Properties

Label 6001.2.a.d.1.19
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9182262530\)
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 1.19
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.08098 q^{2} -2.15379 q^{3} +2.33048 q^{4} +2.78537 q^{5} +4.48200 q^{6} -3.81134 q^{7} -0.687730 q^{8} +1.63882 q^{9} +O(q^{10})\) \(q-2.08098 q^{2} -2.15379 q^{3} +2.33048 q^{4} +2.78537 q^{5} +4.48200 q^{6} -3.81134 q^{7} -0.687730 q^{8} +1.63882 q^{9} -5.79629 q^{10} +0.743233 q^{11} -5.01938 q^{12} -5.06784 q^{13} +7.93133 q^{14} -5.99910 q^{15} -3.22981 q^{16} +1.00000 q^{17} -3.41036 q^{18} +4.09994 q^{19} +6.49125 q^{20} +8.20884 q^{21} -1.54665 q^{22} -5.66096 q^{23} +1.48123 q^{24} +2.75826 q^{25} +10.5461 q^{26} +2.93169 q^{27} -8.88227 q^{28} -3.71663 q^{29} +12.4840 q^{30} +4.90174 q^{31} +8.09664 q^{32} -1.60077 q^{33} -2.08098 q^{34} -10.6160 q^{35} +3.81925 q^{36} -10.8577 q^{37} -8.53190 q^{38} +10.9151 q^{39} -1.91558 q^{40} -4.19522 q^{41} -17.0825 q^{42} -2.59069 q^{43} +1.73209 q^{44} +4.56472 q^{45} +11.7804 q^{46} -8.44901 q^{47} +6.95635 q^{48} +7.52634 q^{49} -5.73988 q^{50} -2.15379 q^{51} -11.8105 q^{52} -0.962978 q^{53} -6.10080 q^{54} +2.07017 q^{55} +2.62117 q^{56} -8.83042 q^{57} +7.73425 q^{58} -2.93377 q^{59} -13.9808 q^{60} +3.77942 q^{61} -10.2004 q^{62} -6.24612 q^{63} -10.3893 q^{64} -14.1158 q^{65} +3.33117 q^{66} -12.7041 q^{67} +2.33048 q^{68} +12.1925 q^{69} +22.0917 q^{70} +15.2528 q^{71} -1.12707 q^{72} +9.11944 q^{73} +22.5946 q^{74} -5.94072 q^{75} +9.55484 q^{76} -2.83271 q^{77} -22.7141 q^{78} -2.53796 q^{79} -8.99621 q^{80} -11.2307 q^{81} +8.73017 q^{82} -0.619691 q^{83} +19.1306 q^{84} +2.78537 q^{85} +5.39118 q^{86} +8.00486 q^{87} -0.511143 q^{88} -6.89607 q^{89} -9.49910 q^{90} +19.3153 q^{91} -13.1928 q^{92} -10.5573 q^{93} +17.5822 q^{94} +11.4198 q^{95} -17.4385 q^{96} -0.244151 q^{97} -15.6622 q^{98} +1.21803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.08098 −1.47148 −0.735738 0.677266i \(-0.763165\pi\)
−0.735738 + 0.677266i \(0.763165\pi\)
\(3\) −2.15379 −1.24349 −0.621746 0.783219i \(-0.713577\pi\)
−0.621746 + 0.783219i \(0.713577\pi\)
\(4\) 2.33048 1.16524
\(5\) 2.78537 1.24565 0.622827 0.782360i \(-0.285984\pi\)
0.622827 + 0.782360i \(0.285984\pi\)
\(6\) 4.48200 1.82977
\(7\) −3.81134 −1.44055 −0.720276 0.693687i \(-0.755985\pi\)
−0.720276 + 0.693687i \(0.755985\pi\)
\(8\) −0.687730 −0.243149
\(9\) 1.63882 0.546274
\(10\) −5.79629 −1.83295
\(11\) 0.743233 0.224093 0.112047 0.993703i \(-0.464259\pi\)
0.112047 + 0.993703i \(0.464259\pi\)
\(12\) −5.01938 −1.44897
\(13\) −5.06784 −1.40557 −0.702783 0.711404i \(-0.748060\pi\)
−0.702783 + 0.711404i \(0.748060\pi\)
\(14\) 7.93133 2.11974
\(15\) −5.99910 −1.54896
\(16\) −3.22981 −0.807453
\(17\) 1.00000 0.242536
\(18\) −3.41036 −0.803830
\(19\) 4.09994 0.940591 0.470295 0.882509i \(-0.344147\pi\)
0.470295 + 0.882509i \(0.344147\pi\)
\(20\) 6.49125 1.45149
\(21\) 8.20884 1.79132
\(22\) −1.54665 −0.329748
\(23\) −5.66096 −1.18039 −0.590196 0.807260i \(-0.700950\pi\)
−0.590196 + 0.807260i \(0.700950\pi\)
\(24\) 1.48123 0.302354
\(25\) 2.75826 0.551652
\(26\) 10.5461 2.06826
\(27\) 2.93169 0.564204
\(28\) −8.88227 −1.67859
\(29\) −3.71663 −0.690162 −0.345081 0.938573i \(-0.612148\pi\)
−0.345081 + 0.938573i \(0.612148\pi\)
\(30\) 12.4840 2.27926
\(31\) 4.90174 0.880379 0.440190 0.897905i \(-0.354911\pi\)
0.440190 + 0.897905i \(0.354911\pi\)
\(32\) 8.09664 1.43130
\(33\) −1.60077 −0.278658
\(34\) −2.08098 −0.356885
\(35\) −10.6160 −1.79443
\(36\) 3.81925 0.636542
\(37\) −10.8577 −1.78499 −0.892495 0.451058i \(-0.851047\pi\)
−0.892495 + 0.451058i \(0.851047\pi\)
\(38\) −8.53190 −1.38406
\(39\) 10.9151 1.74781
\(40\) −1.91558 −0.302880
\(41\) −4.19522 −0.655183 −0.327592 0.944819i \(-0.606237\pi\)
−0.327592 + 0.944819i \(0.606237\pi\)
\(42\) −17.0825 −2.63588
\(43\) −2.59069 −0.395077 −0.197538 0.980295i \(-0.563295\pi\)
−0.197538 + 0.980295i \(0.563295\pi\)
\(44\) 1.73209 0.261123
\(45\) 4.56472 0.680469
\(46\) 11.7804 1.73692
\(47\) −8.44901 −1.23241 −0.616207 0.787584i \(-0.711332\pi\)
−0.616207 + 0.787584i \(0.711332\pi\)
\(48\) 6.95635 1.00406
\(49\) 7.52634 1.07519
\(50\) −5.73988 −0.811742
\(51\) −2.15379 −0.301591
\(52\) −11.8105 −1.63782
\(53\) −0.962978 −0.132275 −0.0661376 0.997811i \(-0.521068\pi\)
−0.0661376 + 0.997811i \(0.521068\pi\)
\(54\) −6.10080 −0.830213
\(55\) 2.07017 0.279142
\(56\) 2.62117 0.350269
\(57\) −8.83042 −1.16962
\(58\) 7.73425 1.01556
\(59\) −2.93377 −0.381945 −0.190972 0.981595i \(-0.561164\pi\)
−0.190972 + 0.981595i \(0.561164\pi\)
\(60\) −13.9808 −1.80491
\(61\) 3.77942 0.483905 0.241952 0.970288i \(-0.422212\pi\)
0.241952 + 0.970288i \(0.422212\pi\)
\(62\) −10.2004 −1.29546
\(63\) −6.24612 −0.786937
\(64\) −10.3893 −1.29867
\(65\) −14.1158 −1.75085
\(66\) 3.33117 0.410039
\(67\) −12.7041 −1.55205 −0.776025 0.630703i \(-0.782767\pi\)
−0.776025 + 0.630703i \(0.782767\pi\)
\(68\) 2.33048 0.282613
\(69\) 12.1925 1.46781
\(70\) 22.0917 2.64046
