Properties

Label 8003.2.a.b.1.7
Level 8003
Weight 2
Character 8003.1
Self dual yes
Analytic conductor 63.904
Analytic rank 1
Dimension 153
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.55787 q^{2} -0.498344 q^{3} +4.54269 q^{4} +3.86602 q^{5} +1.27470 q^{6} -1.47646 q^{7} -6.50388 q^{8} -2.75165 q^{9} +O(q^{10})\) \(q-2.55787 q^{2} -0.498344 q^{3} +4.54269 q^{4} +3.86602 q^{5} +1.27470 q^{6} -1.47646 q^{7} -6.50388 q^{8} -2.75165 q^{9} -9.88878 q^{10} +3.73534 q^{11} -2.26382 q^{12} +2.20288 q^{13} +3.77659 q^{14} -1.92661 q^{15} +7.55068 q^{16} -5.19471 q^{17} +7.03837 q^{18} +3.91132 q^{19} +17.5622 q^{20} +0.735785 q^{21} -9.55450 q^{22} +1.19239 q^{23} +3.24117 q^{24} +9.94613 q^{25} -5.63468 q^{26} +2.86630 q^{27} -6.70710 q^{28} -0.523105 q^{29} +4.92801 q^{30} -10.1374 q^{31} -6.30589 q^{32} -1.86148 q^{33} +13.2874 q^{34} -5.70803 q^{35} -12.4999 q^{36} +1.39561 q^{37} -10.0047 q^{38} -1.09779 q^{39} -25.1441 q^{40} -5.31569 q^{41} -1.88204 q^{42} -3.78237 q^{43} +16.9685 q^{44} -10.6380 q^{45} -3.04997 q^{46} +2.79800 q^{47} -3.76283 q^{48} -4.82007 q^{49} -25.4409 q^{50} +2.58875 q^{51} +10.0070 q^{52} -1.00000 q^{53} -7.33162 q^{54} +14.4409 q^{55} +9.60271 q^{56} -1.94918 q^{57} +1.33803 q^{58} -6.75570 q^{59} -8.75199 q^{60} -0.471212 q^{61} +25.9301 q^{62} +4.06270 q^{63} +1.02828 q^{64} +8.51639 q^{65} +4.76143 q^{66} -8.90921 q^{67} -23.5980 q^{68} -0.594220 q^{69} +14.6004 q^{70} -3.84201 q^{71} +17.8964 q^{72} -4.56953 q^{73} -3.56980 q^{74} -4.95660 q^{75} +17.7679 q^{76} -5.51507 q^{77} +2.80801 q^{78} +11.4530 q^{79} +29.1911 q^{80} +6.82656 q^{81} +13.5968 q^{82} -0.252093 q^{83} +3.34244 q^{84} -20.0829 q^{85} +9.67480 q^{86} +0.260686 q^{87} -24.2942 q^{88} -6.37869 q^{89} +27.2105 q^{90} -3.25246 q^{91} +5.41666 q^{92} +5.05190 q^{93} -7.15691 q^{94} +15.1213 q^{95} +3.14250 q^{96} +5.29260 q^{97} +12.3291 q^{98} -10.2784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55787 −1.80869 −0.904343 0.426806i \(-0.859639\pi\)
−0.904343 + 0.426806i \(0.859639\pi\)
\(3\) −0.498344 −0.287719 −0.143859 0.989598i \(-0.545951\pi\)
−0.143859 + 0.989598i \(0.545951\pi\)
\(4\) 4.54269 2.27135
\(5\) 3.86602 1.72894 0.864469 0.502686i \(-0.167655\pi\)
0.864469 + 0.502686i \(0.167655\pi\)
\(6\) 1.27470 0.520393
\(7\) −1.47646 −0.558049 −0.279025 0.960284i \(-0.590011\pi\)
−0.279025 + 0.960284i \(0.590011\pi\)
\(8\) −6.50388 −2.29947
\(9\) −2.75165 −0.917218
\(10\) −9.88878 −3.12711
\(11\) 3.73534 1.12625 0.563123 0.826373i \(-0.309600\pi\)
0.563123 + 0.826373i \(0.309600\pi\)
\(12\) −2.26382 −0.653510
\(13\) 2.20288 0.610969 0.305485 0.952197i \(-0.401182\pi\)
0.305485 + 0.952197i \(0.401182\pi\)
\(14\) 3.77659 1.00934
\(15\) −1.92661 −0.497448
\(16\) 7.55068 1.88767
\(17\) −5.19471 −1.25990 −0.629951 0.776635i \(-0.716925\pi\)
−0.629951 + 0.776635i \(0.716925\pi\)
\(18\) 7.03837 1.65896
\(19\) 3.91132 0.897319 0.448660 0.893703i \(-0.351902\pi\)
0.448660 + 0.893703i \(0.351902\pi\)
\(20\) 17.5622 3.92702
\(21\) 0.735785 0.160561
\(22\) −9.55450 −2.03703
\(23\) 1.19239 0.248630 0.124315 0.992243i \(-0.460327\pi\)
0.124315 + 0.992243i \(0.460327\pi\)
\(24\) 3.24117 0.661600
\(25\) 9.94613 1.98923
\(26\) −5.63468 −1.10505
\(27\) 2.86630 0.551620
\(28\) −6.70710 −1.26752
\(29\) −0.523105 −0.0971381 −0.0485690 0.998820i \(-0.515466\pi\)
−0.0485690 + 0.998820i \(0.515466\pi\)
\(30\) 4.92801 0.899728
\(31\) −10.1374 −1.82073 −0.910364 0.413809i \(-0.864198\pi\)
−0.910364 + 0.413809i \(0.864198\pi\)
\(32\) −6.30589 −1.11473
\(33\) −1.86148 −0.324042
\(34\) 13.2874 2.27877
\(35\) −5.70803 −0.964832
\(36\) −12.4999 −2.08332
\(37\) 1.39561 0.229437 0.114719 0.993398i \(-0.463403\pi\)
0.114719 + 0.993398i \(0.463403\pi\)
\(38\) −10.0047 −1.62297
\(39\) −1.09779 −0.175787
\(40\) −25.1441 −3.97564
\(41\) −5.31569 −0.830172 −0.415086 0.909782i \(-0.636248\pi\)
−0.415086 + 0.909782i \(0.636248\pi\)
\(42\) −1.88204 −0.290405
\(43\) −3.78237 −0.576805 −0.288403 0.957509i \(-0.593124\pi\)
−0.288403 + 0.957509i \(0.593124\pi\)
\(44\) 16.9685 2.55810
\(45\) −10.6380 −1.58581
\(46\) −3.04997 −0.449694
\(47\) 2.79800 0.408130 0.204065 0.978957i \(-0.434585\pi\)
0.204065 + 0.978957i \(0.434585\pi\)
\(48\) −3.76283 −0.543118
\(49\) −4.82007 −0.688581
\(50\) −25.4409 −3.59789
\(51\) 2.58875 0.362498
\(52\) 10.0070 1.38772
\(53\) −1.00000 −0.137361
\(54\) −7.33162 −0.997708
\(55\) 14.4409 1.94721
\(56\) 9.60271 1.28322
\(57\) −1.94918 −0.258176
\(58\) 1.33803 0.175692
\(59\) −6.75570 −0.879517 −0.439759 0.898116i \(-0.644936\pi\)
−0.439759 + 0.898116i \(0.644936\pi\)
\(60\) −8.75199 −1.12988
\(61\) −0.471212 −0.0603325 −0.0301662 0.999545i \(-0.509604\pi\)
−0.0301662 + 0.999545i \(0.509604\pi\)
\(62\) 25.9301 3.29312
\(63\) 4.06270 0.511853
\(64\) 1.02828 0.128535
\(65\) 8.51639 1.05633
\(66\) 4.76143 0.586091
\(67\) −8.90921 −1.08843 −0.544216 0.838945i \(-0.683173\pi\)
−0.544216 + 0.838945i \(0.683173\pi\)
\(68\) −23.5980 −2.86167
\(69\) −0.594220 −0.0715357
\(70\) 14.6004 1.74508
\(71\) −3.84201 −0.455962 −0.227981 0.973666i \(-0.573212\pi\)
