Properties

Label 6017.2.a.f.1.13
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 1.13
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.32206 q^{2} +0.535084 q^{3} +3.39196 q^{4} -0.511363 q^{5} -1.24250 q^{6} +3.83500 q^{7} -3.23221 q^{8} -2.71368 q^{9} +O(q^{10})\) \(q-2.32206 q^{2} +0.535084 q^{3} +3.39196 q^{4} -0.511363 q^{5} -1.24250 q^{6} +3.83500 q^{7} -3.23221 q^{8} -2.71368 q^{9} +1.18742 q^{10} -1.00000 q^{11} +1.81498 q^{12} +1.58554 q^{13} -8.90510 q^{14} -0.273622 q^{15} +0.721461 q^{16} +5.58922 q^{17} +6.30134 q^{18} +6.53126 q^{19} -1.73452 q^{20} +2.05205 q^{21} +2.32206 q^{22} -3.91383 q^{23} -1.72950 q^{24} -4.73851 q^{25} -3.68173 q^{26} -3.05730 q^{27} +13.0082 q^{28} +0.712066 q^{29} +0.635367 q^{30} +4.98368 q^{31} +4.78914 q^{32} -0.535084 q^{33} -12.9785 q^{34} -1.96108 q^{35} -9.20470 q^{36} +3.92575 q^{37} -15.1660 q^{38} +0.848400 q^{39} +1.65283 q^{40} -2.55719 q^{41} -4.76498 q^{42} +7.01225 q^{43} -3.39196 q^{44} +1.38768 q^{45} +9.08815 q^{46} +1.87117 q^{47} +0.386043 q^{48} +7.70725 q^{49} +11.0031 q^{50} +2.99071 q^{51} +5.37810 q^{52} -8.57947 q^{53} +7.09924 q^{54} +0.511363 q^{55} -12.3955 q^{56} +3.49478 q^{57} -1.65346 q^{58} +6.46824 q^{59} -0.928116 q^{60} +10.8232 q^{61} -11.5724 q^{62} -10.4070 q^{63} -12.5636 q^{64} -0.810789 q^{65} +1.24250 q^{66} +4.01160 q^{67} +18.9584 q^{68} -2.09423 q^{69} +4.55374 q^{70} -15.2159 q^{71} +8.77119 q^{72} +1.42979 q^{73} -9.11582 q^{74} -2.53550 q^{75} +22.1538 q^{76} -3.83500 q^{77} -1.97003 q^{78} -7.90726 q^{79} -0.368928 q^{80} +6.50514 q^{81} +5.93794 q^{82} +3.88440 q^{83} +6.96047 q^{84} -2.85812 q^{85} -16.2828 q^{86} +0.381015 q^{87} +3.23221 q^{88} -4.21218 q^{89} -3.22227 q^{90} +6.08057 q^{91} -13.2756 q^{92} +2.66669 q^{93} -4.34497 q^{94} -3.33985 q^{95} +2.56259 q^{96} -13.1317 q^{97} -17.8967 q^{98} +2.71368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32206 −1.64194 −0.820972 0.570969i \(-0.806568\pi\)
−0.820972 + 0.570969i \(0.806568\pi\)
\(3\) 0.535084 0.308931 0.154466 0.987998i \(-0.450634\pi\)
0.154466 + 0.987998i \(0.450634\pi\)
\(4\) 3.39196 1.69598
\(5\) −0.511363 −0.228689 −0.114344 0.993441i \(-0.536477\pi\)
−0.114344 + 0.993441i \(0.536477\pi\)
\(6\) −1.24250 −0.507248
\(7\) 3.83500 1.44950 0.724748 0.689014i \(-0.241956\pi\)
0.724748 + 0.689014i \(0.241956\pi\)
\(8\) −3.23221 −1.14276
\(9\) −2.71368 −0.904562
\(10\) 1.18742 0.375494
\(11\) −1.00000 −0.301511
\(12\) 1.81498 0.523941
\(13\) 1.58554 0.439751 0.219875 0.975528i \(-0.429435\pi\)
0.219875 + 0.975528i \(0.429435\pi\)
\(14\) −8.90510 −2.37999
\(15\) −0.273622 −0.0706490
\(16\) 0.721461 0.180365
\(17\) 5.58922 1.35559 0.677793 0.735253i \(-0.262937\pi\)
0.677793 + 0.735253i \(0.262937\pi\)
\(18\) 6.30134 1.48524
\(19\) 6.53126 1.49837 0.749187 0.662359i \(-0.230444\pi\)
0.749187 + 0.662359i \(0.230444\pi\)
\(20\) −1.73452 −0.387851
\(21\) 2.05205 0.447794
\(22\) 2.32206 0.495065
\(23\) −3.91383 −0.816091 −0.408045 0.912962i \(-0.633789\pi\)
−0.408045 + 0.912962i \(0.633789\pi\)
\(24\) −1.72950 −0.353034
\(25\) −4.73851 −0.947702
\(26\) −3.68173 −0.722046
\(27\) −3.05730 −0.588378
\(28\) 13.0082 2.45831
\(29\) 0.712066 0.132227 0.0661137 0.997812i \(-0.478940\pi\)
0.0661137 + 0.997812i \(0.478940\pi\)
\(30\) 0.635367 0.116002
\(31\) 4.98368 0.895095 0.447548 0.894260i \(-0.352297\pi\)
0.447548 + 0.894260i \(0.352297\pi\)
\(32\) 4.78914 0.846608
\(33\) −0.535084 −0.0931463
\(34\) −12.9785 −2.22579
\(35\) −1.96108 −0.331483
\(36\) −9.20470 −1.53412
\(37\) 3.92575 0.645389 0.322695 0.946503i \(-0.395411\pi\)
0.322695 + 0.946503i \(0.395411\pi\)
\(38\) −15.1660 −2.46025
\(39\) 0.848400 0.135853
\(40\) 1.65283 0.261336
\(41\) −2.55719 −0.399365 −0.199683 0.979861i \(-0.563991\pi\)
−0.199683 + 0.979861i \(0.563991\pi\)
\(42\) −4.76498 −0.735253
\(43\) 7.01225 1.06936 0.534679 0.845055i \(-0.320433\pi\)
0.534679 + 0.845055i \(0.320433\pi\)
\(44\) −3.39196 −0.511357
\(45\) 1.38768 0.206863
\(46\) 9.08815 1.33997
\(47\) 1.87117 0.272938 0.136469 0.990644i \(-0.456425\pi\)
0.136469 + 0.990644i \(0.456425\pi\)
\(48\) 0.386043 0.0557204
\(49\) 7.70725 1.10104
\(50\) 11.0031 1.55607
\(51\) 2.99071 0.418783
\(52\) 5.37810 0.745808
\(53\) −8.57947 −1.17848 −0.589240 0.807958i \(-0.700573\pi\)
−0.589240 + 0.807958i \(0.700573\pi\)
\(54\) 7.09924 0.966084
\(55\) 0.511363 0.0689522
\(56\) −12.3955 −1.65642
\(57\) 3.49478 0.462894
\(58\) −1.65346 −0.217110
\(59\) 6.46824 0.842093 0.421046 0.907039i \(-0.361663\pi\)
0.421046 + 0.907039i \(0.361663\pi\)
\(60\) −0.928116 −0.119819
\(61\) 10.8232 1.38577 0.692886 0.721047i \(-0.256339\pi\)
0.692886 + 0.721047i \(0.256339\pi\)
\(62\) −11.5724 −1.46970
\(63\) −10.4070 −1.31116
\(64\) −12.5636 −1.57045
\(65\) −0.810789 −0.100566
\(66\) 1.24250 0.152941
\(67\) 4.01160 0.490095 0.245048 0.969511i \(-0.421196\pi\)
0.245048 + 0.969511i \(0.421196\pi\)
\(68\) 18.9584 2.29904
\(69\) −2.09423 −0.252116
\(70\) 4.55374 0.544276
\(71\) −15.2159 −1.80579 −0.902896 0.429859i \(-0.858563\pi\)
−0.902896 + 0.429859i \(0.858563\pi\)
