Properties

Label 4334.2.a.a.1.1
Level $4334$
Weight $2$
Character 4334.1
Self dual yes
Analytic conductor $34.607$
Analytic rank $1$
Dimension $15$
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] = [4334,2,Mod(1,4334)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4334, 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("4334.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4334 = 2 \cdot 11 \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4334.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: \(34.6071642360\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.16186\) of defining polynomial
Character \(\chi\) \(=\) 4334.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.16186 q^{3} +1.00000 q^{4} -1.61035 q^{5} +3.16186 q^{6} +0.0905305 q^{7} -1.00000 q^{8} +6.99733 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.16186 q^{3} +1.00000 q^{4} -1.61035 q^{5} +3.16186 q^{6} +0.0905305 q^{7} -1.00000 q^{8} +6.99733 q^{9} +1.61035 q^{10} +1.00000 q^{11} -3.16186 q^{12} +0.481640 q^{13} -0.0905305 q^{14} +5.09170 q^{15} +1.00000 q^{16} +0.419983 q^{17} -6.99733 q^{18} -1.64931 q^{19} -1.61035 q^{20} -0.286244 q^{21} -1.00000 q^{22} +0.827258 q^{23} +3.16186 q^{24} -2.40677 q^{25} -0.481640 q^{26} -12.6390 q^{27} +0.0905305 q^{28} -0.561896 q^{29} -5.09170 q^{30} -8.42633 q^{31} -1.00000 q^{32} -3.16186 q^{33} -0.419983 q^{34} -0.145786 q^{35} +6.99733 q^{36} +1.21121 q^{37} +1.64931 q^{38} -1.52288 q^{39} +1.61035 q^{40} -7.62488 q^{41} +0.286244 q^{42} +7.99759 q^{43} +1.00000 q^{44} -11.2682 q^{45} -0.827258 q^{46} +12.0094 q^{47} -3.16186 q^{48} -6.99180 q^{49} +2.40677 q^{50} -1.32793 q^{51} +0.481640 q^{52} +1.16240 q^{53} +12.6390 q^{54} -1.61035 q^{55} -0.0905305 q^{56} +5.21489 q^{57} +0.561896 q^{58} +6.82384 q^{59} +5.09170 q^{60} -2.12051 q^{61} +8.42633 q^{62} +0.633472 q^{63} +1.00000 q^{64} -0.775610 q^{65} +3.16186 q^{66} +8.17063 q^{67} +0.419983 q^{68} -2.61567 q^{69} +0.145786 q^{70} +3.26805 q^{71} -6.99733 q^{72} -0.788272 q^{73} -1.21121 q^{74} +7.60986 q^{75} -1.64931 q^{76} +0.0905305 q^{77} +1.52288 q^{78} +11.1043 q^{79} -1.61035 q^{80} +18.9707 q^{81} +7.62488 q^{82} -7.46511 q^{83} -0.286244 q^{84} -0.676320 q^{85} -7.99759 q^{86} +1.77663 q^{87} -1.00000 q^{88} -8.38001 q^{89} +11.2682 q^{90} +0.0436031 q^{91} +0.827258 q^{92} +26.6428 q^{93} -12.0094 q^{94} +2.65597 q^{95} +3.16186 q^{96} +14.5344 q^{97} +6.99180 q^{98} +6.99733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 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
\(3\) −3.16186 −1.82550 −0.912749 0.408520i \(-0.866045\pi\)
−0.912749 + 0.408520i \(0.866045\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.61035 −0.720171 −0.360085 0.932919i \(-0.617252\pi\)
−0.360085 + 0.932919i \(0.617252\pi\)
\(6\) 3.16186 1.29082
\(7\) 0.0905305 0.0342173 0.0171087 0.999854i \(-0.494554\pi\)
0.0171087 + 0.999854i \(0.494554\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.99733 2.33244
\(10\) 1.61035 0.509238
\(11\) 1.00000 0.301511
\(12\) −3.16186 −0.912749
\(13\) 0.481640 0.133583 0.0667915 0.997767i \(-0.478724\pi\)
0.0667915 + 0.997767i \(0.478724\pi\)
\(14\) −0.0905305 −0.0241953
\(15\) 5.09170 1.31467
\(16\) 1.00000 0.250000
\(17\) 0.419983 0.101861 0.0509305 0.998702i \(-0.483781\pi\)
0.0509305 + 0.998702i \(0.483781\pi\)
\(18\) −6.99733 −1.64929
\(19\) −1.64931 −0.378379 −0.189189 0.981941i \(-0.560586\pi\)
−0.189189 + 0.981941i \(0.560586\pi\)
\(20\) −1.61035 −0.360085
\(21\) −0.286244 −0.0624637
\(22\) −1.00000 −0.213201
\(23\) 0.827258 0.172495 0.0862476 0.996274i \(-0.472512\pi\)
0.0862476 + 0.996274i \(0.472512\pi\)
\(24\) 3.16186 0.645411
\(25\) −2.40677 −0.481354
\(26\) −0.481640 −0.0944574
\(27\) −12.6390 −2.43238
\(28\) 0.0905305 0.0171087
\(29\) −0.561896 −0.104341 −0.0521707 0.998638i \(-0.516614\pi\)
−0.0521707 + 0.998638i \(0.516614\pi\)
\(30\) −5.09170 −0.929612
\(31\) −8.42633 −1.51341 −0.756707 0.653754i \(-0.773193\pi\)
−0.756707 + 0.653754i \(0.773193\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.16186 −0.550408
\(34\) −0.419983 −0.0720265
\(35\) −0.145786 −0.0246423
\(36\) 6.99733 1.16622
\(37\) 1.21121 0.199121 0.0995605 0.995032i \(-0.468256\pi\)
0.0995605 + 0.995032i \(0.468256\pi\)
\(38\) 1.64931 0.267554
\(39\) −1.52288 −0.243855
\(40\) 1.61035 0.254619
\(41\) −7.62488 −1.19081 −0.595403 0.803427i \(-0.703008\pi\)
−0.595403 + 0.803427i \(0.703008\pi\)
\(42\) 0.286244 0.0441685
\(43\) 7.99759 1.21962 0.609811 0.792547i \(-0.291245\pi\)
0.609811 + 0.792547i \(0.291245\pi\)
\(44\) 1.00000 0.150756
\(45\) −11.2682 −1.67976
\(46\) −0.827258 −0.121972
\(47\) 12.0094 1.75175 0.875873 0.482542i \(-0.160286\pi\)
0.875873 + 0.482542i \(0.160286\pi\)
\(48\) −3.16186 −0.456375
\(49\) −6.99180 −0.998829
\(50\) 2.40677 0.340369
\(51\) −1.32793 −0.185947
\(52\) 0.481640 0.0667915
\(53\) 1.16240 0.159667 0.0798337 0.996808i \(-0.474561\pi\)
0.0798337 + 0.996808i \(0.474561\pi\)
\(54\) 12.6390 1.71995
\(55\) −1.61035 −0.217140
\(56\) −0.0905305 −0.0120976
\(57\) 5.21489 0.690730
\(58\) 0.561896 0.0737805
\(59\) 6.82384 0.888389 0.444194 0.895930i \(-0.353490\pi\)
0.444194 + 0.895930i \(0.353490\pi\)
\(60\) 5.09170 0.657335