\(71\) 15.2528 1.81017 0.905085 0.425230i \(-0.139807\pi\)
0.905085 + 0.425230i \(0.139807\pi\)
\(72\) −1.12707 −0.132826
\(73\) 9.11944 1.06735 0.533675 0.845690i \(-0.320811\pi\)
0.533675 + 0.845690i \(0.320811\pi\)
\(74\) 22.5946 2.62657
\(75\) −5.94072 −0.685975
\(76\) 9.55484 1.09602
\(77\) −2.83271 −0.322818
\(78\) −22.7141 −2.57186
\(79\) −2.53796 −0.285543 −0.142771 0.989756i \(-0.545601\pi\)
−0.142771 + 0.989756i \(0.545601\pi\)
\(80\) −8.99621 −1.00581
\(81\) −11.2307 −1.24786
\(82\) 8.73017 0.964086
\(83\) −0.619691 −0.0680199 −0.0340099 0.999421i \(-0.510828\pi\)
−0.0340099 + 0.999421i \(0.510828\pi\)
\(84\) 19.1306 2.08732
\(85\) 2.78537 0.302115
\(86\) 5.39118 0.581346
\(87\) 8.00486 0.858211
\(88\) −0.511143 −0.0544881
\(89\) −6.89607 −0.730982 −0.365491 0.930815i \(-0.619099\pi\)
−0.365491 + 0.930815i \(0.619099\pi\)
\(90\) −9.49910 −1.00129
\(91\) 19.3153 2.02479
\(92\) −13.1928 −1.37544
\(93\) −10.5573 −1.09475
\(94\) 17.5822 1.81347
\(95\) 11.4198 1.17165
\(96\) −17.4385 −1.77981
\(97\) −0.244151 −0.0247898 −0.0123949 0.999923i \(-0.503946\pi\)
−0.0123949 + 0.999923i \(0.503946\pi\)
\(98\) −15.6622 −1.58212
\(99\) 1.21803 0.122416
\(100\) 6.42808 0.642808
\(101\) 4.41972 0.439778 0.219889 0.975525i \(-0.429430\pi\)
0.219889 + 0.975525i \(0.429430\pi\)
\(102\) 4.48200 0.443784
\(103\) 19.4775 1.91918 0.959588 0.281409i \(-0.0908016\pi\)
0.959588 + 0.281409i \(0.0908016\pi\)
\(104\) 3.48531 0.341762
\(105\) 22.8646 2.23136
\(106\) 2.00394 0.194640
\(107\) −8.73059 −0.844018 −0.422009 0.906592i \(-0.638675\pi\)
−0.422009 + 0.906592i \(0.638675\pi\)
\(108\) 6.83226 0.657435
\(109\) 3.44283 0.329763 0.164882 0.986313i \(-0.447276\pi\)
0.164882 + 0.986313i \(0.447276\pi\)
\(110\) −4.30799 −0.410751
\(111\) 23.3852 2.21962
\(112\) 12.3099 1.16318
\(113\) −11.1282 −1.04685 −0.523426 0.852071i \(-0.675346\pi\)
−0.523426 + 0.852071i \(0.675346\pi\)
\(114\) 18.3759 1.72106
\(115\) −15.7679 −1.47036
\(116\) −8.66155 −0.804205
\(117\) −8.30530 −0.767825
\(118\) 6.10513 0.562023
\(119\) −3.81134 −0.349385
\(120\) 4.12576 0.376629
\(121\) −10.4476 −0.949782
\(122\) −7.86490 −0.712055
\(123\) 9.03563 0.814716
\(124\) 11.4234 1.02585
\(125\) −6.24407 −0.558486
\(126\) 12.9981 1.15796
\(127\) 16.8043 1.49114 0.745570 0.666427i \(-0.232177\pi\)
0.745570 + 0.666427i \(0.232177\pi\)
\(128\) 5.42673 0.479659
\(129\) 5.57982 0.491275
\(130\) 29.3747 2.57633
\(131\) −5.25032 −0.458723 −0.229361 0.973341i \(-0.573664\pi\)
−0.229361 + 0.973341i \(0.573664\pi\)
\(132\) −3.73057 −0.324704
\(133\) −15.6263 −1.35497
\(134\) 26.4369 2.28380
\(135\) 8.16583 0.702803
\(136\) −0.687730 −0.0589723
\(137\) 11.9521 1.02114 0.510570 0.859836i \(-0.329435\pi\)
0.510570 + 0.859836i \(0.329435\pi\)
\(138\) −25.3725 −2.15985
\(139\) 3.30237 0.280103 0.140052 0.990144i \(-0.455273\pi\)
0.140052 + 0.990144i \(0.455273\pi\)
\(140\) −24.7404 −2.09094
\(141\) 18.1974 1.53250
\(142\) −31.7407 −2.66362
\(143\) −3.76659 −0.314978
\(144\) −5.29309 −0.441091
\(145\) −10.3522 −0.859702
\(146\) −18.9774 −1.57058
\(147\) −16.2102 −1.33699
\(148\) −25.3036 −2.07994
\(149\) −17.4617 −1.43052 −0.715260 0.698859i \(-0.753692\pi\)
−0.715260 + 0.698859i \(0.753692\pi\)
\(150\) 12.3625 1.00940
\(151\) 15.3816 1.25174 0.625868 0.779929i \(-0.284745\pi\)
0.625868 + 0.779929i \(0.284745\pi\)
\(152\) −2.81965 −0.228704
\(153\) 1.63882 0.132491
\(154\) 5.89483 0.475019
\(155\) 13.6531 1.09665
\(156\) 25.4374 2.03662
\(157\) −9.86811 −0.787561 −0.393781 0.919204i \(-0.628833\pi\)
−0.393781 + 0.919204i \(0.628833\pi\)
\(158\) 5.28144 0.420169
\(159\) 2.07406 0.164483
\(160\) 22.5521 1.78290
\(161\) 21.5759 1.70042
\(162\) 23.3709 1.83619
\(163\) 8.51855 0.667224 0.333612 0.942710i \(-0.391732\pi\)
0.333612 + 0.942710i \(0.391732\pi\)
\(164\) −9.77689 −0.763447
\(165\) −4.45873 −0.347111
\(166\) 1.28956 0.100090
\(167\) −14.4885 −1.12115 −0.560576 0.828103i \(-0.689420\pi\)
−0.560576 + 0.828103i \(0.689420\pi\)
\(168\) −5.64547 −0.435557
\(169\) 12.6830 0.975617
\(170\) −5.79629 −0.444555
\(171\) 6.71908 0.513821
\(172\) −6.03757 −0.460360
\(173\) −17.0012 −1.29258 −0.646288 0.763094i \(-0.723679\pi\)
−0.646288 + 0.763094i \(0.723679\pi\)
\(174\) −16.6580 −1.26284
\(175\) −10.5127 −0.794683
\(176\) −2.40050 −0.180945
\(177\) 6.31874 0.474946
\(178\) 14.3506 1.07562
\(179\) 2.16205 0.161599 0.0807995 0.996730i \(-0.474253\pi\)
0.0807995 + 0.996730i \(0.474253\pi\)
\(180\) 10.6380 0.792910
\(181\) −8.46010 −0.628834 −0.314417 0.949285i \(-0.601809\pi\)
−0.314417 + 0.949285i \(0.601809\pi\)
\(182\) −40.1947 −2.97943
\(183\) −8.14008 −0.601732
\(184\) 3.89321 0.287012
\(185\) −30.2426 −2.22348
\(186\) 21.9696 1.61089
\(187\) 0.743233 0.0543506
\(188\) −19.6903 −1.43606
\(189\) −11.1737 −0.812766
\(190\) −23.7645 −1.72405
\(191\) 6.99666 0.506261 0.253130 0.967432i \(-0.418540\pi\)
0.253130 + 0.967432i \(0.418540\pi\)
\(192\) 22.3765 1.61488
\(193\) −17.6170 −1.26810 −0.634050 0.773292i \(-0.718609\pi\)
−0.634050 + 0.773292i \(0.718609\pi\)
\(194\) 0.508073 0.0364775
