Properties

Label 8007.2.a.f.1.47
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 1.47
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.55264 q^{2} -1.00000 q^{3} +4.51600 q^{4} -2.02616 q^{5} -2.55264 q^{6} -3.46941 q^{7} +6.42244 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.55264 q^{2} -1.00000 q^{3} +4.51600 q^{4} -2.02616 q^{5} -2.55264 q^{6} -3.46941 q^{7} +6.42244 q^{8} +1.00000 q^{9} -5.17206 q^{10} +2.24180 q^{11} -4.51600 q^{12} +2.20934 q^{13} -8.85617 q^{14} +2.02616 q^{15} +7.36222 q^{16} -1.00000 q^{17} +2.55264 q^{18} +1.23709 q^{19} -9.15012 q^{20} +3.46941 q^{21} +5.72251 q^{22} -6.14774 q^{23} -6.42244 q^{24} -0.894688 q^{25} +5.63965 q^{26} -1.00000 q^{27} -15.6678 q^{28} +6.11937 q^{29} +5.17206 q^{30} +7.08825 q^{31} +5.94826 q^{32} -2.24180 q^{33} -2.55264 q^{34} +7.02957 q^{35} +4.51600 q^{36} -8.56157 q^{37} +3.15784 q^{38} -2.20934 q^{39} -13.0129 q^{40} -10.8548 q^{41} +8.85617 q^{42} +0.242642 q^{43} +10.1239 q^{44} -2.02616 q^{45} -15.6930 q^{46} +5.56049 q^{47} -7.36222 q^{48} +5.03681 q^{49} -2.28382 q^{50} +1.00000 q^{51} +9.97735 q^{52} -2.50875 q^{53} -2.55264 q^{54} -4.54223 q^{55} -22.2821 q^{56} -1.23709 q^{57} +15.6206 q^{58} +2.25565 q^{59} +9.15012 q^{60} -5.32578 q^{61} +18.0938 q^{62} -3.46941 q^{63} +0.459342 q^{64} -4.47646 q^{65} -5.72251 q^{66} -4.75839 q^{67} -4.51600 q^{68} +6.14774 q^{69} +17.9440 q^{70} -7.79895 q^{71} +6.42244 q^{72} +9.40328 q^{73} -21.8547 q^{74} +0.894688 q^{75} +5.58668 q^{76} -7.77771 q^{77} -5.63965 q^{78} -2.68310 q^{79} -14.9170 q^{80} +1.00000 q^{81} -27.7085 q^{82} -7.70340 q^{83} +15.6678 q^{84} +2.02616 q^{85} +0.619378 q^{86} -6.11937 q^{87} +14.3978 q^{88} +1.43390 q^{89} -5.17206 q^{90} -7.66509 q^{91} -27.7632 q^{92} -7.08825 q^{93} +14.1940 q^{94} -2.50653 q^{95} -5.94826 q^{96} -8.34075 q^{97} +12.8572 q^{98} +2.24180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.55264 1.80499 0.902496 0.430698i \(-0.141732\pi\)
0.902496 + 0.430698i \(0.141732\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.51600 2.25800
\(5\) −2.02616 −0.906125 −0.453062 0.891479i \(-0.649669\pi\)
−0.453062 + 0.891479i \(0.649669\pi\)
\(6\) −2.55264 −1.04211
\(7\) −3.46941 −1.31131 −0.655657 0.755059i \(-0.727608\pi\)
−0.655657 + 0.755059i \(0.727608\pi\)
\(8\) 6.42244 2.27068
\(9\) 1.00000 0.333333
\(10\) −5.17206 −1.63555
\(11\) 2.24180 0.675927 0.337964 0.941159i \(-0.390262\pi\)
0.337964 + 0.941159i \(0.390262\pi\)
\(12\) −4.51600 −1.30366
\(13\) 2.20934 0.612759 0.306380 0.951909i \(-0.400882\pi\)
0.306380 + 0.951909i \(0.400882\pi\)
\(14\) −8.85617 −2.36691
\(15\) 2.02616 0.523151
\(16\) 7.36222 1.84056
\(17\) −1.00000 −0.242536
\(18\) 2.55264 0.601664
\(19\) 1.23709 0.283807 0.141904 0.989880i \(-0.454678\pi\)
0.141904 + 0.989880i \(0.454678\pi\)
\(20\) −9.15012 −2.04603
\(21\) 3.46941 0.757087
\(22\) 5.72251 1.22004
\(23\) −6.14774 −1.28189 −0.640946 0.767586i \(-0.721458\pi\)
−0.640946 + 0.767586i \(0.721458\pi\)
\(24\) −6.42244 −1.31098
\(25\) −0.894688 −0.178938
\(26\) 5.63965 1.10603
\(27\) −1.00000 −0.192450
\(28\) −15.6678 −2.96094
\(29\) 6.11937 1.13634 0.568169 0.822912i \(-0.307652\pi\)
0.568169 + 0.822912i \(0.307652\pi\)
\(30\) 5.17206 0.944284
\(31\) 7.08825 1.27309 0.636544 0.771240i \(-0.280363\pi\)
0.636544 + 0.771240i \(0.280363\pi\)
\(32\) 5.94826 1.05151
\(33\) −2.24180 −0.390247
\(34\) −2.55264 −0.437775
\(35\) 7.02957 1.18821
\(36\) 4.51600 0.752666
\(37\) −8.56157 −1.40751 −0.703757 0.710441i \(-0.748496\pi\)
−0.703757 + 0.710441i \(0.748496\pi\)
\(38\) 3.15784 0.512270
\(39\) −2.20934 −0.353777
\(40\) −13.0129 −2.05752
\(41\) −10.8548 −1.69524 −0.847619 0.530605i \(-0.821965\pi\)
−0.847619 + 0.530605i \(0.821965\pi\)
\(42\) 8.85617 1.36654
\(43\) 0.242642 0.0370025 0.0185012 0.999829i \(-0.494111\pi\)
0.0185012 + 0.999829i \(0.494111\pi\)
\(44\) 10.1239 1.52624
\(45\) −2.02616 −0.302042
\(46\) −15.6930 −2.31381
\(47\) 5.56049 0.811081 0.405541 0.914077i \(-0.367083\pi\)
0.405541 + 0.914077i \(0.367083\pi\)
\(48\) −7.36222 −1.06265
\(49\) 5.03681 0.719544
\(50\) −2.28382 −0.322981
\(51\) 1.00000 0.140028
\(52\) 9.97735 1.38361
\(53\) −2.50875 −0.344603 −0.172301 0.985044i \(-0.555120\pi\)
−0.172301 + 0.985044i \(0.555120\pi\)
\(54\) −2.55264 −0.347371
\(55\) −4.54223 −0.612474
\(56\) −22.2821 −2.97757
\(57\) −1.23709 −0.163856
\(58\) 15.6206 2.05108
\(59\) 2.25565 0.293661 0.146830 0.989162i \(-0.453093\pi\)
0.146830 + 0.989162i \(0.453093\pi\)
\(60\) 9.15012 1.18127
\(61\) −5.32578 −0.681896 −0.340948 0.940082i \(-0.610748\pi\)
−0.340948 + 0.940082i \(0.610748\pi\)
\(62\) 18.0938 2.29791
\(63\) −3.46941 −0.437105
\(64\) 0.459342 0.0574178
\(65\) −4.47646 −0.555237
\(66\) −5.72251 −0.704392
\(67\) −4.75839 −0.581330 −0.290665 0.956825i \(-0.593876\pi\)
−0.290665 + 0.956825i \(0.593876\pi\)
\(68\) −4.51600 −0.547645
\(69\) 6.14774 0.740101
\(70\) 17.9440 2.14472
\(71\) −7.79895 −0.925565 −0.462782 0.886472i \(-0.653149\pi\)
−0.462782 + 0.886472i \(0.653149\pi\)
\(72\) 6.42244 0.756892
