Properties

Label 8007.2.a.f.1.3
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 1.3
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.52044 q^{2} -1.00000 q^{3} +4.35263 q^{4} -1.87454 q^{5} +2.52044 q^{6} -3.72156 q^{7} -5.92968 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.52044 q^{2} -1.00000 q^{3} +4.35263 q^{4} -1.87454 q^{5} +2.52044 q^{6} -3.72156 q^{7} -5.92968 q^{8} +1.00000 q^{9} +4.72466 q^{10} -2.94696 q^{11} -4.35263 q^{12} -4.80391 q^{13} +9.37999 q^{14} +1.87454 q^{15} +6.24016 q^{16} -1.00000 q^{17} -2.52044 q^{18} -2.96492 q^{19} -8.15917 q^{20} +3.72156 q^{21} +7.42764 q^{22} -3.55424 q^{23} +5.92968 q^{24} -1.48611 q^{25} +12.1080 q^{26} -1.00000 q^{27} -16.1986 q^{28} -2.12919 q^{29} -4.72466 q^{30} -1.66517 q^{31} -3.86860 q^{32} +2.94696 q^{33} +2.52044 q^{34} +6.97620 q^{35} +4.35263 q^{36} +0.184027 q^{37} +7.47290 q^{38} +4.80391 q^{39} +11.1154 q^{40} +12.0088 q^{41} -9.37999 q^{42} +0.542752 q^{43} -12.8270 q^{44} -1.87454 q^{45} +8.95825 q^{46} +8.00368 q^{47} -6.24016 q^{48} +6.85003 q^{49} +3.74566 q^{50} +1.00000 q^{51} -20.9097 q^{52} +5.77316 q^{53} +2.52044 q^{54} +5.52418 q^{55} +22.0677 q^{56} +2.96492 q^{57} +5.36651 q^{58} -4.76000 q^{59} +8.15917 q^{60} -8.87761 q^{61} +4.19697 q^{62} -3.72156 q^{63} -2.72973 q^{64} +9.00510 q^{65} -7.42764 q^{66} +6.37330 q^{67} -4.35263 q^{68} +3.55424 q^{69} -17.5831 q^{70} +0.652176 q^{71} -5.92968 q^{72} -10.6625 q^{73} -0.463829 q^{74} +1.48611 q^{75} -12.9052 q^{76} +10.9673 q^{77} -12.1080 q^{78} +5.92951 q^{79} -11.6974 q^{80} +1.00000 q^{81} -30.2675 q^{82} +7.36907 q^{83} +16.1986 q^{84} +1.87454 q^{85} -1.36797 q^{86} +2.12919 q^{87} +17.4745 q^{88} +13.2204 q^{89} +4.72466 q^{90} +17.8780 q^{91} -15.4703 q^{92} +1.66517 q^{93} -20.1728 q^{94} +5.55784 q^{95} +3.86860 q^{96} -6.53499 q^{97} -17.2651 q^{98} -2.94696 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52044 −1.78222 −0.891111 0.453785i \(-0.850073\pi\)
−0.891111 + 0.453785i \(0.850073\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.35263 2.17632
\(5\) −1.87454 −0.838318 −0.419159 0.907913i \(-0.637675\pi\)
−0.419159 + 0.907913i \(0.637675\pi\)
\(6\) 2.52044 1.02897
\(7\) −3.72156 −1.40662 −0.703309 0.710884i \(-0.748295\pi\)
−0.703309 + 0.710884i \(0.748295\pi\)
\(8\) −5.92968 −2.09646
\(9\) 1.00000 0.333333
\(10\) 4.72466 1.49407
\(11\) −2.94696 −0.888542 −0.444271 0.895893i \(-0.646537\pi\)
−0.444271 + 0.895893i \(0.646537\pi\)
\(12\) −4.35263 −1.25650
\(13\) −4.80391 −1.33236 −0.666182 0.745789i \(-0.732073\pi\)
−0.666182 + 0.745789i \(0.732073\pi\)
\(14\) 9.37999 2.50691
\(15\) 1.87454 0.484003
\(16\) 6.24016 1.56004
\(17\) −1.00000 −0.242536
\(18\) −2.52044 −0.594074
\(19\) −2.96492 −0.680198 −0.340099 0.940390i \(-0.610461\pi\)
−0.340099 + 0.940390i \(0.610461\pi\)
\(20\) −8.15917 −1.82445
\(21\) 3.72156 0.812112
\(22\) 7.42764 1.58358
\(23\) −3.55424 −0.741110 −0.370555 0.928811i \(-0.620832\pi\)
−0.370555 + 0.928811i \(0.620832\pi\)
\(24\) 5.92968 1.21039
\(25\) −1.48611 −0.297223
\(26\) 12.1080 2.37457
\(27\) −1.00000 −0.192450
\(28\) −16.1986 −3.06125
\(29\) −2.12919 −0.395381 −0.197691 0.980264i \(-0.563344\pi\)
−0.197691 + 0.980264i \(0.563344\pi\)
\(30\) −4.72466 −0.862601
\(31\) −1.66517 −0.299074 −0.149537 0.988756i \(-0.547778\pi\)
−0.149537 + 0.988756i \(0.547778\pi\)
\(32\) −3.86860 −0.683878
\(33\) 2.94696 0.513000
\(34\) 2.52044 0.432252
\(35\) 6.97620 1.17919
\(36\) 4.35263 0.725439
\(37\) 0.184027 0.0302538 0.0151269 0.999886i \(-0.495185\pi\)
0.0151269 + 0.999886i \(0.495185\pi\)
\(38\) 7.47290 1.21226
\(39\) 4.80391 0.769241
\(40\) 11.1154 1.75750
\(41\) 12.0088 1.87546 0.937729 0.347368i \(-0.112925\pi\)
0.937729 + 0.347368i \(0.112925\pi\)
\(42\) −9.37999 −1.44736
\(43\) 0.542752 0.0827689 0.0413844 0.999143i \(-0.486823\pi\)
0.0413844 + 0.999143i \(0.486823\pi\)
\(44\) −12.8270 −1.93375
\(45\) −1.87454 −0.279439
\(46\) 8.95825 1.32082
\(47\) 8.00368 1.16746 0.583728 0.811949i \(-0.301593\pi\)
0.583728 + 0.811949i \(0.301593\pi\)
\(48\) −6.24016 −0.900689
\(49\) 6.85003 0.978575
\(50\) 3.74566 0.529717
\(51\) 1.00000 0.140028
\(52\) −20.9097 −2.89965
\(53\) 5.77316 0.793004 0.396502 0.918034i \(-0.370224\pi\)
0.396502 + 0.918034i \(0.370224\pi\)
\(54\) 2.52044 0.342989
\(55\) 5.52418 0.744881
\(56\) 22.0677 2.94892
\(57\) 2.96492 0.392713
\(58\) 5.36651 0.704658
\(59\) −4.76000 −0.619700 −0.309850 0.950786i \(-0.600279\pi\)
−0.309850 + 0.950786i \(0.600279\pi\)
\(60\) 8.15917 1.05334
\(61\) −8.87761 −1.13666 −0.568330 0.822800i \(-0.692410\pi\)
−0.568330 + 0.822800i \(0.692410\pi\)
\(62\) 4.19697 0.533016
\(63\) −3.72156 −0.468873
\(64\) −2.72973 −0.341216
\(65\) 9.00510 1.11695
\(66\) −7.42764 −0.914280
\(67\) 6.37330 0.778623 0.389311 0.921106i \(-0.372713\pi\)
0.389311 + 0.921106i \(0.372713\pi\)
\(68\) −4.35263 −0.527834
\(69\) 3.55424 0.427880
\(70\) −17.5831 −2.10159
\(71\) 0.652176 0.0773990 0.0386995 0.999251i \(-0.487678\pi\)
0.0386995 + 0.999251i \(0.487678\pi\)
\(72\) −5.92968 −0.698820
