Properties

Label 8007.2.a.f.1.35
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 1.35
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.36019 q^{2} -1.00000 q^{3} -0.149892 q^{4} -3.22830 q^{5} -1.36019 q^{6} +2.99593 q^{7} -2.92425 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.36019 q^{2} -1.00000 q^{3} -0.149892 q^{4} -3.22830 q^{5} -1.36019 q^{6} +2.99593 q^{7} -2.92425 q^{8} +1.00000 q^{9} -4.39109 q^{10} -3.10094 q^{11} +0.149892 q^{12} +1.97983 q^{13} +4.07502 q^{14} +3.22830 q^{15} -3.67775 q^{16} -1.00000 q^{17} +1.36019 q^{18} -0.710503 q^{19} +0.483896 q^{20} -2.99593 q^{21} -4.21786 q^{22} +6.91202 q^{23} +2.92425 q^{24} +5.42193 q^{25} +2.69294 q^{26} -1.00000 q^{27} -0.449065 q^{28} +9.35128 q^{29} +4.39109 q^{30} -7.97012 q^{31} +0.846083 q^{32} +3.10094 q^{33} -1.36019 q^{34} -9.67175 q^{35} -0.149892 q^{36} -4.06302 q^{37} -0.966417 q^{38} -1.97983 q^{39} +9.44038 q^{40} -0.959933 q^{41} -4.07502 q^{42} -1.47429 q^{43} +0.464806 q^{44} -3.22830 q^{45} +9.40163 q^{46} +5.23028 q^{47} +3.67775 q^{48} +1.97557 q^{49} +7.37484 q^{50} +1.00000 q^{51} -0.296760 q^{52} +4.09703 q^{53} -1.36019 q^{54} +10.0108 q^{55} -8.76085 q^{56} +0.710503 q^{57} +12.7195 q^{58} +2.47378 q^{59} -0.483896 q^{60} +8.55814 q^{61} -10.8409 q^{62} +2.99593 q^{63} +8.50633 q^{64} -6.39148 q^{65} +4.21786 q^{66} -5.39634 q^{67} +0.149892 q^{68} -6.91202 q^{69} -13.1554 q^{70} -0.392945 q^{71} -2.92425 q^{72} -3.98267 q^{73} -5.52647 q^{74} -5.42193 q^{75} +0.106499 q^{76} -9.29019 q^{77} -2.69294 q^{78} -5.00199 q^{79} +11.8729 q^{80} +1.00000 q^{81} -1.30569 q^{82} +13.6271 q^{83} +0.449065 q^{84} +3.22830 q^{85} -2.00531 q^{86} -9.35128 q^{87} +9.06794 q^{88} +9.10587 q^{89} -4.39109 q^{90} +5.93142 q^{91} -1.03605 q^{92} +7.97012 q^{93} +7.11416 q^{94} +2.29372 q^{95} -0.846083 q^{96} -15.0235 q^{97} +2.68715 q^{98} -3.10094 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36019 0.961797 0.480899 0.876776i \(-0.340310\pi\)
0.480899 + 0.876776i \(0.340310\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.149892 −0.0749459
\(5\) −3.22830 −1.44374 −0.721870 0.692028i \(-0.756717\pi\)
−0.721870 + 0.692028i \(0.756717\pi\)
\(6\) −1.36019 −0.555294
\(7\) 2.99593 1.13235 0.566177 0.824284i \(-0.308422\pi\)
0.566177 + 0.824284i \(0.308422\pi\)
\(8\) −2.92425 −1.03388
\(9\) 1.00000 0.333333
\(10\) −4.39109 −1.38859
\(11\) −3.10094 −0.934969 −0.467485 0.884001i \(-0.654840\pi\)
−0.467485 + 0.884001i \(0.654840\pi\)
\(12\) 0.149892 0.0432700
\(13\) 1.97983 0.549105 0.274553 0.961572i \(-0.411470\pi\)
0.274553 + 0.961572i \(0.411470\pi\)
\(14\) 4.07502 1.08909
\(15\) 3.22830 0.833544
\(16\) −3.67775 −0.919437
\(17\) −1.00000 −0.242536
\(18\) 1.36019 0.320599
\(19\) −0.710503 −0.163001 −0.0815003 0.996673i \(-0.525971\pi\)
−0.0815003 + 0.996673i \(0.525971\pi\)
\(20\) 0.483896 0.108202
\(21\) −2.99593 −0.653765
\(22\) −4.21786 −0.899251
\(23\) 6.91202 1.44125 0.720627 0.693323i \(-0.243854\pi\)
0.720627 + 0.693323i \(0.243854\pi\)
\(24\) 2.92425 0.596911
\(25\) 5.42193 1.08439
\(26\) 2.69294 0.528128
\(27\) −1.00000 −0.192450
\(28\) −0.449065 −0.0848652
\(29\) 9.35128 1.73649 0.868244 0.496137i \(-0.165249\pi\)
0.868244 + 0.496137i \(0.165249\pi\)
\(30\) 4.39109 0.801700
\(31\) −7.97012 −1.43148 −0.715738 0.698369i \(-0.753909\pi\)
−0.715738 + 0.698369i \(0.753909\pi\)
\(32\) 0.846083 0.149568
\(33\) 3.10094 0.539805
\(34\) −1.36019 −0.233270
\(35\) −9.67175 −1.63482
\(36\) −0.149892 −0.0249820
\(37\) −4.06302 −0.667957 −0.333978 0.942581i \(-0.608391\pi\)
−0.333978 + 0.942581i \(0.608391\pi\)
\(38\) −0.966417 −0.156774
\(39\) −1.97983 −0.317026
\(40\) 9.44038 1.49265
\(41\) −0.959933 −0.149916 −0.0749582 0.997187i \(-0.523882\pi\)
−0.0749582 + 0.997187i \(0.523882\pi\)
\(42\) −4.07502 −0.628789
\(43\) −1.47429 −0.224828 −0.112414 0.993661i \(-0.535858\pi\)
−0.112414 + 0.993661i \(0.535858\pi\)
\(44\) 0.464806 0.0700721
\(45\) −3.22830 −0.481247
\(46\) 9.40163 1.38620
\(47\) 5.23028 0.762915 0.381457 0.924386i \(-0.375422\pi\)
0.381457 + 0.924386i \(0.375422\pi\)
\(48\) 3.67775 0.530837
\(49\) 1.97557 0.282225
\(50\) 7.37484 1.04296
\(51\) 1.00000 0.140028
\(52\) −0.296760 −0.0411532
\(53\) 4.09703 0.562770 0.281385 0.959595i \(-0.409206\pi\)
0.281385 + 0.959595i \(0.409206\pi\)
\(54\) −1.36019 −0.185098
\(55\) 10.0108 1.34985
\(56\) −8.76085 −1.17072
\(57\) 0.710503 0.0941085
\(58\) 12.7195 1.67015
\(59\) 2.47378 0.322059 0.161029 0.986950i \(-0.448519\pi\)
0.161029 + 0.986950i \(0.448519\pi\)
\(60\) −0.483896 −0.0624707
\(61\) 8.55814 1.09576 0.547879 0.836558i \(-0.315435\pi\)
0.547879 + 0.836558i \(0.315435\pi\)
\(62\) −10.8409 −1.37679
\(63\) 2.99593 0.377451
\(64\) 8.50633 1.06329
\(65\) −6.39148 −0.792766
\(66\) 4.21786 0.519183
\(67\) −5.39634 −0.659267 −0.329634 0.944109i \(-0.606925\pi\)
−0.329634 + 0.944109i \(0.606925\pi\)
\(68\) 0.149892 0.0181770
\(69\) −6.91202 −0.832109
\(70\) −13.1554 −1.57237
\(71\) −0.392945 −0.0466340 −0.0233170 0.999728i \(-0.507423\pi\)
−0.0233170 + 0.999728i \(0.507423\pi\)
\(72\) −2.92425 −0.344627