\(72\) 8.77119 1.03369
\(73\) 1.42979 0.167345 0.0836723 0.996493i \(-0.473335\pi\)
0.0836723 + 0.996493i \(0.473335\pi\)
\(74\) −9.11582 −1.05969
\(75\) −2.53550 −0.292775
\(76\) 22.1538 2.54121
\(77\) −3.83500 −0.437039
\(78\) −1.97003 −0.223062
\(79\) −7.90726 −0.889636 −0.444818 0.895621i \(-0.646732\pi\)
−0.444818 + 0.895621i \(0.646732\pi\)
\(80\) −0.368928 −0.0412475
\(81\) 6.50514 0.722793
\(82\) 5.93794 0.655735
\(83\) 3.88440 0.426368 0.213184 0.977012i \(-0.431617\pi\)
0.213184 + 0.977012i \(0.431617\pi\)
\(84\) 6.96047 0.759450
\(85\) −2.85812 −0.310007
\(86\) −16.2828 −1.75582
\(87\) 0.381015 0.0408491
\(88\) 3.23221 0.344554
\(89\) −4.21218 −0.446491 −0.223245 0.974762i \(-0.571665\pi\)
−0.223245 + 0.974762i \(0.571665\pi\)
\(90\) −3.22227 −0.339657
\(91\) 6.08057 0.637417
\(92\) −13.2756 −1.38407
\(93\) 2.66669 0.276523
\(94\) −4.34497 −0.448149
\(95\) −3.33985 −0.342661
\(96\) 2.56259 0.261544
\(97\) −13.1317 −1.33332 −0.666662 0.745361i \(-0.732277\pi\)
−0.666662 + 0.745361i \(0.732277\pi\)
\(98\) −17.8967 −1.80784
\(99\) 2.71368 0.272736
\(100\) −16.0728 −1.60728
\(101\) 6.69632 0.666309 0.333154 0.942872i \(-0.391887\pi\)
0.333154 + 0.942872i \(0.391887\pi\)
\(102\) −6.94459 −0.687617
\(103\) 2.57956 0.254172 0.127086 0.991892i \(-0.459438\pi\)
0.127086 + 0.991892i \(0.459438\pi\)
\(104\) −5.12481 −0.502529
\(105\) −1.04934 −0.102405
\(106\) 19.9220 1.93500
\(107\) −5.09966 −0.493003 −0.246501 0.969142i \(-0.579281\pi\)
−0.246501 + 0.969142i \(0.579281\pi\)
\(108\) −10.3702 −0.997877
\(109\) 0.985401 0.0943843 0.0471921 0.998886i \(-0.484973\pi\)
0.0471921 + 0.998886i \(0.484973\pi\)
\(110\) −1.18742 −0.113216
\(111\) 2.10061 0.199381
\(112\) 2.76681 0.261439
\(113\) 12.0717 1.13561 0.567803 0.823164i \(-0.307793\pi\)
0.567803 + 0.823164i \(0.307793\pi\)
\(114\) −8.11508 −0.760047
\(115\) 2.00139 0.186631
\(116\) 2.41530 0.224255
\(117\) −4.30267 −0.397782
\(118\) −15.0196 −1.38267
\(119\) 21.4347 1.96491
\(120\) 0.884404 0.0807347
\(121\) 1.00000 0.0909091
\(122\) −25.1322 −2.27536
\(123\) −1.36831 −0.123376
\(124\) 16.9044 1.51806
\(125\) 4.97991 0.445417
\(126\) 24.1656 2.15285
\(127\) −6.01434 −0.533687 −0.266843 0.963740i \(-0.585981\pi\)
−0.266843 + 0.963740i \(0.585981\pi\)
\(128\) 19.5951 1.73198
\(129\) 3.75214 0.330358
\(130\) 1.88270 0.165124
\(131\) 12.1508 1.06162 0.530812 0.847490i \(-0.321887\pi\)
0.530812 + 0.847490i \(0.321887\pi\)
\(132\) −1.81498 −0.157974
\(133\) 25.0474 2.17189
\(134\) −9.31518 −0.804709
\(135\) 1.56339 0.134555
\(136\) −18.0655 −1.54911
\(137\) 5.39118 0.460600 0.230300 0.973120i \(-0.426029\pi\)
0.230300 + 0.973120i \(0.426029\pi\)
\(138\) 4.86293 0.413960
\(139\) 17.2878 1.46633 0.733167 0.680048i \(-0.238041\pi\)
0.733167 + 0.680048i \(0.238041\pi\)
\(140\) −6.65190 −0.562188
\(141\) 1.00123 0.0843191
\(142\) 35.3322 2.96501
\(143\) −1.58554 −0.132590
\(144\) −1.95782 −0.163151
\(145\) −0.364124 −0.0302389
\(146\) −3.32006 −0.274770
\(147\) 4.12403 0.340144
\(148\) 13.3160 1.09457
\(149\) 17.8974 1.46621 0.733107 0.680114i \(-0.238070\pi\)
0.733107 + 0.680114i \(0.238070\pi\)
\(150\) 5.88758 0.480719
\(151\) 19.5040 1.58722 0.793608 0.608429i \(-0.208200\pi\)
0.793608 + 0.608429i \(0.208200\pi\)
\(152\) −21.1104 −1.71228
\(153\) −15.1674 −1.22621
\(154\) 8.90510 0.717594
\(155\) −2.54847 −0.204698
\(156\) 2.87774 0.230403
\(157\) −8.23540 −0.657257 −0.328628 0.944459i \(-0.606586\pi\)
−0.328628 + 0.944459i \(0.606586\pi\)
\(158\) 18.3611 1.46073
\(159\) −4.59074 −0.364069
\(160\) −2.44899 −0.193610
\(161\) −15.0096 −1.18292
\(162\) −15.1053 −1.18679
\(163\) −10.1968 −0.798677 −0.399338 0.916804i \(-0.630760\pi\)
−0.399338 + 0.916804i \(0.630760\pi\)
\(164\) −8.67386 −0.677315
\(165\) 0.273622 0.0213015
\(166\) −9.01980 −0.700072
\(167\) 8.31389 0.643348 0.321674 0.946850i \(-0.395754\pi\)
0.321674 + 0.946850i \(0.395754\pi\)
\(168\) −6.63265 −0.511720
\(169\) −10.4861 −0.806619
\(170\) 6.63673 0.509014
\(171\) −17.7238 −1.35537
\(172\) 23.7852 1.81361
\(173\) 6.30465 0.479334 0.239667 0.970855i \(-0.422962\pi\)
0.239667 + 0.970855i \(0.422962\pi\)
\(174\) −0.884740 −0.0670720
\(175\) −18.1722 −1.37369
\(176\) −0.721461 −0.0543822
\(177\) 3.46105 0.260149
\(178\) 9.78094 0.733112
\(179\) −17.2773 −1.29136 −0.645682 0.763606i \(-0.723427\pi\)
−0.645682 + 0.763606i \(0.723427\pi\)
\(180\) 4.70694 0.350835
\(181\) 22.7089 1.68794 0.843969 0.536392i \(-0.180213\pi\)
0.843969 + 0.536392i \(0.180213\pi\)
\(182\) −14.1194 −1.04660
\(183\) 5.79134 0.428108
\(184\) 12.6503 0.932594
\(185\) −2.00748 −0.147593
\(186\) −6.19221 −0.454035
\(187\) −5.58922 −0.408724
\(188\) 6.34693 0.462897
\(189\) −11.7248 −0.852852
\(190\) 7.75532 0.562630
\(191\) 10.8194 0.782862 0.391431 0.920208i \(-0.371980\pi\)
0.391431 + 0.920208i \(0.371980\pi\)
\(192\) −6.72258 −0.485160
\(193\) −23.0050 −1.65594 −0.827968 0.560775i \(-0.810503\pi\)
−0.827968 + 0.560775i \(0.810503\pi\)
\(194\) 30.4926 2.18924
\(195\) −0.433840 −0.0310680
\(196\) 26.1427 1.86733