\(73\) −10.6625 −1.24795 −0.623973 0.781446i \(-0.714483\pi\)
−0.623973 + 0.781446i \(0.714483\pi\)
\(74\) −0.463829 −0.0539191
\(75\) 1.48611 0.171602
\(76\) −12.9052 −1.48033
\(77\) 10.9673 1.24984
\(78\) −12.1080 −1.37096
\(79\) 5.92951 0.667122 0.333561 0.942729i \(-0.391750\pi\)
0.333561 + 0.942729i \(0.391750\pi\)
\(80\) −11.6974 −1.30781
\(81\) 1.00000 0.111111
\(82\) −30.2675 −3.34248
\(83\) 7.36907 0.808861 0.404430 0.914569i \(-0.367470\pi\)
0.404430 + 0.914569i \(0.367470\pi\)
\(84\) 16.1986 1.76741
\(85\) 1.87454 0.203322
\(86\) −1.36797 −0.147513
\(87\) 2.12919 0.228274
\(88\) 17.4745 1.86279
\(89\) 13.2204 1.40136 0.700679 0.713477i \(-0.252880\pi\)
0.700679 + 0.713477i \(0.252880\pi\)
\(90\) 4.72466 0.498023
\(91\) 17.8780 1.87413
\(92\) −15.4703 −1.61289
\(93\) 1.66517 0.172670
\(94\) −20.1728 −2.08067
\(95\) 5.55784 0.570223
\(96\) 3.86860 0.394837
\(97\) −6.53499 −0.663528 −0.331764 0.943362i \(-0.607644\pi\)
−0.331764 + 0.943362i \(0.607644\pi\)
\(98\) −17.2651 −1.74404
\(99\) −2.94696 −0.296181
\(100\) −6.46851 −0.646851
\(101\) 3.06380 0.304860 0.152430 0.988314i \(-0.451290\pi\)
0.152430 + 0.988314i \(0.451290\pi\)
\(102\) −2.52044 −0.249561
\(103\) −1.87708 −0.184954 −0.0924769 0.995715i \(-0.529478\pi\)
−0.0924769 + 0.995715i \(0.529478\pi\)
\(104\) 28.4856 2.79325
\(105\) −6.97620 −0.680808
\(106\) −14.5509 −1.41331
\(107\) 3.64074 0.351964 0.175982 0.984393i \(-0.443690\pi\)
0.175982 + 0.984393i \(0.443690\pi\)
\(108\) −4.35263 −0.418832
\(109\) 19.4663 1.86454 0.932269 0.361766i \(-0.117826\pi\)
0.932269 + 0.361766i \(0.117826\pi\)
\(110\) −13.9234 −1.32754
\(111\) −0.184027 −0.0174671
\(112\) −23.2231 −2.19438
\(113\) −13.1276 −1.23494 −0.617471 0.786594i \(-0.711843\pi\)
−0.617471 + 0.786594i \(0.711843\pi\)
\(114\) −7.47290 −0.699901
\(115\) 6.66255 0.621286
\(116\) −9.26760 −0.860475
\(117\) −4.80391 −0.444122
\(118\) 11.9973 1.10444
\(119\) 3.72156 0.341155
\(120\) −11.1154 −1.01469
\(121\) −2.31543 −0.210494
\(122\) 22.3755 2.02578
\(123\) −12.0088 −1.08280
\(124\) −7.24788 −0.650879
\(125\) 12.1585 1.08749
\(126\) 9.37999 0.835636
\(127\) 16.0950 1.42820 0.714102 0.700042i \(-0.246835\pi\)
0.714102 + 0.700042i \(0.246835\pi\)
\(128\) 14.6173 1.29200
\(129\) −0.542752 −0.0477866
\(130\) −22.6969 −1.99065
\(131\) 9.54456 0.833912 0.416956 0.908927i \(-0.363097\pi\)
0.416956 + 0.908927i \(0.363097\pi\)
\(132\) 12.8270 1.11645
\(133\) 11.0341 0.956779
\(134\) −16.0635 −1.38768
\(135\) 1.87454 0.161334
\(136\) 5.92968 0.508466
\(137\) −4.90688 −0.419223 −0.209612 0.977785i \(-0.567220\pi\)
−0.209612 + 0.977785i \(0.567220\pi\)
\(138\) −8.95825 −0.762577
\(139\) 14.5218 1.23172 0.615862 0.787854i \(-0.288808\pi\)
0.615862 + 0.787854i \(0.288808\pi\)
\(140\) 30.3649 2.56630
\(141\) −8.00368 −0.674031
\(142\) −1.64377 −0.137942
\(143\) 14.1569 1.18386
\(144\) 6.24016 0.520013
\(145\) 3.99125 0.331455
\(146\) 26.8741 2.22412
\(147\) −6.85003 −0.564981
\(148\) 0.801002 0.0658419
\(149\) 4.60363 0.377144 0.188572 0.982059i \(-0.439614\pi\)
0.188572 + 0.982059i \(0.439614\pi\)
\(150\) −3.74566 −0.305832
\(151\) −18.6599 −1.51852 −0.759260 0.650788i \(-0.774439\pi\)
−0.759260 + 0.650788i \(0.774439\pi\)
\(152\) 17.5810 1.42601
\(153\) −1.00000 −0.0808452
\(154\) −27.6424 −2.22749
\(155\) 3.12142 0.250719
\(156\) 20.9097 1.67411
\(157\) −1.00000 −0.0798087
\(158\) −14.9450 −1.18896
\(159\) −5.77316 −0.457841
\(160\) 7.25183 0.573307
\(161\) 13.2273 1.04246
\(162\) −2.52044 −0.198025
\(163\) −9.35777 −0.732957 −0.366479 0.930426i \(-0.619437\pi\)
−0.366479 + 0.930426i \(0.619437\pi\)
\(164\) 52.2699 4.08159
\(165\) −5.52418 −0.430057
\(166\) −18.5733 −1.44157
\(167\) −9.19729 −0.711708 −0.355854 0.934542i \(-0.615810\pi\)
−0.355854 + 0.934542i \(0.615810\pi\)
\(168\) −22.0677 −1.70256
\(169\) 10.0775 0.775195
\(170\) −4.72466 −0.362365
\(171\) −2.96492 −0.226733
\(172\) 2.36240 0.180131
\(173\) −17.9279 −1.36304 −0.681518 0.731801i \(-0.738680\pi\)
−0.681518 + 0.731801i \(0.738680\pi\)
\(174\) −5.36651 −0.406834
\(175\) 5.53066 0.418079
\(176\) −18.3895 −1.38616
\(177\) 4.76000 0.357784
\(178\) −33.3212 −2.49753
\(179\) −7.01235 −0.524128 −0.262064 0.965050i \(-0.584403\pi\)
−0.262064 + 0.965050i \(0.584403\pi\)
\(180\) −8.15917 −0.608149
\(181\) −15.9778 −1.18762 −0.593811 0.804605i \(-0.702377\pi\)
−0.593811 + 0.804605i \(0.702377\pi\)
\(182\) −45.0606 −3.34011
\(183\) 8.87761 0.656251
\(184\) 21.0755 1.55371
\(185\) −0.344965 −0.0253623
\(186\) −4.19697 −0.307737
\(187\) 2.94696 0.215503
\(188\) 34.8371 2.54076
\(189\) 3.72156 0.270704
\(190\) −14.0082 −1.01626
\(191\) 5.28229 0.382213 0.191107 0.981569i \(-0.438792\pi\)
0.191107 + 0.981569i \(0.438792\pi\)
\(192\) 2.72973 0.197001
\(193\) −2.97462 −0.214118 −0.107059 0.994253i \(-0.534143\pi\)
−0.107059 + 0.994253i \(0.534143\pi\)
\(194\) 16.4711 1.18255
\(195\) −9.00510 −0.644869
\(196\) 29.8157 2.12969
\(197\) −24.3458 −1.73457 −0.867283 0.497815i \(-0.834136\pi\)
−0.867283 + 0.497815i \(0.834136\pi\)
\(198\) 7.42764 0.527860
