Properties

Label 6017.2.a.f.1.10
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.54623 q^{2} -1.76925 q^{3} +4.48328 q^{4} -0.663879 q^{5} +4.50492 q^{6} -3.59601 q^{7} -6.32301 q^{8} +0.130248 q^{9} +O(q^{10})\) \(q-2.54623 q^{2} -1.76925 q^{3} +4.48328 q^{4} -0.663879 q^{5} +4.50492 q^{6} -3.59601 q^{7} -6.32301 q^{8} +0.130248 q^{9} +1.69039 q^{10} -1.00000 q^{11} -7.93205 q^{12} +2.37087 q^{13} +9.15627 q^{14} +1.17457 q^{15} +7.13326 q^{16} +0.864490 q^{17} -0.331642 q^{18} -0.433464 q^{19} -2.97636 q^{20} +6.36225 q^{21} +2.54623 q^{22} +7.71083 q^{23} +11.1870 q^{24} -4.55926 q^{25} -6.03679 q^{26} +5.07731 q^{27} -16.1219 q^{28} +3.04739 q^{29} -2.99072 q^{30} +6.27472 q^{31} -5.51689 q^{32} +1.76925 q^{33} -2.20119 q^{34} +2.38732 q^{35} +0.583939 q^{36} +5.25374 q^{37} +1.10370 q^{38} -4.19467 q^{39} +4.19771 q^{40} -0.827912 q^{41} -16.1997 q^{42} +3.20055 q^{43} -4.48328 q^{44} -0.0864690 q^{45} -19.6335 q^{46} -2.66970 q^{47} -12.6205 q^{48} +5.93131 q^{49} +11.6089 q^{50} -1.52950 q^{51} +10.6293 q^{52} +0.411986 q^{53} -12.9280 q^{54} +0.663879 q^{55} +22.7376 q^{56} +0.766906 q^{57} -7.75936 q^{58} -11.0557 q^{59} +5.26592 q^{60} -3.37352 q^{61} -15.9769 q^{62} -0.468374 q^{63} -0.219240 q^{64} -1.57397 q^{65} -4.50492 q^{66} +10.4408 q^{67} +3.87575 q^{68} -13.6424 q^{69} -6.07866 q^{70} -7.58971 q^{71} -0.823560 q^{72} -11.1191 q^{73} -13.3772 q^{74} +8.06648 q^{75} -1.94334 q^{76} +3.59601 q^{77} +10.6806 q^{78} -7.43624 q^{79} -4.73562 q^{80} -9.37378 q^{81} +2.10805 q^{82} +8.56768 q^{83} +28.5238 q^{84} -0.573917 q^{85} -8.14934 q^{86} -5.39160 q^{87} +6.32301 q^{88} -2.14094 q^{89} +0.220170 q^{90} -8.52569 q^{91} +34.5698 q^{92} -11.1015 q^{93} +6.79766 q^{94} +0.287768 q^{95} +9.76077 q^{96} +15.9031 q^{97} -15.1025 q^{98} -0.130248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54623 −1.80046 −0.900228 0.435419i \(-0.856600\pi\)
−0.900228 + 0.435419i \(0.856600\pi\)
\(3\) −1.76925 −1.02148 −0.510739 0.859736i \(-0.670628\pi\)
−0.510739 + 0.859736i \(0.670628\pi\)
\(4\) 4.48328 2.24164
\(5\) −0.663879 −0.296896 −0.148448 0.988920i \(-0.547428\pi\)
−0.148448 + 0.988920i \(0.547428\pi\)
\(6\) 4.50492 1.83912
\(7\) −3.59601 −1.35917 −0.679583 0.733599i \(-0.737839\pi\)
−0.679583 + 0.733599i \(0.737839\pi\)
\(8\) −6.32301 −2.23552
\(9\) 0.130248 0.0434160
\(10\) 1.69039 0.534548
\(11\) −1.00000 −0.301511
\(12\) −7.93205 −2.28979
\(13\) 2.37087 0.657562 0.328781 0.944406i \(-0.393362\pi\)
0.328781 + 0.944406i \(0.393362\pi\)
\(14\) 9.15627 2.44712
\(15\) 1.17457 0.303272
\(16\) 7.13326 1.78331
\(17\) 0.864490 0.209670 0.104835 0.994490i \(-0.466569\pi\)
0.104835 + 0.994490i \(0.466569\pi\)
\(18\) −0.331642 −0.0781687
\(19\) −0.433464 −0.0994435 −0.0497217 0.998763i \(-0.515833\pi\)
−0.0497217 + 0.998763i \(0.515833\pi\)
\(20\) −2.97636 −0.665534
\(21\) 6.36225 1.38836
\(22\) 2.54623 0.542858
\(23\) 7.71083 1.60782 0.803910 0.594751i \(-0.202749\pi\)
0.803910 + 0.594751i \(0.202749\pi\)
\(24\) 11.1870 2.28353
\(25\) −4.55926 −0.911853
\(26\) −6.03679 −1.18391
\(27\) 5.07731 0.977129
\(28\) −16.1219 −3.04676
\(29\) 3.04739 0.565887 0.282943 0.959137i \(-0.408689\pi\)
0.282943 + 0.959137i \(0.408689\pi\)
\(30\) −2.99072 −0.546028
\(31\) 6.27472 1.12697 0.563486 0.826125i \(-0.309460\pi\)
0.563486 + 0.826125i \(0.309460\pi\)
\(32\) −5.51689 −0.975258
\(33\) 1.76925 0.307987
\(34\) −2.20119 −0.377501
\(35\) 2.38732 0.403530
\(36\) 0.583939 0.0973232
\(37\) 5.25374 0.863710 0.431855 0.901943i \(-0.357859\pi\)
0.431855 + 0.901943i \(0.357859\pi\)
\(38\) 1.10370 0.179044
\(39\) −4.19467 −0.671685
\(40\) 4.19771 0.663716
\(41\) −0.827912 −0.129298 −0.0646490 0.997908i \(-0.520593\pi\)
−0.0646490 + 0.997908i \(0.520593\pi\)
\(42\) −16.1997 −2.49967
\(43\) 3.20055 0.488080 0.244040 0.969765i \(-0.421527\pi\)
0.244040 + 0.969765i \(0.421527\pi\)
\(44\) −4.48328 −0.675880
\(45\) −0.0864690 −0.0128900
\(46\) −19.6335 −2.89481
\(47\) −2.66970 −0.389415 −0.194708 0.980861i \(-0.562376\pi\)
−0.194708 + 0.980861i \(0.562376\pi\)
\(48\) −12.6205 −1.82161
\(49\) 5.93131 0.847330
\(50\) 11.6089 1.64175
\(51\) −1.52950 −0.214173
\(52\) 10.6293 1.47402
\(53\) 0.411986 0.0565906 0.0282953 0.999600i \(-0.490992\pi\)
0.0282953 + 0.999600i \(0.490992\pi\)
\(54\) −12.9280 −1.75928
\(55\) 0.663879 0.0895174
\(56\) 22.7376 3.03844
\(57\) 0.766906 0.101579
\(58\) −7.75936 −1.01885
\(59\) −11.0557 −1.43933 −0.719663 0.694324i \(-0.755704\pi\)
−0.719663 + 0.694324i \(0.755704\pi\)
\(60\) 5.26592 0.679828
\(61\) −3.37352 −0.431935 −0.215968 0.976401i \(-0.569291\pi\)
−0.215968 + 0.976401i \(0.569291\pi\)
\(62\) −15.9769 −2.02906
\(63\) −0.468374 −0.0590096
\(64\) −0.219240 −0.0274050
\(65\) −1.57397 −0.195227
\(66\) −4.50492 −0.554517
\(67\) 10.4408 1.27555 0.637773 0.770224i \(-0.279856\pi\)
0.637773 + 0.770224i \(0.279856\pi\)
\(68\) 3.87575 0.470004
\(69\) −13.6424 −1.64235
\(70\) −6.07866 −0.726539
\(71\) −7.58971 −0.900733 −0.450366 0.892844i \(-0.648707\pi\)
−0.450366 + 0.892844i \(0.648707\pi\)
