Properties

Label 6026.2.a.f.1.5
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $1$
Dimension $20$
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] = [6026,2,Mod(1,6026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6026, 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("6026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6026.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: \(48.1178522580\)
Analytic rank: \(1\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 5 x^{19} - 17 x^{18} + 115 x^{17} + 78 x^{16} - 1083 x^{15} + 248 x^{14} + 5359 x^{13} - 3723 x^{12} - 14776 x^{11} + 14837 x^{10} + 21886 x^{9} - 28084 x^{8} - 14682 x^{7} + \cdots - 18 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.76837\) of defining polynomial
Character \(\chi\) \(=\) 6026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.76837 q^{3} +1.00000 q^{4} +1.49209 q^{5} -1.76837 q^{6} +3.65436 q^{7} +1.00000 q^{8} +0.127121 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.76837 q^{3} +1.00000 q^{4} +1.49209 q^{5} -1.76837 q^{6} +3.65436 q^{7} +1.00000 q^{8} +0.127121 q^{9} +1.49209 q^{10} -3.80342 q^{11} -1.76837 q^{12} +1.15241 q^{13} +3.65436 q^{14} -2.63855 q^{15} +1.00000 q^{16} -6.90897 q^{17} +0.127121 q^{18} -1.36683 q^{19} +1.49209 q^{20} -6.46224 q^{21} -3.80342 q^{22} +1.00000 q^{23} -1.76837 q^{24} -2.77368 q^{25} +1.15241 q^{26} +5.08030 q^{27} +3.65436 q^{28} +10.2612 q^{29} -2.63855 q^{30} -4.85848 q^{31} +1.00000 q^{32} +6.72584 q^{33} -6.90897 q^{34} +5.45261 q^{35} +0.127121 q^{36} -3.49596 q^{37} -1.36683 q^{38} -2.03788 q^{39} +1.49209 q^{40} -4.95721 q^{41} -6.46224 q^{42} -11.4310 q^{43} -3.80342 q^{44} +0.189675 q^{45} +1.00000 q^{46} +1.92948 q^{47} -1.76837 q^{48} +6.35432 q^{49} -2.77368 q^{50} +12.2176 q^{51} +1.15241 q^{52} -11.6074 q^{53} +5.08030 q^{54} -5.67503 q^{55} +3.65436 q^{56} +2.41706 q^{57} +10.2612 q^{58} -6.12808 q^{59} -2.63855 q^{60} -10.6230 q^{61} -4.85848 q^{62} +0.464544 q^{63} +1.00000 q^{64} +1.71949 q^{65} +6.72584 q^{66} -1.94680 q^{67} -6.90897 q^{68} -1.76837 q^{69} +5.45261 q^{70} -9.55777 q^{71} +0.127121 q^{72} +0.982039 q^{73} -3.49596 q^{74} +4.90488 q^{75} -1.36683 q^{76} -13.8990 q^{77} -2.03788 q^{78} +5.33190 q^{79} +1.49209 q^{80} -9.36520 q^{81} -4.95721 q^{82} +3.48726 q^{83} -6.46224 q^{84} -10.3088 q^{85} -11.4310 q^{86} -18.1456 q^{87} -3.80342 q^{88} +12.5179 q^{89} +0.189675 q^{90} +4.21132 q^{91} +1.00000 q^{92} +8.59158 q^{93} +1.92948 q^{94} -2.03943 q^{95} -1.76837 q^{96} +12.5598 q^{97} +6.35432 q^{98} -0.483493 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 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
\(3\) −1.76837 −1.02097 −0.510483 0.859888i \(-0.670534\pi\)
−0.510483 + 0.859888i \(0.670534\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.49209 0.667281 0.333641 0.942700i \(-0.391723\pi\)
0.333641 + 0.942700i \(0.391723\pi\)
\(6\) −1.76837 −0.721933
\(7\) 3.65436 1.38122 0.690608 0.723229i \(-0.257343\pi\)
0.690608 + 0.723229i \(0.257343\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.127121 0.0423736
\(10\) 1.49209 0.471839
\(11\) −3.80342 −1.14677 −0.573387 0.819285i \(-0.694371\pi\)
−0.573387 + 0.819285i \(0.694371\pi\)
\(12\) −1.76837 −0.510483
\(13\) 1.15241 0.319621 0.159811 0.987148i \(-0.448912\pi\)
0.159811 + 0.987148i \(0.448912\pi\)
\(14\) 3.65436 0.976668
\(15\) −2.63855 −0.681272
\(16\) 1.00000 0.250000
\(17\) −6.90897 −1.67567 −0.837836 0.545922i \(-0.816179\pi\)
−0.837836 + 0.545922i \(0.816179\pi\)
\(18\) 0.127121 0.0299626
\(19\) −1.36683 −0.313573 −0.156786 0.987633i \(-0.550113\pi\)
−0.156786 + 0.987633i \(0.550113\pi\)
\(20\) 1.49209 0.333641
\(21\) −6.46224 −1.41018
\(22\) −3.80342 −0.810891
\(23\) 1.00000 0.208514
\(24\) −1.76837 −0.360966
\(25\) −2.77368 −0.554736
\(26\) 1.15241 0.226006
\(27\) 5.08030 0.977705
\(28\) 3.65436 0.690608
\(29\) 10.2612 1.90546 0.952729 0.303821i \(-0.0982625\pi\)
0.952729 + 0.303821i \(0.0982625\pi\)
\(30\) −2.63855 −0.481732
\(31\) −4.85848 −0.872609 −0.436305 0.899799i \(-0.643713\pi\)
−0.436305 + 0.899799i \(0.643713\pi\)
\(32\) 1.00000 0.176777
\(33\) 6.72584 1.17082
\(34\) −6.90897 −1.18488
\(35\) 5.45261 0.921660
\(36\) 0.127121 0.0211868
\(37\) −3.49596 −0.574733 −0.287367 0.957821i \(-0.592780\pi\)
−0.287367 + 0.957821i \(0.592780\pi\)
\(38\) −1.36683 −0.221729
\(39\) −2.03788 −0.326323
\(40\) 1.49209 0.235919
\(41\) −4.95721 −0.774186 −0.387093 0.922041i \(-0.626521\pi\)
−0.387093 + 0.922041i \(0.626521\pi\)
\(42\) −6.46224 −0.997146
\(43\) −11.4310 −1.74321 −0.871604 0.490211i \(-0.836920\pi\)
−0.871604 + 0.490211i \(0.836920\pi\)
\(44\) −3.80342 −0.573387
\(45\) 0.189675 0.0282751
\(46\) 1.00000 0.147442
\(47\) 1.92948 0.281444 0.140722 0.990049i \(-0.455058\pi\)
0.140722 + 0.990049i \(0.455058\pi\)
\(48\) −1.76837 −0.255242
\(49\) 6.35432 0.907760
\(50\) −2.77368 −0.392258
\(51\) 12.2176 1.71081
\(52\) 1.15241 0.159811
\(53\) −11.6074 −1.59440 −0.797202 0.603712i \(-0.793688\pi\)
−0.797202 + 0.603712i \(0.793688\pi\)
\(54\) 5.08030 0.691342
\(55\) −5.67503 −0.765220
\(56\) 3.65436 0.488334
\(57\) 2.41706 0.320147
\(58\) 10.2612 1.34736