\(73\) 9.40328 1.10057 0.550285 0.834977i \(-0.314519\pi\)
0.550285 + 0.834977i \(0.314519\pi\)
\(74\) −21.8547 −2.54055
\(75\) 0.894688 0.103310
\(76\) 5.58668 0.640836
\(77\) −7.77771 −0.886352
\(78\) −5.63965 −0.638564
\(79\) −2.68310 −0.301872 −0.150936 0.988544i \(-0.548229\pi\)
−0.150936 + 0.988544i \(0.548229\pi\)
\(80\) −14.9170 −1.66777
\(81\) 1.00000 0.111111
\(82\) −27.7085 −3.05989
\(83\) −7.70340 −0.845558 −0.422779 0.906233i \(-0.638945\pi\)
−0.422779 + 0.906233i \(0.638945\pi\)
\(84\) 15.6678 1.70950
\(85\) 2.02616 0.219768
\(86\) 0.619378 0.0667892
\(87\) −6.11937 −0.656065
\(88\) 14.3978 1.53481
\(89\) 1.43390 0.151993 0.0759967 0.997108i \(-0.475786\pi\)
0.0759967 + 0.997108i \(0.475786\pi\)
\(90\) −5.17206 −0.545183
\(91\) −7.66509 −0.803520
\(92\) −27.7632 −2.89451
\(93\) −7.08825 −0.735018
\(94\) 14.1940 1.46400
\(95\) −2.50653 −0.257165
\(96\) −5.94826 −0.607092
\(97\) −8.34075 −0.846875 −0.423438 0.905925i \(-0.639177\pi\)
−0.423438 + 0.905925i \(0.639177\pi\)
\(98\) 12.8572 1.29877
\(99\) 2.24180 0.225309
\(100\) −4.04041 −0.404041
\(101\) 3.40536 0.338846 0.169423 0.985543i \(-0.445810\pi\)
0.169423 + 0.985543i \(0.445810\pi\)
\(102\) 2.55264 0.252749
\(103\) −11.6200 −1.14495 −0.572477 0.819921i \(-0.694018\pi\)
−0.572477 + 0.819921i \(0.694018\pi\)
\(104\) 14.1893 1.39138
\(105\) −7.02957 −0.686016
\(106\) −6.40394 −0.622006
\(107\) −12.3157 −1.19061 −0.595303 0.803501i \(-0.702968\pi\)
−0.595303 + 0.803501i \(0.702968\pi\)
\(108\) −4.51600 −0.434552
\(109\) −12.3401 −1.18197 −0.590986 0.806682i \(-0.701261\pi\)
−0.590986 + 0.806682i \(0.701261\pi\)
\(110\) −11.5947 −1.10551
\(111\) 8.56157 0.812628
\(112\) −25.5426 −2.41355
\(113\) −14.4391 −1.35832 −0.679158 0.733992i \(-0.737655\pi\)
−0.679158 + 0.733992i \(0.737655\pi\)
\(114\) −3.15784 −0.295759
\(115\) 12.4563 1.16155
\(116\) 27.6350 2.56585
\(117\) 2.20934 0.204253
\(118\) 5.75787 0.530055
\(119\) 3.46941 0.318040
\(120\) 13.0129 1.18791
\(121\) −5.97435 −0.543123
\(122\) −13.5948 −1.23082
\(123\) 10.8548 0.978746
\(124\) 32.0105 2.87463
\(125\) 11.9436 1.06826
\(126\) −8.85617 −0.788971
\(127\) −0.415656 −0.0368835 −0.0184417 0.999830i \(-0.505871\pi\)
−0.0184417 + 0.999830i \(0.505871\pi\)
\(128\) −10.7240 −0.947875
\(129\) −0.242642 −0.0213634
\(130\) −11.4268 −1.00220
\(131\) 8.39104 0.733129 0.366564 0.930393i \(-0.380534\pi\)
0.366564 + 0.930393i \(0.380534\pi\)
\(132\) −10.1239 −0.881176
\(133\) −4.29196 −0.372160
\(134\) −12.1465 −1.04930
\(135\) 2.02616 0.174384
\(136\) −6.42244 −0.550720
\(137\) 16.0274 1.36931 0.684655 0.728867i \(-0.259953\pi\)
0.684655 + 0.728867i \(0.259953\pi\)
\(138\) 15.6930 1.33588
\(139\) −21.4805 −1.82195 −0.910975 0.412462i \(-0.864669\pi\)
−0.910975 + 0.412462i \(0.864669\pi\)
\(140\) 31.7455 2.68298
\(141\) −5.56049 −0.468278
\(142\) −19.9079 −1.67064
\(143\) 4.95288 0.414181
\(144\) 7.36222 0.613519
\(145\) −12.3988 −1.02966
\(146\) 24.0032 1.98652
\(147\) −5.03681 −0.415429
\(148\) −38.6640 −3.17816
\(149\) 18.0206 1.47630 0.738151 0.674636i \(-0.235699\pi\)
0.738151 + 0.674636i \(0.235699\pi\)
\(150\) 2.28382 0.186473
\(151\) −5.61690 −0.457097 −0.228549 0.973533i \(-0.573398\pi\)
−0.228549 + 0.973533i \(0.573398\pi\)
\(152\) 7.94512 0.644434
\(153\) −1.00000 −0.0808452
\(154\) −19.8537 −1.59986
\(155\) −14.3619 −1.15358
\(156\) −9.97735 −0.798827
\(157\) −1.00000 −0.0798087
\(158\) −6.84899 −0.544876
\(159\) 2.50875 0.198957
\(160\) −12.0521 −0.952803
\(161\) 21.3290 1.68096
\(162\) 2.55264 0.200555
\(163\) −7.04223 −0.551590 −0.275795 0.961216i \(-0.588941\pi\)
−0.275795 + 0.961216i \(0.588941\pi\)
\(164\) −49.0203 −3.82785
\(165\) 4.54223 0.353612
\(166\) −19.6640 −1.52623
\(167\) 1.98324 0.153467 0.0767337 0.997052i \(-0.475551\pi\)
0.0767337 + 0.997052i \(0.475551\pi\)
\(168\) 22.2821 1.71910
\(169\) −8.11884 −0.624526
\(170\) 5.17206 0.396679
\(171\) 1.23709 0.0946024
\(172\) 1.09577 0.0835515
\(173\) −18.7223 −1.42343 −0.711714 0.702470i \(-0.752081\pi\)
−0.711714 + 0.702470i \(0.752081\pi\)
\(174\) −15.6206 −1.18419
\(175\) 3.10404 0.234643
\(176\) 16.5046 1.24408
\(177\) −2.25565 −0.169545
\(178\) 3.66024 0.274347
\(179\) −17.3665 −1.29804 −0.649018 0.760773i \(-0.724820\pi\)
−0.649018 + 0.760773i \(0.724820\pi\)
\(180\) −9.15012 −0.682009
\(181\) 16.7875 1.24781 0.623903 0.781502i \(-0.285546\pi\)
0.623903 + 0.781502i \(0.285546\pi\)
\(182\) −19.5663 −1.45035
\(183\) 5.32578 0.393693
\(184\) −39.4835 −2.91076
\(185\) 17.3471 1.27538
\(186\) −18.0938 −1.32670
\(187\) −2.24180 −0.163936
\(188\) 25.1112 1.83142
\(189\) 3.46941 0.252362
\(190\) −6.39828 −0.464180
\(191\) −11.1355 −0.805734 −0.402867 0.915259i \(-0.631986\pi\)
−0.402867 + 0.915259i \(0.631986\pi\)
\(192\) −0.459342 −0.0331502
\(193\) 13.7983 0.993221 0.496610 0.867974i \(-0.334578\pi\)
0.496610 + 0.867974i \(0.334578\pi\)
\(194\) −21.2910 −1.52860
\(195\) 4.47646 0.320566
\(196\) 22.7462 1.62473
\(197\) −3.21636 −0.229156 −0.114578 0.993414i \(-0.536552\pi\)
−0.114578 + 0.993414i \(0.536552\pi\)