\(61\) −2.12051 −0.271503 −0.135752 0.990743i \(-0.543345\pi\)
−0.135752 + 0.990743i \(0.543345\pi\)
\(62\) 8.42633 1.07015
\(63\) 0.633472 0.0798100
\(64\) 1.00000 0.125000
\(65\) −0.775610 −0.0962025
\(66\) 3.16186 0.389198
\(67\) 8.17063 0.998201 0.499101 0.866544i \(-0.333664\pi\)
0.499101 + 0.866544i \(0.333664\pi\)
\(68\) 0.419983 0.0509305
\(69\) −2.61567 −0.314890
\(70\) 0.145786 0.0174247
\(71\) 3.26805 0.387846 0.193923 0.981017i \(-0.437879\pi\)
0.193923 + 0.981017i \(0.437879\pi\)
\(72\) −6.99733 −0.824644
\(73\) −0.788272 −0.0922602 −0.0461301 0.998935i \(-0.514689\pi\)
−0.0461301 + 0.998935i \(0.514689\pi\)
\(74\) −1.21121 −0.140800
\(75\) 7.60986 0.878711
\(76\) −1.64931 −0.189189
\(77\) 0.0905305 0.0103169
\(78\) 1.52288 0.172432
\(79\) 11.1043 1.24933 0.624665 0.780893i \(-0.285236\pi\)
0.624665 + 0.780893i \(0.285236\pi\)
\(80\) −1.61035 −0.180043
\(81\) 18.9707 2.10785
\(82\) 7.62488 0.842027
\(83\) −7.46511 −0.819403 −0.409701 0.912220i \(-0.634367\pi\)
−0.409701 + 0.912220i \(0.634367\pi\)
\(84\) −0.286244 −0.0312318
\(85\) −0.676320 −0.0733572
\(86\) −7.99759 −0.862403
\(87\) 1.77663 0.190475
\(88\) −1.00000 −0.106600
\(89\) −8.38001 −0.888280 −0.444140 0.895958i \(-0.646491\pi\)
−0.444140 + 0.895958i \(0.646491\pi\)
\(90\) 11.2682 1.18777
\(91\) 0.0436031 0.00457085
\(92\) 0.827258 0.0862476
\(93\) 26.6428 2.76273
\(94\) −12.0094 −1.23867
\(95\) 2.65597 0.272497
\(96\) 3.16186 0.322706
\(97\) 14.5344 1.47574 0.737872 0.674940i \(-0.235831\pi\)
0.737872 + 0.674940i \(0.235831\pi\)
\(98\) 6.99180 0.706279
\(99\) 6.99733 0.703259
\(100\) −2.40677 −0.240677
\(101\) −2.15350 −0.214282 −0.107141 0.994244i \(-0.534170\pi\)
−0.107141 + 0.994244i \(0.534170\pi\)
\(102\) 1.32793 0.131484
\(103\) −14.1960 −1.39877 −0.699387 0.714743i \(-0.746544\pi\)
−0.699387 + 0.714743i \(0.746544\pi\)
\(104\) −0.481640 −0.0472287
\(105\) 0.460954 0.0449845
\(106\) −1.16240 −0.112902
\(107\) 14.9970 1.44982 0.724909 0.688845i \(-0.241882\pi\)
0.724909 + 0.688845i \(0.241882\pi\)
\(108\) −12.6390 −1.21619
\(109\) 12.6556 1.21219 0.606095 0.795392i \(-0.292735\pi\)
0.606095 + 0.795392i \(0.292735\pi\)
\(110\) 1.61035 0.153541
\(111\) −3.82966 −0.363495
\(112\) 0.0905305 0.00855433
\(113\) −3.43974 −0.323583 −0.161792 0.986825i \(-0.551727\pi\)
−0.161792 + 0.986825i \(0.551727\pi\)
\(114\) −5.21489 −0.488420
\(115\) −1.33218 −0.124226
\(116\) −0.561896 −0.0521707
\(117\) 3.37020 0.311575
\(118\) −6.82384 −0.628186
\(119\) 0.0380213 0.00348541
\(120\) −5.09170 −0.464806
\(121\) 1.00000 0.0909091
\(122\) 2.12051 0.191982
\(123\) 24.1088 2.17381
\(124\) −8.42633 −0.756707
\(125\) 11.9275 1.06683
\(126\) −0.633472 −0.0564342
\(127\) −10.0677 −0.893364 −0.446682 0.894693i \(-0.647394\pi\)
−0.446682 + 0.894693i \(0.647394\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −25.2872 −2.22642
\(130\) 0.775610 0.0680255
\(131\) 3.84049 0.335545 0.167773 0.985826i \(-0.446343\pi\)
0.167773 + 0.985826i \(0.446343\pi\)
\(132\) −3.16186 −0.275204
\(133\) −0.149313 −0.0129471
\(134\) −8.17063 −0.705835
\(135\) 20.3532 1.75173
\(136\) −0.419983 −0.0360133
\(137\) −2.88628 −0.246591 −0.123296 0.992370i \(-0.539346\pi\)
−0.123296 + 0.992370i \(0.539346\pi\)
\(138\) 2.61567 0.222661
\(139\) −10.3432 −0.877296 −0.438648 0.898659i \(-0.644543\pi\)
−0.438648 + 0.898659i \(0.644543\pi\)
\(140\) −0.145786 −0.0123212
\(141\) −37.9719 −3.19781
\(142\) −3.26805 −0.274248
\(143\) 0.481640 0.0402768
\(144\) 6.99733 0.583111
\(145\) 0.904849 0.0751436
\(146\) 0.788272 0.0652378
\(147\) 22.1071 1.82336
\(148\) 1.21121 0.0995605
\(149\) −10.9026 −0.893175 −0.446587 0.894740i \(-0.647361\pi\)
−0.446587 + 0.894740i \(0.647361\pi\)
\(150\) −7.60986 −0.621343
\(151\) 1.16138 0.0945119 0.0472560 0.998883i \(-0.484952\pi\)
0.0472560 + 0.998883i \(0.484952\pi\)
\(152\) 1.64931 0.133777
\(153\) 2.93876 0.237585
\(154\) −0.0905305 −0.00729516
\(155\) 13.5693 1.08992
\(156\) −1.52288 −0.121928
\(157\) 12.4185 0.991105 0.495553 0.868578i \(-0.334966\pi\)
0.495553 + 0.868578i \(0.334966\pi\)
\(158\) −11.1043 −0.883409
\(159\) −3.67533 −0.291473
\(160\) 1.61035 0.127309
\(161\) 0.0748921 0.00590232
\(162\) −18.9707 −1.49048
\(163\) −1.80088 −0.141056 −0.0705278 0.997510i \(-0.522468\pi\)
−0.0705278 + 0.997510i \(0.522468\pi\)
\(164\) −7.62488 −0.595403
\(165\) 5.09170 0.396388
\(166\) 7.46511 0.579405
\(167\) 14.4726 1.11992 0.559962 0.828518i \(-0.310816\pi\)
0.559962 + 0.828518i \(0.310816\pi\)
\(168\) 0.286244 0.0220842
\(169\) −12.7680 −0.982156
\(170\) 0.676320 0.0518714
\(171\) −11.5408 −0.882547
\(172\) 7.99759 0.609811
\(173\) 16.6108 1.26289 0.631447 0.775419i \(-0.282461\pi\)
0.631447 + 0.775419i \(0.282461\pi\)
\(174\) −1.77663 −0.134686
\(175\) −0.217886 −0.0164706
\(176\) 1.00000 0.0753778
\(177\) −21.5760 −1.62175
\(178\) 8.38001 0.628108
\(179\) 14.6241 1.09306 0.546529 0.837440i \(-0.315949\pi\)
0.546529 + 0.837440i \(0.315949\pi\)
\(180\) −11.2682 −0.839879
\(181\) −22.8349 −1.69731 −0.848653 0.528950i \(-0.822586\pi\)
−0.848653 + 0.528950i \(0.822586\pi\)
\(182\) −0.0436031 −0.00323208
\(183\) 6.70475 0.495629
\(184\) −0.827258 −0.0609862
\(185\) −1.95047 −0.143401
\(186\) −26.6428 −1.95355