−0.227981 + 0.973666i \(0.573212\pi\)
\(72\) 17.8964 2.10911
\(73\) −4.56953 −0.534823 −0.267411 0.963582i \(-0.586168\pi\)
−0.267411 + 0.963582i \(0.586168\pi\)
\(74\) −3.56980 −0.414980
\(75\) −4.95660 −0.572338
\(76\) 17.7679 2.03812
\(77\) −5.51507 −0.628501
\(78\) 2.80801 0.317944
\(79\) 11.4530 1.28856 0.644279 0.764790i \(-0.277157\pi\)
0.644279 + 0.764790i \(0.277157\pi\)
\(80\) 29.1911 3.26366
\(81\) 6.82656 0.758506
\(82\) 13.5968 1.50152
\(83\) −0.252093 −0.0276709 −0.0138354 0.999904i \(-0.504404\pi\)
−0.0138354 + 0.999904i \(0.504404\pi\)
\(84\) 3.34244 0.364690
\(85\) −20.0829 −2.17829
\(86\) 9.67480 1.04326
\(87\) 0.260686 0.0279485
\(88\) −24.2942 −2.58977
\(89\) −6.37869 −0.676139 −0.338070 0.941121i \(-0.609774\pi\)
−0.338070 + 0.941121i \(0.609774\pi\)
\(90\) 27.2105 2.86824
\(91\) −3.25246 −0.340951
\(92\) 5.41666 0.564726
\(93\) 5.05190 0.523858
\(94\) −7.15691 −0.738179
\(95\) 15.1213 1.55141
\(96\) 3.14250 0.320730
\(97\) 5.29260 0.537382 0.268691 0.963226i \(-0.413409\pi\)
0.268691 + 0.963226i \(0.413409\pi\)
\(98\) 12.3291 1.24543
\(99\) −10.2784 −1.03301
\(100\) 45.1822 4.51822
\(101\) 14.6039 1.45314 0.726572 0.687091i \(-0.241113\pi\)
0.726572 + 0.687091i \(0.241113\pi\)
\(102\) −6.62168 −0.655644
\(103\) −0.942775 −0.0928944 −0.0464472 0.998921i \(-0.514790\pi\)
−0.0464472 + 0.998921i \(0.514790\pi\)
\(104\) −14.3273 −1.40490
\(105\) 2.84456 0.277601
\(106\) 2.55787 0.248442
\(107\) −11.9403 −1.15431 −0.577155 0.816634i \(-0.695837\pi\)
−0.577155 + 0.816634i \(0.695837\pi\)
\(108\) 13.0207 1.25292
\(109\) −1.38902 −0.133044 −0.0665220 0.997785i \(-0.521190\pi\)
−0.0665220 + 0.997785i \(0.521190\pi\)
\(110\) −36.9379 −3.52189
\(111\) −0.695496 −0.0660135
\(112\) −11.1483 −1.05341
\(113\) 2.74152 0.257900 0.128950 0.991651i \(-0.458839\pi\)
0.128950 + 0.991651i \(0.458839\pi\)
\(114\) 4.98576 0.466959
\(115\) 4.60980 0.429866
\(116\) −2.37630 −0.220634
\(117\) −6.06156 −0.560392
\(118\) 17.2802 1.59077
\(119\) 7.66977 0.703087
\(120\) 12.5304 1.14387
\(121\) 2.95274 0.268431
\(122\) 1.20530 0.109123
\(123\) 2.64904 0.238856
\(124\) −46.0510 −4.13550
\(125\) 19.1219 1.71031
\(126\) −10.3919 −0.925781
\(127\) −2.21926 −0.196927 −0.0984636 0.995141i \(-0.531393\pi\)
−0.0984636 + 0.995141i \(0.531393\pi\)
\(128\) 9.98157 0.882254
\(129\) 1.88492 0.165958
\(130\) −21.7838 −1.91057
\(131\) −18.2513 −1.59463 −0.797313 0.603566i \(-0.793746\pi\)
−0.797313 + 0.603566i \(0.793746\pi\)
\(132\) −8.45614 −0.736013
\(133\) −5.77491 −0.500748
\(134\) 22.7886 1.96863
\(135\) 11.0812 0.953717
\(136\) 33.7857 2.89710
\(137\) −9.32578 −0.796755 −0.398378 0.917221i \(-0.630427\pi\)
−0.398378 + 0.917221i \(0.630427\pi\)
\(138\) 1.51994 0.129386
\(139\) 17.3178 1.46888 0.734439 0.678675i \(-0.237445\pi\)
0.734439 + 0.678675i \(0.237445\pi\)
\(140\) −25.9298 −2.19147
\(141\) −1.39437 −0.117427
\(142\) 9.82735 0.824693
\(143\) 8.22850 0.688102
\(144\) −20.7768 −1.73140
\(145\) −2.02233 −0.167946
\(146\) 11.6883 0.967327
\(147\) 2.40205 0.198118
\(148\) 6.33985 0.521132
\(149\) 1.73880 0.142448 0.0712241 0.997460i \(-0.477309\pi\)
0.0712241 + 0.997460i \(0.477309\pi\)
\(150\) 12.6783 1.03518
\(151\) −1.00000 −0.0813788
\(152\) −25.4388 −2.06336
\(153\) 14.2940 1.15560
\(154\) 14.1068 1.13676
\(155\) −39.1913 −3.14792
\(156\) −4.98693 −0.399274
\(157\) −17.6203 −1.40625 −0.703125 0.711066i \(-0.748213\pi\)
−0.703125 + 0.711066i \(0.748213\pi\)
\(158\) −29.2952 −2.33060
\(159\) 0.498344 0.0395212
\(160\) −24.3787 −1.92731
\(161\) −1.76051 −0.138748
\(162\) −17.4614 −1.37190
\(163\) −22.0972 −1.73079 −0.865394 0.501092i \(-0.832932\pi\)
−0.865394 + 0.501092i \(0.832932\pi\)
\(164\) −24.1476 −1.88561
\(165\) −7.19653 −0.560249
\(166\) 0.644822 0.0500479
\(167\) −24.1689 −1.87024 −0.935121 0.354329i \(-0.884709\pi\)
−0.935121 + 0.354329i \(0.884709\pi\)
\(168\) −4.78545 −0.369206
\(169\) −8.14732 −0.626717
\(170\) 51.3693 3.93985
\(171\) −10.7626 −0.823037
\(172\) −17.1821 −1.31013
\(173\) −14.3251 −1.08912 −0.544560 0.838722i \(-0.683304\pi\)
−0.544560 + 0.838722i \(0.683304\pi\)
\(174\) −0.666801 −0.0505500
\(175\) −14.6851 −1.11009
\(176\) 28.2043 2.12598
\(177\) 3.36666 0.253054
\(178\) 16.3158 1.22292
\(179\) 13.9938 1.04594 0.522972 0.852350i \(-0.324823\pi\)
0.522972 + 0.852350i \(0.324823\pi\)
\(180\) −48.3250 −3.60193
\(181\) −5.43395 −0.403902 −0.201951 0.979396i \(-0.564728\pi\)
−0.201951 + 0.979396i \(0.564728\pi\)
\(182\) 8.31938 0.616673
\(183\) 0.234826 0.0173588
\(184\) −7.75515 −0.571717
\(185\) 5.39547 0.396683
\(186\) −12.9221 −0.947495
\(187\) −19.4040 −1.41896
\(188\) 12.7105 0.927005
\(189\) −4.23198 −0.307831
\(190\) −38.6782 −2.80601
\(191\) 7.15902 0.518008 0.259004 0.965876i \(-0.416606\pi\)
0.259004 + 0.965876i \(0.416606\pi\)
\(192\) −0.512438 −0.0369820
\(193\) −1.55393 −0.111854 −0.0559272 0.998435i \(-0.517811\pi\)
−0.0559272 + 0.998435i \(0.517811\pi\)
\(194\) −13.5378 −0.971956
\(195\) −4.24409 −0.303926
\(196\) −21.8961 −1.56401
