Properties

Label 6026.2.a.k.1.10
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $0$
Dimension $35$
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: \(0\)
Dimension: \(35\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.74363 q^{3} +1.00000 q^{4} +1.36417 q^{5} -1.74363 q^{6} +0.246249 q^{7} +1.00000 q^{8} +0.0402388 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.74363 q^{3} +1.00000 q^{4} +1.36417 q^{5} -1.74363 q^{6} +0.246249 q^{7} +1.00000 q^{8} +0.0402388 q^{9} +1.36417 q^{10} +0.997185 q^{11} -1.74363 q^{12} +1.44270 q^{13} +0.246249 q^{14} -2.37860 q^{15} +1.00000 q^{16} +7.37189 q^{17} +0.0402388 q^{18} +0.127079 q^{19} +1.36417 q^{20} -0.429367 q^{21} +0.997185 q^{22} -1.00000 q^{23} -1.74363 q^{24} -3.13905 q^{25} +1.44270 q^{26} +5.16072 q^{27} +0.246249 q^{28} +3.04044 q^{29} -2.37860 q^{30} -7.07979 q^{31} +1.00000 q^{32} -1.73872 q^{33} +7.37189 q^{34} +0.335924 q^{35} +0.0402388 q^{36} +2.76502 q^{37} +0.127079 q^{38} -2.51553 q^{39} +1.36417 q^{40} +9.95597 q^{41} -0.429367 q^{42} +8.18686 q^{43} +0.997185 q^{44} +0.0548924 q^{45} -1.00000 q^{46} -11.5529 q^{47} -1.74363 q^{48} -6.93936 q^{49} -3.13905 q^{50} -12.8538 q^{51} +1.44270 q^{52} +3.11372 q^{53} +5.16072 q^{54} +1.36033 q^{55} +0.246249 q^{56} -0.221579 q^{57} +3.04044 q^{58} +10.4811 q^{59} -2.37860 q^{60} -2.02027 q^{61} -7.07979 q^{62} +0.00990876 q^{63} +1.00000 q^{64} +1.96808 q^{65} -1.73872 q^{66} -14.1574 q^{67} +7.37189 q^{68} +1.74363 q^{69} +0.335924 q^{70} +9.72966 q^{71} +0.0402388 q^{72} -2.07341 q^{73} +2.76502 q^{74} +5.47334 q^{75} +0.127079 q^{76} +0.245556 q^{77} -2.51553 q^{78} -10.9624 q^{79} +1.36417 q^{80} -9.11910 q^{81} +9.95597 q^{82} -0.120817 q^{83} -0.429367 q^{84} +10.0565 q^{85} +8.18686 q^{86} -5.30140 q^{87} +0.997185 q^{88} +0.217175 q^{89} +0.0548924 q^{90} +0.355262 q^{91} -1.00000 q^{92} +12.3445 q^{93} -11.5529 q^{94} +0.173357 q^{95} -1.74363 q^{96} +11.2033 q^{97} -6.93936 q^{98} +0.0401255 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 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
\(3\) −1.74363 −1.00668 −0.503342 0.864087i \(-0.667896\pi\)
−0.503342 + 0.864087i \(0.667896\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.36417 0.610074 0.305037 0.952341i \(-0.401331\pi\)
0.305037 + 0.952341i \(0.401331\pi\)
\(6\) −1.74363 −0.711833
\(7\) 0.246249 0.0930733 0.0465367 0.998917i \(-0.485182\pi\)
0.0465367 + 0.998917i \(0.485182\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.0402388 0.0134129
\(10\) 1.36417 0.431387
\(11\) 0.997185 0.300663 0.150331 0.988636i \(-0.451966\pi\)
0.150331 + 0.988636i \(0.451966\pi\)
\(12\) −1.74363 −0.503342
\(13\) 1.44270 0.400132 0.200066 0.979782i \(-0.435884\pi\)
0.200066 + 0.979782i \(0.435884\pi\)
\(14\) 0.246249 0.0658128
\(15\) −2.37860 −0.614152
\(16\) 1.00000 0.250000
\(17\) 7.37189 1.78795 0.893973 0.448120i \(-0.147906\pi\)
0.893973 + 0.448120i \(0.147906\pi\)
\(18\) 0.0402388 0.00948437
\(19\) 0.127079 0.0291539 0.0145770 0.999894i \(-0.495360\pi\)
0.0145770 + 0.999894i \(0.495360\pi\)
\(20\) 1.36417 0.305037
\(21\) −0.429367 −0.0936955
\(22\) 0.997185 0.212601
\(23\) −1.00000 −0.208514
\(24\) −1.74363 −0.355917
\(25\) −3.13905 −0.627810
\(26\) 1.44270 0.282936
\(27\) 5.16072 0.993182
\(28\) 0.246249 0.0465367
\(29\) 3.04044 0.564595 0.282298 0.959327i \(-0.408903\pi\)
0.282298 + 0.959327i \(0.408903\pi\)
\(30\) −2.37860 −0.434271
\(31\) −7.07979 −1.27157 −0.635784 0.771867i \(-0.719323\pi\)
−0.635784 + 0.771867i \(0.719323\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.73872 −0.302672
\(34\) 7.37189 1.26427
\(35\) 0.335924 0.0567816
\(36\) 0.0402388 0.00670646
\(37\) 2.76502 0.454566 0.227283 0.973829i \(-0.427016\pi\)
0.227283 + 0.973829i \(0.427016\pi\)
\(38\) 0.127079 0.0206149
\(39\) −2.51553 −0.402807
\(40\) 1.36417 0.215694
\(41\) 9.95597 1.55486 0.777430 0.628969i \(-0.216523\pi\)
0.777430 + 0.628969i \(0.216523\pi\)
\(42\) −0.429367 −0.0662527
\(43\) 8.18686 1.24849 0.624243 0.781231i \(-0.285408\pi\)
0.624243 + 0.781231i \(0.285408\pi\)
\(44\) 0.997185 0.150331
\(45\) 0.0548924 0.00818288
\(46\) −1.00000 −0.147442
\(47\) −11.5529 −1.68516 −0.842580 0.538572i \(-0.818964\pi\)
−0.842580 + 0.538572i \(0.818964\pi\)
\(48\) −1.74363 −0.251671
\(49\) −6.93936 −0.991337
\(50\) −3.13905 −0.443929
\(51\) −12.8538 −1.79990
\(52\) 1.44270 0.200066
\(53\) 3.11372 0.427703 0.213851 0.976866i \(-0.431399\pi\)
0.213851 + 0.976866i \(0.431399\pi\)
\(54\) 5.16072 0.702285
\(55\) 1.36033 0.183426
\(56\) 0.246249 0.0329064
\(57\) −0.221579 −0.0293488
\(58\) 3.04044 0.399229
\(59\) 10.4811 1.36452 0.682262 0.731108i \(-0.260996\pi\)
0.682262 + 0.731108i \(0.260996\pi\)
\(60\) −2.37860 −0.307076
\(61\) −2.02027 −0.258668 −0.129334 0.991601i \(-0.541284\pi\)
−0.129334 + 0.991601i \(0.541284\pi\)
\(62\) −7.07979 −0.899135
\(63\) 0.00990876 0.00124839
\(64\) 1.00000 0.125000
\(65\) 1.96808 0.244110
\(66\) −1.73872 −0.214022
\(67\) −14.1574 −1.72960 −0.864800 0.502117i \(-0.832555\pi\)
−0.864800 + 0.502117i \(0.832555\pi\)
\(68\) 7.37189 0.893973
\(69\) 1.74363 0.209908
\(70\) 0.335924 0.0401507