\(73\) −3.98267 −0.466136 −0.233068 0.972460i \(-0.574876\pi\)
−0.233068 + 0.972460i \(0.574876\pi\)
\(74\) −5.52647 −0.642439
\(75\) −5.42193 −0.626071
\(76\) 0.106499 0.0122162
\(77\) −9.29019 −1.05872
\(78\) −2.69294 −0.304915
\(79\) −5.00199 −0.562768 −0.281384 0.959595i \(-0.590794\pi\)
−0.281384 + 0.959595i \(0.590794\pi\)
\(80\) 11.8729 1.32743
\(81\) 1.00000 0.111111
\(82\) −1.30569 −0.144189
\(83\) 13.6271 1.49577 0.747884 0.663830i \(-0.231070\pi\)
0.747884 + 0.663830i \(0.231070\pi\)
\(84\) 0.449065 0.0489970
\(85\) 3.22830 0.350159
\(86\) −2.00531 −0.216239
\(87\) −9.35128 −1.00256
\(88\) 9.06794 0.966646
\(89\) 9.10587 0.965220 0.482610 0.875835i \(-0.339689\pi\)
0.482610 + 0.875835i \(0.339689\pi\)
\(90\) −4.39109 −0.462862
\(91\) 5.93142 0.621781
\(92\) −1.03605 −0.108016
\(93\) 7.97012 0.826463
\(94\) 7.11416 0.733769
\(95\) 2.29372 0.235331
\(96\) −0.846083 −0.0863530
\(97\) −15.0235 −1.52541 −0.762704 0.646747i \(-0.776129\pi\)
−0.762704 + 0.646747i \(0.776129\pi\)
\(98\) 2.68715 0.271443
\(99\) −3.10094 −0.311656
\(100\) −0.812703 −0.0812703
\(101\) −11.0817 −1.10267 −0.551337 0.834283i \(-0.685882\pi\)
−0.551337 + 0.834283i \(0.685882\pi\)
\(102\) 1.36019 0.134679
\(103\) 0.479670 0.0472633 0.0236317 0.999721i \(-0.492477\pi\)
0.0236317 + 0.999721i \(0.492477\pi\)
\(104\) −5.78952 −0.567709
\(105\) 9.67175 0.943867
\(106\) 5.57272 0.541271
\(107\) −7.15167 −0.691378 −0.345689 0.938349i \(-0.612355\pi\)
−0.345689 + 0.938349i \(0.612355\pi\)
\(108\) 0.149892 0.0144233
\(109\) 13.1173 1.25641 0.628203 0.778050i \(-0.283791\pi\)
0.628203 + 0.778050i \(0.283791\pi\)
\(110\) 13.6165 1.29829
\(111\) 4.06302 0.385645
\(112\) −11.0183 −1.04113
\(113\) −17.8656 −1.68066 −0.840328 0.542078i \(-0.817638\pi\)
−0.840328 + 0.542078i \(0.817638\pi\)
\(114\) 0.966417 0.0905133
\(115\) −22.3141 −2.08080
\(116\) −1.40168 −0.130143
\(117\) 1.97983 0.183035
\(118\) 3.36480 0.309755
\(119\) −2.99593 −0.274636
\(120\) −9.44038 −0.861785
\(121\) −1.38416 −0.125832
\(122\) 11.6407 1.05390
\(123\) 0.959933 0.0865543
\(124\) 1.19466 0.107283
\(125\) −1.36213 −0.121833
\(126\) 4.07502 0.363032
\(127\) −7.44419 −0.660565 −0.330282 0.943882i \(-0.607144\pi\)
−0.330282 + 0.943882i \(0.607144\pi\)
\(128\) 9.87803 0.873103
\(129\) 1.47429 0.129804
\(130\) −8.69361 −0.762480
\(131\) 10.7794 0.941804 0.470902 0.882185i \(-0.343928\pi\)
0.470902 + 0.882185i \(0.343928\pi\)
\(132\) −0.464806 −0.0404561
\(133\) −2.12862 −0.184574
\(134\) −7.34003 −0.634082
\(135\) 3.22830 0.277848
\(136\) 2.92425 0.250753
\(137\) −13.1892 −1.12683 −0.563415 0.826174i \(-0.690513\pi\)
−0.563415 + 0.826174i \(0.690513\pi\)
\(138\) −9.40163 −0.800320
\(139\) 20.3422 1.72540 0.862701 0.505714i \(-0.168771\pi\)
0.862701 + 0.505714i \(0.168771\pi\)
\(140\) 1.44972 0.122523
\(141\) −5.23028 −0.440469
\(142\) −0.534479 −0.0448525
\(143\) −6.13933 −0.513397
\(144\) −3.67775 −0.306479
\(145\) −30.1887 −2.50704
\(146\) −5.41717 −0.448328
\(147\) −1.97557 −0.162942
\(148\) 0.609014 0.0500606
\(149\) 20.1066 1.64720 0.823600 0.567171i \(-0.191962\pi\)
0.823600 + 0.567171i \(0.191962\pi\)
\(150\) −7.37484 −0.602153
\(151\) −22.9247 −1.86558 −0.932792 0.360416i \(-0.882635\pi\)
−0.932792 + 0.360416i \(0.882635\pi\)
\(152\) 2.07769 0.168523
\(153\) −1.00000 −0.0808452
\(154\) −12.6364 −1.01827
\(155\) 25.7300 2.06668
\(156\) 0.296760 0.0237598
\(157\) −1.00000 −0.0798087
\(158\) −6.80365 −0.541269
\(159\) −4.09703 −0.324915
\(160\) −2.73141 −0.215937
\(161\) 20.7079 1.63201
\(162\) 1.36019 0.106866
\(163\) 7.59890 0.595192 0.297596 0.954692i \(-0.403815\pi\)
0.297596 + 0.954692i \(0.403815\pi\)
\(164\) 0.143886 0.0112356
\(165\) −10.0108 −0.779338
\(166\) 18.5354 1.43862
\(167\) 1.04495 0.0808609 0.0404305 0.999182i \(-0.487127\pi\)
0.0404305 + 0.999182i \(0.487127\pi\)
\(168\) 8.76085 0.675914
\(169\) −9.08028 −0.698483
\(170\) 4.39109 0.336782
\(171\) −0.710503 −0.0543336
\(172\) 0.220984 0.0168499
\(173\) −16.3423 −1.24248 −0.621242 0.783619i \(-0.713372\pi\)
−0.621242 + 0.783619i \(0.713372\pi\)
\(174\) −12.7195 −0.964261
\(175\) 16.2437 1.22791
\(176\) 11.4045 0.859646
\(177\) −2.47378 −0.185941
\(178\) 12.3857 0.928346
\(179\) −10.6512 −0.796111 −0.398056 0.917361i \(-0.630315\pi\)
−0.398056 + 0.917361i \(0.630315\pi\)
\(180\) 0.483896 0.0360675
\(181\) −13.6692 −1.01602 −0.508010 0.861351i \(-0.669619\pi\)
−0.508010 + 0.861351i \(0.669619\pi\)
\(182\) 8.06783 0.598028
\(183\) −8.55814 −0.632636
\(184\) −20.2125 −1.49008
\(185\) 13.1167 0.964357
\(186\) 10.8409 0.794890
\(187\) 3.10094 0.226763
\(188\) −0.783976 −0.0571773
\(189\) −2.99593 −0.217922
\(190\) 3.11989 0.226340
\(191\) −8.15314 −0.589940 −0.294970 0.955506i \(-0.595310\pi\)
−0.294970 + 0.955506i \(0.595310\pi\)
\(192\) −8.50633 −0.613891
\(193\) −23.0830 −1.66155 −0.830776 0.556607i \(-0.812103\pi\)
−0.830776 + 0.556607i \(0.812103\pi\)
\(194\) −20.4348 −1.46713
\(195\) 6.39148 0.457703
\(196\) −0.296122 −0.0211516
\(197\) −26.6711 −1.90024 −0.950120 0.311885i \(-0.899040\pi\)
−0.950120 + 0.311885i \(0.899040\pi\)