\(195\) 30.4025 2.17717
\(196\) 17.5400 1.25286
\(197\) 10.0886 0.718781 0.359391 0.933187i \(-0.382985\pi\)
0.359391 + 0.933187i \(0.382985\pi\)
\(198\) −2.53469 −0.180133
\(199\) −16.9610 −1.20233 −0.601165 0.799125i \(-0.705297\pi\)
−0.601165 + 0.799125i \(0.705297\pi\)
\(200\) −1.89694 −0.134134
\(201\) 27.3619 1.92996
\(202\) −9.19735 −0.647123
\(203\) 14.1654 0.994214
\(204\) −5.01938 −0.351427
\(205\) −11.6852 −0.816131
\(206\) −40.5323 −2.82402
\(207\) −9.27732 −0.644818
\(208\) 16.3682 1.13493
\(209\) 3.04721 0.210780
\(210\) −47.5809 −3.28339
\(211\) −6.78599 −0.467167 −0.233583 0.972337i \(-0.575045\pi\)
−0.233583 + 0.972337i \(0.575045\pi\)
\(212\) −2.24420 −0.154133
\(213\) −32.8513 −2.25093
\(214\) 18.1682 1.24195
\(215\) −7.21603 −0.492129
\(216\) −2.01621 −0.137186
\(217\) −18.6822 −1.26823
\(218\) −7.16446 −0.485239
\(219\) −19.6414 −1.32724
\(220\) 4.82451 0.325268
\(221\) −5.06784 −0.340900
\(222\) −48.6641 −3.26612
\(223\) 7.12216 0.476935 0.238468 0.971150i \(-0.423355\pi\)
0.238468 + 0.971150i \(0.423355\pi\)
\(224\) −30.8591 −2.06186
\(225\) 4.52030 0.301353
\(226\) 23.1575 1.54042
\(227\) 10.9284 0.725345 0.362672 0.931917i \(-0.381864\pi\)
0.362672 + 0.931917i \(0.381864\pi\)
\(228\) −20.5792 −1.36289
\(229\) −0.0999594 −0.00660550 −0.00330275 0.999995i \(-0.501051\pi\)
−0.00330275 + 0.999995i \(0.501051\pi\)
\(230\) 32.8126 2.16360
\(231\) 6.10108 0.401422
\(232\) 2.55604 0.167812
\(233\) 20.3987 1.33636 0.668182 0.743998i \(-0.267073\pi\)
0.668182 + 0.743998i \(0.267073\pi\)
\(234\) 17.2832 1.12984
\(235\) −23.5336 −1.53516
\(236\) −6.83711 −0.445058
\(237\) 5.46623 0.355070
\(238\) 7.93133 0.514112
\(239\) 3.51462 0.227342 0.113671 0.993518i \(-0.463739\pi\)
0.113671 + 0.993518i \(0.463739\pi\)
\(240\) 19.3760 1.25071
\(241\) −21.9391 −1.41322 −0.706612 0.707601i \(-0.749777\pi\)
−0.706612 + 0.707601i \(0.749777\pi\)
\(242\) 21.7413 1.39758
\(243\) 15.3936 0.987499
\(244\) 8.80787 0.563866
\(245\) 20.9636 1.33932
\(246\) −18.8030 −1.19883
\(247\) −20.7778 −1.32206
\(248\) −3.37107 −0.214063
\(249\) 1.33469 0.0845822
\(250\) 12.9938 0.821799
\(251\) −4.47079 −0.282194 −0.141097 0.989996i \(-0.545063\pi\)
−0.141097 + 0.989996i \(0.545063\pi\)
\(252\) −14.5565 −0.916972
\(253\) −4.20741 −0.264518
\(254\) −34.9694 −2.19418
\(255\) −5.99910 −0.375678
\(256\) 9.48575 0.592860
\(257\) 10.7571 0.671012 0.335506 0.942038i \(-0.391093\pi\)
0.335506 + 0.942038i \(0.391093\pi\)
\(258\) −11.6115 −0.722900
\(259\) 41.3823 2.57137
\(260\) −32.8966 −2.04016
\(261\) −6.09091 −0.377018
\(262\) 10.9258 0.674999
\(263\) −15.0055 −0.925277 −0.462638 0.886547i \(-0.653097\pi\)
−0.462638 + 0.886547i \(0.653097\pi\)
\(264\) 1.10090 0.0677555
\(265\) −2.68225 −0.164769
\(266\) 32.5180 1.99381
\(267\) 14.8527 0.908971
\(268\) −29.6066 −1.80851
\(269\) −5.94447 −0.362440 −0.181220 0.983443i \(-0.558005\pi\)
−0.181220 + 0.983443i \(0.558005\pi\)
\(270\) −16.9929 −1.03416
\(271\) −22.0157 −1.33736 −0.668680 0.743550i \(-0.733140\pi\)
−0.668680 + 0.743550i \(0.733140\pi\)
\(272\) −3.22981 −0.195836
\(273\) −41.6011 −2.51781
\(274\) −24.8722 −1.50258
\(275\) 2.05003 0.123621
\(276\) 28.4145 1.71035
\(277\) −14.4584 −0.868719 −0.434359 0.900740i \(-0.643025\pi\)
−0.434359 + 0.900740i \(0.643025\pi\)
\(278\) −6.87217 −0.412165
\(279\) 8.03309 0.480929
\(280\) 7.30093 0.436314
\(281\) −23.6017 −1.40796 −0.703980 0.710220i \(-0.748595\pi\)
−0.703980 + 0.710220i \(0.748595\pi\)
\(282\) −37.8685 −2.25503
\(283\) 4.66267 0.277167 0.138583 0.990351i \(-0.455745\pi\)
0.138583 + 0.990351i \(0.455745\pi\)
\(284\) 35.5463 2.10929
\(285\) −24.5960 −1.45694
\(286\) 7.83819 0.463482
\(287\) 15.9894 0.943826
\(288\) 13.2690 0.781881
\(289\) 1.00000 0.0588235
\(290\) 21.5427 1.26503
\(291\) 0.525850 0.0308259
\(292\) 21.2527 1.24372
\(293\) −2.76152 −0.161330 −0.0806649 0.996741i \(-0.525704\pi\)
−0.0806649 + 0.996741i \(0.525704\pi\)
\(294\) 33.7331 1.96735
\(295\) −8.17163 −0.475771
\(296\) 7.46714 0.434019
\(297\) 2.17893 0.126434
\(298\) 36.3375 2.10497
\(299\) 28.6889 1.65912
\(300\) −13.8447 −0.799327
\(301\) 9.87402 0.569129
\(302\) −32.0088 −1.84190
\(303\) −9.51916 −0.546861
\(304\) −13.2420 −0.759483
\(305\) 10.5271 0.602778
\(306\) −3.41036 −0.194957
\(307\) 14.6785 0.837747 0.418873 0.908045i \(-0.362425\pi\)
0.418873 + 0.908045i \(0.362425\pi\)
\(308\) −6.60160 −0.376161
\(309\) −41.9505 −2.38648
\(310\) −28.4119 −1.61369
\(311\) −13.1652 −0.746530 −0.373265 0.927725i \(-0.621762\pi\)
−0.373265 + 0.927725i \(0.621762\pi\)
\(312\) −7.50663 −0.424979
\(313\) 0.481557 0.0272192 0.0136096 0.999907i \(-0.495668\pi\)
0.0136096 + 0.999907i \(0.495668\pi\)
\(314\) 20.5354 1.15888
\(315\) −17.3977 −0.980251
\(316\) −5.91467 −0.332726
\(317\) −1.76821 −0.0993126 −0.0496563 0.998766i \(-0.515813\pi\)
−0.0496563 + 0.998766i \(0.515813\pi\)
\(318\) −4.31607 −0.242033
\(319\) −2.76232 −0.154660
\(320\) −28.9381 −1.61769
\(321\) 18.8039 1.04953
\(322\) −44.8990 −2.50212
\(323\) 4.09994 0.228127
\(324\) −26.1730 −1.45406
