Properties

Label 8003.2.a.b.1.6
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 1.6
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.62408 q^{2} -2.48215 q^{3} +4.88578 q^{4} -3.25865 q^{5} +6.51336 q^{6} +0.610888 q^{7} -7.57250 q^{8} +3.16108 q^{9} +O(q^{10})\) \(q-2.62408 q^{2} -2.48215 q^{3} +4.88578 q^{4} -3.25865 q^{5} +6.51336 q^{6} +0.610888 q^{7} -7.57250 q^{8} +3.16108 q^{9} +8.55094 q^{10} +6.56696 q^{11} -12.1272 q^{12} -0.553887 q^{13} -1.60302 q^{14} +8.08846 q^{15} +10.0993 q^{16} +6.81718 q^{17} -8.29493 q^{18} +7.03627 q^{19} -15.9210 q^{20} -1.51632 q^{21} -17.2322 q^{22} -1.85353 q^{23} +18.7961 q^{24} +5.61878 q^{25} +1.45344 q^{26} -0.399838 q^{27} +2.98466 q^{28} +6.42256 q^{29} -21.2247 q^{30} -1.64144 q^{31} -11.3562 q^{32} -16.3002 q^{33} -17.8888 q^{34} -1.99067 q^{35} +15.4444 q^{36} -2.92399 q^{37} -18.4637 q^{38} +1.37483 q^{39} +24.6761 q^{40} +4.41849 q^{41} +3.97893 q^{42} -2.75943 q^{43} +32.0847 q^{44} -10.3009 q^{45} +4.86381 q^{46} +0.122965 q^{47} -25.0679 q^{48} -6.62682 q^{49} -14.7441 q^{50} -16.9213 q^{51} -2.70617 q^{52} -1.00000 q^{53} +1.04920 q^{54} -21.3994 q^{55} -4.62595 q^{56} -17.4651 q^{57} -16.8533 q^{58} +2.05909 q^{59} +39.5184 q^{60} -8.14786 q^{61} +4.30725 q^{62} +1.93107 q^{63} +9.60108 q^{64} +1.80492 q^{65} +42.7729 q^{66} -5.00407 q^{67} +33.3072 q^{68} +4.60075 q^{69} +5.22366 q^{70} +0.658063 q^{71} -23.9373 q^{72} +5.08046 q^{73} +7.67277 q^{74} -13.9467 q^{75} +34.3777 q^{76} +4.01167 q^{77} -3.60767 q^{78} -9.53151 q^{79} -32.9099 q^{80} -8.49080 q^{81} -11.5945 q^{82} -0.567433 q^{83} -7.40839 q^{84} -22.2148 q^{85} +7.24097 q^{86} -15.9418 q^{87} -49.7282 q^{88} -2.38038 q^{89} +27.0302 q^{90} -0.338363 q^{91} -9.05594 q^{92} +4.07430 q^{93} -0.322669 q^{94} -22.9287 q^{95} +28.1879 q^{96} -12.0139 q^{97} +17.3893 q^{98} +20.7587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62408 −1.85550 −0.927751 0.373200i \(-0.878261\pi\)
−0.927751 + 0.373200i \(0.878261\pi\)
\(3\) −2.48215 −1.43307 −0.716536 0.697550i \(-0.754273\pi\)
−0.716536 + 0.697550i \(0.754273\pi\)
\(4\) 4.88578 2.44289
\(5\) −3.25865 −1.45731 −0.728656 0.684880i \(-0.759855\pi\)
−0.728656 + 0.684880i \(0.759855\pi\)
\(6\) 6.51336 2.65907
\(7\) 0.610888 0.230894 0.115447 0.993314i \(-0.463170\pi\)
0.115447 + 0.993314i \(0.463170\pi\)
\(8\) −7.57250 −2.67728
\(9\) 3.16108 1.05369
\(10\) 8.55094 2.70404
\(11\) 6.56696 1.98001 0.990006 0.141027i \(-0.0450403\pi\)
0.990006 + 0.141027i \(0.0450403\pi\)
\(12\) −12.1272 −3.50083
\(13\) −0.553887 −0.153621 −0.0768104 0.997046i \(-0.524474\pi\)
−0.0768104 + 0.997046i \(0.524474\pi\)
\(14\) −1.60302 −0.428424
\(15\) 8.08846 2.08843
\(16\) 10.0993 2.52481
\(17\) 6.81718 1.65341 0.826705 0.562636i \(-0.190213\pi\)
0.826705 + 0.562636i \(0.190213\pi\)
\(18\) −8.29493 −1.95513
\(19\) 7.03627 1.61423 0.807116 0.590393i \(-0.201027\pi\)
0.807116 + 0.590393i \(0.201027\pi\)
\(20\) −15.9210 −3.56005
\(21\) −1.51632 −0.330888
\(22\) −17.2322 −3.67392
\(23\) −1.85353 −0.386488 −0.193244 0.981151i \(-0.561901\pi\)
−0.193244 + 0.981151i \(0.561901\pi\)
\(24\) 18.7961 3.83674
\(25\) 5.61878 1.12376
\(26\) 1.45344 0.285044
\(27\) −0.399838 −0.0769488
\(28\) 2.98466 0.564048
\(29\) 6.42256 1.19264 0.596320 0.802747i \(-0.296629\pi\)
0.596320 + 0.802747i \(0.296629\pi\)
\(30\) −21.2247 −3.87509
\(31\) −1.64144 −0.294811 −0.147405 0.989076i \(-0.547092\pi\)
−0.147405 + 0.989076i \(0.547092\pi\)
\(32\) −11.3562 −2.00752
\(33\) −16.3002 −2.83750
\(34\) −17.8888 −3.06791
\(35\) −1.99067 −0.336484
\(36\) 15.4444 2.57406
\(37\) −2.92399 −0.480701 −0.240350 0.970686i \(-0.577262\pi\)
−0.240350 + 0.970686i \(0.577262\pi\)
\(38\) −18.4637 −2.99521
\(39\) 1.37483 0.220150
\(40\) 24.6761 3.90163
\(41\) 4.41849 0.690053 0.345026 0.938593i \(-0.387870\pi\)
0.345026 + 0.938593i \(0.387870\pi\)
\(42\) 3.97893 0.613963
\(43\) −2.75943 −0.420810 −0.210405 0.977614i \(-0.567478\pi\)
−0.210405 + 0.977614i \(0.567478\pi\)
\(44\) 32.0847 4.83695
\(45\) −10.3009 −1.53556
\(46\) 4.86381 0.717129
\(47\) 0.122965 0.0179362 0.00896812 0.999960i \(-0.497145\pi\)
0.00896812 + 0.999960i \(0.497145\pi\)
\(48\) −25.0679 −3.61824
\(49\) −6.62682 −0.946688
\(50\) −14.7441 −2.08513
\(51\) −16.9213 −2.36946
\(52\) −2.70617 −0.375278
\(53\) −1.00000 −0.137361
\(54\) 1.04920 0.142779
\(55\) −21.3994 −2.88549
\(56\) −4.62595 −0.618168
\(57\) −17.4651 −2.31331
\(58\) −16.8533 −2.21295
\(59\) 2.05909 0.268071 0.134035 0.990977i \(-0.457206\pi\)
0.134035 + 0.990977i \(0.457206\pi\)
\(60\) 39.5184 5.10181
\(61\) −8.14786 −1.04323 −0.521613 0.853182i \(-0.674670\pi\)
−0.521613 + 0.853182i \(0.674670\pi\)
\(62\) 4.30725 0.547022
\(63\) 1.93107 0.243292
\(64\) 9.60108 1.20014
\(65\) 1.80492 0.223873
\(66\) 42.7729 5.26499
\(67\) −5.00407 −0.611344 −0.305672 0.952137i \(-0.598881\pi\)
−0.305672 + 0.952137i \(0.598881\pi\)
\(68\) 33.3072 4.03910
\(69\) 4.60075 0.553865
\(70\) 5.22366 0.624347
\(71\) 0.658063 0.0780977 0.0390488 0.999237i \(-0.487567\pi\)
