Properties

Label 8003.2.a.b.1.1
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 1.1
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.82377 q^{2} +0.0811365 q^{3} +5.97367 q^{4} +1.22528 q^{5} -0.229111 q^{6} +1.93678 q^{7} -11.2207 q^{8} -2.99342 q^{9} +O(q^{10})\) \(q-2.82377 q^{2} +0.0811365 q^{3} +5.97367 q^{4} +1.22528 q^{5} -0.229111 q^{6} +1.93678 q^{7} -11.2207 q^{8} -2.99342 q^{9} -3.45990 q^{10} +1.10465 q^{11} +0.484682 q^{12} -6.90923 q^{13} -5.46902 q^{14} +0.0994147 q^{15} +19.7374 q^{16} +1.76873 q^{17} +8.45272 q^{18} +7.08725 q^{19} +7.31940 q^{20} +0.157144 q^{21} -3.11928 q^{22} +7.96464 q^{23} -0.910409 q^{24} -3.49869 q^{25} +19.5101 q^{26} -0.486285 q^{27} +11.5697 q^{28} -5.37427 q^{29} -0.280724 q^{30} -2.15671 q^{31} -33.2923 q^{32} +0.0896277 q^{33} -4.99450 q^{34} +2.37310 q^{35} -17.8817 q^{36} -3.79792 q^{37} -20.0128 q^{38} -0.560591 q^{39} -13.7485 q^{40} +9.77275 q^{41} -0.443737 q^{42} -6.40853 q^{43} +6.59883 q^{44} -3.66777 q^{45} -22.4903 q^{46} -1.80885 q^{47} +1.60142 q^{48} -3.24887 q^{49} +9.87950 q^{50} +0.143509 q^{51} -41.2735 q^{52} -1.00000 q^{53} +1.37316 q^{54} +1.35351 q^{55} -21.7321 q^{56} +0.575035 q^{57} +15.1757 q^{58} -2.90833 q^{59} +0.593871 q^{60} -4.10954 q^{61} +6.09004 q^{62} -5.79760 q^{63} +54.5351 q^{64} -8.46573 q^{65} -0.253088 q^{66} +11.3085 q^{67} +10.5658 q^{68} +0.646223 q^{69} -6.70107 q^{70} -12.9010 q^{71} +33.5883 q^{72} +5.22639 q^{73} +10.7244 q^{74} -0.283872 q^{75} +42.3369 q^{76} +2.13947 q^{77} +1.58298 q^{78} -6.41878 q^{79} +24.1838 q^{80} +8.94080 q^{81} -27.5960 q^{82} +5.11469 q^{83} +0.938724 q^{84} +2.16719 q^{85} +18.0962 q^{86} -0.436050 q^{87} -12.3950 q^{88} +10.1425 q^{89} +10.3569 q^{90} -13.3817 q^{91} +47.5781 q^{92} -0.174988 q^{93} +5.10776 q^{94} +8.68385 q^{95} -2.70122 q^{96} -9.09837 q^{97} +9.17407 q^{98} -3.30669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.82377 −1.99671 −0.998353 0.0573723i \(-0.981728\pi\)
−0.998353 + 0.0573723i \(0.981728\pi\)
\(3\) 0.0811365 0.0468442 0.0234221 0.999726i \(-0.492544\pi\)
0.0234221 + 0.999726i \(0.492544\pi\)
\(4\) 5.97367 2.98683
\(5\) 1.22528 0.547961 0.273980 0.961735i \(-0.411660\pi\)
0.273980 + 0.961735i \(0.411660\pi\)
\(6\) −0.229111 −0.0935340
\(7\) 1.93678 0.732035 0.366017 0.930608i \(-0.380721\pi\)
0.366017 + 0.930608i \(0.380721\pi\)
\(8\) −11.2207 −3.96712
\(9\) −2.99342 −0.997806
\(10\) −3.45990 −1.09412
\(11\) 1.10465 0.333066 0.166533 0.986036i \(-0.446743\pi\)
0.166533 + 0.986036i \(0.446743\pi\)
\(12\) 0.484682 0.139916
\(13\) −6.90923 −1.91628 −0.958138 0.286307i \(-0.907572\pi\)
−0.958138 + 0.286307i \(0.907572\pi\)
\(14\) −5.46902 −1.46166
\(15\) 0.0994147 0.0256688
\(16\) 19.7374 4.93434
\(17\) 1.76873 0.428981 0.214491 0.976726i \(-0.431191\pi\)
0.214491 + 0.976726i \(0.431191\pi\)
\(18\) 8.45272 1.99232
\(19\) 7.08725 1.62593 0.812964 0.582314i \(-0.197853\pi\)
0.812964 + 0.582314i \(0.197853\pi\)
\(20\) 7.31940 1.63667
\(21\) 0.157144 0.0342916
\(22\) −3.11928 −0.665034
\(23\) 7.96464 1.66074 0.830371 0.557211i \(-0.188129\pi\)
0.830371 + 0.557211i \(0.188129\pi\)
\(24\) −0.910409 −0.185837
\(25\) −3.49869 −0.699739
\(26\) 19.5101 3.82624
\(27\) −0.486285 −0.0935855
\(28\) 11.5697 2.18647
\(29\) −5.37427 −0.997977 −0.498989 0.866608i \(-0.666295\pi\)
−0.498989 + 0.866608i \(0.666295\pi\)
\(30\) −0.280724 −0.0512530
\(31\) −2.15671 −0.387356 −0.193678 0.981065i \(-0.562042\pi\)
−0.193678 + 0.981065i \(0.562042\pi\)
\(32\) −33.2923 −5.88531
\(33\) 0.0896277 0.0156022
\(34\) −4.99450 −0.856549
\(35\) 2.37310 0.401126
\(36\) −17.8817 −2.98028
\(37\) −3.79792 −0.624374 −0.312187 0.950021i \(-0.601061\pi\)
−0.312187 + 0.950021i \(0.601061\pi\)
\(38\) −20.0128 −3.24650
\(39\) −0.560591 −0.0897664
\(40\) −13.7485 −2.17383
\(41\) 9.77275 1.52625 0.763124 0.646252i \(-0.223665\pi\)
0.763124 + 0.646252i \(0.223665\pi\)
\(42\) −0.443737 −0.0684702
\(43\) −6.40853 −0.977291 −0.488646 0.872482i \(-0.662509\pi\)
−0.488646 + 0.872482i \(0.662509\pi\)
\(44\) 6.59883 0.994811
\(45\) −3.66777 −0.546758
\(46\) −22.4903 −3.31601
\(47\) −1.80885 −0.263847 −0.131924 0.991260i \(-0.542115\pi\)
−0.131924 + 0.991260i \(0.542115\pi\)
\(48\) 1.60142 0.231145
\(49\) −3.24887 −0.464125
\(50\) 9.87950 1.39717
\(51\) 0.143509 0.0200953
\(52\) −41.2735 −5.72360
\(53\) −1.00000 −0.137361
\(54\) 1.37316 0.186863
\(55\) 1.35351 0.182507
\(56\) −21.7321 −2.90407
\(57\) 0.575035 0.0761652
\(58\) 15.1757 1.99267
\(59\) −2.90833 −0.378633 −0.189316 0.981916i \(-0.560627\pi\)
−0.189316 + 0.981916i \(0.560627\pi\)
\(60\) 0.593871 0.0766684
\(61\) −4.10954 −0.526173 −0.263086 0.964772i \(-0.584740\pi\)
−0.263086 + 0.964772i \(0.584740\pi\)
\(62\) 6.09004 0.773436
\(63\) −5.79760 −0.730428
\(64\) 54.5351 6.81688
\(65\) −8.46573 −1.05004
\(66\) −0.253088 −0.0311530
\(67\) 11.3085 1.38155 0.690774 0.723071i \(-0.257270\pi\)
0.690774 + 0.723071i \(0.257270\pi\)
\(68\) 10.5658 1.28130
\(69\) 0.646223 0.0777961
\(70\) −6.70107 −0.800932
\(71\) −12.9010 −1.53106 −0.765531 0.643399i \(-0.777523\pi\)
