Properties

Label 6037.2.a.b.1.19
Level $6037$
Weight $2$
Character 6037.1
Self dual yes
Analytic conductor $48.206$
Analytic rank $0$
Dimension $259$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.19
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.38315 q^{2} -2.49497 q^{3} +3.67942 q^{4} -2.67299 q^{5} +5.94590 q^{6} -2.23204 q^{7} -4.00231 q^{8} +3.22488 q^{9} +O(q^{10})\) \(q-2.38315 q^{2} -2.49497 q^{3} +3.67942 q^{4} -2.67299 q^{5} +5.94590 q^{6} -2.23204 q^{7} -4.00231 q^{8} +3.22488 q^{9} +6.37013 q^{10} -3.56753 q^{11} -9.18004 q^{12} +0.171041 q^{13} +5.31929 q^{14} +6.66902 q^{15} +2.17928 q^{16} +3.04647 q^{17} -7.68537 q^{18} +3.24564 q^{19} -9.83503 q^{20} +5.56887 q^{21} +8.50198 q^{22} -1.37245 q^{23} +9.98564 q^{24} +2.14485 q^{25} -0.407618 q^{26} -0.561058 q^{27} -8.21261 q^{28} +3.33676 q^{29} -15.8933 q^{30} -6.95962 q^{31} +2.81106 q^{32} +8.90089 q^{33} -7.26021 q^{34} +5.96621 q^{35} +11.8657 q^{36} -4.36072 q^{37} -7.73486 q^{38} -0.426743 q^{39} +10.6981 q^{40} +8.86840 q^{41} -13.2715 q^{42} +8.33722 q^{43} -13.1264 q^{44} -8.62005 q^{45} +3.27076 q^{46} +4.76900 q^{47} -5.43724 q^{48} -2.01800 q^{49} -5.11151 q^{50} -7.60086 q^{51} +0.629332 q^{52} +4.79417 q^{53} +1.33709 q^{54} +9.53597 q^{55} +8.93331 q^{56} -8.09778 q^{57} -7.95201 q^{58} -2.55132 q^{59} +24.5381 q^{60} -12.5381 q^{61} +16.5858 q^{62} -7.19805 q^{63} -11.0578 q^{64} -0.457191 q^{65} -21.2122 q^{66} +4.09006 q^{67} +11.2092 q^{68} +3.42422 q^{69} -14.2184 q^{70} -0.238225 q^{71} -12.9069 q^{72} -4.75265 q^{73} +10.3923 q^{74} -5.35134 q^{75} +11.9421 q^{76} +7.96288 q^{77} +1.01699 q^{78} -13.4382 q^{79} -5.82518 q^{80} -8.27480 q^{81} -21.1348 q^{82} +12.3750 q^{83} +20.4902 q^{84} -8.14318 q^{85} -19.8689 q^{86} -8.32512 q^{87} +14.2784 q^{88} +17.0413 q^{89} +20.5429 q^{90} -0.381771 q^{91} -5.04982 q^{92} +17.3640 q^{93} -11.3652 q^{94} -8.67555 q^{95} -7.01352 q^{96} -9.50023 q^{97} +4.80920 q^{98} -11.5049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38315 −1.68514 −0.842572 0.538584i \(-0.818959\pi\)
−0.842572 + 0.538584i \(0.818959\pi\)
\(3\) −2.49497 −1.44047 −0.720236 0.693729i \(-0.755966\pi\)
−0.720236 + 0.693729i \(0.755966\pi\)
\(4\) 3.67942 1.83971
\(5\) −2.67299 −1.19540 −0.597698 0.801722i \(-0.703918\pi\)
−0.597698 + 0.801722i \(0.703918\pi\)
\(6\) 5.94590 2.42740
\(7\) −2.23204 −0.843632 −0.421816 0.906682i \(-0.638607\pi\)
−0.421816 + 0.906682i \(0.638607\pi\)
\(8\) −4.00231 −1.41503
\(9\) 3.22488 1.07496
\(10\) 6.37013 2.01441
\(11\) −3.56753 −1.07565 −0.537826 0.843056i \(-0.680754\pi\)
−0.537826 + 0.843056i \(0.680754\pi\)
\(12\) −9.18004 −2.65005
\(13\) 0.171041 0.0474383 0.0237192 0.999719i \(-0.492449\pi\)
0.0237192 + 0.999719i \(0.492449\pi\)
\(14\) 5.31929 1.42164
\(15\) 6.66902 1.72193
\(16\) 2.17928 0.544820
\(17\) 3.04647 0.738878 0.369439 0.929255i \(-0.379550\pi\)
0.369439 + 0.929255i \(0.379550\pi\)
\(18\) −7.68537 −1.81146
\(19\) 3.24564 0.744601 0.372301 0.928112i \(-0.378569\pi\)
0.372301 + 0.928112i \(0.378569\pi\)
\(20\) −9.83503 −2.19918
\(21\) 5.56887 1.21523
\(22\) 8.50198 1.81263
\(23\) −1.37245 −0.286176 −0.143088 0.989710i \(-0.545703\pi\)
−0.143088 + 0.989710i \(0.545703\pi\)
\(24\) 9.98564 2.03831
\(25\) 2.14485 0.428970
\(26\) −0.407618 −0.0799404
\(27\) −0.561058 −0.107976
\(28\) −8.21261 −1.55204
\(29\) 3.33676 0.619621 0.309811 0.950798i \(-0.399734\pi\)
0.309811 + 0.950798i \(0.399734\pi\)
\(30\) −15.8933 −2.90170
\(31\) −6.95962 −1.24998 −0.624992 0.780631i \(-0.714898\pi\)
−0.624992 + 0.780631i \(0.714898\pi\)
\(32\) 2.81106 0.496931
\(33\) 8.90089 1.54945
\(34\) −7.26021 −1.24512
\(35\) 5.96621 1.00847
\(36\) 11.8657 1.97761
\(37\) −4.36072 −0.716898 −0.358449 0.933549i \(-0.616694\pi\)
−0.358449 + 0.933549i \(0.616694\pi\)
\(38\) −7.73486 −1.25476
\(39\) −0.426743 −0.0683335
\(40\) 10.6981 1.69152
\(41\) 8.86840 1.38501 0.692506 0.721412i \(-0.256507\pi\)
0.692506 + 0.721412i \(0.256507\pi\)
\(42\) −13.2715 −2.04783
\(43\) 8.33722 1.27141 0.635707 0.771930i \(-0.280709\pi\)
0.635707 + 0.771930i \(0.280709\pi\)
\(44\) −13.1264 −1.97889
\(45\) −8.62005 −1.28500
\(46\) 3.27076 0.482247
\(47\) 4.76900 0.695629 0.347815 0.937563i \(-0.386924\pi\)
0.347815 + 0.937563i \(0.386924\pi\)
\(48\) −5.43724 −0.784797
\(49\) −2.01800 −0.288286
\(50\) −5.11151 −0.722877
\(51\) −7.60086 −1.06433
\(52\) 0.629332 0.0872727
\(53\) 4.79417 0.658530 0.329265 0.944237i \(-0.393199\pi\)
0.329265 + 0.944237i \(0.393199\pi\)
\(54\) 1.33709 0.181955
\(55\) 9.53597 1.28583
\(56\) 8.93331 1.19376
\(57\) −8.09778 −1.07258
\(58\) −7.95201 −1.04415
\(59\) −2.55132 −0.332154 −0.166077 0.986113i \(-0.553110\pi\)
−0.166077 + 0.986113i \(0.553110\pi\)
\(60\) 24.5381 3.16786
\(61\) −12.5381 −1.60534 −0.802670 0.596423i \(-0.796588\pi\)
−0.802670 + 0.596423i \(0.796588\pi\)
\(62\) 16.5858 2.10640
\(63\) −7.19805 −0.906869
\(64\) −11.0578 −1.38222
\(65\) −0.457191 −0.0567075
\(66\) −21.2122 −2.61104
\(67\) 4.09006 0.499680 0.249840 0.968287i \(-0.419622\pi\)
0.249840 + 0.968287i \(0.419622\pi\)
