Properties

Label 1441.2.a.c.1.15
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $1$
Dimension $23$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1441,2,Mod(1,1441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1441, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1441.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(11.5064429313\)
Analytic rank: \(1\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 1441.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.495822 q^{2} -0.133739 q^{3} -1.75416 q^{4} -0.493567 q^{5} -0.0663105 q^{6} +1.67893 q^{7} -1.86140 q^{8} -2.98211 q^{9} +O(q^{10})\) \(q+0.495822 q^{2} -0.133739 q^{3} -1.75416 q^{4} -0.493567 q^{5} -0.0663105 q^{6} +1.67893 q^{7} -1.86140 q^{8} -2.98211 q^{9} -0.244721 q^{10} +1.00000 q^{11} +0.234599 q^{12} +5.28022 q^{13} +0.832448 q^{14} +0.0660089 q^{15} +2.58540 q^{16} +1.59160 q^{17} -1.47860 q^{18} -7.18138 q^{19} +0.865796 q^{20} -0.224537 q^{21} +0.495822 q^{22} -1.46229 q^{23} +0.248940 q^{24} -4.75639 q^{25} +2.61805 q^{26} +0.800039 q^{27} -2.94510 q^{28} -8.57087 q^{29} +0.0327287 q^{30} +1.89658 q^{31} +5.00469 q^{32} -0.133739 q^{33} +0.789150 q^{34} -0.828662 q^{35} +5.23111 q^{36} +6.08431 q^{37} -3.56069 q^{38} -0.706169 q^{39} +0.918723 q^{40} +1.95977 q^{41} -0.111330 q^{42} -8.81508 q^{43} -1.75416 q^{44} +1.47187 q^{45} -0.725034 q^{46} -8.75989 q^{47} -0.345768 q^{48} -4.18121 q^{49} -2.35832 q^{50} -0.212858 q^{51} -9.26235 q^{52} -6.71231 q^{53} +0.396677 q^{54} -0.493567 q^{55} -3.12514 q^{56} +0.960428 q^{57} -4.24963 q^{58} -3.43339 q^{59} -0.115790 q^{60} -5.71897 q^{61} +0.940366 q^{62} -5.00675 q^{63} -2.68937 q^{64} -2.60614 q^{65} -0.0663105 q^{66} -7.92404 q^{67} -2.79192 q^{68} +0.195564 q^{69} -0.410869 q^{70} -7.56641 q^{71} +5.55089 q^{72} -3.61848 q^{73} +3.01674 q^{74} +0.636113 q^{75} +12.5973 q^{76} +1.67893 q^{77} -0.350134 q^{78} +15.0966 q^{79} -1.27607 q^{80} +8.83935 q^{81} +0.971698 q^{82} -0.0259306 q^{83} +0.393874 q^{84} -0.785561 q^{85} -4.37071 q^{86} +1.14626 q^{87} -1.86140 q^{88} -13.2543 q^{89} +0.729787 q^{90} +8.86509 q^{91} +2.56509 q^{92} -0.253646 q^{93} -4.34334 q^{94} +3.54449 q^{95} -0.669320 q^{96} -8.69413 q^{97} -2.07314 q^{98} -2.98211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.495822 0.350599 0.175300 0.984515i \(-0.443911\pi\)
0.175300 + 0.984515i \(0.443911\pi\)
\(3\) −0.133739 −0.0772140 −0.0386070 0.999254i \(-0.512292\pi\)
−0.0386070 + 0.999254i \(0.512292\pi\)
\(4\) −1.75416 −0.877080
\(5\) −0.493567 −0.220730 −0.110365 0.993891i \(-0.535202\pi\)
−0.110365 + 0.993891i \(0.535202\pi\)
\(6\) −0.0663105 −0.0270712
\(7\) 1.67893 0.634574 0.317287 0.948330i \(-0.397228\pi\)
0.317287 + 0.948330i \(0.397228\pi\)
\(8\) −1.86140 −0.658103
\(9\) −2.98211 −0.994038
\(10\) −0.244721 −0.0773877
\(11\) 1.00000 0.301511
\(12\) 0.234599 0.0677229
\(13\) 5.28022 1.46447 0.732234 0.681053i \(-0.238478\pi\)
0.732234 + 0.681053i \(0.238478\pi\)
\(14\) 0.832448 0.222481
\(15\) 0.0660089 0.0170434
\(16\) 2.58540 0.646350
\(17\) 1.59160 0.386020 0.193010 0.981197i \(-0.438175\pi\)
0.193010 + 0.981197i \(0.438175\pi\)
\(18\) −1.47860 −0.348509
\(19\) −7.18138 −1.64752 −0.823761 0.566937i \(-0.808128\pi\)
−0.823761 + 0.566937i \(0.808128\pi\)
\(20\) 0.865796 0.193598
\(21\) −0.224537 −0.0489980
\(22\) 0.495822 0.105710
\(23\) −1.46229 −0.304908 −0.152454 0.988311i \(-0.548718\pi\)
−0.152454 + 0.988311i \(0.548718\pi\)
\(24\) 0.248940 0.0508147
\(25\) −4.75639 −0.951278
\(26\) 2.61805 0.513441
\(27\) 0.800039 0.153968
\(28\) −2.94510 −0.556572
\(29\) −8.57087 −1.59157 −0.795786 0.605578i \(-0.792942\pi\)
−0.795786 + 0.605578i \(0.792942\pi\)
\(30\) 0.0327287 0.00597541
\(31\) 1.89658 0.340636 0.170318 0.985389i \(-0.445521\pi\)
0.170318 + 0.985389i \(0.445521\pi\)
\(32\) 5.00469 0.884712
\(33\) −0.133739 −0.0232809
\(34\) 0.789150 0.135338
\(35\) −0.828662 −0.140069
\(36\) 5.23111 0.871851
\(37\) 6.08431 1.00026 0.500128 0.865952i \(-0.333286\pi\)
0.500128 + 0.865952i \(0.333286\pi\)
\(38\) −3.56069 −0.577620
\(39\) −0.706169 −0.113077
\(40\) 0.918723 0.145263
\(41\) 1.95977 0.306065 0.153033 0.988221i \(-0.451096\pi\)
0.153033 + 0.988221i \(0.451096\pi\)
\(42\) −0.111330 −0.0171786
\(43\) −8.81508 −1.34429 −0.672143 0.740421i \(-0.734626\pi\)
−0.672143 + 0.740421i \(0.734626\pi\)
\(44\) −1.75416 −0.264450
\(45\) 1.47187 0.219414
\(46\) −0.725034 −0.106900
\(47\) −8.75989 −1.27776 −0.638880 0.769306i \(-0.720602\pi\)
−0.638880 + 0.769306i \(0.720602\pi\)
\(48\) −0.345768 −0.0499073
\(49\) −4.18121 −0.597316
\(50\) −2.35832 −0.333517
\(51\) −0.212858 −0.0298061
\(52\) −9.26235 −1.28446
\(53\) −6.71231 −0.922006 −0.461003 0.887399i \(-0.652510\pi\)
−0.461003 + 0.887399i \(0.652510\pi\)
\(54\) 0.396677 0.0539809
\(55\) −0.493567 −0.0665525
\(56\) −3.12514 −0.417615
\(57\) 0.960428 0.127212
\(58\) −4.24963 −0.558003
\(59\) −3.43339 −0.446989 −0.223494 0.974705i \(-0.571746\pi\)
−0.223494 + 0.974705i \(0.571746\pi\)
\(60\) −0.115790 −0.0149485
\(61\) −5.71897 −0.732240 −0.366120 0.930568i \(-0.619314\pi\)
−0.366120 + 0.930568i \(0.619314\pi\)
\(62\) 0.940366 0.119427
\(63\) −5.00675 −0.630791
\(64\) −2.68937 −0.336171
