Properties

Label 8007.2.a.f.1.45
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 1.45
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.45513 q^{2} -1.00000 q^{3} +4.02764 q^{4} +0.940315 q^{5} -2.45513 q^{6} -2.20409 q^{7} +4.97812 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.45513 q^{2} -1.00000 q^{3} +4.02764 q^{4} +0.940315 q^{5} -2.45513 q^{6} -2.20409 q^{7} +4.97812 q^{8} +1.00000 q^{9} +2.30859 q^{10} -2.19163 q^{11} -4.02764 q^{12} +1.05565 q^{13} -5.41133 q^{14} -0.940315 q^{15} +4.16662 q^{16} -1.00000 q^{17} +2.45513 q^{18} +2.34063 q^{19} +3.78725 q^{20} +2.20409 q^{21} -5.38072 q^{22} -4.57089 q^{23} -4.97812 q^{24} -4.11581 q^{25} +2.59176 q^{26} -1.00000 q^{27} -8.87730 q^{28} -0.413086 q^{29} -2.30859 q^{30} -5.18661 q^{31} +0.273335 q^{32} +2.19163 q^{33} -2.45513 q^{34} -2.07254 q^{35} +4.02764 q^{36} -4.26539 q^{37} +5.74653 q^{38} -1.05565 q^{39} +4.68100 q^{40} -1.99957 q^{41} +5.41133 q^{42} +5.39509 q^{43} -8.82710 q^{44} +0.940315 q^{45} -11.2221 q^{46} +0.440846 q^{47} -4.16662 q^{48} -2.14197 q^{49} -10.1048 q^{50} +1.00000 q^{51} +4.25179 q^{52} +2.47520 q^{53} -2.45513 q^{54} -2.06082 q^{55} -10.9722 q^{56} -2.34063 q^{57} -1.01418 q^{58} -6.59905 q^{59} -3.78725 q^{60} -7.41297 q^{61} -12.7338 q^{62} -2.20409 q^{63} -7.66216 q^{64} +0.992646 q^{65} +5.38072 q^{66} +12.6240 q^{67} -4.02764 q^{68} +4.57089 q^{69} -5.08835 q^{70} -4.61020 q^{71} +4.97812 q^{72} -16.5399 q^{73} -10.4721 q^{74} +4.11581 q^{75} +9.42721 q^{76} +4.83056 q^{77} -2.59176 q^{78} +2.07978 q^{79} +3.91793 q^{80} +1.00000 q^{81} -4.90918 q^{82} +5.79676 q^{83} +8.87730 q^{84} -0.940315 q^{85} +13.2456 q^{86} +0.413086 q^{87} -10.9102 q^{88} -0.0466153 q^{89} +2.30859 q^{90} -2.32676 q^{91} -18.4099 q^{92} +5.18661 q^{93} +1.08233 q^{94} +2.20093 q^{95} -0.273335 q^{96} +15.6767 q^{97} -5.25880 q^{98} -2.19163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.45513 1.73604 0.868018 0.496533i \(-0.165394\pi\)
0.868018 + 0.496533i \(0.165394\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.02764 2.01382
\(5\) 0.940315 0.420522 0.210261 0.977645i \(-0.432569\pi\)
0.210261 + 0.977645i \(0.432569\pi\)
\(6\) −2.45513 −1.00230
\(7\) −2.20409 −0.833069 −0.416535 0.909120i \(-0.636756\pi\)
−0.416535 + 0.909120i \(0.636756\pi\)
\(8\) 4.97812 1.76003
\(9\) 1.00000 0.333333
\(10\) 2.30859 0.730041
\(11\) −2.19163 −0.660801 −0.330400 0.943841i \(-0.607184\pi\)
−0.330400 + 0.943841i \(0.607184\pi\)
\(12\) −4.02764 −1.16268
\(13\) 1.05565 0.292785 0.146393 0.989227i \(-0.453234\pi\)
0.146393 + 0.989227i \(0.453234\pi\)
\(14\) −5.41133 −1.44624
\(15\) −0.940315 −0.242788
\(16\) 4.16662 1.04165
\(17\) −1.00000 −0.242536
\(18\) 2.45513 0.578679
\(19\) 2.34063 0.536977 0.268488 0.963283i \(-0.413476\pi\)
0.268488 + 0.963283i \(0.413476\pi\)
\(20\) 3.78725 0.846856
\(21\) 2.20409 0.480973
\(22\) −5.38072 −1.14717
\(23\) −4.57089 −0.953097 −0.476548 0.879148i \(-0.658112\pi\)
−0.476548 + 0.879148i \(0.658112\pi\)
\(24\) −4.97812 −1.01615
\(25\) −4.11581 −0.823161
\(26\) 2.59176 0.508286
\(27\) −1.00000 −0.192450
\(28\) −8.87730 −1.67765
\(29\) −0.413086 −0.0767081 −0.0383540 0.999264i \(-0.512211\pi\)
−0.0383540 + 0.999264i \(0.512211\pi\)
\(30\) −2.30859 −0.421489
\(31\) −5.18661 −0.931543 −0.465772 0.884905i \(-0.654223\pi\)
−0.465772 + 0.884905i \(0.654223\pi\)
\(32\) 0.273335 0.0483193
\(33\) 2.19163 0.381514
\(34\) −2.45513 −0.421051
\(35\) −2.07254 −0.350324
\(36\) 4.02764 0.671274
\(37\) −4.26539 −0.701227 −0.350613 0.936520i \(-0.614027\pi\)
−0.350613 + 0.936520i \(0.614027\pi\)
\(38\) 5.74653 0.932211
\(39\) −1.05565 −0.169040
\(40\) 4.68100 0.740131
\(41\) −1.99957 −0.312280 −0.156140 0.987735i \(-0.549905\pi\)
−0.156140 + 0.987735i \(0.549905\pi\)
\(42\) 5.41133 0.834986
\(43\) 5.39509 0.822744 0.411372 0.911468i \(-0.365050\pi\)
0.411372 + 0.911468i \(0.365050\pi\)
\(44\) −8.82710 −1.33073
\(45\) 0.940315 0.140174
\(46\) −11.2221 −1.65461
\(47\) 0.440846 0.0643040 0.0321520 0.999483i \(-0.489764\pi\)
0.0321520 + 0.999483i \(0.489764\pi\)
\(48\) −4.16662 −0.601399
\(49\) −2.14197 −0.305995
\(50\) −10.1048 −1.42904
\(51\) 1.00000 0.140028
\(52\) 4.25179 0.589617
\(53\) 2.47520 0.339994 0.169997 0.985445i \(-0.445624\pi\)
0.169997 + 0.985445i \(0.445624\pi\)
\(54\) −2.45513 −0.334100
\(55\) −2.06082 −0.277881
\(56\) −10.9722 −1.46623
\(57\) −2.34063 −0.310024
\(58\) −1.01418 −0.133168
\(59\) −6.59905 −0.859123 −0.429562 0.903038i \(-0.641332\pi\)
−0.429562 + 0.903038i \(0.641332\pi\)
\(60\) −3.78725 −0.488932
\(61\) −7.41297 −0.949134 −0.474567 0.880220i \(-0.657395\pi\)
−0.474567 + 0.880220i \(0.657395\pi\)
\(62\) −12.7338 −1.61719
\(63\) −2.20409 −0.277690
\(64\) −7.66216 −0.957770
\(65\) 0.992646 0.123123
\(66\) 5.38072 0.662321
\(67\) 12.6240 1.54226 0.771131 0.636676i \(-0.219691\pi\)
0.771131 + 0.636676i \(0.219691\pi\)
\(68\) −4.02764 −0.488423
\(69\) 4.57089 0.550271
\(70\) −5.08835 −0.608175
\(71\) −4.61020 −0.547130 −0.273565 0.961854i \(-0.588203\pi\)
−0.273565 + 0.961854i \(0.588203\pi\)
\(72\) 4.97812 0.586677