\(59\) −6.12808 −0.797808 −0.398904 0.916993i \(-0.630609\pi\)
−0.398904 + 0.916993i \(0.630609\pi\)
\(60\) −2.63855 −0.340636
\(61\) −10.6230 −1.36014 −0.680068 0.733149i \(-0.738050\pi\)
−0.680068 + 0.733149i \(0.738050\pi\)
\(62\) −4.85848 −0.617028
\(63\) 0.464544 0.0585271
\(64\) 1.00000 0.125000
\(65\) 1.71949 0.213277
\(66\) 6.72584 0.827893
\(67\) −1.94680 −0.237839 −0.118920 0.992904i \(-0.537943\pi\)
−0.118920 + 0.992904i \(0.537943\pi\)
\(68\) −6.90897 −0.837836
\(69\) −1.76837 −0.212886
\(70\) 5.45261 0.651712
\(71\) −9.55777 −1.13430 −0.567150 0.823615i \(-0.691954\pi\)
−0.567150 + 0.823615i \(0.691954\pi\)
\(72\) 0.127121 0.0149813
\(73\) 0.982039 0.114939 0.0574695 0.998347i \(-0.481697\pi\)
0.0574695 + 0.998347i \(0.481697\pi\)
\(74\) −3.49596 −0.406398
\(75\) 4.90488 0.566367
\(76\) −1.36683 −0.156786
\(77\) −13.8990 −1.58394
\(78\) −2.03788 −0.230745
\(79\) 5.33190 0.599886 0.299943 0.953957i \(-0.403032\pi\)
0.299943 + 0.953957i \(0.403032\pi\)
\(80\) 1.49209 0.166820
\(81\) −9.36520 −1.04058
\(82\) −4.95721 −0.547432
\(83\) 3.48726 0.382776 0.191388 0.981514i \(-0.438701\pi\)
0.191388 + 0.981514i \(0.438701\pi\)
\(84\) −6.46224 −0.705088
\(85\) −10.3088 −1.11814
\(86\) −11.4310 −1.23263
\(87\) −18.1456 −1.94541
\(88\) −3.80342 −0.405446
\(89\) 12.5179 1.32690 0.663448 0.748223i \(-0.269093\pi\)
0.663448 + 0.748223i \(0.269093\pi\)
\(90\) 0.189675 0.0199935
\(91\) 4.21132 0.441466
\(92\) 1.00000 0.104257
\(93\) 8.59158 0.890905
\(94\) 1.92948 0.199011
\(95\) −2.03943 −0.209241
\(96\) −1.76837 −0.180483
\(97\) 12.5598 1.27526 0.637629 0.770343i \(-0.279915\pi\)
0.637629 + 0.770343i \(0.279915\pi\)
\(98\) 6.35432 0.641883
\(99\) −0.483493 −0.0485929
\(100\) −2.77368 −0.277368
\(101\) −4.07669 −0.405646 −0.202823 0.979215i \(-0.565012\pi\)
−0.202823 + 0.979215i \(0.565012\pi\)
\(102\) 12.2176 1.20972
\(103\) −11.2455 −1.10805 −0.554026 0.832500i \(-0.686909\pi\)
−0.554026 + 0.832500i \(0.686909\pi\)
\(104\) 1.15241 0.113003
\(105\) −9.64222 −0.940984
\(106\) −11.6074 −1.12741
\(107\) 13.1940 1.27551 0.637755 0.770239i \(-0.279863\pi\)
0.637755 + 0.770239i \(0.279863\pi\)
\(108\) 5.08030 0.488852
\(109\) −1.49354 −0.143055 −0.0715276 0.997439i \(-0.522787\pi\)
−0.0715276 + 0.997439i \(0.522787\pi\)
\(110\) −5.67503 −0.541092
\(111\) 6.18215 0.586784
\(112\) 3.65436 0.345304
\(113\) 4.90373 0.461304 0.230652 0.973036i \(-0.425914\pi\)
0.230652 + 0.973036i \(0.425914\pi\)
\(114\) 2.41706 0.226378
\(115\) 1.49209 0.139138
\(116\) 10.2612 0.952729
\(117\) 0.146495 0.0135435
\(118\) −6.12808 −0.564135
\(119\) −25.2478 −2.31447
\(120\) −2.63855 −0.240866
\(121\) 3.46599 0.315090
\(122\) −10.6230 −0.961761
\(123\) 8.76617 0.790419
\(124\) −4.85848 −0.436305
\(125\) −11.5990 −1.03745
\(126\) 0.464544 0.0413849
\(127\) 3.66865 0.325540 0.162770 0.986664i \(-0.447957\pi\)
0.162770 + 0.986664i \(0.447957\pi\)
\(128\) 1.00000 0.0883883
\(129\) 20.2142 1.77976
\(130\) 1.71949 0.150810
\(131\) −1.00000 −0.0873704
\(132\) 6.72584 0.585409
\(133\) −4.99489 −0.433112
\(134\) −1.94680 −0.168178
\(135\) 7.58025 0.652404
\(136\) −6.90897 −0.592439
\(137\) −6.11041 −0.522048 −0.261024 0.965332i \(-0.584060\pi\)
−0.261024 + 0.965332i \(0.584060\pi\)
\(138\) −1.76837 −0.150533
\(139\) 6.89890 0.585157 0.292579 0.956241i \(-0.405487\pi\)
0.292579 + 0.956241i \(0.405487\pi\)
\(140\) 5.45261 0.460830
\(141\) −3.41203 −0.287345
\(142\) −9.55777 −0.802071
\(143\) −4.38310 −0.366533
\(144\) 0.127121 0.0105934
\(145\) 15.3106 1.27148
\(146\) 0.982039 0.0812741
\(147\) −11.2368 −0.926793
\(148\) −3.49596 −0.287367
\(149\) 9.97008 0.816781 0.408390 0.912807i \(-0.366090\pi\)
0.408390 + 0.912807i \(0.366090\pi\)
\(150\) 4.90488 0.400482
\(151\) −7.46498 −0.607491 −0.303746 0.952753i \(-0.598237\pi\)
−0.303746 + 0.952753i \(0.598237\pi\)
\(152\) −1.36683 −0.110865
\(153\) −0.878273 −0.0710042
\(154\) −13.8990 −1.12002
\(155\) −7.24927 −0.582276
\(156\) −2.03788 −0.163161
\(157\) −0.950697 −0.0758739 −0.0379369 0.999280i \(-0.512079\pi\)
−0.0379369 + 0.999280i \(0.512079\pi\)
\(158\) 5.33190 0.424183
\(159\) 20.5262 1.62783
\(160\) 1.49209 0.117960
\(161\) 3.65436 0.288004
\(162\) −9.36520 −0.735800
\(163\) 15.2119 1.19149 0.595745 0.803174i \(-0.296857\pi\)
0.595745 + 0.803174i \(0.296857\pi\)
\(164\) −4.95721 −0.387093
\(165\) 10.0355 0.781265
\(166\) 3.48726 0.270664
\(167\) 2.51551 0.194656 0.0973280 0.995252i \(-0.468970\pi\)
0.0973280 + 0.995252i \(0.468970\pi\)
\(168\) −6.46224 −0.498573
\(169\) −11.6720 −0.897842
\(170\) −10.3088 −0.790647
\(171\) −0.173753 −0.0132872
\(172\) −11.4310 −0.871604
\(173\) −11.3846 −0.865556 −0.432778 0.901500i \(-0.642467\pi\)
−0.432778 + 0.901500i \(0.642467\pi\)
\(174\) −18.1456 −1.37561
\(175\) −10.1360 −0.766211
\(176\) −3.80342 −0.286693
\(177\) 10.8367 0.814536
\(178\) 12.5179 0.938257
\(179\) −7.42749 −0.555157 −0.277579 0.960703i \(-0.589532\pi\)
−0.277579 + 0.960703i \(0.589532\pi\)
\(180\) 0.189675 0.0141375
\(181\) −6.58423 −0.489402 −0.244701 0.969599i \(-0.578690\pi\)
−0.244701 + 0.969599i \(0.578690\pi\)
\(182\) 4.21132 0.312164
\(183\) 18.7854 1.38865
\(184\) 1.00000 0.0737210
\(185\) −5.21628 −0.383508