\(198\) −4.21786 −0.299750
\(199\) −0.433103 −0.0307019 −0.0153509 0.999882i \(-0.504887\pi\)
−0.0153509 + 0.999882i \(0.504887\pi\)
\(200\) −15.8551 −1.12113
\(201\) 5.39634 0.380628
\(202\) −15.0732 −1.06055
\(203\) 28.0157 1.96632
\(204\) −0.149892 −0.0104945
\(205\) 3.09895 0.216440
\(206\) 0.652441 0.0454577
\(207\) 6.91202 0.480418
\(208\) −7.28131 −0.504868
\(209\) 2.20323 0.152401
\(210\) 13.1554 0.907808
\(211\) −23.9319 −1.64754 −0.823771 0.566923i \(-0.808134\pi\)
−0.823771 + 0.566923i \(0.808134\pi\)
\(212\) −0.614110 −0.0421773
\(213\) 0.392945 0.0269242
\(214\) −9.72760 −0.664965
\(215\) 4.75946 0.324593
\(216\) 2.92425 0.198970
\(217\) −23.8779 −1.62094
\(218\) 17.8419 1.20841
\(219\) 3.98267 0.269124
\(220\) −1.50053 −0.101166
\(221\) −1.97983 −0.133178
\(222\) 5.52647 0.370912
\(223\) −19.9609 −1.33668 −0.668339 0.743857i \(-0.732995\pi\)
−0.668339 + 0.743857i \(0.732995\pi\)
\(224\) 2.53480 0.169364
\(225\) 5.42193 0.361462
\(226\) −24.3006 −1.61645
\(227\) −5.50929 −0.365665 −0.182832 0.983144i \(-0.558527\pi\)
−0.182832 + 0.983144i \(0.558527\pi\)
\(228\) −0.106499 −0.00705304
\(229\) −20.3676 −1.34593 −0.672964 0.739675i \(-0.734979\pi\)
−0.672964 + 0.739675i \(0.734979\pi\)
\(230\) −30.3513 −2.00131
\(231\) 9.29019 0.611250
\(232\) −27.3455 −1.79532
\(233\) −11.2941 −0.739900 −0.369950 0.929052i \(-0.620625\pi\)
−0.369950 + 0.929052i \(0.620625\pi\)
\(234\) 2.69294 0.176043
\(235\) −16.8849 −1.10145
\(236\) −0.370799 −0.0241370
\(237\) 5.00199 0.324914
\(238\) −4.07502 −0.264144
\(239\) 0.941056 0.0608718 0.0304359 0.999537i \(-0.490310\pi\)
0.0304359 + 0.999537i \(0.490310\pi\)
\(240\) −11.8729 −0.766391
\(241\) 11.0760 0.713470 0.356735 0.934206i \(-0.383890\pi\)
0.356735 + 0.934206i \(0.383890\pi\)
\(242\) −1.88271 −0.121025
\(243\) −1.00000 −0.0641500
\(244\) −1.28280 −0.0821225
\(245\) −6.37775 −0.407459
\(246\) 1.30569 0.0832477
\(247\) −1.40667 −0.0895045
\(248\) 23.3067 1.47997
\(249\) −13.6271 −0.863582
\(250\) −1.85275 −0.117178
\(251\) −8.17534 −0.516023 −0.258011 0.966142i \(-0.583067\pi\)
−0.258011 + 0.966142i \(0.583067\pi\)
\(252\) −0.449065 −0.0282884
\(253\) −21.4338 −1.34753
\(254\) −10.1255 −0.635330
\(255\) −3.22830 −0.202164
\(256\) −3.57669 −0.223543
\(257\) 18.4333 1.14984 0.574919 0.818210i \(-0.305034\pi\)
0.574919 + 0.818210i \(0.305034\pi\)
\(258\) 2.00531 0.124845
\(259\) −12.1725 −0.756364
\(260\) 0.958030 0.0594145
\(261\) 9.35128 0.578829
\(262\) 14.6621 0.905825
\(263\) 23.5480 1.45203 0.726015 0.687679i \(-0.241370\pi\)
0.726015 + 0.687679i \(0.241370\pi\)
\(264\) −9.06794 −0.558093
\(265\) −13.2264 −0.812494
\(266\) −2.89531 −0.177523
\(267\) −9.10587 −0.557270
\(268\) 0.808866 0.0494094
\(269\) −1.74484 −0.106385 −0.0531923 0.998584i \(-0.516940\pi\)
−0.0531923 + 0.998584i \(0.516940\pi\)
\(270\) 4.39109 0.267233
\(271\) −20.1218 −1.22231 −0.611155 0.791511i \(-0.709295\pi\)
−0.611155 + 0.791511i \(0.709295\pi\)
\(272\) 3.67775 0.222996
\(273\) −5.93142 −0.358986
\(274\) −17.9398 −1.08378
\(275\) −16.8131 −1.01387
\(276\) 1.03605 0.0623631
\(277\) 1.60990 0.0967296 0.0483648 0.998830i \(-0.484599\pi\)
0.0483648 + 0.998830i \(0.484599\pi\)
\(278\) 27.6692 1.65949
\(279\) −7.97012 −0.477159
\(280\) 28.2827 1.69021
\(281\) 21.7941 1.30013 0.650064 0.759879i \(-0.274742\pi\)
0.650064 + 0.759879i \(0.274742\pi\)
\(282\) −7.11416 −0.423642
\(283\) 2.77076 0.164704 0.0823522 0.996603i \(-0.473757\pi\)
0.0823522 + 0.996603i \(0.473757\pi\)
\(284\) 0.0588993 0.00349503
\(285\) −2.29372 −0.135868
\(286\) −8.35064 −0.493783
\(287\) −2.87589 −0.169758
\(288\) 0.846083 0.0498559
\(289\) 1.00000 0.0588235
\(290\) −41.0623 −2.41126
\(291\) 15.0235 0.880695
\(292\) 0.596969 0.0349350
\(293\) 0.402509 0.0235148 0.0117574 0.999931i \(-0.496257\pi\)
0.0117574 + 0.999931i \(0.496257\pi\)
\(294\) −2.68715 −0.156718
\(295\) −7.98611 −0.464969
\(296\) 11.8813 0.690587
\(297\) 3.10094 0.179935
\(298\) 27.3488 1.58427
\(299\) 13.6846 0.791401
\(300\) 0.812703 0.0469214
\(301\) −4.41687 −0.254584
\(302\) −31.1818 −1.79431
\(303\) 11.0817 0.636629
\(304\) 2.61305 0.149869
\(305\) −27.6283 −1.58199
\(306\) −1.36019 −0.0777567
\(307\) 29.0637 1.65875 0.829376 0.558691i \(-0.188696\pi\)
0.829376 + 0.558691i \(0.188696\pi\)
\(308\) 1.39252 0.0793464
\(309\) −0.479670 −0.0272875
\(310\) 34.9975 1.98773
\(311\) 1.51575 0.0859502 0.0429751 0.999076i \(-0.486316\pi\)
0.0429751 + 0.999076i \(0.486316\pi\)
\(312\) 5.78952 0.327767
\(313\) 14.5943 0.824916 0.412458 0.910977i \(-0.364670\pi\)
0.412458 + 0.910977i \(0.364670\pi\)
\(314\) −1.36019 −0.0767598
\(315\) −9.67175 −0.544942
\(316\) 0.749758 0.0421772
\(317\) 4.00663 0.225035 0.112517 0.993650i \(-0.464109\pi\)
0.112517 + 0.993650i \(0.464109\pi\)
\(318\) −5.57272 −0.312503
\(319\) −28.9978 −1.62356
\(320\) −27.4610 −1.53512
\(321\) 7.15167 0.399167
\(322\) 28.1666 1.56966
\(323\) 0.710503 0.0395335
\(324\) −0.149892 −0.00832732
\(325\) 10.7345 0.595443
\(326\) 10.3359 0.572454
\(327\) −13.1173 −0.725386
\(328\) 2.80709 0.154996
\(329\) 15.6695 0.863889
\(330\) −13.6165 −0.749565