\(325\) −13.9784 −0.775383
\(326\) −17.7269 −0.981805
\(327\) −7.41514 −0.410058
\(328\) 2.88518 0.159307
\(329\) 32.2021 1.77536
\(330\) 9.27853 0.510766
\(331\) −7.15496 −0.393272 −0.196636 0.980477i \(-0.563002\pi\)
−0.196636 + 0.980477i \(0.563002\pi\)
\(332\) −1.44418 −0.0792596
\(333\) −17.7938 −0.975094
\(334\) 30.1502 1.64975
\(335\) −35.3855 −1.93331
\(336\) −26.5130 −1.44640
\(337\) 31.9959 1.74293 0.871463 0.490462i \(-0.163172\pi\)
0.871463 + 0.490462i \(0.163172\pi\)
\(338\) −26.3931 −1.43560
\(339\) 23.9678 1.30175
\(340\) 6.49125 0.352037
\(341\) 3.64314 0.197287
\(342\) −13.9823 −0.756075
\(343\) −2.00606 −0.108317
\(344\) 1.78170 0.0960627
\(345\) 33.9607 1.82838
\(346\) 35.3791 1.90199
\(347\) 10.2570 0.550624 0.275312 0.961355i \(-0.411219\pi\)
0.275312 + 0.961355i \(0.411219\pi\)
\(348\) 18.6552 1.00002
\(349\) −30.9523 −1.65684 −0.828420 0.560107i \(-0.810760\pi\)
−0.828420 + 0.560107i \(0.810760\pi\)
\(350\) 21.8767 1.16936
\(351\) −14.8574 −0.793027
\(352\) 6.01769 0.320744
\(353\) −1.00000 −0.0532246
\(354\) −13.1492 −0.698871
\(355\) 42.4845 2.25484
\(356\) −16.0712 −0.851771
\(357\) 8.20884 0.434458
\(358\) −4.49918 −0.237789
\(359\) 33.4823 1.76713 0.883564 0.468310i \(-0.155137\pi\)
0.883564 + 0.468310i \(0.155137\pi\)
\(360\) −3.13930 −0.165455
\(361\) −2.19049 −0.115289
\(362\) 17.6053 0.925315
\(363\) 22.5020 1.18105
\(364\) 45.0139 2.35937
\(365\) 25.4010 1.32955
\(366\) 16.9394 0.885435
\(367\) −5.98550 −0.312441 −0.156220 0.987722i \(-0.549931\pi\)
−0.156220 + 0.987722i \(0.549931\pi\)
\(368\) 18.2839 0.953112
\(369\) −6.87522 −0.357910
\(370\) 62.9342 3.27179
\(371\) 3.67024 0.190549
\(372\) −24.6037 −1.27564
\(373\) 33.7873 1.74944 0.874719 0.484630i \(-0.161046\pi\)
0.874719 + 0.484630i \(0.161046\pi\)
\(374\) −1.54665 −0.0799755
\(375\) 13.4484 0.694474
\(376\) 5.81063 0.299661
\(377\) 18.8353 0.970068
\(378\) 23.2522 1.19597
\(379\) 35.5902 1.82814 0.914072 0.405551i \(-0.132920\pi\)
0.914072 + 0.405551i \(0.132920\pi\)
\(380\) 26.6137 1.36526
\(381\) −36.1930 −1.85422
\(382\) −14.5599 −0.744951
\(383\) 3.73217 0.190705 0.0953525 0.995444i \(-0.469602\pi\)
0.0953525 + 0.995444i \(0.469602\pi\)
\(384\) −11.6880 −0.596453
\(385\) −7.89015 −0.402119
\(386\) 36.6607 1.86598
\(387\) −4.24569 −0.215820
\(388\) −0.568989 −0.0288861
\(389\) 32.5963 1.65270 0.826348 0.563159i \(-0.190414\pi\)
0.826348 + 0.563159i \(0.190414\pi\)
\(390\) −63.2670 −3.20365
\(391\) −5.66096 −0.286287
\(392\) −5.17609 −0.261432
\(393\) 11.3081 0.570418
\(394\) −20.9941 −1.05767
\(395\) −7.06914 −0.355687
\(396\) 2.83859 0.142645
\(397\) −0.982787 −0.0493247 −0.0246623 0.999696i \(-0.507851\pi\)
−0.0246623 + 0.999696i \(0.507851\pi\)
\(398\) 35.2954 1.76920
\(399\) 33.6558 1.68490
\(400\) −8.90866 −0.445433
\(401\) 25.8784 1.29231 0.646153 0.763208i \(-0.276377\pi\)
0.646153 + 0.763208i \(0.276377\pi\)
\(402\) −56.9397 −2.83989
\(403\) −24.8413 −1.23743
\(404\) 10.3001 0.512448
\(405\) −31.2817 −1.55440
\(406\) −29.4779 −1.46296
\(407\) −8.06977 −0.400004
\(408\) 1.48123 0.0733317
\(409\) −33.7517 −1.66891 −0.834456 0.551075i \(-0.814218\pi\)
−0.834456 + 0.551075i \(0.814218\pi\)
\(410\) 24.3167 1.20092
\(411\) −25.7424 −1.26978
\(412\) 45.3920 2.23630
\(413\) 11.1816 0.550212
\(414\) 19.3059 0.948835
\(415\) −1.72606 −0.0847292
\(416\) −41.0325 −2.01178
\(417\) −7.11262 −0.348306
\(418\) −6.34119 −0.310158
\(419\) −18.5921 −0.908282 −0.454141 0.890930i \(-0.650054\pi\)
−0.454141 + 0.890930i \(0.650054\pi\)
\(420\) 53.2856 2.60007
\(421\) 10.5884 0.516048 0.258024 0.966139i \(-0.416929\pi\)
0.258024 + 0.966139i \(0.416929\pi\)
\(422\) 14.1215 0.687425
\(423\) −13.8464 −0.673236
\(424\) 0.662269 0.0321626
\(425\) 2.75826 0.133795
\(426\) 68.3629 3.31220
\(427\) −14.4047 −0.697090
\(428\) −20.3465 −0.983485
\(429\) 8.11244 0.391672
\(430\) 15.0164 0.724156
\(431\) 31.7185 1.52783 0.763914 0.645318i \(-0.223275\pi\)
0.763914 + 0.645318i \(0.223275\pi\)
\(432\) −9.46882 −0.455569
\(433\) −14.8066 −0.711559 −0.355779 0.934570i \(-0.615785\pi\)
−0.355779 + 0.934570i \(0.615785\pi\)
\(434\) 38.8774 1.86617
\(435\) 22.2965 1.06903
\(436\) 8.02346 0.384254
\(437\) −23.2096 −1.11027
\(438\) 40.8734 1.95300
\(439\) 16.4258 0.783961 0.391981 0.919973i \(-0.371790\pi\)
0.391981 + 0.919973i \(0.371790\pi\)
\(440\) −1.42372 −0.0678732
\(441\) 12.3343 0.587350
\(442\) 10.5461 0.501626
\(443\) −18.7722 −0.891895 −0.445947 0.895059i \(-0.647133\pi\)
−0.445947 + 0.895059i \(0.647133\pi\)
\(444\) 54.4987 2.58640
\(445\) −19.2081 −0.910550
\(446\) −14.8211 −0.701799
\(447\) 37.6089 1.77884
\(448\) 39.5973 1.87080
\(449\) −11.7121 −0.552728 −0.276364 0.961053i \(-0.589130\pi\)
−0.276364 + 0.961053i \(0.589130\pi\)
\(450\) −9.40666 −0.443434
\(451\) −3.11802 −0.146822
\(452\) −25.9340 −1.21983
\(453\) −33.1287 −1.55652
\(454\) −22.7418 −1.06733
\(455\) 53.8001 2.52219
\(456\) 6.07295 0.284392
\(457\) −8.98974 −0.420523 −0.210261 0.977645i \(-0.567431\pi\)
−0.210261 + 0.977645i \(0.567431\pi\)
\(458\) 0.208014 0.00971984
