Properties

Label 4017.2.a.i.1.18
Level $4017$
Weight $2$
Character 4017.1
Self dual yes
Analytic conductor $32.076$
Analytic rank $1$
Dimension $25$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4017,2,Mod(1,4017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4017.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(1\)
Dimension: \(25\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 4017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.25624 q^{2} -1.00000 q^{3} -0.421872 q^{4} +0.726022 q^{5} -1.25624 q^{6} +0.867951 q^{7} -3.04244 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.25624 q^{2} -1.00000 q^{3} -0.421872 q^{4} +0.726022 q^{5} -1.25624 q^{6} +0.867951 q^{7} -3.04244 q^{8} +1.00000 q^{9} +0.912055 q^{10} +3.59453 q^{11} +0.421872 q^{12} -1.00000 q^{13} +1.09035 q^{14} -0.726022 q^{15} -2.97828 q^{16} -0.939676 q^{17} +1.25624 q^{18} -5.25134 q^{19} -0.306288 q^{20} -0.867951 q^{21} +4.51558 q^{22} +1.49063 q^{23} +3.04244 q^{24} -4.47289 q^{25} -1.25624 q^{26} -1.00000 q^{27} -0.366164 q^{28} +4.96362 q^{29} -0.912055 q^{30} -7.44554 q^{31} +2.34346 q^{32} -3.59453 q^{33} -1.18045 q^{34} +0.630151 q^{35} -0.421872 q^{36} -4.77506 q^{37} -6.59692 q^{38} +1.00000 q^{39} -2.20888 q^{40} -3.53461 q^{41} -1.09035 q^{42} -2.89646 q^{43} -1.51643 q^{44} +0.726022 q^{45} +1.87258 q^{46} +6.80278 q^{47} +2.97828 q^{48} -6.24666 q^{49} -5.61901 q^{50} +0.939676 q^{51} +0.421872 q^{52} +5.61780 q^{53} -1.25624 q^{54} +2.60971 q^{55} -2.64069 q^{56} +5.25134 q^{57} +6.23548 q^{58} +4.52457 q^{59} +0.306288 q^{60} +12.6769 q^{61} -9.35335 q^{62} +0.867951 q^{63} +8.90050 q^{64} -0.726022 q^{65} -4.51558 q^{66} -4.89316 q^{67} +0.396423 q^{68} -1.49063 q^{69} +0.791619 q^{70} +6.74725 q^{71} -3.04244 q^{72} +4.99757 q^{73} -5.99859 q^{74} +4.47289 q^{75} +2.21539 q^{76} +3.11988 q^{77} +1.25624 q^{78} -10.8189 q^{79} -2.16230 q^{80} +1.00000 q^{81} -4.44030 q^{82} -11.5859 q^{83} +0.366164 q^{84} -0.682225 q^{85} -3.63864 q^{86} -4.96362 q^{87} -10.9361 q^{88} -6.84189 q^{89} +0.912055 q^{90} -0.867951 q^{91} -0.628853 q^{92} +7.44554 q^{93} +8.54589 q^{94} -3.81259 q^{95} -2.34346 q^{96} -4.46972 q^{97} -7.84728 q^{98} +3.59453 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.25624 0.888293 0.444146 0.895954i \(-0.353507\pi\)
0.444146 + 0.895954i \(0.353507\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.421872 −0.210936
\(5\) 0.726022 0.324687 0.162343 0.986734i \(-0.448095\pi\)
0.162343 + 0.986734i \(0.448095\pi\)
\(6\) −1.25624 −0.512856
\(7\) 0.867951 0.328055 0.164027 0.986456i \(-0.447551\pi\)
0.164027 + 0.986456i \(0.447551\pi\)
\(8\) −3.04244 −1.07567
\(9\) 1.00000 0.333333
\(10\) 0.912055 0.288417
\(11\) 3.59453 1.08379 0.541896 0.840446i \(-0.317707\pi\)
0.541896 + 0.840446i \(0.317707\pi\)
\(12\) 0.421872 0.121784
\(13\) −1.00000 −0.277350
\(14\) 1.09035 0.291409
\(15\) −0.726022 −0.187458
\(16\) −2.97828 −0.744570
\(17\) −0.939676 −0.227905 −0.113952 0.993486i \(-0.536351\pi\)
−0.113952 + 0.993486i \(0.536351\pi\)
\(18\) 1.25624 0.296098
\(19\) −5.25134 −1.20474 −0.602370 0.798217i \(-0.705777\pi\)
−0.602370 + 0.798217i \(0.705777\pi\)
\(20\) −0.306288 −0.0684881
\(21\) −0.867951 −0.189402
\(22\) 4.51558 0.962724
\(23\) 1.49063 0.310817 0.155408 0.987850i \(-0.450331\pi\)
0.155408 + 0.987850i \(0.450331\pi\)
\(24\) 3.04244 0.621036
\(25\) −4.47289 −0.894578
\(26\) −1.25624 −0.246368
\(27\) −1.00000 −0.192450
\(28\) −0.366164 −0.0691985
\(29\) 4.96362 0.921722 0.460861 0.887472i \(-0.347541\pi\)
0.460861 + 0.887472i \(0.347541\pi\)
\(30\) −0.912055 −0.166518
\(31\) −7.44554 −1.33726 −0.668629 0.743596i \(-0.733119\pi\)
−0.668629 + 0.743596i \(0.733119\pi\)
\(32\) 2.34346 0.414269
\(33\) −3.59453 −0.625727
\(34\) −1.18045 −0.202446
\(35\) 0.630151 0.106515
\(36\) −0.421872 −0.0703120
\(37\) −4.77506 −0.785014 −0.392507 0.919749i \(-0.628392\pi\)
−0.392507 + 0.919749i \(0.628392\pi\)
\(38\) −6.59692 −1.07016
\(39\) 1.00000 0.160128
\(40\) −2.20888 −0.349254
\(41\) −3.53461 −0.552013 −0.276006 0.961156i \(-0.589011\pi\)
−0.276006 + 0.961156i \(0.589011\pi\)
\(42\) −1.09035 −0.168245
\(43\) −2.89646 −0.441706 −0.220853 0.975307i \(-0.570884\pi\)
−0.220853 + 0.975307i \(0.570884\pi\)
\(44\) −1.51643 −0.228611
\(45\) 0.726022 0.108229
\(46\) 1.87258 0.276096
\(47\) 6.80278 0.992287 0.496144 0.868240i \(-0.334749\pi\)
0.496144 + 0.868240i \(0.334749\pi\)
\(48\) 2.97828 0.429878
\(49\) −6.24666 −0.892380
\(50\) −5.61901 −0.794648
\(51\) 0.939676 0.131581
\(52\) 0.421872 0.0585031
\(53\) 5.61780 0.771664 0.385832 0.922569i \(-0.373914\pi\)
0.385832 + 0.922569i \(0.373914\pi\)
\(54\) −1.25624 −0.170952
\(55\) 2.60971 0.351893
\(56\) −2.64069 −0.352877
\(57\) 5.25134 0.695557
\(58\) 6.23548 0.818759
\(59\) 4.52457 0.589049 0.294524 0.955644i \(-0.404839\pi\)
0.294524 + 0.955644i \(0.404839\pi\)
\(60\) 0.306288 0.0395416
\(61\) 12.6769 1.62311 0.811556 0.584275i \(-0.198621\pi\)
0.811556 + 0.584275i \(0.198621\pi\)
\(62\) −9.35335 −1.18788
\(63\) 0.867951 0.109352
\(64\) 8.90050 1.11256
\(65\) −0.726022 −0.0900519
\(66\) −4.51558 −0.555829