−0.765531 + 0.643399i \(0.777523\pi\)
\(72\) 33.5883 3.95842
\(73\) 5.22639 0.611703 0.305851 0.952079i \(-0.401059\pi\)
0.305851 + 0.952079i \(0.401059\pi\)
\(74\) 10.7244 1.24669
\(75\) −0.283872 −0.0327787
\(76\) 42.3369 4.85637
\(77\) 2.13947 0.243816
\(78\) 1.58298 0.179237
\(79\) −6.41878 −0.722169 −0.361085 0.932533i \(-0.617593\pi\)
−0.361085 + 0.932533i \(0.617593\pi\)
\(80\) 24.1838 2.70383
\(81\) 8.94080 0.993422
\(82\) −27.5960 −3.04747
\(83\) 5.11469 0.561410 0.280705 0.959794i \(-0.409432\pi\)
0.280705 + 0.959794i \(0.409432\pi\)
\(84\) 0.938724 0.102423
\(85\) 2.16719 0.235065
\(86\) 18.0962 1.95136
\(87\) −0.436050 −0.0467494
\(88\) −12.3950 −1.32131
\(89\) 10.1425 1.07511 0.537554 0.843230i \(-0.319349\pi\)
0.537554 + 0.843230i \(0.319349\pi\)
\(90\) 10.3569 1.09172
\(91\) −13.3817 −1.40278
\(92\) 47.5781 4.96036
\(93\) −0.174988 −0.0181454
\(94\) 5.10776 0.526826
\(95\) 8.68385 0.890945
\(96\) −2.70122 −0.275692
\(97\) −9.09837 −0.923799 −0.461900 0.886932i \(-0.652832\pi\)
−0.461900 + 0.886932i \(0.652832\pi\)
\(98\) 9.17407 0.926721
\(99\) −3.30669 −0.332335
\(100\) −20.9000 −2.09000
\(101\) 13.1521 1.30869 0.654343 0.756198i \(-0.272945\pi\)
0.654343 + 0.756198i \(0.272945\pi\)
\(102\) −0.405236 −0.0401243
\(103\) −9.75259 −0.960951 −0.480475 0.877008i \(-0.659536\pi\)
−0.480475 + 0.877008i \(0.659536\pi\)
\(104\) 77.5265 7.60210
\(105\) 0.192545 0.0187904
\(106\) 2.82377 0.274269
\(107\) −11.5027 −1.11200 −0.556002 0.831181i \(-0.687665\pi\)
−0.556002 + 0.831181i \(0.687665\pi\)
\(108\) −2.90490 −0.279524
\(109\) 4.31270 0.413082 0.206541 0.978438i \(-0.433779\pi\)
0.206541 + 0.978438i \(0.433779\pi\)
\(110\) −3.82199 −0.364413
\(111\) −0.308150 −0.0292483
\(112\) 38.2270 3.61211
\(113\) −1.67681 −0.157741 −0.0788703 0.996885i \(-0.525131\pi\)
−0.0788703 + 0.996885i \(0.525131\pi\)
\(114\) −1.62376 −0.152080
\(115\) 9.75889 0.910021
\(116\) −32.1041 −2.98079
\(117\) 20.6822 1.91207
\(118\) 8.21246 0.756018
\(119\) 3.42565 0.314029
\(120\) −1.11550 −0.101831
\(121\) −9.77974 −0.889067
\(122\) 11.6044 1.05061
\(123\) 0.792927 0.0714958
\(124\) −12.8834 −1.15697
\(125\) −10.4133 −0.931390
\(126\) 16.3711 1.45845
\(127\) −7.80232 −0.692344 −0.346172 0.938171i \(-0.612519\pi\)
−0.346172 + 0.938171i \(0.612519\pi\)
\(128\) −87.4097 −7.72600
\(129\) −0.519965 −0.0457804
\(130\) 23.9053 2.09663
\(131\) 1.94212 0.169683 0.0848417 0.996394i \(-0.472962\pi\)
0.0848417 + 0.996394i \(0.472962\pi\)
\(132\) 0.535406 0.0466011
\(133\) 13.7265 1.19024
\(134\) −31.9325 −2.75854
\(135\) −0.595834 −0.0512812
\(136\) −19.8465 −1.70182
\(137\) −1.23048 −0.105127 −0.0525636 0.998618i \(-0.516739\pi\)
−0.0525636 + 0.998618i \(0.516739\pi\)
\(138\) −1.82478 −0.155336
\(139\) 1.84023 0.156086 0.0780430 0.996950i \(-0.475133\pi\)
0.0780430 + 0.996950i \(0.475133\pi\)
\(140\) 14.1761 1.19810
\(141\) −0.146763 −0.0123597
\(142\) 36.4293 3.05708
\(143\) −7.63231 −0.638245
\(144\) −59.0822 −4.92351
\(145\) −6.58498 −0.546853
\(146\) −14.7581 −1.22139
\(147\) −0.263602 −0.0217415
\(148\) −22.6875 −1.86490
\(149\) 10.0824 0.825979 0.412989 0.910736i \(-0.364485\pi\)
0.412989 + 0.910736i \(0.364485\pi\)
\(150\) 0.801588 0.0654494
\(151\) −1.00000 −0.0813788
\(152\) −79.5240 −6.45025
\(153\) −5.29456 −0.428040
\(154\) −6.04138 −0.486828
\(155\) −2.64256 −0.212256
\(156\) −3.34878 −0.268117
\(157\) −4.48934 −0.358288 −0.179144 0.983823i \(-0.557333\pi\)
−0.179144 + 0.983823i \(0.557333\pi\)
\(158\) 18.1251 1.44196
\(159\) −0.0811365 −0.00643454
\(160\) −40.7923 −3.22492
\(161\) 15.4258 1.21572
\(162\) −25.2467 −1.98357
\(163\) −8.44188 −0.661219 −0.330610 0.943768i \(-0.607254\pi\)
−0.330610 + 0.943768i \(0.607254\pi\)
\(164\) 58.3792 4.55865
\(165\) 0.109819 0.00854938
\(166\) −14.4427 −1.12097
\(167\) 4.04845 0.313278 0.156639 0.987656i \(-0.449934\pi\)
0.156639 + 0.987656i \(0.449934\pi\)
\(168\) −1.76326 −0.136039
\(169\) 34.7375 2.67211
\(170\) −6.11965 −0.469356
\(171\) −21.2151 −1.62236
\(172\) −38.2824 −2.91901
\(173\) −4.53681 −0.344927 −0.172464 0.985016i \(-0.555173\pi\)
−0.172464 + 0.985016i \(0.555173\pi\)
\(174\) 1.23130 0.0933448
\(175\) −6.77621 −0.512233
\(176\) 21.8029 1.64346
\(177\) −0.235972 −0.0177367
\(178\) −28.6402 −2.14667
\(179\) −15.8720 −1.18633 −0.593164 0.805082i \(-0.702121\pi\)
−0.593164 + 0.805082i \(0.702121\pi\)
\(180\) −21.9100 −1.63308
\(181\) −1.85688 −0.138021 −0.0690106 0.997616i \(-0.521984\pi\)
−0.0690106 + 0.997616i \(0.521984\pi\)
\(182\) 37.7868 2.80094
\(183\) −0.333434 −0.0246481
\(184\) −89.3689 −6.58836
\(185\) −4.65350 −0.342132
\(186\) 0.494124 0.0362310
\(187\) 1.95384 0.142879
\(188\) −10.8054 −0.788068
\(189\) −0.941828 −0.0685079
\(190\) −24.5212 −1.77895
\(191\) 1.25950 0.0911343 0.0455671 0.998961i \(-0.485491\pi\)
0.0455671 + 0.998961i \(0.485491\pi\)
\(192\) 4.42478 0.319331
\(193\) −10.1036 −0.727274 −0.363637 0.931541i \(-0.618465\pi\)
−0.363637 + 0.931541i \(0.618465\pi\)
\(194\) 25.6917 1.84456
\(195\) −0.686879 −0.0491885
\(196\) −19.4077 −1.38626
\(197\) −11.8175 −0.841963 −0.420981 0.907069i \(-0.638314\pi\)