\(459\) 2.93169 0.136840
\(460\) −36.7467 −1.71332
\(461\) −1.15092 −0.0536037 −0.0268018 0.999641i \(-0.508532\pi\)
−0.0268018 + 0.999641i \(0.508532\pi\)
\(462\) −12.6962 −0.590682
\(463\) 5.78963 0.269067 0.134534 0.990909i \(-0.457046\pi\)
0.134534 + 0.990909i \(0.457046\pi\)
\(464\) 12.0040 0.557273
\(465\) −29.4060 −1.36367
\(466\) −42.4493 −1.96643
\(467\) −5.11421 −0.236658 −0.118329 0.992974i \(-0.537754\pi\)
−0.118329 + 0.992974i \(0.537754\pi\)
\(468\) −19.3554 −0.894702
\(469\) 48.4196 2.23581
\(470\) 48.9729 2.25895
\(471\) 21.2539 0.979327
\(472\) 2.01764 0.0928696
\(473\) −1.92549 −0.0885340
\(474\) −11.3751 −0.522477
\(475\) 11.3087 0.518879
\(476\) −8.88227 −0.407118
\(477\) −1.57815 −0.0722586
\(478\) −7.31386 −0.334528
\(479\) 31.5929 1.44352 0.721758 0.692146i \(-0.243334\pi\)
0.721758 + 0.692146i \(0.243334\pi\)
\(480\) −48.5726 −2.21702
\(481\) 55.0249 2.50892
\(482\) 45.6549 2.07953
\(483\) −46.4700 −2.11446
\(484\) −24.3480 −1.10673
\(485\) −0.680049 −0.0308794
\(486\) −32.0338 −1.45308
\(487\) 33.1645 1.50283 0.751414 0.659831i \(-0.229372\pi\)
0.751414 + 0.659831i \(0.229372\pi\)
\(488\) −2.59922 −0.117661
\(489\) −18.3472 −0.829689
\(490\) −43.6249 −1.97077
\(491\) −41.0532 −1.85270 −0.926352 0.376660i \(-0.877073\pi\)
−0.926352 + 0.376660i \(0.877073\pi\)
\(492\) 21.0574 0.949341
\(493\) −3.71663 −0.167389
\(494\) 43.2383 1.94538
\(495\) 3.39265 0.152488
\(496\) −15.8317 −0.710865
\(497\) −58.1335 −2.60765
\(498\) −2.77746 −0.124461
\(499\) −14.1234 −0.632250 −0.316125 0.948718i \(-0.602382\pi\)
−0.316125 + 0.948718i \(0.602382\pi\)
\(500\) −14.5517 −0.650772
\(501\) 31.2052 1.39414
\(502\) 9.30363 0.415241
\(503\) −36.3167 −1.61928 −0.809641 0.586926i \(-0.800338\pi\)
−0.809641 + 0.586926i \(0.800338\pi\)
\(504\) 4.29564 0.191343
\(505\) 12.3105 0.547811
\(506\) 8.75555 0.389232
\(507\) −27.3166 −1.21317
\(508\) 39.1621 1.73754
\(509\) 25.6235 1.13574 0.567871 0.823117i \(-0.307767\pi\)
0.567871 + 0.823117i \(0.307767\pi\)
\(510\) 12.4840 0.552801
\(511\) −34.7573 −1.53757
\(512\) −30.5931 −1.35204
\(513\) 12.0198 0.530686
\(514\) −22.3854 −0.987378
\(515\) 54.2520 2.39063
\(516\) 13.0037 0.572455
\(517\) −6.27958 −0.276176
\(518\) −86.1158 −3.78371
\(519\) 36.6170 1.60731
\(520\) 9.70785 0.425717
\(521\) 35.5352 1.55683 0.778413 0.627753i \(-0.216025\pi\)
0.778413 + 0.627753i \(0.216025\pi\)
\(522\) 12.6751 0.554772
\(523\) −3.41724 −0.149425 −0.0747127 0.997205i \(-0.523804\pi\)
−0.0747127 + 0.997205i \(0.523804\pi\)
\(524\) −12.2358 −0.534523
\(525\) 22.6421 0.988183
\(526\) 31.2261 1.36152
\(527\) 4.90174 0.213523
\(528\) 5.17019 0.225003
\(529\) 9.04651 0.393327
\(530\) 5.58170 0.242454
\(531\) −4.80794 −0.208647
\(532\) −36.4168 −1.57887
\(533\) 21.2607 0.920903
\(534\) −30.9082 −1.33753
\(535\) −24.3179 −1.05135
\(536\) 8.73697 0.377380
\(537\) −4.65660 −0.200947
\(538\) 12.3703 0.533322
\(539\) 5.59382 0.240943
\(540\) 19.0303 0.818935
\(541\) 5.90273 0.253778 0.126889 0.991917i \(-0.459501\pi\)
0.126889 + 0.991917i \(0.459501\pi\)
\(542\) 45.8143 1.96789
\(543\) 18.2213 0.781951
\(544\) 8.09664 0.347141
\(545\) 9.58954 0.410771
\(546\) 86.5712 3.70490
\(547\) −37.7269 −1.61309 −0.806544 0.591174i \(-0.798665\pi\)
−0.806544 + 0.591174i \(0.798665\pi\)
\(548\) 27.8542 1.18987
\(549\) 6.19380 0.264345
\(550\) −4.26607 −0.181906
\(551\) −15.2380 −0.649160
\(552\) −8.38518 −0.356897
\(553\) 9.67303 0.411339
\(554\) 30.0876 1.27830
\(555\) 65.1362 2.76488
\(556\) 7.69612 0.326388
\(557\) 20.0306 0.848724 0.424362 0.905493i \(-0.360498\pi\)
0.424362 + 0.905493i \(0.360498\pi\)
\(558\) −16.7167 −0.707675
\(559\) 13.1292 0.555307
\(560\) 34.2876 1.44892
\(561\) −1.60077 −0.0675845
\(562\) 49.1147 2.07178
\(563\) 12.8469 0.541431 0.270716 0.962659i \(-0.412740\pi\)
0.270716 + 0.962659i \(0.412740\pi\)
\(564\) 42.4088 1.78573
\(565\) −30.9960 −1.30401
\(566\) −9.70292 −0.407844
\(567\) 42.8042 1.79761
\(568\) −10.4898 −0.440142
\(569\) −13.2603 −0.555903 −0.277951 0.960595i \(-0.589655\pi\)
−0.277951 + 0.960595i \(0.589655\pi\)
\(570\) 51.1837 2.14385
\(571\) 23.7341 0.993241 0.496620 0.867968i \(-0.334574\pi\)
0.496620 + 0.867968i \(0.334574\pi\)
\(572\) −8.77796 −0.367025
\(573\) −15.0694 −0.629532
\(574\) −33.2737 −1.38882
\(575\) −15.6144 −0.651166
\(576\) −17.0263 −0.709428
\(577\) −5.64670 −0.235075 −0.117538 0.993068i \(-0.537500\pi\)
−0.117538 + 0.993068i \(0.537500\pi\)
\(578\) −2.08098 −0.0865574
\(579\) 37.9434 1.57687
\(580\) −24.1256 −1.00176
\(581\) 2.36185 0.0979862
\(582\) −1.09428 −0.0453595
\(583\) −0.715717 −0.0296420
\(584\) −6.27171 −0.259525
\(585\) −23.1333 −0.956444
\(586\) 5.74667 0.237393
\(587\) 23.5827 0.973363 0.486681 0.873580i \(-0.338207\pi\)
0.486681 + 0.873580i \(0.338207\pi\)
\(588\) −37.7775 −1.55792
\(589\) 20.0969 0.828076
\(590\) 17.0050 0.700085
\(591\) −21.7287 −0.893800
\(592\) 35.0682 1.44130
\(593\) −35.6186 −1.46268 −0.731339 0.682014i \(-0.761104\pi\)
−0.731339 + 0.682014i \(0.761104\pi\)
\(594\) −4.53431 −0.186045
\(595\) −10.6160 −0.435213
