Properties

Label 6037.2.a.b.1.12
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 1.12
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.56682 q^{2} +2.69132 q^{3} +4.58858 q^{4} +1.90137 q^{5} -6.90815 q^{6} -1.37100 q^{7} -6.64441 q^{8} +4.24322 q^{9} +O(q^{10})\) \(q-2.56682 q^{2} +2.69132 q^{3} +4.58858 q^{4} +1.90137 q^{5} -6.90815 q^{6} -1.37100 q^{7} -6.64441 q^{8} +4.24322 q^{9} -4.88048 q^{10} -2.14344 q^{11} +12.3493 q^{12} +6.04183 q^{13} +3.51912 q^{14} +5.11720 q^{15} +7.87787 q^{16} +4.83137 q^{17} -10.8916 q^{18} -2.20557 q^{19} +8.72457 q^{20} -3.68982 q^{21} +5.50184 q^{22} -0.879951 q^{23} -17.8823 q^{24} -1.38480 q^{25} -15.5083 q^{26} +3.34591 q^{27} -6.29096 q^{28} +2.12672 q^{29} -13.1349 q^{30} +7.97686 q^{31} -6.93227 q^{32} -5.76870 q^{33} -12.4013 q^{34} -2.60679 q^{35} +19.4703 q^{36} -1.36540 q^{37} +5.66131 q^{38} +16.2605 q^{39} -12.6335 q^{40} +2.73926 q^{41} +9.47110 q^{42} +1.23490 q^{43} -9.83535 q^{44} +8.06793 q^{45} +2.25868 q^{46} +8.84089 q^{47} +21.2019 q^{48} -5.12035 q^{49} +3.55453 q^{50} +13.0028 q^{51} +27.7234 q^{52} -6.94173 q^{53} -8.58835 q^{54} -4.07548 q^{55} +9.10952 q^{56} -5.93590 q^{57} -5.45891 q^{58} +14.3717 q^{59} +23.4806 q^{60} +8.87593 q^{61} -20.4752 q^{62} -5.81747 q^{63} +2.03816 q^{64} +11.4877 q^{65} +14.8072 q^{66} -8.94665 q^{67} +22.1691 q^{68} -2.36823 q^{69} +6.69115 q^{70} +3.40699 q^{71} -28.1937 q^{72} -0.293088 q^{73} +3.50474 q^{74} -3.72693 q^{75} -10.1204 q^{76} +2.93867 q^{77} -41.7378 q^{78} -0.569011 q^{79} +14.9787 q^{80} -3.72474 q^{81} -7.03119 q^{82} +0.837098 q^{83} -16.9310 q^{84} +9.18621 q^{85} -3.16977 q^{86} +5.72369 q^{87} +14.2419 q^{88} -4.33353 q^{89} -20.7089 q^{90} -8.28337 q^{91} -4.03772 q^{92} +21.4683 q^{93} -22.6930 q^{94} -4.19360 q^{95} -18.6570 q^{96} -2.53026 q^{97} +13.1430 q^{98} -9.09510 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56682 −1.81502 −0.907509 0.420033i \(-0.862018\pi\)
−0.907509 + 0.420033i \(0.862018\pi\)
\(3\) 2.69132 1.55384 0.776918 0.629602i \(-0.216782\pi\)
0.776918 + 0.629602i \(0.216782\pi\)
\(4\) 4.58858 2.29429
\(5\) 1.90137 0.850318 0.425159 0.905119i \(-0.360218\pi\)
0.425159 + 0.905119i \(0.360218\pi\)
\(6\) −6.90815 −2.82024
\(7\) −1.37100 −0.518191 −0.259096 0.965852i \(-0.583424\pi\)
−0.259096 + 0.965852i \(0.583424\pi\)
\(8\) −6.64441 −2.34915
\(9\) 4.24322 1.41441
\(10\) −4.88048 −1.54334
\(11\) −2.14344 −0.646273 −0.323136 0.946352i \(-0.604737\pi\)
−0.323136 + 0.946352i \(0.604737\pi\)
\(12\) 12.3493 3.56495
\(13\) 6.04183 1.67570 0.837851 0.545899i \(-0.183812\pi\)
0.837851 + 0.545899i \(0.183812\pi\)
\(14\) 3.51912 0.940526
\(15\) 5.11720 1.32125
\(16\) 7.87787 1.96947
\(17\) 4.83137 1.17178 0.585889 0.810391i \(-0.300745\pi\)
0.585889 + 0.810391i \(0.300745\pi\)
\(18\) −10.8916 −2.56717
\(19\) −2.20557 −0.505992 −0.252996 0.967467i \(-0.581416\pi\)
−0.252996 + 0.967467i \(0.581416\pi\)
\(20\) 8.72457 1.95087
\(21\) −3.68982 −0.805184
\(22\) 5.50184 1.17300
\(23\) −0.879951 −0.183482 −0.0917412 0.995783i \(-0.529243\pi\)
−0.0917412 + 0.995783i \(0.529243\pi\)
\(24\) −17.8823 −3.65020
\(25\) −1.38480 −0.276959
\(26\) −15.5083 −3.04143
\(27\) 3.34591 0.643920
\(28\) −6.29096 −1.18888
\(29\) 2.12672 0.394922 0.197461 0.980311i \(-0.436730\pi\)
0.197461 + 0.980311i \(0.436730\pi\)
\(30\) −13.1349 −2.39810
\(31\) 7.97686 1.43269 0.716343 0.697748i \(-0.245815\pi\)
0.716343 + 0.697748i \(0.245815\pi\)
\(32\) −6.93227 −1.22546
\(33\) −5.76870 −1.00420
\(34\) −12.4013 −2.12680
\(35\) −2.60679 −0.440627
\(36\) 19.4703 3.24506
\(37\) −1.36540 −0.224471 −0.112235 0.993682i \(-0.535801\pi\)
−0.112235 + 0.993682i \(0.535801\pi\)
\(38\) 5.66131 0.918385
\(39\) 16.2605 2.60377
\(40\) −12.6335 −1.99753
\(41\) 2.73926 0.427800 0.213900 0.976856i \(-0.431383\pi\)
0.213900 + 0.976856i \(0.431383\pi\)
\(42\) 9.47110 1.46142
\(43\) 1.23490 0.188320 0.0941602 0.995557i \(-0.469983\pi\)
0.0941602 + 0.995557i \(0.469983\pi\)
\(44\) −9.83535 −1.48274
\(45\) 8.06793 1.20270
\(46\) 2.25868 0.333024
\(47\) 8.84089 1.28958 0.644788 0.764362i \(-0.276946\pi\)
0.644788 + 0.764362i \(0.276946\pi\)
\(48\) 21.2019 3.06023
\(49\) −5.12035 −0.731478
\(50\) 3.55453 0.502686
\(51\) 13.0028 1.82075
\(52\) 27.7234 3.84454
\(53\) −6.94173 −0.953520 −0.476760 0.879034i \(-0.658189\pi\)
−0.476760 + 0.879034i \(0.658189\pi\)
\(54\) −8.58835 −1.16873
\(55\) −4.07548 −0.549537
\(56\) 9.10952 1.21731
\(57\) −5.93590 −0.786229
\(58\) −5.45891 −0.716791
\(59\) 14.3717 1.87104 0.935519 0.353276i \(-0.114932\pi\)
0.935519 + 0.353276i \(0.114932\pi\)
\(60\) 23.4806 3.03134
\(61\) 8.87593 1.13645 0.568223 0.822874i \(-0.307631\pi\)
0.568223 + 0.822874i \(0.307631\pi\)
\(62\) −20.4752 −2.60035
\(63\) −5.81747 −0.732933
\(64\) 2.03816 0.254770
\(65\) 11.4877 1.42488
\(66\) 14.8072 1.82264
\(67\) −8.94665 −1.09301 −0.546503 0.837457i \(-0.684041\pi\)
−0.546503 + 0.837457i \(0.684041\pi\)
\(68\) 22.1691 2.68840
\(69\) −2.36823 −0.285102
\(70\) 6.69115 0.799746
\(71\) 3.40699 0.404335 0.202168 0.979351i \(-0.435201\pi\)