\(72\) −0.823560 −0.0970574
\(73\) −11.1191 −1.30139 −0.650695 0.759339i \(-0.725522\pi\)
−0.650695 + 0.759339i \(0.725522\pi\)
\(74\) −13.3772 −1.55507
\(75\) 8.06648 0.931437
\(76\) −1.94334 −0.222917
\(77\) 3.59601 0.409804
\(78\) 10.6806 1.20934
\(79\) −7.43624 −0.836642 −0.418321 0.908299i \(-0.637381\pi\)
−0.418321 + 0.908299i \(0.637381\pi\)
\(80\) −4.73562 −0.529458
\(81\) −9.37378 −1.04153
\(82\) 2.10805 0.232795
\(83\) 8.56768 0.940425 0.470212 0.882553i \(-0.344177\pi\)
0.470212 + 0.882553i \(0.344177\pi\)
\(84\) 28.5238 3.11220
\(85\) −0.573917 −0.0622501
\(86\) −8.14934 −0.878766
\(87\) −5.39160 −0.578040
\(88\) 6.32301 0.674035
\(89\) −2.14094 −0.226939 −0.113470 0.993541i \(-0.536196\pi\)
−0.113470 + 0.993541i \(0.536196\pi\)
\(90\) 0.220170 0.0232079
\(91\) −8.52569 −0.893735
\(92\) 34.5698 3.60416
\(93\) −11.1015 −1.15118
\(94\) 6.79766 0.701125
\(95\) 0.287768 0.0295243
\(96\) 9.76077 0.996204
\(97\) 15.9031 1.61471 0.807356 0.590065i \(-0.200898\pi\)
0.807356 + 0.590065i \(0.200898\pi\)
\(98\) −15.1025 −1.52558
\(99\) −0.130248 −0.0130904
\(100\) −20.4405 −2.04405
\(101\) −18.5255 −1.84336 −0.921680 0.387950i \(-0.873183\pi\)
−0.921680 + 0.387950i \(0.873183\pi\)
\(102\) 3.89446 0.385609
\(103\) −4.56476 −0.449779 −0.224890 0.974384i \(-0.572202\pi\)
−0.224890 + 0.974384i \(0.572202\pi\)
\(104\) −14.9910 −1.46999
\(105\) −4.22376 −0.412197
\(106\) −1.04901 −0.101889
\(107\) −11.8468 −1.14528 −0.572638 0.819808i \(-0.694080\pi\)
−0.572638 + 0.819808i \(0.694080\pi\)
\(108\) 22.7630 2.19037
\(109\) 8.58578 0.822369 0.411184 0.911552i \(-0.365115\pi\)
0.411184 + 0.911552i \(0.365115\pi\)
\(110\) −1.69039 −0.161172
\(111\) −9.29519 −0.882261
\(112\) −25.6513 −2.42382
\(113\) 2.69394 0.253425 0.126712 0.991940i \(-0.459557\pi\)
0.126712 + 0.991940i \(0.459557\pi\)
\(114\) −1.95272 −0.182889
\(115\) −5.11906 −0.477355
\(116\) 13.6623 1.26851
\(117\) 0.308802 0.0285487
\(118\) 28.1503 2.59144
\(119\) −3.10872 −0.284976
\(120\) −7.42680 −0.677971
\(121\) 1.00000 0.0909091
\(122\) 8.58976 0.777681
\(123\) 1.46478 0.132075
\(124\) 28.1313 2.52627
\(125\) 6.34620 0.567621
\(126\) 1.19259 0.106244
\(127\) −7.28935 −0.646825 −0.323413 0.946258i \(-0.604830\pi\)
−0.323413 + 0.946258i \(0.604830\pi\)
\(128\) 11.5920 1.02460
\(129\) −5.66258 −0.498562
\(130\) 4.00770 0.351498
\(131\) 9.39709 0.821028 0.410514 0.911854i \(-0.365349\pi\)
0.410514 + 0.911854i \(0.365349\pi\)
\(132\) 7.93205 0.690396
\(133\) 1.55874 0.135160
\(134\) −26.5847 −2.29656
\(135\) −3.37072 −0.290105
\(136\) −5.46618 −0.468721
\(137\) −14.9699 −1.27896 −0.639480 0.768807i \(-0.720850\pi\)
−0.639480 + 0.768807i \(0.720850\pi\)
\(138\) 34.7367 2.95698
\(139\) 10.5242 0.892651 0.446325 0.894871i \(-0.352732\pi\)
0.446325 + 0.894871i \(0.352732\pi\)
\(140\) 10.7030 0.904570
\(141\) 4.72336 0.397779
\(142\) 19.3251 1.62173
\(143\) −2.37087 −0.198262
\(144\) 0.929093 0.0774244
\(145\) −2.02310 −0.168009
\(146\) 28.3117 2.34309
\(147\) −10.4940 −0.865529
\(148\) 23.5540 1.93613
\(149\) 2.16860 0.177658 0.0888292 0.996047i \(-0.471687\pi\)
0.0888292 + 0.996047i \(0.471687\pi\)
\(150\) −20.5391 −1.67701
\(151\) 10.6063 0.863129 0.431565 0.902082i \(-0.357962\pi\)
0.431565 + 0.902082i \(0.357962\pi\)
\(152\) 2.74080 0.222308
\(153\) 0.112598 0.00910303
\(154\) −9.15627 −0.737834
\(155\) −4.16565 −0.334593
\(156\) −18.8059 −1.50568
\(157\) 2.43305 0.194179 0.0970893 0.995276i \(-0.469047\pi\)
0.0970893 + 0.995276i \(0.469047\pi\)
\(158\) 18.9344 1.50634
\(159\) −0.728906 −0.0578060
\(160\) 3.66255 0.289550
\(161\) −27.7283 −2.18529
\(162\) 23.8678 1.87523
\(163\) 6.30007 0.493459 0.246730 0.969084i \(-0.420644\pi\)
0.246730 + 0.969084i \(0.420644\pi\)
\(164\) −3.71176 −0.289840
\(165\) −1.17457 −0.0914400
\(166\) −21.8153 −1.69319
\(167\) −8.23261 −0.637059 −0.318529 0.947913i \(-0.603189\pi\)
−0.318529 + 0.947913i \(0.603189\pi\)
\(168\) −40.2285 −3.10370
\(169\) −7.37896 −0.567612
\(170\) 1.46132 0.112078
\(171\) −0.0564579 −0.00431744
\(172\) 14.3490 1.09410
\(173\) −10.5745 −0.803962 −0.401981 0.915648i \(-0.631678\pi\)
−0.401981 + 0.915648i \(0.631678\pi\)
\(174\) 13.7283 1.04074
\(175\) 16.3952 1.23936
\(176\) −7.13326 −0.537689
\(177\) 19.5602 1.47024
\(178\) 5.45133 0.408594
\(179\) −0.395686 −0.0295749 −0.0147875 0.999891i \(-0.504707\pi\)
−0.0147875 + 0.999891i \(0.504707\pi\)
\(180\) −0.387665 −0.0288948
\(181\) 8.98573 0.667904 0.333952 0.942590i \(-0.391618\pi\)
0.333952 + 0.942590i \(0.391618\pi\)
\(182\) 21.7084 1.60913
\(183\) 5.96861 0.441212
\(184\) −48.7556 −3.59431
\(185\) −3.48785 −0.256432
\(186\) 28.2671 2.07264
\(187\) −0.864490 −0.0632178
\(188\) −11.9690 −0.872929
\(189\) −18.2581 −1.32808
\(190\) −0.732722 −0.0531573
\(191\) 10.7584 0.778449 0.389225 0.921143i \(-0.372743\pi\)
0.389225 + 0.921143i \(0.372743\pi\)
\(192\) 0.387891 0.0279936
\(193\) 19.4827 1.40239 0.701197 0.712967i \(-0.252649\pi\)
0.701197 + 0.712967i \(0.252649\pi\)
\(194\) −40.4929 −2.90722
\(195\) 2.78475 0.199420
\(196\) 26.5918 1.89941
