Properties

Label 6037.2.a.b.1.4
Level 6037
Weight 2
Character 6037.1
Self dual yes
Analytic conductor 48.206
Analytic rank 0
Dimension 259
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65707 q^{2} +2.92115 q^{3} +5.06000 q^{4} +0.928477 q^{5} -7.76170 q^{6} +3.41739 q^{7} -8.13063 q^{8} +5.53314 q^{9} +O(q^{10})\) \(q-2.65707 q^{2} +2.92115 q^{3} +5.06000 q^{4} +0.928477 q^{5} -7.76170 q^{6} +3.41739 q^{7} -8.13063 q^{8} +5.53314 q^{9} -2.46702 q^{10} +3.81271 q^{11} +14.7810 q^{12} +0.216731 q^{13} -9.08022 q^{14} +2.71222 q^{15} +11.4836 q^{16} -1.11046 q^{17} -14.7019 q^{18} +2.30245 q^{19} +4.69809 q^{20} +9.98271 q^{21} -10.1306 q^{22} +9.12530 q^{23} -23.7508 q^{24} -4.13793 q^{25} -0.575869 q^{26} +7.39969 q^{27} +17.2920 q^{28} +0.567784 q^{29} -7.20656 q^{30} -8.02797 q^{31} -14.2515 q^{32} +11.1375 q^{33} +2.95057 q^{34} +3.17296 q^{35} +27.9977 q^{36} -4.36760 q^{37} -6.11776 q^{38} +0.633105 q^{39} -7.54910 q^{40} +3.05078 q^{41} -26.5247 q^{42} +7.90720 q^{43} +19.2923 q^{44} +5.13739 q^{45} -24.2465 q^{46} +6.04383 q^{47} +33.5454 q^{48} +4.67853 q^{49} +10.9948 q^{50} -3.24382 q^{51} +1.09666 q^{52} -8.67944 q^{53} -19.6615 q^{54} +3.54001 q^{55} -27.7855 q^{56} +6.72581 q^{57} -1.50864 q^{58} -0.276534 q^{59} +13.7239 q^{60} +1.01388 q^{61} +21.3308 q^{62} +18.9089 q^{63} +14.8999 q^{64} +0.201230 q^{65} -29.5931 q^{66} -5.11816 q^{67} -5.61893 q^{68} +26.6564 q^{69} -8.43077 q^{70} -1.17876 q^{71} -44.9879 q^{72} -2.92582 q^{73} +11.6050 q^{74} -12.0875 q^{75} +11.6504 q^{76} +13.0295 q^{77} -1.68220 q^{78} +5.80150 q^{79} +10.6623 q^{80} +5.01621 q^{81} -8.10611 q^{82} +6.36225 q^{83} +50.5125 q^{84} -1.03104 q^{85} -21.0100 q^{86} +1.65858 q^{87} -30.9997 q^{88} +11.9820 q^{89} -13.6504 q^{90} +0.740654 q^{91} +46.1740 q^{92} -23.4509 q^{93} -16.0589 q^{94} +2.13777 q^{95} -41.6308 q^{96} -11.2544 q^{97} -12.4312 q^{98} +21.0962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65707 −1.87883 −0.939415 0.342782i \(-0.888631\pi\)
−0.939415 + 0.342782i \(0.888631\pi\)
\(3\) 2.92115 1.68653 0.843264 0.537499i \(-0.180631\pi\)
0.843264 + 0.537499i \(0.180631\pi\)
\(4\) 5.06000 2.53000
\(5\) 0.928477 0.415227 0.207614 0.978211i \(-0.433430\pi\)
0.207614 + 0.978211i \(0.433430\pi\)
\(6\) −7.76170 −3.16870
\(7\) 3.41739 1.29165 0.645825 0.763485i \(-0.276513\pi\)
0.645825 + 0.763485i \(0.276513\pi\)
\(8\) −8.13063 −2.87461
\(9\) 5.53314 1.84438
\(10\) −2.46702 −0.780142
\(11\) 3.81271 1.14958 0.574788 0.818303i \(-0.305085\pi\)
0.574788 + 0.818303i \(0.305085\pi\)
\(12\) 14.7810 4.26692
\(13\) 0.216731 0.0601104 0.0300552 0.999548i \(-0.490432\pi\)
0.0300552 + 0.999548i \(0.490432\pi\)
\(14\) −9.08022 −2.42679
\(15\) 2.71222 0.700293
\(16\) 11.4836 2.87091
\(17\) −1.11046 −0.269326 −0.134663 0.990891i \(-0.542995\pi\)
−0.134663 + 0.990891i \(0.542995\pi\)
\(18\) −14.7019 −3.46528
\(19\) 2.30245 0.528218 0.264109 0.964493i \(-0.414922\pi\)
0.264109 + 0.964493i \(0.414922\pi\)
\(20\) 4.69809 1.05053
\(21\) 9.98271 2.17841
\(22\) −10.1306 −2.15986
\(23\) 9.12530 1.90276 0.951378 0.308025i \(-0.0996682\pi\)
0.951378 + 0.308025i \(0.0996682\pi\)
\(24\) −23.7508 −4.84812
\(25\) −4.13793 −0.827586
\(26\) −0.575869 −0.112937
\(27\) 7.39969 1.42407
\(28\) 17.2920 3.26788
\(29\) 0.567784 0.105435 0.0527174 0.998609i \(-0.483212\pi\)
0.0527174 + 0.998609i \(0.483212\pi\)
\(30\) −7.20656 −1.31573
\(31\) −8.02797 −1.44187 −0.720933 0.693005i \(-0.756286\pi\)
−0.720933 + 0.693005i \(0.756286\pi\)
\(32\) −14.2515 −2.51933
\(33\) 11.1375 1.93879
\(34\) 2.95057 0.506018
\(35\) 3.17296 0.536329
\(36\) 27.9977 4.66628
\(37\) −4.36760 −0.718030 −0.359015 0.933332i \(-0.616887\pi\)
−0.359015 + 0.933332i \(0.616887\pi\)
\(38\) −6.11776 −0.992432
\(39\) 0.633105 0.101378
\(40\) −7.54910 −1.19362
\(41\) 3.05078 0.476451 0.238226 0.971210i \(-0.423434\pi\)
0.238226 + 0.971210i \(0.423434\pi\)
\(42\) −26.5247 −4.09285
\(43\) 7.90720 1.20584 0.602918 0.797803i \(-0.294004\pi\)
0.602918 + 0.797803i \(0.294004\pi\)
\(44\) 19.2923 2.90843
\(45\) 5.13739 0.765837
\(46\) −24.2465 −3.57496
\(47\) 6.04383 0.881584 0.440792 0.897609i \(-0.354698\pi\)
0.440792 + 0.897609i \(0.354698\pi\)
\(48\) 33.5454 4.84187
\(49\) 4.67853 0.668361
\(50\) 10.9948 1.55489
\(51\) −3.24382 −0.454226
\(52\) 1.09666 0.152079
\(53\) −8.67944 −1.19221 −0.596107 0.802905i \(-0.703286\pi\)
−0.596107 + 0.802905i \(0.703286\pi\)
\(54\) −19.6615 −2.67559
\(55\) 3.54001 0.477335
\(56\) −27.7855 −3.71299
\(57\) 6.72581 0.890855
\(58\) −1.50864 −0.198094
\(59\) −0.276534 −0.0360017 −0.0180008 0.999838i \(-0.505730\pi\)
−0.0180008 + 0.999838i \(0.505730\pi\)
\(60\) 13.7239 1.77174
\(61\) 1.01388 0.129813 0.0649067 0.997891i \(-0.479325\pi\)
0.0649067 + 0.997891i \(0.479325\pi\)
\(62\) 21.3308 2.70902
\(63\) 18.9089 2.38229
\(64\) 14.8999 1.86249
\(65\) 0.201230 0.0249595
\(66\) −29.5931 −3.64266
\(67\) −5.11816 −0.625283 −0.312641 0.949871i \(-0.601214\pi\)
−0.312641 + 0.949871i \(0.601214\pi\)
\(68\) −5.61893 −0.681395
\(69\) 26.6564 3.20905