\(187\) 0.419983 0.0307122
\(188\) 12.0094 0.875873
\(189\) −1.14421 −0.0832294
\(190\) −2.65597 −0.192685
\(191\) 20.0238 1.44887 0.724435 0.689343i \(-0.242101\pi\)
0.724435 + 0.689343i \(0.242101\pi\)
\(192\) −3.16186 −0.228187
\(193\) −12.5215 −0.901316 −0.450658 0.892697i \(-0.648811\pi\)
−0.450658 + 0.892697i \(0.648811\pi\)
\(194\) −14.5344 −1.04351
\(195\) 2.45237 0.175618
\(196\) −6.99180 −0.499415
\(197\) 1.00000 0.0712470
\(198\) −6.99733 −0.497279
\(199\) −6.27326 −0.444699 −0.222350 0.974967i \(-0.571373\pi\)
−0.222350 + 0.974967i \(0.571373\pi\)
\(200\) 2.40677 0.170184
\(201\) −25.8344 −1.82222
\(202\) 2.15350 0.151520
\(203\) −0.0508687 −0.00357028
\(204\) −1.32793 −0.0929735
\(205\) 12.2787 0.857583
\(206\) 14.1960 0.989083
\(207\) 5.78860 0.402335
\(208\) 0.481640 0.0333957
\(209\) −1.64931 −0.114085
\(210\) −0.460954 −0.0318088
\(211\) 5.76182 0.396660 0.198330 0.980135i \(-0.436448\pi\)
0.198330 + 0.980135i \(0.436448\pi\)
\(212\) 1.16240 0.0798337
\(213\) −10.3331 −0.708012
\(214\) −14.9970 −1.02518
\(215\) −12.8789 −0.878336
\(216\) 12.6390 0.859975
\(217\) −0.762840 −0.0517850
\(218\) −12.6556 −0.857148
\(219\) 2.49240 0.168421
\(220\) −1.61035 −0.108570
\(221\) 0.202281 0.0136069
\(222\) 3.82966 0.257030
\(223\) −6.56179 −0.439410 −0.219705 0.975566i \(-0.570509\pi\)
−0.219705 + 0.975566i \(0.570509\pi\)
\(224\) −0.0905305 −0.00604882
\(225\) −16.8410 −1.12273
\(226\) 3.43974 0.228808
\(227\) 23.2625 1.54399 0.771995 0.635629i \(-0.219259\pi\)
0.771995 + 0.635629i \(0.219259\pi\)
\(228\) 5.21489 0.345365
\(229\) −26.6070 −1.75824 −0.879120 0.476600i \(-0.841869\pi\)
−0.879120 + 0.476600i \(0.841869\pi\)
\(230\) 1.33218 0.0878410
\(231\) −0.286244 −0.0188335
\(232\) 0.561896 0.0368903
\(233\) −3.84104 −0.251635 −0.125817 0.992053i \(-0.540155\pi\)
−0.125817 + 0.992053i \(0.540155\pi\)
\(234\) −3.37020 −0.220317
\(235\) −19.3393 −1.26156
\(236\) 6.82384 0.444194
\(237\) −35.1101 −2.28065
\(238\) −0.0380213 −0.00246456
\(239\) −22.6659 −1.46613 −0.733067 0.680156i \(-0.761912\pi\)
−0.733067 + 0.680156i \(0.761912\pi\)
\(240\) 5.09170 0.328668
\(241\) 8.64726 0.557019 0.278510 0.960433i \(-0.410160\pi\)
0.278510 + 0.960433i \(0.410160\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −22.0656 −1.41551
\(244\) −2.12051 −0.135752
\(245\) 11.2593 0.719328
\(246\) −24.1088 −1.53712
\(247\) −0.794376 −0.0505449
\(248\) 8.42633 0.535073
\(249\) 23.6036 1.49582
\(250\) −11.9275 −0.754361
\(251\) 9.71156 0.612988 0.306494 0.951873i \(-0.400844\pi\)
0.306494 + 0.951873i \(0.400844\pi\)
\(252\) 0.633472 0.0399050
\(253\) 0.827258 0.0520092
\(254\) 10.0677 0.631703
\(255\) 2.13843 0.133914
\(256\) 1.00000 0.0625000
\(257\) 7.38542 0.460690 0.230345 0.973109i \(-0.426015\pi\)
0.230345 + 0.973109i \(0.426015\pi\)
\(258\) 25.2872 1.57431
\(259\) 0.109651 0.00681339
\(260\) −0.775610 −0.0481013
\(261\) −3.93177 −0.243371
\(262\) −3.84049 −0.237266
\(263\) −7.42250 −0.457691 −0.228845 0.973463i \(-0.573495\pi\)
−0.228845 + 0.973463i \(0.573495\pi\)
\(264\) 3.16186 0.194599
\(265\) −1.87187 −0.114988
\(266\) 0.149313 0.00915498
\(267\) 26.4964 1.62155
\(268\) 8.17063 0.499101
\(269\) −20.6674 −1.26011 −0.630056 0.776550i \(-0.716968\pi\)
−0.630056 + 0.776550i \(0.716968\pi\)
\(270\) −20.3532 −1.23866
\(271\) −20.5331 −1.24730 −0.623649 0.781704i \(-0.714351\pi\)
−0.623649 + 0.781704i \(0.714351\pi\)
\(272\) 0.419983 0.0254652
\(273\) −0.137867 −0.00834408
\(274\) 2.88628 0.174366
\(275\) −2.40677 −0.145134
\(276\) −2.61567 −0.157445
\(277\) 13.5361 0.813307 0.406653 0.913583i \(-0.366696\pi\)
0.406653 + 0.913583i \(0.366696\pi\)
\(278\) 10.3432 0.620342
\(279\) −58.9619 −3.52995
\(280\) 0.145786 0.00871237
\(281\) −9.89976 −0.590570 −0.295285 0.955409i \(-0.595415\pi\)
−0.295285 + 0.955409i \(0.595415\pi\)
\(282\) 37.9719 2.26119
\(283\) 1.91549 0.113864 0.0569320 0.998378i \(-0.481868\pi\)
0.0569320 + 0.998378i \(0.481868\pi\)
\(284\) 3.26805 0.193923
\(285\) −8.39781 −0.497443
\(286\) −0.481640 −0.0284800
\(287\) −0.690284 −0.0407462
\(288\) −6.99733 −0.412322
\(289\) −16.8236 −0.989624
\(290\) −0.904849 −0.0531346
\(291\) −45.9557 −2.69397
\(292\) −0.788272 −0.0461301
\(293\) 8.73898 0.510537 0.255268 0.966870i \(-0.417836\pi\)
0.255268 + 0.966870i \(0.417836\pi\)
\(294\) −22.1071 −1.28931
\(295\) −10.9888 −0.639791
\(296\) −1.21121 −0.0703999
\(297\) −12.6390 −0.733389
\(298\) 10.9026 0.631570
\(299\) 0.398441 0.0230424
\(300\) 7.60986 0.439356
\(301\) 0.724026 0.0417322
\(302\) −1.16138 −0.0668300
\(303\) 6.80907 0.391171
\(304\) −1.64931 −0.0945947
\(305\) 3.41476 0.195529
\(306\) −2.93876 −0.167998
\(307\) −29.4724 −1.68208 −0.841040 0.540972i \(-0.818056\pi\)
−0.841040 + 0.540972i \(0.818056\pi\)
\(308\) 0.0905305 0.00515846
\(309\) 44.8857 2.55346
\(310\) −13.5693 −0.770687
\(311\) 15.7060 0.890607 0.445303 0.895380i \(-0.353096\pi\)
0.445303 + 0.895380i \(0.353096\pi\)
\(312\) 1.52288 0.0862159
\(313\) −9.38008 −0.530194 −0.265097 0.964222i \(-0.585404\pi\)
−0.265097 + 0.964222i \(0.585404\pi\)
\(314\) −12.4185 −0.700817
\(315\) −1.02011 −0.0574768
\(316\) 11.1043 0.624665
\(317\) 0.406226 0.0228159 0.0114080 0.999935i \(-0.496369\pi\)