\(197\) −16.4192 −1.16982 −0.584910 0.811098i \(-0.698870\pi\)
−0.584910 + 0.811098i \(0.698870\pi\)
\(198\) 0.331642 0.0235687
\(199\) 6.44984 0.457217 0.228609 0.973518i \(-0.426582\pi\)
0.228609 + 0.973518i \(0.426582\pi\)
\(200\) 28.8283 2.03847
\(201\) −18.4724 −1.30294
\(202\) 47.1703 3.31889
\(203\) −10.9585 −0.769134
\(204\) −6.85718 −0.480099
\(205\) 0.549633 0.0383880
\(206\) 11.6229 0.809807
\(207\) 1.00432 0.0698052
\(208\) 16.9120 1.17264
\(209\) 0.433464 0.0299833
\(210\) 10.7547 0.742143
\(211\) −19.0062 −1.30844 −0.654222 0.756303i \(-0.727004\pi\)
−0.654222 + 0.756303i \(0.727004\pi\)
\(212\) 1.84705 0.126856
\(213\) 13.4281 0.920078
\(214\) 30.1647 2.06202
\(215\) −2.12478 −0.144909
\(216\) −32.1039 −2.18439
\(217\) −22.5640 −1.53174
\(218\) −21.8614 −1.48064
\(219\) 19.6724 1.32934
\(220\) 2.97636 0.200666
\(221\) 2.04960 0.137871
\(222\) 23.6677 1.58847
\(223\) 21.3514 1.42979 0.714896 0.699231i \(-0.246474\pi\)
0.714896 + 0.699231i \(0.246474\pi\)
\(224\) 19.8388 1.32554
\(225\) −0.593836 −0.0395890
\(226\) −6.85939 −0.456280
\(227\) 16.9954 1.12802 0.564011 0.825767i \(-0.309258\pi\)
0.564011 + 0.825767i \(0.309258\pi\)
\(228\) 3.43826 0.227704
\(229\) −10.5687 −0.698398 −0.349199 0.937049i \(-0.613546\pi\)
−0.349199 + 0.937049i \(0.613546\pi\)
\(230\) 13.0343 0.859456
\(231\) −6.36225 −0.418605
\(232\) −19.2687 −1.26505
\(233\) −6.02817 −0.394919 −0.197459 0.980311i \(-0.563269\pi\)
−0.197459 + 0.980311i \(0.563269\pi\)
\(234\) −0.786280 −0.0514007
\(235\) 1.77236 0.115616
\(236\) −49.5657 −3.22645
\(237\) 13.1566 0.854611
\(238\) 7.91551 0.513086
\(239\) −24.6934 −1.59728 −0.798642 0.601807i \(-0.794448\pi\)
−0.798642 + 0.601807i \(0.794448\pi\)
\(240\) 8.37850 0.540830
\(241\) 7.96234 0.512899 0.256450 0.966558i \(-0.417447\pi\)
0.256450 + 0.966558i \(0.417447\pi\)
\(242\) −2.54623 −0.163678
\(243\) 1.35263 0.0867716
\(244\) −15.1245 −0.968244
\(245\) −3.93767 −0.251569
\(246\) −3.72967 −0.237795
\(247\) −1.02769 −0.0653902
\(248\) −39.6751 −2.51937
\(249\) −15.1584 −0.960623
\(250\) −16.1589 −1.02198
\(251\) −4.45640 −0.281285 −0.140643 0.990060i \(-0.544917\pi\)
−0.140643 + 0.990060i \(0.544917\pi\)
\(252\) −2.09985 −0.132278
\(253\) −7.71083 −0.484776
\(254\) 18.5604 1.16458
\(255\) 1.01540 0.0635870
\(256\) −29.0775 −1.81734
\(257\) 19.1814 1.19650 0.598250 0.801310i \(-0.295863\pi\)
0.598250 + 0.801310i \(0.295863\pi\)
\(258\) 14.4182 0.897639
\(259\) −18.8925 −1.17393
\(260\) −7.05657 −0.437630
\(261\) 0.396917 0.0245686
\(262\) −23.9271 −1.47822
\(263\) −18.8486 −1.16225 −0.581127 0.813813i \(-0.697388\pi\)
−0.581127 + 0.813813i \(0.697388\pi\)
\(264\) −11.1870 −0.688511
\(265\) −0.273509 −0.0168015
\(266\) −3.96891 −0.243350
\(267\) 3.78786 0.231813
\(268\) 46.8090 2.85932
\(269\) 1.81484 0.110653 0.0553265 0.998468i \(-0.482380\pi\)
0.0553265 + 0.998468i \(0.482380\pi\)
\(270\) 8.58263 0.522322
\(271\) −5.58690 −0.339380 −0.169690 0.985498i \(-0.554277\pi\)
−0.169690 + 0.985498i \(0.554277\pi\)
\(272\) 6.16663 0.373907
\(273\) 15.0841 0.912931
\(274\) 38.1167 2.30271
\(275\) 4.55926 0.274934
\(276\) −61.1627 −3.68156
\(277\) 17.6667 1.06149 0.530745 0.847531i \(-0.321912\pi\)
0.530745 + 0.847531i \(0.321912\pi\)
\(278\) −26.7970 −1.60718
\(279\) 0.817270 0.0489287
\(280\) −15.0950 −0.902100
\(281\) −7.69962 −0.459321 −0.229660 0.973271i \(-0.573762\pi\)
−0.229660 + 0.973271i \(0.573762\pi\)
\(282\) −12.0268 −0.716183
\(283\) −9.64049 −0.573068 −0.286534 0.958070i \(-0.592503\pi\)
−0.286534 + 0.958070i \(0.592503\pi\)
\(284\) −34.0268 −2.01912
\(285\) −0.509133 −0.0301584
\(286\) 6.03679 0.356963
\(287\) 2.97718 0.175737
\(288\) −0.718565 −0.0423418
\(289\) −16.2527 −0.956039
\(290\) 5.15128 0.302493
\(291\) −28.1365 −1.64939
\(292\) −49.8500 −2.91725
\(293\) −16.8094 −0.982013 −0.491007 0.871156i \(-0.663371\pi\)
−0.491007 + 0.871156i \(0.663371\pi\)
\(294\) 26.7201 1.55835
\(295\) 7.33963 0.427330
\(296\) −33.2195 −1.93084
\(297\) −5.07731 −0.294615
\(298\) −5.52175 −0.319866
\(299\) 18.2814 1.05724
\(300\) 36.1643 2.08795
\(301\) −11.5092 −0.663381
\(302\) −27.0061 −1.55403
\(303\) 32.7763 1.88295
\(304\) −3.09201 −0.177339
\(305\) 2.23961 0.128240
\(306\) −0.286701 −0.0163896
\(307\) 7.08964 0.404627 0.202314 0.979321i \(-0.435154\pi\)
0.202314 + 0.979321i \(0.435154\pi\)
\(308\) 16.1219 0.918633
\(309\) 8.07620 0.459439
\(310\) 10.6067 0.602421
\(311\) −11.5590 −0.655451 −0.327725 0.944773i \(-0.606282\pi\)
−0.327725 + 0.944773i \(0.606282\pi\)
\(312\) 26.5229 1.50156
\(313\) −26.1214 −1.47647 −0.738234 0.674545i \(-0.764340\pi\)
−0.738234 + 0.674545i \(0.764340\pi\)
\(314\) −6.19511 −0.349610
\(315\) 0.310944 0.0175197
\(316\) −33.3387 −1.87545
\(317\) 24.0659 1.35168 0.675839 0.737049i \(-0.263782\pi\)
0.675839 + 0.737049i \(0.263782\pi\)
\(318\) 1.85596 0.104077
\(319\) −3.04739 −0.170621
\(320\) 0.145549 0.00813644
\(321\) 20.9600 1.16987
\(322\) 70.6025 3.93452
\(323\) −0.374725 −0.0208503
\(324\) −42.0253 −2.33474
\(325\) −10.8094 −0.599600
\(326\) −16.0414 −0.888451
\(327\) −15.1904 −0.840031