\(197\) 0.380963 0.0271425 0.0135712 0.999908i \(-0.495680\pi\)
0.0135712 + 0.999908i \(0.495680\pi\)
\(198\) 26.2907 1.86840
\(199\) 4.01035 0.284286 0.142143 0.989846i \(-0.454601\pi\)
0.142143 + 0.989846i \(0.454601\pi\)
\(200\) −64.6884 −4.57416
\(201\) 4.43985 0.313163
\(202\) −37.3549 −2.62828
\(203\) 0.772343 0.0542078
\(204\) 11.7599 0.823358
\(205\) −20.5506 −1.43532
\(206\) 2.41150 0.168017
\(207\) −3.28104 −0.228048
\(208\) 16.6332 1.15331
\(209\) 14.6101 1.01060
\(210\) −7.27601 −0.502092
\(211\) 12.8248 0.882895 0.441448 0.897287i \(-0.354465\pi\)
0.441448 + 0.897287i \(0.354465\pi\)
\(212\) −4.54269 −0.311993
\(213\) 1.91464 0.131189
\(214\) 30.5417 2.08779
\(215\) −14.6227 −0.997261
\(216\) −18.6421 −1.26843
\(217\) 14.9674 1.01606
\(218\) 3.55293 0.240635
\(219\) 2.27720 0.153879
\(220\) 65.6006 4.42279
\(221\) −11.4433 −0.769761
\(222\) 1.77899 0.119398
\(223\) 11.8414 0.792956 0.396478 0.918044i \(-0.370232\pi\)
0.396478 + 0.918044i \(0.370232\pi\)
\(224\) 9.31039 0.622076
\(225\) −27.3683 −1.82455
\(226\) −7.01244 −0.466460
\(227\) −15.1989 −1.00879 −0.504395 0.863473i \(-0.668284\pi\)
−0.504395 + 0.863473i \(0.668284\pi\)
\(228\) −8.85454 −0.586407
\(229\) −4.11371 −0.271842 −0.135921 0.990720i \(-0.543399\pi\)
−0.135921 + 0.990720i \(0.543399\pi\)
\(230\) −11.7913 −0.777493
\(231\) 2.74840 0.180832
\(232\) 3.40221 0.223366
\(233\) −11.2145 −0.734684 −0.367342 0.930086i \(-0.619732\pi\)
−0.367342 + 0.930086i \(0.619732\pi\)
\(234\) 15.5047 1.01357
\(235\) 10.8171 0.705632
\(236\) −30.6891 −1.99769
\(237\) −5.70751 −0.370743
\(238\) −19.6183 −1.27166
\(239\) 15.6200 1.01037 0.505186 0.863011i \(-0.331424\pi\)
0.505186 + 0.863011i \(0.331424\pi\)
\(240\) −14.5472 −0.939018
\(241\) −1.54545 −0.0995514 −0.0497757 0.998760i \(-0.515851\pi\)
−0.0497757 + 0.998760i \(0.515851\pi\)
\(242\) −7.55272 −0.485507
\(243\) −12.0009 −0.769857
\(244\) −2.14057 −0.137036
\(245\) −18.6345 −1.19051
\(246\) −6.77590 −0.432016
\(247\) 8.61618 0.548234
\(248\) 65.9323 4.18670
\(249\) 0.125629 0.00796143
\(250\) −48.9112 −3.09342
\(251\) −7.18530 −0.453532 −0.226766 0.973949i \(-0.572815\pi\)
−0.226766 + 0.973949i \(0.572815\pi\)
\(252\) 18.4556 1.16259
\(253\) 4.45397 0.280019
\(254\) 5.67657 0.356179
\(255\) 10.0082 0.626736
\(256\) −27.5881 −1.72426
\(257\) −0.575534 −0.0359008 −0.0179504 0.999839i \(-0.505714\pi\)
−0.0179504 + 0.999839i \(0.505714\pi\)
\(258\) −4.82138 −0.300166
\(259\) −2.06057 −0.128037
\(260\) 38.6873 2.39929
\(261\) 1.43940 0.0890968
\(262\) 46.6845 2.88418
\(263\) −12.6617 −0.780754 −0.390377 0.920655i \(-0.627655\pi\)
−0.390377 + 0.920655i \(0.627655\pi\)
\(264\) 12.1069 0.745125
\(265\) −3.86602 −0.237488
\(266\) 14.7715 0.905696
\(267\) 3.17878 0.194538
\(268\) −40.4718 −2.47221
\(269\) 17.2352 1.05085 0.525424 0.850840i \(-0.323907\pi\)
0.525424 + 0.850840i \(0.323907\pi\)
\(270\) −28.3442 −1.72497
\(271\) 18.9175 1.14916 0.574579 0.818449i \(-0.305166\pi\)
0.574579 + 0.818449i \(0.305166\pi\)
\(272\) −39.2235 −2.37828
\(273\) 1.62085 0.0980980
\(274\) 23.8541 1.44108
\(275\) 37.1522 2.24036
\(276\) −2.69936 −0.162482
\(277\) 6.10063 0.366551 0.183276 0.983062i \(-0.441330\pi\)
0.183276 + 0.983062i \(0.441330\pi\)
\(278\) −44.2967 −2.65674
\(279\) 27.8946 1.67000
\(280\) 37.1243 2.21860
\(281\) 6.83223 0.407577 0.203788 0.979015i \(-0.434675\pi\)
0.203788 + 0.979015i \(0.434675\pi\)
\(282\) 3.56660 0.212388
\(283\) −25.0753 −1.49057 −0.745286 0.666745i \(-0.767687\pi\)
−0.745286 + 0.666745i \(0.767687\pi\)
\(284\) −17.4531 −1.03565
\(285\) −7.53559 −0.446370
\(286\) −21.0474 −1.24456
\(287\) 7.84840 0.463277
\(288\) 17.3516 1.02245
\(289\) 9.98497 0.587351
\(290\) 5.17287 0.303761
\(291\) −2.63754 −0.154615
\(292\) −20.7580 −1.21477
\(293\) 0.848859 0.0495909 0.0247954 0.999693i \(-0.492107\pi\)
0.0247954 + 0.999693i \(0.492107\pi\)
\(294\) −6.14413 −0.358333
\(295\) −26.1177 −1.52063
\(296\) −9.07690 −0.527584
\(297\) 10.7066 0.621260
\(298\) −4.44763 −0.257644
\(299\) 2.62669 0.151905
\(300\) −22.5163 −1.29998
\(301\) 5.58451 0.321886
\(302\) 2.55787 0.147189
\(303\) −7.27777 −0.418097
\(304\) 29.5331 1.69384
\(305\) −1.82172 −0.104311
\(306\) −36.5623 −2.09013
\(307\) −15.5248 −0.886048 −0.443024 0.896510i \(-0.646094\pi\)
−0.443024 + 0.896510i \(0.646094\pi\)
\(308\) −25.0533 −1.42754
\(309\) 0.469826 0.0267275
\(310\) 100.246 5.69361
\(311\) 10.9980 0.623641 0.311821 0.950141i \(-0.399061\pi\)
0.311821 + 0.950141i \(0.399061\pi\)
\(312\) 7.13990 0.404217
\(313\) 4.16627 0.235492 0.117746 0.993044i \(-0.462433\pi\)
0.117746 + 0.993044i \(0.462433\pi\)
\(314\) 45.0703 2.54347
\(315\) 15.7065 0.884962
\(316\) 52.0273 2.92676
\(317\) −7.57168 −0.425268 −0.212634 0.977132i \(-0.568204\pi\)
−0.212634 + 0.977132i \(0.568204\pi\)
\(318\) −1.27470 −0.0714815
\(319\) −1.95397 −0.109401
\(320\) 3.97536 0.222229
\(321\) 5.95037 0.332117
\(322\) 4.50316 0.250951
\(323\) −20.3182 −1.13053
\(324\) 31.0110 1.72283
\(325\) 21.9101 1.21536
\(326\) 56.5218 3.13045
\(327\) 0.692210 0.0382793
\(328\) 34.5726 1.90895