\(70\) −8.43077 −1.00767
\(71\) −1.17876 −0.139892 −0.0699462 0.997551i \(-0.522283\pi\)
−0.0699462 + 0.997551i \(0.522283\pi\)
\(72\) −44.9879 −5.30188
\(73\) −2.92582 −0.342441 −0.171221 0.985233i \(-0.554771\pi\)
−0.171221 + 0.985233i \(0.554771\pi\)
\(74\) 11.6050 1.34906
\(75\) −12.0875 −1.39575
\(76\) 11.6504 1.33639
\(77\) 13.0295 1.48485
\(78\) −1.68220 −0.190472
\(79\) 5.80150 0.652719 0.326360 0.945246i \(-0.394178\pi\)
0.326360 + 0.945246i \(0.394178\pi\)
\(80\) 10.6623 1.19208
\(81\) 5.01621 0.557357
\(82\) −8.10611 −0.895170
\(83\) 6.36225 0.698348 0.349174 0.937058i \(-0.386462\pi\)
0.349174 + 0.937058i \(0.386462\pi\)
\(84\) 50.5125 5.51137
\(85\) −1.03104 −0.111832
\(86\) −21.0100 −2.26556
\(87\) 1.65858 0.177819
\(88\) −30.9997 −3.30458
\(89\) 11.9820 1.27009 0.635047 0.772473i \(-0.280981\pi\)
0.635047 + 0.772473i \(0.280981\pi\)
\(90\) −13.6504 −1.43888
\(91\) 0.740654 0.0776416
\(92\) 46.1740 4.81398
\(93\) −23.4509 −2.43175
\(94\) −16.0589 −1.65635
\(95\) 2.13777 0.219331
\(96\) −41.6308 −4.24892
\(97\) −11.2544 −1.14271 −0.571357 0.820702i \(-0.693583\pi\)
−0.571357 + 0.820702i \(0.693583\pi\)
\(98\) −12.4312 −1.25574
\(99\) 21.0962 2.12025
\(100\) −20.9379 −2.09379
\(101\) −1.85556 −0.184635 −0.0923177 0.995730i \(-0.529428\pi\)
−0.0923177 + 0.995730i \(0.529428\pi\)
\(102\) 8.61906 0.853414
\(103\) −4.75261 −0.468289 −0.234144 0.972202i \(-0.575229\pi\)
−0.234144 + 0.972202i \(0.575229\pi\)
\(104\) −1.76216 −0.172794
\(105\) 9.26871 0.904534
\(106\) 23.0619 2.23997
\(107\) −8.94794 −0.865030 −0.432515 0.901627i \(-0.642374\pi\)
−0.432515 + 0.901627i \(0.642374\pi\)
\(108\) 37.4424 3.60290
\(109\) −8.54537 −0.818498 −0.409249 0.912423i \(-0.634209\pi\)
−0.409249 + 0.912423i \(0.634209\pi\)
\(110\) −9.40604 −0.896831
\(111\) −12.7584 −1.21098
\(112\) 39.2440 3.70821
\(113\) 4.04230 0.380268 0.190134 0.981758i \(-0.439108\pi\)
0.190134 + 0.981758i \(0.439108\pi\)
\(114\) −17.8709 −1.67377
\(115\) 8.47263 0.790076
\(116\) 2.87299 0.266750
\(117\) 1.19920 0.110866
\(118\) 0.734770 0.0676411
\(119\) −3.79487 −0.347875
\(120\) −22.0521 −2.01307
\(121\) 3.53675 0.321523
\(122\) −2.69393 −0.243897
\(123\) 8.91178 0.803548
\(124\) −40.6215 −3.64792
\(125\) −8.48436 −0.758864
\(126\) −50.2421 −4.47593
\(127\) −21.4121 −1.90002 −0.950009 0.312223i \(-0.898926\pi\)
−0.950009 + 0.312223i \(0.898926\pi\)
\(128\) −11.0871 −0.979967
\(129\) 23.0982 2.03368
\(130\) −0.534681 −0.0468946
\(131\) −0.256110 −0.0223765 −0.0111882 0.999937i \(-0.503561\pi\)
−0.0111882 + 0.999937i \(0.503561\pi\)
\(132\) 56.3558 4.90515
\(133\) 7.86836 0.682273
\(134\) 13.5993 1.17480
\(135\) 6.87044 0.591313
\(136\) 9.02874 0.774208
\(137\) 20.4368 1.74603 0.873017 0.487689i \(-0.162160\pi\)
0.873017 + 0.487689i \(0.162160\pi\)
\(138\) −70.8278 −6.02926
\(139\) 10.3999 0.882110 0.441055 0.897480i \(-0.354604\pi\)
0.441055 + 0.897480i \(0.354604\pi\)
\(140\) 16.0552 1.35691
\(141\) 17.6550 1.48682
\(142\) 3.13203 0.262834
\(143\) 0.826332 0.0691014
\(144\) 63.5405 5.29504
\(145\) 0.527174 0.0437794
\(146\) 7.77410 0.643389
\(147\) 13.6667 1.12721
\(148\) −22.1001 −1.81662
\(149\) −3.10424 −0.254309 −0.127154 0.991883i \(-0.540584\pi\)
−0.127154 + 0.991883i \(0.540584\pi\)
\(150\) 32.1174 2.62237
\(151\) −8.44808 −0.687495 −0.343748 0.939062i \(-0.611696\pi\)
−0.343748 + 0.939062i \(0.611696\pi\)
\(152\) −18.7204 −1.51842
\(153\) −6.14433 −0.496740
\(154\) −34.6202 −2.78978
\(155\) −7.45378 −0.598702
\(156\) 3.20351 0.256486
\(157\) −8.02902 −0.640785 −0.320393 0.947285i \(-0.603815\pi\)
−0.320393 + 0.947285i \(0.603815\pi\)
\(158\) −15.4150 −1.22635
\(159\) −25.3540 −2.01070
\(160\) −13.2322 −1.04610
\(161\) 31.1847 2.45770
\(162\) −13.3284 −1.04718
\(163\) 10.0422 0.786568 0.393284 0.919417i \(-0.371339\pi\)
0.393284 + 0.919417i \(0.371339\pi\)
\(164\) 15.4369 1.20542
\(165\) 10.3409 0.805039
\(166\) −16.9049 −1.31208
\(167\) 4.39680 0.340235 0.170117 0.985424i \(-0.445585\pi\)
0.170117 + 0.985424i \(0.445585\pi\)
\(168\) −81.1657 −6.26207
\(169\) −12.9530 −0.996387
\(170\) 2.73953 0.210112
\(171\) 12.7398 0.974235
\(172\) 40.0105 3.05077
\(173\) −8.81909 −0.670503 −0.335251 0.942129i \(-0.608821\pi\)
−0.335251 + 0.942129i \(0.608821\pi\)
\(174\) −4.40697 −0.334091
\(175\) −14.1409 −1.06895
\(176\) 43.7837 3.30032
\(177\) −0.807799 −0.0607179
\(178\) −31.8371 −2.38629
\(179\) −14.4810 −1.08236 −0.541180 0.840907i \(-0.682022\pi\)
−0.541180 + 0.840907i \(0.682022\pi\)
\(180\) 25.9952 1.93757
\(181\) 14.5720 1.08313 0.541565 0.840659i \(-0.317832\pi\)
0.541565 + 0.840659i \(0.317832\pi\)
\(182\) −1.96797 −0.145875
\(183\) 2.96169 0.218934
\(184\) −74.1944 −5.46969
\(185\) −4.05522 −0.298146
\(186\) 62.3107 4.56884
\(187\) −4.23386 −0.309611
\(188\) 30.5818 2.23041
\(189\) 25.2876 1.83940
\(190\) −5.68020 −0.412085
\(191\) 10.9393 0.791538 0.395769 0.918350i \(-0.370478\pi\)
0.395769 + 0.918350i \(0.370478\pi\)
\(192\) 43.5249 3.14114
\(193\) 18.1844 1.30894 0.654471 0.756087i \(-0.272891\pi\)
0.654471 + 0.756087i \(0.272891\pi\)