−0.420981 + 0.907069i \(0.638314\pi\)
\(198\) 9.33732 0.663574
\(199\) 8.75342 0.620514 0.310257 0.950653i \(-0.399585\pi\)
0.310257 + 0.950653i \(0.399585\pi\)
\(200\) 39.2579 2.77595
\(201\) 0.917529 0.0647175
\(202\) −37.1386 −2.61306
\(203\) −10.4088 −0.730554
\(204\) 0.857275 0.0600212
\(205\) 11.9743 0.836324
\(206\) 27.5390 1.91874
\(207\) −23.8415 −1.65710
\(208\) −136.370 −9.45556
\(209\) 7.82896 0.541540
\(210\) −0.543702 −0.0375190
\(211\) −11.1938 −0.770610 −0.385305 0.922789i \(-0.625904\pi\)
−0.385305 + 0.922789i \(0.625904\pi\)
\(212\) −5.97367 −0.410273
\(213\) −1.04674 −0.0717213
\(214\) 32.4808 2.22034
\(215\) −7.85223 −0.535517
\(216\) 5.45646 0.371265
\(217\) −4.17707 −0.283558
\(218\) −12.1781 −0.824803
\(219\) 0.424051 0.0286547
\(220\) 8.08540 0.545118
\(221\) −12.2206 −0.822047
\(222\) 0.870143 0.0584002
\(223\) −25.4096 −1.70155 −0.850777 0.525526i \(-0.823869\pi\)
−0.850777 + 0.525526i \(0.823869\pi\)
\(224\) −64.4800 −4.30825
\(225\) 10.4731 0.698203
\(226\) 4.73491 0.314962
\(227\) 29.3348 1.94702 0.973511 0.228640i \(-0.0734279\pi\)
0.973511 + 0.228640i \(0.0734279\pi\)
\(228\) 3.43507 0.227493
\(229\) −8.40064 −0.555130 −0.277565 0.960707i \(-0.589527\pi\)
−0.277565 + 0.960707i \(0.589527\pi\)
\(230\) −27.5569 −1.81704
\(231\) 0.173589 0.0114213
\(232\) 60.3032 3.95910
\(233\) 15.2658 1.00009 0.500047 0.865998i \(-0.333316\pi\)
0.500047 + 0.865998i \(0.333316\pi\)
\(234\) −58.4018 −3.81784
\(235\) −2.21634 −0.144578
\(236\) −17.3734 −1.13091
\(237\) −0.520797 −0.0338294
\(238\) −9.67325 −0.627024
\(239\) 20.0737 1.29846 0.649231 0.760592i \(-0.275091\pi\)
0.649231 + 0.760592i \(0.275091\pi\)
\(240\) 1.96218 0.126658
\(241\) 16.2200 1.04482 0.522411 0.852694i \(-0.325033\pi\)
0.522411 + 0.852694i \(0.325033\pi\)
\(242\) 27.6157 1.77521
\(243\) 2.18428 0.140122
\(244\) −24.5490 −1.57159
\(245\) −3.98077 −0.254322
\(246\) −2.23904 −0.142756
\(247\) −48.9675 −3.11573
\(248\) 24.1998 1.53669
\(249\) 0.414988 0.0262988
\(250\) 29.4046 1.85971
\(251\) 5.96305 0.376385 0.188192 0.982132i \(-0.439737\pi\)
0.188192 + 0.982132i \(0.439737\pi\)
\(252\) −34.6329 −2.18167
\(253\) 8.79816 0.553136
\(254\) 22.0319 1.38241
\(255\) 0.175838 0.0110114
\(256\) 137.755 8.60967
\(257\) 5.03217 0.313898 0.156949 0.987607i \(-0.449834\pi\)
0.156949 + 0.987607i \(0.449834\pi\)
\(258\) 1.46826 0.0914100
\(259\) −7.35574 −0.457063
\(260\) −50.5714 −3.13631
\(261\) 16.0874 0.995788
\(262\) −5.48409 −0.338808
\(263\) −20.7176 −1.27750 −0.638751 0.769413i \(-0.720549\pi\)
−0.638751 + 0.769413i \(0.720549\pi\)
\(264\) −1.00569 −0.0618957
\(265\) −1.22528 −0.0752682
\(266\) −38.7604 −2.37655
\(267\) 0.822930 0.0503625
\(268\) 67.5530 4.12645
\(269\) 9.32887 0.568792 0.284396 0.958707i \(-0.408207\pi\)
0.284396 + 0.958707i \(0.408207\pi\)
\(270\) 1.68250 0.102393
\(271\) −20.4843 −1.24434 −0.622168 0.782884i \(-0.713748\pi\)
−0.622168 + 0.782884i \(0.713748\pi\)
\(272\) 34.9102 2.11674
\(273\) −1.08574 −0.0657121
\(274\) 3.47460 0.209908
\(275\) −3.86484 −0.233059
\(276\) 3.86032 0.232364
\(277\) −18.3536 −1.10276 −0.551380 0.834254i \(-0.685898\pi\)
−0.551380 + 0.834254i \(0.685898\pi\)
\(278\) −5.19638 −0.311658
\(279\) 6.45592 0.386506
\(280\) −26.6278 −1.59132
\(281\) 20.4488 1.21987 0.609935 0.792451i \(-0.291196\pi\)
0.609935 + 0.792451i \(0.291196\pi\)
\(282\) 0.414426 0.0246787
\(283\) 14.9635 0.889486 0.444743 0.895658i \(-0.353295\pi\)
0.444743 + 0.895658i \(0.353295\pi\)
\(284\) −77.0660 −4.57303
\(285\) 0.704577 0.0417356
\(286\) 21.5519 1.27439
\(287\) 18.9277 1.11727
\(288\) 99.6578 5.87239
\(289\) −13.8716 −0.815975
\(290\) 18.5945 1.09190
\(291\) −0.738210 −0.0432746
\(292\) 31.2207 1.82705
\(293\) 21.6604 1.26541 0.632706 0.774392i \(-0.281944\pi\)
0.632706 + 0.774392i \(0.281944\pi\)
\(294\) 0.744352 0.0434115
\(295\) −3.56352 −0.207476
\(296\) 42.6153 2.47697
\(297\) −0.537176 −0.0311701
\(298\) −28.4702 −1.64924
\(299\) −55.0295 −3.18244
\(300\) −1.69576 −0.0979045
\(301\) −12.4119 −0.715411
\(302\) 2.82377 0.162490
\(303\) 1.06712 0.0613043
\(304\) 139.884 8.02288
\(305\) −5.03533 −0.288322
\(306\) 14.9506 0.854670
\(307\) 28.8136 1.64448 0.822240 0.569141i \(-0.192724\pi\)
0.822240 + 0.569141i \(0.192724\pi\)
\(308\) 12.7805 0.728237
\(309\) −0.791290 −0.0450149
\(310\) 7.46199 0.423813
\(311\) 2.74194 0.155481 0.0777407 0.996974i \(-0.475229\pi\)
0.0777407 + 0.996974i \(0.475229\pi\)
\(312\) 6.29023 0.356114
\(313\) −25.8282 −1.45989 −0.729947 0.683504i \(-0.760455\pi\)
−0.729947 + 0.683504i \(0.760455\pi\)
\(314\) 12.6769 0.715396
\(315\) −7.10367 −0.400246
\(316\) −38.3437 −2.15700
\(317\) −34.9778 −1.96455 −0.982274 0.187450i \(-0.939978\pi\)
−0.982274 + 0.187450i \(0.939978\pi\)
\(318\) 0.229111 0.0128479
\(319\) −5.93671 −0.332392
\(320\) 66.8206 3.73539
\(321\) −0.933285 −0.0520909
\(322\) −43.5588 −2.42744
\(323\) 12.5355 0.697492
\(324\) 53.4093 2.96719
\(325\) 24.1733 1.34089
\(326\) 23.8379 1.32026
\(327\) 0.349917 0.0193505
\(328\) −109.657 −6.05481
\(329\) −3.50334 −0.193145