\(329\) −4.13113 −0.227757
\(330\) 18.4078 1.01332
\(331\) −19.1549 −1.05285 −0.526424 0.850222i \(-0.676468\pi\)
−0.526424 + 0.850222i \(0.676468\pi\)
\(332\) −1.14518 −0.0628501
\(333\) −3.84025 −0.210444
\(334\) 61.8208 3.38268
\(335\) −34.4432 −1.88183
\(336\) 5.55567 0.303087
\(337\) 18.6914 1.01818 0.509092 0.860712i \(-0.329981\pi\)
0.509092 + 0.860712i \(0.329981\pi\)
\(338\) 20.8398 1.13353
\(339\) −1.36622 −0.0742027
\(340\) −91.2302 −4.94765
\(341\) −37.8665 −2.05059
\(342\) 27.5293 1.48862
\(343\) 17.4518 0.942311
\(344\) 24.6000 1.32635
\(345\) −2.29727 −0.123681
\(346\) 36.6419 1.96988
\(347\) 24.4392 1.31196 0.655982 0.754777i \(-0.272255\pi\)
0.655982 + 0.754777i \(0.272255\pi\)
\(348\) 1.18422 0.0634807
\(349\) 11.5737 0.619524 0.309762 0.950814i \(-0.399751\pi\)
0.309762 + 0.950814i \(0.399751\pi\)
\(350\) 37.5625 2.00780
\(351\) 6.31412 0.337023
\(352\) −23.5546 −1.25547
\(353\) −5.28568 −0.281328 −0.140664 0.990057i \(-0.544924\pi\)
−0.140664 + 0.990057i \(0.544924\pi\)
\(354\) −8.61148 −0.457695
\(355\) −14.8533 −0.788330
\(356\) −28.9764 −1.53575
\(357\) −3.82218 −0.202291
\(358\) −35.7942 −1.89178
\(359\) 12.9836 0.685248 0.342624 0.939473i \(-0.388684\pi\)
0.342624 + 0.939473i \(0.388684\pi\)
\(360\) 69.1879 3.64652
\(361\) −3.70155 −0.194819
\(362\) 13.8993 0.730532
\(363\) −1.47148 −0.0772327
\(364\) −14.7749 −0.774418
\(365\) −17.6659 −0.924676
\(366\) −0.600653 −0.0313966
\(367\) −23.4425 −1.22369 −0.611843 0.790979i \(-0.709572\pi\)
−0.611843 + 0.790979i \(0.709572\pi\)
\(368\) 9.00334 0.469332
\(369\) 14.6269 0.761448
\(370\) −13.8009 −0.717476
\(371\) 1.47646 0.0766540
\(372\) 22.9492 1.18986
\(373\) −22.4783 −1.16388 −0.581942 0.813230i \(-0.697707\pi\)
−0.581942 + 0.813230i \(0.697707\pi\)
\(374\) 49.6328 2.56645
\(375\) −9.52927 −0.492089
\(376\) −18.1978 −0.938482
\(377\) −1.15234 −0.0593484
\(378\) 10.8248 0.556770
\(379\) 5.91795 0.303985 0.151992 0.988382i \(-0.451431\pi\)
0.151992 + 0.988382i \(0.451431\pi\)
\(380\) 68.6913 3.52379
\(381\) 1.10595 0.0566597
\(382\) −18.3118 −0.936914
\(383\) 22.4080 1.14499 0.572497 0.819907i \(-0.305975\pi\)
0.572497 + 0.819907i \(0.305975\pi\)
\(384\) −4.97425 −0.253841
\(385\) −21.3214 −1.08664
\(386\) 3.97475 0.202310
\(387\) 10.4078 0.529056
\(388\) 24.0427 1.22058
\(389\) 17.7006 0.897454 0.448727 0.893669i \(-0.351877\pi\)
0.448727 + 0.893669i \(0.351877\pi\)
\(390\) 10.8558 0.549706
\(391\) −6.19411 −0.313250
\(392\) 31.3491 1.58337
\(393\) 9.09544 0.458804
\(394\) −0.974453 −0.0490922
\(395\) 44.2774 2.22784
\(396\) −46.6914 −2.34633
\(397\) −4.35991 −0.218818 −0.109409 0.993997i \(-0.534896\pi\)
−0.109409 + 0.993997i \(0.534896\pi\)
\(398\) −10.2579 −0.514184
\(399\) 2.87789 0.144075
\(400\) 75.1000 3.75500
\(401\) −35.7386 −1.78470 −0.892351 0.451343i \(-0.850945\pi\)
−0.892351 + 0.451343i \(0.850945\pi\)
\(402\) −11.3566 −0.566413
\(403\) −22.3314 −1.11241
\(404\) 66.3411 3.30059
\(405\) 26.3916 1.31141
\(406\) −1.97555 −0.0980450
\(407\) 5.21309 0.258403
\(408\) −16.8369 −0.833551
\(409\) −7.67047 −0.379281 −0.189640 0.981854i \(-0.560732\pi\)
−0.189640 + 0.981854i \(0.560732\pi\)
\(410\) 52.5657 2.59604
\(411\) 4.64745 0.229242
\(412\) −4.28274 −0.210995
\(413\) 9.97452 0.490814
\(414\) 8.39247 0.412468
\(415\) −0.974599 −0.0478412
\(416\) −13.8911 −0.681068
\(417\) −8.63023 −0.422624
\(418\) −37.3707 −1.82786
\(419\) 37.8057 1.84693 0.923464 0.383686i \(-0.125345\pi\)
0.923464 + 0.383686i \(0.125345\pi\)
\(420\) 12.9220 0.630527
\(421\) 18.9542 0.923770 0.461885 0.886940i \(-0.347173\pi\)
0.461885 + 0.886940i \(0.347173\pi\)
\(422\) −32.8041 −1.59688
\(423\) −7.69912 −0.374344
\(424\) 6.50388 0.315856
\(425\) −51.6672 −2.50623
\(426\) −4.89740 −0.237280
\(427\) 0.695725 0.0336685
\(428\) −54.2410 −2.62184
\(429\) −4.10062 −0.197980
\(430\) 37.4030 1.80373
\(431\) 37.0324 1.78379 0.891894 0.452244i \(-0.149376\pi\)
0.891894 + 0.452244i \(0.149376\pi\)
\(432\) 21.6425 1.04128
\(433\) −30.2702 −1.45469 −0.727347 0.686270i \(-0.759247\pi\)
−0.727347 + 0.686270i \(0.759247\pi\)
\(434\) −38.2847 −1.83773
\(435\) 1.00782 0.0483212
\(436\) −6.30990 −0.302189
\(437\) 4.66382 0.223101
\(438\) −5.82477 −0.278318
\(439\) 10.8536 0.518014 0.259007 0.965875i \(-0.416605\pi\)
0.259007 + 0.965875i \(0.416605\pi\)
\(440\) −93.9218 −4.47755
\(441\) 13.2632 0.631579
\(442\) 29.2705 1.39226
\(443\) −4.71355 −0.223947 −0.111974 0.993711i \(-0.535717\pi\)
−0.111974 + 0.993711i \(0.535717\pi\)
\(444\) −3.15942 −0.149940
\(445\) −24.6602 −1.16900
\(446\) −30.2886 −1.43421
\(447\) −0.866521 −0.0409850
\(448\) −1.51822 −0.0717290
\(449\) −36.2134 −1.70902 −0.854508 0.519439i \(-0.826141\pi\)
−0.854508 + 0.519439i \(0.826141\pi\)
\(450\) 70.0046 3.30005
\(451\) −19.8559 −0.934978
\(452\) 12.4539 0.585780
\(453\) 0.498344 0.0234142
\(454\) 38.8769 1.82458
\(455\) −12.5741 −0.589483
\(456\) 12.6773 0.593667
\(457\) −35.8642 −1.67766 −0.838829 0.544396i \(-0.816759\pi\)
−0.838829 + 0.544396i \(0.816759\pi\)
\(458\) 10.5223 0.491676
\(459\) −14.8896 −0.694987