\(71\) 9.72966 1.15470 0.577349 0.816497i \(-0.304087\pi\)
0.577349 + 0.816497i \(0.304087\pi\)
\(72\) 0.0402388 0.00474219
\(73\) −2.07341 −0.242674 −0.121337 0.992611i \(-0.538718\pi\)
−0.121337 + 0.992611i \(0.538718\pi\)
\(74\) 2.76502 0.321427
\(75\) 5.47334 0.632006
\(76\) 0.127079 0.0145770
\(77\) 0.245556 0.0279837
\(78\) −2.51553 −0.284827
\(79\) −10.9624 −1.23336 −0.616681 0.787213i \(-0.711523\pi\)
−0.616681 + 0.787213i \(0.711523\pi\)
\(80\) 1.36417 0.152518
\(81\) −9.11910 −1.01323
\(82\) 9.95597 1.09945
\(83\) −0.120817 −0.0132614 −0.00663068 0.999978i \(-0.502111\pi\)
−0.00663068 + 0.999978i \(0.502111\pi\)
\(84\) −0.429367 −0.0468477
\(85\) 10.0565 1.09078
\(86\) 8.18686 0.882812
\(87\) −5.30140 −0.568369
\(88\) 0.997185 0.106300
\(89\) 0.217175 0.0230205 0.0115103 0.999934i \(-0.496336\pi\)
0.0115103 + 0.999934i \(0.496336\pi\)
\(90\) 0.0548924 0.00578617
\(91\) 0.355262 0.0372416
\(92\) −1.00000 −0.104257
\(93\) 12.3445 1.28007
\(94\) −11.5529 −1.19159
\(95\) 0.173357 0.0177860
\(96\) −1.74363 −0.177958
\(97\) 11.2033 1.13752 0.568762 0.822502i \(-0.307423\pi\)
0.568762 + 0.822502i \(0.307423\pi\)
\(98\) −6.93936 −0.700981
\(99\) 0.0401255 0.00403277
\(100\) −3.13905 −0.313905
\(101\) 8.93549 0.889115 0.444557 0.895750i \(-0.353361\pi\)
0.444557 + 0.895750i \(0.353361\pi\)
\(102\) −12.8538 −1.27272
\(103\) −9.02603 −0.889361 −0.444680 0.895689i \(-0.646683\pi\)
−0.444680 + 0.895689i \(0.646683\pi\)
\(104\) 1.44270 0.141468
\(105\) −0.585727 −0.0571611
\(106\) 3.11372 0.302432
\(107\) 13.9188 1.34559 0.672793 0.739831i \(-0.265095\pi\)
0.672793 + 0.739831i \(0.265095\pi\)
\(108\) 5.16072 0.496591
\(109\) 10.4582 1.00172 0.500859 0.865529i \(-0.333018\pi\)
0.500859 + 0.865529i \(0.333018\pi\)
\(110\) 1.36033 0.129702
\(111\) −4.82116 −0.457605
\(112\) 0.246249 0.0232683
\(113\) 19.5060 1.83497 0.917484 0.397773i \(-0.130217\pi\)
0.917484 + 0.397773i \(0.130217\pi\)
\(114\) −0.221579 −0.0207527
\(115\) −1.36417 −0.127209
\(116\) 3.04044 0.282298
\(117\) 0.0580524 0.00536694
\(118\) 10.4811 0.964864
\(119\) 1.81532 0.166410
\(120\) −2.37860 −0.217135
\(121\) −10.0056 −0.909602
\(122\) −2.02027 −0.182906
\(123\) −17.3595 −1.56525
\(124\) −7.07979 −0.635784
\(125\) −11.1030 −0.993084
\(126\) 0.00990876 0.000882742 0
\(127\) 15.2538 1.35355 0.676776 0.736189i \(-0.263376\pi\)
0.676776 + 0.736189i \(0.263376\pi\)
\(128\) 1.00000 0.0883883
\(129\) −14.2748 −1.25683
\(130\) 1.96808 0.172612
\(131\) −1.00000 −0.0873704
\(132\) −1.73872 −0.151336
\(133\) 0.0312931 0.00271345
\(134\) −14.1574 −1.22301
\(135\) 7.04008 0.605914
\(136\) 7.37189 0.632135
\(137\) −6.20057 −0.529751 −0.264875 0.964283i \(-0.585331\pi\)
−0.264875 + 0.964283i \(0.585331\pi\)
\(138\) 1.74363 0.148427
\(139\) 10.1560 0.861419 0.430709 0.902491i \(-0.358263\pi\)
0.430709 + 0.902491i \(0.358263\pi\)
\(140\) 0.335924 0.0283908
\(141\) 20.1439 1.69642
\(142\) 9.72966 0.816495
\(143\) 1.43864 0.120305
\(144\) 0.0402388 0.00335323
\(145\) 4.14766 0.344445
\(146\) −2.07341 −0.171597
\(147\) 12.0997 0.997964
\(148\) 2.76502 0.227283
\(149\) −9.75595 −0.799239 −0.399619 0.916681i \(-0.630858\pi\)
−0.399619 + 0.916681i \(0.630858\pi\)
\(150\) 5.47334 0.446896
\(151\) −3.15127 −0.256447 −0.128224 0.991745i \(-0.540927\pi\)
−0.128224 + 0.991745i \(0.540927\pi\)
\(152\) 0.127079 0.0103075
\(153\) 0.296636 0.0239816
\(154\) 0.245556 0.0197875
\(155\) −9.65802 −0.775751
\(156\) −2.51553 −0.201403
\(157\) 10.0010 0.798169 0.399084 0.916914i \(-0.369328\pi\)
0.399084 + 0.916914i \(0.369328\pi\)
\(158\) −10.9624 −0.872119
\(159\) −5.42918 −0.430562
\(160\) 1.36417 0.107847
\(161\) −0.246249 −0.0194071
\(162\) −9.11910 −0.716464
\(163\) −2.38311 −0.186660 −0.0933299 0.995635i \(-0.529751\pi\)
−0.0933299 + 0.995635i \(0.529751\pi\)
\(164\) 9.95597 0.777430
\(165\) −2.37190 −0.184652
\(166\) −0.120817 −0.00937719
\(167\) 19.8944 1.53947 0.769736 0.638362i \(-0.220388\pi\)
0.769736 + 0.638362i \(0.220388\pi\)
\(168\) −0.429367 −0.0331263
\(169\) −10.9186 −0.839894
\(170\) 10.0565 0.771297
\(171\) 0.00511351 0.000391040 0
\(172\) 8.18686 0.624243
\(173\) −11.9110 −0.905577 −0.452788 0.891618i \(-0.649571\pi\)
−0.452788 + 0.891618i \(0.649571\pi\)
\(174\) −5.30140 −0.401898
\(175\) −0.772988 −0.0584324
\(176\) 0.997185 0.0751657
\(177\) −18.2752 −1.37364
\(178\) 0.217175 0.0162780
\(179\) 2.85347 0.213278 0.106639 0.994298i \(-0.465991\pi\)
0.106639 + 0.994298i \(0.465991\pi\)
\(180\) 0.0548924 0.00409144
\(181\) 6.40380 0.475990 0.237995 0.971266i \(-0.423510\pi\)
0.237995 + 0.971266i \(0.423510\pi\)
\(182\) 0.355262 0.0263338
\(183\) 3.52259 0.260397
\(184\) −1.00000 −0.0737210
\(185\) 3.77194 0.277319
\(186\) 12.3445 0.905145
\(187\) 7.35114 0.537569
\(188\) −11.5529 −0.842580
\(189\) 1.27082 0.0924387
\(190\) 0.173357 0.0125766
\(191\) −1.54073 −0.111483 −0.0557416 0.998445i \(-0.517752\pi\)
−0.0557416 + 0.998445i \(0.517752\pi\)
\(192\) −1.74363 −0.125836
\(193\) −10.3850 −0.747529 −0.373764 0.927524i \(-0.621933\pi\)
−0.373764 + 0.927524i \(0.621933\pi\)
\(194\) 11.2033 0.804351
\(195\) −3.43160 −0.245742
\(196\) −6.93936 −0.495669
\(197\) 23.0211 1.64019 0.820094 0.572229i \(-0.193921\pi\)