0.0390488 + 0.999237i \(0.487567\pi\)
\(72\) −23.9373 −2.82104
\(73\) 5.08046 0.594622 0.297311 0.954781i \(-0.403910\pi\)
0.297311 + 0.954781i \(0.403910\pi\)
\(74\) 7.67277 0.891942
\(75\) −13.9467 −1.61042
\(76\) 34.3777 3.94339
\(77\) 4.01167 0.457173
\(78\) −3.60767 −0.408488
\(79\) −9.53151 −1.07238 −0.536189 0.844098i \(-0.680137\pi\)
−0.536189 + 0.844098i \(0.680137\pi\)
\(80\) −32.9099 −3.67944
\(81\) −8.49080 −0.943422
\(82\) −11.5945 −1.28039
\(83\) −0.567433 −0.0622839 −0.0311419 0.999515i \(-0.509914\pi\)
−0.0311419 + 0.999515i \(0.509914\pi\)
\(84\) −7.40839 −0.808321
\(85\) −22.2148 −2.40953
\(86\) 7.24097 0.780814
\(87\) −15.9418 −1.70914
\(88\) −49.7282 −5.30105
\(89\) −2.38038 −0.252320 −0.126160 0.992010i \(-0.540265\pi\)
−0.126160 + 0.992010i \(0.540265\pi\)
\(90\) 27.0302 2.84924
\(91\) −0.338363 −0.0354701
\(92\) −9.05594 −0.944147
\(93\) 4.07430 0.422485
\(94\) −0.322669 −0.0332807
\(95\) −22.9287 −2.35244
\(96\) 28.1879 2.87691
\(97\) −12.0139 −1.21982 −0.609911 0.792470i \(-0.708795\pi\)
−0.609911 + 0.792470i \(0.708795\pi\)
\(98\) 17.3893 1.75658
\(99\) 20.7587 2.08633
\(100\) 27.4521 2.74521
\(101\) 7.81888 0.778007 0.389004 0.921236i \(-0.372819\pi\)
0.389004 + 0.921236i \(0.372819\pi\)
\(102\) 44.4028 4.39653
\(103\) −4.44738 −0.438213 −0.219107 0.975701i \(-0.570314\pi\)
−0.219107 + 0.975701i \(0.570314\pi\)
\(104\) 4.19431 0.411286
\(105\) 4.94114 0.482206
\(106\) 2.62408 0.254873
\(107\) 1.68699 0.163088 0.0815439 0.996670i \(-0.474015\pi\)
0.0815439 + 0.996670i \(0.474015\pi\)
\(108\) −1.95352 −0.187977
\(109\) −7.52303 −0.720575 −0.360288 0.932841i \(-0.617321\pi\)
−0.360288 + 0.932841i \(0.617321\pi\)
\(110\) 56.1536 5.35404
\(111\) 7.25779 0.688879
\(112\) 6.16951 0.582964
\(113\) −9.84428 −0.926072 −0.463036 0.886340i \(-0.653240\pi\)
−0.463036 + 0.886340i \(0.653240\pi\)
\(114\) 45.8298 4.29235
\(115\) 6.04000 0.563233
\(116\) 31.3792 2.91349
\(117\) −1.75088 −0.161869
\(118\) −5.40321 −0.497406
\(119\) 4.16454 0.381762
\(120\) −61.2498 −5.59132
\(121\) 32.1249 2.92045
\(122\) 21.3806 1.93571
\(123\) −10.9674 −0.988896
\(124\) −8.01969 −0.720189
\(125\) −2.01640 −0.180352
\(126\) −5.06727 −0.451428
\(127\) −18.4441 −1.63665 −0.818323 0.574758i \(-0.805096\pi\)
−0.818323 + 0.574758i \(0.805096\pi\)
\(128\) −2.48153 −0.219338
\(129\) 6.84934 0.603051
\(130\) −4.73626 −0.415397
\(131\) 7.41549 0.647894 0.323947 0.946075i \(-0.394990\pi\)
0.323947 + 0.946075i \(0.394990\pi\)
\(132\) −79.6391 −6.93169
\(133\) 4.29837 0.372716
\(134\) 13.1310 1.13435
\(135\) 1.30293 0.112138
\(136\) −51.6231 −4.42664
\(137\) 6.68839 0.571428 0.285714 0.958315i \(-0.407769\pi\)
0.285714 + 0.958315i \(0.407769\pi\)
\(138\) −12.0727 −1.02770
\(139\) −5.83713 −0.495099 −0.247549 0.968875i \(-0.579625\pi\)
−0.247549 + 0.968875i \(0.579625\pi\)
\(140\) −9.72596 −0.821993
\(141\) −0.305217 −0.0257039
\(142\) −1.72681 −0.144910
\(143\) −3.63735 −0.304171
\(144\) 31.9246 2.66038
\(145\) −20.9289 −1.73805
\(146\) −13.3315 −1.10332
\(147\) 16.4488 1.35667
\(148\) −14.2860 −1.17430
\(149\) −19.5185 −1.59902 −0.799508 0.600656i \(-0.794906\pi\)
−0.799508 + 0.600656i \(0.794906\pi\)
\(150\) 36.5972 2.98815
\(151\) −1.00000 −0.0813788
\(152\) −53.2821 −4.32175
\(153\) 21.5497 1.74219
\(154\) −10.5269 −0.848285
\(155\) 5.34886 0.429631
\(156\) 6.71713 0.537801
\(157\) −3.54755 −0.283125 −0.141563 0.989929i \(-0.545213\pi\)
−0.141563 + 0.989929i \(0.545213\pi\)
\(158\) 25.0114 1.98980
\(159\) 2.48215 0.196848
\(160\) 37.0059 2.92558
\(161\) −1.13230 −0.0892377
\(162\) 22.2805 1.75052
\(163\) −0.226666 −0.0177539 −0.00887693 0.999961i \(-0.502826\pi\)
−0.00887693 + 0.999961i \(0.502826\pi\)
\(164\) 21.5878 1.68572
\(165\) 53.1166 4.13512
\(166\) 1.48899 0.115568
\(167\) −7.25741 −0.561595 −0.280797 0.959767i \(-0.590599\pi\)
−0.280797 + 0.959767i \(0.590599\pi\)
\(168\) 11.4823 0.885879
\(169\) −12.6932 −0.976401
\(170\) 58.2933 4.47089
\(171\) 22.2423 1.70091
\(172\) −13.4820 −1.02799
\(173\) −22.8210 −1.73505 −0.867525 0.497393i \(-0.834291\pi\)
−0.867525 + 0.497393i \(0.834291\pi\)
\(174\) 41.8324 3.17131
\(175\) 3.43245 0.259469
\(176\) 66.3214 4.99916
\(177\) −5.11098 −0.384164
\(178\) 6.24630 0.468180
\(179\) 11.8175 0.883284 0.441642 0.897191i \(-0.354396\pi\)
0.441642 + 0.897191i \(0.354396\pi\)
\(180\) −50.3277 −3.75121
\(181\) 0.285597 0.0212282 0.0106141 0.999944i \(-0.496621\pi\)
0.0106141 + 0.999944i \(0.496621\pi\)
\(182\) 0.887890 0.0658148
\(183\) 20.2242 1.49502
\(184\) 14.0359 1.03474
\(185\) 9.52825 0.700531
\(186\) −10.6913 −0.783921
\(187\) 44.7681 3.27377
\(188\) 0.600778 0.0438162
\(189\) −0.244256 −0.0177670
\(190\) 60.1667 4.36495
\(191\) −25.2649 −1.82810 −0.914052 0.405596i \(-0.867064\pi\)
−0.914052 + 0.405596i \(0.867064\pi\)
\(192\) −23.8314 −1.71988
\(193\) 3.29886 0.237457 0.118729 0.992927i \(-0.462118\pi\)
0.118729 + 0.992927i \(0.462118\pi\)
\(194\) 31.5253 2.26338
\(195\) −4.48010 −0.320826
\(196\) −32.3771 −2.31265
\(197\) −2.84106 −0.202417 −0.101209 0.994865i \(-0.532271\pi\)