\(460\) 20.9409 0.976376
\(461\) 5.46205 0.254393 0.127196 0.991878i \(-0.459402\pi\)
0.127196 + 0.991878i \(0.459402\pi\)
\(462\) −7.03005 −0.327068
\(463\) −19.4865 −0.905615 −0.452807 0.891608i \(-0.649578\pi\)
−0.452807 + 0.891608i \(0.649578\pi\)
\(464\) −3.94979 −0.183365
\(465\) 19.5308 0.905718
\(466\) 28.6851 1.32881
\(467\) 23.4282 1.08413 0.542063 0.840338i \(-0.317643\pi\)
0.542063 + 0.840338i \(0.317643\pi\)
\(468\) −27.5358 −1.27284
\(469\) 13.1541 0.607399
\(470\) −27.6688 −1.27627
\(471\) 8.78095 0.404605
\(472\) 43.9382 2.02242
\(473\) −14.1284 −0.649625
\(474\) 14.5991 0.670557
\(475\) 38.9025 1.78497
\(476\) 34.8414 1.59695
\(477\) 2.75165 0.125990
\(478\) −39.9538 −1.82745
\(479\) −12.6939 −0.580000 −0.290000 0.957027i \(-0.593655\pi\)
−0.290000 + 0.957027i \(0.593655\pi\)
\(480\) 12.1490 0.554523
\(481\) 3.07437 0.140179
\(482\) 3.95307 0.180057
\(483\) 0.877341 0.0399204
\(484\) 13.4134 0.609700
\(485\) 20.4613 0.929101
\(486\) 30.6967 1.39243
\(487\) 7.80000 0.353452 0.176726 0.984260i \(-0.443449\pi\)
0.176726 + 0.984260i \(0.443449\pi\)
\(488\) 3.06470 0.138733
\(489\) 11.0120 0.497980
\(490\) 47.6646 2.15327
\(491\) 20.8642 0.941587 0.470793 0.882243i \(-0.343968\pi\)
0.470793 + 0.882243i \(0.343968\pi\)
\(492\) 12.0338 0.542525
\(493\) 2.71737 0.122384
\(494\) −22.0391 −0.991584
\(495\) −39.7363 −1.78602
\(496\) −76.5441 −3.43693
\(497\) 5.67257 0.254449
\(498\) −0.321343 −0.0143997
\(499\) 9.37157 0.419529 0.209765 0.977752i \(-0.432730\pi\)
0.209765 + 0.977752i \(0.432730\pi\)
\(500\) 86.8648 3.88471
\(501\) 12.0444 0.538104
\(502\) 18.3791 0.820298
\(503\) 20.0239 0.892823 0.446411 0.894828i \(-0.352702\pi\)
0.446411 + 0.894828i \(0.352702\pi\)
\(504\) −26.4233 −1.17699
\(505\) 56.4590 2.51239
\(506\) −11.3927 −0.506466
\(507\) 4.06017 0.180318
\(508\) −10.0814 −0.447290
\(509\) 31.6688 1.40369 0.701847 0.712328i \(-0.252359\pi\)
0.701847 + 0.712328i \(0.252359\pi\)
\(510\) −25.5996 −1.13357
\(511\) 6.74672 0.298457
\(512\) 50.6036 2.23638
\(513\) 11.2110 0.494979
\(514\) 1.47214 0.0649333
\(515\) −3.64479 −0.160609
\(516\) 8.56261 0.376948
\(517\) 10.4515 0.459655
\(518\) 5.27066 0.231580
\(519\) 7.13885 0.313361
\(520\) −55.3895 −2.42899
\(521\) 6.52949 0.286062 0.143031 0.989718i \(-0.454315\pi\)
0.143031 + 0.989718i \(0.454315\pi\)
\(522\) −3.68180 −0.161148
\(523\) −13.5258 −0.591442 −0.295721 0.955274i \(-0.595560\pi\)
−0.295721 + 0.955274i \(0.595560\pi\)
\(524\) −82.9102 −3.62195
\(525\) 7.31821 0.319393
\(526\) 32.3870 1.41214
\(527\) 52.6607 2.29394
\(528\) −14.0555 −0.611685
\(529\) −21.5782 −0.938183
\(530\) 9.88878 0.429541
\(531\) 18.5893 0.806709
\(532\) −26.2336 −1.13737
\(533\) −11.7098 −0.507209
\(534\) −8.13090 −0.351859
\(535\) −46.1614 −1.99573
\(536\) 57.9444 2.50282
\(537\) −6.97371 −0.300938
\(538\) −44.0854 −1.90066
\(539\) −18.0046 −0.775512
\(540\) 50.3384 2.16622
\(541\) 3.39391 0.145916 0.0729579 0.997335i \(-0.476756\pi\)
0.0729579 + 0.997335i \(0.476756\pi\)
\(542\) −48.3885 −2.07847
\(543\) 2.70797 0.116210
\(544\) 32.7572 1.40445
\(545\) −5.36999 −0.230025
\(546\) −4.14591 −0.177429
\(547\) 37.1288 1.58751 0.793757 0.608235i \(-0.208122\pi\)
0.793757 + 0.608235i \(0.208122\pi\)
\(548\) −42.3642 −1.80971
\(549\) 1.29661 0.0553380
\(550\) −95.0304 −4.05211
\(551\) −2.04603 −0.0871638
\(552\) 3.86473 0.164494
\(553\) −16.9098 −0.719079
\(554\) −15.6046 −0.662976
\(555\) −2.68880 −0.114133
\(556\) 78.6695 3.33633
\(557\) 30.4257 1.28918 0.644589 0.764530i \(-0.277029\pi\)
0.644589 + 0.764530i \(0.277029\pi\)
\(558\) −71.3506 −3.02051
\(559\) −8.33210 −0.352410
\(560\) −43.0995 −1.82128
\(561\) 9.66985 0.408262
\(562\) −17.4760 −0.737179
\(563\) −12.8657 −0.542223 −0.271112 0.962548i \(-0.587391\pi\)
−0.271112 + 0.962548i \(0.587391\pi\)
\(564\) −6.33418 −0.266717
\(565\) 10.5988 0.445893
\(566\) 64.1393 2.69598
\(567\) −10.0791 −0.423284
\(568\) 24.9879 1.04847
\(569\) −13.2534 −0.555613 −0.277807 0.960637i \(-0.589607\pi\)
−0.277807 + 0.960637i \(0.589607\pi\)
\(570\) 19.2751 0.807343
\(571\) 2.86523 0.119906 0.0599530 0.998201i \(-0.480905\pi\)
0.0599530 + 0.998201i \(0.480905\pi\)
\(572\) 37.3796 1.56292
\(573\) −3.56765 −0.149041
\(574\) −20.0752 −0.837922
\(575\) 11.8597 0.494582
\(576\) −2.82947 −0.117895
\(577\) −44.6372 −1.85827 −0.929136 0.369738i \(-0.879447\pi\)
−0.929136 + 0.369738i \(0.879447\pi\)
\(578\) −25.5402 −1.06233
\(579\) 0.774392 0.0321826
\(580\) −9.18684 −0.381463
\(581\) 0.372206 0.0154417
\(582\) 6.74647 0.279650
\(583\) −3.73534 −0.154702
\(584\) 29.7196 1.22981
\(585\) −23.4341 −0.968883
\(586\) −2.17127 −0.0896944
\(587\) −32.7787 −1.35292 −0.676460 0.736479i \(-0.736487\pi\)
−0.676460 + 0.736479i \(0.736487\pi\)
\(588\) 10.9118 0.449994
\(589\) −39.6506 −1.63377
\(590\) 66.8056 2.75034
\(591\) −0.189851 −0.00780941
\(592\) 10.5378 0.433102
\(593\) 33.8525 1.39016 0.695079 0.718934i \(-0.255369\pi\)
0.695079 + 0.718934i \(0.255369\pi\)
\(594\) −27.3861 −1.12366
\(595\) 29.6515 1.21559
\(596\) 7.89884 0.323549
\(597\) −1.99853 −0.0817945