\(330\) −0.310103 −0.0170706
\(331\) −11.8999 −0.654076 −0.327038 0.945011i \(-0.606050\pi\)
−0.327038 + 0.945011i \(0.606050\pi\)
\(332\) 30.5535 1.67684
\(333\) 11.3687 0.623003
\(334\) −11.4319 −0.625524
\(335\) 13.8560 0.757034
\(336\) 3.10160 0.169206
\(337\) −6.54525 −0.356542 −0.178271 0.983981i \(-0.557050\pi\)
−0.178271 + 0.983981i \(0.557050\pi\)
\(338\) −98.0906 −5.33543
\(339\) −0.136050 −0.00738923
\(340\) 12.9461 0.702100
\(341\) −2.38241 −0.129015
\(342\) 59.9065 3.23937
\(343\) −19.8498 −1.07179
\(344\) 71.9083 3.87703
\(345\) 0.791802 0.0426292
\(346\) 12.8109 0.688718
\(347\) −14.5490 −0.781033 −0.390517 0.920596i \(-0.627704\pi\)
−0.390517 + 0.920596i \(0.627704\pi\)
\(348\) −2.60482 −0.139633
\(349\) −19.0582 −1.02016 −0.510082 0.860126i \(-0.670385\pi\)
−0.510082 + 0.860126i \(0.670385\pi\)
\(350\) 19.1344 1.02278
\(351\) 3.35985 0.179336
\(352\) −36.7765 −1.96019
\(353\) 8.64074 0.459900 0.229950 0.973202i \(-0.426144\pi\)
0.229950 + 0.973202i \(0.426144\pi\)
\(354\) 0.666330 0.0354150
\(355\) −15.8072 −0.838962
\(356\) 60.5882 3.21117
\(357\) 0.277946 0.0147104
\(358\) 44.8188 2.36875
\(359\) −27.2990 −1.44079 −0.720394 0.693565i \(-0.756039\pi\)
−0.720394 + 0.693565i \(0.756039\pi\)
\(360\) 41.1550 2.16906
\(361\) 31.2291 1.64364
\(362\) 5.24341 0.275588
\(363\) −0.793494 −0.0416476
\(364\) −79.9377 −4.18987
\(365\) 6.40378 0.335189
\(366\) 0.941539 0.0492151
\(367\) −9.09308 −0.474655 −0.237327 0.971430i \(-0.576271\pi\)
−0.237327 + 0.971430i \(0.576271\pi\)
\(368\) 157.201 8.19467
\(369\) −29.2539 −1.52290
\(370\) 13.1404 0.683138
\(371\) −1.93678 −0.100553
\(372\) −1.04532 −0.0541972
\(373\) −24.3983 −1.26330 −0.631649 0.775254i \(-0.717622\pi\)
−0.631649 + 0.775254i \(0.717622\pi\)
\(374\) −5.51719 −0.285287
\(375\) −0.844895 −0.0436302
\(376\) 20.2966 1.04671
\(377\) 37.1321 1.91240
\(378\) 2.65950 0.136790
\(379\) −37.6829 −1.93564 −0.967820 0.251643i \(-0.919029\pi\)
−0.967820 + 0.251643i \(0.919029\pi\)
\(380\) 51.8745 2.66110
\(381\) −0.633053 −0.0324323
\(382\) −3.55654 −0.181968
\(383\) −7.77167 −0.397114 −0.198557 0.980089i \(-0.563625\pi\)
−0.198557 + 0.980089i \(0.563625\pi\)
\(384\) −7.09212 −0.361918
\(385\) 2.62145 0.133601
\(386\) 28.5303 1.45215
\(387\) 19.1834 0.975147
\(388\) −54.3506 −2.75924
\(389\) −0.723666 −0.0366913 −0.0183457 0.999832i \(-0.505840\pi\)
−0.0183457 + 0.999832i \(0.505840\pi\)
\(390\) 1.93959 0.0982149
\(391\) 14.0873 0.712427
\(392\) 36.4547 1.84124
\(393\) 0.157576 0.00794868
\(394\) 33.3699 1.68115
\(395\) −7.86479 −0.395720
\(396\) −19.7531 −0.992628
\(397\) −10.2245 −0.513152 −0.256576 0.966524i \(-0.582594\pi\)
−0.256576 + 0.966524i \(0.582594\pi\)
\(398\) −24.7176 −1.23898
\(399\) 1.11372 0.0557556
\(400\) −69.0550 −3.45275
\(401\) −31.0775 −1.55194 −0.775969 0.630771i \(-0.782739\pi\)
−0.775969 + 0.630771i \(0.782739\pi\)
\(402\) −2.59089 −0.129222
\(403\) 14.9012 0.742281
\(404\) 78.5665 3.90883
\(405\) 10.9550 0.544356
\(406\) 29.3920 1.45870
\(407\) −4.19538 −0.207957
\(408\) −1.61027 −0.0797204
\(409\) 17.9693 0.888525 0.444263 0.895897i \(-0.353466\pi\)
0.444263 + 0.895897i \(0.353466\pi\)
\(410\) −33.8128 −1.66989
\(411\) −0.0998370 −0.00492459
\(412\) −58.2587 −2.87020
\(413\) −5.63281 −0.277172
\(414\) 67.3228 3.30874
\(415\) 6.26692 0.307631
\(416\) 230.024 11.2779
\(417\) 0.149310 0.00731172
\(418\) −22.1072 −1.08130
\(419\) −3.31775 −0.162083 −0.0810414 0.996711i \(-0.525825\pi\)
−0.0810414 + 0.996711i \(0.525825\pi\)
\(420\) 1.15020 0.0561239
\(421\) 14.4108 0.702338 0.351169 0.936312i \(-0.385784\pi\)
0.351169 + 0.936312i \(0.385784\pi\)
\(422\) 31.6086 1.53868
\(423\) 5.41463 0.263268
\(424\) 11.2207 0.544926
\(425\) −6.18826 −0.300175
\(426\) 2.95574 0.143206
\(427\) −7.95929 −0.385177
\(428\) −68.7130 −3.32137
\(429\) −0.619258 −0.0298981
\(430\) 22.1729 1.06927
\(431\) 17.0058 0.819140 0.409570 0.912279i \(-0.365679\pi\)
0.409570 + 0.912279i \(0.365679\pi\)
\(432\) −9.59798 −0.461783
\(433\) −3.49382 −0.167902 −0.0839511 0.996470i \(-0.526754\pi\)
−0.0839511 + 0.996470i \(0.526754\pi\)
\(434\) 11.7951 0.566182
\(435\) −0.534282 −0.0256169
\(436\) 25.7626 1.23381
\(437\) 56.4474 2.70024
\(438\) −1.19742 −0.0572150
\(439\) −30.4567 −1.45362 −0.726809 0.686840i \(-0.758997\pi\)
−0.726809 + 0.686840i \(0.758997\pi\)
\(440\) −15.1873 −0.724027
\(441\) 9.72524 0.463107
\(442\) 34.5081 1.64138
\(443\) 10.8599 0.515969 0.257985 0.966149i \(-0.416942\pi\)
0.257985 + 0.966149i \(0.416942\pi\)
\(444\) −1.84078 −0.0873597
\(445\) 12.4274 0.589117
\(446\) 71.7509 3.39750
\(447\) 0.818047 0.0386923
\(448\) 105.623 4.99020
\(449\) −36.3079 −1.71348 −0.856738 0.515752i \(-0.827512\pi\)
−0.856738 + 0.515752i \(0.827512\pi\)
\(450\) −29.5735 −1.39411
\(451\) 10.7955 0.508340
\(452\) −10.0167 −0.471145
\(453\) −0.0811365 −0.00381212
\(454\) −82.8348 −3.88763
\(455\) −16.3963 −0.768669
\(456\) −6.45230 −0.302157
\(457\) −11.0568 −0.517217 −0.258608 0.965982i \(-0.583264\pi\)
−0.258608 + 0.965982i \(0.583264\pi\)
\(458\) 23.7215 1.10843
\(459\) −0.860109 −0.0401464
\(460\) 58.2964 2.71808