\(197\) −13.2646 −0.945061 −0.472531 0.881314i \(-0.656659\pi\)
−0.472531 + 0.881314i \(0.656659\pi\)
\(198\) −6.30134 −0.447816
\(199\) −15.9498 −1.13065 −0.565327 0.824867i \(-0.691250\pi\)
−0.565327 + 0.824867i \(0.691250\pi\)
\(200\) 15.3158 1.08299
\(201\) 2.14655 0.151406
\(202\) −15.5493 −1.09404
\(203\) 2.73078 0.191663
\(204\) 10.1443 0.710246
\(205\) 1.30765 0.0913302
\(206\) −5.98990 −0.417336
\(207\) 10.6209 0.738204
\(208\) 1.14391 0.0793157
\(209\) −6.53126 −0.451777
\(210\) 2.43664 0.168144
\(211\) 3.34523 0.230295 0.115148 0.993348i \(-0.463266\pi\)
0.115148 + 0.993348i \(0.463266\pi\)
\(212\) −29.1012 −1.99868
\(213\) −8.14178 −0.557865
\(214\) 11.8417 0.809482
\(215\) −3.58580 −0.244550
\(216\) 9.88184 0.672374
\(217\) 19.1124 1.29744
\(218\) −2.28816 −0.154974
\(219\) 0.765060 0.0516980
\(220\) 1.73452 0.116941
\(221\) 8.86195 0.596120
\(222\) −4.87773 −0.327372
\(223\) 7.75735 0.519470 0.259735 0.965680i \(-0.416365\pi\)
0.259735 + 0.965680i \(0.416365\pi\)
\(224\) 18.3664 1.22715
\(225\) 12.8588 0.857254
\(226\) −28.0311 −1.86460
\(227\) −9.32991 −0.619248 −0.309624 0.950859i \(-0.600203\pi\)
−0.309624 + 0.950859i \(0.600203\pi\)
\(228\) 11.8541 0.785059
\(229\) 4.62785 0.305817 0.152909 0.988240i \(-0.451136\pi\)
0.152909 + 0.988240i \(0.451136\pi\)
\(230\) −4.64734 −0.306437
\(231\) −2.05205 −0.135015
\(232\) −2.30154 −0.151104
\(233\) −4.93453 −0.323272 −0.161636 0.986850i \(-0.551677\pi\)
−0.161636 + 0.986850i \(0.551677\pi\)
\(234\) 9.99104 0.653135
\(235\) −0.956847 −0.0624178
\(236\) 21.9400 1.42817
\(237\) −4.23105 −0.274836
\(238\) −49.7726 −3.22628
\(239\) −25.9547 −1.67887 −0.839434 0.543462i \(-0.817113\pi\)
−0.839434 + 0.543462i \(0.817113\pi\)
\(240\) −0.197408 −0.0127426
\(241\) −10.0236 −0.645675 −0.322838 0.946454i \(-0.604637\pi\)
−0.322838 + 0.946454i \(0.604637\pi\)
\(242\) −2.32206 −0.149268
\(243\) 12.6527 0.811672
\(244\) 36.7119 2.35024
\(245\) −3.94120 −0.251794
\(246\) 3.17730 0.202577
\(247\) 10.3556 0.658911
\(248\) −16.1083 −1.02288
\(249\) 2.07848 0.131718
\(250\) −11.5637 −0.731350
\(251\) 1.46742 0.0926226 0.0463113 0.998927i \(-0.485253\pi\)
0.0463113 + 0.998927i \(0.485253\pi\)
\(252\) −35.3001 −2.22370
\(253\) 3.91383 0.246061
\(254\) 13.9657 0.876283
\(255\) −1.52934 −0.0957707
\(256\) −20.3738 −1.27336
\(257\) −6.41556 −0.400192 −0.200096 0.979776i \(-0.564125\pi\)
−0.200096 + 0.979776i \(0.564125\pi\)
\(258\) −8.71270 −0.542429
\(259\) 15.0553 0.935489
\(260\) −2.75016 −0.170558
\(261\) −1.93232 −0.119608
\(262\) −28.2150 −1.74313
\(263\) 0.626901 0.0386564 0.0193282 0.999813i \(-0.493847\pi\)
0.0193282 + 0.999813i \(0.493847\pi\)
\(264\) 1.72950 0.106444
\(265\) 4.38722 0.269505
\(266\) −58.1616 −3.56611
\(267\) −2.25387 −0.137935
\(268\) 13.6072 0.831192
\(269\) 15.8922 0.968963 0.484482 0.874801i \(-0.339008\pi\)
0.484482 + 0.874801i \(0.339008\pi\)
\(270\) −3.63029 −0.220932
\(271\) 14.0706 0.854726 0.427363 0.904080i \(-0.359443\pi\)
0.427363 + 0.904080i \(0.359443\pi\)
\(272\) 4.03240 0.244500
\(273\) 3.25362 0.196918
\(274\) −12.5186 −0.756279
\(275\) 4.73851 0.285743
\(276\) −7.10354 −0.427583
\(277\) 29.5429 1.77506 0.887529 0.460752i \(-0.152420\pi\)
0.887529 + 0.460752i \(0.152420\pi\)
\(278\) −40.1434 −2.40764
\(279\) −13.5241 −0.809669
\(280\) 6.33861 0.378805
\(281\) 4.46193 0.266176 0.133088 0.991104i \(-0.457511\pi\)
0.133088 + 0.991104i \(0.457511\pi\)
\(282\) −2.32492 −0.138447
\(283\) 0.471128 0.0280057 0.0140028 0.999902i \(-0.495543\pi\)
0.0140028 + 0.999902i \(0.495543\pi\)
\(284\) −51.6116 −3.06258
\(285\) −1.78710 −0.105859
\(286\) 3.68173 0.217705
\(287\) −9.80682 −0.578878
\(288\) −12.9962 −0.765809
\(289\) 14.2394 0.837611
\(290\) 0.845518 0.0496505
\(291\) −7.02657 −0.411905
\(292\) 4.84980 0.283813
\(293\) −8.91018 −0.520538 −0.260269 0.965536i \(-0.583811\pi\)
−0.260269 + 0.965536i \(0.583811\pi\)
\(294\) −9.57624 −0.558498
\(295\) −3.30762 −0.192577
\(296\) −12.6888 −0.737524
\(297\) 3.05730 0.177403
\(298\) −41.5589 −2.40744
\(299\) −6.20555 −0.358876
\(300\) −8.60032 −0.496539
\(301\) 26.8920 1.55003
\(302\) −45.2895 −2.60612
\(303\) 3.58310 0.205844
\(304\) 4.71205 0.270255
\(305\) −5.53460 −0.316910
\(306\) 35.2196 2.01337
\(307\) −6.28255 −0.358564 −0.179282 0.983798i \(-0.557377\pi\)
−0.179282 + 0.983798i \(0.557377\pi\)
\(308\) −13.0082 −0.741209
\(309\) 1.38028 0.0785217
\(310\) 5.91770 0.336103
\(311\) −21.1922 −1.20170 −0.600850 0.799362i \(-0.705171\pi\)
−0.600850 + 0.799362i \(0.705171\pi\)
\(312\) −2.74220 −0.155247
\(313\) 27.3794 1.54757 0.773787 0.633446i \(-0.218360\pi\)
0.773787 + 0.633446i \(0.218360\pi\)
\(314\) 19.1231 1.07918
\(315\) 5.32175 0.299847
\(316\) −26.8211 −1.50880
\(317\) −20.0952 −1.12866 −0.564331 0.825549i \(-0.690866\pi\)
−0.564331 + 0.825549i \(0.690866\pi\)
\(318\) 10.6600 0.597781
\(319\) −0.712066 −0.0398680
\(320\) 6.42455 0.359143
\(321\) −2.72875 −0.152304
\(322\) 34.8531 1.94229
\(323\) 36.5047 2.03117
\(324\) 22.0652 1.22584
\(325\) −7.51311 −0.416752
\(326\) 23.6776 1.31138
\(327\) 0.527273 0.0291582