\(199\) 17.3592 1.23056 0.615282 0.788307i \(-0.289042\pi\)
0.615282 + 0.788307i \(0.289042\pi\)
\(200\) 8.81218 0.623115
\(201\) −6.37330 −0.449538
\(202\) −7.72213 −0.543328
\(203\) 7.92393 0.556151
\(204\) 4.35263 0.304745
\(205\) −22.5109 −1.57223
\(206\) 4.73106 0.329629
\(207\) −3.55424 −0.247037
\(208\) −29.9771 −2.07854
\(209\) 8.73748 0.604384
\(210\) 17.5831 1.21335
\(211\) 9.45719 0.651060 0.325530 0.945532i \(-0.394457\pi\)
0.325530 + 0.945532i \(0.394457\pi\)
\(212\) 25.1284 1.72583
\(213\) −0.652176 −0.0446863
\(214\) −9.17628 −0.627278
\(215\) −1.01741 −0.0693866
\(216\) 5.92968 0.403464
\(217\) 6.19704 0.420682
\(218\) −49.0638 −3.32302
\(219\) 10.6625 0.720502
\(220\) 24.0447 1.62110
\(221\) 4.80391 0.323146
\(222\) 0.463829 0.0311302
\(223\) −28.9506 −1.93868 −0.969338 0.245732i \(-0.920972\pi\)
−0.969338 + 0.245732i \(0.920972\pi\)
\(224\) 14.3972 0.961955
\(225\) −1.48611 −0.0990742
\(226\) 33.0874 2.20094
\(227\) 7.60202 0.504563 0.252282 0.967654i \(-0.418819\pi\)
0.252282 + 0.967654i \(0.418819\pi\)
\(228\) 12.9052 0.854667
\(229\) 13.6198 0.900019 0.450010 0.893024i \(-0.351421\pi\)
0.450010 + 0.893024i \(0.351421\pi\)
\(230\) −16.7926 −1.10727
\(231\) −10.9673 −0.721595
\(232\) 12.6254 0.828901
\(233\) −4.67412 −0.306212 −0.153106 0.988210i \(-0.548928\pi\)
−0.153106 + 0.988210i \(0.548928\pi\)
\(234\) 12.1080 0.791523
\(235\) −15.0032 −0.978700
\(236\) −20.7186 −1.34866
\(237\) −5.92951 −0.385163
\(238\) −9.37999 −0.608014
\(239\) 25.2415 1.63274 0.816369 0.577530i \(-0.195983\pi\)
0.816369 + 0.577530i \(0.195983\pi\)
\(240\) 11.6974 0.755064
\(241\) −9.47592 −0.610398 −0.305199 0.952289i \(-0.598723\pi\)
−0.305199 + 0.952289i \(0.598723\pi\)
\(242\) 5.83591 0.375147
\(243\) −1.00000 −0.0641500
\(244\) −38.6410 −2.47373
\(245\) −12.8406 −0.820358
\(246\) 30.2675 1.92978
\(247\) 14.2432 0.906272
\(248\) 9.87393 0.626995
\(249\) −7.36907 −0.466996
\(250\) −30.6447 −1.93814
\(251\) −11.4885 −0.725148 −0.362574 0.931955i \(-0.618102\pi\)
−0.362574 + 0.931955i \(0.618102\pi\)
\(252\) −16.1986 −1.02042
\(253\) 10.4742 0.658507
\(254\) −40.5666 −2.54538
\(255\) −1.87454 −0.117388
\(256\) −31.3827 −1.96142
\(257\) −7.47709 −0.466408 −0.233204 0.972428i \(-0.574921\pi\)
−0.233204 + 0.972428i \(0.574921\pi\)
\(258\) 1.36797 0.0851664
\(259\) −0.684868 −0.0425556
\(260\) 39.1959 2.43083
\(261\) −2.12919 −0.131794
\(262\) −24.0565 −1.48622
\(263\) 1.86511 0.115007 0.0575037 0.998345i \(-0.481686\pi\)
0.0575037 + 0.998345i \(0.481686\pi\)
\(264\) −17.4745 −1.07548
\(265\) −10.8220 −0.664790
\(266\) −27.8109 −1.70519
\(267\) −13.2204 −0.809075
\(268\) 27.7406 1.69453
\(269\) 29.4837 1.79765 0.898827 0.438303i \(-0.144420\pi\)
0.898827 + 0.438303i \(0.144420\pi\)
\(270\) −4.72466 −0.287534
\(271\) 18.5631 1.12763 0.563813 0.825902i \(-0.309334\pi\)
0.563813 + 0.825902i \(0.309334\pi\)
\(272\) −6.24016 −0.378365
\(273\) −17.8780 −1.08203
\(274\) 12.3675 0.747149
\(275\) 4.37951 0.264095
\(276\) 15.4703 0.931202
\(277\) 19.9779 1.20036 0.600178 0.799866i \(-0.295096\pi\)
0.600178 + 0.799866i \(0.295096\pi\)
\(278\) −36.6014 −2.19520
\(279\) −1.66517 −0.0996912
\(280\) −41.3667 −2.47213
\(281\) −19.7369 −1.17740 −0.588702 0.808350i \(-0.700361\pi\)
−0.588702 + 0.808350i \(0.700361\pi\)
\(282\) 20.1728 1.20127
\(283\) −15.7621 −0.936957 −0.468478 0.883475i \(-0.655198\pi\)
−0.468478 + 0.883475i \(0.655198\pi\)
\(284\) 2.83868 0.168445
\(285\) −5.55784 −0.329218
\(286\) −35.6817 −2.10990
\(287\) −44.6915 −2.63805
\(288\) −3.86860 −0.227959
\(289\) 1.00000 0.0588235
\(290\) −10.0597 −0.590727
\(291\) 6.53499 0.383088
\(292\) −46.4098 −2.71593
\(293\) 16.1592 0.944028 0.472014 0.881591i \(-0.343527\pi\)
0.472014 + 0.881591i \(0.343527\pi\)
\(294\) 17.2651 1.00692
\(295\) 8.92280 0.519505
\(296\) −1.09122 −0.0634259
\(297\) 2.94696 0.171000
\(298\) −11.6032 −0.672154
\(299\) 17.0742 0.987428
\(300\) 6.46851 0.373459
\(301\) −2.01988 −0.116424
\(302\) 47.0312 2.70634
\(303\) −3.06380 −0.176011
\(304\) −18.5015 −1.06114
\(305\) 16.6414 0.952883
\(306\) 2.52044 0.144084
\(307\) 22.9476 1.30969 0.654846 0.755763i \(-0.272734\pi\)
0.654846 + 0.755763i \(0.272734\pi\)
\(308\) 47.7366 2.72005
\(309\) 1.87708 0.106783
\(310\) −7.86737 −0.446837
\(311\) 28.3295 1.60642 0.803210 0.595696i \(-0.203124\pi\)
0.803210 + 0.595696i \(0.203124\pi\)
\(312\) −28.4856 −1.61268
\(313\) −12.2451 −0.692134 −0.346067 0.938210i \(-0.612483\pi\)
−0.346067 + 0.938210i \(0.612483\pi\)
\(314\) 2.52044 0.142237
\(315\) 6.97620 0.393065
\(316\) 25.8090 1.45187
\(317\) 8.74468 0.491150 0.245575 0.969378i \(-0.421023\pi\)
0.245575 + 0.969378i \(0.421023\pi\)
\(318\) 14.5509 0.815975
\(319\) 6.27465 0.351313
\(320\) 5.11698 0.286048
\(321\) −3.64074 −0.203206
\(322\) −33.3387 −1.85789
\(323\) 2.96492 0.164972
\(324\) 4.35263 0.241813
\(325\) 7.13915 0.396009
\(326\) 23.5857 1.30629
\(327\) −19.4663 −1.07649
\(328\) −71.2083 −3.93182
\(329\) −29.7862 −1.64217
\(330\) 13.9234 0.766457
\(331\) −7.30026 −0.401259 −0.200629 0.979667i \(-0.564299\pi\)
