Properties

Label 6037.2.a.b.1.8
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 1.8
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.60071 q^{2} -0.749599 q^{3} +4.76372 q^{4} -3.60076 q^{5} +1.94949 q^{6} -2.40322 q^{7} -7.18764 q^{8} -2.43810 q^{9} +O(q^{10})\) \(q-2.60071 q^{2} -0.749599 q^{3} +4.76372 q^{4} -3.60076 q^{5} +1.94949 q^{6} -2.40322 q^{7} -7.18764 q^{8} -2.43810 q^{9} +9.36455 q^{10} +2.22014 q^{11} -3.57088 q^{12} -2.00163 q^{13} +6.25010 q^{14} +2.69912 q^{15} +9.16557 q^{16} +4.82130 q^{17} +6.34081 q^{18} -2.15015 q^{19} -17.1530 q^{20} +1.80145 q^{21} -5.77395 q^{22} +1.89464 q^{23} +5.38785 q^{24} +7.96546 q^{25} +5.20568 q^{26} +4.07639 q^{27} -11.4483 q^{28} -2.11811 q^{29} -7.01965 q^{30} +0.688943 q^{31} -9.46175 q^{32} -1.66421 q^{33} -12.5388 q^{34} +8.65343 q^{35} -11.6144 q^{36} +4.93426 q^{37} +5.59193 q^{38} +1.50042 q^{39} +25.8810 q^{40} -1.43704 q^{41} -4.68507 q^{42} -9.03240 q^{43} +10.5761 q^{44} +8.77902 q^{45} -4.92742 q^{46} +7.66993 q^{47} -6.87050 q^{48} -1.22452 q^{49} -20.7159 q^{50} -3.61404 q^{51} -9.53522 q^{52} -1.61201 q^{53} -10.6015 q^{54} -7.99419 q^{55} +17.2735 q^{56} +1.61175 q^{57} +5.50859 q^{58} -6.77799 q^{59} +12.8579 q^{60} -9.48597 q^{61} -1.79174 q^{62} +5.85930 q^{63} +6.27617 q^{64} +7.20740 q^{65} +4.32814 q^{66} +3.30456 q^{67} +22.9673 q^{68} -1.42022 q^{69} -22.5051 q^{70} +4.23793 q^{71} +17.5242 q^{72} +4.90703 q^{73} -12.8326 q^{74} -5.97090 q^{75} -10.2427 q^{76} -5.33549 q^{77} -3.90217 q^{78} -13.0263 q^{79} -33.0030 q^{80} +4.25865 q^{81} +3.73732 q^{82} -14.0724 q^{83} +8.58161 q^{84} -17.3603 q^{85} +23.4907 q^{86} +1.58773 q^{87} -15.9576 q^{88} -10.5387 q^{89} -22.8317 q^{90} +4.81038 q^{91} +9.02553 q^{92} -0.516431 q^{93} -19.9473 q^{94} +7.74217 q^{95} +7.09251 q^{96} -17.5159 q^{97} +3.18462 q^{98} -5.41293 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60071 −1.83898 −0.919492 0.393110i \(-0.871399\pi\)
−0.919492 + 0.393110i \(0.871399\pi\)
\(3\) −0.749599 −0.432781 −0.216390 0.976307i \(-0.569428\pi\)
−0.216390 + 0.976307i \(0.569428\pi\)
\(4\) 4.76372 2.38186
\(5\) −3.60076 −1.61031 −0.805154 0.593066i \(-0.797917\pi\)
−0.805154 + 0.593066i \(0.797917\pi\)
\(6\) 1.94949 0.795877
\(7\) −2.40322 −0.908333 −0.454167 0.890917i \(-0.650063\pi\)
−0.454167 + 0.890917i \(0.650063\pi\)
\(8\) −7.18764 −2.54121
\(9\) −2.43810 −0.812701
\(10\) 9.36455 2.96133
\(11\) 2.22014 0.669397 0.334699 0.942325i \(-0.391366\pi\)
0.334699 + 0.942325i \(0.391366\pi\)
\(12\) −3.57088 −1.03082
\(13\) −2.00163 −0.555154 −0.277577 0.960703i \(-0.589531\pi\)
−0.277577 + 0.960703i \(0.589531\pi\)
\(14\) 6.25010 1.67041
\(15\) 2.69912 0.696911
\(16\) 9.16557 2.29139
\(17\) 4.82130 1.16934 0.584669 0.811272i \(-0.301225\pi\)
0.584669 + 0.811272i \(0.301225\pi\)
\(18\) 6.34081 1.49454
\(19\) −2.15015 −0.493278 −0.246639 0.969107i \(-0.579326\pi\)
−0.246639 + 0.969107i \(0.579326\pi\)
\(20\) −17.1530 −3.83553
\(21\) 1.80145 0.393109
\(22\) −5.77395 −1.23101
\(23\) 1.89464 0.395060 0.197530 0.980297i \(-0.436708\pi\)
0.197530 + 0.980297i \(0.436708\pi\)
\(24\) 5.38785 1.09979
\(25\) 7.96546 1.59309
\(26\) 5.20568 1.02092
\(27\) 4.07639 0.784502
\(28\) −11.4483 −2.16352
\(29\) −2.11811 −0.393322 −0.196661 0.980472i \(-0.563010\pi\)
−0.196661 + 0.980472i \(0.563010\pi\)
\(30\) −7.01965 −1.28161
\(31\) 0.688943 0.123738 0.0618689 0.998084i \(-0.480294\pi\)
0.0618689 + 0.998084i \(0.480294\pi\)
\(32\) −9.46175 −1.67262
\(33\) −1.66421 −0.289702
\(34\) −12.5388 −2.15039
\(35\) 8.65343 1.46270
\(36\) −11.6144 −1.93574
\(37\) 4.93426 0.811188 0.405594 0.914053i \(-0.367065\pi\)
0.405594 + 0.914053i \(0.367065\pi\)
\(38\) 5.59193 0.907131
\(39\) 1.50042 0.240260
\(40\) 25.8810 4.09214
\(41\) −1.43704 −0.224427 −0.112214 0.993684i \(-0.535794\pi\)
−0.112214 + 0.993684i \(0.535794\pi\)
\(42\) −4.68507 −0.722921
\(43\) −9.03240 −1.37743 −0.688714 0.725033i \(-0.741824\pi\)
−0.688714 + 0.725033i \(0.741824\pi\)
\(44\) 10.5761 1.59441
\(45\) 8.77902 1.30870
\(46\) −4.92742 −0.726509
\(47\) 7.66993 1.11877 0.559387 0.828907i \(-0.311037\pi\)
0.559387 + 0.828907i \(0.311037\pi\)
\(48\) −6.87050 −0.991671
\(49\) −1.22452 −0.174931
\(50\) −20.7159 −2.92967
\(51\) −3.61404 −0.506067
\(52\) −9.53522 −1.32230
\(53\) −1.61201 −0.221427 −0.110714 0.993852i \(-0.535314\pi\)
−0.110714 + 0.993852i \(0.535314\pi\)
\(54\) −10.6015 −1.44269
\(55\) −7.99419 −1.07794
\(56\) 17.2735 2.30827
\(57\) 1.61175 0.213481
\(58\) 5.50859 0.723313
\(59\) −6.77799 −0.882419 −0.441209 0.897404i \(-0.645450\pi\)
−0.441209 + 0.897404i \(0.645450\pi\)
\(60\) 12.8579 1.65994
\(61\) −9.48597 −1.21455 −0.607277 0.794490i \(-0.707738\pi\)
−0.607277 + 0.794490i \(0.707738\pi\)
\(62\) −1.79174 −0.227552
\(63\) 5.85930 0.738203
\(64\) 6.27617 0.784522
\(65\) 7.20740 0.893969
\(66\) 4.32814 0.532758
\(67\) 3.30456 0.403717 0.201858 0.979415i \(-0.435302\pi\)
0.201858 + 0.979415i \(0.435302\pi\)
\(68\) 22.9673 2.78520
\(69\) −1.42022 −0.170974
\(70\) −22.5051 −2.68987