\(65\) −2.60614 −0.323252
\(66\) −0.0663105 −0.00816226
\(67\) −7.92404 −0.968075 −0.484038 0.875047i \(-0.660830\pi\)
−0.484038 + 0.875047i \(0.660830\pi\)
\(68\) −2.79192 −0.338570
\(69\) 0.195564 0.0235432
\(70\) −0.410869 −0.0491082
\(71\) −7.56641 −0.897967 −0.448984 0.893540i \(-0.648214\pi\)
−0.448984 + 0.893540i \(0.648214\pi\)
\(72\) 5.55089 0.654179
\(73\) −3.61848 −0.423511 −0.211756 0.977323i \(-0.567918\pi\)
−0.211756 + 0.977323i \(0.567918\pi\)
\(74\) 3.01674 0.350689
\(75\) 0.636113 0.0734520
\(76\) 12.5973 1.44501
\(77\) 1.67893 0.191331
\(78\) −0.350134 −0.0396449
\(79\) 15.0966 1.69850 0.849250 0.527992i \(-0.177055\pi\)
0.849250 + 0.527992i \(0.177055\pi\)
\(80\) −1.27607 −0.142669
\(81\) 8.83935 0.982150
\(82\) 0.971698 0.107306
\(83\) −0.0259306 −0.00284625 −0.00142312 0.999999i \(-0.500453\pi\)
−0.00142312 + 0.999999i \(0.500453\pi\)
\(84\) 0.393874 0.0429752
\(85\) −0.785561 −0.0852060
\(86\) −4.37071 −0.471306
\(87\) 1.14626 0.122892
\(88\) −1.86140 −0.198425
\(89\) −13.2543 −1.40495 −0.702474 0.711709i \(-0.747921\pi\)
−0.702474 + 0.711709i \(0.747921\pi\)
\(90\) 0.729787 0.0769263
\(91\) 8.86509 0.929314
\(92\) 2.56509 0.267429
\(93\) −0.253646 −0.0263019
\(94\) −4.34334 −0.447982
\(95\) 3.54449 0.363657
\(96\) −0.669320 −0.0683122
\(97\) −8.69413 −0.882756 −0.441378 0.897321i \(-0.645510\pi\)
−0.441378 + 0.897321i \(0.645510\pi\)
\(98\) −2.07314 −0.209418
\(99\) −2.98211 −0.299714
\(100\) 8.34347 0.834347
\(101\) 9.03831 0.899346 0.449673 0.893193i \(-0.351541\pi\)
0.449673 + 0.893193i \(0.351541\pi\)
\(102\) −0.105540 −0.0104500
\(103\) −0.951482 −0.0937523 −0.0468762 0.998901i \(-0.514927\pi\)
−0.0468762 + 0.998901i \(0.514927\pi\)
\(104\) −9.82857 −0.963771
\(105\) 0.110824 0.0108153
\(106\) −3.32811 −0.323254
\(107\) 9.86449 0.953636 0.476818 0.879002i \(-0.341790\pi\)
0.476818 + 0.879002i \(0.341790\pi\)
\(108\) −1.40340 −0.135042
\(109\) 20.7918 1.99149 0.995747 0.0921260i \(-0.0293663\pi\)
0.995747 + 0.0921260i \(0.0293663\pi\)
\(110\) −0.244721 −0.0233333
\(111\) −0.813707 −0.0772337
\(112\) 4.34069 0.410157
\(113\) −14.4582 −1.36011 −0.680054 0.733162i \(-0.738044\pi\)
−0.680054 + 0.733162i \(0.738044\pi\)
\(114\) 0.476201 0.0446003
\(115\) 0.721737 0.0673023
\(116\) 15.0347 1.39594
\(117\) −15.7462 −1.45574
\(118\) −1.70235 −0.156714
\(119\) 2.67218 0.244958
\(120\) −0.122869 −0.0112163
\(121\) 1.00000 0.0909091
\(122\) −2.83559 −0.256723
\(123\) −0.262097 −0.0236325
\(124\) −3.32691 −0.298765
\(125\) 4.81543 0.430705
\(126\) −2.48245 −0.221155
\(127\) −4.96659 −0.440713 −0.220357 0.975419i \(-0.570722\pi\)
−0.220357 + 0.975419i \(0.570722\pi\)
\(128\) −11.3428 −1.00257
\(129\) 1.17892 0.103798
\(130\) −1.29218 −0.113332
\(131\) 1.00000 0.0873704
\(132\) 0.234599 0.0204192
\(133\) −12.0570 −1.04547
\(134\) −3.92891 −0.339406
\(135\) −0.394873 −0.0339852
\(136\) −2.96260 −0.254040
\(137\) 11.2713 0.962971 0.481485 0.876454i \(-0.340097\pi\)
0.481485 + 0.876454i \(0.340097\pi\)
\(138\) 0.0969650 0.00825421
\(139\) −12.0592 −1.02285 −0.511423 0.859329i \(-0.670882\pi\)
−0.511423 + 0.859329i \(0.670882\pi\)
\(140\) 1.45361 0.122852
\(141\) 1.17153 0.0986610
\(142\) −3.75159 −0.314827
\(143\) 5.28022 0.441554
\(144\) −7.70996 −0.642497
\(145\) 4.23030 0.351307
\(146\) −1.79412 −0.148483
\(147\) 0.559189 0.0461211
\(148\) −10.6729 −0.877304
\(149\) 1.01857 0.0834447 0.0417223 0.999129i \(-0.486716\pi\)
0.0417223 + 0.999129i \(0.486716\pi\)
\(150\) 0.315399 0.0257522
\(151\) 20.9376 1.70388 0.851939 0.523642i \(-0.175427\pi\)
0.851939 + 0.523642i \(0.175427\pi\)
\(152\) 13.3674 1.08424
\(153\) −4.74633 −0.383718
\(154\) 0.832448 0.0670806
\(155\) −0.936089 −0.0751885
\(156\) 1.23873 0.0991780
\(157\) 5.75439 0.459250 0.229625 0.973279i \(-0.426250\pi\)
0.229625 + 0.973279i \(0.426250\pi\)
\(158\) 7.48522 0.595492
\(159\) 0.897694 0.0711918
\(160\) −2.47015 −0.195282
\(161\) −2.45507 −0.193487
\(162\) 4.38274 0.344341
\(163\) 0.379296 0.0297088 0.0148544 0.999890i \(-0.495272\pi\)
0.0148544 + 0.999890i \(0.495272\pi\)
\(164\) −3.43776 −0.268444
\(165\) 0.0660089 0.00513879
\(166\) −0.0128569 −0.000997892 0
\(167\) −20.7913 −1.60888 −0.804439 0.594036i \(-0.797534\pi\)
−0.804439 + 0.594036i \(0.797534\pi\)
\(168\) 0.417952 0.0322457
\(169\) 14.8807 1.14467
\(170\) −0.389498 −0.0298731
\(171\) 21.4157 1.63770
\(172\) 15.4631 1.17905
\(173\) 1.07921 0.0820509 0.0410255 0.999158i \(-0.486938\pi\)
0.0410255 + 0.999158i \(0.486938\pi\)
\(174\) 0.568339 0.0430857
\(175\) −7.98563 −0.603657
\(176\) 2.58540 0.194882
\(177\) 0.459176 0.0345138
\(178\) −6.57175 −0.492574
\(179\) −15.2854 −1.14249 −0.571244 0.820780i \(-0.693539\pi\)
−0.571244 + 0.820780i \(0.693539\pi\)
\(180\) −2.58190 −0.192444
\(181\) −21.0127 −1.56186 −0.780931 0.624618i \(-0.785255\pi\)
−0.780931 + 0.624618i \(0.785255\pi\)
\(182\) 4.39551 0.325817
\(183\) 0.764847 0.0565391
\(184\) 2.72189 0.200661
\(185\) −3.00302 −0.220786
\(186\) −0.125763 −0.00922141
\(187\) 1.59160 0.116389
\(188\) 15.3662 1.12070
\(189\) 1.34321 0.0977039
\(190\) 1.75744 0.127498
\(191\) −16.7701 −1.21344 −0.606720 0.794916i \(-0.707515\pi\)
−0.606720 + 0.794916i \(0.707515\pi\)