\(598\) −6.71873 −0.274749
\(599\) −7.30303 −0.298394 −0.149197 0.988807i \(-0.547669\pi\)
−0.149197 + 0.988807i \(0.547669\pi\)
\(600\) 32.2371 1.31607
\(601\) −17.2323 −0.702918 −0.351459 0.936203i \(-0.614314\pi\)
−0.351459 + 0.936203i \(0.614314\pi\)
\(602\) −14.2844 −0.582190
\(603\) 24.5151 0.998330
\(604\) −4.54269 −0.184840
\(605\) 11.4154 0.464100
\(606\) 18.6156 0.756206
\(607\) −33.3527 −1.35375 −0.676873 0.736100i \(-0.736665\pi\)
−0.676873 + 0.736100i \(0.736665\pi\)
\(608\) −24.6644 −1.00027
\(609\) −0.384892 −0.0155966
\(610\) 4.65971 0.188666
\(611\) 6.16366 0.249355
\(612\) 64.9334 2.62478
\(613\) 7.05887 0.285105 0.142553 0.989787i \(-0.454469\pi\)
0.142553 + 0.989787i \(0.454469\pi\)
\(614\) 39.7104 1.60258
\(615\) 10.2413 0.412967
\(616\) 35.8694 1.44522
\(617\) −28.4749 −1.14636 −0.573179 0.819430i \(-0.694290\pi\)
−0.573179 + 0.819430i \(0.694290\pi\)
\(618\) −1.20175 −0.0483416
\(619\) 2.07817 0.0835289 0.0417644 0.999127i \(-0.486702\pi\)
0.0417644 + 0.999127i \(0.486702\pi\)
\(620\) −178.034 −7.15003
\(621\) 3.41775 0.137149
\(622\) −28.1315 −1.12797
\(623\) 9.41787 0.377319
\(624\) −8.28907 −0.331828
\(625\) 24.1949 0.967796
\(626\) −10.6568 −0.425931
\(627\) −7.28086 −0.290769
\(628\) −80.0435 −3.19408
\(629\) −7.24980 −0.289069
\(630\) −40.1752 −1.60062
\(631\) 7.69549 0.306353 0.153176 0.988199i \(-0.451050\pi\)
0.153176 + 0.988199i \(0.451050\pi\)
\(632\) −74.4886 −2.96300
\(633\) −6.39116 −0.254026
\(634\) 19.3674 0.769176
\(635\) −8.57970 −0.340475
\(636\) 2.26382 0.0897664
\(637\) −10.6180 −0.420702
\(638\) 4.99800 0.197873
\(639\) 10.5719 0.418217
\(640\) 38.5890 1.52536
\(641\) −0.932262 −0.0368221 −0.0184111 0.999831i \(-0.505861\pi\)
−0.0184111 + 0.999831i \(0.505861\pi\)
\(642\) −15.2203 −0.600696
\(643\) 40.5834 1.60046 0.800228 0.599697i \(-0.204712\pi\)
0.800228 + 0.599697i \(0.204712\pi\)
\(644\) −7.99747 −0.315145
\(645\) 7.28714 0.286931
\(646\) 51.9712 2.04478
\(647\) 25.0302 0.984040 0.492020 0.870584i \(-0.336259\pi\)
0.492020 + 0.870584i \(0.336259\pi\)
\(648\) −44.3991 −1.74416
\(649\) −25.2348 −0.990553
\(650\) −56.0433 −2.19820
\(651\) −7.45893 −0.292338
\(652\) −100.381 −3.93122
\(653\) 43.0165 1.68336 0.841682 0.539973i \(-0.181566\pi\)
0.841682 + 0.539973i \(0.181566\pi\)
\(654\) −1.77058 −0.0692353
\(655\) −70.5600 −2.75701
\(656\) −40.1371 −1.56709
\(657\) 12.5738 0.490549
\(658\) 10.5669 0.411940
\(659\) 7.51317 0.292671 0.146336 0.989235i \(-0.453252\pi\)
0.146336 + 0.989235i \(0.453252\pi\)
\(660\) −32.6916 −1.27252
\(661\) −33.8268 −1.31571 −0.657854 0.753145i \(-0.728536\pi\)
−0.657854 + 0.753145i \(0.728536\pi\)
\(662\) 48.9957 1.90427
\(663\) 5.70271 0.221475
\(664\) 1.63958 0.0636282
\(665\) −22.3259 −0.865763
\(666\) 9.82284 0.380627
\(667\) −0.623744 −0.0241515
\(668\) −109.792 −4.24797
\(669\) −5.90107 −0.228148
\(670\) 88.1012 3.40365
\(671\) −1.76014 −0.0679493
\(672\) −4.63977 −0.178983
\(673\) −19.3024 −0.744052 −0.372026 0.928222i \(-0.621337\pi\)
−0.372026 + 0.928222i \(0.621337\pi\)
\(674\) −47.8100 −1.84157
\(675\) 28.5086 1.09730
\(676\) −37.0108 −1.42349
\(677\) 0.844994 0.0324758 0.0162379 0.999868i \(-0.494831\pi\)
0.0162379 + 0.999868i \(0.494831\pi\)
\(678\) 3.49460 0.134209
\(679\) −7.81431 −0.299886
\(680\) 130.616 5.00891
\(681\) 7.57430 0.290248
\(682\) 96.8576 3.70887
\(683\) −36.6169 −1.40111 −0.700553 0.713600i \(-0.747063\pi\)
−0.700553 + 0.713600i \(0.747063\pi\)
\(684\) −48.8912 −1.86940
\(685\) −36.0537 −1.37754
\(686\) −44.6395 −1.70435
\(687\) 2.05004 0.0782140
\(688\) −28.5594 −1.08882
\(689\) −2.20288 −0.0839231
\(690\) 5.87611 0.223700
\(691\) −1.03405 −0.0393371 −0.0196686 0.999807i \(-0.506261\pi\)
−0.0196686 + 0.999807i \(0.506261\pi\)
\(692\) −65.0748 −2.47377
\(693\) 15.1756 0.576472
\(694\) −62.5122 −2.37293
\(695\) 66.9511 2.53960
\(696\) −1.69547 −0.0642666
\(697\) 27.6135 1.04593
\(698\) −29.6039 −1.12053
\(699\) 5.58866 0.211383
\(700\) −66.7097 −2.52139
\(701\) −26.3603 −0.995615 −0.497807 0.867288i \(-0.665861\pi\)
−0.497807 + 0.867288i \(0.665861\pi\)
\(702\) −16.1507 −0.609569
\(703\) 5.45870 0.205879
\(704\) 3.84098 0.144762
\(705\) −5.39065 −0.203024
\(706\) 13.5201 0.508835
\(707\) −21.5621 −0.810925
\(708\) 15.2937 0.574773
\(709\) −42.7996 −1.60737 −0.803686 0.595054i \(-0.797131\pi\)
−0.803686 + 0.595054i \(0.797131\pi\)
\(710\) 37.9927 1.42584
\(711\) −31.5146 −1.18189
\(712\) 41.4862 1.55476
\(713\) −12.0877 −0.452688
\(714\) 9.77665 0.365882
\(715\) 31.8116 1.18969
\(716\) 63.5694 2.37570
\(717\) −7.78412 −0.290703
\(718\) −33.2103 −1.23940
\(719\) 1.29433 0.0482705 0.0241353 0.999709i \(-0.492317\pi\)
0.0241353 + 0.999709i \(0.492317\pi\)
\(720\) −80.3238 −2.99349
\(721\) 1.39197 0.0518397
\(722\) 9.46809 0.352366
\(723\) 0.770167 0.0286428
\(724\) −24.6847 −0.917401
\(725\) −5.20287 −0.193230
\(726\) 3.76385 0.139690
\(727\) −21.5499 −0.799242 −0.399621 0.916681i \(-0.630858\pi\)
−0.399621 + 0.916681i \(0.630858\pi\)
\(728\) 21.1536 0.784005
\(729\) −14.4991 −0.537004
\(730\) 45.1871 1.67245