\(71\) 4.23793 0.502950 0.251475 0.967864i \(-0.419084\pi\)
0.251475 + 0.967864i \(0.419084\pi\)
\(72\) 17.5242 2.06525
\(73\) 4.90703 0.574325 0.287162 0.957882i \(-0.407288\pi\)
0.287162 + 0.957882i \(0.407288\pi\)
\(74\) −12.8326 −1.49176
\(75\) −5.97090 −0.689460
\(76\) −10.2427 −1.17492
\(77\) −5.33549 −0.608036
\(78\) −3.90217 −0.441834
\(79\) −13.0263 −1.46558 −0.732789 0.680456i \(-0.761782\pi\)
−0.732789 + 0.680456i \(0.761782\pi\)
\(80\) −33.0030 −3.68985
\(81\) 4.25865 0.473183
\(82\) 3.73732 0.412718
\(83\) −14.0724 −1.54465 −0.772324 0.635229i \(-0.780906\pi\)
−0.772324 + 0.635229i \(0.780906\pi\)
\(84\) 8.58161 0.936331
\(85\) −17.3603 −1.88299
\(86\) 23.4907 2.53307
\(87\) 1.58773 0.170222
\(88\) −15.9576 −1.70108
\(89\) −10.5387 −1.11710 −0.558550 0.829471i \(-0.688642\pi\)
−0.558550 + 0.829471i \(0.688642\pi\)
\(90\) −22.8317 −2.40667
\(91\) 4.81038 0.504264
\(92\) 9.02553 0.940977
\(93\) −0.516431 −0.0535513
\(94\) −19.9473 −2.05741
\(95\) 7.74217 0.794330
\(96\) 7.09251 0.723877
\(97\) −17.5159 −1.77847 −0.889236 0.457448i \(-0.848763\pi\)
−0.889236 + 0.457448i \(0.848763\pi\)
\(98\) 3.18462 0.321695
\(99\) −5.41293 −0.544019
\(100\) 37.9452 3.79452
\(101\) −14.1313 −1.40612 −0.703061 0.711130i \(-0.748184\pi\)
−0.703061 + 0.711130i \(0.748184\pi\)
\(102\) 9.39909 0.930648
\(103\) −11.3083 −1.11424 −0.557119 0.830433i \(-0.688093\pi\)
−0.557119 + 0.830433i \(0.688093\pi\)
\(104\) 14.3870 1.41076
\(105\) −6.48660 −0.633027
\(106\) 4.19239 0.407201
\(107\) 8.81988 0.852650 0.426325 0.904570i \(-0.359808\pi\)
0.426325 + 0.904570i \(0.359808\pi\)
\(108\) 19.4188 1.86857
\(109\) 9.55008 0.914731 0.457366 0.889279i \(-0.348793\pi\)
0.457366 + 0.889279i \(0.348793\pi\)
\(110\) 20.7906 1.98231
\(111\) −3.69872 −0.351067
\(112\) −22.0269 −2.08135
\(113\) −5.40354 −0.508322 −0.254161 0.967162i \(-0.581799\pi\)
−0.254161 + 0.967162i \(0.581799\pi\)
\(114\) −4.19170 −0.392589
\(115\) −6.82214 −0.636168
\(116\) −10.0901 −0.936838
\(117\) 4.88019 0.451174
\(118\) 17.6276 1.62275
\(119\) −11.5867 −1.06215
\(120\) −19.4003 −1.77100
\(121\) −6.07098 −0.551907
\(122\) 24.6703 2.23354
\(123\) 1.07720 0.0971279
\(124\) 3.28193 0.294726
\(125\) −10.6779 −0.955063
\(126\) −15.2384 −1.35754
\(127\) −12.4562 −1.10531 −0.552656 0.833410i \(-0.686386\pi\)
−0.552656 + 0.833410i \(0.686386\pi\)
\(128\) 2.60096 0.229895
\(129\) 6.77067 0.596125
\(130\) −18.7444 −1.64399
\(131\) 14.6621 1.28103 0.640517 0.767944i \(-0.278720\pi\)
0.640517 + 0.767944i \(0.278720\pi\)
\(132\) −7.92784 −0.690030
\(133\) 5.16729 0.448061
\(134\) −8.59422 −0.742428
\(135\) −14.6781 −1.26329
\(136\) −34.6538 −2.97154
\(137\) 2.45492 0.209738 0.104869 0.994486i \(-0.466558\pi\)
0.104869 + 0.994486i \(0.466558\pi\)
\(138\) 3.69359 0.314419
\(139\) −0.0244488 −0.00207372 −0.00103686 0.999999i \(-0.500330\pi\)
−0.00103686 + 0.999999i \(0.500330\pi\)
\(140\) 41.2225 3.48394
\(141\) −5.74937 −0.484184
\(142\) −11.0216 −0.924916
\(143\) −4.44391 −0.371618
\(144\) −22.3466 −1.86222
\(145\) 7.62679 0.633370
\(146\) −12.7618 −1.05617
\(147\) 0.917896 0.0757068
\(148\) 23.5054 1.93213
\(149\) 7.07311 0.579451 0.289726 0.957110i \(-0.406436\pi\)
0.289726 + 0.957110i \(0.406436\pi\)
\(150\) 15.5286 1.26791
\(151\) −3.14779 −0.256163 −0.128082 0.991764i \(-0.540882\pi\)
−0.128082 + 0.991764i \(0.540882\pi\)
\(152\) 15.4545 1.25353
\(153\) −11.7548 −0.950321
\(154\) 13.8761 1.11817
\(155\) −2.48072 −0.199256
\(156\) 7.14759 0.572265
\(157\) −6.32853 −0.505072 −0.252536 0.967588i \(-0.581265\pi\)
−0.252536 + 0.967588i \(0.581265\pi\)
\(158\) 33.8778 2.69517
\(159\) 1.20836 0.0958295
\(160\) 34.0695 2.69343
\(161\) −4.55325 −0.358846
\(162\) −11.0755 −0.870176
\(163\) 2.47104 0.193547 0.0967733 0.995306i \(-0.469148\pi\)
0.0967733 + 0.995306i \(0.469148\pi\)
\(164\) −6.84564 −0.534555
\(165\) 5.99243 0.466510
\(166\) 36.5983 2.84058
\(167\) 4.65532 0.360240 0.180120 0.983645i \(-0.442351\pi\)
0.180120 + 0.983645i \(0.442351\pi\)
\(168\) −12.9482 −0.998975
\(169\) −8.99346 −0.691804
\(170\) 45.1493 3.46279
\(171\) 5.24229 0.400888
\(172\) −43.0278 −3.28084
\(173\) 16.9623 1.28962 0.644811 0.764342i \(-0.276936\pi\)
0.644811 + 0.764342i \(0.276936\pi\)
\(174\) −4.12923 −0.313036
\(175\) −19.1428 −1.44706
\(176\) 20.3488 1.53385
\(177\) 5.08077 0.381894
\(178\) 27.4082 2.05433
\(179\) −2.81310 −0.210261 −0.105131 0.994458i \(-0.533526\pi\)
−0.105131 + 0.994458i \(0.533526\pi\)
\(180\) 41.8208 3.11714
\(181\) 7.92772 0.589263 0.294631 0.955611i \(-0.404803\pi\)
0.294631 + 0.955611i \(0.404803\pi\)
\(182\) −12.5104 −0.927334
\(183\) 7.11067 0.525636
\(184\) −13.6180 −1.00393
\(185\) −17.7671 −1.30626
\(186\) 1.34309 0.0984800
\(187\) 10.7040 0.782751
\(188\) 36.5374 2.66476
\(189\) −9.79648 −0.712589
\(190\) −20.1352 −1.46076
\(191\) −26.0936 −1.88807 −0.944033 0.329851i \(-0.893001\pi\)
−0.944033 + 0.329851i \(0.893001\pi\)
\(192\) −4.70461 −0.339526
\(193\) −1.58426 −0.114037 −0.0570187 0.998373i \(-0.518159\pi\)
−0.0570187 + 0.998373i \(0.518159\pi\)
\(194\) 45.5539 3.27058