0.202168 + 0.979351i \(0.435201\pi\)
\(72\) −28.1937 −3.32266
\(73\) −0.293088 −0.0343034 −0.0171517 0.999853i \(-0.505460\pi\)
−0.0171517 + 0.999853i \(0.505460\pi\)
\(74\) 3.50474 0.407418
\(75\) −3.72693 −0.430349
\(76\) −10.1204 −1.16089
\(77\) 2.93867 0.334893
\(78\) −41.7378 −4.72588
\(79\) −0.569011 −0.0640187 −0.0320093 0.999488i \(-0.510191\pi\)
−0.0320093 + 0.999488i \(0.510191\pi\)
\(80\) 14.9787 1.67467
\(81\) −3.72474 −0.413860
\(82\) −7.03119 −0.776465
\(83\) 0.837098 0.0918834 0.0459417 0.998944i \(-0.485371\pi\)
0.0459417 + 0.998944i \(0.485371\pi\)
\(84\) −16.9310 −1.84732
\(85\) 9.18621 0.996385
\(86\) −3.16977 −0.341805
\(87\) 5.72369 0.613644
\(88\) 14.2419 1.51819
\(89\) −4.33353 −0.459353 −0.229677 0.973267i \(-0.573767\pi\)
−0.229677 + 0.973267i \(0.573767\pi\)
\(90\) −20.7089 −2.18291
\(91\) −8.28337 −0.868334
\(92\) −4.03772 −0.420962
\(93\) 21.4683 2.22616
\(94\) −22.6930 −2.34060
\(95\) −4.19360 −0.430255
\(96\) −18.6570 −1.90417
\(97\) −2.53026 −0.256909 −0.128455 0.991715i \(-0.541002\pi\)
−0.128455 + 0.991715i \(0.541002\pi\)
\(98\) 13.1430 1.32765
\(99\) −9.09510 −0.914092
\(100\) −6.35424 −0.635424
\(101\) 0.658159 0.0654893 0.0327447 0.999464i \(-0.489575\pi\)
0.0327447 + 0.999464i \(0.489575\pi\)
\(102\) −33.3758 −3.30470
\(103\) −7.45126 −0.734194 −0.367097 0.930183i \(-0.619648\pi\)
−0.367097 + 0.930183i \(0.619648\pi\)
\(104\) −40.1444 −3.93648
\(105\) −7.01570 −0.684662
\(106\) 17.8182 1.73065
\(107\) 4.68313 0.452735 0.226368 0.974042i \(-0.427315\pi\)
0.226368 + 0.974042i \(0.427315\pi\)
\(108\) 15.3529 1.47734
\(109\) −8.80386 −0.843256 −0.421628 0.906769i \(-0.638541\pi\)
−0.421628 + 0.906769i \(0.638541\pi\)
\(110\) 10.4610 0.997420
\(111\) −3.67474 −0.348791
\(112\) −10.8006 −1.02056
\(113\) 6.00184 0.564606 0.282303 0.959325i \(-0.408902\pi\)
0.282303 + 0.959325i \(0.408902\pi\)
\(114\) 15.2364 1.42702
\(115\) −1.67311 −0.156018
\(116\) 9.75862 0.906065
\(117\) 25.6368 2.37012
\(118\) −36.8896 −3.39597
\(119\) −6.62383 −0.607205
\(120\) −34.0008 −3.10383
\(121\) −6.40565 −0.582332
\(122\) −22.7829 −2.06267
\(123\) 7.37223 0.664731
\(124\) 36.6024 3.28699
\(125\) −12.1399 −1.08582
\(126\) 14.9324 1.33029
\(127\) 0.660547 0.0586141 0.0293070 0.999570i \(-0.490670\pi\)
0.0293070 + 0.999570i \(0.490670\pi\)
\(128\) 8.63294 0.763052
\(129\) 3.32351 0.292619
\(130\) −29.4870 −2.58618
\(131\) −1.22830 −0.107317 −0.0536584 0.998559i \(-0.517088\pi\)
−0.0536584 + 0.998559i \(0.517088\pi\)
\(132\) −26.4701 −2.30393
\(133\) 3.02385 0.262201
\(134\) 22.9645 1.98383
\(135\) 6.36180 0.547537
\(136\) −32.1016 −2.75269
\(137\) 11.0761 0.946295 0.473148 0.880983i \(-0.343118\pi\)
0.473148 + 0.880983i \(0.343118\pi\)
\(138\) 6.07883 0.517465
\(139\) −3.23645 −0.274512 −0.137256 0.990536i \(-0.543828\pi\)
−0.137256 + 0.990536i \(0.543828\pi\)
\(140\) −11.9614 −1.01093
\(141\) 23.7937 2.00379
\(142\) −8.74514 −0.733876
\(143\) −12.9503 −1.08296
\(144\) 33.4275 2.78563
\(145\) 4.04368 0.335809
\(146\) 0.752305 0.0622612
\(147\) −13.7805 −1.13660
\(148\) −6.26525 −0.515000
\(149\) −10.3101 −0.844640 −0.422320 0.906447i \(-0.638784\pi\)
−0.422320 + 0.906447i \(0.638784\pi\)
\(150\) 9.56638 0.781091
\(151\) 21.7952 1.77367 0.886833 0.462090i \(-0.152900\pi\)
0.886833 + 0.462090i \(0.152900\pi\)
\(152\) 14.6547 1.18865
\(153\) 20.5006 1.65737
\(154\) −7.54305 −0.607836
\(155\) 15.1669 1.21824
\(156\) 74.6126 5.97379
\(157\) −19.0156 −1.51761 −0.758806 0.651317i \(-0.774217\pi\)
−0.758806 + 0.651317i \(0.774217\pi\)
\(158\) 1.46055 0.116195
\(159\) −18.6824 −1.48161
\(160\) −13.1808 −1.04203
\(161\) 1.20642 0.0950790
\(162\) 9.56075 0.751164
\(163\) 20.6691 1.61893 0.809463 0.587171i \(-0.199759\pi\)
0.809463 + 0.587171i \(0.199759\pi\)
\(164\) 12.5693 0.981497
\(165\) −10.9684 −0.853891
\(166\) −2.14868 −0.166770
\(167\) 9.00270 0.696650 0.348325 0.937374i \(-0.386751\pi\)
0.348325 + 0.937374i \(0.386751\pi\)
\(168\) 24.5167 1.89150
\(169\) 23.5037 1.80798
\(170\) −23.5794 −1.80846
\(171\) −9.35872 −0.715679
\(172\) 5.66643 0.432061
\(173\) 15.7179 1.19501 0.597505 0.801865i \(-0.296159\pi\)
0.597505 + 0.801865i \(0.296159\pi\)
\(174\) −14.6917 −1.11378
\(175\) 1.89856 0.143518
\(176\) −16.8858 −1.27281
\(177\) 38.6789 2.90729
\(178\) 11.1234 0.833734
\(179\) −4.33605 −0.324092 −0.162046 0.986783i \(-0.551809\pi\)
−0.162046 + 0.986783i \(0.551809\pi\)
\(180\) 37.0203 2.75933
\(181\) 7.03983 0.523267 0.261633 0.965167i \(-0.415739\pi\)
0.261633 + 0.965167i \(0.415739\pi\)
\(182\) 21.2619 1.57604
\(183\) 23.8880 1.76585
\(184\) 5.84676 0.431029
\(185\) −2.59613 −0.190871
\(186\) −55.1053 −4.04052
\(187\) −10.3558 −0.757289
\(188\) 40.5671 2.95866
\(189\) −4.58725 −0.333674
\(190\) 10.7642 0.780919
\(191\) −16.8139 −1.21661 −0.608305 0.793703i \(-0.708150\pi\)
−0.608305 + 0.793703i \(0.708150\pi\)
\(192\) 5.48535 0.395871
\(193\) −6.48067 −0.466489 −0.233244 0.972418i \(-0.574934\pi\)
−0.233244 + 0.972418i \(0.574934\pi\)
\(194\) 6.49473 0.466295
\(195\) 30.9172 2.21403