\(461\) 38.1048 1.77472 0.887359 0.461079i \(-0.152537\pi\)
0.887359 + 0.461079i \(0.152537\pi\)
\(462\) −0.490176 −0.0228050
\(463\) −6.44200 −0.299385 −0.149693 0.988733i \(-0.547828\pi\)
−0.149693 + 0.988733i \(0.547828\pi\)
\(464\) −106.074 −4.92436
\(465\) −0.214408 −0.00994295
\(466\) −43.1070 −1.99689
\(467\) −40.3737 −1.86827 −0.934135 0.356919i \(-0.883827\pi\)
−0.934135 + 0.356919i \(0.883827\pi\)
\(468\) 123.549 5.71104
\(469\) 21.9020 1.01134
\(470\) 6.25843 0.288680
\(471\) −0.364249 −0.0167837
\(472\) 32.6336 1.50208
\(473\) −7.07920 −0.325502
\(474\) 1.47061 0.0675474
\(475\) −24.7961 −1.13772
\(476\) 20.4637 0.937953
\(477\) 2.99342 0.137059
\(478\) −56.6835 −2.59264
\(479\) −31.5792 −1.44289 −0.721445 0.692471i \(-0.756522\pi\)
−0.721445 + 0.692471i \(0.756522\pi\)
\(480\) −3.30975 −0.151069
\(481\) 26.2407 1.19647
\(482\) −45.8015 −2.08620
\(483\) 1.25159 0.0569494
\(484\) −58.4209 −2.65550
\(485\) −11.1480 −0.506206
\(486\) −6.16790 −0.279782
\(487\) 32.7210 1.48273 0.741366 0.671101i \(-0.234178\pi\)
0.741366 + 0.671101i \(0.234178\pi\)
\(488\) 46.1120 2.08739
\(489\) −0.684944 −0.0309743
\(490\) 11.2408 0.507807
\(491\) 16.3507 0.737896 0.368948 0.929450i \(-0.379718\pi\)
0.368948 + 0.929450i \(0.379718\pi\)
\(492\) 4.73668 0.213546
\(493\) −9.50566 −0.428114
\(494\) 138.273 6.22119
\(495\) −4.05161 −0.182106
\(496\) −42.5677 −1.91135
\(497\) −24.9863 −1.12079
\(498\) −1.17183 −0.0525110
\(499\) 26.6948 1.19502 0.597511 0.801861i \(-0.296156\pi\)
0.597511 + 0.801861i \(0.296156\pi\)
\(500\) −62.2054 −2.78191
\(501\) 0.328477 0.0146753
\(502\) −16.8383 −0.751529
\(503\) 33.3942 1.48898 0.744488 0.667636i \(-0.232694\pi\)
0.744488 + 0.667636i \(0.232694\pi\)
\(504\) 65.0532 2.89770
\(505\) 16.1150 0.717109
\(506\) −24.8440 −1.10445
\(507\) 2.81848 0.125173
\(508\) −46.6085 −2.06792
\(509\) −43.2833 −1.91850 −0.959248 0.282565i \(-0.908815\pi\)
−0.959248 + 0.282565i \(0.908815\pi\)
\(510\) −0.496527 −0.0219866
\(511\) 10.1224 0.447788
\(512\) −214.168 −9.46498
\(513\) −3.44642 −0.152163
\(514\) −14.2097 −0.626762
\(515\) −11.9496 −0.526563
\(516\) −3.10610 −0.136738
\(517\) −1.99815 −0.0878785
\(518\) 20.7709 0.912621
\(519\) −0.368101 −0.0161578
\(520\) 94.9915 4.16565
\(521\) 0.0361531 0.00158390 0.000791949 1.00000i \(-0.499748\pi\)
0.000791949 1.00000i \(0.499748\pi\)
\(522\) −45.4272 −1.98829
\(523\) 11.7968 0.515840 0.257920 0.966166i \(-0.416963\pi\)
0.257920 + 0.966166i \(0.416963\pi\)
\(524\) 11.6016 0.506816
\(525\) −0.549798 −0.0239951
\(526\) 58.5017 2.55080
\(527\) −3.81464 −0.166168
\(528\) 1.76901 0.0769865
\(529\) 40.4354 1.75806
\(530\) 3.45990 0.150288
\(531\) 8.70586 0.377802
\(532\) 81.9973 3.55504
\(533\) −67.5222 −2.92471
\(534\) −2.32376 −0.100559
\(535\) −14.0940 −0.609335
\(536\) −126.889 −5.48077
\(537\) −1.28780 −0.0555725
\(538\) −26.3426 −1.13571
\(539\) −3.58888 −0.154584
\(540\) −3.55931 −0.153168
\(541\) −3.42784 −0.147374 −0.0736871 0.997281i \(-0.523477\pi\)
−0.0736871 + 0.997281i \(0.523477\pi\)
\(542\) 57.8431 2.48457
\(543\) −0.150661 −0.00646548
\(544\) −58.8853 −2.52469
\(545\) 5.28426 0.226353
\(546\) 3.06588 0.131208
\(547\) −15.1618 −0.648272 −0.324136 0.946011i \(-0.605074\pi\)
−0.324136 + 0.946011i \(0.605074\pi\)
\(548\) −7.35049 −0.313997
\(549\) 12.3016 0.525018
\(550\) 10.9134 0.465350
\(551\) −38.0888 −1.62264
\(552\) −7.25108 −0.308626
\(553\) −12.4318 −0.528653
\(554\) 51.8262 2.20189
\(555\) −0.377569 −0.0160269
\(556\) 10.9929 0.466203
\(557\) −43.6401 −1.84909 −0.924545 0.381073i \(-0.875554\pi\)
−0.924545 + 0.381073i \(0.875554\pi\)
\(558\) −18.2300 −0.771739
\(559\) 44.2780 1.87276
\(560\) 46.8387 1.97930
\(561\) 0.158528 0.00669304
\(562\) −57.7425 −2.43572
\(563\) −46.5469 −1.96172 −0.980858 0.194723i \(-0.937619\pi\)
−0.980858 + 0.194723i \(0.937619\pi\)
\(564\) −0.876716 −0.0369164
\(565\) −2.05455 −0.0864357
\(566\) −42.2534 −1.77604
\(567\) 17.3164 0.727219
\(568\) 144.758 6.07391
\(569\) 36.4341 1.52740 0.763698 0.645574i \(-0.223382\pi\)
0.763698 + 0.645574i \(0.223382\pi\)
\(570\) −1.98956 −0.0833336
\(571\) −10.8218 −0.452877 −0.226438 0.974026i \(-0.572708\pi\)
−0.226438 + 0.974026i \(0.572708\pi\)
\(572\) −45.5929 −1.90633
\(573\) 0.102191 0.00426911
\(574\) −53.4474 −2.23085
\(575\) −27.8658 −1.16209
\(576\) −163.246 −6.80192
\(577\) 6.12082 0.254813 0.127407 0.991851i \(-0.459335\pi\)
0.127407 + 0.991851i \(0.459335\pi\)
\(578\) 39.1701 1.62926
\(579\) −0.819772 −0.0340686
\(580\) −39.3365 −1.63336
\(581\) 9.90604 0.410972
\(582\) 2.08453 0.0864067
\(583\) −1.10465 −0.0457501
\(584\) −58.6439 −2.42670
\(585\) 25.3415 1.04774
\(586\) −61.1639 −2.52666
\(587\) 32.1446 1.32675 0.663374 0.748288i \(-0.269124\pi\)
0.663374 + 0.748288i \(0.269124\pi\)
\(588\) −1.57467 −0.0649384
\(589\) −15.2851 −0.629813
\(590\) 10.0625 0.414268
\(591\) −0.958831 −0.0394410
\(592\) −74.9609 −3.08087
\(593\) 4.61461 0.189499 0.0947496 0.995501i \(-0.469795\pi\)
0.0947496 + 0.995501i \(0.469795\pi\)
\(594\) 1.51686 0.0622375
\(595\) 4.19738 0.172076
\(596\) 60.2286 2.46706
