 −0.468513 0.883457i \(-0.655210\pi\)
−0.468513 + 0.883457i \(0.655210\pi\)
\(542\) −18.2688 −0.784710
\(543\) −1.97516 −0.0847623
\(544\) −2.18772 −0.0937977
\(545\) 15.0525 0.644780
\(546\) 8.63741 0.369647
\(547\) −28.8135 −1.23198 −0.615989 0.787755i \(-0.711243\pi\)
−0.615989 + 0.787755i \(0.711243\pi\)
\(548\) −8.71705 −0.372374
\(549\) −11.7945 −0.503378
\(550\) −47.0806 −2.00752
\(551\) 0.695720 0.0296387
\(552\) 0.996474 0.0424128
\(553\) −34.5080 −1.46743
\(554\) −19.8976 −0.845368
\(555\) 29.1304 1.23652
\(556\) 3.32059 0.140824
\(557\) 11.8907 0.503826 0.251913 0.967750i \(-0.418940\pi\)
0.251913 + 0.967750i \(0.418940\pi\)
\(558\) −14.8435 −0.628374
\(559\) −4.29552 −0.181681
\(560\) 65.4662 2.76645
\(561\) 3.85540 0.162775
\(562\) −34.6997 −1.46372
\(563\) 13.3514 0.562696 0.281348 0.959606i \(-0.409218\pi\)
0.281348 + 0.959606i \(0.409218\pi\)
\(564\) 3.15768 0.132962
\(565\) 10.9544 0.460854
\(566\) −1.59588 −0.0670800
\(567\) −3.93711 −0.165343
\(568\) 30.1894 1.26672
\(569\) −4.47621 −0.187653 −0.0938263 0.995589i \(-0.529910\pi\)
−0.0938263 + 0.995589i \(0.529910\pi\)
\(570\) −0.809854 −0.0339211
\(571\) 35.2715 1.47607 0.738033 0.674764i \(-0.235755\pi\)
0.738033 + 0.674764i \(0.235755\pi\)
\(572\) −2.14406 −0.0896477
\(573\) 18.7075 0.781519
\(574\) 18.2104 0.760089
\(575\) −3.16370 −0.131935
\(576\) 5.87722 0.244884
\(577\) 19.2534 0.801530 0.400765 0.916181i \(-0.368744\pi\)
0.400765 + 0.916181i \(0.368744\pi\)
\(578\) −1.54663 −0.0643312
\(579\) 5.35036 0.222353
\(580\) −6.71741 −0.278925
\(581\) 26.3309 1.09239
\(582\) −17.3856 −0.720657
\(583\) 18.1107 0.750070
\(584\) 15.8845 0.657304
\(585\) −5.09380 −0.210603
\(586\) −22.6722 −0.936579
\(587\) −4.00735 −0.165401 −0.0827005 0.996574i \(-0.526354\pi\)
−0.0827005 + 0.996574i \(0.526354\pi\)
\(588\) −3.33278 −0.137442
\(589\) −1.39943 −0.0576624
\(590\) 49.8903 2.05395
\(591\) 4.07175 0.167489
\(592\) 37.5616 1.54377
\(593\) −35.0361 −1.43876 −0.719381 0.694616i \(-0.755574\pi\)
−0.719381 + 0.694616i \(0.755574\pi\)
\(594\) 5.96287 0.244660
\(595\) 14.1383 0.579615
\(596\) 1.55407 0.0636574
\(597\) −2.43646 −0.0997178
\(598\) −0.879054 −0.0359472
\(599\) −23.8079 −0.972765 −0.486382 0.873746i \(-0.661684\pi\)
−0.486382 + 0.873746i \(0.661684\pi\)
\(600\) −19.6355 −0.801618
\(601\) 18.5378 0.756171 0.378086 0.925771i \(-0.376583\pi\)
0.378086 + 0.925771i \(0.376583\pi\)
\(602\) 18.4399 0.751553
\(603\) −5.49370 −0.223721
\(604\) −3.65681 −0.148794
