Properties

Label 8003.2.a.b.1.18
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 1.18
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.34979 q^{2} -2.55203 q^{3} +3.52153 q^{4} +3.27958 q^{5} +5.99675 q^{6} +4.82178 q^{7} -3.57528 q^{8} +3.51287 q^{9} +O(q^{10})\) \(q-2.34979 q^{2} -2.55203 q^{3} +3.52153 q^{4} +3.27958 q^{5} +5.99675 q^{6} +4.82178 q^{7} -3.57528 q^{8} +3.51287 q^{9} -7.70633 q^{10} +3.08273 q^{11} -8.98706 q^{12} -3.47250 q^{13} -11.3302 q^{14} -8.36959 q^{15} +1.35811 q^{16} -4.04990 q^{17} -8.25452 q^{18} +3.40481 q^{19} +11.5491 q^{20} -12.3053 q^{21} -7.24379 q^{22} -8.59467 q^{23} +9.12423 q^{24} +5.75564 q^{25} +8.15966 q^{26} -1.30887 q^{27} +16.9800 q^{28} -0.344181 q^{29} +19.6668 q^{30} -2.73850 q^{31} +3.95928 q^{32} -7.86724 q^{33} +9.51643 q^{34} +15.8134 q^{35} +12.3707 q^{36} -8.28001 q^{37} -8.00061 q^{38} +8.86194 q^{39} -11.7254 q^{40} +2.78767 q^{41} +28.9150 q^{42} -12.7978 q^{43} +10.8559 q^{44} +11.5207 q^{45} +20.1957 q^{46} -1.37067 q^{47} -3.46595 q^{48} +16.2496 q^{49} -13.5246 q^{50} +10.3355 q^{51} -12.2285 q^{52} -1.00000 q^{53} +3.07556 q^{54} +10.1101 q^{55} -17.2392 q^{56} -8.68920 q^{57} +0.808754 q^{58} +14.2547 q^{59} -29.4738 q^{60} +12.5301 q^{61} +6.43490 q^{62} +16.9383 q^{63} -12.0197 q^{64} -11.3883 q^{65} +18.4864 q^{66} -4.86324 q^{67} -14.2619 q^{68} +21.9339 q^{69} -37.1582 q^{70} -13.6656 q^{71} -12.5595 q^{72} +4.28647 q^{73} +19.4563 q^{74} -14.6886 q^{75} +11.9902 q^{76} +14.8643 q^{77} -20.8237 q^{78} -13.2510 q^{79} +4.45404 q^{80} -7.19835 q^{81} -6.55045 q^{82} +4.59159 q^{83} -43.3336 q^{84} -13.2820 q^{85} +30.0723 q^{86} +0.878361 q^{87} -11.0216 q^{88} -8.51377 q^{89} -27.0714 q^{90} -16.7436 q^{91} -30.2664 q^{92} +6.98873 q^{93} +3.22080 q^{94} +11.1664 q^{95} -10.1042 q^{96} +7.60135 q^{97} -38.1831 q^{98} +10.8292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34979 −1.66155 −0.830777 0.556605i \(-0.812104\pi\)
−0.830777 + 0.556605i \(0.812104\pi\)
\(3\) −2.55203 −1.47342 −0.736708 0.676211i \(-0.763621\pi\)
−0.736708 + 0.676211i \(0.763621\pi\)
\(4\) 3.52153 1.76076
\(5\) 3.27958 1.46667 0.733336 0.679866i \(-0.237962\pi\)
0.733336 + 0.679866i \(0.237962\pi\)
\(6\) 5.99675 2.44816
\(7\) 4.82178 1.82246 0.911231 0.411896i \(-0.135133\pi\)
0.911231 + 0.411896i \(0.135133\pi\)
\(8\) −3.57528 −1.26405
\(9\) 3.51287 1.17096
\(10\) −7.70633 −2.43696
\(11\) 3.08273 0.929479 0.464739 0.885447i \(-0.346148\pi\)
0.464739 + 0.885447i \(0.346148\pi\)
\(12\) −8.98706 −2.59434
\(13\) −3.47250 −0.963099 −0.481549 0.876419i \(-0.659926\pi\)
−0.481549 + 0.876419i \(0.659926\pi\)
\(14\) −11.3302 −3.02812
\(15\) −8.36959 −2.16102
\(16\) 1.35811 0.339528
\(17\) −4.04990 −0.982246 −0.491123 0.871090i \(-0.663413\pi\)
−0.491123 + 0.871090i \(0.663413\pi\)
\(18\) −8.25452 −1.94561
\(19\) 3.40481 0.781118 0.390559 0.920578i \(-0.372282\pi\)
0.390559 + 0.920578i \(0.372282\pi\)
\(20\) 11.5491 2.58246
\(21\) −12.3053 −2.68525
\(22\) −7.24379 −1.54438
\(23\) −8.59467 −1.79211 −0.896056 0.443940i \(-0.853580\pi\)
−0.896056 + 0.443940i \(0.853580\pi\)
\(24\) 9.12423 1.86248
\(25\) 5.75564 1.15113
\(26\) 8.15966 1.60024
\(27\) −1.30887 −0.251891
\(28\) 16.9800 3.20893
\(29\) −0.344181 −0.0639128 −0.0319564 0.999489i \(-0.510174\pi\)
−0.0319564 + 0.999489i \(0.510174\pi\)
\(30\) 19.6668 3.59065
\(31\) −2.73850 −0.491848 −0.245924 0.969289i \(-0.579091\pi\)
−0.245924 + 0.969289i \(0.579091\pi\)
\(32\) 3.95928 0.699908
\(33\) −7.86724 −1.36951
\(34\) 9.51643 1.63205
\(35\) 15.8134 2.67295
\(36\) 12.3707 2.06178
\(37\) −8.28001 −1.36123 −0.680613 0.732643i \(-0.738286\pi\)
−0.680613 + 0.732643i \(0.738286\pi\)
\(38\) −8.00061 −1.29787
\(39\) 8.86194 1.41905
\(40\) −11.7254 −1.85395
\(41\) 2.78767 0.435361 0.217680 0.976020i \(-0.430151\pi\)
0.217680 + 0.976020i \(0.430151\pi\)
\(42\) 28.9150 4.46168
\(43\) −12.7978 −1.95165 −0.975826 0.218549i \(-0.929868\pi\)
−0.975826 + 0.218549i \(0.929868\pi\)
\(44\) 10.8559 1.63659
\(45\) 11.5207 1.71741
\(46\) 20.1957 2.97769
\(47\) −1.37067 −0.199933 −0.0999666 0.994991i \(-0.531874\pi\)
−0.0999666 + 0.994991i \(0.531874\pi\)
\(48\) −3.46595 −0.500266
\(49\) 16.2496 2.32137
\(50\) −13.5246 −1.91266
\(51\) 10.3355 1.44726
\(52\) −12.2285 −1.69579
\(53\) −1.00000 −0.137361
\(54\) 3.07556 0.418531
\(55\) 10.1101 1.36324
\(56\) −17.2392 −2.30369
\(57\) −8.68920 −1.15091
\(58\) 0.808754 0.106195
\(59\) 14.2547 1.85580 0.927902 0.372825i \(-0.121611\pi\)
0.927902 + 0.372825i \(0.121611\pi\)
\(60\) −29.4738 −3.80505
\(61\) 12.5301 1.60431 0.802156 0.597114i \(-0.203686\pi\)
0.802156 + 0.597114i \(0.203686\pi\)
\(62\) 6.43490 0.817233
\(63\) 16.9383 2.13402
\(64\) −12.0197 −1.50246
\(65\) −11.3883 −1.41255
\(66\) 18.4864 2.27552
\(67\) −4.86324 −0.594139 −0.297069 0.954856i \(-0.596009\pi\)
−0.297069 + 0.954856i \(0.596009\pi\)
\(68\) −14.2619 −1.72950
\(69\) 21.9339 2.64053
\(70\) −37.1582 −4.44126
\(71\) −13.6656 −1.62180 −0.810902 0.585182i \(-0.801023\pi\)