\(195\) −5.40266 −0.386893
\(196\) −5.83325 −0.416661
\(197\) 10.3233 0.735508 0.367754 0.929923i \(-0.380127\pi\)
0.367754 + 0.929923i \(0.380127\pi\)
\(198\) 14.0775 1.00044
\(199\) −3.30085 −0.233991 −0.116996 0.993132i \(-0.537326\pi\)
−0.116996 + 0.993132i \(0.537326\pi\)
\(200\) −57.2529 −4.04839
\(201\) −2.47710 −0.174721
\(202\) 36.7516 2.58583
\(203\) 5.09028 0.357268
\(204\) −17.2163 −1.20538
\(205\) 5.17442 0.361397
\(206\) 29.4096 2.04907
\(207\) −4.61933 −0.321065
\(208\) −18.3461 −1.27207
\(209\) −4.77363 −0.330199
\(210\) 16.8698 1.16413
\(211\) 3.58875 0.247060 0.123530 0.992341i \(-0.460579\pi\)
0.123530 + 0.992341i \(0.460579\pi\)
\(212\) −7.67918 −0.527408
\(213\) −3.17675 −0.217667
\(214\) −22.9380 −1.56801
\(215\) 32.5235 2.21808
\(216\) −29.2997 −1.99359
\(217\) −1.65568 −0.112395
\(218\) −24.8370 −1.68218
\(219\) −3.67830 −0.248557
\(220\) −38.0820 −2.56749
\(221\) −9.65048 −0.649162
\(222\) 9.61930 0.645605
\(223\) −9.95968 −0.666949 −0.333475 0.942759i \(-0.608221\pi\)
−0.333475 + 0.942759i \(0.608221\pi\)
\(224\) 22.7387 1.51929
\(225\) −19.4206 −1.29471
\(226\) 14.0531 0.934796
\(227\) 17.4185 1.15610 0.578052 0.816000i \(-0.303813\pi\)
0.578052 + 0.816000i \(0.303813\pi\)
\(228\) 7.67792 0.508483
\(229\) −13.8102 −0.912603 −0.456302 0.889825i \(-0.650826\pi\)
−0.456302 + 0.889825i \(0.650826\pi\)
\(230\) 17.7425 1.16990
\(231\) 3.99948 0.263146
\(232\) 15.2242 0.999516
\(233\) 3.23572 0.211979 0.105989 0.994367i \(-0.466199\pi\)
0.105989 + 0.994367i \(0.466199\pi\)
\(234\) −12.6920 −0.829701
\(235\) −27.6176 −1.80157
\(236\) −32.2884 −2.10180
\(237\) 9.76452 0.634274
\(238\) 30.1336 1.95327
\(239\) 17.9609 1.16179 0.580896 0.813978i \(-0.302702\pi\)
0.580896 + 0.813978i \(0.302702\pi\)
\(240\) 24.7390 1.59690
\(241\) 17.3752 1.11924 0.559619 0.828750i \(-0.310948\pi\)
0.559619 + 0.828750i \(0.310948\pi\)
\(242\) 15.7889 1.01495
\(243\) −15.4215 −0.989287
\(244\) −45.1885 −2.89290
\(245\) 4.40919 0.281693
\(246\) −2.80149 −0.178617
\(247\) 4.30382 0.273845
\(248\) −4.95187 −0.314444
\(249\) 10.5487 0.668494
\(250\) 27.7702 1.75634
\(251\) 1.62952 0.102855 0.0514273 0.998677i \(-0.483623\pi\)
0.0514273 + 0.998677i \(0.483623\pi\)
\(252\) 27.9121 1.75830
\(253\) 4.20637 0.264452
\(254\) 32.3951 2.03265
\(255\) 13.0133 0.814924
\(256\) −19.3167 −1.20729
\(257\) 6.18870 0.386041 0.193020 0.981195i \(-0.438172\pi\)
0.193020 + 0.981195i \(0.438172\pi\)
\(258\) −17.6086 −1.09626
\(259\) −11.8581 −0.736829
\(260\) 34.3340 2.12931
\(261\) 5.16416 0.319653
\(262\) −38.1319 −2.35580
\(263\) 3.91256 0.241259 0.120629 0.992698i \(-0.461509\pi\)
0.120629 + 0.992698i \(0.461509\pi\)
\(264\) 11.9618 0.736196
\(265\) 5.80448 0.356566
\(266\) −13.4387 −0.823977
\(267\) 7.89980 0.483460
\(268\) 15.7420 0.961596
\(269\) −7.57471 −0.461838 −0.230919 0.972973i \(-0.574173\pi\)
−0.230919 + 0.972973i \(0.574173\pi\)
\(270\) 38.1736 2.32317
\(271\) −18.5223 −1.12515 −0.562575 0.826746i \(-0.690189\pi\)
−0.562575 + 0.826746i \(0.690189\pi\)
\(272\) 44.1900 2.67941
\(273\) −3.60585 −0.218236
\(274\) −6.38455 −0.385705
\(275\) 17.6844 1.06641
\(276\) −6.76553 −0.407237
\(277\) 12.5043 0.751311 0.375655 0.926759i \(-0.377418\pi\)
0.375655 + 0.926759i \(0.377418\pi\)
\(278\) 0.0635843 0.00381353
\(279\) −1.67971 −0.100562
\(280\) −62.1977 −3.71703
\(281\) −4.42222 −0.263807 −0.131904 0.991263i \(-0.542109\pi\)
−0.131904 + 0.991263i \(0.542109\pi\)
\(282\) 14.9525 0.890406
\(283\) 17.1801 1.02125 0.510625 0.859803i \(-0.329414\pi\)
0.510625 + 0.859803i \(0.329414\pi\)
\(284\) 20.1883 1.19796
\(285\) −5.80352 −0.343771
\(286\) 11.5573 0.683400
\(287\) 3.45352 0.203855
\(288\) 23.0687 1.35934
\(289\) 6.24494 0.367349
\(290\) −19.8351 −1.16476
\(291\) 13.1299 0.769689
\(292\) 23.3757 1.36796
\(293\) −4.68421 −0.273654 −0.136827 0.990595i \(-0.543691\pi\)
−0.136827 + 0.990595i \(0.543691\pi\)
\(294\) −2.38719 −0.139223
\(295\) 24.4059 1.42097
\(296\) −35.4657 −2.06140
\(297\) 9.05016 0.525144
\(298\) −18.3951 −1.06560
\(299\) −3.79238 −0.219319
\(300\) −28.4437 −1.64220
\(301\) 21.7069 1.25116
\(302\) 8.18650 0.471080
\(303\) 10.5928 0.608542
\(304\) −19.7074 −1.13029
\(305\) 34.1567 1.95581
\(306\) 30.5709 1.74762
\(307\) −28.6823 −1.63699 −0.818494 0.574515i \(-0.805191\pi\)
−0.818494 + 0.574515i \(0.805191\pi\)
\(308\) −25.4168 −1.44825
\(309\) 8.47667 0.482221
\(310\) 6.45164 0.366428
\(311\) −16.3627 −0.927844 −0.463922 0.885876i \(-0.653558\pi\)
−0.463922 + 0.885876i \(0.653558\pi\)
\(312\) −10.7845 −0.610552
\(313\) 15.5165 0.877042 0.438521 0.898721i \(-0.355502\pi\)
0.438521 + 0.898721i \(0.355502\pi\)
\(314\) 16.4587 0.928818
\(315\) −21.0979 −1.18873
\(316\) −62.0538 −3.49080
\(317\) −17.3276 −0.973214 −0.486607 0.873621i \(-0.661766\pi\)
−0.486607 + 0.873621i \(0.661766\pi\)
\(318\) −3.14261 −0.176229
\(319\) −4.70249 −0.263289
\(320\) −22.5990 −1.26332
\(321\) −6.61137 −0.369010
\(322\) 11.8417 0.659912
\(323\) −10.3665 −0.576809
\(324\) 20.2870 1.12706
\(325\) −15.9440 −0.884411
\(326\) −6.42647 −0.355929