\(194\) 29.9037 2.14696
\(195\) 0.587823 0.0420949
\(196\) 23.6734 1.69096
\(197\) −10.0282 −0.714481 −0.357241 0.934012i \(-0.616282\pi\)
−0.357241 + 0.934012i \(0.616282\pi\)
\(198\) −56.0541 −3.98359
\(199\) −8.42428 −0.597181 −0.298591 0.954381i \(-0.596516\pi\)
−0.298591 + 0.954381i \(0.596516\pi\)
\(200\) 33.6440 2.37899
\(201\) −14.9509 −1.05456
\(202\) 4.93035 0.346899
\(203\) 1.94034 0.136185
\(204\) −16.4138 −1.14919
\(205\) 2.83257 0.197835
\(206\) 12.6280 0.879835
\(207\) 50.4915 3.50940
\(208\) 2.48886 0.172571
\(209\) 8.77857 0.607226
\(210\) −24.6276 −1.69947
\(211\) 9.58370 0.659769 0.329884 0.944021i \(-0.392990\pi\)
0.329884 + 0.944021i \(0.392990\pi\)
\(212\) −43.9180 −3.01630
\(213\) −3.44332 −0.235933
\(214\) 23.7753 1.62524
\(215\) 7.34165 0.500696
\(216\) −60.1641 −4.09365
\(217\) −27.4347 −1.86239
\(218\) 22.7056 1.53782
\(219\) −8.54677 −0.577537
\(220\) 17.9125 1.20766
\(221\) −0.240671 −0.0161893
\(222\) 33.9000 2.27522
\(223\) 6.19198 0.414645 0.207323 0.978273i \(-0.433525\pi\)
0.207323 + 0.978273i \(0.433525\pi\)
\(224\) −48.7028 −3.25410
\(225\) −22.8957 −1.52638
\(226\) −10.7407 −0.714458
\(227\) −2.19145 −0.145452 −0.0727260 0.997352i \(-0.523170\pi\)
−0.0727260 + 0.997352i \(0.523170\pi\)
\(228\) 34.0326 2.25386
\(229\) 8.12996 0.537243 0.268621 0.963246i \(-0.413432\pi\)
0.268621 + 0.963246i \(0.413432\pi\)
\(230\) −22.5123 −1.48442
\(231\) 38.0612 2.50424
\(232\) −4.61644 −0.303084
\(233\) −19.6215 −1.28545 −0.642725 0.766097i \(-0.722196\pi\)
−0.642725 + 0.766097i \(0.722196\pi\)
\(234\) −3.18636 −0.208299
\(235\) 5.61156 0.366058
\(236\) −1.39926 −0.0910843
\(237\) 16.9471 1.10083
\(238\) 10.0832 0.653598
\(239\) 4.24206 0.274396 0.137198 0.990544i \(-0.456190\pi\)
0.137198 + 0.990544i \(0.456190\pi\)
\(240\) 31.1461 2.01047
\(241\) 20.0319 1.29037 0.645184 0.764028i \(-0.276781\pi\)
0.645184 + 0.764028i \(0.276781\pi\)
\(242\) −9.39738 −0.604087
\(243\) −7.54594 −0.484072
\(244\) 5.13021 0.328428
\(245\) 4.34391 0.277522
\(246\) −23.6792 −1.50973
\(247\) 0.499012 0.0317514
\(248\) 65.2725 4.14481
\(249\) 18.5851 1.17778
\(250\) 22.5435 1.42578
\(251\) −11.7713 −0.742996 −0.371498 0.928434i \(-0.621156\pi\)
−0.371498 + 0.928434i \(0.621156\pi\)
\(252\) 95.6790 6.02721
\(253\) 34.7921 2.18736
\(254\) 56.8934 3.56981
\(255\) −3.01181 −0.188607
\(256\) −0.340740 −0.0212962
\(257\) 5.52632 0.344723 0.172361 0.985034i \(-0.444860\pi\)
0.172361 + 0.985034i \(0.444860\pi\)
\(258\) −61.3733 −3.82094
\(259\) −14.9258 −0.927443
\(260\) 1.01822 0.0631475
\(261\) 3.14163 0.194462
\(262\) 0.680502 0.0420416
\(263\) 16.1830 0.997889 0.498944 0.866634i \(-0.333721\pi\)
0.498944 + 0.866634i \(0.333721\pi\)
\(264\) −90.5550 −5.57327
\(265\) −8.05866 −0.495039
\(266\) −20.9068 −1.28188
\(267\) 35.0014 2.14205
\(268\) −25.8979 −1.58197
\(269\) 9.33375 0.569089 0.284544 0.958663i \(-0.408158\pi\)
0.284544 + 0.958663i \(0.408158\pi\)
\(270\) −18.2552 −1.11098
\(271\) 4.16548 0.253035 0.126517 0.991964i \(-0.459620\pi\)
0.126517 + 0.991964i \(0.459620\pi\)
\(272\) −12.7521 −0.773210
\(273\) 2.16356 0.130945
\(274\) −54.3020 −3.28050
\(275\) −15.7767 −0.951372
\(276\) 134.881 8.11891
\(277\) −12.7210 −0.764333 −0.382166 0.924093i \(-0.624822\pi\)
−0.382166 + 0.924093i \(0.624822\pi\)
\(278\) −27.6333 −1.65733
\(279\) −44.4199 −2.65935
\(280\) −25.7982 −1.54174
\(281\) −0.499785 −0.0298147 −0.0149073 0.999889i \(-0.504745\pi\)
−0.0149073 + 0.999889i \(0.504745\pi\)
\(282\) −46.9104 −2.79348
\(283\) 25.9117 1.54029 0.770147 0.637867i \(-0.220183\pi\)
0.770147 + 0.637867i \(0.220183\pi\)
\(284\) −5.96450 −0.353928
\(285\) 6.24476 0.369907
\(286\) −2.19562 −0.129830
\(287\) 10.4257 0.615408
\(288\) −78.8555 −4.64660
\(289\) −15.7669 −0.927463
\(290\) −1.40074 −0.0822541
\(291\) −32.8759 −1.92722
\(292\) −14.8047 −0.866377
\(293\) 23.8129 1.39117 0.695583 0.718445i \(-0.255146\pi\)
0.695583 + 0.718445i \(0.255146\pi\)
\(294\) −36.3133 −2.11784
\(295\) −0.256756 −0.0149489
\(296\) 35.5114 2.06406
\(297\) 28.2129 1.63708
\(298\) 8.24816 0.477803
\(299\) 1.97774 0.114375
\(300\) −61.1630 −3.53124
\(301\) 27.0220 1.55752
\(302\) 22.4471 1.29169
\(303\) −5.42038 −0.311393
\(304\) 26.4405 1.51646
\(305\) 0.941360 0.0539021
\(306\) 16.3259 0.933289
\(307\) −26.6855 −1.52302 −0.761510 0.648154i \(-0.775542\pi\)
−0.761510 + 0.648154i \(0.775542\pi\)
\(308\) 65.9293 3.75667
\(309\) −13.8831 −0.789783
\(310\) 19.8052 1.12486
\(311\) −28.2797 −1.60360 −0.801799 0.597594i \(-0.796123\pi\)
−0.801799 + 0.597594i \(0.796123\pi\)
\(312\) −5.14754 −0.291422
\(313\) −0.894123 −0.0505388 −0.0252694 0.999681i \(-0.508044\pi\)
−0.0252694 + 0.999681i \(0.508044\pi\)
\(314\) 21.3336 1.20393
\(315\) 17.5564 0.989194
\(316\) 29.3556 1.65138
\(317\) 31.5491 1.77197 0.885986 0.463713i \(-0.153483\pi\)
0.885986 + 0.463713i \(0.153483\pi\)
\(318\) 67.3672 3.77777
\(319\) 2.16480 0.121205
\(320\) 13.8342 0.773356
\(321\) −26.1383 −1.45890
\(322\) −82.8597 −4.61759
\(323\) −2.55678 −0.142263
\(324\) 25.3820 1.41011
\(325\) −0.896818 −0.0497465