\(186\) 8.59158 0.629965
\(187\) 26.2777 1.92162
\(188\) 1.92948 0.140722
\(189\) 18.5652 1.35042
\(190\) −2.03943 −0.147956
\(191\) 19.7052 1.42582 0.712910 0.701255i \(-0.247377\pi\)
0.712910 + 0.701255i \(0.247377\pi\)
\(192\) −1.76837 −0.127621
\(193\) −13.0842 −0.941818 −0.470909 0.882182i \(-0.656074\pi\)
−0.470909 + 0.882182i \(0.656074\pi\)
\(194\) 12.5598 0.901744
\(195\) −3.04070 −0.217749
\(196\) 6.35432 0.453880
\(197\) 2.45311 0.174777 0.0873884 0.996174i \(-0.472148\pi\)
0.0873884 + 0.996174i \(0.472148\pi\)
\(198\) −0.483493 −0.0343604
\(199\) −9.16778 −0.649887 −0.324943 0.945733i \(-0.605345\pi\)
−0.324943 + 0.945733i \(0.605345\pi\)
\(200\) −2.77368 −0.196129
\(201\) 3.44265 0.242826
\(202\) −4.07669 −0.286835
\(203\) 37.4981 2.63185
\(204\) 12.2176 0.855403
\(205\) −7.39658 −0.516600
\(206\) −11.2455 −0.783511
\(207\) 0.127121 0.00883550
\(208\) 1.15241 0.0799053
\(209\) 5.19863 0.359597
\(210\) −9.64222 −0.665376
\(211\) −10.3828 −0.714780 −0.357390 0.933955i \(-0.616333\pi\)
−0.357390 + 0.933955i \(0.616333\pi\)
\(212\) −11.6074 −0.797202
\(213\) 16.9016 1.15808
\(214\) 13.1940 0.901922
\(215\) −17.0560 −1.16321
\(216\) 5.08030 0.345671
\(217\) −17.7546 −1.20526
\(218\) −1.49354 −0.101155
\(219\) −1.73660 −0.117349
\(220\) −5.67503 −0.382610
\(221\) −7.96197 −0.535580
\(222\) 6.18215 0.414919
\(223\) 19.9461 1.33569 0.667844 0.744302i \(-0.267217\pi\)
0.667844 + 0.744302i \(0.267217\pi\)
\(224\) 3.65436 0.244167
\(225\) −0.352592 −0.0235062
\(226\) 4.90373 0.326192
\(227\) 4.12615 0.273862 0.136931 0.990581i \(-0.456276\pi\)
0.136931 + 0.990581i \(0.456276\pi\)
\(228\) 2.41706 0.160074
\(229\) 19.7304 1.30382 0.651911 0.758295i \(-0.273967\pi\)
0.651911 + 0.758295i \(0.273967\pi\)
\(230\) 1.49209 0.0983852
\(231\) 24.5786 1.61715
\(232\) 10.2612 0.673681
\(233\) −20.4976 −1.34284 −0.671421 0.741076i \(-0.734316\pi\)
−0.671421 + 0.741076i \(0.734316\pi\)
\(234\) 0.146495 0.00957669
\(235\) 2.87895 0.187802
\(236\) −6.12808 −0.398904
\(237\) −9.42875 −0.612463
\(238\) −25.2478 −1.63657
\(239\) −24.7053 −1.59805 −0.799025 0.601298i \(-0.794651\pi\)
−0.799025 + 0.601298i \(0.794651\pi\)
\(240\) −2.63855 −0.170318
\(241\) −0.352041 −0.0226770 −0.0113385 0.999936i \(-0.503609\pi\)
−0.0113385 + 0.999936i \(0.503609\pi\)
\(242\) 3.46599 0.222802
\(243\) 1.32020 0.0846909
\(244\) −10.6230 −0.680068
\(245\) 9.48119 0.605731
\(246\) 8.76617 0.558910
\(247\) −1.57515 −0.100224
\(248\) −4.85848 −0.308514
\(249\) −6.16675 −0.390802
\(250\) −11.5990 −0.733585
\(251\) 15.9077 1.00408 0.502042 0.864844i \(-0.332582\pi\)
0.502042 + 0.864844i \(0.332582\pi\)
\(252\) 0.464544 0.0292636
\(253\) −3.80342 −0.239119
\(254\) 3.66865 0.230191
\(255\) 18.2297 1.14159
\(256\) 1.00000 0.0625000
\(257\) −0.558890 −0.0348626 −0.0174313 0.999848i \(-0.505549\pi\)
−0.0174313 + 0.999848i \(0.505549\pi\)
\(258\) 20.2142 1.25848
\(259\) −12.7755 −0.793831
\(260\) 1.71949 0.106639
\(261\) 1.30441 0.0807411
\(262\) −1.00000 −0.0617802
\(263\) 17.8238 1.09906 0.549531 0.835473i \(-0.314806\pi\)
0.549531 + 0.835473i \(0.314806\pi\)
\(264\) 6.72584 0.413947
\(265\) −17.3193 −1.06392
\(266\) −4.99489 −0.306256
\(267\) −22.1362 −1.35472
\(268\) −1.94680 −0.118920
\(269\) −7.74721 −0.472356 −0.236178 0.971710i \(-0.575895\pi\)
−0.236178 + 0.971710i \(0.575895\pi\)
\(270\) 7.58025 0.461319
\(271\) −5.30801 −0.322438 −0.161219 0.986919i \(-0.551543\pi\)
−0.161219 + 0.986919i \(0.551543\pi\)
\(272\) −6.90897 −0.418918
\(273\) −7.44715 −0.450722
\(274\) −6.11041 −0.369143
\(275\) 10.5495 0.636157
\(276\) −1.76837 −0.106443
\(277\) −3.63363 −0.218324 −0.109162 0.994024i \(-0.534817\pi\)
−0.109162 + 0.994024i \(0.534817\pi\)
\(278\) 6.89890 0.413769
\(279\) −0.617614 −0.0369756
\(280\) 5.45261 0.325856
\(281\) −16.9276 −1.00981 −0.504906 0.863174i \(-0.668473\pi\)
−0.504906 + 0.863174i \(0.668473\pi\)
\(282\) −3.41203 −0.203183
\(283\) −31.8013 −1.89039 −0.945195 0.326506i \(-0.894129\pi\)
−0.945195 + 0.326506i \(0.894129\pi\)
\(284\) −9.55777 −0.567150
\(285\) 3.60646 0.213628
\(286\) −4.38310 −0.259178
\(287\) −18.1154 −1.06932
\(288\) 0.127121 0.00749066
\(289\) 30.7339 1.80787
\(290\) 15.3106 0.899069
\(291\) −22.2104 −1.30200
\(292\) 0.982039 0.0574695
\(293\) 4.80599 0.280769 0.140384 0.990097i \(-0.455166\pi\)
0.140384 + 0.990097i \(0.455166\pi\)
\(294\) −11.2368 −0.655342
\(295\) −9.14362 −0.532362
\(296\) −3.49596 −0.203199
\(297\) −19.3225 −1.12121
\(298\) 9.97008 0.577551
\(299\) 1.15241 0.0666456
\(300\) 4.90488 0.283184
\(301\) −41.7729 −2.40775
\(302\) −7.46498 −0.429561
\(303\) 7.20908 0.414151
\(304\) −1.36683 −0.0783932
\(305\) −15.8504 −0.907593
\(306\) −0.878273 −0.0502075
\(307\) −19.8325 −1.13190 −0.565950 0.824440i \(-0.691490\pi\)
−0.565950 + 0.824440i \(0.691490\pi\)
\(308\) −13.8990 −0.791972
\(309\) 19.8862 1.13128
\(310\) −7.24927 −0.411731
\(311\) −23.5442 −1.33507 −0.667535 0.744578i \(-0.732651\pi\)
−0.667535 + 0.744578i \(0.732651\pi\)
\(312\) −2.03788 −0.115372
\(313\) −19.8159 −1.12006 −0.560030 0.828472i \(-0.689210\pi\)
−0.560030 + 0.828472i \(0.689210\pi\)
\(314\) −0.950697 −0.0536509
\(315\) 0.693140 0.0390540
\(316\) 5.33190 0.299943