\(327\) −7.15872 −0.395878
\(328\) 10.3289 0.570318
\(329\) −18.4325 −1.01622
\(330\) −15.5846 −0.857904
\(331\) 5.82367 0.320098 0.160049 0.987109i \(-0.448835\pi\)
0.160049 + 0.987109i \(0.448835\pi\)
\(332\) −67.0370 −3.67913
\(333\) −12.0302 −0.659253
\(334\) −12.1072 −0.662475
\(335\) −11.8989 −0.650108
\(336\) 16.5113 0.900767
\(337\) −7.52521 −0.409924 −0.204962 0.978770i \(-0.565707\pi\)
−0.204962 + 0.978770i \(0.565707\pi\)
\(338\) 23.3894 1.27222
\(339\) 4.05049 0.219992
\(340\) −82.6998 −4.48502
\(341\) 1.52955 0.0828297
\(342\) −13.6337 −0.737226
\(343\) 19.7654 1.06723
\(344\) 64.9216 3.50034
\(345\) 5.11387 0.275322
\(346\) −44.1142 −2.37159
\(347\) 2.79302 0.149937 0.0749687 0.997186i \(-0.476114\pi\)
0.0749687 + 0.997186i \(0.476114\pi\)
\(348\) 7.56349 0.405446
\(349\) −33.1385 −1.77387 −0.886933 0.461898i \(-0.847169\pi\)
−0.886933 + 0.461898i \(0.847169\pi\)
\(350\) 49.7849 2.66112
\(351\) −8.15945 −0.435519
\(352\) −21.0064 −1.11964
\(353\) 4.63827 0.246870 0.123435 0.992353i \(-0.460609\pi\)
0.123435 + 0.992353i \(0.460609\pi\)
\(354\) −13.2136 −0.702296
\(355\) −15.2598 −0.809904
\(356\) −50.2034 −2.66077
\(357\) 8.68535 0.459677
\(358\) 7.31608 0.386667
\(359\) −26.0910 −1.37703 −0.688515 0.725222i \(-0.741737\pi\)
−0.688515 + 0.725222i \(0.741737\pi\)
\(360\) −63.1004 −3.32568
\(361\) −14.3769 −0.756676
\(362\) −20.6177 −1.08364
\(363\) 4.55080 0.238855
\(364\) 22.9153 1.20109
\(365\) −17.6690 −0.924840
\(366\) −18.4928 −0.966635
\(367\) −18.7059 −0.976440 −0.488220 0.872721i \(-0.662354\pi\)
−0.488220 + 0.872721i \(0.662354\pi\)
\(368\) 17.3655 0.905237
\(369\) 3.50364 0.182392
\(370\) 46.2071 2.40219
\(371\) 3.87403 0.201130
\(372\) −2.46013 −0.127552
\(373\) −3.42892 −0.177543 −0.0887714 0.996052i \(-0.528294\pi\)
−0.0887714 + 0.996052i \(0.528294\pi\)
\(374\) −27.8379 −1.43947
\(375\) 8.00416 0.413333
\(376\) −55.1287 −2.84304
\(377\) 4.23967 0.218354
\(378\) 25.4779 1.31044
\(379\) −30.5237 −1.56790 −0.783949 0.620825i \(-0.786798\pi\)
−0.783949 + 0.620825i \(0.786798\pi\)
\(380\) 36.8815 1.89198
\(381\) 9.33717 0.478358
\(382\) 67.8620 3.47212
\(383\) −6.67146 −0.340896 −0.170448 0.985367i \(-0.554521\pi\)
−0.170448 + 0.985367i \(0.554521\pi\)
\(384\) −1.94968 −0.0994940
\(385\) 19.2118 0.979125
\(386\) 4.12020 0.209713
\(387\) 22.0219 1.11944
\(388\) −83.4409 −4.23607
\(389\) −18.0381 −0.914569 −0.457284 0.889321i \(-0.651178\pi\)
−0.457284 + 0.889321i \(0.651178\pi\)
\(390\) 14.0508 0.711489
\(391\) 9.13463 0.461958
\(392\) 8.80138 0.444537
\(393\) −10.9907 −0.554407
\(394\) −26.8481 −1.35259
\(395\) 46.9047 2.36003
\(396\) −25.7856 −1.29578
\(397\) 14.9013 0.747874 0.373937 0.927454i \(-0.378008\pi\)
0.373937 + 0.927454i \(0.378008\pi\)
\(398\) 8.58458 0.430306
\(399\) −3.87340 −0.193912
\(400\) 73.0080 3.65040
\(401\) −10.0752 −0.503132 −0.251566 0.967840i \(-0.580946\pi\)
−0.251566 + 0.967840i \(0.580946\pi\)
\(402\) 6.44222 0.321309
\(403\) −1.37901 −0.0686935
\(404\) −67.3177 −3.34918
\(405\) −15.3344 −0.761971
\(406\) −13.2384 −0.657009
\(407\) 10.9547 0.543007
\(408\) 25.9764 1.28602
\(409\) −10.8222 −0.535122 −0.267561 0.963541i \(-0.586218\pi\)
−0.267561 + 0.963541i \(0.586218\pi\)
\(410\) −13.4572 −0.664604
\(411\) −1.84020 −0.0907706
\(412\) −53.8695 −2.65396
\(413\) 16.2890 0.801530
\(414\) 12.0136 0.590434
\(415\) 50.6714 2.48736
\(416\) 18.9390 0.928559
\(417\) 0.0183268 0.000897465 0
\(418\) 12.4149 0.607231
\(419\) 17.0887 0.834838 0.417419 0.908714i \(-0.362935\pi\)
0.417419 + 0.908714i \(0.362935\pi\)
\(420\) −30.9003 −1.50778
\(421\) 17.9307 0.873891 0.436946 0.899488i \(-0.356060\pi\)
0.436946 + 0.899488i \(0.356060\pi\)
\(422\) −9.33331 −0.454338
\(423\) −18.7001 −0.909228
\(424\) 11.5866 0.562694
\(425\) 38.4039 1.86286
\(426\) 8.26181 0.400286
\(427\) 22.7969 1.10322
\(428\) 42.0154 2.03089
\(429\) 3.33115 0.160829
\(430\) −84.5843 −4.07902
\(431\) 22.0254 1.06092 0.530462 0.847708i \(-0.322018\pi\)
0.530462 + 0.847708i \(0.322018\pi\)
\(432\) 37.3625 1.79760
\(433\) 29.2860 1.40739 0.703697 0.710501i \(-0.251531\pi\)
0.703697 + 0.710501i \(0.251531\pi\)
\(434\) 4.30596 0.206693
\(435\) −5.71703 −0.274111
\(436\) 45.4939 2.17876
\(437\) −4.07376 −0.194875
\(438\) 9.56622 0.457092
\(439\) −22.1269 −1.05606 −0.528031 0.849225i \(-0.677069\pi\)
−0.528031 + 0.849225i \(0.677069\pi\)
\(440\) 57.4593 2.73927
\(441\) 2.98550 0.142166
\(442\) 25.0982 1.19380
\(443\) −18.8566 −0.895903 −0.447951 0.894058i \(-0.647846\pi\)
−0.447951 + 0.894058i \(0.647846\pi\)
\(444\) −17.6196 −0.836191
\(445\) 37.9473 1.79888
\(446\) 25.9023 1.22651
\(447\) −5.30199 −0.250775
\(448\) −15.0830 −0.712607
\(449\) 24.0191 1.13353 0.566766 0.823879i \(-0.308195\pi\)
0.566766 + 0.823879i \(0.308195\pi\)
\(450\) 50.5075 2.38095
\(451\) −3.19042 −0.150231
\(452\) −25.7409 −1.21075
\(453\) 2.35958 0.110863
\(454\) −45.3005 −2.12606
\(455\) −17.3210 −0.812021
\(456\) −11.5847 −0.542502
\(457\) 19.8939 0.930597 0.465298 0.885154i \(-0.345947\pi\)
0.465298 + 0.885154i \(0.345947\pi\)