0.820094 + 0.572229i \(0.193921\pi\)
\(198\) 0.0401255 0.00285160
\(199\) −13.8274 −0.980196 −0.490098 0.871667i \(-0.663039\pi\)
−0.490098 + 0.871667i \(0.663039\pi\)
\(200\) −3.13905 −0.221964
\(201\) 24.6852 1.74116
\(202\) 8.93549 0.628699
\(203\) 0.748705 0.0525488
\(204\) −12.8538 −0.899949
\(205\) 13.5816 0.948580
\(206\) −9.02603 −0.628873
\(207\) −0.0402388 −0.00279679
\(208\) 1.44270 0.100033
\(209\) 0.126721 0.00876550
\(210\) −0.585727 −0.0404190
\(211\) 0.717238 0.0493767 0.0246883 0.999695i \(-0.492141\pi\)
0.0246883 + 0.999695i \(0.492141\pi\)
\(212\) 3.11372 0.213851
\(213\) −16.9649 −1.16242
\(214\) 13.9188 0.951473
\(215\) 11.1682 0.761668
\(216\) 5.16072 0.351143
\(217\) −1.74339 −0.118349
\(218\) 10.4582 0.708321
\(219\) 3.61526 0.244296
\(220\) 1.36033 0.0917132
\(221\) 10.6354 0.715415
\(222\) −4.82116 −0.323575
\(223\) 28.0974 1.88154 0.940771 0.339041i \(-0.110103\pi\)
0.940771 + 0.339041i \(0.110103\pi\)
\(224\) 0.246249 0.0164532
\(225\) −0.126312 −0.00842077
\(226\) 19.5060 1.29752
\(227\) −10.8000 −0.716820 −0.358410 0.933564i \(-0.616681\pi\)
−0.358410 + 0.933564i \(0.616681\pi\)
\(228\) −0.221579 −0.0146744
\(229\) −3.86486 −0.255397 −0.127698 0.991813i \(-0.540759\pi\)
−0.127698 + 0.991813i \(0.540759\pi\)
\(230\) −1.36417 −0.0899505
\(231\) −0.428158 −0.0281707
\(232\) 3.04044 0.199615
\(233\) 9.20161 0.602817 0.301409 0.953495i \(-0.402543\pi\)
0.301409 + 0.953495i \(0.402543\pi\)
\(234\) 0.0580524 0.00379500
\(235\) −15.7600 −1.02807
\(236\) 10.4811 0.682262
\(237\) 19.1143 1.24161
\(238\) 1.81532 0.117670
\(239\) −7.41788 −0.479823 −0.239912 0.970795i \(-0.577118\pi\)
−0.239912 + 0.970795i \(0.577118\pi\)
\(240\) −2.37860 −0.153538
\(241\) 14.9370 0.962177 0.481089 0.876672i \(-0.340242\pi\)
0.481089 + 0.876672i \(0.340242\pi\)
\(242\) −10.0056 −0.643186
\(243\) 0.418146 0.0268241
\(244\) −2.02027 −0.129334
\(245\) −9.46644 −0.604789
\(246\) −17.3595 −1.10680
\(247\) 0.183337 0.0116654
\(248\) −7.07979 −0.449567
\(249\) 0.210659 0.0133500
\(250\) −11.1030 −0.702217
\(251\) 9.89554 0.624601 0.312300 0.949983i \(-0.398900\pi\)
0.312300 + 0.949983i \(0.398900\pi\)
\(252\) 0.00990876 0.000624193 0
\(253\) −0.997185 −0.0626925
\(254\) 15.2538 0.957106
\(255\) −17.5348 −1.09807
\(256\) 1.00000 0.0625000
\(257\) 9.73200 0.607066 0.303533 0.952821i \(-0.401834\pi\)
0.303533 + 0.952821i \(0.401834\pi\)
\(258\) −14.2748 −0.888713
\(259\) 0.680883 0.0423080
\(260\) 1.96808 0.122055
\(261\) 0.122344 0.00757288
\(262\) −1.00000 −0.0617802
\(263\) −27.9012 −1.72046 −0.860231 0.509904i \(-0.829681\pi\)
−0.860231 + 0.509904i \(0.829681\pi\)
\(264\) −1.73872 −0.107011
\(265\) 4.24764 0.260930
\(266\) 0.0312931 0.00191870
\(267\) −0.378672 −0.0231744
\(268\) −14.1574 −0.864800
\(269\) 29.5144 1.79953 0.899763 0.436380i \(-0.143739\pi\)
0.899763 + 0.436380i \(0.143739\pi\)
\(270\) 7.04008 0.428446
\(271\) 5.94548 0.361162 0.180581 0.983560i \(-0.442202\pi\)
0.180581 + 0.983560i \(0.442202\pi\)
\(272\) 7.37189 0.446987
\(273\) −0.619446 −0.0374906
\(274\) −6.20057 −0.374590
\(275\) −3.13022 −0.188759
\(276\) 1.74363 0.104954
\(277\) 4.76161 0.286097 0.143049 0.989716i \(-0.454309\pi\)
0.143049 + 0.989716i \(0.454309\pi\)
\(278\) 10.1560 0.609115
\(279\) −0.284882 −0.0170555
\(280\) 0.335924 0.0200753
\(281\) −2.55357 −0.152333 −0.0761666 0.997095i \(-0.524268\pi\)
−0.0761666 + 0.997095i \(0.524268\pi\)
\(282\) 20.1439 1.19955
\(283\) 19.0982 1.13527 0.567636 0.823279i \(-0.307858\pi\)
0.567636 + 0.823279i \(0.307858\pi\)
\(284\) 9.72966 0.577349
\(285\) −0.302270 −0.0179049
\(286\) 1.43864 0.0850683
\(287\) 2.45165 0.144716
\(288\) 0.0402388 0.00237109
\(289\) 37.3448 2.19675
\(290\) 4.14766 0.243559
\(291\) −19.5344 −1.14513
\(292\) −2.07341 −0.121337
\(293\) 25.3806 1.48275 0.741376 0.671089i \(-0.234173\pi\)
0.741376 + 0.671089i \(0.234173\pi\)
\(294\) 12.0997 0.705667
\(295\) 14.2980 0.832460
\(296\) 2.76502 0.160713
\(297\) 5.14620 0.298613
\(298\) −9.75595 −0.565147
\(299\) −1.44270 −0.0834333
\(300\) 5.47334 0.316003
\(301\) 2.01601 0.116201
\(302\) −3.15127 −0.181335
\(303\) −15.5802 −0.895058
\(304\) 0.127079 0.00728848
\(305\) −2.75598 −0.157807
\(306\) 0.296636 0.0169576
\(307\) −28.7690 −1.64193 −0.820967 0.570975i \(-0.806565\pi\)
−0.820967 + 0.570975i \(0.806565\pi\)
\(308\) 0.245556 0.0139918
\(309\) 15.7380 0.895305
\(310\) −9.65802 −0.548539
\(311\) 7.33784 0.416091 0.208046 0.978119i \(-0.433290\pi\)
0.208046 + 0.978119i \(0.433290\pi\)
\(312\) −2.51553 −0.142414
\(313\) −23.4443 −1.32515 −0.662576 0.748995i \(-0.730537\pi\)
−0.662576 + 0.748995i \(0.730537\pi\)
\(314\) 10.0010 0.564391
\(315\) 0.0135172 0.000761608 0
\(316\) −10.9624 −0.616681
\(317\) 7.85505 0.441183 0.220592 0.975366i \(-0.429201\pi\)
0.220592 + 0.975366i \(0.429201\pi\)
\(318\) −5.42918 −0.304453
\(319\) 3.03188 0.169753
\(320\) 1.36417 0.0762592
\(321\) −24.2693 −1.35458
\(322\) −0.246249 −0.0137229
\(323\) 0.936813 0.0521257
\(324\) −9.11910 −0.506617
\(325\) −4.52870 −0.251207
\(326\) −2.38311 −0.131988
\(327\) −18.2353 −1.00841
\(328\) 9.95597 0.549726
\(329\) −2.84488 −0.156843