\(317\) −6.59785 −0.370572 −0.185286 0.982685i \(-0.559321\pi\)
−0.185286 + 0.982685i \(0.559321\pi\)
\(318\) 20.5262 1.15105
\(319\) −39.0277 −2.18513
\(320\) 1.49209 0.0834101
\(321\) −23.3318 −1.30225
\(322\) 3.65436 0.203649
\(323\) 9.44340 0.525445
\(324\) −9.36520 −0.520289
\(325\) −3.19642 −0.177305
\(326\) 15.2119 0.842510
\(327\) 2.64113 0.146055
\(328\) −4.95721 −0.273716
\(329\) 7.05101 0.388735
\(330\) 10.0355 0.552438
\(331\) −21.6708 −1.19113 −0.595567 0.803306i \(-0.703073\pi\)
−0.595567 + 0.803306i \(0.703073\pi\)
\(332\) 3.48726 0.191388
\(333\) −0.444410 −0.0243535
\(334\) 2.51551 0.137643
\(335\) −2.90479 −0.158706
\(336\) −6.46224 −0.352544
\(337\) −1.89195 −0.103061 −0.0515307 0.998671i \(-0.516410\pi\)
−0.0515307 + 0.998671i \(0.516410\pi\)
\(338\) −11.6720 −0.634870
\(339\) −8.67160 −0.470977
\(340\) −10.3088 −0.559072
\(341\) 18.4788 1.00069
\(342\) −0.173753 −0.00939547
\(343\) −2.35954 −0.127403
\(344\) −11.4310 −0.616317
\(345\) −2.63855 −0.142055
\(346\) −11.3846 −0.612041
\(347\) 7.18382 0.385648 0.192824 0.981233i \(-0.438235\pi\)
0.192824 + 0.981233i \(0.438235\pi\)
\(348\) −18.1456 −0.972705
\(349\) 11.8172 0.632560 0.316280 0.948666i \(-0.397566\pi\)
0.316280 + 0.948666i \(0.397566\pi\)
\(350\) −10.1360 −0.541793
\(351\) 5.85459 0.312495
\(352\) −3.80342 −0.202723
\(353\) −19.9397 −1.06128 −0.530642 0.847596i \(-0.678049\pi\)
−0.530642 + 0.847596i \(0.678049\pi\)
\(354\) 10.8367 0.575964
\(355\) −14.2610 −0.756896
\(356\) 12.5179 0.663448
\(357\) 44.6474 2.36299
\(358\) −7.42749 −0.392555
\(359\) 31.0530 1.63891 0.819457 0.573141i \(-0.194275\pi\)
0.819457 + 0.573141i \(0.194275\pi\)
\(360\) 0.189675 0.00999675
\(361\) −17.1318 −0.901672
\(362\) −6.58423 −0.346059
\(363\) −6.12914 −0.321696
\(364\) 4.21132 0.220733
\(365\) 1.46529 0.0766966
\(366\) 18.7854 0.981926
\(367\) 13.2547 0.691887 0.345944 0.938255i \(-0.387559\pi\)
0.345944 + 0.938255i \(0.387559\pi\)
\(368\) 1.00000 0.0521286
\(369\) −0.630164 −0.0328050
\(370\) −5.21628 −0.271181
\(371\) −42.4177 −2.20222
\(372\) 8.59158 0.445453
\(373\) −33.2382 −1.72101 −0.860505 0.509442i \(-0.829852\pi\)
−0.860505 + 0.509442i \(0.829852\pi\)
\(374\) 26.2777 1.35879
\(375\) 20.5113 1.05920
\(376\) 1.92948 0.0995054
\(377\) 11.8251 0.609025
\(378\) 18.5652 0.954893
\(379\) −4.97231 −0.255410 −0.127705 0.991812i \(-0.540761\pi\)
−0.127705 + 0.991812i \(0.540761\pi\)
\(380\) −2.03943 −0.104621
\(381\) −6.48751 −0.332365
\(382\) 19.7052 1.00821
\(383\) 30.2486 1.54563 0.772814 0.634632i \(-0.218848\pi\)
0.772814 + 0.634632i \(0.218848\pi\)
\(384\) −1.76837 −0.0902416
\(385\) −20.7386 −1.05694
\(386\) −13.0842 −0.665966
\(387\) −1.45311 −0.0738659
\(388\) 12.5598 0.637629
\(389\) 13.7779 0.698566 0.349283 0.937017i \(-0.386425\pi\)
0.349283 + 0.937017i \(0.386425\pi\)
\(390\) −3.04070 −0.153972
\(391\) −6.90897 −0.349402
\(392\) 6.35432 0.320942
\(393\) 1.76837 0.0892023
\(394\) 2.45311 0.123586
\(395\) 7.95565 0.400292
\(396\) −0.483493 −0.0242965
\(397\) −23.3680 −1.17281 −0.586403 0.810020i \(-0.699456\pi\)
−0.586403 + 0.810020i \(0.699456\pi\)
\(398\) −9.16778 −0.459539
\(399\) 8.83280 0.442193
\(400\) −2.77368 −0.138684
\(401\) −0.577445 −0.0288362 −0.0144181 0.999896i \(-0.504590\pi\)
−0.0144181 + 0.999896i \(0.504590\pi\)
\(402\) 3.44265 0.171704
\(403\) −5.59896 −0.278904
\(404\) −4.07669 −0.202823
\(405\) −13.9737 −0.694358
\(406\) 37.4981 1.86100
\(407\) 13.2966 0.659089
\(408\) 12.2176 0.604861
\(409\) 32.9261 1.62809 0.814045 0.580802i \(-0.197261\pi\)
0.814045 + 0.580802i \(0.197261\pi\)
\(410\) −7.39658 −0.365291
\(411\) 10.8054 0.532993
\(412\) −11.2455 −0.554026
\(413\) −22.3942 −1.10195
\(414\) 0.127121 0.00624764
\(415\) 5.20329 0.255419
\(416\) 1.15241 0.0565015
\(417\) −12.1998 −0.597426
\(418\) 5.19863 0.254273
\(419\) 9.40549 0.459488 0.229744 0.973251i \(-0.426211\pi\)
0.229744 + 0.973251i \(0.426211\pi\)
\(420\) −9.64222 −0.470492
\(421\) −2.40395 −0.117161 −0.0585806 0.998283i \(-0.518657\pi\)
−0.0585806 + 0.998283i \(0.518657\pi\)
\(422\) −10.3828 −0.505426
\(423\) 0.245277 0.0119258
\(424\) −11.6074 −0.563707
\(425\) 19.1633 0.929555
\(426\) 16.9016 0.818888
\(427\) −38.8202 −1.87864
\(428\) 13.1940 0.637755
\(429\) 7.75092 0.374218
\(430\) −17.0560 −0.822513
\(431\) 11.7801 0.567428 0.283714 0.958909i \(-0.408433\pi\)
0.283714 + 0.958909i \(0.408433\pi\)
\(432\) 5.08030 0.244426
\(433\) −18.0802 −0.868881 −0.434440 0.900701i \(-0.643054\pi\)
−0.434440 + 0.900701i \(0.643054\pi\)
\(434\) −17.7546 −0.852249
\(435\) −27.0748 −1.29814
\(436\) −1.49354 −0.0715276
\(437\) −1.36683 −0.0653844
\(438\) −1.73660 −0.0829782
\(439\) −3.48237 −0.166204 −0.0831022 0.996541i \(-0.526483\pi\)
−0.0831022 + 0.996541i \(0.526483\pi\)
\(440\) −5.67503 −0.270546
\(441\) 0.807766 0.0384650
\(442\) −7.96197 −0.378712
\(443\) −21.5689 −1.02477 −0.512384 0.858756i \(-0.671238\pi\)
−0.512384 + 0.858756i \(0.671238\pi\)
\(444\) 6.18215 0.293392
\(445\) 18.6778 0.885412
\(446\) 19.9461 0.944474
\(447\) −17.6308 −0.833906
\(448\) 3.65436 0.172652
\(449\) −16.8096 −0.793296 −0.396648 0.917971i \(-0.629827\pi\)
−0.396648 + 0.917971i \(0.629827\pi\)
