Properties

Label 4010.2.a.l.1.6
Level $4010$
Weight $2$
Character 4010.1
Self dual yes
Analytic conductor $32.020$
Analytic rank $0$
Dimension $17$
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] = [4010,2,Mod(1,4010)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4010, 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("4010.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4010.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: \(32.0200112105\)
Analytic rank: \(0\)
Dimension: \(17\)
Coefficient field: \(\mathbb{Q}[x]/(x^{17} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + 2544 x^{9} - 6415 x^{8} - 2573 x^{7} + 6456 x^{6} + 485 x^{5} - 1839 x^{4} + \cdots - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.548857\) of defining polynomial
Character \(\chi\) \(=\) 4010.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.548857 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.548857 q^{6} -1.86676 q^{7} -1.00000 q^{8} -2.69876 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.548857 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.548857 q^{6} -1.86676 q^{7} -1.00000 q^{8} -2.69876 q^{9} +1.00000 q^{10} +0.761515 q^{11} -0.548857 q^{12} -4.22069 q^{13} +1.86676 q^{14} +0.548857 q^{15} +1.00000 q^{16} +1.77958 q^{17} +2.69876 q^{18} -7.51631 q^{19} -1.00000 q^{20} +1.02458 q^{21} -0.761515 q^{22} +2.16755 q^{23} +0.548857 q^{24} +1.00000 q^{25} +4.22069 q^{26} +3.12780 q^{27} -1.86676 q^{28} -1.35794 q^{29} -0.548857 q^{30} +2.74334 q^{31} -1.00000 q^{32} -0.417963 q^{33} -1.77958 q^{34} +1.86676 q^{35} -2.69876 q^{36} -8.22343 q^{37} +7.51631 q^{38} +2.31655 q^{39} +1.00000 q^{40} -11.9509 q^{41} -1.02458 q^{42} -11.2893 q^{43} +0.761515 q^{44} +2.69876 q^{45} -2.16755 q^{46} +3.51558 q^{47} -0.548857 q^{48} -3.51520 q^{49} -1.00000 q^{50} -0.976737 q^{51} -4.22069 q^{52} +11.0125 q^{53} -3.12780 q^{54} -0.761515 q^{55} +1.86676 q^{56} +4.12537 q^{57} +1.35794 q^{58} -12.1732 q^{59} +0.548857 q^{60} +6.48721 q^{61} -2.74334 q^{62} +5.03794 q^{63} +1.00000 q^{64} +4.22069 q^{65} +0.417963 q^{66} +7.99847 q^{67} +1.77958 q^{68} -1.18967 q^{69} -1.86676 q^{70} -4.51275 q^{71} +2.69876 q^{72} +16.3206 q^{73} +8.22343 q^{74} -0.548857 q^{75} -7.51631 q^{76} -1.42157 q^{77} -2.31655 q^{78} -13.9449 q^{79} -1.00000 q^{80} +6.37956 q^{81} +11.9509 q^{82} -0.0586654 q^{83} +1.02458 q^{84} -1.77958 q^{85} +11.2893 q^{86} +0.745313 q^{87} -0.761515 q^{88} -0.122663 q^{89} -2.69876 q^{90} +7.87902 q^{91} +2.16755 q^{92} -1.50570 q^{93} -3.51558 q^{94} +7.51631 q^{95} +0.548857 q^{96} -2.83378 q^{97} +3.51520 q^{98} -2.05514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.548857 −0.316883 −0.158441 0.987368i \(-0.550647\pi\)
−0.158441 + 0.987368i \(0.550647\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0.548857 0.224070
\(7\) −1.86676 −0.705570 −0.352785 0.935704i \(-0.614765\pi\)
−0.352785 + 0.935704i \(0.614765\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.69876 −0.899585
\(10\) 1.00000 0.316228
\(11\) 0.761515 0.229606 0.114803 0.993388i \(-0.463376\pi\)
0.114803 + 0.993388i \(0.463376\pi\)
\(12\) −0.548857 −0.158441
\(13\) −4.22069 −1.17061 −0.585304 0.810814i \(-0.699025\pi\)
−0.585304 + 0.810814i \(0.699025\pi\)
\(14\) 1.86676 0.498913
\(15\) 0.548857 0.141714
\(16\) 1.00000 0.250000
\(17\) 1.77958 0.431613 0.215806 0.976436i \(-0.430762\pi\)
0.215806 + 0.976436i \(0.430762\pi\)
\(18\) 2.69876 0.636103
\(19\) −7.51631 −1.72436 −0.862179 0.506603i \(-0.830901\pi\)
−0.862179 + 0.506603i \(0.830901\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.02458 0.223583
\(22\) −0.761515 −0.162356
\(23\) 2.16755 0.451965 0.225982 0.974131i \(-0.427441\pi\)
0.225982 + 0.974131i \(0.427441\pi\)
\(24\) 0.548857 0.112035
\(25\) 1.00000 0.200000
\(26\) 4.22069 0.827745
\(27\) 3.12780 0.601945
\(28\) −1.86676 −0.352785
\(29\) −1.35794 −0.252163 −0.126081 0.992020i \(-0.540240\pi\)
−0.126081 + 0.992020i \(0.540240\pi\)
\(30\) −0.548857 −0.100207
\(31\) 2.74334 0.492719 0.246359 0.969179i \(-0.420766\pi\)
0.246359 + 0.969179i \(0.420766\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.417963 −0.0727580
\(34\) −1.77958 −0.305196
\(35\) 1.86676 0.315540
\(36\) −2.69876 −0.449793
\(37\) −8.22343 −1.35192 −0.675962 0.736937i \(-0.736271\pi\)
−0.675962 + 0.736937i \(0.736271\pi\)
\(38\) 7.51631 1.21931
\(39\) 2.31655 0.370945
\(40\) 1.00000 0.158114
\(41\) −11.9509 −1.86642 −0.933209 0.359333i \(-0.883004\pi\)
−0.933209 + 0.359333i \(0.883004\pi\)
\(42\) −1.02458 −0.158097
\(43\) −11.2893 −1.72161 −0.860803 0.508938i \(-0.830038\pi\)
−0.860803 + 0.508938i \(0.830038\pi\)
\(44\) 0.761515 0.114803
\(45\) 2.69876 0.402307
\(46\) −2.16755 −0.319587
\(47\) 3.51558 0.512799 0.256400 0.966571i \(-0.417464\pi\)
0.256400 + 0.966571i \(0.417464\pi\)
\(48\) −0.548857 −0.0792206
\(49\) −3.51520 −0.502171
\(50\) −1.00000 −0.141421
\(51\) −0.976737 −0.136770
\(52\) −4.22069 −0.585304
\(53\) 11.0125 1.51269 0.756344 0.654174i \(-0.226983\pi\)
0.756344 + 0.654174i \(0.226983\pi\)
\(54\) −3.12780 −0.425640
\(55\) −0.761515 −0.102683
\(56\) 1.86676 0.249457
\(57\) 4.12537 0.546419
\(58\) 1.35794 0.178306