\(326\) −26.6829 −1.47783
\(327\) −24.9623 −1.38042
\(328\) −24.8047 −1.36961
\(329\) 20.6541 1.13870
\(330\) −27.4765 −1.51253
\(331\) −10.8083 −0.594076 −0.297038 0.954866i \(-0.595999\pi\)
−0.297038 + 0.954866i \(0.595999\pi\)
\(332\) 32.1930 1.76682
\(333\) −24.1666 −1.32432
\(334\) −11.6826 −0.639244
\(335\) −4.75209 −0.259635
\(336\) 114.638 6.25400
\(337\) −23.0281 −1.25442 −0.627212 0.778849i \(-0.715804\pi\)
−0.627212 + 0.778849i \(0.715804\pi\)
\(338\) 34.4171 1.87204
\(339\) 11.8082 0.641333
\(340\) −5.21704 −0.282934
\(341\) −30.6083 −1.65753
\(342\) −33.8504 −1.83042
\(343\) −7.93336 −0.428361
\(344\) −64.2905 −3.46631
\(345\) 24.7498 1.33249
\(346\) 23.4329 1.25976
\(347\) 3.71783 0.199584 0.0997918 0.995008i \(-0.468182\pi\)
0.0997918 + 0.995008i \(0.468182\pi\)
\(348\) 8.39244 0.449882
\(349\) −10.8487 −0.580716 −0.290358 0.956918i \(-0.593774\pi\)
−0.290358 + 0.956918i \(0.593774\pi\)
\(350\) 37.5733 2.00838
\(351\) 1.60374 0.0856014
\(352\) −54.3368 −2.89616
\(353\) 13.7699 0.732900 0.366450 0.930438i \(-0.380573\pi\)
0.366450 + 0.930438i \(0.380573\pi\)
\(354\) 2.14638 0.114079
\(355\) −1.09445 −0.0580872
\(356\) 60.6292 3.21334
\(357\) −11.0854 −0.586702
\(358\) 38.4770 2.03357
\(359\) −18.2381 −0.962568 −0.481284 0.876565i \(-0.659829\pi\)
−0.481284 + 0.876565i \(0.659829\pi\)
\(360\) −41.7702 −2.20148
\(361\) −13.6987 −0.720986
\(362\) −38.7189 −2.03502
\(363\) 10.3314 0.542257
\(364\) 3.74771 0.196433
\(365\) −2.71655 −0.142191
\(366\) −7.86940 −0.411340
\(367\) −23.7312 −1.23876 −0.619379 0.785092i \(-0.712616\pi\)
−0.619379 + 0.785092i \(0.712616\pi\)
\(368\) 104.791 5.46263
\(369\) 16.8804 0.878757
\(370\) 10.7750 0.560165
\(371\) −29.6610 −1.53992
\(372\) −118.662 −6.15233
\(373\) 23.7322 1.22880 0.614402 0.788993i \(-0.289397\pi\)
0.614402 + 0.788993i \(0.289397\pi\)
\(374\) 11.2496 0.581705
\(375\) −24.7841 −1.27985
\(376\) −49.1402 −2.53421
\(377\) 0.123056 0.00633773
\(378\) −67.1908 −3.45592
\(379\) −29.5080 −1.51573 −0.757863 0.652414i \(-0.773756\pi\)
−0.757863 + 0.652414i \(0.773756\pi\)
\(380\) 10.8171 0.554907
\(381\) −62.5481 −3.20443
\(382\) −29.0664 −1.48716
\(383\) −24.2379 −1.23850 −0.619250 0.785194i \(-0.712563\pi\)
−0.619250 + 0.785194i \(0.712563\pi\)
\(384\) −32.3870 −1.65274
\(385\) 12.0976 0.616550
\(386\) −48.3172 −2.45928
\(387\) 43.7516 2.22402
\(388\) −56.9474 −2.89107
\(389\) −30.8281 −1.56305 −0.781523 0.623877i \(-0.785557\pi\)
−0.781523 + 0.623877i \(0.785557\pi\)
\(390\) −1.56188 −0.0790891
\(391\) −10.1333 −0.512462
\(392\) −38.0394 −1.92128
\(393\) −0.748138 −0.0377385
\(394\) 26.6457 1.34239
\(395\) 5.38655 0.271027
\(396\) 106.747 5.36424
\(397\) −20.1646 −1.01203 −0.506015 0.862524i \(-0.668882\pi\)
−0.506015 + 0.862524i \(0.668882\pi\)
\(398\) 22.3839 1.12200
\(399\) 22.9847 1.15067
\(400\) −47.5184 −2.37592
\(401\) 1.54569 0.0771879 0.0385939 0.999255i \(-0.487712\pi\)
0.0385939 + 0.999255i \(0.487712\pi\)
\(402\) 39.7256 1.98133
\(403\) −1.73991 −0.0866711
\(404\) −9.38915 −0.467128
\(405\) 4.65743 0.231430
\(406\) −5.15561 −0.255868
\(407\) −16.6524 −0.825429
\(408\) 26.3743 1.30572
\(409\) −36.7548 −1.81741 −0.908704 0.417442i \(-0.862927\pi\)
−0.908704 + 0.417442i \(0.862927\pi\)
\(410\) −7.52634 −0.371699
\(411\) 59.6991 2.94474
\(412\) −24.0482 −1.18477
\(413\) −0.945024 −0.0465016
\(414\) −134.159 −6.59357
\(415\) 5.90720 0.289973
\(416\) −3.08874 −0.151438
\(417\) 30.3798 1.48770
\(418\) −23.3252 −1.14087
\(419\) 17.1981 0.840182 0.420091 0.907482i \(-0.361998\pi\)
0.420091 + 0.907482i \(0.361998\pi\)
\(420\) 46.8997 2.28847
\(421\) 10.6017 0.516693 0.258347 0.966052i \(-0.416822\pi\)
0.258347 + 0.966052i \(0.416822\pi\)
\(422\) −25.4645 −1.23959
\(423\) 33.4414 1.62598
\(424\) 70.5693 3.42715
\(425\) 4.59501 0.222891
\(426\) 9.14914 0.443277
\(427\) 3.46480 0.167674
\(428\) −45.2766 −2.18853
\(429\) 2.41384 0.116541
\(430\) −19.5073 −0.940723
\(431\) −11.2876 −0.543704 −0.271852 0.962339i \(-0.587636\pi\)
−0.271852 + 0.962339i \(0.587636\pi\)
\(432\) 84.9752 4.08837
\(433\) −6.71586 −0.322743 −0.161372 0.986894i \(-0.551592\pi\)
−0.161372 + 0.986894i \(0.551592\pi\)
\(434\) 72.8958 3.49911
\(435\) 1.53996 0.0738353
\(436\) −43.2396 −2.07080
\(437\) 21.0105 1.00507
\(438\) 22.7093 1.08509
\(439\) 41.2325 1.96792 0.983959 0.178392i \(-0.0570895\pi\)
0.983959 + 0.178392i \(0.0570895\pi\)
\(440\) −28.7825 −1.37215
\(441\) 25.8870 1.23271
\(442\) 0.639479 0.0304169
\(443\) −32.3888 −1.53884 −0.769418 0.638745i \(-0.779454\pi\)
−0.769418 + 0.638745i \(0.779454\pi\)
\(444\) −64.5577 −3.06378
\(445\) 11.1250 0.527378
\(446\) −16.4525 −0.779048
\(447\) −9.06795 −0.428899
\(448\) 50.9187 2.40568
\(449\) −36.6881 −1.73142 −0.865710 0.500546i \(-0.833133\pi\)
−0.865710 + 0.500546i \(0.833133\pi\)
\(450\) 60.8355 2.86781
\(451\) 11.6317 0.547716
\(452\) 20.4541 0.962078
\(453\) −24.6781 −1.15948
\(454\) 5.82284 0.273279
\(455\) 0.687679 0.0322389
\(456\) −54.6851 −2.56086
\(457\) −35.2168 −1.64737 −0.823686 0.567047i \(-0.808086\pi\)