\(198\) 5.72251 0.406681
\(199\) 9.70222 0.687772 0.343886 0.939011i \(-0.388257\pi\)
0.343886 + 0.939011i \(0.388257\pi\)
\(200\) −5.74608 −0.406309
\(201\) 4.75839 0.335631
\(202\) 8.69268 0.611614
\(203\) −21.2306 −1.49010
\(204\) 4.51600 0.316183
\(205\) 21.9936 1.53610
\(206\) −29.6618 −2.06663
\(207\) −6.14774 −0.427297
\(208\) 16.2656 1.12782
\(209\) 2.77330 0.191833
\(210\) −17.9440 −1.23825
\(211\) 24.6814 1.69914 0.849568 0.527479i \(-0.176863\pi\)
0.849568 + 0.527479i \(0.176863\pi\)
\(212\) −11.3295 −0.778112
\(213\) 7.79895 0.534375
\(214\) −31.4377 −2.14903
\(215\) −0.491630 −0.0335289
\(216\) −6.42244 −0.436992
\(217\) −24.5921 −1.66942
\(218\) −31.5000 −2.13345
\(219\) −9.40328 −0.635415
\(220\) −20.5127 −1.38297
\(221\) −2.20934 −0.148616
\(222\) 21.8547 1.46679
\(223\) −27.6445 −1.85121 −0.925605 0.378490i \(-0.876443\pi\)
−0.925605 + 0.378490i \(0.876443\pi\)
\(224\) −20.6369 −1.37886
\(225\) −0.894688 −0.0596459
\(226\) −36.8579 −2.45175
\(227\) −18.6791 −1.23977 −0.619887 0.784691i \(-0.712822\pi\)
−0.619887 + 0.784691i \(0.712822\pi\)
\(228\) −5.58668 −0.369987
\(229\) −4.98225 −0.329236 −0.164618 0.986357i \(-0.552639\pi\)
−0.164618 + 0.986357i \(0.552639\pi\)
\(230\) 31.7965 2.09660
\(231\) 7.77771 0.511736
\(232\) 39.3013 2.58026
\(233\) 15.7438 1.03141 0.515707 0.856765i \(-0.327529\pi\)
0.515707 + 0.856765i \(0.327529\pi\)
\(234\) 5.63965 0.368675
\(235\) −11.2664 −0.734941
\(236\) 10.1865 0.663085
\(237\) 2.68310 0.174286
\(238\) 8.85617 0.574060
\(239\) 10.6517 0.689004 0.344502 0.938786i \(-0.388048\pi\)
0.344502 + 0.938786i \(0.388048\pi\)
\(240\) 14.9170 0.962890
\(241\) 20.4804 1.31926 0.659629 0.751591i \(-0.270713\pi\)
0.659629 + 0.751591i \(0.270713\pi\)
\(242\) −15.2504 −0.980332
\(243\) −1.00000 −0.0641500
\(244\) −24.0512 −1.53972
\(245\) −10.2054 −0.651997
\(246\) 27.7085 1.76663
\(247\) 2.73314 0.173905
\(248\) 45.5239 2.89077
\(249\) 7.70340 0.488183
\(250\) 30.4877 1.92821
\(251\) 22.1050 1.39526 0.697628 0.716460i \(-0.254239\pi\)
0.697628 + 0.716460i \(0.254239\pi\)
\(252\) −15.6678 −0.986981
\(253\) −13.7820 −0.866465
\(254\) −1.06102 −0.0665744
\(255\) −2.02616 −0.126883
\(256\) −28.2932 −1.76832
\(257\) 2.02310 0.126198 0.0630988 0.998007i \(-0.479902\pi\)
0.0630988 + 0.998007i \(0.479902\pi\)
\(258\) −0.619378 −0.0385608
\(259\) 29.7036 1.84569
\(260\) −20.2157 −1.25372
\(261\) 6.11937 0.378779
\(262\) 21.4193 1.32329
\(263\) 2.18794 0.134914 0.0674572 0.997722i \(-0.478511\pi\)
0.0674572 + 0.997722i \(0.478511\pi\)
\(264\) −14.3978 −0.886124
\(265\) 5.08311 0.312253
\(266\) −10.9559 −0.671746
\(267\) −1.43390 −0.0877534
\(268\) −21.4889 −1.31264
\(269\) −10.5208 −0.641463 −0.320731 0.947170i \(-0.603929\pi\)
−0.320731 + 0.947170i \(0.603929\pi\)
\(270\) 5.17206 0.314761
\(271\) −21.3957 −1.29970 −0.649849 0.760063i \(-0.725168\pi\)
−0.649849 + 0.760063i \(0.725168\pi\)
\(272\) −7.36222 −0.446400
\(273\) 7.66509 0.463912
\(274\) 40.9122 2.47159
\(275\) −2.00571 −0.120949
\(276\) 27.7632 1.67115
\(277\) 10.2537 0.616087 0.308044 0.951372i \(-0.400326\pi\)
0.308044 + 0.951372i \(0.400326\pi\)
\(278\) −54.8320 −3.28860
\(279\) 7.08825 0.424363
\(280\) 45.1470 2.69805
\(281\) −16.8624 −1.00593 −0.502964 0.864308i \(-0.667757\pi\)
−0.502964 + 0.864308i \(0.667757\pi\)
\(282\) −14.1940 −0.845238
\(283\) −8.82997 −0.524887 −0.262444 0.964947i \(-0.584528\pi\)
−0.262444 + 0.964947i \(0.584528\pi\)
\(284\) −35.2200 −2.08992
\(285\) 2.50653 0.148474
\(286\) 12.6429 0.747593
\(287\) 37.6598 2.22299
\(288\) 5.94826 0.350504
\(289\) 1.00000 0.0588235
\(290\) −31.6497 −1.85854
\(291\) 8.34075 0.488944
\(292\) 42.4652 2.48509
\(293\) −32.7904 −1.91563 −0.957816 0.287381i \(-0.907215\pi\)
−0.957816 + 0.287381i \(0.907215\pi\)
\(294\) −12.8572 −0.749846
\(295\) −4.57030 −0.266093
\(296\) −54.9862 −3.19601
\(297\) −2.24180 −0.130082
\(298\) 46.0001 2.66471
\(299\) −13.5824 −0.785491
\(300\) 4.04041 0.233273
\(301\) −0.841823 −0.0485219
\(302\) −14.3380 −0.825057
\(303\) −3.40536 −0.195633
\(304\) 9.10771 0.522363
\(305\) 10.7909 0.617883
\(306\) −2.55264 −0.145925
\(307\) 23.3845 1.33462 0.667312 0.744778i \(-0.267445\pi\)
0.667312 + 0.744778i \(0.267445\pi\)
\(308\) −35.1241 −2.00138
\(309\) 11.6200 0.661040
\(310\) −36.6609 −2.08220
\(311\) −2.92766 −0.166012 −0.0830062 0.996549i \(-0.526452\pi\)
−0.0830062 + 0.996549i \(0.526452\pi\)
\(312\) −14.1893 −0.803313
\(313\) 3.54376 0.200305 0.100153 0.994972i \(-0.468067\pi\)
0.100153 + 0.994972i \(0.468067\pi\)
\(314\) −2.55264 −0.144054
\(315\) 7.02957 0.396071
\(316\) −12.1168 −0.681626
\(317\) −27.9163 −1.56794 −0.783968 0.620801i \(-0.786808\pi\)
−0.783968 + 0.620801i \(0.786808\pi\)
\(318\) 6.40394 0.359115
\(319\) 13.7184 0.768081
\(320\) −0.930699 −0.0520277
\(321\) 12.3157 0.687397
\(322\) 54.4454 3.03412
\(323\) −1.23709 −0.0688333
\(324\) 4.51600 0.250889
\(325\) −1.97667 −0.109646
\(326\) −17.9763 −0.995616
\(327\) 12.3401 0.682412
\(328\) −69.7145 −3.84934
\(329\) −19.2916 −1.06358