\(59\) −12.1732 −1.58482 −0.792409 0.609991i \(-0.791173\pi\)
−0.792409 + 0.609991i \(0.791173\pi\)
\(60\) 0.548857 0.0708571
\(61\) 6.48721 0.830601 0.415301 0.909684i \(-0.363676\pi\)
0.415301 + 0.909684i \(0.363676\pi\)
\(62\) −2.74334 −0.348405
\(63\) 5.03794 0.634720
\(64\) 1.00000 0.125000
\(65\) 4.22069 0.523512
\(66\) 0.417963 0.0514477
\(67\) 7.99847 0.977168 0.488584 0.872517i \(-0.337514\pi\)
0.488584 + 0.872517i \(0.337514\pi\)
\(68\) 1.77958 0.215806
\(69\) −1.18967 −0.143220
\(70\) −1.86676 −0.223121
\(71\) −4.51275 −0.535564 −0.267782 0.963479i \(-0.586291\pi\)
−0.267782 + 0.963479i \(0.586291\pi\)
\(72\) 2.69876 0.318051
\(73\) 16.3206 1.91018 0.955091 0.296313i \(-0.0957570\pi\)
0.955091 + 0.296313i \(0.0957570\pi\)
\(74\) 8.22343 0.955954
\(75\) −0.548857 −0.0633765
\(76\) −7.51631 −0.862179
\(77\) −1.42157 −0.162003
\(78\) −2.31655 −0.262298
\(79\) −13.9449 −1.56893 −0.784465 0.620174i \(-0.787062\pi\)
−0.784465 + 0.620174i \(0.787062\pi\)
\(80\) −1.00000 −0.111803
\(81\) 6.37956 0.708840
\(82\) 11.9509 1.31976
\(83\) −0.0586654 −0.00643936 −0.00321968 0.999995i \(-0.501025\pi\)
−0.00321968 + 0.999995i \(0.501025\pi\)
\(84\) 1.02458 0.111791
\(85\) −1.77958 −0.193023
\(86\) 11.2893 1.21736
\(87\) 0.745313 0.0799059
\(88\) −0.761515 −0.0811778
\(89\) −0.122663 −0.0130022 −0.00650111 0.999979i \(-0.502069\pi\)
−0.00650111 + 0.999979i \(0.502069\pi\)
\(90\) −2.69876 −0.284474
\(91\) 7.87902 0.825945
\(92\) 2.16755 0.225982
\(93\) −1.50570 −0.156134
\(94\) −3.51558 −0.362604
\(95\) 7.51631 0.771157
\(96\) 0.548857 0.0560174
\(97\) −2.83378 −0.287727 −0.143863 0.989598i \(-0.545953\pi\)
−0.143863 + 0.989598i \(0.545953\pi\)
\(98\) 3.51520 0.355089
\(99\) −2.05514 −0.206550
\(100\) 1.00000 0.100000
\(101\) 0.212072 0.0211020 0.0105510 0.999944i \(-0.496641\pi\)
0.0105510 + 0.999944i \(0.496641\pi\)
\(102\) 0.976737 0.0967113
\(103\) 1.08106 0.106520 0.0532600 0.998581i \(-0.483039\pi\)
0.0532600 + 0.998581i \(0.483039\pi\)
\(104\) 4.22069 0.413872
\(105\) −1.02458 −0.0999892
\(106\) −11.0125 −1.06963
\(107\) 11.8016 1.14091 0.570453 0.821330i \(-0.306768\pi\)
0.570453 + 0.821330i \(0.306768\pi\)
\(108\) 3.12780 0.300973
\(109\) 18.0977 1.73345 0.866723 0.498790i \(-0.166222\pi\)
0.866723 + 0.498790i \(0.166222\pi\)
\(110\) 0.761515 0.0726077
\(111\) 4.51348 0.428401
\(112\) −1.86676 −0.176392
\(113\) −6.50418 −0.611862 −0.305931 0.952054i \(-0.598968\pi\)
−0.305931 + 0.952054i \(0.598968\pi\)
\(114\) −4.12537 −0.386377
\(115\) −2.16755 −0.202125
\(116\) −1.35794 −0.126081
\(117\) 11.3906 1.05306
\(118\) 12.1732 1.12063
\(119\) −3.32206 −0.304533
\(120\) −0.548857 −0.0501035
\(121\) −10.4201 −0.947281
\(122\) −6.48721 −0.587324
\(123\) 6.55934 0.591435
\(124\) 2.74334 0.246359
\(125\) −1.00000 −0.0894427
\(126\) −5.03794 −0.448815
\(127\) −21.3259 −1.89237 −0.946183 0.323633i \(-0.895096\pi\)
−0.946183 + 0.323633i \(0.895096\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 6.19622 0.545547
\(130\) −4.22069 −0.370179
\(131\) 11.9874 1.04735 0.523674 0.851919i \(-0.324561\pi\)
0.523674 + 0.851919i \(0.324561\pi\)
\(132\) −0.417963 −0.0363790
\(133\) 14.0312 1.21666
\(134\) −7.99847 −0.690962
\(135\) −3.12780 −0.269198
\(136\) −1.77958 −0.152598
\(137\) −8.61417 −0.735959 −0.367979 0.929834i \(-0.619950\pi\)
−0.367979 + 0.929834i \(0.619950\pi\)
\(138\) 1.18967 0.101272
\(139\) 0.313769 0.0266135 0.0133068 0.999911i \(-0.495764\pi\)
0.0133068 + 0.999911i \(0.495764\pi\)
\(140\) 1.86676 0.157770
\(141\) −1.92955 −0.162497
\(142\) 4.51275 0.378701
\(143\) −3.21412 −0.268778
\(144\) −2.69876 −0.224896
\(145\) 1.35794 0.112771
\(146\) −16.3206 −1.35070
\(147\) 1.92934 0.159129
\(148\) −8.22343 −0.675962
\(149\) −17.3878 −1.42447 −0.712234 0.701942i \(-0.752316\pi\)
−0.712234 + 0.701942i \(0.752316\pi\)
\(150\) 0.548857 0.0448140
\(151\) 11.6514 0.948176 0.474088 0.880478i \(-0.342778\pi\)
0.474088 + 0.880478i \(0.342778\pi\)
\(152\) 7.51631 0.609653
\(153\) −4.80266 −0.388272
\(154\) 1.42157 0.114553
\(155\) −2.74334 −0.220351
\(156\) 2.31655 0.185473
\(157\) 15.9952 1.27656 0.638279 0.769805i \(-0.279647\pi\)
0.638279 + 0.769805i \(0.279647\pi\)
\(158\) 13.9449 1.10940
\(159\) −6.04431 −0.479345
\(160\) 1.00000 0.0790569
\(161\) −4.04629 −0.318893
\(162\) −6.37956 −0.501225
\(163\) 7.07887 0.554460 0.277230 0.960804i \(-0.410584\pi\)
0.277230 + 0.960804i \(0.410584\pi\)
\(164\) −11.9509 −0.933209
\(165\) 0.417963 0.0325384
\(166\) 0.0586654 0.00455332
\(167\) 12.2111 0.944924 0.472462 0.881351i \(-0.343365\pi\)
0.472462 + 0.881351i \(0.343365\pi\)
\(168\) −1.02458 −0.0790484
\(169\) 4.81419 0.370322
\(170\) 1.77958 0.136488
\(171\) 20.2847 1.55121
\(172\) −11.2893 −0.860803
\(173\) −17.3158 −1.31650 −0.658248 0.752801i \(-0.728702\pi\)
−0.658248 + 0.752801i \(0.728702\pi\)
\(174\) −0.745313 −0.0565020
\(175\) −1.86676 −0.141114
\(176\) 0.761515 0.0574014
\(177\) 6.68135 0.502201
\(178\) 0.122663 0.00919395
\(179\) 10.8140 0.808274 0.404137 0.914698i \(-0.367572\pi\)
0.404137 + 0.914698i \(0.367572\pi\)
\(180\) 2.69876 0.201153
\(181\) 14.7439 1.09591 0.547954 0.836508i \(-0.315407\pi\)
0.547954 + 0.836508i \(0.315407\pi\)
\(182\) −7.87902 −0.584032
\(183\) −3.56055 −0.263203
