Properties

Label 8007.2.a.f.1.30
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 1.30
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.803950 q^{2} -1.00000 q^{3} -1.35366 q^{4} -0.904757 q^{5} -0.803950 q^{6} +1.61084 q^{7} -2.69618 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.803950 q^{2} -1.00000 q^{3} -1.35366 q^{4} -0.904757 q^{5} -0.803950 q^{6} +1.61084 q^{7} -2.69618 q^{8} +1.00000 q^{9} -0.727380 q^{10} -1.65375 q^{11} +1.35366 q^{12} -0.0916358 q^{13} +1.29503 q^{14} +0.904757 q^{15} +0.539733 q^{16} -1.00000 q^{17} +0.803950 q^{18} -5.68127 q^{19} +1.22474 q^{20} -1.61084 q^{21} -1.32954 q^{22} +5.14537 q^{23} +2.69618 q^{24} -4.18141 q^{25} -0.0736706 q^{26} -1.00000 q^{27} -2.18053 q^{28} +7.70133 q^{29} +0.727380 q^{30} +4.00116 q^{31} +5.82628 q^{32} +1.65375 q^{33} -0.803950 q^{34} -1.45742 q^{35} -1.35366 q^{36} +9.54524 q^{37} -4.56746 q^{38} +0.0916358 q^{39} +2.43939 q^{40} +0.791309 q^{41} -1.29503 q^{42} -1.21613 q^{43} +2.23863 q^{44} -0.904757 q^{45} +4.13662 q^{46} -0.249380 q^{47} -0.539733 q^{48} -4.40521 q^{49} -3.36165 q^{50} +1.00000 q^{51} +0.124044 q^{52} -2.79921 q^{53} -0.803950 q^{54} +1.49625 q^{55} -4.34310 q^{56} +5.68127 q^{57} +6.19149 q^{58} -3.55467 q^{59} -1.22474 q^{60} -1.36280 q^{61} +3.21674 q^{62} +1.61084 q^{63} +3.60457 q^{64} +0.0829082 q^{65} +1.32954 q^{66} +8.35596 q^{67} +1.35366 q^{68} -5.14537 q^{69} -1.17169 q^{70} -10.6303 q^{71} -2.69618 q^{72} +6.03964 q^{73} +7.67390 q^{74} +4.18141 q^{75} +7.69053 q^{76} -2.66393 q^{77} +0.0736706 q^{78} +4.64140 q^{79} -0.488328 q^{80} +1.00000 q^{81} +0.636173 q^{82} -13.3886 q^{83} +2.18053 q^{84} +0.904757 q^{85} -0.977709 q^{86} -7.70133 q^{87} +4.45882 q^{88} -10.9910 q^{89} -0.727380 q^{90} -0.147610 q^{91} -6.96510 q^{92} -4.00116 q^{93} -0.200489 q^{94} +5.14017 q^{95} -5.82628 q^{96} -0.693595 q^{97} -3.54157 q^{98} -1.65375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.803950 0.568479 0.284239 0.958753i \(-0.408259\pi\)
0.284239 + 0.958753i \(0.408259\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.35366 −0.676832
\(5\) −0.904757 −0.404620 −0.202310 0.979322i \(-0.564845\pi\)
−0.202310 + 0.979322i \(0.564845\pi\)
\(6\) −0.803950 −0.328211
\(7\) 1.61084 0.608839 0.304419 0.952538i \(-0.401538\pi\)
0.304419 + 0.952538i \(0.401538\pi\)
\(8\) −2.69618 −0.953243
\(9\) 1.00000 0.333333
\(10\) −0.727380 −0.230018
\(11\) −1.65375 −0.498625 −0.249313 0.968423i \(-0.580205\pi\)
−0.249313 + 0.968423i \(0.580205\pi\)
\(12\) 1.35366 0.390769
\(13\) −0.0916358 −0.0254152 −0.0127076 0.999919i \(-0.504045\pi\)
−0.0127076 + 0.999919i \(0.504045\pi\)
\(14\) 1.29503 0.346112
\(15\) 0.904757 0.233607
\(16\) 0.539733 0.134933
\(17\) −1.00000 −0.242536
\(18\) 0.803950 0.189493
\(19\) −5.68127 −1.30337 −0.651687 0.758488i \(-0.725938\pi\)
−0.651687 + 0.758488i \(0.725938\pi\)
\(20\) 1.22474 0.273860
\(21\) −1.61084 −0.351513
\(22\) −1.32954 −0.283458
\(23\) 5.14537 1.07288 0.536442 0.843937i \(-0.319768\pi\)
0.536442 + 0.843937i \(0.319768\pi\)
\(24\) 2.69618 0.550355
\(25\) −4.18141 −0.836283
\(26\) −0.0736706 −0.0144480
\(27\) −1.00000 −0.192450
\(28\) −2.18053 −0.412082
\(29\) 7.70133 1.43010 0.715051 0.699072i \(-0.246404\pi\)
0.715051 + 0.699072i \(0.246404\pi\)
\(30\) 0.727380 0.132801
\(31\) 4.00116 0.718630 0.359315 0.933216i \(-0.383010\pi\)
0.359315 + 0.933216i \(0.383010\pi\)
\(32\) 5.82628 1.02995
\(33\) 1.65375 0.287882
\(34\) −0.803950 −0.137876
\(35\) −1.45742 −0.246348
\(36\) −1.35366 −0.225611
\(37\) 9.54524 1.56923 0.784613 0.619985i \(-0.212861\pi\)
0.784613 + 0.619985i \(0.212861\pi\)
\(38\) −4.56746 −0.740940
\(39\) 0.0916358 0.0146735
\(40\) 2.43939 0.385701
\(41\) 0.791309 0.123582 0.0617908 0.998089i \(-0.480319\pi\)
0.0617908 + 0.998089i \(0.480319\pi\)
\(42\) −1.29503 −0.199828
\(43\) −1.21613 −0.185458 −0.0927291 0.995691i \(-0.529559\pi\)
−0.0927291 + 0.995691i \(0.529559\pi\)
\(44\) 2.23863 0.337486
\(45\) −0.904757 −0.134873
\(46\) 4.13662 0.609912
\(47\) −0.249380 −0.0363758 −0.0181879 0.999835i \(-0.505790\pi\)
−0.0181879 + 0.999835i \(0.505790\pi\)
\(48\) −0.539733 −0.0779038
\(49\) −4.40521 −0.629315
\(50\) −3.36165 −0.475409
\(51\) 1.00000 0.140028
\(52\) 0.124044 0.0172018
\(53\) −2.79921 −0.384502 −0.192251 0.981346i \(-0.561579\pi\)
−0.192251 + 0.981346i \(0.561579\pi\)
\(54\) −0.803950 −0.109404
\(55\) 1.49625 0.201754
\(56\) −4.34310 −0.580372
\(57\) 5.68127 0.752503
\(58\) 6.19149 0.812982
\(59\) −3.55467 −0.462779 −0.231389 0.972861i \(-0.574327\pi\)
−0.231389 + 0.972861i \(0.574327\pi\)
\(60\) −1.22474 −0.158113
\(61\) −1.36280 −0.174488 −0.0872442 0.996187i \(-0.527806\pi\)
−0.0872442 + 0.996187i \(0.527806\pi\)
\(62\) 3.21674 0.408526
\(63\) 1.61084 0.202946
\(64\) 3.60457 0.450571
\(65\) 0.0829082 0.0102835
\(66\) 1.32954 0.163655
\(67\) 8.35596 1.02084 0.510421 0.859924i \(-0.329489\pi\)
0.510421 + 0.859924i \(0.329489\pi\)
\(68\) 1.35366 0.164156
\(69\) −5.14537 −0.619430
\(70\) −1.17169 −0.140044
\(71\) −10.6303 −1.26158 −0.630791 0.775953i \(-0.717269\pi\)
−0.630791 + 0.775953i \(0.717269\pi\)
\(72\) −2.69618 −0.317748