\(330\) 11.5947 0.638267
\(331\) −2.18898 −0.120317 −0.0601587 0.998189i \(-0.519161\pi\)
−0.0601587 + 0.998189i \(0.519161\pi\)
\(332\) −34.7885 −1.90927
\(333\) −8.56157 −0.469171
\(334\) 5.06249 0.277007
\(335\) 9.64124 0.526757
\(336\) 25.5426 1.39346
\(337\) −32.6741 −1.77987 −0.889936 0.456085i \(-0.849251\pi\)
−0.889936 + 0.456085i \(0.849251\pi\)
\(338\) −20.7245 −1.12726
\(339\) 14.4391 0.784224
\(340\) 9.15012 0.496235
\(341\) 15.8904 0.860514
\(342\) 3.15784 0.170757
\(343\) 6.81112 0.367766
\(344\) 1.55835 0.0840207
\(345\) −12.4563 −0.670624
\(346\) −47.7913 −2.56928
\(347\) 28.1445 1.51087 0.755437 0.655221i \(-0.227424\pi\)
0.755437 + 0.655221i \(0.227424\pi\)
\(348\) −27.6350 −1.48139
\(349\) 26.0053 1.39203 0.696017 0.718025i \(-0.254954\pi\)
0.696017 + 0.718025i \(0.254954\pi\)
\(350\) 7.92351 0.423530
\(351\) −2.20934 −0.117926
\(352\) 13.3348 0.710746
\(353\) −10.9923 −0.585061 −0.292530 0.956256i \(-0.594497\pi\)
−0.292530 + 0.956256i \(0.594497\pi\)
\(354\) −5.75787 −0.306027
\(355\) 15.8019 0.838677
\(356\) 6.47550 0.343201
\(357\) −3.46941 −0.183621
\(358\) −44.3306 −2.34294
\(359\) 22.3832 1.18134 0.590670 0.806913i \(-0.298863\pi\)
0.590670 + 0.806913i \(0.298863\pi\)
\(360\) −13.0129 −0.685839
\(361\) −17.4696 −0.919454
\(362\) 42.8525 2.25228
\(363\) 5.97435 0.313572
\(364\) −34.6155 −1.81435
\(365\) −19.0525 −0.997254
\(366\) 13.5948 0.710613
\(367\) 4.08640 0.213308 0.106654 0.994296i \(-0.465986\pi\)
0.106654 + 0.994296i \(0.465986\pi\)
\(368\) −45.2610 −2.35939
\(369\) −10.8548 −0.565080
\(370\) 44.2810 2.30206
\(371\) 8.70387 0.451882
\(372\) −32.0105 −1.65967
\(373\) −3.90386 −0.202134 −0.101067 0.994880i \(-0.532226\pi\)
−0.101067 + 0.994880i \(0.532226\pi\)
\(374\) −5.72251 −0.295904
\(375\) −11.9436 −0.616763
\(376\) 35.7119 1.84170
\(377\) 13.5197 0.696302
\(378\) 8.85617 0.455512
\(379\) −30.3176 −1.55731 −0.778656 0.627451i \(-0.784098\pi\)
−0.778656 + 0.627451i \(0.784098\pi\)
\(380\) −11.3195 −0.580677
\(381\) 0.415656 0.0212947
\(382\) −28.4249 −1.45434
\(383\) 31.0815 1.58819 0.794096 0.607792i \(-0.207945\pi\)
0.794096 + 0.607792i \(0.207945\pi\)
\(384\) 10.7240 0.547256
\(385\) 15.7589 0.803146
\(386\) 35.2221 1.79276
\(387\) 0.242642 0.0123342
\(388\) −37.6668 −1.91224
\(389\) −14.2062 −0.720285 −0.360142 0.932897i \(-0.617272\pi\)
−0.360142 + 0.932897i \(0.617272\pi\)
\(390\) 11.4268 0.578619
\(391\) 6.14774 0.310904
\(392\) 32.3486 1.63385
\(393\) −8.39104 −0.423272
\(394\) −8.21022 −0.413625
\(395\) 5.43637 0.273534
\(396\) 10.1239 0.508747
\(397\) 31.2065 1.56621 0.783104 0.621891i \(-0.213635\pi\)
0.783104 + 0.621891i \(0.213635\pi\)
\(398\) 24.7663 1.24142
\(399\) 4.29196 0.214867
\(400\) −6.58689 −0.329345
\(401\) 3.77384 0.188457 0.0942284 0.995551i \(-0.469962\pi\)
0.0942284 + 0.995551i \(0.469962\pi\)
\(402\) 12.1465 0.605811
\(403\) 15.6603 0.780096
\(404\) 15.3786 0.765114
\(405\) −2.02616 −0.100681
\(406\) −54.1942 −2.68961
\(407\) −19.1933 −0.951376
\(408\) 6.42244 0.317958
\(409\) 17.3296 0.856893 0.428447 0.903567i \(-0.359061\pi\)
0.428447 + 0.903567i \(0.359061\pi\)
\(410\) 56.1418 2.77265
\(411\) −16.0274 −0.790572
\(412\) −52.4760 −2.58530
\(413\) −7.82577 −0.385081
\(414\) −15.6930 −0.771268
\(415\) 15.6083 0.766181
\(416\) 13.1417 0.644325
\(417\) 21.4805 1.05190
\(418\) 7.07924 0.346257
\(419\) 10.0593 0.491427 0.245714 0.969342i \(-0.420978\pi\)
0.245714 + 0.969342i \(0.420978\pi\)
\(420\) −31.7455 −1.54902
\(421\) −11.2473 −0.548161 −0.274080 0.961707i \(-0.588373\pi\)
−0.274080 + 0.961707i \(0.588373\pi\)
\(422\) 63.0028 3.06693
\(423\) 5.56049 0.270360
\(424\) −16.1123 −0.782482
\(425\) 0.894688 0.0433987
\(426\) 19.9079 0.964543
\(427\) 18.4773 0.894180
\(428\) −55.6178 −2.68839
\(429\) −4.95288 −0.239127
\(430\) −1.25496 −0.0605194
\(431\) −3.75504 −0.180874 −0.0904370 0.995902i \(-0.528826\pi\)
−0.0904370 + 0.995902i \(0.528826\pi\)
\(432\) −7.36222 −0.354215
\(433\) 30.4843 1.46498 0.732491 0.680777i \(-0.238358\pi\)
0.732491 + 0.680777i \(0.238358\pi\)
\(434\) −62.7748 −3.01329
\(435\) 12.3988 0.594477
\(436\) −55.7280 −2.66889
\(437\) −7.60528 −0.363810
\(438\) −24.0032 −1.14692
\(439\) 23.0191 1.09864 0.549321 0.835611i \(-0.314886\pi\)
0.549321 + 0.835611i \(0.314886\pi\)
\(440\) −29.1722 −1.39073
\(441\) 5.03681 0.239848
\(442\) −5.63965 −0.268251
\(443\) 24.6124 1.16937 0.584685 0.811260i \(-0.301218\pi\)
0.584685 + 0.811260i \(0.301218\pi\)
\(444\) 38.6640 1.83491
\(445\) −2.90531 −0.137725
\(446\) −70.5665 −3.34142
\(447\) −18.0206 −0.852343
\(448\) −1.59365 −0.0752927
\(449\) 14.0696 0.663987 0.331993 0.943282i \(-0.392279\pi\)
0.331993 + 0.943282i \(0.392279\pi\)
\(450\) −2.28382 −0.107660
\(451\) −24.3343 −1.14586
\(452\) −65.2069 −3.06707
\(453\) 5.61690 0.263905
\(454\) −47.6811 −2.23778
\(455\) 15.5307 0.728089
\(456\) −7.94512 −0.372064
\(457\) −21.1847 −0.990977 −0.495489 0.868614i \(-0.665011\pi\)
−0.495489 + 0.868614i \(0.665011\pi\)
\(458\) −12.7179 −0.594269
\(459\) 1.00000 0.0466760
\(460\) 56.2525 2.62279