−0.200629 + 0.979667i \(0.564299\pi\)
\(332\) 32.0749 1.76034
\(333\) 0.184027 0.0100846
\(334\) 23.1812 1.26842
\(335\) −11.9470 −0.652733
\(336\) 23.2231 1.26693
\(337\) −29.7260 −1.61928 −0.809639 0.586929i \(-0.800337\pi\)
−0.809639 + 0.586929i \(0.800337\pi\)
\(338\) −25.3999 −1.38157
\(339\) 13.1276 0.712994
\(340\) 8.15917 0.442493
\(341\) 4.90719 0.265739
\(342\) 7.47290 0.404088
\(343\) 0.558131 0.0301363
\(344\) −3.21834 −0.173522
\(345\) −6.66255 −0.358699
\(346\) 45.1864 2.42923
\(347\) 12.8598 0.690352 0.345176 0.938538i \(-0.387819\pi\)
0.345176 + 0.938538i \(0.387819\pi\)
\(348\) 9.26760 0.496796
\(349\) 17.3968 0.931231 0.465616 0.884987i \(-0.345833\pi\)
0.465616 + 0.884987i \(0.345833\pi\)
\(350\) −13.9397 −0.745109
\(351\) 4.80391 0.256414
\(352\) 11.4006 0.607654
\(353\) 15.2555 0.811969 0.405984 0.913880i \(-0.366929\pi\)
0.405984 + 0.913880i \(0.366929\pi\)
\(354\) −11.9973 −0.637650
\(355\) −1.22253 −0.0648850
\(356\) 57.5435 3.04980
\(357\) −3.72156 −0.196966
\(358\) 17.6742 0.934113
\(359\) 22.1169 1.16729 0.583643 0.812011i \(-0.301627\pi\)
0.583643 + 0.812011i \(0.301627\pi\)
\(360\) 11.1154 0.585833
\(361\) −10.2093 −0.537330
\(362\) 40.2712 2.11661
\(363\) 2.31543 0.121529
\(364\) 77.8166 4.07870
\(365\) 19.9872 1.04618
\(366\) −22.3755 −1.16959
\(367\) −28.8081 −1.50377 −0.751886 0.659293i \(-0.770856\pi\)
−0.751886 + 0.659293i \(0.770856\pi\)
\(368\) −22.1790 −1.15616
\(369\) 12.0088 0.625152
\(370\) 0.869465 0.0452013
\(371\) −21.4852 −1.11545
\(372\) 7.24788 0.375785
\(373\) −12.7252 −0.658887 −0.329443 0.944175i \(-0.606861\pi\)
−0.329443 + 0.944175i \(0.606861\pi\)
\(374\) −7.42764 −0.384074
\(375\) −12.1585 −0.627860
\(376\) −47.4593 −2.44752
\(377\) 10.2285 0.526792
\(378\) −9.37999 −0.482454
\(379\) 26.1581 1.34365 0.671825 0.740710i \(-0.265511\pi\)
0.671825 + 0.740710i \(0.265511\pi\)
\(380\) 24.1913 1.24099
\(381\) −16.0950 −0.824574
\(382\) −13.3137 −0.681189
\(383\) −17.3823 −0.888195 −0.444098 0.895978i \(-0.646476\pi\)
−0.444098 + 0.895978i \(0.646476\pi\)
\(384\) −14.6173 −0.745937
\(385\) −20.5586 −1.04776
\(386\) 7.49737 0.381606
\(387\) 0.542752 0.0275896
\(388\) −28.4444 −1.44405
\(389\) −10.2237 −0.518362 −0.259181 0.965829i \(-0.583453\pi\)
−0.259181 + 0.965829i \(0.583453\pi\)
\(390\) 22.6969 1.14930
\(391\) 3.55424 0.179745
\(392\) −40.6185 −2.05154
\(393\) −9.54456 −0.481459
\(394\) 61.3622 3.09138
\(395\) −11.1151 −0.559260
\(396\) −12.8270 −0.644583
\(397\) −18.2914 −0.918018 −0.459009 0.888432i \(-0.651795\pi\)
−0.459009 + 0.888432i \(0.651795\pi\)
\(398\) −43.7530 −2.19314
\(399\) −11.0341 −0.552397
\(400\) −9.27358 −0.463679
\(401\) 22.9681 1.14697 0.573486 0.819215i \(-0.305591\pi\)
0.573486 + 0.819215i \(0.305591\pi\)
\(402\) 16.0635 0.801177
\(403\) 7.99933 0.398475
\(404\) 13.3356 0.663471
\(405\) −1.87454 −0.0931465
\(406\) −19.9718 −0.991184
\(407\) −0.542320 −0.0268818
\(408\) −5.92968 −0.293563
\(409\) 3.02331 0.149493 0.0747466 0.997203i \(-0.476185\pi\)
0.0747466 + 0.997203i \(0.476185\pi\)
\(410\) 56.7375 2.80206
\(411\) 4.90688 0.242039
\(412\) −8.17022 −0.402518
\(413\) 17.7146 0.871681
\(414\) 8.95825 0.440274
\(415\) −13.8136 −0.678083
\(416\) 18.5844 0.911175
\(417\) −14.5218 −0.711136
\(418\) −22.0223 −1.07715
\(419\) −0.892352 −0.0435942 −0.0217971 0.999762i \(-0.506939\pi\)
−0.0217971 + 0.999762i \(0.506939\pi\)
\(420\) −30.3649 −1.48165
\(421\) 24.3328 1.18591 0.592954 0.805236i \(-0.297961\pi\)
0.592954 + 0.805236i \(0.297961\pi\)
\(422\) −23.8363 −1.16033
\(423\) 8.00368 0.389152
\(424\) −34.2330 −1.66250
\(425\) 1.48611 0.0720871
\(426\) 1.64377 0.0796410
\(427\) 33.0386 1.59885
\(428\) 15.8468 0.765985
\(429\) −14.1569 −0.683503
\(430\) 2.56432 0.123662
\(431\) 9.42564 0.454017 0.227009 0.973893i \(-0.427105\pi\)
0.227009 + 0.973893i \(0.427105\pi\)
\(432\) −6.24016 −0.300230
\(433\) −7.29466 −0.350559 −0.175279 0.984519i \(-0.556083\pi\)
−0.175279 + 0.984519i \(0.556083\pi\)
\(434\) −15.6193 −0.749750
\(435\) −3.99125 −0.191366
\(436\) 84.7299 4.05783
\(437\) 10.5380 0.504101
\(438\) −26.8741 −1.28410
\(439\) 13.7761 0.657498 0.328749 0.944417i \(-0.393373\pi\)
0.328749 + 0.944417i \(0.393373\pi\)
\(440\) −32.7566 −1.56161
\(441\) 6.85003 0.326192
\(442\) −12.1080 −0.575918
\(443\) −3.46706 −0.164725 −0.0823625 0.996602i \(-0.526247\pi\)
−0.0823625 + 0.996602i \(0.526247\pi\)
\(444\) −0.801002 −0.0380139
\(445\) −24.7821 −1.17478
\(446\) 72.9683 3.45515
\(447\) −4.60363 −0.217744
\(448\) 10.1589 0.479961
\(449\) −10.4236 −0.491921 −0.245961 0.969280i \(-0.579103\pi\)
−0.245961 + 0.969280i \(0.579103\pi\)
\(450\) 3.74566 0.176572
\(451\) −35.3894 −1.66642
\(452\) −57.1397 −2.68762
\(453\) 18.6599 0.876718
\(454\) −19.1604 −0.899244
\(455\) −33.5131 −1.57112
\(456\) −17.5810 −0.823306
\(457\) 26.5846 1.24357 0.621787 0.783186i \(-0.286407\pi\)
0.621787 + 0.783186i \(0.286407\pi\)
\(458\) −34.3278 −1.60403
\(459\) 1.00000 0.0466760
\(460\) 28.9996 1.35211
\(461\) 32.9053 1.53255 0.766275 0.642513i \(-0.222108\pi\)