−0.823686 + 0.567047i \(0.808086\pi\)
\(458\) −21.6018 −1.00939
\(459\) −8.21706 −0.383539
\(460\) 42.8715 1.99889
\(461\) 16.5160 0.769228 0.384614 0.923077i \(-0.374335\pi\)
0.384614 + 0.923077i \(0.374335\pi\)
\(462\) −101.131 −4.70504
\(463\) 34.2064 1.58971 0.794853 0.606802i \(-0.207548\pi\)
0.794853 + 0.606802i \(0.207548\pi\)
\(464\) 6.52022 0.302693
\(465\) −21.7736 −1.00973
\(466\) 52.1357 2.41514
\(467\) −3.25276 −0.150520 −0.0752599 0.997164i \(-0.523979\pi\)
−0.0752599 + 0.997164i \(0.523979\pi\)
\(468\) 6.06797 0.280492
\(469\) −17.4907 −0.807647
\(470\) −14.9103 −0.687760
\(471\) −23.4540 −1.08070
\(472\) 2.24840 0.103491
\(473\) 30.1479 1.38620
\(474\) −45.0295 −2.06827
\(475\) −9.52738 −0.437146
\(476\) −19.2021 −0.880125
\(477\) −48.0246 −2.19889
\(478\) −11.2714 −0.515544
\(479\) −0.133163 −0.00608438 −0.00304219 0.999995i \(-0.500968\pi\)
−0.00304219 + 0.999995i \(0.500968\pi\)
\(480\) −38.6532 −1.76427
\(481\) −0.946595 −0.0431610
\(482\) −53.2261 −2.42438
\(483\) 91.0952 4.14498
\(484\) 17.8960 0.813453
\(485\) −10.4495 −0.474486
\(486\) 20.0501 0.909490
\(487\) −38.4819 −1.74378 −0.871892 0.489699i \(-0.837107\pi\)
−0.871892 + 0.489699i \(0.837107\pi\)
\(488\) −8.24345 −0.373163
\(489\) 29.3349 1.32657
\(490\) −11.5420 −0.521416
\(491\) −8.38529 −0.378423 −0.189211 0.981936i \(-0.560593\pi\)
−0.189211 + 0.981936i \(0.560593\pi\)
\(492\) 45.0936 2.03298
\(493\) −0.630501 −0.0283964
\(494\) −1.32591 −0.0596554
\(495\) 19.5874 0.880387
\(496\) −92.1902 −4.13946
\(497\) −4.02826 −0.180692
\(498\) −49.3819 −2.21286
\(499\) −33.4695 −1.49830 −0.749151 0.662399i \(-0.769538\pi\)
−0.749151 + 0.662399i \(0.769538\pi\)
\(500\) −42.9309 −1.91993
\(501\) 12.8437 0.573816
\(502\) 31.2770 1.39596
\(503\) 30.3689 1.35408 0.677042 0.735944i \(-0.263262\pi\)
0.677042 + 0.735944i \(0.263262\pi\)
\(504\) −153.741 −6.84817
\(505\) −1.72285 −0.0766657
\(506\) −92.4449 −4.10968
\(507\) −37.8378 −1.68044
\(508\) −108.345 −4.80705
\(509\) −19.0336 −0.843651 −0.421826 0.906677i \(-0.638611\pi\)
−0.421826 + 0.906677i \(0.638611\pi\)
\(510\) 8.00259 0.354361
\(511\) −9.99865 −0.442314
\(512\) 23.0795 1.01998
\(513\) 17.0374 0.752220
\(514\) −14.6838 −0.647675
\(515\) −4.41269 −0.194446
\(516\) 116.877 5.14521
\(517\) 23.0434 1.01345
\(518\) 39.6588 1.74251
\(519\) −25.7619 −1.13082
\(520\) −1.63612 −0.0717488
\(521\) 12.6476 0.554100 0.277050 0.960855i \(-0.410643\pi\)
0.277050 + 0.960855i \(0.410643\pi\)
\(522\) −8.34751 −0.365361
\(523\) 35.7242 1.56211 0.781054 0.624463i \(-0.214682\pi\)
0.781054 + 0.624463i \(0.214682\pi\)
\(524\) −1.29592 −0.0566125
\(525\) −41.3078 −1.80282
\(526\) −42.9994 −1.87486
\(527\) 8.91474 0.388332
\(528\) 127.899 5.56609
\(529\) 60.2711 2.62048
\(530\) 21.4124 0.930095
\(531\) −1.53010 −0.0664008
\(532\) 39.8139 1.72615
\(533\) 0.661198 0.0286396
\(534\) −93.0010 −4.02455
\(535\) −8.30796 −0.359184
\(536\) 41.6139 1.79745
\(537\) −42.3012 −1.82543
\(538\) −24.8004 −1.06922
\(539\) 17.8379 0.768332
\(540\) 34.7644 1.49602
\(541\) 29.9478 1.28756 0.643779 0.765212i \(-0.277366\pi\)
0.643779 + 0.765212i \(0.277366\pi\)
\(542\) −11.0680 −0.475410
\(543\) 42.5671 1.82673
\(544\) 15.8257 0.678521
\(545\) −7.93418 −0.339863
\(546\) −5.74873 −0.246023
\(547\) −8.30101 −0.354925 −0.177463 0.984128i \(-0.556789\pi\)
−0.177463 + 0.984128i \(0.556789\pi\)
\(548\) 103.410 4.41747
\(549\) 5.60991 0.239425
\(550\) 41.9198 1.78747
\(551\) 1.30729 0.0556926
\(552\) −216.733 −9.22478
\(553\) 19.8260 0.843085
\(554\) 33.8006 1.43605
\(555\) −11.8459 −0.502831
\(556\) 52.6236 2.23174
\(557\) 24.9047 1.05525 0.527623 0.849479i \(-0.323083\pi\)
0.527623 + 0.849479i \(0.323083\pi\)
\(558\) 118.027 4.99646
\(559\) 1.71374 0.0724833
\(560\) 36.4371 1.53975
\(561\) −12.3678 −0.522167
\(562\) 1.32796 0.0560167
\(563\) 21.1368 0.890810 0.445405 0.895329i \(-0.353060\pi\)
0.445405 + 0.895329i \(0.353060\pi\)
\(564\) 89.3342 3.76165
\(565\) 3.75318 0.157898
\(566\) −68.8492 −2.89395
\(567\) 17.1423 0.719910
\(568\) 9.58402 0.402137
\(569\) 14.3064 0.599757 0.299879 0.953977i \(-0.403054\pi\)
0.299879 + 0.953977i \(0.403054\pi\)
\(570\) −16.5927 −0.694993
\(571\) −6.16416 −0.257962 −0.128981 0.991647i \(-0.541171\pi\)
−0.128981 + 0.991647i \(0.541171\pi\)
\(572\) 4.18124 0.174827
\(573\) 31.9553 1.33495
\(574\) −27.7017 −1.15625
\(575\) −37.7599 −1.57469
\(576\) 82.4432 3.43514
\(577\) −1.97725 −0.0823139 −0.0411570 0.999153i \(-0.513104\pi\)
−0.0411570 + 0.999153i \(0.513104\pi\)
\(578\) 41.8936 1.74255
\(579\) 53.1194 2.20757
\(580\) 2.66750 0.110762
\(581\) 21.7423 0.902022
\(582\) 87.3534 3.62092
\(583\) −33.0922 −1.37054
\(584\) 23.7888 0.984386
\(585\) 1.11343 0.0460347
\(586\) −63.2726 −2.61377
\(587\) 8.38286 0.345998 0.172999 0.984922i \(-0.444654\pi\)
0.172999 + 0.984922i \(0.444654\pi\)
\(588\) 69.1536 2.85184
\(589\) −18.4840 −0.761620
\(590\) 0.682217 0.0280864
\(591\) −29.2940 −1.20499
\(592\) −50.1559 −2.06140
\(593\) −23.2981 −0.956738 −0.478369 0.878159i \(-0.658772\pi\)
−0.478369 + 0.878159i \(0.658772\pi\)