\(597\) 0.710222 0.0290674
\(598\) 155.391 6.35439
\(599\) −25.1452 −1.02741 −0.513704 0.857968i \(-0.671727\pi\)
−0.513704 + 0.857968i \(0.671727\pi\)
\(600\) 3.18524 0.130037
\(601\) 22.1039 0.901636 0.450818 0.892616i \(-0.351132\pi\)
0.450818 + 0.892616i \(0.351132\pi\)
\(602\) 35.0484 1.42847
\(603\) −33.8509 −1.37852
\(604\) −5.97367 −0.243065
\(605\) −11.9829 −0.487174
\(606\) −3.01329 −0.122407
\(607\) −0.102767 −0.00417119 −0.00208559 0.999998i \(-0.500664\pi\)
−0.00208559 + 0.999998i \(0.500664\pi\)
\(608\) −235.951 −9.56908
\(609\) −0.844533 −0.0342222
\(610\) 14.2186 0.575694
\(611\) 12.4977 0.505604
\(612\) −31.6279 −1.27848
\(613\) −26.9614 −1.08896 −0.544481 0.838773i \(-0.683273\pi\)
−0.544481 + 0.838773i \(0.683273\pi\)
\(614\) −81.3630 −3.28354
\(615\) 0.971556 0.0391769
\(616\) −24.0064 −0.967246
\(617\) 24.2051 0.974459 0.487229 0.873274i \(-0.338008\pi\)
0.487229 + 0.873274i \(0.338008\pi\)
\(618\) 2.23442 0.0898816
\(619\) −7.80737 −0.313805 −0.156902 0.987614i \(-0.550151\pi\)
−0.156902 + 0.987614i \(0.550151\pi\)
\(620\) −15.7858 −0.633973
\(621\) −3.87308 −0.155421
\(622\) −7.74262 −0.310451
\(623\) 19.6439 0.787016
\(624\) −11.0646 −0.442938
\(625\) 4.73433 0.189373
\(626\) 72.9328 2.91498
\(627\) 0.635214 0.0253680
\(628\) −26.8178 −1.07015
\(629\) −6.71751 −0.267845
\(630\) 20.0591 0.799174
\(631\) 7.70459 0.306715 0.153358 0.988171i \(-0.450991\pi\)
0.153358 + 0.988171i \(0.450991\pi\)
\(632\) 72.0233 2.86493
\(633\) −0.908222 −0.0360986
\(634\) 98.7692 3.92263
\(635\) −9.56001 −0.379377
\(636\) −0.484682 −0.0192189
\(637\) 22.4472 0.889392
\(638\) 16.7639 0.663689
\(639\) 38.6179 1.52770
\(640\) −107.101 −4.23355
\(641\) 20.3954 0.805570 0.402785 0.915295i \(-0.368042\pi\)
0.402785 + 0.915295i \(0.368042\pi\)
\(642\) 2.63538 0.104010
\(643\) −17.4909 −0.689776 −0.344888 0.938644i \(-0.612083\pi\)
−0.344888 + 0.938644i \(0.612083\pi\)
\(644\) 92.1484 3.63116
\(645\) −0.637102 −0.0250859
\(646\) −35.3973 −1.39269
\(647\) 28.3210 1.11341 0.556707 0.830709i \(-0.312065\pi\)
0.556707 + 0.830709i \(0.312065\pi\)
\(648\) −100.322 −3.94103
\(649\) −3.21270 −0.126110
\(650\) −68.2598 −2.67737
\(651\) −0.338913 −0.0132830
\(652\) −50.4290 −1.97495
\(653\) 17.4540 0.683026 0.341513 0.939877i \(-0.389061\pi\)
0.341513 + 0.939877i \(0.389061\pi\)
\(654\) −0.988085 −0.0386372
\(655\) 2.37963 0.0929799
\(656\) 192.888 7.53103
\(657\) −15.6448 −0.610361
\(658\) 9.89263 0.385655
\(659\) −12.7872 −0.498120 −0.249060 0.968488i \(-0.580122\pi\)
−0.249060 + 0.968488i \(0.580122\pi\)
\(660\) 0.656021 0.0255356
\(661\) 20.9020 0.812992 0.406496 0.913653i \(-0.366751\pi\)
0.406496 + 0.913653i \(0.366751\pi\)
\(662\) 33.6025 1.30600
\(663\) −0.991536 −0.0385081
\(664\) −57.3905 −2.22718
\(665\) 16.8187 0.652202
\(666\) −32.1027 −1.24395
\(667\) −42.8041 −1.65738
\(668\) 24.1841 0.935710
\(669\) −2.06165 −0.0797079
\(670\) −39.1261 −1.51157
\(671\) −4.53962 −0.175250
\(672\) −5.23168 −0.201816
\(673\) −24.1019 −0.929061 −0.464530 0.885557i \(-0.653777\pi\)
−0.464530 + 0.885557i \(0.653777\pi\)
\(674\) 18.4823 0.711910
\(675\) 1.70136 0.0654854
\(676\) 207.510 7.98116
\(677\) −12.3085 −0.473054 −0.236527 0.971625i \(-0.576009\pi\)
−0.236527 + 0.971625i \(0.576009\pi\)
\(678\) 0.384174 0.0147541
\(679\) −17.6216 −0.676253
\(680\) −24.3174 −0.932531
\(681\) 2.38013 0.0912066
\(682\) 6.72738 0.257605
\(683\) −1.46615 −0.0561005 −0.0280503 0.999607i \(-0.508930\pi\)
−0.0280503 + 0.999607i \(0.508930\pi\)
\(684\) −126.732 −4.84572
\(685\) −1.50768 −0.0576056
\(686\) 56.0513 2.14005
\(687\) −0.681598 −0.0260046
\(688\) −126.487 −4.82229
\(689\) 6.90923 0.263221
\(690\) −2.23587 −0.0851180
\(691\) 45.0709 1.71458 0.857289 0.514836i \(-0.172147\pi\)
0.857289 + 0.514836i \(0.172147\pi\)
\(692\) −27.1014 −1.03024
\(693\) −6.40433 −0.243281
\(694\) 41.0831 1.55949
\(695\) 2.25479 0.0855291
\(696\) 4.89279 0.185461
\(697\) 17.2854 0.654732
\(698\) 53.8161 2.03697
\(699\) 1.23861 0.0468486
\(700\) −40.4788 −1.52996
\(701\) 36.8357 1.39127 0.695633 0.718398i \(-0.255124\pi\)
0.695633 + 0.718398i \(0.255124\pi\)
\(702\) −9.48745 −0.358081
\(703\) −26.9168 −1.01519
\(704\) 60.2423 2.27047
\(705\) −0.179826 −0.00677264
\(706\) −24.3995 −0.918286
\(707\) 25.4728 0.958004
\(708\) −1.40962 −0.0529767
\(709\) 26.2623 0.986301 0.493150 0.869944i \(-0.335845\pi\)
0.493150 + 0.869944i \(0.335845\pi\)
\(710\) 44.6360 1.67516
\(711\) 19.2141 0.720584
\(712\) −113.807 −4.26508
\(713\) −17.1774 −0.643298
\(714\) −0.784854 −0.0293724
\(715\) −9.35170 −0.349734
\(716\) −94.8139 −3.54336
\(717\) 1.62871 0.0608253
\(718\) 77.0861 2.87683
\(719\) −24.2956 −0.906074 −0.453037 0.891492i \(-0.649659\pi\)
−0.453037 + 0.891492i \(0.649659\pi\)
\(720\) −72.3921 −2.69789
\(721\) −18.8886 −0.703450
\(722\) −88.1839 −3.28186
\(723\) 1.31603 0.0489438
\(724\) −11.0924 −0.412246
\(725\) 18.8029 0.698324
\(726\) 2.24064 0.0831580
\(727\) −3.31603 −0.122985 −0.0614923 0.998108i \(-0.519586\pi\)
−0.0614923 + 0.998108i \(0.519586\pi\)
\(728\) 150.152 5.56500
\(729\) −26.6452 −0.986858