0.766275 + 0.642513i \(0.222108\pi\)
\(462\) 27.6424 1.28604
\(463\) 23.5261 1.09335 0.546675 0.837345i \(-0.315893\pi\)
0.546675 + 0.837345i \(0.315893\pi\)
\(464\) −13.2865 −0.616810
\(465\) −3.12142 −0.144753
\(466\) 11.7809 0.545738
\(467\) 3.00725 0.139159 0.0695795 0.997576i \(-0.477834\pi\)
0.0695795 + 0.997576i \(0.477834\pi\)
\(468\) −20.9097 −0.966549
\(469\) −23.7186 −1.09522
\(470\) 37.8147 1.74426
\(471\) 1.00000 0.0460776
\(472\) 28.2253 1.29917
\(473\) −1.59947 −0.0735436
\(474\) 14.9450 0.686446
\(475\) 4.40620 0.202170
\(476\) 16.1986 0.742462
\(477\) 5.77316 0.264335
\(478\) −63.6198 −2.90990
\(479\) 3.88205 0.177375 0.0886876 0.996059i \(-0.471733\pi\)
0.0886876 + 0.996059i \(0.471733\pi\)
\(480\) −7.25183 −0.330999
\(481\) −0.884048 −0.0403091
\(482\) 23.8835 1.08786
\(483\) −13.2273 −0.601864
\(484\) −10.0782 −0.458101
\(485\) 12.2501 0.556247
\(486\) 2.52044 0.114330
\(487\) −24.2239 −1.09769 −0.548844 0.835925i \(-0.684932\pi\)
−0.548844 + 0.835925i \(0.684932\pi\)
\(488\) 52.6414 2.38296
\(489\) 9.35777 0.423173
\(490\) 32.3641 1.46206
\(491\) 9.01271 0.406738 0.203369 0.979102i \(-0.434811\pi\)
0.203369 + 0.979102i \(0.434811\pi\)
\(492\) −52.2699 −2.35651
\(493\) 2.12919 0.0958941
\(494\) −35.8991 −1.61518
\(495\) 5.52418 0.248294
\(496\) −10.3909 −0.466566
\(497\) −2.42711 −0.108871
\(498\) 18.5733 0.832291
\(499\) 1.66247 0.0744223 0.0372112 0.999307i \(-0.488153\pi\)
0.0372112 + 0.999307i \(0.488153\pi\)
\(500\) 52.9213 2.36671
\(501\) 9.19729 0.410905
\(502\) 28.9561 1.29237
\(503\) −0.185198 −0.00825757 −0.00412878 0.999991i \(-0.501314\pi\)
−0.00412878 + 0.999991i \(0.501314\pi\)
\(504\) 22.0677 0.982973
\(505\) −5.74321 −0.255569
\(506\) −26.3996 −1.17361
\(507\) −10.0775 −0.447559
\(508\) 70.0558 3.10822
\(509\) −19.1100 −0.847036 −0.423518 0.905888i \(-0.639205\pi\)
−0.423518 + 0.905888i \(0.639205\pi\)
\(510\) 4.72466 0.209212
\(511\) 39.6810 1.75538
\(512\) 49.8636 2.20368
\(513\) 2.96492 0.130904
\(514\) 18.8456 0.831243
\(515\) 3.51865 0.155050
\(516\) −2.36240 −0.103999
\(517\) −23.5865 −1.03733
\(518\) 1.72617 0.0758436
\(519\) 17.9279 0.786949
\(520\) −53.3974 −2.34163
\(521\) −21.5567 −0.944415 −0.472207 0.881487i \(-0.656543\pi\)
−0.472207 + 0.881487i \(0.656543\pi\)
\(522\) 5.36651 0.234886
\(523\) 9.44195 0.412868 0.206434 0.978461i \(-0.433814\pi\)
0.206434 + 0.978461i \(0.433814\pi\)
\(524\) 41.5440 1.81486
\(525\) −5.53066 −0.241378
\(526\) −4.70089 −0.204969
\(527\) 1.66517 0.0725360
\(528\) 18.3895 0.800300
\(529\) −10.3674 −0.450757
\(530\) 27.2762 1.18480
\(531\) −4.76000 −0.206567
\(532\) 48.0275 2.08226
\(533\) −57.6891 −2.49879
\(534\) 33.3212 1.44195
\(535\) −6.82470 −0.295058
\(536\) −37.7916 −1.63235
\(537\) 7.01235 0.302605
\(538\) −74.3121 −3.20382
\(539\) −20.1868 −0.869505
\(540\) 8.15917 0.351115
\(541\) −23.7931 −1.02294 −0.511472 0.859300i \(-0.670900\pi\)
−0.511472 + 0.859300i \(0.670900\pi\)
\(542\) −46.7872 −2.00968
\(543\) 15.9778 0.685674
\(544\) 3.86860 0.165865
\(545\) −36.4904 −1.56308
\(546\) 45.0606 1.92842
\(547\) 15.3382 0.655814 0.327907 0.944710i \(-0.393657\pi\)
0.327907 + 0.944710i \(0.393657\pi\)
\(548\) −21.3579 −0.912362
\(549\) −8.87761 −0.378887
\(550\) −11.0383 −0.470675
\(551\) 6.31288 0.268938
\(552\) −21.0755 −0.897032
\(553\) −22.0670 −0.938386
\(554\) −50.3532 −2.13930
\(555\) 0.344965 0.0146430
\(556\) 63.2081 2.68062
\(557\) 0.0226634 0.000960279 0 0.000480139 1.00000i \(-0.499847\pi\)
0.000480139 1.00000i \(0.499847\pi\)
\(558\) 4.19697 0.177672
\(559\) −2.60733 −0.110278
\(560\) 43.5326 1.83959
\(561\) −2.94696 −0.124421
\(562\) 49.7457 2.09839
\(563\) −2.00033 −0.0843038 −0.0421519 0.999111i \(-0.513421\pi\)
−0.0421519 + 0.999111i \(0.513421\pi\)
\(564\) −34.8371 −1.46691
\(565\) 24.6082 1.03527
\(566\) 39.7274 1.66987
\(567\) −3.72156 −0.156291
\(568\) −3.86719 −0.162264
\(569\) −25.6981 −1.07732 −0.538660 0.842523i \(-0.681069\pi\)
−0.538660 + 0.842523i \(0.681069\pi\)
\(570\) 14.0082 0.586740
\(571\) −22.2678 −0.931879 −0.465939 0.884817i \(-0.654284\pi\)
−0.465939 + 0.884817i \(0.654284\pi\)
\(572\) 61.6199 2.57646
\(573\) −5.28229 −0.220671
\(574\) 112.642 4.70160
\(575\) 5.28200 0.220275
\(576\) −2.72973 −0.113739
\(577\) −26.7484 −1.11355 −0.556775 0.830663i \(-0.687962\pi\)
−0.556775 + 0.830663i \(0.687962\pi\)
\(578\) −2.52044 −0.104837
\(579\) 2.97462 0.123621
\(580\) 17.3725 0.721352
\(581\) −27.4245 −1.13776
\(582\) −16.4711 −0.682748
\(583\) −17.0133 −0.704617
\(584\) 63.2250 2.61627
\(585\) 9.00510 0.372315
\(586\) −40.7282 −1.68247
\(587\) 5.45070 0.224974 0.112487 0.993653i \(-0.464118\pi\)
0.112487 + 0.993653i \(0.464118\pi\)
\(588\) −29.8157 −1.22958
\(589\) 4.93709 0.203429
\(590\) −22.4894 −0.925874
\(591\) 24.3458 1.00145
\(592\) 1.14836 0.0471972
\(593\) 23.5888 0.968675 0.484337 0.874881i \(-0.339061\pi\)
0.484337 + 0.874881i \(0.339061\pi\)
\(594\) −7.42764 −0.304760
\(595\) −6.97620 −0.285997
\(596\) 20.0379 0.820785
\(597\) −17.3592 −0.710466
\(598\) −43.0346 −1.75982