\(328\) 8.26535 0.456378
\(329\) 7.17594 0.395622
\(330\) −0.635367 −0.0349758
\(331\) −12.6702 −0.696415 −0.348207 0.937418i \(-0.613209\pi\)
−0.348207 + 0.937418i \(0.613209\pi\)
\(332\) 13.1757 0.723111
\(333\) −10.6532 −0.583794
\(334\) −19.3053 −1.05634
\(335\) −2.05139 −0.112079
\(336\) 1.48047 0.0807665
\(337\) 3.25249 0.177175 0.0885873 0.996068i \(-0.471765\pi\)
0.0885873 + 0.996068i \(0.471765\pi\)
\(338\) 24.3492 1.32442
\(339\) 6.45936 0.350824
\(340\) −9.69463 −0.525765
\(341\) −4.98368 −0.269881
\(342\) 41.1557 2.22544
\(343\) 2.71232 0.146452
\(344\) −22.6650 −1.22202
\(345\) 1.07091 0.0576560
\(346\) −14.6398 −0.787039
\(347\) 5.52353 0.296518 0.148259 0.988949i \(-0.452633\pi\)
0.148259 + 0.988949i \(0.452633\pi\)
\(348\) 1.29239 0.0692793
\(349\) −2.62547 −0.140538 −0.0702691 0.997528i \(-0.522386\pi\)
−0.0702691 + 0.997528i \(0.522386\pi\)
\(350\) 42.1969 2.25552
\(351\) −4.84749 −0.258740
\(352\) −4.78914 −0.255262
\(353\) −20.2212 −1.07627 −0.538134 0.842859i \(-0.680871\pi\)
−0.538134 + 0.842859i \(0.680871\pi\)
\(354\) −8.03677 −0.427150
\(355\) 7.78084 0.412964
\(356\) −14.2876 −0.757239
\(357\) 11.4694 0.607023
\(358\) 40.1189 2.12035
\(359\) 7.67286 0.404958 0.202479 0.979287i \(-0.435100\pi\)
0.202479 + 0.979287i \(0.435100\pi\)
\(360\) −4.48526 −0.236394
\(361\) 23.6574 1.24512
\(362\) −52.7313 −2.77150
\(363\) 0.535084 0.0280847
\(364\) 20.6250 1.08104
\(365\) −0.731143 −0.0382698
\(366\) −13.4478 −0.702930
\(367\) 2.20396 0.115046 0.0575228 0.998344i \(-0.481680\pi\)
0.0575228 + 0.998344i \(0.481680\pi\)
\(368\) −2.82368 −0.147194
\(369\) 6.93939 0.361250
\(370\) 4.66149 0.242340
\(371\) −32.9023 −1.70820
\(372\) 9.04530 0.468977
\(373\) −13.2353 −0.685297 −0.342648 0.939464i \(-0.611324\pi\)
−0.342648 + 0.939464i \(0.611324\pi\)
\(374\) 12.9785 0.671102
\(375\) 2.66467 0.137603
\(376\) −6.04801 −0.311902
\(377\) 1.12901 0.0581471
\(378\) 27.2256 1.40033
\(379\) 20.0253 1.02863 0.514315 0.857601i \(-0.328046\pi\)
0.514315 + 0.857601i \(0.328046\pi\)
\(380\) −11.3286 −0.581146
\(381\) −3.21818 −0.164872
\(382\) −25.1232 −1.28541
\(383\) −2.22060 −0.113467 −0.0567336 0.998389i \(-0.518069\pi\)
−0.0567336 + 0.998389i \(0.518069\pi\)
\(384\) 10.4850 0.535062
\(385\) 1.96108 0.0999458
\(386\) 53.4190 2.71895
\(387\) −19.0290 −0.967300
\(388\) −44.5422 −2.26129
\(389\) 12.2727 0.622249 0.311124 0.950369i \(-0.399294\pi\)
0.311124 + 0.950369i \(0.399294\pi\)
\(390\) 1.00740 0.0510118
\(391\) −21.8753 −1.10628
\(392\) −24.9114 −1.25822
\(393\) 6.50173 0.327969
\(394\) 30.8011 1.55174
\(395\) 4.04348 0.203450
\(396\) 9.20470 0.462554
\(397\) −0.0859503 −0.00431372 −0.00215686 0.999998i \(-0.500687\pi\)
−0.00215686 + 0.999998i \(0.500687\pi\)
\(398\) 37.0365 1.85647
\(399\) 13.4025 0.670963
\(400\) −3.41865 −0.170932
\(401\) 28.2346 1.40997 0.704984 0.709224i \(-0.250954\pi\)
0.704984 + 0.709224i \(0.250954\pi\)
\(402\) −4.98441 −0.248600
\(403\) 7.90184 0.393619
\(404\) 22.7136 1.13005
\(405\) −3.32649 −0.165294
\(406\) −6.34102 −0.314700
\(407\) −3.92575 −0.194592
\(408\) −9.66658 −0.478567
\(409\) −0.718707 −0.0355378 −0.0177689 0.999842i \(-0.505656\pi\)
−0.0177689 + 0.999842i \(0.505656\pi\)
\(410\) −3.03644 −0.149959
\(411\) 2.88474 0.142294
\(412\) 8.74977 0.431070
\(413\) 24.8057 1.22061
\(414\) −24.6624 −1.21209
\(415\) −1.98634 −0.0975054
\(416\) 7.59339 0.372297
\(417\) 9.25045 0.452996
\(418\) 15.1660 0.741792
\(419\) −37.5851 −1.83615 −0.918075 0.396406i \(-0.870257\pi\)
−0.918075 + 0.396406i \(0.870257\pi\)
\(420\) −3.55933 −0.173677
\(421\) 13.8651 0.675746 0.337873 0.941192i \(-0.390293\pi\)
0.337873 + 0.941192i \(0.390293\pi\)
\(422\) −7.76782 −0.378131
\(423\) −5.07776 −0.246889
\(424\) 27.7306 1.34672
\(425\) −26.4846 −1.28469
\(426\) 18.9057 0.915984
\(427\) 41.5071 2.00867
\(428\) −17.2978 −0.836122
\(429\) −0.848400 −0.0409611
\(430\) 8.32645 0.401537
\(431\) 22.7350 1.09511 0.547553 0.836771i \(-0.315559\pi\)
0.547553 + 0.836771i \(0.315559\pi\)
\(432\) −2.20573 −0.106123
\(433\) 5.10427 0.245296 0.122648 0.992450i \(-0.460861\pi\)
0.122648 + 0.992450i \(0.460861\pi\)
\(434\) −44.3802 −2.13032
\(435\) −0.194837 −0.00934173
\(436\) 3.34244 0.160074
\(437\) −25.5623 −1.22281
\(438\) −1.77651 −0.0848852
\(439\) 3.12851 0.149316 0.0746579 0.997209i \(-0.476214\pi\)
0.0746579 + 0.997209i \(0.476214\pi\)
\(440\) −1.65283 −0.0787956
\(441\) −20.9151 −0.995955
\(442\) −20.5780 −0.978795
\(443\) 23.8040 1.13096 0.565481 0.824762i \(-0.308691\pi\)
0.565481 + 0.824762i \(0.308691\pi\)
\(444\) 7.12517 0.338146
\(445\) 2.15396 0.102107
\(446\) −18.0130 −0.852941
\(447\) 9.57663 0.452959
\(448\) −48.1814 −2.27636
\(449\) −21.0284 −0.992391 −0.496196 0.868211i \(-0.665270\pi\)
−0.496196 + 0.868211i \(0.665270\pi\)
\(450\) −29.8589 −1.40756
\(451\) 2.55719 0.120413
\(452\) 40.9466 1.92596
\(453\) 10.4363 0.490340
\(454\) 21.6646 1.01677
\(455\) −3.10938 −0.145770
\(456\) −11.2958 −0.528976
\(457\) 17.4770 0.817539 0.408769 0.912638i \(-0.365958\pi\)
0.408769 + 0.912638i \(0.365958\pi\)