\(192\) 0.359672 0.0259571
\(193\) −18.0268 −1.29760 −0.648799 0.760960i \(-0.724728\pi\)
−0.648799 + 0.760960i \(0.724728\pi\)
\(194\) −4.31074 −0.309493
\(195\) 0.348541 0.0249596
\(196\) 7.33452 0.523894
\(197\) 13.1321 0.935626 0.467813 0.883827i \(-0.345042\pi\)
0.467813 + 0.883827i \(0.345042\pi\)
\(198\) −1.47860 −0.105079
\(199\) 18.2178 1.29142 0.645711 0.763582i \(-0.276561\pi\)
0.645711 + 0.763582i \(0.276561\pi\)
\(200\) 8.85353 0.626039
\(201\) 1.05975 0.0747490
\(202\) 4.48139 0.315310
\(203\) −14.3899 −1.00997
\(204\) 0.373387 0.0261423
\(205\) −0.967279 −0.0675577
\(206\) −0.471766 −0.0328695
\(207\) 4.36071 0.303090
\(208\) 13.6515 0.946560
\(209\) −7.18138 −0.496747
\(210\) 0.0549490 0.00379184
\(211\) 4.70567 0.323951 0.161976 0.986795i \(-0.448213\pi\)
0.161976 + 0.986795i \(0.448213\pi\)
\(212\) 11.7745 0.808673
\(213\) 1.01192 0.0693356
\(214\) 4.89103 0.334344
\(215\) 4.35083 0.296724
\(216\) −1.48919 −0.101326
\(217\) 3.18422 0.216159
\(218\) 10.3090 0.698216
\(219\) 0.483930 0.0327010
\(220\) 0.865796 0.0583719
\(221\) 8.40399 0.565314
\(222\) −0.403454 −0.0270781
\(223\) 27.3812 1.83358 0.916790 0.399370i \(-0.130771\pi\)
0.916790 + 0.399370i \(0.130771\pi\)
\(224\) 8.40250 0.561415
\(225\) 14.1841 0.945607
\(226\) −7.16867 −0.476853
\(227\) −13.4949 −0.895690 −0.447845 0.894111i \(-0.647808\pi\)
−0.447845 + 0.894111i \(0.647808\pi\)
\(228\) −1.68474 −0.111575
\(229\) 17.2225 1.13809 0.569047 0.822305i \(-0.307312\pi\)
0.569047 + 0.822305i \(0.307312\pi\)
\(230\) 0.357853 0.0235961
\(231\) −0.224537 −0.0147734
\(232\) 15.9538 1.04742
\(233\) 24.1856 1.58445 0.792226 0.610227i \(-0.208922\pi\)
0.792226 + 0.610227i \(0.208922\pi\)
\(234\) −7.80732 −0.510380
\(235\) 4.32359 0.282040
\(236\) 6.02271 0.392045
\(237\) −2.01900 −0.131148
\(238\) 1.32492 0.0858820
\(239\) 22.4259 1.45061 0.725307 0.688426i \(-0.241698\pi\)
0.725307 + 0.688426i \(0.241698\pi\)
\(240\) 0.170659 0.0110160
\(241\) −9.62695 −0.620127 −0.310063 0.950716i \(-0.600350\pi\)
−0.310063 + 0.950716i \(0.600350\pi\)
\(242\) 0.495822 0.0318726
\(243\) −3.58228 −0.229803
\(244\) 10.0320 0.642233
\(245\) 2.06371 0.131845
\(246\) −0.129954 −0.00828553
\(247\) −37.9193 −2.41275
\(248\) −3.53029 −0.224173
\(249\) 0.00346792 0.000219770 0
\(250\) 2.38760 0.151005
\(251\) 12.4381 0.785083 0.392542 0.919734i \(-0.371596\pi\)
0.392542 + 0.919734i \(0.371596\pi\)
\(252\) 8.78264 0.553254
\(253\) −1.46229 −0.0919332
\(254\) −2.46254 −0.154514
\(255\) 0.105060 0.00657910
\(256\) −0.245289 −0.0153305
\(257\) −14.8275 −0.924912 −0.462456 0.886642i \(-0.653032\pi\)
−0.462456 + 0.886642i \(0.653032\pi\)
\(258\) 0.584532 0.0363914
\(259\) 10.2151 0.634736
\(260\) 4.57159 0.283518
\(261\) 25.5593 1.58208
\(262\) 0.495822 0.0306320
\(263\) −14.3548 −0.885153 −0.442576 0.896731i \(-0.645935\pi\)
−0.442576 + 0.896731i \(0.645935\pi\)
\(264\) 0.248940 0.0153212
\(265\) 3.31297 0.203514
\(266\) −5.97813 −0.366543
\(267\) 1.77260 0.108482
\(268\) 13.9000 0.849080
\(269\) 11.3186 0.690106 0.345053 0.938583i \(-0.387861\pi\)
0.345053 + 0.938583i \(0.387861\pi\)
\(270\) −0.195787 −0.0119152
\(271\) −11.8010 −0.716860 −0.358430 0.933557i \(-0.616688\pi\)
−0.358430 + 0.933557i \(0.616688\pi\)
\(272\) 4.11492 0.249504
\(273\) −1.18560 −0.0717560
\(274\) 5.58855 0.337617
\(275\) −4.75639 −0.286821
\(276\) −0.343051 −0.0206492
\(277\) −15.4341 −0.927345 −0.463673 0.886007i \(-0.653469\pi\)
−0.463673 + 0.886007i \(0.653469\pi\)
\(278\) −5.97921 −0.358609
\(279\) −5.65582 −0.338605
\(280\) 1.54247 0.0921800
\(281\) −12.6262 −0.753218 −0.376609 0.926372i \(-0.622910\pi\)
−0.376609 + 0.926372i \(0.622910\pi\)
\(282\) 0.580872 0.0345905
\(283\) −16.2670 −0.966975 −0.483488 0.875351i \(-0.660630\pi\)
−0.483488 + 0.875351i \(0.660630\pi\)
\(284\) 13.2727 0.787589
\(285\) −0.474035 −0.0280794
\(286\) 2.61805 0.154808
\(287\) 3.29031 0.194221
\(288\) −14.9246 −0.879438
\(289\) −14.4668 −0.850989
\(290\) 2.09748 0.123168
\(291\) 1.16274 0.0681611
\(292\) 6.34740 0.371453
\(293\) 32.2542 1.88431 0.942155 0.335176i \(-0.108796\pi\)
0.942155 + 0.335176i \(0.108796\pi\)
\(294\) 0.277258 0.0161700
\(295\) 1.69461 0.0986637
\(296\) −11.3253 −0.658271
\(297\) 0.800039 0.0464230
\(298\) 0.505030 0.0292556
\(299\) −7.72119 −0.446528
\(300\) −1.11584 −0.0644233
\(301\) −14.7999 −0.853050
\(302\) 10.3813 0.597378
\(303\) −1.20877 −0.0694421
\(304\) −18.5668 −1.06488
\(305\) 2.82270 0.161627
\(306\) −2.35333 −0.134531
\(307\) 11.3179 0.645949 0.322974 0.946408i \(-0.395317\pi\)
0.322974 + 0.946408i \(0.395317\pi\)
\(308\) −2.94510 −0.167813
\(309\) 0.127250 0.00723899
\(310\) −0.464134 −0.0263610
\(311\) 20.4740 1.16097 0.580487 0.814270i \(-0.302862\pi\)
0.580487 + 0.814270i \(0.302862\pi\)
\(312\) 1.31446 0.0744166
\(313\) −8.88910 −0.502442 −0.251221 0.967930i \(-0.580832\pi\)
−0.251221 + 0.967930i \(0.580832\pi\)
\(314\) 2.85315 0.161013
\(315\) 2.47116 0.139234
\(316\) −26.4818 −1.48972
\(317\) −18.3295 −1.02949 −0.514744 0.857344i \(-0.672113\pi\)
−0.514744 + 0.857344i \(0.672113\pi\)
\(318\) 0.445096 0.0249598
\(319\) −8.57087 −0.479877
\(320\) 1.32738 0.0742029
\(321\) −1.31926 −0.0736341
\(322\) −1.21728 −0.0678362