\(73\) −16.5399 −1.93585 −0.967926 0.251234i \(-0.919164\pi\)
−0.967926 + 0.251234i \(0.919164\pi\)
\(74\) −10.4721 −1.21735
\(75\) 4.11581 0.475252
\(76\) 9.42721 1.08137
\(77\) 4.83056 0.550493
\(78\) −2.59176 −0.293459
\(79\) 2.07978 0.233993 0.116997 0.993132i \(-0.462673\pi\)
0.116997 + 0.993132i \(0.462673\pi\)
\(80\) 3.91793 0.438038
\(81\) 1.00000 0.111111
\(82\) −4.90918 −0.542129
\(83\) 5.79676 0.636277 0.318138 0.948044i \(-0.396942\pi\)
0.318138 + 0.948044i \(0.396942\pi\)
\(84\) 8.87730 0.968593
\(85\) −0.940315 −0.101992
\(86\) 13.2456 1.42831
\(87\) 0.413086 0.0442874
\(88\) −10.9102 −1.16303
\(89\) −0.0466153 −0.00494122 −0.00247061 0.999997i \(-0.500786\pi\)
−0.00247061 + 0.999997i \(0.500786\pi\)
\(90\) 2.30859 0.243347
\(91\) −2.32676 −0.243911
\(92\) −18.4099 −1.91937
\(93\) 5.18661 0.537827
\(94\) 1.08233 0.111634
\(95\) 2.20093 0.225810
\(96\) −0.273335 −0.0278971
\(97\) 15.6767 1.59173 0.795863 0.605477i \(-0.207017\pi\)
0.795863 + 0.605477i \(0.207017\pi\)
\(98\) −5.25880 −0.531219
\(99\) −2.19163 −0.220267
\(100\) −16.5770 −1.65770
\(101\) −13.9930 −1.39236 −0.696178 0.717869i \(-0.745118\pi\)
−0.696178 + 0.717869i \(0.745118\pi\)
\(102\) 2.45513 0.243094
\(103\) 5.35560 0.527703 0.263851 0.964563i \(-0.415007\pi\)
0.263851 + 0.964563i \(0.415007\pi\)
\(104\) 5.25516 0.515311
\(105\) 2.07254 0.202260
\(106\) 6.07692 0.590243
\(107\) −4.13977 −0.400207 −0.200103 0.979775i \(-0.564128\pi\)
−0.200103 + 0.979775i \(0.564128\pi\)
\(108\) −4.02764 −0.387560
\(109\) 2.64234 0.253091 0.126545 0.991961i \(-0.459611\pi\)
0.126545 + 0.991961i \(0.459611\pi\)
\(110\) −5.05958 −0.482412
\(111\) 4.26539 0.404853
\(112\) −9.18362 −0.867770
\(113\) 17.6980 1.66489 0.832446 0.554107i \(-0.186940\pi\)
0.832446 + 0.554107i \(0.186940\pi\)
\(114\) −5.74653 −0.538212
\(115\) −4.29808 −0.400798
\(116\) −1.66376 −0.154476
\(117\) 1.05565 0.0975951
\(118\) −16.2015 −1.49147
\(119\) 2.20409 0.202049
\(120\) −4.68100 −0.427315
\(121\) −6.19676 −0.563342
\(122\) −18.1998 −1.64773
\(123\) 1.99957 0.180295
\(124\) −20.8898 −1.87596
\(125\) −8.57173 −0.766679
\(126\) −5.41133 −0.482079
\(127\) −4.61078 −0.409141 −0.204570 0.978852i \(-0.565580\pi\)
−0.204570 + 0.978852i \(0.565580\pi\)
\(128\) −19.3582 −1.71104
\(129\) −5.39509 −0.475011
\(130\) 2.43707 0.213745
\(131\) 2.20540 0.192687 0.0963434 0.995348i \(-0.469285\pi\)
0.0963434 + 0.995348i \(0.469285\pi\)
\(132\) 8.82710 0.768300
\(133\) −5.15896 −0.447339
\(134\) 30.9934 2.67742
\(135\) −0.940315 −0.0809295
\(136\) −4.97812 −0.426870
\(137\) −18.0456 −1.54174 −0.770870 0.636992i \(-0.780178\pi\)
−0.770870 + 0.636992i \(0.780178\pi\)
\(138\) 11.2221 0.955290
\(139\) −6.19172 −0.525175 −0.262588 0.964908i \(-0.584576\pi\)
−0.262588 + 0.964908i \(0.584576\pi\)
\(140\) −8.34746 −0.705489
\(141\) −0.440846 −0.0371259
\(142\) −11.3186 −0.949837
\(143\) −2.31360 −0.193473
\(144\) 4.16662 0.347218
\(145\) −0.388431 −0.0322574
\(146\) −40.6076 −3.36071
\(147\) 2.14197 0.176667
\(148\) −17.1795 −1.41214
\(149\) 10.0318 0.821835 0.410917 0.911673i \(-0.365208\pi\)
0.410917 + 0.911673i \(0.365208\pi\)
\(150\) 10.1048 0.825055
\(151\) 1.64782 0.134098 0.0670489 0.997750i \(-0.478642\pi\)
0.0670489 + 0.997750i \(0.478642\pi\)
\(152\) 11.6519 0.945095
\(153\) −1.00000 −0.0808452
\(154\) 11.8596 0.955676
\(155\) −4.87705 −0.391734
\(156\) −4.25179 −0.340416
\(157\) −1.00000 −0.0798087
\(158\) 5.10612 0.406221
\(159\) −2.47520 −0.196296
\(160\) 0.257021 0.0203193
\(161\) 10.0747 0.793996
\(162\) 2.45513 0.192893
\(163\) −18.3450 −1.43689 −0.718447 0.695582i \(-0.755147\pi\)
−0.718447 + 0.695582i \(0.755147\pi\)
\(164\) −8.05353 −0.628875
\(165\) 2.06082 0.160435
\(166\) 14.2318 1.10460
\(167\) 4.40543 0.340902 0.170451 0.985366i \(-0.445477\pi\)
0.170451 + 0.985366i \(0.445477\pi\)
\(168\) 10.9722 0.846527
\(169\) −11.8856 −0.914277
\(170\) −2.30859 −0.177061
\(171\) 2.34063 0.178992
\(172\) 21.7295 1.65686
\(173\) −5.98786 −0.455248 −0.227624 0.973749i \(-0.573096\pi\)
−0.227624 + 0.973749i \(0.573096\pi\)
\(174\) 1.01418 0.0768846
\(175\) 9.07163 0.685751
\(176\) −9.13168 −0.688326
\(177\) 6.59905 0.496015
\(178\) −0.114447 −0.00857813
\(179\) 5.98666 0.447464 0.223732 0.974651i \(-0.428176\pi\)
0.223732 + 0.974651i \(0.428176\pi\)
\(180\) 3.78725 0.282285
\(181\) −17.1545 −1.27508 −0.637542 0.770416i \(-0.720049\pi\)
−0.637542 + 0.770416i \(0.720049\pi\)
\(182\) −5.71248 −0.423437
\(183\) 7.41297 0.547982
\(184\) −22.7544 −1.67748
\(185\) −4.01082 −0.294881
\(186\) 12.7338 0.933687
\(187\) 2.19163 0.160268
\(188\) 1.77557 0.129497
\(189\) 2.20409 0.160324
\(190\) 5.40355 0.392015
\(191\) 11.7739 0.851926 0.425963 0.904741i \(-0.359935\pi\)
0.425963 + 0.904741i \(0.359935\pi\)
\(192\) 7.66216 0.552969
\(193\) −10.4745 −0.753968 −0.376984 0.926220i \(-0.623039\pi\)
−0.376984 + 0.926220i \(0.623039\pi\)
\(194\) 38.4882 2.76329
\(195\) −0.992646 −0.0710849
\(196\) −8.62708 −0.616220
\(197\) −15.6245 −1.11320 −0.556599 0.830781i \(-0.687894\pi\)
−0.556599 + 0.830781i \(0.687894\pi\)