\(328\) 5.23489 0.289048
\(329\) 9.60026 0.529280
\(330\) 2.99072 0.164634
\(331\) 6.32706 0.347767 0.173883 0.984766i \(-0.444368\pi\)
0.173883 + 0.984766i \(0.444368\pi\)
\(332\) 38.4113 2.10809
\(333\) 0.684290 0.0374989
\(334\) 20.9621 1.14700
\(335\) −6.93143 −0.378704
\(336\) 45.3836 2.47588
\(337\) 33.6648 1.83384 0.916919 0.399073i \(-0.130668\pi\)
0.916919 + 0.399073i \(0.130668\pi\)
\(338\) 18.7885 1.02196
\(339\) −4.76626 −0.258868
\(340\) −2.57303 −0.139542
\(341\) −6.27472 −0.339795
\(342\) 0.143755 0.00777336
\(343\) 3.84301 0.207503
\(344\) −20.2371 −1.09111
\(345\) 9.05690 0.487607
\(346\) 26.9250 1.44750
\(347\) −17.9486 −0.963531 −0.481766 0.876300i \(-0.660004\pi\)
−0.481766 + 0.876300i \(0.660004\pi\)
\(348\) −24.1721 −1.29576
\(349\) −10.2951 −0.551082 −0.275541 0.961289i \(-0.588857\pi\)
−0.275541 + 0.961289i \(0.588857\pi\)
\(350\) −41.7459 −2.23141
\(351\) 12.0377 0.642523
\(352\) 5.51689 0.294051
\(353\) −19.6296 −1.04478 −0.522389 0.852707i \(-0.674959\pi\)
−0.522389 + 0.852707i \(0.674959\pi\)
\(354\) −49.8049 −2.64710
\(355\) 5.03865 0.267424
\(356\) −9.59844 −0.508717
\(357\) 5.50010 0.291096
\(358\) 1.00751 0.0532484
\(359\) 18.6737 0.985561 0.492780 0.870154i \(-0.335981\pi\)
0.492780 + 0.870154i \(0.335981\pi\)
\(360\) 0.546744 0.0288159
\(361\) −18.8121 −0.990111
\(362\) −22.8797 −1.20253
\(363\) −1.76925 −0.0928616
\(364\) −38.2231 −2.00343
\(365\) 7.38172 0.386377
\(366\) −15.1974 −0.794383
\(367\) −4.28026 −0.223428 −0.111714 0.993740i \(-0.535634\pi\)
−0.111714 + 0.993740i \(0.535634\pi\)
\(368\) 55.0033 2.86725
\(369\) −0.107834 −0.00561361
\(370\) 8.88087 0.461694
\(371\) −1.48151 −0.0769160
\(372\) −49.7714 −2.58053
\(373\) −2.33403 −0.120851 −0.0604257 0.998173i \(-0.519246\pi\)
−0.0604257 + 0.998173i \(0.519246\pi\)
\(374\) 2.20119 0.113821
\(375\) −11.2280 −0.579812
\(376\) 16.8805 0.870545
\(377\) 7.22498 0.372106
\(378\) 46.4892 2.39115
\(379\) 8.57064 0.440244 0.220122 0.975472i \(-0.429354\pi\)
0.220122 + 0.975472i \(0.429354\pi\)
\(380\) 1.29014 0.0661830
\(381\) 12.8967 0.660717
\(382\) −27.3933 −1.40156
\(383\) 19.0896 0.975431 0.487715 0.873003i \(-0.337830\pi\)
0.487715 + 0.873003i \(0.337830\pi\)
\(384\) −20.5092 −1.04661
\(385\) −2.38732 −0.121669
\(386\) −49.6074 −2.52495
\(387\) 0.416866 0.0211905
\(388\) 71.2979 3.61960
\(389\) −7.91748 −0.401432 −0.200716 0.979649i \(-0.564327\pi\)
−0.200716 + 0.979649i \(0.564327\pi\)
\(390\) −7.09062 −0.359048
\(391\) 6.66594 0.337111
\(392\) −37.5037 −1.89422
\(393\) −16.6258 −0.838661
\(394\) 41.8071 2.10621
\(395\) 4.93676 0.248395
\(396\) −0.583939 −0.0293440
\(397\) −4.53224 −0.227466 −0.113733 0.993511i \(-0.536281\pi\)
−0.113733 + 0.993511i \(0.536281\pi\)
\(398\) −16.4228 −0.823200
\(399\) −2.75781 −0.138063
\(400\) −32.5224 −1.62612
\(401\) −24.4009 −1.21852 −0.609260 0.792970i \(-0.708533\pi\)
−0.609260 + 0.792970i \(0.708533\pi\)
\(402\) 47.0349 2.34589
\(403\) 14.8766 0.741054
\(404\) −83.0553 −4.13215
\(405\) 6.22306 0.309226
\(406\) 27.9028 1.38479
\(407\) −5.25374 −0.260418
\(408\) 9.67104 0.478788
\(409\) −31.2051 −1.54299 −0.771497 0.636233i \(-0.780492\pi\)
−0.771497 + 0.636233i \(0.780492\pi\)
\(410\) −1.39949 −0.0691160
\(411\) 26.4854 1.30643
\(412\) −20.4651 −1.00824
\(413\) 39.7563 1.95628
\(414\) −2.55723 −0.125681
\(415\) −5.68790 −0.279208
\(416\) −13.0799 −0.641293
\(417\) −18.6199 −0.911823
\(418\) −1.10370 −0.0539837
\(419\) 25.7468 1.25781 0.628907 0.777481i \(-0.283503\pi\)
0.628907 + 0.777481i \(0.283503\pi\)
\(420\) −18.9363 −0.923998
\(421\) 2.01752 0.0983277 0.0491639 0.998791i \(-0.484344\pi\)
0.0491639 + 0.998791i \(0.484344\pi\)
\(422\) 48.3942 2.35579
\(423\) −0.347723 −0.0169069
\(424\) −2.60499 −0.126509
\(425\) −3.94144 −0.191188
\(426\) −34.1910 −1.65656
\(427\) 12.1312 0.587072
\(428\) −53.1127 −2.56730
\(429\) 4.19467 0.202521
\(430\) 5.41017 0.260902
\(431\) −24.4643 −1.17840 −0.589201 0.807987i \(-0.700557\pi\)
−0.589201 + 0.807987i \(0.700557\pi\)
\(432\) 36.2178 1.74253
\(433\) 4.98047 0.239346 0.119673 0.992813i \(-0.461815\pi\)
0.119673 + 0.992813i \(0.461815\pi\)
\(434\) 57.4530 2.75783
\(435\) 3.57937 0.171618
\(436\) 38.4925 1.84346
\(437\) −3.34237 −0.159887
\(438\) −50.0905 −2.39342
\(439\) 32.4820 1.55028 0.775141 0.631788i \(-0.217679\pi\)
0.775141 + 0.631788i \(0.217679\pi\)
\(440\) −4.19771 −0.200118
\(441\) 0.772542 0.0367877
\(442\) −5.21874 −0.248230
\(443\) −2.52365 −0.119902 −0.0599510 0.998201i \(-0.519094\pi\)
−0.0599510 + 0.998201i \(0.519094\pi\)
\(444\) −41.6730 −1.97771
\(445\) 1.42133 0.0673773
\(446\) −54.3654 −2.57428
\(447\) −3.83679 −0.181474
\(448\) 0.788391 0.0372480
\(449\) −18.2746 −0.862431 −0.431216 0.902249i \(-0.641915\pi\)
−0.431216 + 0.902249i \(0.641915\pi\)
\(450\) 1.51204 0.0712783
\(451\) 0.827912 0.0389848
\(452\) 12.0777 0.568087
\(453\) −18.7652 −0.881667
\(454\) −43.2741 −2.03095
\(455\) 5.66003 0.265346
\(456\) −4.84915 −0.227082
\(457\) 12.6503 0.591756 0.295878 0.955226i \(-0.404388\pi\)
0.295878 + 0.955226i \(0.404388\pi\)