−0.810902 + 0.585182i \(0.801023\pi\)
\(72\) −12.5595 −1.48015
\(73\) 4.28647 0.501693 0.250847 0.968027i \(-0.419291\pi\)
0.250847 + 0.968027i \(0.419291\pi\)
\(74\) 19.4563 2.26175
\(75\) −14.6886 −1.69609
\(76\) 11.9902 1.37537
\(77\) 14.8643 1.69394
\(78\) −20.8237 −2.35782
\(79\) −13.2510 −1.49085 −0.745427 0.666588i \(-0.767754\pi\)
−0.745427 + 0.666588i \(0.767754\pi\)
\(80\) 4.45404 0.497976
\(81\) −7.19835 −0.799816
\(82\) −6.55045 −0.723376
\(83\) 4.59159 0.503993 0.251996 0.967728i \(-0.418913\pi\)
0.251996 + 0.967728i \(0.418913\pi\)
\(84\) −43.3336 −4.72809
\(85\) −13.2820 −1.44063
\(86\) 30.0723 3.24278
\(87\) 0.878361 0.0941702
\(88\) −11.0216 −1.17491
\(89\) −8.51377 −0.902458 −0.451229 0.892408i \(-0.649014\pi\)
−0.451229 + 0.892408i \(0.649014\pi\)
\(90\) −27.0714 −2.85357
\(91\) −16.7436 −1.75521
\(92\) −30.2664 −3.15549
\(93\) 6.98873 0.724698
\(94\) 3.22080 0.332200
\(95\) 11.1664 1.14564
\(96\) −10.1042 −1.03126
\(97\) 7.60135 0.771800 0.385900 0.922541i \(-0.373891\pi\)
0.385900 + 0.922541i \(0.373891\pi\)
\(98\) −38.1831 −3.85708
\(99\) 10.8292 1.08838
\(100\) 20.2686 2.02686
\(101\) 1.21450 0.120847 0.0604237 0.998173i \(-0.480755\pi\)
0.0604237 + 0.998173i \(0.480755\pi\)
\(102\) −24.2863 −2.40470
\(103\) −7.85027 −0.773510 −0.386755 0.922182i \(-0.626404\pi\)
−0.386755 + 0.922182i \(0.626404\pi\)
\(104\) 12.4152 1.21741
\(105\) −40.3563 −3.93838
\(106\) 2.34979 0.228232
\(107\) 7.83343 0.757286 0.378643 0.925543i \(-0.376391\pi\)
0.378643 + 0.925543i \(0.376391\pi\)
\(108\) −4.60921 −0.443521
\(109\) −6.10668 −0.584914 −0.292457 0.956279i \(-0.594473\pi\)
−0.292457 + 0.956279i \(0.594473\pi\)
\(110\) −23.7566 −2.26510
\(111\) 21.1309 2.00565
\(112\) 6.54852 0.618777
\(113\) 0.695341 0.0654122 0.0327061 0.999465i \(-0.489587\pi\)
0.0327061 + 0.999465i \(0.489587\pi\)
\(114\) 20.4178 1.91230
\(115\) −28.1869 −2.62844
\(116\) −1.21204 −0.112535
\(117\) −12.1985 −1.12775
\(118\) −33.4956 −3.08352
\(119\) −19.5277 −1.79011
\(120\) 29.9236 2.73164
\(121\) −1.49676 −0.136069
\(122\) −29.4431 −2.66565
\(123\) −7.11422 −0.641468
\(124\) −9.64369 −0.866029
\(125\) 2.47817 0.221654
\(126\) −39.8015 −3.54580
\(127\) −11.3199 −1.00448 −0.502241 0.864728i \(-0.667491\pi\)
−0.502241 + 0.864728i \(0.667491\pi\)
\(128\) 20.3253 1.79652
\(129\) 32.6605 2.87560
\(130\) 26.7602 2.34703
\(131\) 6.17924 0.539883 0.269941 0.962877i \(-0.412996\pi\)
0.269941 + 0.962877i \(0.412996\pi\)
\(132\) −27.7047 −2.41138
\(133\) 16.4173 1.42356
\(134\) 11.4276 0.987195
\(135\) −4.29253 −0.369442
\(136\) 14.4795 1.24161
\(137\) −18.3273 −1.56580 −0.782902 0.622145i \(-0.786261\pi\)
−0.782902 + 0.622145i \(0.786261\pi\)
\(138\) −51.5401 −4.38738
\(139\) −12.8690 −1.09153 −0.545766 0.837938i \(-0.683761\pi\)
−0.545766 + 0.837938i \(0.683761\pi\)
\(140\) 55.6874 4.70644
\(141\) 3.49800 0.294585
\(142\) 32.1113 2.69472
\(143\) −10.7048 −0.895180
\(144\) 4.77087 0.397573
\(145\) −1.12877 −0.0937391
\(146\) −10.0723 −0.833591
\(147\) −41.4694 −3.42034
\(148\) −29.1583 −2.39680
\(149\) 1.74075 0.142608 0.0713038 0.997455i \(-0.477284\pi\)
0.0713038 + 0.997455i \(0.477284\pi\)
\(150\) 34.5151 2.81815
\(151\) −1.00000 −0.0813788
\(152\) −12.1732 −0.987374
\(153\) −14.2268 −1.15017
\(154\) −34.9279 −2.81457
\(155\) −8.98111 −0.721380
\(156\) 31.2076 2.49861
\(157\) −7.11405 −0.567763 −0.283881 0.958859i \(-0.591622\pi\)
−0.283881 + 0.958859i \(0.591622\pi\)
\(158\) 31.1371 2.47713
\(159\) 2.55203 0.202389
\(160\) 12.9848 1.02654
\(161\) −41.4416 −3.26606
\(162\) 16.9146 1.32894
\(163\) 23.5364 1.84351 0.921756 0.387771i \(-0.126755\pi\)
0.921756 + 0.387771i \(0.126755\pi\)
\(164\) 9.81686 0.766568
\(165\) −25.8012 −2.00862
\(166\) −10.7893 −0.837412
\(167\) −22.3933 −1.73284 −0.866422 0.499312i \(-0.833586\pi\)
−0.866422 + 0.499312i \(0.833586\pi\)
\(168\) 43.9951 3.39429
\(169\) −0.941736 −0.0724412
\(170\) 31.2099 2.39369
\(171\) 11.9607 0.914656
\(172\) −45.0680 −3.43640
\(173\) 14.2454 1.08306 0.541529 0.840682i \(-0.317846\pi\)
0.541529 + 0.840682i \(0.317846\pi\)
\(174\) −2.06397 −0.156469
\(175\) 27.7524 2.09789
\(176\) 4.18670 0.315584
\(177\) −36.3785 −2.73437
\(178\) 20.0056 1.49948
\(179\) −2.61927 −0.195774 −0.0978868 0.995198i \(-0.531208\pi\)
−0.0978868 + 0.995198i \(0.531208\pi\)
\(180\) 40.5706 3.02396
\(181\) −5.17426 −0.384599 −0.192300 0.981336i \(-0.561595\pi\)
−0.192300 + 0.981336i \(0.561595\pi\)
\(182\) 39.3441 2.91638
\(183\) −31.9772 −2.36382
\(184\) 30.7284 2.26532
\(185\) −27.1550 −1.99647
\(186\) −16.4221 −1.20412
\(187\) −12.4848 −0.912977
\(188\) −4.82687 −0.352035
\(189\) −6.31106 −0.459062
\(190\) −26.2386 −1.90355
\(191\) 23.6082 1.70823 0.854114 0.520086i \(-0.174100\pi\)
0.854114 + 0.520086i \(0.174100\pi\)
\(192\) 30.6747 2.21376
\(193\) −4.40647 −0.317184 −0.158592 0.987344i \(-0.550696\pi\)
−0.158592 + 0.987344i \(0.550696\pi\)
\(194\) −17.8616 −1.28239
\(195\) 29.0634 2.08127
\(196\) 57.2233 4.08738
\(197\) −11.7995 −0.840681 −0.420340 0.907366i \(-0.638089\pi\)
