Properties

Label 4033.2.a.d.1.64
Level $4033$
Weight $2$
Character 4033.1
Self dual yes
Analytic conductor $32.204$
Analytic rank $1$
Dimension $79$
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] = [4033,2,Mod(1,4033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4033, 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("4033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4033 = 37 \cdot 109 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4033.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: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.64
Character \(\chi\) \(=\) 4033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.63648 q^{2} +1.67074 q^{3} +0.678051 q^{4} +1.47944 q^{5} +2.73412 q^{6} -2.83994 q^{7} -2.16334 q^{8} -0.208643 q^{9} +O(q^{10})\) \(q+1.63648 q^{2} +1.67074 q^{3} +0.678051 q^{4} +1.47944 q^{5} +2.73412 q^{6} -2.83994 q^{7} -2.16334 q^{8} -0.208643 q^{9} +2.42106 q^{10} +1.80916 q^{11} +1.13284 q^{12} -4.94134 q^{13} -4.64749 q^{14} +2.47175 q^{15} -4.89635 q^{16} -1.34129 q^{17} -0.341439 q^{18} +2.42257 q^{19} +1.00313 q^{20} -4.74479 q^{21} +2.96065 q^{22} -1.31284 q^{23} -3.61436 q^{24} -2.81126 q^{25} -8.08637 q^{26} -5.36079 q^{27} -1.92562 q^{28} -9.70408 q^{29} +4.04496 q^{30} +3.85932 q^{31} -3.68608 q^{32} +3.02263 q^{33} -2.19498 q^{34} -4.20151 q^{35} -0.141471 q^{36} -1.00000 q^{37} +3.96448 q^{38} -8.25567 q^{39} -3.20052 q^{40} -4.26082 q^{41} -7.76473 q^{42} +1.97772 q^{43} +1.22670 q^{44} -0.308674 q^{45} -2.14843 q^{46} +12.1650 q^{47} -8.18050 q^{48} +1.06525 q^{49} -4.60056 q^{50} -2.24094 q^{51} -3.35048 q^{52} -11.6517 q^{53} -8.77281 q^{54} +2.67654 q^{55} +6.14374 q^{56} +4.04748 q^{57} -15.8805 q^{58} +4.85443 q^{59} +1.67597 q^{60} -6.17621 q^{61} +6.31567 q^{62} +0.592533 q^{63} +3.76052 q^{64} -7.31040 q^{65} +4.94646 q^{66} -9.53293 q^{67} -0.909462 q^{68} -2.19341 q^{69} -6.87567 q^{70} +7.27131 q^{71} +0.451365 q^{72} +15.8618 q^{73} -1.63648 q^{74} -4.69688 q^{75} +1.64263 q^{76} -5.13791 q^{77} -13.5102 q^{78} +8.53665 q^{79} -7.24384 q^{80} -8.33054 q^{81} -6.97272 q^{82} +0.979738 q^{83} -3.21721 q^{84} -1.98435 q^{85} +3.23649 q^{86} -16.2130 q^{87} -3.91383 q^{88} +0.458112 q^{89} -0.505138 q^{90} +14.0331 q^{91} -0.890173 q^{92} +6.44789 q^{93} +19.9078 q^{94} +3.58405 q^{95} -6.15846 q^{96} -18.0435 q^{97} +1.74326 q^{98} -0.377469 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.63648 1.15716 0.578581 0.815625i \(-0.303607\pi\)
0.578581 + 0.815625i \(0.303607\pi\)
\(3\) 1.67074 0.964600 0.482300 0.876006i \(-0.339802\pi\)
0.482300 + 0.876006i \(0.339802\pi\)
\(4\) 0.678051 0.339026
\(5\) 1.47944 0.661625 0.330812 0.943697i \(-0.392677\pi\)
0.330812 + 0.943697i \(0.392677\pi\)
\(6\) 2.73412 1.11620
\(7\) −2.83994 −1.07340 −0.536698 0.843774i \(-0.680329\pi\)
−0.536698 + 0.843774i \(0.680329\pi\)
\(8\) −2.16334 −0.764855
\(9\) −0.208643 −0.0695476
\(10\) 2.42106 0.765608
\(11\) 1.80916 0.545483 0.272742 0.962087i \(-0.412070\pi\)
0.272742 + 0.962087i \(0.412070\pi\)
\(12\) 1.13284 0.327024
\(13\) −4.94134 −1.37048 −0.685240 0.728317i \(-0.740303\pi\)
−0.685240 + 0.728317i \(0.740303\pi\)
\(14\) −4.64749 −1.24209
\(15\) 2.47175 0.638203
\(16\) −4.89635 −1.22409
\(17\) −1.34129 −0.325310 −0.162655 0.986683i \(-0.552006\pi\)
−0.162655 + 0.986683i \(0.552006\pi\)
\(18\) −0.341439 −0.0804779
\(19\) 2.42257 0.555776 0.277888 0.960613i \(-0.410366\pi\)
0.277888 + 0.960613i \(0.410366\pi\)
\(20\) 1.00313 0.224308
\(21\) −4.74479 −1.03540
\(22\) 2.96065 0.631213
\(23\) −1.31284 −0.273746 −0.136873 0.990589i \(-0.543705\pi\)
−0.136873 + 0.990589i \(0.543705\pi\)
\(24\) −3.61436 −0.737779
\(25\) −2.81126 −0.562253
\(26\) −8.08637 −1.58587
\(27\) −5.36079 −1.03169
\(28\) −1.92562 −0.363909
\(29\) −9.70408 −1.80200 −0.901001 0.433816i \(-0.857167\pi\)
−0.901001 + 0.433816i \(0.857167\pi\)
\(30\) 4.04496 0.738505
\(31\) 3.85932 0.693153 0.346577 0.938022i \(-0.387344\pi\)
0.346577 + 0.938022i \(0.387344\pi\)
\(32\) −3.68608 −0.651613
\(33\) 3.02263 0.526173
\(34\) −2.19498 −0.376437
\(35\) −4.20151 −0.710185
\(36\) −0.141471 −0.0235784
\(37\) −1.00000 −0.164399
\(38\) 3.96448 0.643124
\(39\) −8.25567 −1.32196
\(40\) −3.20052 −0.506047
\(41\) −4.26082 −0.665428 −0.332714 0.943028i \(-0.607964\pi\)
−0.332714 + 0.943028i \(0.607964\pi\)
\(42\) −7.76473 −1.19812
\(43\) 1.97772 0.301599 0.150800 0.988564i \(-0.451815\pi\)
0.150800 + 0.988564i \(0.451815\pi\)
\(44\) 1.22670 0.184933
\(45\) −0.308674 −0.0460144
\(46\) −2.14843 −0.316769
\(47\) 12.1650 1.77445 0.887226 0.461336i \(-0.152630\pi\)
0.887226 + 0.461336i \(0.152630\pi\)
\(48\) −8.18050 −1.18075
\(49\) 1.06525 0.152179
\(50\) −4.60056 −0.650618
\(51\) −2.24094 −0.313794
\(52\) −3.35048 −0.464628
\(53\) −11.6517 −1.60048 −0.800240 0.599680i \(-0.795295\pi\)
−0.800240 + 0.599680i \(0.795295\pi\)
\(54\) −8.77281 −1.19383
\(55\) 2.67654 0.360905
\(56\) 6.14374 0.820992
\(57\) 4.04748 0.536102
\(58\) −15.8805 −2.08521
\(59\) 4.85443 0.631994 0.315997 0.948760i \(-0.397661\pi\)
0.315997 + 0.948760i \(0.397661\pi\)
\(60\) 1.67597 0.216367
\(61\) −6.17621 −0.790782 −0.395391 0.918513i \(-0.629391\pi\)