\(458\) 26.9103 1.25744
\(459\) 4.38929 0.204874
\(460\) −22.9502 −1.07006
\(461\) 4.80598 0.223837 0.111918 0.993717i \(-0.464300\pi\)
0.111918 + 0.993717i \(0.464300\pi\)
\(462\) 16.1997 0.753680
\(463\) 36.7310 1.70704 0.853518 0.521064i \(-0.174465\pi\)
0.853518 + 0.521064i \(0.174465\pi\)
\(464\) 21.7378 1.00915
\(465\) 7.37009 0.341780
\(466\) 15.3491 0.711034
\(467\) 32.3530 1.49712 0.748559 0.663068i \(-0.230746\pi\)
0.748559 + 0.663068i \(0.230746\pi\)
\(468\) 1.38445 0.0639960
\(469\) −37.5452 −1.73368
\(470\) −4.51282 −0.208161
\(471\) −4.30468 −0.198349
\(472\) 69.9051 3.21764
\(473\) −3.20055 −0.147162
\(474\) −33.4996 −1.53869
\(475\) 1.97628 0.0906778
\(476\) −13.9373 −0.638814
\(477\) 0.0536604 0.00245694
\(478\) 62.8751 2.87584
\(479\) 17.6184 0.805004 0.402502 0.915419i \(-0.368141\pi\)
0.402502 + 0.915419i \(0.368141\pi\)
\(480\) −6.47997 −0.295769
\(481\) 12.4560 0.567943
\(482\) −20.2739 −0.923453
\(483\) 49.0582 2.23223
\(484\) 4.48328 0.203786
\(485\) −10.5577 −0.479401
\(486\) −3.44412 −0.156228
\(487\) −14.9484 −0.677377 −0.338688 0.940899i \(-0.609983\pi\)
−0.338688 + 0.940899i \(0.609983\pi\)
\(488\) 21.3308 0.965600
\(489\) −11.1464 −0.504057
\(490\) 10.0262 0.452939
\(491\) −14.7603 −0.666123 −0.333061 0.942905i \(-0.608082\pi\)
−0.333061 + 0.942905i \(0.608082\pi\)
\(492\) 6.56704 0.296065
\(493\) 2.63444 0.118649
\(494\) 2.61673 0.117732
\(495\) 0.0864690 0.00388649
\(496\) 44.7592 2.00975
\(497\) 27.2927 1.22424
\(498\) 38.5967 1.72956
\(499\) 40.6004 1.81752 0.908762 0.417315i \(-0.137029\pi\)
0.908762 + 0.417315i \(0.137029\pi\)
\(500\) 28.4518 1.27240
\(501\) 14.5656 0.650741
\(502\) 11.3470 0.506442
\(503\) −22.6138 −1.00830 −0.504149 0.863616i \(-0.668194\pi\)
−0.504149 + 0.863616i \(0.668194\pi\)
\(504\) 2.96153 0.131917
\(505\) 12.2987 0.547286
\(506\) 19.6335 0.872818
\(507\) 13.0552 0.579803
\(508\) −32.6802 −1.44995
\(509\) 31.3724 1.39056 0.695279 0.718740i \(-0.255281\pi\)
0.695279 + 0.718740i \(0.255281\pi\)
\(510\) −2.58545 −0.114486
\(511\) 39.9844 1.76880
\(512\) 50.8538 2.24744
\(513\) −2.20083 −0.0971691
\(514\) −48.8401 −2.15425
\(515\) 3.03045 0.133538
\(516\) −25.3869 −1.11760
\(517\) 2.66970 0.117413
\(518\) 48.1047 2.11360
\(519\) 18.7089 0.821229
\(520\) 9.95224 0.436435
\(521\) 31.1167 1.36325 0.681623 0.731704i \(-0.261274\pi\)
0.681623 + 0.731704i \(0.261274\pi\)
\(522\) −1.01064 −0.0442346
\(523\) 17.9552 0.785126 0.392563 0.919725i \(-0.371589\pi\)
0.392563 + 0.919725i \(0.371589\pi\)
\(524\) 42.1298 1.84045
\(525\) −29.0072 −1.26598
\(526\) 47.9928 2.09259
\(527\) 5.42443 0.236292
\(528\) 12.6205 0.549238
\(529\) 36.4570 1.58508
\(530\) 0.696416 0.0302504
\(531\) −1.43998 −0.0624898
\(532\) 6.98828 0.302980
\(533\) −1.96287 −0.0850215
\(534\) −9.64476 −0.417370
\(535\) 7.86486 0.340028
\(536\) −66.0172 −2.85151
\(537\) 0.700067 0.0302101
\(538\) −4.62101 −0.199226
\(539\) −5.93131 −0.255480
\(540\) −15.1119 −0.650312
\(541\) 3.39609 0.146009 0.0730046 0.997332i \(-0.476741\pi\)
0.0730046 + 0.997332i \(0.476741\pi\)
\(542\) 14.2255 0.611038
\(543\) −15.8980 −0.682249
\(544\) −4.76930 −0.204482
\(545\) −5.69992 −0.244158
\(546\) −38.4075 −1.64369
\(547\) 1.00000 0.0427569
\(548\) −67.1141 −2.86697
\(549\) −0.439395 −0.0187529
\(550\) −11.6089 −0.495007
\(551\) −1.32094 −0.0562737
\(552\) 86.2610 3.67151
\(553\) 26.7408 1.13713
\(554\) −44.9835 −1.91117
\(555\) 6.17088 0.261939
\(556\) 47.1830 2.00100
\(557\) 37.3688 1.58336 0.791682 0.610933i \(-0.209205\pi\)
0.791682 + 0.610933i \(0.209205\pi\)
\(558\) −2.08096 −0.0880939
\(559\) 7.58810 0.320943
\(560\) 17.0294 0.719621
\(561\) 1.52950 0.0645756
\(562\) 19.6050 0.826987
\(563\) 2.81180 0.118503 0.0592516 0.998243i \(-0.481129\pi\)
0.0592516 + 0.998243i \(0.481129\pi\)
\(564\) 21.1762 0.891677
\(565\) −1.78845 −0.0752407
\(566\) 24.5469 1.03178
\(567\) 33.7082 1.41561
\(568\) 47.9898 2.01361
\(569\) −18.8624 −0.790752 −0.395376 0.918519i \(-0.629386\pi\)
−0.395376 + 0.918519i \(0.629386\pi\)
\(570\) 1.29637 0.0542989
\(571\) −25.5974 −1.07122 −0.535610 0.844466i \(-0.679918\pi\)
−0.535610 + 0.844466i \(0.679918\pi\)
\(572\) −10.6293 −0.444433
\(573\) −19.0343 −0.795168
\(574\) −7.58059 −0.316408
\(575\) −35.1557 −1.46610
\(576\) −0.0285556 −0.00118982
\(577\) −26.4065 −1.09932 −0.549658 0.835389i \(-0.685242\pi\)
−0.549658 + 0.835389i \(0.685242\pi\)
\(578\) 41.3830 1.72131
\(579\) −34.4698 −1.43251
\(580\) −9.07013 −0.376617
\(581\) −30.8095 −1.27819
\(582\) 71.6420 2.96966
\(583\) −0.411986 −0.0170627
\(584\) 70.3060 2.90928
\(585\) −0.205007 −0.00847600
\(586\) 42.8005 1.76807
\(587\) 9.99745 0.412639 0.206320 0.978485i \(-0.433851\pi\)
0.206320 + 0.978485i \(0.433851\pi\)
\(588\) −47.0475 −1.94021
\(589\) −2.71986 −0.112070
\(590\) −18.6884 −0.769388
\(591\) 29.0497 1.19495
\(592\) 37.4763 1.54027
\(593\) −34.2421 −1.40616 −0.703078 0.711113i \(-0.748192\pi\)
−0.703078 + 0.711113i \(0.748192\pi\)
\(594\) 12.9280 0.530442
\(595\) 2.06381 0.0846081
\(596\) 9.72244 0.398246
\(597\) −11.4114 −0.467037