−0.420340 + 0.907366i \(0.638089\pi\)
\(198\) −25.4465 −1.80840
\(199\) 5.83666 0.413750 0.206875 0.978367i \(-0.433671\pi\)
0.206875 + 0.978367i \(0.433671\pi\)
\(200\) −20.5780 −1.45509
\(201\) 12.4111 0.875414
\(202\) −2.85383 −0.200795
\(203\) −1.65956 −0.116479
\(204\) 36.3967 2.54828
\(205\) 9.14238 0.638532
\(206\) 18.4465 1.28523
\(207\) −30.1920 −2.09849
\(208\) −4.71605 −0.326999
\(209\) 10.4961 0.726033
\(210\) 94.8291 6.54383
\(211\) −26.1322 −1.79901 −0.899507 0.436906i \(-0.856074\pi\)
−0.899507 + 0.436906i \(0.856074\pi\)
\(212\) −3.52153 −0.241860
\(213\) 34.8750 2.38959
\(214\) −18.4069 −1.25827
\(215\) −41.9715 −2.86243
\(216\) 4.67956 0.318404
\(217\) −13.2044 −0.896375
\(218\) 14.3494 0.971866
\(219\) −10.9392 −0.739203
\(220\) 35.6029 2.40035
\(221\) 14.0633 0.945999
\(222\) −49.6532 −3.33250
\(223\) 11.3643 0.761007 0.380504 0.924779i \(-0.375751\pi\)
0.380504 + 0.924779i \(0.375751\pi\)
\(224\) 19.0908 1.27556
\(225\) 20.2188 1.34792
\(226\) −1.63391 −0.108686
\(227\) −18.2321 −1.21010 −0.605052 0.796186i \(-0.706848\pi\)
−0.605052 + 0.796186i \(0.706848\pi\)
\(228\) −30.5993 −2.02649
\(229\) 13.6210 0.900102 0.450051 0.893003i \(-0.351406\pi\)
0.450051 + 0.893003i \(0.351406\pi\)
\(230\) 66.2334 4.36730
\(231\) −37.9341 −2.49588
\(232\) 1.23054 0.0807891
\(233\) 14.3590 0.940692 0.470346 0.882482i \(-0.344129\pi\)
0.470346 + 0.882482i \(0.344129\pi\)
\(234\) 28.6638 1.87381
\(235\) −4.49523 −0.293236
\(236\) 50.1983 3.26763
\(237\) 33.8170 2.19665
\(238\) 45.8862 2.97436
\(239\) −25.7499 −1.66563 −0.832813 0.553555i \(-0.813271\pi\)
−0.832813 + 0.553555i \(0.813271\pi\)
\(240\) −11.3668 −0.733727
\(241\) −11.3817 −0.733158 −0.366579 0.930387i \(-0.619471\pi\)
−0.366579 + 0.930387i \(0.619471\pi\)
\(242\) 3.51707 0.226086
\(243\) 22.2970 1.43035
\(244\) 44.1251 2.82482
\(245\) 53.2917 3.40468
\(246\) 16.7170 1.06583
\(247\) −11.8232 −0.752294
\(248\) 9.79089 0.621722
\(249\) −11.7179 −0.742592
\(250\) −5.82318 −0.368290
\(251\) 22.0126 1.38942 0.694712 0.719288i \(-0.255532\pi\)
0.694712 + 0.719288i \(0.255532\pi\)
\(252\) 59.6487 3.75752
\(253\) −26.4951 −1.66573
\(254\) 26.5995 1.66900
\(255\) 33.8960 2.12265
\(256\) −23.7208 −1.48255
\(257\) 1.24375 0.0775829 0.0387914 0.999247i \(-0.487649\pi\)
0.0387914 + 0.999247i \(0.487649\pi\)
\(258\) −76.7454 −4.77796
\(259\) −39.9244 −2.48078
\(260\) −40.1044 −2.48717
\(261\) −1.20906 −0.0748391
\(262\) −14.5199 −0.897045
\(263\) 28.3305 1.74693 0.873467 0.486883i \(-0.161866\pi\)
0.873467 + 0.486883i \(0.161866\pi\)
\(264\) 28.1276 1.73113
\(265\) −3.27958 −0.201463
\(266\) −38.5772 −2.36532
\(267\) 21.7274 1.32970
\(268\) −17.1260 −1.04614
\(269\) 4.85106 0.295774 0.147887 0.989004i \(-0.452753\pi\)
0.147887 + 0.989004i \(0.452753\pi\)
\(270\) 10.0866 0.613848
\(271\) 4.70926 0.286067 0.143034 0.989718i \(-0.454314\pi\)
0.143034 + 0.989718i \(0.454314\pi\)
\(272\) −5.50022 −0.333500
\(273\) 42.7303 2.58616
\(274\) 43.0653 2.60167
\(275\) 17.7431 1.06995
\(276\) 77.2408 4.64935
\(277\) −4.56836 −0.274486 −0.137243 0.990537i \(-0.543824\pi\)
−0.137243 + 0.990537i \(0.543824\pi\)
\(278\) 30.2394 1.81364
\(279\) −9.61998 −0.575933
\(280\) −56.5374 −3.37875
\(281\) −3.77999 −0.225495 −0.112748 0.993624i \(-0.535965\pi\)
−0.112748 + 0.993624i \(0.535965\pi\)
\(282\) −8.21958 −0.489469
\(283\) 0.740790 0.0440354 0.0220177 0.999758i \(-0.492991\pi\)
0.0220177 + 0.999758i \(0.492991\pi\)
\(284\) −48.1237 −2.85562
\(285\) −28.4969 −1.68801
\(286\) 25.1541 1.48739
\(287\) 13.4415 0.793428
\(288\) 13.9084 0.819562
\(289\) −0.598292 −0.0351937
\(290\) 2.65237 0.155753
\(291\) −19.3989 −1.13718
\(292\) 15.0949 0.883363
\(293\) −2.09295 −0.122272 −0.0611358 0.998129i \(-0.519472\pi\)
−0.0611358 + 0.998129i \(0.519472\pi\)
\(294\) 97.4446 5.68309
\(295\) 46.7494 2.72186
\(296\) 29.6034 1.72066
\(297\) −4.03488 −0.234128
\(298\) −4.09040 −0.236950
\(299\) 29.8450 1.72598
\(300\) −51.7262 −2.98642
\(301\) −61.7084 −3.55681
\(302\) 2.34979 0.135215
\(303\) −3.09945 −0.178059
\(304\) 4.62412 0.265211
\(305\) 41.0934 2.35300
\(306\) 33.4300 1.91107
\(307\) 24.8316 1.41721 0.708607 0.705604i \(-0.249324\pi\)
0.708607 + 0.705604i \(0.249324\pi\)
\(308\) 52.3449 2.98263
\(309\) 20.0342 1.13970
\(310\) 21.1038 1.19861
\(311\) 32.4115 1.83789 0.918944 0.394389i \(-0.129044\pi\)
0.918944 + 0.394389i \(0.129044\pi\)
\(312\) −31.6839 −1.79375
\(313\) −21.4248 −1.21100 −0.605499 0.795846i \(-0.707027\pi\)
−0.605499 + 0.795846i \(0.707027\pi\)
\(314\) 16.7165 0.943369
\(315\) 55.5505 3.12991
\(316\) −46.6638 −2.62504
\(317\) −29.4016 −1.65136 −0.825679 0.564141i \(-0.809207\pi\)
−0.825679 + 0.564141i \(0.809207\pi\)
\(318\) −5.99675 −0.336281
\(319\) −1.06102 −0.0594056
\(320\) −39.4196 −2.20362
\(321\) −19.9912 −1.11580
\(322\) 97.3792 5.42673
\(323\) −13.7892 −0.767250
\(324\) −25.3492 −1.40829
\(325\) −19.9865 −1.10865
\(326\) −55.3056 −3.06310
\(327\) 15.5844 0.861822
\(328\) −9.96670 −0.550319
\(329\) −6.60908 −0.364371
