Properties

Label 6034.2.a.p.1.15
Level $6034$
Weight $2$
Character 6034.1
Self dual yes
Analytic conductor $48.182$
Analytic rank $0$
Dimension $27$
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] = [6034,2,Mod(1,6034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6034, 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("6034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6034.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: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 6034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.396413 q^{3} +1.00000 q^{4} -1.85319 q^{5} -0.396413 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.84286 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.396413 q^{3} +1.00000 q^{4} -1.85319 q^{5} -0.396413 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.84286 q^{9} +1.85319 q^{10} +4.50165 q^{11} +0.396413 q^{12} -5.91310 q^{13} -1.00000 q^{14} -0.734628 q^{15} +1.00000 q^{16} -7.27375 q^{17} +2.84286 q^{18} +8.32838 q^{19} -1.85319 q^{20} +0.396413 q^{21} -4.50165 q^{22} +4.63014 q^{23} -0.396413 q^{24} -1.56569 q^{25} +5.91310 q^{26} -2.31618 q^{27} +1.00000 q^{28} +4.78767 q^{29} +0.734628 q^{30} -2.20360 q^{31} -1.00000 q^{32} +1.78451 q^{33} +7.27375 q^{34} -1.85319 q^{35} -2.84286 q^{36} +4.81524 q^{37} -8.32838 q^{38} -2.34403 q^{39} +1.85319 q^{40} +0.513367 q^{41} -0.396413 q^{42} -9.72662 q^{43} +4.50165 q^{44} +5.26835 q^{45} -4.63014 q^{46} -2.59821 q^{47} +0.396413 q^{48} +1.00000 q^{49} +1.56569 q^{50} -2.88341 q^{51} -5.91310 q^{52} +0.359603 q^{53} +2.31618 q^{54} -8.34241 q^{55} -1.00000 q^{56} +3.30148 q^{57} -4.78767 q^{58} -13.9736 q^{59} -0.734628 q^{60} -6.74430 q^{61} +2.20360 q^{62} -2.84286 q^{63} +1.00000 q^{64} +10.9581 q^{65} -1.78451 q^{66} +13.8107 q^{67} -7.27375 q^{68} +1.83545 q^{69} +1.85319 q^{70} +2.79743 q^{71} +2.84286 q^{72} -7.79200 q^{73} -4.81524 q^{74} -0.620660 q^{75} +8.32838 q^{76} +4.50165 q^{77} +2.34403 q^{78} -5.54692 q^{79} -1.85319 q^{80} +7.61040 q^{81} -0.513367 q^{82} +16.1813 q^{83} +0.396413 q^{84} +13.4796 q^{85} +9.72662 q^{86} +1.89789 q^{87} -4.50165 q^{88} -3.71243 q^{89} -5.26835 q^{90} -5.91310 q^{91} +4.63014 q^{92} -0.873537 q^{93} +2.59821 q^{94} -15.4341 q^{95} -0.396413 q^{96} -13.5994 q^{97} -1.00000 q^{98} -12.7976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.396413 0.228869 0.114435 0.993431i \(-0.463494\pi\)
0.114435 + 0.993431i \(0.463494\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.85319 −0.828771 −0.414386 0.910101i \(-0.636004\pi\)
−0.414386 + 0.910101i \(0.636004\pi\)
\(6\) −0.396413 −0.161835
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) −2.84286 −0.947619
\(10\) 1.85319 0.586030
\(11\) 4.50165 1.35730 0.678650 0.734462i \(-0.262565\pi\)
0.678650 + 0.734462i \(0.262565\pi\)
\(12\) 0.396413 0.114435
\(13\) −5.91310 −1.64000 −0.819999 0.572365i \(-0.806026\pi\)
−0.819999 + 0.572365i \(0.806026\pi\)
\(14\) −1.00000 −0.267261
\(15\) −0.734628 −0.189680
\(16\) 1.00000 0.250000
\(17\) −7.27375 −1.76414 −0.882071 0.471116i \(-0.843851\pi\)
−0.882071 + 0.471116i \(0.843851\pi\)
\(18\) 2.84286 0.670068
\(19\) 8.32838 1.91066 0.955330 0.295540i \(-0.0954997\pi\)