\(331\) −6.98207 −0.383769 −0.191885 0.981418i \(-0.561460\pi\)
−0.191885 + 0.981418i \(0.561460\pi\)
\(332\) −2.04259 −0.112102
\(333\) −4.06302 −0.222652
\(334\) 1.42133 0.0777718
\(335\) 17.4210 0.951811
\(336\) 11.0183 0.601096
\(337\) 26.8163 1.46078 0.730389 0.683031i \(-0.239339\pi\)
0.730389 + 0.683031i \(0.239339\pi\)
\(338\) −12.3509 −0.671799
\(339\) 17.8656 0.970327
\(340\) −0.483896 −0.0262429
\(341\) 24.7149 1.33839
\(342\) −0.966417 −0.0522579
\(343\) −15.0528 −0.812775
\(344\) 4.31121 0.232445
\(345\) 22.3141 1.20135
\(346\) −22.2286 −1.19502
\(347\) −35.8479 −1.92441 −0.962207 0.272317i \(-0.912210\pi\)
−0.962207 + 0.272317i \(0.912210\pi\)
\(348\) 1.40168 0.0751379
\(349\) −24.5337 −1.31326 −0.656628 0.754214i \(-0.728018\pi\)
−0.656628 + 0.754214i \(0.728018\pi\)
\(350\) 22.0945 1.18100
\(351\) −1.97983 −0.105675
\(352\) −2.62366 −0.139841
\(353\) 26.8289 1.42796 0.713979 0.700167i \(-0.246891\pi\)
0.713979 + 0.700167i \(0.246891\pi\)
\(354\) −3.36480 −0.178837
\(355\) 1.26855 0.0673274
\(356\) −1.36489 −0.0723393
\(357\) 2.99593 0.158561
\(358\) −14.4877 −0.765698
\(359\) 22.1075 1.16679 0.583396 0.812188i \(-0.301724\pi\)
0.583396 + 0.812188i \(0.301724\pi\)
\(360\) 9.44038 0.497552
\(361\) −18.4952 −0.973431
\(362\) −18.5926 −0.977206
\(363\) 1.38416 0.0726494
\(364\) −0.889070 −0.0466000
\(365\) 12.8573 0.672980
\(366\) −11.6407 −0.608468
\(367\) −23.5498 −1.22929 −0.614646 0.788803i \(-0.710701\pi\)
−0.614646 + 0.788803i \(0.710701\pi\)
\(368\) −25.4207 −1.32514
\(369\) −0.959933 −0.0499721
\(370\) 17.8411 0.927516
\(371\) 12.2744 0.637254
\(372\) −1.19466 −0.0619400
\(373\) 8.36700 0.433227 0.216614 0.976257i \(-0.430499\pi\)
0.216614 + 0.976257i \(0.430499\pi\)
\(374\) 4.21786 0.218100
\(375\) 1.36213 0.0703402
\(376\) −15.2947 −0.788762
\(377\) 18.5139 0.953515
\(378\) −4.07502 −0.209596
\(379\) −0.731209 −0.0375597 −0.0187798 0.999824i \(-0.505978\pi\)
−0.0187798 + 0.999824i \(0.505978\pi\)
\(380\) −0.343810 −0.0176371
\(381\) 7.44419 0.381377
\(382\) −11.0898 −0.567403
\(383\) 11.8672 0.606385 0.303192 0.952929i \(-0.401947\pi\)
0.303192 + 0.952929i \(0.401947\pi\)
\(384\) −9.87803 −0.504086
\(385\) 29.9916 1.52851
\(386\) −31.3972 −1.59808
\(387\) −1.47429 −0.0749425
\(388\) 2.25190 0.114323
\(389\) −28.3872 −1.43929 −0.719645 0.694342i \(-0.755696\pi\)
−0.719645 + 0.694342i \(0.755696\pi\)
\(390\) 8.69361 0.440218
\(391\) −6.91202 −0.349556
\(392\) −5.77708 −0.291786
\(393\) −10.7794 −0.543751
\(394\) −36.2777 −1.82765
\(395\) 16.1479 0.812491
\(396\) 0.464806 0.0233574
\(397\) 23.2632 1.16755 0.583773 0.811917i \(-0.301576\pi\)
0.583773 + 0.811917i \(0.301576\pi\)
\(398\) −0.589101 −0.0295290
\(399\) 2.12862 0.106564
\(400\) −19.9405 −0.997026
\(401\) −34.3264 −1.71418 −0.857090 0.515167i \(-0.827730\pi\)
−0.857090 + 0.515167i \(0.827730\pi\)
\(402\) 7.34003 0.366087
\(403\) −15.7795 −0.786031
\(404\) 1.66106 0.0826408
\(405\) −3.22830 −0.160416
\(406\) 38.1066 1.89120
\(407\) 12.5992 0.624519
\(408\) −2.92425 −0.144772
\(409\) 25.1427 1.24323 0.621614 0.783324i \(-0.286477\pi\)
0.621614 + 0.783324i \(0.286477\pi\)
\(410\) 4.21516 0.208172
\(411\) 13.1892 0.650576
\(412\) −0.0718986 −0.00354219
\(413\) 7.41126 0.364684
\(414\) 9.40163 0.462065
\(415\) −43.9924 −2.15950
\(416\) 1.67510 0.0821285
\(417\) −20.3422 −0.996161
\(418\) 2.99680 0.146578
\(419\) −36.6041 −1.78823 −0.894114 0.447839i \(-0.852194\pi\)
−0.894114 + 0.447839i \(0.852194\pi\)
\(420\) −1.44972 −0.0707389
\(421\) −30.7382 −1.49809 −0.749044 0.662520i \(-0.769487\pi\)
−0.749044 + 0.662520i \(0.769487\pi\)
\(422\) −32.5519 −1.58460
\(423\) 5.23028 0.254305
\(424\) −11.9807 −0.581837
\(425\) −5.42193 −0.263002
\(426\) 0.534479 0.0258956
\(427\) 25.6396 1.24079
\(428\) 1.07198 0.0518159
\(429\) 6.13933 0.296410
\(430\) 6.47376 0.312192
\(431\) 3.65106 0.175865 0.0879326 0.996126i \(-0.471974\pi\)
0.0879326 + 0.996126i \(0.471974\pi\)
\(432\) 3.67775 0.176946
\(433\) −11.1690 −0.536749 −0.268374 0.963315i \(-0.586486\pi\)
−0.268374 + 0.963315i \(0.586486\pi\)
\(434\) −32.4784 −1.55901
\(435\) 30.1887 1.44744
\(436\) −1.96617 −0.0941624
\(437\) −4.91101 −0.234925
\(438\) 5.41717 0.258843
\(439\) −15.9845 −0.762900 −0.381450 0.924389i \(-0.624575\pi\)
−0.381450 + 0.924389i \(0.624575\pi\)
\(440\) −29.2741 −1.39559
\(441\) 1.97557 0.0940749
\(442\) −2.69294 −0.128090
\(443\) −20.6925 −0.983131 −0.491566 0.870841i \(-0.663575\pi\)
−0.491566 + 0.870841i \(0.663575\pi\)
\(444\) −0.609014 −0.0289025
\(445\) −29.3965 −1.39353
\(446\) −27.1505 −1.28561
\(447\) −20.1066 −0.951011
\(448\) 25.4843 1.20402
\(449\) 10.9512 0.516818 0.258409 0.966036i \(-0.416802\pi\)
0.258409 + 0.966036i \(0.416802\pi\)
\(450\) 7.37484 0.347653
\(451\) 2.97670 0.140167
\(452\) 2.67791 0.125958
\(453\) 22.9247 1.07710
\(454\) −7.49367 −0.351695
\(455\) −19.1484 −0.897691
\(456\) −2.07769 −0.0972969
\(457\) 20.1929 0.944585 0.472293 0.881442i \(-0.343427\pi\)
0.472293 + 0.881442i \(0.343427\pi\)
\(458\) −27.7037 −1.29451
\(459\) 1.00000 0.0466760
\(460\) 3.34470 0.155947