\(458\) −10.7461 −0.502134
\(459\) −17.0879 −0.797597
\(460\) 6.78863 0.316521
\(461\) −20.4826 −0.953969 −0.476985 0.878912i \(-0.658270\pi\)
−0.476985 + 0.878912i \(0.658270\pi\)
\(462\) 4.76498 0.221687
\(463\) −3.52212 −0.163687 −0.0818435 0.996645i \(-0.526081\pi\)
−0.0818435 + 0.996645i \(0.526081\pi\)
\(464\) 0.513728 0.0238492
\(465\) −1.36365 −0.0632376
\(466\) 11.4583 0.530794
\(467\) −21.9680 −1.01656 −0.508280 0.861192i \(-0.669718\pi\)
−0.508280 + 0.861192i \(0.669718\pi\)
\(468\) −14.5945 −0.674629
\(469\) 15.3845 0.710391
\(470\) 2.22185 0.102487
\(471\) −4.40664 −0.203047
\(472\) −20.9067 −0.962308
\(473\) −7.01225 −0.322423
\(474\) 9.82475 0.451266
\(475\) −30.9484 −1.42001
\(476\) 72.7055 3.33245
\(477\) 23.2820 1.06601
\(478\) 60.2683 2.75661
\(479\) −23.9165 −1.09277 −0.546386 0.837534i \(-0.683997\pi\)
−0.546386 + 0.837534i \(0.683997\pi\)
\(480\) −1.31042 −0.0598120
\(481\) 6.22445 0.283810
\(482\) 23.2753 1.06016
\(483\) −8.03139 −0.365441
\(484\) 3.39196 0.154180
\(485\) 6.71507 0.304916
\(486\) −29.3803 −1.33272
\(487\) 23.5503 1.06717 0.533584 0.845747i \(-0.320845\pi\)
0.533584 + 0.845747i \(0.320845\pi\)
\(488\) −34.9829 −1.58360
\(489\) −5.45616 −0.246736
\(490\) 9.15171 0.413432
\(491\) 14.7853 0.667253 0.333627 0.942705i \(-0.391727\pi\)
0.333627 + 0.942705i \(0.391727\pi\)
\(492\) −4.64125 −0.209244
\(493\) 3.97989 0.179245
\(494\) −24.0463 −1.08189
\(495\) −1.38768 −0.0623715
\(496\) 3.59553 0.161444
\(497\) −58.3529 −2.61749
\(498\) −4.82635 −0.216274
\(499\) −34.8161 −1.55858 −0.779292 0.626661i \(-0.784421\pi\)
−0.779292 + 0.626661i \(0.784421\pi\)
\(500\) 16.8917 0.755418
\(501\) 4.44863 0.198750
\(502\) −3.40743 −0.152081
\(503\) 7.20245 0.321141 0.160571 0.987024i \(-0.448667\pi\)
0.160571 + 0.987024i \(0.448667\pi\)
\(504\) 33.6376 1.49834
\(505\) −3.42425 −0.152377
\(506\) −9.08815 −0.404018
\(507\) −5.61092 −0.249190
\(508\) −20.4004 −0.905121
\(509\) 32.9017 1.45834 0.729171 0.684332i \(-0.239906\pi\)
0.729171 + 0.684332i \(0.239906\pi\)
\(510\) 3.55121 0.157250
\(511\) 5.48326 0.242565
\(512\) 8.11900 0.358812
\(513\) −19.9680 −0.881611
\(514\) 14.8973 0.657092
\(515\) −1.31909 −0.0581262
\(516\) 12.7271 0.560280
\(517\) −1.87117 −0.0822939
\(518\) −34.9592 −1.53602
\(519\) 3.37352 0.148081
\(520\) 2.62064 0.114923
\(521\) −0.603507 −0.0264401 −0.0132201 0.999913i \(-0.504208\pi\)
−0.0132201 + 0.999913i \(0.504208\pi\)
\(522\) 4.48697 0.196389
\(523\) 40.4316 1.76795 0.883975 0.467534i \(-0.154858\pi\)
0.883975 + 0.467534i \(0.154858\pi\)
\(524\) 41.2151 1.80049
\(525\) −9.72366 −0.424375
\(526\) −1.45570 −0.0634716
\(527\) 27.8549 1.21338
\(528\) −0.386043 −0.0168003
\(529\) −7.68191 −0.333996
\(530\) −10.1874 −0.442512
\(531\) −17.5528 −0.761725
\(532\) 84.9598 3.68347
\(533\) −4.05453 −0.175621
\(534\) 5.23363 0.226481
\(535\) 2.60778 0.112744
\(536\) −12.9663 −0.560060
\(537\) −9.24481 −0.398943
\(538\) −36.9026 −1.59098
\(539\) −7.70725 −0.331975
\(540\) 5.30296 0.228203
\(541\) 13.8931 0.597311 0.298655 0.954361i \(-0.403462\pi\)
0.298655 + 0.954361i \(0.403462\pi\)
\(542\) −32.6727 −1.40341
\(543\) 12.1512 0.521456
\(544\) 26.7676 1.14765
\(545\) −0.503898 −0.0215846
\(546\) −7.55509 −0.323328
\(547\) 1.00000 0.0427569
\(548\) 18.2867 0.781168
\(549\) −29.3708 −1.25352
\(550\) −11.0031 −0.469174
\(551\) 4.65069 0.198126
\(552\) 6.76899 0.288107
\(553\) −30.3244 −1.28952
\(554\) −68.6003 −2.91455
\(555\) −1.07417 −0.0455961
\(556\) 58.6396 2.48687
\(557\) 38.5965 1.63539 0.817693 0.575654i \(-0.195253\pi\)
0.817693 + 0.575654i \(0.195253\pi\)
\(558\) 31.4038 1.32943
\(559\) 11.1182 0.470251
\(560\) −1.41484 −0.0597880
\(561\) −2.99071 −0.126268
\(562\) −10.3609 −0.437047
\(563\) 15.3573 0.647234 0.323617 0.946188i \(-0.395101\pi\)
0.323617 + 0.946188i \(0.395101\pi\)
\(564\) 3.39614 0.143003
\(565\) −6.17300 −0.259700
\(566\) −1.09399 −0.0459837
\(567\) 24.9472 1.04769
\(568\) 49.1809 2.06358
\(569\) 29.8962 1.25331 0.626657 0.779296i \(-0.284423\pi\)
0.626657 + 0.779296i \(0.284423\pi\)
\(570\) 4.14975 0.173814
\(571\) −1.28845 −0.0539200 −0.0269600 0.999637i \(-0.508583\pi\)
−0.0269600 + 0.999637i \(0.508583\pi\)
\(572\) −5.37810 −0.224870
\(573\) 5.78927 0.241850
\(574\) 22.7720 0.950485
\(575\) 18.5457 0.773410
\(576\) 34.0936 1.42057
\(577\) 28.2462 1.17590 0.587952 0.808896i \(-0.299934\pi\)
0.587952 + 0.808896i \(0.299934\pi\)
\(578\) −33.0647 −1.37531
\(579\) −12.3096 −0.511570
\(580\) −1.23509 −0.0512845
\(581\) 14.8967 0.618018
\(582\) 16.3161 0.676325
\(583\) 8.57947 0.355325
\(584\) −4.62139 −0.191234
\(585\) 2.20022 0.0909681
\(586\) 20.6900 0.854694
\(587\) 43.5216 1.79633 0.898164 0.439661i \(-0.144901\pi\)
0.898164 + 0.439661i \(0.144901\pi\)
\(588\) 13.9885 0.576878
\(589\) 32.5497 1.34119
\(590\) 7.68048 0.316201
\(591\) −7.09766 −0.291959
\(592\) 2.83227 0.116406
\(593\) 24.0740 0.988600 0.494300 0.869291i \(-0.335424\pi\)
0.494300 + 0.869291i \(0.335424\pi\)
\(594\) −7.09924 −0.291285
\(595\) −10.9609 −0.449353
\(596\) 60.7073 2.48667