\(461\) −10.6532 −0.496167 −0.248084 0.968739i \(-0.579801\pi\)
−0.248084 + 0.968739i \(0.579801\pi\)
\(462\) 19.8537 0.923679
\(463\) 38.2845 1.77923 0.889616 0.456709i \(-0.150972\pi\)
0.889616 + 0.456709i \(0.150972\pi\)
\(464\) 45.0521 2.09149
\(465\) 14.3619 0.666018
\(466\) 40.1884 1.86169
\(467\) −28.5102 −1.31929 −0.659647 0.751575i \(-0.729294\pi\)
−0.659647 + 0.751575i \(0.729294\pi\)
\(468\) 9.97735 0.461203
\(469\) 16.5088 0.762306
\(470\) −28.7592 −1.32656
\(471\) 1.00000 0.0460776
\(472\) 14.4868 0.666808
\(473\) 0.543953 0.0250110
\(474\) 6.84899 0.314585
\(475\) −1.10681 −0.0507838
\(476\) 15.6678 0.718134
\(477\) −2.50875 −0.114868
\(478\) 27.1901 1.24365
\(479\) −9.40074 −0.429531 −0.214765 0.976666i \(-0.568899\pi\)
−0.214765 + 0.976666i \(0.568899\pi\)
\(480\) 12.0521 0.550101
\(481\) −18.9154 −0.862467
\(482\) 52.2792 2.38125
\(483\) −21.3290 −0.970504
\(484\) −26.9801 −1.22637
\(485\) 16.8997 0.767375
\(486\) −2.55264 −0.115790
\(487\) 25.7599 1.16729 0.583647 0.812008i \(-0.301625\pi\)
0.583647 + 0.812008i \(0.301625\pi\)
\(488\) −34.2045 −1.54837
\(489\) 7.04223 0.318461
\(490\) −26.0507 −1.17685
\(491\) −23.1486 −1.04468 −0.522341 0.852737i \(-0.674941\pi\)
−0.522341 + 0.852737i \(0.674941\pi\)
\(492\) 49.0203 2.21001
\(493\) −6.11937 −0.275602
\(494\) 6.97673 0.313898
\(495\) −4.54223 −0.204158
\(496\) 52.1853 2.34319
\(497\) 27.0578 1.21371
\(498\) 19.6640 0.881167
\(499\) 11.6616 0.522047 0.261023 0.965332i \(-0.415940\pi\)
0.261023 + 0.965332i \(0.415940\pi\)
\(500\) 53.9371 2.41214
\(501\) −1.98324 −0.0886044
\(502\) 56.4262 2.51843
\(503\) 27.1431 1.21025 0.605125 0.796131i \(-0.293123\pi\)
0.605125 + 0.796131i \(0.293123\pi\)
\(504\) −22.2821 −0.992523
\(505\) −6.89979 −0.307037
\(506\) −35.1805 −1.56396
\(507\) 8.11884 0.360570
\(508\) −1.87710 −0.0832829
\(509\) 41.4022 1.83512 0.917560 0.397596i \(-0.130156\pi\)
0.917560 + 0.397596i \(0.130156\pi\)
\(510\) −5.17206 −0.229023
\(511\) −32.6238 −1.44319
\(512\) −50.7745 −2.24394
\(513\) −1.23709 −0.0546187
\(514\) 5.16426 0.227786
\(515\) 23.5440 1.03747
\(516\) −1.09577 −0.0482385
\(517\) 12.4655 0.548232
\(518\) 75.8227 3.33146
\(519\) 18.7223 0.821816
\(520\) −28.7498 −1.26076
\(521\) 0.305682 0.0133922 0.00669608 0.999978i \(-0.497869\pi\)
0.00669608 + 0.999978i \(0.497869\pi\)
\(522\) 15.6206 0.683694
\(523\) 1.77085 0.0774337 0.0387168 0.999250i \(-0.487673\pi\)
0.0387168 + 0.999250i \(0.487673\pi\)
\(524\) 37.8939 1.65540
\(525\) −3.10404 −0.135471
\(526\) 5.58505 0.243520
\(527\) −7.08825 −0.308769
\(528\) −16.5046 −0.718271
\(529\) 14.7947 0.643247
\(530\) 12.9754 0.563615
\(531\) 2.25565 0.0978868
\(532\) −19.3825 −0.840337
\(533\) −23.9819 −1.03877
\(534\) −3.66024 −0.158394
\(535\) 24.9536 1.07884
\(536\) −30.5605 −1.32001
\(537\) 17.3665 0.749421
\(538\) −26.8558 −1.15784
\(539\) 11.2915 0.486359
\(540\) 9.15012 0.393758
\(541\) −22.0126 −0.946397 −0.473198 0.880956i \(-0.656901\pi\)
−0.473198 + 0.880956i \(0.656901\pi\)
\(542\) −54.6157 −2.34595
\(543\) −16.7875 −0.720421
\(544\) −5.94826 −0.255029
\(545\) 25.0031 1.07101
\(546\) 19.5663 0.837358
\(547\) −34.3621 −1.46922 −0.734609 0.678491i \(-0.762634\pi\)
−0.734609 + 0.678491i \(0.762634\pi\)
\(548\) 72.3795 3.09190
\(549\) −5.32578 −0.227299
\(550\) −5.11986 −0.218312
\(551\) 7.57018 0.322501
\(552\) 39.4835 1.68053
\(553\) 9.30876 0.395849
\(554\) 26.1741 1.11203
\(555\) −17.3471 −0.736343
\(556\) −97.0057 −4.11396
\(557\) −18.7764 −0.795581 −0.397790 0.917476i \(-0.630223\pi\)
−0.397790 + 0.917476i \(0.630223\pi\)
\(558\) 18.0938 0.765971
\(559\) 0.536077 0.0226736
\(560\) 51.7533 2.18697
\(561\) 2.24180 0.0946487
\(562\) −43.0438 −1.81569
\(563\) 16.4630 0.693834 0.346917 0.937896i \(-0.387229\pi\)
0.346917 + 0.937896i \(0.387229\pi\)
\(564\) −25.1112 −1.05737
\(565\) 29.2559 1.23080
\(566\) −22.5398 −0.947417
\(567\) −3.46941 −0.145702
\(568\) −50.0883 −2.10166
\(569\) −29.2442 −1.22598 −0.612990 0.790091i \(-0.710033\pi\)
−0.612990 + 0.790091i \(0.710033\pi\)
\(570\) 6.39828 0.267995
\(571\) 6.78996 0.284151 0.142075 0.989856i \(-0.454622\pi\)
0.142075 + 0.989856i \(0.454622\pi\)
\(572\) 22.3672 0.935219
\(573\) 11.1355 0.465190
\(574\) 96.1322 4.01248
\(575\) 5.50031 0.229379
\(576\) 0.459342 0.0191393
\(577\) −5.25392 −0.218723 −0.109362 0.994002i \(-0.534881\pi\)
−0.109362 + 0.994002i \(0.534881\pi\)
\(578\) 2.55264 0.106176
\(579\) −13.7983 −0.573436
\(580\) −55.9929 −2.32498
\(581\) 26.7262 1.10879
\(582\) 21.2910 0.882540
\(583\) −5.62410 −0.232926
\(584\) 60.3920 2.49904
\(585\) −4.47646 −0.185079
\(586\) −83.7021 −3.45770
\(587\) 29.1675 1.20387 0.601935 0.798545i \(-0.294396\pi\)
0.601935 + 0.798545i \(0.294396\pi\)
\(588\) −22.7462 −0.938038
\(589\) 8.76878 0.361311
\(590\) −11.6664 −0.480296
\(591\) 3.21636 0.132303
\(592\) −63.0322 −2.59061
\(593\) 3.43837 0.141197 0.0705985 0.997505i \(-0.477509\pi\)
0.0705985 + 0.997505i \(0.477509\pi\)
\(594\) −5.72251 −0.234797
\(595\) −7.02957 −0.288184
\(596\) 81.3808 3.33349