\(184\) −2.16755 −0.159794
\(185\) 8.22343 0.604598
\(186\) 1.50570 0.110403
\(187\) 1.35518 0.0991006
\(188\) 3.51558 0.256400
\(189\) −5.83886 −0.424715
\(190\) −7.51631 −0.545290
\(191\) −6.89586 −0.498967 −0.249483 0.968379i \(-0.580261\pi\)
−0.249483 + 0.968379i \(0.580261\pi\)
\(192\) −0.548857 −0.0396103
\(193\) 11.5661 0.832543 0.416272 0.909240i \(-0.363337\pi\)
0.416272 + 0.909240i \(0.363337\pi\)
\(194\) 2.83378 0.203454
\(195\) −2.31655 −0.165892
\(196\) −3.51520 −0.251086
\(197\) 25.0540 1.78502 0.892511 0.451026i \(-0.148942\pi\)
0.892511 + 0.451026i \(0.148942\pi\)
\(198\) 2.05514 0.146053
\(199\) 10.1371 0.718599 0.359299 0.933222i \(-0.383016\pi\)
0.359299 + 0.933222i \(0.383016\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −4.39001 −0.309647
\(202\) −0.212072 −0.0149214
\(203\) 2.53495 0.177918
\(204\) −0.976737 −0.0683852
\(205\) 11.9509 0.834688
\(206\) −1.08106 −0.0753210
\(207\) −5.84968 −0.406581
\(208\) −4.22069 −0.292652
\(209\) −5.72378 −0.395922
\(210\) 1.02458 0.0707031
\(211\) 10.9855 0.756274 0.378137 0.925750i \(-0.376565\pi\)
0.378137 + 0.925750i \(0.376565\pi\)
\(212\) 11.0125 0.756344
\(213\) 2.47685 0.169711
\(214\) −11.8016 −0.806743
\(215\) 11.2893 0.769926
\(216\) −3.12780 −0.212820
\(217\) −5.12117 −0.347648
\(218\) −18.0977 −1.22573
\(219\) −8.95767 −0.605303
\(220\) −0.761515 −0.0513414
\(221\) −7.51107 −0.505249
\(222\) −4.51348 −0.302925
\(223\) 10.1950 0.682711 0.341355 0.939934i \(-0.389114\pi\)
0.341355 + 0.939934i \(0.389114\pi\)
\(224\) 1.86676 0.124728
\(225\) −2.69876 −0.179917
\(226\) 6.50418 0.432652
\(227\) 19.1164 1.26880 0.634398 0.773006i \(-0.281248\pi\)
0.634398 + 0.773006i \(0.281248\pi\)
\(228\) 4.12537 0.273210
\(229\) 12.7450 0.842211 0.421105 0.907012i \(-0.361642\pi\)
0.421105 + 0.907012i \(0.361642\pi\)
\(230\) 2.16755 0.142924
\(231\) 0.780237 0.0513358
\(232\) 1.35794 0.0891529
\(233\) −19.0509 −1.24807 −0.624033 0.781398i \(-0.714507\pi\)
−0.624033 + 0.781398i \(0.714507\pi\)
\(234\) −11.3906 −0.744627
\(235\) −3.51558 −0.229331
\(236\) −12.1732 −0.792409
\(237\) 7.65378 0.497166
\(238\) 3.32206 0.215337
\(239\) 14.2195 0.919783 0.459892 0.887975i \(-0.347888\pi\)
0.459892 + 0.887975i \(0.347888\pi\)
\(240\) 0.548857 0.0354285
\(241\) −25.0784 −1.61544 −0.807721 0.589564i \(-0.799299\pi\)
−0.807721 + 0.589564i \(0.799299\pi\)
\(242\) 10.4201 0.669829
\(243\) −12.8849 −0.826564
\(244\) 6.48721 0.415301
\(245\) 3.51520 0.224578
\(246\) −6.55934 −0.418208
\(247\) 31.7240 2.01855
\(248\) −2.74334 −0.174202
\(249\) 0.0321989 0.00204052
\(250\) 1.00000 0.0632456
\(251\) −16.2113 −1.02325 −0.511623 0.859210i \(-0.670955\pi\)
−0.511623 + 0.859210i \(0.670955\pi\)
\(252\) 5.03794 0.317360
\(253\) 1.65062 0.103774
\(254\) 21.3259 1.33810
\(255\) 0.976737 0.0611656
\(256\) 1.00000 0.0625000
\(257\) −4.87073 −0.303828 −0.151914 0.988394i \(-0.548544\pi\)
−0.151914 + 0.988394i \(0.548544\pi\)
\(258\) −6.19622 −0.385760
\(259\) 15.3512 0.953876
\(260\) 4.22069 0.261756
\(261\) 3.66474 0.226842
\(262\) −11.9874 −0.740587
\(263\) −0.362645 −0.0223617 −0.0111808 0.999937i \(-0.503559\pi\)
−0.0111808 + 0.999937i \(0.503559\pi\)
\(264\) 0.417963 0.0257238
\(265\) −11.0125 −0.676495
\(266\) −14.0312 −0.860305
\(267\) 0.0673242 0.00412017
\(268\) 7.99847 0.488584
\(269\) −20.9121 −1.27503 −0.637517 0.770436i \(-0.720039\pi\)
−0.637517 + 0.770436i \(0.720039\pi\)
\(270\) 3.12780 0.190352
\(271\) −9.56595 −0.581090 −0.290545 0.956861i \(-0.593837\pi\)
−0.290545 + 0.956861i \(0.593837\pi\)
\(272\) 1.77958 0.107903
\(273\) −4.32445 −0.261728
\(274\) 8.61417 0.520401
\(275\) 0.761515 0.0459211
\(276\) −1.18967 −0.0716098
\(277\) −5.26163 −0.316141 −0.158070 0.987428i \(-0.550527\pi\)
−0.158070 + 0.987428i \(0.550527\pi\)
\(278\) −0.313769 −0.0188186
\(279\) −7.40361 −0.443243
\(280\) −1.86676 −0.111560
\(281\) −15.0816 −0.899691 −0.449845 0.893106i \(-0.648521\pi\)
−0.449845 + 0.893106i \(0.648521\pi\)
\(282\) 1.92955 0.114903
\(283\) 21.4410 1.27453 0.637267 0.770643i \(-0.280065\pi\)
0.637267 + 0.770643i \(0.280065\pi\)
\(284\) −4.51275 −0.267782
\(285\) −4.12537 −0.244366
\(286\) 3.21412 0.190055
\(287\) 22.3095 1.31689
\(288\) 2.69876 0.159026
\(289\) −13.8331 −0.813711
\(290\) −1.35794 −0.0797408
\(291\) 1.55534 0.0911756
\(292\) 16.3206 0.955091
\(293\) −2.88070 −0.168292 −0.0841461 0.996453i \(-0.526816\pi\)
−0.0841461 + 0.996453i \(0.526816\pi\)
\(294\) −1.92934 −0.112521
\(295\) 12.1732 0.708752
\(296\) 8.22343 0.477977
\(297\) 2.38187 0.138210
\(298\) 17.3878 1.00725
\(299\) −9.14853 −0.529073
\(300\) −0.548857 −0.0316883
\(301\) 21.0745 1.21471
\(302\) −11.6514 −0.670462
\(303\) −0.116397 −0.00668685
\(304\) −7.51631 −0.431090
\(305\) −6.48721 −0.371456
\(306\) 4.80266 0.274550
\(307\) −17.1239 −0.977313 −0.488657 0.872476i \(-0.662513\pi\)
−0.488657 + 0.872476i \(0.662513\pi\)
\(308\) −1.42157 −0.0810014
\(309\) −0.593347 −0.0337543
\(310\) 2.74334 0.155811
\(311\) −16.7400 −0.949238 −0.474619 0.880191i \(-0.657414\pi\)
−0.474619 + 0.880191i \(0.657414\pi\)
\(312\) −2.31655 −0.131149
\(313\) −12.5325 −0.708378 −0.354189 0.935174i \(-0.615243\pi\)
−0.354189 + 0.935174i \(0.615243\pi\)