\(461\) −28.0471 −1.30628 −0.653142 0.757235i \(-0.726550\pi\)
−0.653142 + 0.757235i \(0.726550\pi\)
\(462\) 12.6364 0.587898
\(463\) 11.4533 0.532278 0.266139 0.963935i \(-0.414252\pi\)
0.266139 + 0.963935i \(0.414252\pi\)
\(464\) −34.3916 −1.59659
\(465\) −25.7300 −1.19320
\(466\) −15.3621 −0.711634
\(467\) 18.4240 0.852563 0.426281 0.904591i \(-0.359823\pi\)
0.426281 + 0.904591i \(0.359823\pi\)
\(468\) −0.296760 −0.0137177
\(469\) −16.1670 −0.746524
\(470\) −22.9667 −1.05937
\(471\) 1.00000 0.0460776
\(472\) −7.23396 −0.332970
\(473\) 4.57170 0.210207
\(474\) 6.80365 0.312502
\(475\) −3.85230 −0.176756
\(476\) 0.449065 0.0205828
\(477\) 4.09703 0.187590
\(478\) 1.28001 0.0585464
\(479\) −35.4383 −1.61922 −0.809609 0.586969i \(-0.800321\pi\)
−0.809609 + 0.586969i \(0.800321\pi\)
\(480\) 2.73141 0.124671
\(481\) −8.04409 −0.366779
\(482\) 15.0655 0.686214
\(483\) −20.7079 −0.942241
\(484\) 0.207474 0.00943062
\(485\) 48.5005 2.20229
\(486\) −1.36019 −0.0616993
\(487\) 17.7572 0.804654 0.402327 0.915496i \(-0.368201\pi\)
0.402327 + 0.915496i \(0.368201\pi\)
\(488\) −25.0262 −1.13288
\(489\) −7.59890 −0.343634
\(490\) −8.67493 −0.391893
\(491\) 27.0554 1.22099 0.610497 0.792019i \(-0.290970\pi\)
0.610497 + 0.792019i \(0.290970\pi\)
\(492\) −0.143886 −0.00648689
\(493\) −9.35128 −0.421160
\(494\) −1.91334 −0.0860852
\(495\) 10.0108 0.449951
\(496\) 29.3121 1.31615
\(497\) −1.17723 −0.0528062
\(498\) −18.5354 −0.830590
\(499\) 34.2567 1.53354 0.766769 0.641923i \(-0.221863\pi\)
0.766769 + 0.641923i \(0.221863\pi\)
\(500\) 0.204172 0.00913087
\(501\) −1.04495 −0.0466851
\(502\) −11.1200 −0.496310
\(503\) −0.407685 −0.0181778 −0.00908888 0.999959i \(-0.502893\pi\)
−0.00908888 + 0.999959i \(0.502893\pi\)
\(504\) −8.76085 −0.390239
\(505\) 35.7752 1.59197
\(506\) −29.1539 −1.29605
\(507\) 9.08028 0.403270
\(508\) 1.11582 0.0495066
\(509\) −32.9394 −1.46001 −0.730007 0.683439i \(-0.760483\pi\)
−0.730007 + 0.683439i \(0.760483\pi\)
\(510\) −4.39109 −0.194441
\(511\) −11.9318 −0.527831
\(512\) −24.6210 −1.08811
\(513\) 0.710503 0.0313695
\(514\) 25.0727 1.10591
\(515\) −1.54852 −0.0682360
\(516\) −0.220984 −0.00972829
\(517\) −16.2188 −0.713302
\(518\) −16.5569 −0.727468
\(519\) 16.3423 0.717348
\(520\) 18.6903 0.819625
\(521\) 35.0986 1.53770 0.768848 0.639431i \(-0.220830\pi\)
0.768848 + 0.639431i \(0.220830\pi\)
\(522\) 12.7195 0.556717
\(523\) −35.8291 −1.56670 −0.783348 0.621583i \(-0.786490\pi\)
−0.783348 + 0.621583i \(0.786490\pi\)
\(524\) −1.61575 −0.0705843
\(525\) −16.2437 −0.708934
\(526\) 32.0296 1.39656
\(527\) 7.97012 0.347184
\(528\) −11.4045 −0.496317
\(529\) 24.7760 1.07722
\(530\) −17.9904 −0.781454
\(531\) 2.47378 0.107353
\(532\) 0.319062 0.0138331
\(533\) −1.90050 −0.0823199
\(534\) −12.3857 −0.535981
\(535\) 23.0877 0.998170
\(536\) 15.7803 0.681603
\(537\) 10.6512 0.459635
\(538\) −2.37330 −0.102320
\(539\) −6.12614 −0.263871
\(540\) −0.483896 −0.0208236
\(541\) 29.9432 1.28736 0.643679 0.765295i \(-0.277407\pi\)
0.643679 + 0.765295i \(0.277407\pi\)
\(542\) −27.3694 −1.17562
\(543\) 13.6692 0.586600
\(544\) −0.846083 −0.0362755
\(545\) −42.3465 −1.81392
\(546\) −8.06783 −0.345271
\(547\) −26.9190 −1.15097 −0.575487 0.817811i \(-0.695187\pi\)
−0.575487 + 0.817811i \(0.695187\pi\)
\(548\) 1.97695 0.0844513
\(549\) 8.55814 0.365253
\(550\) −22.8690 −0.975136
\(551\) −6.64411 −0.283049
\(552\) 20.2125 0.860301
\(553\) −14.9856 −0.637253
\(554\) 2.18977 0.0930342
\(555\) −13.1167 −0.556772
\(556\) −3.04913 −0.129312
\(557\) 25.5205 1.08134 0.540670 0.841235i \(-0.318171\pi\)
0.540670 + 0.841235i \(0.318171\pi\)
\(558\) −10.8409 −0.458930
\(559\) −2.91885 −0.123454
\(560\) 35.5703 1.50312
\(561\) −3.10094 −0.130922
\(562\) 29.6441 1.25046
\(563\) 32.5667 1.37252 0.686261 0.727355i \(-0.259251\pi\)
0.686261 + 0.727355i \(0.259251\pi\)
\(564\) 0.783976 0.0330113
\(565\) 57.6756 2.42643
\(566\) 3.76875 0.158412
\(567\) 2.99593 0.125817
\(568\) 1.14907 0.0482140
\(569\) −18.8148 −0.788756 −0.394378 0.918948i \(-0.629040\pi\)
−0.394378 + 0.918948i \(0.629040\pi\)
\(570\) −3.11989 −0.130678
\(571\) 18.1739 0.760555 0.380278 0.924872i \(-0.375828\pi\)
0.380278 + 0.924872i \(0.375828\pi\)
\(572\) 0.920235 0.0384770
\(573\) 8.15314 0.340602
\(574\) −3.91175 −0.163273
\(575\) 37.4765 1.56288
\(576\) 8.50633 0.354430
\(577\) −0.495928 −0.0206458 −0.0103229 0.999947i \(-0.503286\pi\)
−0.0103229 + 0.999947i \(0.503286\pi\)
\(578\) 1.36019 0.0565763
\(579\) 23.0830 0.959297
\(580\) 4.52504 0.187892
\(581\) 40.8257 1.69374
\(582\) 20.4348 0.847050
\(583\) −12.7046 −0.526173
\(584\) 11.6463 0.481929
\(585\) −6.39148 −0.264255
\(586\) 0.547488 0.0226165
\(587\) 41.3693 1.70749 0.853747 0.520688i \(-0.174325\pi\)
0.853747 + 0.520688i \(0.174325\pi\)
\(588\) 0.296122 0.0122119
\(589\) 5.66280 0.233331
\(590\) −10.8626 −0.447206
\(591\) 26.6711 1.09710
\(592\) 14.9428 0.614145
\(593\) 38.7697 1.59208 0.796041 0.605243i \(-0.206924\pi\)
0.796041 + 0.605243i \(0.206924\pi\)
\(594\) 4.21786 0.173061
\(595\) 9.67175 0.396503
\(596\) −3.01382 −0.123451
\(597\) 0.433103 0.0177257