\(67\) −4.89316 −0.597795 −0.298897 0.954285i \(-0.596619\pi\)
−0.298897 + 0.954285i \(0.596619\pi\)
\(68\) 0.396423 0.0480733
\(69\) −1.49063 −0.179450
\(70\) 0.791619 0.0946165
\(71\) 6.74725 0.800751 0.400375 0.916351i \(-0.368880\pi\)
0.400375 + 0.916351i \(0.368880\pi\)
\(72\) −3.04244 −0.358555
\(73\) 4.99757 0.584921 0.292461 0.956278i \(-0.405526\pi\)
0.292461 + 0.956278i \(0.405526\pi\)
\(74\) −5.99859 −0.697323
\(75\) 4.47289 0.516485
\(76\) 2.21539 0.254123
\(77\) 3.11988 0.355543
\(78\) 1.25624 0.142241
\(79\) −10.8189 −1.21722 −0.608609 0.793470i \(-0.708272\pi\)
−0.608609 + 0.793470i \(0.708272\pi\)
\(80\) −2.16230 −0.241752
\(81\) 1.00000 0.111111
\(82\) −4.44030 −0.490349
\(83\) −11.5859 −1.27171 −0.635857 0.771807i \(-0.719353\pi\)
−0.635857 + 0.771807i \(0.719353\pi\)
\(84\) 0.366164 0.0399518
\(85\) −0.682225 −0.0739977
\(86\) −3.63864 −0.392365
\(87\) −4.96362 −0.532156
\(88\) −10.9361 −1.16580
\(89\) −6.84189 −0.725238 −0.362619 0.931937i \(-0.618117\pi\)
−0.362619 + 0.931937i \(0.618117\pi\)
\(90\) 0.912055 0.0961390
\(91\) −0.867951 −0.0909860
\(92\) −0.628853 −0.0655624
\(93\) 7.44554 0.772066
\(94\) 8.54589 0.881442
\(95\) −3.81259 −0.391163
\(96\) −2.34346 −0.239178
\(97\) −4.46972 −0.453832 −0.226916 0.973914i \(-0.572864\pi\)
−0.226916 + 0.973914i \(0.572864\pi\)
\(98\) −7.84728 −0.792695
\(99\) 3.59453 0.361264
\(100\) 1.88699 0.188699
\(101\) −18.9754 −1.88813 −0.944063 0.329765i \(-0.893030\pi\)
−0.944063 + 0.329765i \(0.893030\pi\)
\(102\) 1.18045 0.116882
\(103\) −1.00000 −0.0985329
\(104\) 3.04244 0.298336
\(105\) −0.630151 −0.0614965
\(106\) 7.05728 0.685464
\(107\) −12.5998 −1.21807 −0.609034 0.793144i \(-0.708443\pi\)
−0.609034 + 0.793144i \(0.708443\pi\)
\(108\) 0.421872 0.0405946
\(109\) −19.1826 −1.83736 −0.918681 0.395001i \(-0.870744\pi\)
−0.918681 + 0.395001i \(0.870744\pi\)
\(110\) 3.27841 0.312584
\(111\) 4.77506 0.453228
\(112\) −2.58500 −0.244260
\(113\) −17.7441 −1.66922 −0.834610 0.550841i \(-0.814307\pi\)
−0.834610 + 0.550841i \(0.814307\pi\)
\(114\) 6.59692 0.617859
\(115\) 1.08223 0.100918
\(116\) −2.09401 −0.194424
\(117\) −1.00000 −0.0924500
\(118\) 5.68393 0.523248
\(119\) −0.815593 −0.0747652
\(120\) 2.20888 0.201642
\(121\) 1.92065 0.174604
\(122\) 15.9252 1.44180
\(123\) 3.53461 0.318705
\(124\) 3.14106 0.282076
\(125\) −6.87753 −0.615145
\(126\) 1.09035 0.0971362
\(127\) −15.4264 −1.36887 −0.684437 0.729072i \(-0.739952\pi\)
−0.684437 + 0.729072i \(0.739952\pi\)
\(128\) 6.49421 0.574012
\(129\) 2.89646 0.255019
\(130\) −0.912055 −0.0799925
\(131\) 11.5715 1.01101 0.505504 0.862824i \(-0.331307\pi\)
0.505504 + 0.862824i \(0.331307\pi\)
\(132\) 1.51643 0.131988
\(133\) −4.55791 −0.395221
\(134\) −6.14696 −0.531017
\(135\) −0.726022 −0.0624860
\(136\) 2.85891 0.245149
\(137\) −3.27157 −0.279509 −0.139754 0.990186i \(-0.544631\pi\)
−0.139754 + 0.990186i \(0.544631\pi\)
\(138\) −1.87258 −0.159404
\(139\) −21.1187 −1.79126 −0.895632 0.444796i \(-0.853276\pi\)
−0.895632 + 0.444796i \(0.853276\pi\)
\(140\) −0.265843 −0.0224678
\(141\) −6.80278 −0.572897
\(142\) 8.47613 0.711301
\(143\) −3.59453 −0.300590
\(144\) −2.97828 −0.248190
\(145\) 3.60370 0.299271
\(146\) 6.27813 0.519582
\(147\) 6.24666 0.515216
\(148\) 2.01446 0.165588
\(149\) −3.53031 −0.289215 −0.144607 0.989489i \(-0.546192\pi\)
−0.144607 + 0.989489i \(0.546192\pi\)
\(150\) 5.61901 0.458790
\(151\) 11.1317 0.905882 0.452941 0.891540i \(-0.350375\pi\)
0.452941 + 0.891540i \(0.350375\pi\)
\(152\) 15.9769 1.29590
\(153\) −0.939676 −0.0759683
\(154\) 3.91930 0.315826
\(155\) −5.40562 −0.434190
\(156\) −0.421872 −0.0337768
\(157\) 4.76685 0.380436 0.190218 0.981742i \(-0.439080\pi\)
0.190218 + 0.981742i \(0.439080\pi\)
\(158\) −13.5911 −1.08125
\(159\) −5.61780 −0.445521
\(160\) 1.70140 0.134508
\(161\) 1.29379 0.101965
\(162\) 1.25624 0.0986992
\(163\) −16.2779 −1.27499 −0.637494 0.770456i \(-0.720029\pi\)
−0.637494 + 0.770456i \(0.720029\pi\)
\(164\) 1.49115 0.116439
\(165\) −2.60971 −0.203165
\(166\) −14.5546 −1.12965
\(167\) 6.63100 0.513122 0.256561 0.966528i \(-0.417411\pi\)
0.256561 + 0.966528i \(0.417411\pi\)
\(168\) 2.64069 0.203734
\(169\) 1.00000 0.0769231
\(170\) −0.857036 −0.0657316
\(171\) −5.25134 −0.401580
\(172\) 1.22194 0.0931717
\(173\) 15.4319 1.17326 0.586632 0.809854i \(-0.300453\pi\)
0.586632 + 0.809854i \(0.300453\pi\)
\(174\) −6.23548 −0.472711
\(175\) −3.88225 −0.293471
\(176\) −10.7055 −0.806959
\(177\) −4.52457 −0.340087
\(178\) −8.59502 −0.644224
\(179\) −18.3875 −1.37435 −0.687174 0.726493i \(-0.741149\pi\)
−0.687174 + 0.726493i \(0.741149\pi\)
\(180\) −0.306288 −0.0228294
\(181\) 14.2111 1.05630 0.528150 0.849151i \(-0.322886\pi\)
0.528150 + 0.849151i \(0.322886\pi\)
\(182\) −1.09035 −0.0808222
\(183\) −12.6769 −0.937104
\(184\) −4.53514 −0.334335
\(185\) −3.46679 −0.254884
\(186\) 9.35335 0.685821
\(187\) −3.37769 −0.247001
\(188\) −2.86990 −0.209309
\(189\) −0.867951 −0.0631341
\(190\) −4.78951 −0.347468
\(191\) −2.61191 −0.188991 −0.0944955 0.995525i \(-0.530124\pi\)
−0.0944955 + 0.995525i \(0.530124\pi\)
\(192\) −8.90050 −0.642338
\(193\) 13.2196 0.951570 0.475785 0.879562i \(-0.342164\pi\)