\(596\) −40.6942 −1.66690
\(597\) 36.5304 1.49509
\(598\) −59.7010 −2.44136
\(599\) −21.9541 −0.897020 −0.448510 0.893778i \(-0.648045\pi\)
−0.448510 + 0.893778i \(0.648045\pi\)
\(600\) 4.08561 0.166794
\(601\) 21.6928 0.884869 0.442435 0.896801i \(-0.354115\pi\)
0.442435 + 0.896801i \(0.354115\pi\)
\(602\) −20.5477 −0.837460
\(603\) −20.8197 −0.847845
\(604\) 35.8465 1.45857
\(605\) −29.1004 −1.18310
\(606\) 19.8092 0.804693
\(607\) −36.9906 −1.50140 −0.750701 0.660642i \(-0.770284\pi\)
−0.750701 + 0.660642i \(0.770284\pi\)
\(608\) 33.1958 1.34627
\(609\) −30.5093 −1.23630
\(610\) −21.9066 −0.886973
\(611\) 42.8182 1.73224
\(612\) 3.81925 0.154384
\(613\) 18.6944 0.755060 0.377530 0.925997i \(-0.376774\pi\)
0.377530 + 0.925997i \(0.376774\pi\)
\(614\) −30.5457 −1.23272
\(615\) 25.1675 1.01485
\(616\) 1.94814 0.0784929
\(617\) 25.6353 1.03204 0.516020 0.856577i \(-0.327413\pi\)
0.516020 + 0.856577i \(0.327413\pi\)
\(618\) 87.2983 3.51165
\(619\) 36.5340 1.46842 0.734212 0.678920i \(-0.237552\pi\)
0.734212 + 0.678920i \(0.237552\pi\)
\(620\) 31.8184 1.27786
\(621\) −16.5962 −0.665983
\(622\) 27.3966 1.09850
\(623\) 26.2833 1.05302
\(624\) −35.2537 −1.41128
\(625\) −31.1833 −1.24733
\(626\) −1.00211 −0.0400525
\(627\) −6.56306 −0.262103
\(628\) −22.9975 −0.917699
\(629\) −10.8577 −0.432924
\(630\) 36.2043 1.44242
\(631\) 9.37028 0.373025 0.186513 0.982453i \(-0.440282\pi\)
0.186513 + 0.982453i \(0.440282\pi\)
\(632\) 1.74543 0.0694294
\(633\) 14.6156 0.580919
\(634\) 3.67961 0.146136
\(635\) 46.8061 1.85744
\(636\) 4.83355 0.191663
\(637\) −38.1423 −1.51125
\(638\) 5.74834 0.227579
\(639\) 24.9966 0.988850
\(640\) 15.1154 0.597489
\(641\) 33.2885 1.31482 0.657409 0.753534i \(-0.271652\pi\)
0.657409 + 0.753534i \(0.271652\pi\)
\(642\) −39.1305 −1.54436
\(643\) 15.4710 0.610117 0.305058 0.952334i \(-0.401324\pi\)
0.305058 + 0.952334i \(0.401324\pi\)
\(644\) 50.2822 1.98140
\(645\) 15.5418 0.611959
\(646\) −8.53190 −0.335683
\(647\) 46.3055 1.82046 0.910229 0.414106i \(-0.135906\pi\)
0.910229 + 0.414106i \(0.135906\pi\)
\(648\) 7.72371 0.303416
\(649\) −2.18048 −0.0855912
\(650\) 29.0888 1.14096
\(651\) 40.2376 1.57704
\(652\) 19.8523 0.777478
\(653\) 32.8928 1.28720 0.643598 0.765364i \(-0.277441\pi\)
0.643598 + 0.765364i \(0.277441\pi\)
\(654\) 15.4308 0.603391
\(655\) −14.6241 −0.571409
\(656\) 13.5498 0.529030
\(657\) 14.9452 0.583066
\(658\) −67.0119 −2.61240
\(659\) 42.4294 1.65281 0.826407 0.563074i \(-0.190381\pi\)
0.826407 + 0.563074i \(0.190381\pi\)
\(660\) −10.3910 −0.404469
\(661\) −8.94012 −0.347730 −0.173865 0.984769i \(-0.555626\pi\)
−0.173865 + 0.984769i \(0.555626\pi\)
\(662\) 14.8893 0.578690
\(663\) 10.9151 0.423907
\(664\) 0.426180 0.0165390
\(665\) −43.5249 −1.68782
\(666\) 37.0286 1.43483
\(667\) 21.0397 0.814662
\(668\) −33.7651 −1.30641
\(669\) −15.3397 −0.593066
\(670\) 73.6365 2.84483
\(671\) 2.80899 0.108440
\(672\) 66.4641 2.56391
\(673\) 28.1335 1.08447 0.542233 0.840228i \(-0.317579\pi\)
0.542233 + 0.840228i \(0.317579\pi\)
\(674\) −66.5828 −2.56467
\(675\) 8.08637 0.311244
\(676\) 29.5576 1.13683
\(677\) 9.73626 0.374195 0.187097 0.982341i \(-0.440092\pi\)
0.187097 + 0.982341i \(0.440092\pi\)
\(678\) −49.8765 −1.91550
\(679\) 0.930542 0.0357109
\(680\) −1.91558 −0.0734591
\(681\) −23.5376 −0.901961
\(682\) −7.58130 −0.290303
\(683\) −23.0088 −0.880407 −0.440203 0.897898i \(-0.645094\pi\)
−0.440203 + 0.897898i \(0.645094\pi\)
\(684\) 15.6587 0.598725
\(685\) 33.2910 1.27199
\(686\) 4.17456 0.159386
\(687\) 0.215292 0.00821390
\(688\) 8.36746 0.319006
\(689\) 4.88022 0.185922
\(690\) −70.6716 −2.69042
\(691\) 50.6196 1.92566 0.962830 0.270107i \(-0.0870592\pi\)
0.962830 + 0.270107i \(0.0870592\pi\)
\(692\) −39.6209 −1.50616
\(693\) −4.64232 −0.176347
\(694\) −21.3446 −0.810230
\(695\) 9.19830 0.348911
\(696\) −5.50518 −0.208673
\(697\) −4.19522 −0.158905
\(698\) 64.4112 2.43800
\(699\) −43.9346 −1.66176
\(700\) −24.4996 −0.925998
\(701\) 45.4185 1.71543 0.857717 0.514122i \(-0.171882\pi\)
0.857717 + 0.514122i \(0.171882\pi\)
\(702\) 30.9179 1.16692
\(703\) −44.5158 −1.67894
\(704\) −7.72169 −0.291022
\(705\) 50.6864 1.90896
\(706\) 2.08098 0.0783188
\(707\) −16.8451 −0.633524
\(708\) 14.7257 0.553427
\(709\) 37.9095 1.42372 0.711860 0.702321i \(-0.247853\pi\)
0.711860 + 0.702321i \(0.247853\pi\)
\(710\) −88.4095 −3.31795
\(711\) −4.15926 −0.155985
\(712\) 4.74263 0.177738
\(713\) −27.7486 −1.03919
\(714\) −17.0825 −0.639295
\(715\) −10.4913 −0.392353
\(716\) 5.03861 0.188302
\(717\) −7.56977 −0.282698
\(718\) −69.6760 −2.60029
\(719\) 45.5640 1.69925 0.849625 0.527387i \(-0.176828\pi\)
0.849625 + 0.527387i \(0.176828\pi\)
\(720\) −14.7432 −0.549447
\(721\) −74.2355 −2.76467
\(722\) 4.55836 0.169645
\(723\) 47.2524 1.75733
\(724\) −19.7161 −0.732744
\(725\) −10.2514 −0.380729
\(726\) −46.8262 −1.73788
\(727\) 27.0469 1.00312 0.501558 0.865124i \(-0.332760\pi\)
0.501558 + 0.865124i \(0.332760\pi\)
\(728\) −13.2837 −0.492327
\(729\) 0.537592 0.0199108
\(730\) −52.8590 −1.95640