\(68\) 11.2092 1.35932
\(69\) 3.42422 0.412228
\(70\) −14.2184 −1.69942
\(71\) −0.238225 −0.0282721 −0.0141360 0.999900i \(-0.504500\pi\)
−0.0141360 + 0.999900i \(0.504500\pi\)
\(72\) −12.9069 −1.52110
\(73\) −4.75265 −0.556256 −0.278128 0.960544i \(-0.589714\pi\)
−0.278128 + 0.960544i \(0.589714\pi\)
\(74\) 10.3923 1.20808
\(75\) −5.35134 −0.617920
\(76\) 11.9421 1.36985
\(77\) 7.96288 0.907454
\(78\) 1.01699 0.115152
\(79\) −13.4382 −1.51192 −0.755959 0.654619i \(-0.772829\pi\)
−0.755959 + 0.654619i \(0.772829\pi\)
\(80\) −5.82518 −0.651275
\(81\) −8.27480 −0.919423
\(82\) −21.1348 −2.33394
\(83\) 12.3750 1.35833 0.679166 0.733985i \(-0.262342\pi\)
0.679166 + 0.733985i \(0.262342\pi\)
\(84\) 20.4902 2.23566
\(85\) −8.14318 −0.883252
\(86\) −19.8689 −2.14252
\(87\) −8.32512 −0.892547
\(88\) 14.2784 1.52208
\(89\) 17.0413 1.80637 0.903187 0.429248i \(-0.141221\pi\)
0.903187 + 0.429248i \(0.141221\pi\)
\(90\) 20.5429 2.16541
\(91\) −0.381771 −0.0400205
\(92\) −5.04982 −0.526480
\(93\) 17.3640 1.80057
\(94\) −11.3652 −1.17224
\(95\) −8.67555 −0.890093
\(96\) −7.01352 −0.715814
\(97\) −9.50023 −0.964603 −0.482301 0.876005i \(-0.660199\pi\)
−0.482301 + 0.876005i \(0.660199\pi\)
\(98\) 4.80920 0.485802
\(99\) −11.5049 −1.15628
\(100\) 7.89181 0.789181
\(101\) −14.9381 −1.48640 −0.743198 0.669071i \(-0.766692\pi\)
−0.743198 + 0.669071i \(0.766692\pi\)
\(102\) 18.1140 1.79355
\(103\) 10.1803 1.00310 0.501548 0.865130i \(-0.332764\pi\)
0.501548 + 0.865130i \(0.332764\pi\)
\(104\) −0.684560 −0.0671266
\(105\) −14.8855 −1.45268
\(106\) −11.4252 −1.10972
\(107\) 13.8725 1.34111 0.670555 0.741860i \(-0.266056\pi\)
0.670555 + 0.741860i \(0.266056\pi\)
\(108\) −2.06437 −0.198644
\(109\) −8.28011 −0.793091 −0.396545 0.918015i \(-0.629791\pi\)
−0.396545 + 0.918015i \(0.629791\pi\)
\(110\) −22.7257 −2.16681
\(111\) 10.8799 1.03267
\(112\) −4.86424 −0.459627
\(113\) −11.4873 −1.08063 −0.540315 0.841463i \(-0.681695\pi\)
−0.540315 + 0.841463i \(0.681695\pi\)
\(114\) 19.2982 1.80745
\(115\) 3.66854 0.342093
\(116\) 12.2773 1.13992
\(117\) 0.551587 0.0509942
\(118\) 6.08019 0.559727
\(119\) −6.79985 −0.623341
\(120\) −26.6915 −2.43659
\(121\) 1.72730 0.157027
\(122\) 29.8802 2.70523
\(123\) −22.1264 −1.99507
\(124\) −25.6073 −2.29961
\(125\) 7.63177 0.682606
\(126\) 17.1541 1.52820
\(127\) 0.455660 0.0404333 0.0202166 0.999796i \(-0.493564\pi\)
0.0202166 + 0.999796i \(0.493564\pi\)
\(128\) 20.7302 1.83231
\(129\) −20.8011 −1.83144
\(130\) 1.08956 0.0955604
\(131\) −16.2877 −1.42306 −0.711532 0.702654i \(-0.751998\pi\)
−0.711532 + 0.702654i \(0.751998\pi\)
\(132\) 32.7501 2.85053
\(133\) −7.24440 −0.628169
\(134\) −9.74723 −0.842033
\(135\) 1.49970 0.129074
\(136\) −12.1929 −1.04553
\(137\) 2.07152 0.176982 0.0884908 0.996077i \(-0.471796\pi\)
0.0884908 + 0.996077i \(0.471796\pi\)
\(138\) −8.16044 −0.694663
\(139\) 19.9400 1.69129 0.845643 0.533748i \(-0.179217\pi\)
0.845643 + 0.533748i \(0.179217\pi\)
\(140\) 21.9522 1.85530
\(141\) −11.8985 −1.00203
\(142\) 0.567726 0.0476425
\(143\) −0.610196 −0.0510271
\(144\) 7.02790 0.585659
\(145\) −8.91912 −0.740692
\(146\) 11.3263 0.937370
\(147\) 5.03485 0.415267
\(148\) −16.0449 −1.31888
\(149\) −8.57850 −0.702778 −0.351389 0.936230i \(-0.614291\pi\)
−0.351389 + 0.936230i \(0.614291\pi\)
\(150\) 12.7531 1.04128
\(151\) 7.11675 0.579153 0.289576 0.957155i \(-0.406486\pi\)
0.289576 + 0.957155i \(0.406486\pi\)
\(152\) −12.9901 −1.05363
\(153\) 9.82450 0.794264
\(154\) −18.9768 −1.52919
\(155\) 18.6030 1.49423
\(156\) −1.57017 −0.125714
\(157\) −22.3094 −1.78049 −0.890243 0.455486i \(-0.849466\pi\)
−0.890243 + 0.455486i \(0.849466\pi\)
\(158\) 32.0253 2.54780
\(159\) −11.9613 −0.948594
\(160\) −7.51393 −0.594029
\(161\) 3.06336 0.241427
\(162\) 19.7201 1.54936
\(163\) −1.08447 −0.0849421 −0.0424711 0.999098i \(-0.513523\pi\)
−0.0424711 + 0.999098i \(0.513523\pi\)
\(164\) 32.6306 2.54802
\(165\) −23.7920 −1.85220
\(166\) −29.4915 −2.28898
\(167\) 2.54198 0.196704 0.0983520 0.995152i \(-0.468643\pi\)
0.0983520 + 0.995152i \(0.468643\pi\)
\(168\) −22.2883 −1.71958
\(169\) −12.9707 −0.997750
\(170\) 19.4064 1.48841
\(171\) 10.4668 0.800416
\(172\) 30.6761 2.33903
\(173\) −11.3261 −0.861106 −0.430553 0.902565i \(-0.641682\pi\)
−0.430553 + 0.902565i \(0.641682\pi\)
\(174\) 19.8400 1.50407
\(175\) −4.78740 −0.361893
\(176\) −7.77465 −0.586036
\(177\) 6.36548 0.478458
\(178\) −40.6120 −3.04400
\(179\) 8.72191 0.651907 0.325953 0.945386i \(-0.394315\pi\)
0.325953 + 0.945386i \(0.394315\pi\)
\(180\) −31.7168 −2.36403
\(181\) −24.2768 −1.80448 −0.902239 0.431236i \(-0.858078\pi\)
−0.902239 + 0.431236i \(0.858078\pi\)
\(182\) 0.909818 0.0674402
\(183\) 31.2822 2.31245
\(184\) 5.49297 0.404947
\(185\) 11.6561 0.856977
\(186\) −41.3811 −3.03421
\(187\) −10.8684 −0.794776
\(188\) 17.5471 1.27976
\(189\) 1.25230 0.0910917
\(190\) 20.6752 1.49993
\(191\) 2.12136 0.153496 0.0767480 0.997051i \(-0.475546\pi\)
0.0767480 + 0.997051i \(0.475546\pi\)
\(192\) 27.5888 1.99105
\(193\) 8.52268 0.613476 0.306738 0.951794i \(-0.400762\pi\)