\(594\) −74.9634 −3.07579
\(595\) −3.52345 −0.144447
\(596\) −15.7074 −0.643402
\(597\) −24.6086 −1.00716
\(598\) −5.25497 −0.214892
\(599\) 10.9090 0.445728 0.222864 0.974850i \(-0.428459\pi\)
0.222864 + 0.974850i \(0.428459\pi\)
\(600\) 98.2793 4.01223
\(601\) 39.1730 1.59790 0.798950 0.601398i \(-0.205389\pi\)
0.798950 + 0.601398i \(0.205389\pi\)
\(602\) −71.7992 −2.92631
\(603\) −28.3195 −1.15326
\(604\) −42.7473 −1.73936
\(605\) 3.28379 0.133505
\(606\) 14.4023 0.585054
\(607\) −17.4809 −0.709527 −0.354763 0.934956i \(-0.615439\pi\)
−0.354763 + 0.934956i \(0.615439\pi\)
\(608\) −32.8133 −1.33076
\(609\) 5.66802 0.229680
\(610\) −2.50126 −0.101273
\(611\) 1.30989 0.0529923
\(612\) −31.0903 −1.25675
\(613\) 13.5173 0.545957 0.272978 0.962020i \(-0.411991\pi\)
0.272978 + 0.962020i \(0.411991\pi\)
\(614\) 70.9050 2.86149
\(615\) 8.27438 0.333655
\(616\) −105.938 −4.26837
\(617\) 42.1812 1.69815 0.849075 0.528273i \(-0.177160\pi\)
0.849075 + 0.528273i \(0.177160\pi\)
\(618\) 36.8884 1.48387
\(619\) 24.1302 0.969874 0.484937 0.874549i \(-0.338843\pi\)
0.484937 + 0.874549i \(0.338843\pi\)
\(620\) −37.7162 −1.51472
\(621\) 67.5244 2.70966
\(622\) 75.1412 3.01289
\(623\) 40.9473 1.64052
\(624\) 7.27033 0.291046
\(625\) 12.8121 0.512485
\(626\) 2.37574 0.0949538
\(627\) 25.6436 1.02410
\(628\) −40.6269 −1.62119
\(629\) 4.85005 0.193384
\(630\) −46.6486 −1.85853
\(631\) −24.5942 −0.979080 −0.489540 0.871981i \(-0.662835\pi\)
−0.489540 + 0.871981i \(0.662835\pi\)
\(632\) −47.1698 −1.87632
\(633\) 27.9955 1.11272
\(634\) −83.8279 −3.32923
\(635\) −19.8806 −0.788939
\(636\) −128.291 −5.08708
\(637\) 1.01398 0.0401754
\(638\) −5.75200 −0.227724
\(639\) −6.52222 −0.258015
\(640\) −10.2941 −0.406909
\(641\) −29.7856 −1.17646 −0.588231 0.808693i \(-0.700175\pi\)
−0.588231 + 0.808693i \(0.700175\pi\)
\(642\) 69.4513 2.74102
\(643\) −0.763355 −0.0301038 −0.0150519 0.999887i \(-0.504791\pi\)
−0.0150519 + 0.999887i \(0.504791\pi\)
\(644\) 157.795 6.21797
\(645\) 21.4461 0.844439
\(646\) 6.79353 0.267288
\(647\) 9.33095 0.366838 0.183419 0.983035i \(-0.441284\pi\)
0.183419 + 0.983035i \(0.441284\pi\)
\(648\) −40.7850 −1.60218
\(649\) −1.05434 −0.0413866
\(650\) 2.38291 0.0934652
\(651\) −80.1409 −3.14097
\(652\) 50.8137 1.99002
\(653\) −6.28140 −0.245810 −0.122905 0.992418i \(-0.539221\pi\)
−0.122905 + 0.992418i \(0.539221\pi\)
\(654\) 66.3266 2.59358
\(655\) −0.237792 −0.00929132
\(656\) 35.0339 1.36785
\(657\) −16.1890 −0.631592
\(658\) −54.8794 −2.13942
\(659\) −29.7976 −1.16075 −0.580375 0.814349i \(-0.697094\pi\)
−0.580375 + 0.814349i \(0.697094\pi\)
\(660\) 52.3251 2.03675
\(661\) −2.41915 −0.0940942 −0.0470471 0.998893i \(-0.514981\pi\)
−0.0470471 + 0.998893i \(0.514981\pi\)
\(662\) 28.7183 1.11617
\(663\) −0.703037 −0.0273037
\(664\) −51.7291 −2.00748
\(665\) 7.30559 0.283299
\(666\) 64.2122 2.48817
\(667\) 5.18120 0.200617
\(668\) 22.2478 0.860795
\(669\) 18.0877 0.699311
\(670\) 12.6266 0.487809
\(671\) 3.86561 0.149230
\(672\) −142.268 −5.48813
\(673\) 33.6552 1.29731 0.648656 0.761081i \(-0.275331\pi\)
0.648656 + 0.761081i \(0.275331\pi\)
\(674\) 61.1873 2.35685
\(675\) −30.6194 −1.17854
\(676\) −65.5424 −2.52086
\(677\) 23.5998 0.907015 0.453508 0.891252i \(-0.350172\pi\)
0.453508 + 0.891252i \(0.350172\pi\)
\(678\) −31.3751 −1.20495
\(679\) −38.4607 −1.47599
\(680\) 8.38297 0.321472
\(681\) −6.40158 −0.245309
\(682\) 81.3283 3.11422
\(683\) −13.1054 −0.501465 −0.250733 0.968056i \(-0.580671\pi\)
−0.250733 + 0.968056i \(0.580671\pi\)
\(684\) 64.4633 2.46482
\(685\) 18.9751 0.725001
\(686\) 21.0795 0.804818
\(687\) 23.7489 0.906075
\(688\) 90.8033 3.46184
\(689\) −1.88110 −0.0716644
\(690\) −65.7620 −2.50352
\(691\) −0.156446 −0.00595149 −0.00297575 0.999996i \(-0.500947\pi\)
−0.00297575 + 0.999996i \(0.500947\pi\)
\(692\) −44.6246 −1.69637
\(693\) 72.0940 2.73863
\(694\) −9.87852 −0.374984
\(695\) 9.65609 0.366276
\(696\) −13.4853 −0.511160
\(697\) −3.38776 −0.128321
\(698\) 28.8257 1.09107
\(699\) −57.3175 −2.16795
\(700\) −71.5530 −2.70445
\(701\) 18.4837 0.698121 0.349060 0.937100i \(-0.386501\pi\)
0.349060 + 0.937100i \(0.386501\pi\)
\(702\) −4.26125 −0.160830
\(703\) −10.0562 −0.379276
\(704\) 56.8090 2.14107
\(705\) 16.3922 0.617367
\(706\) −36.5877 −1.37700
\(707\) −6.34118 −0.238484
\(708\) −4.08747 −0.153616
\(709\) 47.1285 1.76995 0.884973 0.465642i \(-0.154177\pi\)
0.884973 + 0.465642i \(0.154177\pi\)
\(710\) 2.90802 0.109136
\(711\) 32.1005 1.20386
\(712\) −97.4216 −3.65103
\(713\) −73.2576 −2.74352
\(714\) 29.4546 1.10231
\(715\) 0.767230 0.0286928
\(716\) −73.2738 −2.73837
\(717\) 12.3917 0.462777
\(718\) 48.4598 1.80850
\(719\) −17.6068 −0.656622 −0.328311 0.944570i \(-0.606479\pi\)
−0.328311 + 0.944570i \(0.606479\pi\)
\(720\) 58.9958 2.19865
\(721\) −16.2415 −0.604866
\(722\) 36.3984 1.35461
\(723\) 58.5162 2.17624
\(724\) 73.7345 2.74032
\(725\) −2.34945 −0.0872564
\(726\) −27.4512 −1.01881
\(727\) 35.6057 1.32054 0.660272 0.751027i \(-0.270441\pi\)
0.660272 + 0.751027i \(0.270441\pi\)