\(330\) 60.6275 3.33744
\(331\) −18.3859 −1.01058 −0.505290 0.862949i \(-0.668615\pi\)
−0.505290 + 0.862949i \(0.668615\pi\)
\(332\) 16.1694 0.887413
\(333\) −29.0866 −1.59394
\(334\) 52.6196 2.87922
\(335\) −15.9494 −0.871407
\(336\) −16.7120 −0.911716
\(337\) −11.6946 −0.637045 −0.318522 0.947915i \(-0.603187\pi\)
−0.318522 + 0.947915i \(0.603187\pi\)
\(338\) 2.21288 0.120365
\(339\) −1.77453 −0.0963794
\(340\) −46.7729 −2.53661
\(341\) −8.44205 −0.457163
\(342\) −28.1051 −1.51975
\(343\) 44.5994 2.40814
\(344\) 45.7559 2.46699
\(345\) 71.9339 3.87279
\(346\) −33.4738 −1.79956
\(347\) 12.2023 0.655053 0.327527 0.944842i \(-0.393785\pi\)
0.327527 + 0.944842i \(0.393785\pi\)
\(348\) 3.09317 0.165811
\(349\) −35.7783 −1.91517 −0.957584 0.288153i \(-0.906959\pi\)
−0.957584 + 0.288153i \(0.906959\pi\)
\(350\) −65.2124 −3.48575
\(351\) 4.54504 0.242596
\(352\) 12.2054 0.650550
\(353\) −26.5979 −1.41566 −0.707831 0.706381i \(-0.750326\pi\)
−0.707831 + 0.706381i \(0.750326\pi\)
\(354\) 85.4819 4.54331
\(355\) −44.8173 −2.37865
\(356\) −29.9815 −1.58902
\(357\) 49.8354 2.63757
\(358\) 6.15475 0.325289
\(359\) −35.4096 −1.86884 −0.934422 0.356167i \(-0.884083\pi\)
−0.934422 + 0.356167i \(0.884083\pi\)
\(360\) −41.1899 −2.17090
\(361\) −7.40724 −0.389855
\(362\) 12.1584 0.639033
\(363\) 3.81978 0.200486
\(364\) −58.9632 −3.09051
\(365\) 14.0578 0.735819
\(366\) 75.1398 3.92762
\(367\) 3.80542 0.198641 0.0993206 0.995055i \(-0.468333\pi\)
0.0993206 + 0.995055i \(0.468333\pi\)
\(368\) −11.6725 −0.608473
\(369\) 9.79272 0.509789
\(370\) 63.8085 3.31725
\(371\) −4.82178 −0.250334
\(372\) 24.6110 1.27602
\(373\) 8.36767 0.433261 0.216631 0.976254i \(-0.430493\pi\)
0.216631 + 0.976254i \(0.430493\pi\)
\(374\) 29.3366 1.51696
\(375\) −6.32436 −0.326589
\(376\) 4.90054 0.252726
\(377\) 1.19517 0.0615543
\(378\) 14.8297 0.762757
\(379\) −29.8927 −1.53548 −0.767742 0.640760i \(-0.778620\pi\)
−0.767742 + 0.640760i \(0.778620\pi\)
\(380\) 39.3227 2.01721
\(381\) 28.8889 1.48002
\(382\) −55.4744 −2.83831
\(383\) 8.91615 0.455594 0.227797 0.973709i \(-0.426848\pi\)
0.227797 + 0.973709i \(0.426848\pi\)
\(384\) −51.8708 −2.64702
\(385\) 48.7485 2.48445
\(386\) 10.3543 0.527019
\(387\) −44.9572 −2.28530
\(388\) 26.7684 1.35896
\(389\) −2.03711 −0.103285 −0.0516427 0.998666i \(-0.516446\pi\)
−0.0516427 + 0.998666i \(0.516446\pi\)
\(390\) −68.2930 −3.45815
\(391\) 34.8076 1.76029
\(392\) −58.0968 −2.93433
\(393\) −15.7696 −0.795473
\(394\) 27.7264 1.39684
\(395\) −43.4577 −2.18659
\(396\) 38.1355 1.91638
\(397\) 10.4502 0.524481 0.262240 0.965003i \(-0.415539\pi\)
0.262240 + 0.965003i \(0.415539\pi\)
\(398\) −13.7149 −0.687468
\(399\) −41.8974 −2.09749
\(400\) 7.81680 0.390840
\(401\) 6.54172 0.326678 0.163339 0.986570i \(-0.447774\pi\)
0.163339 + 0.986570i \(0.447774\pi\)
\(402\) −29.1636 −1.45455
\(403\) 9.50943 0.473698
\(404\) 4.27690 0.212784
\(405\) −23.6075 −1.17307
\(406\) 3.89963 0.193536
\(407\) −25.5251 −1.26523
\(408\) −36.9523 −1.82941
\(409\) −17.7146 −0.875930 −0.437965 0.898992i \(-0.644301\pi\)
−0.437965 + 0.898992i \(0.644301\pi\)
\(410\) −21.4827 −1.06096
\(411\) 46.7718 2.30708
\(412\) −27.6450 −1.36197
\(413\) 68.7330 3.38213
\(414\) 70.9449 3.48675
\(415\) 15.0585 0.739192
\(416\) −13.7486 −0.674080
\(417\) 32.8420 1.60828
\(418\) −24.6637 −1.20634
\(419\) −14.5429 −0.710466 −0.355233 0.934778i \(-0.615598\pi\)
−0.355233 + 0.934778i \(0.615598\pi\)
\(420\) −142.116 −6.93455
\(421\) 23.3232 1.13670 0.568350 0.822787i \(-0.307582\pi\)
0.568350 + 0.822787i \(0.307582\pi\)
\(422\) 61.4053 2.98916
\(423\) −4.81500 −0.234113
\(424\) 3.57528 0.173631
\(425\) −23.3098 −1.13069
\(426\) −81.9490 −3.97044
\(427\) 60.4173 2.92380
\(428\) 27.5857 1.33340
\(429\) 27.3190 1.31897
\(430\) 98.6244 4.75609
\(431\) 3.86468 0.186155 0.0930775 0.995659i \(-0.470330\pi\)
0.0930775 + 0.995659i \(0.470330\pi\)
\(432\) −1.77759 −0.0855241
\(433\) −11.6182 −0.558333 −0.279167 0.960243i \(-0.590058\pi\)
−0.279167 + 0.960243i \(0.590058\pi\)
\(434\) 31.0277 1.48938
\(435\) 2.88065 0.138117
\(436\) −21.5049 −1.02990
\(437\) −29.2633 −1.39985
\(438\) 25.7049 1.22823
\(439\) −17.9477 −0.856596 −0.428298 0.903638i \(-0.640887\pi\)
−0.428298 + 0.903638i \(0.640887\pi\)
\(440\) −36.1463 −1.72321
\(441\) 57.0827 2.71822
\(442\) −33.0458 −1.57183
\(443\) −26.3122 −1.25013 −0.625066 0.780572i \(-0.714928\pi\)
−0.625066 + 0.780572i \(0.714928\pi\)
\(444\) 74.4130 3.53148
\(445\) −27.9216 −1.32361
\(446\) −26.7037 −1.26446
\(447\) −4.44244 −0.210120
\(448\) −57.9564 −2.73818
\(449\) 20.5011 0.967506 0.483753 0.875205i \(-0.339273\pi\)
0.483753 + 0.875205i \(0.339273\pi\)
\(450\) −47.5100 −2.23964
\(451\) 8.59364 0.404659
\(452\) 2.44866 0.115176
\(453\) 2.55203 0.119905
\(454\) 42.8416 2.01065
\(455\) −54.9121 −2.57432
\(456\) 31.0663 1.45481
\(457\) −28.1733 −1.31789 −0.658946 0.752190i \(-0.728998\pi\)
−0.658946 + 0.752190i \(0.728998\pi\)
\(458\) −32.0066 −1.49557
\(459\) 5.30078 0.247419
\(460\) −99.2610 −4.62807