\(450\) −0.352592 −0.0166214
\(451\) 18.8543 0.887816
\(452\) 4.90373 0.230652
\(453\) 13.2008 0.620228
\(454\) 4.12615 0.193650
\(455\) 6.28365 0.294582
\(456\) 2.41706 0.113189
\(457\) −34.5898 −1.61804 −0.809021 0.587780i \(-0.800002\pi\)
−0.809021 + 0.587780i \(0.800002\pi\)
\(458\) 19.7304 0.921942
\(459\) −35.0997 −1.63831
\(460\) 1.49209 0.0695689
\(461\) 39.4992 1.83966 0.919831 0.392315i \(-0.128326\pi\)
0.919831 + 0.392315i \(0.128326\pi\)
\(462\) 24.5786 1.14350
\(463\) 26.6234 1.23730 0.618648 0.785668i \(-0.287681\pi\)
0.618648 + 0.785668i \(0.287681\pi\)
\(464\) 10.2612 0.476365
\(465\) 12.8194 0.594484
\(466\) −20.4976 −0.949533
\(467\) 24.1096 1.11566 0.557831 0.829955i \(-0.311634\pi\)
0.557831 + 0.829955i \(0.311634\pi\)
\(468\) 0.146495 0.00677174
\(469\) −7.11430 −0.328508
\(470\) 2.87895 0.132796
\(471\) 1.68118 0.0774647
\(472\) −6.12808 −0.282068
\(473\) 43.4768 1.99906
\(474\) −9.42875 −0.433077
\(475\) 3.79116 0.173950
\(476\) −25.2478 −1.15723
\(477\) −1.47555 −0.0675606
\(478\) −24.7053 −1.12999
\(479\) 31.6140 1.44448 0.722239 0.691643i \(-0.243113\pi\)
0.722239 + 0.691643i \(0.243113\pi\)
\(480\) −2.63855 −0.120433
\(481\) −4.02878 −0.183697
\(482\) −0.352041 −0.0160350
\(483\) −6.46224 −0.294042
\(484\) 3.46599 0.157545
\(485\) 18.7404 0.850956
\(486\) 1.32020 0.0598855
\(487\) 27.4000 1.24161 0.620805 0.783965i \(-0.286806\pi\)
0.620805 + 0.783965i \(0.286806\pi\)
\(488\) −10.6230 −0.480881
\(489\) −26.9002 −1.21647
\(490\) 9.48119 0.428317
\(491\) 38.5933 1.74169 0.870846 0.491556i \(-0.163572\pi\)
0.870846 + 0.491556i \(0.163572\pi\)
\(492\) 8.76617 0.395209
\(493\) −70.8944 −3.19292
\(494\) −1.57515 −0.0708694
\(495\) −0.721413 −0.0324251
\(496\) −4.85848 −0.218152
\(497\) −34.9275 −1.56671
\(498\) −6.16675 −0.276339
\(499\) 18.9661 0.849040 0.424520 0.905419i \(-0.360443\pi\)
0.424520 + 0.905419i \(0.360443\pi\)
\(500\) −11.5990 −0.518723
\(501\) −4.44835 −0.198737
\(502\) 15.9077 0.709994
\(503\) −36.2209 −1.61501 −0.807504 0.589862i \(-0.799182\pi\)
−0.807504 + 0.589862i \(0.799182\pi\)
\(504\) 0.464544 0.0206925
\(505\) −6.08277 −0.270680
\(506\) −3.80342 −0.169083
\(507\) 20.6403 0.916667
\(508\) 3.66865 0.162770
\(509\) −17.5489 −0.777842 −0.388921 0.921271i \(-0.627152\pi\)
−0.388921 + 0.921271i \(0.627152\pi\)
\(510\) 18.2297 0.807224
\(511\) 3.58872 0.158756
\(512\) 1.00000 0.0441942
\(513\) −6.94392 −0.306582
\(514\) −0.558890 −0.0246516
\(515\) −16.7792 −0.739382
\(516\) 20.2142 0.889879
\(517\) −7.33862 −0.322752
\(518\) −12.7755 −0.561323
\(519\) 20.1322 0.883704
\(520\) 1.71949 0.0754048
\(521\) −0.369981 −0.0162091 −0.00810457 0.999967i \(-0.502580\pi\)
−0.00810457 + 0.999967i \(0.502580\pi\)
\(522\) 1.30441 0.0570926
\(523\) 20.3547 0.890049 0.445025 0.895518i \(-0.353195\pi\)
0.445025 + 0.895518i \(0.353195\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 17.9242 0.782276
\(526\) 17.8238 0.777155
\(527\) 33.5671 1.46221
\(528\) 6.72584 0.292705
\(529\) 1.00000 0.0434783
\(530\) −17.3193 −0.752302
\(531\) −0.779006 −0.0338060
\(532\) −4.99489 −0.216556
\(533\) −5.71274 −0.247446
\(534\) −22.1362 −0.957929
\(535\) 19.6866 0.851124
\(536\) −1.94680 −0.0840889
\(537\) 13.1345 0.566797
\(538\) −7.74721 −0.334006
\(539\) −24.1681 −1.04100
\(540\) 7.58025 0.326202
\(541\) −1.06724 −0.0458843 −0.0229422 0.999737i \(-0.507303\pi\)
−0.0229422 + 0.999737i \(0.507303\pi\)
\(542\) −5.30801 −0.227998
\(543\) 11.6433 0.499663
\(544\) −6.90897 −0.296220
\(545\) −2.22849 −0.0954580
\(546\) −7.44715 −0.318709
\(547\) −41.9510 −1.79370 −0.896848 0.442338i \(-0.854149\pi\)
−0.896848 + 0.442338i \(0.854149\pi\)
\(548\) −6.11041 −0.261024
\(549\) −1.35040 −0.0576338
\(550\) 10.5495 0.449831
\(551\) −14.0253 −0.597500
\(552\) −1.76837 −0.0752667
\(553\) 19.4847 0.828572
\(554\) −3.63363 −0.154378
\(555\) 9.22429 0.391549
\(556\) 6.89890 0.292579
\(557\) 22.2132 0.941204 0.470602 0.882346i \(-0.344037\pi\)
0.470602 + 0.882346i \(0.344037\pi\)
\(558\) −0.617614 −0.0261457
\(559\) −13.1732 −0.557166
\(560\) 5.45261 0.230415
\(561\) −46.4686 −1.96191
\(562\) −16.9276 −0.714046
\(563\) 41.1487 1.73421 0.867104 0.498126i \(-0.165978\pi\)
0.867104 + 0.498126i \(0.165978\pi\)
\(564\) −3.41203 −0.143672
\(565\) 7.31679 0.307820
\(566\) −31.8013 −1.33671
\(567\) −34.2238 −1.43726
\(568\) −9.55777 −0.401035
\(569\) −7.53567 −0.315912 −0.157956 0.987446i \(-0.550490\pi\)
−0.157956 + 0.987446i \(0.550490\pi\)
\(570\) 3.60646 0.151058
\(571\) −34.2929 −1.43511 −0.717557 0.696500i \(-0.754740\pi\)
−0.717557 + 0.696500i \(0.754740\pi\)
\(572\) −4.38310 −0.183266
\(573\) −34.8461 −1.45572
\(574\) −18.1154 −0.756123
\(575\) −2.77368 −0.115670
\(576\) 0.127121 0.00529670
\(577\) −20.0143 −0.833208 −0.416604 0.909088i \(-0.636780\pi\)
−0.416604 + 0.909088i \(0.636780\pi\)
\(578\) 30.7339 1.27836
\(579\) 23.1376 0.961565
\(580\) 15.3106 0.635738
\(581\) 12.7437 0.528697
\(582\) −22.2104 −0.920651
\(583\) 44.1479 1.82842
\(584\) 0.982039 0.0406371
\(585\) 0.218583 0.00903731
\(586\) 4.80599 0.198534
\(587\) 6.48741 0.267764 0.133882 0.990997i \(-0.457256\pi\)
0.133882 + 0.990997i \(0.457256\pi\)
\(588\) −11.2368 −0.463397
\(589\) 6.64073 0.273627