\(458\) 35.9164 1.67826
\(459\) 19.6535 0.917348
\(460\) −32.4988 −1.51526
\(461\) 38.3823 1.78764 0.893821 0.448425i \(-0.148015\pi\)
0.893821 + 0.448425i \(0.148015\pi\)
\(462\) −10.4015 −0.483921
\(463\) −16.1933 −0.752567 −0.376283 0.926505i \(-0.622798\pi\)
−0.376283 + 0.926505i \(0.622798\pi\)
\(464\) −19.4136 −0.901256
\(465\) 1.85954 0.0862342
\(466\) −8.41518 −0.389826
\(467\) −8.67187 −0.401286 −0.200643 0.979664i \(-0.564303\pi\)
−0.200643 + 0.979664i \(0.564303\pi\)
\(468\) 23.2478 1.07463
\(469\) −7.94160 −0.366709
\(470\) 71.8254 3.31306
\(471\) 4.74386 0.218585
\(472\) 48.7177 2.24242
\(473\) −20.0532 −0.922046
\(474\) −25.3947 −1.16642
\(475\) −17.1270 −0.785838
\(476\) −55.1956 −2.52989
\(477\) 3.93026 0.179954
\(478\) −46.7111 −2.13652
\(479\) 3.99940 0.182737 0.0913687 0.995817i \(-0.470876\pi\)
0.0913687 + 0.995817i \(0.470876\pi\)
\(480\) −25.5384 −1.16566
\(481\) −9.87659 −0.450334
\(482\) −45.1881 −2.05826
\(483\) 3.41311 0.155302
\(484\) −28.9204 −1.31457
\(485\) 63.0706 2.86389
\(486\) 40.1068 1.81928
\(487\) 14.9384 0.676925 0.338463 0.940980i \(-0.390093\pi\)
0.338463 + 0.940980i \(0.390093\pi\)
\(488\) 68.1817 3.08644
\(489\) −1.85229 −0.0837633
\(490\) −11.4670 −0.518028
\(491\) 13.8028 0.622913 0.311457 0.950260i \(-0.399183\pi\)
0.311457 + 0.950260i \(0.399183\pi\)
\(492\) 5.13148 0.231345
\(493\) −10.2120 −0.459926
\(494\) −11.1930 −0.503597
\(495\) 19.4906 0.876039
\(496\) 6.31455 0.283532
\(497\) −10.1847 −0.456846
\(498\) −27.4341 −1.22935
\(499\) 35.6685 1.59674 0.798371 0.602166i \(-0.205695\pi\)
0.798371 + 0.602166i \(0.205695\pi\)
\(500\) −50.8666 −2.27482
\(501\) −3.48962 −0.155905
\(502\) −4.23793 −0.189148
\(503\) −30.0654 −1.34055 −0.670275 0.742113i \(-0.733824\pi\)
−0.670275 + 0.742113i \(0.733824\pi\)
\(504\) −42.1146 −1.87593
\(505\) 50.8836 2.26429
\(506\) −10.9396 −0.486323
\(507\) 6.74148 0.299400
\(508\) −59.3379 −2.63270
\(509\) −16.0537 −0.711569 −0.355785 0.934568i \(-0.615786\pi\)
−0.355785 + 0.934568i \(0.615786\pi\)
\(510\) −33.8438 −1.49863
\(511\) −11.7927 −0.521678
\(512\) 45.0353 1.99030
\(513\) −8.76486 −0.386978
\(514\) −16.0950 −0.709922
\(515\) 40.7184 1.79427
\(516\) 32.2536 1.41988
\(517\) 17.0283 0.748904
\(518\) 30.8396 1.35502
\(519\) −12.7149 −0.558124
\(520\) −51.8042 −2.27177
\(521\) −42.8894 −1.87902 −0.939508 0.342526i \(-0.888718\pi\)
−0.939508 + 0.342526i \(0.888718\pi\)
\(522\) −13.4305 −0.587837
\(523\) 5.15590 0.225452 0.112726 0.993626i \(-0.464042\pi\)
0.112726 + 0.993626i \(0.464042\pi\)
\(524\) 69.8461 3.05124
\(525\) 14.3494 0.626260
\(526\) −10.1754 −0.443670
\(527\) 3.32160 0.144691
\(528\) −15.2535 −0.663822
\(529\) −19.4103 −0.843928
\(530\) −15.0958 −0.655719
\(531\) 16.5254 0.717142
\(532\) 24.6155 1.06722
\(533\) 2.87642 0.124592
\(534\) −20.5451 −0.889074
\(535\) −31.7582 −1.37303
\(536\) −23.7520 −1.02593
\(537\) 2.10870 0.0909970
\(538\) 19.6997 0.849313
\(539\) −2.71860 −0.117098
\(540\) −69.9224 −3.00898
\(541\) −10.7502 −0.462188 −0.231094 0.972931i \(-0.574230\pi\)
−0.231094 + 0.972931i \(0.574230\pi\)
\(542\) 48.1712 2.06913
\(543\) −5.94261 −0.255022
\(544\) −45.6179 −1.95585
\(545\) −34.3875 −1.47300
\(546\) 9.37779 0.401332
\(547\) 28.5128 1.21912 0.609559 0.792741i \(-0.291347\pi\)
0.609559 + 0.792741i \(0.291347\pi\)
\(548\) 11.6945 0.499566
\(549\) 23.1278 0.987069
\(550\) −45.9922 −1.96111
\(551\) 4.55425 0.194017
\(552\) 10.2080 0.434483
\(553\) 31.3052 1.33123
\(554\) −32.5201 −1.38165
\(555\) 13.3182 0.565325
\(556\) −0.116467 −0.00493930
\(557\) 15.7892 0.669010 0.334505 0.942394i \(-0.391431\pi\)
0.334505 + 0.942394i \(0.391431\pi\)
\(558\) 4.36845 0.184931
\(559\) 18.0796 0.764684
\(560\) 79.3136 3.35161
\(561\) −8.02367 −0.338760
\(562\) 11.5009 0.485137
\(563\) 7.82334 0.329714 0.164857 0.986317i \(-0.447284\pi\)
0.164857 + 0.986317i \(0.447284\pi\)
\(564\) −27.3884 −1.15326
\(565\) 19.4568 0.818556
\(566\) −44.6805 −1.87806
\(567\) −10.2345 −0.429808
\(568\) −30.4607 −1.27810
\(569\) −25.9007 −1.08581 −0.542907 0.839793i \(-0.682676\pi\)
−0.542907 + 0.839793i \(0.682676\pi\)
\(570\) 15.0933 0.632189
\(571\) −1.20933 −0.0506087 −0.0253044 0.999680i \(-0.508055\pi\)
−0.0253044 + 0.999680i \(0.508055\pi\)
\(572\) −21.1695 −0.885142
\(573\) 19.5597 0.817119
\(574\) −8.98162 −0.374886
\(575\) 15.0917 0.629367
\(576\) −15.3020 −0.637581
\(577\) 36.0838 1.50219 0.751095 0.660194i \(-0.229526\pi\)
0.751095 + 0.660194i \(0.229526\pi\)
\(578\) −16.2413 −0.675549
\(579\) 1.18756 0.0493532
\(580\) 36.3319 1.50860
\(581\) 33.8192 1.40305
\(582\) −34.1472 −1.41544
\(583\) −3.57890 −0.148223
\(584\) −35.2700 −1.45948
\(585\) −17.5724 −0.726529
\(586\) 12.1823 0.503246
\(587\) −7.23567 −0.298648 −0.149324 0.988788i \(-0.547710\pi\)
−0.149324 + 0.988788i \(0.547710\pi\)
\(588\) 4.37260 0.180323
\(589\) −1.48133 −0.0610372
\(590\) −63.4728 −2.61313
\(591\) −7.73837 −0.318314
\(592\) 45.2253 1.85875
\(593\) −11.6987 −0.480408 −0.240204 0.970722i \(-0.577214\pi\)
−0.240204 + 0.970722i \(0.577214\pi\)
\(594\) −23.5369 −0.965730