−0.395391 + 0.918513i \(0.629391\pi\)
\(62\) 6.31567 0.802091
\(63\) 0.592533 0.0746522
\(64\) 3.76052 0.470065
\(65\) −7.31040 −0.906744
\(66\) 4.94646 0.608867
\(67\) −9.53293 −1.16463 −0.582317 0.812962i \(-0.697854\pi\)
−0.582317 + 0.812962i \(0.697854\pi\)
\(68\) −0.909462 −0.110288
\(69\) −2.19341 −0.264056
\(70\) −6.87567 −0.821800
\(71\) 7.27131 0.862946 0.431473 0.902126i \(-0.357994\pi\)
0.431473 + 0.902126i \(0.357994\pi\)
\(72\) 0.451365 0.0531939
\(73\) 15.8618 1.85648 0.928239 0.371984i \(-0.121323\pi\)
0.928239 + 0.371984i \(0.121323\pi\)
\(74\) −1.63648 −0.190236
\(75\) −4.69688 −0.542349
\(76\) 1.64263 0.188422
\(77\) −5.13791 −0.585519
\(78\) −13.5102 −1.52973
\(79\) 8.53665 0.960449 0.480224 0.877146i \(-0.340555\pi\)
0.480224 + 0.877146i \(0.340555\pi\)
\(80\) −7.24384 −0.809886
\(81\) −8.33054 −0.925615
\(82\) −6.97272 −0.770008
\(83\) 0.979738 0.107540 0.0537701 0.998553i \(-0.482876\pi\)
0.0537701 + 0.998553i \(0.482876\pi\)
\(84\) −3.21721 −0.351026
\(85\) −1.98435 −0.215233
\(86\) 3.23649 0.348999
\(87\) −16.2130 −1.73821
\(88\) −3.91383 −0.417215
\(89\) 0.458112 0.0485597 0.0242799 0.999705i \(-0.492271\pi\)
0.0242799 + 0.999705i \(0.492271\pi\)
\(90\) −0.505138 −0.0532462
\(91\) 14.0331 1.47107
\(92\) −0.890173 −0.0928070
\(93\) 6.44789 0.668616
\(94\) 19.9078 2.05333
\(95\) 3.58405 0.367715
\(96\) −6.15846 −0.628546
\(97\) −18.0435 −1.83204 −0.916020 0.401132i \(-0.868617\pi\)
−0.916020 + 0.401132i \(0.868617\pi\)
\(98\) 1.74326 0.176096
\(99\) −0.377469 −0.0379371
\(100\) −1.90618 −0.190618
\(101\) 7.48057 0.744345 0.372172 0.928164i \(-0.378613\pi\)
0.372172 + 0.928164i \(0.378613\pi\)
\(102\) −3.66724 −0.363111
\(103\) 7.66146 0.754906 0.377453 0.926029i \(-0.376800\pi\)
0.377453 + 0.926029i \(0.376800\pi\)
\(104\) 10.6898 1.04822
\(105\) −7.01962 −0.685045
\(106\) −19.0677 −1.85202
\(107\) −15.6190 −1.50995 −0.754975 0.655754i \(-0.772351\pi\)
−0.754975 + 0.655754i \(0.772351\pi\)
\(108\) −3.63489 −0.349768
\(109\) −1.00000 −0.0957826
\(110\) 4.38010 0.417626
\(111\) −1.67074 −0.158579
\(112\) 13.9053 1.31393
\(113\) −7.46276 −0.702037 −0.351019 0.936368i \(-0.614165\pi\)
−0.351019 + 0.936368i \(0.614165\pi\)
\(114\) 6.62360 0.620357
\(115\) −1.94227 −0.181117
\(116\) −6.57986 −0.610925
\(117\) 1.03097 0.0953137
\(118\) 7.94416 0.731319
\(119\) 3.80918 0.349187
\(120\) −5.34723 −0.488133
\(121\) −7.72693 −0.702448
\(122\) −10.1072 −0.915064
\(123\) −7.11870 −0.641872
\(124\) 2.61681 0.234997
\(125\) −11.5563 −1.03363
\(126\) 0.969666 0.0863847
\(127\) 11.0196 0.977832 0.488916 0.872331i \(-0.337393\pi\)
0.488916 + 0.872331i \(0.337393\pi\)
\(128\) 13.5262 1.19555
\(129\) 3.30425 0.290923
\(130\) −11.9633 −1.04925
\(131\) 2.23657 0.195410 0.0977049 0.995215i \(-0.468850\pi\)
0.0977049 + 0.995215i \(0.468850\pi\)
\(132\) 2.04950 0.178386
\(133\) −6.87996 −0.596568
\(134\) −15.6004 −1.34767
\(135\) −7.93096 −0.682588
\(136\) 2.90166 0.248815
\(137\) −8.04851 −0.687631 −0.343816 0.939037i \(-0.611719\pi\)
−0.343816 + 0.939037i \(0.611719\pi\)
\(138\) −3.58946 −0.305555
\(139\) 21.9618 1.86277 0.931387 0.364030i \(-0.118599\pi\)
0.931387 + 0.364030i \(0.118599\pi\)
\(140\) −2.84884 −0.240771
\(141\) 20.3245 1.71164
\(142\) 11.8993 0.998569
\(143\) −8.93968 −0.747574
\(144\) 1.02159 0.0851324
\(145\) −14.3566 −1.19225
\(146\) 25.9574 2.14825
\(147\) 1.77975 0.146792
\(148\) −0.678051 −0.0557355
\(149\) −10.2006 −0.835667 −0.417833 0.908524i \(-0.637210\pi\)
−0.417833 + 0.908524i \(0.637210\pi\)
\(150\) −7.68632 −0.627586
\(151\) −16.1784 −1.31658 −0.658289 0.752765i \(-0.728719\pi\)
−0.658289 + 0.752765i \(0.728719\pi\)
\(152\) −5.24084 −0.425088
\(153\) 0.279850 0.0226246
\(154\) −8.40806 −0.677541
\(155\) 5.70962 0.458607
\(156\) −5.59776 −0.448180
\(157\) 12.1022 0.965859 0.482929 0.875659i \(-0.339573\pi\)
0.482929 + 0.875659i \(0.339573\pi\)
\(158\) 13.9700 1.11140
\(159\) −19.4669 −1.54382
\(160\) −5.45333 −0.431123
\(161\) 3.72839 0.293838
\(162\) −13.6327 −1.07109
\(163\) 5.05421 0.395877 0.197938 0.980214i \(-0.436575\pi\)
0.197938 + 0.980214i \(0.436575\pi\)
\(164\) −2.88905 −0.225597
\(165\) 4.47180 0.348129
\(166\) 1.60332 0.124442
\(167\) −0.659764 −0.0510541 −0.0255270 0.999674i \(-0.508126\pi\)
−0.0255270 + 0.999674i \(0.508126\pi\)
\(168\) 10.2646 0.791929
\(169\) 11.4168 0.878215
\(170\) −3.24734 −0.249060
\(171\) −0.505453 −0.0386529
\(172\) 1.34099 0.102250
\(173\) 13.8511 1.05308 0.526540 0.850150i \(-0.323489\pi\)
0.526540 + 0.850150i \(0.323489\pi\)
\(174\) −26.5321 −2.01139
\(175\) 7.98382 0.603520
\(176\) −8.85829 −0.667719
\(177\) 8.11048 0.609621
\(178\) 0.749688 0.0561915
\(179\) −7.27609 −0.543840 −0.271920 0.962320i \(-0.587659\pi\)
−0.271920 + 0.962320i \(0.587659\pi\)
\(180\) −0.209297 −0.0156001
\(181\) −4.51957 −0.335937 −0.167968 0.985792i \(-0.553721\pi\)
−0.167968 + 0.985792i \(0.553721\pi\)
\(182\) 22.9648 1.70226
\(183\) −10.3188 −0.762788
\(184\) 2.84012 0.209376
\(185\) −1.47944 −0.108770
\(186\) 10.5518 0.773697
\(187\) −2.42661 −0.177451
\(188\) 8.24851 0.601584
\(189\) 15.2243 1.10741
\(190\) 5.86520 0.425507