\(599\) −5.20121 −0.212516 −0.106258 0.994339i \(-0.533887\pi\)
−0.106258 + 0.994339i \(0.533887\pi\)
\(600\) −8.81218 −0.359756
\(601\) 29.5637 1.20593 0.602964 0.797768i \(-0.293986\pi\)
0.602964 + 0.797768i \(0.293986\pi\)
\(602\) 5.09100 0.207494
\(603\) 6.37330 0.259541
\(604\) −81.2196 −3.30478
\(605\) 4.34036 0.176461
\(606\) 7.72213 0.313690
\(607\) −15.6165 −0.633854 −0.316927 0.948450i \(-0.602651\pi\)
−0.316927 + 0.948450i \(0.602651\pi\)
\(608\) 11.4701 0.465173
\(609\) −7.92393 −0.321094
\(610\) −41.9437 −1.69825
\(611\) −38.4489 −1.55548
\(612\) −4.35263 −0.175945
\(613\) 33.6331 1.35843 0.679214 0.733940i \(-0.262321\pi\)
0.679214 + 0.733940i \(0.262321\pi\)
\(614\) −57.8382 −2.33416
\(615\) 22.5109 0.907727
\(616\) −65.0325 −2.62024
\(617\) 10.8403 0.436414 0.218207 0.975902i \(-0.429979\pi\)
0.218207 + 0.975902i \(0.429979\pi\)
\(618\) −4.73106 −0.190311
\(619\) −29.4100 −1.18209 −0.591044 0.806640i \(-0.701284\pi\)
−0.591044 + 0.806640i \(0.701284\pi\)
\(620\) 13.5864 0.545644
\(621\) 3.55424 0.142627
\(622\) −71.4030 −2.86300
\(623\) −49.2005 −1.97118
\(624\) 29.9771 1.20005
\(625\) −15.3609 −0.614436
\(626\) 30.8631 1.23354
\(627\) −8.73748 −0.348942
\(628\) −4.35263 −0.173689
\(629\) −0.184027 −0.00733763
\(630\) −17.5831 −0.700529
\(631\) −39.4954 −1.57229 −0.786143 0.618045i \(-0.787925\pi\)
−0.786143 + 0.618045i \(0.787925\pi\)
\(632\) −35.1601 −1.39859
\(633\) −9.45719 −0.375890
\(634\) −22.0405 −0.875339
\(635\) −30.1707 −1.19729
\(636\) −25.1284 −0.996408
\(637\) −32.9069 −1.30382
\(638\) −15.8149 −0.626118
\(639\) 0.652176 0.0257997
\(640\) −27.4007 −1.08311
\(641\) −14.3591 −0.567151 −0.283576 0.958950i \(-0.591521\pi\)
−0.283576 + 0.958950i \(0.591521\pi\)
\(642\) 9.17628 0.362159
\(643\) 45.3534 1.78856 0.894282 0.447503i \(-0.147687\pi\)
0.894282 + 0.447503i \(0.147687\pi\)
\(644\) 57.5737 2.26872
\(645\) 1.01741 0.0400604
\(646\) −7.47290 −0.294017
\(647\) 6.48076 0.254785 0.127392 0.991852i \(-0.459339\pi\)
0.127392 + 0.991852i \(0.459339\pi\)
\(648\) −5.92968 −0.232940
\(649\) 14.0275 0.550629
\(650\) −17.9938 −0.705776
\(651\) −6.19704 −0.242881
\(652\) −40.7310 −1.59515
\(653\) −3.05164 −0.119420 −0.0597099 0.998216i \(-0.519018\pi\)
−0.0597099 + 0.998216i \(0.519018\pi\)
\(654\) 49.0638 1.91855
\(655\) −17.8916 −0.699084
\(656\) 74.9367 2.92579
\(657\) −10.6625 −0.415982
\(658\) 75.0744 2.92671
\(659\) −10.9964 −0.428357 −0.214179 0.976794i \(-0.568708\pi\)
−0.214179 + 0.976794i \(0.568708\pi\)
\(660\) −24.0447 −0.935940
\(661\) 43.6844 1.69913 0.849563 0.527487i \(-0.176865\pi\)
0.849563 + 0.527487i \(0.176865\pi\)
\(662\) 18.3999 0.715132
\(663\) −4.80391 −0.186568
\(664\) −43.6963 −1.69574
\(665\) −20.6839 −0.802086
\(666\) −0.463829 −0.0179730
\(667\) 7.56766 0.293021
\(668\) −40.0324 −1.54890
\(669\) 28.9506 1.11929
\(670\) 30.1117 1.16332
\(671\) 26.1619 1.00997
\(672\) −14.3972 −0.555385
\(673\) −16.5922 −0.639584 −0.319792 0.947488i \(-0.603613\pi\)
−0.319792 + 0.947488i \(0.603613\pi\)
\(674\) 74.9226 2.88591
\(675\) 1.48611 0.0572005
\(676\) 43.8639 1.68707
\(677\) 7.05970 0.271326 0.135663 0.990755i \(-0.456683\pi\)
0.135663 + 0.990755i \(0.456683\pi\)
\(678\) −33.0874 −1.27071
\(679\) 24.3204 0.933330
\(680\) −11.1154 −0.426256
\(681\) −7.60202 −0.291310
\(682\) −12.3683 −0.473607
\(683\) 15.2706 0.584315 0.292157 0.956370i \(-0.405627\pi\)
0.292157 + 0.956370i \(0.405627\pi\)
\(684\) −12.9052 −0.493442
\(685\) 9.19813 0.351442
\(686\) −1.40674 −0.0537095
\(687\) −13.6198 −0.519626
\(688\) 3.38686 0.129123
\(689\) −27.7337 −1.05657
\(690\) 16.7926 0.639282
\(691\) −10.6766 −0.406155 −0.203078 0.979163i \(-0.565094\pi\)
−0.203078 + 0.979163i \(0.565094\pi\)
\(692\) −78.0338 −2.96640
\(693\) 10.9673 0.416613
\(694\) −32.4125 −1.23036
\(695\) −27.2216 −1.03258
\(696\) −12.6254 −0.478566
\(697\) −12.0088 −0.454865
\(698\) −43.8477 −1.65966
\(699\) 4.67412 0.176792
\(700\) 24.0730 0.909872
\(701\) 25.0522 0.946210 0.473105 0.881006i \(-0.343133\pi\)
0.473105 + 0.881006i \(0.343133\pi\)
\(702\) −12.1080 −0.456986
\(703\) −0.545624 −0.0205786
\(704\) 8.04441 0.303185
\(705\) 15.0032 0.565053
\(706\) −38.4507 −1.44711
\(707\) −11.4021 −0.428821
\(708\) 20.7186 0.778651
\(709\) −41.8013 −1.56988 −0.784941 0.619571i \(-0.787307\pi\)
−0.784941 + 0.619571i \(0.787307\pi\)
\(710\) 3.08131 0.115640
\(711\) 5.92951 0.222374
\(712\) −78.3927 −2.93789
\(713\) 5.91841 0.221646
\(714\) 9.37999 0.351037
\(715\) −26.5377 −0.992453
\(716\) −30.5222 −1.14067
\(717\) −25.2415 −0.942662
\(718\) −55.7444 −2.08036
\(719\) −1.31995 −0.0492257 −0.0246129 0.999697i \(-0.507835\pi\)
−0.0246129 + 0.999697i \(0.507835\pi\)
\(720\) −11.6974 −0.435936
\(721\) 6.98565 0.260159
\(722\) 25.7319 0.957642
\(723\) 9.47592 0.352413
\(724\) −69.5456 −2.58464
\(725\) 3.16422 0.117516
\(726\) −5.83591 −0.216591
\(727\) 7.40415 0.274605 0.137302 0.990529i \(-0.456157\pi\)
0.137302 + 0.990529i \(0.456157\pi\)
\(728\) −106.011 −3.92903
\(729\) 1.00000 0.0370370
\(730\) −50.3765 −1.86452