\(196\) −23.4951 −1.67822
\(197\) 20.8090 1.48258 0.741289 0.671186i \(-0.234215\pi\)
0.741289 + 0.671186i \(0.234215\pi\)
\(198\) 23.3455 1.65909
\(199\) 12.1650 0.862352 0.431176 0.902268i \(-0.358099\pi\)
0.431176 + 0.902268i \(0.358099\pi\)
\(200\) 9.20116 0.650620
\(201\) −24.0783 −1.69835
\(202\) −1.68938 −0.118864
\(203\) −2.91574 −0.204645
\(204\) 59.6642 4.17733
\(205\) 5.20834 0.363766
\(206\) 19.1261 1.33258
\(207\) −3.73383 −0.259519
\(208\) 47.5967 3.30024
\(209\) 4.72752 0.327009
\(210\) 18.0081 1.24267
\(211\) 7.42566 0.511204 0.255602 0.966782i \(-0.417726\pi\)
0.255602 + 0.966782i \(0.417726\pi\)
\(212\) −31.8526 −2.18765
\(213\) 9.16931 0.628271
\(214\) −12.0208 −0.821722
\(215\) 2.34800 0.160132
\(216\) −22.2316 −1.51267
\(217\) −10.9363 −0.742405
\(218\) 22.5979 1.53053
\(219\) −0.788795 −0.0533018
\(220\) −18.7006 −1.26080
\(221\) 29.1903 1.96355
\(222\) 9.43240 0.633061
\(223\) −2.91726 −0.195354 −0.0976770 0.995218i \(-0.531141\pi\)
−0.0976770 + 0.995218i \(0.531141\pi\)
\(224\) 9.50418 0.635024
\(225\) −5.87600 −0.391733
\(226\) −15.4057 −1.02477
\(227\) −17.6984 −1.17469 −0.587343 0.809338i \(-0.699826\pi\)
−0.587343 + 0.809338i \(0.699826\pi\)
\(228\) −27.2373 −1.80384
\(229\) 10.9722 0.725066 0.362533 0.931971i \(-0.381912\pi\)
0.362533 + 0.931971i \(0.381912\pi\)
\(230\) 4.29458 0.283176
\(231\) 7.90891 0.520368
\(232\) −14.1308 −0.927733
\(233\) 26.8740 1.76057 0.880286 0.474444i \(-0.157351\pi\)
0.880286 + 0.474444i \(0.157351\pi\)
\(234\) −65.8051 −4.30182
\(235\) 16.8098 1.09655
\(236\) 65.9457 4.29270
\(237\) −1.53139 −0.0994746
\(238\) 17.0022 1.10209
\(239\) 15.1902 0.982575 0.491288 0.870997i \(-0.336526\pi\)
0.491288 + 0.870997i \(0.336526\pi\)
\(240\) 40.3126 2.60217
\(241\) −8.37058 −0.539196 −0.269598 0.962973i \(-0.586891\pi\)
−0.269598 + 0.962973i \(0.586891\pi\)
\(242\) 16.4422 1.05694
\(243\) −20.0622 −1.28699
\(244\) 40.7279 2.60734
\(245\) −9.73567 −0.621989
\(246\) −18.9232 −1.20650
\(247\) −13.3257 −0.847892
\(248\) −53.0015 −3.36560
\(249\) 2.25290 0.142772
\(250\) 31.1608 1.97078
\(251\) −14.4246 −0.910470 −0.455235 0.890371i \(-0.650445\pi\)
−0.455235 + 0.890371i \(0.650445\pi\)
\(252\) −26.6939 −1.68156
\(253\) 1.88613 0.118580
\(254\) −1.69551 −0.106386
\(255\) 24.7231 1.54822
\(256\) −26.2356 −1.63972
\(257\) −24.2749 −1.51423 −0.757114 0.653283i \(-0.773391\pi\)
−0.757114 + 0.653283i \(0.773391\pi\)
\(258\) −8.53087 −0.531109
\(259\) 1.87197 0.116319
\(260\) 52.7124 3.26908
\(261\) 9.02415 0.558581
\(262\) 3.15282 0.194782
\(263\) 18.5427 1.14339 0.571697 0.820465i \(-0.306285\pi\)
0.571697 + 0.820465i \(0.306285\pi\)
\(264\) 38.3296 2.35902
\(265\) −13.1988 −0.810795
\(266\) −7.76168 −0.475899
\(267\) −11.6629 −0.713760
\(268\) −41.0524 −2.50767
\(269\) −7.11462 −0.433786 −0.216893 0.976195i \(-0.569592\pi\)
−0.216893 + 0.976195i \(0.569592\pi\)
\(270\) −16.3296 −0.993789
\(271\) 18.0415 1.09594 0.547970 0.836498i \(-0.315401\pi\)
0.547970 + 0.836498i \(0.315401\pi\)
\(272\) 38.0609 2.30778
\(273\) −22.2932 −1.34925
\(274\) −28.4304 −1.71754
\(275\) 2.96823 0.178991
\(276\) −10.8668 −0.654105
\(277\) −16.8741 −1.01386 −0.506932 0.861986i \(-0.669221\pi\)
−0.506932 + 0.861986i \(0.669221\pi\)
\(278\) 8.30738 0.498244
\(279\) 33.8476 2.02640
\(280\) 17.3206 1.03510
\(281\) −1.59345 −0.0950571 −0.0475286 0.998870i \(-0.515135\pi\)
−0.0475286 + 0.998870i \(0.515135\pi\)
\(282\) −61.0741 −3.63691
\(283\) −20.0622 −1.19257 −0.596287 0.802771i \(-0.703358\pi\)
−0.596287 + 0.802771i \(0.703358\pi\)
\(284\) 15.6332 0.927662
\(285\) −11.2863 −0.668545
\(286\) 33.2412 1.96559
\(287\) −3.75553 −0.221682
\(288\) −29.4152 −1.73330
\(289\) 6.34211 0.373065
\(290\) −10.3794 −0.609500
\(291\) −6.80975 −0.399195
\(292\) −1.34486 −0.0787018
\(293\) −14.2969 −0.835232 −0.417616 0.908624i \(-0.637134\pi\)
−0.417616 + 0.908624i \(0.637134\pi\)
\(294\) 35.3721 2.06294
\(295\) 27.3259 1.59098
\(296\) 9.07229 0.527316
\(297\) −7.17176 −0.416148
\(298\) 26.4643 1.53304
\(299\) −5.31651 −0.307462
\(300\) −17.1013 −0.987345
\(301\) −1.69305 −0.0975859
\(302\) −55.9443 −3.21923
\(303\) 1.77132 0.101760
\(304\) −17.3752 −0.996536
\(305\) 16.8764 0.966341
\(306\) −52.6213 −3.00816
\(307\) 27.3330 1.55998 0.779989 0.625793i \(-0.215225\pi\)
0.779989 + 0.625793i \(0.215225\pi\)
\(308\) 13.4843 0.768340
\(309\) −20.0537 −1.14082
\(310\) −38.9309 −2.21112
\(311\) 34.2429 1.94174 0.970869 0.239613i \(-0.0770205\pi\)
0.970869 + 0.239613i \(0.0770205\pi\)
\(312\) −108.042 −6.11665
\(313\) −11.7966 −0.666785 −0.333393 0.942788i \(-0.608193\pi\)
−0.333393 + 0.942788i \(0.608193\pi\)
\(314\) 48.8097 2.75449
\(315\) −11.0612 −0.623226
\(316\) −2.61095 −0.146877
\(317\) 12.8499 0.721721 0.360861 0.932620i \(-0.382483\pi\)
0.360861 + 0.932620i \(0.382483\pi\)
\(318\) 47.9545 2.68915
\(319\) −4.55851 −0.255227
\(320\) 3.87530 0.216636
\(321\) 12.6038 0.703477
\(322\) −3.09666 −0.172570
\(323\) −10.6559 −0.592911
\(324\) −17.0913 −0.949515
\(325\) −8.36670 −0.464101
\(326\) −53.0538 −2.93838