0.306738 + 0.951794i \(0.400762\pi\)
\(194\) 22.6405 1.62549
\(195\) 1.14068 0.0816856
\(196\) −7.42506 −0.530361
\(197\) −8.78306 −0.625767 −0.312883 0.949792i \(-0.601295\pi\)
−0.312883 + 0.949792i \(0.601295\pi\)
\(198\) 27.4178 1.94850
\(199\) 0.326298 0.0231307 0.0115653 0.999933i \(-0.496319\pi\)
0.0115653 + 0.999933i \(0.496319\pi\)
\(200\) −8.58436 −0.607006
\(201\) −10.2046 −0.719775
\(202\) 35.5998 2.50479
\(203\) −7.44778 −0.522732
\(204\) −27.9667 −1.95806
\(205\) −23.7051 −1.65564
\(206\) −24.2612 −1.69036
\(207\) −4.42598 −0.307627
\(208\) 0.372747 0.0258453
\(209\) −11.5789 −0.800932
\(210\) 35.4745 2.44797
\(211\) 21.7473 1.49715 0.748574 0.663051i \(-0.230739\pi\)
0.748574 + 0.663051i \(0.230739\pi\)
\(212\) 17.6398 1.21150
\(213\) 0.594364 0.0407251
\(214\) −33.0604 −2.25996
\(215\) −22.2853 −1.51984
\(216\) 2.24553 0.152789
\(217\) 15.5341 1.05453
\(218\) 19.7328 1.33647
\(219\) 11.8577 0.801270
\(220\) 35.0868 2.36555
\(221\) 0.521073 0.0350511
\(222\) −25.9284 −1.74020
\(223\) −11.1124 −0.744145 −0.372072 0.928204i \(-0.621353\pi\)
−0.372072 + 0.928204i \(0.621353\pi\)
\(224\) −6.27441 −0.419226
\(225\) 6.91688 0.461125
\(226\) 27.3759 1.82102
\(227\) −21.6852 −1.43930 −0.719650 0.694337i \(-0.755698\pi\)
−0.719650 + 0.694337i \(0.755698\pi\)
\(228\) −29.7951 −1.97323
\(229\) 9.11007 0.602011 0.301005 0.953622i \(-0.402678\pi\)
0.301005 + 0.953622i \(0.402678\pi\)
\(230\) −8.74269 −0.576476
\(231\) −19.8671 −1.30716
\(232\) −13.3548 −0.876782
\(233\) −14.5692 −0.954463 −0.477231 0.878778i \(-0.658360\pi\)
−0.477231 + 0.878778i \(0.658360\pi\)
\(234\) −1.31452 −0.0859326
\(235\) −12.7475 −0.831552
\(236\) −9.38738 −0.611067
\(237\) 33.5279 2.17787
\(238\) 16.2051 1.05042
\(239\) −14.9631 −0.967881 −0.483940 0.875101i \(-0.660795\pi\)
−0.483940 + 0.875101i \(0.660795\pi\)
\(240\) 14.5337 0.938143
\(241\) −10.6052 −0.683143 −0.341572 0.939856i \(-0.610959\pi\)
−0.341572 + 0.939856i \(0.610959\pi\)
\(242\) −4.11642 −0.264614
\(243\) 22.3286 1.43238
\(244\) −46.1329 −2.95336
\(245\) 5.39408 0.344615
\(246\) 52.7306 3.36198
\(247\) 0.555139 0.0353226
\(248\) 27.8545 1.76876
\(249\) −30.8752 −1.95664
\(250\) −18.1877 −1.15029
\(251\) −17.5875 −1.11011 −0.555056 0.831813i \(-0.687303\pi\)
−0.555056 + 0.831813i \(0.687303\pi\)
\(252\) −26.4846 −1.66838
\(253\) 4.89626 0.307825
\(254\) −1.08591 −0.0681359
\(255\) 20.3170 1.27230
\(256\) −27.2877 −1.70548
\(257\) −15.6901 −0.978724 −0.489362 0.872081i \(-0.662770\pi\)
−0.489362 + 0.872081i \(0.662770\pi\)
\(258\) 49.5723 3.08623
\(259\) 9.73330 0.604798
\(260\) −1.68220 −0.104325
\(261\) 10.7606 0.666067
\(262\) 38.8161 2.39807
\(263\) −8.97221 −0.553250 −0.276625 0.960978i \(-0.589216\pi\)
−0.276625 + 0.960978i \(0.589216\pi\)
\(264\) −35.6241 −2.19251
\(265\) −12.8148 −0.787204
\(266\) 17.2645 1.05856
\(267\) −42.5175 −2.60203
\(268\) 15.0490 0.919266
\(269\) −0.339949 −0.0207271 −0.0103635 0.999946i \(-0.503299\pi\)
−0.0103635 + 0.999946i \(0.503299\pi\)
\(270\) −3.57402 −0.217508
\(271\) −7.45834 −0.453062 −0.226531 0.974004i \(-0.572738\pi\)
−0.226531 + 0.974004i \(0.572738\pi\)
\(272\) 6.63911 0.402555
\(273\) 0.952507 0.0576483
\(274\) −4.93674 −0.298239
\(275\) −7.65183 −0.461423
\(276\) 12.5991 0.758379
\(277\) −23.7532 −1.42719 −0.713595 0.700559i \(-0.752934\pi\)
−0.713595 + 0.700559i \(0.752934\pi\)
\(278\) −47.5200 −2.85006
\(279\) −22.4439 −1.34368
\(280\) −23.8786 −1.42702
\(281\) 12.7096 0.758193 0.379097 0.925357i \(-0.376235\pi\)
0.379097 + 0.925357i \(0.376235\pi\)
\(282\) 28.3559 1.68857
\(283\) 11.6001 0.689554 0.344777 0.938685i \(-0.387955\pi\)
0.344777 + 0.938685i \(0.387955\pi\)
\(284\) −0.876529 −0.0520124
\(285\) 21.6452 1.28215
\(286\) 1.45419 0.0859880
\(287\) −19.7946 −1.16844
\(288\) 9.06533 0.534180
\(289\) −7.71900 −0.454059
\(290\) 21.2556 1.24817
\(291\) 23.7028 1.38948
\(292\) −17.4870 −1.02335
\(293\) −6.10147 −0.356452 −0.178226 0.983990i \(-0.557036\pi\)
−0.178226 + 0.983990i \(0.557036\pi\)
\(294\) −11.9988 −0.699785
\(295\) 6.81965 0.397055
\(296\) 17.4530 1.01443
\(297\) 2.00159 0.116144
\(298\) 20.4439 1.18428
\(299\) −0.234746 −0.0135757
\(300\) −19.6898 −1.13679
\(301\) −18.6090 −1.07261
\(302\) −16.9603 −0.975955
\(303\) 37.2701 2.14111
\(304\) 7.07316 0.405673
\(305\) 33.5142 1.91902
\(306\) −23.4133 −1.33845
\(307\) 0.405309 0.0231322 0.0115661 0.999933i \(-0.496318\pi\)
0.0115661 + 0.999933i \(0.496318\pi\)
\(308\) 29.2988 1.66945
\(309\) −25.3996 −1.44493
\(310\) −44.3337 −2.51798
\(311\) −11.6930 −0.663048 −0.331524 0.943447i \(-0.607563\pi\)
−0.331524 + 0.943447i \(0.607563\pi\)
\(312\) 1.70796 0.0966940
\(313\) 18.2376 1.03085 0.515426 0.856934i \(-0.327634\pi\)
0.515426 + 0.856934i \(0.327634\pi\)
\(314\) 53.1668 3.00037
\(315\) 19.2403 1.08407
\(316\) −49.4448 −2.78149
\(317\) 27.0250 1.51788 0.758939 0.651162i \(-0.225718\pi\)
0.758939 + 0.651162i \(0.225718\pi\)
\(318\) 28.5057 1.59852
\(319\) −11.9040 −0.666497
\(320\) 29.5572 1.65230
\(321\) −34.6116 −1.93183
\(322\) −7.30046 −0.406839
\(323\) 9.88776 0.550170