0.0114080 + 0.999935i \(0.496369\pi\)
\(318\) 3.67533 0.206102
\(319\) −0.561896 −0.0314601
\(320\) −1.61035 −0.0900213
\(321\) −47.4185 −2.64664
\(322\) −0.0748921 −0.00417357
\(323\) −0.692684 −0.0385420
\(324\) 18.9707 1.05393
\(325\) −1.15920 −0.0643007
\(326\) 1.80088 0.0997414
\(327\) −40.0153 −2.21285
\(328\) 7.62488 0.421013
\(329\) 1.08721 0.0599400
\(330\) −5.09170 −0.280289
\(331\) 32.8525 1.80573 0.902867 0.429919i \(-0.141458\pi\)
0.902867 + 0.429919i \(0.141458\pi\)
\(332\) −7.46511 −0.409701
\(333\) 8.47521 0.464439
\(334\) −14.4726 −0.791906
\(335\) −13.1576 −0.718875
\(336\) −0.286244 −0.0156159
\(337\) −1.57192 −0.0856279 −0.0428139 0.999083i \(-0.513632\pi\)
−0.0428139 + 0.999083i \(0.513632\pi\)
\(338\) 12.7680 0.694489
\(339\) 10.8760 0.590701
\(340\) −0.676320 −0.0366786
\(341\) −8.42633 −0.456311
\(342\) 11.5408 0.624055
\(343\) −1.26669 −0.0683946
\(344\) −7.99759 −0.431201
\(345\) 4.21215 0.226774
\(346\) −16.6108 −0.893001
\(347\) −33.0672 −1.77514 −0.887571 0.460671i \(-0.847609\pi\)
−0.887571 + 0.460671i \(0.847609\pi\)
\(348\) 1.77663 0.0952376
\(349\) −17.8947 −0.957879 −0.478939 0.877848i \(-0.658979\pi\)
−0.478939 + 0.877848i \(0.658979\pi\)
\(350\) 0.217886 0.0116465
\(351\) −6.08745 −0.324924
\(352\) −1.00000 −0.0533002
\(353\) 0.965407 0.0513834 0.0256917 0.999670i \(-0.491821\pi\)
0.0256917 + 0.999670i \(0.491821\pi\)
\(354\) 21.5760 1.14675
\(355\) −5.26270 −0.279315
\(356\) −8.38001 −0.444140
\(357\) −0.120218 −0.00636261
\(358\) −14.6241 −0.772909
\(359\) 4.14233 0.218624 0.109312 0.994008i \(-0.465135\pi\)
0.109312 + 0.994008i \(0.465135\pi\)
\(360\) 11.2682 0.593884
\(361\) −16.2798 −0.856830
\(362\) 22.8349 1.20018
\(363\) −3.16186 −0.165954
\(364\) 0.0436031 0.00228543
\(365\) 1.26939 0.0664431
\(366\) −6.70475 −0.350463
\(367\) −34.2662 −1.78868 −0.894340 0.447388i \(-0.852354\pi\)
−0.894340 + 0.447388i \(0.852354\pi\)
\(368\) 0.827258 0.0431238
\(369\) −53.3538 −2.77749
\(370\) 1.95047 0.101400
\(371\) 0.105232 0.00546339
\(372\) 26.6428 1.38137
\(373\) −22.9046 −1.18596 −0.592979 0.805218i \(-0.702048\pi\)
−0.592979 + 0.805218i \(0.702048\pi\)
\(374\) −0.419983 −0.0217168
\(375\) −37.7130 −1.94749
\(376\) −12.0094 −0.619336
\(377\) −0.270632 −0.0139382
\(378\) 1.14421 0.0588521
\(379\) 0.208774 0.0107240 0.00536200 0.999986i \(-0.498293\pi\)
0.00536200 + 0.999986i \(0.498293\pi\)
\(380\) 2.65597 0.136249
\(381\) 31.8326 1.63083
\(382\) −20.0238 −1.02451
\(383\) −24.4168 −1.24764 −0.623819 0.781569i \(-0.714420\pi\)
−0.623819 + 0.781569i \(0.714420\pi\)
\(384\) 3.16186 0.161353
\(385\) −0.145786 −0.00742994
\(386\) 12.5215 0.637327
\(387\) 55.9618 2.84470
\(388\) 14.5344 0.737872
\(389\) 2.00470 0.101642 0.0508211 0.998708i \(-0.483816\pi\)
0.0508211 + 0.998708i \(0.483816\pi\)
\(390\) −2.45237 −0.124180
\(391\) 0.347434 0.0175705
\(392\) 6.99180 0.353139
\(393\) −12.1431 −0.612537
\(394\) −1.00000 −0.0503793
\(395\) −17.8818 −0.899730
\(396\) 6.99733 0.351629
\(397\) 4.97318 0.249597 0.124798 0.992182i \(-0.460172\pi\)
0.124798 + 0.992182i \(0.460172\pi\)
\(398\) 6.27326 0.314450
\(399\) 0.472107 0.0236349
\(400\) −2.40677 −0.120339
\(401\) −5.06123 −0.252746 −0.126373 0.991983i \(-0.540334\pi\)
−0.126373 + 0.991983i \(0.540334\pi\)
\(402\) 25.8344 1.28850
\(403\) −4.05846 −0.202166
\(404\) −2.15350 −0.107141
\(405\) −30.5494 −1.51801
\(406\) 0.0508687 0.00252457
\(407\) 1.21121 0.0600372
\(408\) 1.32793 0.0657422
\(409\) 13.7553 0.680158 0.340079 0.940397i \(-0.389546\pi\)
0.340079 + 0.940397i \(0.389546\pi\)
\(410\) −12.2787 −0.606403
\(411\) 9.12599 0.450152
\(412\) −14.1960 −0.699387
\(413\) 0.617766 0.0303983
\(414\) −5.78860 −0.284494
\(415\) 12.0215 0.590110
\(416\) −0.481640 −0.0236144
\(417\) 32.7036 1.60150
\(418\) 1.64931 0.0806706
\(419\) −1.85667 −0.0907042 −0.0453521 0.998971i \(-0.514441\pi\)
−0.0453521 + 0.998971i \(0.514441\pi\)
\(420\) 0.460954 0.0224923
\(421\) 6.84016 0.333369 0.166684 0.986010i \(-0.446694\pi\)
0.166684 + 0.986010i \(0.446694\pi\)
\(422\) −5.76182 −0.280481
\(423\) 84.0335 4.08585
\(424\) −1.16240 −0.0564509
\(425\) −1.01080 −0.0490312
\(426\) 10.3331 0.500640
\(427\) −0.191971 −0.00929012
\(428\) 14.9970 0.724909
\(429\) −1.52288 −0.0735252
\(430\) 12.8789 0.621077
\(431\) −5.73620 −0.276303 −0.138152 0.990411i \(-0.544116\pi\)
−0.138152 + 0.990411i \(0.544116\pi\)
\(432\) −12.6390 −0.608094
\(433\) 16.0484 0.771236 0.385618 0.922659i \(-0.373988\pi\)
0.385618 + 0.922659i \(0.373988\pi\)
\(434\) 0.762840 0.0366175
\(435\) −2.86100 −0.137175
\(436\) 12.6556 0.606095
\(437\) −1.36441 −0.0652685
\(438\) −2.49240 −0.119092
\(439\) −14.8135 −0.707012 −0.353506 0.935432i \(-0.615011\pi\)
−0.353506 + 0.935432i \(0.615011\pi\)
\(440\) 1.61035 0.0767705
\(441\) −48.9240 −2.32971
\(442\) −0.202281 −0.00962152
\(443\) −15.7001 −0.745933 −0.372966 0.927845i \(-0.621659\pi\)
−0.372966 + 0.927845i \(0.621659\pi\)
\(444\) −3.82966 −0.181748
\(445\) 13.4948 0.639713
\(446\) 6.56179 0.310710
\(447\) 34.4724 1.63049
\(448\) 0.0905305 0.00427717
\(449\) 12.0150 0.567021 0.283511 0.958969i \(-0.408501\pi\)
0.283511 + 0.958969i \(0.408501\pi\)
\(450\) 16.8410 0.793891
\(451\) −7.62488 −0.359041