\(595\) 41.7208 1.71039
\(596\) 33.6943 1.38017
\(597\) 2.47432 0.101267
\(598\) 9.86290 0.403324
\(599\) −14.9465 −0.610696 −0.305348 0.952241i \(-0.598773\pi\)
−0.305348 + 0.952241i \(0.598773\pi\)
\(600\) 42.9167 1.75207
\(601\) −7.63701 −0.311520 −0.155760 0.987795i \(-0.549783\pi\)
−0.155760 + 0.987795i \(0.549783\pi\)
\(602\) −56.4534 −2.30087
\(603\) −8.05686 −0.328101
\(604\) −14.9952 −0.610145
\(605\) 21.8601 0.888741
\(606\) −27.5489 −1.11910
\(607\) 19.2133 0.779845 0.389923 0.920848i \(-0.372502\pi\)
0.389923 + 0.920848i \(0.372502\pi\)
\(608\) 20.3442 0.825066
\(609\) −3.81567 −0.154619
\(610\) −88.8318 −3.59669
\(611\) −15.3524 −0.621091
\(612\) −55.9967 −2.26353
\(613\) 16.3596 0.660758 0.330379 0.943848i \(-0.392823\pi\)
0.330379 + 0.943848i \(0.392823\pi\)
\(614\) 74.5946 3.01039
\(615\) −3.87874 −0.156406
\(616\) 38.3496 1.54515
\(617\) 48.0225 1.93331 0.966656 0.256077i \(-0.0824302\pi\)
0.966656 + 0.256077i \(0.0824302\pi\)
\(618\) −22.0454 −0.886796
\(619\) −6.57799 −0.264392 −0.132196 0.991224i \(-0.542203\pi\)
−0.132196 + 0.991224i \(0.542203\pi\)
\(620\) −11.8174 −0.474600
\(621\) 7.72330 0.309925
\(622\) 42.5547 1.70629
\(623\) 25.3269 1.01470
\(624\) 13.7522 0.550530
\(625\) −1.37869 −0.0551477
\(626\) −40.3539 −1.61287
\(627\) 3.57831 0.142904
\(628\) −30.1473 −1.20301
\(629\) 23.7896 0.948552
\(630\) 54.8697 2.18606
\(631\) −44.0453 −1.75341 −0.876707 0.481025i \(-0.840265\pi\)
−0.876707 + 0.481025i \(0.840265\pi\)
\(632\) 93.6286 3.72435
\(633\) −2.69012 −0.106923
\(634\) 45.0641 1.78972
\(635\) 44.8519 1.77989
\(636\) 5.75630 0.228252
\(637\) 2.45103 0.0971135
\(638\) 12.2298 0.484184
\(639\) −10.3325 −0.408748
\(640\) −9.36544 −0.370201
\(641\) 23.4674 0.926909 0.463454 0.886121i \(-0.346610\pi\)
0.463454 + 0.886121i \(0.346610\pi\)
\(642\) 17.1943 0.678604
\(643\) 1.32958 0.0524334 0.0262167 0.999656i \(-0.491654\pi\)
0.0262167 + 0.999656i \(0.491654\pi\)
\(644\) −21.6904 −0.854721
\(645\) −24.3796 −0.959944
\(646\) 26.9604 1.06074
\(647\) −9.42766 −0.370640 −0.185320 0.982678i \(-0.559332\pi\)
−0.185320 + 0.982678i \(0.559332\pi\)
\(648\) −30.6096 −1.20246
\(649\) −15.0481 −0.590688
\(650\) 41.4657 1.62642
\(651\) 1.24110 0.0486425
\(652\) 11.7713 0.461001
\(653\) 25.5048 0.998080 0.499040 0.866579i \(-0.333686\pi\)
0.499040 + 0.866579i \(0.333686\pi\)
\(654\) 18.6178 0.728014
\(655\) −52.7947 −2.06286
\(656\) −13.1713 −0.514251
\(657\) −11.9638 −0.466754
\(658\) 47.9378 1.86881
\(659\) 21.6617 0.843820 0.421910 0.906638i \(-0.361360\pi\)
0.421910 + 0.906638i \(0.361360\pi\)
\(660\) 28.5462 1.11116
\(661\) 37.3586 1.45308 0.726541 0.687123i \(-0.241127\pi\)
0.726541 + 0.687123i \(0.241127\pi\)
\(662\) −15.1457 −0.588655
\(663\) 7.23399 0.280945
\(664\) 101.147 3.92528
\(665\) −18.6062 −0.721517
\(666\) 31.2872 1.21235
\(667\) −4.01305 −0.155386
\(668\) 22.1766 0.858040
\(669\) 7.46576 0.288643
\(670\) 30.9457 1.19554
\(671\) −21.0602 −0.813019
\(672\) −17.0449 −0.657521
\(673\) −3.20604 −0.123584 −0.0617918 0.998089i \(-0.519681\pi\)
−0.0617918 + 0.998089i \(0.519681\pi\)
\(674\) 19.5709 0.753844
\(675\) 32.4704 1.24979
\(676\) −42.8423 −1.64778
\(677\) −4.16865 −0.160214 −0.0801071 0.996786i \(-0.525526\pi\)
−0.0801071 + 0.996786i \(0.525526\pi\)
\(678\) −10.5342 −0.404562
\(679\) 42.0947 1.61545
\(680\) 124.780 4.78509
\(681\) −13.0569 −0.500340
\(682\) −3.97792 −0.152322
\(683\) −1.11078 −0.0425029 −0.0212514 0.999774i \(-0.506765\pi\)
−0.0212514 + 0.999774i \(0.506765\pi\)
\(684\) 24.9728 0.954858
\(685\) −8.83958 −0.337743
\(686\) −51.4040 −1.96262
\(687\) 10.3521 0.394957
\(688\) −82.7871 −3.15623
\(689\) 3.22666 0.122926
\(690\) −13.2997 −0.506312
\(691\) 45.7674 1.74107 0.870537 0.492104i \(-0.163772\pi\)
0.870537 + 0.492104i \(0.163772\pi\)
\(692\) 80.8038 3.07170
\(693\) 13.0085 0.494151
\(694\) −7.26386 −0.275732
\(695\) 0.0880341 0.00333932
\(696\) −11.4120 −0.432572
\(697\) −6.92839 −0.262431
\(698\) 86.1839 3.26211
\(699\) −2.42549 −0.0917404
\(700\) −91.1909 −3.44669
\(701\) 13.7643 0.519872 0.259936 0.965626i \(-0.416298\pi\)
0.259936 + 0.965626i \(0.416298\pi\)
\(702\) 21.2204 0.800913
\(703\) −10.6094 −0.400141
\(704\) 13.9340 0.525157
\(705\) 20.7021 0.779685
\(706\) −12.0628 −0.453991
\(707\) 33.9608 1.27723
\(708\) 24.2033 0.909617
\(709\) 49.9855 1.87724 0.938622 0.344947i \(-0.112103\pi\)
0.938622 + 0.344947i \(0.112103\pi\)
\(710\) 39.6863 1.48940
\(711\) 31.7595 1.19108
\(712\) 75.7484 2.83879
\(713\) 1.30530 0.0488838
\(714\) −22.5881 −0.845339
\(715\) 16.0014 0.598420
\(716\) −13.4008 −0.500813
\(717\) −13.4634 −0.502801
\(718\) 67.8552 2.53233
\(719\) 4.38691 0.163604 0.0818022 0.996649i \(-0.473932\pi\)
0.0818022 + 0.996649i \(0.473932\pi\)
\(720\) 80.4647 2.99874
\(721\) 27.1763 1.01210
\(722\) 37.3901 1.39152
\(723\) −13.0245 −0.484385
\(724\) 37.7654 1.40354
\(725\) −16.8717 −0.626599
\(726\) −11.8353 −0.439250
\(727\) −8.21876 −0.304817 −0.152409 0.988318i \(-0.548703\pi\)
−0.152409 + 0.988318i \(0.548703\pi\)
\(728\) −34.5753 −1.28144