\(731\) −0.542752 −0.0200744
\(732\) 38.6410 1.42821
\(733\) 17.4941 0.646160 0.323080 0.946372i \(-0.395282\pi\)
0.323080 + 0.946372i \(0.395282\pi\)
\(734\) 72.6093 2.68006
\(735\) 12.8406 0.473634
\(736\) 13.7499 0.506828
\(737\) −18.7819 −0.691839
\(738\) −30.2675 −1.11416
\(739\) −0.456404 −0.0167891 −0.00839455 0.999965i \(-0.502672\pi\)
−0.00839455 + 0.999965i \(0.502672\pi\)
\(740\) −1.50151 −0.0551965
\(741\) −14.2432 −0.523236
\(742\) 54.1521 1.98799
\(743\) −42.8477 −1.57193 −0.785965 0.618271i \(-0.787833\pi\)
−0.785965 + 0.618271i \(0.787833\pi\)
\(744\) −9.87393 −0.361996
\(745\) −8.62967 −0.316167
\(746\) 32.0732 1.17428
\(747\) 7.36907 0.269620
\(748\) 12.8270 0.469003
\(749\) −13.5492 −0.495079
\(750\) 30.6447 1.11899
\(751\) −10.3788 −0.378729 −0.189365 0.981907i \(-0.560643\pi\)
−0.189365 + 0.981907i \(0.560643\pi\)
\(752\) 49.9442 1.82128
\(753\) 11.4885 0.418664
\(754\) −25.7802 −0.938861
\(755\) 34.9786 1.27300
\(756\) 16.1986 0.589137
\(757\) 50.9710 1.85257 0.926286 0.376821i \(-0.122983\pi\)
0.926286 + 0.376821i \(0.122983\pi\)
\(758\) −65.9299 −2.39468
\(759\) −10.4742 −0.380189
\(760\) −32.9562 −1.19545
\(761\) 16.7766 0.608151 0.304075 0.952648i \(-0.401653\pi\)
0.304075 + 0.952648i \(0.401653\pi\)
\(762\) 40.5666 1.46957
\(763\) −72.4452 −2.62269
\(764\) 22.9919 0.831818
\(765\) 1.87454 0.0677740
\(766\) 43.8112 1.58296
\(767\) 22.8666 0.825666
\(768\) 31.3827 1.13243
\(769\) 12.7734 0.460619 0.230310 0.973117i \(-0.426026\pi\)
0.230310 + 0.973117i \(0.426026\pi\)
\(770\) 51.8168 1.86735
\(771\) 7.47709 0.269281
\(772\) −12.9474 −0.465989
\(773\) −26.7526 −0.962224 −0.481112 0.876659i \(-0.659767\pi\)
−0.481112 + 0.876659i \(0.659767\pi\)
\(774\) −1.36797 −0.0491708
\(775\) 2.47463 0.0888914
\(776\) 38.7504 1.39106
\(777\) 0.684868 0.0245695
\(778\) 25.7683 0.923837
\(779\) −35.6050 −1.27568
\(780\) −39.1959 −1.40344
\(781\) −1.92194 −0.0687723
\(782\) −8.95825 −0.320346
\(783\) 2.12919 0.0760912
\(784\) 42.7452 1.52662
\(785\) 1.87454 0.0669051
\(786\) 24.0565 0.858068
\(787\) 30.0905 1.07261 0.536305 0.844024i \(-0.319820\pi\)
0.536305 + 0.844024i \(0.319820\pi\)
\(788\) −105.968 −3.77497
\(789\) −1.86511 −0.0663995
\(790\) 28.0149 0.996727
\(791\) 48.8552 1.73709
\(792\) 17.4745 0.620930
\(793\) 42.6472 1.51445
\(794\) 46.1024 1.63611
\(795\) 10.8220 0.383817
\(796\) 75.5584 2.67810
\(797\) 27.2747 0.966120 0.483060 0.875587i \(-0.339525\pi\)
0.483060 + 0.875587i \(0.339525\pi\)
\(798\) 27.8109 0.984494
\(799\) −8.00368 −0.283150
\(800\) 5.74917 0.203264
\(801\) 13.2204 0.467119
\(802\) −57.8898 −2.04416
\(803\) 31.4218 1.10885
\(804\) −27.7406 −0.978337
\(805\) −24.7951 −0.873912
\(806\) −20.1619 −0.710171
\(807\) −29.4837 −1.03788
\(808\) −18.1674 −0.639125
\(809\) −11.4849 −0.403789 −0.201894 0.979407i \(-0.564710\pi\)
−0.201894 + 0.979407i \(0.564710\pi\)
\(810\) 4.72466 0.166008
\(811\) 47.8148 1.67901 0.839503 0.543355i \(-0.182846\pi\)
0.839503 + 0.543355i \(0.182846\pi\)
\(812\) 34.4900 1.21036
\(813\) −18.5631 −0.651035
\(814\) 1.36689 0.0479093
\(815\) 17.5415 0.614452
\(816\) 6.24016 0.218449
\(817\) −1.60921 −0.0562992
\(818\) −7.62009 −0.266430
\(819\) 17.8780 0.624710
\(820\) −97.9818 −3.42167
\(821\) −16.3535 −0.570741 −0.285370 0.958417i \(-0.592117\pi\)
−0.285370 + 0.958417i \(0.592117\pi\)
\(822\) −12.3675 −0.431367
\(823\) 3.95095 0.137721 0.0688607 0.997626i \(-0.478064\pi\)
0.0688607 + 0.997626i \(0.478064\pi\)
\(824\) 11.1305 0.387748
\(825\) −4.37951 −0.152475
\(826\) −44.6488 −1.55353
\(827\) −42.7224 −1.48560 −0.742801 0.669512i \(-0.766503\pi\)
−0.742801 + 0.669512i \(0.766503\pi\)
\(828\) −15.4703 −0.537630
\(829\) −3.02966 −0.105225 −0.0526123 0.998615i \(-0.516755\pi\)
−0.0526123 + 0.998615i \(0.516755\pi\)
\(830\) 34.8164 1.20849
\(831\) −19.9779 −0.693026
\(832\) 13.1134 0.454625
\(833\) −6.85003 −0.237339
\(834\) 36.6014 1.26740
\(835\) 17.2407 0.596638
\(836\) 38.0311 1.31533
\(837\) 1.66517 0.0575567
\(838\) 2.24912 0.0776946
\(839\) −8.76015 −0.302434 −0.151217 0.988501i \(-0.548319\pi\)
−0.151217 + 0.988501i \(0.548319\pi\)
\(840\) 41.3667 1.42729
\(841\) −24.4665 −0.843674
\(842\) −61.3295 −2.11355
\(843\) 19.7369 0.679774
\(844\) 41.1637 1.41691
\(845\) −18.8907 −0.649860
\(846\) −20.1728 −0.693556
\(847\) 8.61702 0.296084
\(848\) 36.0254 1.23712
\(849\) 15.7621 0.540952
\(850\) −3.74566 −0.128475
\(851\) −0.654075 −0.0224214
\(852\) −2.83868 −0.0972517
\(853\) −23.1819 −0.793732 −0.396866 0.917877i \(-0.629902\pi\)
−0.396866 + 0.917877i \(0.629902\pi\)
\(854\) −83.2718 −2.84950
\(855\) 5.55784 0.190074
\(856\) −21.5884 −0.737877
\(857\) −49.0605 −1.67587 −0.837937 0.545767i \(-0.816239\pi\)
−0.837937 + 0.545767i \(0.816239\pi\)
\(858\) 35.6817 1.21815
\(859\) −27.5243 −0.939118 −0.469559 0.882901i \(-0.655587\pi\)
−0.469559 + 0.882901i \(0.655587\pi\)
\(860\) −4.42840 −0.151007
\(861\) 44.6915 1.52308
\(862\) −23.7568 −0.809160
\(863\) 6.70822 0.228351 0.114175 0.993461i \(-0.463577\pi\)
0.114175 + 0.993461i \(0.463577\pi\)