\(191\) −8.53849 −0.617824 −0.308912 0.951091i \(-0.599965\pi\)
−0.308912 + 0.951091i \(0.599965\pi\)
\(192\) 6.28283 0.453424
\(193\) −6.57047 −0.472952 −0.236476 0.971637i \(-0.575993\pi\)
−0.236476 + 0.971637i \(0.575993\pi\)
\(194\) −29.5278 −2.11997
\(195\) −12.2137 −0.874644
\(196\) 0.722295 0.0515925
\(197\) −9.97993 −0.711041 −0.355520 0.934669i \(-0.615696\pi\)
−0.355520 + 0.934669i \(0.615696\pi\)
\(198\) −0.617719 −0.0438994
\(199\) −17.9787 −1.27448 −0.637240 0.770666i \(-0.719924\pi\)
−0.637240 + 0.770666i \(0.719924\pi\)
\(200\) 6.08171 0.430042
\(201\) −15.9270 −1.12340
\(202\) 12.2418 0.861328
\(203\) 27.5590 1.93426
\(204\) −1.51947 −0.106384
\(205\) −6.30362 −0.440264
\(206\) 12.5378 0.873549
\(207\) 0.273915 0.0190384
\(208\) 24.1945 1.67759
\(209\) 4.38283 0.303167
\(210\) −11.4874 −0.792708
\(211\) −6.82591 −0.469915 −0.234957 0.972006i \(-0.575495\pi\)
−0.234957 + 0.972006i \(0.575495\pi\)
\(212\) −7.90043 −0.542604
\(213\) 12.1484 0.832397
\(214\) −25.5602 −1.74726
\(215\) 2.92591 0.199546
\(216\) 11.5972 0.789090
\(217\) −10.9602 −0.744028
\(218\) −1.63648 −0.110836
\(219\) 26.5008 1.79076
\(220\) 1.81483 0.122356
\(221\) 6.62775 0.445831
\(222\) −2.73412 −0.183502
\(223\) −3.65951 −0.245059 −0.122530 0.992465i \(-0.539101\pi\)
−0.122530 + 0.992465i \(0.539101\pi\)
\(224\) 10.4682 0.699439
\(225\) 0.586550 0.0391033
\(226\) −12.2126 −0.812372
\(227\) 18.1893 1.20727 0.603634 0.797262i \(-0.293719\pi\)
0.603634 + 0.797262i \(0.293719\pi\)
\(228\) 2.74440 0.181752
\(229\) −7.02896 −0.464486 −0.232243 0.972658i \(-0.574607\pi\)
−0.232243 + 0.972658i \(0.574607\pi\)
\(230\) −3.17847 −0.209582
\(231\) −8.58409 −0.564792
\(232\) 20.9932 1.37827
\(233\) 14.4277 0.945188 0.472594 0.881280i \(-0.343318\pi\)
0.472594 + 0.881280i \(0.343318\pi\)
\(234\) 1.68716 0.110293
\(235\) 17.9974 1.17402
\(236\) 3.29155 0.214262
\(237\) 14.2625 0.926448
\(238\) 6.23362 0.404066
\(239\) −13.0374 −0.843316 −0.421658 0.906755i \(-0.638552\pi\)
−0.421658 + 0.906755i \(0.638552\pi\)
\(240\) −12.1025 −0.781216
\(241\) 8.67524 0.558821 0.279411 0.960172i \(-0.409861\pi\)
0.279411 + 0.960172i \(0.409861\pi\)
\(242\) −12.6449 −0.812847
\(243\) 2.16425 0.138837
\(244\) −4.18778 −0.268095
\(245\) 1.57597 0.100685
\(246\) −11.6496 −0.742750
\(247\) −11.9707 −0.761681
\(248\) −8.34900 −0.530162
\(249\) 1.63688 0.103733
\(250\) −18.9116 −1.19607
\(251\) 21.2054 1.33848 0.669238 0.743048i \(-0.266621\pi\)
0.669238 + 0.743048i \(0.266621\pi\)
\(252\) 0.401768 0.0253090
\(253\) −2.37514 −0.149324
\(254\) 18.0333 1.13151
\(255\) −3.31533 −0.207614
\(256\) 14.6142 0.913386
\(257\) 14.1597 0.883260 0.441630 0.897197i \(-0.354400\pi\)
0.441630 + 0.897197i \(0.354400\pi\)
\(258\) 5.40732 0.336645
\(259\) 2.83994 0.176465
\(260\) −4.95682 −0.307409
\(261\) 2.02469 0.125325
\(262\) 3.66009 0.226121
\(263\) 15.7356 0.970299 0.485149 0.874431i \(-0.338765\pi\)
0.485149 + 0.874431i \(0.338765\pi\)
\(264\) −6.53897 −0.402446
\(265\) −17.2379 −1.05892
\(266\) −11.2589 −0.690326
\(267\) 0.765383 0.0468407
\(268\) −6.46382 −0.394840
\(269\) −5.11460 −0.311843 −0.155921 0.987769i \(-0.549835\pi\)
−0.155921 + 0.987769i \(0.549835\pi\)
\(270\) −12.9788 −0.789866
\(271\) −18.6072 −1.13031 −0.565153 0.824986i \(-0.691183\pi\)
−0.565153 + 0.824986i \(0.691183\pi\)
\(272\) 6.56741 0.398208
\(273\) 23.4456 1.41899
\(274\) −13.1712 −0.795701
\(275\) −5.08603 −0.306699
\(276\) −1.48724 −0.0895216
\(277\) −9.02972 −0.542543 −0.271272 0.962503i \(-0.587444\pi\)
−0.271272 + 0.962503i \(0.587444\pi\)
\(278\) 35.9399 2.15553
\(279\) −0.805219 −0.0482072
\(280\) 9.08929 0.543189
\(281\) 13.5343 0.807391 0.403696 0.914893i \(-0.367725\pi\)
0.403696 + 0.914893i \(0.367725\pi\)
\(282\) 33.2606 1.98064
\(283\) 21.0111 1.24898 0.624491 0.781032i \(-0.285306\pi\)
0.624491 + 0.781032i \(0.285306\pi\)
\(284\) 4.93032 0.292561
\(285\) 5.98799 0.354698
\(286\) −14.6296 −0.865064
\(287\) 12.1005 0.714268
\(288\) 0.769075 0.0453182
\(289\) −15.2009 −0.894173
\(290\) −23.4942 −1.37963
\(291\) −30.1459 −1.76719
\(292\) 10.7551 0.629393
\(293\) 0.185923 0.0108617 0.00543086 0.999985i \(-0.498271\pi\)
0.00543086 + 0.999985i \(0.498271\pi\)
\(294\) 2.91252 0.169862
\(295\) 7.18184 0.418143
\(296\) 2.16334 0.125741
\(297\) −9.69855 −0.562767
\(298\) −16.6931 −0.967003
\(299\) 6.48719 0.375164
\(300\) −3.18472 −0.183870
\(301\) −5.61660 −0.323736
\(302\) −26.4755 −1.52349
\(303\) 12.4981 0.717995
\(304\) −11.8618 −0.680319
\(305\) −9.13732 −0.523201
\(306\) 0.457968 0.0261803
\(307\) −24.9431 −1.42358 −0.711788 0.702395i \(-0.752114\pi\)
−0.711788 + 0.702395i \(0.752114\pi\)
\(308\) −3.48377 −0.198506
\(309\) 12.8003 0.728182
\(310\) 9.34365 0.530683
\(311\) −6.04246 −0.342637 −0.171318 0.985216i \(-0.554803\pi\)
−0.171318 + 0.985216i \(0.554803\pi\)
\(312\) 17.8598 1.01111
\(313\) −16.0560 −0.907538 −0.453769 0.891119i \(-0.649921\pi\)
−0.453769 + 0.891119i \(0.649921\pi\)
\(314\) 19.8049 1.11766
\(315\) 0.876616 0.0493917
\(316\) 5.78829 0.325617
\(317\) −6.02432 −0.338359 −0.169180 0.985585i \(-0.554112\pi\)
−0.169180 + 0.985585i \(0.554112\pi\)