\(73\) 6.03964 0.706886 0.353443 0.935456i \(-0.385011\pi\)
0.353443 + 0.935456i \(0.385011\pi\)
\(74\) 7.67390 0.892072
\(75\) 4.18141 0.482828
\(76\) 7.69053 0.882164
\(77\) −2.66393 −0.303583
\(78\) 0.0736706 0.00834156
\(79\) 4.64140 0.522198 0.261099 0.965312i \(-0.415915\pi\)
0.261099 + 0.965312i \(0.415915\pi\)
\(80\) −0.488328 −0.0545967
\(81\) 1.00000 0.111111
\(82\) 0.636173 0.0702536
\(83\) −13.3886 −1.46959 −0.734795 0.678289i \(-0.762722\pi\)
−0.734795 + 0.678289i \(0.762722\pi\)
\(84\) 2.18053 0.237915
\(85\) 0.904757 0.0981347
\(86\) −0.977709 −0.105429
\(87\) −7.70133 −0.825670
\(88\) 4.45882 0.475311
\(89\) −10.9910 −1.16504 −0.582521 0.812816i \(-0.697934\pi\)
−0.582521 + 0.812816i \(0.697934\pi\)
\(90\) −0.727380 −0.0766726
\(91\) −0.147610 −0.0154738
\(92\) −6.96510 −0.726162
\(93\) −4.00116 −0.414901
\(94\) −0.200489 −0.0206789
\(95\) 5.14017 0.527371
\(96\) −5.82628 −0.594642
\(97\) −0.693595 −0.0704239 −0.0352120 0.999380i \(-0.511211\pi\)
−0.0352120 + 0.999380i \(0.511211\pi\)
\(98\) −3.54157 −0.357752
\(99\) −1.65375 −0.166208
\(100\) 5.66023 0.566023
\(101\) 8.68888 0.864576 0.432288 0.901736i \(-0.357706\pi\)
0.432288 + 0.901736i \(0.357706\pi\)
\(102\) 0.803950 0.0796029
\(103\) 5.02979 0.495600 0.247800 0.968811i \(-0.420292\pi\)
0.247800 + 0.968811i \(0.420292\pi\)
\(104\) 0.247067 0.0242269
\(105\) 1.45742 0.142229
\(106\) −2.25043 −0.218581
\(107\) 8.73839 0.844772 0.422386 0.906416i \(-0.361193\pi\)
0.422386 + 0.906416i \(0.361193\pi\)
\(108\) 1.35366 0.130256
\(109\) −15.6798 −1.50185 −0.750926 0.660386i \(-0.770392\pi\)
−0.750926 + 0.660386i \(0.770392\pi\)
\(110\) 1.20291 0.114693
\(111\) −9.54524 −0.905994
\(112\) 0.869422 0.0821526
\(113\) 8.44997 0.794906 0.397453 0.917622i \(-0.369894\pi\)
0.397453 + 0.917622i \(0.369894\pi\)
\(114\) 4.56746 0.427782
\(115\) −4.65531 −0.434110
\(116\) −10.4250 −0.967938
\(117\) −0.0916358 −0.00847173
\(118\) −2.85778 −0.263080
\(119\) −1.61084 −0.147665
\(120\) −2.43939 −0.222685
\(121\) −8.26510 −0.751373
\(122\) −1.09562 −0.0991930
\(123\) −0.791309 −0.0713499
\(124\) −5.41623 −0.486392
\(125\) 8.30695 0.742996
\(126\) 1.29503 0.115371
\(127\) 11.0619 0.981583 0.490792 0.871277i \(-0.336708\pi\)
0.490792 + 0.871277i \(0.336708\pi\)
\(128\) −8.75466 −0.773810
\(129\) 1.21613 0.107074
\(130\) 0.0666540 0.00584595
\(131\) 16.0262 1.40021 0.700106 0.714039i \(-0.253136\pi\)
0.700106 + 0.714039i \(0.253136\pi\)
\(132\) −2.23863 −0.194847
\(133\) −9.15160 −0.793544
\(134\) 6.71777 0.580327
\(135\) 0.904757 0.0778691
\(136\) 2.69618 0.231195
\(137\) −5.73989 −0.490392 −0.245196 0.969474i \(-0.578852\pi\)
−0.245196 + 0.969474i \(0.578852\pi\)
\(138\) −4.13662 −0.352133
\(139\) 5.11048 0.433465 0.216732 0.976231i \(-0.430460\pi\)
0.216732 + 0.976231i \(0.430460\pi\)
\(140\) 1.97285 0.166736
\(141\) 0.249380 0.0210016
\(142\) −8.54621 −0.717182
\(143\) 0.151543 0.0126727
\(144\) 0.539733 0.0449778
\(145\) −6.96784 −0.578647
\(146\) 4.85557 0.401850
\(147\) 4.40521 0.363335
\(148\) −12.9210 −1.06210
\(149\) −14.4213 −1.18144 −0.590720 0.806876i \(-0.701156\pi\)
−0.590720 + 0.806876i \(0.701156\pi\)
\(150\) 3.36165 0.274478
\(151\) −9.67344 −0.787213 −0.393607 0.919279i \(-0.628773\pi\)
−0.393607 + 0.919279i \(0.628773\pi\)
\(152\) 15.3177 1.24243
\(153\) −1.00000 −0.0808452
\(154\) −2.14166 −0.172580
\(155\) −3.62008 −0.290772
\(156\) −0.124044 −0.00993147
\(157\) −1.00000 −0.0798087
\(158\) 3.73145 0.296858
\(159\) 2.79921 0.221992
\(160\) −5.27137 −0.416738
\(161\) 8.28835 0.653213
\(162\) 0.803950 0.0631643
\(163\) −11.9782 −0.938201 −0.469101 0.883145i \(-0.655422\pi\)
−0.469101 + 0.883145i \(0.655422\pi\)
\(164\) −1.07117 −0.0836440
\(165\) −1.49625 −0.116483
\(166\) −10.7638 −0.835430
\(167\) 18.4715 1.42937 0.714684 0.699447i \(-0.246571\pi\)
0.714684 + 0.699447i \(0.246571\pi\)
\(168\) 4.34310 0.335078
\(169\) −12.9916 −0.999354
\(170\) 0.727380 0.0557875
\(171\) −5.68127 −0.434458
\(172\) 1.64623 0.125524
\(173\) 23.5239 1.78849 0.894243 0.447581i \(-0.147714\pi\)
0.894243 + 0.447581i \(0.147714\pi\)
\(174\) −6.19149 −0.469376
\(175\) −6.73557 −0.509161
\(176\) −0.892586 −0.0672812
\(177\) 3.55467 0.267185
\(178\) −8.83620 −0.662302
\(179\) −26.1494 −1.95450 −0.977248 0.212101i \(-0.931969\pi\)
−0.977248 + 0.212101i \(0.931969\pi\)
\(180\) 1.22474 0.0912865
\(181\) −15.3791 −1.14312 −0.571558 0.820562i \(-0.693661\pi\)
−0.571558 + 0.820562i \(0.693661\pi\)
\(182\) −0.118671 −0.00879650
\(183\) 1.36280 0.100741
\(184\) −13.8728 −1.02272
\(185\) −8.63612 −0.634940
\(186\) −3.21674 −0.235863
\(187\) 1.65375 0.120934
\(188\) 0.337577 0.0246203
\(189\) −1.61084 −0.117171
\(190\) 4.13244 0.299799
\(191\) 6.93828 0.502036 0.251018 0.967982i \(-0.419235\pi\)
0.251018 + 0.967982i \(0.419235\pi\)
\(192\) −3.60457 −0.260138
\(193\) 0.330525 0.0237917 0.0118959 0.999929i \(-0.496213\pi\)
0.0118959 + 0.999929i \(0.496213\pi\)
\(194\) −0.557616 −0.0400345
\(195\) −0.0829082 −0.00593718
\(196\) 5.96317 0.425941
\(197\) −15.7318 −1.12084 −0.560421 0.828208i \(-0.689361\pi\)
−0.560421 + 0.828208i \(0.689361\pi\)