−0.101209 + 0.994865i \(0.532271\pi\)
\(198\) −54.4724 −3.87119
\(199\) −13.3172 −0.944034 −0.472017 0.881589i \(-0.656474\pi\)
−0.472017 + 0.881589i \(0.656474\pi\)
\(200\) −42.5482 −3.00861
\(201\) 12.4209 0.876100
\(202\) −20.5173 −1.44359
\(203\) 3.92346 0.275373
\(204\) −82.6737 −5.78831
\(205\) −14.3983 −1.00562
\(206\) 11.6703 0.813105
\(207\) −5.85917 −0.407240
\(208\) −5.59385 −0.387864
\(209\) 46.2069 3.19620
\(210\) −12.9659 −0.894735
\(211\) 8.10242 0.557794 0.278897 0.960321i \(-0.410031\pi\)
0.278897 + 0.960321i \(0.410031\pi\)
\(212\) −4.88578 −0.335556
\(213\) −1.63341 −0.111920
\(214\) −4.42680 −0.302610
\(215\) 8.99203 0.613251
\(216\) 3.02777 0.206014
\(217\) −1.00273 −0.0680700
\(218\) 19.7410 1.33703
\(219\) −12.6105 −0.852137
\(220\) −104.553 −7.04894
\(221\) −3.77595 −0.253998
\(222\) −19.0450 −1.27822
\(223\) −12.9999 −0.870536 −0.435268 0.900301i \(-0.643346\pi\)
−0.435268 + 0.900301i \(0.643346\pi\)
\(224\) −6.93738 −0.463523
\(225\) 17.7615 1.18410
\(226\) 25.8321 1.71833
\(227\) −19.2694 −1.27895 −0.639476 0.768811i \(-0.720849\pi\)
−0.639476 + 0.768811i \(0.720849\pi\)
\(228\) −85.3306 −5.65116
\(229\) −10.3824 −0.686090 −0.343045 0.939319i \(-0.611458\pi\)
−0.343045 + 0.939319i \(0.611458\pi\)
\(230\) −15.8494 −1.04508
\(231\) −9.95759 −0.655161
\(232\) −48.6348 −3.19303
\(233\) 12.6518 0.828846 0.414423 0.910084i \(-0.363983\pi\)
0.414423 + 0.910084i \(0.363983\pi\)
\(234\) 4.59446 0.300349
\(235\) −0.400699 −0.0261387
\(236\) 10.0602 0.654866
\(237\) 23.6587 1.53680
\(238\) −10.9281 −0.708361
\(239\) 0.236038 0.0152680 0.00763402 0.999971i \(-0.497570\pi\)
0.00763402 + 0.999971i \(0.497570\pi\)
\(240\) 81.6874 5.27290
\(241\) 11.9739 0.771304 0.385652 0.922644i \(-0.373976\pi\)
0.385652 + 0.922644i \(0.373976\pi\)
\(242\) −84.2982 −5.41889
\(243\) 22.2750 1.42894
\(244\) −39.8086 −2.54849
\(245\) 21.5945 1.37962
\(246\) 28.7792 1.83490
\(247\) −3.89730 −0.247979
\(248\) 12.4298 0.789291
\(249\) 1.40846 0.0892573
\(250\) 5.29118 0.334643
\(251\) −23.0954 −1.45777 −0.728885 0.684636i \(-0.759961\pi\)
−0.728885 + 0.684636i \(0.759961\pi\)
\(252\) 9.43477 0.594334
\(253\) −12.1721 −0.765251
\(254\) 48.3987 3.03680
\(255\) 55.1405 3.45303
\(256\) −12.6904 −0.793153
\(257\) −13.6842 −0.853599 −0.426800 0.904346i \(-0.640359\pi\)
−0.426800 + 0.904346i \(0.640359\pi\)
\(258\) −17.9732 −1.11896
\(259\) −1.78623 −0.110991
\(260\) 8.81845 0.546897
\(261\) 20.3023 1.25668
\(262\) −19.4588 −1.20217
\(263\) 25.8285 1.59266 0.796328 0.604865i \(-0.206773\pi\)
0.796328 + 0.604865i \(0.206773\pi\)
\(264\) 123.433 7.59678
\(265\) 3.25865 0.200177
\(266\) −11.2793 −0.691576
\(267\) 5.90847 0.361592
\(268\) −24.4487 −1.49344
\(269\) −11.7068 −0.713779 −0.356889 0.934147i \(-0.616163\pi\)
−0.356889 + 0.934147i \(0.616163\pi\)
\(270\) −3.41899 −0.208073
\(271\) 26.6988 1.62184 0.810918 0.585159i \(-0.198968\pi\)
0.810918 + 0.585159i \(0.198968\pi\)
\(272\) 68.8485 4.17455
\(273\) 0.839869 0.0508312
\(274\) −17.5509 −1.06029
\(275\) 36.8983 2.22505
\(276\) 22.4782 1.35303
\(277\) 2.31899 0.139335 0.0696674 0.997570i \(-0.477806\pi\)
0.0696674 + 0.997570i \(0.477806\pi\)
\(278\) 15.3171 0.918656
\(279\) −5.18872 −0.310640
\(280\) 15.0743 0.900863
\(281\) 13.0713 0.779770 0.389885 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(282\) 0.800913 0.0476937
\(283\) −31.7668 −1.88834 −0.944170 0.329460i \(-0.893133\pi\)
−0.944170 + 0.329460i \(0.893133\pi\)
\(284\) 3.21515 0.190784
\(285\) 56.9126 3.37121
\(286\) 9.54469 0.564390
\(287\) 2.69920 0.159329
\(288\) −35.8980 −2.11531
\(289\) 29.4740 1.73377
\(290\) 54.9189 3.22495
\(291\) 29.8202 1.74809
\(292\) 24.8220 1.45260
\(293\) −26.8730 −1.56994 −0.784969 0.619535i \(-0.787321\pi\)
−0.784969 + 0.619535i \(0.787321\pi\)
\(294\) −43.1628 −2.51731
\(295\) −6.70985 −0.390662
\(296\) 22.1419 1.28697
\(297\) −2.62572 −0.152359
\(298\) 51.2180 2.96698
\(299\) 1.02665 0.0593725
\(300\) −68.1404 −3.93409
\(301\) −1.68571 −0.0971624
\(302\) 2.62408 0.150999
\(303\) −19.4077 −1.11494
\(304\) 71.0611 4.07563
\(305\) 26.5510 1.52031
\(306\) −56.5481 −3.23264
\(307\) −30.9630 −1.76715 −0.883576 0.468288i \(-0.844871\pi\)
−0.883576 + 0.468288i \(0.844871\pi\)
\(308\) 19.6001 1.11682
\(309\) 11.0391 0.627991
\(310\) −14.0358 −0.797181
\(311\) −14.7720 −0.837643 −0.418821 0.908069i \(-0.637557\pi\)
−0.418821 + 0.908069i \(0.637557\pi\)
\(312\) −10.4109 −0.589402
\(313\) 25.1441 1.42123 0.710615 0.703581i \(-0.248417\pi\)
0.710615 + 0.703581i \(0.248417\pi\)
\(314\) 9.30903 0.525339
\(315\) −6.29267 −0.354552
\(316\) −46.5688 −2.61970
\(317\) −18.9254 −1.06296 −0.531479 0.847071i \(-0.678364\pi\)
−0.531479 + 0.847071i \(0.678364\pi\)
\(318\) −6.51336 −0.365251
\(319\) 42.1767 2.36144
\(320\) −31.2865 −1.74897
\(321\) −4.18738 −0.233716
\(322\) 2.97124 0.165581
\(323\) 47.9676 2.66899
\(324\) −41.4841 −2.30467
\(325\) −3.11217 −0.172632
\(326\) 0.594789 0.0329423
\(327\) 18.6733 1.03264
\(328\) −33.4590 −1.84747
\(329\) 0.0751177 0.00414137