\(730\) −18.0828 −0.669274
\(731\) −11.3350 −0.419240
\(732\) −1.99182 −0.0736199
\(733\) −28.0806 −1.03718 −0.518590 0.855023i \(-0.673543\pi\)
−0.518590 + 0.855023i \(0.673543\pi\)
\(734\) 25.6768 0.947746
\(735\) −0.322986 −0.0119135
\(736\) −265.161 −9.77397
\(737\) 12.4919 0.460146
\(738\) 82.6063 3.04078
\(739\) 3.63715 0.133795 0.0668974 0.997760i \(-0.478690\pi\)
0.0668974 + 0.997760i \(0.478690\pi\)
\(740\) −27.7985 −1.02189
\(741\) −3.97305 −0.145954
\(742\) 5.46902 0.200774
\(743\) 49.0671 1.80010 0.900050 0.435788i \(-0.143530\pi\)
0.900050 + 0.435788i \(0.143530\pi\)
\(744\) 1.96349 0.0719849
\(745\) 12.3537 0.452604
\(746\) 68.8953 2.52243
\(747\) −15.3104 −0.560178
\(748\) 11.6716 0.426755
\(749\) −22.2781 −0.814026
\(750\) 2.38579 0.0871167
\(751\) 22.6939 0.828114 0.414057 0.910251i \(-0.364111\pi\)
0.414057 + 0.910251i \(0.364111\pi\)
\(752\) −35.7019 −1.30191
\(753\) 0.483821 0.0176314
\(754\) −104.852 −3.81850
\(755\) −1.22528 −0.0445924
\(756\) −5.62616 −0.204622
\(757\) −40.5323 −1.47317 −0.736586 0.676343i \(-0.763564\pi\)
−0.736586 + 0.676343i \(0.763564\pi\)
\(758\) 106.408 3.86490
\(759\) 0.713852 0.0259112
\(760\) −97.4390 −3.53449
\(761\) −11.8092 −0.428083 −0.214042 0.976825i \(-0.568663\pi\)
−0.214042 + 0.976825i \(0.568663\pi\)
\(762\) 1.78759 0.0647577
\(763\) 8.35276 0.302390
\(764\) 7.52384 0.272203
\(765\) −6.48731 −0.234549
\(766\) 21.9454 0.792919
\(767\) 20.0944 0.725565
\(768\) 11.1769 0.403313
\(769\) 12.2726 0.442561 0.221280 0.975210i \(-0.428976\pi\)
0.221280 + 0.975210i \(0.428976\pi\)
\(770\) −7.40236 −0.266763
\(771\) 0.408292 0.0147043
\(772\) −60.3556 −2.17225
\(773\) −27.0527 −0.973018 −0.486509 0.873675i \(-0.661730\pi\)
−0.486509 + 0.873675i \(0.661730\pi\)
\(774\) −54.1695 −1.94708
\(775\) 7.54566 0.271048
\(776\) 102.090 3.66483
\(777\) −0.596819 −0.0214107
\(778\) 2.04347 0.0732618
\(779\) 69.2620 2.48157
\(780\) −4.10319 −0.146918
\(781\) −14.2511 −0.509944
\(782\) −39.7794 −1.42251
\(783\) 2.61343 0.0933963
\(784\) −64.1242 −2.29015
\(785\) −5.50069 −0.196328
\(786\) −0.444959 −0.0158712
\(787\) 26.0946 0.930174 0.465087 0.885265i \(-0.346023\pi\)
0.465087 + 0.885265i \(0.346023\pi\)
\(788\) −70.5939 −2.51480
\(789\) −1.68095 −0.0598435
\(790\) 22.2083 0.790137
\(791\) −3.24761 −0.115472
\(792\) 37.1034 1.31841
\(793\) 28.3938 1.00829
\(794\) 28.8715 1.02461
\(795\) −0.0994147 −0.00352588
\(796\) 52.2900 1.85337
\(797\) 14.7113 0.521101 0.260551 0.965460i \(-0.416096\pi\)
0.260551 + 0.965460i \(0.416096\pi\)
\(798\) −3.14488 −0.111327
\(799\) −3.19937 −0.113186
\(800\) 116.480 4.11818
\(801\) −30.3609 −1.07275
\(802\) 87.7558 3.09876
\(803\) 5.77335 0.203737
\(804\) 5.48101 0.193300
\(805\) 18.9008 0.666167
\(806\) −42.0775 −1.48212
\(807\) 0.756912 0.0266446
\(808\) −147.576 −5.19172
\(809\) −21.6964 −0.762804 −0.381402 0.924409i \(-0.624559\pi\)
−0.381402 + 0.924409i \(0.624559\pi\)
\(810\) −30.9343 −1.08692
\(811\) 3.32491 0.116754 0.0583768 0.998295i \(-0.481408\pi\)
0.0583768 + 0.998295i \(0.481408\pi\)
\(812\) −62.1787 −2.18204
\(813\) −1.66203 −0.0582899
\(814\) 11.8468 0.415230
\(815\) −10.3436 −0.362322
\(816\) 2.83249 0.0991569
\(817\) −45.4189 −1.58900
\(818\) −50.7412 −1.77412
\(819\) 40.0569 1.39970
\(820\) 71.5307 2.49796
\(821\) 15.5133 0.541417 0.270708 0.962661i \(-0.412742\pi\)
0.270708 + 0.962661i \(0.412742\pi\)
\(822\) 0.281916 0.00983296
\(823\) −49.6057 −1.72915 −0.864574 0.502506i \(-0.832411\pi\)
−0.864574 + 0.502506i \(0.832411\pi\)
\(824\) 109.431 3.81221
\(825\) −0.313580 −0.0109174
\(826\) 15.9057 0.553432
\(827\) 29.5445 1.02736 0.513682 0.857981i \(-0.328281\pi\)
0.513682 + 0.857981i \(0.328281\pi\)
\(828\) −142.421 −4.94947
\(829\) 37.9640 1.31854 0.659272 0.751904i \(-0.270864\pi\)
0.659272 + 0.751904i \(0.270864\pi\)
\(830\) −17.6963 −0.614248
\(831\) −1.48914 −0.0516579
\(832\) −376.795 −13.0630
\(833\) −5.74640 −0.199101
\(834\) −0.421616 −0.0145994
\(835\) 4.96047 0.171664
\(836\) 46.7676 1.61749
\(837\) 1.04877 0.0362509
\(838\) 9.36856 0.323632
\(839\) −49.8255 −1.72017 −0.860084 0.510152i \(-0.829589\pi\)
−0.860084 + 0.510152i \(0.829589\pi\)
\(840\) −2.16049 −0.0745440
\(841\) −0.117188 −0.00404096
\(842\) −40.6927 −1.40236
\(843\) 1.65914 0.0571438
\(844\) −66.8678 −2.30168
\(845\) 42.5631 1.46421
\(846\) −15.2897 −0.525670
\(847\) −18.9412 −0.650828
\(848\) −19.7374 −0.677784
\(849\) 1.21408 0.0416672
\(850\) 17.4742 0.599361
\(851\) −30.2490 −1.03692
\(852\) −6.25286 −0.214220
\(853\) −36.7361 −1.25782 −0.628909 0.777479i \(-0.716498\pi\)
−0.628909 + 0.777479i \(0.716498\pi\)
\(854\) 22.4752 0.769085
\(855\) −25.9944 −0.888989
\(856\) 129.068 4.41146
\(857\) −2.56397 −0.0875835 −0.0437917 0.999041i \(-0.513944\pi\)
−0.0437917 + 0.999041i \(0.513944\pi\)
\(858\) 1.74864 0.0596977
\(859\) 40.0871 1.36775 0.683877 0.729597i \(-0.260293\pi\)
0.683877 + 0.729597i \(0.260293\pi\)
\(860\) −46.9066 −1.59950
\(861\) 1.53573 0.0523374
\(862\) −48.0204 −1.63558
\(863\) −14.4172 −0.490767 −0.245383 0.969426i \(-0.578914\pi\)