\(327\) −23.6940 −1.31028
\(328\) −18.2008 −1.00497
\(329\) −12.1209 −0.668247
\(330\) 28.1540 1.54983
\(331\) 23.4672 1.28988 0.644938 0.764235i \(-0.276883\pi\)
0.644938 + 0.764235i \(0.276883\pi\)
\(332\) 3.84109 0.210807
\(333\) −5.79370 −0.317493
\(334\) −23.1083 −1.26443
\(335\) −17.0109 −0.929404
\(336\) −29.0679 −1.58578
\(337\) −13.2298 −0.720671 −0.360335 0.932823i \(-0.617338\pi\)
−0.360335 + 0.932823i \(0.617338\pi\)
\(338\) −60.3298 −3.28151
\(339\) 16.1529 0.877305
\(340\) 42.1516 2.28599
\(341\) −17.0979 −0.925906
\(342\) 24.0222 1.29897
\(343\) 16.6171 0.897236
\(344\) −8.20518 −0.442394
\(345\) −4.50288 −0.242427
\(346\) −40.3451 −2.16896
\(347\) 9.05366 0.486026 0.243013 0.970023i \(-0.421864\pi\)
0.243013 + 0.970023i \(0.421864\pi\)
\(348\) 26.2636 1.40788
\(349\) −9.13038 −0.488738 −0.244369 0.969682i \(-0.578581\pi\)
−0.244369 + 0.969682i \(0.578581\pi\)
\(350\) −4.87327 −0.260487
\(351\) 20.2154 1.07902
\(352\) 14.8589 0.791984
\(353\) −16.2929 −0.867184 −0.433592 0.901109i \(-0.642754\pi\)
−0.433592 + 0.901109i \(0.642754\pi\)
\(354\) −99.2819 −5.27678
\(355\) 6.47795 0.343814
\(356\) −19.8847 −1.05389
\(357\) −17.8269 −0.943497
\(358\) 11.1299 0.588232
\(359\) 20.9286 1.10457 0.552283 0.833656i \(-0.313757\pi\)
0.552283 + 0.833656i \(0.313757\pi\)
\(360\) −53.6066 −2.82532
\(361\) −14.1355 −0.743972
\(362\) −18.0700 −0.949738
\(363\) −17.2397 −0.904848
\(364\) −38.0089 −1.99221
\(365\) −0.557268 −0.0291688
\(366\) −61.3163 −3.20505
\(367\) −19.0853 −0.996245 −0.498123 0.867107i \(-0.665977\pi\)
−0.498123 + 0.867107i \(0.665977\pi\)
\(368\) −6.93214 −0.361363
\(369\) 11.6233 0.605083
\(370\) 6.66381 0.346435
\(371\) 9.51714 0.494105
\(372\) 98.5089 5.10745
\(373\) 0.638680 0.0330696 0.0165348 0.999863i \(-0.494737\pi\)
0.0165348 + 0.999863i \(0.494737\pi\)
\(374\) 26.5814 1.37449
\(375\) −32.6723 −1.68719
\(376\) −58.7425 −3.02941
\(377\) 12.8493 0.661772
\(378\) 11.7747 0.605623
\(379\) −16.1832 −0.831274 −0.415637 0.909531i \(-0.636441\pi\)
−0.415637 + 0.909531i \(0.636441\pi\)
\(380\) −19.2427 −0.987128
\(381\) 1.77775 0.0910767
\(382\) 43.1583 2.20817
\(383\) 19.5900 1.00100 0.500502 0.865735i \(-0.333149\pi\)
0.500502 + 0.865735i \(0.333149\pi\)
\(384\) 23.2340 1.18566
\(385\) 5.58750 0.284765
\(386\) 16.6347 0.846685
\(387\) 5.23995 0.266362
\(388\) −11.6103 −0.589424
\(389\) 20.8032 1.05476 0.527382 0.849628i \(-0.323174\pi\)
0.527382 + 0.849628i \(0.323174\pi\)
\(390\) −79.3590 −4.01850
\(391\) −4.25137 −0.215001
\(392\) 34.0217 1.71835
\(393\) −3.30574 −0.166753
\(394\) −53.4129 −2.69090
\(395\) −1.08190 −0.0544363
\(396\) −41.7336 −2.09719
\(397\) −9.99438 −0.501604 −0.250802 0.968038i \(-0.580694\pi\)
−0.250802 + 0.968038i \(0.580694\pi\)
\(398\) −31.2253 −1.56518
\(399\) 8.13815 0.407417
\(400\) −10.9092 −0.545462
\(401\) −33.6694 −1.68137 −0.840684 0.541526i \(-0.817847\pi\)
−0.840684 + 0.541526i \(0.817847\pi\)
\(402\) 61.8048 3.08254
\(403\) 48.1948 2.40075
\(404\) 3.02001 0.150251
\(405\) −7.08211 −0.351913
\(406\) 7.48420 0.371434
\(407\) 2.92666 0.145069
\(408\) −86.3958 −4.27723
\(409\) 19.8889 0.983444 0.491722 0.870752i \(-0.336368\pi\)
0.491722 + 0.870752i \(0.336368\pi\)
\(410\) −13.3689 −0.660242
\(411\) 29.8094 1.47039
\(412\) −34.1907 −1.68445
\(413\) −19.7037 −0.969555
\(414\) 9.58407 0.471031
\(415\) 1.59163 0.0781301
\(416\) −41.8836 −2.05351
\(417\) −8.71032 −0.426546
\(418\) −12.1347 −0.593527
\(419\) 23.9655 1.17079 0.585395 0.810748i \(-0.300939\pi\)
0.585395 + 0.810748i \(0.300939\pi\)
\(420\) −32.1921 −1.57081
\(421\) 11.8667 0.578349 0.289174 0.957276i \(-0.406619\pi\)
0.289174 + 0.957276i \(0.406619\pi\)
\(422\) −19.0604 −0.927844
\(423\) 37.5138 1.82398
\(424\) 46.1237 2.23997
\(425\) −6.69046 −0.324535
\(426\) −23.5360 −1.14032
\(427\) −12.1689 −0.588897
\(428\) 21.4889 1.03871
\(429\) −34.8535 −1.68274
\(430\) −6.02690 −0.290643
\(431\) 32.5370 1.56725 0.783627 0.621232i \(-0.213368\pi\)
0.783627 + 0.621232i \(0.213368\pi\)
\(432\) 26.3586 1.26818
\(433\) −1.20791 −0.0580484 −0.0290242 0.999579i \(-0.509240\pi\)
−0.0290242 + 0.999579i \(0.509240\pi\)
\(434\) 28.0716 1.34748
\(435\) 10.8829 0.521793
\(436\) −40.3972 −1.93467
\(437\) 1.94079 0.0928408
\(438\) 2.02470 0.0967437
\(439\) −4.93160 −0.235372 −0.117686 0.993051i \(-0.537548\pi\)
−0.117686 + 0.993051i \(0.537548\pi\)
\(440\) 27.0792 1.29095
\(441\) −21.7268 −1.03461
\(442\) −74.9263 −3.56388
\(443\) 15.3256 0.728140 0.364070 0.931372i \(-0.381387\pi\)
0.364070 + 0.931372i \(0.381387\pi\)
\(444\) −16.8618 −0.800226
\(445\) −8.23964 −0.390596
\(446\) 7.48808 0.354571
\(447\) −27.7479 −1.31243
\(448\) −2.79433 −0.132020
\(449\) −10.7969 −0.509536 −0.254768 0.967002i \(-0.581999\pi\)
−0.254768 + 0.967002i \(0.581999\pi\)
\(450\) 15.0826 0.711002
\(451\) −5.87144 −0.276476
\(452\) 27.5399 1.29537
\(453\) 58.6578 2.75599
\(454\) 45.4287 2.13208
\(455\) −15.7498 −0.738360
\(456\) 39.4406 1.84697
\(457\) 27.9278 1.30641 0.653204 0.757182i \(-0.273424\pi\)
0.653204 + 0.757182i \(0.273424\pi\)