\(198\) −1.32954 −0.0944860
\(199\) −23.6125 −1.67385 −0.836923 0.547320i \(-0.815648\pi\)
−0.836923 + 0.547320i \(0.815648\pi\)
\(200\) 11.2738 0.797181
\(201\) −8.35596 −0.589384
\(202\) 6.98543 0.491493
\(203\) 12.4056 0.870701
\(204\) −1.35366 −0.0947754
\(205\) −0.715942 −0.0500036
\(206\) 4.04370 0.281738
\(207\) 5.14537 0.357628
\(208\) −0.0494589 −0.00342936
\(209\) 9.39542 0.649895
\(210\) 1.17169 0.0808543
\(211\) 27.8021 1.91397 0.956986 0.290134i \(-0.0936998\pi\)
0.956986 + 0.290134i \(0.0936998\pi\)
\(212\) 3.78919 0.260243
\(213\) 10.6303 0.728374
\(214\) 7.02523 0.480235
\(215\) 1.10030 0.0750401
\(216\) 2.69618 0.183452
\(217\) 6.44522 0.437530
\(218\) −12.6058 −0.853771
\(219\) −6.03964 −0.408121
\(220\) −2.02541 −0.136553
\(221\) 0.0916358 0.00616409
\(222\) −7.67390 −0.515038
\(223\) −8.02098 −0.537124 −0.268562 0.963262i \(-0.586548\pi\)
−0.268562 + 0.963262i \(0.586548\pi\)
\(224\) 9.38518 0.627074
\(225\) −4.18141 −0.278761
\(226\) 6.79336 0.451887
\(227\) 6.55387 0.434996 0.217498 0.976061i \(-0.430210\pi\)
0.217498 + 0.976061i \(0.430210\pi\)
\(228\) −7.69053 −0.509318
\(229\) 10.1111 0.668157 0.334079 0.942545i \(-0.391575\pi\)
0.334079 + 0.942545i \(0.391575\pi\)
\(230\) −3.74264 −0.246782
\(231\) 2.66393 0.175273
\(232\) −20.7642 −1.36323
\(233\) 5.50557 0.360682 0.180341 0.983604i \(-0.442280\pi\)
0.180341 + 0.983604i \(0.442280\pi\)
\(234\) −0.0736706 −0.00481600
\(235\) 0.225629 0.0147184
\(236\) 4.81183 0.313223
\(237\) −4.64140 −0.301491
\(238\) −1.29503 −0.0839445
\(239\) −23.7783 −1.53809 −0.769046 0.639193i \(-0.779269\pi\)
−0.769046 + 0.639193i \(0.779269\pi\)
\(240\) 0.488328 0.0315214
\(241\) −2.65562 −0.171063 −0.0855317 0.996335i \(-0.527259\pi\)
−0.0855317 + 0.996335i \(0.527259\pi\)
\(242\) −6.64473 −0.427139
\(243\) −1.00000 −0.0641500
\(244\) 1.84477 0.118099
\(245\) 3.98564 0.254633
\(246\) −0.636173 −0.0405609
\(247\) 0.520608 0.0331255
\(248\) −10.7879 −0.685030
\(249\) 13.3886 0.848468
\(250\) 6.67838 0.422378
\(251\) 24.7174 1.56015 0.780074 0.625687i \(-0.215181\pi\)
0.780074 + 0.625687i \(0.215181\pi\)
\(252\) −2.18053 −0.137361
\(253\) −8.50917 −0.534967
\(254\) 8.89321 0.558009
\(255\) −0.904757 −0.0566581
\(256\) −14.2475 −0.890466
\(257\) −13.6334 −0.850427 −0.425214 0.905093i \(-0.639801\pi\)
−0.425214 + 0.905093i \(0.639801\pi\)
\(258\) 0.977709 0.0608695
\(259\) 15.3758 0.955406
\(260\) −0.112230 −0.00696019
\(261\) 7.70133 0.476701
\(262\) 12.8842 0.795990
\(263\) −8.51665 −0.525159 −0.262580 0.964910i \(-0.584573\pi\)
−0.262580 + 0.964910i \(0.584573\pi\)
\(264\) −4.45882 −0.274421
\(265\) 2.53261 0.155577
\(266\) −7.35743 −0.451113
\(267\) 10.9910 0.672637
\(268\) −11.3112 −0.690939
\(269\) −12.3629 −0.753782 −0.376891 0.926258i \(-0.623007\pi\)
−0.376891 + 0.926258i \(0.623007\pi\)
\(270\) 0.727380 0.0442669
\(271\) 2.18769 0.132892 0.0664462 0.997790i \(-0.478834\pi\)
0.0664462 + 0.997790i \(0.478834\pi\)
\(272\) −0.539733 −0.0327261
\(273\) 0.147610 0.00893378
\(274\) −4.61459 −0.278777
\(275\) 6.91503 0.416992
\(276\) 6.96510 0.419250
\(277\) −29.8676 −1.79457 −0.897285 0.441453i \(-0.854463\pi\)
−0.897285 + 0.441453i \(0.854463\pi\)
\(278\) 4.10857 0.246416
\(279\) 4.00116 0.239543
\(280\) 3.92945 0.234830
\(281\) −15.2973 −0.912563 −0.456281 0.889836i \(-0.650819\pi\)
−0.456281 + 0.889836i \(0.650819\pi\)
\(282\) 0.200489 0.0119390
\(283\) −8.20474 −0.487721 −0.243861 0.969810i \(-0.578414\pi\)
−0.243861 + 0.969810i \(0.578414\pi\)
\(284\) 14.3898 0.853878
\(285\) −5.14017 −0.304478
\(286\) 0.121833 0.00720414
\(287\) 1.27467 0.0752413
\(288\) 5.82628 0.343317
\(289\) 1.00000 0.0588235
\(290\) −5.60180 −0.328949
\(291\) 0.693595 0.0406593
\(292\) −8.17564 −0.478443
\(293\) 20.2152 1.18098 0.590491 0.807044i \(-0.298934\pi\)
0.590491 + 0.807044i \(0.298934\pi\)
\(294\) 3.54157 0.206548
\(295\) 3.21612 0.187249
\(296\) −25.7357 −1.49586
\(297\) 1.65375 0.0959605
\(298\) −11.5940 −0.671624
\(299\) −0.471500 −0.0272675
\(300\) −5.66023 −0.326793
\(301\) −1.95899 −0.112914
\(302\) −7.77696 −0.447514
\(303\) −8.68888 −0.499163
\(304\) −3.06637 −0.175868
\(305\) 1.23300 0.0706015
\(306\) −0.803950 −0.0459588
\(307\) −18.2955 −1.04418 −0.522090 0.852890i \(-0.674847\pi\)
−0.522090 + 0.852890i \(0.674847\pi\)
\(308\) 3.60606 0.205474
\(309\) −5.02979 −0.286135
\(310\) −2.91037 −0.165298
\(311\) −12.0568 −0.683678 −0.341839 0.939759i \(-0.611050\pi\)
−0.341839 + 0.939759i \(0.611050\pi\)
\(312\) −0.247067 −0.0139874
\(313\) −3.26567 −0.184586 −0.0922932 0.995732i \(-0.529420\pi\)
−0.0922932 + 0.995732i \(0.529420\pi\)
\(314\) −0.803950 −0.0453695
\(315\) −1.45742 −0.0821161
\(316\) −6.28289 −0.353440
\(317\) −7.25078 −0.407244 −0.203622 0.979050i \(-0.565271\pi\)
−0.203622 + 0.979050i \(0.565271\pi\)
\(318\) 2.25043 0.126198
\(319\) −12.7361 −0.713085
\(320\) −3.26126 −0.182310
\(321\) −8.73839 −0.487729
\(322\) 6.66342 0.371338
\(323\) 5.68127 0.316114
\(324\) −1.35366 −0.0752035
\(325\) 0.383167 0.0212543
\(326\) −9.62984 −0.533347
\(327\) 15.6798 0.867095
\(328\) −2.13351 −0.117803
\(329\) −0.401711 −0.0221470