\(330\) −2.37190 −0.130569
\(331\) 5.10693 0.280702 0.140351 0.990102i \(-0.455177\pi\)
0.140351 + 0.990102i \(0.455177\pi\)
\(332\) −0.120817 −0.00663068
\(333\) 0.111261 0.00609706
\(334\) 19.8944 1.08857
\(335\) −19.3130 −1.05518
\(336\) −0.429367 −0.0234239
\(337\) −5.56800 −0.303308 −0.151654 0.988434i \(-0.548460\pi\)
−0.151654 + 0.988434i \(0.548460\pi\)
\(338\) −10.9186 −0.593895
\(339\) −34.0112 −1.84723
\(340\) 10.0565 0.545390
\(341\) −7.05987 −0.382313
\(342\) 0.00511351 0.000276507 0
\(343\) −3.43255 −0.185340
\(344\) 8.18686 0.441406
\(345\) 2.37860 0.128059
\(346\) −11.9110 −0.640339
\(347\) 23.3865 1.25545 0.627727 0.778434i \(-0.283986\pi\)
0.627727 + 0.778434i \(0.283986\pi\)
\(348\) −5.30140 −0.284185
\(349\) −11.2297 −0.601113 −0.300557 0.953764i \(-0.597172\pi\)
−0.300557 + 0.953764i \(0.597172\pi\)
\(350\) −0.772988 −0.0413179
\(351\) 7.44536 0.397404
\(352\) 0.997185 0.0531502
\(353\) −18.4868 −0.983952 −0.491976 0.870609i \(-0.663725\pi\)
−0.491976 + 0.870609i \(0.663725\pi\)
\(354\) −18.2752 −0.971314
\(355\) 13.2729 0.704451
\(356\) 0.217175 0.0115103
\(357\) −3.16524 −0.167522
\(358\) 2.85347 0.150810
\(359\) 15.5631 0.821390 0.410695 0.911773i \(-0.365286\pi\)
0.410695 + 0.911773i \(0.365286\pi\)
\(360\) 0.0548924 0.00289308
\(361\) −18.9839 −0.999150
\(362\) 6.40380 0.336576
\(363\) 17.4461 0.915682
\(364\) 0.355262 0.0186208
\(365\) −2.82848 −0.148049
\(366\) 3.52259 0.184129
\(367\) −6.14723 −0.320883 −0.160441 0.987045i \(-0.551292\pi\)
−0.160441 + 0.987045i \(0.551292\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 0.400616 0.0208552
\(370\) 3.77194 0.196094
\(371\) 0.766751 0.0398077
\(372\) 12.3445 0.640034
\(373\) 11.8605 0.614115 0.307057 0.951691i \(-0.400656\pi\)
0.307057 + 0.951691i \(0.400656\pi\)
\(374\) 7.35114 0.380119
\(375\) 19.3595 0.999722
\(376\) −11.5529 −0.595794
\(377\) 4.38643 0.225913
\(378\) 1.27082 0.0653640
\(379\) −34.6762 −1.78120 −0.890600 0.454788i \(-0.849715\pi\)
−0.890600 + 0.454788i \(0.849715\pi\)
\(380\) 0.173357 0.00889302
\(381\) −26.5969 −1.36260
\(382\) −1.54073 −0.0788306
\(383\) 34.3641 1.75592 0.877962 0.478730i \(-0.158903\pi\)
0.877962 + 0.478730i \(0.158903\pi\)
\(384\) −1.74363 −0.0889791
\(385\) 0.334979 0.0170721
\(386\) −10.3850 −0.528583
\(387\) 0.329429 0.0167458
\(388\) 11.2033 0.568762
\(389\) 16.8196 0.852790 0.426395 0.904537i \(-0.359783\pi\)
0.426395 + 0.904537i \(0.359783\pi\)
\(390\) −3.43160 −0.173766
\(391\) −7.37189 −0.372813
\(392\) −6.93936 −0.350491
\(393\) 1.74363 0.0879544
\(394\) 23.0211 1.15979
\(395\) −14.9545 −0.752442
\(396\) 0.0401255 0.00201638
\(397\) 14.1294 0.709134 0.354567 0.935031i \(-0.384628\pi\)
0.354567 + 0.935031i \(0.384628\pi\)
\(398\) −13.8274 −0.693103
\(399\) −0.0545635 −0.00273159
\(400\) −3.13905 −0.156953
\(401\) −5.45756 −0.272538 −0.136269 0.990672i \(-0.543511\pi\)
−0.136269 + 0.990672i \(0.543511\pi\)
\(402\) 24.6852 1.23119
\(403\) −10.2140 −0.508795
\(404\) 8.93549 0.444557
\(405\) −12.4400 −0.618147
\(406\) 0.748705 0.0371576
\(407\) 2.75724 0.136671
\(408\) −12.8538 −0.636360
\(409\) 39.2662 1.94159 0.970794 0.239914i \(-0.0771192\pi\)
0.970794 + 0.239914i \(0.0771192\pi\)
\(410\) 13.5816 0.670747
\(411\) 10.8115 0.533291
\(412\) −9.02603 −0.444680
\(413\) 2.58096 0.127001
\(414\) −0.0402388 −0.00197763
\(415\) −0.164814 −0.00809040
\(416\) 1.44270 0.0707340
\(417\) −17.7082 −0.867176
\(418\) 0.126721 0.00619814
\(419\) 1.83398 0.0895958 0.0447979 0.998996i \(-0.485736\pi\)
0.0447979 + 0.998996i \(0.485736\pi\)
\(420\) −0.585727 −0.0285806
\(421\) −1.43510 −0.0699424 −0.0349712 0.999388i \(-0.511134\pi\)
−0.0349712 + 0.999388i \(0.511134\pi\)
\(422\) 0.717238 0.0349146
\(423\) −0.464874 −0.0226029
\(424\) 3.11372 0.151216
\(425\) −23.1407 −1.12249
\(426\) −16.9649 −0.821953
\(427\) −0.497488 −0.0240751
\(428\) 13.9188 0.672793
\(429\) −2.50845 −0.121109
\(430\) 11.1682 0.538581
\(431\) −8.27409 −0.398549 −0.199275 0.979944i \(-0.563859\pi\)
−0.199275 + 0.979944i \(0.563859\pi\)
\(432\) 5.16072 0.248295
\(433\) 18.7308 0.900146 0.450073 0.892992i \(-0.351398\pi\)
0.450073 + 0.892992i \(0.351398\pi\)
\(434\) −1.74339 −0.0836855
\(435\) −7.23198 −0.346747
\(436\) 10.4582 0.500859
\(437\) −0.127079 −0.00607901
\(438\) 3.61526 0.172744
\(439\) 7.31923 0.349328 0.174664 0.984628i \(-0.444116\pi\)
0.174664 + 0.984628i \(0.444116\pi\)
\(440\) 1.36033 0.0648510
\(441\) −0.279231 −0.0132967
\(442\) 10.6354 0.505875
\(443\) −9.31350 −0.442498 −0.221249 0.975217i \(-0.571013\pi\)
−0.221249 + 0.975217i \(0.571013\pi\)
\(444\) −4.82116 −0.228802
\(445\) 0.296263 0.0140442
\(446\) 28.0974 1.33045
\(447\) 17.0108 0.804581
\(448\) 0.246249 0.0116342
\(449\) 11.8291 0.558252 0.279126 0.960254i \(-0.409955\pi\)
0.279126 + 0.960254i \(0.409955\pi\)
\(450\) −0.126312 −0.00595439
\(451\) 9.92794 0.467489
\(452\) 19.5060 0.917484
\(453\) 5.49465 0.258161
\(454\) −10.8000 −0.506868
\(455\) 0.484637 0.0227201
\(456\) −0.221579 −0.0103764
\(457\) −7.75579 −0.362801 −0.181400 0.983409i \(-0.558063\pi\)
−0.181400 + 0.983409i \(0.558063\pi\)
\(458\) −3.86486 −0.180593
\(459\) 38.0443 1.77576
\(460\) −1.36417 −0.0636046