\(731\) 19.6483 0.726718
\(732\) 1.06674 0.0394279
\(733\) 7.96269 0.294109 0.147054 0.989128i \(-0.453021\pi\)
0.147054 + 0.989128i \(0.453021\pi\)
\(734\) 59.9627 2.21326
\(735\) 9.28639 0.342534
\(736\) −7.51907 −0.277157
\(737\) −33.2789 −1.22584
\(738\) −37.4138 −1.37722
\(739\) 52.1757 1.91931 0.959657 0.281172i \(-0.0907232\pi\)
0.959657 + 0.281172i \(0.0907232\pi\)
\(740\) 24.5100 0.901005
\(741\) −4.29382 −0.157737
\(742\) −3.77659 −0.138643
\(743\) 4.07451 0.149479 0.0747396 0.997203i \(-0.476187\pi\)
0.0747396 + 0.997203i \(0.476187\pi\)
\(744\) −32.8569 −1.20459
\(745\) 6.72224 0.246284
\(746\) 57.4967 2.10510
\(747\) 0.693674 0.0253802
\(748\) −88.1463 −3.22295
\(749\) 17.6293 0.644162
\(750\) 24.3746 0.890035
\(751\) −10.9751 −0.400487 −0.200243 0.979746i \(-0.564173\pi\)
−0.200243 + 0.979746i \(0.564173\pi\)
\(752\) 21.1268 0.770415
\(753\) 3.58075 0.130490
\(754\) 2.94753 0.107343
\(755\) −3.86602 −0.140699
\(756\) −19.2246 −0.699191
\(757\) −12.2752 −0.446151 −0.223075 0.974801i \(-0.571610\pi\)
−0.223075 + 0.974801i \(0.571610\pi\)
\(758\) −15.1373 −0.549813
\(759\) −2.21961 −0.0805668
\(760\) −98.3468 −3.56741
\(761\) 17.2888 0.626717 0.313358 0.949635i \(-0.398546\pi\)
0.313358 + 0.949635i \(0.398546\pi\)
\(762\) −2.82888 −0.102480
\(763\) 2.05083 0.0742451
\(764\) 32.5212 1.17658
\(765\) 55.2611 1.99797
\(766\) −57.3166 −2.07093
\(767\) −14.8820 −0.537358
\(768\) 13.7484 0.496101
\(769\) 4.07055 0.146788 0.0733939 0.997303i \(-0.476617\pi\)
0.0733939 + 0.997303i \(0.476617\pi\)
\(770\) 54.5373 1.96539
\(771\) 0.286814 0.0103293
\(772\) −7.05903 −0.254060
\(773\) −26.0782 −0.937968 −0.468984 0.883207i \(-0.655380\pi\)
−0.468984 + 0.883207i \(0.655380\pi\)
\(774\) −26.6217 −0.956897
\(775\) −100.828 −3.62184
\(776\) −34.4224 −1.23569
\(777\) 1.02687 0.0368388
\(778\) −45.2757 −1.62321
\(779\) −20.7914 −0.744929
\(780\) −19.2796 −0.690320
\(781\) −14.3512 −0.513526
\(782\) 15.8437 0.566570
\(783\) −1.49938 −0.0535833
\(784\) −36.3948 −1.29981
\(785\) −68.1203 −2.43132
\(786\) −23.2649 −0.829833
\(787\) −46.0299 −1.64079 −0.820393 0.571799i \(-0.806246\pi\)
−0.820393 + 0.571799i \(0.806246\pi\)
\(788\) 1.73060 0.0616500
\(789\) 6.30988 0.224638
\(790\) −113.256 −4.02946
\(791\) −4.04774 −0.143921
\(792\) 66.8491 2.37538
\(793\) −1.03802 −0.0368613
\(794\) 11.1521 0.395772
\(795\) 1.92661 0.0683298
\(796\) 18.2178 0.645712
\(797\) −4.65884 −0.165025 −0.0825123 0.996590i \(-0.526294\pi\)
−0.0825123 + 0.996590i \(0.526294\pi\)
\(798\) −7.36127 −0.260586
\(799\) −14.5348 −0.514204
\(800\) −62.7192 −2.21746
\(801\) 17.5519 0.620167
\(802\) 91.4147 3.22796
\(803\) −17.0687 −0.602342
\(804\) 20.1689 0.711301
\(805\) −6.80619 −0.239887
\(806\) 57.1209 2.01200
\(807\) −8.58906 −0.302349
\(808\) −94.9820 −3.34146
\(809\) −45.4005 −1.59620 −0.798098 0.602527i \(-0.794160\pi\)
−0.798098 + 0.602527i \(0.794160\pi\)
\(810\) −67.5063 −2.37193
\(811\) −46.3228 −1.62661 −0.813306 0.581836i \(-0.802335\pi\)
−0.813306 + 0.581836i \(0.802335\pi\)
\(812\) 3.50852 0.123125
\(813\) −9.42743 −0.330634
\(814\) −13.3344 −0.467370
\(815\) −85.4283 −2.99242
\(816\) 19.5468 0.684275
\(817\) −14.7941 −0.517578
\(818\) 19.6201 0.686000
\(819\) 8.94965 0.312726
\(820\) −93.3550 −3.26010
\(821\) −18.4985 −0.645604 −0.322802 0.946467i \(-0.604625\pi\)
−0.322802 + 0.946467i \(0.604625\pi\)
\(822\) −11.8876 −0.414626
\(823\) −42.2939 −1.47427 −0.737136 0.675744i \(-0.763822\pi\)
−0.737136 + 0.675744i \(0.763822\pi\)
\(824\) 6.13169 0.213608
\(825\) −18.5146 −0.644594
\(826\) −25.5135 −0.887728
\(827\) 43.3852 1.50865 0.754325 0.656501i \(-0.227964\pi\)
0.754325 + 0.656501i \(0.227964\pi\)
\(828\) −14.9048 −0.517976
\(829\) 30.8204 1.07044 0.535218 0.844714i \(-0.320230\pi\)
0.535218 + 0.844714i \(0.320230\pi\)
\(830\) 2.49290 0.0865297
\(831\) −3.04021 −0.105464
\(832\) 2.26518 0.0785311
\(833\) 25.0388 0.867544
\(834\) 22.0750 0.764395
\(835\) −93.4373 −3.23353
\(836\) 66.3692 2.29543
\(837\) −29.0568 −1.00435
\(838\) −96.7019 −3.34051
\(839\) 45.2318 1.56157 0.780787 0.624797i \(-0.214818\pi\)
0.780787 + 0.624797i \(0.214818\pi\)
\(840\) −18.5007 −0.638334
\(841\) −28.7264 −0.990564
\(842\) −48.4823 −1.67081
\(843\) −3.40480 −0.117268
\(844\) 58.2591 2.00536
\(845\) −31.4977 −1.08355
\(846\) 19.6933 0.677071
\(847\) −4.35960 −0.149798
\(848\) −7.55068 −0.259291
\(849\) 12.4961 0.428866
\(850\) 132.158 4.53298
\(851\) 1.66411 0.0570451
\(852\) 8.69762 0.297976
\(853\) −17.4016 −0.595818 −0.297909 0.954594i \(-0.596289\pi\)
−0.297909 + 0.954594i \(0.596289\pi\)
\(854\) −1.77957 −0.0608958
\(855\) −41.6085 −1.42298
\(856\) 77.6581 2.65430
\(857\) −6.42925 −0.219619 −0.109810 0.993953i \(-0.535024\pi\)
−0.109810 + 0.993953i \(0.535024\pi\)
\(858\) 10.4889 0.358084
\(859\) −21.0255 −0.717380 −0.358690 0.933457i \(-0.616776\pi\)
−0.358690 + 0.933457i \(0.616776\pi\)
\(860\) −66.4265 −2.26513
\(861\) −3.91120 −0.133293
\(862\) −94.7241 −3.22631
\(863\) −23.8923 −0.813302 −0.406651 0.913584i \(-0.633304\pi\)
−0.406651 + 0.913584i \(0.633304\pi\)