\(729\) −1.21604 −0.0450386
\(730\) 45.9521 1.70076
\(731\) −43.5479 −1.61068
\(732\) 33.8732 1.25199
\(733\) −31.7146 −1.17140 −0.585702 0.810526i \(-0.699181\pi\)
−0.585702 + 0.810526i \(0.699181\pi\)
\(734\) 48.6487 1.79566
\(735\) −3.30512 −0.121911
\(736\) −17.9266 −0.660784
\(737\) 7.33659 0.270247
\(738\) −9.11198 −0.335416
\(739\) 14.5846 0.536504 0.268252 0.963349i \(-0.413554\pi\)
0.268252 + 0.963349i \(0.413554\pi\)
\(740\) −84.6374 −3.11133
\(741\) −3.22613 −0.118515
\(742\) −10.0753 −0.369874
\(743\) 16.7750 0.615415 0.307708 0.951481i \(-0.400438\pi\)
0.307708 + 0.951481i \(0.400438\pi\)
\(744\) 3.71192 0.136085
\(745\) −25.4685 −0.933095
\(746\) 8.91764 0.326498
\(747\) 34.3100 1.25534
\(748\) 50.9906 1.86440
\(749\) −21.1961 −0.774490
\(750\) −20.8165 −0.760112
\(751\) −23.3405 −0.851706 −0.425853 0.904792i \(-0.640026\pi\)
−0.425853 + 0.904792i \(0.640026\pi\)
\(752\) 70.2992 2.56355
\(753\) −1.22149 −0.0445135
\(754\) −11.0262 −0.401550
\(755\) 11.3344 0.412502
\(756\) −46.6677 −1.69729
\(757\) −0.728092 −0.0264630 −0.0132315 0.999912i \(-0.504212\pi\)
−0.0132315 + 0.999912i \(0.504212\pi\)
\(758\) 79.3835 2.88334
\(759\) −3.15309 −0.114450
\(760\) −55.6480 −2.01856
\(761\) 37.8199 1.37097 0.685485 0.728087i \(-0.259590\pi\)
0.685485 + 0.728087i \(0.259590\pi\)
\(762\) −24.2833 −0.879692
\(763\) −22.9510 −0.830881
\(764\) −124.302 −4.49711
\(765\) 42.3263 1.53031
\(766\) 17.3506 0.626902
\(767\) 13.5671 0.489878
\(768\) 14.4798 0.522494
\(769\) 7.96338 0.287167 0.143583 0.989638i \(-0.454137\pi\)
0.143583 + 0.989638i \(0.454137\pi\)
\(770\) −49.9645 −1.80059
\(771\) −4.63904 −0.167071
\(772\) −7.54695 −0.271621
\(773\) 15.3892 0.553511 0.276756 0.960940i \(-0.410741\pi\)
0.276756 + 0.960940i \(0.410741\pi\)
\(774\) −57.2727 −2.05863
\(775\) 5.48775 0.197126
\(776\) 125.898 4.51948
\(777\) 8.88884 0.318885
\(778\) 46.9120 1.68188
\(779\) 3.08985 0.110705
\(780\) −25.7367 −0.921523
\(781\) 9.40879 0.336673
\(782\) −23.7566 −0.849533
\(783\) −8.63423 −0.308562
\(784\) −11.2234 −0.400835
\(785\) 22.7875 0.813321
\(786\) 28.5837 1.01955
\(787\) −41.2252 −1.46952 −0.734761 0.678327i \(-0.762705\pi\)
−0.734761 + 0.678327i \(0.762705\pi\)
\(788\) 49.1775 1.75188
\(789\) −2.93285 −0.104412
\(790\) −121.986 −4.34006
\(791\) 12.9859 0.461726
\(792\) 38.9062 1.38247
\(793\) 18.9874 0.674264
\(794\) −38.7540 −1.37533
\(795\) −4.35103 −0.154315
\(796\) −15.7243 −0.557334
\(797\) −29.2361 −1.03560 −0.517798 0.855503i \(-0.673248\pi\)
−0.517798 + 0.855503i \(0.673248\pi\)
\(798\) 10.0736 0.356601
\(799\) 36.9790 1.30822
\(800\) −75.3672 −2.66463
\(801\) 25.6944 0.907868
\(802\) 26.2027 0.925251
\(803\) 10.8943 0.384451
\(804\) −11.8002 −0.416160
\(805\) 16.3951 0.577853
\(806\) 3.58642 0.126326
\(807\) 5.67799 0.199875
\(808\) 101.571 3.57326
\(809\) −12.4998 −0.439470 −0.219735 0.975560i \(-0.570519\pi\)
−0.219735 + 0.975560i \(0.570519\pi\)
\(810\) 39.8803 1.40125
\(811\) −33.4708 −1.17532 −0.587660 0.809108i \(-0.699951\pi\)
−0.587660 + 0.809108i \(0.699951\pi\)
\(812\) 24.2487 0.850961
\(813\) 13.8843 0.486944
\(814\) −28.4902 −0.998580
\(815\) −8.89761 −0.311670
\(816\) −33.1247 −1.15960
\(817\) 19.4210 0.679456
\(818\) 28.1454 0.984080
\(819\) −11.7282 −0.409816
\(820\) 24.6495 0.860798
\(821\) −38.9331 −1.35878 −0.679388 0.733779i \(-0.737755\pi\)
−0.679388 + 0.733779i \(0.737755\pi\)
\(822\) 4.78585 0.166926
\(823\) 21.3407 0.743889 0.371944 0.928255i \(-0.378691\pi\)
0.371944 + 0.928255i \(0.378691\pi\)
\(824\) 81.2799 2.83152
\(825\) −13.2562 −0.461523
\(826\) −42.3631 −1.47400
\(827\) 35.2637 1.22624 0.613120 0.789990i \(-0.289914\pi\)
0.613120 + 0.789990i \(0.289914\pi\)
\(828\) −22.0052 −0.764733
\(829\) 44.0741 1.53076 0.765379 0.643580i \(-0.222552\pi\)
0.765379 + 0.643580i \(0.222552\pi\)
\(830\) −131.782 −4.57421
\(831\) −9.37321 −0.325153
\(832\) −12.5626 −0.435530
\(833\) −5.90376 −0.204553
\(834\) −0.0476627 −0.00165042
\(835\) −16.7627 −0.580097
\(836\) −22.7402 −0.786488
\(837\) 2.80840 0.0970726
\(838\) −44.4429 −1.53525
\(839\) −25.4543 −0.878779 −0.439389 0.898297i \(-0.644805\pi\)
−0.439389 + 0.898297i \(0.644805\pi\)
\(840\) 46.6233 1.60866
\(841\) −24.5136 −0.845298
\(842\) −46.6328 −1.60707
\(843\) 3.31489 0.114171
\(844\) 17.0958 0.588461
\(845\) 32.3833 1.11402
\(846\) 48.6335 1.67206
\(847\) 14.5899 0.501316
\(848\) −14.7750 −0.507377
\(849\) −12.8782 −0.441978
\(850\) −99.8776 −3.42577
\(851\) 9.34865 0.320468
\(852\) −15.1331 −0.518452
\(853\) −2.16771 −0.0742210 −0.0371105 0.999311i \(-0.511815\pi\)
−0.0371105 + 0.999311i \(0.511815\pi\)
\(854\) −59.2882 −2.02880
\(855\) −18.8762 −0.645553
\(856\) −63.3941 −2.16677
\(857\) −4.45040 −0.152023 −0.0760114 0.997107i \(-0.524219\pi\)
−0.0760114 + 0.997107i \(0.524219\pi\)
\(858\) −8.66336 −0.295762
\(859\) 25.8007 0.880309 0.440155 0.897922i \(-0.354924\pi\)
0.440155 + 0.897922i \(0.354924\pi\)
\(860\) 154.933 5.28316
\(861\) −2.58875 −0.0882245
\(862\) −57.2817 −1.95102
\(863\) 31.8885 1.08550 0.542748 0.839896i \(-0.317384\pi\)