\(324\) −30.4465 −1.69147
\(325\) 0.366858 0.0203496
\(326\) 2.58445 0.143140
\(327\) 20.6586 1.14242
\(328\) −35.4941 −1.95983
\(329\) −10.6446 −0.586855
\(330\) 56.6999 3.12122
\(331\) −21.1684 −1.16352 −0.581761 0.813360i \(-0.697636\pi\)
−0.581761 + 0.813360i \(0.697636\pi\)
\(332\) 45.5327 2.49893
\(333\) −14.0628 −0.770636
\(334\) −6.05792 −0.331474
\(335\) −10.9327 −0.597315
\(336\) 12.1361 0.662080
\(337\) −13.5243 −0.736717 −0.368358 0.929684i \(-0.620080\pi\)
−0.368358 + 0.929684i \(0.620080\pi\)
\(338\) 30.9113 1.68135
\(339\) 28.6604 1.55662
\(340\) −29.9622 −1.62493
\(341\) 24.8287 1.34455
\(342\) −24.9440 −1.34882
\(343\) 20.1285 1.08684
\(344\) −33.3681 −1.79909
\(345\) −9.15289 −0.492775
\(346\) 26.9918 1.45109
\(347\) −6.02881 −0.323643 −0.161822 0.986820i \(-0.551737\pi\)
−0.161822 + 0.986820i \(0.551737\pi\)
\(348\) −30.6316 −1.64203
\(349\) −12.2753 −0.657081 −0.328540 0.944490i \(-0.606557\pi\)
−0.328540 + 0.944490i \(0.606557\pi\)
\(350\) 11.4091 0.609842
\(351\) −0.0959641 −0.00512219
\(352\) −10.0286 −0.534524
\(353\) 3.07296 0.163557 0.0817785 0.996651i \(-0.473940\pi\)
0.0817785 + 0.996651i \(0.473940\pi\)
\(354\) −15.1699 −0.806271
\(355\) 0.636772 0.0337963
\(356\) 62.7020 3.32320
\(357\) 16.9654 0.897905
\(358\) −20.7857 −1.09856
\(359\) −13.4613 −0.710463 −0.355231 0.934778i \(-0.615598\pi\)
−0.355231 + 0.934778i \(0.615598\pi\)
\(360\) 34.5001 1.81831
\(361\) −8.46581 −0.445569
\(362\) 57.8553 3.04080
\(363\) −4.30956 −0.226194
\(364\) −1.40469 −0.0736260
\(365\) 12.7038 0.664945
\(366\) −74.5503 −3.89681
\(367\) −18.3817 −0.959516 −0.479758 0.877401i \(-0.659275\pi\)
−0.479758 + 0.877401i \(0.659275\pi\)
\(368\) −2.99095 −0.155914
\(369\) 28.5995 1.48883
\(370\) −27.7784 −1.44413
\(371\) −10.7008 −0.555557
\(372\) 63.8895 3.31252
\(373\) 6.94259 0.359473 0.179737 0.983715i \(-0.442475\pi\)
0.179737 + 0.983715i \(0.442475\pi\)
\(374\) 25.9011 1.33931
\(375\) −19.0410 −0.983275
\(376\) −19.0870 −0.984336
\(377\) 0.570724 0.0293938
\(378\) −2.98443 −0.153503
\(379\) 11.3470 0.582856 0.291428 0.956593i \(-0.405870\pi\)
0.291428 + 0.956593i \(0.405870\pi\)
\(380\) −31.9210 −1.63751
\(381\) −1.13686 −0.0582430
\(382\) −5.05552 −0.258663
\(383\) −36.1993 −1.84970 −0.924849 0.380335i \(-0.875809\pi\)
−0.924849 + 0.380335i \(0.875809\pi\)
\(384\) −51.7212 −2.63939
\(385\) −21.2847 −1.08477
\(386\) −20.3108 −1.03379
\(387\) 26.8865 1.36672
\(388\) −34.9553 −1.77459
\(389\) 27.9468 1.41696 0.708480 0.705731i \(-0.249381\pi\)
0.708480 + 0.705731i \(0.249381\pi\)
\(390\) −2.71841 −0.137652
\(391\) −4.18113 −0.211449
\(392\) 8.07665 0.407933
\(393\) 40.6374 2.04988
\(394\) 20.9314 1.05451
\(395\) 35.9202 1.80734
\(396\) −42.3312 −2.12722
\(397\) 27.5452 1.38245 0.691226 0.722639i \(-0.257071\pi\)
0.691226 + 0.722639i \(0.257071\pi\)
\(398\) −0.777619 −0.0389785
\(399\) 18.0746 0.904860
\(400\) 4.67423 0.233712
\(401\) −32.8563 −1.64077 −0.820384 0.571813i \(-0.806240\pi\)
−0.820384 + 0.571813i \(0.806240\pi\)
\(402\) 24.3191 1.21292
\(403\) −1.19038 −0.0592971
\(404\) −54.9635 −2.73454
\(405\) 22.1184 1.09907
\(406\) 17.7492 0.880878
\(407\) 15.5570 0.771133
\(408\) 30.4210 1.50606
\(409\) 11.6168 0.574415 0.287208 0.957868i \(-0.407273\pi\)
0.287208 + 0.957868i \(0.407273\pi\)
\(410\) 56.4929 2.78999
\(411\) −5.16837 −0.254937
\(412\) 37.4576 1.84540
\(413\) 5.69465 0.280216
\(414\) 10.5478 0.518395
\(415\) −33.0782 −1.62374
\(416\) 0.480808 0.0235735
\(417\) −49.7497 −2.43625
\(418\) 27.5944 1.34969
\(419\) 15.3202 0.748441 0.374221 0.927340i \(-0.377910\pi\)
0.374221 + 0.927340i \(0.377910\pi\)
\(420\) −54.7700 −2.67250
\(421\) 22.4446 1.09388 0.546941 0.837171i \(-0.315792\pi\)
0.546941 + 0.837171i \(0.315792\pi\)
\(422\) −51.8272 −2.52291
\(423\) 15.3794 0.747773
\(424\) −19.1878 −0.931840
\(425\) 6.53423 0.316957
\(426\) −1.41646 −0.0686277
\(427\) 27.9856 1.35432
\(428\) 51.0429 2.46725
\(429\) 1.52242 0.0735031
\(430\) 53.1092 2.56115
\(431\) −21.9342 −1.05653 −0.528265 0.849079i \(-0.677157\pi\)
−0.528265 + 0.849079i \(0.677157\pi\)
\(432\) −1.22270 −0.0588273
\(433\) 36.7281 1.76504 0.882520 0.470274i \(-0.155845\pi\)
0.882520 + 0.470274i \(0.155845\pi\)
\(434\) −37.0202 −1.77703
\(435\) 22.2529 1.06695
\(436\) −30.4660 −1.45906
\(437\) −4.45448 −0.213087
\(438\) −28.2588 −1.35026
\(439\) 33.6811 1.60751 0.803755 0.594960i \(-0.202832\pi\)
0.803755 + 0.594960i \(0.202832\pi\)
\(440\) −38.1659 −1.81949
\(441\) −6.50779 −0.309895
\(442\) −1.24180 −0.0590662
\(443\) 12.0761 0.573752 0.286876 0.957968i \(-0.407383\pi\)
0.286876 + 0.957968i \(0.407383\pi\)
\(444\) 40.0316 1.89981
\(445\) −45.5511 −2.15933
\(446\) 26.4827 1.25399
\(447\) 21.4031 1.01233
\(448\) 24.6813 1.16608
\(449\) 28.7540 1.35698 0.678492 0.734608i \(-0.262634\pi\)
0.678492 + 0.734608i \(0.262634\pi\)
\(450\) −16.4840 −0.777063
\(451\) −31.6383 −1.48979
\(452\) −42.2664 −1.98805
\(453\) −17.7561 −0.834253
\(454\) 51.6792 2.42543
\(455\) 1.02047 0.0478403
\(456\) 32.4098 1.51773
\(457\) 31.7539 1.48538 0.742692 0.669634i \(-0.233549\pi\)