\(598\) −46.5487 −1.90352
\(599\) 26.3043 1.07477 0.537383 0.843338i \(-0.319413\pi\)
0.537383 + 0.843338i \(0.319413\pi\)
\(600\) −51.0044 −2.08225
\(601\) −20.6853 −0.843771 −0.421885 0.906649i \(-0.638632\pi\)
−0.421885 + 0.906649i \(0.638632\pi\)
\(602\) 29.3051 1.19439
\(603\) 1.35989 0.0553792
\(604\) 47.5511 1.93483
\(605\) −0.663879 −0.0269905
\(606\) −83.4561 −3.39017
\(607\) 9.78395 0.397118 0.198559 0.980089i \(-0.436374\pi\)
0.198559 + 0.980089i \(0.436374\pi\)
\(608\) 2.39137 0.0969830
\(609\) 19.3883 0.785653
\(610\) −5.70256 −0.230890
\(611\) −6.32951 −0.256065
\(612\) 0.504810 0.0204057
\(613\) −28.8933 −1.16699 −0.583495 0.812116i \(-0.698315\pi\)
−0.583495 + 0.812116i \(0.698315\pi\)
\(614\) −18.0519 −0.728514
\(615\) −0.972439 −0.0392125
\(616\) −22.7376 −0.916125
\(617\) 22.4455 0.903621 0.451811 0.892114i \(-0.350778\pi\)
0.451811 + 0.892114i \(0.350778\pi\)
\(618\) −20.5639 −0.827200
\(619\) 15.8897 0.638661 0.319331 0.947643i \(-0.396542\pi\)
0.319331 + 0.947643i \(0.396542\pi\)
\(620\) −18.6758 −0.750038
\(621\) 39.1503 1.57105
\(622\) 29.4319 1.18011
\(623\) 7.69885 0.308448
\(624\) −29.9217 −1.19782
\(625\) 18.5832 0.743329
\(626\) 66.5110 2.65831
\(627\) −0.766906 −0.0306273
\(628\) 10.9081 0.435279
\(629\) 4.54181 0.181094
\(630\) −0.791734 −0.0315434
\(631\) 46.2269 1.84026 0.920131 0.391610i \(-0.128082\pi\)
0.920131 + 0.391610i \(0.128082\pi\)
\(632\) 47.0194 1.87033
\(633\) 33.6268 1.33655
\(634\) −61.2774 −2.43364
\(635\) 4.83925 0.192040
\(636\) −3.26789 −0.129580
\(637\) 14.0624 0.557172
\(638\) 7.75936 0.307196
\(639\) −0.988545 −0.0391062
\(640\) −7.69570 −0.304199
\(641\) 18.9648 0.749063 0.374532 0.927214i \(-0.377804\pi\)
0.374532 + 0.927214i \(0.377804\pi\)
\(642\) −53.3690 −2.10631
\(643\) 35.0808 1.38345 0.691726 0.722160i \(-0.256851\pi\)
0.691726 + 0.722160i \(0.256851\pi\)
\(644\) −124.314 −4.89864
\(645\) 3.75927 0.148021
\(646\) 0.954137 0.0375400
\(647\) −20.0508 −0.788276 −0.394138 0.919051i \(-0.628957\pi\)
−0.394138 + 0.919051i \(0.628957\pi\)
\(648\) 59.2705 2.32836
\(649\) 11.0557 0.433973
\(650\) 27.5233 1.07955
\(651\) 39.9213 1.56464
\(652\) 28.2450 1.10616
\(653\) −6.78128 −0.265372 −0.132686 0.991158i \(-0.542360\pi\)
−0.132686 + 0.991158i \(0.542360\pi\)
\(654\) 38.6782 1.51244
\(655\) −6.23853 −0.243760
\(656\) −5.90571 −0.230579
\(657\) −1.44824 −0.0565012
\(658\) −24.4445 −0.952945
\(659\) −37.0129 −1.44182 −0.720908 0.693030i \(-0.756275\pi\)
−0.720908 + 0.693030i \(0.756275\pi\)
\(660\) −5.26592 −0.204976
\(661\) 5.62057 0.218615 0.109307 0.994008i \(-0.465137\pi\)
0.109307 + 0.994008i \(0.465137\pi\)
\(662\) −16.1101 −0.626138
\(663\) −3.62625 −0.140832
\(664\) −54.1735 −2.10234
\(665\) −1.03482 −0.0401285
\(666\) −1.74236 −0.0675151
\(667\) 23.4979 0.909844
\(668\) −36.9091 −1.42806
\(669\) −37.7759 −1.46050
\(670\) 17.6490 0.681840
\(671\) 3.37352 0.130233
\(672\) −35.0998 −1.35401
\(673\) 20.5314 0.791429 0.395714 0.918374i \(-0.370497\pi\)
0.395714 + 0.918374i \(0.370497\pi\)
\(674\) −85.7183 −3.30174
\(675\) −23.1488 −0.890998
\(676\) −33.0820 −1.27238
\(677\) 18.4013 0.707219 0.353610 0.935393i \(-0.384954\pi\)
0.353610 + 0.935393i \(0.384954\pi\)
\(678\) 12.1360 0.466080
\(679\) −57.1876 −2.19466
\(680\) 3.62888 0.139161
\(681\) −30.0690 −1.15225
\(682\) 15.9769 0.611786
\(683\) 5.41507 0.207202 0.103601 0.994619i \(-0.466964\pi\)
0.103601 + 0.994619i \(0.466964\pi\)
\(684\) −0.253117 −0.00967815
\(685\) 9.93817 0.379718
\(686\) −9.78519 −0.373600
\(687\) 18.6987 0.713398
\(688\) 22.8304 0.870399
\(689\) 0.976766 0.0372118
\(690\) −23.0609 −0.877915
\(691\) 37.1200 1.41211 0.706055 0.708157i \(-0.250473\pi\)
0.706055 + 0.708157i \(0.250473\pi\)
\(692\) −47.4083 −1.80219
\(693\) 0.468374 0.0177921
\(694\) 45.7012 1.73480
\(695\) −6.98680 −0.265024
\(696\) 34.0911 1.29222
\(697\) −0.715722 −0.0271099
\(698\) 26.2136 0.992200
\(699\) 10.6653 0.403400
\(700\) 73.5042 2.77820
\(701\) −7.93806 −0.299817 −0.149908 0.988700i \(-0.547898\pi\)
−0.149908 + 0.988700i \(0.547898\pi\)
\(702\) −30.6506 −1.15683
\(703\) −2.27731 −0.0858903
\(704\) 0.219240 0.00826293
\(705\) −3.13574 −0.118099
\(706\) 49.9814 1.88108
\(707\) 66.6181 2.50543
\(708\) 87.6941 3.29575
\(709\) 9.62710 0.361553 0.180777 0.983524i \(-0.442139\pi\)
0.180777 + 0.983524i \(0.442139\pi\)
\(710\) −12.8296 −0.481484
\(711\) −0.968556 −0.0363237
\(712\) 13.5372 0.507327
\(713\) 48.3833 1.81197
\(714\) −14.0045 −0.524106
\(715\) 1.57397 0.0588633
\(716\) −1.77397 −0.0662964
\(717\) 43.6888 1.63159
\(718\) −47.5476 −1.77446
\(719\) 17.1560 0.639811 0.319905 0.947449i \(-0.396349\pi\)
0.319905 + 0.947449i \(0.396349\pi\)
\(720\) −0.616805 −0.0229870
\(721\) 16.4149 0.611324
\(722\) 47.8999 1.78265
\(723\) −14.0874 −0.523915
\(724\) 40.2856 1.49720
\(725\) −13.8939 −0.516005
\(726\) 4.50492 0.167193
\(727\) 3.74979 0.139072 0.0695360 0.997579i \(-0.477848\pi\)
0.0695360 + 0.997579i \(0.477848\pi\)
\(728\) 53.9080 1.99796
\(729\) 25.7282 0.952896
\(730\) −18.7956 −0.695655
\(731\) 2.76685 0.102336