\(330\) −1.20291 −0.0662179
\(331\) −2.46217 −0.135333 −0.0676666 0.997708i \(-0.521555\pi\)
−0.0676666 + 0.997708i \(0.521555\pi\)
\(332\) 18.1237 0.994665
\(333\) 9.54524 0.523076
\(334\) 14.8502 0.812565
\(335\) −7.56011 −0.413053
\(336\) −0.869422 −0.0474308
\(337\) −22.8291 −1.24358 −0.621791 0.783183i \(-0.713595\pi\)
−0.621791 + 0.783183i \(0.713595\pi\)
\(338\) −10.4446 −0.568112
\(339\) −8.44997 −0.458939
\(340\) −1.22474 −0.0664207
\(341\) −6.61694 −0.358327
\(342\) −4.56746 −0.246980
\(343\) −18.3719 −0.991990
\(344\) 3.27891 0.176787
\(345\) 4.65531 0.250633
\(346\) 18.9120 1.01672
\(347\) −22.1051 −1.18667 −0.593333 0.804957i \(-0.702188\pi\)
−0.593333 + 0.804957i \(0.702188\pi\)
\(348\) 10.4250 0.558840
\(349\) 1.63160 0.0873374 0.0436687 0.999046i \(-0.486095\pi\)
0.0436687 + 0.999046i \(0.486095\pi\)
\(350\) −5.41507 −0.289447
\(351\) 0.0916358 0.00489116
\(352\) −9.63523 −0.513559
\(353\) −5.25543 −0.279718 −0.139859 0.990171i \(-0.544665\pi\)
−0.139859 + 0.990171i \(0.544665\pi\)
\(354\) 2.85778 0.151889
\(355\) 9.61782 0.510461
\(356\) 14.8781 0.788537
\(357\) 1.61084 0.0852545
\(358\) −21.0228 −1.11109
\(359\) −36.6056 −1.93197 −0.965985 0.258598i \(-0.916739\pi\)
−0.965985 + 0.258598i \(0.916739\pi\)
\(360\) 2.43939 0.128567
\(361\) 13.2768 0.698781
\(362\) −12.3640 −0.649837
\(363\) 8.26510 0.433805
\(364\) 0.199815 0.0104731
\(365\) −5.46440 −0.286020
\(366\) 1.09562 0.0572691
\(367\) −28.3117 −1.47786 −0.738929 0.673783i \(-0.764668\pi\)
−0.738929 + 0.673783i \(0.764668\pi\)
\(368\) 2.77713 0.144768
\(369\) 0.791309 0.0411939
\(370\) −6.94301 −0.360950
\(371\) −4.50907 −0.234099
\(372\) 5.41623 0.280819
\(373\) −14.8154 −0.767111 −0.383555 0.923518i \(-0.625301\pi\)
−0.383555 + 0.923518i \(0.625301\pi\)
\(374\) 1.32954 0.0687487
\(375\) −8.30695 −0.428969
\(376\) 0.672374 0.0346750
\(377\) −0.705718 −0.0363463
\(378\) −1.29503 −0.0666093
\(379\) −10.5079 −0.539755 −0.269878 0.962895i \(-0.586983\pi\)
−0.269878 + 0.962895i \(0.586983\pi\)
\(380\) −6.95806 −0.356941
\(381\) −11.0619 −0.566717
\(382\) 5.57803 0.285397
\(383\) −5.65256 −0.288832 −0.144416 0.989517i \(-0.546130\pi\)
−0.144416 + 0.989517i \(0.546130\pi\)
\(384\) 8.75466 0.446759
\(385\) 2.41021 0.122835
\(386\) 0.265726 0.0135251
\(387\) −1.21613 −0.0618194
\(388\) 0.938895 0.0476652
\(389\) −15.4207 −0.781859 −0.390930 0.920421i \(-0.627846\pi\)
−0.390930 + 0.920421i \(0.627846\pi\)
\(390\) −0.0666540 −0.00337516
\(391\) −5.14537 −0.260212
\(392\) 11.8772 0.599891
\(393\) −16.0262 −0.808412
\(394\) −12.6476 −0.637175
\(395\) −4.19934 −0.211292
\(396\) 2.23863 0.112495
\(397\) 11.7381 0.589116 0.294558 0.955634i \(-0.404828\pi\)
0.294558 + 0.955634i \(0.404828\pi\)
\(398\) −18.9833 −0.951546
\(399\) 9.15160 0.458153
\(400\) −2.25685 −0.112842
\(401\) −9.53240 −0.476025 −0.238013 0.971262i \(-0.576496\pi\)
−0.238013 + 0.971262i \(0.576496\pi\)
\(402\) −6.71777 −0.335052
\(403\) −0.366650 −0.0182641
\(404\) −11.7618 −0.585173
\(405\) −0.904757 −0.0449578
\(406\) 9.97347 0.494975
\(407\) −15.7855 −0.782457
\(408\) −2.69618 −0.133481
\(409\) −24.1096 −1.19214 −0.596072 0.802931i \(-0.703273\pi\)
−0.596072 + 0.802931i \(0.703273\pi\)
\(410\) −0.575582 −0.0284260
\(411\) 5.73989 0.283128
\(412\) −6.80865 −0.335438
\(413\) −5.72599 −0.281758
\(414\) 4.13662 0.203304
\(415\) 12.1134 0.594625
\(416\) −0.533896 −0.0261764
\(417\) −5.11048 −0.250261
\(418\) 7.55345 0.369452
\(419\) 22.7111 1.10951 0.554755 0.832014i \(-0.312812\pi\)
0.554755 + 0.832014i \(0.312812\pi\)
\(420\) −1.97285 −0.0962653
\(421\) 4.02437 0.196136 0.0980678 0.995180i \(-0.468734\pi\)
0.0980678 + 0.995180i \(0.468734\pi\)
\(422\) 22.3515 1.08805
\(423\) −0.249380 −0.0121253
\(424\) 7.54718 0.366524
\(425\) 4.18141 0.202828
\(426\) 8.54621 0.414065
\(427\) −2.19524 −0.106235
\(428\) −11.8288 −0.571768
\(429\) −0.151543 −0.00731657
\(430\) 0.884590 0.0426587
\(431\) −32.7346 −1.57677 −0.788385 0.615182i \(-0.789082\pi\)
−0.788385 + 0.615182i \(0.789082\pi\)
\(432\) −0.539733 −0.0259679
\(433\) −9.99326 −0.480245 −0.240123 0.970743i \(-0.577188\pi\)
−0.240123 + 0.970743i \(0.577188\pi\)
\(434\) 5.18164 0.248727
\(435\) 6.96784 0.334082
\(436\) 21.2252 1.01650
\(437\) −29.2322 −1.39837
\(438\) −4.85557 −0.232008
\(439\) −17.1750 −0.819716 −0.409858 0.912149i \(-0.634422\pi\)
−0.409858 + 0.912149i \(0.634422\pi\)
\(440\) −4.03415 −0.192320
\(441\) −4.40521 −0.209772
\(442\) 0.0736706 0.00350415
\(443\) 7.84031 0.372505 0.186252 0.982502i \(-0.440366\pi\)
0.186252 + 0.982502i \(0.440366\pi\)
\(444\) 12.9210 0.613205
\(445\) 9.94417 0.471399
\(446\) −6.44847 −0.305344
\(447\) 14.4213 0.682105
\(448\) 5.80637 0.274325
\(449\) −3.45648 −0.163121 −0.0815607 0.996668i \(-0.525990\pi\)
−0.0815607 + 0.996668i \(0.525990\pi\)
\(450\) −3.36165 −0.158470
\(451\) −1.30863 −0.0616210
\(452\) −11.4384 −0.538018
\(453\) 9.67344 0.454498
\(454\) 5.26899 0.247286
\(455\) 0.133551 0.00626099
\(456\) −15.3177 −0.717318
\(457\) −9.24640 −0.432528 −0.216264 0.976335i \(-0.569387\pi\)
−0.216264 + 0.976335i \(0.569387\pi\)
\(458\) 8.12879 0.379833
\(459\) 1.00000 0.0466760