\(590\) −9.14362 −0.376437
\(591\) −4.33800 −0.178441
\(592\) −3.49596 −0.143683
\(593\) 14.0991 0.578981 0.289490 0.957181i \(-0.406514\pi\)
0.289490 + 0.957181i \(0.406514\pi\)
\(594\) −19.3225 −0.792813
\(595\) −37.6719 −1.54440
\(596\) 9.97008 0.408390
\(597\) 16.2120 0.663513
\(598\) 1.15241 0.0471255
\(599\) 3.65675 0.149411 0.0747054 0.997206i \(-0.476198\pi\)
0.0747054 + 0.997206i \(0.476198\pi\)
\(600\) 4.90488 0.200241
\(601\) −24.3062 −0.991471 −0.495735 0.868474i \(-0.665101\pi\)
−0.495735 + 0.868474i \(0.665101\pi\)
\(602\) −41.7729 −1.70253
\(603\) −0.247478 −0.0100781
\(604\) −7.46498 −0.303746
\(605\) 5.17155 0.210253
\(606\) 7.20908 0.292849
\(607\) −31.4760 −1.27757 −0.638785 0.769385i \(-0.720563\pi\)
−0.638785 + 0.769385i \(0.720563\pi\)
\(608\) −1.36683 −0.0554324
\(609\) −66.3104 −2.68703
\(610\) −15.8504 −0.641765
\(611\) 2.22355 0.0899554
\(612\) −0.878273 −0.0355021
\(613\) 31.3452 1.26602 0.633011 0.774143i \(-0.281819\pi\)
0.633011 + 0.774143i \(0.281819\pi\)
\(614\) −19.8325 −0.800374
\(615\) 13.0799 0.527431
\(616\) −13.8990 −0.560008
\(617\) −12.2805 −0.494396 −0.247198 0.968965i \(-0.579510\pi\)
−0.247198 + 0.968965i \(0.579510\pi\)
\(618\) 19.8862 0.799939
\(619\) 24.3545 0.978892 0.489446 0.872034i \(-0.337199\pi\)
0.489446 + 0.872034i \(0.337199\pi\)
\(620\) −7.24927 −0.291138
\(621\) 5.08030 0.203866
\(622\) −23.5442 −0.944037
\(623\) 45.7449 1.83273
\(624\) −2.03788 −0.0815806
\(625\) −3.43830 −0.137532
\(626\) −19.8159 −0.792002
\(627\) −9.19309 −0.367137
\(628\) −0.950697 −0.0379369
\(629\) 24.1535 0.963064
\(630\) 0.693140 0.0276154
\(631\) 14.4076 0.573556 0.286778 0.957997i \(-0.407416\pi\)
0.286778 + 0.957997i \(0.407416\pi\)
\(632\) 5.33190 0.212092
\(633\) 18.3606 0.729767
\(634\) −6.59785 −0.262034
\(635\) 5.47393 0.217226
\(636\) 20.5262 0.813917
\(637\) 7.32278 0.290139
\(638\) −39.0277 −1.54512
\(639\) −1.21499 −0.0480643
\(640\) 1.49209 0.0589799
\(641\) −1.04081 −0.0411094 −0.0205547 0.999789i \(-0.506543\pi\)
−0.0205547 + 0.999789i \(0.506543\pi\)
\(642\) −23.3318 −0.920833
\(643\) −13.2422 −0.522219 −0.261110 0.965309i \(-0.584088\pi\)
−0.261110 + 0.965309i \(0.584088\pi\)
\(644\) 3.65436 0.144002
\(645\) 30.1613 1.18760
\(646\) 9.44340 0.371546
\(647\) −11.4589 −0.450496 −0.225248 0.974301i \(-0.572319\pi\)
−0.225248 + 0.974301i \(0.572319\pi\)
\(648\) −9.36520 −0.367900
\(649\) 23.3076 0.914905
\(650\) −3.19642 −0.125374
\(651\) 31.3967 1.23053
\(652\) 15.2119 0.595745
\(653\) −20.0278 −0.783750 −0.391875 0.920019i \(-0.628173\pi\)
−0.391875 + 0.920019i \(0.628173\pi\)
\(654\) 2.64113 0.103276
\(655\) −1.49209 −0.0583006
\(656\) −4.95721 −0.193547
\(657\) 0.124837 0.00487037
\(658\) 7.05101 0.274877
\(659\) 1.88462 0.0734143 0.0367072 0.999326i \(-0.488313\pi\)
0.0367072 + 0.999326i \(0.488313\pi\)
\(660\) 10.0355 0.390632
\(661\) −34.7164 −1.35031 −0.675155 0.737676i \(-0.735923\pi\)
−0.675155 + 0.737676i \(0.735923\pi\)
\(662\) −21.6708 −0.842259
\(663\) 14.0797 0.546809
\(664\) 3.48726 0.135332
\(665\) −7.45281 −0.289007
\(666\) −0.444410 −0.0172205
\(667\) 10.2612 0.397315
\(668\) 2.51551 0.0973280
\(669\) −35.2720 −1.36369
\(670\) −2.90479 −0.112222
\(671\) 40.4037 1.55977
\(672\) −6.46224 −0.249286
\(673\) 3.79605 0.146327 0.0731634 0.997320i \(-0.476691\pi\)
0.0731634 + 0.997320i \(0.476691\pi\)
\(674\) −1.89195 −0.0728754
\(675\) −14.0911 −0.542368
\(676\) −11.6720 −0.448921
\(677\) −16.5157 −0.634750 −0.317375 0.948300i \(-0.602801\pi\)
−0.317375 + 0.948300i \(0.602801\pi\)
\(678\) −8.67160 −0.333031
\(679\) 45.8981 1.76141
\(680\) −10.3088 −0.395323
\(681\) −7.29654 −0.279604
\(682\) 18.4788 0.707591
\(683\) −20.8222 −0.796740 −0.398370 0.917225i \(-0.630424\pi\)
−0.398370 + 0.917225i \(0.630424\pi\)
\(684\) −0.173753 −0.00664360
\(685\) −9.11726 −0.348353
\(686\) −2.35954 −0.0900878
\(687\) −34.8906 −1.33116
\(688\) −11.4310 −0.435802
\(689\) −13.3765 −0.509605
\(690\) −2.63855 −0.100448
\(691\) 31.0286 1.18038 0.590191 0.807263i \(-0.299052\pi\)
0.590191 + 0.807263i \(0.299052\pi\)
\(692\) −11.3846 −0.432778
\(693\) −1.76686 −0.0671173
\(694\) 7.18382 0.272694
\(695\) 10.2938 0.390464
\(696\) −18.1456 −0.687806
\(697\) 34.2492 1.29728
\(698\) 11.8172 0.447287
\(699\) 36.2473 1.37100
\(700\) −10.1360 −0.383105
\(701\) 32.5687 1.23010 0.615052 0.788486i \(-0.289135\pi\)
0.615052 + 0.788486i \(0.289135\pi\)
\(702\) 5.85459 0.220967
\(703\) 4.77840 0.180221
\(704\) −3.80342 −0.143347
\(705\) −5.09104 −0.191740
\(706\) −19.9397 −0.750441
\(707\) −14.8977 −0.560284
\(708\) 10.8367 0.407268
\(709\) 51.5471 1.93589 0.967946 0.251159i \(-0.0808118\pi\)
0.967946 + 0.251159i \(0.0808118\pi\)
\(710\) −14.2610 −0.535206
\(711\) 0.677795 0.0254193
\(712\) 12.5179 0.469128
\(713\) −4.85848 −0.181952
\(714\) 44.6474 1.67089
\(715\) −6.53996 −0.244580
\(716\) −7.42749 −0.277579
\(717\) 43.6880 1.63156
\(718\) 31.0530 1.15889
\(719\) 14.2049 0.529755 0.264877 0.964282i \(-0.414669\pi\)
0.264877 + 0.964282i \(0.414669\pi\)
\(720\) 0.189675 0.00706877
\(721\) −41.0950 −1.53046
\(722\) −17.1318 −0.637578
\(723\) 0.622538 0.0231524
\(724\) −6.58423 −0.244701
\(725\) −28.4613 −1.05703