\(732\) 26.7590 0.989039
\(733\) −34.0730 −1.25851 −0.629257 0.777197i \(-0.716641\pi\)
−0.629257 + 0.777197i \(0.716641\pi\)
\(734\) 10.8985 0.402272
\(735\) 6.96673 0.256972
\(736\) −42.5398 −1.56804
\(737\) −10.4408 −0.384592
\(738\) 0.274570 0.0101071
\(739\) 18.1980 0.669426 0.334713 0.942320i \(-0.391361\pi\)
0.334713 + 0.942320i \(0.391361\pi\)
\(740\) −15.6370 −0.574828
\(741\) 1.81824 0.0667946
\(742\) 3.77226 0.138484
\(743\) 44.6648 1.63859 0.819297 0.573370i \(-0.194364\pi\)
0.819297 + 0.573370i \(0.194364\pi\)
\(744\) 70.1951 2.57348
\(745\) −1.43969 −0.0527460
\(746\) 5.94298 0.217588
\(747\) 1.11592 0.0408295
\(748\) −3.87575 −0.141712
\(749\) 42.6014 1.55662
\(750\) 28.5891 1.04393
\(751\) −15.9881 −0.583416 −0.291708 0.956507i \(-0.594224\pi\)
−0.291708 + 0.956507i \(0.594224\pi\)
\(752\) −19.0436 −0.694450
\(753\) 7.88448 0.287327
\(754\) −18.3965 −0.669960
\(755\) −7.04131 −0.256259
\(756\) −81.8561 −2.97708
\(757\) 49.3497 1.79365 0.896823 0.442389i \(-0.145869\pi\)
0.896823 + 0.442389i \(0.145869\pi\)
\(758\) −21.8228 −0.792640
\(759\) 13.6424 0.495188
\(760\) −1.81956 −0.0660023
\(761\) −28.9266 −1.04859 −0.524294 0.851537i \(-0.675671\pi\)
−0.524294 + 0.851537i \(0.675671\pi\)
\(762\) −32.8379 −1.18959
\(763\) −30.8746 −1.11774
\(764\) 48.2329 1.74500
\(765\) −0.0747516 −0.00270265
\(766\) −48.6064 −1.75622
\(767\) −26.2116 −0.946446
\(768\) 51.4453 1.85637
\(769\) 21.4805 0.774607 0.387303 0.921952i \(-0.373407\pi\)
0.387303 + 0.921952i \(0.373407\pi\)
\(770\) 6.07866 0.219060
\(771\) −33.9366 −1.22220
\(772\) 87.3464 3.14367
\(773\) −39.5584 −1.42282 −0.711408 0.702780i \(-0.751942\pi\)
−0.711408 + 0.702780i \(0.751942\pi\)
\(774\) −1.06144 −0.0381525
\(775\) −28.6081 −1.02763
\(776\) −100.555 −3.60972
\(777\) 33.4256 1.19914
\(778\) 20.1597 0.722761
\(779\) 0.358870 0.0128578
\(780\) 12.4848 0.447029
\(781\) 7.58971 0.271581
\(782\) −16.9730 −0.606954
\(783\) 15.4726 0.552944
\(784\) 42.3096 1.51106
\(785\) −1.61525 −0.0576508
\(786\) 42.3331 1.50997
\(787\) 26.9185 0.959540 0.479770 0.877394i \(-0.340720\pi\)
0.479770 + 0.877394i \(0.340720\pi\)
\(788\) −73.6120 −2.62232
\(789\) 33.3479 1.18722
\(790\) −12.5701 −0.447225
\(791\) −9.68745 −0.344446
\(792\) 0.823560 0.0292639
\(793\) −7.99820 −0.284024
\(794\) 11.5401 0.409543
\(795\) 0.483906 0.0171624
\(796\) 28.9165 1.02492
\(797\) −12.0097 −0.425405 −0.212703 0.977117i \(-0.568227\pi\)
−0.212703 + 0.977117i \(0.568227\pi\)
\(798\) 7.02201 0.248576
\(799\) −2.30793 −0.0816486
\(800\) 25.1530 0.889292
\(801\) −0.278854 −0.00985281
\(802\) 62.1302 2.19389
\(803\) 11.1191 0.392384
\(804\) −82.8169 −2.92073
\(805\) 18.4082 0.648804
\(806\) −37.8791 −1.33424
\(807\) −3.21091 −0.113030
\(808\) 117.137 4.12087
\(809\) 8.61994 0.303061 0.151530 0.988453i \(-0.451580\pi\)
0.151530 + 0.988453i \(0.451580\pi\)
\(810\) −15.8453 −0.556748
\(811\) −0.230276 −0.00808608 −0.00404304 0.999992i \(-0.501287\pi\)
−0.00404304 + 0.999992i \(0.501287\pi\)
\(812\) −49.1299 −1.72412
\(813\) 9.88462 0.346669
\(814\) 13.3772 0.468872
\(815\) −4.18248 −0.146506
\(816\) −10.9103 −0.381938
\(817\) −1.38732 −0.0485363
\(818\) 79.4554 2.77809
\(819\) −1.11046 −0.0388025
\(820\) 2.46416 0.0860522
\(821\) −31.5401 −1.10076 −0.550378 0.834915i \(-0.685516\pi\)
−0.550378 + 0.834915i \(0.685516\pi\)
\(822\) −67.4380 −2.35217
\(823\) −51.3808 −1.79102 −0.895511 0.445040i \(-0.853189\pi\)
−0.895511 + 0.445040i \(0.853189\pi\)
\(824\) 28.8630 1.00549
\(825\) −8.06648 −0.280839
\(826\) −101.229 −3.52220
\(827\) 45.2084 1.57205 0.786025 0.618195i \(-0.212136\pi\)
0.786025 + 0.618195i \(0.212136\pi\)
\(828\) 4.50266 0.156478
\(829\) −34.5407 −1.19965 −0.599824 0.800132i \(-0.704763\pi\)
−0.599824 + 0.800132i \(0.704763\pi\)
\(830\) 14.4827 0.502702
\(831\) −31.2569 −1.08429
\(832\) −0.519791 −0.0180205
\(833\) 5.12756 0.177660
\(834\) 47.4106 1.64170
\(835\) 5.46546 0.189140
\(836\) 1.94334 0.0672119
\(837\) 31.8587 1.10120
\(838\) −65.5573 −2.26464
\(839\) 43.2213 1.49217 0.746083 0.665853i \(-0.231932\pi\)
0.746083 + 0.665853i \(0.231932\pi\)
\(840\) 26.7069 0.921475
\(841\) −19.7134 −0.679772
\(842\) −5.13706 −0.177035
\(843\) 13.6226 0.469186
\(844\) −85.2103 −2.93306
\(845\) 4.89874 0.168522
\(846\) 0.885382 0.0304401
\(847\) −3.59601 −0.123560
\(848\) 2.93880 0.100919
\(849\) 17.0564 0.585376
\(850\) 10.0358 0.344225
\(851\) 40.5108 1.38869
\(852\) 60.2019 2.06248
\(853\) −33.0952 −1.13316 −0.566580 0.824007i \(-0.691734\pi\)
−0.566580 + 0.824007i \(0.691734\pi\)
\(854\) −30.8889 −1.05700
\(855\) 0.0374812 0.00128183
\(856\) 74.9076 2.56029
\(857\) 3.76327 0.128551 0.0642754 0.997932i \(-0.479526\pi\)
0.0642754 + 0.997932i \(0.479526\pi\)
\(858\) −10.6806 −0.364629
\(859\) 12.6305 0.430945 0.215473 0.976510i \(-0.430871\pi\)
0.215473 + 0.976510i \(0.430871\pi\)
\(860\) −9.52598 −0.324833
\(861\) −5.26738 −0.179512
\(862\) 62.2916 2.12166
\(863\) −1.22511 −0.0417032 −0.0208516 0.999783i \(-0.506638\pi\)
−0.0208516 + 0.999783i \(0.506638\pi\)
\(864\) −28.0110 −0.952953