\(198\) −5.38072 −0.382391
\(199\) 13.0676 0.926338 0.463169 0.886270i \(-0.346712\pi\)
0.463169 + 0.886270i \(0.346712\pi\)
\(200\) −20.4890 −1.44879
\(201\) −12.6240 −0.890425
\(202\) −34.3546 −2.41718
\(203\) 0.910480 0.0639031
\(204\) 4.02764 0.281991
\(205\) −1.88022 −0.131320
\(206\) 13.1487 0.916111
\(207\) −4.57089 −0.317699
\(208\) 4.39850 0.304981
\(209\) −5.12978 −0.354835
\(210\) 5.08835 0.351130
\(211\) 5.69321 0.391937 0.195969 0.980610i \(-0.437215\pi\)
0.195969 + 0.980610i \(0.437215\pi\)
\(212\) 9.96921 0.684688
\(213\) 4.61020 0.315885
\(214\) −10.1637 −0.694773
\(215\) 5.07309 0.345982
\(216\) −4.97812 −0.338718
\(217\) 11.4318 0.776040
\(218\) 6.48729 0.439374
\(219\) 16.5399 1.11767
\(220\) −8.30025 −0.559603
\(221\) −1.05565 −0.0710109
\(222\) 10.4721 0.702840
\(223\) −0.272673 −0.0182596 −0.00912978 0.999958i \(-0.502906\pi\)
−0.00912978 + 0.999958i \(0.502906\pi\)
\(224\) −0.602456 −0.0402533
\(225\) −4.11581 −0.274387
\(226\) 43.4509 2.89031
\(227\) 28.5750 1.89659 0.948296 0.317387i \(-0.102805\pi\)
0.948296 + 0.317387i \(0.102805\pi\)
\(228\) −9.42721 −0.624332
\(229\) −20.5559 −1.35837 −0.679187 0.733965i \(-0.737667\pi\)
−0.679187 + 0.733965i \(0.737667\pi\)
\(230\) −10.5523 −0.695800
\(231\) −4.83056 −0.317827
\(232\) −2.05639 −0.135008
\(233\) 4.92520 0.322661 0.161330 0.986900i \(-0.448422\pi\)
0.161330 + 0.986900i \(0.448422\pi\)
\(234\) 2.59176 0.169429
\(235\) 0.414534 0.0270412
\(236\) −26.5786 −1.73012
\(237\) −2.07978 −0.135096
\(238\) 5.41133 0.350764
\(239\) 8.12516 0.525573 0.262786 0.964854i \(-0.415359\pi\)
0.262786 + 0.964854i \(0.415359\pi\)
\(240\) −3.91793 −0.252902
\(241\) −10.8644 −0.699836 −0.349918 0.936780i \(-0.613791\pi\)
−0.349918 + 0.936780i \(0.613791\pi\)
\(242\) −15.2138 −0.977982
\(243\) −1.00000 −0.0641500
\(244\) −29.8568 −1.91139
\(245\) −2.01413 −0.128678
\(246\) 4.90918 0.312998
\(247\) 2.47089 0.157219
\(248\) −25.8196 −1.63954
\(249\) −5.79676 −0.367355
\(250\) −21.0447 −1.33098
\(251\) −27.2575 −1.72048 −0.860240 0.509889i \(-0.829687\pi\)
−0.860240 + 0.509889i \(0.829687\pi\)
\(252\) −8.87730 −0.559218
\(253\) 10.0177 0.629807
\(254\) −11.3200 −0.710283
\(255\) 0.940315 0.0588848
\(256\) −32.2026 −2.01266
\(257\) 12.7933 0.798025 0.399013 0.916945i \(-0.369353\pi\)
0.399013 + 0.916945i \(0.369353\pi\)
\(258\) −13.2456 −0.824637
\(259\) 9.40133 0.584170
\(260\) 3.99802 0.247947
\(261\) −0.413086 −0.0255694
\(262\) 5.41453 0.334511
\(263\) −20.8358 −1.28479 −0.642396 0.766373i \(-0.722059\pi\)
−0.642396 + 0.766373i \(0.722059\pi\)
\(264\) 10.9102 0.671475
\(265\) 2.32747 0.142975
\(266\) −12.6659 −0.776596
\(267\) 0.0466153 0.00285281
\(268\) 50.8448 3.10584
\(269\) 11.1293 0.678567 0.339283 0.940684i \(-0.389815\pi\)
0.339283 + 0.940684i \(0.389815\pi\)
\(270\) −2.30859 −0.140496
\(271\) 24.8663 1.51052 0.755260 0.655426i \(-0.227511\pi\)
0.755260 + 0.655426i \(0.227511\pi\)
\(272\) −4.16662 −0.252638
\(273\) 2.32676 0.140822
\(274\) −44.3043 −2.67652
\(275\) 9.02032 0.543946
\(276\) 18.4099 1.10815
\(277\) −13.4048 −0.805418 −0.402709 0.915328i \(-0.631931\pi\)
−0.402709 + 0.915328i \(0.631931\pi\)
\(278\) −15.2015 −0.911723
\(279\) −5.18661 −0.310514
\(280\) −10.3174 −0.616580
\(281\) 6.36966 0.379982 0.189991 0.981786i \(-0.439154\pi\)
0.189991 + 0.981786i \(0.439154\pi\)
\(282\) −1.08233 −0.0644520
\(283\) 2.44477 0.145326 0.0726631 0.997357i \(-0.476850\pi\)
0.0726631 + 0.997357i \(0.476850\pi\)
\(284\) −18.5682 −1.10182
\(285\) −2.20093 −0.130372
\(286\) −5.68018 −0.335876
\(287\) 4.40723 0.260151
\(288\) 0.273335 0.0161064
\(289\) 1.00000 0.0588235
\(290\) −0.953646 −0.0560000
\(291\) −15.6767 −0.918984
\(292\) −66.6169 −3.89846
\(293\) 22.5516 1.31748 0.658739 0.752371i \(-0.271090\pi\)
0.658739 + 0.752371i \(0.271090\pi\)
\(294\) 5.25880 0.306699
\(295\) −6.20519 −0.361280
\(296\) −21.2336 −1.23418
\(297\) 2.19163 0.127171
\(298\) 24.6293 1.42673
\(299\) −4.82527 −0.279053
\(300\) 16.5770 0.957073
\(301\) −11.8913 −0.685403
\(302\) 4.04561 0.232799
\(303\) 13.9930 0.803877
\(304\) 9.75249 0.559344
\(305\) −6.97053 −0.399131
\(306\) −2.45513 −0.140350
\(307\) −11.3143 −0.645741 −0.322871 0.946443i \(-0.604648\pi\)
−0.322871 + 0.946443i \(0.604648\pi\)
\(308\) 19.4558 1.10859
\(309\) −5.35560 −0.304669
\(310\) −11.9738 −0.680065
\(311\) −6.53583 −0.370613 −0.185306 0.982681i \(-0.559328\pi\)
−0.185306 + 0.982681i \(0.559328\pi\)
\(312\) −5.25516 −0.297515
\(313\) 23.2867 1.31624 0.658121 0.752912i \(-0.271352\pi\)
0.658121 + 0.752912i \(0.271352\pi\)
\(314\) −2.45513 −0.138551
\(315\) −2.07254 −0.116775
\(316\) 8.37661 0.471221
\(317\) −12.3194 −0.691924 −0.345962 0.938249i \(-0.612447\pi\)
−0.345962 + 0.938249i \(0.612447\pi\)
\(318\) −6.07692 −0.340777
\(319\) 0.905330 0.0506888
\(320\) −7.20485 −0.402763
\(321\) 4.13977 0.231059
\(322\) 24.7346 1.37841
\(323\) −2.34063 −0.130236
\(324\) 4.02764 0.223758
\(325\) −4.34486 −0.241010
\(326\) −45.0393 −2.49450
\(327\) −2.64234 −0.146122
\(328\) −9.95407 −0.549621
\(329\) −0.971667 −0.0535697