\(864\) −18.0746 −0.614910
\(865\) −55.3814 −1.88302
\(866\) 77.4273 2.63109
\(867\) −4.97595 −0.168992
\(868\) 67.9924 2.30781
\(869\) 42.7807 1.45123
\(870\) −2.57787 −0.0873979
\(871\) −19.6259 −0.664999
\(872\) 9.03402 0.305931
\(873\) −14.5634 −0.492897
\(874\) −11.9294 −0.403519
\(875\) −28.2327 −0.954438
\(876\) 10.3446 0.349512
\(877\) 4.61639 0.155885 0.0779423 0.996958i \(-0.475165\pi\)
0.0779423 + 0.996958i \(0.475165\pi\)
\(878\) −27.7621 −0.936924
\(879\) −0.423024 −0.0142682
\(880\) 109.039 3.67569
\(881\) 43.9708 1.48141 0.740707 0.671828i \(-0.234491\pi\)
0.740707 + 0.671828i \(0.234491\pi\)
\(882\) −33.9254 −1.14233
\(883\) 12.4428 0.418734 0.209367 0.977837i \(-0.432860\pi\)
0.209367 + 0.977837i \(0.432860\pi\)
\(884\) −51.9835 −1.74839
\(885\) 13.0156 0.437514
\(886\) 12.0566 0.405051
\(887\) 22.9618 0.770983 0.385491 0.922711i \(-0.374032\pi\)
0.385491 + 0.922711i \(0.374032\pi\)
\(888\) 4.52342 0.151796
\(889\) 3.27664 0.109895
\(890\) 63.0774 2.11436
\(891\) 25.4995 0.854265
\(892\) 53.7917 1.80108
\(893\) 10.9439 0.366223
\(894\) 2.21645 0.0741291
\(895\) 54.1003 1.80837
\(896\) −14.7374 −0.492341
\(897\) −1.30900 −0.0437061
\(898\) 92.6291 3.09107
\(899\) 5.30291 0.176862
\(900\) −124.326 −4.14420
\(901\) 5.19471 0.173061
\(902\) 50.7888 1.69108
\(903\) −2.78301 −0.0926127
\(904\) −17.8305 −0.593033
\(905\) −21.0078 −0.698322
\(906\) −1.27470 −0.0423490
\(907\) −25.1422 −0.834832 −0.417416 0.908715i \(-0.637064\pi\)
−0.417416 + 0.908715i \(0.637064\pi\)
\(908\) −69.0442 −2.29131
\(909\) −40.1849 −1.33285
\(910\) 32.1629 1.06619
\(911\) 30.1805 0.999925 0.499963 0.866047i \(-0.333347\pi\)
0.499963 + 0.866047i \(0.333347\pi\)
\(912\) −14.7177 −0.487350
\(913\) −0.941654 −0.0311642
\(914\) 91.7360 3.03436
\(915\) 0.907841 0.0300123
\(916\) −18.6873 −0.617446
\(917\) 26.9473 0.889880
\(918\) 38.0856 1.25701
\(919\) −22.9841 −0.758175 −0.379088 0.925361i \(-0.623762\pi\)
−0.379088 + 0.925361i \(0.623762\pi\)
\(920\) −29.9816 −0.988464
\(921\) 7.73669 0.254933
\(922\) −13.9712 −0.460117
\(923\) −8.46348 −0.278579
\(924\) 12.4852 0.410731
\(925\) 13.8810 0.456403
\(926\) 49.8439 1.63797
\(927\) 2.59419 0.0852044
\(928\) 3.29864 0.108283
\(929\) 20.0132 0.656613 0.328306 0.944571i \(-0.393522\pi\)
0.328306 + 0.944571i \(0.393522\pi\)
\(930\) −49.9571 −1.63816
\(931\) −18.8528 −0.617877
\(932\) −50.9439 −1.66872
\(933\) −5.48080 −0.179433
\(934\) −59.9262 −1.96084
\(935\) −75.0162 −2.45329
\(936\) 39.4237 1.28860
\(937\) 8.28447 0.270642 0.135321 0.990802i \(-0.456793\pi\)
0.135321 + 0.990802i \(0.456793\pi\)
\(938\) −33.6464 −1.09859
\(939\) −2.07624 −0.0677554
\(940\) 49.1389 1.60273
\(941\) 11.6577 0.380031 0.190015 0.981781i \(-0.439146\pi\)
0.190015 + 0.981781i \(0.439146\pi\)
\(942\) −22.4605 −0.731803
\(943\) −6.33837 −0.206406
\(944\) −51.0101 −1.66024
\(945\) −16.3609 −0.532221
\(946\) 36.1386 1.17497
\(947\) 51.4962 1.67340 0.836700 0.547661i \(-0.184482\pi\)
0.836700 + 0.547661i \(0.184482\pi\)
\(948\) −25.9275 −0.842085
\(949\) −10.0661 −0.326760
\(950\) −99.5076 −3.22845
\(951\) 3.77330 0.122358
\(952\) −49.8833 −1.61673
\(953\) 18.2894 0.592453 0.296226 0.955118i \(-0.404272\pi\)
0.296226 + 0.955118i \(0.404272\pi\)
\(954\) −7.03837 −0.227876
\(955\) 27.6769 0.895604
\(956\) 70.9567 2.29490
\(957\) 0.973750 0.0314769
\(958\) 32.4694 1.04904
\(959\) 13.7691 0.444629
\(960\) −1.98110 −0.0639396
\(961\) 71.7665 2.31505
\(962\) −7.86384 −0.253540
\(963\) 32.8555 1.05875
\(964\) −7.02052 −0.226116
\(965\) −6.00753 −0.193389
\(966\) −2.24412 −0.0722035
\(967\) 28.4295 0.914231 0.457115 0.889407i \(-0.348883\pi\)
0.457115 + 0.889407i \(0.348883\pi\)
\(968\) −19.2043 −0.617248
\(969\) 10.1254 0.325276
\(970\) −52.3374 −1.68045
\(971\) −6.45816 −0.207252 −0.103626 0.994616i \(-0.533045\pi\)
−0.103626 + 0.994616i \(0.533045\pi\)
\(972\) −54.5163 −1.74861
\(973\) −25.5691 −0.819706
\(974\) −19.9514 −0.639284
\(975\) −10.9188 −0.349681
\(976\) −3.55797 −0.113888
\(977\) 32.9445 1.05399 0.526993 0.849869i \(-0.323319\pi\)
0.526993 + 0.849869i \(0.323319\pi\)
\(978\) −28.1673 −0.900690
\(979\) −23.8265 −0.761500
\(980\) −84.6508 −2.70407
\(981\) 3.82210 0.122030
\(982\) −53.3678 −1.70304
\(983\) −58.3607 −1.86142 −0.930708 0.365763i \(-0.880808\pi\)
−0.930708 + 0.365763i \(0.880808\pi\)
\(984\) −17.2290 −0.549242
\(985\) 1.47281 0.0469277
\(986\) −6.95069 −0.221355
\(987\) 2.05872 0.0655299
\(988\) 39.1407 1.24523
\(989\) −4.51005 −0.143411
\(990\) 101.640 3.23034
\(991\) 0.429961 0.0136582 0.00682908 0.999977i \(-0.497826\pi\)
0.00682908 + 0.999977i \(0.497826\pi\)
\(992\) 63.9252 2.02963
\(993\) 9.54573 0.302925
\(994\) −14.5097 −0.460219
\(995\) 15.5041 0.491513
\(996\) 0.570695 0.0180832
\(997\) 55.6201 1.76151 0.880753 0.473577i \(-0.157037\pi\)
0.880753 + 0.473577i \(0.157037\pi\)
\(998\) −23.9712 −0.758796
\(999\) 4.00025 0.126562
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 8003.2.a.b.1.7 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.7 153 1.1 even 1 trivial