0.475785 + 0.879562i \(0.342164\pi\)
\(194\) −5.61503 −0.403135
\(195\) 0.726022 0.0519915
\(196\) 2.63529 0.188235
\(197\) −5.50978 −0.392556 −0.196278 0.980548i \(-0.562885\pi\)
−0.196278 + 0.980548i \(0.562885\pi\)
\(198\) 4.51558 0.320908
\(199\) 8.20184 0.581413 0.290707 0.956812i \(-0.406110\pi\)
0.290707 + 0.956812i \(0.406110\pi\)
\(200\) 13.6085 0.962267
\(201\) 4.89316 0.345137
\(202\) −23.8376 −1.67721
\(203\) 4.30818 0.302375
\(204\) −0.396423 −0.0277551
\(205\) −2.56620 −0.179231
\(206\) −1.25624 −0.0875261
\(207\) 1.49063 0.103606
\(208\) 2.97828 0.206507
\(209\) −18.8761 −1.30569
\(210\) −0.791619 −0.0546269
\(211\) −4.45695 −0.306829 −0.153415 0.988162i \(-0.549027\pi\)
−0.153415 + 0.988162i \(0.549027\pi\)
\(212\) −2.36999 −0.162772
\(213\) −6.74725 −0.462314
\(214\) −15.8283 −1.08200
\(215\) −2.10289 −0.143416
\(216\) 3.04244 0.207012
\(217\) −6.46236 −0.438694
\(218\) −24.0979 −1.63212
\(219\) −4.99757 −0.337705
\(220\) −1.10096 −0.0742268
\(221\) 0.939676 0.0632094
\(222\) 5.99859 0.402599
\(223\) 17.3716 1.16329 0.581643 0.813444i \(-0.302410\pi\)
0.581643 + 0.813444i \(0.302410\pi\)
\(224\) 2.03401 0.135903
\(225\) −4.47289 −0.298193
\(226\) −22.2907 −1.48276
\(227\) 0.396107 0.0262906 0.0131453 0.999914i \(-0.495816\pi\)
0.0131453 + 0.999914i \(0.495816\pi\)
\(228\) −2.21539 −0.146718
\(229\) −13.0026 −0.859235 −0.429618 0.903011i \(-0.641352\pi\)
−0.429618 + 0.903011i \(0.641352\pi\)
\(230\) 1.35953 0.0896449
\(231\) −3.11988 −0.205273
\(232\) −15.1015 −0.991465
\(233\) 0.00103394 6.77358e−5 0 3.38679e−5 1.00000i \(-0.499989\pi\)
3.38679e−5 1.00000i \(0.499989\pi\)
\(234\) −1.25624 −0.0821227
\(235\) 4.93897 0.322183
\(236\) −1.90879 −0.124252
\(237\) 10.8189 0.702762
\(238\) −1.02458 −0.0664134
\(239\) 20.8018 1.34556 0.672778 0.739844i \(-0.265101\pi\)
0.672778 + 0.739844i \(0.265101\pi\)
\(240\) 2.16230 0.139576
\(241\) −13.7419 −0.885196 −0.442598 0.896720i \(-0.645943\pi\)
−0.442598 + 0.896720i \(0.645943\pi\)
\(242\) 2.41279 0.155100
\(243\) −1.00000 −0.0641500
\(244\) −5.34803 −0.342373
\(245\) −4.53521 −0.289744
\(246\) 4.44030 0.283103
\(247\) 5.25134 0.334135
\(248\) 22.6526 1.43844
\(249\) 11.5859 0.734224
\(250\) −8.63980 −0.546429
\(251\) −1.28495 −0.0811051 −0.0405525 0.999177i \(-0.512912\pi\)
−0.0405525 + 0.999177i \(0.512912\pi\)
\(252\) −0.366164 −0.0230662
\(253\) 5.35810 0.336861
\(254\) −19.3792 −1.21596
\(255\) 0.682225 0.0427226
\(256\) −9.64275 −0.602672
\(257\) 13.6547 0.851757 0.425878 0.904780i \(-0.359965\pi\)
0.425878 + 0.904780i \(0.359965\pi\)
\(258\) 3.63864 0.226532
\(259\) −4.14451 −0.257528
\(260\) 0.306288 0.0189952
\(261\) 4.96362 0.307241
\(262\) 14.5366 0.898071
\(263\) −22.7598 −1.40343 −0.701714 0.712459i \(-0.747581\pi\)
−0.701714 + 0.712459i \(0.747581\pi\)
\(264\) 10.9361 0.673074
\(265\) 4.07865 0.250549
\(266\) −5.72581 −0.351072
\(267\) 6.84189 0.418717
\(268\) 2.06429 0.126096
\(269\) 1.40354 0.0855756 0.0427878 0.999084i \(-0.486376\pi\)
0.0427878 + 0.999084i \(0.486376\pi\)
\(270\) −0.912055 −0.0555059
\(271\) 0.793915 0.0482269 0.0241135 0.999709i \(-0.492324\pi\)
0.0241135 + 0.999709i \(0.492324\pi\)
\(272\) 2.79862 0.169691
\(273\) 0.867951 0.0525308
\(274\) −4.10986 −0.248286
\(275\) −16.0779 −0.969537
\(276\) 0.628853 0.0378525
\(277\) 9.18431 0.551832 0.275916 0.961182i \(-0.411019\pi\)
0.275916 + 0.961182i \(0.411019\pi\)
\(278\) −26.5301 −1.59117
\(279\) −7.44554 −0.445753
\(280\) −1.91720 −0.114575
\(281\) 25.3899 1.51464 0.757319 0.653046i \(-0.226509\pi\)
0.757319 + 0.653046i \(0.226509\pi\)
\(282\) −8.54589 −0.508901
\(283\) 1.44014 0.0856073 0.0428036 0.999084i \(-0.486371\pi\)
0.0428036 + 0.999084i \(0.486371\pi\)
\(284\) −2.84647 −0.168907
\(285\) 3.81259 0.225838
\(286\) −4.51558 −0.267012
\(287\) −3.06786 −0.181090
\(288\) 2.34346 0.138090
\(289\) −16.1170 −0.948059
\(290\) 4.52710 0.265840
\(291\) 4.46972 0.262020
\(292\) −2.10833 −0.123381
\(293\) −23.1478 −1.35231 −0.676155 0.736759i \(-0.736355\pi\)
−0.676155 + 0.736759i \(0.736355\pi\)
\(294\) 7.84728 0.457663
\(295\) 3.28494 0.191256
\(296\) 14.5278 0.844413
\(297\) −3.59453 −0.208576
\(298\) −4.43491 −0.256907
\(299\) −1.49063 −0.0862051
\(300\) −1.88699 −0.108945
\(301\) −2.51399 −0.144904
\(302\) 13.9840 0.804689
\(303\) 18.9754 1.09011
\(304\) 15.6400 0.897014
\(305\) 9.20371 0.527003
\(306\) −1.18045 −0.0674821
\(307\) 19.2794 1.10033 0.550167 0.835054i \(-0.314564\pi\)
0.550167 + 0.835054i \(0.314564\pi\)
\(308\) −1.31619 −0.0749967
\(309\) 1.00000 0.0568880
\(310\) −6.79074 −0.385688
\(311\) 23.7591 1.34726 0.673628 0.739071i \(-0.264735\pi\)
0.673628 + 0.739071i \(0.264735\pi\)
\(312\) −3.04244 −0.172244
\(313\) −13.7303 −0.776085 −0.388042 0.921642i \(-0.626849\pi\)
−0.388042 + 0.921642i \(0.626849\pi\)
\(314\) 5.98829 0.337939
\(315\) 0.630151 0.0355050
\(316\) 4.56418 0.256755
\(317\) −7.62491 −0.428258 −0.214129 0.976805i \(-0.568691\pi\)
−0.214129 + 0.976805i \(0.568691\pi\)
\(318\) −7.05728 −0.395753
\(319\) 17.8419 0.998955
\(320\) 6.46196 0.361234
\(321\) 12.5998 0.703252
\(322\) 1.62530 0.0905747