\(598\) 18.6136 0.761167
\(599\) −29.3493 −1.19918 −0.599589 0.800308i \(-0.704669\pi\)
−0.599589 + 0.800308i \(0.704669\pi\)
\(600\) 15.8551 0.647282
\(601\) −40.1888 −1.63934 −0.819668 0.572839i \(-0.805842\pi\)
−0.819668 + 0.572839i \(0.805842\pi\)
\(602\) −6.00777 −0.244859
\(603\) −5.39634 −0.219756
\(604\) 3.43622 0.139818
\(605\) 4.46848 0.181669
\(606\) 15.0732 0.612308
\(607\) −16.5081 −0.670043 −0.335021 0.942211i \(-0.608744\pi\)
−0.335021 + 0.942211i \(0.608744\pi\)
\(608\) −0.601145 −0.0243796
\(609\) −28.0157 −1.13525
\(610\) −37.5796 −1.52155
\(611\) 10.3551 0.418921
\(612\) 0.149892 0.00605902
\(613\) −25.2978 −1.02177 −0.510885 0.859649i \(-0.670682\pi\)
−0.510885 + 0.859649i \(0.670682\pi\)
\(614\) 39.5320 1.59538
\(615\) −3.09895 −0.124962
\(616\) 27.1669 1.09459
\(617\) −2.50442 −0.100824 −0.0504120 0.998729i \(-0.516053\pi\)
−0.0504120 + 0.998729i \(0.516053\pi\)
\(618\) −0.652441 −0.0262450
\(619\) −1.82866 −0.0735000 −0.0367500 0.999324i \(-0.511701\pi\)
−0.0367500 + 0.999324i \(0.511701\pi\)
\(620\) −3.85671 −0.154889
\(621\) −6.91202 −0.277370
\(622\) 2.06170 0.0826666
\(623\) 27.2805 1.09297
\(624\) 7.28131 0.291486
\(625\) −22.7123 −0.908492
\(626\) 19.8509 0.793402
\(627\) −2.20323 −0.0879885
\(628\) 0.149892 0.00598133
\(629\) 4.06302 0.162003
\(630\) −13.1554 −0.524123
\(631\) −16.9691 −0.675528 −0.337764 0.941231i \(-0.609671\pi\)
−0.337764 + 0.941231i \(0.609671\pi\)
\(632\) 14.6271 0.581835
\(633\) 23.9319 0.951208
\(634\) 5.44977 0.216438
\(635\) 24.0321 0.953684
\(636\) 0.614110 0.0243511
\(637\) 3.91129 0.154971
\(638\) −39.4424 −1.56154
\(639\) −0.392945 −0.0155447
\(640\) −31.8893 −1.26053
\(641\) −15.1783 −0.599506 −0.299753 0.954017i \(-0.596904\pi\)
−0.299753 + 0.954017i \(0.596904\pi\)
\(642\) 9.72760 0.383918
\(643\) −26.8376 −1.05837 −0.529186 0.848506i \(-0.677503\pi\)
−0.529186 + 0.848506i \(0.677503\pi\)
\(644\) −3.10394 −0.122312
\(645\) −4.75946 −0.187404
\(646\) 0.966417 0.0380232
\(647\) −14.3159 −0.562817 −0.281409 0.959588i \(-0.590802\pi\)
−0.281409 + 0.959588i \(0.590802\pi\)
\(648\) −2.92425 −0.114876
\(649\) −7.67105 −0.301115
\(650\) 14.6009 0.572695
\(651\) 23.8779 0.935848
\(652\) −1.13901 −0.0446072
\(653\) −30.5029 −1.19367 −0.596836 0.802364i \(-0.703576\pi\)
−0.596836 + 0.802364i \(0.703576\pi\)
\(654\) −17.8419 −0.697675
\(655\) −34.7993 −1.35972
\(656\) 3.53039 0.137839
\(657\) −3.98267 −0.155379
\(658\) 21.3135 0.830886
\(659\) 1.12394 0.0437824 0.0218912 0.999760i \(-0.493031\pi\)
0.0218912 + 0.999760i \(0.493031\pi\)
\(660\) 1.50053 0.0584082
\(661\) 19.5244 0.759411 0.379706 0.925107i \(-0.376025\pi\)
0.379706 + 0.925107i \(0.376025\pi\)
\(662\) −9.49692 −0.369108
\(663\) 1.97983 0.0768901
\(664\) −39.8491 −1.54644
\(665\) 6.87181 0.266478
\(666\) −5.52647 −0.214146
\(667\) 64.6362 2.50272
\(668\) −0.156630 −0.00606019
\(669\) 19.9609 0.771732
\(670\) 23.6958 0.915449
\(671\) −26.5383 −1.02450
\(672\) −2.53480 −0.0977821
\(673\) −40.8207 −1.57352 −0.786762 0.617257i \(-0.788244\pi\)
−0.786762 + 0.617257i \(0.788244\pi\)
\(674\) 36.4752 1.40497
\(675\) −5.42193 −0.208690
\(676\) 1.36106 0.0523484
\(677\) −14.5913 −0.560790 −0.280395 0.959885i \(-0.590465\pi\)
−0.280395 + 0.959885i \(0.590465\pi\)
\(678\) 24.3006 0.933258
\(679\) −45.0094 −1.72730
\(680\) −9.44038 −0.362022
\(681\) 5.50929 0.211117
\(682\) 33.6169 1.28726
\(683\) 4.41012 0.168749 0.0843744 0.996434i \(-0.473111\pi\)
0.0843744 + 0.996434i \(0.473111\pi\)
\(684\) 0.106499 0.00407208
\(685\) 42.5787 1.62685
\(686\) −20.4746 −0.781725
\(687\) 20.3676 0.777072
\(688\) 5.42208 0.206715
\(689\) 8.11141 0.309020
\(690\) 30.3513 1.15545
\(691\) −21.1419 −0.804277 −0.402138 0.915579i \(-0.631733\pi\)
−0.402138 + 0.915579i \(0.631733\pi\)
\(692\) 2.44958 0.0931190
\(693\) −9.29019 −0.352905
\(694\) −48.7598 −1.85090
\(695\) −65.6707 −2.49103
\(696\) 27.3455 1.03653
\(697\) 0.959933 0.0363601
\(698\) −33.3704 −1.26309
\(699\) 11.2941 0.427181
\(700\) −2.43480 −0.0920267
\(701\) 12.4713 0.471034 0.235517 0.971870i \(-0.424322\pi\)
0.235517 + 0.971870i \(0.424322\pi\)
\(702\) −2.69294 −0.101638
\(703\) 2.88679 0.108877
\(704\) −26.3776 −0.994145
\(705\) 16.8849 0.635923
\(706\) 36.4923 1.37341
\(707\) −33.2000 −1.24862
\(708\) 0.370799 0.0139355
\(709\) −11.4412 −0.429682 −0.214841 0.976649i \(-0.568923\pi\)
−0.214841 + 0.976649i \(0.568923\pi\)
\(710\) 1.72546 0.0647553
\(711\) −5.00199 −0.187589
\(712\) −26.6279 −0.997922
\(713\) −55.0896 −2.06312
\(714\) 4.07502 0.152504
\(715\) 19.8196 0.741212
\(716\) 1.59653 0.0596653
\(717\) −0.941056 −0.0351444
\(718\) 30.0704 1.12222
\(719\) −34.4197 −1.28364 −0.641819 0.766856i \(-0.721820\pi\)
−0.641819 + 0.766856i \(0.721820\pi\)
\(720\) 11.8729 0.442476
\(721\) 1.43706 0.0535188
\(722\) −25.1569 −0.936243
\(723\) −11.0760 −0.411922
\(724\) 2.04889 0.0761465
\(725\) 50.7020 1.88303
\(726\) 1.88271 0.0698740
\(727\) −0.566545 −0.0210120 −0.0105060 0.999945i \(-0.503344\pi\)
−0.0105060 + 0.999945i \(0.503344\pi\)
\(728\) −17.3450 −0.642847
\(729\) 1.00000 0.0370370