0.955330 + 0.295540i \(0.0954997\pi\)
\(20\) −1.85319 −0.414386
\(21\) 0.396413 0.0865044
\(22\) −4.50165 −0.959756
\(23\) 4.63014 0.965451 0.482726 0.875772i \(-0.339647\pi\)
0.482726 + 0.875772i \(0.339647\pi\)
\(24\) −0.396413 −0.0809175
\(25\) −1.56569 −0.313138
\(26\) 5.91310 1.15965
\(27\) −2.31618 −0.445750
\(28\) 1.00000 0.188982
\(29\) 4.78767 0.889048 0.444524 0.895767i \(-0.353373\pi\)
0.444524 + 0.895767i \(0.353373\pi\)
\(30\) 0.734628 0.134124
\(31\) −2.20360 −0.395779 −0.197890 0.980224i \(-0.563409\pi\)
−0.197890 + 0.980224i \(0.563409\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.78451 0.310644
\(34\) 7.27375 1.24744
\(35\) −1.85319 −0.313246
\(36\) −2.84286 −0.473809
\(37\) 4.81524 0.791620 0.395810 0.918332i \(-0.370464\pi\)
0.395810 + 0.918332i \(0.370464\pi\)
\(38\) −8.32838 −1.35104
\(39\) −2.34403 −0.375345
\(40\) 1.85319 0.293015
\(41\) 0.513367 0.0801745 0.0400872 0.999196i \(-0.487236\pi\)
0.0400872 + 0.999196i \(0.487236\pi\)
\(42\) −0.396413 −0.0611678
\(43\) −9.72662 −1.48330 −0.741648 0.670789i \(-0.765956\pi\)
−0.741648 + 0.670789i \(0.765956\pi\)
\(44\) 4.50165 0.678650
\(45\) 5.26835 0.785359
\(46\) −4.63014 −0.682677
\(47\) −2.59821 −0.378987 −0.189494 0.981882i \(-0.560685\pi\)
−0.189494 + 0.981882i \(0.560685\pi\)
\(48\) 0.396413 0.0572173
\(49\) 1.00000 0.142857
\(50\) 1.56569 0.221422
\(51\) −2.88341 −0.403758
\(52\) −5.91310 −0.819999
\(53\) 0.359603 0.0493953 0.0246977 0.999695i \(-0.492138\pi\)
0.0246977 + 0.999695i \(0.492138\pi\)
\(54\) 2.31618 0.315193
\(55\) −8.34241 −1.12489
\(56\) −1.00000 −0.133631
\(57\) 3.30148 0.437291
\(58\) −4.78767 −0.628652
\(59\) −13.9736 −1.81921 −0.909604 0.415477i \(-0.863615\pi\)
−0.909604 + 0.415477i \(0.863615\pi\)
\(60\) −0.734628 −0.0948401
\(61\) −6.74430 −0.863519 −0.431759 0.901989i \(-0.642107\pi\)
−0.431759 + 0.901989i \(0.642107\pi\)
\(62\) 2.20360 0.279858
\(63\) −2.84286 −0.358166
\(64\) 1.00000 0.125000
\(65\) 10.9581 1.35918
\(66\) −1.78451 −0.219658
\(67\) 13.8107 1.68725 0.843624 0.536935i \(-0.180418\pi\)
0.843624 + 0.536935i \(0.180418\pi\)
\(68\) −7.27375 −0.882071
\(69\) 1.83545 0.220962
\(70\) 1.85319 0.221498
\(71\) 2.79743 0.331994 0.165997 0.986126i \(-0.446916\pi\)
0.165997 + 0.986126i \(0.446916\pi\)
\(72\) 2.84286 0.335034
\(73\) −7.79200 −0.911984 −0.455992 0.889984i \(-0.650715\pi\)
−0.455992 + 0.889984i \(0.650715\pi\)
\(74\) −4.81524 −0.559760
\(75\) −0.620660 −0.0716677
\(76\) 8.32838 0.955330
\(77\) 4.50165 0.513011
\(78\) 2.34403 0.265409
\(79\) −5.54692 −0.624077 −0.312039 0.950069i \(-0.601012\pi\)
−0.312039 + 0.950069i \(0.601012\pi\)
\(80\) −1.85319 −0.207193
\(81\) 7.61040 0.845601
\(82\) −0.513367 −0.0566919
\(83\) 16.1813 1.77613 0.888065 0.459718i \(-0.152050\pi\)
0.888065 + 0.459718i \(0.152050\pi\)
\(84\) 0.396413 0.0432522
\(85\) 13.4796 1.46207
\(86\) 9.72662 1.04885
\(87\) 1.89789 0.203476
\(88\) −4.50165 −0.479878
\(89\) −3.71243 −0.393517 −0.196758 0.980452i \(-0.563041\pi\)
−0.196758 + 0.980452i \(0.563041\pi\)
\(90\) −5.26835 −0.555333
\(91\) −5.91310 −0.619861
\(92\) 4.63014 0.482726
\(93\) −0.873537 −0.0905816
\(94\) 2.59821 0.267985
\(95\) −15.4341 −1.58350