\(318\) −31.8570 −1.78645
\(319\) −17.5563 −0.982962
\(320\) 5.56346 0.311007
\(321\) −26.0953 −1.45650
\(322\) 6.10141 0.340018
\(323\) −3.24937 −0.180800
\(324\) −5.64853 −0.313807
\(325\) 13.8914 0.770556
\(326\) 8.27110 0.458094
\(327\) −1.67074 −0.0923919
\(328\) 9.21758 0.508956
\(329\) −34.5479 −1.90469
\(330\) 7.31798 0.402842
\(331\) 25.6176 1.40807 0.704034 0.710166i \(-0.251380\pi\)
0.704034 + 0.710166i \(0.251380\pi\)
\(332\) 0.664313 0.0364589
\(333\) 0.208643 0.0114336
\(334\) −1.07969 −0.0590779
\(335\) −14.1034 −0.770550
\(336\) 23.2321 1.26742
\(337\) −18.0292 −0.982111 −0.491056 0.871128i \(-0.663389\pi\)
−0.491056 + 0.871128i \(0.663389\pi\)
\(338\) 18.6833 1.01624
\(339\) −12.4683 −0.677185
\(340\) −1.34549 −0.0729696
\(341\) 6.98213 0.378103
\(342\) −0.827161 −0.0447277
\(343\) 16.8543 0.910048
\(344\) −4.27847 −0.230680
\(345\) −3.24501 −0.174706
\(346\) 22.6670 1.21859
\(347\) −9.82600 −0.527487 −0.263744 0.964593i \(-0.584957\pi\)
−0.263744 + 0.964593i \(0.584957\pi\)
\(348\) −10.9932 −0.589298
\(349\) 18.2946 0.979285 0.489643 0.871923i \(-0.337127\pi\)
0.489643 + 0.871923i \(0.337127\pi\)
\(350\) 13.0653 0.698371
\(351\) 26.4895 1.41390
\(352\) −6.66872 −0.355444
\(353\) −15.0098 −0.798889 −0.399445 0.916757i \(-0.630797\pi\)
−0.399445 + 0.916757i \(0.630797\pi\)
\(354\) 13.2726 0.705430
\(355\) 10.7575 0.570946
\(356\) 0.310623 0.0164630
\(357\) 6.36413 0.336825
\(358\) −11.9071 −0.629312
\(359\) 19.5629 1.03249 0.516246 0.856440i \(-0.327329\pi\)
0.516246 + 0.856440i \(0.327329\pi\)
\(360\) 0.667766 0.0351944
\(361\) −13.1311 −0.691113
\(362\) −7.39616 −0.388734
\(363\) −12.9097 −0.677581
\(364\) 9.51515 0.498729
\(365\) 23.4665 1.22829
\(366\) −16.8865 −0.882670
\(367\) −7.55573 −0.394406 −0.197203 0.980363i \(-0.563186\pi\)
−0.197203 + 0.980363i \(0.563186\pi\)
\(368\) 6.42813 0.335089
\(369\) 0.888990 0.0462790
\(370\) −2.42106 −0.125865
\(371\) 33.0900 1.71795
\(372\) 4.37200 0.226678
\(373\) 22.9616 1.18891 0.594455 0.804129i \(-0.297368\pi\)
0.594455 + 0.804129i \(0.297368\pi\)
\(374\) −3.97108 −0.205340
\(375\) −19.3075 −0.997034
\(376\) −26.3170 −1.35720
\(377\) 47.9511 2.46961
\(378\) 24.9142 1.28145
\(379\) 8.67330 0.445518 0.222759 0.974874i \(-0.428494\pi\)
0.222759 + 0.974874i \(0.428494\pi\)
\(380\) 2.43017 0.124665
\(381\) 18.4108 0.943216
\(382\) −13.9730 −0.714922
\(383\) 4.82530 0.246561 0.123281 0.992372i \(-0.460658\pi\)
0.123281 + 0.992372i \(0.460658\pi\)
\(384\) 22.5986 1.15323
\(385\) −7.60122 −0.387394
\(386\) −10.7524 −0.547283
\(387\) −0.412637 −0.0209755
\(388\) −12.2344 −0.621109
\(389\) 2.87282 0.145658 0.0728289 0.997344i \(-0.476797\pi\)
0.0728289 + 0.997344i \(0.476797\pi\)
\(390\) −19.9875 −1.01211
\(391\) 1.76090 0.0890524
\(392\) −2.30450 −0.116395
\(393\) 3.73671 0.188492
\(394\) −16.3319 −0.822790
\(395\) 12.6295 0.635457
\(396\) −0.255943 −0.0128616
\(397\) −30.1383 −1.51260 −0.756299 0.654227i \(-0.772994\pi\)
−0.756299 + 0.654227i \(0.772994\pi\)
\(398\) −29.4218 −1.47478
\(399\) −11.4946 −0.575449
\(400\) 13.7649 0.688246
\(401\) 28.5336 1.42490 0.712450 0.701723i \(-0.247586\pi\)
0.712450 + 0.701723i \(0.247586\pi\)
\(402\) −26.0642 −1.29996
\(403\) −19.0702 −0.949953
\(404\) 5.07221 0.252352
\(405\) −12.3245 −0.612410
\(406\) 45.0996 2.23826
\(407\) −1.80916 −0.0896769
\(408\) 4.84790 0.240007
\(409\) −2.35976 −0.116683 −0.0583413 0.998297i \(-0.518581\pi\)
−0.0583413 + 0.998297i \(0.518581\pi\)
\(410\) −10.3157 −0.509457
\(411\) −13.4469 −0.663289
\(412\) 5.19486 0.255932
\(413\) −13.7863 −0.678379
\(414\) 0.448255 0.0220305
\(415\) 1.44946 0.0711513
\(416\) 18.2142 0.893023
\(417\) 36.6923 1.79683
\(418\) 7.17239 0.350813
\(419\) 27.9186 1.36391 0.681957 0.731392i \(-0.261129\pi\)
0.681957 + 0.731392i \(0.261129\pi\)
\(420\) −4.75966 −0.232248
\(421\) −27.9350 −1.36147 −0.680733 0.732531i \(-0.738339\pi\)
−0.680733 + 0.732531i \(0.738339\pi\)
\(422\) −11.1704 −0.543768
\(423\) −2.53815 −0.123409
\(424\) 25.2065 1.22414
\(425\) 3.77071 0.182906
\(426\) 19.8806 0.963219
\(427\) 17.5401 0.848823
\(428\) −10.5905 −0.511911
\(429\) −14.9358 −0.721109
\(430\) 4.78818 0.230907
\(431\) −14.8397 −0.714803 −0.357402 0.933951i \(-0.616337\pi\)
−0.357402 + 0.933951i \(0.616337\pi\)
\(432\) 26.2483 1.26287
\(433\) 1.35115 0.0649323 0.0324662 0.999473i \(-0.489664\pi\)
0.0324662 + 0.999473i \(0.489664\pi\)
\(434\) −17.9361 −0.860962
\(435\) −23.9861 −1.15004
\(436\) −0.678051 −0.0324728
\(437\) −3.18045 −0.152142
\(438\) 43.3679 2.07220
\(439\) −2.43036 −0.115995 −0.0579973 0.998317i \(-0.518471\pi\)
−0.0579973 + 0.998317i \(0.518471\pi\)
\(440\) −5.79027 −0.276040
\(441\) −0.222257 −0.0105837
\(442\) 10.8462 0.515899
\(443\) −19.7248 −0.937155 −0.468577 0.883422i \(-0.655233\pi\)
−0.468577 + 0.883422i \(0.655233\pi\)
\(444\) −1.13284 −0.0537624
\(445\) 0.677748 0.0321283
\(446\) −5.98870 −0.283573
\(447\) −17.0425 −0.806084
\(448\) −10.6796 −0.504566
\(449\) 11.3367 0.535011 0.267505 0.963556i \(-0.413801\pi\)
0.267505 + 0.963556i \(0.413801\pi\)
\(450\) 0.959875 0.0452489
\(451\) −7.70851 −0.362980
\(452\) −5.06013 −0.238009
\(453\) −27.0298 −1.26997