\(452\) −3.43974 −0.161792
\(453\) −3.67212 −0.172531
\(454\) −23.2625 −1.09177
\(455\) −0.0702163 −0.00329179
\(456\) −5.21489 −0.244210
\(457\) 1.13638 0.0531574 0.0265787 0.999647i \(-0.491539\pi\)
0.0265787 + 0.999647i \(0.491539\pi\)
\(458\) 26.6070 1.24326
\(459\) −5.30817 −0.247764
\(460\) −1.33218 −0.0621130
\(461\) 16.5049 0.768710 0.384355 0.923185i \(-0.374424\pi\)
0.384355 + 0.923185i \(0.374424\pi\)
\(462\) 0.286244 0.0133173
\(463\) −37.7903 −1.75626 −0.878131 0.478420i \(-0.841210\pi\)
−0.878131 + 0.478420i \(0.841210\pi\)
\(464\) −0.561896 −0.0260854
\(465\) −42.9043 −1.98964
\(466\) 3.84104 0.177933
\(467\) 1.47313 0.0681685 0.0340843 0.999419i \(-0.489149\pi\)
0.0340843 + 0.999419i \(0.489149\pi\)
\(468\) 3.37020 0.155787
\(469\) 0.739691 0.0341558
\(470\) 19.3393 0.892055
\(471\) −39.2656 −1.80926
\(472\) −6.82384 −0.314093
\(473\) 7.99759 0.367730
\(474\) 35.1101 1.61266
\(475\) 3.96952 0.182134
\(476\) 0.0380213 0.00174270
\(477\) 8.13367 0.372415
\(478\) 22.6659 1.03671
\(479\) 8.78124 0.401225 0.200612 0.979671i \(-0.435707\pi\)
0.200612 + 0.979671i \(0.435707\pi\)
\(480\) −5.09170 −0.232403
\(481\) 0.583365 0.0265992
\(482\) −8.64726 −0.393872
\(483\) −0.236798 −0.0107747
\(484\) 1.00000 0.0454545
\(485\) −23.4055 −1.06279
\(486\) 22.0656 1.00091
\(487\) 38.7747 1.75705 0.878525 0.477697i \(-0.158528\pi\)
0.878525 + 0.477697i \(0.158528\pi\)
\(488\) 2.12051 0.0959910
\(489\) 5.69412 0.257497
\(490\) −11.2593 −0.508641
\(491\) −12.6103 −0.569094 −0.284547 0.958662i \(-0.591843\pi\)
−0.284547 + 0.958662i \(0.591843\pi\)
\(492\) 24.1088 1.08691
\(493\) −0.235987 −0.0106283
\(494\) 0.794376 0.0357407
\(495\) −11.2682 −0.506466
\(496\) −8.42633 −0.378353
\(497\) 0.295858 0.0132710
\(498\) −23.6036 −1.05770
\(499\) 40.8293 1.82777 0.913885 0.405974i \(-0.133068\pi\)
0.913885 + 0.405974i \(0.133068\pi\)
\(500\) 11.9275 0.533414
\(501\) −45.7603 −2.04442
\(502\) −9.71156 −0.433448
\(503\) 0.743243 0.0331396 0.0165698 0.999863i \(-0.494725\pi\)
0.0165698 + 0.999863i \(0.494725\pi\)
\(504\) −0.633472 −0.0282171
\(505\) 3.46790 0.154319
\(506\) −0.827258 −0.0367761
\(507\) 40.3707 1.79292
\(508\) −10.0677 −0.446682
\(509\) 9.84334 0.436298 0.218149 0.975915i \(-0.429998\pi\)
0.218149 + 0.975915i \(0.429998\pi\)
\(510\) −2.13843 −0.0946912
\(511\) −0.0713627 −0.00315690
\(512\) −1.00000 −0.0441942
\(513\) 20.8457 0.920359
\(514\) −7.38542 −0.325757
\(515\) 22.8606 1.00736
\(516\) −25.2872 −1.11321
\(517\) 12.0094 0.528171
\(518\) −0.109651 −0.00481779
\(519\) −52.5209 −2.30541
\(520\) 0.775610 0.0340127
\(521\) 3.77380 0.165333 0.0826667 0.996577i \(-0.473656\pi\)
0.0826667 + 0.996577i \(0.473656\pi\)
\(522\) 3.93177 0.172089
\(523\) 8.14264 0.356053 0.178026 0.984026i \(-0.443029\pi\)
0.178026 + 0.984026i \(0.443029\pi\)
\(524\) 3.84049 0.167773
\(525\) 0.688925 0.0300671
\(526\) 7.42250 0.323636
\(527\) −3.53892 −0.154158
\(528\) −3.16186 −0.137602
\(529\) −22.3156 −0.970245
\(530\) 1.87187 0.0813086
\(531\) 47.7487 2.07212
\(532\) −0.149313 −0.00647355
\(533\) −3.67245 −0.159071
\(534\) −26.4964 −1.14661
\(535\) −24.1505 −1.04412
\(536\) −8.17063 −0.352917
\(537\) −46.2394 −1.99538
\(538\) 20.6674 0.891033
\(539\) −6.99180 −0.301158
\(540\) 20.3532 0.875863
\(541\) −31.8864 −1.37090 −0.685452 0.728118i \(-0.740395\pi\)
−0.685452 + 0.728118i \(0.740395\pi\)
\(542\) 20.5331 0.881973
\(543\) 72.2007 3.09843
\(544\) −0.419983 −0.0180066
\(545\) −20.3800 −0.872984
\(546\) 0.137867 0.00590016
\(547\) −29.2911 −1.25240 −0.626198 0.779664i \(-0.715390\pi\)
−0.626198 + 0.779664i \(0.715390\pi\)
\(548\) −2.88628 −0.123296
\(549\) −14.8379 −0.633267
\(550\) 2.40677 0.102625
\(551\) 0.926743 0.0394806
\(552\) 2.61567 0.111330
\(553\) 1.00528 0.0427487
\(554\) −13.5361 −0.575095
\(555\) 6.16709 0.261779
\(556\) −10.3432 −0.438648
\(557\) −18.4722 −0.782691 −0.391346 0.920244i \(-0.627990\pi\)
−0.391346 + 0.920244i \(0.627990\pi\)
\(558\) 58.9619 2.49605
\(559\) 3.85196 0.162921
\(560\) −0.145786 −0.00616058
\(561\) −1.32793 −0.0560651
\(562\) 9.89976 0.417596
\(563\) −15.1463 −0.638338 −0.319169 0.947698i \(-0.603404\pi\)
−0.319169 + 0.947698i \(0.603404\pi\)
\(564\) −37.9719 −1.59890
\(565\) 5.53918 0.233035
\(566\) −1.91549 −0.0805140
\(567\) 1.71743 0.0721251
\(568\) −3.26805 −0.137124
\(569\) −39.5200 −1.65677 −0.828383 0.560162i \(-0.810739\pi\)
−0.828383 + 0.560162i \(0.810739\pi\)
\(570\) 8.39781 0.351745
\(571\) −2.41783 −0.101183 −0.0505916 0.998719i \(-0.516111\pi\)
−0.0505916 + 0.998719i \(0.516111\pi\)
\(572\) 0.481640 0.0201384
\(573\) −63.3123 −2.64491
\(574\) 0.690284 0.0288119
\(575\) −1.99102 −0.0830313
\(576\) 6.99733 0.291556
\(577\) −20.2179 −0.841683 −0.420841 0.907134i \(-0.638265\pi\)
−0.420841 + 0.907134i \(0.638265\pi\)
\(578\) 16.8236 0.699770
\(579\) 39.5911 1.64535
\(580\) 0.904849 0.0375718
\(581\) −0.675821 −0.0280378
\(582\) 45.9557 1.90492
\(583\) 1.16240 0.0481415
\(584\) 0.788272 0.0326189
\(585\) −5.42720 −0.224387
\(586\) −8.73898 −0.361004
\(587\) −37.3524 −1.54170 −0.770848 0.637019i \(-0.780167\pi\)
−0.770848 + 0.637019i \(0.780167\pi\)
\(588\) 22.1071 0.911681
\(589\) 13.8977 0.572643
\(590\) 10.9888 0.452401
\(591\) −3.16186 −0.130061