0.742692 + 0.669634i \(0.233549\pi\)
\(458\) −21.7107 −1.01447
\(459\) −1.70925 −0.0797809
\(460\) 13.4981 0.629351
\(461\) −35.4539 −1.65125 −0.825626 0.564217i \(-0.809178\pi\)
−0.825626 + 0.564217i \(0.809178\pi\)
\(462\) 47.3464 2.20276
\(463\) 2.79877 0.130070 0.0650348 0.997883i \(-0.479284\pi\)
0.0650348 + 0.997883i \(0.479284\pi\)
\(464\) 7.27173 0.337582
\(465\) −46.4138 −2.15239
\(466\) 34.7207 1.60841
\(467\) 35.2041 1.62905 0.814527 0.580126i \(-0.196997\pi\)
0.814527 + 0.580126i \(0.196997\pi\)
\(468\) 2.02952 0.0938145
\(469\) −9.12917 −0.421546
\(470\) 30.3791 1.40128
\(471\) 55.6613 2.56474
\(472\) 10.2112 0.470008
\(473\) −29.7433 −1.36760
\(474\) −79.9022 −3.67003
\(475\) 6.96142 0.319412
\(476\) −25.0195 −1.14677
\(477\) 15.4606 0.707893
\(478\) 35.6593 1.63102
\(479\) 2.50788 0.114588 0.0572940 0.998357i \(-0.481753\pi\)
0.0572940 + 0.998357i \(0.481753\pi\)
\(480\) 18.7470 0.855681
\(481\) −0.745863 −0.0340084
\(482\) 25.2739 1.15119
\(483\) −7.64300 −0.347768
\(484\) 6.35546 0.288885
\(485\) 25.3940 1.15308
\(486\) −53.2124 −2.41376
\(487\) 16.6538 0.754655 0.377328 0.926080i \(-0.376843\pi\)
0.377328 + 0.926080i \(0.376843\pi\)
\(488\) 50.1814 2.27160
\(489\) 2.70572 0.122357
\(490\) −12.8549 −0.580726
\(491\) 6.26557 0.282761 0.141381 0.989955i \(-0.454846\pi\)
0.141381 + 0.989955i \(0.454846\pi\)
\(492\) −81.4123 −3.67035
\(493\) 10.1654 0.457825
\(494\) −1.32298 −0.0595237
\(495\) 30.7523 1.38221
\(496\) −15.1669 −0.681016
\(497\) 0.531727 0.0238512
\(498\) 73.5804 3.29722
\(499\) −30.2723 −1.35518 −0.677588 0.735442i \(-0.736975\pi\)
−0.677588 + 0.735442i \(0.736975\pi\)
\(500\) 28.0805 1.25580
\(501\) −6.34215 −0.283347
\(502\) 41.9137 1.87070
\(503\) 21.4391 0.955923 0.477962 0.878381i \(-0.341376\pi\)
0.477962 + 0.878381i \(0.341376\pi\)
\(504\) 28.8088 1.28325
\(505\) 39.9293 1.77683
\(506\) −11.6685 −0.518730
\(507\) 32.3616 1.43723
\(508\) 1.67656 0.0743855
\(509\) 16.0886 0.713116 0.356558 0.934273i \(-0.383950\pi\)
0.356558 + 0.934273i \(0.383950\pi\)
\(510\) −48.4185 −2.14401
\(511\) 10.6081 0.469275
\(512\) 23.5704 1.04167
\(513\) −1.82099 −0.0803989
\(514\) 37.3920 1.64929
\(515\) −27.2118 −1.19910
\(516\) −76.5360 −3.36931
\(517\) −17.0136 −0.748255
\(518\) −23.1959 −1.01917
\(519\) 28.2582 1.24040
\(520\) 1.82982 0.0802429
\(521\) 21.8917 0.959094 0.479547 0.877516i \(-0.340801\pi\)
0.479547 + 0.877516i \(0.340801\pi\)
\(522\) −25.6443 −1.12242
\(523\) 34.7802 1.52083 0.760416 0.649436i \(-0.224995\pi\)
0.760416 + 0.649436i \(0.224995\pi\)
\(524\) −59.9293 −2.61802
\(525\) 11.9444 0.521297
\(526\) 21.3822 0.932306
\(527\) −21.2023 −0.923586
\(528\) 19.3975 0.844169
\(529\) −21.1164 −0.918104
\(530\) 30.5395 1.32655
\(531\) −8.22770 −0.357052
\(532\) −26.6552 −1.15565
\(533\) 1.51686 0.0657026
\(534\) 101.326 4.38479
\(535\) −37.0811 −1.60316
\(536\) −16.3697 −0.707062
\(537\) −21.7609 −0.939053
\(538\) 0.810151 0.0349281
\(539\) 7.19928 0.310095
\(540\) 5.51802 0.237458
\(541\) −4.86709 −0.209252 −0.104626 0.994512i \(-0.533365\pi\)
−0.104626 + 0.994512i \(0.533365\pi\)
\(542\) 17.7744 0.763475
\(543\) 60.5698 2.59930
\(544\) 8.56383 0.367171
\(545\) 22.1326 0.948057
\(546\) −2.26997 −0.0971457
\(547\) −30.1606 −1.28957 −0.644787 0.764363i \(-0.723054\pi\)
−0.644787 + 0.764363i \(0.723054\pi\)
\(548\) 7.62197 0.325595
\(549\) −40.4338 −1.72567
\(550\) 18.2355 0.777564
\(551\) 10.8299 0.461371
\(552\) −13.7048 −0.583315
\(553\) 29.9946 1.27550
\(554\) 56.6074 2.40502
\(555\) −29.0817 −1.23445
\(556\) 73.3675 3.11148
\(557\) −15.7159 −0.665906 −0.332953 0.942943i \(-0.608045\pi\)
−0.332953 + 0.942943i \(0.608045\pi\)
\(558\) 53.4872 2.26430
\(559\) 1.42601 0.0603138
\(560\) 13.0020 0.549436
\(561\) 27.1163 1.14485
\(562\) −30.2890 −1.27766
\(563\) −5.15528 −0.217269 −0.108635 0.994082i \(-0.534648\pi\)
−0.108635 + 0.994082i \(0.534648\pi\)
\(564\) −43.7796 −1.84345
\(565\) 30.7053 1.29178
\(566\) −27.6448 −1.16200
\(567\) 18.4697 0.775654
\(568\) 0.953449 0.0400058
\(569\) 17.5813 0.737045 0.368523 0.929619i \(-0.379864\pi\)
0.368523 + 0.929619i \(0.379864\pi\)
\(570\) −51.5839 −2.16061
\(571\) 23.9075 1.00050 0.500248 0.865882i \(-0.333242\pi\)
0.500248 + 0.865882i \(0.333242\pi\)
\(572\) −2.24516 −0.0938750
\(573\) −5.29272 −0.221107
\(574\) 47.1736 1.96899
\(575\) −2.94370 −0.122761
\(576\) −35.6599 −1.48583
\(577\) −6.80087 −0.283124 −0.141562 0.989929i \(-0.545212\pi\)
−0.141562 + 0.989929i \(0.545212\pi\)
\(578\) 18.3956 0.765154
\(579\) −21.2638 −0.883695
\(580\) −32.8172 −1.36266
\(581\) −27.6215 −1.14593
\(582\) −56.4874 −2.34148
\(583\) −17.1034 −0.708350
\(584\) 19.0216 0.787118
\(585\) −1.47438 −0.0609583
\(586\) 14.5407 0.600673
\(587\) −12.2824 −0.506947 −0.253474 0.967342i \(-0.581573\pi\)
−0.253474 + 0.967342i \(0.581573\pi\)
\(588\) 18.5253 0.763971
\(589\) −22.5884 −0.930740
\(590\) −16.2523 −0.669095
\(591\) 21.9135 0.901399
\(592\) −9.50323 −0.390580
\(593\) −14.2660 −0.585833 −0.292917 0.956138i \(-0.594626\pi\)
−0.292917 + 0.956138i \(0.594626\pi\)