\(461\) 18.7101 0.871416 0.435708 0.900088i \(-0.356498\pi\)
0.435708 + 0.900088i \(0.356498\pi\)
\(462\) 89.1373 4.14704
\(463\) 16.0866 0.747607 0.373803 0.927508i \(-0.378054\pi\)
0.373803 + 0.927508i \(0.378054\pi\)
\(464\) −0.467436 −0.0217002
\(465\) 22.9201 1.06289
\(466\) −33.7408 −1.56301
\(467\) 5.53290 0.256032 0.128016 0.991772i \(-0.459139\pi\)
0.128016 + 0.991772i \(0.459139\pi\)
\(468\) −42.9572 −1.98570
\(469\) −23.4495 −1.08280
\(470\) 10.5629 0.487228
\(471\) 18.1553 0.836551
\(472\) −50.9645 −2.34583
\(473\) −39.4523 −1.81402
\(474\) −79.4629 −3.64985
\(475\) 19.5969 0.899166
\(476\) −68.7675 −3.15195
\(477\) −3.51287 −0.160843
\(478\) 60.5070 2.76753
\(479\) 3.68528 0.168385 0.0841924 0.996450i \(-0.473169\pi\)
0.0841924 + 0.996450i \(0.473169\pi\)
\(480\) −33.1375 −1.51252
\(481\) 28.7524 1.31099
\(482\) 26.7446 1.21818
\(483\) 105.760 4.81226
\(484\) −5.27088 −0.239585
\(485\) 24.9292 1.13198
\(486\) −52.3934 −2.37661
\(487\) −10.5871 −0.479749 −0.239874 0.970804i \(-0.577106\pi\)
−0.239874 + 0.970804i \(0.577106\pi\)
\(488\) −44.7986 −2.02794
\(489\) −60.0656 −2.71626
\(490\) −125.225 −5.65707
\(491\) −18.0523 −0.814688 −0.407344 0.913275i \(-0.633545\pi\)
−0.407344 + 0.913275i \(0.633545\pi\)
\(492\) −25.0530 −1.12947
\(493\) 1.39390 0.0627780
\(494\) 27.7821 1.24998
\(495\) 35.5154 1.59630
\(496\) −3.71918 −0.166996
\(497\) −65.8924 −2.95568
\(498\) 27.5346 1.23386
\(499\) −25.8090 −1.15537 −0.577685 0.816260i \(-0.696044\pi\)
−0.577685 + 0.816260i \(0.696044\pi\)
\(500\) 8.72694 0.390281
\(501\) 57.1484 2.55320
\(502\) −51.7251 −2.30860
\(503\) −29.1621 −1.30027 −0.650136 0.759818i \(-0.725288\pi\)
−0.650136 + 0.759818i \(0.725288\pi\)
\(504\) −60.5592 −2.69752
\(505\) 3.98305 0.177244
\(506\) 62.2579 2.76770
\(507\) 2.40334 0.106736
\(508\) −39.8635 −1.76866
\(509\) −19.8330 −0.879083 −0.439542 0.898222i \(-0.644859\pi\)
−0.439542 + 0.898222i \(0.644859\pi\)
\(510\) −79.6487 −3.52690
\(511\) 20.6684 0.914316
\(512\) 15.0884 0.666820
\(513\) −4.45644 −0.196757
\(514\) −2.92255 −0.128908
\(515\) −25.7456 −1.13449
\(516\) 115.015 5.06325
\(517\) −4.22542 −0.185834
\(518\) 93.8141 4.12196
\(519\) −36.3548 −1.59580
\(520\) 40.7165 1.78554
\(521\) 5.54609 0.242979 0.121489 0.992593i \(-0.461233\pi\)
0.121489 + 0.992593i \(0.461233\pi\)
\(522\) 2.84105 0.124349
\(523\) 28.4244 1.24291 0.621456 0.783449i \(-0.286542\pi\)
0.621456 + 0.783449i \(0.286542\pi\)
\(524\) 21.7604 0.950607
\(525\) −70.8251 −3.09106
\(526\) −66.5709 −2.90263
\(527\) 11.0906 0.483116
\(528\) −10.6846 −0.464987
\(529\) 50.8684 2.21167
\(530\) 7.70633 0.334742
\(531\) 50.0749 2.17307
\(532\) 57.8139 2.50655
\(533\) −9.68019 −0.419295
\(534\) −51.0549 −2.20936
\(535\) 25.6903 1.11069
\(536\) 17.3874 0.751023
\(537\) 6.68447 0.288456
\(538\) −11.3990 −0.491445
\(539\) 50.0931 2.15766
\(540\) −15.1163 −0.650500
\(541\) −12.5006 −0.537443 −0.268722 0.963218i \(-0.586601\pi\)
−0.268722 + 0.963218i \(0.586601\pi\)
\(542\) −11.0658 −0.475317
\(543\) 13.2049 0.566675
\(544\) −16.0347 −0.687482
\(545\) −20.0273 −0.857877
\(546\) −100.407 −4.29704
\(547\) −25.1384 −1.07484 −0.537420 0.843314i \(-0.680601\pi\)
−0.537420 + 0.843314i \(0.680601\pi\)
\(548\) −64.5400 −2.75701
\(549\) 44.0166 1.87858
\(550\) −41.6926 −1.77778
\(551\) −1.17187 −0.0499234
\(552\) −78.4198 −3.33777
\(553\) −63.8934 −2.71702
\(554\) 10.7347 0.456074
\(555\) 69.3003 2.94164
\(556\) −45.3184 −1.92193
\(557\) −21.9044 −0.928117 −0.464059 0.885804i \(-0.653607\pi\)
−0.464059 + 0.885804i \(0.653607\pi\)
\(558\) 22.6050 0.956945
\(559\) 44.4405 1.87963
\(560\) 21.4764 0.907543
\(561\) 31.8615 1.34520
\(562\) 8.88219 0.374672
\(563\) 34.0753 1.43610 0.718052 0.695990i \(-0.245034\pi\)
0.718052 + 0.695990i \(0.245034\pi\)
\(564\) 12.3183 0.518695
\(565\) 2.28043 0.0959382
\(566\) −1.74070 −0.0731672
\(567\) −34.7089 −1.45763
\(568\) 48.8582 2.05005
\(569\) 10.2760 0.430794 0.215397 0.976527i \(-0.430896\pi\)
0.215397 + 0.976527i \(0.430896\pi\)
\(570\) 66.9618 2.80472
\(571\) −6.82983 −0.285819 −0.142910 0.989736i \(-0.545646\pi\)
−0.142910 + 0.989736i \(0.545646\pi\)
\(572\) −37.6972 −1.57620
\(573\) −60.2489 −2.51693
\(574\) −31.5848 −1.31832
\(575\) −49.4678 −2.06295
\(576\) −42.2237 −1.75932
\(577\) −25.5250 −1.06262 −0.531309 0.847178i \(-0.678300\pi\)
−0.531309 + 0.847178i \(0.678300\pi\)
\(578\) 1.40586 0.0584762
\(579\) 11.2455 0.467345
\(580\) −3.97499 −0.165052
\(581\) 22.1397 0.918508
\(582\) 45.5834 1.88949
\(583\) −3.08273 −0.127674
\(584\) −15.3253 −0.634166
\(585\) −40.0058 −1.65404
\(586\) 4.91801 0.203161
\(587\) 29.0087 1.19732 0.598658 0.801005i \(-0.295701\pi\)
0.598658 + 0.801005i \(0.295701\pi\)
\(588\) −146.036 −6.02242
\(589\) −9.32407 −0.384192
\(590\) −109.851 −4.52251
\(591\) 30.1128 1.23867
\(592\) −11.2452 −0.462174
\(593\) 26.7625 1.09900 0.549502 0.835492i \(-0.314817\pi\)
0.549502 + 0.835492i \(0.314817\pi\)
\(594\) 9.48114 0.389016
\(595\) −64.0428 −2.62550
\(596\) 6.13009 0.251098