\(728\) −6.02198 −0.223189
\(729\) −37.0915 −1.37376
\(730\) 7.21807 0.267153
\(731\) −8.78063 −0.324763
\(732\) 14.9861 0.553904
\(733\) −31.8583 −1.17671 −0.588356 0.808602i \(-0.700225\pi\)
−0.588356 + 0.808602i \(0.700225\pi\)
\(734\) 63.0554 2.32742
\(735\) 12.6892 0.468049
\(736\) −130.049 −4.79367
\(737\) −19.5141 −0.718810
\(738\) −44.8522 −1.65103
\(739\) −5.59398 −0.205778 −0.102889 0.994693i \(-0.532809\pi\)
−0.102889 + 0.994693i \(0.532809\pi\)
\(740\) −20.5194 −0.754309
\(741\) 1.45769 0.0535496
\(742\) 78.8113 2.89325
\(743\) 40.5598 1.48799 0.743997 0.668183i \(-0.232928\pi\)
0.743997 + 0.668183i \(0.232928\pi\)
\(744\) 190.671 6.99033
\(745\) −2.88221 −0.105596
\(746\) −63.0579 −2.30871
\(747\) 35.2032 1.28802
\(748\) −21.4233 −0.783315
\(749\) −30.5786 −1.11732
\(750\) 65.8530 2.40461
\(751\) −5.47987 −0.199963 −0.0999816 0.994989i \(-0.531878\pi\)
−0.0999816 + 0.994989i \(0.531878\pi\)
\(752\) 69.4051 2.53094
\(753\) −34.3857 −1.25308
\(754\) −0.326969 −0.0119075
\(755\) −7.84385 −0.285467
\(756\) 127.955 4.65369
\(757\) 20.8712 0.758577 0.379289 0.925278i \(-0.376169\pi\)
0.379289 + 0.925278i \(0.376169\pi\)
\(758\) 78.4048 2.84779
\(759\) 101.633 3.68905
\(760\) −17.3814 −0.630490
\(761\) 44.8125 1.62445 0.812225 0.583344i \(-0.198256\pi\)
0.812225 + 0.583344i \(0.198256\pi\)
\(762\) 166.194 6.02059
\(763\) −29.2028 −1.05721
\(764\) 55.3527 2.00259
\(765\) −5.70487 −0.206260
\(766\) 64.4018 2.32693
\(767\) −0.0599335 −0.00216407
\(768\) −0.995353 −0.0359167
\(769\) 32.3485 1.16652 0.583258 0.812287i \(-0.301778\pi\)
0.583258 + 0.812287i \(0.301778\pi\)
\(770\) −32.1441 −1.15839
\(771\) 16.1432 0.581385
\(772\) 92.0131 3.31163
\(773\) −45.6741 −1.64278 −0.821391 0.570365i \(-0.806802\pi\)
−0.821391 + 0.570365i \(0.806802\pi\)
\(774\) −116.251 −4.17856
\(775\) 33.2192 1.19327
\(776\) 91.5055 3.28486
\(777\) −43.6005 −1.56416
\(778\) 81.9122 2.93670
\(779\) 7.02426 0.251670
\(780\) 2.97438 0.106500
\(781\) −4.49425 −0.160817
\(782\) 26.9248 0.962829
\(783\) 4.20142 0.150147
\(784\) 53.7265 1.91880
\(785\) −7.45476 −0.266072
\(786\) 1.98785 0.0709043
\(787\) −8.86566 −0.316027 −0.158013 0.987437i \(-0.550509\pi\)
−0.158013 + 0.987437i \(0.550509\pi\)
\(788\) −50.7428 −1.80764
\(789\) 47.2731 1.68297
\(790\) −14.3124 −0.509214
\(791\) 13.8141 0.491173
\(792\) −171.526 −6.09490
\(793\) 0.219738 0.00780313
\(794\) 53.5786 1.90143
\(795\) −23.5406 −0.834898
\(796\) −42.6269 −1.51087
\(797\) −45.0509 −1.59579 −0.797893 0.602800i \(-0.794052\pi\)
−0.797893 + 0.602800i \(0.794052\pi\)
\(798\) −61.0718 −2.16192
\(799\) −6.71143 −0.237433
\(800\) 58.9717 2.08496
\(801\) 66.2983 2.34254
\(802\) −4.10699 −0.145023
\(803\) −11.1553 −0.393662
\(804\) −75.6518 −2.66803
\(805\) 28.9542 1.02050
\(806\) 4.62306 0.162840
\(807\) 27.2653 0.959785
\(808\) 15.0869 0.530755
\(809\) −23.2365 −0.816952 −0.408476 0.912769i \(-0.633940\pi\)
−0.408476 + 0.912769i \(0.633940\pi\)
\(810\) −12.3751 −0.434817
\(811\) 26.9919 0.947814 0.473907 0.880575i \(-0.342843\pi\)
0.473907 + 0.880575i \(0.342843\pi\)
\(812\) 9.81811 0.344548
\(813\) 12.1680 0.426751
\(814\) 44.2465 1.55084
\(815\) 9.32398 0.326605
\(816\) −37.2508 −1.30404
\(817\) 18.2059 0.636945
\(818\) 97.6599 3.41460
\(819\) 4.09814 0.143201
\(820\) 14.3328 0.500524
\(821\) 9.63379 0.336222 0.168111 0.985768i \(-0.446233\pi\)
0.168111 + 0.985768i \(0.446233\pi\)
\(822\) −158.624 −5.53266
\(823\) −19.4544 −0.678138 −0.339069 0.940762i \(-0.610112\pi\)
−0.339069 + 0.940762i \(0.610112\pi\)
\(824\) 38.6417 1.34615
\(825\) −46.0862 −1.60452
\(826\) 2.51099 0.0873686
\(827\) 3.46264 0.120408 0.0602040 0.998186i \(-0.480825\pi\)
0.0602040 + 0.998186i \(0.480825\pi\)
\(828\) 255.487 8.87880
\(829\) 10.9182 0.379203 0.189602 0.981861i \(-0.439280\pi\)
0.189602 + 0.981861i \(0.439280\pi\)
\(830\) −15.6958 −0.544810
\(831\) −37.1601 −1.28907
\(832\) 3.22927 0.111955
\(833\) −5.19532 −0.180007
\(834\) −80.7211 −2.79514
\(835\) 4.08233 0.141275
\(836\) 44.4196 1.53628
\(837\) −59.4045 −2.05332
\(838\) −45.6965 −1.57856
\(839\) 31.3279 1.08156 0.540780 0.841164i \(-0.318129\pi\)
0.540780 + 0.841164i \(0.318129\pi\)
\(840\) −75.3605 −2.60018
\(841\) −28.6776 −0.988883
\(842\) −28.1693 −0.970779
\(843\) −1.45995 −0.0502833
\(844\) 48.4935 1.66922
\(845\) −12.0266 −0.413727
\(846\) −88.8560 −3.05493
\(847\) 12.0864 0.415295
\(848\) −99.6714 −3.42273
\(849\) 75.6922 2.59775
\(850\) −12.2092 −0.418773
\(851\) −39.8557 −1.36624
\(852\) −17.4232 −0.596910
\(853\) 21.5084 0.736433 0.368217 0.929740i \(-0.379968\pi\)
0.368217 + 0.929740i \(0.379968\pi\)
\(854\) −9.20622 −0.315030
\(855\) 11.8286 0.404529
\(856\) 72.7524 2.48663
\(857\) 40.1034 1.36991 0.684954 0.728587i \(-0.259822\pi\)
0.684954 + 0.728587i \(0.259822\pi\)
\(858\) −6.41374 −0.218962
\(859\) −5.10522 −0.174188 −0.0870939 0.996200i \(-0.527758\pi\)
−0.0870939 + 0.996200i \(0.527758\pi\)
\(860\) 37.1488 1.26676
\(861\) 30.4550 1.03790
\(862\) 29.9919 1.02153
\(863\) −36.0059 −1.22566 −0.612828 0.790216i \(-0.709968\pi\)