\(314\) −15.9952 −0.902663
\(315\) −5.03794 −0.283856
\(316\) −13.9449 −0.784465
\(317\) 33.5037 1.88176 0.940879 0.338744i \(-0.110002\pi\)
0.940879 + 0.338744i \(0.110002\pi\)
\(318\) 6.04431 0.338948
\(319\) −1.03409 −0.0578979
\(320\) −1.00000 −0.0559017
\(321\) −6.47740 −0.361533
\(322\) 4.04629 0.225491
\(323\) −13.3759 −0.744255
\(324\) 6.37956 0.354420
\(325\) −4.22069 −0.234122
\(326\) −7.07887 −0.392062
\(327\) −9.93304 −0.549298
\(328\) 11.9509 0.659879
\(329\) −6.56274 −0.361816
\(330\) −0.417963 −0.0230081
\(331\) 34.0309 1.87051 0.935255 0.353976i \(-0.115170\pi\)
0.935255 + 0.353976i \(0.115170\pi\)
\(332\) −0.0586654 −0.00321968
\(333\) 22.1930 1.21617
\(334\) −12.2111 −0.668162
\(335\) −7.99847 −0.437003
\(336\) 1.02458 0.0558957
\(337\) 17.9001 0.975083 0.487541 0.873100i \(-0.337894\pi\)
0.487541 + 0.873100i \(0.337894\pi\)
\(338\) −4.81419 −0.261858
\(339\) 3.56986 0.193888
\(340\) −1.77958 −0.0965115
\(341\) 2.08910 0.113131
\(342\) −20.2847 −1.09687
\(343\) 19.6294 1.05989
\(344\) 11.2893 0.608680
\(345\) 1.18967 0.0640498
\(346\) 17.3158 0.930903
\(347\) −12.1406 −0.651740 −0.325870 0.945415i \(-0.605657\pi\)
−0.325870 + 0.945415i \(0.605657\pi\)
\(348\) 0.745313 0.0399530
\(349\) −22.3750 −1.19771 −0.598854 0.800858i \(-0.704377\pi\)
−0.598854 + 0.800858i \(0.704377\pi\)
\(350\) 1.86676 0.0997826
\(351\) −13.2015 −0.704642
\(352\) −0.761515 −0.0405889
\(353\) 19.9913 1.06403 0.532014 0.846735i \(-0.321435\pi\)
0.532014 + 0.846735i \(0.321435\pi\)
\(354\) −6.68135 −0.355110
\(355\) 4.51275 0.239512
\(356\) −0.122663 −0.00650111
\(357\) 1.82333 0.0965011
\(358\) −10.8140 −0.571536
\(359\) −18.1630 −0.958608 −0.479304 0.877649i \(-0.659111\pi\)
−0.479304 + 0.877649i \(0.659111\pi\)
\(360\) −2.69876 −0.142237
\(361\) 37.4949 1.97341
\(362\) −14.7439 −0.774924
\(363\) 5.71914 0.300177
\(364\) 7.87902 0.412973
\(365\) −16.3206 −0.854259
\(366\) 3.56055 0.186113
\(367\) 19.8279 1.03501 0.517504 0.855681i \(-0.326861\pi\)
0.517504 + 0.855681i \(0.326861\pi\)
\(368\) 2.16755 0.112991
\(369\) 32.2526 1.67900
\(370\) −8.22343 −0.427516
\(371\) −20.5578 −1.06731
\(372\) −1.50570 −0.0780670
\(373\) −4.64418 −0.240467 −0.120233 0.992746i \(-0.538364\pi\)
−0.120233 + 0.992746i \(0.538364\pi\)
\(374\) −1.35518 −0.0700747
\(375\) 0.548857 0.0283428
\(376\) −3.51558 −0.181302
\(377\) 5.73143 0.295183
\(378\) 5.83886 0.300319
\(379\) 33.5715 1.72445 0.862225 0.506525i \(-0.169070\pi\)
0.862225 + 0.506525i \(0.169070\pi\)
\(380\) 7.51631 0.385578
\(381\) 11.7048 0.599658
\(382\) 6.89586 0.352823
\(383\) 12.1617 0.621435 0.310717 0.950502i \(-0.399431\pi\)
0.310717 + 0.950502i \(0.399431\pi\)
\(384\) 0.548857 0.0280087
\(385\) 1.42157 0.0724498
\(386\) −11.5661 −0.588697
\(387\) 30.4672 1.54873
\(388\) −2.83378 −0.143863
\(389\) −22.6068 −1.14621 −0.573106 0.819481i \(-0.694262\pi\)
−0.573106 + 0.819481i \(0.694262\pi\)
\(390\) 2.31655 0.117303
\(391\) 3.85733 0.195074
\(392\) 3.51520 0.177544
\(393\) −6.57939 −0.331886
\(394\) −25.0540 −1.26220
\(395\) 13.9449 0.701646
\(396\) −2.05514 −0.103275
\(397\) −8.63801 −0.433529 −0.216765 0.976224i \(-0.569550\pi\)
−0.216765 + 0.976224i \(0.569550\pi\)
\(398\) −10.1371 −0.508126
\(399\) −7.70109 −0.385537
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) 4.39001 0.218954
\(403\) −11.5788 −0.576780
\(404\) 0.212072 0.0105510
\(405\) −6.37956 −0.317003
\(406\) −2.53495 −0.125807
\(407\) −6.26227 −0.310409
\(408\) 0.976737 0.0483557
\(409\) 24.3843 1.20573 0.602864 0.797844i \(-0.294026\pi\)
0.602864 + 0.797844i \(0.294026\pi\)
\(410\) −11.9509 −0.590213
\(411\) 4.72795 0.233212
\(412\) 1.08106 0.0532600
\(413\) 22.7245 1.11820
\(414\) 5.84968 0.287496
\(415\) 0.0586654 0.00287977
\(416\) 4.22069 0.206936
\(417\) −0.172214 −0.00843336
\(418\) 5.72378 0.279959
\(419\) −6.20803 −0.303282 −0.151641 0.988436i \(-0.548456\pi\)
−0.151641 + 0.988436i \(0.548456\pi\)
\(420\) −1.02458 −0.0499946
\(421\) 36.0429 1.75662 0.878311 0.478090i \(-0.158671\pi\)
0.878311 + 0.478090i \(0.158671\pi\)
\(422\) −10.9855 −0.534766
\(423\) −9.48768 −0.461307
\(424\) −11.0125 −0.534816
\(425\) 1.77958 0.0863225
\(426\) −2.47685 −0.120004
\(427\) −12.1101 −0.586047
\(428\) 11.8016 0.570453
\(429\) 1.76409 0.0851711
\(430\) −11.2893 −0.544420
\(431\) 26.0536 1.25496 0.627480 0.778633i \(-0.284086\pi\)
0.627480 + 0.778633i \(0.284086\pi\)
\(432\) 3.12780 0.150486
\(433\) −0.698973 −0.0335905 −0.0167952 0.999859i \(-0.505346\pi\)
−0.0167952 + 0.999859i \(0.505346\pi\)
\(434\) 5.12117 0.245824
\(435\) −0.745313 −0.0357350
\(436\) 18.0977 0.866723
\(437\) −16.2919 −0.779349
\(438\) 8.95767 0.428014
\(439\) −12.6681 −0.604614 −0.302307 0.953211i \(-0.597757\pi\)
−0.302307 + 0.953211i \(0.597757\pi\)
\(440\) 0.761515 0.0363038
\(441\) 9.48666 0.451746
\(442\) 7.51107 0.357265
\(443\) 25.6499 1.21866 0.609331 0.792916i \(-0.291438\pi\)
0.609331 + 0.792916i \(0.291438\pi\)
\(444\) 4.51348 0.214200
\(445\) 0.122663 0.00581477
\(446\) −10.1950 −0.482749
\(447\) 9.54343 0.451389
\(448\) −1.86676 −0.0881962
\(449\) 34.0187 1.60544 0.802721 0.596354i \(-0.203385\pi\)
0.802721 + 0.596354i \(0.203385\pi\)
\(450\) 2.69876 0.127221
\(451\) −9.10080 −0.428540