\(605\) 13.8763 0.564153
\(606\) 1.94645 0.0790692
\(607\) −14.2576 −0.578698 −0.289349 0.957224i \(-0.593439\pi\)
−0.289349 + 0.957224i \(0.593439\pi\)
\(608\) −0.319001 −0.0129372
\(609\) −18.7850 −0.761207
\(610\) 65.5069 2.65230
\(611\) 11.4247 0.462193
\(612\) −0.392054 −0.0158479
\(613\) −28.1775 −1.13808 −0.569039 0.822310i \(-0.692685\pi\)
−0.569039 + 0.822310i \(0.692685\pi\)
\(614\) −32.4760 −1.31062
\(615\) −10.7394 −0.433053
\(616\) −37.7489 −1.52095
\(617\) −25.3219 −1.01942 −0.509711 0.860346i \(-0.670248\pi\)
−0.509711 + 0.860346i \(0.670248\pi\)
\(618\) −16.5947 −0.667537
\(619\) −33.7829 −1.35785 −0.678925 0.734208i \(-0.737554\pi\)
−0.678925 + 0.734208i \(0.737554\pi\)
\(620\) 13.5119 0.542652
\(621\) 0.400691 0.0160792
\(622\) −7.88579 −0.316191
\(623\) 28.2638 1.13237
\(624\) −6.56810 −0.262934
\(625\) −2.13732 −0.0854928
\(626\) 40.4128 1.61522
\(627\) 0.562174 0.0224510
\(628\) −0.392054 −0.0156447
\(629\) 8.11194 0.323444
\(630\) 21.8667 0.871191
\(631\) 13.9029 0.553464 0.276732 0.960947i \(-0.410749\pi\)
0.276732 + 0.960947i \(0.410749\pi\)
\(632\) 21.7971 0.867044
\(633\) 6.39005 0.253982
\(634\) 30.3343 1.20473
\(635\) 29.7125 1.17911
\(636\) −1.84167 −0.0730270
\(637\) −12.0582 −0.477762
\(638\) 28.4505 1.12637
\(639\) 12.1394 0.480227
\(640\) −48.3545 −1.91138
\(641\) −38.0252 −1.50191 −0.750953 0.660355i \(-0.770406\pi\)
−0.750953 + 0.660355i \(0.770406\pi\)
\(642\) −19.3592 −0.764048
\(643\) −38.6521 −1.52429 −0.762146 0.647406i \(-0.775854\pi\)
−0.762146 + 0.647406i \(0.775854\pi\)
\(644\) 0.618490 0.0243719
\(645\) −10.8747 −0.428190
\(646\) −0.225520 −0.00887298
\(647\) 19.4338 0.764021 0.382011 0.924158i \(-0.375232\pi\)
0.382011 + 0.924158i \(0.375232\pi\)
\(648\) 2.48689 0.0976943
\(649\) −34.6322 −1.35943
\(650\) 17.3218 0.679416
\(651\) 37.7857 1.48094
\(652\) 5.38047 0.210715
\(653\) 45.7883 1.79183 0.895917 0.444222i \(-0.146520\pi\)
0.895917 + 0.444222i \(0.146520\pi\)
\(654\) 6.48297 0.253504
\(655\) 12.3078 0.480904
\(656\) −13.8477 −0.540660
\(657\) 6.38728 0.249192
\(658\) −49.0439 −1.91193
\(659\) −3.29596 −0.128392 −0.0641961 0.997937i \(-0.520448\pi\)
−0.0641961 + 0.997937i \(0.520448\pi\)
\(660\) −5.42797 −0.211283
\(661\) 16.2719 0.632902 0.316451 0.948609i \(-0.397509\pi\)
0.316451 + 0.948609i \(0.397509\pi\)
\(662\) 28.1203 1.09293
\(663\) −1.41847 −0.0550889
\(664\) −16.6320 −0.645448
\(665\) 2.06157 0.0799444
\(666\) 12.5461 0.486153
\(667\) 1.91180 0.0740254