\(597\) −8.53451 −0.349294
\(598\) 14.4097 0.589255
\(599\) −24.0120 −0.981104 −0.490552 0.871412i \(-0.663205\pi\)
−0.490552 + 0.871412i \(0.663205\pi\)
\(600\) 8.19527 0.334570
\(601\) 11.8849 0.484797 0.242398 0.970177i \(-0.422066\pi\)
0.242398 + 0.970177i \(0.422066\pi\)
\(602\) −62.4448 −2.54506
\(603\) −10.8862 −0.443322
\(604\) 66.1569 2.69188
\(605\) −0.511363 −0.0207899
\(606\) −8.32016 −0.337984
\(607\) −23.9979 −0.974047 −0.487023 0.873389i \(-0.661917\pi\)
−0.487023 + 0.873389i \(0.661917\pi\)
\(608\) 31.2791 1.26854
\(609\) 1.46120 0.0592106
\(610\) 12.8517 0.520349
\(611\) 2.96682 0.120025
\(612\) −51.4471 −2.07963
\(613\) 20.5271 0.829081 0.414540 0.910031i \(-0.363942\pi\)
0.414540 + 0.910031i \(0.363942\pi\)
\(614\) 14.5885 0.588742
\(615\) 0.699703 0.0282148
\(616\) 12.3955 0.499430
\(617\) 20.5495 0.827293 0.413647 0.910438i \(-0.364255\pi\)
0.413647 + 0.910438i \(0.364255\pi\)
\(618\) −3.20510 −0.128928
\(619\) 2.72676 0.109598 0.0547989 0.998497i \(-0.482548\pi\)
0.0547989 + 0.998497i \(0.482548\pi\)
\(620\) −8.64430 −0.347163
\(621\) 11.9658 0.480170
\(622\) 49.2095 1.97312
\(623\) −16.1537 −0.647186
\(624\) 0.612087 0.0245031
\(625\) 21.1460 0.845840
\(626\) −63.5765 −2.54103
\(627\) −3.49478 −0.139568
\(628\) −27.9341 −1.11469
\(629\) 21.9419 0.874880
\(630\) −12.3574 −0.492331
\(631\) 47.0291 1.87220 0.936100 0.351735i \(-0.114408\pi\)
0.936100 + 0.351735i \(0.114408\pi\)
\(632\) 25.5579 1.01664
\(633\) 1.78998 0.0711453
\(634\) 46.6623 1.85320
\(635\) 3.07551 0.122048
\(636\) −15.5716 −0.617454
\(637\) 12.2202 0.484182
\(638\) 1.65346 0.0654611
\(639\) 41.2911 1.63345
\(640\) −10.0202 −0.396084
\(641\) 9.34444 0.369083 0.184542 0.982825i \(-0.440920\pi\)
0.184542 + 0.982825i \(0.440920\pi\)
\(642\) 6.33631 0.250074
\(643\) −20.3819 −0.803785 −0.401892 0.915687i \(-0.631647\pi\)
−0.401892 + 0.915687i \(0.631647\pi\)
\(644\) −50.9118 −2.00621
\(645\) −1.91871 −0.0755490
\(646\) −84.7660 −3.33507
\(647\) 11.5584 0.454409 0.227204 0.973847i \(-0.427041\pi\)
0.227204 + 0.973847i \(0.427041\pi\)
\(648\) −21.0260 −0.825978
\(649\) −6.46824 −0.253901
\(650\) 17.4459 0.684284
\(651\) 10.2268 0.400819
\(652\) −34.5872 −1.35454
\(653\) 19.1569 0.749666 0.374833 0.927092i \(-0.377700\pi\)
0.374833 + 0.927092i \(0.377700\pi\)
\(654\) −1.22436 −0.0478762
\(655\) −6.21349 −0.242781
\(656\) −1.84491 −0.0720316
\(657\) −3.88001 −0.151374
\(658\) −16.6630 −0.649590
\(659\) −17.7388 −0.691005 −0.345503 0.938418i \(-0.612292\pi\)
−0.345503 + 0.938418i \(0.612292\pi\)
\(660\) 0.928116 0.0361269
\(661\) −18.8366 −0.732660 −0.366330 0.930485i \(-0.619386\pi\)
−0.366330 + 0.930485i \(0.619386\pi\)
\(662\) 29.4208 1.14347
\(663\) 4.74189 0.184160
\(664\) −12.5552 −0.487235
\(665\) −12.8083 −0.496685
\(666\) 24.7375 0.958557
\(667\) −2.78691 −0.107909
\(668\) 28.2004 1.09110
\(669\) 4.15084 0.160481
\(670\) 4.76344 0.184028
\(671\) −10.8232 −0.417826
\(672\) 9.82756 0.379106
\(673\) 47.0527 1.81375 0.906874 0.421403i \(-0.138462\pi\)
0.906874 + 0.421403i \(0.138462\pi\)
\(674\) −7.55248 −0.290911
\(675\) 14.4871 0.557607
\(676\) −35.5682 −1.36801
\(677\) −15.4235 −0.592774 −0.296387 0.955068i \(-0.595782\pi\)
−0.296387 + 0.955068i \(0.595782\pi\)
\(678\) −14.9990 −0.576034
\(679\) −50.3602 −1.93265
\(680\) 9.23804 0.354263
\(681\) −4.99229 −0.191305
\(682\) 11.5724 0.443130
\(683\) 5.77772 0.221078 0.110539 0.993872i \(-0.464742\pi\)
0.110539 + 0.993872i \(0.464742\pi\)
\(684\) −60.1183 −2.29868
\(685\) −2.75685 −0.105334
\(686\) −6.29817 −0.240465
\(687\) 2.47629 0.0944764
\(688\) 5.05906 0.192875
\(689\) −13.6031 −0.518238
\(690\) −2.48672 −0.0946679
\(691\) 25.6592 0.976120 0.488060 0.872810i \(-0.337705\pi\)
0.488060 + 0.872810i \(0.337705\pi\)
\(692\) 21.3851 0.812940
\(693\) 10.4070 0.395329
\(694\) −12.8260 −0.486867
\(695\) −8.84036 −0.335334
\(696\) −1.23152 −0.0466807
\(697\) −14.2927 −0.541374
\(698\) 6.09649 0.230756
\(699\) −2.64039 −0.0998688
\(700\) −61.6393 −2.32975
\(701\) 10.6531 0.402361 0.201181 0.979554i \(-0.435522\pi\)
0.201181 + 0.979554i \(0.435522\pi\)
\(702\) 11.2562 0.424836
\(703\) 25.6401 0.967035
\(704\) 12.5636 0.473508
\(705\) −0.511994 −0.0192828
\(706\) 46.9549 1.76717
\(707\) 25.6804 0.965812
\(708\) 11.7397 0.441207
\(709\) −28.0448 −1.05324 −0.526622 0.850100i \(-0.676542\pi\)
−0.526622 + 0.850100i \(0.676542\pi\)
\(710\) −18.0676 −0.678063
\(711\) 21.4578 0.804731
\(712\) 13.6147 0.510231
\(713\) −19.5053 −0.730479
\(714\) −26.6325 −0.996698
\(715\) 0.810789 0.0303218
\(716\) −58.6038 −2.19013
\(717\) −13.8879 −0.518655
\(718\) −17.8168 −0.664918
\(719\) 41.2641 1.53889 0.769445 0.638713i \(-0.220533\pi\)
0.769445 + 0.638713i \(0.220533\pi\)
\(720\) 1.00116 0.0373109
\(721\) 9.89264 0.368421
\(722\) −54.9338 −2.04442
\(723\) −5.36346 −0.199469
\(724\) 77.0275 2.86271
\(725\) −3.37413 −0.125312
\(726\) −1.24250 −0.0461134
\(727\) −5.13660 −0.190506 −0.0952530 0.995453i \(-0.530366\pi\)
−0.0952530 + 0.995453i \(0.530366\pi\)
\(728\) −19.6537 −0.728413
\(729\) −12.7451 −0.472042