\(460\) 6.30172 0.293819
\(461\) 36.9374 1.72035 0.860174 0.510001i \(-0.170355\pi\)
0.860174 + 0.510001i \(0.170355\pi\)
\(462\) 2.14166 0.0996392
\(463\) −10.2255 −0.475219 −0.237609 0.971361i \(-0.576364\pi\)
−0.237609 + 0.971361i \(0.576364\pi\)
\(464\) 4.15667 0.192968
\(465\) 3.62008 0.167877
\(466\) 4.42621 0.205040
\(467\) −7.02356 −0.325012 −0.162506 0.986708i \(-0.551958\pi\)
−0.162506 + 0.986708i \(0.551958\pi\)
\(468\) 0.124044 0.00573394
\(469\) 13.4601 0.621529
\(470\) 0.181394 0.00836709
\(471\) 1.00000 0.0460776
\(472\) 9.58403 0.441141
\(473\) 2.01118 0.0924742
\(474\) −3.73145 −0.171391
\(475\) 23.7557 1.08999
\(476\) 2.18053 0.0999444
\(477\) −2.79921 −0.128167
\(478\) −19.1166 −0.874373
\(479\) 17.0977 0.781215 0.390608 0.920557i \(-0.372265\pi\)
0.390608 + 0.920557i \(0.372265\pi\)
\(480\) 5.27137 0.240604
\(481\) −0.874685 −0.0398822
\(482\) −2.13498 −0.0972459
\(483\) −8.28835 −0.377133
\(484\) 11.1882 0.508553
\(485\) 0.627536 0.0284949
\(486\) −0.803950 −0.0364679
\(487\) 33.9184 1.53699 0.768494 0.639857i \(-0.221006\pi\)
0.768494 + 0.639857i \(0.221006\pi\)
\(488\) 3.67435 0.166330
\(489\) 11.9782 0.541671
\(490\) 3.20426 0.144754
\(491\) −2.45805 −0.110930 −0.0554651 0.998461i \(-0.517664\pi\)
−0.0554651 + 0.998461i \(0.517664\pi\)
\(492\) 1.07117 0.0482919
\(493\) −7.70133 −0.346851
\(494\) 0.418543 0.0188311
\(495\) 1.49625 0.0672512
\(496\) 2.15956 0.0969672
\(497\) −17.1236 −0.768100
\(498\) 10.7638 0.482336
\(499\) −6.31577 −0.282733 −0.141366 0.989957i \(-0.545150\pi\)
−0.141366 + 0.989957i \(0.545150\pi\)
\(500\) −11.2448 −0.502884
\(501\) −18.4715 −0.825246
\(502\) 19.8716 0.886911
\(503\) −1.23700 −0.0551552 −0.0275776 0.999620i \(-0.508779\pi\)
−0.0275776 + 0.999620i \(0.508779\pi\)
\(504\) −4.34310 −0.193457
\(505\) −7.86133 −0.349825
\(506\) −6.84095 −0.304117
\(507\) 12.9916 0.576977
\(508\) −14.9741 −0.664367
\(509\) −30.6654 −1.35922 −0.679609 0.733574i \(-0.737851\pi\)
−0.679609 + 0.733574i \(0.737851\pi\)
\(510\) −0.727380 −0.0322089
\(511\) 9.72886 0.430380
\(512\) 6.05507 0.267599
\(513\) 5.68127 0.250834
\(514\) −10.9606 −0.483450
\(515\) −4.55074 −0.200530
\(516\) −1.64623 −0.0724714
\(517\) 0.412413 0.0181379
\(518\) 12.3614 0.543128
\(519\) −23.5239 −1.03258
\(520\) −0.223535 −0.00980267
\(521\) 19.8837 0.871119 0.435560 0.900160i \(-0.356550\pi\)
0.435560 + 0.900160i \(0.356550\pi\)
\(522\) 6.19149 0.270994
\(523\) −35.7865 −1.56483 −0.782416 0.622756i \(-0.786013\pi\)
−0.782416 + 0.622756i \(0.786013\pi\)
\(524\) −21.6940 −0.947708
\(525\) 6.73557 0.293964
\(526\) −6.84696 −0.298542
\(527\) −4.00116 −0.174293
\(528\) 0.892586 0.0388448
\(529\) 3.47482 0.151079
\(530\) 2.03609 0.0884422
\(531\) −3.55467 −0.154260
\(532\) 12.3882 0.537096
\(533\) −0.0725122 −0.00314085
\(534\) 8.83620 0.382380
\(535\) −7.90612 −0.341811
\(536\) −22.5292 −0.973111
\(537\) 26.1494 1.12843
\(538\) −9.93919 −0.428509
\(539\) 7.28513 0.313793
\(540\) −1.22474 −0.0527043
\(541\) −10.0756 −0.433183 −0.216592 0.976262i \(-0.569494\pi\)
−0.216592 + 0.976262i \(0.569494\pi\)
\(542\) 1.75879 0.0755466
\(543\) 15.3791 0.659978
\(544\) −5.82628 −0.249800
\(545\) 14.1864 0.607679
\(546\) 0.118671 0.00507866
\(547\) −9.16606 −0.391912 −0.195956 0.980613i \(-0.562781\pi\)
−0.195956 + 0.980613i \(0.562781\pi\)
\(548\) 7.76988 0.331913
\(549\) −1.36280 −0.0581628
\(550\) 5.55934 0.237051
\(551\) −43.7534 −1.86396
\(552\) 13.8728 0.590467
\(553\) 7.47653 0.317934
\(554\) −24.0121 −1.02017
\(555\) 8.63612 0.366583
\(556\) −6.91787 −0.293383
\(557\) 8.31472 0.352306 0.176153 0.984363i \(-0.443635\pi\)
0.176153 + 0.984363i \(0.443635\pi\)
\(558\) 3.21674 0.136175
\(559\) 0.111441 0.00471346
\(560\) −0.786616 −0.0332406
\(561\) −1.65375 −0.0698215
\(562\) −12.2983 −0.518773
\(563\) −5.47764 −0.230855 −0.115427 0.993316i \(-0.536824\pi\)
−0.115427 + 0.993316i \(0.536824\pi\)
\(564\) −0.337577 −0.0142146
\(565\) −7.64517 −0.321635
\(566\) −6.59621 −0.277259
\(567\) 1.61084 0.0676488
\(568\) 28.6611 1.20259
\(569\) 9.02752 0.378453 0.189227 0.981933i \(-0.439402\pi\)
0.189227 + 0.981933i \(0.439402\pi\)
\(570\) −4.13244 −0.173089
\(571\) −15.3469 −0.642247 −0.321124 0.947037i \(-0.604061\pi\)
−0.321124 + 0.947037i \(0.604061\pi\)
\(572\) −0.205138 −0.00857726
\(573\) −6.93828 −0.289851
\(574\) 1.02477 0.0427731
\(575\) −21.5149 −0.897234
\(576\) 3.60457 0.150190
\(577\) 20.2804 0.844285 0.422142 0.906529i \(-0.361278\pi\)
0.422142 + 0.906529i \(0.361278\pi\)
\(578\) 0.803950 0.0334399
\(579\) −0.330525 −0.0137361
\(580\) 9.43211 0.391647
\(581\) −21.5668 −0.894743
\(582\) 0.557616 0.0231139
\(583\) 4.62921 0.191722
\(584\) −16.2839 −0.673834
\(585\) 0.0829082 0.00342783
\(586\) 16.2520 0.671364
\(587\) 32.5848 1.34492 0.672459 0.740134i \(-0.265238\pi\)
0.672459 + 0.740134i \(0.265238\pi\)
\(588\) −5.96317 −0.245917
\(589\) −22.7317 −0.936644
\(590\) 2.58560 0.106447
\(591\) 15.7318 0.647119
\(592\) 5.15188 0.211741
\(593\) 33.6310 1.38106 0.690530 0.723304i \(-0.257378\pi\)
0.690530 + 0.723304i \(0.257378\pi\)
\(594\) 1.32954 0.0545515
\(595\) 1.45742 0.0597482