\(454\) 29.7664 1.39700
\(455\) 20.7611 0.973295
\(456\) −8.75606 −0.410040
\(457\) −12.9011 −0.603488 −0.301744 0.953389i \(-0.597569\pi\)
−0.301744 + 0.953389i \(0.597569\pi\)
\(458\) −11.5027 −0.537486
\(459\) 7.19037 0.335618
\(460\) −1.31696 −0.0614034
\(461\) 13.0158 0.606206 0.303103 0.952958i \(-0.401977\pi\)
0.303103 + 0.952958i \(0.401977\pi\)
\(462\) −14.0477 −0.653556
\(463\) −28.5795 −1.32820 −0.664100 0.747644i \(-0.731185\pi\)
−0.664100 + 0.747644i \(0.731185\pi\)
\(464\) 47.5146 2.20581
\(465\) 9.53926 0.442373
\(466\) 23.6105 1.09374
\(467\) −4.93454 −0.228343 −0.114172 0.993461i \(-0.536421\pi\)
−0.114172 + 0.993461i \(0.536421\pi\)
\(468\) 0.699054 0.0323138
\(469\) 27.0729 1.25011
\(470\) 29.4523 1.35853
\(471\) 20.2195 0.931667
\(472\) −10.5018 −0.483383
\(473\) 3.57802 0.164517
\(474\) 23.3402 1.07205
\(475\) −6.81049 −0.312487
\(476\) 2.58282 0.118383
\(477\) 2.43104 0.111310
\(478\) −21.3353 −0.975854
\(479\) −32.8105 −1.49915 −0.749576 0.661919i \(-0.769742\pi\)
−0.749576 + 0.661919i \(0.769742\pi\)
\(480\) −9.11107 −0.415861
\(481\) 4.94134 0.225306
\(482\) 14.1968 0.646647
\(483\) 6.22915 0.283436
\(484\) −5.23925 −0.238148
\(485\) −26.6943 −1.21212
\(486\) 3.54175 0.160657
\(487\) −10.5021 −0.475897 −0.237948 0.971278i \(-0.576475\pi\)
−0.237948 + 0.971278i \(0.576475\pi\)
\(488\) 13.3612 0.604834
\(489\) 8.44426 0.381862
\(490\) 2.57904 0.116509
\(491\) −0.536109 −0.0241943 −0.0120971 0.999927i \(-0.503851\pi\)
−0.0120971 + 0.999927i \(0.503851\pi\)
\(492\) −4.82684 −0.217611
\(493\) 13.0160 0.586210
\(494\) −19.5898 −0.881388
\(495\) −0.558442 −0.0251001
\(496\) −18.8966 −0.848480
\(497\) −20.6501 −0.926282
\(498\) 2.67872 0.120036
\(499\) −14.5312 −0.650507 −0.325253 0.945627i \(-0.605450\pi\)
−0.325253 + 0.945627i \(0.605450\pi\)
\(500\) −7.83575 −0.350425
\(501\) −1.10229 −0.0492467
\(502\) 34.7022 1.54883
\(503\) −11.3529 −0.506202 −0.253101 0.967440i \(-0.581450\pi\)
−0.253101 + 0.967440i \(0.581450\pi\)
\(504\) −1.28185 −0.0570981
\(505\) 11.0670 0.492477
\(506\) −3.88686 −0.172792
\(507\) 19.0745 0.847126
\(508\) 7.47185 0.331510
\(509\) 1.34841 0.0597673 0.0298836 0.999553i \(-0.490486\pi\)
0.0298836 + 0.999553i \(0.490486\pi\)
\(510\) −5.42545 −0.240243
\(511\) −45.0464 −1.99274
\(512\) −3.13657 −0.138618
\(513\) −12.9869 −0.573386
\(514\) 23.1721 1.02208
\(515\) 11.3347 0.499464
\(516\) 2.24045 0.0986302
\(517\) 22.0085 0.967933
\(518\) 4.64749 0.204199
\(519\) 23.1415 1.01580
\(520\) 15.8149 0.693527
\(521\) 4.02602 0.176383 0.0881915 0.996104i \(-0.471891\pi\)
0.0881915 + 0.996104i \(0.471891\pi\)
\(522\) 3.31335 0.145021
\(523\) 33.0997 1.44735 0.723673 0.690143i \(-0.242452\pi\)
0.723673 + 0.690143i \(0.242452\pi\)
\(524\) 1.51651 0.0662489
\(525\) 13.3388 0.582155
\(526\) 25.7509 1.12279
\(527\) −5.17645 −0.225490
\(528\) −14.7999 −0.644081
\(529\) −21.2764 −0.925063
\(530\) −28.2094 −1.22534
\(531\) −1.01284 −0.0439537
\(532\) −4.66496 −0.202252
\(533\) 21.0541 0.911956
\(534\) 1.25253 0.0542023
\(535\) −23.1074 −0.999020
\(536\) 20.6229 0.890776
\(537\) −12.1564 −0.524588
\(538\) −8.36992 −0.360853
\(539\) 1.92721 0.0830110
\(540\) −5.37760 −0.231415
\(541\) −8.07535 −0.347186 −0.173593 0.984817i \(-0.555538\pi\)
−0.173593 + 0.984817i \(0.555538\pi\)
\(542\) −30.4502 −1.30795
\(543\) −7.55101 −0.324045
\(544\) 4.94409 0.211976
\(545\) −1.47944 −0.0633722
\(546\) 38.3681 1.64200
\(547\) 12.5640 0.537198 0.268599 0.963252i \(-0.413439\pi\)
0.268599 + 0.963252i \(0.413439\pi\)
\(548\) −5.45730 −0.233124
\(549\) 1.28862 0.0549971
\(550\) −8.32317 −0.354901
\(551\) −23.5088 −1.00151
\(552\) 4.74508 0.201964
\(553\) −24.2436 −1.03094
\(554\) −14.7769 −0.627811
\(555\) −2.47175 −0.104920
\(556\) 14.8912 0.631528
\(557\) −32.4676 −1.37570 −0.687848 0.725855i \(-0.741444\pi\)
−0.687848 + 0.725855i \(0.741444\pi\)
\(558\) −1.31772 −0.0557836
\(559\) −9.77257 −0.413336
\(560\) 20.5721 0.869329
\(561\) −4.05422 −0.171169
\(562\) 22.1486 0.934283
\(563\) −29.7715 −1.25472 −0.627360 0.778729i \(-0.715865\pi\)
−0.627360 + 0.778729i \(0.715865\pi\)
\(564\) 13.7811 0.580288
\(565\) −11.0407 −0.464485
\(566\) 34.3842 1.44528
\(567\) 23.6582 0.993552
\(568\) −15.7303 −0.660028
\(569\) 14.3759 0.602669 0.301334 0.953519i \(-0.402568\pi\)
0.301334 + 0.953519i \(0.402568\pi\)
\(570\) 9.79920 0.410444
\(571\) −25.9384 −1.08549 −0.542744 0.839898i \(-0.682614\pi\)
−0.542744 + 0.839898i \(0.682614\pi\)
\(572\) −6.06156 −0.253447
\(573\) −14.2656 −0.595952
\(574\) 19.8021 0.826524
\(575\) 3.69074 0.153915
\(576\) −0.784606 −0.0326919
\(577\) 30.4494 1.26763 0.633814 0.773486i \(-0.281489\pi\)
0.633814 + 0.773486i \(0.281489\pi\)
\(578\) −24.8760 −1.03470
\(579\) −10.9775 −0.456210
\(580\) −9.73450 −0.404203
\(581\) −2.78240 −0.115433
\(582\) −49.3331 −2.04492
\(583\) −21.0798 −0.873035
\(584\) −34.3143 −1.41994
\(585\) 1.52526 0.0630619
\(586\) 0.304258 0.0125688
\(587\) −6.23333 −0.257277 −0.128638 0.991692i \(-0.541061\pi\)
−0.128638 + 0.991692i \(0.541061\pi\)
\(588\) 1.20676 0.0497661
\(589\) 9.34947 0.385238
\(590\) 11.7529 0.483859
\(591\) −16.6738 −0.685869
\(592\) 4.89635 0.201239