\(458\) −28.1638 −1.31601
\(459\) 16.1653 0.754532
\(460\) −7.67720 −0.357951
\(461\) −16.4439 −0.765871 −0.382935 0.923775i \(-0.625087\pi\)
−0.382935 + 0.923775i \(0.625087\pi\)
\(462\) −20.3008 −0.944478
\(463\) −40.2349 −1.86988 −0.934938 0.354812i \(-0.884545\pi\)
−0.934938 + 0.354812i \(0.884545\pi\)
\(464\) 16.7540 0.777787
\(465\) 40.8192 1.89294
\(466\) −68.9807 −3.19547
\(467\) −14.4985 −0.670909 −0.335454 0.942056i \(-0.608890\pi\)
−0.335454 + 0.942056i \(0.608890\pi\)
\(468\) 117.636 5.43775
\(469\) 12.2659 0.566386
\(470\) −43.1477 −1.99026
\(471\) −51.1772 −2.35812
\(472\) −95.4916 −4.39536
\(473\) −2.64694 −0.121706
\(474\) 3.93081 0.180548
\(475\) 3.05426 0.140139
\(476\) −30.3939 −1.39310
\(477\) −29.4553 −1.34866
\(478\) −38.9907 −1.78339
\(479\) −9.10772 −0.416143 −0.208071 0.978114i \(-0.566719\pi\)
−0.208071 + 0.978114i \(0.566719\pi\)
\(480\) −35.4738 −1.61915
\(481\) −8.24952 −0.376146
\(482\) 21.4858 0.978650
\(483\) 3.24686 0.147737
\(484\) −29.3928 −1.33604
\(485\) −4.81096 −0.218455
\(486\) 51.4961 2.33591
\(487\) −11.9093 −0.539662 −0.269831 0.962908i \(-0.586968\pi\)
−0.269831 + 0.962908i \(0.586968\pi\)
\(488\) −58.9754 −2.66969
\(489\) 55.6271 2.51554
\(490\) 24.9897 1.12892
\(491\) −22.5739 −1.01874 −0.509372 0.860546i \(-0.670122\pi\)
−0.509372 + 0.860546i \(0.670122\pi\)
\(492\) 33.8280 1.52508
\(493\) 10.2750 0.462761
\(494\) 34.2046 1.53894
\(495\) −17.2931 −0.777269
\(496\) 62.8407 2.82163
\(497\) −4.67100 −0.209523
\(498\) −5.78280 −0.259133
\(499\) 28.0609 1.25618 0.628090 0.778141i \(-0.283837\pi\)
0.628090 + 0.778141i \(0.283837\pi\)
\(500\) −55.7046 −2.49119
\(501\) 24.2292 1.08248
\(502\) 37.0253 1.65252
\(503\) −3.31337 −0.147736 −0.0738680 0.997268i \(-0.523534\pi\)
−0.0738680 + 0.997268i \(0.523534\pi\)
\(504\) 38.6537 1.72177
\(505\) 1.25140 0.0556867
\(506\) −4.84135 −0.215224
\(507\) 63.2560 2.80930
\(508\) 3.03097 0.134478
\(509\) −16.5201 −0.732239 −0.366119 0.930568i \(-0.619314\pi\)
−0.366119 + 0.930568i \(0.619314\pi\)
\(510\) −63.4597 −2.81004
\(511\) 0.401825 0.0177757
\(512\) 50.0761 2.21307
\(513\) −7.37963 −0.325819
\(514\) 62.3094 2.74835
\(515\) −14.1676 −0.624299
\(516\) 15.2502 0.671352
\(517\) −18.9499 −0.833418
\(518\) −4.80502 −0.211120
\(519\) 42.3020 1.85685
\(520\) −76.3293 −3.34726
\(521\) 14.8787 0.651846 0.325923 0.945396i \(-0.394325\pi\)
0.325923 + 0.945396i \(0.394325\pi\)
\(522\) −23.1634 −1.01383
\(523\) −17.3698 −0.759530 −0.379765 0.925083i \(-0.623995\pi\)
−0.379765 + 0.925083i \(0.623995\pi\)
\(524\) −5.63613 −0.246216
\(525\) 5.10964 0.223003
\(526\) −47.5959 −2.07528
\(527\) 38.5391 1.67879
\(528\) −45.4451 −1.97774
\(529\) −22.2257 −0.966334
\(530\) 33.8789 1.47161
\(531\) 60.9824 2.64641
\(532\) 13.8751 0.601564
\(533\) 16.5501 0.716865
\(534\) 29.9367 1.29549
\(535\) 8.90436 0.384969
\(536\) 59.4452 2.56764
\(537\) −11.6697 −0.503585
\(538\) 18.2620 0.787329
\(539\) 10.9752 0.472734
\(540\) 29.1916 1.25621
\(541\) −27.6955 −1.19072 −0.595361 0.803458i \(-0.702991\pi\)
−0.595361 + 0.803458i \(0.702991\pi\)
\(542\) −46.3092 −1.98915
\(543\) 18.9465 0.813071
\(544\) −33.4923 −1.43597
\(545\) −16.7394 −0.717036
\(546\) 57.2228 2.44891
\(547\) −16.2671 −0.695533 −0.347766 0.937581i \(-0.613060\pi\)
−0.347766 + 0.937581i \(0.613060\pi\)
\(548\) 50.8235 2.17107
\(549\) 37.6625 1.60740
\(550\) −7.61893 −0.324872
\(551\) −4.69063 −0.199828
\(552\) 15.7355 0.669748
\(553\) 0.780116 0.0331739
\(554\) 43.3127 1.84018
\(555\) −6.98703 −0.296583
\(556\) −14.8507 −0.629809
\(557\) −25.0501 −1.06141 −0.530703 0.847558i \(-0.678072\pi\)
−0.530703 + 0.847558i \(0.678072\pi\)
\(558\) −86.8807 −3.67795
\(559\) 7.46105 0.315569
\(560\) −20.5359 −0.867801
\(561\) −27.8707 −1.17670
\(562\) 4.09010 0.172530
\(563\) 42.9879 1.81172 0.905861 0.423574i \(-0.139225\pi\)
0.905861 + 0.423574i \(0.139225\pi\)
\(564\) 109.179 4.59727
\(565\) 11.4117 0.480094
\(566\) 51.4961 2.16454
\(567\) 5.10664 0.214459
\(568\) −22.6375 −0.949846
\(569\) −21.3839 −0.896458 −0.448229 0.893919i \(-0.647945\pi\)
−0.448229 + 0.893919i \(0.647945\pi\)
\(570\) 28.9700 1.21342
\(571\) −13.0658 −0.546787 −0.273394 0.961902i \(-0.588146\pi\)
−0.273394 + 0.961902i \(0.588146\pi\)
\(572\) −59.4235 −2.48462
\(573\) −45.2516 −1.89041
\(574\) 9.63979 0.402357
\(575\) 1.21855 0.0508172
\(576\) 8.64837 0.360349
\(577\) −22.3901 −0.932111 −0.466055 0.884755i \(-0.654325\pi\)
−0.466055 + 0.884755i \(0.654325\pi\)
\(578\) −16.2791 −0.677120
\(579\) −17.4416 −0.724847
\(580\) 18.5547 0.770443
\(581\) −1.14767 −0.0476132
\(582\) 17.4794 0.724546
\(583\) 14.8792 0.616234
\(584\) 1.94740 0.0805839
\(585\) 48.7450 2.01536
\(586\) 36.6975 1.51596
\(587\) −5.02060 −0.207222 −0.103611 0.994618i \(-0.533040\pi\)
−0.103611 + 0.994618i \(0.533040\pi\)
\(588\) −63.2329 −2.60768
\(589\) −17.5935 −0.724928
\(590\) −70.1408 −2.88765
\(591\) 56.0037 2.30368
\(592\) −10.7565 −0.442088
\(593\) 13.6921 0.562269 0.281135 0.959668i \(-0.409289\pi\)
0.281135 + 0.959668i \(0.409289\pi\)
\(594\) 18.4086 0.755316