\(596\) 19.5216 0.799637
\(597\) 23.6125 0.966396
\(598\) −0.379063 −0.0155010
\(599\) 5.60394 0.228971 0.114485 0.993425i \(-0.463478\pi\)
0.114485 + 0.993425i \(0.463478\pi\)
\(600\) −11.2738 −0.460253
\(601\) 3.29883 0.134562 0.0672811 0.997734i \(-0.478568\pi\)
0.0672811 + 0.997734i \(0.478568\pi\)
\(602\) −1.57493 −0.0641893
\(603\) 8.35596 0.340281
\(604\) 13.0946 0.532811
\(605\) 7.47791 0.304020
\(606\) −6.98543 −0.283764
\(607\) 30.6868 1.24554 0.622769 0.782406i \(-0.286008\pi\)
0.622769 + 0.782406i \(0.286008\pi\)
\(608\) −33.1007 −1.34241
\(609\) −12.4056 −0.502700
\(610\) 0.991272 0.0401354
\(611\) 0.0228522 0.000924499 0
\(612\) 1.35366 0.0547186
\(613\) 40.5002 1.63579 0.817894 0.575369i \(-0.195141\pi\)
0.817894 + 0.575369i \(0.195141\pi\)
\(614\) −14.7087 −0.593594
\(615\) 0.715942 0.0288696
\(616\) 7.18242 0.289388
\(617\) 7.41310 0.298440 0.149220 0.988804i \(-0.452324\pi\)
0.149220 + 0.988804i \(0.452324\pi\)
\(618\) −4.04370 −0.162662
\(619\) 2.32291 0.0933656 0.0466828 0.998910i \(-0.485135\pi\)
0.0466828 + 0.998910i \(0.485135\pi\)
\(620\) 4.90038 0.196804
\(621\) −5.14537 −0.206477
\(622\) −9.69306 −0.388656
\(623\) −17.7047 −0.709323
\(624\) 0.0494589 0.00197994
\(625\) 13.3913 0.535652
\(626\) −2.62543 −0.104933
\(627\) −9.39542 −0.375217
\(628\) 1.35366 0.0540171
\(629\) −9.54524 −0.380593
\(630\) −1.17169 −0.0466812
\(631\) −23.7123 −0.943972 −0.471986 0.881606i \(-0.656463\pi\)
−0.471986 + 0.881606i \(0.656463\pi\)
\(632\) −12.5140 −0.497782
\(633\) −27.8021 −1.10503
\(634\) −5.82927 −0.231510
\(635\) −10.0083 −0.397168
\(636\) −3.78919 −0.150251
\(637\) 0.403675 0.0159942
\(638\) −10.2392 −0.405374
\(639\) −10.6303 −0.420527
\(640\) 7.92084 0.313099
\(641\) −13.8543 −0.547213 −0.273606 0.961842i \(-0.588217\pi\)
−0.273606 + 0.961842i \(0.588217\pi\)
\(642\) −7.02523 −0.277264
\(643\) 18.6936 0.737203 0.368602 0.929587i \(-0.379837\pi\)
0.368602 + 0.929587i \(0.379837\pi\)
\(644\) −11.2196 −0.442115
\(645\) −1.10030 −0.0433244
\(646\) 4.56746 0.179704
\(647\) 10.4629 0.411340 0.205670 0.978621i \(-0.434063\pi\)
0.205670 + 0.978621i \(0.434063\pi\)
\(648\) −2.69618 −0.105916
\(649\) 5.87855 0.230753
\(650\) 0.308047 0.0120826
\(651\) −6.44522 −0.252608
\(652\) 16.2144 0.635004
\(653\) 25.2592 0.988469 0.494235 0.869328i \(-0.335448\pi\)
0.494235 + 0.869328i \(0.335448\pi\)
\(654\) 12.6058 0.492925
\(655\) −14.4998 −0.566553
\(656\) 0.427096 0.0166753
\(657\) 6.03964 0.235629
\(658\) −0.322955 −0.0125901
\(659\) 25.9584 1.01119 0.505597 0.862770i \(-0.331272\pi\)
0.505597 + 0.862770i \(0.331272\pi\)
\(660\) 2.02541 0.0788391
\(661\) −33.8501 −1.31662 −0.658309 0.752748i \(-0.728728\pi\)
−0.658309 + 0.752748i \(0.728728\pi\)
\(662\) −1.97947 −0.0769341
\(663\) −0.0916358 −0.00355884
\(664\) 36.0981 1.40088
\(665\) 8.27997 0.321084
\(666\) 7.67390 0.297357
\(667\) 39.6262 1.53433
\(668\) −25.0042 −0.967442
\(669\) 8.02098 0.310109
\(670\) −6.07796 −0.234812
\(671\) 2.25373 0.0870044
\(672\) −9.38518 −0.362041
\(673\) −36.7361 −1.41607 −0.708036 0.706176i \(-0.750419\pi\)
−0.708036 + 0.706176i \(0.750419\pi\)
\(674\) −18.3535 −0.706950
\(675\) 4.18141 0.160943
\(676\) 17.5863 0.676395
\(677\) −27.9614 −1.07465 −0.537323 0.843377i \(-0.680564\pi\)
−0.537323 + 0.843377i \(0.680564\pi\)
\(678\) −6.79336 −0.260897
\(679\) −1.11727 −0.0428768
\(680\) −2.43939 −0.0935463
\(681\) −6.55387 −0.251145
\(682\) −5.31969 −0.203702
\(683\) 28.4644 1.08916 0.544579 0.838709i \(-0.316689\pi\)
0.544579 + 0.838709i \(0.316689\pi\)
\(684\) 7.69053 0.294055
\(685\) 5.19321 0.198422
\(686\) −14.7701 −0.563925
\(687\) −10.1111 −0.385761
\(688\) −0.656386 −0.0250245
\(689\) 0.256508 0.00977218
\(690\) 3.74264 0.142480
\(691\) 7.99042 0.303970 0.151985 0.988383i \(-0.451433\pi\)
0.151985 + 0.988383i \(0.451433\pi\)
\(692\) −31.8434 −1.21050
\(693\) −2.66393 −0.101194
\(694\) −17.7714 −0.674595
\(695\) −4.62374 −0.175389
\(696\) 20.7642 0.787064
\(697\) −0.791309 −0.0299730
\(698\) 1.31172 0.0496494
\(699\) −5.50557 −0.208240
\(700\) 9.11770 0.344617
\(701\) −21.2227 −0.801571 −0.400785 0.916172i \(-0.631263\pi\)
−0.400785 + 0.916172i \(0.631263\pi\)
\(702\) 0.0736706 0.00278052
\(703\) −54.2291 −2.04529
\(704\) −5.96107 −0.224666
\(705\) −0.225629 −0.00849767
\(706\) −4.22511 −0.159014
\(707\) 13.9964 0.526388
\(708\) −4.81183 −0.180840
\(709\) 11.6853 0.438851 0.219425 0.975629i \(-0.429582\pi\)
0.219425 + 0.975629i \(0.429582\pi\)
\(710\) 7.73225 0.290186
\(711\) 4.64140 0.174066
\(712\) 29.6337 1.11057
\(713\) 20.5875 0.771007
\(714\) 1.29503 0.0484654
\(715\) −0.137110 −0.00512761
\(716\) 35.3975 1.32286
\(717\) 23.7783 0.888018
\(718\) −29.4291 −1.09828
\(719\) 42.7654 1.59488 0.797441 0.603397i \(-0.206187\pi\)
0.797441 + 0.603397i \(0.206187\pi\)
\(720\) −0.488328 −0.0181989
\(721\) 8.10217 0.301741
\(722\) 10.6739 0.397242
\(723\) 2.65562 0.0987635
\(724\) 20.8181 0.773697
\(725\) −32.2025 −1.19597
\(726\) 6.64473 0.246609
\(727\) −13.7752 −0.510893 −0.255447 0.966823i \(-0.582223\pi\)
−0.255447 + 0.966823i \(0.582223\pi\)
\(728\) 0.397984 0.0147503
\(729\) 1.00000 0.0370370