\(730\) 1.69776 0.0628368
\(731\) 39.1930 1.44961
\(732\) 19.6440 0.726063
\(733\) −22.6014 −0.834802 −0.417401 0.908722i \(-0.637059\pi\)
−0.417401 + 0.908722i \(0.637059\pi\)
\(734\) −5.11772 −0.188898
\(735\) −2.10888 −0.0777871
\(736\) −18.7439 −0.690909
\(737\) −4.01160 −0.147769
\(738\) −16.1137 −0.593153
\(739\) −31.3649 −1.15378 −0.576888 0.816823i \(-0.695733\pi\)
−0.576888 + 0.816823i \(0.695733\pi\)
\(740\) −6.80930 −0.250315
\(741\) 5.54112 0.203558
\(742\) 76.4011 2.80477
\(743\) 8.10292 0.297267 0.148634 0.988892i \(-0.452512\pi\)
0.148634 + 0.988892i \(0.452512\pi\)
\(744\) −8.61929 −0.315999
\(745\) −9.15208 −0.335306
\(746\) 30.7331 1.12522
\(747\) −10.5410 −0.385676
\(748\) −18.9584 −0.693188
\(749\) −19.5572 −0.714605
\(750\) −6.18753 −0.225937
\(751\) −9.94714 −0.362976 −0.181488 0.983393i \(-0.558091\pi\)
−0.181488 + 0.983393i \(0.558091\pi\)
\(752\) 1.34998 0.0492285
\(753\) 0.785193 0.0286140
\(754\) −2.62163 −0.0954742
\(755\) −9.97364 −0.362978
\(756\) −39.7699 −1.44642
\(757\) 19.9049 0.723457 0.361728 0.932284i \(-0.382187\pi\)
0.361728 + 0.932284i \(0.382187\pi\)
\(758\) −46.4999 −1.68895
\(759\) 2.09423 0.0760158
\(760\) 10.7951 0.391578
\(761\) 16.8165 0.609599 0.304800 0.952417i \(-0.401411\pi\)
0.304800 + 0.952417i \(0.401411\pi\)
\(762\) 7.47281 0.270711
\(763\) 3.77902 0.136810
\(764\) 36.6988 1.32772
\(765\) 7.75604 0.280420
\(766\) 5.15636 0.186307
\(767\) 10.2557 0.370311
\(768\) −10.9017 −0.393382
\(769\) −11.6024 −0.418394 −0.209197 0.977874i \(-0.567085\pi\)
−0.209197 + 0.977874i \(0.567085\pi\)
\(770\) −4.55374 −0.164105
\(771\) −3.43287 −0.123632
\(772\) −78.0320 −2.80843
\(773\) −3.08532 −0.110971 −0.0554856 0.998459i \(-0.517671\pi\)
−0.0554856 + 0.998459i \(0.517671\pi\)
\(774\) 44.1865 1.58825
\(775\) −23.6152 −0.848283
\(776\) 42.4444 1.52367
\(777\) 8.05584 0.289002
\(778\) −28.4979 −1.02170
\(779\) −16.7016 −0.598399
\(780\) −1.47157 −0.0526906
\(781\) 15.2159 0.544467
\(782\) 50.7957 1.81645
\(783\) −2.17700 −0.0777997
\(784\) 5.56048 0.198589
\(785\) 4.21128 0.150307
\(786\) −15.0974 −0.538506
\(787\) −27.8226 −0.991770 −0.495885 0.868388i \(-0.665156\pi\)
−0.495885 + 0.868388i \(0.665156\pi\)
\(788\) −44.9929 −1.60280
\(789\) 0.335445 0.0119422
\(790\) −9.38920 −0.334053
\(791\) 46.2949 1.64606
\(792\) −8.77119 −0.311671
\(793\) 17.1607 0.609394
\(794\) 0.199582 0.00708289
\(795\) 2.34754 0.0832585
\(796\) −54.1012 −1.91757
\(797\) −34.8594 −1.23478 −0.617391 0.786656i \(-0.711810\pi\)
−0.617391 + 0.786656i \(0.711810\pi\)
\(798\) −31.1213 −1.10168
\(799\) 10.4584 0.369991
\(800\) −22.6934 −0.802332
\(801\) 11.4305 0.403878
\(802\) −65.5623 −2.31509
\(803\) −1.42979 −0.0504563
\(804\) 7.28100 0.256781
\(805\) 7.67534 0.270520
\(806\) −18.3485 −0.646300
\(807\) 8.50366 0.299343
\(808\) −21.6439 −0.761430
\(809\) −5.69898 −0.200365 −0.100183 0.994969i \(-0.531943\pi\)
−0.100183 + 0.994969i \(0.531943\pi\)
\(810\) 7.72430 0.271404
\(811\) 17.4954 0.614346 0.307173 0.951654i \(-0.400617\pi\)
0.307173 + 0.951654i \(0.400617\pi\)
\(812\) 9.26267 0.325056
\(813\) 7.52894 0.264051
\(814\) 9.11582 0.319509
\(815\) 5.21428 0.182648
\(816\) 2.15768 0.0755338
\(817\) 45.7988 1.60230
\(818\) 1.66888 0.0583510
\(819\) −16.5007 −0.576583
\(820\) 4.43549 0.154894
\(821\) −7.87520 −0.274846 −0.137423 0.990512i \(-0.543882\pi\)
−0.137423 + 0.990512i \(0.543882\pi\)
\(822\) −6.69853 −0.233638
\(823\) −30.5507 −1.06493 −0.532466 0.846451i \(-0.678735\pi\)
−0.532466 + 0.846451i \(0.678735\pi\)
\(824\) −8.33769 −0.290457
\(825\) 2.53550 0.0882748
\(826\) −57.6003 −2.00417
\(827\) −9.64557 −0.335409 −0.167705 0.985837i \(-0.553635\pi\)
−0.167705 + 0.985837i \(0.553635\pi\)
\(828\) 36.0257 1.25198
\(829\) 16.0498 0.557433 0.278717 0.960373i \(-0.410091\pi\)
0.278717 + 0.960373i \(0.410091\pi\)
\(830\) 4.61239 0.160098
\(831\) 15.8079 0.548371
\(832\) −19.9201 −0.690606
\(833\) 43.0775 1.49255
\(834\) −21.4801 −0.743795
\(835\) −4.25142 −0.147126
\(836\) −22.1538 −0.766204
\(837\) −15.2366 −0.526655
\(838\) 87.2748 3.01486
\(839\) −0.0291175 −0.00100525 −0.000502624 1.00000i \(-0.500160\pi\)
−0.000502624 1.00000i \(0.500160\pi\)
\(840\) 3.39169 0.117025
\(841\) −28.4930 −0.982516
\(842\) −32.1957 −1.10954
\(843\) 2.38751 0.0822302
\(844\) 11.3469 0.390575
\(845\) 5.36218 0.184465
\(846\) 11.7909 0.405378
\(847\) 3.83500 0.131772
\(848\) −6.18975 −0.212557
\(849\) 0.252093 0.00865182
\(850\) 61.4987 2.10939
\(851\) −15.3647 −0.526696
\(852\) −27.6166 −0.946128
\(853\) 0.807124 0.0276354 0.0138177 0.999905i \(-0.495602\pi\)
0.0138177 + 0.999905i \(0.495602\pi\)
\(854\) −96.3820 −3.29812
\(855\) 9.06329 0.309958
\(856\) 16.4832 0.563383
\(857\) 33.9410 1.15940 0.579701 0.814829i \(-0.303169\pi\)
0.579701 + 0.814829i \(0.303169\pi\)
\(858\) 1.97003 0.0672559
\(859\) 50.7405 1.73124 0.865621 0.500700i \(-0.166924\pi\)
0.865621 + 0.500700i \(0.166924\pi\)
\(860\) −12.1629 −0.414751
\(861\) −5.24747 −0.178833
\(862\) −52.7920 −1.79810
\(863\) 19.7754 0.673162 0.336581 0.941655i \(-0.390729\pi\)