0.542748 + 0.839896i \(0.317384\pi\)
\(864\) −38.5698 −1.31217
\(865\) −61.0773 −2.07669
\(866\) −76.1644 −2.58817
\(867\) −4.68120 −0.158982
\(868\) −7.88721 −0.267709
\(869\) −28.9203 −0.981053
\(870\) 14.8684 0.504085
\(871\) −6.61453 −0.224125
\(872\) −68.6425 −2.32453
\(873\) 42.7056 1.44537
\(874\) 10.5947 0.358371
\(875\) 25.6614 0.867515
\(876\) −17.5224 −0.592027
\(877\) −14.0514 −0.474483 −0.237241 0.971451i \(-0.576243\pi\)
−0.237241 + 0.971451i \(0.576243\pi\)
\(878\) 57.5459 1.94208
\(879\) 3.51128 0.118432
\(880\) −73.2713 −2.46997
\(881\) 19.0071 0.640366 0.320183 0.947356i \(-0.396256\pi\)
0.320183 + 0.947356i \(0.396256\pi\)
\(882\) −7.76442 −0.261442
\(883\) 14.1755 0.477044 0.238522 0.971137i \(-0.423337\pi\)
0.238522 + 0.971137i \(0.423337\pi\)
\(884\) −45.9722 −1.54621
\(885\) −18.2946 −0.614967
\(886\) 49.0406 1.64755
\(887\) 38.8125 1.30320 0.651598 0.758564i \(-0.274099\pi\)
0.651598 + 0.758564i \(0.274099\pi\)
\(888\) 26.5850 0.892136
\(889\) 29.9351 1.00399
\(890\) −98.6902 −3.30810
\(891\) 9.45479 0.316747
\(892\) −47.4451 −1.58858
\(893\) −16.4915 −0.551867
\(894\) 13.7890 0.461172
\(895\) 10.1293 0.338585
\(896\) −6.25069 −0.208821
\(897\) 2.84276 0.0949171
\(898\) −62.4668 −2.08454
\(899\) −1.45925 −0.0486688
\(900\) −92.5143 −3.08381
\(901\) −7.77201 −0.258923
\(902\) 8.29738 0.276272
\(903\) −16.2714 −0.541480
\(904\) 38.8387 1.29176
\(905\) −28.5458 −0.948895
\(906\) −6.13659 −0.203874
\(907\) −29.5282 −0.980468 −0.490234 0.871591i \(-0.663089\pi\)
−0.490234 + 0.871591i \(0.663089\pi\)
\(908\) 82.9767 2.75368
\(909\) 34.4537 1.14276
\(910\) 45.0470 1.49329
\(911\) 5.98340 0.198239 0.0991194 0.995076i \(-0.468397\pi\)
0.0991194 + 0.995076i \(0.468397\pi\)
\(912\) 14.7726 0.489170
\(913\) −31.2427 −1.03398
\(914\) −51.7383 −1.71135
\(915\) −25.6038 −0.846435
\(916\) −65.7878 −2.17369
\(917\) −35.2363 −1.16361
\(918\) −51.1132 −1.68699
\(919\) 14.1985 0.468366 0.234183 0.972193i \(-0.424759\pi\)
0.234183 + 0.972193i \(0.424759\pi\)
\(920\) 49.0351 1.61664
\(921\) 21.5002 0.708457
\(922\) −99.8214 −3.28744
\(923\) −8.48279 −0.279214
\(924\) 19.0524 0.626777
\(925\) 39.3037 1.29230
\(926\) 42.1142 1.38396
\(927\) 27.5707 0.905542
\(928\) 20.0410 0.657877
\(929\) 20.5986 0.675819 0.337909 0.941179i \(-0.390280\pi\)
0.337909 + 0.941179i \(0.390280\pi\)
\(930\) −4.83614 −0.158583
\(931\) 2.63290 0.0862896
\(932\) 15.4140 0.504904
\(933\) 12.2655 0.401553
\(934\) 22.5531 0.737959
\(935\) −38.5424 −1.26047
\(936\) −35.0771 −1.14653
\(937\) −24.9845 −0.816207 −0.408103 0.912936i \(-0.633810\pi\)
−0.408103 + 0.912936i \(0.633810\pi\)
\(938\) 20.6538 0.674372
\(939\) −11.6311 −0.379567
\(940\) −131.562 −4.29109
\(941\) −54.8706 −1.78873 −0.894366 0.447337i \(-0.852373\pi\)
−0.894366 + 0.447337i \(0.852373\pi\)
\(942\) −12.3374 −0.401975
\(943\) −2.72267 −0.0886623
\(944\) −62.1241 −2.02197
\(945\) 35.2748 1.14749
\(946\) 52.1526 1.69563
\(947\) −17.8703 −0.580706 −0.290353 0.956920i \(-0.593773\pi\)
−0.290353 + 0.956920i \(0.593773\pi\)
\(948\) 46.5154 1.51075
\(949\) −9.82208 −0.318838
\(950\) 44.5423 1.44514
\(951\) 12.9887 0.421188
\(952\) 83.2808 2.69915
\(953\) −10.1087 −0.327454 −0.163727 0.986506i \(-0.552352\pi\)
−0.163727 + 0.986506i \(0.552352\pi\)
\(954\) −10.2215 −0.330932
\(955\) 93.9567 3.04037
\(956\) 85.5605 2.76722
\(957\) 3.52498 0.113946
\(958\) −10.4013 −0.336051
\(959\) −5.89972 −0.190512
\(960\) 16.9402 0.546742
\(961\) −30.5254 −0.984689
\(962\) 25.6862 0.828156
\(963\) −21.5038 −0.692949
\(964\) 82.7707 2.66587
\(965\) 5.70453 0.183635
\(966\) −8.87652 −0.285597
\(967\) −6.79599 −0.218544 −0.109272 0.994012i \(-0.534852\pi\)
−0.109272 + 0.994012i \(0.534852\pi\)
\(968\) 43.6360 1.40252
\(969\) 7.77073 0.249632
\(970\) −164.029 −5.26664
\(971\) 16.8683 0.541329 0.270664 0.962674i \(-0.412757\pi\)
0.270664 + 0.962674i \(0.412757\pi\)
\(972\) −73.4635 −2.35634
\(973\) 0.0587558 0.00188363
\(974\) −38.8506 −1.24485
\(975\) 11.9516 0.382756
\(976\) −86.9443 −2.78302
\(977\) −36.4954 −1.16759 −0.583796 0.811900i \(-0.698433\pi\)
−0.583796 + 0.811900i \(0.698433\pi\)
\(978\) 4.81727 0.154039
\(979\) −23.3974 −0.747784
\(980\) 21.0041 0.670952
\(981\) −23.2841 −0.743403
\(982\) −35.8972 −1.14553
\(983\) 13.0504 0.416242 0.208121 0.978103i \(-0.433265\pi\)
0.208121 + 0.978103i \(0.433265\pi\)
\(984\) −7.74253 −0.246823
\(985\) −37.1719 −1.18439
\(986\) 26.5586 0.845797
\(987\) 13.8170 0.439800
\(988\) 20.5022 0.652261
\(989\) −17.1132 −0.544167
\(990\) −50.6896 −1.61102
\(991\) 14.0462 0.446193 0.223096 0.974796i \(-0.428384\pi\)
0.223096 + 0.974796i \(0.428384\pi\)
\(992\) −6.51860 −0.206966
\(993\) −4.36542 −0.138532
\(994\) 26.4875 0.840132
\(995\) 11.8856 0.376798
\(996\) 50.2508 1.59226
\(997\) −39.4626 −1.24979 −0.624896 0.780708i \(-0.714859\pi\)
−0.624896 + 0.780708i \(0.714859\pi\)
\(998\) −92.7637 −2.93638
\(999\) 20.1140 0.636379
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.1.8 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.8 259 1.1 even 1 trivial