\(461\) −14.4336 −0.672242 −0.336121 0.941819i \(-0.609115\pi\)
−0.336121 + 0.941819i \(0.609115\pi\)
\(462\) −0.428158 −0.0199197
\(463\) −3.16041 −0.146877 −0.0734383 0.997300i \(-0.523397\pi\)
−0.0734383 + 0.997300i \(0.523397\pi\)
\(464\) 3.04044 0.141149
\(465\) 16.8400 0.780936
\(466\) 9.20161 0.426256
\(467\) −24.0200 −1.11151 −0.555757 0.831345i \(-0.687572\pi\)
−0.555757 + 0.831345i \(0.687572\pi\)
\(468\) 0.0580524 0.00268347
\(469\) −3.48624 −0.160980
\(470\) −15.7600 −0.726956
\(471\) −17.4381 −0.803504
\(472\) 10.4811 0.482432
\(473\) 8.16382 0.375373
\(474\) 19.1143 0.877949
\(475\) −0.398908 −0.0183031
\(476\) 1.81532 0.0832051
\(477\) 0.125293 0.00573675
\(478\) −7.41788 −0.339286
\(479\) 9.17663 0.419291 0.209646 0.977777i \(-0.432769\pi\)
0.209646 + 0.977777i \(0.432769\pi\)
\(480\) −2.37860 −0.108568
\(481\) 3.98908 0.181887
\(482\) 14.9370 0.680362
\(483\) 0.429367 0.0195369
\(484\) −10.0056 −0.454801
\(485\) 15.2832 0.693973
\(486\) 0.418146 0.0189675
\(487\) 20.1543 0.913279 0.456640 0.889652i \(-0.349053\pi\)
0.456640 + 0.889652i \(0.349053\pi\)
\(488\) −2.02027 −0.0914531
\(489\) 4.15526 0.187907
\(490\) −9.46644 −0.427650
\(491\) 35.6510 1.60891 0.804454 0.594015i \(-0.202458\pi\)
0.804454 + 0.594015i \(0.202458\pi\)
\(492\) −17.3595 −0.782627
\(493\) 22.4138 1.00947
\(494\) 0.183337 0.00824870
\(495\) 0.0547379 0.00246029
\(496\) −7.07979 −0.317892
\(497\) 2.39592 0.107472
\(498\) 0.210659 0.00943987
\(499\) −28.9004 −1.29376 −0.646879 0.762593i \(-0.723926\pi\)
−0.646879 + 0.762593i \(0.723926\pi\)
\(500\) −11.1030 −0.496542
\(501\) −34.6884 −1.54976
\(502\) 9.89554 0.441659
\(503\) 19.1967 0.855941 0.427970 0.903793i \(-0.359229\pi\)
0.427970 + 0.903793i \(0.359229\pi\)
\(504\) 0.00990876 0.000441371 0
\(505\) 12.1895 0.542426
\(506\) −0.997185 −0.0443303
\(507\) 19.0380 0.845508
\(508\) 15.2538 0.676776
\(509\) 4.21290 0.186733 0.0933667 0.995632i \(-0.470237\pi\)
0.0933667 + 0.995632i \(0.470237\pi\)
\(510\) −17.5348 −0.776453
\(511\) −0.510575 −0.0225865
\(512\) 1.00000 0.0441942
\(513\) 0.655820 0.0289551
\(514\) 9.73200 0.429260
\(515\) −12.3130 −0.542576
\(516\) −14.2748 −0.628415
\(517\) −11.5204 −0.506665
\(518\) 0.680883 0.0299163
\(519\) 20.7684 0.911630
\(520\) 1.96808 0.0863059
\(521\) −33.7554 −1.47885 −0.739426 0.673238i \(-0.764903\pi\)
−0.739426 + 0.673238i \(0.764903\pi\)
\(522\) 0.122344 0.00535483
\(523\) −32.4611 −1.41943 −0.709713 0.704491i \(-0.751175\pi\)
−0.709713 + 0.704491i \(0.751175\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 1.34780 0.0588229
\(526\) −27.9012 −1.21655
\(527\) −52.1915 −2.27350
\(528\) −1.73872 −0.0756681
\(529\) 1.00000 0.0434783
\(530\) 4.24764 0.184506
\(531\) 0.421747 0.0183023
\(532\) 0.0312931 0.00135673
\(533\) 14.3634 0.622150
\(534\) −0.378672 −0.0163868
\(535\) 18.9876 0.820906
\(536\) −14.1574 −0.611506
\(537\) −4.97539 −0.214704
\(538\) 29.5144 1.27246
\(539\) −6.91983 −0.298058
\(540\) 7.04008 0.302957
\(541\) 12.8940 0.554356 0.277178 0.960819i \(-0.410601\pi\)
0.277178 + 0.960819i \(0.410601\pi\)
\(542\) 5.94548 0.255380
\(543\) −11.1658 −0.479172
\(544\) 7.37189 0.316067
\(545\) 14.2668 0.611121
\(546\) −0.619446 −0.0265098
\(547\) 3.71031 0.158641 0.0793206 0.996849i \(-0.474725\pi\)
0.0793206 + 0.996849i \(0.474725\pi\)
\(548\) −6.20057 −0.264875
\(549\) −0.0812930 −0.00346950
\(550\) −3.13022 −0.133473
\(551\) 0.386376 0.0164602
\(552\) 1.74363 0.0742137
\(553\) −2.69947 −0.114793
\(554\) 4.76161 0.202301
\(555\) −6.57687 −0.279173
\(556\) 10.1560 0.430709
\(557\) 6.88278 0.291633 0.145816 0.989312i \(-0.453419\pi\)
0.145816 + 0.989312i \(0.453419\pi\)
\(558\) −0.284882 −0.0120600
\(559\) 11.8112 0.499559
\(560\) 0.335924 0.0141954
\(561\) −12.8177 −0.541162
\(562\) −2.55357 −0.107716
\(563\) −31.3575 −1.32156 −0.660780 0.750579i \(-0.729775\pi\)
−0.660780 + 0.750579i \(0.729775\pi\)
\(564\) 20.1439 0.848212
\(565\) 26.6094 1.11947
\(566\) 19.0982 0.802759
\(567\) −2.24557 −0.0943050
\(568\) 9.72966 0.408248
\(569\) 0.412572 0.0172959 0.00864796 0.999963i \(-0.497247\pi\)
0.00864796 + 0.999963i \(0.497247\pi\)
\(570\) −0.302270 −0.0126607
\(571\) −16.4158 −0.686981 −0.343491 0.939156i \(-0.611609\pi\)
−0.343491 + 0.939156i \(0.611609\pi\)
\(572\) 1.43864 0.0601524
\(573\) 2.68646 0.112228
\(574\) 2.45165 0.102330
\(575\) 3.13905 0.130907
\(576\) 0.0402388 0.00167662
\(577\) 31.4910 1.31099 0.655493 0.755201i \(-0.272461\pi\)
0.655493 + 0.755201i \(0.272461\pi\)
\(578\) 37.3448 1.55334
\(579\) 18.1076 0.752525
\(580\) 4.14766 0.172222
\(581\) −0.0297510 −0.00123428
\(582\) −19.5344 −0.809727
\(583\) 3.10496 0.128594
\(584\) −2.07341 −0.0857983
\(585\) 0.0791931 0.00327423
\(586\) 25.3806 1.04846
\(587\) −12.8077 −0.528630 −0.264315 0.964436i \(-0.585146\pi\)
−0.264315 + 0.964436i \(0.585146\pi\)
\(588\) 12.0997 0.498982
\(589\) −0.899694 −0.0370712
\(590\) 14.2980 0.588638
\(591\) −40.1403 −1.65115
\(592\) 2.76502 0.113642
\(593\) −45.6946 −1.87645 −0.938226 0.346024i \(-0.887531\pi\)
−0.938226 + 0.346024i \(0.887531\pi\)
\(594\) 5.14620 0.211151
\(595\) 2.47640 0.101522
\(596\) −9.75595 −0.399619