\(731\) −2.59069 −0.0958202
\(732\) −18.9703 −0.701164
\(733\) −3.01302 −0.111289 −0.0556443 0.998451i \(-0.517721\pi\)
−0.0556443 + 0.998451i \(0.517721\pi\)
\(734\) 12.4557 0.459749
\(735\) −45.1512 −1.66543
\(736\) −45.8348 −1.68949
\(737\) −9.44208 −0.347803
\(738\) 14.3072 0.526656
\(739\) −20.8382 −0.766545 −0.383272 0.923635i \(-0.625203\pi\)
−0.383272 + 0.923635i \(0.625203\pi\)
\(740\) −70.4798 −2.59089
\(741\) 44.7512 1.64398
\(742\) −7.63770 −0.280389
\(743\) −10.1357 −0.371842 −0.185921 0.982565i \(-0.559527\pi\)
−0.185921 + 0.982565i \(0.559527\pi\)
\(744\) 7.26060 0.266186
\(745\) −48.6372 −1.78193
\(746\) −70.3107 −2.57426
\(747\) −1.01556 −0.0371575
\(748\) 1.73209 0.0633315
\(749\) 33.2753 1.21585
\(750\) −27.9859 −1.02190
\(751\) −24.8327 −0.906159 −0.453080 0.891470i \(-0.649675\pi\)
−0.453080 + 0.891470i \(0.649675\pi\)
\(752\) 27.2887 0.995117
\(753\) 9.62916 0.350906
\(754\) −39.1959 −1.42743
\(755\) 42.8433 1.55923
\(756\) −26.0401 −0.947069
\(757\) −7.21502 −0.262234 −0.131117 0.991367i \(-0.541856\pi\)
−0.131117 + 0.991367i \(0.541856\pi\)
\(758\) −74.0625 −2.69007
\(759\) 9.06190 0.328926
\(760\) −7.85376 −0.284886
\(761\) 26.3039 0.953517 0.476758 0.879034i \(-0.341812\pi\)
0.476758 + 0.879034i \(0.341812\pi\)
\(762\) 75.3169 2.72844
\(763\) −13.1218 −0.475041
\(764\) 16.3056 0.589916
\(765\) 4.56472 0.165038
\(766\) −7.76658 −0.280618
\(767\) 14.8679 0.536849
\(768\) −20.4303 −0.737217
\(769\) −28.8070 −1.03881 −0.519403 0.854530i \(-0.673846\pi\)
−0.519403 + 0.854530i \(0.673846\pi\)
\(770\) 16.4192 0.591709
\(771\) −23.1687 −0.834399
\(772\) −41.0562 −1.47764
\(773\) −11.0591 −0.397768 −0.198884 0.980023i \(-0.563732\pi\)
−0.198884 + 0.980023i \(0.563732\pi\)
\(774\) 8.83520 0.317575
\(775\) 13.5203 0.485663
\(776\) 0.167910 0.00602761
\(777\) −89.1289 −3.19748
\(778\) −67.8322 −2.43190
\(779\) −17.2001 −0.616259
\(780\) 70.8525 2.53693
\(781\) 11.3364 0.405647
\(782\) 11.7804 0.421265
\(783\) −10.8960 −0.389392
\(784\) −24.3087 −0.868167
\(785\) −27.4863 −0.981028
\(786\) −23.5319 −0.839357
\(787\) −10.4784 −0.373513 −0.186757 0.982406i \(-0.559798\pi\)
−0.186757 + 0.982406i \(0.559798\pi\)
\(788\) 23.5113 0.837554
\(789\) 32.3187 1.15058
\(790\) 14.7107 0.523385
\(791\) 42.4133 1.50804
\(792\) −0.837674 −0.0297654
\(793\) −19.1535 −0.680161
\(794\) 2.04516 0.0725801
\(795\) 5.77700 0.204889
\(796\) −39.5272 −1.40101
\(797\) −5.05869 −0.179188 −0.0895940 0.995978i \(-0.528557\pi\)
−0.0895940 + 0.995978i \(0.528557\pi\)
\(798\) −70.0370 −2.47928
\(799\) −8.44901 −0.298904
\(800\) 22.3326 0.789578
\(801\) −11.3014 −0.399317
\(802\) −53.8525 −1.90160
\(803\) 6.77787 0.239186
\(804\) 63.7665 2.24887
\(805\) 60.0967 2.11813
\(806\) 51.6942 1.82085
\(807\) 12.8031 0.450692
\(808\) −3.03957 −0.106932
\(809\) −2.73948 −0.0963150 −0.0481575 0.998840i \(-0.515335\pi\)
−0.0481575 + 0.998840i \(0.515335\pi\)
\(810\) 65.0966 2.28726
\(811\) −15.3648 −0.539532 −0.269766 0.962926i \(-0.586946\pi\)
−0.269766 + 0.962926i \(0.586946\pi\)
\(812\) 33.0122 1.15850
\(813\) 47.4173 1.66300
\(814\) 16.7930 0.588596
\(815\) 23.7273 0.831130
\(816\) 6.95635 0.243521
\(817\) −10.6217 −0.371606
\(818\) 70.2366 2.45576
\(819\) 31.6543 1.10609
\(820\) −27.2322 −0.950990
\(821\) 54.6365 1.90683 0.953413 0.301667i \(-0.0975432\pi\)
0.953413 + 0.301667i \(0.0975432\pi\)
\(822\) 53.5695 1.86845
\(823\) 12.8741 0.448764 0.224382 0.974501i \(-0.427964\pi\)
0.224382 + 0.974501i \(0.427964\pi\)
\(824\) −13.3953 −0.466646
\(825\) −4.41534 −0.153722
\(826\) −23.2687 −0.809623
\(827\) −2.79009 −0.0970208 −0.0485104 0.998823i \(-0.515447\pi\)
−0.0485104 + 0.998823i \(0.515447\pi\)
\(828\) −21.6206 −0.751369
\(829\) 55.5290 1.92860 0.964301 0.264808i \(-0.0853084\pi\)
0.964301 + 0.264808i \(0.0853084\pi\)
\(830\) 3.59191 0.124677
\(831\) 31.1403 1.08025
\(832\) 52.6515 1.82536
\(833\) 7.52634 0.260772
\(834\) 14.8012 0.512525
\(835\) −40.3557 −1.39657
\(836\) 7.10147 0.245610
\(837\) 14.3704 0.496714
\(838\) 38.6897 1.33652
\(839\) 37.2970 1.28763 0.643817 0.765179i \(-0.277350\pi\)
0.643817 + 0.765179i \(0.277350\pi\)
\(840\) −15.7247 −0.542553
\(841\) −15.1866 −0.523677
\(842\) −22.0343 −0.759352
\(843\) 50.8332 1.75079
\(844\) −15.8146 −0.544362
\(845\) 35.3268 1.21528
\(846\) 28.8142 0.990651
\(847\) 39.8194 1.36821
\(848\) 3.11024 0.106806
\(849\) −10.0424 −0.344655
\(850\) −5.73988 −0.196876
\(851\) 61.4649 2.10699
\(852\) −76.5594 −2.62288
\(853\) −16.4601 −0.563582 −0.281791 0.959476i \(-0.590929\pi\)
−0.281791 + 0.959476i \(0.590929\pi\)
\(854\) 29.9758 1.02575
\(855\) 18.7151 0.640042
\(856\) 6.00429 0.205222
\(857\) −33.9556 −1.15990 −0.579950 0.814652i \(-0.696928\pi\)
−0.579950 + 0.814652i \(0.696928\pi\)
\(858\) −16.8818 −0.576337
\(859\) −45.2067 −1.54243 −0.771217 0.636572i \(-0.780352\pi\)
−0.771217 + 0.636572i \(0.780352\pi\)
\(860\) −16.8168 −0.573449
\(861\) −34.4379 −1.17364
\(862\) −66.0057 −2.24816
\(863\) 25.0753 0.853573 0.426786 0.904352i \(-0.359646\pi\)
0.426786 + 0.904352i \(0.359646\pi\)