\(323\) 4.93456 0.274566
\(324\) −0.421872 −0.0234373
\(325\) 4.47289 0.248111
\(326\) −20.4489 −1.13256
\(327\) 19.1826 1.06080
\(328\) 10.7538 0.593781
\(329\) 5.90448 0.325524
\(330\) −3.27841 −0.180470
\(331\) −28.2691 −1.55381 −0.776904 0.629619i \(-0.783211\pi\)
−0.776904 + 0.629619i \(0.783211\pi\)
\(332\) 4.88775 0.268250
\(333\) −4.77506 −0.261671
\(334\) 8.33010 0.455803
\(335\) −3.55254 −0.194096
\(336\) 2.58500 0.141023
\(337\) 20.2030 1.10053 0.550264 0.834991i \(-0.314527\pi\)
0.550264 + 0.834991i \(0.314527\pi\)
\(338\) 1.25624 0.0683302
\(339\) 17.7441 0.963725
\(340\) 0.287812 0.0156088
\(341\) −26.7632 −1.44931
\(342\) −6.59692 −0.356721
\(343\) −11.4975 −0.620804
\(344\) 8.81232 0.475128
\(345\) −1.08223 −0.0582651
\(346\) 19.3861 1.04220
\(347\) −10.3588 −0.556088 −0.278044 0.960568i \(-0.589686\pi\)
−0.278044 + 0.960568i \(0.589686\pi\)
\(348\) 2.09401 0.112251
\(349\) 25.8477 1.38359 0.691797 0.722092i \(-0.256819\pi\)
0.691797 + 0.722092i \(0.256819\pi\)
\(350\) −4.87702 −0.260688
\(351\) 1.00000 0.0533761
\(352\) 8.42364 0.448982
\(353\) −4.88716 −0.260117 −0.130059 0.991506i \(-0.541517\pi\)
−0.130059 + 0.991506i \(0.541517\pi\)
\(354\) −5.68393 −0.302097
\(355\) 4.89865 0.259993
\(356\) 2.88640 0.152979
\(357\) 0.815593 0.0431657
\(358\) −23.0991 −1.22082
\(359\) −31.5578 −1.66556 −0.832778 0.553608i \(-0.813251\pi\)
−0.832778 + 0.553608i \(0.813251\pi\)
\(360\) −2.20888 −0.116418
\(361\) 8.57660 0.451400
\(362\) 17.8525 0.938304
\(363\) −1.92065 −0.100808
\(364\) 0.366164 0.0191922
\(365\) 3.62835 0.189916
\(366\) −15.9252 −0.832423
\(367\) 23.6613 1.23511 0.617554 0.786529i \(-0.288124\pi\)
0.617554 + 0.786529i \(0.288124\pi\)
\(368\) −4.43950 −0.231425
\(369\) −3.53461 −0.184004
\(370\) −4.35511 −0.226411
\(371\) 4.87598 0.253148
\(372\) −3.14106 −0.162856
\(373\) 17.2299 0.892131 0.446066 0.895000i \(-0.352825\pi\)
0.446066 + 0.895000i \(0.352825\pi\)
\(374\) −4.24318 −0.219410
\(375\) 6.87753 0.355154
\(376\) −20.6971 −1.06737
\(377\) −4.96362 −0.255640
\(378\) −1.09035 −0.0560816
\(379\) −5.53919 −0.284529 −0.142265 0.989829i \(-0.545438\pi\)
−0.142265 + 0.989829i \(0.545438\pi\)
\(380\) 1.60842 0.0825104
\(381\) 15.4264 0.790320
\(382\) −3.28117 −0.167879
\(383\) 29.7856 1.52198 0.760988 0.648766i \(-0.224715\pi\)
0.760988 + 0.648766i \(0.224715\pi\)
\(384\) −6.49421 −0.331406
\(385\) 2.26510 0.115440
\(386\) 16.6070 0.845273
\(387\) −2.89646 −0.147235
\(388\) 1.88565 0.0957294
\(389\) 6.13688 0.311152 0.155576 0.987824i \(-0.450277\pi\)
0.155576 + 0.987824i \(0.450277\pi\)
\(390\) 0.912055 0.0461837
\(391\) −1.40070 −0.0708367
\(392\) 19.0051 0.959903
\(393\) −11.5715 −0.583706
\(394\) −6.92159 −0.348705
\(395\) −7.85474 −0.395215
\(396\) −1.51643 −0.0762035
\(397\) −11.6171 −0.583046 −0.291523 0.956564i \(-0.594162\pi\)
−0.291523 + 0.956564i \(0.594162\pi\)
\(398\) 10.3034 0.516465
\(399\) 4.55791 0.228181
\(400\) 13.3215 0.666076
\(401\) 35.9050 1.79301 0.896505 0.443034i \(-0.146098\pi\)
0.896505 + 0.443034i \(0.146098\pi\)
\(402\) 6.14696 0.306583
\(403\) 7.44554 0.370889
\(404\) 8.00520 0.398274
\(405\) 0.726022 0.0360763
\(406\) 5.41209 0.268598
\(407\) −17.1641 −0.850792
\(408\) −2.85891 −0.141537
\(409\) −13.5194 −0.668491 −0.334245 0.942486i \(-0.608481\pi\)
−0.334245 + 0.942486i \(0.608481\pi\)
\(410\) −3.22375 −0.159210
\(411\) 3.27157 0.161375
\(412\) 0.421872 0.0207841
\(413\) 3.92710 0.193240
\(414\) 1.87258 0.0920321
\(415\) −8.41159 −0.412909
\(416\) −2.34346 −0.114898
\(417\) 21.1187 1.03419
\(418\) −23.7128 −1.15983
\(419\) 26.8040 1.30946 0.654730 0.755863i \(-0.272782\pi\)
0.654730 + 0.755863i \(0.272782\pi\)
\(420\) 0.265843 0.0129718
\(421\) 32.0554 1.56228 0.781142 0.624354i \(-0.214638\pi\)
0.781142 + 0.624354i \(0.214638\pi\)
\(422\) −5.59898 −0.272554
\(423\) 6.80278 0.330762
\(424\) −17.0918 −0.830053
\(425\) 4.20307 0.203879
\(426\) −8.47613 −0.410670
\(427\) 11.0029 0.532469
\(428\) 5.31550 0.256934
\(429\) 3.59453 0.173546
\(430\) −2.64173 −0.127396
\(431\) −14.1512 −0.681640 −0.340820 0.940129i \(-0.610705\pi\)
−0.340820 + 0.940129i \(0.610705\pi\)
\(432\) 2.97828 0.143293
\(433\) −18.9607 −0.911193 −0.455597 0.890186i \(-0.650574\pi\)
−0.455597 + 0.890186i \(0.650574\pi\)
\(434\) −8.11825 −0.389688
\(435\) −3.60370 −0.172784
\(436\) 8.09260 0.387565
\(437\) −7.82778 −0.374454
\(438\) −6.27813 −0.299981
\(439\) −11.8097 −0.563645 −0.281822 0.959467i \(-0.590939\pi\)
−0.281822 + 0.959467i \(0.590939\pi\)
\(440\) −7.93988 −0.378519
\(441\) −6.24666 −0.297460
\(442\) 1.18045 0.0561485
\(443\) −28.3908 −1.34889 −0.674443 0.738327i \(-0.735616\pi\)
−0.674443 + 0.738327i \(0.735616\pi\)
\(444\) −2.01446 −0.0956021
\(445\) −4.96736 −0.235475
\(446\) 21.8228 1.03334
\(447\) 3.53031 0.166978
\(448\) 7.72520 0.364981
\(449\) −7.86773 −0.371301 −0.185651 0.982616i \(-0.559439\pi\)
−0.185651 + 0.982616i \(0.559439\pi\)
\(450\) −5.61901 −0.264883
\(451\) −12.7052 −0.598267
\(452\) 7.48572 0.352098
\(453\) −11.1317 −0.523011
\(454\) 0.497604 0.0233537
\(455\) −0.630151 −0.0295420
\(456\) −15.9769 −0.748187
\(457\) 10.3630 0.484761 0.242381 0.970181i \(-0.422072\pi\)