\(594\) −4.77011 −0.195720
\(595\) 18.1759 0.745139
\(596\) −31.5639 −1.29291
\(597\) −0.814105 −0.0333191
\(598\) 0.559434 0.0228770
\(599\) 0.498134 0.0203532 0.0101766 0.999948i \(-0.496761\pi\)
0.0101766 + 0.999948i \(0.496761\pi\)
\(600\) 21.4177 0.874375
\(601\) −21.6279 −0.882221 −0.441110 0.897453i \(-0.645415\pi\)
−0.441110 + 0.897453i \(0.645415\pi\)
\(602\) 44.3481 1.80749
\(603\) 13.1899 0.537135
\(604\) 26.1855 1.06547
\(605\) −4.61705 −0.187710
\(606\) −88.8204 −3.60808
\(607\) −24.1356 −0.979633 −0.489817 0.871826i \(-0.662936\pi\)
−0.489817 + 0.871826i \(0.662936\pi\)
\(608\) 9.12371 0.370015
\(609\) 18.5820 0.752981
\(610\) −79.8694 −3.23382
\(611\) 0.815695 0.0329995
\(612\) 36.1484 1.46121
\(613\) −29.3641 −1.18600 −0.593002 0.805201i \(-0.702057\pi\)
−0.593002 + 0.805201i \(0.702057\pi\)
\(614\) −0.965913 −0.0389811
\(615\) 59.1436 2.38490
\(616\) −31.8699 −1.28407
\(617\) 14.0470 0.565512 0.282756 0.959192i \(-0.408751\pi\)
0.282756 + 0.959192i \(0.408751\pi\)
\(618\) 60.5311 2.43492
\(619\) −14.5848 −0.586214 −0.293107 0.956080i \(-0.594689\pi\)
−0.293107 + 0.956080i \(0.594689\pi\)
\(620\) 68.4480 2.74894
\(621\) 0.770024 0.0309000
\(622\) 27.8662 1.11733
\(623\) −38.0368 −1.52391
\(624\) −0.929992 −0.0372295
\(625\) −31.1239 −1.24495
\(626\) −43.4631 −1.73713
\(627\) 28.8891 1.15372
\(628\) −82.0857 −3.27558
\(629\) −13.2848 −0.529700
\(630\) −45.8525 −1.82681
\(631\) 15.8228 0.629895 0.314947 0.949109i \(-0.398013\pi\)
0.314947 + 0.949109i \(0.398013\pi\)
\(632\) 53.7839 2.13941
\(633\) −54.2589 −2.15660
\(634\) −64.4048 −2.55784
\(635\) −1.21797 −0.0483338
\(636\) −44.0107 −1.74514
\(637\) −0.345161 −0.0136758
\(638\) 28.3691 1.12314
\(639\) −0.768246 −0.0303913
\(640\) −55.4115 −2.19033
\(641\) 1.27998 0.0505564 0.0252782 0.999680i \(-0.491953\pi\)
0.0252782 + 0.999680i \(0.491953\pi\)
\(642\) 82.4847 3.25541
\(643\) 30.2649 1.19353 0.596765 0.802416i \(-0.296452\pi\)
0.596765 + 0.802416i \(0.296452\pi\)
\(644\) 11.2714 0.444155
\(645\) 55.6011 2.18929
\(646\) −23.5640 −0.927115
\(647\) 14.0216 0.551246 0.275623 0.961266i \(-0.411116\pi\)
0.275623 + 0.961266i \(0.411116\pi\)
\(648\) 33.1183 1.30101
\(649\) 9.10193 0.357282
\(650\) −0.874279 −0.0342921
\(651\) −38.7572 −1.51901
\(652\) −3.99021 −0.156269
\(653\) 31.7172 1.24119 0.620595 0.784131i \(-0.286891\pi\)
0.620595 + 0.784131i \(0.286891\pi\)
\(654\) −49.2327 −1.92515
\(655\) 43.5368 1.70112
\(656\) 19.3267 0.754582
\(657\) −15.3267 −0.597952
\(658\) 25.3677 0.988935
\(659\) 48.4984 1.88923 0.944614 0.328182i \(-0.106436\pi\)
0.944614 + 0.328182i \(0.106436\pi\)
\(660\) −87.5405 −3.40751
\(661\) 34.9661 1.36003 0.680013 0.733201i \(-0.261974\pi\)
0.680013 + 0.733201i \(0.261974\pi\)
\(662\) 50.4476 1.96070
\(663\) −1.30006 −0.0504902
\(664\) −49.5285 −1.92208
\(665\) 19.3642 0.750911
\(666\) 33.5138 1.29863
\(667\) −4.57954 −0.177320
\(668\) 9.35299 0.361878
\(669\) 27.7252 1.07192
\(670\) 26.0542 1.00656
\(671\) 44.7301 1.72679
\(672\) 15.6545 0.603884
\(673\) −24.0260 −0.926135 −0.463067 0.886323i \(-0.653251\pi\)
−0.463067 + 0.886323i \(0.653251\pi\)
\(674\) 32.2305 1.24147
\(675\) −1.20339 −0.0463184
\(676\) −47.7248 −1.83557
\(677\) −38.3303 −1.47315 −0.736576 0.676354i \(-0.763559\pi\)
−0.736576 + 0.676354i \(0.763559\pi\)
\(678\) −68.3020 −2.62312
\(679\) 21.2049 0.813769
\(680\) 32.5915 1.24983
\(681\) 54.1040 2.07327
\(682\) −59.1705 −2.26576
\(683\) 23.5458 0.900955 0.450478 0.892788i \(-0.351254\pi\)
0.450478 + 0.892788i \(0.351254\pi\)
\(684\) 38.5117 1.47253
\(685\) −5.53713 −0.211563
\(686\) −47.9694 −1.83148
\(687\) −22.7294 −0.867179
\(688\) 18.1691 0.692692
\(689\) 0.820002 0.0312396
\(690\) 21.8127 0.830397
\(691\) −27.3120 −1.03900 −0.519499 0.854471i \(-0.673881\pi\)
−0.519499 + 0.854471i \(0.673881\pi\)
\(692\) −41.6734 −1.58418
\(693\) 25.6793 0.975476
\(694\) 14.3676 0.545385
\(695\) −53.2993 −2.02176
\(696\) 33.3197 1.26298
\(697\) 27.0174 1.02336
\(698\) 29.2539 1.10728
\(699\) 36.3498 1.37488
\(700\) −17.6148 −0.665778
\(701\) −52.1011 −1.96783 −0.983917 0.178628i \(-0.942834\pi\)
−0.983917 + 0.178628i \(0.942834\pi\)
\(702\) 0.228697 0.00863162
\(703\) −14.1533 −0.533803
\(704\) 39.4489 1.48679
\(705\) 31.8045 1.19783
\(706\) −7.32333 −0.275617
\(707\) 33.3424 1.25397
\(708\) 23.4212 0.880224
\(709\) 0.596094 0.0223868 0.0111934 0.999937i \(-0.496437\pi\)
0.0111934 + 0.999937i \(0.496437\pi\)
\(710\) −1.51752 −0.0569517
\(711\) −43.3366 −1.62525
\(712\) −68.2045 −2.55607
\(713\) 9.55172 0.357715
\(714\) −40.4312 −1.51310
\(715\) 1.63104 0.0609976
\(716\) 32.0916 1.19932
\(717\) 37.3324 1.39421
\(718\) 32.0804 1.19723
\(719\) 36.8292 1.37350 0.686749 0.726895i \(-0.259037\pi\)
0.686749 + 0.726895i \(0.259037\pi\)
\(720\) −18.7855 −0.700094
\(721\) −22.7229 −0.846244
\(722\) 20.1753 0.750847
\(723\) 26.4597 0.984048
\(724\) −89.3244 −3.31971
\(725\) 7.15686 0.265799
\(726\) 10.2704 0.381169
\(727\) 5.47852 0.203187 0.101594 0.994826i \(-0.467606\pi\)
0.101594 + 0.994826i \(0.467606\pi\)
\(728\) 1.52797 0.0566302