\(726\) −6.12914 −0.227474
\(727\) −45.7525 −1.69687 −0.848433 0.529303i \(-0.822454\pi\)
−0.848433 + 0.529303i \(0.822454\pi\)
\(728\) 4.21132 0.156082
\(729\) 25.7610 0.954111
\(730\) 1.46529 0.0542327
\(731\) 78.9763 2.92104
\(732\) 18.7854 0.694327
\(733\) 37.5072 1.38536 0.692680 0.721245i \(-0.256430\pi\)
0.692680 + 0.721245i \(0.256430\pi\)
\(734\) 13.2547 0.489238
\(735\) −16.7662 −0.618431
\(736\) 1.00000 0.0368605
\(737\) 7.40449 0.272748
\(738\) −0.630164 −0.0231967
\(739\) 45.7613 1.68336 0.841678 0.539979i \(-0.181568\pi\)
0.841678 + 0.539979i \(0.181568\pi\)
\(740\) −5.21628 −0.191754
\(741\) 2.78544 0.102326
\(742\) −42.4177 −1.55720
\(743\) 8.96576 0.328922 0.164461 0.986384i \(-0.447412\pi\)
0.164461 + 0.986384i \(0.447412\pi\)
\(744\) 8.59158 0.314983
\(745\) 14.8762 0.545022
\(746\) −33.2382 −1.21694
\(747\) 0.443303 0.0162196
\(748\) 26.2777 0.960808
\(749\) 48.2155 1.76176
\(750\) 20.5113 0.748966
\(751\) 5.17286 0.188760 0.0943801 0.995536i \(-0.469913\pi\)
0.0943801 + 0.995536i \(0.469913\pi\)
\(752\) 1.92948 0.0703609
\(753\) −28.1306 −1.02514
\(754\) 11.8251 0.430645
\(755\) −11.1384 −0.405367
\(756\) 18.5652 0.675211
\(757\) 33.4756 1.21669 0.608347 0.793671i \(-0.291833\pi\)
0.608347 + 0.793671i \(0.291833\pi\)
\(758\) −4.97231 −0.180602
\(759\) 6.72584 0.244132
\(760\) −2.03943 −0.0739779
\(761\) −14.2812 −0.517694 −0.258847 0.965918i \(-0.583343\pi\)
−0.258847 + 0.965918i \(0.583343\pi\)
\(762\) −6.48751 −0.235018
\(763\) −5.45793 −0.197590
\(764\) 19.7052 0.712910
\(765\) −1.31046 −0.0473797
\(766\) 30.2486 1.09292
\(767\) −7.06206 −0.254996
\(768\) −1.76837 −0.0638104
\(769\) 5.87258 0.211771 0.105885 0.994378i \(-0.466232\pi\)
0.105885 + 0.994378i \(0.466232\pi\)
\(770\) −20.7386 −0.747366
\(771\) 0.988323 0.0355936
\(772\) −13.0842 −0.470909
\(773\) 0.706883 0.0254248 0.0127124 0.999919i \(-0.495953\pi\)
0.0127124 + 0.999919i \(0.495953\pi\)
\(774\) −1.45311 −0.0522311
\(775\) 13.4759 0.484068
\(776\) 12.5598 0.450872
\(777\) 22.5918 0.810475
\(778\) 13.7779 0.493961
\(779\) 6.77567 0.242764
\(780\) −3.04070 −0.108874
\(781\) 36.3522 1.30078
\(782\) −6.90897 −0.247064
\(783\) 52.1300 1.86298
\(784\) 6.35432 0.226940
\(785\) −1.41852 −0.0506292
\(786\) 1.76837 0.0630756
\(787\) 11.4425 0.407880 0.203940 0.978983i \(-0.434625\pi\)
0.203940 + 0.978983i \(0.434625\pi\)
\(788\) 2.45311 0.0873884
\(789\) −31.5190 −1.12211
\(790\) 7.95565 0.283049
\(791\) 17.9200 0.637162
\(792\) −0.483493 −0.0171802
\(793\) −12.2421 −0.434728
\(794\) −23.3680 −0.829298
\(795\) 30.6269 1.08622
\(796\) −9.16778 −0.324943
\(797\) −26.3884 −0.934724 −0.467362 0.884066i \(-0.654796\pi\)
−0.467362 + 0.884066i \(0.654796\pi\)
\(798\) 8.83280 0.312678
\(799\) −13.3307 −0.471607
\(800\) −2.77368 −0.0980644
\(801\) 1.59129 0.0562253
\(802\) −0.577445 −0.0203903
\(803\) −3.73510 −0.131809
\(804\) 3.44265 0.121413
\(805\) 5.45261 0.192179
\(806\) −5.59896 −0.197215
\(807\) 13.6999 0.482260
\(808\) −4.07669 −0.143417
\(809\) −2.12707 −0.0747839 −0.0373919 0.999301i \(-0.511905\pi\)
−0.0373919 + 0.999301i \(0.511905\pi\)
\(810\) −13.9737 −0.490985
\(811\) 37.2203 1.30698 0.653492 0.756934i \(-0.273303\pi\)
0.653492 + 0.756934i \(0.273303\pi\)
\(812\) 37.4981 1.31593
\(813\) 9.38650 0.329199
\(814\) 13.2966 0.466046
\(815\) 22.6975 0.795058
\(816\) 12.2176 0.427701
\(817\) 15.6242 0.546622
\(818\) 32.9261 1.15123
\(819\) 0.535346 0.0187065
\(820\) −7.39658 −0.258300
\(821\) −23.9603 −0.836219 −0.418109 0.908397i \(-0.637307\pi\)
−0.418109 + 0.908397i \(0.637307\pi\)
\(822\) 10.8054 0.376883
\(823\) −4.50535 −0.157047 −0.0785234 0.996912i \(-0.525021\pi\)
−0.0785234 + 0.996912i \(0.525021\pi\)
\(824\) −11.2455 −0.391755
\(825\) −18.6553 −0.649495
\(826\) −22.3942 −0.779193
\(827\) 14.9884 0.521196 0.260598 0.965447i \(-0.416080\pi\)
0.260598 + 0.965447i \(0.416080\pi\)
\(828\) 0.127121 0.00441775
\(829\) −39.2151 −1.36200 −0.680999 0.732284i \(-0.738454\pi\)
−0.680999 + 0.732284i \(0.738454\pi\)
\(830\) 5.20329 0.180609
\(831\) 6.42560 0.222902
\(832\) 1.15241 0.0399526
\(833\) −43.9018 −1.52111
\(834\) −12.1998 −0.422444
\(835\) 3.75336 0.129890
\(836\) 5.19863 0.179798
\(837\) −24.6826 −0.853154
\(838\) 9.40549 0.324907
\(839\) 18.3997 0.635227 0.317614 0.948220i \(-0.397119\pi\)
0.317614 + 0.948220i \(0.397119\pi\)
\(840\) −9.64222 −0.332688
\(841\) 76.2924 2.63077
\(842\) −2.40395 −0.0828454
\(843\) 29.9341 1.03099
\(844\) −10.3828 −0.357390
\(845\) −17.4156 −0.599113
\(846\) 0.245277 0.00843280
\(847\) 12.6660 0.435207
\(848\) −11.6074 −0.398601
\(849\) 56.2363 1.93003
\(850\) 19.1633 0.657295
\(851\) −3.49596 −0.119840
\(852\) 16.9016 0.579041
\(853\) −19.1200 −0.654655 −0.327328 0.944911i \(-0.606148\pi\)
−0.327328 + 0.944911i \(0.606148\pi\)
\(854\) −38.8202 −1.32840
\(855\) −0.259254 −0.00886630
\(856\) 13.1940 0.450961
\(857\) 4.98827 0.170396 0.0851980 0.996364i \(-0.472848\pi\)
0.0851980 + 0.996364i \(0.472848\pi\)
\(858\) 7.75092 0.264612
\(859\) 15.0504 0.513512 0.256756 0.966476i \(-0.417346\pi\)
0.256756 + 0.966476i \(0.417346\pi\)
\(860\) −17.0560 −0.581605
\(861\) 32.0347 1.09174
\(862\) 11.7801 0.401232