\(323\) −11.4299 −0.635976
\(324\) −15.5056 −0.861424
\(325\) −25.1148 −1.39312
\(326\) 0.188063 0.0104159
\(327\) −2.78067 −0.153771
\(328\) −3.64791 −0.201422
\(329\) −14.7072 −0.810834
\(330\) 0.0327287 0.00180165
\(331\) 23.8825 1.31270 0.656349 0.754457i \(-0.272100\pi\)
0.656349 + 0.754457i \(0.272100\pi\)
\(332\) 0.0454864 0.00249639
\(333\) −18.1441 −0.994292
\(334\) −10.3088 −0.564071
\(335\) 3.91104 0.213683
\(336\) −0.580518 −0.0316699
\(337\) 17.9902 0.979990 0.489995 0.871725i \(-0.336999\pi\)
0.489995 + 0.871725i \(0.336999\pi\)
\(338\) 7.37817 0.401320
\(339\) 1.93361 0.105019
\(340\) 1.37800 0.0747325
\(341\) 1.89658 0.102706
\(342\) 10.6184 0.574176
\(343\) −18.7724 −1.01362
\(344\) 16.4083 0.884679
\(345\) −0.0965240 −0.00519668
\(346\) 0.535097 0.0287670
\(347\) −14.2631 −0.765682 −0.382841 0.923814i \(-0.625054\pi\)
−0.382841 + 0.923814i \(0.625054\pi\)
\(348\) −2.01072 −0.107786
\(349\) −19.5360 −1.04574 −0.522870 0.852413i \(-0.675139\pi\)
−0.522870 + 0.852413i \(0.675139\pi\)
\(350\) −3.95945 −0.211641
\(351\) 4.22438 0.225481
\(352\) 5.00469 0.266751
\(353\) 15.1166 0.804576 0.402288 0.915513i \(-0.368215\pi\)
0.402288 + 0.915513i \(0.368215\pi\)
\(354\) 0.227670 0.0121005
\(355\) 3.73453 0.198208
\(356\) 23.2501 1.23225
\(357\) −0.357373 −0.0189142
\(358\) −7.57886 −0.400555
\(359\) −0.696301 −0.0367494 −0.0183747 0.999831i \(-0.505849\pi\)
−0.0183747 + 0.999831i \(0.505849\pi\)
\(360\) −2.73974 −0.144397
\(361\) 32.5723 1.71433
\(362\) −10.4186 −0.547587
\(363\) −0.133739 −0.00701945
\(364\) −15.5508 −0.815083
\(365\) 1.78596 0.0934815
\(366\) 0.379228 0.0198226
\(367\) 17.2552 0.900714 0.450357 0.892849i \(-0.351297\pi\)
0.450357 + 0.892849i \(0.351297\pi\)
\(368\) −3.78060 −0.197077
\(369\) −5.84427 −0.304240
\(370\) −1.48896 −0.0774074
\(371\) −11.2695 −0.585081
\(372\) 0.444936 0.0230688
\(373\) 36.4711 1.88840 0.944201 0.329371i \(-0.106837\pi\)
0.944201 + 0.329371i \(0.106837\pi\)
\(374\) 0.789150 0.0408060
\(375\) −0.644009 −0.0332565
\(376\) 16.3056 0.840898
\(377\) −45.2561 −2.33081
\(378\) 0.665991 0.0342549
\(379\) −15.7902 −0.811088 −0.405544 0.914076i \(-0.632918\pi\)
−0.405544 + 0.914076i \(0.632918\pi\)
\(380\) −6.21761 −0.318957
\(381\) 0.664224 0.0340292
\(382\) −8.31497 −0.425431
\(383\) 28.0572 1.43366 0.716828 0.697251i \(-0.245593\pi\)
0.716828 + 0.697251i \(0.245593\pi\)
\(384\) 1.51697 0.0774127
\(385\) −0.828662 −0.0422325
\(386\) −8.93809 −0.454937
\(387\) 26.2876 1.33627
\(388\) 15.2509 0.774248
\(389\) 35.1657 1.78297 0.891487 0.453046i \(-0.149663\pi\)
0.891487 + 0.453046i \(0.149663\pi\)
\(390\) 0.172814 0.00875080
\(391\) −2.32738 −0.117700
\(392\) 7.78289 0.393095
\(393\) −0.133739 −0.00674622
\(394\) 6.51120 0.328030
\(395\) −7.45118 −0.374909
\(396\) 5.23111 0.262873
\(397\) 3.92453 0.196966 0.0984832 0.995139i \(-0.468601\pi\)
0.0984832 + 0.995139i \(0.468601\pi\)
\(398\) 9.03277 0.452772
\(399\) 1.61249 0.0807253
\(400\) −12.2972 −0.614859
\(401\) −29.5493 −1.47562 −0.737810 0.675008i \(-0.764140\pi\)
−0.737810 + 0.675008i \(0.764140\pi\)
\(402\) 0.525447 0.0262069
\(403\) 10.0144 0.498851
\(404\) −15.8547 −0.788798
\(405\) −4.36281 −0.216790
\(406\) −7.13481 −0.354095
\(407\) 6.08431 0.301588
\(408\) 0.396213 0.0196155
\(409\) 11.7281 0.579915 0.289957 0.957040i \(-0.406359\pi\)
0.289957 + 0.957040i \(0.406359\pi\)
\(410\) −0.479598 −0.0236857
\(411\) −1.50741 −0.0743548
\(412\) 1.66905 0.0822283
\(413\) −5.76440 −0.283647
\(414\) 2.16213 0.106263
\(415\) 0.0127985 0.000628252 0
\(416\) 26.4258 1.29563
\(417\) 1.61278 0.0789781
\(418\) −3.56069 −0.174159
\(419\) −11.5393 −0.563733 −0.281866 0.959454i \(-0.590953\pi\)
−0.281866 + 0.959454i \(0.590953\pi\)
\(420\) −0.194403 −0.00948590
\(421\) −33.0198 −1.60928 −0.804642 0.593760i \(-0.797643\pi\)
−0.804642 + 0.593760i \(0.797643\pi\)
\(422\) 2.33317 0.113577
\(423\) 26.1230 1.27014
\(424\) 12.4943 0.606775
\(425\) −7.57027 −0.367212
\(426\) 0.501732 0.0243090
\(427\) −9.60173 −0.464660
\(428\) −17.3039 −0.836416
\(429\) −0.706169 −0.0340941
\(430\) 2.15724 0.104031
\(431\) 1.04523 0.0503467 0.0251734 0.999683i \(-0.491986\pi\)
0.0251734 + 0.999683i \(0.491986\pi\)
\(432\) 2.06842 0.0995170
\(433\) −6.26433 −0.301045 −0.150522 0.988607i \(-0.548096\pi\)
−0.150522 + 0.988607i \(0.548096\pi\)
\(434\) 1.57880 0.0757850
\(435\) −0.565754 −0.0271258
\(436\) −36.4722 −1.74670
\(437\) 10.5012 0.502343
\(438\) 0.239943 0.0114649
\(439\) −0.0715349 −0.00341418 −0.00170709 0.999999i \(-0.500543\pi\)
−0.00170709 + 0.999999i \(0.500543\pi\)
\(440\) 0.918723 0.0437984
\(441\) 12.4688 0.593755
\(442\) 4.16688 0.198198
\(443\) −14.0540 −0.667727 −0.333863 0.942621i \(-0.608352\pi\)
−0.333863 + 0.942621i \(0.608352\pi\)
\(444\) 1.42737 0.0677402
\(445\) 6.54186 0.310114
\(446\) 13.5762 0.642851
\(447\) −0.136222 −0.00644310
\(448\) −4.51524 −0.213325
\(449\) 12.9572 0.611489 0.305745 0.952114i \(-0.401095\pi\)
0.305745 + 0.952114i \(0.401095\pi\)
\(450\) 7.03279 0.331529
\(451\) 1.95977 0.0922821
\(452\) 25.3619 1.19292
\(453\) −2.80016 −0.131563
\(454\) −6.69108 −0.314028
\(455\) −4.37551 −0.205127
\(456\) −1.78774 −0.0837184