\(330\) −139.382 −7.67272
\(331\) −3.59576 −0.197641 −0.0988205 0.995105i \(-0.531507\pi\)
−0.0988205 + 0.995105i \(0.531507\pi\)
\(332\) −2.77235 −0.152153
\(333\) −9.24298 −0.506512
\(334\) 19.0440 1.04204
\(335\) 16.3065 0.890918
\(336\) −15.3137 −0.835429
\(337\) −19.9423 −1.08633 −0.543163 0.839627i \(-0.682774\pi\)
−0.543163 + 0.839627i \(0.682774\pi\)
\(338\) 33.3079 1.81171
\(339\) 24.4350 1.32713
\(340\) −108.537 −5.88622
\(341\) −10.7792 −0.583728
\(342\) −58.3654 −3.15604
\(343\) −8.32446 −0.449478
\(344\) 20.8958 1.12663
\(345\) −14.9922 −0.807154
\(346\) 59.8841 3.21939
\(347\) −12.8463 −0.689624 −0.344812 0.938672i \(-0.612057\pi\)
−0.344812 + 0.938672i \(0.612057\pi\)
\(348\) −77.8880 −4.17523
\(349\) −14.6891 −0.786288 −0.393144 0.919477i \(-0.628613\pi\)
−0.393144 + 0.919477i \(0.628613\pi\)
\(350\) −9.00700 −0.481444
\(351\) 0.221465 0.0118209
\(352\) −74.5758 −3.97490
\(353\) 31.0255 1.65132 0.825660 0.564168i \(-0.190803\pi\)
0.825660 + 0.564168i \(0.190803\pi\)
\(354\) 13.4116 0.712818
\(355\) −2.14439 −0.113813
\(356\) −11.6300 −0.616389
\(357\) −10.3370 −0.547093
\(358\) −31.0101 −1.63894
\(359\) −0.915912 −0.0483400 −0.0241700 0.999708i \(-0.507694\pi\)
−0.0241700 + 0.999708i \(0.507694\pi\)
\(360\) 78.0032 4.11113
\(361\) 30.5091 1.60574
\(362\) −0.749427 −0.0393890
\(363\) −79.7389 −4.18521
\(364\) −1.65317 −0.0866494
\(365\) −16.5554 −0.866550
\(366\) −53.0700 −2.77401
\(367\) −20.3916 −1.06443 −0.532217 0.846608i \(-0.678641\pi\)
−0.532217 + 0.846608i \(0.678641\pi\)
\(368\) −18.7193 −0.975810
\(369\) 13.9672 0.727105
\(370\) −25.0029 −1.29984
\(371\) −0.610888 −0.0317157
\(372\) 19.9061 1.03208
\(373\) 27.9887 1.44920 0.724601 0.689169i \(-0.242024\pi\)
0.724601 + 0.689169i \(0.242024\pi\)
\(374\) −117.475 −6.07449
\(375\) 5.00500 0.258457
\(376\) −0.931150 −0.0480204
\(377\) −3.55738 −0.183214
\(378\) 0.640946 0.0329667
\(379\) 2.93247 0.150631 0.0753155 0.997160i \(-0.476004\pi\)
0.0753155 + 0.997160i \(0.476004\pi\)
\(380\) −112.025 −5.74674
\(381\) 45.7810 2.34543
\(382\) 66.2970 3.39205
\(383\) −28.5613 −1.45942 −0.729708 0.683759i \(-0.760344\pi\)
−0.729708 + 0.683759i \(0.760344\pi\)
\(384\) 6.15953 0.314327
\(385\) −13.0726 −0.666243
\(386\) −8.65647 −0.440603
\(387\) −8.72281 −0.443405
\(388\) −58.6970 −2.97989
\(389\) 24.0747 1.22064 0.610318 0.792156i \(-0.291041\pi\)
0.610318 + 0.792156i \(0.291041\pi\)
\(390\) 11.7561 0.595294
\(391\) −12.6359 −0.639023
\(392\) 50.1815 2.53455
\(393\) −18.4064 −0.928479
\(394\) 7.45516 0.375586
\(395\) 31.0598 1.56279
\(396\) 101.422 5.09667
\(397\) 10.1374 0.508782 0.254391 0.967101i \(-0.418125\pi\)
0.254391 + 0.967101i \(0.418125\pi\)
\(398\) 34.9455 1.75166
\(399\) −10.6692 −0.534129
\(400\) 56.7455 2.83728
\(401\) 4.33304 0.216382 0.108191 0.994130i \(-0.465494\pi\)
0.108191 + 0.994130i \(0.465494\pi\)
\(402\) −32.5933 −1.62560
\(403\) 0.909171 0.0452890
\(404\) 38.2013 1.90058
\(405\) 27.6685 1.37486
\(406\) −10.2955 −0.510956
\(407\) −19.2017 −0.951794
\(408\) 128.136 6.34370
\(409\) 8.95975 0.443031 0.221516 0.975157i \(-0.428900\pi\)
0.221516 + 0.975157i \(0.428900\pi\)
\(410\) 37.7823 1.86593
\(411\) −16.6016 −0.818898
\(412\) −21.7289 −1.07051
\(413\) 1.25787 0.0618959
\(414\) 15.3749 0.755635
\(415\) 1.84906 0.0907670
\(416\) 6.29007 0.308396
\(417\) 14.4886 0.709512
\(418\) −121.250 −5.93055
\(419\) −33.1607 −1.62001 −0.810003 0.586425i \(-0.800535\pi\)
−0.810003 + 0.586425i \(0.800535\pi\)
\(420\) 24.1413 1.17798
\(421\) 25.2215 1.22922 0.614611 0.788830i \(-0.289313\pi\)
0.614611 + 0.788830i \(0.289313\pi\)
\(422\) −21.2614 −1.03499
\(423\) 0.388702 0.0188993
\(424\) 7.57250 0.367753
\(425\) 38.3043 1.85803
\(426\) 4.28620 0.207667
\(427\) −4.97743 −0.240875
\(428\) 8.24227 0.398405
\(429\) 9.02847 0.435899
\(430\) −23.5958 −1.13789
\(431\) −18.3840 −0.885527 −0.442763 0.896638i \(-0.646002\pi\)
−0.442763 + 0.896638i \(0.646002\pi\)
\(432\) −4.03806 −0.194281
\(433\) 21.5689 1.03653 0.518267 0.855219i \(-0.326577\pi\)
0.518267 + 0.855219i \(0.326577\pi\)
\(434\) 2.63125 0.126304
\(435\) 51.9486 2.49075
\(436\) −36.7558 −1.76028
\(437\) −13.0419 −0.623881
\(438\) 33.0908 1.58114
\(439\) 29.1914 1.39323 0.696616 0.717444i \(-0.254688\pi\)
0.696616 + 0.717444i \(0.254688\pi\)
\(440\) 162.047 7.72528
\(441\) −20.9479 −0.997520
\(442\) 9.90839 0.471294
\(443\) 29.4471 1.39908 0.699538 0.714596i \(-0.253389\pi\)
0.699538 + 0.714596i \(0.253389\pi\)
\(444\) 35.4599 1.68285
\(445\) 7.75682 0.367709
\(446\) 34.1127 1.61528
\(447\) 48.4478 2.29150
\(448\) 5.86518 0.277104
\(449\) −31.0829 −1.46689 −0.733446 0.679748i \(-0.762089\pi\)
−0.733446 + 0.679748i \(0.762089\pi\)
\(450\) −46.6074 −2.19709
\(451\) 29.0161 1.36631
\(452\) −48.0969 −2.26229
\(453\) 2.48215 0.116622
\(454\) 50.5643 2.37310
\(455\) 1.10261 0.0516910
\(456\) 132.254 6.19338
\(457\) 8.29414 0.387984 0.193992 0.981003i \(-0.437856\pi\)
0.193992 + 0.981003i \(0.437856\pi\)
\(458\) 27.2443 1.27304
\(459\) −2.72577 −0.127228
\(460\) 29.5101 1.37592