\(864\) 3.86860 0.131612
\(865\) 33.6066 1.14266
\(866\) 18.3858 0.624774
\(867\) −1.00000 −0.0339618
\(868\) 26.9734 0.915538
\(869\) −17.4740 −0.592766
\(870\) 10.0597 0.341057
\(871\) −30.6168 −1.03741
\(872\) −115.429 −3.90893
\(873\) −6.53499 −0.221176
\(874\) −26.5605 −0.898421
\(875\) −45.2485 −1.52968
\(876\) 46.4098 1.56804
\(877\) 24.1639 0.815957 0.407979 0.912991i \(-0.366234\pi\)
0.407979 + 0.912991i \(0.366234\pi\)
\(878\) −34.7219 −1.17181
\(879\) −16.1592 −0.545035
\(880\) 34.4718 1.16204
\(881\) 21.3942 0.720790 0.360395 0.932800i \(-0.382642\pi\)
0.360395 + 0.932800i \(0.382642\pi\)
\(882\) −17.2651 −0.581346
\(883\) 15.5395 0.522947 0.261474 0.965211i \(-0.415792\pi\)
0.261474 + 0.965211i \(0.415792\pi\)
\(884\) 20.9097 0.703268
\(885\) −8.92280 −0.299937
\(886\) 8.73853 0.293577
\(887\) 28.3488 0.951858 0.475929 0.879484i \(-0.342112\pi\)
0.475929 + 0.879484i \(0.342112\pi\)
\(888\) 1.09122 0.0366190
\(889\) −59.8987 −2.00894
\(890\) 62.4619 2.09373
\(891\) −2.94696 −0.0987268
\(892\) −126.011 −4.21917
\(893\) −23.7302 −0.794102
\(894\) 11.6032 0.388069
\(895\) 13.1449 0.439386
\(896\) −54.3993 −1.81735
\(897\) −17.0742 −0.570092
\(898\) 26.2722 0.876713
\(899\) 3.54547 0.118248
\(900\) −6.46851 −0.215617
\(901\) −5.77316 −0.192332
\(902\) 89.1970 2.96993
\(903\) 2.01988 0.0672175
\(904\) 77.8425 2.58900
\(905\) 29.9510 0.995605
\(906\) −47.0312 −1.56251
\(907\) −47.6943 −1.58366 −0.791832 0.610739i \(-0.790873\pi\)
−0.791832 + 0.610739i \(0.790873\pi\)
\(908\) 33.0888 1.09809
\(909\) 3.06380 0.101620
\(910\) 84.4677 2.80008
\(911\) 53.2038 1.76272 0.881360 0.472446i \(-0.156629\pi\)
0.881360 + 0.472446i \(0.156629\pi\)
\(912\) 18.5015 0.612647
\(913\) −21.7164 −0.718707
\(914\) −67.0049 −2.21633
\(915\) −16.6414 −0.550148
\(916\) 59.2818 1.95873
\(917\) −35.5207 −1.17300
\(918\) −2.52044 −0.0831870
\(919\) −49.1423 −1.62106 −0.810528 0.585700i \(-0.800820\pi\)
−0.810528 + 0.585700i \(0.800820\pi\)
\(920\) −39.5068 −1.30250
\(921\) −22.9476 −0.756151
\(922\) −82.9358 −2.73135
\(923\) −3.13299 −0.103124
\(924\) −47.7366 −1.57042
\(925\) −0.273485 −0.00899212
\(926\) −59.2961 −1.94859
\(927\) −1.87708 −0.0616512
\(928\) 8.23699 0.270393
\(929\) −8.68961 −0.285097 −0.142548 0.989788i \(-0.545530\pi\)
−0.142548 + 0.989788i \(0.545530\pi\)
\(930\) 7.86737 0.257981
\(931\) −20.3098 −0.665625
\(932\) −20.3447 −0.666414
\(933\) −28.3295 −0.927467
\(934\) −7.57960 −0.248012
\(935\) −5.52418 −0.180660
\(936\) 28.4856 0.931083
\(937\) −48.0327 −1.56916 −0.784580 0.620027i \(-0.787121\pi\)
−0.784580 + 0.620027i \(0.787121\pi\)
\(938\) 59.7815 1.95193
\(939\) 12.2451 0.399604
\(940\) −65.3034 −2.12996
\(941\) −51.7791 −1.68795 −0.843975 0.536383i \(-0.819790\pi\)
−0.843975 + 0.536383i \(0.819790\pi\)
\(942\) −2.52044 −0.0821205
\(943\) −42.6821 −1.38992
\(944\) −29.7032 −0.966756
\(945\) −6.97620 −0.226936
\(946\) 4.03137 0.131071
\(947\) 18.6060 0.604614 0.302307 0.953211i \(-0.402243\pi\)
0.302307 + 0.953211i \(0.402243\pi\)
\(948\) −25.8090 −0.838237
\(949\) 51.2215 1.66272
\(950\) −11.1056 −0.360312
\(951\) −8.74468 −0.283566
\(952\) −22.0677 −0.715218
\(953\) 3.94458 0.127778 0.0638888 0.997957i \(-0.479650\pi\)
0.0638888 + 0.997957i \(0.479650\pi\)
\(954\) −14.5509 −0.471103
\(955\) −9.90185 −0.320416
\(956\) 109.867 3.55336
\(957\) −6.27465 −0.202831
\(958\) −9.78448 −0.316122
\(959\) 18.2613 0.589687
\(960\) −5.11698 −0.165150
\(961\) −28.2272 −0.910555
\(962\) 2.22819 0.0718399
\(963\) 3.64074 0.117321
\(964\) −41.2452 −1.32842
\(965\) 5.57604 0.179499
\(966\) 33.3387 1.07265
\(967\) 10.6783 0.343392 0.171696 0.985150i \(-0.445075\pi\)
0.171696 + 0.985150i \(0.445075\pi\)
\(968\) 13.7298 0.441292
\(969\) −2.96492 −0.0952468
\(970\) −30.8756 −0.991357
\(971\) −10.0143 −0.321374 −0.160687 0.987005i \(-0.551371\pi\)
−0.160687 + 0.987005i \(0.551371\pi\)
\(972\) −4.35263 −0.139611
\(973\) −54.0438 −1.73256
\(974\) 61.0548 1.95632
\(975\) −7.13915 −0.228636
\(976\) −55.3976 −1.77324
\(977\) −45.4519 −1.45413 −0.727067 0.686566i \(-0.759117\pi\)
−0.727067 + 0.686566i \(0.759117\pi\)
\(978\) −23.5857 −0.754189
\(979\) −38.9599 −1.24517
\(980\) −55.8906 −1.78536
\(981\) 19.4663 0.621513
\(982\) −22.7160 −0.724897
\(983\) 27.0407 0.862465 0.431233 0.902241i \(-0.358079\pi\)
0.431233 + 0.902241i \(0.358079\pi\)
\(984\) 71.2083 2.27004
\(985\) 45.6371 1.45412
\(986\) −5.36651 −0.170905
\(987\) 29.7862 0.948105
\(988\) 61.9954 1.97234
\(989\) −1.92907 −0.0613408
\(990\) −13.9234 −0.442514
\(991\) −4.95423 −0.157376 −0.0786881 0.996899i \(-0.525073\pi\)
−0.0786881 + 0.996899i \(0.525073\pi\)
\(992\) 6.44188 0.204530
\(993\) 7.30026 0.231667
\(994\) 6.11740 0.194032
\(995\) −32.5405 −1.03160
\(996\) −32.0749 −1.01633
\(997\) 22.5256 0.713394 0.356697 0.934220i \(-0.383903\pi\)
0.356697 + 0.934220i \(0.383903\pi\)
\(998\) −4.19016 −0.132637
\(999\) −0.184027 −0.00582235
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.1.3 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.3 48 1.1 even 1 trivial