\(597\) 24.1098 0.986748
\(598\) −1.44270 −0.0589963
\(599\) −44.7825 −1.82976 −0.914882 0.403722i \(-0.867716\pi\)
−0.914882 + 0.403722i \(0.867716\pi\)
\(600\) 5.47334 0.223448
\(601\) −24.2363 −0.988619 −0.494309 0.869286i \(-0.664579\pi\)
−0.494309 + 0.869286i \(0.664579\pi\)
\(602\) 2.01601 0.0821663
\(603\) −0.569676 −0.0231990
\(604\) −3.15127 −0.128224
\(605\) −13.6493 −0.554924
\(606\) −15.5802 −0.632901
\(607\) 6.32673 0.256794 0.128397 0.991723i \(-0.459017\pi\)
0.128397 + 0.991723i \(0.459017\pi\)
\(608\) 0.127079 0.00515374
\(609\) −1.30546 −0.0529000
\(610\) −2.75598 −0.111586
\(611\) −16.6673 −0.674286
\(612\) 0.296636 0.0119908
\(613\) 4.42348 0.178663 0.0893314 0.996002i \(-0.471527\pi\)
0.0893314 + 0.996002i \(0.471527\pi\)
\(614\) −28.7690 −1.16102
\(615\) −23.6812 −0.954920
\(616\) 0.245556 0.00989373
\(617\) 28.2911 1.13896 0.569478 0.822007i \(-0.307145\pi\)
0.569478 + 0.822007i \(0.307145\pi\)
\(618\) 15.7380 0.633076
\(619\) −5.85911 −0.235497 −0.117749 0.993043i \(-0.537568\pi\)
−0.117749 + 0.993043i \(0.537568\pi\)
\(620\) −9.65802 −0.387875
\(621\) −5.16072 −0.207093
\(622\) 7.33784 0.294221
\(623\) 0.0534791 0.00214260
\(624\) −2.51553 −0.100702
\(625\) 0.548889 0.0219556
\(626\) −23.4443 −0.937024
\(627\) −0.220955 −0.00882409
\(628\) 10.0010 0.399084
\(629\) 20.3834 0.812740
\(630\) 0.0135172 0.000538538 0
\(631\) 7.60584 0.302784 0.151392 0.988474i \(-0.451624\pi\)
0.151392 + 0.988474i \(0.451624\pi\)
\(632\) −10.9624 −0.436060
\(633\) −1.25060 −0.0497067
\(634\) 7.85505 0.311964
\(635\) 20.8087 0.825767
\(636\) −5.42918 −0.215281
\(637\) −10.0114 −0.396666
\(638\) 3.03188 0.120033
\(639\) 0.391510 0.0154879
\(640\) 1.36417 0.0539234
\(641\) −11.8032 −0.466199 −0.233099 0.972453i \(-0.574887\pi\)
−0.233099 + 0.972453i \(0.574887\pi\)
\(642\) −24.2693 −0.957833
\(643\) −8.95080 −0.352985 −0.176492 0.984302i \(-0.556475\pi\)
−0.176492 + 0.984302i \(0.556475\pi\)
\(644\) −0.246249 −0.00970357
\(645\) −19.4733 −0.766759
\(646\) 0.936813 0.0368584
\(647\) −35.2340 −1.38519 −0.692596 0.721325i \(-0.743533\pi\)
−0.692596 + 0.721325i \(0.743533\pi\)
\(648\) −9.11910 −0.358232
\(649\) 10.4516 0.410262
\(650\) −4.52870 −0.177630
\(651\) 3.03983 0.119140
\(652\) −2.38311 −0.0933299
\(653\) −33.1240 −1.29624 −0.648120 0.761538i \(-0.724445\pi\)
−0.648120 + 0.761538i \(0.724445\pi\)
\(654\) −18.2353 −0.713055
\(655\) −1.36417 −0.0533024
\(656\) 9.95597 0.388715
\(657\) −0.0834315 −0.00325497
\(658\) −2.84488 −0.110905
\(659\) −0.0712961 −0.00277730 −0.00138865 0.999999i \(-0.500442\pi\)
−0.00138865 + 0.999999i \(0.500442\pi\)
\(660\) −2.37190 −0.0923262
\(661\) −32.6138 −1.26853 −0.634265 0.773116i \(-0.718697\pi\)
−0.634265 + 0.773116i \(0.718697\pi\)
\(662\) 5.10693 0.198486
\(663\) −18.5442 −0.720197
\(664\) −0.120817 −0.00468860
\(665\) 0.0426890 0.00165541
\(666\) 0.111261 0.00431128
\(667\) −3.04044 −0.117726
\(668\) 19.8944 0.769736
\(669\) −48.9915 −1.89412
\(670\) −19.3130 −0.746127
\(671\) −2.01458 −0.0777720
\(672\) −0.429367 −0.0165632
\(673\) 18.4365 0.710675 0.355338 0.934738i \(-0.384366\pi\)
0.355338 + 0.934738i \(0.384366\pi\)
\(674\) −5.56800 −0.214471
\(675\) −16.1998 −0.623529
\(676\) −10.9186 −0.419947
\(677\) 17.2492 0.662939 0.331470 0.943466i \(-0.392456\pi\)
0.331470 + 0.943466i \(0.392456\pi\)
\(678\) −34.0112 −1.30619
\(679\) 2.75880 0.105873
\(680\) 10.0565 0.385649
\(681\) 18.8311 0.721611
\(682\) −7.05987 −0.270336
\(683\) 21.8802 0.837224 0.418612 0.908165i \(-0.362517\pi\)
0.418612 + 0.908165i \(0.362517\pi\)
\(684\) 0.00511351 0.000195520 0
\(685\) −8.45861 −0.323187
\(686\) −3.43255 −0.131055
\(687\) 6.73887 0.257104
\(688\) 8.18686 0.312121
\(689\) 4.49216 0.171138
\(690\) 2.37860 0.0905517
\(691\) −21.4768 −0.817017 −0.408509 0.912754i \(-0.633951\pi\)
−0.408509 + 0.912754i \(0.633951\pi\)
\(692\) −11.9110 −0.452788
\(693\) 0.00988087 0.000375343 0
\(694\) 23.3865 0.887740
\(695\) 13.8544 0.525529
\(696\) −5.30140 −0.200949
\(697\) 73.3943 2.78001
\(698\) −11.2297 −0.425051
\(699\) −16.0442 −0.606847
\(700\) −0.772988 −0.0292162
\(701\) −36.7402 −1.38766 −0.693830 0.720139i \(-0.744078\pi\)
−0.693830 + 0.720139i \(0.744078\pi\)
\(702\) 7.44536 0.281007
\(703\) 0.351376 0.0132524
\(704\) 0.997185 0.0375828
\(705\) 27.4796 1.03494
\(706\) −18.4868 −0.695759
\(707\) 2.20036 0.0827529
\(708\) −18.2752 −0.686822
\(709\) 13.3657 0.501961 0.250980 0.967992i \(-0.419247\pi\)
0.250980 + 0.967992i \(0.419247\pi\)
\(710\) 13.2729 0.498122
\(711\) −0.441112 −0.0165430
\(712\) 0.217175 0.00813898
\(713\) 7.07979 0.265140
\(714\) −3.16524 −0.118456
\(715\) 1.96254 0.0733948
\(716\) 2.85347 0.106639
\(717\) 12.9340 0.483030
\(718\) 15.5631 0.580810
\(719\) 0.603503 0.0225069 0.0112534 0.999937i \(-0.496418\pi\)
0.0112534 + 0.999937i \(0.496418\pi\)
\(720\) 0.0548924 0.00204572
\(721\) −2.22265 −0.0827758
\(722\) −18.9839 −0.706506
\(723\) −26.0446 −0.968609
\(724\) 6.40380 0.237995
\(725\) −9.54409 −0.354459
\(726\) 17.4461 0.647485
\(727\) 28.8113 1.06855 0.534276 0.845310i \(-0.320584\pi\)
0.534276 + 0.845310i \(0.320584\pi\)
\(728\) 0.355262 0.0131669
\(729\) 26.6282 0.986230