−0.612828 + 0.790216i \(0.709968\pi\)
\(864\) −105.457 −3.58771
\(865\) −8.18831 −0.278411
\(866\) 17.8445 0.606380
\(867\) −46.0575 −1.56419
\(868\) −138.820 −4.71184
\(869\) 22.1194 0.750350
\(870\) −4.09177 −0.138724
\(871\) −1.10926 −0.0375860
\(872\) 69.4793 2.35286
\(873\) −62.2723 −2.10760
\(874\) −55.8264 −1.88836
\(875\) −28.9943 −0.980187
\(876\) −43.2467 −1.46117
\(877\) 3.43723 0.116067 0.0580335 0.998315i \(-0.481517\pi\)
0.0580335 + 0.998315i \(0.481517\pi\)
\(878\) −109.557 −3.69738
\(879\) 69.5613 2.34624
\(880\) 40.6521 1.37038
\(881\) 33.9638 1.14427 0.572136 0.820159i \(-0.306115\pi\)
0.572136 + 0.820159i \(0.306115\pi\)
\(882\) −68.7834 −2.31606
\(883\) 29.7487 1.00112 0.500562 0.865701i \(-0.333127\pi\)
0.500562 + 0.865701i \(0.333127\pi\)
\(884\) −1.21780 −0.0409589
\(885\) −0.750022 −0.0252117
\(886\) 86.0591 2.89121
\(887\) 44.7362 1.50209 0.751047 0.660249i \(-0.229549\pi\)
0.751047 + 0.660249i \(0.229549\pi\)
\(888\) 103.734 3.48109
\(889\) −73.1735 −2.45416
\(890\) −29.5600 −0.990853
\(891\) 19.1254 0.640723
\(892\) 31.3314 1.04905
\(893\) 13.9156 0.465668
\(894\) 24.0941 0.805829
\(895\) −13.4453 −0.449425
\(896\) −37.8888 −1.26578
\(897\) 5.77727 0.192897
\(898\) 97.4828 3.25304
\(899\) −4.55815 −0.152023
\(900\) −115.853 −3.86175
\(901\) 9.63817 0.321094
\(902\) −30.9062 −1.02907
\(903\) 78.9353 2.62680
\(904\) −32.8665 −1.09312
\(905\) 13.5298 0.449745
\(906\) 65.5715 2.17847
\(907\) 18.4734 0.613400 0.306700 0.951806i \(-0.400775\pi\)
0.306700 + 0.951806i \(0.400775\pi\)
\(908\) −11.0888 −0.367994
\(909\) −10.2671 −0.340538
\(910\) −1.82721 −0.0605714
\(911\) −44.2452 −1.46591 −0.732955 0.680277i \(-0.761859\pi\)
−0.732955 + 0.680277i \(0.761859\pi\)
\(912\) 77.2366 2.55756
\(913\) 24.2574 0.802804
\(914\) 93.5733 3.09513
\(915\) 2.74986 0.0909074
\(916\) 41.1376 1.35922
\(917\) −0.875228 −0.0289026
\(918\) 21.8333 0.720605
\(919\) 8.17401 0.269636 0.134818 0.990870i \(-0.456955\pi\)
0.134818 + 0.990870i \(0.456955\pi\)
\(920\) −68.8878 −2.27116
\(921\) −77.9523 −2.56862
\(922\) −43.8842 −1.44525
\(923\) −0.255473 −0.00840899
\(924\) 192.590 6.33573
\(925\) 18.0728 0.594231
\(926\) −90.8887 −2.98679
\(927\) −26.2969 −0.863702
\(928\) −8.09177 −0.265625
\(929\) −20.7450 −0.680621 −0.340310 0.940313i \(-0.610532\pi\)
−0.340310 + 0.940313i \(0.610532\pi\)
\(930\) 57.8540 1.89711
\(931\) 10.7721 0.353041
\(932\) −99.2851 −3.25219
\(933\) −82.6095 −2.70451
\(934\) 8.64281 0.282801
\(935\) −3.93104 −0.128559
\(936\) −9.75028 −0.318698
\(937\) 1.42837 0.0466629 0.0233315 0.999728i \(-0.492573\pi\)
0.0233315 + 0.999728i \(0.492573\pi\)
\(938\) 46.4740 1.51743
\(939\) −2.61187 −0.0852351
\(940\) 28.3945 0.926126
\(941\) 4.63184 0.150994 0.0754968 0.997146i \(-0.475946\pi\)
0.0754968 + 0.997146i \(0.475946\pi\)
\(942\) 62.3188 2.03046
\(943\) 27.8392 0.906570
\(944\) −3.17561 −0.103357
\(945\) 23.4789 0.763770
\(946\) −80.1049 −2.60443
\(947\) −9.36568 −0.304344 −0.152172 0.988354i \(-0.548627\pi\)
−0.152172 + 0.988354i \(0.548627\pi\)
\(948\) 85.7522 2.78510
\(949\) −0.634116 −0.0205843
\(950\) 25.3149 0.821323
\(951\) 92.1596 2.98848
\(952\) 30.8547 1.00001
\(953\) −21.1901 −0.686414 −0.343207 0.939260i \(-0.611513\pi\)
−0.343207 + 0.939260i \(0.611513\pi\)
\(954\) 127.604 4.13135
\(955\) 10.1569 0.328668
\(956\) 21.4648 0.694223
\(957\) 6.32370 0.204416
\(958\) 0.353823 0.0114315
\(959\) 69.8405 2.25527
\(960\) 40.4119 1.30429
\(961\) 33.4483 1.07898
\(962\) 2.51517 0.0810922
\(963\) −49.5102 −1.59544
\(964\) 101.361 3.26463
\(965\) 16.8838 0.543509
\(966\) −242.046 −7.78770
\(967\) 52.7597 1.69664 0.848319 0.529485i \(-0.177615\pi\)
0.848319 + 0.529485i \(0.177615\pi\)
\(968\) −28.7560 −0.924253
\(969\) −7.46874 −0.239931
\(970\) 27.7649 0.891478
\(971\) −6.43887 −0.206633 −0.103317 0.994649i \(-0.532945\pi\)
−0.103317 + 0.994649i \(0.532945\pi\)
\(972\) −38.1825 −1.22470
\(973\) 35.5406 1.13938
\(974\) 102.249 3.27627
\(975\) −2.61974 −0.0838989
\(976\) 11.6430 0.372682
\(977\) −2.35728 −0.0754161 −0.0377080 0.999289i \(-0.512006\pi\)
−0.0377080 + 0.999289i \(0.512006\pi\)
\(978\) −77.9448 −2.49240
\(979\) 45.6840 1.46007
\(980\) 21.9802 0.702131
\(981\) −47.2827 −1.50962
\(982\) 22.2803 0.710992
\(983\) 25.2175 0.804313 0.402156 0.915571i \(-0.368261\pi\)
0.402156 + 0.915571i \(0.368261\pi\)
\(984\) −72.4584 −2.30989
\(985\) −9.31097 −0.296672
\(986\) 1.67528 0.0533519
\(987\) 60.3338 1.92045
\(988\) 2.52500 0.0803310
\(989\) 72.1556 2.29441
\(990\) −52.0450 −1.65410
\(991\) −26.8966 −0.854399 −0.427200 0.904157i \(-0.640500\pi\)
−0.427200 + 0.904157i \(0.640500\pi\)
\(992\) 114.410 3.63254
\(993\) −31.5726 −1.00193
\(994\) 10.7034 0.339490
\(995\) −7.82174 −0.247966
\(996\) 94.0408 2.97980
\(997\) −8.01923 −0.253971 −0.126986 0.991905i \(-0.540530\pi\)
−0.126986 + 0.991905i \(0.540530\pi\)
\(998\) 88.9308 2.81506
\(999\) −32.3189 −1.02252
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 6037.2.a.b.1.4 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.4 259 1.1 even 1 trivial