\(461\) −15.1643 −0.706271 −0.353135 0.935572i \(-0.614885\pi\)
−0.353135 + 0.935572i \(0.614885\pi\)
\(462\) 26.1295 1.21565
\(463\) −13.0326 −0.605677 −0.302838 0.953042i \(-0.597934\pi\)
−0.302838 + 0.953042i \(0.597934\pi\)
\(464\) 64.8631 3.01119
\(465\) −13.2767 −0.615692
\(466\) −33.1992 −1.53792
\(467\) −1.15375 −0.0533891 −0.0266946 0.999644i \(-0.508498\pi\)
−0.0266946 + 0.999644i \(0.508498\pi\)
\(468\) −8.55443 −0.395429
\(469\) −3.05692 −0.141156
\(470\) 1.05146 0.0485004
\(471\) 8.80556 0.405739
\(472\) −15.5924 −0.717700
\(473\) −18.1211 −0.833208
\(474\) −62.0821 −2.85153
\(475\) 39.5353 1.81400
\(476\) 20.3470 0.932603
\(477\) −3.16108 −0.144736
\(478\) −0.619382 −0.0283299
\(479\) −29.9037 −1.36634 −0.683168 0.730262i \(-0.739398\pi\)
−0.683168 + 0.730262i \(0.739398\pi\)
\(480\) −91.8544 −4.19256
\(481\) 1.61956 0.0738456
\(482\) −31.4203 −1.43116
\(483\) 2.81054 0.127884
\(484\) 156.955 7.13432
\(485\) 39.1489 1.77766
\(486\) −58.4512 −2.65140
\(487\) −7.16599 −0.324722 −0.162361 0.986731i \(-0.551911\pi\)
−0.162361 + 0.986731i \(0.551911\pi\)
\(488\) 61.6996 2.79301
\(489\) 0.562620 0.0254425
\(490\) −56.6655 −2.55989
\(491\) −18.0096 −0.812762 −0.406381 0.913704i \(-0.633209\pi\)
−0.406381 + 0.913704i \(0.633209\pi\)
\(492\) −53.5842 −2.41576
\(493\) 43.7838 1.97192
\(494\) 10.2268 0.460126
\(495\) −67.6453 −3.04043
\(496\) −16.5773 −0.744342
\(497\) 0.402002 0.0180323
\(498\) −3.69590 −0.165617
\(499\) 33.9682 1.52062 0.760312 0.649558i \(-0.225046\pi\)
0.760312 + 0.649558i \(0.225046\pi\)
\(500\) −9.85166 −0.440579
\(501\) 18.0140 0.804806
\(502\) 60.6042 2.70490
\(503\) 34.9480 1.55825 0.779126 0.626867i \(-0.215663\pi\)
0.779126 + 0.626867i \(0.215663\pi\)
\(504\) −14.6230 −0.651361
\(505\) −25.4790 −1.13380
\(506\) 31.9404 1.41992
\(507\) 31.5065 1.39925
\(508\) −90.1136 −3.99814
\(509\) −18.3056 −0.811382 −0.405691 0.914010i \(-0.632969\pi\)
−0.405691 + 0.914010i \(0.632969\pi\)
\(510\) −144.693 −6.40711
\(511\) 3.10359 0.137295
\(512\) 38.2638 1.69104
\(513\) −2.81337 −0.124213
\(514\) 35.9085 1.58386
\(515\) 14.4924 0.638613
\(516\) 33.4643 1.47319
\(517\) 0.807504 0.0355140
\(518\) 4.68720 0.205944
\(519\) 56.6453 2.48645
\(520\) −13.6678 −0.599372
\(521\) −36.0676 −1.58015 −0.790076 0.613009i \(-0.789959\pi\)
−0.790076 + 0.613009i \(0.789959\pi\)
\(522\) −53.2747 −2.33177
\(523\) −35.3948 −1.54771 −0.773853 0.633365i \(-0.781673\pi\)
−0.773853 + 0.633365i \(0.781673\pi\)
\(524\) 36.2304 1.58273
\(525\) −8.51986 −0.371837
\(526\) −67.7761 −2.95518
\(527\) −11.1900 −0.487443
\(528\) −164.620 −7.16416
\(529\) −19.5644 −0.850627
\(530\) −8.55094 −0.371429
\(531\) 6.50896 0.282465
\(532\) 21.0009 0.910504
\(533\) −2.44735 −0.106006
\(534\) −15.5043 −0.670936
\(535\) −5.49732 −0.237670
\(536\) 37.8933 1.63674
\(537\) −29.3329 −1.26581
\(538\) 30.7196 1.32442
\(539\) −43.5180 −1.87445
\(540\) 6.36582 0.273941
\(541\) 31.9562 1.37390 0.686952 0.726703i \(-0.258948\pi\)
0.686952 + 0.726703i \(0.258948\pi\)
\(542\) −70.0597 −3.00932
\(543\) −0.708895 −0.0304216
\(544\) −77.4175 −3.31925
\(545\) 24.5149 1.05010
\(546\) −2.20388 −0.0943174
\(547\) −15.7117 −0.671784 −0.335892 0.941900i \(-0.609038\pi\)
−0.335892 + 0.941900i \(0.609038\pi\)
\(548\) 32.6780 1.39593
\(549\) −25.7561 −1.09924
\(550\) −96.8239 −4.12859
\(551\) 45.1909 1.92520
\(552\) −34.8391 −1.48285
\(553\) −5.82268 −0.247606
\(554\) −6.08522 −0.258536
\(555\) −23.6506 −1.00391
\(556\) −28.5189 −1.20947
\(557\) 26.5186 1.12363 0.561814 0.827264i \(-0.310104\pi\)
0.561814 + 0.827264i \(0.310104\pi\)
\(558\) 13.6156 0.576394
\(559\) 1.52842 0.0646451
\(560\) −20.1043 −0.849560
\(561\) −111.121 −4.69155
\(562\) −34.3002 −1.44687
\(563\) 8.16045 0.343922 0.171961 0.985104i \(-0.444990\pi\)
0.171961 + 0.985104i \(0.444990\pi\)
\(564\) −1.49122 −0.0627918
\(565\) 32.0790 1.34957
\(566\) 83.3585 3.50382
\(567\) −5.18692 −0.217830
\(568\) −4.98318 −0.209089
\(569\) −43.7433 −1.83381 −0.916907 0.399101i \(-0.869322\pi\)
−0.916907 + 0.399101i \(0.869322\pi\)
\(570\) −149.343 −6.25529
\(571\) −8.93501 −0.373919 −0.186959 0.982368i \(-0.559863\pi\)
−0.186959 + 0.982368i \(0.559863\pi\)
\(572\) −17.7713 −0.743055
\(573\) 62.7114 2.61981
\(574\) −7.08292 −0.295635
\(575\) −10.4146 −0.434318
\(576\) 30.3498 1.26458
\(577\) −32.6009 −1.35720 −0.678598 0.734510i \(-0.737412\pi\)
−0.678598 + 0.734510i \(0.737412\pi\)
\(578\) −77.3420 −3.21700
\(579\) −8.18829 −0.340294
\(580\) −102.254 −4.24586
\(581\) −0.346638 −0.0143810
\(582\) −78.2506 −3.24359
\(583\) −6.56696 −0.271976
\(584\) −38.4717 −1.59197
\(585\) 5.70552 0.235894
\(586\) 70.5168 2.91302
\(587\) 23.2205 0.958414 0.479207 0.877702i \(-0.340924\pi\)
0.479207 + 0.877702i \(0.340924\pi\)
\(588\) 80.3650 3.31420
\(589\) −11.5496 −0.475893
\(590\) 17.6071 0.724875
\(591\) 7.05195 0.290078
\(592\) −29.5301 −1.21368
\(593\) −7.00612 −0.287707 −0.143853 0.989599i \(-0.545949\pi\)
−0.143853 + 0.989599i \(0.545949\pi\)
\(594\) 6.89008 0.282703
\(595\) −13.5708 −0.556347
\(596\) −95.3629 −3.90622