\(330\) 5.05958 0.278521
\(331\) −11.0849 −0.609280 −0.304640 0.952468i \(-0.598536\pi\)
−0.304640 + 0.952468i \(0.598536\pi\)
\(332\) 23.3473 1.28135
\(333\) −4.26539 −0.233742
\(334\) 10.8159 0.591819
\(335\) 11.8705 0.648555
\(336\) 9.18362 0.501007
\(337\) 6.03457 0.328724 0.164362 0.986400i \(-0.447443\pi\)
0.164362 + 0.986400i \(0.447443\pi\)
\(338\) −29.1806 −1.58722
\(339\) −17.6980 −0.961226
\(340\) −3.78725 −0.205393
\(341\) 11.3671 0.615565
\(342\) 5.74653 0.310737
\(343\) 20.1498 1.08798
\(344\) 26.8574 1.44805
\(345\) 4.29808 0.231401
\(346\) −14.7009 −0.790328
\(347\) −31.7272 −1.70320 −0.851602 0.524188i \(-0.824369\pi\)
−0.851602 + 0.524188i \(0.824369\pi\)
\(348\) 1.66376 0.0891869
\(349\) 23.7228 1.26985 0.634925 0.772574i \(-0.281031\pi\)
0.634925 + 0.772574i \(0.281031\pi\)
\(350\) 22.2720 1.19049
\(351\) −1.05565 −0.0563466
\(352\) −0.599049 −0.0319294
\(353\) −12.5431 −0.667601 −0.333801 0.942644i \(-0.608331\pi\)
−0.333801 + 0.942644i \(0.608331\pi\)
\(354\) 16.2015 0.861100
\(355\) −4.33504 −0.230080
\(356\) −0.187750 −0.00995072
\(357\) −2.20409 −0.116653
\(358\) 14.6980 0.776814
\(359\) 0.542532 0.0286338 0.0143169 0.999898i \(-0.495443\pi\)
0.0143169 + 0.999898i \(0.495443\pi\)
\(360\) 4.68100 0.246710
\(361\) −13.5215 −0.711656
\(362\) −42.1164 −2.21359
\(363\) 6.19676 0.325246
\(364\) −9.37135 −0.491192
\(365\) −15.5528 −0.814068
\(366\) 18.1998 0.951317
\(367\) 21.7498 1.13533 0.567665 0.823260i \(-0.307847\pi\)
0.567665 + 0.823260i \(0.307847\pi\)
\(368\) −19.0452 −0.992797
\(369\) −1.99957 −0.104093
\(370\) −9.84706 −0.511924
\(371\) −5.45557 −0.283239
\(372\) 20.8898 1.08309
\(373\) 10.6254 0.550161 0.275080 0.961421i \(-0.411296\pi\)
0.275080 + 0.961421i \(0.411296\pi\)
\(374\) 5.38072 0.278231
\(375\) 8.57173 0.442642
\(376\) 2.19458 0.113177
\(377\) −0.436075 −0.0224590
\(378\) 5.41133 0.278329
\(379\) −0.111443 −0.00572445 −0.00286222 0.999996i \(-0.500911\pi\)
−0.00286222 + 0.999996i \(0.500911\pi\)
\(380\) 8.86455 0.454742
\(381\) 4.61078 0.236218
\(382\) 28.9063 1.47897
\(383\) −2.38124 −0.121676 −0.0608379 0.998148i \(-0.519377\pi\)
−0.0608379 + 0.998148i \(0.519377\pi\)
\(384\) 19.3582 0.987871
\(385\) 4.54225 0.231494
\(386\) −25.7161 −1.30891
\(387\) 5.39509 0.274248
\(388\) 63.1401 3.20545
\(389\) 10.7283 0.543945 0.271973 0.962305i \(-0.412324\pi\)
0.271973 + 0.962305i \(0.412324\pi\)
\(390\) −2.43707 −0.123406
\(391\) 4.57089 0.231160
\(392\) −10.6630 −0.538561
\(393\) −2.20540 −0.111248
\(394\) −38.3600 −1.93255
\(395\) 1.95565 0.0983993
\(396\) −8.82710 −0.443578
\(397\) −12.8204 −0.643438 −0.321719 0.946835i \(-0.604261\pi\)
−0.321719 + 0.946835i \(0.604261\pi\)
\(398\) 32.0826 1.60816
\(399\) 5.15896 0.258271
\(400\) −17.1490 −0.857450
\(401\) −30.0760 −1.50193 −0.750963 0.660345i \(-0.770410\pi\)
−0.750963 + 0.660345i \(0.770410\pi\)
\(402\) −30.9934 −1.54581
\(403\) −5.47526 −0.272742
\(404\) −56.3588 −2.80396
\(405\) 0.940315 0.0467246
\(406\) 2.23534 0.110938
\(407\) 9.34816 0.463371
\(408\) 4.97812 0.246453
\(409\) −10.7624 −0.532169 −0.266084 0.963950i \(-0.585730\pi\)
−0.266084 + 0.963950i \(0.585730\pi\)
\(410\) −4.61618 −0.227977
\(411\) 18.0456 0.890124
\(412\) 21.5704 1.06270
\(413\) 14.5449 0.715709
\(414\) −11.2221 −0.551537
\(415\) 5.45078 0.267568
\(416\) 0.288547 0.0141472
\(417\) 6.19172 0.303210
\(418\) −12.5943 −0.616006
\(419\) 10.5383 0.514830 0.257415 0.966301i \(-0.417129\pi\)
0.257415 + 0.966301i \(0.417129\pi\)
\(420\) 8.34746 0.407315
\(421\) 25.9671 1.26556 0.632780 0.774332i \(-0.281914\pi\)
0.632780 + 0.774332i \(0.281914\pi\)
\(422\) 13.9776 0.680417
\(423\) 0.440846 0.0214347
\(424\) 12.3218 0.598400
\(425\) 4.11581 0.199646
\(426\) 11.3186 0.548389
\(427\) 16.3389 0.790694
\(428\) −16.6735 −0.805945
\(429\) 2.31360 0.111702
\(430\) 12.4551 0.600637
\(431\) 21.4917 1.03522 0.517610 0.855616i \(-0.326822\pi\)
0.517610 + 0.855616i \(0.326822\pi\)
\(432\) −4.16662 −0.200466
\(433\) 0.277977 0.0133587 0.00667936 0.999978i \(-0.497874\pi\)
0.00667936 + 0.999978i \(0.497874\pi\)
\(434\) 28.0665 1.34723
\(435\) 0.388431 0.0186238
\(436\) 10.6424 0.509679
\(437\) −10.6988 −0.511791
\(438\) 40.6076 1.94031
\(439\) −8.46535 −0.404029 −0.202015 0.979382i \(-0.564749\pi\)
−0.202015 + 0.979382i \(0.564749\pi\)
\(440\) −10.2590 −0.489079
\(441\) −2.14197 −0.101998
\(442\) −2.59176 −0.123277
\(443\) 1.49565 0.0710606 0.0355303 0.999369i \(-0.488688\pi\)
0.0355303 + 0.999369i \(0.488688\pi\)
\(444\) 17.1795 0.815302
\(445\) −0.0438331 −0.00207789
\(446\) −0.669447 −0.0316992
\(447\) −10.0318 −0.474487
\(448\) 16.8881 0.797889
\(449\) 32.2081 1.51999 0.759997 0.649927i \(-0.225200\pi\)
0.759997 + 0.649927i \(0.225200\pi\)
\(450\) −10.1048 −0.476346
\(451\) 4.38230 0.206355
\(452\) 71.2814 3.35279
\(453\) −1.64782 −0.0774214
\(454\) 70.1553 3.29255
\(455\) −2.18789 −0.102570
\(456\) −11.6519 −0.545651
\(457\) −0.271547 −0.0127024 −0.00635121 0.999980i \(-0.502022\pi\)
−0.00635121 + 0.999980i \(0.502022\pi\)
\(458\) −50.4674 −2.35819
\(459\) 1.00000 0.0466760
\(460\) −17.3111 −0.807135