\(595\) −12.5943 −0.516318
\(596\) −47.3089 −1.93785
\(597\) 32.7399 1.33995
\(598\) 13.6465 0.558049
\(599\) −3.09833 −0.126594 −0.0632972 0.997995i \(-0.520162\pi\)
−0.0632972 + 0.997995i \(0.520162\pi\)
\(600\) 24.7633 1.01096
\(601\) −36.8331 −1.50245 −0.751227 0.660044i \(-0.770537\pi\)
−0.751227 + 0.660044i \(0.770537\pi\)
\(602\) 4.34577 0.177120
\(603\) −37.9626 −1.54596
\(604\) 100.009 4.06930
\(605\) −12.1795 −0.495167
\(606\) −4.54666 −0.184696
\(607\) 5.82139 0.236283 0.118141 0.992997i \(-0.462306\pi\)
0.118141 + 0.992997i \(0.462306\pi\)
\(608\) 15.2896 0.620076
\(609\) −7.84721 −0.317985
\(610\) −43.3188 −1.75393
\(611\) 53.4151 2.16094
\(612\) 94.0683 3.80249
\(613\) −18.6308 −0.752489 −0.376245 0.926520i \(-0.622785\pi\)
−0.376245 + 0.926520i \(0.622785\pi\)
\(614\) −70.1590 −2.83139
\(615\) 14.0173 0.565233
\(616\) −19.5257 −0.786715
\(617\) −38.5096 −1.55034 −0.775170 0.631753i \(-0.782336\pi\)
−0.775170 + 0.631753i \(0.782336\pi\)
\(618\) 51.4744 2.07060
\(619\) 21.5289 0.865319 0.432660 0.901557i \(-0.357575\pi\)
0.432660 + 0.901557i \(0.357575\pi\)
\(620\) 69.5947 2.79499
\(621\) −2.94423 −0.118148
\(622\) −87.8954 −3.52429
\(623\) 5.94129 0.238033
\(624\) 128.098 5.12803
\(625\) −16.1584 −0.646334
\(626\) 30.2799 1.21023
\(627\) 12.7233 0.508119
\(628\) −87.2546 −3.48184
\(629\) −6.59676 −0.263030
\(630\) 28.3920 1.13117
\(631\) −36.9158 −1.46960 −0.734798 0.678286i \(-0.762723\pi\)
−0.734798 + 0.678286i \(0.762723\pi\)
\(632\) 3.78074 0.150390
\(633\) 19.9849 0.794327
\(634\) −32.9833 −1.30994
\(635\) 1.25594 0.0498406
\(636\) −85.7258 −3.39925
\(637\) −30.9363 −1.22574
\(638\) 11.7009 0.463242
\(639\) 14.4566 0.571895
\(640\) 16.4144 0.648836
\(641\) 28.9775 1.14454 0.572272 0.820064i \(-0.306062\pi\)
0.572272 + 0.820064i \(0.306062\pi\)
\(642\) −32.3518 −1.27682
\(643\) 20.8654 0.822853 0.411426 0.911443i \(-0.365031\pi\)
0.411426 + 0.911443i \(0.365031\pi\)
\(644\) 5.53574 0.218139
\(645\) 6.31923 0.248819
\(646\) 27.3518 1.07614
\(647\) −5.75667 −0.226318 −0.113159 0.993577i \(-0.536097\pi\)
−0.113159 + 0.993577i \(0.536097\pi\)
\(648\) 24.7487 0.972222
\(649\) −30.8050 −1.20920
\(650\) 21.4758 0.842351
\(651\) −29.4331 −1.15358
\(652\) 94.8415 3.71428
\(653\) −4.59160 −0.179683 −0.0898415 0.995956i \(-0.528636\pi\)
−0.0898415 + 0.995956i \(0.528636\pi\)
\(654\) 60.8183 2.37819
\(655\) −2.33545 −0.0912534
\(656\) 21.5795 0.842539
\(657\) −1.24364 −0.0485189
\(658\) 31.1122 1.21288
\(659\) 10.0323 0.390805 0.195402 0.980723i \(-0.437399\pi\)
0.195402 + 0.980723i \(0.437399\pi\)
\(660\) −50.3295 −1.95907
\(661\) −0.152534 −0.00593290 −0.00296645 0.999996i \(-0.500944\pi\)
−0.00296645 + 0.999996i \(0.500944\pi\)
\(662\) −60.2362 −2.34115
\(663\) 78.5605 3.05104
\(664\) −5.56202 −0.215848
\(665\) 5.74945 0.222954
\(666\) 14.8714 0.576255
\(667\) −1.87141 −0.0724613
\(668\) 41.3096 1.59831
\(669\) −7.85128 −0.303548
\(670\) 43.6639 1.68688
\(671\) −19.0251 −0.734454
\(672\) 25.5788 0.986724
\(673\) −9.93306 −0.382891 −0.191446 0.981503i \(-0.561318\pi\)
−0.191446 + 0.981503i \(0.561318\pi\)
\(674\) 33.9584 1.30803
\(675\) −4.63340 −0.178340
\(676\) 107.848 4.14802
\(677\) 32.6068 1.25318 0.626591 0.779348i \(-0.284450\pi\)
0.626591 + 0.779348i \(0.284450\pi\)
\(678\) −41.4616 −1.59232
\(679\) 3.46900 0.133128
\(680\) −61.0370 −2.34066
\(681\) −47.6322 −1.82527
\(682\) 43.8874 1.68053
\(683\) −22.2685 −0.852080 −0.426040 0.904704i \(-0.640092\pi\)
−0.426040 + 0.904704i \(0.640092\pi\)
\(684\) −42.9432 −1.64197
\(685\) 21.0598 0.804652
\(686\) −42.6530 −1.62850
\(687\) 29.5299 1.12663
\(688\) 9.72838 0.370891
\(689\) −41.9407 −1.59781
\(690\) 11.5581 0.440009
\(691\) −0.521065 −0.0198222 −0.00991112 0.999951i \(-0.503155\pi\)
−0.00991112 + 0.999951i \(0.503155\pi\)
\(692\) 72.1228 2.74170
\(693\) 12.4694 0.473674
\(694\) −23.2391 −0.882146
\(695\) −6.15368 −0.233422
\(696\) −38.0306 −1.44155
\(697\) 13.2344 0.501287
\(698\) 23.4361 0.887068
\(699\) 72.3265 2.73564
\(700\) 8.71169 0.329271
\(701\) 5.50549 0.207939 0.103970 0.994580i \(-0.466845\pi\)
0.103970 + 0.994580i \(0.466845\pi\)
\(702\) −51.8893 −1.95844
\(703\) 3.01149 0.113580
\(704\) −4.36869 −0.164651
\(705\) 45.2406 1.70386
\(706\) 41.8210 1.57395
\(707\) −0.902340 −0.0339360
\(708\) 177.481 6.67015
\(709\) 42.3712 1.59129 0.795643 0.605766i \(-0.207133\pi\)
0.795643 + 0.605766i \(0.207133\pi\)
\(710\) −16.6277 −0.624028
\(711\) −2.41444 −0.0905485
\(712\) 28.7938 1.07909
\(713\) −7.01924 −0.262873
\(714\) 45.7584 1.71246
\(715\) −24.6233 −0.920861
\(716\) −19.8963 −0.743560
\(717\) 40.8819 1.52676
\(718\) −53.7199 −2.00481
\(719\) 14.2530 0.531549 0.265774 0.964035i \(-0.414372\pi\)
0.265774 + 0.964035i \(0.414372\pi\)
\(720\) 63.5581 2.36867
\(721\) 10.2157 0.380453
\(722\) 36.2832 1.35032
\(723\) −22.5279 −0.837822
\(724\) 32.3028 1.20052
\(725\) −2.94507 −0.109377
\(726\) 44.2512 1.64231
\(727\) −26.6318 −0.987718 −0.493859 0.869542i \(-0.664414\pi\)
−0.493859 + 0.869542i \(0.664414\pi\)
\(728\) 55.0382 2.03985