\(730\) −4.39311 −0.162596
\(731\) 1.21613 0.0449802
\(732\) −1.84477 −0.0681847
\(733\) 12.4182 0.458676 0.229338 0.973347i \(-0.426344\pi\)
0.229338 + 0.973347i \(0.426344\pi\)
\(734\) −22.7612 −0.840131
\(735\) −3.98564 −0.147013
\(736\) 29.9783 1.10502
\(737\) −13.8187 −0.509018
\(738\) 0.636173 0.0234179
\(739\) 16.7363 0.615654 0.307827 0.951442i \(-0.400398\pi\)
0.307827 + 0.951442i \(0.400398\pi\)
\(740\) 11.6904 0.429748
\(741\) −0.520608 −0.0191250
\(742\) −3.62507 −0.133081
\(743\) 26.6018 0.975927 0.487963 0.872864i \(-0.337740\pi\)
0.487963 + 0.872864i \(0.337740\pi\)
\(744\) 10.7879 0.395502
\(745\) 13.0478 0.478034
\(746\) −11.9108 −0.436086
\(747\) −13.3886 −0.489863
\(748\) −2.23863 −0.0818523
\(749\) 14.0761 0.514330
\(750\) −6.67838 −0.243860
\(751\) −23.4297 −0.854961 −0.427480 0.904025i \(-0.640599\pi\)
−0.427480 + 0.904025i \(0.640599\pi\)
\(752\) −0.134599 −0.00490831
\(753\) −24.7174 −0.900752
\(754\) −0.567362 −0.0206621
\(755\) 8.75211 0.318522
\(756\) 2.18053 0.0793051
\(757\) 26.5306 0.964271 0.482135 0.876097i \(-0.339861\pi\)
0.482135 + 0.876097i \(0.339861\pi\)
\(758\) −8.44784 −0.306840
\(759\) 8.50917 0.308863
\(760\) −13.8588 −0.502712
\(761\) −13.2481 −0.480242 −0.240121 0.970743i \(-0.577187\pi\)
−0.240121 + 0.970743i \(0.577187\pi\)
\(762\) −8.89321 −0.322167
\(763\) −25.2576 −0.914386
\(764\) −9.39209 −0.339794
\(765\) 0.904757 0.0327116
\(766\) −4.54438 −0.164195
\(767\) 0.325735 0.0117616
\(768\) 14.2475 0.514111
\(769\) 11.5443 0.416299 0.208150 0.978097i \(-0.433256\pi\)
0.208150 + 0.978097i \(0.433256\pi\)
\(770\) 1.93769 0.0698294
\(771\) 13.6334 0.490995
\(772\) −0.447420 −0.0161030
\(773\) 17.4946 0.629237 0.314618 0.949218i \(-0.398123\pi\)
0.314618 + 0.949218i \(0.398123\pi\)
\(774\) −0.977709 −0.0351430
\(775\) −16.7305 −0.600978
\(776\) 1.87006 0.0671312
\(777\) −15.3758 −0.551604
\(778\) −12.3975 −0.444470
\(779\) −4.49564 −0.161073
\(780\) 0.112230 0.00401847
\(781\) 17.5799 0.629057
\(782\) −4.13662 −0.147925
\(783\) −7.70133 −0.275223
\(784\) −2.37764 −0.0849156
\(785\) 0.904757 0.0322922
\(786\) −12.8842 −0.459565
\(787\) 12.7278 0.453696 0.226848 0.973930i \(-0.427158\pi\)
0.226848 + 0.973930i \(0.427158\pi\)
\(788\) 21.2955 0.758622
\(789\) 8.51665 0.303201
\(790\) −3.37606 −0.120115
\(791\) 13.6115 0.483970
\(792\) 4.45882 0.158437
\(793\) 0.124881 0.00443466
\(794\) 9.43682 0.334900
\(795\) −2.53261 −0.0898224
\(796\) 31.9634 1.13291
\(797\) −4.20025 −0.148781 −0.0743903 0.997229i \(-0.523701\pi\)
−0.0743903 + 0.997229i \(0.523701\pi\)
\(798\) 7.35743 0.260450
\(799\) 0.249380 0.00882244
\(800\) −24.3621 −0.861330
\(801\) −10.9910 −0.388347
\(802\) −7.66357 −0.270610
\(803\) −9.98807 −0.352471
\(804\) 11.3112 0.398914
\(805\) −7.49894 −0.264303
\(806\) −0.294768 −0.0103828
\(807\) 12.3629 0.435196
\(808\) −23.4268 −0.824152
\(809\) 35.9815 1.26504 0.632521 0.774543i \(-0.282020\pi\)
0.632521 + 0.774543i \(0.282020\pi\)
\(810\) −0.727380 −0.0255575
\(811\) −17.8320 −0.626167 −0.313083 0.949726i \(-0.601362\pi\)
−0.313083 + 0.949726i \(0.601362\pi\)
\(812\) −16.7930 −0.589318
\(813\) −2.18769 −0.0767255
\(814\) −12.6907 −0.444810
\(815\) 10.8373 0.379615
\(816\) 0.539733 0.0188944
\(817\) 6.90917 0.241721
\(818\) −19.3829 −0.677708
\(819\) −0.147610 −0.00515792
\(820\) 0.969145 0.0338440
\(821\) 5.28531 0.184459 0.0922293 0.995738i \(-0.470601\pi\)
0.0922293 + 0.995738i \(0.470601\pi\)
\(822\) 4.61459 0.160952
\(823\) −25.4428 −0.886881 −0.443440 0.896304i \(-0.646242\pi\)
−0.443440 + 0.896304i \(0.646242\pi\)
\(824\) −13.5612 −0.472427
\(825\) −6.91503 −0.240750
\(826\) −4.60341 −0.160173
\(827\) −27.1093 −0.942681 −0.471341 0.881951i \(-0.656230\pi\)
−0.471341 + 0.881951i \(0.656230\pi\)
\(828\) −6.96510 −0.242054
\(829\) −37.8778 −1.31555 −0.657775 0.753215i \(-0.728502\pi\)
−0.657775 + 0.753215i \(0.728502\pi\)
\(830\) 9.73860 0.338032
\(831\) 29.8676 1.03609
\(832\) −0.330308 −0.0114514
\(833\) 4.40521 0.152631
\(834\) −4.10857 −0.142268
\(835\) −16.7122 −0.578351
\(836\) −12.7182 −0.439870
\(837\) −4.00116 −0.138300
\(838\) 18.2586 0.630733
\(839\) 26.5124 0.915309 0.457654 0.889130i \(-0.348690\pi\)
0.457654 + 0.889130i \(0.348690\pi\)
\(840\) −3.92945 −0.135579
\(841\) 30.3105 1.04519
\(842\) 3.23539 0.111499
\(843\) 15.2973 0.526868
\(844\) −37.6346 −1.29544
\(845\) 11.7542 0.404358
\(846\) −0.200489 −0.00689297
\(847\) −13.3137 −0.457465
\(848\) −1.51083 −0.0518821
\(849\) 8.20474 0.281586
\(850\) 3.36165 0.115304
\(851\) 49.1138 1.68360
\(852\) −14.3898 −0.492987
\(853\) −33.7541 −1.15572 −0.577858 0.816137i \(-0.696111\pi\)
−0.577858 + 0.816137i \(0.696111\pi\)
\(854\) −1.76487 −0.0603925
\(855\) 5.14017 0.175790
\(856\) −23.5603 −0.805273
\(857\) −42.5808 −1.45453 −0.727267 0.686355i \(-0.759210\pi\)
−0.727267 + 0.686355i \(0.759210\pi\)
\(858\) −0.121833 −0.00415931
\(859\) −15.9109 −0.542872 −0.271436 0.962457i \(-0.587498\pi\)
−0.271436 + 0.962457i \(0.587498\pi\)
\(860\) −1.48944 −0.0507895
\(861\) −1.27467 −0.0434406
\(862\) −26.3170 −0.896360
\(863\) 33.0354 1.12454 0.562269 0.826954i \(-0.309928\pi\)