\(597\) 33.0554 1.35287
\(598\) −2.69400 −0.110166
\(599\) −33.3961 −1.36453 −0.682264 0.731106i \(-0.739004\pi\)
−0.682264 + 0.731106i \(0.739004\pi\)
\(600\) 105.611 4.31156
\(601\) 37.4337 1.52695 0.763476 0.645836i \(-0.223491\pi\)
0.763476 + 0.645836i \(0.223491\pi\)
\(602\) 4.42342 0.180285
\(603\) −15.8183 −0.644170
\(604\) −4.88578 −0.198799
\(605\) −104.684 −4.25600
\(606\) 50.9272 2.06877
\(607\) 4.71995 0.191577 0.0957885 0.995402i \(-0.469463\pi\)
0.0957885 + 0.995402i \(0.469463\pi\)
\(608\) −79.9055 −3.24059
\(609\) −9.73864 −0.394630
\(610\) −69.6719 −2.82093
\(611\) −0.0681086 −0.00275538
\(612\) 105.287 4.25597
\(613\) −21.0932 −0.851946 −0.425973 0.904736i \(-0.640068\pi\)
−0.425973 + 0.904736i \(0.640068\pi\)
\(614\) 81.2493 3.27895
\(615\) 35.7388 1.44113
\(616\) −30.3784 −1.22398
\(617\) 36.2892 1.46095 0.730473 0.682941i \(-0.239299\pi\)
0.730473 + 0.682941i \(0.239299\pi\)
\(618\) −28.9674 −1.16524
\(619\) −43.3640 −1.74295 −0.871473 0.490444i \(-0.836835\pi\)
−0.871473 + 0.490444i \(0.836835\pi\)
\(620\) 26.1333 1.04954
\(621\) 0.741111 0.0297398
\(622\) 38.7628 1.55425
\(623\) −1.45415 −0.0582591
\(624\) 13.8848 0.555837
\(625\) −21.5232 −0.860928
\(626\) −65.9801 −2.63710
\(627\) −114.693 −4.58038
\(628\) −17.3325 −0.691643
\(629\) −19.9334 −0.794796
\(630\) 16.5124 0.657872
\(631\) −22.2315 −0.885022 −0.442511 0.896763i \(-0.645912\pi\)
−0.442511 + 0.896763i \(0.645912\pi\)
\(632\) 72.1773 2.87106
\(633\) −20.1115 −0.799358
\(634\) 49.6618 1.97232
\(635\) 60.1027 2.38510
\(636\) 12.1272 0.480877
\(637\) 3.67051 0.145431
\(638\) −110.675 −4.38166
\(639\) 2.08019 0.0822911
\(640\) 8.08642 0.319644
\(641\) 26.9528 1.06457 0.532285 0.846565i \(-0.321333\pi\)
0.532285 + 0.846565i \(0.321333\pi\)
\(642\) 10.9880 0.433661
\(643\) 6.94492 0.273881 0.136941 0.990579i \(-0.456273\pi\)
0.136941 + 0.990579i \(0.456273\pi\)
\(644\) −5.53216 −0.217998
\(645\) −22.3196 −0.878833
\(646\) −125.871 −4.95231
\(647\) −2.19558 −0.0863171 −0.0431586 0.999068i \(-0.513742\pi\)
−0.0431586 + 0.999068i \(0.513742\pi\)
\(648\) 64.2965 2.52581
\(649\) 13.5219 0.530783
\(650\) 8.16658 0.320320
\(651\) 2.48894 0.0975492
\(652\) −1.10744 −0.0433707
\(653\) −15.9755 −0.625168 −0.312584 0.949890i \(-0.601195\pi\)
−0.312584 + 0.949890i \(0.601195\pi\)
\(654\) −49.0002 −1.91606
\(655\) −24.1645 −0.944183
\(656\) 44.6235 1.74226
\(657\) 16.0598 0.626551
\(658\) −0.197114 −0.00768432
\(659\) −31.7292 −1.23599 −0.617996 0.786181i \(-0.712055\pi\)
−0.617996 + 0.786181i \(0.712055\pi\)
\(660\) 259.516 10.1016
\(661\) 8.11186 0.315515 0.157757 0.987478i \(-0.449574\pi\)
0.157757 + 0.987478i \(0.449574\pi\)
\(662\) 9.43556 0.366723
\(663\) 9.37249 0.363997
\(664\) 4.29688 0.166751
\(665\) −14.0069 −0.543164
\(666\) 24.2543 0.939834
\(667\) −11.9044 −0.460941
\(668\) −35.4581 −1.37191
\(669\) 32.2677 1.24754
\(670\) −42.7895 −1.65310
\(671\) −53.5066 −2.06560
\(672\) 17.2196 0.664262
\(673\) −33.1516 −1.27790 −0.638949 0.769249i \(-0.720631\pi\)
−0.638949 + 0.769249i \(0.720631\pi\)
\(674\) 52.3301 2.01568
\(675\) −2.24660 −0.0864717
\(676\) −62.0162 −2.38524
\(677\) −23.4270 −0.900372 −0.450186 0.892935i \(-0.648642\pi\)
−0.450186 + 0.892935i \(0.648642\pi\)
\(678\) −64.1193 −2.46249
\(679\) −7.33912 −0.281650
\(680\) 168.221 6.45100
\(681\) 47.8295 1.83283
\(682\) 28.2855 1.08311
\(683\) 9.70710 0.371432 0.185716 0.982603i \(-0.440540\pi\)
0.185716 + 0.982603i \(0.440540\pi\)
\(684\) 108.671 4.15513
\(685\) −21.7951 −0.832749
\(686\) 21.8440 0.834008
\(687\) 25.7708 0.983217
\(688\) −27.8682 −1.06247
\(689\) 0.553887 0.0211014
\(690\) 39.3407 1.49768
\(691\) −16.7230 −0.636172 −0.318086 0.948062i \(-0.603040\pi\)
−0.318086 + 0.948062i \(0.603040\pi\)
\(692\) −111.498 −4.23853
\(693\) 12.6812 0.481720
\(694\) 33.7096 1.27960
\(695\) 19.0211 0.721513
\(696\) 120.719 4.57584
\(697\) 30.1217 1.14094
\(698\) 38.5453 1.45896
\(699\) −31.4037 −1.18780
\(700\) 16.7702 0.633853
\(701\) −14.6816 −0.554517 −0.277259 0.960795i \(-0.589426\pi\)
−0.277259 + 0.960795i \(0.589426\pi\)
\(702\) −0.581141 −0.0219338
\(703\) −20.5740 −0.775963
\(704\) 63.0499 2.37628
\(705\) 0.994596 0.0374586
\(706\) −81.4132 −3.06403
\(707\) 4.77646 0.179637
\(708\) −24.9711 −0.938471
\(709\) −23.2063 −0.871531 −0.435766 0.900060i \(-0.643522\pi\)
−0.435766 + 0.900060i \(0.643522\pi\)
\(710\) 5.62705 0.211180
\(711\) −30.1299 −1.12996
\(712\) 18.0254 0.675531
\(713\) 3.04245 0.113941
\(714\) 27.1251 1.01513
\(715\) 11.8529 0.443272
\(716\) 57.7379 2.15776
\(717\) −0.585883 −0.0218802
\(718\) 2.40342 0.0896950
\(719\) 50.5760 1.88617 0.943083 0.332556i \(-0.107911\pi\)
0.943083 + 0.332556i \(0.107911\pi\)
\(720\) −104.031 −3.87701
\(721\) −2.71685 −0.101181
\(722\) −80.0583 −2.97946
\(723\) −29.7210 −1.10533
\(724\) 1.39536 0.0518582
\(725\) 36.0870 1.34024
\(726\) 209.241 7.76566
\(727\) 25.1604 0.933148 0.466574 0.884482i \(-0.345488\pi\)
0.466574 + 0.884482i \(0.345488\pi\)
\(728\) 2.56225 0.0949634
\(729\) −29.8175 −1.10435