\(597\) −14.8953 −0.609626
\(598\) −70.1296 −2.86781
\(599\) −0.661074 −0.0270107 −0.0135054 0.999909i \(-0.504299\pi\)
−0.0135054 + 0.999909i \(0.504299\pi\)
\(600\) 52.5158 2.14395
\(601\) 28.3595 1.15681 0.578404 0.815750i \(-0.303676\pi\)
0.578404 + 0.815750i \(0.303676\pi\)
\(602\) 145.002 5.90984
\(603\) −17.0839 −0.695711
\(604\) −3.52153 −0.143289
\(605\) −4.90874 −0.199569
\(606\) 7.28306 0.295854
\(607\) 9.81288 0.398292 0.199146 0.979970i \(-0.436183\pi\)
0.199146 + 0.979970i \(0.436183\pi\)
\(608\) 13.4806 0.546711
\(609\) 4.23526 0.171622
\(610\) −96.5610 −3.90964
\(611\) 4.75966 0.192555
\(612\) −50.1001 −2.02517
\(613\) −19.1643 −0.774040 −0.387020 0.922071i \(-0.626496\pi\)
−0.387020 + 0.922071i \(0.626496\pi\)
\(614\) −58.3491 −2.35478
\(615\) −23.3317 −0.940823
\(616\) −53.1439 −2.14123
\(617\) 3.29263 0.132556 0.0662781 0.997801i \(-0.478888\pi\)
0.0662781 + 0.997801i \(0.478888\pi\)
\(618\) −47.0761 −1.89368
\(619\) 13.1219 0.527412 0.263706 0.964603i \(-0.415055\pi\)
0.263706 + 0.964603i \(0.415055\pi\)
\(620\) −31.6273 −1.27018
\(621\) 11.2493 0.451418
\(622\) −76.1603 −3.05375
\(623\) −41.0515 −1.64469
\(624\) 12.0355 0.481806
\(625\) −20.6508 −0.826033
\(626\) 50.3438 2.01214
\(627\) −26.7865 −1.06975
\(628\) −25.0523 −0.999697
\(629\) 33.5332 1.33706
\(630\) −130.532 −5.20053
\(631\) 48.7161 1.93936 0.969679 0.244384i \(-0.0785856\pi\)
0.969679 + 0.244384i \(0.0785856\pi\)
\(632\) 47.3760 1.88452
\(633\) 66.6902 2.65070
\(634\) 69.0876 2.74382
\(635\) −37.1246 −1.47325
\(636\) 8.98706 0.356360
\(637\) −56.4267 −2.23571
\(638\) 2.49317 0.0987056
\(639\) −48.0054 −1.89906
\(640\) 66.6584 2.63490
\(641\) 41.5587 1.64147 0.820736 0.571308i \(-0.193564\pi\)
0.820736 + 0.571308i \(0.193564\pi\)
\(642\) 46.9751 1.85396
\(643\) 31.4097 1.23868 0.619338 0.785124i \(-0.287401\pi\)
0.619338 + 0.785124i \(0.287401\pi\)
\(644\) −145.938 −5.75076
\(645\) 107.113 4.21756
\(646\) 32.4017 1.27483
\(647\) 32.1926 1.26562 0.632811 0.774306i \(-0.281901\pi\)
0.632811 + 0.774306i \(0.281901\pi\)
\(648\) 25.7361 1.01101
\(649\) 43.9434 1.72493
\(650\) 46.9640 1.84208
\(651\) 33.6981 1.32073
\(652\) 82.8840 3.24599
\(653\) −47.1808 −1.84633 −0.923163 0.384408i \(-0.874406\pi\)
−0.923163 + 0.384408i \(0.874406\pi\)
\(654\) −36.6202 −1.43196
\(655\) 20.2653 0.791831
\(656\) 3.78597 0.147817
\(657\) 15.0578 0.587461
\(658\) 15.5300 0.605422
\(659\) −9.56067 −0.372431 −0.186215 0.982509i \(-0.559622\pi\)
−0.186215 + 0.982509i \(0.559622\pi\)
\(660\) −90.8598 −3.53671
\(661\) −40.2832 −1.56683 −0.783417 0.621496i \(-0.786525\pi\)
−0.783417 + 0.621496i \(0.786525\pi\)
\(662\) 43.2031 1.67914
\(663\) −35.8900 −1.39385
\(664\) −16.4162 −0.637074
\(665\) 53.8417 2.08789
\(666\) 68.3476 2.64841
\(667\) 2.95812 0.114539
\(668\) −78.8586 −3.05113
\(669\) −29.0020 −1.12128
\(670\) 37.4777 1.44789
\(671\) 38.6269 1.49117
\(672\) −48.7203 −1.87943
\(673\) 17.4256 0.671709 0.335855 0.941914i \(-0.390975\pi\)
0.335855 + 0.941914i \(0.390975\pi\)
\(674\) 27.4799 1.05849
\(675\) −7.53335 −0.289959
\(676\) −3.31635 −0.127552
\(677\) −40.0720 −1.54009 −0.770047 0.637988i \(-0.779767\pi\)
−0.770047 + 0.637988i \(0.779767\pi\)
\(678\) 4.16979 0.160140
\(679\) 36.6521 1.40658
\(680\) 47.4868 1.82103
\(681\) 46.5288 1.78299
\(682\) 19.8371 0.759601
\(683\) −35.8465 −1.37163 −0.685814 0.727777i \(-0.740554\pi\)
−0.685814 + 0.727777i \(0.740554\pi\)
\(684\) 42.1199 1.61049
\(685\) −60.1057 −2.29652
\(686\) −104.799 −4.00126
\(687\) −34.7613 −1.32622
\(688\) −17.3809 −0.662641
\(689\) 3.47250 0.132292
\(690\) −169.030 −6.43485
\(691\) −16.3774 −0.623025 −0.311512 0.950242i \(-0.600836\pi\)
−0.311512 + 0.950242i \(0.600836\pi\)
\(692\) 50.1656 1.90701
\(693\) 52.2162 1.98353
\(694\) −28.6729 −1.08841
\(695\) −42.2048 −1.60092
\(696\) −3.14039 −0.119036
\(697\) −11.2898 −0.427631
\(698\) 84.0716 3.18216
\(699\) −36.6448 −1.38603
\(700\) 97.7310 3.69388
\(701\) 37.6420 1.42172 0.710860 0.703334i \(-0.248306\pi\)
0.710860 + 0.703334i \(0.248306\pi\)
\(702\) −10.6799 −0.403087
\(703\) −28.1919 −1.06328
\(704\) −37.0536 −1.39651
\(705\) 11.4720 0.432060
\(706\) 62.4996 2.35220
\(707\) 5.85606 0.220240
\(708\) −128.108 −4.81459
\(709\) −15.5997 −0.585861 −0.292930 0.956134i \(-0.594630\pi\)
−0.292930 + 0.956134i \(0.594630\pi\)
\(710\) 105.311 3.95227
\(711\) −46.5490 −1.74573
\(712\) 30.4391 1.14075
\(713\) 23.5365 0.881448
\(714\) −117.103 −4.38247
\(715\) −35.1072 −1.31294
\(716\) −9.22385 −0.344711
\(717\) 65.7147 2.45416
\(718\) 83.2051 3.10519
\(719\) 45.1328 1.68317 0.841586 0.540124i \(-0.181623\pi\)
0.841586 + 0.540124i \(0.181623\pi\)
\(720\) 15.6465 0.583109
\(721\) −37.8523 −1.40969
\(722\) 17.4055 0.647765
\(723\) 29.0464 1.08025
\(724\) −18.2213 −0.677189
\(725\) −1.98098 −0.0735717
\(726\) −8.97569 −0.333119
\(727\) 37.2070 1.37993 0.689965 0.723843i \(-0.257626\pi\)
0.689965 + 0.723843i \(0.257626\pi\)
\(728\) 59.8632 2.21868
\(729\) −35.3077 −1.30769
\(730\) −33.0329 −1.22260