\(668\) 2.14485 0.0829866
\(669\) −15.7994 −0.610841
\(670\) 30.5120 1.17878
\(671\) −45.4727 −1.75545
\(672\) 8.61329 0.332265
\(673\) −10.3424 −0.398672 −0.199336 0.979931i \(-0.563878\pi\)
−0.199336 + 0.979931i \(0.563878\pi\)
\(674\) 49.7366 1.91578
\(675\) −7.89562 −0.303902
\(676\) −4.30787 −0.165687
\(677\) 24.6411 0.947036 0.473518 0.880784i \(-0.342984\pi\)
0.473518 + 0.880784i \(0.342984\pi\)
\(678\) 4.71793 0.181191
\(679\) 44.2570 1.69843
\(680\) −8.93055 −0.342471
\(681\) −22.3025 −0.854632
\(682\) −57.2276 −2.19136
\(683\) −1.94550 −0.0744423 −0.0372212 0.999307i \(-0.511851\pi\)
−0.0372212 + 0.999307i \(0.511851\pi\)
\(684\) −0.0571672 −0.00218584
\(685\) −79.8444 −3.05070
\(686\) 9.13880 0.348921
\(687\) −8.60868 −0.328442
\(688\) −14.0221 −0.534588
\(689\) −6.66326 −0.253850
\(690\) −2.22544 −0.0847210
\(691\) 10.8166 0.411484 0.205742 0.978606i \(-0.434039\pi\)
0.205742 + 0.978606i \(0.434039\pi\)
\(692\) −3.66356 −0.139268
\(693\) −15.1791 −0.576608
\(694\) 7.51023 0.285085
\(695\) 30.4151 1.15371
\(696\) 11.8656 0.449766
\(697\) −2.99059 −0.113277
\(698\) 2.67842 0.101380
\(699\) −16.5862 −0.627348
\(700\) −12.1874 −0.460639
\(701\) −7.31867 −0.276422 −0.138211 0.990403i \(-0.544135\pi\)
−0.138211 + 0.990403i \(0.544135\pi\)
\(702\) −2.19385 −0.0828014
\(703\) 1.18284 0.0446116
\(704\) 22.6591 0.853995
\(705\) 28.9230 1.08930
\(706\) 17.0732 0.642557
\(707\) −4.95491 −0.186348
\(708\) 3.52173 0.132355
\(709\) 30.5669 1.14797 0.573983 0.818867i \(-0.305398\pi\)
0.573983 + 0.818867i \(0.305398\pi\)
\(710\) −67.4223 −2.53031
\(711\) 8.76482 0.328706
\(712\) −17.8530 −0.669068
\(713\) −3.84556 −0.144017
\(714\) 6.08924 0.227884
\(715\) −19.6387 −0.734445
\(716\) 1.18389 0.0442441
\(717\) 20.8882 0.780086
\(718\) −49.1465 −1.83413
\(719\) −39.3686 −1.46820 −0.734100 0.679041i \(-0.762396\pi\)
−0.734100 + 0.679041i \(0.762396\pi\)
\(720\) −16.6280 −0.619689
\(721\) 42.2436 1.57324
\(722\) 29.3530 1.09241
\(723\) 14.4173 0.536185
\(724\) 0.774370 0.0287792
\(725\) −37.6722 −1.39911
\(726\) 5.97639 0.221805
\(727\) −2.95851 −0.109725 −0.0548626 0.998494i \(-0.517472\pi\)
−0.0548626 + 0.998494i \(0.517472\pi\)
\(728\) 13.8885 0.514742
\(729\) 1.00000 0.0370370
\(730\) −35.4750 −1.31299
\(731\) −3.02827 −0.112005
\(732\) 4.62410 0.170912
\(733\) −0.125750 −0.00464466 −0.00232233 0.999997i \(-0.500739\pi\)
−0.00232233 + 0.999997i \(0.500739\pi\)
\(734\) 4.04581 0.149333
\(735\) −30.5268 −1.12600