\(452\) −6.50418 −0.305931
\(453\) −6.39494 −0.300460
\(454\) −19.1164 −0.897175
\(455\) −7.87902 −0.369374
\(456\) −4.12537 −0.193188
\(457\) 15.8036 0.739260 0.369630 0.929179i \(-0.379484\pi\)
0.369630 + 0.929179i \(0.379484\pi\)
\(458\) −12.7450 −0.595533
\(459\) 5.56618 0.259807
\(460\) −2.16755 −0.101062
\(461\) 19.6388 0.914671 0.457336 0.889294i \(-0.348804\pi\)
0.457336 + 0.889294i \(0.348804\pi\)
\(462\) −0.780237 −0.0362999
\(463\) 6.91455 0.321346 0.160673 0.987008i \(-0.448634\pi\)
0.160673 + 0.987008i \(0.448634\pi\)
\(464\) −1.35794 −0.0630406
\(465\) 1.50570 0.0698252
\(466\) 19.0509 0.882516
\(467\) 4.65442 0.215381 0.107691 0.994184i \(-0.465654\pi\)
0.107691 + 0.994184i \(0.465654\pi\)
\(468\) 11.3906 0.526531
\(469\) −14.9312 −0.689460
\(470\) 3.51558 0.162161
\(471\) −8.77909 −0.404519
\(472\) 12.1732 0.560317
\(473\) −8.59700 −0.395290
\(474\) −7.65378 −0.351550
\(475\) −7.51631 −0.344872
\(476\) −3.32206 −0.152266
\(477\) −29.7202 −1.36079
\(478\) −14.2195 −0.650385
\(479\) −19.0202 −0.869054 −0.434527 0.900659i \(-0.643084\pi\)
−0.434527 + 0.900659i \(0.643084\pi\)
\(480\) −0.548857 −0.0250518
\(481\) 34.7085 1.58257
\(482\) 25.0784 1.14229
\(483\) 2.22083 0.101051
\(484\) −10.4201 −0.473641
\(485\) 2.83378 0.128675
\(486\) 12.8849 0.584469
\(487\) 2.44044 0.110587 0.0552934 0.998470i \(-0.482391\pi\)
0.0552934 + 0.998470i \(0.482391\pi\)
\(488\) −6.48721 −0.293662
\(489\) −3.88529 −0.175699
\(490\) −3.51520 −0.158800
\(491\) 19.6388 0.886287 0.443144 0.896451i \(-0.353863\pi\)
0.443144 + 0.896451i \(0.353863\pi\)
\(492\) 6.55934 0.295718
\(493\) −2.41656 −0.108837
\(494\) −31.7240 −1.42733
\(495\) 2.05514 0.0923719
\(496\) 2.74334 0.123180
\(497\) 8.42422 0.377878
\(498\) −0.0321989 −0.00144287
\(499\) 43.4800 1.94643 0.973216 0.229893i \(-0.0738376\pi\)
0.973216 + 0.229893i \(0.0738376\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −6.70215 −0.299430
\(502\) 16.2113 0.723544
\(503\) −23.3736 −1.04218 −0.521089 0.853502i \(-0.674474\pi\)
−0.521089 + 0.853502i \(0.674474\pi\)
\(504\) −5.03794 −0.224408
\(505\) −0.212072 −0.00943709
\(506\) −1.65062 −0.0733790
\(507\) −2.64230 −0.117349
\(508\) −21.3259 −0.946183
\(509\) −26.8089 −1.18828 −0.594142 0.804360i \(-0.702508\pi\)
−0.594142 + 0.804360i \(0.702508\pi\)
\(510\) −0.976737 −0.0432506
\(511\) −30.4667 −1.34777
\(512\) −1.00000 −0.0441942
\(513\) −23.5095 −1.03797
\(514\) 4.87073 0.214839
\(515\) −1.08106 −0.0476372
\(516\) 6.19622 0.272774
\(517\) 2.67717 0.117742
\(518\) −15.3512 −0.674492
\(519\) 9.50389 0.417174
\(520\) −4.22069 −0.185089
\(521\) 1.15191 0.0504660 0.0252330 0.999682i \(-0.491967\pi\)
0.0252330 + 0.999682i \(0.491967\pi\)
\(522\) −3.66474 −0.160401
\(523\) 13.9791 0.611265 0.305632 0.952150i \(-0.401132\pi\)
0.305632 + 0.952150i \(0.401132\pi\)
\(524\) 11.9874 0.523674
\(525\) 1.02458 0.0447165
\(526\) 0.362645 0.0158121
\(527\) 4.88201 0.212664
\(528\) −0.417963 −0.0181895
\(529\) −18.3017 −0.795728
\(530\) 11.0125 0.478354
\(531\) 32.8525 1.42568
\(532\) 14.0312 0.608328
\(533\) 50.4410 2.18484
\(534\) −0.0673242 −0.00291340
\(535\) −11.8016 −0.510229
\(536\) −7.99847 −0.345481
\(537\) −5.93532 −0.256128
\(538\) 20.9121 0.901586
\(539\) −2.67688 −0.115301
\(540\) −3.12780 −0.134599
\(541\) −15.9678 −0.686510 −0.343255 0.939242i \(-0.611530\pi\)
−0.343255 + 0.939242i \(0.611530\pi\)
\(542\) 9.56595 0.410893
\(543\) −8.09231 −0.347274
\(544\) −1.77958 −0.0762990
\(545\) −18.0977 −0.775220
\(546\) 4.32445 0.185069
\(547\) −20.7081 −0.885413 −0.442706 0.896667i \(-0.645982\pi\)
−0.442706 + 0.896667i \(0.645982\pi\)
\(548\) −8.61417 −0.367979
\(549\) −17.5074 −0.747197
\(550\) −0.761515 −0.0324711
\(551\) 10.2067 0.434819
\(552\) 1.18967 0.0506358
\(553\) 26.0319 1.10699
\(554\) 5.26163 0.223545
\(555\) −4.51348 −0.191587
\(556\) 0.313769 0.0133068
\(557\) −31.3637 −1.32892 −0.664461 0.747323i \(-0.731339\pi\)
−0.664461 + 0.747323i \(0.731339\pi\)
\(558\) 7.40361 0.313420
\(559\) 47.6487 2.01533
\(560\) 1.86676 0.0788851
\(561\) −0.743800 −0.0314033
\(562\) 15.0816 0.636178
\(563\) −28.1159 −1.18494 −0.592471 0.805592i \(-0.701848\pi\)
−0.592471 + 0.805592i \(0.701848\pi\)
\(564\) −1.92955 −0.0812486
\(565\) 6.50418 0.273633
\(566\) −21.4410 −0.901231
\(567\) −11.9091 −0.500136
\(568\) 4.51275 0.189351
\(569\) 23.5546 0.987460 0.493730 0.869615i \(-0.335633\pi\)
0.493730 + 0.869615i \(0.335633\pi\)
\(570\) 4.12537 0.172793
\(571\) −25.2957 −1.05859 −0.529296 0.848437i \(-0.677544\pi\)
−0.529296 + 0.848437i \(0.677544\pi\)
\(572\) −3.21412 −0.134389
\(573\) 3.78484 0.158114
\(574\) −22.3095 −0.931181
\(575\) 2.16755 0.0903929
\(576\) −2.69876 −0.112448
\(577\) −40.5453 −1.68792 −0.843961 0.536404i \(-0.819782\pi\)
−0.843961 + 0.536404i \(0.819782\pi\)
\(578\) 13.8331 0.575380
\(579\) −6.34811 −0.263818
\(580\) 1.35794 0.0563853
\(581\) 0.109514 0.00454342
\(582\) −1.55534 −0.0644709
\(583\) 8.38622 0.347322
\(584\) −16.3206 −0.675351
\(585\) −11.3906 −0.470944
\(586\) 2.88070 0.119001
\(587\) 8.72727 0.360213 0.180106 0.983647i \(-0.442356\pi\)
0.180106 + 0.983647i \(0.442356\pi\)
\(588\) 1.92934 0.0795646
\(589\) −20.6198 −0.849624