\(729\) −30.8847 −1.14388
\(730\) −30.2750 −1.12053
\(731\) 25.3991 0.939421
\(732\) 115.100 4.25423
\(733\) 34.9544 1.29107 0.645535 0.763731i \(-0.276634\pi\)
0.645535 + 0.763731i \(0.276634\pi\)
\(734\) 43.8063 1.61692
\(735\) −13.4581 −0.496408
\(736\) −3.85804 −0.142209
\(737\) −14.5914 −0.537482
\(738\) −68.1570 −2.50889
\(739\) 16.7379 0.615714 0.307857 0.951433i \(-0.400388\pi\)
0.307857 + 0.951433i \(0.400388\pi\)
\(740\) 42.8878 1.57659
\(741\) −1.38505 −0.0508813
\(742\) 25.5016 0.936194
\(743\) −37.3283 −1.36944 −0.684722 0.728805i \(-0.740076\pi\)
−0.684722 + 0.728805i \(0.740076\pi\)
\(744\) −69.4962 −2.54786
\(745\) 22.9302 0.840098
\(746\) −16.5452 −0.605764
\(747\) 39.9078 1.46015
\(748\) −39.9894 −1.46216
\(749\) −30.9641 −1.13140
\(750\) 45.3777 1.65696
\(751\) −9.92872 −0.362304 −0.181152 0.983455i \(-0.557983\pi\)
−0.181152 + 0.983455i \(0.557983\pi\)
\(752\) 10.3930 0.378993
\(753\) 43.8802 1.59908
\(754\) −1.36012 −0.0495327
\(755\) −19.0230 −0.692317
\(756\) 4.60775 0.167582
\(757\) −0.302253 −0.0109856 −0.00549279 0.999985i \(-0.501748\pi\)
−0.00549279 + 0.999985i \(0.501748\pi\)
\(758\) −27.0416 −0.982197
\(759\) −12.2160 −0.443414
\(760\) 34.7222 1.25951
\(761\) 21.5937 0.782769 0.391385 0.920227i \(-0.371996\pi\)
0.391385 + 0.920227i \(0.371996\pi\)
\(762\) 2.70931 0.0981478
\(763\) 18.4815 0.669077
\(764\) 7.80536 0.282388
\(765\) −26.2607 −0.949459
\(766\) 86.2685 3.11701
\(767\) −0.436382 −0.0157568
\(768\) 68.0820 2.45670
\(769\) −4.25428 −0.153413 −0.0767067 0.997054i \(-0.524440\pi\)
−0.0767067 + 0.997054i \(0.524440\pi\)
\(770\) 50.7246 1.82799
\(771\) 39.1464 1.40982
\(772\) 31.3585 1.12862
\(773\) 21.6549 0.778872 0.389436 0.921054i \(-0.372670\pi\)
0.389436 + 0.921054i \(0.372670\pi\)
\(774\) −64.0747 −2.30312
\(775\) −14.9273 −0.536206
\(776\) 38.0229 1.36494
\(777\) −24.2843 −0.871194
\(778\) −66.6015 −2.38778
\(779\) 28.7837 1.03128
\(780\) 4.19703 0.150278
\(781\) 0.849875 0.0304109
\(782\) 9.96427 0.356322
\(783\) −1.87212 −0.0669040
\(784\) −4.39778 −0.157064
\(785\) 59.6328 2.12838
\(786\) −96.8450 −3.45435
\(787\) 38.9198 1.38734 0.693670 0.720293i \(-0.255993\pi\)
0.693670 + 0.720293i \(0.255993\pi\)
\(788\) −32.3165 −1.15123
\(789\) 22.3854 0.796942
\(790\) −85.6032 −3.04563
\(791\) 25.6400 0.911654
\(792\) 46.0460 1.63617
\(793\) −2.14453 −0.0761546
\(794\) −65.6443 −2.32963
\(795\) 31.9724 1.13395
\(796\) 1.20059 0.0425537
\(797\) 0.932362 0.0330260 0.0165130 0.999864i \(-0.494744\pi\)
0.0165130 + 0.999864i \(0.494744\pi\)
\(798\) −43.0745 −1.52482
\(799\) 14.5286 0.513985
\(800\) 6.02932 0.213168
\(801\) 54.9560 1.94178
\(802\) 78.3017 2.76493
\(803\) 16.9552 0.598337
\(804\) −37.5469 −1.32418
\(805\) −8.18832 −0.288600
\(806\) 2.83686 0.0999242
\(807\) 0.848164 0.0298568
\(808\) 59.7869 2.10330
\(809\) −41.2075 −1.44878 −0.724389 0.689392i \(-0.757878\pi\)
−0.724389 + 0.689392i \(0.757878\pi\)
\(810\) −52.7116 −1.85210
\(811\) 38.7356 1.36019 0.680096 0.733123i \(-0.261938\pi\)
0.680096 + 0.733123i \(0.261938\pi\)
\(812\) −27.4035 −0.961675
\(813\) 18.6083 0.652623
\(814\) −37.0748 −1.29947
\(815\) 2.89877 0.101539
\(816\) −16.5644 −0.579870
\(817\) 27.0596 0.946697
\(818\) −27.6847 −0.967972
\(819\) −1.23116 −0.0430203
\(820\) −87.2210 −3.04589
\(821\) 29.3522 1.02440 0.512200 0.858866i \(-0.328831\pi\)
0.512200 + 0.858866i \(0.328831\pi\)
\(822\) 12.3170 0.429605
\(823\) −27.0107 −0.941535 −0.470768 0.882257i \(-0.656023\pi\)
−0.470768 + 0.882257i \(0.656023\pi\)
\(824\) −40.7448 −1.41941
\(825\) 19.0911 0.664667
\(826\) −13.5712 −0.472204
\(827\) 12.9494 0.450295 0.225147 0.974325i \(-0.427714\pi\)
0.225147 + 0.974325i \(0.427714\pi\)
\(828\) −16.2850 −0.565944
\(829\) −0.270202 −0.00938449 −0.00469225 0.999989i \(-0.501494\pi\)
−0.00469225 + 0.999989i \(0.501494\pi\)
\(830\) 78.8303 2.73624
\(831\) 59.2634 2.05583
\(832\) −1.89133 −0.0655701
\(833\) −6.14778 −0.213008
\(834\) 118.561 4.10543
\(835\) −6.79466 −0.235139
\(836\) −42.6038 −1.47348
\(837\) 3.90475 0.134968
\(838\) −36.5104 −1.26123
\(839\) 6.54256 0.225874 0.112937 0.993602i \(-0.463974\pi\)
0.112937 + 0.993602i \(0.463974\pi\)
\(840\) 59.5764 2.05558
\(841\) −17.8660 −0.616070
\(842\) −53.4889 −1.84335
\(843\) −31.7102 −1.09216
\(844\) 80.0175 2.75432
\(845\) 34.6706 1.19271
\(846\) −36.6515 −1.26010
\(847\) −3.85541 −0.132473
\(848\) 10.4478 0.358780
\(849\) −28.9419 −0.993283
\(850\) −15.5721 −0.534118
\(851\) 5.98487 0.205159
\(852\) 2.18691 0.0749224
\(853\) −1.50858 −0.0516528 −0.0258264 0.999666i \(-0.508222\pi\)
−0.0258264 + 0.999666i \(0.508222\pi\)
\(854\) −66.6939 −2.28222
\(855\) −27.9776 −0.956813
\(856\) −55.5222 −1.89771
\(857\) 19.2304 0.656897 0.328448 0.944522i \(-0.393474\pi\)
0.328448 + 0.944522i \(0.393474\pi\)
\(858\) −3.62816 −0.123863
\(859\) −28.0626 −0.957485 −0.478743 0.877955i \(-0.658907\pi\)
−0.478743 + 0.877955i \(0.658907\pi\)
\(860\) −81.9968 −2.79607
\(861\) 49.3870 1.68310
\(862\) 52.2724 1.78041
\(863\) −15.6969 −0.534328 −0.267164 0.963651i \(-0.586087\pi\)
−0.267164 + 0.963651i \(0.586087\pi\)