\(730\) −2.82848 −0.104687
\(731\) 60.3527 2.23222
\(732\) 3.52259 0.130199
\(733\) 45.3067 1.67344 0.836720 0.547631i \(-0.184470\pi\)
0.836720 + 0.547631i \(0.184470\pi\)
\(734\) −6.14723 −0.226898
\(735\) 16.5060 0.608831
\(736\) −1.00000 −0.0368605
\(737\) −14.1175 −0.520026
\(738\) 0.400616 0.0147469
\(739\) −44.2885 −1.62918 −0.814589 0.580039i \(-0.803037\pi\)
−0.814589 + 0.580039i \(0.803037\pi\)
\(740\) 3.77194 0.138659
\(741\) −0.319671 −0.0117434
\(742\) 0.766751 0.0281483
\(743\) −19.8217 −0.727189 −0.363594 0.931557i \(-0.618451\pi\)
−0.363594 + 0.931557i \(0.618451\pi\)
\(744\) 12.3445 0.452572
\(745\) −13.3087 −0.487595
\(746\) 11.8605 0.434245
\(747\) −0.00486152 −0.000177874 0
\(748\) 7.35114 0.268784
\(749\) 3.42750 0.125238
\(750\) 19.3595 0.706910
\(751\) 21.3947 0.780703 0.390352 0.920666i \(-0.372353\pi\)
0.390352 + 0.920666i \(0.372353\pi\)
\(752\) −11.5529 −0.421290
\(753\) −17.2541 −0.628776
\(754\) 4.38643 0.159744
\(755\) −4.29886 −0.156452
\(756\) 1.27082 0.0462194
\(757\) 37.7286 1.37127 0.685635 0.727945i \(-0.259524\pi\)
0.685635 + 0.727945i \(0.259524\pi\)
\(758\) −34.6762 −1.25950
\(759\) 1.73872 0.0631116
\(760\) 0.173357 0.00628832
\(761\) 10.0487 0.364266 0.182133 0.983274i \(-0.441700\pi\)
0.182133 + 0.983274i \(0.441700\pi\)
\(762\) −26.5969 −0.963504
\(763\) 2.57533 0.0932331
\(764\) −1.54073 −0.0557416
\(765\) 0.404661 0.0146305
\(766\) 34.3641 1.24163
\(767\) 15.1211 0.545990
\(768\) −1.74363 −0.0629178
\(769\) −11.8606 −0.427705 −0.213852 0.976866i \(-0.568601\pi\)
−0.213852 + 0.976866i \(0.568601\pi\)
\(770\) 0.334979 0.0120718
\(771\) −16.9690 −0.611123
\(772\) −10.3850 −0.373764
\(773\) −38.6458 −1.38999 −0.694996 0.719013i \(-0.744594\pi\)
−0.694996 + 0.719013i \(0.744594\pi\)
\(774\) 0.329429 0.0118411
\(775\) 22.2238 0.798304
\(776\) 11.2033 0.402175
\(777\) −1.18721 −0.0425908
\(778\) 16.8196 0.603013
\(779\) 1.26519 0.0453303
\(780\) −3.43160 −0.122871
\(781\) 9.70228 0.347175
\(782\) −7.37189 −0.263618
\(783\) 15.6909 0.560746
\(784\) −6.93936 −0.247834
\(785\) 13.6431 0.486942
\(786\) 1.74363 0.0621932
\(787\) −27.7596 −0.989524 −0.494762 0.869028i \(-0.664745\pi\)
−0.494762 + 0.869028i \(0.664745\pi\)
\(788\) 23.0211 0.820094
\(789\) 48.6493 1.73196
\(790\) −14.9545 −0.532057
\(791\) 4.80332 0.170787
\(792\) 0.0401255 0.00142580
\(793\) −2.91463 −0.103502
\(794\) 14.1294 0.501433
\(795\) −7.40630 −0.262674
\(796\) −13.8274 −0.490098
\(797\) 0.721464 0.0255556 0.0127778 0.999918i \(-0.495933\pi\)
0.0127778 + 0.999918i \(0.495933\pi\)
\(798\) −0.0545635 −0.00193153
\(799\) −85.1665 −3.01298
\(800\) −3.13905 −0.110982
\(801\) 0.00873886 0.000308772 0
\(802\) −5.45756 −0.192713
\(803\) −2.06757 −0.0729631
\(804\) 24.6852 0.870580
\(805\) −0.335924 −0.0118398
\(806\) −10.2140 −0.359773
\(807\) −51.4622 −1.81155
\(808\) 8.93549 0.314350
\(809\) 38.2714 1.34555 0.672775 0.739847i \(-0.265102\pi\)
0.672775 + 0.739847i \(0.265102\pi\)
\(810\) −12.4400 −0.437096
\(811\) −35.8424 −1.25860 −0.629298 0.777164i \(-0.716658\pi\)
−0.629298 + 0.777164i \(0.716658\pi\)
\(812\) 0.748705 0.0262744
\(813\) −10.3667 −0.363576
\(814\) 2.75724 0.0966411
\(815\) −3.25096 −0.113876
\(816\) −12.8538 −0.449974
\(817\) 1.04038 0.0363982
\(818\) 39.2662 1.37291
\(819\) 0.0142953 0.000499519 0
\(820\) 13.5816 0.474290
\(821\) 13.1870 0.460230 0.230115 0.973163i \(-0.426090\pi\)
0.230115 + 0.973163i \(0.426090\pi\)
\(822\) 10.8115 0.377094
\(823\) 11.6916 0.407542 0.203771 0.979019i \(-0.434680\pi\)
0.203771 + 0.979019i \(0.434680\pi\)
\(824\) −9.02603 −0.314437
\(825\) 5.45793 0.190021
\(826\) 2.58096 0.0898031
\(827\) 35.0321 1.21819 0.609093 0.793099i \(-0.291533\pi\)
0.609093 + 0.793099i \(0.291533\pi\)
\(828\) −0.0402388 −0.00139839
\(829\) 35.4622 1.23165 0.615827 0.787882i \(-0.288822\pi\)
0.615827 + 0.787882i \(0.288822\pi\)
\(830\) −0.164814 −0.00572078
\(831\) −8.30247 −0.288010
\(832\) 1.44270 0.0500165
\(833\) −51.1562 −1.77246
\(834\) −17.7082 −0.613186
\(835\) 27.1392 0.939191
\(836\) 0.126721 0.00438275
\(837\) −36.5369 −1.26290
\(838\) 1.83398 0.0633538
\(839\) 12.1039 0.417872 0.208936 0.977929i \(-0.433000\pi\)
0.208936 + 0.977929i \(0.433000\pi\)
\(840\) −0.585727 −0.0202095
\(841\) −19.7557 −0.681232
\(842\) −1.43510 −0.0494568
\(843\) 4.45248 0.153351
\(844\) 0.717238 0.0246883
\(845\) −14.8948 −0.512397
\(846\) −0.464874 −0.0159827
\(847\) −2.46387 −0.0846597
\(848\) 3.11372 0.106926
\(849\) −33.3002 −1.14286
\(850\) −23.1407 −0.793721
\(851\) −2.76502 −0.0947836
\(852\) −16.9649 −0.581208
\(853\) −58.0382 −1.98719 −0.993595 0.112998i \(-0.963955\pi\)
−0.993595 + 0.112998i \(0.963955\pi\)
\(854\) −0.497488 −0.0170237
\(855\) 0.00697567 0.000238563 0
\(856\) 13.9188 0.475736
\(857\) −16.2303 −0.554415 −0.277207 0.960810i \(-0.589409\pi\)
−0.277207 + 0.960810i \(0.589409\pi\)
\(858\) −2.50845 −0.0856369
\(859\) −22.6080 −0.771375 −0.385688 0.922629i \(-0.626036\pi\)
−0.385688 + 0.922629i \(0.626036\pi\)
\(860\) 11.1682 0.380834
\(861\) −4.27476 −0.145683
\(862\) −8.27409 −0.281817
\(863\) −21.6136 −0.735735 −0.367868 0.929878i \(-0.619912\pi\)
−0.367868 + 0.929878i \(0.619912\pi\)