\(590\) −12.1732 −0.501163
\(591\) −13.7510 −0.565642
\(592\) −8.22343 −0.337981
\(593\) 44.2149 1.81569 0.907844 0.419308i \(-0.137727\pi\)
0.907844 + 0.419308i \(0.137727\pi\)
\(594\) −2.38187 −0.0977292
\(595\) 3.32206 0.136191
\(596\) −17.3878 −0.712234
\(597\) −5.56381 −0.227711
\(598\) 9.14853 0.374111
\(599\) −26.3992 −1.07864 −0.539322 0.842100i \(-0.681319\pi\)
−0.539322 + 0.842100i \(0.681319\pi\)
\(600\) 0.548857 0.0224070
\(601\) 13.0659 0.532970 0.266485 0.963839i \(-0.414138\pi\)
0.266485 + 0.963839i \(0.414138\pi\)
\(602\) −21.0745 −0.858932
\(603\) −21.5859 −0.879046
\(604\) 11.6514 0.474088
\(605\) 10.4201 0.423637
\(606\) 0.116397 0.00472832
\(607\) −0.0516183 −0.00209512 −0.00104756 0.999999i \(-0.500333\pi\)
−0.00104756 + 0.999999i \(0.500333\pi\)
\(608\) 7.51631 0.304826
\(609\) −1.39132 −0.0563792
\(610\) 6.48721 0.262659
\(611\) −14.8381 −0.600287
\(612\) −4.80266 −0.194136
\(613\) −18.0550 −0.729234 −0.364617 0.931158i \(-0.618800\pi\)
−0.364617 + 0.931158i \(0.618800\pi\)
\(614\) 17.1239 0.691065
\(615\) −6.55934 −0.264498
\(616\) 1.42157 0.0572766
\(617\) 19.9740 0.804124 0.402062 0.915612i \(-0.368294\pi\)
0.402062 + 0.915612i \(0.368294\pi\)
\(618\) 0.593347 0.0238679
\(619\) 10.9321 0.439397 0.219698 0.975568i \(-0.429493\pi\)
0.219698 + 0.975568i \(0.429493\pi\)
\(620\) −2.74334 −0.110175
\(621\) 6.77965 0.272058
\(622\) 16.7400 0.671213
\(623\) 0.228982 0.00917397
\(624\) 2.31655 0.0927363
\(625\) 1.00000 0.0400000
\(626\) 12.5325 0.500899
\(627\) 3.14154 0.125461
\(628\) 15.9952 0.638279
\(629\) −14.6343 −0.583507
\(630\) 5.03794 0.200716
\(631\) −25.8454 −1.02889 −0.514445 0.857523i \(-0.672002\pi\)
−0.514445 + 0.857523i \(0.672002\pi\)
\(632\) 13.9449 0.554700
\(633\) −6.02947 −0.239650
\(634\) −33.5037 −1.33060
\(635\) 21.3259 0.846292
\(636\) −6.04431 −0.239672
\(637\) 14.8366 0.587846
\(638\) 1.03409 0.0409400
\(639\) 12.1788 0.481786
\(640\) 1.00000 0.0395285
\(641\) 28.3830 1.12106 0.560531 0.828133i \(-0.310597\pi\)
0.560531 + 0.828133i \(0.310597\pi\)
\(642\) 6.47740 0.255643
\(643\) −9.24838 −0.364720 −0.182360 0.983232i \(-0.558374\pi\)
−0.182360 + 0.983232i \(0.558374\pi\)
\(644\) −4.04629 −0.159446
\(645\) −6.19622 −0.243976
\(646\) 13.3759 0.526268
\(647\) 15.2499 0.599537 0.299769 0.954012i \(-0.403091\pi\)
0.299769 + 0.954012i \(0.403091\pi\)
\(648\) −6.37956 −0.250613
\(649\) −9.27009 −0.363883
\(650\) 4.22069 0.165549
\(651\) 2.81079 0.110163
\(652\) 7.07887 0.277230
\(653\) −44.5302 −1.74260 −0.871301 0.490750i \(-0.836723\pi\)
−0.871301 + 0.490750i \(0.836723\pi\)
\(654\) 9.93304 0.388413
\(655\) −11.9874 −0.468388
\(656\) −11.9509 −0.466605
\(657\) −44.0453 −1.71837
\(658\) 6.56274 0.255842
\(659\) −0.386052 −0.0150384 −0.00751922 0.999972i \(-0.502393\pi\)
−0.00751922 + 0.999972i \(0.502393\pi\)
\(660\) 0.417963 0.0162692
\(661\) 26.2732 1.02191 0.510955 0.859608i \(-0.329292\pi\)
0.510955 + 0.859608i \(0.329292\pi\)
\(662\) −34.0309 −1.32265
\(663\) 4.12250 0.160105
\(664\) 0.0586654 0.00227666
\(665\) −14.0312 −0.544105
\(666\) −22.1930 −0.859962
\(667\) −2.94339 −0.113969
\(668\) 12.2111 0.472462
\(669\) −5.59562 −0.216339
\(670\) 7.99847 0.309008
\(671\) 4.94011 0.190711
\(672\) −1.02458 −0.0395242
\(673\) 2.29890 0.0886161 0.0443081 0.999018i \(-0.485892\pi\)
0.0443081 + 0.999018i \(0.485892\pi\)
\(674\) −17.9001 −0.689488
\(675\) 3.12780 0.120389
\(676\) 4.81419 0.185161
\(677\) −24.3399 −0.935457 −0.467728 0.883872i \(-0.654927\pi\)
−0.467728 + 0.883872i \(0.654927\pi\)
\(678\) −3.56986 −0.137100
\(679\) 5.29000 0.203011
\(680\) 1.77958 0.0682439
\(681\) −10.4921 −0.402060
\(682\) −2.08910 −0.0799957
\(683\) 2.65464 0.101577 0.0507885 0.998709i \(-0.483827\pi\)
0.0507885 + 0.998709i \(0.483827\pi\)
\(684\) 20.2847 0.775604
\(685\) 8.61417 0.329131
\(686\) −19.6294 −0.749453
\(687\) −6.99516 −0.266882
\(688\) −11.2893 −0.430402
\(689\) −46.4805 −1.77077
\(690\) −1.18967 −0.0452900
\(691\) 0.454025 0.0172719 0.00863596 0.999963i \(-0.497251\pi\)
0.00863596 + 0.999963i \(0.497251\pi\)
\(692\) −17.3158 −0.658248
\(693\) 3.83647 0.145735
\(694\) 12.1406 0.460850
\(695\) −0.313769 −0.0119019
\(696\) −0.745313 −0.0282510
\(697\) −21.2677 −0.805570
\(698\) 22.3750 0.846907
\(699\) 10.4562 0.395490
\(700\) −1.86676 −0.0705570
\(701\) −40.8562 −1.54312 −0.771558 0.636159i \(-0.780522\pi\)
−0.771558 + 0.636159i \(0.780522\pi\)
\(702\) 13.2015 0.498257
\(703\) 61.8098 2.33120
\(704\) 0.761515 0.0287007
\(705\) 1.92955 0.0726709
\(706\) −19.9913 −0.752382
\(707\) −0.395888 −0.0148889
\(708\) 6.68135 0.251100
\(709\) −19.0442 −0.715219 −0.357609 0.933871i \(-0.616408\pi\)
−0.357609 + 0.933871i \(0.616408\pi\)
\(710\) −4.51275 −0.169360
\(711\) 37.6340 1.41139
\(712\) 0.122663 0.00459698
\(713\) 5.94632 0.222691
\(714\) −1.82333 −0.0682366
\(715\) 3.21412 0.120201
\(716\) 10.8140 0.404137
\(717\) −7.80447 −0.291463
\(718\) 18.1630 0.677838
\(719\) −36.0186 −1.34327 −0.671633 0.740884i \(-0.734407\pi\)
−0.671633 + 0.740884i \(0.734407\pi\)
\(720\) 2.69876 0.100577
\(721\) −2.01808 −0.0751573
\(722\) −37.4949 −1.39541
\(723\) 13.7645 0.511906
\(724\) 14.7439 0.547954
\(725\) −1.35794 −0.0504325
\(726\) −5.71914 −0.212257