0.242381 + 0.970181i \(0.422072\pi\)
\(458\) −16.3343 −0.763252
\(459\) 0.939676 0.0438603
\(460\) −0.456561 −0.0212873
\(461\) 26.2629 1.22319 0.611593 0.791173i \(-0.290529\pi\)
0.611593 + 0.791173i \(0.290529\pi\)
\(462\) −3.91930 −0.182342
\(463\) −19.4088 −0.902005 −0.451002 0.892523i \(-0.648933\pi\)
−0.451002 + 0.892523i \(0.648933\pi\)
\(464\) −14.7831 −0.686287
\(465\) 5.40562 0.250680
\(466\) 0.00129887 6.01692e−5 0
\(467\) 5.99903 0.277602 0.138801 0.990320i \(-0.455675\pi\)
0.138801 + 0.990320i \(0.455675\pi\)
\(468\) 0.421872 0.0195010
\(469\) −4.24702 −0.196109
\(470\) 6.20451 0.286192
\(471\) −4.76685 −0.219645
\(472\) −13.7657 −0.633619
\(473\) −10.4114 −0.478718
\(474\) 13.5911 0.624258
\(475\) 23.4887 1.07773
\(476\) 0.344075 0.0157707
\(477\) 5.61780 0.257221
\(478\) 26.1320 1.19525
\(479\) 20.2738 0.926334 0.463167 0.886271i \(-0.346713\pi\)
0.463167 + 0.886271i \(0.346713\pi\)
\(480\) −1.70140 −0.0776581
\(481\) 4.77506 0.217724
\(482\) −17.2631 −0.786313
\(483\) −1.29379 −0.0588695
\(484\) −0.810268 −0.0368303
\(485\) −3.24512 −0.147353
\(486\) −1.25624 −0.0569840
\(487\) −17.7279 −0.803328 −0.401664 0.915787i \(-0.631568\pi\)
−0.401664 + 0.915787i \(0.631568\pi\)
\(488\) −38.5688 −1.74593
\(489\) 16.2779 0.736114
\(490\) −5.69730 −0.257378
\(491\) −12.9916 −0.586303 −0.293152 0.956066i \(-0.594704\pi\)
−0.293152 + 0.956066i \(0.594704\pi\)
\(492\) −1.49115 −0.0672263
\(493\) −4.66420 −0.210065
\(494\) 6.59692 0.296810
\(495\) 2.60971 0.117298
\(496\) 22.1749 0.995683
\(497\) 5.85628 0.262690
\(498\) 14.5546 0.652206
\(499\) −16.3797 −0.733254 −0.366627 0.930368i \(-0.619488\pi\)
−0.366627 + 0.930368i \(0.619488\pi\)
\(500\) 2.90143 0.129756
\(501\) −6.63100 −0.296251
\(502\) −1.61420 −0.0720451
\(503\) 22.5897 1.00723 0.503613 0.863930i \(-0.332004\pi\)
0.503613 + 0.863930i \(0.332004\pi\)
\(504\) −2.64069 −0.117626
\(505\) −13.7766 −0.613050
\(506\) 6.73103 0.299231
\(507\) −1.00000 −0.0444116
\(508\) 6.50798 0.288745
\(509\) 38.1459 1.69079 0.845393 0.534145i \(-0.179367\pi\)
0.845393 + 0.534145i \(0.179367\pi\)
\(510\) 0.857036 0.0379502
\(511\) 4.33765 0.191886
\(512\) −25.1020 −1.10936
\(513\) 5.25134 0.231852
\(514\) 17.1535 0.756609
\(515\) −0.726022 −0.0319923
\(516\) −1.22194 −0.0537927
\(517\) 24.4528 1.07543
\(518\) −5.20649 −0.228760
\(519\) −15.4319 −0.677384
\(520\) 2.20888 0.0968658
\(521\) 11.6402 0.509965 0.254983 0.966946i \(-0.417930\pi\)
0.254983 + 0.966946i \(0.417930\pi\)
\(522\) 6.23548 0.272920
\(523\) −2.03449 −0.0889620 −0.0444810 0.999010i \(-0.514163\pi\)
−0.0444810 + 0.999010i \(0.514163\pi\)
\(524\) −4.88170 −0.213258
\(525\) 3.88225 0.169435
\(526\) −28.5916 −1.24665
\(527\) 6.99639 0.304768
\(528\) 10.7055 0.465898
\(529\) −20.7780 −0.903393
\(530\) 5.12374 0.222561
\(531\) 4.52457 0.196350
\(532\) 1.92285 0.0833662
\(533\) 3.53461 0.153101
\(534\) 8.59502 0.371943
\(535\) −9.14772 −0.395491
\(536\) 14.8872 0.643027
\(537\) 18.3875 0.793480
\(538\) 1.76318 0.0760162
\(539\) −22.4538 −0.967154
\(540\) 0.306288 0.0131805
\(541\) 19.4194 0.834907 0.417454 0.908698i \(-0.362923\pi\)
0.417454 + 0.908698i \(0.362923\pi\)
\(542\) 0.997344 0.0428396
\(543\) −14.2111 −0.609855
\(544\) −2.20209 −0.0944140
\(545\) −13.9270 −0.596567
\(546\) 1.09035 0.0466627
\(547\) −4.06957 −0.174002 −0.0870011 0.996208i \(-0.527728\pi\)
−0.0870011 + 0.996208i \(0.527728\pi\)
\(548\) 1.38018 0.0589584
\(549\) 12.6769 0.541037
\(550\) −20.1977 −0.861232
\(551\) −26.0657 −1.11044
\(552\) 4.53514 0.193028
\(553\) −9.39026 −0.399314
\(554\) 11.5377 0.490188
\(555\) 3.46679 0.147157
\(556\) 8.90938 0.377842
\(557\) −28.7020 −1.21614 −0.608071 0.793883i \(-0.708056\pi\)
−0.608071 + 0.793883i \(0.708056\pi\)
\(558\) −9.35335 −0.395959
\(559\) 2.89646 0.122507
\(560\) −1.87677 −0.0793079
\(561\) 3.37769 0.142606
\(562\) 31.8958 1.34544
\(563\) 5.74931 0.242305 0.121152 0.992634i \(-0.461341\pi\)
0.121152 + 0.992634i \(0.461341\pi\)
\(564\) 2.86990 0.120845
\(565\) −12.8826 −0.541974
\(566\) 1.80915 0.0760443
\(567\) 0.867951 0.0364505
\(568\) −20.5281 −0.861340
\(569\) 24.9949 1.04784 0.523920 0.851768i \(-0.324469\pi\)
0.523920 + 0.851768i \(0.324469\pi\)
\(570\) 4.78951 0.200611
\(571\) 18.6578 0.780803 0.390402 0.920645i \(-0.372336\pi\)
0.390402 + 0.920645i \(0.372336\pi\)
\(572\) 1.51643 0.0634052
\(573\) 2.61191 0.109114
\(574\) −3.85396 −0.160861
\(575\) −6.66741 −0.278050
\(576\) 8.90050 0.370854
\(577\) −14.9335 −0.621691 −0.310845 0.950460i \(-0.600612\pi\)
−0.310845 + 0.950460i \(0.600612\pi\)
\(578\) −20.2468 −0.842154
\(579\) −13.2196 −0.549389
\(580\) −1.52030 −0.0631270
\(581\) −10.0560 −0.417192
\(582\) 5.61503 0.232750
\(583\) 20.1934 0.836324
\(584\) −15.2048 −0.629180
\(585\) −0.726022 −0.0300173
\(586\) −29.0791 −1.20125
\(587\) −12.8503 −0.530388 −0.265194 0.964195i \(-0.585436\pi\)
−0.265194 + 0.964195i \(0.585436\pi\)
\(588\) −2.63529 −0.108678
\(589\) 39.0991 1.61105
\(590\) 4.12665 0.169892
\(591\) 5.50978 0.226642
\(592\) 14.2215 0.584498
\(593\) −30.4911 −1.25212 −0.626059 0.779775i \(-0.715333\pi\)
−0.626059 + 0.779775i \(0.715333\pi\)