\(597\) −9.70222 −0.397085
\(598\) −34.6711 −1.41781
\(599\) 2.03705 0.0832314 0.0416157 0.999134i \(-0.486749\pi\)
0.0416157 + 0.999134i \(0.486749\pi\)
\(600\) 5.74608 0.234583
\(601\) −7.62119 −0.310875 −0.155437 0.987846i \(-0.549679\pi\)
−0.155437 + 0.987846i \(0.549679\pi\)
\(602\) −2.14888 −0.0875816
\(603\) −4.75839 −0.193777
\(604\) −25.3659 −1.03212
\(605\) 12.1050 0.492137
\(606\) −8.69268 −0.353116
\(607\) 2.48850 0.101005 0.0505025 0.998724i \(-0.483918\pi\)
0.0505025 + 0.998724i \(0.483918\pi\)
\(608\) 7.35851 0.298427
\(609\) 21.2306 0.860307
\(610\) 27.5452 1.11527
\(611\) 12.2850 0.496998
\(612\) −4.51600 −0.182548
\(613\) 29.7440 1.20135 0.600674 0.799494i \(-0.294899\pi\)
0.600674 + 0.799494i \(0.294899\pi\)
\(614\) 59.6923 2.40899
\(615\) −21.9936 −0.886867
\(616\) −49.9519 −2.01262
\(617\) −47.1182 −1.89691 −0.948453 0.316919i \(-0.897352\pi\)
−0.948453 + 0.316919i \(0.897352\pi\)
\(618\) 29.6618 1.19317
\(619\) 8.48363 0.340986 0.170493 0.985359i \(-0.445464\pi\)
0.170493 + 0.985359i \(0.445464\pi\)
\(620\) −64.8583 −2.60477
\(621\) 6.14774 0.246700
\(622\) −7.47327 −0.299651
\(623\) −4.97480 −0.199311
\(624\) −16.2656 −0.651146
\(625\) −19.7261 −0.789044
\(626\) 9.04597 0.361549
\(627\) −2.77330 −0.110755
\(628\) −4.51600 −0.180208
\(629\) 8.56157 0.341372
\(630\) 17.9440 0.714906
\(631\) −23.0457 −0.917434 −0.458717 0.888582i \(-0.651691\pi\)
−0.458717 + 0.888582i \(0.651691\pi\)
\(632\) −17.2320 −0.685453
\(633\) −24.6814 −0.980996
\(634\) −71.2604 −2.83011
\(635\) 0.842184 0.0334211
\(636\) 11.3295 0.449243
\(637\) 11.1280 0.440907
\(638\) 35.0181 1.38638
\(639\) −7.79895 −0.308522
\(640\) 21.7285 0.858893
\(641\) 31.8566 1.25826 0.629131 0.777300i \(-0.283411\pi\)
0.629131 + 0.777300i \(0.283411\pi\)
\(642\) 31.4377 1.24075
\(643\) −29.5534 −1.16547 −0.582736 0.812662i \(-0.698018\pi\)
−0.582736 + 0.812662i \(0.698018\pi\)
\(644\) 96.3218 3.79561
\(645\) 0.491630 0.0193579
\(646\) −3.15784 −0.124244
\(647\) 38.1367 1.49931 0.749653 0.661831i \(-0.230220\pi\)
0.749653 + 0.661831i \(0.230220\pi\)
\(648\) 6.42244 0.252297
\(649\) 5.05671 0.198493
\(650\) −5.04573 −0.197910
\(651\) 24.5921 0.963839
\(652\) −31.8027 −1.24549
\(653\) −30.5698 −1.19629 −0.598144 0.801388i \(-0.704095\pi\)
−0.598144 + 0.801388i \(0.704095\pi\)
\(654\) 31.5000 1.23175
\(655\) −17.0016 −0.664306
\(656\) −79.9156 −3.12018
\(657\) 9.40328 0.366857
\(658\) −49.2447 −1.91976
\(659\) 50.6158 1.97171 0.985855 0.167598i \(-0.0536010\pi\)
0.985855 + 0.167598i \(0.0536010\pi\)
\(660\) 20.5127 0.798456
\(661\) 10.7008 0.416211 0.208106 0.978106i \(-0.433270\pi\)
0.208106 + 0.978106i \(0.433270\pi\)
\(662\) −5.58769 −0.217172
\(663\) 2.20934 0.0858035
\(664\) −49.4746 −1.91999
\(665\) 8.69619 0.337224
\(666\) −21.8547 −0.846850
\(667\) −37.6203 −1.45666
\(668\) 8.95628 0.346529
\(669\) 27.6445 1.06880
\(670\) 24.6107 0.950793
\(671\) −11.9393 −0.460912
\(672\) 20.6369 0.796088
\(673\) 5.40360 0.208293 0.104147 0.994562i \(-0.466789\pi\)
0.104147 + 0.994562i \(0.466789\pi\)
\(674\) −83.4054 −3.21266
\(675\) 0.894688 0.0344366
\(676\) −36.6646 −1.41018
\(677\) −3.10063 −0.119167 −0.0595835 0.998223i \(-0.518977\pi\)
−0.0595835 + 0.998223i \(0.518977\pi\)
\(678\) 36.8579 1.41552
\(679\) 28.9375 1.11052
\(680\) 13.0129 0.499021
\(681\) 18.6791 0.715784
\(682\) 40.5626 1.55322
\(683\) 23.3315 0.892755 0.446378 0.894845i \(-0.352714\pi\)
0.446378 + 0.894845i \(0.352714\pi\)
\(684\) 5.58668 0.213612
\(685\) −32.4740 −1.24077
\(686\) 17.3864 0.663815
\(687\) 4.98225 0.190085
\(688\) 1.78638 0.0681052
\(689\) −5.54266 −0.211159
\(690\) −31.7965 −1.21047
\(691\) −9.35985 −0.356065 −0.178033 0.984025i \(-0.556973\pi\)
−0.178033 + 0.984025i \(0.556973\pi\)
\(692\) −84.5497 −3.21410
\(693\) −7.77771 −0.295451
\(694\) 71.8429 2.72712
\(695\) 43.5228 1.65091
\(696\) −39.3013 −1.48971
\(697\) 10.8548 0.411156
\(698\) 66.3824 2.51261
\(699\) −15.7438 −0.595487
\(700\) 14.0178 0.529824
\(701\) 31.5119 1.19019 0.595095 0.803655i \(-0.297114\pi\)
0.595095 + 0.803655i \(0.297114\pi\)
\(702\) −5.63965 −0.212855
\(703\) −10.5914 −0.399462
\(704\) 1.02975 0.0388102
\(705\) 11.2664 0.424318
\(706\) −28.0594 −1.05603
\(707\) −11.8146 −0.444333
\(708\) −10.1865 −0.382832
\(709\) −35.2079 −1.32226 −0.661131 0.750270i \(-0.729923\pi\)
−0.661131 + 0.750270i \(0.729923\pi\)
\(710\) 40.3366 1.51381
\(711\) −2.68310 −0.100624
\(712\) 9.20916 0.345128
\(713\) −43.5767 −1.63196
\(714\) −8.85617 −0.331434
\(715\) −10.0353 −0.375299
\(716\) −78.4272 −2.93096
\(717\) −10.6517 −0.397796
\(718\) 57.1364 2.13231
\(719\) 42.9730 1.60262 0.801311 0.598248i \(-0.204136\pi\)
0.801311 + 0.598248i \(0.204136\pi\)
\(720\) −14.9170 −0.555925
\(721\) 40.3146 1.50139
\(722\) −44.5937 −1.65961
\(723\) −20.4804 −0.761675
\(724\) 75.8123 2.81754
\(725\) −5.47492 −0.203334
\(726\) 15.2504 0.565995
\(727\) 23.5392 0.873022 0.436511 0.899699i \(-0.356214\pi\)
0.436511 + 0.899699i \(0.356214\pi\)
\(728\) −49.2286 −1.82453
\(729\) 1.00000 0.0370370