\(592\) 1.21121 0.0497803
\(593\) 22.3854 0.919260 0.459630 0.888110i \(-0.347982\pi\)
0.459630 + 0.888110i \(0.347982\pi\)
\(594\) 12.6390 0.518584
\(595\) −0.0612276 −0.00251009
\(596\) −10.9026 −0.446587
\(597\) 19.8351 0.811798
\(598\) −0.398441 −0.0162934
\(599\) 25.0022 1.02156 0.510781 0.859711i \(-0.329356\pi\)
0.510781 + 0.859711i \(0.329356\pi\)
\(600\) −7.60986 −0.310671
\(601\) −11.6416 −0.474869 −0.237435 0.971404i \(-0.576307\pi\)
−0.237435 + 0.971404i \(0.576307\pi\)
\(602\) −0.724026 −0.0295091
\(603\) 57.1726 2.32825
\(604\) 1.16138 0.0472560
\(605\) −1.61035 −0.0654701
\(606\) −6.80907 −0.276599
\(607\) 16.5455 0.671561 0.335780 0.941940i \(-0.391000\pi\)
0.335780 + 0.941940i \(0.391000\pi\)
\(608\) 1.64931 0.0668885
\(609\) 0.160840 0.00651755
\(610\) −3.41476 −0.138260
\(611\) 5.78419 0.234003
\(612\) 2.93876 0.118792
\(613\) −39.2445 −1.58507 −0.792536 0.609825i \(-0.791240\pi\)
−0.792536 + 0.609825i \(0.791240\pi\)
\(614\) 29.4724 1.18941
\(615\) −38.8236 −1.56552
\(616\) −0.0905305 −0.00364758
\(617\) 4.59232 0.184880 0.0924400 0.995718i \(-0.470533\pi\)
0.0924400 + 0.995718i \(0.470533\pi\)
\(618\) −44.8857 −1.80557
\(619\) −16.0564 −0.645363 −0.322681 0.946508i \(-0.604584\pi\)
−0.322681 + 0.946508i \(0.604584\pi\)
\(620\) 13.5693 0.544958
\(621\) −10.4557 −0.419573
\(622\) −15.7060 −0.629754
\(623\) −0.758647 −0.0303945
\(624\) −1.52288 −0.0609639
\(625\) −7.17360 −0.286944
\(626\) 9.38008 0.374903
\(627\) 5.21489 0.208263
\(628\) 12.4185 0.495553
\(629\) 0.508686 0.0202826
\(630\) 1.02011 0.0406423
\(631\) −5.86225 −0.233372 −0.116686 0.993169i \(-0.537227\pi\)
−0.116686 + 0.993169i \(0.537227\pi\)
\(632\) −11.1043 −0.441705
\(633\) −18.2180 −0.724102
\(634\) −0.406226 −0.0161333
\(635\) 16.2125 0.643374
\(636\) −3.67533 −0.145736
\(637\) −3.36753 −0.133427
\(638\) 0.561896 0.0222457
\(639\) 22.8676 0.904629
\(640\) 1.61035 0.0636547
\(641\) 19.5228 0.771103 0.385551 0.922686i \(-0.374011\pi\)
0.385551 + 0.922686i \(0.374011\pi\)
\(642\) 47.4185 1.87146
\(643\) 0.210958 0.00831936 0.00415968 0.999991i \(-0.498676\pi\)
0.00415968 + 0.999991i \(0.498676\pi\)
\(644\) 0.0748921 0.00295116
\(645\) 40.7213 1.60340
\(646\) 0.692684 0.0272533
\(647\) 2.15038 0.0845402 0.0422701 0.999106i \(-0.486541\pi\)
0.0422701 + 0.999106i \(0.486541\pi\)
\(648\) −18.9707 −0.745239
\(649\) 6.82384 0.267859
\(650\) 1.15920 0.0454675
\(651\) 2.41199 0.0945334
\(652\) −1.80088 −0.0705278
\(653\) 13.3050 0.520664 0.260332 0.965519i \(-0.416168\pi\)
0.260332 + 0.965519i \(0.416168\pi\)
\(654\) 40.0153 1.56472
\(655\) −6.18453 −0.241650
\(656\) −7.62488 −0.297701
\(657\) −5.51580 −0.215192
\(658\) −1.08721 −0.0423840
\(659\) 6.26635 0.244102 0.122051 0.992524i \(-0.461053\pi\)
0.122051 + 0.992524i \(0.461053\pi\)
\(660\) 5.09170 0.198194
\(661\) −26.6034 −1.03475 −0.517376 0.855758i \(-0.673091\pi\)
−0.517376 + 0.855758i \(0.673091\pi\)
\(662\) −32.8525 −1.27685
\(663\) −0.639583 −0.0248393
\(664\) 7.46511 0.289703
\(665\) 0.240447 0.00932412
\(666\) −8.47521 −0.328408
\(667\) −0.464833 −0.0179984
\(668\) 14.4726 0.559962
\(669\) 20.7474 0.802142
\(670\) 13.1576 0.508322
\(671\) −2.12051 −0.0818614
\(672\) 0.286244 0.0110421
\(673\) 16.9958 0.655139 0.327570 0.944827i \(-0.393770\pi\)
0.327570 + 0.944827i \(0.393770\pi\)
\(674\) 1.57192 0.0605481
\(675\) 30.4192 1.17083
\(676\) −12.7680 −0.491078
\(677\) 8.01111 0.307892 0.153946 0.988079i \(-0.450802\pi\)
0.153946 + 0.988079i \(0.450802\pi\)
\(678\) −10.8760 −0.417689
\(679\) 1.31581 0.0504960
\(680\) 0.676320 0.0259357
\(681\) −73.5528 −2.81855
\(682\) 8.42633 0.322661
\(683\) 39.8758 1.52581 0.762903 0.646513i \(-0.223773\pi\)
0.762903 + 0.646513i \(0.223773\pi\)
\(684\) −11.5408 −0.441274
\(685\) 4.64792 0.177588
\(686\) 1.26669 0.0483623
\(687\) 84.1275 3.20967
\(688\) 7.99759 0.304905
\(689\) 0.559857 0.0213288
\(690\) −4.21215 −0.160354
\(691\) −27.8331 −1.05882 −0.529411 0.848366i \(-0.677587\pi\)
−0.529411 + 0.848366i \(0.677587\pi\)
\(692\) 16.6108 0.631447
\(693\) 0.633472 0.0240636
\(694\) 33.0672 1.25521
\(695\) 16.6561 0.631803
\(696\) −1.77663 −0.0673431
\(697\) −3.20232 −0.121297
\(698\) 17.8947 0.677323
\(699\) 12.1448 0.459359
\(700\) −0.217886 −0.00823532
\(701\) −5.61712 −0.212156 −0.106078 0.994358i \(-0.533829\pi\)
−0.106078 + 0.994358i \(0.533829\pi\)
\(702\) 6.08745 0.229756
\(703\) −1.99766 −0.0753431
\(704\) 1.00000 0.0376889
\(705\) 61.1480 2.30297
\(706\) −0.965407 −0.0363336
\(707\) −0.194958 −0.00733214
\(708\) −21.5760 −0.810876
\(709\) −16.9164 −0.635308 −0.317654 0.948207i \(-0.602895\pi\)
−0.317654 + 0.948207i \(0.602895\pi\)
\(710\) 5.26270 0.197506
\(711\) 77.7004 2.91399
\(712\) 8.38001 0.314054
\(713\) −6.97075 −0.261057
\(714\) 0.120218 0.00449904
\(715\) −0.775610 −0.0290062
\(716\) 14.6241 0.546529
\(717\) 71.6663 2.67643
\(718\) −4.14233 −0.154590
\(719\) 0.492657 0.0183730 0.00918650 0.999958i \(-0.497076\pi\)
0.00918650 + 0.999958i \(0.497076\pi\)
\(720\) −11.2682 −0.419940
\(721\) −1.28517 −0.0478623
\(722\) 16.2798 0.605870
\(723\) −27.3414 −1.01684
\(724\) −22.8349 −0.848653
\(725\) 1.35235 0.0502252
\(726\) 3.16186 0.117347
\(727\) −21.0884 −0.782125 −0.391062 0.920364i \(-0.627892\pi\)