\(864\) −1.57717 −0.0536564
\(865\) 30.2745 1.02936
\(866\) −87.5287 −2.97435
\(867\) 19.2587 0.654059
\(868\) 57.1566 1.94002
\(869\) 47.9413 1.62630
\(870\) −53.0321 −1.79796
\(871\) 0.699569 0.0237040
\(872\) 33.1396 1.12225
\(873\) −30.6371 −1.03691
\(874\) 10.6157 0.359082
\(875\) −17.0344 −0.575868
\(876\) 43.6295 1.47410
\(877\) −14.6274 −0.493934 −0.246967 0.969024i \(-0.579434\pi\)
−0.246967 + 0.969024i \(0.579434\pi\)
\(878\) −80.2672 −2.70889
\(879\) 15.2230 0.513459
\(880\) 20.7815 0.700545
\(881\) 24.6365 0.830024 0.415012 0.909816i \(-0.363777\pi\)
0.415012 + 0.909816i \(0.363777\pi\)
\(882\) 15.5091 0.522218
\(883\) 21.6211 0.727609 0.363804 0.931475i \(-0.381478\pi\)
0.363804 + 0.931475i \(0.381478\pi\)
\(884\) 1.91724 0.0644839
\(885\) −17.0148 −0.571947
\(886\) −28.7792 −0.966855
\(887\) −19.8445 −0.666314 −0.333157 0.942871i \(-0.608114\pi\)
−0.333157 + 0.942871i \(0.608114\pi\)
\(888\) −43.5446 −1.46126
\(889\) −1.01705 −0.0341108
\(890\) 108.555 3.63878
\(891\) 29.5206 0.988979
\(892\) −40.8873 −1.36901
\(893\) 15.4785 0.517967
\(894\) −51.0069 −1.70592
\(895\) −23.3136 −0.779286
\(896\) −46.2706 −1.54579
\(897\) 0.585683 0.0195554
\(898\) −68.5251 −2.28671
\(899\) −23.2226 −0.774516
\(900\) 25.4501 0.848337
\(901\) 14.6053 0.486574
\(902\) 75.3990 2.51051
\(903\) 46.4289 1.54506
\(904\) 45.9756 1.52912
\(905\) 64.8915 2.15707
\(906\) 42.3154 1.40584
\(907\) −57.5316 −1.91031 −0.955153 0.296114i \(-0.904309\pi\)
−0.955153 + 0.296114i \(0.904309\pi\)
\(908\) −79.7890 −2.64789
\(909\) −48.1735 −1.59782
\(910\) −2.43193 −0.0806178
\(911\) 12.7535 0.422543 0.211271 0.977427i \(-0.432240\pi\)
0.211271 + 0.977427i \(0.432240\pi\)
\(912\) −17.6473 −0.584361
\(913\) −44.1482 −1.46109
\(914\) −75.6743 −2.50308
\(915\) −83.6169 −2.76429
\(916\) 33.5198 1.10752
\(917\) 36.3548 1.20054
\(918\) 4.07340 0.134442
\(919\) −1.67382 −0.0552142 −0.0276071 0.999619i \(-0.508789\pi\)
−0.0276071 + 0.999619i \(0.508789\pi\)
\(920\) −14.6826 −0.484072
\(921\) −1.01123 −0.0333213
\(922\) 84.4921 2.78260
\(923\) −0.0407463 −0.00134118
\(924\) −73.0995 −2.40480
\(925\) −9.35310 −0.307528
\(926\) −6.66989 −0.219186
\(927\) 32.8302 1.07829
\(928\) 9.37985 0.307909
\(929\) 1.56230 0.0512573 0.0256287 0.999672i \(-0.491841\pi\)
0.0256287 + 0.999672i \(0.491841\pi\)
\(930\) 110.611 3.62708
\(931\) −6.54970 −0.214658
\(932\) −53.6063 −1.75593
\(933\) 29.1736 0.955102
\(934\) −83.8968 −2.74519
\(935\) 29.0511 0.950072
\(936\) −2.20762 −0.0721583
\(937\) −41.5510 −1.35741 −0.678706 0.734410i \(-0.737459\pi\)
−0.678706 + 0.734410i \(0.737459\pi\)
\(938\) 21.7562 0.710366
\(939\) −45.5023 −1.48491
\(940\) −46.9032 −1.52981
\(941\) −5.02999 −0.163973 −0.0819864 0.996633i \(-0.526126\pi\)
−0.0819864 + 0.996633i \(0.526126\pi\)
\(942\) −132.649 −4.32195
\(943\) −12.1714 −0.396357
\(944\) −5.56004 −0.180964
\(945\) −3.34739 −0.108891
\(946\) 70.8829 2.30460
\(947\) 32.6372 1.06057 0.530284 0.847820i \(-0.322085\pi\)
0.530284 + 0.847820i \(0.322085\pi\)
\(948\) 123.363 4.00665
\(949\) −0.812899 −0.0263878
\(950\) −16.5901 −0.538255
\(951\) −67.4267 −2.18646
\(952\) 27.2151 0.882046
\(953\) −38.9007 −1.26012 −0.630058 0.776548i \(-0.716969\pi\)
−0.630058 + 0.776548i \(0.716969\pi\)
\(954\) −36.8450 −1.19290
\(955\) −5.67035 −0.183488
\(956\) −55.0554 −1.78062
\(957\) 29.7002 0.960070
\(958\) −5.97667 −0.193097
\(959\) −4.62371 −0.149307
\(960\) −73.7444 −2.38009
\(961\) 17.4363 0.562460
\(962\) 1.77751 0.0573091
\(963\) 44.7372 1.44164
\(964\) −39.0211 −1.25678
\(965\) −22.7810 −0.733346
\(966\) 18.2144 0.586040
\(967\) −21.9054 −0.704430 −0.352215 0.935919i \(-0.614571\pi\)
−0.352215 + 0.935919i \(0.614571\pi\)
\(968\) −6.91319 −0.222198
\(969\) −24.6697 −0.792504
\(970\) −60.5178 −1.94311
\(971\) −50.0639 −1.60663 −0.803314 0.595556i \(-0.796932\pi\)
−0.803314 + 0.595556i \(0.796932\pi\)
\(972\) 82.1561 2.63516
\(973\) −44.5068 −1.42682
\(974\) −39.6885 −1.27170
\(975\) −0.915300 −0.0293131
\(976\) −27.3240 −0.874621
\(977\) 53.3465 1.70671 0.853353 0.521333i \(-0.174565\pi\)
0.853353 + 0.521333i \(0.174565\pi\)
\(978\) −6.44814 −0.206189
\(979\) −60.7954 −1.94303
\(980\) 19.8471 0.633992
\(981\) −26.7023 −0.852540
\(982\) −14.9318 −0.476493
\(983\) −48.7942 −1.55629 −0.778147 0.628082i \(-0.783840\pi\)
−0.778147 + 0.628082i \(0.783840\pi\)
\(984\) 88.5567 2.82308
\(985\) 23.4770 0.748039
\(986\) −24.2256 −0.771500
\(987\) 26.5579 0.845348
\(988\) 2.04259 0.0649834
\(989\) −11.4424 −0.363848
\(990\) −73.2875 −2.32923
\(991\) −4.87308 −0.154798 −0.0773992 0.997000i \(-0.524662\pi\)
−0.0773992 + 0.997000i \(0.524662\pi\)
\(992\) −19.5639 −0.621155
\(993\) 52.8146 1.67602
\(994\) −1.26719 −0.0401927
\(995\) −0.872191 −0.0276503
\(996\) −113.603 −3.59964
\(997\) 28.5128 0.903009 0.451504 0.892269i \(-0.350888\pi\)
0.451504 + 0.892269i \(0.350888\pi\)
\(998\) 72.1436 2.28367
\(999\) 2.44662 0.0774076
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.1.19 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.19 259 1.1 even 1 trivial