\(730\) −48.6343 −1.80004
\(731\) −0.242642 −0.00897442
\(732\) 24.0512 0.888957
\(733\) −21.0888 −0.778934 −0.389467 0.921040i \(-0.627341\pi\)
−0.389467 + 0.921040i \(0.627341\pi\)
\(734\) 10.4311 0.385020
\(735\) 10.2054 0.376430
\(736\) −36.5683 −1.34793
\(737\) −10.6673 −0.392936
\(738\) −27.7085 −1.01996
\(739\) −41.2274 −1.51657 −0.758287 0.651921i \(-0.773963\pi\)
−0.758287 + 0.651921i \(0.773963\pi\)
\(740\) 78.3394 2.87981
\(741\) −2.73314 −0.100404
\(742\) 22.2179 0.815644
\(743\) −4.37009 −0.160323 −0.0801616 0.996782i \(-0.525544\pi\)
−0.0801616 + 0.996782i \(0.525544\pi\)
\(744\) −45.5239 −1.66899
\(745\) −36.5125 −1.33771
\(746\) −9.96516 −0.364851
\(747\) −7.70340 −0.281853
\(748\) −10.1239 −0.370168
\(749\) 42.7283 1.56126
\(750\) −30.4877 −1.11325
\(751\) −6.63680 −0.242180 −0.121090 0.992642i \(-0.538639\pi\)
−0.121090 + 0.992642i \(0.538639\pi\)
\(752\) 40.9376 1.49284
\(753\) −22.1050 −0.805551
\(754\) 34.5111 1.25682
\(755\) 11.3807 0.414187
\(756\) 15.6678 0.569834
\(757\) −32.8572 −1.19422 −0.597108 0.802161i \(-0.703684\pi\)
−0.597108 + 0.802161i \(0.703684\pi\)
\(758\) −77.3902 −2.81094
\(759\) 13.7820 0.500254
\(760\) −16.0981 −0.583938
\(761\) −28.3486 −1.02764 −0.513818 0.857899i \(-0.671770\pi\)
−0.513818 + 0.857899i \(0.671770\pi\)
\(762\) 1.06102 0.0384368
\(763\) 42.8130 1.54994
\(764\) −50.2877 −1.81934
\(765\) 2.02616 0.0732559
\(766\) 79.3401 2.86667
\(767\) 4.98349 0.179943
\(768\) 28.2932 1.02094
\(769\) 21.7056 0.782724 0.391362 0.920237i \(-0.372004\pi\)
0.391362 + 0.920237i \(0.372004\pi\)
\(770\) 40.2268 1.44967
\(771\) −2.02310 −0.0728603
\(772\) 62.3129 2.24269
\(773\) −13.2436 −0.476339 −0.238169 0.971224i \(-0.576547\pi\)
−0.238169 + 0.971224i \(0.576547\pi\)
\(774\) 0.619378 0.0222631
\(775\) −6.34178 −0.227803
\(776\) −53.5680 −1.92298
\(777\) −29.7036 −1.06561
\(778\) −36.2635 −1.30011
\(779\) −13.4284 −0.481121
\(780\) 20.2157 0.723837
\(781\) −17.4837 −0.625614
\(782\) 15.6930 0.561180
\(783\) −6.11937 −0.218688
\(784\) 37.0821 1.32436
\(785\) 2.02616 0.0723166
\(786\) −21.4193 −0.764003
\(787\) −7.09225 −0.252811 −0.126406 0.991979i \(-0.540344\pi\)
−0.126406 + 0.991979i \(0.540344\pi\)
\(788\) −14.5251 −0.517434
\(789\) −2.18794 −0.0778929
\(790\) 13.8771 0.493726
\(791\) 50.0951 1.78118
\(792\) 14.3978 0.511604
\(793\) −11.7664 −0.417838
\(794\) 79.6590 2.82699
\(795\) −5.08311 −0.180279
\(796\) 43.8152 1.55299
\(797\) 21.4434 0.759564 0.379782 0.925076i \(-0.375999\pi\)
0.379782 + 0.925076i \(0.375999\pi\)
\(798\) 10.9559 0.387833
\(799\) −5.56049 −0.196716
\(800\) −5.32184 −0.188155
\(801\) 1.43390 0.0506645
\(802\) 9.63328 0.340163
\(803\) 21.0802 0.743905
\(804\) 21.4889 0.757854
\(805\) −43.2159 −1.52316
\(806\) 39.9753 1.40807
\(807\) 10.5208 0.370349
\(808\) 21.8707 0.769410
\(809\) 36.3473 1.27790 0.638951 0.769248i \(-0.279369\pi\)
0.638951 + 0.769248i \(0.279369\pi\)
\(810\) −5.17206 −0.181728
\(811\) 15.7654 0.553597 0.276799 0.960928i \(-0.410726\pi\)
0.276799 + 0.960928i \(0.410726\pi\)
\(812\) −95.8773 −3.36463
\(813\) 21.3957 0.750381
\(814\) −48.9937 −1.71723
\(815\) 14.2687 0.499809
\(816\) 7.36222 0.257729
\(817\) 0.300169 0.0105016
\(818\) 44.2363 1.54669
\(819\) −7.66509 −0.267840
\(820\) 99.3229 3.46851
\(821\) 14.9671 0.522357 0.261178 0.965291i \(-0.415889\pi\)
0.261178 + 0.965291i \(0.415889\pi\)
\(822\) −40.9122 −1.42698
\(823\) 13.1155 0.457177 0.228589 0.973523i \(-0.426589\pi\)
0.228589 + 0.973523i \(0.426589\pi\)
\(824\) −74.6289 −2.59982
\(825\) 2.00571 0.0698298
\(826\) −19.9764 −0.695068
\(827\) 10.5864 0.368126 0.184063 0.982914i \(-0.441075\pi\)
0.184063 + 0.982914i \(0.441075\pi\)
\(828\) −27.7632 −0.964836
\(829\) −31.9709 −1.11040 −0.555198 0.831718i \(-0.687357\pi\)
−0.555198 + 0.831718i \(0.687357\pi\)
\(830\) 39.8424 1.38295
\(831\) −10.2537 −0.355698
\(832\) 1.01484 0.0351833
\(833\) −5.03681 −0.174515
\(834\) 54.8320 1.89868
\(835\) −4.01835 −0.139061
\(836\) 12.5242 0.433158
\(837\) −7.08825 −0.245006
\(838\) 25.6777 0.887023
\(839\) 29.9980 1.03565 0.517823 0.855488i \(-0.326743\pi\)
0.517823 + 0.855488i \(0.326743\pi\)
\(840\) −45.1470 −1.55772
\(841\) 8.44664 0.291263
\(842\) −28.7104 −0.989426
\(843\) 16.8624 0.580772
\(844\) 111.461 3.83664
\(845\) 16.4500 0.565899
\(846\) 14.1940 0.487998
\(847\) 20.7275 0.712204
\(848\) −18.4700 −0.634261
\(849\) 8.82997 0.303044
\(850\) 2.28382 0.0783344
\(851\) 52.6343 1.80428
\(852\) 35.2200 1.20662
\(853\) −29.8090 −1.02064 −0.510321 0.859984i \(-0.670473\pi\)
−0.510321 + 0.859984i \(0.670473\pi\)
\(854\) 47.1660 1.61399
\(855\) −2.50653 −0.0857216
\(856\) −79.0970 −2.70348
\(857\) −16.6775 −0.569691 −0.284846 0.958573i \(-0.591942\pi\)
−0.284846 + 0.958573i \(0.591942\pi\)
\(858\) −12.6429 −0.431623
\(859\) 32.2577 1.10062 0.550309 0.834961i \(-0.314510\pi\)
0.550309 + 0.834961i \(0.314510\pi\)
\(860\) −2.22020 −0.0757081
\(861\) −37.6598 −1.28344
\(862\) −9.58529 −0.326476
\(863\) −55.9577 −1.90482 −0.952411 0.304818i \(-0.901404\pi\)