\(864\) 23.7369 0.807544
\(865\) −47.3545 −1.61010
\(866\) 30.8122 1.04704
\(867\) −2.15379 −0.0731466
\(868\) −43.5386 −1.47780
\(869\) −1.88629 −0.0639881
\(870\) −46.3985 −1.57306
\(871\) 64.3822 2.18151
\(872\) −2.36774 −0.0801817
\(873\) −0.400120 −0.0135420
\(874\) 48.2988 1.63373
\(875\) 23.7983 0.804529
\(876\) −45.7739 −1.54656
\(877\) −17.7065 −0.597908 −0.298954 0.954268i \(-0.596638\pi\)
−0.298954 + 0.954268i \(0.596638\pi\)
\(878\) −34.1818 −1.15358
\(879\) 5.94774 0.200612
\(880\) −6.68628 −0.225394
\(881\) −14.2437 −0.479884 −0.239942 0.970787i \(-0.577128\pi\)
−0.239942 + 0.970787i \(0.577128\pi\)
\(882\) −25.6675 −0.864271
\(883\) −6.38285 −0.214800 −0.107400 0.994216i \(-0.534253\pi\)
−0.107400 + 0.994216i \(0.534253\pi\)
\(884\) −11.8105 −0.397231
\(885\) 17.6000 0.591618
\(886\) 39.0646 1.31240
\(887\) 45.5793 1.53040 0.765201 0.643791i \(-0.222639\pi\)
0.765201 + 0.643791i \(0.222639\pi\)
\(888\) −16.0827 −0.539699
\(889\) −64.0469 −2.14806
\(890\) 39.9716 1.33985
\(891\) −8.34704 −0.279636
\(892\) 16.5981 0.555745
\(893\) −34.6404 −1.15920
\(894\) −78.2634 −2.61752
\(895\) 6.02209 0.201296
\(896\) −20.6831 −0.690974
\(897\) −61.7899 −2.06310
\(898\) 24.3726 0.813326
\(899\) −18.2180 −0.607604
\(900\) 10.5345 0.351149
\(901\) −0.962978 −0.0320814
\(902\) 6.48855 0.216045
\(903\) −21.2666 −0.707708
\(904\) 7.65318 0.254541
\(905\) −23.5645 −0.783310
\(906\) 68.9403 2.29039
\(907\) 41.2481 1.36962 0.684810 0.728722i \(-0.259885\pi\)
0.684810 + 0.728722i \(0.259885\pi\)
\(908\) 25.4685 0.845202
\(909\) 7.24314 0.240240
\(910\) −111.957 −3.71134
\(911\) −45.4589 −1.50612 −0.753061 0.657951i \(-0.771423\pi\)
−0.753061 + 0.657951i \(0.771423\pi\)
\(912\) 28.5206 0.944412
\(913\) −0.460574 −0.0152428
\(914\) 18.7075 0.618789
\(915\) −22.6731 −0.749550
\(916\) −0.232954 −0.00769701
\(917\) 20.0108 0.660814
\(918\) −6.10080 −0.201356
\(919\) 8.35180 0.275501 0.137750 0.990467i \(-0.456013\pi\)
0.137750 + 0.990467i \(0.456013\pi\)
\(920\) 10.8440 0.357517
\(921\) −31.6145 −1.04173
\(922\) 2.39504 0.0788766
\(923\) −77.2986 −2.54431
\(924\) 14.2185 0.467753
\(925\) −29.9483 −0.984692
\(926\) −12.0481 −0.395926
\(927\) 31.9202 1.04840
\(928\) −30.0923 −0.987827
\(929\) −10.3064 −0.338141 −0.169070 0.985604i \(-0.554077\pi\)
−0.169070 + 0.985604i \(0.554077\pi\)
\(930\) 61.1934 2.00661
\(931\) 30.8575 1.01132
\(932\) 47.5389 1.55719
\(933\) 28.3551 0.928305
\(934\) 10.6426 0.348236
\(935\) 2.07017 0.0677019
\(936\) 5.71180 0.186696
\(937\) 49.0054 1.60094 0.800469 0.599374i \(-0.204584\pi\)
0.800469 + 0.599374i \(0.204584\pi\)
\(938\) −100.760 −3.28994
\(939\) −1.03717 −0.0338469
\(940\) −54.8446 −1.78883
\(941\) −1.14819 −0.0374298 −0.0187149 0.999825i \(-0.505957\pi\)
−0.0187149 + 0.999825i \(0.505957\pi\)
\(942\) −44.2289 −1.44106
\(943\) 23.7490 0.773373
\(944\) 9.47554 0.308403
\(945\) −31.1228 −1.01242
\(946\) 4.00690 0.130276
\(947\) −11.7075 −0.380441 −0.190221 0.981741i \(-0.560920\pi\)
−0.190221 + 0.981741i \(0.560920\pi\)
\(948\) 12.7390 0.413742
\(949\) −46.2159 −1.50023
\(950\) −23.5332 −0.763517
\(951\) 3.80836 0.123494
\(952\) 2.62117 0.0849528
\(953\) 31.1758 1.00988 0.504942 0.863153i \(-0.331514\pi\)
0.504942 + 0.863153i \(0.331514\pi\)
\(954\) 3.28410 0.106327
\(955\) 19.4883 0.630625
\(956\) 8.19077 0.264908
\(957\) 5.94947 0.192319
\(958\) −65.7442 −2.12410
\(959\) −45.5537 −1.47100
\(960\) 62.3266 2.01158
\(961\) −6.97292 −0.224933
\(962\) −114.506 −3.69182
\(963\) −14.3079 −0.461065
\(964\) −51.1288 −1.64675
\(965\) −49.0698 −1.57961
\(966\) 96.7031 3.11137
\(967\) −3.39871 −0.109295 −0.0546475 0.998506i \(-0.517404\pi\)
−0.0546475 + 0.998506i \(0.517404\pi\)
\(968\) 7.18513 0.230939
\(969\) −8.83042 −0.283674
\(970\) 1.41517 0.0454383
\(971\) 48.9997 1.57248 0.786238 0.617923i \(-0.212026\pi\)
0.786238 + 0.617923i \(0.212026\pi\)
\(972\) 35.8745 1.15067
\(973\) −12.5865 −0.403503
\(974\) −69.0147 −2.21137
\(975\) 30.1066 0.964183
\(976\) −12.2068 −0.390731
\(977\) 23.2644 0.744295 0.372147 0.928174i \(-0.378622\pi\)
0.372147 + 0.928174i \(0.378622\pi\)
\(978\) 38.1802 1.22087
\(979\) −5.12539 −0.163808
\(980\) 48.8553 1.56063
\(981\) 5.64219 0.180141
\(982\) 85.4309 2.72621
\(983\) −7.69386 −0.245396 −0.122698 0.992444i \(-0.539155\pi\)
−0.122698 + 0.992444i \(0.539155\pi\)
\(984\) −6.21407 −0.198097
\(985\) 28.1004 0.895352
\(986\) 7.73425 0.246309
\(987\) −69.3566 −2.20764
\(988\) −48.4224 −1.54052
\(989\) 14.6658 0.466346
\(990\) −7.06004 −0.224383
\(991\) −40.5001 −1.28653 −0.643264 0.765644i \(-0.722420\pi\)
−0.643264 + 0.765644i \(0.722420\pi\)
\(992\) 39.6877 1.26008
\(993\) 15.4103 0.489031
\(994\) 120.975 3.83709
\(995\) −47.2425 −1.49769
\(996\) 3.11046 0.0985588
\(997\) −37.1530 −1.17665 −0.588323 0.808626i \(-0.700212\pi\)
−0.588323 + 0.808626i \(0.700212\pi\)
\(998\) 29.3905 0.930341
\(999\) −31.8313 −1.00710
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 6001.2.a.d.1.19 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.19 121 1.1 even 1 trivial