\(727\) 3.08100 0.114268 0.0571339 0.998367i \(-0.481804\pi\)
0.0571339 + 0.998367i \(0.481804\pi\)
\(728\) −7.87902 −0.292016
\(729\) −12.0667 −0.446916
\(730\) 16.3206 0.604053
\(731\) −20.0903 −0.743067
\(732\) −3.56055 −0.131602
\(733\) −34.1974 −1.26311 −0.631556 0.775330i \(-0.717583\pi\)
−0.631556 + 0.775330i \(0.717583\pi\)
\(734\) −19.8279 −0.731861
\(735\) −1.92934 −0.0711648
\(736\) −2.16755 −0.0798968
\(737\) 6.09096 0.224363
\(738\) −32.2526 −1.18723
\(739\) 50.3886 1.85357 0.926787 0.375587i \(-0.122559\pi\)
0.926787 + 0.375587i \(0.122559\pi\)
\(740\) 8.22343 0.302299
\(741\) −17.4119 −0.639643
\(742\) 20.5578 0.754700
\(743\) −35.6132 −1.30652 −0.653260 0.757134i \(-0.726599\pi\)
−0.653260 + 0.757134i \(0.726599\pi\)
\(744\) 1.50570 0.0552017
\(745\) 17.3878 0.637041
\(746\) 4.64418 0.170036
\(747\) 0.158324 0.00579276
\(748\) 1.35518 0.0495503
\(749\) −22.0308 −0.804989
\(750\) −0.548857 −0.0200414
\(751\) 29.9318 1.09223 0.546114 0.837711i \(-0.316107\pi\)
0.546114 + 0.837711i \(0.316107\pi\)
\(752\) 3.51558 0.128200
\(753\) 8.89766 0.324249
\(754\) −5.73143 −0.208726
\(755\) −11.6514 −0.424037
\(756\) −5.83886 −0.212357
\(757\) 2.45166 0.0891072 0.0445536 0.999007i \(-0.485813\pi\)
0.0445536 + 0.999007i \(0.485813\pi\)
\(758\) −33.5715 −1.21937
\(759\) −0.905953 −0.0328840
\(760\) −7.51631 −0.272645
\(761\) −47.2602 −1.71318 −0.856590 0.515997i \(-0.827422\pi\)
−0.856590 + 0.515997i \(0.827422\pi\)
\(762\) −11.7048 −0.424022
\(763\) −33.7841 −1.22307
\(764\) −6.89586 −0.249483
\(765\) 4.80266 0.173641
\(766\) −12.1617 −0.439421
\(767\) 51.3793 1.85520
\(768\) −0.548857 −0.0198052
\(769\) −36.5371 −1.31756 −0.658781 0.752335i \(-0.728927\pi\)
−0.658781 + 0.752335i \(0.728927\pi\)
\(770\) −1.42157 −0.0512298
\(771\) 2.67333 0.0962777
\(772\) 11.5661 0.416272
\(773\) −45.1575 −1.62420 −0.812101 0.583517i \(-0.801676\pi\)
−0.812101 + 0.583517i \(0.801676\pi\)
\(774\) −30.4672 −1.09512
\(775\) 2.74334 0.0985438
\(776\) 2.83378 0.101727
\(777\) −8.42560 −0.302267
\(778\) 22.6068 0.810495
\(779\) 89.8267 3.21838
\(780\) −2.31655 −0.0829459
\(781\) −3.43653 −0.122969
\(782\) −3.85733 −0.137938
\(783\) −4.24736 −0.151788
\(784\) −3.51520 −0.125543
\(785\) −15.9952 −0.570894
\(786\) 6.57939 0.234679
\(787\) 40.5568 1.44569 0.722847 0.691008i \(-0.242833\pi\)
0.722847 + 0.691008i \(0.242833\pi\)
\(788\) 25.0540 0.892511
\(789\) 0.199040 0.00708602
\(790\) −13.9449 −0.496139
\(791\) 12.1418 0.431712
\(792\) 2.05514 0.0730264
\(793\) −27.3805 −0.972309
\(794\) 8.63801 0.306551
\(795\) 6.04431 0.214369
\(796\) 10.1371 0.359299
\(797\) 14.8745 0.526883 0.263441 0.964675i \(-0.415142\pi\)
0.263441 + 0.964675i \(0.415142\pi\)
\(798\) 7.70109 0.272616
\(799\) 6.25626 0.221331
\(800\) −1.00000 −0.0353553
\(801\) 0.331036 0.0116966
\(802\) −1.00000 −0.0353112
\(803\) 12.4284 0.438588
\(804\) −4.39001 −0.154824
\(805\) 4.04629 0.142613
\(806\) 11.5788 0.407845
\(807\) 11.4778 0.404036
\(808\) −0.212072 −0.00746068
\(809\) −7.79676 −0.274120 −0.137060 0.990563i \(-0.543765\pi\)
−0.137060 + 0.990563i \(0.543765\pi\)
\(810\) 6.37956 0.224155
\(811\) −31.8247 −1.11752 −0.558759 0.829330i \(-0.688722\pi\)
−0.558759 + 0.829330i \(0.688722\pi\)
\(812\) 2.53495 0.0889591
\(813\) 5.25033 0.184137
\(814\) 6.26227 0.219492
\(815\) −7.07887 −0.247962
\(816\) −0.976737 −0.0341926
\(817\) 84.8541 2.96867
\(818\) −24.3843 −0.852578
\(819\) −21.2636 −0.743009
\(820\) 11.9509 0.417344
\(821\) 23.2473 0.811337 0.405669 0.914020i \(-0.367039\pi\)
0.405669 + 0.914020i \(0.367039\pi\)
\(822\) −4.72795 −0.164906
\(823\) 32.4608 1.13151 0.565757 0.824572i \(-0.308584\pi\)
0.565757 + 0.824572i \(0.308584\pi\)
\(824\) −1.08106 −0.0376605
\(825\) −0.417963 −0.0145516
\(826\) −22.7245 −0.790686
\(827\) 42.7624 1.48699 0.743496 0.668740i \(-0.233166\pi\)
0.743496 + 0.668740i \(0.233166\pi\)
\(828\) −5.84968 −0.203290
\(829\) −16.9781 −0.589674 −0.294837 0.955548i \(-0.595265\pi\)
−0.294837 + 0.955548i \(0.595265\pi\)
\(830\) −0.0586654 −0.00203630
\(831\) 2.88788 0.100180
\(832\) −4.22069 −0.146326
\(833\) −6.25559 −0.216743
\(834\) 0.172214 0.00596328
\(835\) −12.2111 −0.422583
\(836\) −5.72378 −0.197961
\(837\) 8.58063 0.296590
\(838\) 6.20803 0.214453
\(839\) −0.805427 −0.0278064 −0.0139032 0.999903i \(-0.504426\pi\)
−0.0139032 + 0.999903i \(0.504426\pi\)
\(840\) 1.02458 0.0353515
\(841\) −27.1560 −0.936414
\(842\) −36.0429 −1.24212
\(843\) 8.27762 0.285096
\(844\) 10.9855 0.378137
\(845\) −4.81419 −0.165613
\(846\) 9.48768 0.326193
\(847\) 19.4518 0.668373
\(848\) 11.0125 0.378172
\(849\) −11.7680 −0.403877
\(850\) −1.77958 −0.0610392
\(851\) −17.8247 −0.611021
\(852\) 2.47685 0.0848555
\(853\) 19.5314 0.668743 0.334372 0.942441i \(-0.391476\pi\)
0.334372 + 0.942441i \(0.391476\pi\)
\(854\) 12.1101 0.414398
\(855\) −20.2847 −0.693721
\(856\) −11.8016 −0.403371
\(857\) −53.5256 −1.82840 −0.914199 0.405265i \(-0.867179\pi\)
−0.914199 + 0.405265i \(0.867179\pi\)
\(858\) −1.76409 −0.0602250
\(859\) −16.8448 −0.574736 −0.287368 0.957820i \(-0.592780\pi\)
−0.287368 + 0.957820i \(0.592780\pi\)
\(860\) 11.2893 0.384963
\(861\) −12.2447 −0.417299
\(862\) −26.0536 −0.887391