\(863\) −42.9207 −1.46104 −0.730520 0.682892i \(-0.760722\pi\)
−0.730520 + 0.682892i \(0.760722\pi\)
\(864\) 5.08030 0.172835
\(865\) −16.9868 −0.577569
\(866\) −18.0802 −0.614392
\(867\) −54.3488 −1.84578
\(868\) −17.7546 −0.602631
\(869\) −20.2794 −0.687933
\(870\) −27.0748 −0.917920
\(871\) −2.24351 −0.0760185
\(872\) −1.49354 −0.0505777
\(873\) 1.59662 0.0540373
\(874\) −1.36683 −0.0462338
\(875\) −42.3869 −1.43294
\(876\) −1.73660 −0.0586744
\(877\) −53.8301 −1.81771 −0.908856 0.417110i \(-0.863043\pi\)
−0.908856 + 0.417110i \(0.863043\pi\)
\(878\) −3.48237 −0.117524
\(879\) −8.49875 −0.286656
\(880\) −5.67503 −0.191305
\(881\) −42.0254 −1.41587 −0.707936 0.706276i \(-0.750374\pi\)
−0.707936 + 0.706276i \(0.750374\pi\)
\(882\) 0.807766 0.0271989
\(883\) −23.2560 −0.782626 −0.391313 0.920258i \(-0.627979\pi\)
−0.391313 + 0.920258i \(0.627979\pi\)
\(884\) −7.96197 −0.267790
\(885\) 16.1693 0.543524
\(886\) −21.5689 −0.724621
\(887\) 34.6868 1.16467 0.582334 0.812950i \(-0.302140\pi\)
0.582334 + 0.812950i \(0.302140\pi\)
\(888\) 6.18215 0.207459
\(889\) 13.4065 0.449641
\(890\) 18.6778 0.626081
\(891\) 35.6198 1.19331
\(892\) 19.9461 0.667844
\(893\) −2.63728 −0.0882531
\(894\) −17.6308 −0.589661
\(895\) −11.0825 −0.370446
\(896\) 3.65436 0.122083
\(897\) −2.03788 −0.0680429
\(898\) −16.8096 −0.560945
\(899\) −49.8539 −1.66272
\(900\) −0.352592 −0.0117531
\(901\) 80.1955 2.67170
\(902\) 18.8543 0.627781
\(903\) 73.8697 2.45823
\(904\) 4.90373 0.163096
\(905\) −9.82423 −0.326568
\(906\) 13.2008 0.438568
\(907\) −8.03171 −0.266688 −0.133344 0.991070i \(-0.542572\pi\)
−0.133344 + 0.991070i \(0.542572\pi\)
\(908\) 4.12615 0.136931
\(909\) −0.518231 −0.0171887
\(910\) 6.28365 0.208301
\(911\) −33.3845 −1.10608 −0.553039 0.833155i \(-0.686532\pi\)
−0.553039 + 0.833155i \(0.686532\pi\)
\(912\) 2.41706 0.0800369
\(913\) −13.2635 −0.438958
\(914\) −34.5898 −1.14413
\(915\) 28.0294 0.926622
\(916\) 19.7304 0.651911
\(917\) −3.65436 −0.120677
\(918\) −35.0997 −1.15846
\(919\) −8.18635 −0.270043 −0.135021 0.990843i \(-0.543110\pi\)
−0.135021 + 0.990843i \(0.543110\pi\)
\(920\) 1.49209 0.0491926
\(921\) 35.0711 1.15563
\(922\) 39.4992 1.30084
\(923\) −11.0145 −0.362546
\(924\) 24.5786 0.808577
\(925\) 9.69669 0.318825
\(926\) 26.6234 0.874900
\(927\) −1.42954 −0.0469521
\(928\) 10.2612 0.336841
\(929\) −11.5590 −0.379237 −0.189619 0.981858i \(-0.560725\pi\)
−0.189619 + 0.981858i \(0.560725\pi\)
\(930\) 12.8194 0.420364
\(931\) −8.68529 −0.284649
\(932\) −20.4976 −0.671421
\(933\) 41.6348 1.36306
\(934\) 24.1096 0.788892
\(935\) 39.2086 1.28226
\(936\) 0.146495 0.00478835
\(937\) −31.0546 −1.01451 −0.507254 0.861797i \(-0.669339\pi\)
−0.507254 + 0.861797i \(0.669339\pi\)
\(938\) −7.11430 −0.232290
\(939\) 35.0417 1.14354
\(940\) 2.87895 0.0939010
\(941\) −2.41102 −0.0785970 −0.0392985 0.999228i \(-0.512512\pi\)
−0.0392985 + 0.999228i \(0.512512\pi\)
\(942\) 1.68118 0.0547758
\(943\) −4.95721 −0.161429
\(944\) −6.12808 −0.199452
\(945\) 27.7009 0.901111
\(946\) 43.4768 1.41355
\(947\) 29.4598 0.957314 0.478657 0.878002i \(-0.341124\pi\)
0.478657 + 0.878002i \(0.341124\pi\)
\(948\) −9.42875 −0.306232
\(949\) 1.13171 0.0367369
\(950\) 3.79116 0.123001
\(951\) 11.6674 0.378342
\(952\) −25.2478 −0.818287
\(953\) −17.5497 −0.568490 −0.284245 0.958752i \(-0.591743\pi\)
−0.284245 + 0.958752i \(0.591743\pi\)
\(954\) −1.47555 −0.0477726
\(955\) 29.4019 0.951423
\(956\) −24.7053 −0.799025
\(957\) 69.0152 2.23094
\(958\) 31.6140 1.02140
\(959\) −22.3296 −0.721061
\(960\) −2.63855 −0.0851590
\(961\) −7.39514 −0.238553
\(962\) −4.02878 −0.129893
\(963\) 1.67723 0.0540479
\(964\) −0.352041 −0.0113385
\(965\) −19.5227 −0.628457
\(966\) −6.46224 −0.207919
\(967\) 34.5653 1.11155 0.555773 0.831334i \(-0.312423\pi\)
0.555773 + 0.831334i \(0.312423\pi\)
\(968\) 3.46599 0.111401
\(969\) −16.6994 −0.536462
\(970\) 18.7404 0.601717
\(971\) −17.5609 −0.563556 −0.281778 0.959480i \(-0.590924\pi\)
−0.281778 + 0.959480i \(0.590924\pi\)
\(972\) 1.32020 0.0423454
\(973\) 25.2111 0.808229
\(974\) 27.4000 0.877951
\(975\) 5.65244 0.181023
\(976\) −10.6230 −0.340034
\(977\) −18.6995 −0.598249 −0.299125 0.954214i \(-0.596695\pi\)
−0.299125 + 0.954214i \(0.596695\pi\)
\(978\) −26.9002 −0.860175
\(979\) −47.6108 −1.52165
\(980\) 9.48119 0.302866
\(981\) −0.189860 −0.00606176
\(982\) 38.5933 1.23156
\(983\) 33.1212 1.05640 0.528201 0.849119i \(-0.322867\pi\)
0.528201 + 0.849119i \(0.322867\pi\)
\(984\) 8.76617 0.279455
\(985\) 3.66025 0.116625
\(986\) −70.8944 −2.25774
\(987\) −12.4688 −0.396886
\(988\) −1.57515 −0.0501122
\(989\) −11.4310 −0.363484
\(990\) −0.721413 −0.0229280
\(991\) −6.54358 −0.207864 −0.103932 0.994584i \(-0.533142\pi\)
−0.103932 + 0.994584i \(0.533142\pi\)
\(992\) −4.85848 −0.154257
\(993\) 38.3219 1.21611
\(994\) −34.9275 −1.10783
\(995\) −13.6791 −0.433657
\(996\) −6.16675 −0.195401
\(997\) 20.4934 0.649034 0.324517 0.945880i \(-0.394798\pi\)
0.324517 + 0.945880i \(0.394798\pi\)
\(998\) 18.9661 0.600362
\(999\) −17.7606 −0.561919
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 6026.2.a.f.1.5 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.f.1.5 20 1.1 even 1 trivial