\(731\) 51.8300 1.91700
\(732\) −112.609 −4.16213
\(733\) −12.1531 −0.448883 −0.224442 0.974488i \(-0.572056\pi\)
−0.224442 + 0.974488i \(0.572056\pi\)
\(734\) −8.94195 −0.330053
\(735\) −136.002 −5.01652
\(736\) −34.0287 −1.25431
\(737\) −14.9921 −0.552240
\(738\) −23.0109 −0.847042
\(739\) 32.8362 1.20790 0.603949 0.797023i \(-0.293593\pi\)
0.603949 + 0.797023i \(0.293593\pi\)
\(740\) −95.6270 −3.51532
\(741\) 30.1732 1.10844
\(742\) 11.3302 0.415944
\(743\) −13.2548 −0.486270 −0.243135 0.969992i \(-0.578176\pi\)
−0.243135 + 0.969992i \(0.578176\pi\)
\(744\) −24.9867 −0.916056
\(745\) 5.70892 0.209158
\(746\) −19.6623 −0.719888
\(747\) 16.1297 0.590154
\(748\) −43.9655 −1.60754
\(749\) 37.7711 1.38013
\(750\) 14.8610 0.542645
\(751\) −11.3269 −0.413323 −0.206662 0.978412i \(-0.566260\pi\)
−0.206662 + 0.978412i \(0.566260\pi\)
\(752\) −1.86153 −0.0678829
\(753\) −56.1769 −2.04720
\(754\) −2.80840 −0.102276
\(755\) −3.27958 −0.119356
\(756\) −22.2246 −0.808301
\(757\) 39.7099 1.44328 0.721640 0.692268i \(-0.243388\pi\)
0.721640 + 0.692268i \(0.243388\pi\)
\(758\) 70.2416 2.55129
\(759\) 67.6163 2.45432
\(760\) −39.9229 −1.44815
\(761\) 13.0738 0.473924 0.236962 0.971519i \(-0.423848\pi\)
0.236962 + 0.971519i \(0.423848\pi\)
\(762\) −67.8829 −2.45914
\(763\) −29.4451 −1.06598
\(764\) 83.1369 3.00779
\(765\) −46.6579 −1.68692
\(766\) −20.9511 −0.756994
\(767\) −49.4995 −1.78732
\(768\) 60.5363 2.18441
\(769\) −0.692477 −0.0249713 −0.0124857 0.999922i \(-0.503974\pi\)
−0.0124857 + 0.999922i \(0.503974\pi\)
\(770\) −114.549 −4.12806
\(771\) −3.17409 −0.114312
\(772\) −15.5175 −0.558487
\(773\) −20.6488 −0.742684 −0.371342 0.928496i \(-0.621102\pi\)
−0.371342 + 0.928496i \(0.621102\pi\)
\(774\) 105.640 3.79715
\(775\) −15.7618 −0.566180
\(776\) −27.1770 −0.975596
\(777\) 101.888 3.65523
\(778\) 4.78678 0.171614
\(779\) 9.49150 0.340068
\(780\) 102.348 3.66464
\(781\) −42.1273 −1.50743
\(782\) −81.7906 −2.92483
\(783\) 0.450486 0.0160991
\(784\) 22.0687 0.788169
\(785\) −23.3311 −0.832722
\(786\) 37.0554 1.32172
\(787\) −54.4542 −1.94108 −0.970541 0.240935i \(-0.922546\pi\)
−0.970541 + 0.240935i \(0.922546\pi\)
\(788\) −41.5524 −1.48024
\(789\) −72.3004 −2.57396
\(790\) 102.117 3.63314
\(791\) 3.35278 0.119211
\(792\) −38.7176 −1.37577
\(793\) −43.5107 −1.54511
\(794\) −24.5558 −0.871454
\(795\) 8.36959 0.296839
\(796\) 20.5540 0.728516
\(797\) 4.76060 0.168629 0.0843145 0.996439i \(-0.473130\pi\)
0.0843145 + 0.996439i \(0.473130\pi\)
\(798\) 98.4503 3.48510
\(799\) 5.55109 0.196383
\(800\) 22.7882 0.805683
\(801\) −29.9078 −1.05674
\(802\) −15.3717 −0.542793
\(803\) 13.2140 0.466313
\(804\) 43.7062 1.54140
\(805\) −135.911 −4.79023
\(806\) −22.3452 −0.787076
\(807\) −12.3801 −0.435799
\(808\) −4.34218 −0.152757
\(809\) 16.0485 0.564234 0.282117 0.959380i \(-0.408963\pi\)
0.282117 + 0.959380i \(0.408963\pi\)
\(810\) 55.4729 1.94912
\(811\) −17.3718 −0.610007 −0.305004 0.952351i \(-0.598658\pi\)
−0.305004 + 0.952351i \(0.598658\pi\)
\(812\) −5.84421 −0.205091
\(813\) −12.0182 −0.421497
\(814\) 59.9786 2.10225
\(815\) 77.1894 2.70383
\(816\) 14.0367 0.491384
\(817\) −43.5743 −1.52447
\(818\) 41.6256 1.45541
\(819\) −58.8183 −2.05528
\(820\) 32.1952 1.12430
\(821\) −32.1024 −1.12038 −0.560191 0.828363i \(-0.689272\pi\)
−0.560191 + 0.828363i \(0.689272\pi\)
\(822\) −109.904 −3.83334
\(823\) 17.3917 0.606237 0.303118 0.952953i \(-0.401972\pi\)
0.303118 + 0.952953i \(0.401972\pi\)
\(824\) 28.0669 0.977758
\(825\) −45.2809 −1.57648
\(826\) −161.508 −5.61960
\(827\) −7.67010 −0.266716 −0.133358 0.991068i \(-0.542576\pi\)
−0.133358 + 0.991068i \(0.542576\pi\)
\(828\) −106.322 −3.69494
\(829\) −20.8625 −0.724584 −0.362292 0.932065i \(-0.618006\pi\)
−0.362292 + 0.932065i \(0.618006\pi\)
\(830\) −35.3844 −1.22821
\(831\) 11.6586 0.404433
\(832\) 41.7385 1.44702
\(833\) −65.8092 −2.28015
\(834\) −77.1720 −2.67225
\(835\) −73.4405 −2.54151
\(836\) 36.9624 1.27837
\(837\) 3.58432 0.123892
\(838\) 34.1728 1.18048
\(839\) 34.5548 1.19296 0.596482 0.802626i \(-0.296565\pi\)
0.596482 + 0.802626i \(0.296565\pi\)
\(840\) 144.285 4.97831
\(841\) −28.8815 −0.995915
\(842\) −54.8046 −1.88869
\(843\) 9.64665 0.332248
\(844\) −92.0253 −3.16764
\(845\) −3.08850 −0.106247
\(846\) 11.3143 0.388992
\(847\) −7.21704 −0.247980
\(848\) −1.35811 −0.0466378
\(849\) −1.89052 −0.0648825
\(850\) 54.7731 1.87870
\(851\) 71.1640 2.43947
\(852\) 122.813 4.20751
\(853\) −34.8325 −1.19264 −0.596322 0.802746i \(-0.703372\pi\)
−0.596322 + 0.802746i \(0.703372\pi\)
\(854\) −141.968 −4.85805
\(855\) 39.2260 1.34150
\(856\) −28.0067 −0.957250
\(857\) 29.9372 1.02264 0.511318 0.859391i \(-0.329157\pi\)
0.511318 + 0.859391i \(0.329157\pi\)
\(858\) −64.1940 −2.19155
\(859\) 49.1525 1.67706 0.838532 0.544853i \(-0.183415\pi\)
0.838532 + 0.544853i \(0.183415\pi\)
\(860\) −147.804 −5.04007
\(861\) −34.3032 −1.16905
\(862\) −9.08120 −0.309307
\(863\) −12.4598 −0.424135 −0.212068 0.977255i \(-0.568020\pi\)