\(593\) −13.0033 −0.533984 −0.266992 0.963699i \(-0.586030\pi\)
−0.266992 + 0.963699i \(0.586030\pi\)
\(594\) −15.8714 −0.651213
\(595\) 5.63544 0.231030
\(596\) −6.91654 −0.283312
\(597\) −30.0377 −1.22936
\(598\) 10.6161 0.434125
\(599\) −1.27850 −0.0522379 −0.0261190 0.999659i \(-0.508315\pi\)
−0.0261190 + 0.999659i \(0.508315\pi\)
\(600\) 10.1609 0.414818
\(601\) 21.5189 0.877775 0.438887 0.898542i \(-0.355373\pi\)
0.438887 + 0.898542i \(0.355373\pi\)
\(602\) −9.19143 −0.374615
\(603\) 1.98898 0.0809975
\(604\) −10.9698 −0.446353
\(605\) −11.4315 −0.464757
\(606\) 20.4528 0.830836
\(607\) −12.4158 −0.503940 −0.251970 0.967735i \(-0.581078\pi\)
−0.251970 + 0.967735i \(0.581078\pi\)
\(608\) −8.92980 −0.362151
\(609\) 46.0438 1.86579
\(610\) −14.9530 −0.605429
\(611\) −60.1115 −2.43185
\(612\) 0.189753 0.00767030
\(613\) −29.1464 −1.17721 −0.588605 0.808421i \(-0.700323\pi\)
−0.588605 + 0.808421i \(0.700323\pi\)
\(614\) −40.8187 −1.64731
\(615\) −10.5317 −0.424678
\(616\) 11.1150 0.447837
\(617\) 24.0892 0.969794 0.484897 0.874571i \(-0.338857\pi\)
0.484897 + 0.874571i \(0.338857\pi\)
\(618\) 20.9473 0.842625
\(619\) −4.05177 −0.162854 −0.0814272 0.996679i \(-0.525948\pi\)
−0.0814272 + 0.996679i \(0.525948\pi\)
\(620\) 3.87141 0.155480
\(621\) 7.03787 0.282420
\(622\) −9.88834 −0.396486
\(623\) −1.30101 −0.0521238
\(624\) 40.4226 1.61820
\(625\) −3.04048 −0.121619
\(626\) −26.2752 −1.05017
\(627\) 7.32255 0.292434
\(628\) 8.20589 0.327451
\(629\) 1.34129 0.0534807
\(630\) 1.43456 0.0571543
\(631\) −24.8491 −0.989226 −0.494613 0.869113i \(-0.664690\pi\)
−0.494613 + 0.869113i \(0.664690\pi\)
\(632\) −18.4677 −0.734604
\(633\) −11.4043 −0.453280
\(634\) −9.85864 −0.391537
\(635\) 16.3028 0.646958
\(636\) −13.1995 −0.523395
\(637\) −5.26377 −0.208558
\(638\) −28.7304 −1.13745
\(639\) −1.51711 −0.0600158
\(640\) 20.0111 0.791009
\(641\) 6.24215 0.246550 0.123275 0.992373i \(-0.460660\pi\)
0.123275 + 0.992373i \(0.460660\pi\)
\(642\) −42.7043 −1.68540
\(643\) 19.7930 0.780560 0.390280 0.920696i \(-0.372378\pi\)
0.390280 + 0.920696i \(0.372378\pi\)
\(644\) 2.52804 0.0996186
\(645\) 4.88843 0.192482
\(646\) −5.31751 −0.209215
\(647\) −2.46432 −0.0968826 −0.0484413 0.998826i \(-0.515425\pi\)
−0.0484413 + 0.998826i \(0.515425\pi\)
\(648\) 18.0218 0.707962
\(649\) 8.78246 0.344742
\(650\) 22.7329 0.891659
\(651\) −18.3116 −0.717689
\(652\) 3.42702 0.134212
\(653\) −33.9536 −1.32871 −0.664354 0.747418i \(-0.731293\pi\)
−0.664354 + 0.747418i \(0.731293\pi\)
\(654\) −2.73412 −0.106912
\(655\) 3.30886 0.129288
\(656\) 20.8625 0.814542
\(657\) −3.30944 −0.129114
\(658\) −56.5368 −2.20403
\(659\) −17.8783 −0.696438 −0.348219 0.937413i \(-0.613213\pi\)
−0.348219 + 0.937413i \(0.613213\pi\)
\(660\) 3.03211 0.118025
\(661\) −4.66432 −0.181421 −0.0907105 0.995877i \(-0.528914\pi\)
−0.0907105 + 0.995877i \(0.528914\pi\)
\(662\) 41.9225 1.62936
\(663\) 11.0732 0.430048
\(664\) −2.11950 −0.0822527
\(665\) −10.1785 −0.394704
\(666\) 0.341439 0.0132305
\(667\) 12.7399 0.493291
\(668\) −0.447354 −0.0173086
\(669\) −6.11408 −0.236384
\(670\) −23.0798 −0.891652
\(671\) −11.1738 −0.431358
\(672\) 17.4897 0.674678
\(673\) 35.8891 1.38342 0.691712 0.722173i \(-0.256857\pi\)
0.691712 + 0.722173i \(0.256857\pi\)
\(674\) −29.5043 −1.13646
\(675\) 15.0706 0.580068
\(676\) 7.74117 0.297737
\(677\) −35.7238 −1.37298 −0.686488 0.727141i \(-0.740849\pi\)
−0.686488 + 0.727141i \(0.740849\pi\)
\(678\) −20.4041 −0.783613
\(679\) 51.2425 1.96651
\(680\) 4.29282 0.164622
\(681\) 30.3895 1.16453
\(682\) 11.4261 0.437527
\(683\) 4.17252 0.159657 0.0798285 0.996809i \(-0.474563\pi\)
0.0798285 + 0.996809i \(0.474563\pi\)
\(684\) −0.342723 −0.0131043
\(685\) −11.9073 −0.454954
\(686\) 27.5817 1.05307
\(687\) −11.7435 −0.448043
\(688\) −9.68360 −0.369184
\(689\) 57.5748 2.19343
\(690\) −5.31038 −0.202163
\(691\) 50.3769 1.91643 0.958213 0.286054i \(-0.0923437\pi\)
0.958213 + 0.286054i \(0.0923437\pi\)
\(692\) 9.39176 0.357021
\(693\) 1.07199 0.0407215
\(694\) −16.0800 −0.610389
\(695\) 32.4911 1.23246
\(696\) 35.0741 1.32948
\(697\) 5.71498 0.216470
\(698\) 29.9386 1.13319
\(699\) 24.1048 0.911728
\(700\) 5.41343 0.204609
\(701\) 37.4057 1.41279 0.706396 0.707817i \(-0.250320\pi\)
0.706396 + 0.707817i \(0.250320\pi\)
\(702\) 43.3494 1.63612
\(703\) −2.42257 −0.0913691
\(704\) 6.80339 0.256412
\(705\) 30.0689 1.13246
\(706\) −24.5631 −0.924445
\(707\) −21.2444 −0.798977
\(708\) 5.49932 0.206677
\(709\) −14.8459 −0.557549 −0.278774 0.960357i \(-0.589928\pi\)
−0.278774 + 0.960357i \(0.589928\pi\)
\(710\) 17.6043 0.660678
\(711\) −1.78111 −0.0667969
\(712\) −0.991050 −0.0371412
\(713\) −5.06667 −0.189748
\(714\) 10.4147 0.389762
\(715\) −13.2257 −0.494613
\(716\) −4.93356 −0.184376
\(717\) −21.7820 −0.813463
\(718\) 32.0142 1.19476
\(719\) −42.5704 −1.58761 −0.793803 0.608174i \(-0.791902\pi\)
−0.793803 + 0.608174i \(0.791902\pi\)
\(720\) 1.51138 0.0563257
\(721\) −21.7581 −0.810313
\(722\) −21.4888 −0.799730
\(723\) 14.4940 0.539039
\(724\) −3.06450 −0.113891
\(725\) 27.2807 1.01318
\(726\) −21.1263 −0.784072
\(727\) 4.34883 0.161289 0.0806446 0.996743i \(-0.474302\pi\)