\(594\) −4.51558 −0.185276
\(595\) −0.592138 −0.0242753
\(596\) 1.48934 0.0610057
\(597\) −8.20184 −0.335679
\(598\) −1.87258 −0.0765754
\(599\) −40.7333 −1.66432 −0.832158 0.554539i \(-0.812895\pi\)
−0.832158 + 0.554539i \(0.812895\pi\)
\(600\) −13.6085 −0.555565
\(601\) 12.5484 0.511861 0.255930 0.966695i \(-0.417618\pi\)
0.255930 + 0.966695i \(0.417618\pi\)
\(602\) −3.15816 −0.128717
\(603\) −4.89316 −0.199265
\(604\) −4.69614 −0.191083
\(605\) 1.39443 0.0566918
\(606\) 23.8376 0.968337
\(607\) 4.28572 0.173952 0.0869760 0.996210i \(-0.472280\pi\)
0.0869760 + 0.996210i \(0.472280\pi\)
\(608\) −12.3063 −0.499087
\(609\) −4.30818 −0.174576
\(610\) 11.5620 0.468133
\(611\) −6.80278 −0.275211
\(612\) 0.396423 0.0160244
\(613\) 43.6881 1.76454 0.882272 0.470740i \(-0.156013\pi\)
0.882272 + 0.470740i \(0.156013\pi\)
\(614\) 24.2195 0.977420
\(615\) 2.56620 0.103479
\(616\) −9.49204 −0.382445
\(617\) −4.52035 −0.181982 −0.0909911 0.995852i \(-0.529003\pi\)
−0.0909911 + 0.995852i \(0.529003\pi\)
\(618\) 1.25624 0.0505332
\(619\) 24.1932 0.972407 0.486204 0.873846i \(-0.338381\pi\)
0.486204 + 0.873846i \(0.338381\pi\)
\(620\) 2.28048 0.0915863
\(621\) −1.49063 −0.0598167
\(622\) 29.8470 1.19676
\(623\) −5.93842 −0.237918
\(624\) −2.97828 −0.119227
\(625\) 17.3712 0.694849
\(626\) −17.2485 −0.689390
\(627\) 18.8761 0.753839
\(628\) −2.01100 −0.0802476
\(629\) 4.48700 0.178909
\(630\) 0.791619 0.0315388
\(631\) 21.0860 0.839418 0.419709 0.907659i \(-0.362132\pi\)
0.419709 + 0.907659i \(0.362132\pi\)
\(632\) 32.9158 1.30932
\(633\) 4.45695 0.177148
\(634\) −9.57869 −0.380418
\(635\) −11.1999 −0.444456
\(636\) 2.36999 0.0939763
\(637\) 6.24666 0.247502
\(638\) 22.4136 0.887364
\(639\) 6.74725 0.266917
\(640\) 4.71494 0.186374
\(641\) 1.57660 0.0622721 0.0311360 0.999515i \(-0.490087\pi\)
0.0311360 + 0.999515i \(0.490087\pi\)
\(642\) 15.8283 0.624694
\(643\) −34.3478 −1.35455 −0.677273 0.735732i \(-0.736839\pi\)
−0.677273 + 0.735732i \(0.736839\pi\)
\(644\) −0.545813 −0.0215081
\(645\) 2.10289 0.0828014
\(646\) 6.19897 0.243895
\(647\) −39.0306 −1.53445 −0.767226 0.641377i \(-0.778364\pi\)
−0.767226 + 0.641377i \(0.778364\pi\)
\(648\) −3.04244 −0.119518
\(649\) 16.2637 0.638406
\(650\) 5.61901 0.220396
\(651\) 6.46236 0.253280
\(652\) 6.86721 0.268941
\(653\) 15.8978 0.622129 0.311064 0.950389i \(-0.399314\pi\)
0.311064 + 0.950389i \(0.399314\pi\)
\(654\) 24.0979 0.942302
\(655\) 8.40117 0.328261
\(656\) 10.5270 0.411012
\(657\) 4.99757 0.194974
\(658\) 7.41742 0.289161
\(659\) 24.1342 0.940133 0.470067 0.882631i \(-0.344230\pi\)
0.470067 + 0.882631i \(0.344230\pi\)
\(660\) 1.10096 0.0428549
\(661\) −33.0940 −1.28721 −0.643605 0.765358i \(-0.722562\pi\)
−0.643605 + 0.765358i \(0.722562\pi\)
\(662\) −35.5126 −1.38024
\(663\) −0.939676 −0.0364940
\(664\) 35.2493 1.36794
\(665\) −3.30914 −0.128323
\(666\) −5.99859 −0.232441
\(667\) 7.39890 0.286487
\(668\) −2.79743 −0.108236
\(669\) −17.3716 −0.671624
\(670\) −4.46283 −0.172414
\(671\) 45.5675 1.75912
\(672\) −2.03401 −0.0784636
\(673\) 32.7435 1.26217 0.631085 0.775713i \(-0.282610\pi\)
0.631085 + 0.775713i \(0.282610\pi\)
\(674\) 25.3797 0.977591
\(675\) 4.47289 0.172162
\(676\) −0.421872 −0.0162258
\(677\) 11.4719 0.440900 0.220450 0.975398i \(-0.429247\pi\)
0.220450 + 0.975398i \(0.429247\pi\)
\(678\) 22.2907 0.856070
\(679\) −3.87950 −0.148882
\(680\) 2.07563 0.0795968
\(681\) −0.396107 −0.0151789
\(682\) −33.6209 −1.28741
\(683\) 6.59279 0.252266 0.126133 0.992013i \(-0.459743\pi\)
0.126133 + 0.992013i \(0.459743\pi\)
\(684\) 2.21539 0.0847077
\(685\) −2.37523 −0.0907528
\(686\) −14.4435 −0.551456
\(687\) 13.0026 0.496080
\(688\) 8.62648 0.328881
\(689\) −5.61780 −0.214021
\(690\) −1.35953 −0.0517565
\(691\) −32.3009 −1.22878 −0.614392 0.789001i \(-0.710599\pi\)
−0.614392 + 0.789001i \(0.710599\pi\)
\(692\) −6.51027 −0.247483
\(693\) 3.11988 0.118514
\(694\) −13.0131 −0.493969
\(695\) −15.3326 −0.581600
\(696\) 15.1015 0.572422
\(697\) 3.32138 0.125806
\(698\) 32.4708 1.22904
\(699\) −0.00103394 −3.91073e−5 0
\(700\) 1.63781 0.0619035
\(701\) −17.9660 −0.678567 −0.339284 0.940684i \(-0.610185\pi\)
−0.339284 + 0.940684i \(0.610185\pi\)
\(702\) 1.25624 0.0474136
\(703\) 25.0754 0.945738
\(704\) 31.9931 1.20579
\(705\) −4.93897 −0.186012
\(706\) −6.13943 −0.231060
\(707\) −16.4697 −0.619408
\(708\) 1.90879 0.0717366
\(709\) 36.4287 1.36811 0.684053 0.729432i \(-0.260215\pi\)
0.684053 + 0.729432i \(0.260215\pi\)
\(710\) 6.15386 0.230950
\(711\) −10.8189 −0.405740
\(712\) 20.8160 0.780114
\(713\) −11.0985 −0.415642
\(714\) 1.02458 0.0383438
\(715\) −2.60971 −0.0975975
\(716\) 7.75717 0.289899
\(717\) −20.8018 −0.776858
\(718\) −39.6440 −1.47950
\(719\) 41.0784 1.53197 0.765983 0.642861i \(-0.222253\pi\)
0.765983 + 0.642861i \(0.222253\pi\)
\(720\) −2.16230 −0.0805841
\(721\) −0.867951 −0.0323242
\(722\) 10.7742 0.400975
\(723\) 13.7419 0.511068
\(724\) −5.99525 −0.222812
\(725\) −22.2018 −0.824553
\(726\) −2.41279 −0.0895470
\(727\) −13.0105 −0.482534 −0.241267 0.970459i \(-0.577563\pi\)
−0.241267 + 0.970459i \(0.577563\pi\)
\(728\) 2.64069 0.0978705