−0.212068 + 0.977255i \(0.568020\pi\)
\(864\) −5.18216 −0.176301
\(865\) 46.7189 1.58849
\(866\) 27.3003 0.927701
\(867\) 1.52686 0.0518549
\(868\) −46.4998 −1.57831
\(869\) −40.8493 −1.38572
\(870\) −6.76894 −0.229489
\(871\) 16.8876 0.572214
\(872\) 21.8331 0.739362
\(873\) 26.7026 0.903745
\(874\) 68.7626 2.32593
\(875\) 11.9492 0.403956
\(876\) −38.5227 −1.30156
\(877\) −49.2618 −1.66345 −0.831726 0.555186i \(-0.812647\pi\)
−0.831726 + 0.555186i \(0.812647\pi\)
\(878\) 42.1733 1.42328
\(879\) 5.34129 0.180157
\(880\) 13.7306 0.462859
\(881\) 27.4367 0.924365 0.462183 0.886785i \(-0.347066\pi\)
0.462183 + 0.886785i \(0.347066\pi\)
\(882\) −134.132 −4.51647
\(883\) 7.02371 0.236367 0.118183 0.992992i \(-0.462293\pi\)
0.118183 + 0.992992i \(0.462293\pi\)
\(884\) 49.5243 1.66568
\(885\) −119.306 −4.01043
\(886\) 61.8283 2.07716
\(887\) 4.20107 0.141058 0.0705290 0.997510i \(-0.477531\pi\)
0.0705290 + 0.997510i \(0.477531\pi\)
\(888\) −75.5488 −2.53525
\(889\) −54.5823 −1.83063
\(890\) 65.6099 2.19925
\(891\) −22.1906 −0.743412
\(892\) 40.0196 1.33995
\(893\) −4.66689 −0.156171
\(894\) 10.4388 0.349127
\(895\) −8.59011 −0.287136
\(896\) 98.0041 3.27409
\(897\) −76.1654 −2.54309
\(898\) −48.1733 −1.60756
\(899\) 0.942538 0.0314354
\(900\) 71.2011 2.37337
\(901\) 4.04990 0.134922
\(902\) −20.1933 −0.672363
\(903\) 157.482 5.24067
\(904\) −2.48604 −0.0826845
\(905\) −16.9694 −0.564081
\(906\) −5.99675 −0.199229
\(907\) −9.41590 −0.312650 −0.156325 0.987706i \(-0.549965\pi\)
−0.156325 + 0.987706i \(0.549965\pi\)
\(908\) −64.2047 −2.13071
\(909\) 4.26639 0.141507
\(910\) 129.032 4.27737
\(911\) 46.9174 1.55444 0.777221 0.629228i \(-0.216629\pi\)
0.777221 + 0.629228i \(0.216629\pi\)
\(912\) −11.8009 −0.390767
\(913\) 14.1547 0.468451
\(914\) 66.2015 2.18975
\(915\) −104.872 −3.46695
\(916\) 47.9668 1.58487
\(917\) 29.7950 0.983916
\(918\) −12.4557 −0.411100
\(919\) −27.2302 −0.898243 −0.449121 0.893471i \(-0.648263\pi\)
−0.449121 + 0.893471i \(0.648263\pi\)
\(920\) 100.776 3.32249
\(921\) −63.3710 −2.08815
\(922\) −43.9648 −1.44791
\(923\) 47.4537 1.56196
\(924\) −133.586 −4.39466
\(925\) −47.6567 −1.56694
\(926\) −37.8001 −1.24219
\(927\) −27.5770 −0.905748
\(928\) −1.36271 −0.0447331
\(929\) −9.10301 −0.298660 −0.149330 0.988787i \(-0.547712\pi\)
−0.149330 + 0.988787i \(0.547712\pi\)
\(930\) −53.8575 −1.76606
\(931\) 55.3268 1.81326
\(932\) 50.5658 1.65634
\(933\) −82.7152 −2.70797
\(934\) −13.0012 −0.425412
\(935\) −40.9448 −1.33904
\(936\) 43.6129 1.42553
\(937\) 26.6909 0.871953 0.435977 0.899958i \(-0.356403\pi\)
0.435977 + 0.899958i \(0.356403\pi\)
\(938\) 55.1014 1.79912
\(939\) 54.6767 1.78431
\(940\) −15.8301 −0.516320
\(941\) 16.3756 0.533830 0.266915 0.963720i \(-0.413996\pi\)
0.266915 + 0.963720i \(0.413996\pi\)
\(942\) −42.6612 −1.38998
\(943\) −23.9591 −0.780216
\(944\) 19.3595 0.630097
\(945\) −20.6976 −0.673294
\(946\) 92.7048 3.01409
\(947\) 12.7835 0.415407 0.207704 0.978192i \(-0.433401\pi\)
0.207704 + 0.978192i \(0.433401\pi\)
\(948\) 119.087 3.86778
\(949\) −14.8848 −0.483180
\(950\) −46.0486 −1.49401
\(951\) 75.0338 2.43314
\(952\) 69.8172 2.26279
\(953\) 19.3786 0.627736 0.313868 0.949467i \(-0.398375\pi\)
0.313868 + 0.949467i \(0.398375\pi\)
\(954\) 8.25452 0.267250
\(955\) 77.4249 2.50541
\(956\) −90.6792 −2.93277
\(957\) 2.70775 0.0875292
\(958\) −8.65965 −0.279780
\(959\) −88.3700 −2.85362
\(960\) 100.600 3.24685
\(961\) −23.5006 −0.758085
\(962\) −67.5621 −2.17829
\(963\) 27.5178 0.886750
\(964\) −40.0809 −1.29092
\(965\) −14.4514 −0.465206
\(966\) −248.515 −7.99584
\(967\) 25.2675 0.812547 0.406273 0.913752i \(-0.366828\pi\)
0.406273 + 0.913752i \(0.366828\pi\)
\(968\) 5.35133 0.171998
\(969\) 35.1904 1.13048
\(970\) −58.5786 −1.88084
\(971\) −29.0931 −0.933642 −0.466821 0.884352i \(-0.654601\pi\)
−0.466821 + 0.884352i \(0.654601\pi\)
\(972\) 78.5196 2.51852
\(973\) −62.0513 −1.98927
\(974\) 24.8776 0.797129
\(975\) 51.0061 1.63350
\(976\) 17.0173 0.544709
\(977\) −5.47042 −0.175014 −0.0875072 0.996164i \(-0.527890\pi\)
−0.0875072 + 0.996164i \(0.527890\pi\)
\(978\) 141.142 4.51322
\(979\) −26.2457 −0.838815
\(980\) 187.668 5.99485
\(981\) −21.4520 −0.684909
\(982\) 42.4191 1.35365
\(983\) 51.5729 1.64492 0.822460 0.568824i \(-0.192601\pi\)
0.822460 + 0.568824i \(0.192601\pi\)
\(984\) 25.4353 0.810849
\(985\) −38.6974 −1.23300
\(986\) −3.27537 −0.104309
\(987\) 16.8666 0.536870
\(988\) −41.6358 −1.32461
\(989\) 109.993 3.49758
\(990\) −83.4538 −2.65233
\(991\) −5.97771 −0.189888 −0.0949441 0.995483i \(-0.530267\pi\)
−0.0949441 + 0.995483i \(0.530267\pi\)
\(992\) −10.8425 −0.344249
\(993\) 46.9214 1.48901
\(994\) 154.833 4.91102
\(995\) 19.1418 0.606835
\(996\) −41.2649 −1.30753
\(997\) −39.6857 −1.25686 −0.628429 0.777867i \(-0.716302\pi\)
−0.628429 + 0.777867i \(0.716302\pi\)
\(998\) 60.6458 1.91971
\(999\) 10.8374 0.342881
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.1.18 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.18 153 1.1 even 1 trivial