\(736\) −0.876599 −0.0323119
\(737\) −21.1804 −0.780191
\(738\) −4.62533 −0.170261
\(739\) −33.9560 −1.24909 −0.624546 0.780988i \(-0.714716\pi\)
−0.624546 + 0.780988i \(0.714716\pi\)
\(740\) −11.4207 −0.419833
\(741\) −0.206834 −0.00759823
\(742\) 28.6041 1.05009
\(743\) −49.6319 −1.82082 −0.910409 0.413709i \(-0.864233\pi\)
−0.910409 + 0.413709i \(0.864233\pi\)
\(744\) −23.8675 −0.875025
\(745\) 14.2347 0.521517
\(746\) −19.1311 −0.700440
\(747\) −6.68788 −0.244697
\(748\) −1.51153 −0.0552669
\(749\) 49.2810 1.80069
\(750\) 16.0823 0.587242
\(751\) 9.54133 0.348168 0.174084 0.984731i \(-0.444304\pi\)
0.174084 + 0.984731i \(0.444304\pi\)
\(752\) 37.2942 1.35998
\(753\) −23.9164 −0.871561
\(754\) −10.4674 −0.381202
\(755\) −33.4948 −1.21900
\(756\) 1.54356 0.0561387
\(757\) −23.4545 −0.852467 −0.426233 0.904613i \(-0.640160\pi\)
−0.426233 + 0.904613i \(0.640160\pi\)
\(758\) 14.2287 0.516809
\(759\) 1.54482 0.0560736
\(760\) −1.30220 −0.0472358
\(761\) −35.8791 −1.30061 −0.650307 0.759671i \(-0.725360\pi\)
−0.650307 + 0.759671i \(0.725360\pi\)
\(762\) 12.7969 0.463582
\(763\) −16.5031 −0.597453
\(764\) −7.33437 −0.265348
\(765\) −3.59105 −0.129835
\(766\) 53.3652 1.92816
\(767\) 12.7418 0.460080
\(768\) −9.07136 −0.327334
\(769\) 3.71044 0.133802 0.0669009 0.997760i \(-0.478689\pi\)
0.0669009 + 0.997760i \(0.478689\pi\)
\(770\) 84.3051 3.03814
\(771\) −4.37343 −0.157505
\(772\) −2.09763 −0.0754954
\(773\) −28.0966 −1.01056 −0.505282 0.862954i \(-0.668612\pi\)
−0.505282 + 0.862954i \(0.668612\pi\)
\(774\) −4.68361 −0.168349
\(775\) 75.7768 2.72198
\(776\) −27.9551 −1.00353
\(777\) −31.9376 −1.14575
\(778\) 20.6110 0.738942
\(779\) −0.436072 −0.0156239
\(780\) 1.99705 0.0715057
\(781\) 46.8023 1.67472
\(782\) −0.619719 −0.0221611
\(783\) 4.77127 0.170511
\(784\) −39.3622 −1.40579
\(785\) −3.59105 −0.128170
\(786\) 5.30083 0.189074
\(787\) 29.7364 1.05999 0.529995 0.848001i \(-0.322194\pi\)
0.529995 + 0.848001i \(0.322194\pi\)
\(788\) −1.59635 −0.0568675
\(789\) 5.15870 0.183655
\(790\) −48.6799 −1.73195
\(791\) −12.0100 −0.427027
\(792\) 9.58798 0.340694
\(793\) 16.7302 0.594108
\(794\) 6.39898 0.227091
\(795\) −16.8689 −0.598279
\(796\) 0.955225 0.0338571
\(797\) −47.7145 −1.69013 −0.845067 0.534661i \(-0.820439\pi\)
−0.845067 + 0.534661i \(0.820439\pi\)
\(798\) 0.887898 0.0314313
\(799\) 8.05420 0.284937
\(800\) 17.2734 0.610707
\(801\) −7.17883 −0.253651
\(802\) −31.9186 −1.12709
\(803\) 24.6256 0.869017
\(804\) 2.15383 0.0759596