\(457\) 33.9436 1.58781 0.793906 0.608040i \(-0.208044\pi\)
0.793906 + 0.608040i \(0.208044\pi\)
\(458\) 8.53929 0.399015
\(459\) 1.27334 0.0594345
\(460\) −1.26604 −0.0590295
\(461\) 0.0276148 0.00128615 0.000643076 1.00000i \(-0.499795\pi\)
0.000643076 1.00000i \(0.499795\pi\)
\(462\) −0.111330 −0.00517956
\(463\) −6.87111 −0.319327 −0.159664 0.987171i \(-0.551041\pi\)
−0.159664 + 0.987171i \(0.551041\pi\)
\(464\) −22.1591 −1.02871
\(465\) 0.125191 0.00580560
\(466\) 11.9918 0.555508
\(467\) −34.8283 −1.61166 −0.805831 0.592146i \(-0.798281\pi\)
−0.805831 + 0.592146i \(0.798281\pi\)
\(468\) 27.6214 1.27680
\(469\) −13.3039 −0.614315
\(470\) 2.14373 0.0988829
\(471\) −0.769584 −0.0354605
\(472\) 6.39089 0.294164
\(473\) −8.81508 −0.405318
\(474\) −1.00106 −0.0459803
\(475\) 34.1575 1.56725
\(476\) −4.68743 −0.214848
\(477\) 20.0169 0.916509
\(478\) 11.1193 0.508584
\(479\) −23.5724 −1.07705 −0.538526 0.842609i \(-0.681019\pi\)
−0.538526 + 0.842609i \(0.681019\pi\)
\(480\) 0.330354 0.0150785
\(481\) 32.1265 1.46484
\(482\) −4.77326 −0.217416
\(483\) 0.328338 0.0149399
\(484\) −1.75416 −0.0797346
\(485\) 4.29114 0.194850
\(486\) −1.77617 −0.0805688
\(487\) 22.2936 1.01022 0.505110 0.863055i \(-0.331452\pi\)
0.505110 + 0.863055i \(0.331452\pi\)
\(488\) 10.6453 0.481889
\(489\) −0.0507265 −0.00229393
\(490\) 1.02323 0.0462249
\(491\) −31.6498 −1.42834 −0.714168 0.699974i \(-0.753195\pi\)
−0.714168 + 0.699974i \(0.753195\pi\)
\(492\) 0.459761 0.0207276
\(493\) −13.6414 −0.614378
\(494\) −18.8012 −0.845906
\(495\) 1.47187 0.0661558
\(496\) 4.90342 0.220170
\(497\) −12.7034 −0.569827
\(498\) 0.00171947 7.70512e−5 0
\(499\) 22.5760 1.01064 0.505319 0.862933i \(-0.331375\pi\)
0.505319 + 0.862933i \(0.331375\pi\)
\(500\) −8.44704 −0.377763
\(501\) 2.78060 0.124228
\(502\) 6.16706 0.275249
\(503\) −28.0156 −1.24915 −0.624577 0.780963i \(-0.714729\pi\)
−0.624577 + 0.780963i \(0.714729\pi\)
\(504\) 9.31953 0.415125
\(505\) −4.46101 −0.198512
\(506\) −0.725034 −0.0322317
\(507\) −1.99012 −0.0883844
\(508\) 8.71219 0.386541
\(509\) 11.8699 0.526123 0.263062 0.964779i \(-0.415268\pi\)
0.263062 + 0.964779i \(0.415268\pi\)
\(510\) 0.0520909 0.00230663
\(511\) −6.07516 −0.268749
\(512\) 22.5640 0.997199
\(513\) −5.74539 −0.253665
\(514\) −7.35179 −0.324273
\(515\) 0.469620 0.0206939
\(516\) −2.06801 −0.0910390
\(517\) −8.75989 −0.385259
\(518\) 5.06488 0.222538
\(519\) −0.144332 −0.00633548
\(520\) 4.85106 0.212733
\(521\) 14.8079 0.648747 0.324373 0.945929i \(-0.394847\pi\)
0.324373 + 0.945929i \(0.394847\pi\)
\(522\) 12.6729 0.554677
\(523\) −21.0116 −0.918772 −0.459386 0.888237i \(-0.651931\pi\)
−0.459386 + 0.888237i \(0.651931\pi\)
\(524\) −1.75416 −0.0766309
\(525\) 1.06799 0.0466107
\(526\) −7.11741 −0.310334
\(527\) 3.01860 0.131492
\(528\) −0.345768 −0.0150476
\(529\) −20.8617 −0.907031
\(530\) 1.64264 0.0713519
\(531\) 10.2387 0.444324
\(532\) 21.1499 0.916965
\(533\) 10.3480 0.448223
\(534\) 0.878896 0.0380336
\(535\) −4.86879 −0.210496
\(536\) 14.7498 0.637093
\(537\) 2.04425 0.0882161
\(538\) 5.61200 0.241951
\(539\) −4.18121 −0.180097
\(540\) 0.692670 0.0298078
\(541\) 16.0002 0.687902 0.343951 0.938988i \(-0.388235\pi\)
0.343951 + 0.938988i \(0.388235\pi\)
\(542\) −5.85119 −0.251330
\(543\) 2.81021 0.120598
\(544\) 7.96546 0.341516
\(545\) −10.2622 −0.439582
\(546\) −0.587849 −0.0251576
\(547\) −14.4429 −0.617534 −0.308767 0.951138i \(-0.599916\pi\)
−0.308767 + 0.951138i \(0.599916\pi\)
\(548\) −19.7716 −0.844603
\(549\) 17.0546 0.727874
\(550\) −2.35832 −0.100559
\(551\) 61.5507 2.62215
\(552\) −0.364022 −0.0154938
\(553\) 25.3460 1.07782
\(554\) −7.65257 −0.325126
\(555\) 0.401619 0.0170478
\(556\) 21.1537 0.897119
\(557\) −35.5026 −1.50429 −0.752146 0.658997i \(-0.770981\pi\)
−0.752146 + 0.658997i \(0.770981\pi\)
\(558\) −2.80428 −0.118715
\(559\) −46.5455 −1.96867
\(560\) −2.14242 −0.0905339
\(561\) −0.212858 −0.00898688
\(562\) −6.26037 −0.264078
\(563\) −32.0306 −1.34993 −0.674965 0.737850i \(-0.735841\pi\)
−0.674965 + 0.737850i \(0.735841\pi\)
\(564\) −2.05506 −0.0865336
\(565\) 7.13607 0.300217
\(566\) −8.06556 −0.339021
\(567\) 14.8406 0.623247
\(568\) 14.0841 0.590955
\(569\) −29.7085 −1.24544 −0.622722 0.782443i \(-0.713973\pi\)
−0.622722 + 0.782443i \(0.713973\pi\)
\(570\) −0.235037 −0.00984462
\(571\) 10.0609 0.421035 0.210518 0.977590i \(-0.432485\pi\)
0.210518 + 0.977590i \(0.432485\pi\)
\(572\) −9.26235 −0.387278
\(573\) 2.24280 0.0936945
\(574\) 1.63141 0.0680937
\(575\) 6.95521 0.290052
\(576\) 8.02000 0.334167
\(577\) 3.65440 0.152134 0.0760672 0.997103i \(-0.475764\pi\)
0.0760672 + 0.997103i \(0.475764\pi\)
\(578\) −7.17296 −0.298356
\(579\) 2.41088 0.100193
\(580\) −7.42063 −0.308125
\(581\) −0.0435355 −0.00180616
\(582\) 0.576513 0.0238972
\(583\) −6.71231 −0.277995
\(584\) 6.73542 0.278714
\(585\) 7.77181 0.321325
\(586\) 15.9923 0.660638
\(587\) −42.0903 −1.73725 −0.868627 0.495467i \(-0.834997\pi\)
−0.868627 + 0.495467i \(0.834997\pi\)
\(588\) −0.980907 −0.0404519
\(589\) −13.6201 −0.561205
\(590\) 0.840222 0.0345914
\(591\) −1.75627 −0.0722434
\(592\) 15.7304 0.646515
\(593\) −4.67197 −0.191855 −0.0959274 0.995388i \(-0.530582\pi\)
−0.0959274 + 0.995388i \(0.530582\pi\)