\(730\) 43.4427 1.60789
\(731\) −18.8116 −0.695771
\(732\) 98.8111 3.65216
\(733\) −43.2926 −1.59905 −0.799524 0.600635i \(-0.794915\pi\)
−0.799524 + 0.600635i \(0.794915\pi\)
\(734\) 53.5092 1.97506
\(735\) −53.6008 −1.97709
\(736\) 21.0491 0.775880
\(737\) −32.8615 −1.21047
\(738\) −36.6511 −1.34915
\(739\) −47.3007 −1.73998 −0.869992 0.493065i \(-0.835876\pi\)
−0.869992 + 0.493065i \(0.835876\pi\)
\(740\) 46.5529 1.71132
\(741\) 9.67370 0.355372
\(742\) 1.60302 0.0588486
\(743\) 4.94915 0.181567 0.0907834 0.995871i \(-0.471063\pi\)
0.0907834 + 0.995871i \(0.471063\pi\)
\(744\) −30.8526 −1.13111
\(745\) 63.6038 2.33026
\(746\) −73.4446 −2.68900
\(747\) −1.79370 −0.0656282
\(748\) 218.727 7.99746
\(749\) 1.03056 0.0376560
\(750\) −13.1335 −0.479568
\(751\) 1.07182 0.0391112 0.0195556 0.999809i \(-0.493775\pi\)
0.0195556 + 0.999809i \(0.493775\pi\)
\(752\) 1.24185 0.0452857
\(753\) 57.3264 2.08909
\(754\) 9.33482 0.339954
\(755\) 3.25865 0.118594
\(756\) −1.19338 −0.0434028
\(757\) 24.3791 0.886075 0.443037 0.896503i \(-0.353901\pi\)
0.443037 + 0.896503i \(0.353901\pi\)
\(758\) −7.69504 −0.279496
\(759\) 30.2129 1.09666
\(760\) 173.628 6.29814
\(761\) −5.04882 −0.183020 −0.0915098 0.995804i \(-0.529169\pi\)
−0.0915098 + 0.995804i \(0.529169\pi\)
\(762\) −120.133 −4.35195
\(763\) −4.59572 −0.166376
\(764\) −123.439 −4.46585
\(765\) −70.2229 −2.53891
\(766\) 74.9471 2.70795
\(767\) −1.14050 −0.0411812
\(768\) 31.4996 1.13665
\(769\) −22.2005 −0.800572 −0.400286 0.916390i \(-0.631089\pi\)
−0.400286 + 0.916390i \(0.631089\pi\)
\(770\) 34.3036 1.23622
\(771\) 33.9664 1.22327
\(772\) 16.1175 0.580082
\(773\) 15.3380 0.551668 0.275834 0.961205i \(-0.411046\pi\)
0.275834 + 0.961205i \(0.411046\pi\)
\(774\) 22.8893 0.822739
\(775\) −9.22287 −0.331295
\(776\) 90.9749 3.26581
\(777\) 4.43370 0.159058
\(778\) −63.1739 −2.26489
\(779\) 31.0897 1.11391
\(780\) −21.8888 −0.783743
\(781\) 4.32147 0.154634
\(782\) 33.1575 1.18571
\(783\) −2.56798 −0.0917722
\(784\) −66.9259 −2.39021
\(785\) 11.5602 0.412601
\(786\) 48.2997 1.72279
\(787\) −16.4908 −0.587832 −0.293916 0.955831i \(-0.594959\pi\)
−0.293916 + 0.955831i \(0.594959\pi\)
\(788\) −13.8808 −0.494483
\(789\) −64.1104 −2.28239
\(790\) −81.5033 −2.89976
\(791\) −6.01375 −0.213824
\(792\) −157.195 −5.58569
\(793\) 4.51300 0.160261
\(794\) −26.6014 −0.944047
\(795\) −8.08846 −0.286868
\(796\) −65.0651 −2.30617
\(797\) −16.1067 −0.570528 −0.285264 0.958449i \(-0.592081\pi\)
−0.285264 + 0.958449i \(0.592081\pi\)
\(798\) 27.9968 0.991078
\(799\) 0.838273 0.0296560
\(800\) −63.8081 −2.25596
\(801\) −7.52458 −0.265868
\(802\) −11.3702 −0.401497
\(803\) 33.3631 1.17736
\(804\) 60.6855 2.14021
\(805\) 3.68976 0.130047
\(806\) −2.38573 −0.0840339
\(807\) 29.0582 1.02290
\(808\) −59.2084 −2.08295
\(809\) −35.3972 −1.24450 −0.622250 0.782819i \(-0.713781\pi\)
−0.622250 + 0.782819i \(0.713781\pi\)
\(810\) −72.6043 −2.55105
\(811\) 16.7415 0.587874 0.293937 0.955825i \(-0.405034\pi\)
0.293937 + 0.955825i \(0.405034\pi\)
\(812\) 19.1692 0.672706
\(813\) −66.2705 −2.32421
\(814\) 50.3868 1.76605
\(815\) 0.738625 0.0258729
\(816\) −170.892 −5.98243
\(817\) −19.4161 −0.679285
\(818\) −23.5111 −0.822046
\(819\) −1.06959 −0.0373747
\(820\) −70.3470 −2.45662
\(821\) −17.7154 −0.618272 −0.309136 0.951018i \(-0.600040\pi\)
−0.309136 + 0.951018i \(0.600040\pi\)
\(822\) 43.5639 1.51947
\(823\) 21.3083 0.742759 0.371379 0.928481i \(-0.378885\pi\)
0.371379 + 0.928481i \(0.378885\pi\)
\(824\) 33.6777 1.17322
\(825\) −91.5872 −3.18866
\(826\) −3.30075 −0.114848
\(827\) −19.6490 −0.683262 −0.341631 0.939834i \(-0.610979\pi\)
−0.341631 + 0.939834i \(0.610979\pi\)
\(828\) −28.6266 −0.994843
\(829\) −39.7903 −1.38197 −0.690987 0.722867i \(-0.742824\pi\)
−0.690987 + 0.722867i \(0.742824\pi\)
\(830\) −4.85209 −0.168418
\(831\) −5.75610 −0.199677
\(832\) −5.31792 −0.184366
\(833\) −45.1762 −1.56526
\(834\) −38.0193 −1.31650
\(835\) 23.6493 0.818419
\(836\) 225.757 7.80795
\(837\) 0.656308 0.0226853
\(838\) 87.0162 3.00593
\(839\) 10.5594 0.364552 0.182276 0.983247i \(-0.441654\pi\)
0.182276 + 0.983247i \(0.441654\pi\)
\(840\) −37.4168 −1.29100
\(841\) 12.2493 0.422389
\(842\) −66.1832 −2.28082
\(843\) −32.4450 −1.11747
\(844\) 39.5866 1.36263
\(845\) 41.3627 1.42292
\(846\) −1.01998 −0.0350678
\(847\) 19.6247 0.674313
\(848\) −10.0993 −0.346810
\(849\) 78.8500 2.70613
\(850\) −100.513 −3.44758
\(851\) 5.41971 0.185785
\(852\) −7.98049 −0.273407
\(853\) −40.7463 −1.39513 −0.697563 0.716523i \(-0.745732\pi\)
−0.697563 + 0.716523i \(0.745732\pi\)
\(854\) 13.0612 0.446943
\(855\) −72.4797 −2.47875
\(856\) −12.7747 −0.436632
\(857\) 30.8214 1.05284 0.526420 0.850225i \(-0.323534\pi\)
0.526420 + 0.850225i \(0.323534\pi\)
\(858\) −23.6914 −0.808811
\(859\) −14.8826 −0.507789 −0.253895 0.967232i \(-0.581712\pi\)
−0.253895 + 0.967232i \(0.581712\pi\)
\(860\) 43.9330 1.49810
\(861\) −6.69984 −0.228330
\(862\) 48.2411 1.64310
\(863\) 43.9674 1.49667 0.748333 0.663323i \(-0.230854\pi\)
0.748333 + 0.663323i \(0.230854\pi\)