\(864\) 5.16072 0.175571
\(865\) −16.2486 −0.552468
\(866\) 18.7308 0.636499
\(867\) −65.1154 −2.21144
\(868\) −1.74339 −0.0591746
\(869\) −10.9315 −0.370826
\(870\) −7.23198 −0.245187
\(871\) −20.4248 −0.692068
\(872\) 10.4582 0.354160
\(873\) 0.450808 0.0152575
\(874\) −0.127079 −0.00429851
\(875\) −2.73411 −0.0924297
\(876\) 3.61526 0.122148
\(877\) −33.5071 −1.13145 −0.565727 0.824592i \(-0.691404\pi\)
−0.565727 + 0.824592i \(0.691404\pi\)
\(878\) 7.31923 0.247012
\(879\) −44.2544 −1.49266
\(880\) 1.36033 0.0458566
\(881\) 23.2254 0.782483 0.391242 0.920288i \(-0.372046\pi\)
0.391242 + 0.920288i \(0.372046\pi\)
\(882\) −0.279231 −0.00940221
\(883\) −21.6898 −0.729918 −0.364959 0.931024i \(-0.618917\pi\)
−0.364959 + 0.931024i \(0.618917\pi\)
\(884\) 10.6354 0.357707
\(885\) −24.9304 −0.838025
\(886\) −9.31350 −0.312893
\(887\) 22.9021 0.768976 0.384488 0.923130i \(-0.374378\pi\)
0.384488 + 0.923130i \(0.374378\pi\)
\(888\) −4.82116 −0.161788
\(889\) 3.75622 0.125980
\(890\) 0.296263 0.00993075
\(891\) −9.09343 −0.304641
\(892\) 28.0974 0.940771
\(893\) −1.46813 −0.0491290
\(894\) 17.0108 0.568925
\(895\) 3.89260 0.130115
\(896\) 0.246249 0.00822660
\(897\) 2.51553 0.0839910
\(898\) 11.8291 0.394744
\(899\) −21.5257 −0.717922
\(900\) −0.126312 −0.00421039
\(901\) 22.9540 0.764710
\(902\) 9.92794 0.330564
\(903\) −3.51517 −0.116977
\(904\) 19.5060 0.648759
\(905\) 8.73584 0.290389
\(906\) 5.49465 0.182548
\(907\) −23.5007 −0.780329 −0.390165 0.920745i \(-0.627582\pi\)
−0.390165 + 0.920745i \(0.627582\pi\)
\(908\) −10.8000 −0.358410
\(909\) 0.359553 0.0119256
\(910\) 0.484637 0.0160656
\(911\) −33.9597 −1.12514 −0.562568 0.826751i \(-0.690187\pi\)
−0.562568 + 0.826751i \(0.690187\pi\)
\(912\) −0.221579 −0.00733720
\(913\) −0.120477 −0.00398719
\(914\) −7.75579 −0.256539
\(915\) 4.80540 0.158862
\(916\) −3.86486 −0.127698
\(917\) −0.246249 −0.00813186
\(918\) 38.0443 1.25565
\(919\) −40.0329 −1.32056 −0.660282 0.751018i \(-0.729563\pi\)
−0.660282 + 0.751018i \(0.729563\pi\)
\(920\) −1.36417 −0.0449752
\(921\) 50.1625 1.65291
\(922\) −14.4336 −0.475347
\(923\) 14.0369 0.462032
\(924\) −0.428158 −0.0140854
\(925\) −8.67953 −0.285381
\(926\) −3.16041 −0.103857
\(927\) −0.363196 −0.0119289
\(928\) 3.04044 0.0998073
\(929\) −0.704161 −0.0231028 −0.0115514 0.999933i \(-0.503677\pi\)
−0.0115514 + 0.999933i \(0.503677\pi\)
\(930\) 16.8400 0.552205
\(931\) −0.881847 −0.0289014
\(932\) 9.20161 0.301409
\(933\) −12.7945 −0.418872
\(934\) −24.0200 −0.785960
\(935\) 10.0282 0.327957
\(936\) 0.0580524 0.00189750
\(937\) −30.7695 −1.00520 −0.502598 0.864520i \(-0.667622\pi\)
−0.502598 + 0.864520i \(0.667622\pi\)
\(938\) −3.48624 −0.113830
\(939\) 40.8782 1.33401
\(940\) −15.7600 −0.514036
\(941\) 13.7610 0.448596 0.224298 0.974521i \(-0.427991\pi\)
0.224298 + 0.974521i \(0.427991\pi\)
\(942\) −17.4381 −0.568163
\(943\) −9.95597 −0.324211
\(944\) 10.4811 0.341131
\(945\) 1.73361 0.0563944
\(946\) 8.16382 0.265429
\(947\) 18.9787 0.616725 0.308363 0.951269i \(-0.400219\pi\)
0.308363 + 0.951269i \(0.400219\pi\)
\(948\) 19.1143 0.620803
\(949\) −2.99130 −0.0971018
\(950\) −0.398908 −0.0129423
\(951\) −13.6963 −0.444132
\(952\) 1.81532 0.0588349
\(953\) −42.3132 −1.37066 −0.685329 0.728233i \(-0.740342\pi\)
−0.685329 + 0.728233i \(0.740342\pi\)
\(954\) 0.125293 0.00405649
\(955\) −2.10181 −0.0680130
\(956\) −7.41788 −0.239912
\(957\) −5.28647 −0.170887
\(958\) 9.17663 0.296484
\(959\) −1.52688 −0.0493057
\(960\) −2.37860 −0.0767689
\(961\) 19.1235 0.616887
\(962\) 3.98908 0.128613
\(963\) 0.560078 0.0180482
\(964\) 14.9370 0.481089
\(965\) −14.1669 −0.456048
\(966\) 0.429367 0.0138146
\(967\) 17.6001 0.565980 0.282990 0.959123i \(-0.408674\pi\)
0.282990 + 0.959123i \(0.408674\pi\)
\(968\) −10.0056 −0.321593
\(969\) −1.63345 −0.0524741
\(970\) 15.2832 0.490713
\(971\) −24.1878 −0.776225 −0.388112 0.921612i \(-0.626873\pi\)
−0.388112 + 0.921612i \(0.626873\pi\)
\(972\) 0.418146 0.0134120
\(973\) 2.50090 0.0801751
\(974\) 20.1543 0.645786
\(975\) 7.89636 0.252886
\(976\) −2.02027 −0.0646671
\(977\) −9.61496 −0.307610 −0.153805 0.988101i \(-0.549153\pi\)
−0.153805 + 0.988101i \(0.549153\pi\)
\(978\) 4.15526 0.132871
\(979\) 0.216564 0.00692141
\(980\) −9.46644 −0.302394
\(981\) 0.420827 0.0134360
\(982\) 35.6510 1.13767
\(983\) −51.4645 −1.64146 −0.820731 0.571314i \(-0.806434\pi\)
−0.820731 + 0.571314i \(0.806434\pi\)
\(984\) −17.3595 −0.553401
\(985\) 31.4047 1.00064
\(986\) 22.4138 0.713801
\(987\) 4.96042 0.157892
\(988\) 0.183337 0.00583271
\(989\) −8.18686 −0.260327
\(990\) 0.0547379 0.00173968
\(991\) 29.0849 0.923912 0.461956 0.886903i \(-0.347148\pi\)
0.461956 + 0.886903i \(0.347148\pi\)
\(992\) −7.07979 −0.224784
\(993\) −8.90458 −0.282578
\(994\) 2.39592 0.0759939
\(995\) −18.8628 −0.597992
\(996\) 0.210659 0.00667500
\(997\) −39.4162 −1.24832 −0.624162 0.781295i \(-0.714560\pi\)
−0.624162 + 0.781295i \(0.714560\pi\)
\(998\) −28.9004 −0.914825
\(999\) 14.2695 0.451467
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.k.1.10 35
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.k.1.10 35 1.1 even 1 trivial