\(594\) 0.396677 0.0162759
\(595\) −1.31890 −0.0540695
\(596\) −1.78674 −0.0731877
\(597\) −2.43642 −0.0997159
\(598\) −3.82834 −0.156552
\(599\) −7.98355 −0.326199 −0.163100 0.986610i \(-0.552149\pi\)
−0.163100 + 0.986610i \(0.552149\pi\)
\(600\) −1.18406 −0.0483389
\(601\) 9.75081 0.397744 0.198872 0.980025i \(-0.436272\pi\)
0.198872 + 0.980025i \(0.436272\pi\)
\(602\) −7.33809 −0.299078
\(603\) 23.6304 0.962304
\(604\) −36.7279 −1.49444
\(605\) −0.493567 −0.0200663
\(606\) −0.599335 −0.0243463
\(607\) 7.41998 0.301168 0.150584 0.988597i \(-0.451885\pi\)
0.150584 + 0.988597i \(0.451885\pi\)
\(608\) −35.9406 −1.45758
\(609\) 1.92448 0.0779838
\(610\) 1.39955 0.0566663
\(611\) −46.2541 −1.87124
\(612\) 8.32583 0.336552
\(613\) 27.0577 1.09285 0.546426 0.837508i \(-0.315988\pi\)
0.546426 + 0.837508i \(0.315988\pi\)
\(614\) 5.61168 0.226469
\(615\) 0.129362 0.00521640
\(616\) −3.12514 −0.125916
\(617\) 2.03934 0.0821009 0.0410505 0.999157i \(-0.486930\pi\)
0.0410505 + 0.999157i \(0.486930\pi\)
\(618\) 0.0630933 0.00253798
\(619\) −11.0858 −0.445576 −0.222788 0.974867i \(-0.571516\pi\)
−0.222788 + 0.974867i \(0.571516\pi\)
\(620\) 1.64205 0.0659463
\(621\) −1.16989 −0.0469460
\(622\) 10.1515 0.407036
\(623\) −22.2529 −0.891544
\(624\) −1.82573 −0.0730876
\(625\) 21.4052 0.856209
\(626\) −4.40741 −0.176156
\(627\) 0.960428 0.0383558
\(628\) −10.0941 −0.402799
\(629\) 9.68379 0.386118
\(630\) 1.22526 0.0488154
\(631\) −2.14166 −0.0852583 −0.0426291 0.999091i \(-0.513573\pi\)
−0.0426291 + 0.999091i \(0.513573\pi\)
\(632\) −28.1007 −1.11779
\(633\) −0.629329 −0.0250136
\(634\) −9.08818 −0.360938
\(635\) 2.45134 0.0972785
\(636\) −1.57470 −0.0624409
\(637\) −22.0777 −0.874750
\(638\) −4.24963 −0.168244
\(639\) 22.5639 0.892614
\(640\) 5.59844 0.221298
\(641\) 19.3356 0.763710 0.381855 0.924222i \(-0.375285\pi\)
0.381855 + 0.924222i \(0.375285\pi\)
\(642\) −0.654119 −0.0258160
\(643\) −45.6817 −1.80151 −0.900756 0.434325i \(-0.856987\pi\)
−0.900756 + 0.434325i \(0.856987\pi\)
\(644\) 4.30659 0.169703
\(645\) −0.581874 −0.0229113
\(646\) −5.66719 −0.222973
\(647\) −44.2889 −1.74118 −0.870589 0.492012i \(-0.836262\pi\)
−0.870589 + 0.492012i \(0.836262\pi\)
\(648\) −16.4535 −0.646355
\(649\) −3.43339 −0.134772
\(650\) −12.4525 −0.488426
\(651\) −0.425852 −0.0166905
\(652\) −0.665346 −0.0260570
\(653\) 7.33534 0.287054 0.143527 0.989646i \(-0.454156\pi\)
0.143527 + 0.989646i \(0.454156\pi\)
\(654\) −1.37872 −0.0539121
\(655\) −0.493567 −0.0192853
\(656\) 5.06680 0.197825
\(657\) 10.7907 0.420986
\(658\) −7.29215 −0.284278
\(659\) −3.15542 −0.122918 −0.0614588 0.998110i \(-0.519575\pi\)
−0.0614588 + 0.998110i \(0.519575\pi\)
\(660\) −0.115790 −0.00450713
\(661\) 30.3021 1.17862 0.589308 0.807908i \(-0.299400\pi\)
0.589308 + 0.807908i \(0.299400\pi\)
\(662\) 11.8414 0.460231
\(663\) −1.12394 −0.0436501
\(664\) 0.0482670 0.00187312
\(665\) 5.95094 0.230767
\(666\) −8.99625 −0.348598
\(667\) 12.5331 0.485283
\(668\) 36.4712 1.41111
\(669\) −3.66192 −0.141578
\(670\) 1.93918 0.0749171
\(671\) −5.71897 −0.220779
\(672\) −1.12374 −0.0433491
\(673\) 31.2761 1.20561 0.602803 0.797890i \(-0.294050\pi\)
0.602803 + 0.797890i \(0.294050\pi\)
\(674\) 8.91995 0.343583
\(675\) −3.80530 −0.146466
\(676\) −26.1031 −1.00397
\(677\) 40.5803 1.55963 0.779815 0.626011i \(-0.215313\pi\)
0.779815 + 0.626011i \(0.215313\pi\)
\(678\) 0.958727 0.0368197
\(679\) −14.5968 −0.560174
\(680\) 1.46224 0.0560743
\(681\) 1.80479 0.0691598
\(682\) 0.940366 0.0360085
\(683\) −2.36606 −0.0905346 −0.0452673 0.998975i \(-0.514414\pi\)
−0.0452673 + 0.998975i \(0.514414\pi\)
\(684\) −37.5666 −1.43639
\(685\) −5.56313 −0.212556
\(686\) −9.30778 −0.355373
\(687\) −2.30331 −0.0878768
\(688\) −22.7905 −0.868880
\(689\) −35.4424 −1.35025
\(690\) −0.0478587 −0.00182195
\(691\) −23.0434 −0.876613 −0.438307 0.898826i \(-0.644422\pi\)
−0.438307 + 0.898826i \(0.644422\pi\)
\(692\) −1.89311 −0.0719653
\(693\) −5.00675 −0.190191
\(694\) −7.07195 −0.268447
\(695\) 5.95201 0.225773
\(696\) −2.13364 −0.0808753
\(697\) 3.11917 0.118147
\(698\) −9.68639 −0.366635
\(699\) −3.23455 −0.122342
\(700\) 14.0081 0.529455
\(701\) −41.0188 −1.54926 −0.774629 0.632416i \(-0.782063\pi\)
−0.774629 + 0.632416i \(0.782063\pi\)
\(702\) 2.09454 0.0790534
\(703\) −43.6938 −1.64794
\(704\) −2.68937 −0.101359
\(705\) −0.578231 −0.0217774
\(706\) 7.49514 0.282083
\(707\) 15.1747 0.570701
\(708\) −0.805468 −0.0302714
\(709\) 22.1323 0.831197 0.415599 0.909548i \(-0.363572\pi\)
0.415599 + 0.909548i \(0.363572\pi\)
\(710\) 1.85166 0.0694916
\(711\) −45.0198 −1.68837
\(712\) 24.6714 0.924600
\(713\) −2.77335 −0.103863
\(714\) −0.177193 −0.00663129
\(715\) −2.60614 −0.0974641
\(716\) 26.8131 1.00205
\(717\) −2.99921 −0.112008
\(718\) −0.345241 −0.0128843
\(719\) −42.8153 −1.59674 −0.798370 0.602167i \(-0.794304\pi\)
−0.798370 + 0.602167i \(0.794304\pi\)
\(720\) 3.80538 0.141818
\(721\) −1.59747 −0.0594928
\(722\) 16.1500 0.601043
\(723\) 1.28749 0.0478825
\(724\) 36.8596 1.36988
\(725\) 40.7664 1.51403
\(726\) −0.0663105 −0.00246101
\(727\) −3.03429 −0.112536 −0.0562678 0.998416i \(-0.517920\pi\)
−0.0562678 + 0.998416i \(0.517920\pi\)