−0.952411 + 0.304818i \(0.901404\pi\)
\(864\) −5.94826 −0.202364
\(865\) 37.9343 1.28980
\(866\) 77.8156 2.64428
\(867\) −1.00000 −0.0339618
\(868\) −111.058 −3.76954
\(869\) −6.01495 −0.204043
\(870\) 31.6497 1.07303
\(871\) −10.5129 −0.356215
\(872\) −79.2539 −2.68387
\(873\) −8.34075 −0.282292
\(874\) −19.4136 −0.656674
\(875\) −41.4371 −1.40083
\(876\) −42.4652 −1.43476
\(877\) 49.0256 1.65548 0.827739 0.561114i \(-0.189627\pi\)
0.827739 + 0.561114i \(0.189627\pi\)
\(878\) 58.7596 1.98304
\(879\) 32.7904 1.10599
\(880\) −33.4409 −1.12729
\(881\) −4.52658 −0.152504 −0.0762522 0.997089i \(-0.524295\pi\)
−0.0762522 + 0.997089i \(0.524295\pi\)
\(882\) 12.8572 0.432924
\(883\) −43.4739 −1.46301 −0.731507 0.681834i \(-0.761183\pi\)
−0.731507 + 0.681834i \(0.761183\pi\)
\(884\) −9.97735 −0.335575
\(885\) 4.57030 0.153629
\(886\) 62.8267 2.11070
\(887\) 31.7212 1.06509 0.532546 0.846401i \(-0.321235\pi\)
0.532546 + 0.846401i \(0.321235\pi\)
\(888\) 54.9862 1.84522
\(889\) 1.44208 0.0483658
\(890\) −7.41623 −0.248593
\(891\) 2.24180 0.0751030
\(892\) −124.842 −4.18003
\(893\) 6.87881 0.230191
\(894\) −46.0001 −1.53847
\(895\) 35.1873 1.17618
\(896\) 37.2059 1.24296
\(897\) 13.5824 0.453504
\(898\) 35.9148 1.19849
\(899\) 43.3756 1.44666
\(900\) −4.04041 −0.134680
\(901\) 2.50875 0.0835785
\(902\) −62.1168 −2.06826
\(903\) 0.841823 0.0280141
\(904\) −92.7343 −3.08430
\(905\) −34.0141 −1.13067
\(906\) 14.3380 0.476347
\(907\) −20.5033 −0.680802 −0.340401 0.940280i \(-0.610563\pi\)
−0.340401 + 0.940280i \(0.610563\pi\)
\(908\) −84.3546 −2.79941
\(909\) 3.40536 0.112949
\(910\) 39.6443 1.31420
\(911\) 9.12407 0.302294 0.151147 0.988511i \(-0.451703\pi\)
0.151147 + 0.988511i \(0.451703\pi\)
\(912\) −9.10771 −0.301586
\(913\) −17.2694 −0.571535
\(914\) −54.0770 −1.78871
\(915\) −10.7909 −0.356735
\(916\) −22.4998 −0.743414
\(917\) −29.1120 −0.961362
\(918\) 2.55264 0.0842498
\(919\) 2.74670 0.0906054 0.0453027 0.998973i \(-0.485575\pi\)
0.0453027 + 0.998973i \(0.485575\pi\)
\(920\) 79.9998 2.63751
\(921\) −23.3845 −0.770546
\(922\) −27.1937 −0.895578
\(923\) −17.2305 −0.567149
\(924\) 35.1241 1.15550
\(925\) 7.65994 0.251857
\(926\) 97.7268 3.21150
\(927\) −11.6200 −0.381651
\(928\) 36.3996 1.19487
\(929\) 5.53981 0.181755 0.0908777 0.995862i \(-0.471033\pi\)
0.0908777 + 0.995862i \(0.471033\pi\)
\(930\) 36.6609 1.20216
\(931\) 6.23097 0.204212
\(932\) 71.0991 2.32893
\(933\) 2.92766 0.0958473
\(934\) −72.7764 −2.38132
\(935\) 4.54223 0.148547
\(936\) 14.1893 0.463793
\(937\) −14.2715 −0.466228 −0.233114 0.972449i \(-0.574892\pi\)
−0.233114 + 0.972449i \(0.574892\pi\)
\(938\) 42.1411 1.37596
\(939\) −3.54376 −0.115646
\(940\) −50.8791 −1.65949
\(941\) −21.3378 −0.695593 −0.347796 0.937570i \(-0.613070\pi\)
−0.347796 + 0.937570i \(0.613070\pi\)
\(942\) 2.55264 0.0831697
\(943\) 66.7326 2.17311
\(944\) 16.6066 0.540499
\(945\) −7.02957 −0.228672
\(946\) 1.38852 0.0451446
\(947\) 46.8591 1.52271 0.761357 0.648333i \(-0.224533\pi\)
0.761357 + 0.648333i \(0.224533\pi\)
\(948\) 12.1168 0.393537
\(949\) 20.7750 0.674385
\(950\) −2.82528 −0.0916643
\(951\) 27.9163 0.905249
\(952\) 22.2821 0.722167
\(953\) 4.02202 0.130286 0.0651430 0.997876i \(-0.479250\pi\)
0.0651430 + 0.997876i \(0.479250\pi\)
\(954\) −6.40394 −0.207335
\(955\) 22.5622 0.730095
\(956\) 48.1032 1.55577
\(957\) −13.7184 −0.443452
\(958\) −23.9968 −0.775300
\(959\) −55.6055 −1.79560
\(960\) 0.930699 0.0300382
\(961\) 19.2433 0.620753
\(962\) −48.2843 −1.55675
\(963\) −12.3157 −0.396869
\(964\) 92.4894 2.97888
\(965\) −27.9574 −0.899982
\(966\) −54.4454 −1.75175
\(967\) −7.94737 −0.255570 −0.127785 0.991802i \(-0.540787\pi\)
−0.127785 + 0.991802i \(0.540787\pi\)
\(968\) −38.3699 −1.23326
\(969\) 1.23709 0.0397409
\(970\) 43.1389 1.38511
\(971\) 50.0346 1.60569 0.802843 0.596190i \(-0.203320\pi\)
0.802843 + 0.596190i \(0.203320\pi\)
\(972\) −4.51600 −0.144851
\(973\) 74.5246 2.38915
\(974\) 65.7559 2.10696
\(975\) 1.97667 0.0633040
\(976\) −39.2096 −1.25507
\(977\) −13.4519 −0.430366 −0.215183 0.976574i \(-0.569035\pi\)
−0.215183 + 0.976574i \(0.569035\pi\)
\(978\) 17.9763 0.574819
\(979\) 3.21452 0.102736
\(980\) −46.0874 −1.47221
\(981\) −12.3401 −0.393991
\(982\) −59.0902 −1.88564
\(983\) 16.3993 0.523057 0.261529 0.965196i \(-0.415773\pi\)
0.261529 + 0.965196i \(0.415773\pi\)
\(984\) 69.7145 2.22242
\(985\) 6.51684 0.207644
\(986\) −15.6206 −0.497460
\(987\) 19.2916 0.614059
\(988\) 12.3428 0.392678
\(989\) −1.49170 −0.0474332
\(990\) −11.5947 −0.368504
\(991\) 40.6463 1.29117 0.645587 0.763687i \(-0.276613\pi\)
0.645587 + 0.763687i \(0.276613\pi\)
\(992\) 42.1628 1.33867
\(993\) 2.18898 0.0694653
\(994\) 69.0688 2.19073
\(995\) −19.6582 −0.623208
\(996\) 34.7885 1.10232
\(997\) −28.6143 −0.906223 −0.453111 0.891454i \(-0.649686\pi\)
−0.453111 + 0.891454i \(0.649686\pi\)
\(998\) 29.7680 0.942290
\(999\) 8.56157 0.270876
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.1.47 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.47 48 1.1 even 1 trivial