−0.391062 + 0.920364i \(0.627892\pi\)
\(728\) −0.0436031 −0.00161604
\(729\) 12.8561 0.476153
\(730\) −1.26939 −0.0469824
\(731\) 3.35886 0.124232
\(732\) 6.70475 0.247815
\(733\) 24.5006 0.904951 0.452476 0.891777i \(-0.350541\pi\)
0.452476 + 0.891777i \(0.350541\pi\)
\(734\) 34.2662 1.26479
\(735\) −35.6001 −1.31313
\(736\) −0.827258 −0.0304931
\(737\) 8.17063 0.300969
\(738\) 53.3538 1.96398
\(739\) 3.13925 0.115479 0.0577397 0.998332i \(-0.481611\pi\)
0.0577397 + 0.998332i \(0.481611\pi\)
\(740\) −1.95047 −0.0717006
\(741\) 2.51170 0.0922697
\(742\) −0.105232 −0.00386320
\(743\) 24.7621 0.908434 0.454217 0.890891i \(-0.349919\pi\)
0.454217 + 0.890891i \(0.349919\pi\)
\(744\) −26.6428 −0.976774
\(745\) 17.5570 0.643238
\(746\) 22.9046 0.838599
\(747\) −52.2359 −1.91121
\(748\) 0.419983 0.0153561
\(749\) 1.35769 0.0496089
\(750\) 37.7130 1.37709
\(751\) −42.8569 −1.56387 −0.781935 0.623360i \(-0.785767\pi\)
−0.781935 + 0.623360i \(0.785767\pi\)
\(752\) 12.0094 0.437936
\(753\) −30.7066 −1.11901
\(754\) 0.270632 0.00985582
\(755\) −1.87023 −0.0680647
\(756\) −1.14421 −0.0416147
\(757\) −12.8451 −0.466863 −0.233431 0.972373i \(-0.574995\pi\)
−0.233431 + 0.972373i \(0.574995\pi\)
\(758\) −0.208774 −0.00758301
\(759\) −2.61567 −0.0949428
\(760\) −2.65597 −0.0963423
\(761\) −41.1022 −1.48995 −0.744977 0.667090i \(-0.767540\pi\)
−0.744977 + 0.667090i \(0.767540\pi\)
\(762\) −31.8326 −1.15317
\(763\) 1.14572 0.0414779
\(764\) 20.0238 0.724435
\(765\) −4.73244 −0.171102
\(766\) 24.4168 0.882214
\(767\) 3.28664 0.118674
\(768\) −3.16186 −0.114094
\(769\) −14.1741 −0.511132 −0.255566 0.966792i \(-0.582262\pi\)
−0.255566 + 0.966792i \(0.582262\pi\)
\(770\) 0.145786 0.00525376
\(771\) −23.3516 −0.840989
\(772\) −12.5215 −0.450658
\(773\) 16.3094 0.586607 0.293304 0.956019i \(-0.405245\pi\)
0.293304 + 0.956019i \(0.405245\pi\)
\(774\) −55.9618 −2.01151
\(775\) 20.2802 0.728488
\(776\) −14.5344 −0.521755
\(777\) −0.346701 −0.0124378
\(778\) −2.00470 −0.0718719
\(779\) 12.5758 0.450575
\(780\) 2.45237 0.0878088
\(781\) 3.26805 0.116940
\(782\) −0.347434 −0.0124242
\(783\) 7.10180 0.253798
\(784\) −6.99180 −0.249707
\(785\) −19.9982 −0.713765
\(786\) 12.1431 0.433129
\(787\) −5.25108 −0.187181 −0.0935904 0.995611i \(-0.529834\pi\)
−0.0935904 + 0.995611i \(0.529834\pi\)
\(788\) 1.00000 0.0356235
\(789\) 23.4689 0.835514
\(790\) 17.8818 0.636205
\(791\) −0.311401 −0.0110722
\(792\) −6.99733 −0.248639
\(793\) −1.02132 −0.0362682
\(794\) −4.97318 −0.176492
\(795\) 5.91857 0.209910
\(796\) −6.27326 −0.222350
\(797\) 41.2924 1.46265 0.731325 0.682029i \(-0.238902\pi\)
0.731325 + 0.682029i \(0.238902\pi\)
\(798\) −0.472107 −0.0167124
\(799\) 5.04373 0.178434
\(800\) 2.40677 0.0850922
\(801\) −58.6377 −2.07186
\(802\) 5.06123 0.178718
\(803\) −0.788272 −0.0278175
\(804\) −25.8344 −0.911108
\(805\) −0.120602 −0.00425068
\(806\) 4.05846 0.142953
\(807\) 65.3472 2.30033
\(808\) 2.15350 0.0757600
\(809\) −15.5840 −0.547903 −0.273952 0.961743i \(-0.588331\pi\)
−0.273952 + 0.961743i \(0.588331\pi\)
\(810\) 30.5494 1.07340
\(811\) 5.66060 0.198771 0.0993853 0.995049i \(-0.468312\pi\)
0.0993853 + 0.995049i \(0.468312\pi\)
\(812\) −0.0508687 −0.00178514
\(813\) 64.9228 2.27694
\(814\) −1.21121 −0.0424527
\(815\) 2.90004 0.101584
\(816\) −1.32793 −0.0464867
\(817\) −13.1905 −0.461479
\(818\) −13.7553 −0.480944
\(819\) 0.305106 0.0106613
\(820\) 12.2787 0.428792
\(821\) −39.8262 −1.38994 −0.694972 0.719037i \(-0.744583\pi\)
−0.694972 + 0.719037i \(0.744583\pi\)
\(822\) −9.12599 −0.318305
\(823\) −3.71062 −0.129344 −0.0646720 0.997907i \(-0.520600\pi\)
−0.0646720 + 0.997907i \(0.520600\pi\)
\(824\) 14.1960 0.494541
\(825\) 7.60986 0.264941
\(826\) −0.617766 −0.0214948
\(827\) 3.26348 0.113482 0.0567411 0.998389i \(-0.481929\pi\)
0.0567411 + 0.998389i \(0.481929\pi\)
\(828\) 5.78860 0.201168
\(829\) 6.39376 0.222064 0.111032 0.993817i \(-0.464584\pi\)
0.111032 + 0.993817i \(0.464584\pi\)
\(830\) −12.0215 −0.417271
\(831\) −42.7993 −1.48469
\(832\) 0.481640 0.0166979
\(833\) −2.93644 −0.101742
\(834\) −32.7036 −1.13243
\(835\) −23.3060 −0.806537
\(836\) −1.64931 −0.0570427
\(837\) 106.500 3.68119
\(838\) 1.85667 0.0641375
\(839\) 11.5824 0.399869 0.199934 0.979809i \(-0.435927\pi\)
0.199934 + 0.979809i \(0.435927\pi\)
\(840\) −0.460954 −0.0159044
\(841\) −28.6843 −0.989113
\(842\) −6.84016 −0.235727
\(843\) 31.3016 1.07808
\(844\) 5.76182 0.198330
\(845\) 20.5610 0.707320
\(846\) −84.0335 −2.88913
\(847\) 0.0905305 0.00311067
\(848\) 1.16240 0.0399168
\(849\) −6.05650 −0.207859
\(850\) 1.01080 0.0346703
\(851\) 1.00198 0.0343474
\(852\) −10.3331 −0.354006
\(853\) −11.7851 −0.403513 −0.201757 0.979436i \(-0.564665\pi\)
−0.201757 + 0.979436i \(0.564665\pi\)
\(854\) 0.191971 0.00656911
\(855\) 18.5847 0.635585
\(856\) −14.9970 −0.512588
\(857\) −20.3899 −0.696507 −0.348253 0.937400i \(-0.613225\pi\)
−0.348253 + 0.937400i \(0.613225\pi\)
\(858\) 1.52288 0.0519902
\(859\) 26.7342 0.912159 0.456079 0.889939i \(-0.349253\pi\)
0.456079 + 0.889939i \(0.349253\pi\)
\(860\) −12.8789 −0.439168
\(861\) 2.18258 0.0743821
\(862\) 5.73620 0.195376
\(863\) −50.8908 −1.73234 −0.866171 0.499748i \(-0.833426\pi\)