0.562269 + 0.826954i \(0.309928\pi\)
\(864\) −5.82628 −0.198214
\(865\) −21.2834 −0.723657
\(866\) −8.03408 −0.273009
\(867\) −1.00000 −0.0339618
\(868\) −8.72466 −0.296134
\(869\) −7.67573 −0.260381
\(870\) 5.60180 0.189919
\(871\) −0.765705 −0.0259449
\(872\) 42.2755 1.43163
\(873\) −0.693595 −0.0234746
\(874\) −23.5013 −0.794942
\(875\) 13.3811 0.452365
\(876\) 8.17564 0.276229
\(877\) 25.9924 0.877702 0.438851 0.898560i \(-0.355386\pi\)
0.438851 + 0.898560i \(0.355386\pi\)
\(878\) −13.8078 −0.465991
\(879\) −20.2152 −0.681841
\(880\) 0.807573 0.0272233
\(881\) 52.4284 1.76636 0.883179 0.469037i \(-0.155399\pi\)
0.883179 + 0.469037i \(0.155399\pi\)
\(882\) −3.54157 −0.119251
\(883\) −42.5118 −1.43064 −0.715318 0.698799i \(-0.753718\pi\)
−0.715318 + 0.698799i \(0.753718\pi\)
\(884\) −0.124044 −0.00417205
\(885\) −3.21612 −0.108109
\(886\) 6.30322 0.211761
\(887\) −23.5832 −0.791845 −0.395922 0.918284i \(-0.629575\pi\)
−0.395922 + 0.918284i \(0.629575\pi\)
\(888\) 25.7357 0.863632
\(889\) 17.8189 0.597626
\(890\) 7.99462 0.267980
\(891\) −1.65375 −0.0554028
\(892\) 10.8577 0.363543
\(893\) 1.41680 0.0474113
\(894\) 11.5940 0.387762
\(895\) 23.6588 0.790828
\(896\) −14.1023 −0.471125
\(897\) 0.471500 0.0157429
\(898\) −2.77884 −0.0927311
\(899\) 30.8143 1.02771
\(900\) 5.66023 0.188674
\(901\) 2.79921 0.0932553
\(902\) −1.05207 −0.0350302
\(903\) 1.95899 0.0651910
\(904\) −22.7826 −0.757739
\(905\) 13.9143 0.462527
\(906\) 7.77696 0.258372
\(907\) −10.9562 −0.363796 −0.181898 0.983317i \(-0.558224\pi\)
−0.181898 + 0.983317i \(0.558224\pi\)
\(908\) −8.87174 −0.294419
\(909\) 8.68888 0.288192
\(910\) 0.107369 0.00355924
\(911\) −52.1336 −1.72726 −0.863632 0.504122i \(-0.831816\pi\)
−0.863632 + 0.504122i \(0.831816\pi\)
\(912\) 3.06637 0.101538
\(913\) 22.1414 0.732775
\(914\) −7.43365 −0.245883
\(915\) −1.23300 −0.0407618
\(916\) −13.6870 −0.452230
\(917\) 25.8155 0.852503
\(918\) 0.803950 0.0265343
\(919\) −28.1686 −0.929197 −0.464599 0.885521i \(-0.653801\pi\)
−0.464599 + 0.885521i \(0.653801\pi\)
\(920\) 12.5516 0.413812
\(921\) 18.2955 0.602858
\(922\) 29.6959 0.977981
\(923\) 0.974113 0.0320633
\(924\) −3.60606 −0.118631
\(925\) −39.9126 −1.31232
\(926\) −8.22078 −0.270152
\(927\) 5.02979 0.165200
\(928\) 44.8701 1.47293
\(929\) 20.4835 0.672041 0.336020 0.941855i \(-0.390919\pi\)
0.336020 + 0.941855i \(0.390919\pi\)
\(930\) 2.91037 0.0954347
\(931\) 25.0272 0.820233
\(932\) −7.45269 −0.244121
\(933\) 12.0568 0.394721
\(934\) −5.64659 −0.184762
\(935\) −1.49625 −0.0489325
\(936\) 0.247067 0.00807562
\(937\) 4.62838 0.151203 0.0756013 0.997138i \(-0.475912\pi\)
0.0756013 + 0.997138i \(0.475912\pi\)
\(938\) 10.8212 0.353326
\(939\) 3.26567 0.106571
\(940\) −0.305425 −0.00996187
\(941\) 7.94391 0.258964 0.129482 0.991582i \(-0.458669\pi\)
0.129482 + 0.991582i \(0.458669\pi\)
\(942\) 0.803950 0.0261941
\(943\) 4.07158 0.132589
\(944\) −1.91857 −0.0624443
\(945\) 1.45742 0.0474097
\(946\) 1.61689 0.0525696
\(947\) 49.7703 1.61732 0.808659 0.588277i \(-0.200194\pi\)
0.808659 + 0.588277i \(0.200194\pi\)
\(948\) 6.28289 0.204059
\(949\) −0.553447 −0.0179656
\(950\) 19.0984 0.619635
\(951\) 7.25078 0.235123
\(952\) 4.34310 0.140761
\(953\) 20.1753 0.653541 0.326771 0.945104i \(-0.394040\pi\)
0.326771 + 0.945104i \(0.394040\pi\)
\(954\) −2.25043 −0.0728603
\(955\) −6.27746 −0.203134
\(956\) 32.1879 1.04103
\(957\) 12.7361 0.411700
\(958\) 13.7457 0.444104
\(959\) −9.24602 −0.298569
\(960\) 3.26126 0.105257
\(961\) −14.9907 −0.483570
\(962\) −0.703203 −0.0226722
\(963\) 8.73839 0.281591
\(964\) 3.59481 0.115781
\(965\) −0.299045 −0.00962659
\(966\) −6.66342 −0.214392
\(967\) 6.69093 0.215166 0.107583 0.994196i \(-0.465689\pi\)
0.107583 + 0.994196i \(0.465689\pi\)
\(968\) 22.2842 0.716241
\(969\) −5.68127 −0.182509
\(970\) 0.504507 0.0161988
\(971\) 30.3676 0.974542 0.487271 0.873251i \(-0.337992\pi\)
0.487271 + 0.873251i \(0.337992\pi\)
\(972\) 1.35366 0.0434188
\(973\) 8.23214 0.263910
\(974\) 27.2687 0.873745
\(975\) −0.383167 −0.0122712
\(976\) −0.735548 −0.0235443
\(977\) −26.4301 −0.845574 −0.422787 0.906229i \(-0.638948\pi\)
−0.422787 + 0.906229i \(0.638948\pi\)
\(978\) 9.62984 0.307928
\(979\) 18.1764 0.580920
\(980\) −5.39522 −0.172344
\(981\) −15.6798 −0.500617
\(982\) −1.97615 −0.0630615
\(983\) 54.7375 1.74585 0.872927 0.487850i \(-0.162219\pi\)
0.872927 + 0.487850i \(0.162219\pi\)
\(984\) 2.13351 0.0680138
\(985\) 14.2334 0.453515
\(986\) −6.19149 −0.197177
\(987\) 0.401711 0.0127866
\(988\) −0.704728 −0.0224204
\(989\) −6.25744 −0.198975
\(990\) 1.20291 0.0382309
\(991\) 23.2925 0.739910 0.369955 0.929050i \(-0.379373\pi\)
0.369955 + 0.929050i \(0.379373\pi\)
\(992\) 23.3119 0.740153
\(993\) 2.46217 0.0781347
\(994\) −13.7665 −0.436648
\(995\) 21.3636 0.677272
\(996\) −18.1237 −0.574270
\(997\) −18.5796 −0.588421 −0.294210 0.955741i \(-0.595057\pi\)
−0.294210 + 0.955741i \(0.595057\pi\)
\(998\) −5.07757 −0.160728
\(999\) −9.54524 −0.301998
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.1.30 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.30 48 1.1 even 1 trivial