\(805\) 5.66510 0.199668
\(806\) 21.0551 0.741633
\(807\) 23.3617 0.822370
\(808\) 3.12979 0.110106
\(809\) −49.6772 −1.74656 −0.873278 0.487222i \(-0.838010\pi\)
−0.873278 + 0.487222i \(0.838010\pi\)
\(810\) −5.55401 −0.195148
\(811\) −29.3652 −1.03115 −0.515576 0.856844i \(-0.672422\pi\)
−0.515576 + 0.856844i \(0.672422\pi\)
\(812\) 7.36475 0.258452
\(813\) −11.8120 −0.414265
\(814\) 48.3705 1.69538
\(815\) 49.2828 1.72630
\(816\) −4.63040 −0.162096
\(817\) −0.441566 −0.0154484
\(818\) −42.2875 −1.47855
\(819\) 5.58468 0.195144
\(820\) 4.21041 0.147034
\(821\) −15.7994 −0.551402 −0.275701 0.961244i \(-0.588910\pi\)
−0.275701 + 0.961244i \(0.588910\pi\)
\(822\) −34.3882 −1.19942
\(823\) −55.5050 −1.93478 −0.967392 0.253285i \(-0.918489\pi\)
−0.967392 + 0.253285i \(0.918489\pi\)
\(824\) −26.6834 −0.929560
\(825\) −30.4408 −1.05981
\(826\) −54.6981 −1.90319
\(827\) 22.2330 0.773115 0.386558 0.922265i \(-0.373664\pi\)
0.386558 + 0.922265i \(0.373664\pi\)
\(828\) −0.157092 −0.00545934
\(829\) 0.296851 0.0103101 0.00515504 0.999987i \(-0.498359\pi\)
0.00515504 + 0.999987i \(0.498359\pi\)
\(830\) 37.1446 1.28931
\(831\) −12.8652 −0.446287
\(832\) −8.33667 −0.289022
\(833\) −8.50081 −0.294536
\(834\) 13.0995 0.453598
\(835\) 19.6459 0.679873
\(836\) −0.220403 −0.00762278
\(837\) −9.59732 −0.331732
\(838\) 42.5524 1.46995
\(839\) −46.9989 −1.62258 −0.811291 0.584643i \(-0.801235\pi\)
−0.811291 + 0.584643i \(0.801235\pi\)
\(840\) 35.1605 1.21315
\(841\) −6.23494 −0.214998
\(842\) 39.6937 1.36793
\(843\) −22.4357 −0.772727
\(844\) −2.50525 −0.0862342
\(845\) −39.4582 −1.35740
\(846\) 12.4568 0.428275
\(847\) −15.2136 −0.522744
\(848\) −21.7513 −0.746942
\(849\) −1.03185 −0.0354130
\(850\) 12.2116 0.418853
\(851\) 3.25038 0.111422
\(852\) −4.75930 −0.163051
\(853\) 50.4261 1.72656 0.863278 0.504729i \(-0.168407\pi\)
0.863278 + 0.504729i \(0.168407\pi\)
\(854\) −71.8197 −2.45762
\(855\) −0.523626 −0.0179076
\(856\) −31.1286 −1.06395
\(857\) −44.8707 −1.53275 −0.766376 0.642392i \(-0.777942\pi\)
−0.766376 + 0.642392i \(0.777942\pi\)
\(858\) −8.45817 −0.288757
\(859\) −42.3143 −1.44374 −0.721872 0.692027i \(-0.756718\pi\)
−0.721872 + 0.692027i \(0.756718\pi\)
\(860\) 4.26346 0.145383
\(861\) 11.7743 0.401267
\(862\) −16.2020 −0.551841
\(863\) −55.3235 −1.88323 −0.941617 0.336686i \(-0.890694\pi\)
−0.941617 + 0.336686i \(0.890694\pi\)
\(864\) −2.18772 −0.0744277
\(865\) −33.5566 −1.14096
\(866\) 40.3149 1.36995