\(461\) 9.14111 0.425744 0.212872 0.977080i \(-0.431718\pi\)
0.212872 + 0.977080i \(0.431718\pi\)
\(462\) −11.8596 −0.551760
\(463\) 22.6359 1.05198 0.525989 0.850491i \(-0.323695\pi\)
0.525989 + 0.850491i \(0.323695\pi\)
\(464\) −1.72117 −0.0799033
\(465\) 4.87705 0.226168
\(466\) 12.0920 0.560150
\(467\) 22.0765 1.02158 0.510789 0.859706i \(-0.329353\pi\)
0.510789 + 0.859706i \(0.329353\pi\)
\(468\) 4.25179 0.196539
\(469\) −27.8244 −1.28481
\(470\) 1.01773 0.0469446
\(471\) 1.00000 0.0460776
\(472\) −32.8508 −1.51208
\(473\) −11.8240 −0.543670
\(474\) −5.10612 −0.234532
\(475\) −9.63357 −0.442018
\(476\) 8.87730 0.406891
\(477\) 2.47520 0.113331
\(478\) 19.9483 0.912413
\(479\) 26.8567 1.22712 0.613558 0.789650i \(-0.289738\pi\)
0.613558 + 0.789650i \(0.289738\pi\)
\(480\) −0.257021 −0.0117314
\(481\) −4.50278 −0.205309
\(482\) −26.6734 −1.21494
\(483\) −10.0747 −0.458414
\(484\) −24.9583 −1.13447
\(485\) 14.7410 0.669356
\(486\) −2.45513 −0.111367
\(487\) 14.8888 0.674676 0.337338 0.941384i \(-0.390473\pi\)
0.337338 + 0.941384i \(0.390473\pi\)
\(488\) −36.9026 −1.67050
\(489\) 18.3450 0.829591
\(490\) −4.94493 −0.223389
\(491\) −30.6936 −1.38518 −0.692592 0.721329i \(-0.743531\pi\)
−0.692592 + 0.721329i \(0.743531\pi\)
\(492\) 8.05353 0.363081
\(493\) 0.413086 0.0186044
\(494\) 6.06634 0.272938
\(495\) −2.06082 −0.0926271
\(496\) −21.6106 −0.970346
\(497\) 10.1613 0.455797
\(498\) −14.2318 −0.637741
\(499\) 33.9673 1.52059 0.760293 0.649580i \(-0.225055\pi\)
0.760293 + 0.649580i \(0.225055\pi\)
\(500\) −34.5239 −1.54395
\(501\) −4.40543 −0.196820
\(502\) −66.9207 −2.98682
\(503\) −32.9640 −1.46979 −0.734895 0.678180i \(-0.762769\pi\)
−0.734895 + 0.678180i \(0.762769\pi\)
\(504\) −10.9722 −0.488742
\(505\) −13.1578 −0.585516
\(506\) 24.5947 1.09337
\(507\) 11.8856 0.527858
\(508\) −18.5706 −0.823936
\(509\) −20.3173 −0.900549 −0.450275 0.892890i \(-0.648674\pi\)
−0.450275 + 0.892890i \(0.648674\pi\)
\(510\) 2.30859 0.102226
\(511\) 36.4556 1.61270
\(512\) −40.3449 −1.78301
\(513\) −2.34063 −0.103341
\(514\) 31.4092 1.38540
\(515\) 5.03595 0.221910
\(516\) −21.7295 −0.956588
\(517\) −0.966171 −0.0424922
\(518\) 23.0815 1.01414
\(519\) 5.98786 0.262838
\(520\) 4.94151 0.216699
\(521\) −2.83585 −0.124241 −0.0621205 0.998069i \(-0.519786\pi\)
−0.0621205 + 0.998069i \(0.519786\pi\)
\(522\) −1.01418 −0.0443893
\(523\) 28.2833 1.23674 0.618370 0.785887i \(-0.287793\pi\)
0.618370 + 0.785887i \(0.287793\pi\)
\(524\) 8.88256 0.388037
\(525\) −9.07163 −0.395918
\(526\) −51.1546 −2.23044
\(527\) 5.18661 0.225932
\(528\) 9.13168 0.397405
\(529\) −2.10695 −0.0916065
\(530\) 5.71422 0.248210
\(531\) −6.59905 −0.286374
\(532\) −20.7785 −0.900860
\(533\) −2.11085 −0.0914309
\(534\) 0.114447 0.00495258
\(535\) −3.89269 −0.168296
\(536\) 62.8435 2.71443
\(537\) −5.98666 −0.258344
\(538\) 27.3239 1.17802
\(539\) 4.69440 0.202202
\(540\) −3.78725 −0.162977
\(541\) −37.3445 −1.60557 −0.802784 0.596270i \(-0.796649\pi\)
−0.802784 + 0.596270i \(0.796649\pi\)
\(542\) 61.0499 2.62232
\(543\) 17.1545 0.736170
\(544\) −0.273335 −0.0117191
\(545\) 2.48464 0.106430
\(546\) 5.71248 0.244472
\(547\) 4.93348 0.210940 0.105470 0.994422i \(-0.466365\pi\)
0.105470 + 0.994422i \(0.466365\pi\)
\(548\) −72.6813 −3.10479
\(549\) −7.41297 −0.316378
\(550\) 22.1460 0.944310
\(551\) −0.966879 −0.0411904
\(552\) 22.7544 0.968493
\(553\) −4.58403 −0.194933
\(554\) −32.9105 −1.39823
\(555\) 4.01082 0.170250
\(556\) −24.9380 −1.05761
\(557\) −3.32177 −0.140748 −0.0703740 0.997521i \(-0.522419\pi\)
−0.0703740 + 0.997521i \(0.522419\pi\)
\(558\) −12.7338 −0.539064
\(559\) 5.69534 0.240887
\(560\) −8.63549 −0.364916
\(561\) −2.19163 −0.0925306
\(562\) 15.6383 0.659662
\(563\) 17.6284 0.742950 0.371475 0.928443i \(-0.378852\pi\)
0.371475 + 0.928443i \(0.378852\pi\)
\(564\) −1.77557 −0.0747650
\(565\) 16.6417 0.700123
\(566\) 6.00221 0.252292
\(567\) −2.20409 −0.0925633
\(568\) −22.9501 −0.962964
\(569\) −25.1519 −1.05442 −0.527212 0.849734i \(-0.676763\pi\)
−0.527212 + 0.849734i \(0.676763\pi\)
\(570\) −5.40355 −0.226330
\(571\) 16.2381 0.679542 0.339771 0.940508i \(-0.389651\pi\)
0.339771 + 0.940508i \(0.389651\pi\)
\(572\) −9.31835 −0.389620
\(573\) −11.7739 −0.491860
\(574\) 10.8203 0.451631
\(575\) 18.8129 0.784553
\(576\) −7.66216 −0.319257
\(577\) −12.6123 −0.525055 −0.262527 0.964925i \(-0.584556\pi\)
−0.262527 + 0.964925i \(0.584556\pi\)
\(578\) 2.45513 0.102120
\(579\) 10.4745 0.435303
\(580\) −1.56446 −0.0649607
\(581\) −12.7766 −0.530063
\(582\) −38.4882 −1.59539
\(583\) −5.42471 −0.224669
\(584\) −82.3377 −3.40716
\(585\) 0.992646 0.0410409
\(586\) 55.3670 2.28719
\(587\) −17.7162 −0.731225 −0.365612 0.930767i \(-0.619140\pi\)
−0.365612 + 0.930767i \(0.619140\pi\)
\(588\) 8.62708 0.355775
\(589\) −12.1399 −0.500217
\(590\) −15.2345 −0.627195
\(591\) 15.6245 0.642705
\(592\) −17.7723 −0.730436
\(593\) 21.2406 0.872248 0.436124 0.899886i \(-0.356351\pi\)
0.436124 + 0.899886i \(0.356351\pi\)
\(594\) 5.38072 0.220774
\(595\) 2.07254 0.0849660