\(865\) 7.02017 0.238693
\(866\) −12.6814 −0.430932
\(867\) 28.7550 0.976572
\(868\) −101.161 −3.43362
\(869\) 7.43624 0.252257
\(870\) −9.11390 −0.308990
\(871\) 24.7538 0.838751
\(872\) −54.2879 −1.83842
\(873\) 2.07134 0.0701044
\(874\) 8.51044 0.287870
\(875\) −22.8210 −0.771491
\(876\) 88.1971 2.97990
\(877\) −39.9594 −1.34933 −0.674667 0.738122i \(-0.735713\pi\)
−0.674667 + 0.738122i \(0.735713\pi\)
\(878\) −82.7067 −2.79122
\(879\) 29.7400 1.00310
\(880\) 4.73562 0.159638
\(881\) 11.7891 0.397187 0.198593 0.980082i \(-0.436363\pi\)
0.198593 + 0.980082i \(0.436363\pi\)
\(882\) −1.96707 −0.0662347
\(883\) −20.0506 −0.674755 −0.337377 0.941369i \(-0.609540\pi\)
−0.337377 + 0.941369i \(0.609540\pi\)
\(884\) 9.18892 0.309057
\(885\) −12.9856 −0.436508
\(886\) 6.42578 0.215878
\(887\) 4.17582 0.140210 0.0701052 0.997540i \(-0.477666\pi\)
0.0701052 + 0.997540i \(0.477666\pi\)
\(888\) 58.7736 1.97231
\(889\) 26.2126 0.879142
\(890\) −3.61902 −0.121310
\(891\) 9.37378 0.314033
\(892\) 95.7242 3.20508
\(893\) 1.15722 0.0387248
\(894\) 9.76935 0.326736
\(895\) 0.262687 0.00878067
\(896\) −41.6851 −1.39260
\(897\) −32.3444 −1.07995
\(898\) 46.5313 1.55277
\(899\) 19.1215 0.637739
\(900\) −2.66233 −0.0887444
\(901\) 0.356158 0.0118653
\(902\) −2.10805 −0.0701905
\(903\) 20.3627 0.677628
\(904\) −17.0338 −0.566536
\(905\) −5.96544 −0.198298
\(906\) 47.7805 1.58740
\(907\) −2.93935 −0.0975994 −0.0487997 0.998809i \(-0.515540\pi\)
−0.0487997 + 0.998809i \(0.515540\pi\)
\(908\) 76.1950 2.52862
\(909\) −2.41292 −0.0800314
\(910\) −14.4117 −0.477744
\(911\) 5.02116 0.166358 0.0831792 0.996535i \(-0.473493\pi\)
0.0831792 + 0.996535i \(0.473493\pi\)
\(912\) 5.47054 0.181148
\(913\) −8.56768 −0.283549
\(914\) −32.2105 −1.06543
\(915\) −3.96243 −0.130994
\(916\) −47.3824 −1.56556
\(917\) −33.7921 −1.11591
\(918\) −11.1761 −0.368867
\(919\) 16.5767 0.546816 0.273408 0.961898i \(-0.411849\pi\)
0.273408 + 0.961898i \(0.411849\pi\)
\(920\) 32.3679 1.06714
\(921\) −12.5434 −0.413318
\(922\) −12.2371 −0.403008
\(923\) −17.9942 −0.592287
\(924\) −28.5238 −0.938363
\(925\) −23.9532 −0.787577
\(926\) −93.5256 −3.07344
\(927\) −0.594551 −0.0195276
\(928\) −16.8121 −0.551886
\(929\) −28.3954 −0.931621 −0.465811 0.884884i \(-0.654237\pi\)
−0.465811 + 0.884884i \(0.654237\pi\)
\(930\) −18.7659 −0.615359
\(931\) −2.57101 −0.0842615
\(932\) −27.0260 −0.885266
\(933\) 20.4508 0.669528
\(934\) −82.3781 −2.69549
\(935\) 0.573917 0.0187691
\(936\) −1.95256 −0.0638213
\(937\) 19.1184 0.624570 0.312285 0.949988i \(-0.398906\pi\)
0.312285 + 0.949988i \(0.398906\pi\)
\(938\) 95.5988 3.12141
\(939\) 46.2153 1.50818
\(940\) 7.94597 0.259169
\(941\) −11.5339 −0.375995 −0.187998 0.982169i \(-0.560200\pi\)
−0.187998 + 0.982169i \(0.560200\pi\)
\(942\) 10.9607 0.357119
\(943\) −6.38389 −0.207888
\(944\) −78.8629 −2.56677
\(945\) 12.1212 0.394301
\(946\) 8.14934 0.264958
\(947\) −13.3167 −0.432735 −0.216367 0.976312i \(-0.569421\pi\)
−0.216367 + 0.976312i \(0.569421\pi\)
\(948\) 58.9846 1.91573
\(949\) −26.3619 −0.855744
\(950\) −5.03205 −0.163261
\(951\) −42.5787 −1.38071
\(952\) 19.6565 0.637069
\(953\) −33.3553 −1.08048 −0.540242 0.841510i \(-0.681667\pi\)
−0.540242 + 0.841510i \(0.681667\pi\)
\(954\) −0.136632 −0.00442361
\(955\) −7.14227 −0.231118
\(956\) −110.707 −3.58054
\(957\) 5.39160 0.174286
\(958\) −44.8604 −1.44937
\(959\) 53.8318 1.73832
\(960\) −0.257513 −0.00831119
\(961\) 8.37207 0.270067
\(962\) −31.7157 −1.02256
\(963\) −1.54303 −0.0497234
\(964\) 35.6974 1.14974
\(965\) −12.9342 −0.416365
\(966\) −124.914 −4.01903
\(967\) −11.9491 −0.384259 −0.192129 0.981370i \(-0.561539\pi\)
−0.192129 + 0.981370i \(0.561539\pi\)
\(968\) −6.32301 −0.203229
\(969\) 0.662983 0.0212981
\(970\) 26.8824 0.863141
\(971\) 32.5444 1.04440 0.522200 0.852823i \(-0.325112\pi\)
0.522200 + 0.852823i \(0.325112\pi\)
\(972\) 6.06424 0.194511
\(973\) −37.8452 −1.21326
\(974\) 38.0621 1.21959
\(975\) 19.1246 0.612478
\(976\) −24.0642 −0.770276
\(977\) −13.9280 −0.445597 −0.222798 0.974865i \(-0.571519\pi\)
−0.222798 + 0.974865i \(0.571519\pi\)
\(978\) 28.3813 0.907533
\(979\) 2.14094 0.0684248
\(980\) −17.6537 −0.563927
\(981\) 1.11828 0.0357040
\(982\) 37.5831 1.19932
\(983\) 28.5968 0.912096 0.456048 0.889955i \(-0.349265\pi\)
0.456048 + 0.889955i \(0.349265\pi\)
\(984\) −9.26183 −0.295256
\(985\) 10.9004 0.347315
\(986\) −6.70789 −0.213623
\(987\) −16.9853 −0.540647
\(988\) −4.60742 −0.146581
\(989\) 24.6789 0.784744
\(990\) −0.220170 −0.00699746
\(991\) −46.2655 −1.46967 −0.734836 0.678245i \(-0.762741\pi\)
−0.734836 + 0.678245i \(0.762741\pi\)
\(992\) −34.6169 −1.09909
\(993\) −11.1942 −0.355236
\(994\) −69.4934 −2.20420
\(995\) −4.28192 −0.135746
\(996\) −67.9593 −2.15337
\(997\) 14.5092 0.459512 0.229756 0.973248i \(-0.426207\pi\)
0.229756 + 0.973248i \(0.426207\pi\)
\(998\) −103.378 −3.27237
\(999\) 26.6749 0.843956
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 6017.2.a.f.1.10 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.10 121 1.1 even 1 trivial