0.0806446 + 0.996743i \(0.474302\pi\)
\(728\) −30.3583 −1.12515
\(729\) 28.6075 1.05954
\(730\) 38.4023 1.42133
\(731\) −2.65269 −0.0981133
\(732\) −6.99668 −0.258605
\(733\) −11.9813 −0.442538 −0.221269 0.975213i \(-0.571020\pi\)
−0.221269 + 0.975213i \(0.571020\pi\)
\(734\) −12.3648 −0.456392
\(735\) 2.63304 0.0971210
\(736\) 4.83924 0.178377
\(737\) −17.2466 −0.635288
\(738\) 1.45481 0.0535523
\(739\) −5.30437 −0.195124 −0.0975622 0.995229i \(-0.531104\pi\)
−0.0975622 + 0.995229i \(0.531104\pi\)
\(740\) −1.00313 −0.0368760
\(741\) −20.0000 −0.734717
\(742\) 54.1510 1.98795
\(743\) 15.6795 0.575226 0.287613 0.957747i \(-0.407138\pi\)
0.287613 + 0.957747i \(0.407138\pi\)
\(744\) −13.9490 −0.511394
\(745\) −15.0912 −0.552898
\(746\) 37.5762 1.37576
\(747\) −0.204415 −0.00747917
\(748\) −1.64536 −0.0601605
\(749\) 44.3571 1.62077
\(750\) −31.5962 −1.15373
\(751\) −1.42456 −0.0519828 −0.0259914 0.999662i \(-0.508274\pi\)
−0.0259914 + 0.999662i \(0.508274\pi\)
\(752\) −59.5642 −2.17208
\(753\) 35.4287 1.29109
\(754\) 78.4708 2.85774
\(755\) −23.9349 −0.871080
\(756\) 10.3229 0.375439
\(757\) −36.6098 −1.33061 −0.665303 0.746574i \(-0.731698\pi\)
−0.665303 + 0.746574i \(0.731698\pi\)
\(758\) 14.1936 0.515536
\(759\) −3.96823 −0.144038
\(760\) −7.75350 −0.281249
\(761\) 43.5188 1.57755 0.788777 0.614679i \(-0.210715\pi\)
0.788777 + 0.614679i \(0.210715\pi\)
\(762\) 30.1289 1.09145
\(763\) 2.83994 0.102813
\(764\) −5.78953 −0.209458
\(765\) 0.414021 0.0149690
\(766\) 7.89648 0.285311
\(767\) −23.9874 −0.866135
\(768\) 24.4164 0.881052
\(769\) −6.95070 −0.250649 −0.125324 0.992116i \(-0.539997\pi\)
−0.125324 + 0.992116i \(0.539997\pi\)
\(770\) −12.4392 −0.448278
\(771\) 23.6572 0.851992
\(772\) −4.45511 −0.160343
\(773\) 1.98872 0.0715292 0.0357646 0.999360i \(-0.488613\pi\)
0.0357646 + 0.999360i \(0.488613\pi\)
\(774\) −0.675270 −0.0242721
\(775\) −10.8496 −0.389727
\(776\) 39.0342 1.40125
\(777\) 4.74479 0.170218
\(778\) 4.70130 0.168550
\(779\) −10.3221 −0.369829
\(780\) −8.28154 −0.296527
\(781\) 13.1550 0.470722
\(782\) 2.88167 0.103048
\(783\) 52.0216 1.85910
\(784\) −5.21585 −0.186280
\(785\) 17.9044 0.639036
\(786\) 6.11504 0.218116
\(787\) 31.5429 1.12438 0.562192 0.827006i \(-0.309958\pi\)
0.562192 + 0.827006i \(0.309958\pi\)
\(788\) −6.76690 −0.241061
\(789\) 26.2900 0.935950
\(790\) 20.6678 0.735327
\(791\) 21.1938 0.753564
\(792\) 0.816593 0.0290164
\(793\) 30.5187 1.08375
\(794\) −49.3206 −1.75032
\(795\) −28.8000 −1.02143
\(796\) −12.1905 −0.432081
\(797\) 0.669871 0.0237280 0.0118640 0.999930i \(-0.496223\pi\)
0.0118640 + 0.999930i \(0.496223\pi\)
\(798\) −18.8106 −0.665889
\(799\) −16.3168 −0.577247
\(800\) 10.3625 0.366371
\(801\) −0.0955818 −0.00337722
\(802\) 46.6945 1.64884
\(803\) 28.6965 1.01268
\(804\) −10.7993 −0.380863
\(805\) 5.51592 0.194411
\(806\) −31.2079 −1.09925
\(807\) −8.54514 −0.300803
\(808\) −16.1830 −0.569316
\(809\) −6.02851 −0.211951 −0.105976 0.994369i \(-0.533797\pi\)
−0.105976 + 0.994369i \(0.533797\pi\)
\(810\) −20.1688 −0.708658
\(811\) 26.2163 0.920578 0.460289 0.887769i \(-0.347746\pi\)
0.460289 + 0.887769i \(0.347746\pi\)
\(812\) 18.6864 0.655764
\(813\) −31.0877 −1.09029
\(814\) −2.96065 −0.103771
\(815\) 7.47740 0.261922
\(816\) 10.9724 0.384111
\(817\) 4.79117 0.167622
\(818\) −3.86169 −0.135021
\(819\) −2.92791 −0.102309
\(820\) −4.27417 −0.149261
\(821\) 29.2765 1.02176 0.510878 0.859653i \(-0.329320\pi\)
0.510878 + 0.859653i \(0.329320\pi\)
\(822\) −22.0056 −0.767533
\(823\) 31.3133 1.09151 0.545757 0.837944i \(-0.316242\pi\)
0.545757 + 0.837944i \(0.316242\pi\)
\(824\) −16.5743 −0.577394
\(825\) −8.49741 −0.295842
\(826\) −22.5609 −0.784995
\(827\) 25.5755 0.889348 0.444674 0.895693i \(-0.353320\pi\)
0.444674 + 0.895693i \(0.353320\pi\)
\(828\) 0.185728 0.00645451
\(829\) 1.80238 0.0625991 0.0312995 0.999510i \(-0.490035\pi\)
0.0312995 + 0.999510i \(0.490035\pi\)
\(830\) 2.37201 0.0823336
\(831\) −15.0863 −0.523337
\(832\) −18.5820 −0.644215
\(833\) −1.42881 −0.0495053
\(834\) 60.0461 2.07923
\(835\) −0.976080 −0.0337786
\(836\) 2.97178 0.102781
\(837\) −20.6890 −0.715116
\(838\) 45.6881 1.57827
\(839\) −23.5344 −0.812498 −0.406249 0.913762i \(-0.633163\pi\)
−0.406249 + 0.913762i \(0.633163\pi\)
\(840\) 15.1858 0.523960
\(841\) 65.1692 2.24721
\(842\) −45.7149 −1.57544
\(843\) 22.6123 0.778809
\(844\) −4.62831 −0.159313
\(845\) 16.8904 0.581049
\(846\) −4.15361 −0.142804
\(847\) 21.9440 0.754005
\(848\) 57.0506 1.95913
\(849\) 35.1040 1.20477
\(850\) 6.17068 0.211653
\(851\) 1.31284 0.0450036
\(852\) 8.23726 0.282204
\(853\) −12.2079 −0.417990 −0.208995 0.977917i \(-0.567019\pi\)
−0.208995 + 0.977917i \(0.567019\pi\)
\(854\) 28.7039 0.982226
\(855\) −0.747786 −0.0255737
\(856\) 33.7892 1.15489
\(857\) −34.3583 −1.17366 −0.586828 0.809711i \(-0.699624\pi\)
−0.586828 + 0.809711i \(0.699624\pi\)
\(858\) −24.4421 −0.834441
\(859\) 11.1492 0.380404 0.190202 0.981745i \(-0.439086\pi\)
0.190202 + 0.981745i \(0.439086\pi\)
\(860\) 1.98392 0.0676510
\(861\) 20.2167 0.688982
\(862\) −24.2848 −0.827144
\(863\) −4.12069 −0.140270 −0.0701349 0.997538i \(-0.522343\pi\)