\(864\) 4.54064 0.154476
\(865\) 74.3657 2.52851
\(866\) −56.5984 −1.92329
\(867\) −73.1590 −2.48461
\(868\) −4.89913 −0.166287
\(869\) −62.5930 −2.12332
\(870\) −136.317 −4.62159
\(871\) 2.77169 0.0939151
\(872\) 56.9681 1.92918
\(873\) −37.9768 −1.28532
\(874\) 34.2231 1.15761
\(875\) −1.23179 −0.0416422
\(876\) −61.6119 −2.08167
\(877\) −28.9962 −0.979133 −0.489567 0.871966i \(-0.662845\pi\)
−0.489567 + 0.871966i \(0.662845\pi\)
\(878\) −76.6006 −2.58514
\(879\) 66.7029 2.24983
\(880\) −216.118 −7.28533
\(881\) −6.97946 −0.235144 −0.117572 0.993064i \(-0.537511\pi\)
−0.117572 + 0.993064i \(0.537511\pi\)
\(882\) 54.9690 1.85090
\(883\) 52.4084 1.76368 0.881841 0.471547i \(-0.156304\pi\)
0.881841 + 0.471547i \(0.156304\pi\)
\(884\) −18.4485 −0.620489
\(885\) 16.6549 0.559847
\(886\) −77.2715 −2.59599
\(887\) −20.4074 −0.685215 −0.342607 0.939479i \(-0.611310\pi\)
−0.342607 + 0.939479i \(0.611310\pi\)
\(888\) −54.9596 −1.84432
\(889\) −11.2673 −0.377892
\(890\) −20.3545 −0.682284
\(891\) −55.7587 −1.86799
\(892\) −63.5145 −2.12662
\(893\) 0.865213 0.0289533
\(894\) −127.131 −4.25189
\(895\) −38.5092 −1.28722
\(896\) −1.51593 −0.0506438
\(897\) −2.54830 −0.0850851
\(898\) 81.5638 2.72182
\(899\) −10.5422 −0.351603
\(900\) 86.7785 2.89262
\(901\) −6.81718 −0.227113
\(902\) −76.1404 −2.53520
\(903\) 4.18418 0.139241
\(904\) 74.5457 2.47935
\(905\) −0.930659 −0.0309361
\(906\) −6.51336 −0.216392
\(907\) −10.9648 −0.364081 −0.182040 0.983291i \(-0.558270\pi\)
−0.182040 + 0.983291i \(0.558270\pi\)
\(908\) −94.1458 −3.12434
\(909\) 24.7161 0.819783
\(910\) −2.89332 −0.0959127
\(911\) 0.704225 0.0233320 0.0116660 0.999932i \(-0.496287\pi\)
0.0116660 + 0.999932i \(0.496287\pi\)
\(912\) −176.385 −5.84068
\(913\) −3.72631 −0.123323
\(914\) −21.7645 −0.719904
\(915\) −65.9037 −2.17871
\(916\) −50.7262 −1.67604
\(917\) 4.53003 0.149595
\(918\) 7.15262 0.236072
\(919\) 24.9517 0.823081 0.411540 0.911392i \(-0.364991\pi\)
0.411540 + 0.911392i \(0.364991\pi\)
\(920\) −45.7379 −1.50793
\(921\) 76.8549 2.53245
\(922\) 39.7922 1.31049
\(923\) −0.364493 −0.0119974
\(924\) −48.6505 −1.60049
\(925\) −16.4293 −0.540191
\(926\) 34.1986 1.12383
\(927\) −14.0585 −0.461743
\(928\) −72.9360 −2.39424
\(929\) 49.3087 1.61777 0.808883 0.587970i \(-0.200073\pi\)
0.808883 + 0.587970i \(0.200073\pi\)
\(930\) 34.8391 1.14242
\(931\) −46.6281 −1.52817
\(932\) 61.8138 2.02478
\(933\) 36.6664 1.20040
\(934\) 3.02752 0.0990636
\(935\) −145.884 −4.77090
\(936\) 13.2586 0.433370
\(937\) −40.0037 −1.30686 −0.653432 0.756985i \(-0.726671\pi\)
−0.653432 + 0.756985i \(0.726671\pi\)
\(938\) 8.02160 0.261914
\(939\) −62.4116 −2.03673
\(940\) −1.95772 −0.0638539
\(941\) 13.6800 0.445955 0.222977 0.974824i \(-0.428422\pi\)
0.222977 + 0.974824i \(0.428422\pi\)
\(942\) −23.1065 −0.752849
\(943\) −8.18982 −0.266697
\(944\) 20.7953 0.676828
\(945\) 0.795944 0.0258921
\(946\) 47.5511 1.54602
\(947\) 45.8467 1.48982 0.744908 0.667167i \(-0.232493\pi\)
0.744908 + 0.667167i \(0.232493\pi\)
\(948\) 115.591 3.75422
\(949\) −2.81400 −0.0913463
\(950\) −103.744 −3.36589
\(951\) 46.9758 1.52330
\(952\) −31.5359 −1.02209
\(953\) 56.5045 1.83036 0.915179 0.403047i \(-0.132049\pi\)
0.915179 + 0.403047i \(0.132049\pi\)
\(954\) 8.29493 0.268558
\(955\) 82.3294 2.66412
\(956\) 1.15323 0.0372981
\(957\) −104.689 −3.38411
\(958\) 78.4696 2.53524
\(959\) 4.08586 0.131939
\(960\) 77.6580 2.50640
\(961\) −28.3057 −0.913087
\(962\) −4.24985 −0.137021
\(963\) 5.33273 0.171845
\(964\) 58.5016 1.88421
\(965\) −10.7498 −0.346049
\(966\) −7.37507 −0.237289
\(967\) −7.79697 −0.250734 −0.125367 0.992110i \(-0.540011\pi\)
−0.125367 + 0.992110i \(0.540011\pi\)
\(968\) −243.266 −7.81886
\(969\) −119.063 −3.82485
\(970\) −102.730 −3.29845
\(971\) −36.8392 −1.18223 −0.591113 0.806589i \(-0.701311\pi\)
−0.591113 + 0.806589i \(0.701311\pi\)
\(972\) 108.831 3.49074
\(973\) −3.56583 −0.114315
\(974\) 18.8041 0.602522
\(975\) 7.72489 0.247394
\(976\) −82.2873 −2.63395
\(977\) 11.3592 0.363412 0.181706 0.983353i \(-0.441838\pi\)
0.181706 + 0.983353i \(0.441838\pi\)
\(978\) −1.47636 −0.0472087
\(979\) −15.6319 −0.499596
\(980\) 105.506 3.37026
\(981\) −23.7809 −0.759266
\(982\) 47.2585 1.50808
\(983\) 3.31628 0.105773 0.0528864 0.998601i \(-0.483158\pi\)
0.0528864 + 0.998601i \(0.483158\pi\)
\(984\) 83.0505 2.64755
\(985\) 9.25802 0.294985
\(986\) −114.892 −3.65891
\(987\) −0.186454 −0.00593488
\(988\) −19.0413 −0.605786
\(989\) 5.11470 0.162638
\(990\) 177.506 5.64152
\(991\) 44.0319 1.39872 0.699360 0.714770i \(-0.253468\pi\)
0.699360 + 0.714770i \(0.253468\pi\)
\(992\) 18.6405 0.591837
\(993\) 8.92524 0.283234
\(994\) −1.05488 −0.0334589
\(995\) 43.3962 1.37575
\(996\) 6.88140 0.218045
\(997\) −30.5965 −0.969002 −0.484501 0.874791i \(-0.660999\pi\)
−0.484501 + 0.874791i \(0.660999\pi\)
\(998\) −89.1351 −2.82152
\(999\) 1.16912 0.0369894
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.1.6 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.6 153 1.1 even 1 trivial