\(867\) −1.00000 −0.0339618
\(868\) −14.8140 −0.502821
\(869\) 33.7919 1.14631
\(870\) −26.4997 −0.898424
\(871\) 7.79266 0.264044
\(872\) 10.4243 0.353010
\(873\) −11.2410 −0.380450
\(874\) −0.0903639 −0.00305660
\(875\) −40.9392 −1.38400
\(876\) −2.50416 −0.0846077
\(877\) −32.4277 −1.09500 −0.547502 0.836804i \(-0.684421\pi\)
−0.547502 + 0.836804i \(0.684421\pi\)
\(878\) 7.95679 0.268529
\(879\) −14.6591 −0.494440
\(880\) −64.1076 −2.16107
\(881\) 11.8303 0.398572 0.199286 0.979941i \(-0.436138\pi\)
0.199286 + 0.979941i \(0.436138\pi\)
\(882\) −13.1476 −0.442702
\(883\) −32.2787 −1.08626 −0.543132 0.839647i \(-0.682762\pi\)
−0.543132 + 0.839647i \(0.682762\pi\)
\(884\) 0.556118 0.0187043
\(885\) 32.2575 1.08432
\(886\) −47.5947 −1.59898
\(887\) −45.7989 −1.53778 −0.768889 0.639383i \(-0.779190\pi\)
−0.768889 + 0.639383i \(0.779190\pi\)
\(888\) 20.1735 0.676979
\(889\) −32.5758 −1.09256
\(890\) 39.8713 1.33649
\(891\) 3.85540 0.129161
\(892\) 6.19423 0.207398
\(893\) 1.17442 0.0393004
\(894\) 6.13072 0.205042
\(895\) 10.8439 0.362473
\(896\) 53.0143 1.77108
\(897\) −0.568369 −0.0189773
\(898\) −32.1153 −1.07170
\(899\) −45.7914 −1.52723
\(900\) 3.09551 0.103184
\(901\) −4.69749 −0.156496
\(902\) −17.8325 −0.593758
\(903\) 11.9226 0.396761
\(904\) 7.58618 0.252313
\(905\) 7.09290 0.235776
\(906\) −14.4259 −0.479267
\(907\) −48.8416 −1.62176 −0.810879 0.585214i \(-0.801010\pi\)
−0.810879 + 0.585214i \(0.801010\pi\)
\(908\) 8.74377 0.290172
\(909\) 1.25851 0.0417423
\(910\) −31.0174 −1.02822
\(911\) 14.8665 0.492550 0.246275 0.969200i \(-0.420793\pi\)
0.246275 + 0.969200i \(0.420793\pi\)
\(912\) −0.675179 −0.0223574
\(913\) −25.7845 −0.853342
\(914\) 17.1033 0.565728
\(915\) 42.3547 1.40020
\(916\) 3.37507 0.111515
\(917\) −13.4938 −0.445606
\(918\) −1.54663 −0.0510463
\(919\) −22.9265 −0.756275 −0.378137 0.925749i \(-0.623435\pi\)
−0.378137 + 0.925749i \(0.623435\pi\)
\(920\) −3.57839 −0.117976
\(921\) −20.9980 −0.691906
\(922\) 38.3737 1.26377
\(923\) −17.2194 −0.566784
\(924\) 5.95105 0.195775
\(925\) −64.0488 −2.10591
\(926\) −7.39598 −0.243047
\(927\) −10.7296 −0.352407
\(928\) −10.4382 −0.342651
\(929\) −35.1905 −1.15456 −0.577281 0.816546i \(-0.695886\pi\)
−0.577281 + 0.816546i \(0.695886\pi\)
\(930\) 53.3036 1.74789
\(931\) −1.23954 −0.0406243
\(932\) 6.50269 0.213003
\(933\) −5.09870 −0.166924
\(934\) 24.3542 0.796892
\(935\) −13.8449 −0.452778
\(936\) −3.52759 −0.115303
\(937\) 29.5193 0.964355 0.482177 0.876074i \(-0.339846\pi\)