\(729\) −42.8197 −1.58591
\(730\) 1.43041 0.0529418
\(731\) 5.96625 0.220670
\(732\) 109.612 4.05137
\(733\) 32.7962 1.21136 0.605678 0.795710i \(-0.292902\pi\)
0.605678 + 0.795710i \(0.292902\pi\)
\(734\) 48.9886 1.80820
\(735\) −26.2018 −0.966469
\(736\) 6.10006 0.224851
\(737\) 19.1766 0.706380
\(738\) −29.8349 −1.09824
\(739\) −20.2476 −0.744819 −0.372409 0.928069i \(-0.621468\pi\)
−0.372409 + 0.928069i \(0.621468\pi\)
\(740\) −11.9125 −0.437914
\(741\) −35.8637 −1.31749
\(742\) −24.4288 −0.896810
\(743\) 25.2278 0.925519 0.462759 0.886484i \(-0.346859\pi\)
0.462759 + 0.886484i \(0.346859\pi\)
\(744\) −142.644 −5.22959
\(745\) −19.6034 −0.718213
\(746\) −1.63938 −0.0600219
\(747\) 3.55199 0.129961
\(748\) −47.5182 −1.73744
\(749\) −6.42059 −0.234603
\(750\) 83.8639 3.06228
\(751\) −14.4919 −0.528817 −0.264409 0.964411i \(-0.585177\pi\)
−0.264409 + 0.964411i \(0.585177\pi\)
\(752\) 69.6474 2.53978
\(753\) −38.8211 −1.41472
\(754\) −32.9818 −1.20113
\(755\) 41.4407 1.50818
\(756\) −21.0490 −0.765543
\(757\) −9.74964 −0.354357 −0.177178 0.984179i \(-0.556697\pi\)
−0.177178 + 0.984179i \(0.556697\pi\)
\(758\) 41.5393 1.50878
\(759\) 5.07617 0.184253
\(760\) 27.8640 1.01073
\(761\) −7.60272 −0.275598 −0.137799 0.990460i \(-0.544003\pi\)
−0.137799 + 0.990460i \(0.544003\pi\)
\(762\) −4.56316 −0.165306
\(763\) 12.0701 0.436968
\(764\) −77.1518 −2.79126
\(765\) 38.9791 1.40929
\(766\) −50.2842 −1.81684
\(767\) 86.8315 3.13530
\(768\) −70.6083 −2.54786
\(769\) −38.9700 −1.40530 −0.702648 0.711538i \(-0.747999\pi\)
−0.702648 + 0.711538i \(0.747999\pi\)
\(770\) −14.3421 −0.516854
\(771\) −65.3316 −2.35286
\(772\) −29.7370 −1.07026
\(773\) 46.0818 1.65745 0.828723 0.559659i \(-0.189068\pi\)
0.828723 + 0.559659i \(0.189068\pi\)
\(774\) −13.4500 −0.483451
\(775\) −11.0463 −0.396796
\(776\) 16.8121 0.603519
\(777\) 5.03808 0.180740
\(778\) −53.3981 −1.91442
\(779\) −6.04162 −0.216464
\(780\) 141.866 5.07962
\(781\) −7.30269 −0.261311
\(782\) 10.9125 0.390230
\(783\) 7.11581 0.254298
\(784\) −40.3374 −1.44062
\(785\) −36.1557 −1.29045
\(786\) 8.48526 0.302659
\(787\) −6.72581 −0.239749 −0.119875 0.992789i \(-0.538249\pi\)
−0.119875 + 0.992789i \(0.538249\pi\)
\(788\) 95.4835 3.40146
\(789\) 49.9045 1.77665
\(790\) 2.77704 0.0988027
\(791\) −8.22855 −0.292574
\(792\) 60.4316 2.14734
\(793\) 53.6269 1.90435
\(794\) 25.6538 0.910419
\(795\) −35.5222 −1.25984
\(796\) 55.8199 1.97848
\(797\) 14.0542 0.497827 0.248913 0.968526i \(-0.419927\pi\)
0.248913 + 0.968526i \(0.419927\pi\)
\(798\) −20.8892 −0.739469
\(799\) 42.7136 1.51110
\(800\) 9.59978 0.339404
\(801\) −18.3881 −0.649712
\(802\) 86.4233 3.05171
\(803\) 0.628218 0.0221693
\(804\) −110.485 −3.89651
\(805\) 2.29384 0.0808474
\(806\) −123.707 −4.35741
\(807\) −19.1477 −0.674033
\(808\) −4.37308 −0.153844
\(809\) 7.75735 0.272734 0.136367 0.990658i \(-0.456457\pi\)
0.136367 + 0.990658i \(0.456457\pi\)
\(810\) 18.1785 0.638728
\(811\) 20.2257 0.710222 0.355111 0.934824i \(-0.384443\pi\)
0.355111 + 0.934824i \(0.384443\pi\)
\(812\) −13.3791 −0.469515
\(813\) 48.5554 1.70291
\(814\) −7.51222 −0.263303
\(815\) 39.2995 1.37660
\(816\) 102.434 3.58591
\(817\) −2.72366 −0.0952887
\(818\) −51.0513 −1.78497
\(819\) −35.1482 −1.22818
\(820\) 23.8989 0.834584
\(821\) −11.3770 −0.397062 −0.198531 0.980095i \(-0.563617\pi\)
−0.198531 + 0.980095i \(0.563617\pi\)
\(822\) −76.5154 −2.66878
\(823\) 35.3434 1.23199 0.615997 0.787749i \(-0.288753\pi\)
0.615997 + 0.787749i \(0.288753\pi\)
\(824\) 49.5092 1.72474
\(825\) 7.98847 0.278123
\(826\) 50.5759 1.75976
\(827\) −1.44721 −0.0503244 −0.0251622 0.999683i \(-0.508010\pi\)
−0.0251622 + 0.999683i \(0.508010\pi\)
\(828\) −17.1329 −0.595411
\(829\) 28.5404 0.991248 0.495624 0.868537i \(-0.334939\pi\)
0.495624 + 0.868537i \(0.334939\pi\)
\(830\) −4.08544 −0.141808
\(831\) −45.4136 −1.57538
\(832\) 12.3142 0.426919
\(833\) −24.7383 −0.857130
\(834\) 22.3578 0.774189
\(835\) 17.1175 0.592374
\(836\) 21.6926 0.750253
\(837\) 26.6898 0.922535
\(838\) −61.5152 −2.12501
\(839\) −22.9697 −0.793003 −0.396502 0.918034i \(-0.629776\pi\)
−0.396502 + 0.918034i \(0.629776\pi\)
\(840\) 46.6152 1.60838
\(841\) −24.4771 −0.844036
\(842\) −30.4598 −1.04971
\(843\) −4.28848 −0.147703
\(844\) 34.0732 1.17285
\(845\) 44.6892 1.53735
\(846\) −96.2913 −3.31056
\(847\) 8.78217 0.301759
\(848\) −54.6861 −1.87793
\(849\) −53.9939 −1.85306
\(850\) 17.1732 0.589036
\(851\) 1.20149 0.0411864
\(852\) 42.0741 1.44143
\(853\) −23.4767 −0.803826 −0.401913 0.915678i \(-0.631655\pi\)
−0.401913 + 0.915678i \(0.631655\pi\)
\(854\) 31.2355 1.06886
\(855\) −17.7944 −0.608555
\(856\) −31.1166 −1.06355
\(857\) 52.8256 1.80449 0.902245 0.431224i \(-0.141918\pi\)
0.902245 + 0.431224i \(0.141918\pi\)
\(858\) 89.4627 3.05421
\(859\) −46.1838 −1.57577 −0.787885 0.615822i \(-0.788824\pi\)
−0.787885 + 0.615822i \(0.788824\pi\)
\(860\) 10.7740 0.367389
\(861\) −10.1074 −0.344458
\(862\) −83.5167 −2.84459
\(863\) 31.9217 1.08663 0.543313 0.839530i \(-0.317170\pi\)