−0.866171 + 0.499748i \(0.833426\pi\)
\(864\) 12.6390 0.429987
\(865\) −26.7492 −0.909500
\(866\) −16.0484 −0.545346
\(867\) 53.1938 1.80656
\(868\) −0.762840 −0.0258925
\(869\) 11.1043 0.376687
\(870\) 2.86100 0.0969971
\(871\) 3.93530 0.133343
\(872\) −12.6556 −0.428574
\(873\) 101.702 3.44209
\(874\) 1.36441 0.0461518
\(875\) 1.07980 0.0365040
\(876\) 2.49240 0.0842105
\(877\) 2.08367 0.0703604 0.0351802 0.999381i \(-0.488799\pi\)
0.0351802 + 0.999381i \(0.488799\pi\)
\(878\) 14.8135 0.499933
\(879\) −27.6314 −0.931984
\(880\) −1.61035 −0.0542849
\(881\) −18.6018 −0.626712 −0.313356 0.949636i \(-0.601453\pi\)
−0.313356 + 0.949636i \(0.601453\pi\)
\(882\) 48.9240 1.64736
\(883\) 12.2050 0.410732 0.205366 0.978685i \(-0.434161\pi\)
0.205366 + 0.978685i \(0.434161\pi\)
\(884\) 0.202281 0.00680344
\(885\) 34.7449 1.16794
\(886\) 15.7001 0.527454
\(887\) 6.67456 0.224110 0.112055 0.993702i \(-0.464257\pi\)
0.112055 + 0.993702i \(0.464257\pi\)
\(888\) 3.82966 0.128515
\(889\) −0.911434 −0.0305685
\(890\) −13.4948 −0.452345
\(891\) 18.9707 0.635542
\(892\) −6.56179 −0.219705
\(893\) −19.8072 −0.662823
\(894\) −34.4724 −1.15293
\(895\) −23.5500 −0.787188
\(896\) −0.0905305 −0.00302441
\(897\) −1.25981 −0.0420639
\(898\) −12.0150 −0.400945
\(899\) 4.73472 0.157912
\(900\) −16.8410 −0.561366
\(901\) 0.488187 0.0162639
\(902\) 7.62488 0.253881
\(903\) −2.28927 −0.0761820
\(904\) 3.43974 0.114404
\(905\) 36.7722 1.22235
\(906\) 3.67212 0.121998
\(907\) 2.05244 0.0681501 0.0340750 0.999419i \(-0.489151\pi\)
0.0340750 + 0.999419i \(0.489151\pi\)
\(908\) 23.2625 0.771995
\(909\) −15.0688 −0.499800
\(910\) 0.0702163 0.00232765
\(911\) 0.884430 0.0293025 0.0146512 0.999893i \(-0.495336\pi\)
0.0146512 + 0.999893i \(0.495336\pi\)
\(912\) 5.21489 0.172682
\(913\) −7.46511 −0.247059
\(914\) −1.13638 −0.0375880
\(915\) −10.7970 −0.356938
\(916\) −26.6070 −0.879120
\(917\) 0.347681 0.0114815
\(918\) 5.30817 0.175196
\(919\) 48.9391 1.61435 0.807176 0.590311i \(-0.200995\pi\)
0.807176 + 0.590311i \(0.200995\pi\)
\(920\) 1.33218 0.0439205
\(921\) 93.1876 3.07064
\(922\) −16.5049 −0.543560
\(923\) 1.57402 0.0518096
\(924\) −0.286244 −0.00941675
\(925\) −2.91509 −0.0958477
\(926\) 37.7903 1.24186
\(927\) −99.3342 −3.26256
\(928\) 0.561896 0.0184451
\(929\) −13.6229 −0.446954 −0.223477 0.974709i \(-0.571741\pi\)
−0.223477 + 0.974709i \(0.571741\pi\)
\(930\) 42.9043 1.40689
\(931\) 11.5317 0.377936
\(932\) −3.84104 −0.125817
\(933\) −49.6602 −1.62580
\(934\) −1.47313 −0.0482024
\(935\) −0.676320 −0.0221180
\(936\) −3.37020 −0.110158
\(937\) −18.8355 −0.615327 −0.307664 0.951495i \(-0.599547\pi\)
−0.307664 + 0.951495i \(0.599547\pi\)
\(938\) −0.739691 −0.0241518
\(939\) 29.6585 0.967868
\(940\) −19.3393 −0.630778
\(941\) −56.7175 −1.84894 −0.924469 0.381257i \(-0.875491\pi\)
−0.924469 + 0.381257i \(0.875491\pi\)
\(942\) 39.2656 1.27934
\(943\) −6.30774 −0.205408
\(944\) 6.82384 0.222097
\(945\) 1.84259 0.0599394
\(946\) −7.99759 −0.260024
\(947\) 30.7764 1.00010 0.500049 0.865997i \(-0.333315\pi\)
0.500049 + 0.865997i \(0.333315\pi\)
\(948\) −35.1101 −1.14032
\(949\) −0.379663 −0.0123244
\(950\) −3.96952 −0.128788
\(951\) −1.28443 −0.0416505
\(952\) −0.0380213 −0.00123228
\(953\) −32.8697 −1.06475 −0.532377 0.846507i \(-0.678701\pi\)
−0.532377 + 0.846507i \(0.678701\pi\)
\(954\) −8.13367 −0.263337
\(955\) −32.2453 −1.04343
\(956\) −22.6659 −0.733067
\(957\) 1.77663 0.0574304
\(958\) −8.78124 −0.283709
\(959\) −0.261296 −0.00843769
\(960\) 5.09170 0.164334
\(961\) 40.0031 1.29042
\(962\) −0.583365 −0.0188085
\(963\) 104.939 3.38162
\(964\) 8.64726 0.278510
\(965\) 20.1640 0.649102
\(966\) 0.236798 0.00761885
\(967\) 15.2791 0.491341 0.245671 0.969353i \(-0.420992\pi\)
0.245671 + 0.969353i \(0.420992\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 2.19017 0.0703583
\(970\) 23.4055 0.751505
\(971\) −35.4425 −1.13741 −0.568703 0.822543i \(-0.692555\pi\)
−0.568703 + 0.822543i \(0.692555\pi\)
\(972\) −22.0656 −0.707754
\(973\) −0.936372 −0.0300187
\(974\) −38.7747 −1.24242
\(975\) 3.66522 0.117381
\(976\) −2.12051 −0.0678759
\(977\) −54.1371 −1.73200 −0.866000 0.500043i \(-0.833317\pi\)
−0.866000 + 0.500043i \(0.833317\pi\)
\(978\) −5.69412 −0.182078
\(979\) −8.38001 −0.267826
\(980\) 11.2593 0.359664
\(981\) 88.5557 2.82737
\(982\) 12.6103 0.402410
\(983\) 5.14061 0.163960 0.0819800 0.996634i \(-0.473876\pi\)
0.0819800 + 0.996634i \(0.473876\pi\)
\(984\) −24.1088 −0.768559
\(985\) −1.61035 −0.0513100
\(986\) 0.235987 0.00751535
\(987\) −3.43761 −0.109420
\(988\) −0.794376 −0.0252725
\(989\) 6.61607 0.210379
\(990\) 11.2682 0.358126
\(991\) 49.4147 1.56971 0.784855 0.619679i \(-0.212737\pi\)
0.784855 + 0.619679i \(0.212737\pi\)
\(992\) 8.42633 0.267536
\(993\) −103.875 −3.29637
\(994\) −0.295858 −0.00938405
\(995\) 10.1021 0.320259
\(996\) 23.6036 0.747909
\(997\) 60.0884 1.90302 0.951509 0.307621i \(-0.0995328\pi\)
0.951509 + 0.307621i \(0.0995328\pi\)
\(998\) −40.8293 −1.29243
\(999\) −15.3084 −0.484337
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 4334.2.a.a.1.1 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4334.2.a.a.1.1 15 1.1 even 1 trivial