0.482177 + 0.876074i \(0.339846\pi\)
\(938\) −33.4524 −1.09226
\(939\) 26.1297 0.852709
\(940\) −11.3394 −0.369850
\(941\) −33.4722 −1.09116 −0.545581 0.838058i \(-0.683691\pi\)
−0.545581 + 0.838058i \(0.683691\pi\)
\(942\) −1.54663 −0.0503918
\(943\) −1.19830 −0.0390221
\(944\) 41.5938 1.35376
\(945\) 14.1383 0.459920
\(946\) −18.0572 −0.587090
\(947\) 7.38623 0.240020 0.120010 0.992773i \(-0.461707\pi\)
0.120010 + 0.992773i \(0.461707\pi\)
\(948\) −3.43628 −0.111605
\(949\) −9.06018 −0.294106
\(950\) 1.78062 0.0577710
\(951\) 19.6132 0.636002
\(952\) 9.79116 0.317333
\(953\) −41.9183 −1.35787 −0.678934 0.734199i \(-0.737558\pi\)
−0.678934 + 0.734199i \(0.737558\pi\)
\(954\) −7.26527 −0.235222
\(955\) −67.1797 −2.17388
\(956\) −8.18932 −0.264862
\(957\) 18.3952 0.594632
\(958\) −15.9646 −0.515794
\(959\) 87.5388 2.82678
\(960\) −21.1054 −0.681173
\(961\) 61.1086 1.97124
\(962\) −17.7964 −0.573778
\(963\) −12.5171 −0.403357
\(964\) −5.65236 −0.182050
\(965\) −19.2134 −0.618501
\(966\) 2.43990 0.0785025
\(967\) 24.8001 0.797519 0.398759 0.917056i \(-0.369441\pi\)
0.398759 + 0.917056i \(0.369441\pi\)
\(968\) 9.60971 0.308868
\(969\) −0.145814 −0.00468423
\(970\) 62.4325 2.00459
\(971\) 47.0133 1.50873 0.754365 0.656455i \(-0.227945\pi\)
0.754365 + 0.656455i \(0.227945\pi\)
\(972\) −0.392054 −0.0125751
\(973\) −33.3462 −1.06903
\(974\) −38.7481 −1.24157
\(975\) 11.1997 0.358678
\(976\) 54.6134 1.74813
\(977\) 3.12781 0.100067 0.0500337 0.998748i \(-0.484067\pi\)
0.0500337 + 0.998748i \(0.484067\pi\)
\(978\) 21.2256 0.678719
\(979\) −27.6773 −0.884570
\(980\) 11.9682 0.382309
\(981\) 4.19169 0.133830
\(982\) 63.5853 2.02909
\(983\) 14.5096 0.462785 0.231393 0.972860i \(-0.425672\pi\)
0.231393 + 0.972860i \(0.425672\pi\)
\(984\) −7.43728 −0.237092
\(985\) −14.6219 −0.465891
\(986\) −7.37938 −0.235007
\(987\) −31.7103 −1.00935
\(988\) 0.0810900 0.00257982
\(989\) −1.21340 −0.0385839
\(990\) −21.4130 −0.680548
\(991\) −24.3752 −0.774303 −0.387152 0.922016i \(-0.626541\pi\)
−0.387152 + 0.922016i \(0.626541\pi\)
\(992\) 20.9962 0.666631
\(993\) 18.1817 0.576979
\(994\) 73.9196 2.34459
\(995\) 8.74945 0.277376
\(996\) 2.62201 0.0830817
\(997\) 17.2128 0.545136 0.272568 0.962137i \(-0.412127\pi\)
0.272568 + 0.962137i \(0.412127\pi\)
\(998\) −51.4222 −1.62774
\(999\) 8.11194 0.256651
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.1.12 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.12 48 1.1 even 1 trivial