\(596\) 40.4044 1.65503
\(597\) −13.0676 −0.534822
\(598\) −11.8467 −0.484446
\(599\) 11.0157 0.450089 0.225044 0.974349i \(-0.427747\pi\)
0.225044 + 0.974349i \(0.427747\pi\)
\(600\) 20.4890 0.836459
\(601\) −30.0304 −1.22496 −0.612482 0.790484i \(-0.709829\pi\)
−0.612482 + 0.790484i \(0.709829\pi\)
\(602\) −29.1946 −1.18988
\(603\) 12.6240 0.514087
\(604\) 6.63683 0.270049
\(605\) −5.82691 −0.236898
\(606\) 34.3546 1.39556
\(607\) −3.91891 −0.159064 −0.0795318 0.996832i \(-0.525343\pi\)
−0.0795318 + 0.996832i \(0.525343\pi\)
\(608\) 0.639775 0.0259463
\(609\) −0.910480 −0.0368945
\(610\) −17.1135 −0.692906
\(611\) 0.465380 0.0188273
\(612\) −4.02764 −0.162808
\(613\) −29.3736 −1.18639 −0.593193 0.805060i \(-0.702133\pi\)
−0.593193 + 0.805060i \(0.702133\pi\)
\(614\) −27.7780 −1.12103
\(615\) 1.88022 0.0758179
\(616\) 24.0471 0.968884
\(617\) 34.7312 1.39823 0.699113 0.715012i \(-0.253579\pi\)
0.699113 + 0.715012i \(0.253579\pi\)
\(618\) −13.1487 −0.528917
\(619\) 13.9980 0.562626 0.281313 0.959616i \(-0.409230\pi\)
0.281313 + 0.959616i \(0.409230\pi\)
\(620\) −19.6430 −0.788883
\(621\) 4.57089 0.183424
\(622\) −16.0463 −0.643397
\(623\) 0.102745 0.00411638
\(624\) −4.39850 −0.176081
\(625\) 12.5189 0.500756
\(626\) 57.1718 2.28504
\(627\) 5.12978 0.204864
\(628\) −4.02764 −0.160720
\(629\) 4.26539 0.170072
\(630\) −5.08835 −0.202725
\(631\) 15.9550 0.635157 0.317579 0.948232i \(-0.397130\pi\)
0.317579 + 0.948232i \(0.397130\pi\)
\(632\) 10.3534 0.411835
\(633\) −5.69321 −0.226285
\(634\) −30.2456 −1.20120
\(635\) −4.33559 −0.172053
\(636\) −9.96921 −0.395305
\(637\) −2.26117 −0.0895910
\(638\) 2.22270 0.0879975
\(639\) −4.61020 −0.182377
\(640\) −18.2028 −0.719531
\(641\) −10.7062 −0.422870 −0.211435 0.977392i \(-0.567814\pi\)
−0.211435 + 0.977392i \(0.567814\pi\)
\(642\) 10.1637 0.401128
\(643\) −42.8102 −1.68827 −0.844135 0.536131i \(-0.819885\pi\)
−0.844135 + 0.536131i \(0.819885\pi\)
\(644\) 40.5772 1.59897
\(645\) −5.07309 −0.199753
\(646\) −5.74653 −0.226094
\(647\) 32.9112 1.29387 0.646936 0.762544i \(-0.276050\pi\)
0.646936 + 0.762544i \(0.276050\pi\)
\(648\) 4.97812 0.195559
\(649\) 14.4627 0.567709
\(650\) −10.6672 −0.418401
\(651\) −11.4318 −0.448047
\(652\) −73.8872 −2.89365
\(653\) −2.30507 −0.0902043 −0.0451021 0.998982i \(-0.514361\pi\)
−0.0451021 + 0.998982i \(0.514361\pi\)
\(654\) −6.48729 −0.253673
\(655\) 2.07377 0.0810290
\(656\) −8.33142 −0.325287
\(657\) −16.5399 −0.645284
\(658\) −2.38556 −0.0929990
\(659\) 1.57036 0.0611727 0.0305863 0.999532i \(-0.490263\pi\)
0.0305863 + 0.999532i \(0.490263\pi\)
\(660\) 8.30025 0.323087
\(661\) −7.67753 −0.298621 −0.149311 0.988790i \(-0.547705\pi\)
−0.149311 + 0.988790i \(0.547705\pi\)
\(662\) −27.2148 −1.05773
\(663\) 1.05565 0.0409982
\(664\) 28.8569 1.11987
\(665\) −4.85105 −0.188116
\(666\) −10.4721 −0.405785
\(667\) 1.88817 0.0731102
\(668\) 17.7435 0.686517
\(669\) 0.272673 0.0105422
\(670\) 29.1436 1.12591
\(671\) 16.2465 0.627188
\(672\) 0.602456 0.0232403
\(673\) 44.2322 1.70503 0.852514 0.522705i \(-0.175077\pi\)
0.852514 + 0.522705i \(0.175077\pi\)
\(674\) 14.8156 0.570677
\(675\) 4.11581 0.158417
\(676\) −47.8709 −1.84119
\(677\) −26.8378 −1.03146 −0.515731 0.856751i \(-0.672480\pi\)
−0.515731 + 0.856751i \(0.672480\pi\)
\(678\) −43.4509 −1.66872
\(679\) −34.5529 −1.32602
\(680\) −4.68100 −0.179508
\(681\) −28.5750 −1.09500
\(682\) 27.9077 1.06864
\(683\) −37.9479 −1.45204 −0.726018 0.687676i \(-0.758631\pi\)
−0.726018 + 0.687676i \(0.758631\pi\)
\(684\) 9.42721 0.360458
\(685\) −16.9686 −0.648336
\(686\) 49.4702 1.88878
\(687\) 20.5559 0.784258
\(688\) 22.4793 0.857015
\(689\) 2.61295 0.0995454
\(690\) 10.5523 0.401720
\(691\) −6.97120 −0.265197 −0.132599 0.991170i \(-0.542332\pi\)
−0.132599 + 0.991170i \(0.542332\pi\)
\(692\) −24.1170 −0.916789
\(693\) 4.83056 0.183498
\(694\) −77.8942 −2.95682
\(695\) −5.82217 −0.220848
\(696\) 2.05639 0.0779472
\(697\) 1.99957 0.0757389
\(698\) 58.2423 2.20451
\(699\) −4.92520 −0.186288
\(700\) 36.5373 1.38098
\(701\) 8.07668 0.305052 0.152526 0.988299i \(-0.451259\pi\)
0.152526 + 0.988299i \(0.451259\pi\)
\(702\) −2.59176 −0.0978197
\(703\) −9.98370 −0.376542
\(704\) 16.7926 0.632895
\(705\) −0.414534 −0.0156123
\(706\) −30.7949 −1.15898
\(707\) 30.8419 1.15993
\(708\) 26.5786 0.998886
\(709\) 9.25735 0.347667 0.173833 0.984775i \(-0.444385\pi\)
0.173833 + 0.984775i \(0.444385\pi\)
\(710\) −10.6431 −0.399427
\(711\) 2.07978 0.0779978
\(712\) −0.232057 −0.00869669
\(713\) 23.7075 0.887851
\(714\) −5.41133 −0.202514
\(715\) −2.17551 −0.0813595
\(716\) 24.1121 0.901113
\(717\) −8.12516 −0.303440
\(718\) 1.33198 0.0497092
\(719\) 47.6922 1.77862 0.889309 0.457308i \(-0.151186\pi\)
0.889309 + 0.457308i \(0.151186\pi\)
\(720\) 3.91793 0.146013
\(721\) −11.8042 −0.439613
\(722\) −33.1969 −1.23546
\(723\) 10.8644 0.404050
\(724\) −69.0922 −2.56779
\(725\) 1.70018 0.0631431
\(726\) 15.2138 0.564638
\(727\) 17.2580 0.640065 0.320032 0.947407i \(-0.396306\pi\)
0.320032 + 0.947407i \(0.396306\pi\)
\(728\) −11.5829 −0.429290