\(730\) 17.4883 0.647270
\(731\) 1.47429 0.0545287
\(732\) 1.28280 0.0474135
\(733\) 16.6202 0.613881 0.306940 0.951729i \(-0.400695\pi\)
0.306940 + 0.951729i \(0.400695\pi\)
\(734\) −32.0322 −1.18233
\(735\) 6.37775 0.235247
\(736\) 5.84814 0.215565
\(737\) 16.7337 0.616395
\(738\) −1.30569 −0.0480631
\(739\) 0.659089 0.0242450 0.0121225 0.999927i \(-0.496141\pi\)
0.0121225 + 0.999927i \(0.496141\pi\)
\(740\) −1.96608 −0.0722746
\(741\) 1.40667 0.0516755
\(742\) 16.6955 0.612910
\(743\) 20.6658 0.758154 0.379077 0.925365i \(-0.376241\pi\)
0.379077 + 0.925365i \(0.376241\pi\)
\(744\) −23.3067 −0.854464
\(745\) −64.9103 −2.37813
\(746\) 11.3807 0.416677
\(747\) 13.6271 0.498589
\(748\) −0.464806 −0.0169950
\(749\) −21.4259 −0.782884
\(750\) 1.85275 0.0676530
\(751\) 27.6699 1.00969 0.504845 0.863210i \(-0.331550\pi\)
0.504845 + 0.863210i \(0.331550\pi\)
\(752\) −19.2357 −0.701452
\(753\) 8.17534 0.297926
\(754\) 25.1824 0.917088
\(755\) 74.0078 2.69342
\(756\) 0.449065 0.0163323
\(757\) 34.9709 1.27104 0.635519 0.772085i \(-0.280786\pi\)
0.635519 + 0.772085i \(0.280786\pi\)
\(758\) −0.994580 −0.0361248
\(759\) 21.4338 0.777996
\(760\) −6.70742 −0.243304
\(761\) 40.2156 1.45781 0.728907 0.684613i \(-0.240029\pi\)
0.728907 + 0.684613i \(0.240029\pi\)
\(762\) 10.1255 0.366808
\(763\) 39.2983 1.42270
\(764\) 1.22209 0.0442136
\(765\) 3.22830 0.116720
\(766\) 16.1416 0.583219
\(767\) 4.89766 0.176844
\(768\) 3.57669 0.129063
\(769\) −29.1027 −1.04947 −0.524735 0.851266i \(-0.675836\pi\)
−0.524735 + 0.851266i \(0.675836\pi\)
\(770\) 40.7941 1.47012
\(771\) −18.4333 −0.663859
\(772\) 3.45995 0.124526
\(773\) 15.4068 0.554144 0.277072 0.960849i \(-0.410636\pi\)
0.277072 + 0.960849i \(0.410636\pi\)
\(774\) −2.00531 −0.0720795
\(775\) −43.2135 −1.55227
\(776\) 43.9326 1.57709
\(777\) 12.1725 0.436687
\(778\) −38.6120 −1.38431
\(779\) 0.682036 0.0244365
\(780\) −0.958030 −0.0343030
\(781\) 1.21850 0.0436014
\(782\) −9.40163 −0.336202
\(783\) −9.35128 −0.334187
\(784\) −7.26566 −0.259488
\(785\) 3.22830 0.115223
\(786\) −14.6621 −0.522978
\(787\) −23.8310 −0.849482 −0.424741 0.905315i \(-0.639635\pi\)
−0.424741 + 0.905315i \(0.639635\pi\)
\(788\) 3.99778 0.142415
\(789\) −23.5480 −0.838330
\(790\) 21.9642 0.781452
\(791\) −53.5241 −1.90310
\(792\) 9.06794 0.322215
\(793\) 16.9436 0.601686
\(794\) 31.6423 1.12294
\(795\) 13.2264 0.469093
\(796\) 0.0649186 0.00230098
\(797\) 20.1569 0.713993 0.356997 0.934106i \(-0.383801\pi\)
0.356997 + 0.934106i \(0.383801\pi\)
\(798\) 2.89531 0.102493
\(799\) −5.23028 −0.185034
\(800\) 4.58741 0.162189
\(801\) 9.10587 0.321740
\(802\) −46.6903 −1.64869
\(803\) 12.3500 0.435823
\(804\) −0.808866 −0.0285265
\(805\) −66.8513 −2.35620
\(806\) −21.4630 −0.756003
\(807\) 1.74484 0.0614211
\(808\) 32.4058 1.14003
\(809\) −2.16465 −0.0761049 −0.0380525 0.999276i \(-0.512115\pi\)
−0.0380525 + 0.999276i \(0.512115\pi\)
\(810\) −4.39109 −0.154287
\(811\) 27.5859 0.968673 0.484336 0.874882i \(-0.339061\pi\)
0.484336 + 0.874882i \(0.339061\pi\)
\(812\) −4.19933 −0.147367
\(813\) 20.1218 0.705701
\(814\) 17.1373 0.600661
\(815\) −24.5315 −0.859303
\(816\) −3.67775 −0.128747
\(817\) 1.04749 0.0366470
\(818\) 34.1988 1.19573
\(819\) 5.93142 0.207260
\(820\) −0.464508 −0.0162213
\(821\) −25.3863 −0.885987 −0.442994 0.896525i \(-0.646084\pi\)
−0.442994 + 0.896525i \(0.646084\pi\)
\(822\) 17.9398 0.625722
\(823\) −36.1110 −1.25875 −0.629374 0.777102i \(-0.716689\pi\)
−0.629374 + 0.777102i \(0.716689\pi\)
\(824\) −1.40268 −0.0488646
\(825\) 16.8131 0.585357
\(826\) 10.0807 0.350752
\(827\) −10.6867 −0.371614 −0.185807 0.982586i \(-0.559490\pi\)
−0.185807 + 0.982586i \(0.559490\pi\)
\(828\) −1.03605 −0.0360054
\(829\) 13.1639 0.457200 0.228600 0.973520i \(-0.426585\pi\)
0.228600 + 0.973520i \(0.426585\pi\)
\(830\) −59.8378 −2.07700
\(831\) −1.60990 −0.0558468
\(832\) 16.8411 0.583859
\(833\) −1.97557 −0.0684495
\(834\) −27.6692 −0.958105
\(835\) −3.37343 −0.116742
\(836\) −0.330246 −0.0114218
\(837\) 7.97012 0.275488
\(838\) −49.7885 −1.71991
\(839\) −35.1891 −1.21486 −0.607431 0.794372i \(-0.707800\pi\)
−0.607431 + 0.794372i \(0.707800\pi\)
\(840\) −28.2827 −0.975845
\(841\) 58.4464 2.01539
\(842\) −41.8097 −1.44086
\(843\) −21.7941 −0.750629
\(844\) 3.58720 0.123476
\(845\) 29.3139 1.00843
\(846\) 7.11416 0.244590
\(847\) −4.14683 −0.142487
\(848\) −15.0678 −0.517432
\(849\) −2.77076 −0.0950921
\(850\) −7.37484 −0.252955
\(851\) −28.0837 −0.962696
\(852\) −0.0588993 −0.00201786
\(853\) 39.5498 1.35416 0.677080 0.735910i \(-0.263245\pi\)
0.677080 + 0.735910i \(0.263245\pi\)
\(854\) 34.8746 1.19338
\(855\) 2.29372 0.0784436
\(856\) 20.9133 0.714802
\(857\) −41.9770 −1.43391 −0.716953 0.697122i \(-0.754464\pi\)
−0.716953 + 0.697122i \(0.754464\pi\)
\(858\) 8.35064 0.285086
\(859\) 25.7663 0.879134 0.439567 0.898210i \(-0.355132\pi\)
0.439567 + 0.898210i \(0.355132\pi\)
\(860\) −0.713404 −0.0243269
\(861\) 2.87589 0.0980100
\(862\) 4.96612 0.169147
\(863\) −27.6036 −0.939639 −0.469819 0.882763i \(-0.655681\pi\)
−0.469819 + 0.882763i \(0.655681\pi\)