\(729\) 1.00000 0.0370370
\(730\) 4.55806 0.168701
\(731\) 2.72174 0.100667
\(732\) 5.34803 0.197669
\(733\) −5.62091 −0.207613 −0.103807 0.994598i \(-0.533102\pi\)
−0.103807 + 0.994598i \(0.533102\pi\)
\(734\) 29.7241 1.09714
\(735\) 4.53521 0.167284
\(736\) 3.49322 0.128762
\(737\) −17.5886 −0.647885
\(738\) −4.44030 −0.163450
\(739\) −10.6423 −0.391483 −0.195742 0.980655i \(-0.562711\pi\)
−0.195742 + 0.980655i \(0.562711\pi\)
\(740\) 1.46254 0.0537641
\(741\) −5.25134 −0.192913
\(742\) 6.12538 0.224870
\(743\) 7.80516 0.286344 0.143172 0.989698i \(-0.454270\pi\)
0.143172 + 0.989698i \(0.454270\pi\)
\(744\) −22.6526 −0.830485
\(745\) −2.56309 −0.0939042
\(746\) 21.6448 0.792474
\(747\) −11.5859 −0.423905
\(748\) 1.42495 0.0521015
\(749\) −10.9360 −0.399593
\(750\) 8.63980 0.315481
\(751\) −4.12697 −0.150595 −0.0752977 0.997161i \(-0.523991\pi\)
−0.0752977 + 0.997161i \(0.523991\pi\)
\(752\) −20.2606 −0.738827
\(753\) 1.28495 0.0468260
\(754\) −6.23548 −0.227083
\(755\) 8.08184 0.294128
\(756\) 0.366164 0.0133173
\(757\) 5.01666 0.182334 0.0911668 0.995836i \(-0.470940\pi\)
0.0911668 + 0.995836i \(0.470940\pi\)
\(758\) −6.95853 −0.252745
\(759\) −5.35810 −0.194487
\(760\) 11.5996 0.420761
\(761\) −18.4794 −0.669878 −0.334939 0.942240i \(-0.608716\pi\)
−0.334939 + 0.942240i \(0.608716\pi\)
\(762\) 19.3792 0.702036
\(763\) −16.6496 −0.602755
\(764\) 1.10189 0.0398650
\(765\) −0.682225 −0.0246659
\(766\) 37.4178 1.35196
\(767\) −4.52457 −0.163373
\(768\) 9.64275 0.347953
\(769\) 30.3155 1.09321 0.546603 0.837392i \(-0.315921\pi\)
0.546603 + 0.837392i \(0.315921\pi\)
\(770\) 2.84550 0.102545
\(771\) −13.6547 −0.491762
\(772\) −5.57699 −0.200720
\(773\) −36.0205 −1.29557 −0.647783 0.761825i \(-0.724304\pi\)
−0.647783 + 0.761825i \(0.724304\pi\)
\(774\) −3.63864 −0.130788
\(775\) 33.3031 1.19628
\(776\) 13.5989 0.488171
\(777\) 4.14451 0.148684
\(778\) 7.70937 0.276394
\(779\) 18.5614 0.665032
\(780\) −0.306288 −0.0109669
\(781\) 24.2532 0.867847
\(782\) −1.75962 −0.0629237
\(783\) −4.96362 −0.177385
\(784\) 18.6043 0.664440
\(785\) 3.46084 0.123523
\(786\) −14.5366 −0.518502
\(787\) 36.7209 1.30896 0.654479 0.756080i \(-0.272888\pi\)
0.654479 + 0.756080i \(0.272888\pi\)
\(788\) 2.32442 0.0828041
\(789\) 22.7598 0.810269
\(790\) −9.86741 −0.351067
\(791\) −15.4010 −0.547595
\(792\) −10.9361 −0.388599
\(793\) −12.6769 −0.450170
\(794\) −14.5938 −0.517916
\(795\) −4.07865 −0.144655
\(796\) −3.46012 −0.122641
\(797\) −4.15280 −0.147100 −0.0735499 0.997292i \(-0.523433\pi\)
−0.0735499 + 0.997292i \(0.523433\pi\)
\(798\) 5.72581 0.202691
\(799\) −6.39241 −0.226147
\(800\) −10.4820 −0.370596
\(801\) −6.84189 −0.241746
\(802\) 45.1051 1.59272
\(803\) 17.9639 0.633933
\(804\) −2.06429 −0.0728017
\(805\) 0.939319 0.0331067
\(806\) 9.35335 0.329458
\(807\) −1.40354 −0.0494071
\(808\) 57.7316 2.03099
\(809\) −0.877993 −0.0308686 −0.0154343 0.999881i \(-0.504913\pi\)
−0.0154343 + 0.999881i \(0.504913\pi\)
\(810\) 0.912055 0.0320463
\(811\) 12.3049 0.432082 0.216041 0.976384i \(-0.430685\pi\)
0.216041 + 0.976384i \(0.430685\pi\)
\(812\) −1.81750 −0.0637818
\(813\) −0.793915 −0.0278438
\(814\) −21.5621 −0.755752
\(815\) −11.8181 −0.413972
\(816\) −2.79862 −0.0979712
\(817\) 15.2103 0.532142
\(818\) −16.9835 −0.593816
\(819\) −0.867951 −0.0303287
\(820\) 1.08261 0.0378063
\(821\) −4.13970 −0.144477 −0.0722383 0.997387i \(-0.523014\pi\)
−0.0722383 + 0.997387i \(0.523014\pi\)
\(822\) 4.10986 0.143348
\(823\) 29.6230 1.03259 0.516296 0.856410i \(-0.327310\pi\)
0.516296 + 0.856410i \(0.327310\pi\)
\(824\) 3.04244 0.105988
\(825\) 16.0779 0.559762
\(826\) 4.93337 0.171654
\(827\) 0.901506 0.0313484 0.0156742 0.999877i \(-0.495011\pi\)
0.0156742 + 0.999877i \(0.495011\pi\)
\(828\) −0.628853 −0.0218541
\(829\) 19.8674 0.690022 0.345011 0.938599i \(-0.387875\pi\)
0.345011 + 0.938599i \(0.387875\pi\)
\(830\) −10.5669 −0.366784
\(831\) −9.18431 −0.318600
\(832\) −8.90050 −0.308569
\(833\) 5.86984 0.203378
\(834\) 26.5301 0.918661
\(835\) 4.81425 0.166604
\(836\) 7.96330 0.275416
\(837\) 7.44554 0.257355
\(838\) 33.6721 1.16318
\(839\) 22.3484 0.771553 0.385777 0.922592i \(-0.373934\pi\)
0.385777 + 0.922592i \(0.373934\pi\)
\(840\) 1.91720 0.0661496
\(841\) −4.36243 −0.150429
\(842\) 40.2691 1.38777
\(843\) −25.3899 −0.874476
\(844\) 1.88026 0.0647213
\(845\) 0.726022 0.0249759
\(846\) 8.54589 0.293814
\(847\) 1.66703 0.0572798
\(848\) −16.7314 −0.574558
\(849\) −1.44014 −0.0494254
\(850\) 5.28005 0.181104
\(851\) −7.11782 −0.243996
\(852\) 2.84647 0.0975186
\(853\) −36.4578 −1.24829 −0.624146 0.781308i \(-0.714553\pi\)
−0.624146 + 0.781308i \(0.714553\pi\)
\(854\) 13.8223 0.472989
\(855\) −3.81259 −0.130388
\(856\) 38.3341 1.31023
\(857\) 16.9812 0.580067 0.290033 0.957017i \(-0.406334\pi\)
0.290033 + 0.957017i \(0.406334\pi\)
\(858\) 4.51558 0.154159
\(859\) 5.55249 0.189448 0.0947242 0.995504i \(-0.469803\pi\)
0.0947242 + 0.995504i \(0.469803\pi\)
\(860\) 0.887152 0.0302516
\(861\) 3.06786 0.104553
\(862\) −17.7773 −0.605496
\(863\) −4.97423 −0.169325 −0.0846624 0.996410i \(-0.526981\pi\)
−0.0846624 + 0.996410i \(0.526981\pi\)