−0.0701349 + 0.997538i \(0.522343\pi\)
\(864\) 19.7603 0.672260
\(865\) 20.4919 0.696744
\(866\) 2.21113 0.0751373
\(867\) −25.3968 −0.862519
\(868\) −7.43159 −0.252245
\(869\) 15.4442 0.523908
\(870\) −39.2526 −1.33079
\(871\) 47.1054 1.59611
\(872\) 2.16334 0.0732598
\(873\) 3.76465 0.127414
\(874\) −5.20473 −0.176053
\(875\) 32.8191 1.10949
\(876\) 17.9689 0.607113
\(877\) −25.2253 −0.851797 −0.425898 0.904771i \(-0.640042\pi\)
−0.425898 + 0.904771i \(0.640042\pi\)
\(878\) −3.97722 −0.134225
\(879\) 0.310628 0.0104772
\(880\) −13.1053 −0.441779
\(881\) 38.0767 1.28284 0.641418 0.767192i \(-0.278347\pi\)
0.641418 + 0.767192i \(0.278347\pi\)
\(882\) −0.363719 −0.0122470
\(883\) −40.7554 −1.37153 −0.685765 0.727823i \(-0.740532\pi\)
−0.685765 + 0.727823i \(0.740532\pi\)
\(884\) 4.49396 0.151148
\(885\) 11.9989 0.403340
\(886\) −32.2792 −1.08444
\(887\) −1.36291 −0.0457620 −0.0228810 0.999738i \(-0.507284\pi\)
−0.0228810 + 0.999738i \(0.507284\pi\)
\(888\) 3.61436 0.121290
\(889\) −31.2950 −1.04960
\(890\) 1.10912 0.0371777
\(891\) −15.0713 −0.504908
\(892\) −2.48134 −0.0830813
\(893\) 29.4707 0.986198
\(894\) −27.8897 −0.932770
\(895\) −10.7645 −0.359818
\(896\) −38.4135 −1.28330
\(897\) 10.8384 0.361883
\(898\) 18.5522 0.619094
\(899\) −37.4511 −1.24906
\(900\) 0.397711 0.0132570
\(901\) 15.6282 0.520652
\(902\) −12.6148 −0.420027
\(903\) −9.38385 −0.312275
\(904\) 16.1445 0.536957
\(905\) −6.68642 −0.222264
\(906\) −44.2336 −1.46956
\(907\) −37.9353 −1.25962 −0.629811 0.776748i \(-0.716868\pi\)
−0.629811 + 0.776748i \(0.716868\pi\)
\(908\) 12.3333 0.409294
\(909\) −1.56077 −0.0517674
\(910\) 33.9750 1.12626
\(911\) 24.9675 0.827209 0.413605 0.910457i \(-0.364270\pi\)
0.413605 + 0.910457i \(0.364270\pi\)
\(912\) −19.8179 −0.656235
\(913\) 1.77251 0.0586614
\(914\) −21.1123 −0.698334
\(915\) −15.2660 −0.504680
\(916\) −4.76599 −0.157473
\(917\) −6.35171 −0.209752
\(918\) 11.7669 0.388364
\(919\) 4.93453 0.162775 0.0813876 0.996683i \(-0.474065\pi\)
0.0813876 + 0.996683i \(0.474065\pi\)
\(920\) 4.20178 0.138528
\(921\) −41.6732 −1.37318
\(922\) 21.3000 0.701479
\(923\) −35.9300 −1.18265
\(924\) −5.82045 −0.191479
\(925\) 2.81126 0.0924338
\(926\) −46.7696 −1.53694
\(927\) −1.59851 −0.0525019
\(928\) 35.7700 1.17421
\(929\) −33.6674 −1.10459 −0.552295 0.833649i \(-0.686248\pi\)
−0.552295 + 0.833649i \(0.686248\pi\)
\(930\) 15.6108 0.511897
\(931\) 2.58065 0.0845775
\(932\) 9.78269 0.320443
\(933\) −10.0954 −0.330507
\(934\) −8.07526 −0.264231
\(935\) −3.59002 −0.117406
\(936\) −2.23035 −0.0729011
\(937\) −9.86172 −0.322168 −0.161084 0.986941i \(-0.551499\pi\)
−0.161084 + 0.986941i \(0.551499\pi\)
\(938\) 44.3042 1.44658
\(939\) −26.8253 −0.875410
\(940\) 12.2032 0.398023
\(941\) −6.24530 −0.203591 −0.101795 0.994805i \(-0.532459\pi\)
−0.101795 + 0.994805i \(0.532459\pi\)
\(942\) 33.0888 1.07809
\(943\) 5.59378 0.182158
\(944\) −23.7690 −0.773615
\(945\) 22.5234 0.732688
\(946\) 5.85533 0.190373
\(947\) 31.0889 1.01025 0.505127 0.863045i \(-0.331446\pi\)
0.505127 + 0.863045i \(0.331446\pi\)
\(948\) 9.67070 0.314090
\(949\) −78.3783 −2.54427
\(950\) −11.1452 −0.361598
\(951\) −10.0650 −0.326381
\(952\) −8.24053 −0.267077
\(953\) −46.4637 −1.50511 −0.752553 0.658532i \(-0.771178\pi\)
−0.752553 + 0.658532i \(0.771178\pi\)
\(954\) 3.97834 0.128803
\(955\) −12.6322 −0.408767
\(956\) −8.83999 −0.285906
\(957\) −29.3319 −0.948165
\(958\) −53.6936 −1.73476
\(959\) 22.8573 0.738100
\(960\) 9.29506 0.299997
\(961\) −16.1057 −0.519538
\(962\) 8.08637 0.260715
\(963\) 3.25880 0.105013
\(964\) 5.88226 0.189455
\(965\) −9.72060 −0.312917
\(966\) 10.1938 0.327982
\(967\) −55.1039 −1.77202 −0.886011 0.463663i \(-0.846535\pi\)
−0.886011 + 0.463663i \(0.846535\pi\)
\(968\) 16.7160 0.537271
\(969\) −5.42884 −0.174399
\(970\) −43.6845 −1.40262
\(971\) 39.3443 1.26262 0.631310 0.775531i \(-0.282518\pi\)
0.631310 + 0.775531i \(0.282518\pi\)
\(972\) 1.46747 0.0470693
\(973\) −62.3701 −1.99949
\(974\) −17.1865 −0.550690
\(975\) 23.2088 0.743278
\(976\) 30.2409 0.967987
\(977\) 10.7406 0.343623 0.171811 0.985130i \(-0.445038\pi\)
0.171811 + 0.985130i \(0.445038\pi\)
\(978\) 13.8188 0.441877
\(979\) 0.828798 0.0264885
\(980\) 1.06859 0.0341349
\(981\) 0.208643 0.00666146
\(982\) −0.877329 −0.0279967
\(983\) 6.02893 0.192293 0.0961465 0.995367i \(-0.469348\pi\)
0.0961465 + 0.995367i \(0.469348\pi\)
\(984\) 15.4001 0.490939
\(985\) −14.7647 −0.470442
\(986\) 21.3003 0.678340
\(987\) −57.7204 −1.83726
\(988\) −8.11678 −0.258229
\(989\) −2.59643 −0.0825617
\(990\) −0.913876 −0.0290449
\(991\) −41.9959 −1.33404 −0.667021 0.745039i \(-0.732431\pi\)
−0.667021 + 0.745039i \(0.732431\pi\)
\(992\) −14.2257 −0.451668
\(993\) 42.8002 1.35822
\(994\) −33.7933 −1.07186
\(995\) −26.5984 −0.843227
\(996\) 1.10989 0.0351682
\(997\) 7.27669 0.230455 0.115228 0.993339i \(-0.463240\pi\)
0.115228 + 0.993339i \(0.463240\pi\)
\(998\) −23.7800 −0.752742
\(999\) 5.36079 0.169608
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 4033.2.a.d.1.64 79
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.d.1.64 79 1.1 even 1 trivial