\(729\) 1.00000 0.0370370
\(730\) −38.1840 −1.41325
\(731\) −5.39509 −0.199545
\(732\) 29.8568 1.10354
\(733\) 17.3699 0.641571 0.320786 0.947152i \(-0.396053\pi\)
0.320786 + 0.947152i \(0.396053\pi\)
\(734\) 53.3984 1.97097
\(735\) 2.01413 0.0742921
\(736\) −1.24939 −0.0460530
\(737\) −27.6670 −1.01913
\(738\) −4.90918 −0.180710
\(739\) 22.2670 0.819105 0.409553 0.912286i \(-0.365685\pi\)
0.409553 + 0.912286i \(0.365685\pi\)
\(740\) −16.1541 −0.593838
\(741\) −2.47089 −0.0907704
\(742\) −13.3941 −0.491713
\(743\) 27.5352 1.01017 0.505085 0.863070i \(-0.331461\pi\)
0.505085 + 0.863070i \(0.331461\pi\)
\(744\) 25.8196 0.946591
\(745\) 9.43303 0.345599
\(746\) 26.0866 0.955099
\(747\) 5.79676 0.212092
\(748\) 8.82710 0.322751
\(749\) 9.12444 0.333400
\(750\) 21.0447 0.768443
\(751\) −32.9541 −1.20251 −0.601256 0.799056i \(-0.705333\pi\)
−0.601256 + 0.799056i \(0.705333\pi\)
\(752\) 1.83684 0.0669826
\(753\) 27.2575 0.993320
\(754\) −1.07062 −0.0389896
\(755\) 1.54947 0.0563910
\(756\) 8.87730 0.322864
\(757\) 9.13239 0.331922 0.165961 0.986132i \(-0.446927\pi\)
0.165961 + 0.986132i \(0.446927\pi\)
\(758\) −0.273607 −0.00993785
\(759\) −10.0177 −0.363619
\(760\) 10.9565 0.397433
\(761\) 29.3151 1.06267 0.531336 0.847161i \(-0.321690\pi\)
0.531336 + 0.847161i \(0.321690\pi\)
\(762\) 11.3200 0.410082
\(763\) −5.82398 −0.210842
\(764\) 47.4209 1.71563
\(765\) −0.940315 −0.0339972
\(766\) −5.84625 −0.211234
\(767\) −6.96631 −0.251539
\(768\) 32.2026 1.16201
\(769\) −40.9760 −1.47763 −0.738816 0.673908i \(-0.764615\pi\)
−0.738816 + 0.673908i \(0.764615\pi\)
\(770\) 11.1518 0.401882
\(771\) −12.7933 −0.460740
\(772\) −42.1873 −1.51836
\(773\) −26.6535 −0.958661 −0.479331 0.877634i \(-0.659120\pi\)
−0.479331 + 0.877634i \(0.659120\pi\)
\(774\) 13.2456 0.476104
\(775\) 21.3471 0.766811
\(776\) 78.0404 2.80149
\(777\) −9.40133 −0.337271
\(778\) 26.3393 0.944309
\(779\) −4.68023 −0.167687
\(780\) −3.99802 −0.143152
\(781\) 10.1038 0.361544
\(782\) 11.2221 0.401302
\(783\) 0.413086 0.0147625
\(784\) −8.92476 −0.318741
\(785\) −0.940315 −0.0335613
\(786\) −5.41453 −0.193130
\(787\) −37.8563 −1.34943 −0.674716 0.738078i \(-0.735734\pi\)
−0.674716 + 0.738078i \(0.735734\pi\)
\(788\) −62.9298 −2.24178
\(789\) 20.8358 0.741775
\(790\) 4.80136 0.170825
\(791\) −39.0081 −1.38697
\(792\) −10.9102 −0.387676
\(793\) −7.82552 −0.277892
\(794\) −31.4757 −1.11703
\(795\) −2.32747 −0.0825467
\(796\) 52.6316 1.86548
\(797\) −35.6581 −1.26307 −0.631537 0.775346i \(-0.717575\pi\)
−0.631537 + 0.775346i \(0.717575\pi\)
\(798\) 12.6659 0.448368
\(799\) −0.440846 −0.0155960
\(800\) −1.12499 −0.0397746
\(801\) −0.0466153 −0.00164707
\(802\) −73.8404 −2.60740
\(803\) 36.2494 1.27921
\(804\) −50.8448 −1.79316
\(805\) 9.47337 0.333892
\(806\) −13.4425 −0.473490
\(807\) −11.1293 −0.391771
\(808\) −69.6588 −2.45059
\(809\) 41.6208 1.46331 0.731654 0.681676i \(-0.238749\pi\)
0.731654 + 0.681676i \(0.238749\pi\)
\(810\) 2.30859 0.0811157
\(811\) 34.3205 1.20516 0.602578 0.798060i \(-0.294140\pi\)
0.602578 + 0.798060i \(0.294140\pi\)
\(812\) 3.66709 0.128689
\(813\) −24.8663 −0.872099
\(814\) 22.9509 0.804429
\(815\) −17.2501 −0.604245
\(816\) 4.16662 0.145861
\(817\) 12.6279 0.441794
\(818\) −26.4231 −0.923864
\(819\) −2.32676 −0.0813035
\(820\) −7.57286 −0.264456
\(821\) 29.5872 1.03260 0.516300 0.856408i \(-0.327309\pi\)
0.516300 + 0.856408i \(0.327309\pi\)
\(822\) 44.3043 1.54529
\(823\) 12.3456 0.430340 0.215170 0.976577i \(-0.430969\pi\)
0.215170 + 0.976577i \(0.430969\pi\)
\(824\) 26.6608 0.928772
\(825\) −9.02032 −0.314047
\(826\) 35.7096 1.24250
\(827\) −35.6508 −1.23970 −0.619851 0.784720i \(-0.712807\pi\)
−0.619851 + 0.784720i \(0.712807\pi\)
\(828\) −18.4099 −0.639789
\(829\) 2.45389 0.0852271 0.0426136 0.999092i \(-0.486432\pi\)
0.0426136 + 0.999092i \(0.486432\pi\)
\(830\) 13.3824 0.464508
\(831\) 13.4048 0.465008
\(832\) −8.08858 −0.280421
\(833\) 2.14197 0.0742148
\(834\) 15.2015 0.526383
\(835\) 4.14249 0.143357
\(836\) −20.6609 −0.714573
\(837\) 5.18661 0.179276
\(838\) 25.8729 0.893763
\(839\) −35.8108 −1.23632 −0.618162 0.786050i \(-0.712123\pi\)
−0.618162 + 0.786050i \(0.712123\pi\)
\(840\) 10.3174 0.355983
\(841\) −28.8294 −0.994116
\(842\) 63.7525 2.19706
\(843\) −6.36966 −0.219383
\(844\) 22.9302 0.789291
\(845\) −11.1762 −0.384473
\(846\) 1.08233 0.0372114
\(847\) 13.6583 0.469303
\(848\) 10.3132 0.354157
\(849\) −2.44477 −0.0839042
\(850\) 10.1048 0.346593
\(851\) 19.4967 0.668337
\(852\) 18.5682 0.636137
\(853\) 24.0542 0.823600 0.411800 0.911274i \(-0.364900\pi\)
0.411800 + 0.911274i \(0.364900\pi\)
\(854\) 40.1140 1.37267
\(855\) 2.20093 0.0752701
\(856\) −20.6083 −0.704376
\(857\) 13.5708 0.463571 0.231785 0.972767i \(-0.425543\pi\)
0.231785 + 0.972767i \(0.425543\pi\)
\(858\) 5.68018 0.193918
\(859\) 14.9012 0.508422 0.254211 0.967149i \(-0.418184\pi\)
0.254211 + 0.967149i \(0.418184\pi\)
\(860\) 20.4326 0.696745
\(861\) −4.40723 −0.150198
\(862\) 52.7649 1.79718
\(863\) 14.1870 0.482932 0.241466 0.970409i \(-0.422372\pi\)
0.241466 + 0.970409i \(0.422372\pi\)