\(864\) −2.34346 −0.0797262
\(865\) 11.2039 0.380943
\(866\) −23.8191 −0.809406
\(867\) 16.1170 0.547362
\(868\) 2.72629 0.0925362
\(869\) −38.8888 −1.31921
\(870\) −4.52710 −0.153483
\(871\) 4.89316 0.165798
\(872\) 58.3620 1.97639
\(873\) −4.46972 −0.151277
\(874\) −9.83354 −0.332624
\(875\) −5.96936 −0.201801
\(876\) 2.10833 0.0712340
\(877\) 23.2188 0.784042 0.392021 0.919956i \(-0.371776\pi\)
0.392021 + 0.919956i \(0.371776\pi\)
\(878\) −14.8357 −0.500682
\(879\) 23.1478 0.780756
\(880\) −7.77244 −0.262009
\(881\) −47.4334 −1.59807 −0.799035 0.601284i \(-0.794656\pi\)
−0.799035 + 0.601284i \(0.794656\pi\)
\(882\) −7.84728 −0.264232
\(883\) −2.67783 −0.0901163 −0.0450582 0.998984i \(-0.514347\pi\)
−0.0450582 + 0.998984i \(0.514347\pi\)
\(884\) −0.396423 −0.0133331
\(885\) −3.28494 −0.110422
\(886\) −35.6655 −1.19821
\(887\) −44.5623 −1.49626 −0.748128 0.663554i \(-0.769047\pi\)
−0.748128 + 0.663554i \(0.769047\pi\)
\(888\) −14.5278 −0.487522
\(889\) −13.3894 −0.449066
\(890\) −6.24017 −0.209171
\(891\) 3.59453 0.120421
\(892\) −7.32858 −0.245379
\(893\) −35.7237 −1.19545
\(894\) 4.43491 0.148325
\(895\) −13.3497 −0.446233
\(896\) 5.63665 0.188307
\(897\) 1.49063 0.0497705
\(898\) −9.88373 −0.329824
\(899\) −36.9569 −1.23258
\(900\) 1.88699 0.0628996
\(901\) −5.27891 −0.175866
\(902\) −15.9608 −0.531436
\(903\) 2.51399 0.0836602
\(904\) 53.9853 1.79552
\(905\) 10.3175 0.342967
\(906\) −13.9840 −0.464587
\(907\) 49.7051 1.65043 0.825215 0.564819i \(-0.191054\pi\)
0.825215 + 0.564819i \(0.191054\pi\)
\(908\) −0.167106 −0.00554562
\(909\) −18.9754 −0.629375
\(910\) −0.791619 −0.0262419
\(911\) −52.5608 −1.74142 −0.870708 0.491799i \(-0.836339\pi\)
−0.870708 + 0.491799i \(0.836339\pi\)
\(912\) −15.6400 −0.517891
\(913\) −41.6457 −1.37827
\(914\) 13.0184 0.430610
\(915\) −9.20371 −0.304265
\(916\) 5.48542 0.181243
\(917\) 10.0435 0.331666
\(918\) 1.18045 0.0389608
\(919\) −46.7884 −1.54341 −0.771703 0.635983i \(-0.780595\pi\)
−0.771703 + 0.635983i \(0.780595\pi\)
\(920\) −3.29261 −0.108554
\(921\) −19.2794 −0.635279
\(922\) 32.9924 1.08655
\(923\) −6.74725 −0.222088
\(924\) 1.31619 0.0432994
\(925\) 21.3583 0.702257
\(926\) −24.3821 −0.801244
\(927\) −1.00000 −0.0328443
\(928\) 11.6321 0.381841
\(929\) −34.9058 −1.14522 −0.572611 0.819827i \(-0.694069\pi\)
−0.572611 + 0.819827i \(0.694069\pi\)
\(930\) 6.79074 0.222677
\(931\) 32.8034 1.07509
\(932\) −0.000436191 0 −1.42879e−5 0
\(933\) −23.7591 −0.777838
\(934\) 7.53619 0.246592
\(935\) −2.45228 −0.0801981
\(936\) 3.04244 0.0994453
\(937\) 19.7797 0.646174 0.323087 0.946369i \(-0.395279\pi\)
0.323087 + 0.946369i \(0.395279\pi\)
\(938\) −5.33526 −0.174202
\(939\) 13.7303 0.448073
\(940\) −2.08361 −0.0679599
\(941\) 46.7587 1.52429 0.762145 0.647406i \(-0.224146\pi\)
0.762145 + 0.647406i \(0.224146\pi\)
\(942\) −5.98829 −0.195109
\(943\) −5.26877 −0.171575
\(944\) −13.4754 −0.438588
\(945\) −0.630151 −0.0204988
\(946\) −13.0792 −0.425241
\(947\) 24.7249 0.803451 0.401726 0.915760i \(-0.368411\pi\)
0.401726 + 0.915760i \(0.368411\pi\)
\(948\) −4.56418 −0.148238
\(949\) −4.99757 −0.162228
\(950\) 29.5073 0.957344
\(951\) 7.62491 0.247255
\(952\) 2.48139 0.0804224
\(953\) −56.7166 −1.83723 −0.918615 0.395154i \(-0.870691\pi\)
−0.918615 + 0.395154i \(0.870691\pi\)
\(954\) 7.05728 0.228488
\(955\) −1.89630 −0.0613629
\(956\) −8.77569 −0.283826
\(957\) −17.8419 −0.576747
\(958\) 25.4687 0.822855
\(959\) −2.83956 −0.0916942
\(960\) −6.46196 −0.208559
\(961\) 24.4360 0.788259
\(962\) 5.99859 0.193402
\(963\) −12.5998 −0.406023
\(964\) 5.79734 0.186720
\(965\) 9.59775 0.308962
\(966\) −1.62530 −0.0522933
\(967\) −22.6203 −0.727421 −0.363710 0.931512i \(-0.618490\pi\)
−0.363710 + 0.931512i \(0.618490\pi\)
\(968\) −5.84346 −0.187816
\(969\) −4.93456 −0.158521
\(970\) −4.07663 −0.130893
\(971\) 44.5180 1.42865 0.714325 0.699814i \(-0.246734\pi\)
0.714325 + 0.699814i \(0.246734\pi\)
\(972\) 0.421872 0.0135315
\(973\) −18.3300 −0.587632
\(974\) −22.2704 −0.713590
\(975\) −4.47289 −0.143247
\(976\) −37.7554 −1.20852
\(977\) 12.1739 0.389477 0.194738 0.980855i \(-0.437614\pi\)
0.194738 + 0.980855i \(0.437614\pi\)
\(978\) 20.4489 0.653885
\(979\) −24.5934 −0.786007
\(980\) 1.91328 0.0611174
\(981\) −19.1826 −0.612454
\(982\) −16.3205 −0.520809
\(983\) −15.6174 −0.498118 −0.249059 0.968488i \(-0.580121\pi\)
−0.249059 + 0.968488i \(0.580121\pi\)
\(984\) −10.7538 −0.342820
\(985\) −4.00022 −0.127458
\(986\) −5.85933 −0.186599
\(987\) −5.90448 −0.187942
\(988\) −2.21539 −0.0704810
\(989\) −4.31754 −0.137290
\(990\) 3.27841 0.104195
\(991\) 53.0460 1.68506 0.842531 0.538647i \(-0.181064\pi\)
0.842531 + 0.538647i \(0.181064\pi\)
\(992\) −17.4483 −0.553985
\(993\) 28.2691 0.897092
\(994\) 7.35687 0.233346
\(995\) 5.95472 0.188777
\(996\) −4.88775 −0.154874
\(997\) −57.2409 −1.81284 −0.906418 0.422381i \(-0.861194\pi\)
−0.906418 + 0.422381i \(0.861194\pi\)
\(998\) −20.5767 −0.651345
\(999\) 4.77506 0.151076
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 4017.2.a.i.1.18 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4017.2.a.i.1.18 25 1.1 even 1 trivial