\(728\) −16.5014 −0.611584
\(729\) −26.0389 −0.964406
\(730\) 0.885519 0.0327745
\(731\) −14.0301 −0.518921
\(732\) −1.34166 −0.0495894
\(733\) 12.6004 0.465405 0.232702 0.972548i \(-0.425243\pi\)
0.232702 + 0.972548i \(0.425243\pi\)
\(734\) 8.55551 0.315789
\(735\) −0.275997 −0.0101803
\(736\) −7.31829 −0.269756
\(737\) −7.92404 −0.291886
\(738\) −2.89772 −0.106666
\(739\) 12.8976 0.474446 0.237223 0.971455i \(-0.423763\pi\)
0.237223 + 0.971455i \(0.423763\pi\)
\(740\) 5.26777 0.193647
\(741\) 5.07127 0.186298
\(742\) −5.58764 −0.205129
\(743\) −19.7920 −0.726098 −0.363049 0.931770i \(-0.618264\pi\)
−0.363049 + 0.931770i \(0.618264\pi\)
\(744\) 0.472135 0.0173093
\(745\) −0.502733 −0.0184187
\(746\) 18.0832 0.662072
\(747\) 0.0773279 0.00282928
\(748\) −2.79192 −0.102083
\(749\) 16.5617 0.605153
\(750\) −0.319314 −0.0116597
\(751\) 39.9885 1.45920 0.729600 0.683874i \(-0.239706\pi\)
0.729600 + 0.683874i \(0.239706\pi\)
\(752\) −22.6478 −0.825881
\(753\) −1.66345 −0.0606194
\(754\) −22.4390 −0.817179
\(755\) −10.3341 −0.376096
\(756\) −2.35620 −0.0856941
\(757\) −26.4640 −0.961852 −0.480926 0.876761i \(-0.659699\pi\)
−0.480926 + 0.876761i \(0.659699\pi\)
\(758\) −7.82912 −0.284367
\(759\) 0.195564 0.00709853
\(760\) −6.59770 −0.239324
\(761\) 6.70772 0.243155 0.121577 0.992582i \(-0.461205\pi\)
0.121577 + 0.992582i \(0.461205\pi\)
\(762\) 0.329337 0.0119306
\(763\) 34.9079 1.26375
\(764\) 29.4174 1.06428
\(765\) 2.34263 0.0846980
\(766\) 13.9114 0.502638
\(767\) −18.1290 −0.654601
\(768\) 0.0328046 0.00118373
\(769\) 4.82752 0.174085 0.0870423 0.996205i \(-0.472258\pi\)
0.0870423 + 0.996205i \(0.472258\pi\)
\(770\) −0.410869 −0.0148067
\(771\) 1.98300 0.0714162
\(772\) 31.6219 1.13810
\(773\) 42.0235 1.51148 0.755740 0.654872i \(-0.227278\pi\)
0.755740 + 0.654872i \(0.227278\pi\)
\(774\) 13.0340 0.468496
\(775\) −9.02088 −0.324040
\(776\) 16.1832 0.580944
\(777\) −1.36615 −0.0490105
\(778\) 17.4359 0.625109
\(779\) −14.0739 −0.504249
\(780\) −0.611398 −0.0218915
\(781\) −7.56641 −0.270747
\(782\) −1.15396 −0.0412657
\(783\) −6.85704 −0.245050
\(784\) −10.8101 −0.386075
\(785\) −2.84018 −0.101370
\(786\) −0.0663105 −0.00236522
\(787\) 13.4224 0.478457 0.239229 0.970963i \(-0.423105\pi\)
0.239229 + 0.970963i \(0.423105\pi\)
\(788\) −23.0359 −0.820619
\(789\) 1.91979 0.0683462
\(790\) −3.69446 −0.131443
\(791\) −24.2742 −0.863090
\(792\) 5.55089 0.197242
\(793\) −30.1974 −1.07234
\(794\) 1.94587 0.0690562
\(795\) −0.443072 −0.0157141
\(796\) −31.9569 −1.13268
\(797\) −29.5569 −1.04696 −0.523480 0.852038i \(-0.675367\pi\)
−0.523480 + 0.852038i \(0.675367\pi\)
\(798\) 0.799506 0.0283022
\(799\) −13.9422 −0.493241
\(800\) −23.8043 −0.841608
\(801\) 39.5257 1.39657
\(802\) −14.6512 −0.517351
\(803\) −3.61848 −0.127693
\(804\) −1.85897 −0.0655608
\(805\) 1.21174 0.0427083
\(806\) 4.96534 0.174897
\(807\) −1.51373 −0.0532858
\(808\) −16.8239 −0.591862
\(809\) −28.8347 −1.01377 −0.506886 0.862013i \(-0.669204\pi\)
−0.506886 + 0.862013i \(0.669204\pi\)
\(810\) −2.16318 −0.0760063
\(811\) −6.05999 −0.212795 −0.106397 0.994324i \(-0.533932\pi\)
−0.106397 + 0.994324i \(0.533932\pi\)
\(812\) 25.2421 0.885825
\(813\) 1.57825 0.0553516
\(814\) 3.01674 0.105737
\(815\) −0.187208 −0.00655761
\(816\) −0.550324 −0.0192652
\(817\) 63.3045 2.21474
\(818\) 5.81503 0.203318
\(819\) −26.4367 −0.923773
\(820\) 1.69676 0.0592535
\(821\) −13.3298 −0.465214 −0.232607 0.972571i \(-0.574726\pi\)
−0.232607 + 0.972571i \(0.574726\pi\)
\(822\) −0.747405 −0.0260687
\(823\) 14.0190 0.488672 0.244336 0.969691i \(-0.421430\pi\)
0.244336 + 0.969691i \(0.421430\pi\)
\(824\) 1.77108 0.0616986
\(825\) 0.636113 0.0221466
\(826\) −2.85811 −0.0994465
\(827\) 4.30220 0.149602 0.0748011 0.997198i \(-0.476168\pi\)
0.0748011 + 0.997198i \(0.476168\pi\)
\(828\) −7.64938 −0.265834
\(829\) 2.30813 0.0801648 0.0400824 0.999196i \(-0.487238\pi\)
0.0400824 + 0.999196i \(0.487238\pi\)
\(830\) 0.00634576 0.000220265 0
\(831\) 2.06413 0.0716040
\(832\) −14.2004 −0.492312
\(833\) −6.65481 −0.230576
\(834\) 0.799651 0.0276896
\(835\) 10.2619 0.355127
\(836\) 12.5973 0.435687
\(837\) 1.51734 0.0524469
\(838\) −5.72145 −0.197644
\(839\) 3.84974 0.132908 0.0664539 0.997789i \(-0.478831\pi\)
0.0664539 + 0.997789i \(0.478831\pi\)
\(840\) −0.206287 −0.00711759
\(841\) 44.4599 1.53310
\(842\) −16.3719 −0.564214
\(843\) 1.68861 0.0581590
\(844\) −8.25450 −0.284131
\(845\) −7.34462 −0.252663
\(846\) 12.9523 0.445311
\(847\) 1.67893 0.0576885
\(848\) −17.3540 −0.595939
\(849\) 2.17553 0.0746640
\(850\) −3.75351 −0.128744
\(851\) −8.89702 −0.304986
\(852\) −1.77507 −0.0608129
\(853\) 44.7596 1.53254 0.766270 0.642519i \(-0.222111\pi\)
0.766270 + 0.642519i \(0.222111\pi\)
\(854\) −4.76075 −0.162909
\(855\) −10.5701 −0.361489
\(856\) −18.3617 −0.627591
\(857\) 29.9863 1.02431 0.512156 0.858893i \(-0.328847\pi\)
0.512156 + 0.858893i \(0.328847\pi\)
\(858\) −0.350134 −0.0119534
\(859\) 32.9772 1.12517 0.562584 0.826740i \(-0.309807\pi\)
0.562584 + 0.826740i \(0.309807\pi\)
\(860\) −7.63206 −0.260251
\(861\) −0.440042 −0.0149966
\(862\) 0.518246 0.0176515
\(863\) −56.3255 −1.91734 −0.958672 0.284515i \(-0.908167\pi\)