0.543313 + 0.839530i \(0.317170\pi\)
\(864\) −23.1947 −0.789101
\(865\) 29.8855 1.01614
\(866\) 3.10049 0.105359
\(867\) 17.0687 0.579682
\(868\) −50.1821 −1.70329
\(869\) 1.21964 0.0413735
\(870\) −27.9343 −0.947063
\(871\) −54.0541 −1.83155
\(872\) 58.4964 1.98094
\(873\) −10.7365 −0.363374
\(874\) −4.98167 −0.168508
\(875\) 16.6438 0.562663
\(876\) −3.61944 −0.122290
\(877\) −4.73118 −0.159761 −0.0798804 0.996804i \(-0.525454\pi\)
−0.0798804 + 0.996804i \(0.525454\pi\)
\(878\) 12.6585 0.427205
\(879\) −38.4775 −1.29781
\(880\) −32.1061 −1.08230
\(881\) −53.8774 −1.81517 −0.907587 0.419864i \(-0.862078\pi\)
−0.907587 + 0.419864i \(0.862078\pi\)
\(882\) 55.7687 1.87783
\(883\) 19.4987 0.656184 0.328092 0.944646i \(-0.393594\pi\)
0.328092 + 0.944646i \(0.393594\pi\)
\(884\) 133.942 4.50495
\(885\) 73.5429 2.47212
\(886\) −39.3380 −1.32159
\(887\) 36.9991 1.24231 0.621154 0.783689i \(-0.286664\pi\)
0.621154 + 0.783689i \(0.286664\pi\)
\(888\) 24.4165 0.819363
\(889\) −0.905613 −0.0303733
\(890\) 21.1497 0.708939
\(891\) 7.98378 0.267467
\(892\) −13.3861 −0.448198
\(893\) −19.4992 −0.652516
\(894\) 71.2240 2.38209
\(895\) −8.24443 −0.275581
\(896\) −11.8358 −0.395406
\(897\) −14.3085 −0.477745
\(898\) 27.7137 0.924817
\(899\) 16.9645 0.565799
\(900\) −26.9624 −0.898748
\(901\) −33.5380 −1.11731
\(902\) 15.0710 0.501808
\(903\) −4.55655 −0.151633
\(904\) −39.8787 −1.32635
\(905\) 13.3853 0.444943
\(906\) −150.564 −5.00216
\(907\) 7.43751 0.246959 0.123479 0.992347i \(-0.460595\pi\)
0.123479 + 0.992347i \(0.460595\pi\)
\(908\) −81.2106 −2.69507
\(909\) 2.79272 0.0926285
\(910\) 40.4268 1.34014
\(911\) −9.05989 −0.300168 −0.150084 0.988673i \(-0.547954\pi\)
−0.150084 + 0.988673i \(0.547954\pi\)
\(912\) −46.7623 −1.54845
\(913\) −1.79427 −0.0593817
\(914\) −71.6857 −2.37115
\(915\) 45.4199 1.50154
\(916\) 50.3470 1.66351
\(917\) 1.68400 0.0556106
\(918\) −41.4935 −1.36949
\(919\) 23.6266 0.779370 0.389685 0.920948i \(-0.372584\pi\)
0.389685 + 0.920948i \(0.372584\pi\)
\(920\) 11.1168 0.366511
\(921\) 73.5620 2.42395
\(922\) 42.2087 1.39007
\(923\) 20.5845 0.677546
\(924\) 36.2906 1.19387
\(925\) 1.89080 0.0621692
\(926\) 103.276 3.39386
\(927\) −31.6173 −1.03845
\(928\) −14.7430 −0.483963
\(929\) −2.13655 −0.0700981 −0.0350490 0.999386i \(-0.511159\pi\)
−0.0350490 + 0.999386i \(0.511159\pi\)
\(930\) −104.776 −3.43572
\(931\) 11.2933 0.370122
\(932\) 123.313 4.03926
\(933\) 92.1587 3.01714
\(934\) 37.2150 1.21771
\(935\) −19.6901 −0.643936
\(936\) −170.342 −5.56779
\(937\) −18.5034 −0.604480 −0.302240 0.953232i \(-0.597734\pi\)
−0.302240 + 0.953232i \(0.597734\pi\)
\(938\) −31.4844 −1.02800
\(939\) −31.7486 −1.03608
\(940\) 77.1330 2.51580
\(941\) −6.03781 −0.196827 −0.0984136 0.995146i \(-0.531377\pi\)
−0.0984136 + 0.995146i \(0.531377\pi\)
\(942\) 131.363 4.28003
\(943\) −2.41041 −0.0784938
\(944\) 113.219 3.68495
\(945\) −8.72206 −0.283729
\(946\) 6.79422 0.220899
\(947\) 29.5440 0.960052 0.480026 0.877254i \(-0.340627\pi\)
0.480026 + 0.877254i \(0.340627\pi\)
\(948\) −7.02691 −0.228223
\(949\) −1.77079 −0.0574822
\(950\) −7.83975 −0.254355
\(951\) 34.5832 1.12144
\(952\) 44.0114 1.42642
\(953\) −27.4465 −0.889079 −0.444540 0.895759i \(-0.646633\pi\)
−0.444540 + 0.895759i \(0.646633\pi\)
\(954\) 75.6065 2.44785
\(955\) −31.9694 −1.03451
\(956\) 69.7016 2.25431
\(957\) −12.2684 −0.396582
\(958\) 23.3779 0.755306
\(959\) −15.1854 −0.490362
\(960\) 10.4297 0.336616
\(961\) 32.6302 1.05259
\(962\) 21.1751 0.682711
\(963\) 19.8716 0.640352
\(964\) −38.4090 −1.23707
\(965\) −12.3221 −0.396664
\(966\) −8.33411 −0.268145
\(967\) −13.9008 −0.447021 −0.223511 0.974702i \(-0.571752\pi\)
−0.223511 + 0.974702i \(0.571752\pi\)
\(968\) 42.5618 1.36799
\(969\) −28.6785 −0.921287
\(970\) 12.3489 0.396499
\(971\) −28.6176 −0.918382 −0.459191 0.888337i \(-0.651861\pi\)
−0.459191 + 0.888337i \(0.651861\pi\)
\(972\) −92.0570 −2.95273
\(973\) 4.43718 0.142250
\(974\) 30.5691 0.979496
\(975\) −22.5175 −0.721137
\(976\) 69.9235 2.23820
\(977\) 26.7270 0.855072 0.427536 0.903998i \(-0.359382\pi\)
0.427536 + 0.903998i \(0.359382\pi\)
\(978\) −142.785 −4.56576
\(979\) 9.28868 0.296867
\(980\) −44.6728 −1.42702
\(981\) −37.3567 −1.19271
\(982\) 57.9431 1.84904
\(983\) −21.1966 −0.676067 −0.338034 0.941134i \(-0.609762\pi\)
−0.338034 + 0.941134i \(0.609762\pi\)
\(984\) −48.9841 −1.56156
\(985\) 39.5655 1.26066
\(986\) −26.3740 −0.839920
\(987\) −32.6212 −1.03835
\(988\) −61.1459 −1.94531
\(989\) −1.08665 −0.0345535
\(990\) 44.3884 1.41076
\(991\) −14.1723 −0.450198 −0.225099 0.974336i \(-0.572271\pi\)
−0.225099 + 0.974336i \(0.572271\pi\)
\(992\) −55.2977 −1.75570
\(993\) 63.1579 2.00426
\(994\) 11.9896 0.380288
\(995\) 23.1301 0.733274
\(996\) 10.3376 0.327560
\(997\) −13.1149 −0.415353 −0.207677 0.978198i \(-0.566590\pi\)
−0.207677 + 0.978198i \(0.566590\pi\)
\(998\) −72.0274 −2.27999
\(999\) −4.56851 −0.144541
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.1.12 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.12 259 1.1 even 1 trivial