\(864\) −0.273335 −0.00929905
\(865\) −5.63047 −0.191442
\(866\) 0.682468 0.0231912
\(867\) −1.00000 −0.0339618
\(868\) 46.0431 1.56281
\(869\) −4.55810 −0.154623
\(870\) 0.953646 0.0323316
\(871\) 13.3265 0.451552
\(872\) 13.1539 0.445447
\(873\) 15.6767 0.530575
\(874\) −26.2668 −0.888487
\(875\) 18.8929 0.638697
\(876\) 66.6169 2.25078
\(877\) −23.5753 −0.796082 −0.398041 0.917368i \(-0.630310\pi\)
−0.398041 + 0.917368i \(0.630310\pi\)
\(878\) −20.7835 −0.701409
\(879\) −22.5516 −0.760647
\(880\) −8.58666 −0.289456
\(881\) 18.5366 0.624515 0.312257 0.949998i \(-0.398915\pi\)
0.312257 + 0.949998i \(0.398915\pi\)
\(882\) −5.25880 −0.177073
\(883\) −8.96129 −0.301571 −0.150786 0.988566i \(-0.548180\pi\)
−0.150786 + 0.988566i \(0.548180\pi\)
\(884\) −4.25179 −0.143003
\(885\) 6.20519 0.208585
\(886\) 3.67202 0.123364
\(887\) −29.7260 −0.998103 −0.499052 0.866572i \(-0.666318\pi\)
−0.499052 + 0.866572i \(0.666318\pi\)
\(888\) 21.2336 0.712554
\(889\) 10.1626 0.340843
\(890\) −0.107616 −0.00360729
\(891\) −2.19163 −0.0734223
\(892\) −1.09823 −0.0367715
\(893\) 1.03186 0.0345298
\(894\) −24.6293 −0.823726
\(895\) 5.62935 0.188168
\(896\) 42.6674 1.42542
\(897\) 4.82527 0.161111
\(898\) 79.0749 2.63876
\(899\) 2.14252 0.0714569
\(900\) −16.5770 −0.552567
\(901\) −2.47520 −0.0824608
\(902\) 10.7591 0.358239
\(903\) 11.8913 0.395717
\(904\) 88.1029 2.93026
\(905\) −16.1306 −0.536200
\(906\) −4.04561 −0.134406
\(907\) −18.2268 −0.605212 −0.302606 0.953116i \(-0.597857\pi\)
−0.302606 + 0.953116i \(0.597857\pi\)
\(908\) 115.090 3.81940
\(909\) −13.9930 −0.464119
\(910\) −5.37154 −0.178065
\(911\) 12.9167 0.427949 0.213975 0.976839i \(-0.431359\pi\)
0.213975 + 0.976839i \(0.431359\pi\)
\(912\) −9.75249 −0.322937
\(913\) −12.7043 −0.420452
\(914\) −0.666682 −0.0220519
\(915\) 6.97053 0.230439
\(916\) −82.7919 −2.73552
\(917\) −4.86091 −0.160521
\(918\) 2.45513 0.0810312
\(919\) 45.8151 1.51130 0.755650 0.654976i \(-0.227321\pi\)
0.755650 + 0.654976i \(0.227321\pi\)
\(920\) −21.3963 −0.705416
\(921\) 11.3143 0.372819
\(922\) 22.4426 0.739106
\(923\) −4.86677 −0.160192
\(924\) −19.4558 −0.640047
\(925\) 17.5555 0.577223
\(926\) 55.5739 1.82627
\(927\) 5.35560 0.175901
\(928\) −0.112911 −0.00370648
\(929\) 18.0085 0.590841 0.295421 0.955367i \(-0.404540\pi\)
0.295421 + 0.955367i \(0.404540\pi\)
\(930\) 11.9738 0.392636
\(931\) −5.01355 −0.164312
\(932\) 19.8369 0.649781
\(933\) 6.53583 0.213973
\(934\) 54.2005 1.77350
\(935\) 2.06082 0.0673961
\(936\) 5.25516 0.171770
\(937\) 17.5437 0.573126 0.286563 0.958061i \(-0.407487\pi\)
0.286563 + 0.958061i \(0.407487\pi\)
\(938\) −68.3124 −2.23048
\(939\) −23.2867 −0.759933
\(940\) 1.66960 0.0544562
\(941\) 14.1592 0.461578 0.230789 0.973004i \(-0.425869\pi\)
0.230789 + 0.973004i \(0.425869\pi\)
\(942\) 2.45513 0.0799923
\(943\) 9.13980 0.297633
\(944\) −27.4957 −0.894909
\(945\) 2.07254 0.0674198
\(946\) −29.0295 −0.943831
\(947\) 40.7207 1.32325 0.661623 0.749837i \(-0.269868\pi\)
0.661623 + 0.749837i \(0.269868\pi\)
\(948\) −8.37661 −0.272060
\(949\) −17.4604 −0.566789
\(950\) −23.6516 −0.767360
\(951\) 12.3194 0.399482
\(952\) 10.9722 0.355612
\(953\) −28.9513 −0.937825 −0.468913 0.883245i \(-0.655354\pi\)
−0.468913 + 0.883245i \(0.655354\pi\)
\(954\) 6.07692 0.196748
\(955\) 11.0711 0.358253
\(956\) 32.7252 1.05841
\(957\) −0.905330 −0.0292652
\(958\) 65.9367 2.13032
\(959\) 39.7742 1.28438
\(960\) 7.20485 0.232535
\(961\) −4.09903 −0.132227
\(962\) −11.0549 −0.356424
\(963\) −4.13977 −0.133402
\(964\) −43.7578 −1.40934
\(965\) −9.84929 −0.317060
\(966\) −24.7346 −0.795823
\(967\) −57.9945 −1.86498 −0.932489 0.361199i \(-0.882367\pi\)
−0.932489 + 0.361199i \(0.882367\pi\)
\(968\) −30.8482 −0.991499
\(969\) 2.34063 0.0751918
\(970\) 36.1911 1.16203
\(971\) −11.5844 −0.371761 −0.185881 0.982572i \(-0.559514\pi\)
−0.185881 + 0.982572i \(0.559514\pi\)
\(972\) −4.02764 −0.129187
\(973\) 13.6471 0.437507
\(974\) 36.5539 1.17126
\(975\) 4.34486 0.139147
\(976\) −30.8870 −0.988669
\(977\) −41.6869 −1.33368 −0.666841 0.745200i \(-0.732354\pi\)
−0.666841 + 0.745200i \(0.732354\pi\)
\(978\) 45.0393 1.44020
\(979\) 0.102164 0.00326516
\(980\) −8.11218 −0.259134
\(981\) 2.64234 0.0843635
\(982\) −75.3567 −2.40473
\(983\) −42.3156 −1.34966 −0.674829 0.737974i \(-0.735783\pi\)
−0.674829 + 0.737974i \(0.735783\pi\)
\(984\) 9.95407 0.317324
\(985\) −14.6919 −0.468124
\(986\) 1.01418 0.0322980
\(987\) 0.971667 0.0309285
\(988\) 9.95185 0.316611
\(989\) −24.6604 −0.784155
\(990\) −5.05958 −0.160804
\(991\) −53.5139 −1.69993 −0.849963 0.526842i \(-0.823376\pi\)
−0.849963 + 0.526842i \(0.823376\pi\)
\(992\) −1.41768 −0.0450115
\(993\) 11.0849 0.351768
\(994\) 24.9473 0.791280
\(995\) 12.2877 0.389545
\(996\) −23.3473 −0.739787
\(997\) 20.8459 0.660197 0.330098 0.943947i \(-0.392918\pi\)
0.330098 + 0.943947i \(0.392918\pi\)
\(998\) 83.3941 2.63979
\(999\) 4.26539 0.134951
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.1.45 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.45 48 1.1 even 1 trivial