−0.958672 + 0.284515i \(0.908167\pi\)
\(864\) 4.00395 0.136217
\(865\) −0.532663 −0.0181111
\(866\) −3.10599 −0.105546
\(867\) 1.93477 0.0657082
\(868\) −5.58563 −0.189589
\(869\) 15.0966 0.512117
\(870\) −0.280513 −0.00951029
\(871\) −41.8406 −1.41772
\(872\) −38.7018 −1.31061
\(873\) 25.9269 0.877493
\(874\) 5.20675 0.176121
\(875\) 8.08475 0.273314
\(876\) −0.848892 −0.0286814
\(877\) 16.5114 0.557550 0.278775 0.960356i \(-0.410072\pi\)
0.278775 + 0.960356i \(0.410072\pi\)
\(878\) −0.0354686 −0.00119701
\(879\) −4.31363 −0.145495
\(880\) −1.27607 −0.0430162
\(881\) −0.219342 −0.00738981 −0.00369490 0.999993i \(-0.501176\pi\)
−0.00369490 + 0.999993i \(0.501176\pi\)
\(882\) 6.18233 0.208170
\(883\) 32.3565 1.08888 0.544442 0.838799i \(-0.316742\pi\)
0.544442 + 0.838799i \(0.316742\pi\)
\(884\) −14.7419 −0.495825
\(885\) −0.226634 −0.00761822
\(886\) −6.96829 −0.234104
\(887\) −57.3089 −1.92425 −0.962123 0.272617i \(-0.912111\pi\)
−0.962123 + 0.272617i \(0.912111\pi\)
\(888\) 1.51463 0.0508277
\(889\) −8.33852 −0.279665
\(890\) 3.24360 0.108726
\(891\) 8.83935 0.296129
\(892\) −48.0310 −1.60820
\(893\) 62.9081 2.10514
\(894\) −0.0675420 −0.00225894
\(895\) 7.54439 0.252181
\(896\) −19.0438 −0.636207
\(897\) 1.03262 0.0344782
\(898\) 6.42448 0.214388
\(899\) −16.2554 −0.542146
\(900\) −24.8812 −0.829373
\(901\) −10.6833 −0.355912
\(902\) 0.971698 0.0323540
\(903\) 1.97931 0.0658674
\(904\) 26.9123 0.895091
\(905\) 10.3712 0.344749
\(906\) −1.38838 −0.0461259
\(907\) 21.2091 0.704236 0.352118 0.935956i \(-0.385462\pi\)
0.352118 + 0.935956i \(0.385462\pi\)
\(908\) 23.6723 0.785592
\(909\) −26.9533 −0.893984
\(910\) −2.16948 −0.0719174
\(911\) 25.9210 0.858803 0.429401 0.903114i \(-0.358725\pi\)
0.429401 + 0.903114i \(0.358725\pi\)
\(912\) 2.48309 0.0822234
\(913\) −0.0259306 −0.000858176 0
\(914\) 16.8300 0.556686
\(915\) −0.377503 −0.0124799
\(916\) −30.2110 −0.998200
\(917\) 1.67893 0.0554430
\(918\) 0.631351 0.0208377
\(919\) 6.73660 0.222220 0.111110 0.993808i \(-0.464559\pi\)
0.111110 + 0.993808i \(0.464559\pi\)
\(920\) −1.34344 −0.0442918
\(921\) −1.51364 −0.0498763
\(922\) 0.0136920 0.000450924 0
\(923\) −39.9523 −1.31505
\(924\) 0.393874 0.0129575
\(925\) −28.9394 −0.951521
\(926\) −3.40684 −0.111956
\(927\) 2.83743 0.0931934
\(928\) −42.8946 −1.40808
\(929\) 38.9868 1.27911 0.639557 0.768744i \(-0.279118\pi\)
0.639557 + 0.768744i \(0.279118\pi\)
\(930\) 0.0620726 0.00203544
\(931\) 30.0269 0.984091
\(932\) −42.4255 −1.38969
\(933\) −2.73816 −0.0896434
\(934\) −17.2686 −0.565047
\(935\) −0.785561 −0.0256906
\(936\) 29.3099 0.958025
\(937\) 34.4896 1.12673 0.563363 0.826209i \(-0.309507\pi\)
0.563363 + 0.826209i \(0.309507\pi\)
\(938\) −6.59635 −0.215378
\(939\) 1.18882 0.0387955
\(940\) −7.58427 −0.247372
\(941\) 32.6353 1.06388 0.531940 0.846782i \(-0.321463\pi\)
0.531940 + 0.846782i \(0.321463\pi\)
\(942\) −0.381576 −0.0124324
\(943\) −2.86575 −0.0933217
\(944\) −8.87668 −0.288911
\(945\) −0.662962 −0.0215662
\(946\) −4.37071 −0.142104
\(947\) 5.15503 0.167516 0.0837580 0.996486i \(-0.473308\pi\)
0.0837580 + 0.996486i \(0.473308\pi\)
\(948\) 3.54164 0.115027
\(949\) −19.1064 −0.620219
\(950\) 16.9360 0.549477
\(951\) 2.45136 0.0794909
\(952\) −4.97398 −0.161207
\(953\) 24.2889 0.786795 0.393397 0.919369i \(-0.371300\pi\)
0.393397 + 0.919369i \(0.371300\pi\)
\(954\) 9.92480 0.321327
\(955\) 8.27715 0.267842
\(956\) −39.3387 −1.27230
\(957\) 1.14626 0.0370532
\(958\) −11.6877 −0.377613
\(959\) 18.9236 0.611076
\(960\) −0.177522 −0.00572950
\(961\) −27.4030 −0.883967
\(962\) 15.9290 0.513572
\(963\) −29.4170 −0.947951
\(964\) 16.8872 0.543901
\(965\) 8.89744 0.286419
\(966\) 0.162797 0.00523791
\(967\) −59.4072 −1.91041 −0.955203 0.295951i \(-0.904364\pi\)
−0.955203 + 0.295951i \(0.904364\pi\)
\(968\) −1.86140 −0.0598275
\(969\) 1.52862 0.0491062
\(970\) 2.12764 0.0683144
\(971\) −6.97321 −0.223781 −0.111890 0.993721i \(-0.535691\pi\)
−0.111890 + 0.993721i \(0.535691\pi\)
\(972\) 6.28389 0.201556
\(973\) −20.2465 −0.649072
\(974\) 11.0537 0.354182
\(975\) 3.35881 0.107568
\(976\) −14.7858 −0.473283
\(977\) 32.2743 1.03255 0.516273 0.856424i \(-0.327319\pi\)
0.516273 + 0.856424i \(0.327319\pi\)
\(978\) −0.0251513 −0.000804251 0
\(979\) −13.2543 −0.423608
\(980\) −3.62007 −0.115639
\(981\) −62.0036 −1.97962
\(982\) −15.6927 −0.500773
\(983\) −18.8500 −0.601221 −0.300611 0.953747i \(-0.597190\pi\)
−0.300611 + 0.953747i \(0.597190\pi\)
\(984\) 0.487866 0.0155526
\(985\) −6.48159 −0.206521
\(986\) −6.76370 −0.215400
\(987\) 1.96692 0.0626077
\(988\) 66.5165 2.11617
\(989\) 12.8902 0.409884
\(990\) 0.729787 0.0231941
\(991\) −24.5367 −0.779436 −0.389718 0.920934i \(-0.627427\pi\)
−0.389718 + 0.920934i \(0.627427\pi\)
\(992\) 9.49179 0.301365
\(993\) −3.19400 −0.101359
\(994\) −6.29864 −0.199781
\(995\) −8.99168 −0.285056
\(996\) −0.00608328 −0.000192756 0
\(997\) −43.5102 −1.37798 −0.688992 0.724769i \(-0.741946\pi\)
−0.688992 + 0.724769i \(0.741946\pi\)
\(998\) 11.1937 0.354329
\(999\) 4.86769 0.154007
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 1441.2.a.c.1.15 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.c.1.15 23 1.1 even 1 trivial