−0.245383 + 0.969426i \(0.578914\pi\)
\(864\) 16.1895 0.550780
\(865\) −5.55885 −0.189007
\(866\) 9.86573 0.335251
\(867\) −1.12549 −0.0382237
\(868\) −24.9524 −0.846941
\(869\) −7.09053 −0.240530
\(870\) 1.50869 0.0511493
\(871\) −78.1328 −2.64743
\(872\) −48.3916 −1.63875
\(873\) 27.2352 0.921772
\(874\) −159.394 −5.39159
\(875\) −20.1682 −0.681810
\(876\) 2.53314 0.0855869
\(877\) 12.9610 0.437663 0.218831 0.975763i \(-0.429776\pi\)
0.218831 + 0.975763i \(0.429776\pi\)
\(878\) 86.0026 2.90245
\(879\) 1.75745 0.0592772
\(880\) 26.7147 0.900551
\(881\) 0.0190464 0.000641689 0 0.000320845 1.00000i \(-0.499898\pi\)
0.000320845 1.00000i \(0.499898\pi\)
\(882\) −27.4618 −0.924687
\(883\) −38.9098 −1.30942 −0.654709 0.755881i \(-0.727209\pi\)
−0.654709 + 0.755881i \(0.727209\pi\)
\(884\) −73.0018 −2.45532
\(885\) −0.289131 −0.00971904
\(886\) −30.6658 −1.03024
\(887\) 11.7221 0.393590 0.196795 0.980445i \(-0.436947\pi\)
0.196795 + 0.980445i \(0.436947\pi\)
\(888\) 3.45766 0.116031
\(889\) −15.1114 −0.506820
\(890\) −35.0922 −1.17629
\(891\) 9.87648 0.330874
\(892\) −151.789 −5.08226
\(893\) −12.8198 −0.428997
\(894\) −2.30997 −0.0772571
\(895\) −19.4476 −0.650061
\(896\) −169.294 −5.65570
\(897\) −4.46490 −0.149079
\(898\) 102.525 3.42131
\(899\) 11.5907 0.386572
\(900\) 62.5625 2.08542
\(901\) −1.76873 −0.0589251
\(902\) −30.4840 −1.01501
\(903\) −1.00706 −0.0335128
\(904\) 18.8150 0.625776
\(905\) −2.27520 −0.0756302
\(906\) 0.229111 0.00761169
\(907\) −39.7141 −1.31868 −0.659342 0.751843i \(-0.729165\pi\)
−0.659342 + 0.751843i \(0.729165\pi\)
\(908\) 175.237 5.81543
\(909\) −39.3698 −1.30581
\(910\) 46.2993 1.53481
\(911\) −12.3113 −0.407892 −0.203946 0.978982i \(-0.565377\pi\)
−0.203946 + 0.978982i \(0.565377\pi\)
\(912\) 11.3497 0.375825
\(913\) 5.64996 0.186986
\(914\) 31.2219 1.03273
\(915\) −0.408549 −0.0135062
\(916\) −50.1826 −1.65808
\(917\) 3.76146 0.124214
\(918\) 2.42875 0.0801606
\(919\) 22.6517 0.747211 0.373606 0.927588i \(-0.378121\pi\)
0.373606 + 0.927588i \(0.378121\pi\)
\(920\) −109.502 −3.61017
\(921\) 2.33784 0.0770343
\(922\) −107.599 −3.54359
\(923\) 89.1357 2.93394
\(924\) 1.03696 0.0341136
\(925\) 13.2877 0.436898
\(926\) 18.1907 0.597784
\(927\) 29.1936 0.958842
\(928\) 178.922 5.87340
\(929\) −27.4350 −0.900113 −0.450056 0.893000i \(-0.648596\pi\)
−0.450056 + 0.893000i \(0.648596\pi\)
\(930\) 0.605440 0.0198531
\(931\) −23.0256 −0.754633
\(932\) 91.1927 2.98711
\(933\) 0.222472 0.00728340
\(934\) 114.006 3.73039
\(935\) 2.39400 0.0782920
\(936\) −232.069 −7.58542
\(937\) 39.6368 1.29488 0.647438 0.762118i \(-0.275840\pi\)
0.647438 + 0.762118i \(0.275840\pi\)
\(938\) −61.8462 −2.01935
\(939\) −2.09561 −0.0683875
\(940\) −13.2397 −0.431831
\(941\) −57.2313 −1.86569 −0.932844 0.360280i \(-0.882681\pi\)
−0.932844 + 0.360280i \(0.882681\pi\)
\(942\) 1.02856 0.0335121
\(943\) 77.8364 2.53470
\(944\) −57.4029 −1.86830
\(945\) −1.15400 −0.0375396
\(946\) 19.9900 0.649932
\(947\) −49.0227 −1.59302 −0.796511 0.604624i \(-0.793323\pi\)
−0.796511 + 0.604624i \(0.793323\pi\)
\(948\) −3.11107 −0.101043
\(949\) −36.1104 −1.17219
\(950\) 70.0185 2.27170
\(951\) −2.83797 −0.0920276
\(952\) −38.4383 −1.24579
\(953\) −48.3708 −1.56688 −0.783442 0.621465i \(-0.786538\pi\)
−0.783442 + 0.621465i \(0.786538\pi\)
\(954\) −8.45272 −0.273667
\(955\) 1.54324 0.0499380
\(956\) 119.914 3.87829
\(957\) −0.481684 −0.0155706
\(958\) 89.1724 2.88103
\(959\) −2.38317 −0.0769567
\(960\) 5.42159 0.174981
\(961\) −26.3486 −0.849955
\(962\) −74.0976 −2.38900
\(963\) 34.4322 1.10956
\(964\) 96.8929 3.12071
\(965\) −12.3797 −0.398518
\(966\) −3.53421 −0.113711
\(967\) −43.7009 −1.40532 −0.702662 0.711523i \(-0.748006\pi\)
−0.702662 + 0.711523i \(0.748006\pi\)
\(968\) 109.736 3.52704
\(969\) 1.01708 0.0326734
\(970\) 31.4795 1.01074
\(971\) −58.3573 −1.87277 −0.936387 0.350970i \(-0.885852\pi\)
−0.936387 + 0.350970i \(0.885852\pi\)
\(972\) 13.0482 0.418520
\(973\) 3.56412 0.114260
\(974\) −92.3966 −2.96058
\(975\) 1.96134 0.0628130
\(976\) −81.1115 −2.59632
\(977\) 10.0169 0.320469 0.160234 0.987079i \(-0.448775\pi\)
0.160234 + 0.987079i \(0.448775\pi\)
\(978\) 1.93412 0.0618465
\(979\) 11.2040 0.358081
\(980\) −23.7798 −0.759619
\(981\) −12.9097 −0.412175
\(982\) −46.1706 −1.47336
\(983\) 42.8038 1.36523 0.682615 0.730778i \(-0.260843\pi\)
0.682615 + 0.730778i \(0.260843\pi\)
\(984\) −8.89721 −0.283633
\(985\) −14.4797 −0.461363
\(986\) 26.8418 0.854817
\(987\) −0.284249 −0.00904774
\(988\) −292.515 −9.30615
\(989\) −51.0416 −1.62303
\(990\) 11.4408 0.363613
\(991\) −32.6973 −1.03866 −0.519332 0.854573i \(-0.673819\pi\)
−0.519332 + 0.854573i \(0.673819\pi\)
\(992\) 71.8018 2.27971
\(993\) −0.965513 −0.0306396
\(994\) 70.5556 2.23789
\(995\) 10.7254 0.340017
\(996\) 2.47900 0.0785501
\(997\) 9.62079 0.304693 0.152347 0.988327i \(-0.451317\pi\)
0.152347 + 0.988327i \(0.451317\pi\)
\(998\) −75.3798 −2.38611
\(999\) 1.84687 0.0584323
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.1.1 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.1 153 1.1 even 1 trivial