\(864\) −0.846083 −0.0287843
\(865\) 52.7580 1.79382
\(866\) −15.1920 −0.516244
\(867\) −1.00000 −0.0339618
\(868\) 3.57910 0.121483
\(869\) 15.5109 0.526171
\(870\) 41.0623 1.39214
\(871\) −10.6838 −0.362007
\(872\) −38.3582 −1.29897
\(873\) −15.0235 −0.508470
\(874\) −6.67989 −0.225951
\(875\) −4.08085 −0.137958
\(876\) −0.596969 −0.0201697
\(877\) −13.5592 −0.457862 −0.228931 0.973443i \(-0.573523\pi\)
−0.228931 + 0.973443i \(0.573523\pi\)
\(878\) −21.7420 −0.733755
\(879\) −0.402509 −0.0135763
\(880\) −36.8171 −1.24111
\(881\) −42.9425 −1.44677 −0.723384 0.690446i \(-0.757415\pi\)
−0.723384 + 0.690446i \(0.757415\pi\)
\(882\) 2.68715 0.0904810
\(883\) −6.54972 −0.220416 −0.110208 0.993909i \(-0.535152\pi\)
−0.110208 + 0.993909i \(0.535152\pi\)
\(884\) 0.296760 0.00998111
\(885\) 7.98611 0.268450
\(886\) −28.1457 −0.945573
\(887\) 39.1733 1.31531 0.657656 0.753318i \(-0.271548\pi\)
0.657656 + 0.753318i \(0.271548\pi\)
\(888\) −11.8813 −0.398711
\(889\) −22.3022 −0.747993
\(890\) −39.9847 −1.34029
\(891\) −3.10094 −0.103885
\(892\) 2.99197 0.100179
\(893\) −3.71613 −0.124356
\(894\) −27.3488 −0.914680
\(895\) 34.3854 1.14938
\(896\) 29.5938 0.988661
\(897\) −13.6846 −0.456915
\(898\) 14.8957 0.497075
\(899\) −74.5308 −2.48574
\(900\) −0.812703 −0.0270901
\(901\) −4.09703 −0.136492
\(902\) 4.04886 0.134812
\(903\) 4.41687 0.146984
\(904\) 52.2436 1.73760
\(905\) 44.1282 1.46687
\(906\) 31.1818 1.03595
\(907\) 57.7416 1.91728 0.958639 0.284625i \(-0.0918690\pi\)
0.958639 + 0.284625i \(0.0918690\pi\)
\(908\) 0.825798 0.0274051
\(909\) −11.0817 −0.367558
\(910\) −26.0454 −0.863397
\(911\) 23.3402 0.773296 0.386648 0.922227i \(-0.373633\pi\)
0.386648 + 0.922227i \(0.373633\pi\)
\(912\) −2.61305 −0.0865268
\(913\) −42.2568 −1.39850
\(914\) 27.4662 0.908500
\(915\) 27.6283 0.913362
\(916\) 3.05293 0.100872
\(917\) 32.2944 1.06646
\(918\) 1.36019 0.0448929
\(919\) −9.27010 −0.305792 −0.152896 0.988242i \(-0.548860\pi\)
−0.152896 + 0.988242i \(0.548860\pi\)
\(920\) 65.2520 2.15130
\(921\) −29.0637 −0.957681
\(922\) −38.1493 −1.25638
\(923\) −0.777964 −0.0256070
\(924\) −1.39252 −0.0458107
\(925\) −22.0294 −0.724324
\(926\) 15.5786 0.511944
\(927\) 0.479670 0.0157544
\(928\) 7.91196 0.259723
\(929\) 0.753499 0.0247215 0.0123608 0.999924i \(-0.496065\pi\)
0.0123608 + 0.999924i \(0.496065\pi\)
\(930\) −34.9975 −1.14761
\(931\) −1.40365 −0.0460028
\(932\) 1.69289 0.0554524
\(933\) −1.51575 −0.0496233
\(934\) 25.0601 0.819993
\(935\) −10.0108 −0.327387
\(936\) −5.78952 −0.189236
\(937\) −35.2077 −1.15019 −0.575094 0.818088i \(-0.695034\pi\)
−0.575094 + 0.818088i \(0.695034\pi\)
\(938\) −21.9902 −0.718005
\(939\) −14.5943 −0.476265
\(940\) 2.53091 0.0825492
\(941\) 14.2112 0.463271 0.231636 0.972803i \(-0.425592\pi\)
0.231636 + 0.972803i \(0.425592\pi\)
\(942\) 1.36019 0.0443173
\(943\) −6.63507 −0.216068
\(944\) −9.09794 −0.296113
\(945\) 9.67175 0.314622
\(946\) 6.21836 0.202176
\(947\) 11.8458 0.384935 0.192468 0.981303i \(-0.438351\pi\)
0.192468 + 0.981303i \(0.438351\pi\)
\(948\) −0.749758 −0.0243510
\(949\) −7.88500 −0.255958
\(950\) −5.23985 −0.170003
\(951\) −4.00663 −0.129924
\(952\) 8.76085 0.283941
\(953\) −30.4435 −0.986162 −0.493081 0.869983i \(-0.664129\pi\)
−0.493081 + 0.869983i \(0.664129\pi\)
\(954\) 5.57272 0.180424
\(955\) 26.3208 0.851721
\(956\) −0.141056 −0.00456209
\(957\) 28.9978 0.937365
\(958\) −48.2027 −1.55736
\(959\) −39.5139 −1.27597
\(960\) 27.4610 0.886300
\(961\) 32.5228 1.04912
\(962\) −10.9415 −0.352767
\(963\) −7.15167 −0.230459
\(964\) −1.66021 −0.0534717
\(965\) 74.5189 2.39885
\(966\) −28.1666 −0.906245
\(967\) −32.6784 −1.05087 −0.525433 0.850835i \(-0.676097\pi\)
−0.525433 + 0.850835i \(0.676097\pi\)
\(968\) 4.04763 0.130096
\(969\) −0.710503 −0.0228247
\(970\) 65.9697 2.11816
\(971\) −3.81520 −0.122436 −0.0612179 0.998124i \(-0.519498\pi\)
−0.0612179 + 0.998124i \(0.519498\pi\)
\(972\) 0.149892 0.00480778
\(973\) 60.9437 1.95377
\(974\) 24.1531 0.773914
\(975\) −10.7345 −0.343779
\(976\) −31.4747 −1.00748
\(977\) −3.06867 −0.0981753 −0.0490877 0.998794i \(-0.515631\pi\)
−0.0490877 + 0.998794i \(0.515631\pi\)
\(978\) −10.3359 −0.330506
\(979\) −28.2368 −0.902451
\(980\) 0.955971 0.0305374
\(981\) 13.1173 0.418802
\(982\) 36.8004 1.17435
\(983\) 20.1766 0.643533 0.321766 0.946819i \(-0.395723\pi\)
0.321766 + 0.946819i \(0.395723\pi\)
\(984\) −2.80709 −0.0894867
\(985\) 86.1025 2.74345
\(986\) −12.7195 −0.405071
\(987\) −15.6695 −0.498767
\(988\) 0.210849 0.00670800
\(989\) −10.1903 −0.324034
\(990\) 13.6165 0.432762
\(991\) 31.3412 0.995586 0.497793 0.867296i \(-0.334144\pi\)
0.497793 + 0.867296i \(0.334144\pi\)
\(992\) −6.74338 −0.214103
\(993\) 6.98207 0.221569
\(994\) −1.60126 −0.0507889
\(995\) 1.39819 0.0443255
\(996\) 2.04259 0.0647219
\(997\) 22.3368 0.707414 0.353707 0.935356i \(-0.384921\pi\)
0.353707 + 0.935356i \(0.384921\pi\)
\(998\) 46.5954 1.47495
\(999\) 4.06302 0.128548
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.1.35 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.35 48 1.1 even 1 trivial