0.336581 + 0.941655i \(0.390729\pi\)
\(864\) −14.6419 −0.498126
\(865\) −3.22397 −0.109618
\(866\) −11.8524 −0.402761
\(867\) 7.61928 0.258764
\(868\) 64.8286 2.20042
\(869\) 7.90726 0.268235
\(870\) 0.452423 0.0153386
\(871\) 6.36057 0.215520
\(872\) −3.18502 −0.107858
\(873\) 35.6353 1.20607
\(874\) 59.3571 2.00778
\(875\) 19.0980 0.645630
\(876\) 2.59505 0.0876787
\(877\) 44.5437 1.50413 0.752067 0.659086i \(-0.229057\pi\)
0.752067 + 0.659086i \(0.229057\pi\)
\(878\) −7.26459 −0.245168
\(879\) −4.76770 −0.160810
\(880\) 0.368928 0.0124366
\(881\) 7.80297 0.262889 0.131444 0.991324i \(-0.458039\pi\)
0.131444 + 0.991324i \(0.458039\pi\)
\(882\) 48.5660 1.63530
\(883\) 24.0304 0.808687 0.404343 0.914607i \(-0.367500\pi\)
0.404343 + 0.914607i \(0.367500\pi\)
\(884\) 30.0594 1.01101
\(885\) −1.76986 −0.0594930
\(886\) −55.2742 −1.85697
\(887\) 15.1318 0.508076 0.254038 0.967194i \(-0.418241\pi\)
0.254038 + 0.967194i \(0.418241\pi\)
\(888\) −6.78960 −0.227844
\(889\) −23.0650 −0.773576
\(890\) −5.00161 −0.167654
\(891\) −6.50514 −0.217930
\(892\) 26.3126 0.881011
\(893\) 12.2211 0.408963
\(894\) −22.2375 −0.743733
\(895\) 8.83496 0.295320
\(896\) 75.1473 2.51050
\(897\) −3.32050 −0.110868
\(898\) 48.8292 1.62945
\(899\) 3.54871 0.118356
\(900\) 43.6166 1.45389
\(901\) −47.9525 −1.59753
\(902\) −5.93794 −0.197712
\(903\) 14.3895 0.478852
\(904\) −39.0181 −1.29772
\(905\) −11.6125 −0.386012
\(906\) −24.2337 −0.805111
\(907\) 12.5128 0.415480 0.207740 0.978184i \(-0.433389\pi\)
0.207740 + 0.978184i \(0.433389\pi\)
\(908\) −31.6467 −1.05023
\(909\) −18.1717 −0.602717
\(910\) 7.22016 0.239346
\(911\) −33.1250 −1.09748 −0.548741 0.835992i \(-0.684893\pi\)
−0.548741 + 0.835992i \(0.684893\pi\)
\(912\) 2.52134 0.0834901
\(913\) −3.88440 −0.128555
\(914\) −40.5826 −1.34235
\(915\) −2.96148 −0.0979034
\(916\) 15.6975 0.518659
\(917\) 46.5985 1.53882
\(918\) 39.6792 1.30961
\(919\) −31.2214 −1.02990 −0.514950 0.857220i \(-0.672190\pi\)
−0.514950 + 0.857220i \(0.672190\pi\)
\(920\) −6.46891 −0.213274
\(921\) −3.36170 −0.110772
\(922\) 47.5618 1.56636
\(923\) −24.1254 −0.794098
\(924\) −6.96047 −0.228983
\(925\) −18.6022 −0.611636
\(926\) 8.17858 0.268765
\(927\) −7.00012 −0.229914
\(928\) 3.41018 0.111945
\(929\) 58.6317 1.92364 0.961822 0.273674i \(-0.0882390\pi\)
0.961822 + 0.273674i \(0.0882390\pi\)
\(930\) 3.16647 0.103833
\(931\) 50.3381 1.64976
\(932\) −16.7377 −0.548262
\(933\) −11.3396 −0.371242
\(934\) 51.0111 1.66913
\(935\) 2.85812 0.0934706
\(936\) 13.9071 0.454568
\(937\) 53.2436 1.73939 0.869697 0.493587i \(-0.164314\pi\)
0.869697 + 0.493587i \(0.164314\pi\)
\(938\) −35.7238 −1.16642
\(939\) 14.6503 0.478094
\(940\) −3.24558 −0.105859
\(941\) −4.02381 −0.131172 −0.0655862 0.997847i \(-0.520892\pi\)
−0.0655862 + 0.997847i \(0.520892\pi\)
\(942\) 10.2325 0.333392
\(943\) 10.0084 0.325918
\(944\) 4.66658 0.151884
\(945\) 5.99562 0.195037
\(946\) 16.2828 0.529401
\(947\) −8.98501 −0.291974 −0.145987 0.989287i \(-0.546636\pi\)
−0.145987 + 0.989287i \(0.546636\pi\)
\(948\) −14.3516 −0.466117
\(949\) 2.26700 0.0735899
\(950\) 71.8641 2.33158
\(951\) −10.7527 −0.348679
\(952\) −69.2813 −2.24542
\(953\) 46.9602 1.52119 0.760595 0.649226i \(-0.224907\pi\)
0.760595 + 0.649226i \(0.224907\pi\)
\(954\) −54.0621 −1.75033
\(955\) −5.53262 −0.179031
\(956\) −88.0371 −2.84732
\(957\) −0.381015 −0.0123165
\(958\) 55.5354 1.79427
\(959\) 20.6752 0.667637
\(960\) 3.43768 0.110951
\(961\) −6.16293 −0.198804
\(962\) −14.4535 −0.466001
\(963\) 13.8389 0.445951
\(964\) −33.9995 −1.09505
\(965\) 11.7639 0.378694
\(966\) 18.6493 0.600033
\(967\) 46.4368 1.49331 0.746654 0.665213i \(-0.231659\pi\)
0.746654 + 0.665213i \(0.231659\pi\)
\(968\) −3.23221 −0.103887
\(969\) 19.5331 0.627493
\(970\) −15.5928 −0.500654
\(971\) 58.5314 1.87836 0.939180 0.343424i \(-0.111587\pi\)
0.939180 + 0.343424i \(0.111587\pi\)
\(972\) 42.9175 1.37658
\(973\) 66.2989 2.12544
\(974\) −54.6853 −1.75223
\(975\) −4.02015 −0.128748
\(976\) 7.80854 0.249945
\(977\) 12.5090 0.400198 0.200099 0.979776i \(-0.435874\pi\)
0.200099 + 0.979776i \(0.435874\pi\)
\(978\) 12.6695 0.405127
\(979\) 4.21218 0.134622
\(980\) −13.3684 −0.427038
\(981\) −2.67407 −0.0853764
\(982\) −34.3325 −1.09559
\(983\) 10.5568 0.336708 0.168354 0.985727i \(-0.446155\pi\)
0.168354 + 0.985727i \(0.446155\pi\)
\(984\) 4.42266 0.140989
\(985\) 6.78301 0.216125
\(986\) −9.24155 −0.294311
\(987\) 3.83974 0.122220
\(988\) 35.1258 1.11750
\(989\) −27.4448 −0.872693
\(990\) 3.22227 0.102410
\(991\) 7.16396 0.227571 0.113785 0.993505i \(-0.463702\pi\)
0.113785 + 0.993505i \(0.463702\pi\)
\(992\) 23.8675 0.757795
\(993\) −6.77960 −0.215144
\(994\) 135.499 4.29777
\(995\) 8.15616 0.258568
\(996\) 7.05012 0.223391
\(997\) 20.2829 0.642367 0.321183 0.947017i \(-0.395919\pi\)
0.321183 + 0.947017i \(0.395919\pi\)
\(998\) 80.8451 2.55911
\(999\) −12.0022 −0.379733
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.1.13 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.13 121 1.1 even 1 trivial