\(863\) 23.2906 0.792823 0.396411 0.918073i \(-0.370255\pi\)
0.396411 + 0.918073i \(0.370255\pi\)
\(864\) −3.12780 −0.106410
\(865\) 17.3158 0.588755
\(866\) 0.698973 0.0237521
\(867\) 7.59238 0.257851
\(868\) −5.12117 −0.173824
\(869\) −10.6193 −0.360235
\(870\) 0.745313 0.0252685
\(871\) −33.7590 −1.14388
\(872\) −18.0977 −0.612865
\(873\) 7.64768 0.258835
\(874\) 16.2919 0.551083
\(875\) 1.86676 0.0631081
\(876\) −8.95767 −0.302652
\(877\) −32.8314 −1.10864 −0.554319 0.832305i \(-0.687021\pi\)
−0.554319 + 0.832305i \(0.687021\pi\)
\(878\) 12.6681 0.427527
\(879\) 1.58109 0.0533288
\(880\) −0.761515 −0.0256707
\(881\) −40.6644 −1.37002 −0.685010 0.728534i \(-0.740202\pi\)
−0.685010 + 0.728534i \(0.740202\pi\)
\(882\) −9.48666 −0.319433
\(883\) −7.63075 −0.256795 −0.128398 0.991723i \(-0.540983\pi\)
−0.128398 + 0.991723i \(0.540983\pi\)
\(884\) −7.51107 −0.252624
\(885\) −6.68135 −0.224591
\(886\) −25.6499 −0.861725
\(887\) −50.0573 −1.68076 −0.840380 0.541998i \(-0.817668\pi\)
−0.840380 + 0.541998i \(0.817668\pi\)
\(888\) −4.51348 −0.151463
\(889\) 39.8103 1.33520
\(890\) −0.122663 −0.00411166
\(891\) 4.85813 0.162753
\(892\) 10.1950 0.341355
\(893\) −26.4241 −0.884250
\(894\) −9.54343 −0.319180
\(895\) −10.8140 −0.361471
\(896\) 1.86676 0.0623642
\(897\) 5.02123 0.167654
\(898\) −34.0187 −1.13522
\(899\) −3.72529 −0.124245
\(900\) −2.69876 −0.0899585
\(901\) 19.5977 0.652895
\(902\) 9.10080 0.303024
\(903\) −11.5669 −0.384922
\(904\) 6.50418 0.216326
\(905\) −14.7439 −0.490105
\(906\) 6.39494 0.212458
\(907\) −15.6195 −0.518637 −0.259318 0.965792i \(-0.583498\pi\)
−0.259318 + 0.965792i \(0.583498\pi\)
\(908\) 19.1164 0.634398
\(909\) −0.572331 −0.0189830
\(910\) 7.87902 0.261187
\(911\) −5.79468 −0.191986 −0.0959932 0.995382i \(-0.530603\pi\)
−0.0959932 + 0.995382i \(0.530603\pi\)
\(912\) 4.12537 0.136605
\(913\) −0.0446746 −0.00147851
\(914\) −15.8036 −0.522736
\(915\) 3.56055 0.117708
\(916\) 12.7450 0.421105
\(917\) −22.3777 −0.738977
\(918\) −5.56618 −0.183711
\(919\) −57.0861 −1.88310 −0.941549 0.336877i \(-0.890629\pi\)
−0.941549 + 0.336877i \(0.890629\pi\)
\(920\) 2.16755 0.0714619
\(921\) 9.39857 0.309693
\(922\) −19.6388 −0.646770
\(923\) 19.0469 0.626936
\(924\) 0.780237 0.0256679
\(925\) −8.22343 −0.270385
\(926\) −6.91455 −0.227226
\(927\) −2.91752 −0.0958239
\(928\) 1.35794 0.0445765
\(929\) −32.7557 −1.07468 −0.537340 0.843366i \(-0.680571\pi\)
−0.537340 + 0.843366i \(0.680571\pi\)
\(930\) −1.50570 −0.0493739
\(931\) 26.4213 0.865923
\(932\) −19.0509 −0.624033
\(933\) 9.18786 0.300797
\(934\) −4.65442 −0.152297
\(935\) −1.35518 −0.0443192
\(936\) −11.3906 −0.372314
\(937\) 19.3678 0.632719 0.316360 0.948639i \(-0.397539\pi\)
0.316360 + 0.948639i \(0.397539\pi\)
\(938\) 14.9312 0.487522
\(939\) 6.87854 0.224473
\(940\) −3.51558 −0.114665
\(941\) 10.1407 0.330576 0.165288 0.986245i \(-0.447145\pi\)
0.165288 + 0.986245i \(0.447145\pi\)
\(942\) 8.77909 0.286038
\(943\) −25.9041 −0.843555
\(944\) −12.1732 −0.396204
\(945\) 5.83886 0.189938
\(946\) 8.59700 0.279513
\(947\) −17.8730 −0.580796 −0.290398 0.956906i \(-0.593788\pi\)
−0.290398 + 0.956906i \(0.593788\pi\)
\(948\) 7.65378 0.248583
\(949\) −68.8841 −2.23607
\(950\) 7.51631 0.243861
\(951\) −18.3887 −0.596296
\(952\) 3.32206 0.107669
\(953\) −43.4985 −1.40905 −0.704527 0.709677i \(-0.748841\pi\)
−0.704527 + 0.709677i \(0.748841\pi\)
\(954\) 29.7202 0.962226
\(955\) 6.89586 0.223145
\(956\) 14.2195 0.459892
\(957\) 0.567567 0.0183468
\(958\) 19.0202 0.614514
\(959\) 16.0806 0.519270
\(960\) 0.548857 0.0177143
\(961\) −23.4741 −0.757228
\(962\) −34.7085 −1.11905
\(963\) −31.8497 −1.02634
\(964\) −25.0784 −0.807721
\(965\) −11.5661 −0.372325
\(966\) −2.22083 −0.0714542
\(967\) −33.5502 −1.07890 −0.539452 0.842017i \(-0.681368\pi\)
−0.539452 + 0.842017i \(0.681368\pi\)
\(968\) 10.4201 0.334915
\(969\) 7.34145 0.235841
\(970\) −2.83378 −0.0909872
\(971\) 57.3589 1.84073 0.920367 0.391056i \(-0.127890\pi\)
0.920367 + 0.391056i \(0.127890\pi\)
\(972\) −12.8849 −0.413282
\(973\) −0.585732 −0.0187777
\(974\) −2.44044 −0.0781967
\(975\) 2.31655 0.0741890
\(976\) 6.48721 0.207650
\(977\) 10.5052 0.336092 0.168046 0.985779i \(-0.446254\pi\)
0.168046 + 0.985779i \(0.446254\pi\)
\(978\) 3.88529 0.124238
\(979\) −0.0934095 −0.00298538
\(980\) 3.51520 0.112289
\(981\) −48.8413 −1.55938
\(982\) −19.6388 −0.626700
\(983\) 27.3192 0.871347 0.435673 0.900105i \(-0.356510\pi\)
0.435673 + 0.900105i \(0.356510\pi\)
\(984\) −6.55934 −0.209104
\(985\) −25.0540 −0.798286
\(986\) 2.41656 0.0769590
\(987\) 3.60201 0.114653
\(988\) 31.7240 1.00927
\(989\) −24.4701 −0.778105
\(990\) −2.05514 −0.0653168
\(991\) 4.32711 0.137455 0.0687275 0.997635i \(-0.478106\pi\)
0.0687275 + 0.997635i \(0.478106\pi\)
\(992\) −2.74334 −0.0871012
\(993\) −18.6781 −0.592732
\(994\) −8.42422 −0.267200
\(995\) −10.1371 −0.321367
\(996\) 0.0321989 0.00102026
\(997\) 24.9385 0.789811 0.394906 0.918722i \(-0.370777\pi\)
0.394906 + 0.918722i \(0.370777\pi\)
\(998\) −43.4800 −1.37634
\(999\) −25.7212 −0.813784
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 4010.2.a.l.1.6 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.l.1.6 17 1.1 even 1 trivial