\(96\) −0.396413 −0.0404587
\(97\) −13.5994 −1.38081 −0.690406 0.723422i \(-0.742568\pi\)
−0.690406 + 0.723422i \(0.742568\pi\)
\(98\) −1.00000 −0.101015
\(99\) −12.7976 −1.28620
\(100\) −1.56569 −0.156569
\(101\) 9.17375 0.912822 0.456411 0.889769i \(-0.349135\pi\)
0.456411 + 0.889769i \(0.349135\pi\)
\(102\) 2.88341 0.285500
\(103\) 4.11643 0.405604 0.202802 0.979220i \(-0.434995\pi\)
0.202802 + 0.979220i \(0.434995\pi\)
\(104\) 5.91310 0.579827
\(105\) −0.734628 −0.0716924
\(106\) −0.359603 −0.0349278
\(107\) 0.279089 0.0269806 0.0134903 0.999909i \(-0.495706\pi\)
0.0134903 + 0.999909i \(0.495706\pi\)
\(108\) −2.31618 −0.222875
\(109\) 18.3186 1.75460 0.877300 0.479943i \(-0.159343\pi\)
0.877300 + 0.479943i \(0.159343\pi\)
\(110\) 8.34241 0.795418
\(111\) 1.90882 0.181177
\(112\) 1.00000 0.0944911
\(113\) 0.364997 0.0343360 0.0171680 0.999853i \(-0.494535\pi\)
0.0171680 + 0.999853i \(0.494535\pi\)
\(114\) −3.30148 −0.309212
\(115\) −8.58053 −0.800138
\(116\) 4.78767 0.444524
\(117\) 16.8101 1.55409
\(118\) 13.9736 1.28637
\(119\) −7.27375 −0.666783
\(120\) 0.734628 0.0670621
\(121\) 9.26489 0.842262
\(122\) 6.74430 0.610600
\(123\) 0.203505 0.0183495
\(124\) −2.20360 −0.197890
\(125\) 12.1675 1.08829
\(126\) 2.84286 0.253262
\(127\) −6.00997 −0.533299 −0.266649 0.963794i \(-0.585917\pi\)
−0.266649 + 0.963794i \(0.585917\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.85576 −0.339481
\(130\) −10.9581 −0.961088
\(131\) 20.2084 1.76562 0.882808 0.469735i \(-0.155650\pi\)
0.882808 + 0.469735i \(0.155650\pi\)
\(132\) 1.78451 0.155322
\(133\) 8.32838 0.722162
\(134\) −13.8107 −1.19306
\(135\) 4.29233 0.369425
\(136\) 7.27375 0.623719
\(137\) 12.4323 1.06216 0.531082 0.847320i \(-0.321786\pi\)
0.531082 + 0.847320i \(0.321786\pi\)
\(138\) −1.83545 −0.156244
\(139\) 2.95241 0.250420 0.125210 0.992130i \(-0.460040\pi\)
0.125210 + 0.992130i \(0.460040\pi\)
\(140\) −1.85319 −0.156623
\(141\) −1.02996 −0.0867385
\(142\) −2.79743 −0.234755
\(143\) −26.6187 −2.22597
\(144\) −2.84286 −0.236905
\(145\) −8.87245 −0.736817
\(146\) 7.79200 0.644870
\(147\) 0.396413 0.0326956
\(148\) 4.81524 0.395810
\(149\) 2.62018 0.214653 0.107327 0.994224i \(-0.465771\pi\)
0.107327 + 0.994224i \(0.465771\pi\)
\(150\) 0.620660 0.0506767
\(151\) −8.04927 −0.655041 −0.327520 0.944844i \(-0.606213\pi\)
−0.327520 + 0.944844i \(0.606213\pi\)
\(152\) −8.32838 −0.675521
\(153\) 20.6782 1.67173
\(154\) −4.50165 −0.362754
\(155\) 4.08369 0.328010
\(156\) −2.34403 −0.187672
\(157\) 12.2632 0.978707 0.489354 0.872085i \(-0.337233\pi\)
0.489354 + 0.872085i \(0.337233\pi\)
\(158\) 5.54692 0.441289
\(159\) 0.142551 0.0113051
\(160\) 1.85319 0.146507
\(161\) 4.63014 0.364906
\(162\) −7.61040 −0.597930
\(163\) 13.3927 1.04899 0.524497 0.851413i \(-0.324254\pi\)
0.524497 + 0.851413i \(0.324254\pi\)
\(164\) 0.513367 0.0400872
\(165\) −3.30704 −0.257453
\(166\) −16.1813 −1.25591
\(167\) −11.5887 −0.896761 −0.448380 0.893843i \(-0.647999\pi\)
−0.448380 + 0.893843i \(0.647999\pi\)
\(168\) −0.396413 −0.0305839
\(169\) 21.9647 1.68959
\(170\) −13.4796 −1.03384
\(171\) −23.6764 −1.81058
\(172\) −9.72662 −0.741648
\(173\) −9.41841 −0.716068 −0.358034 0.933709i \(-0.616553\pi\)
−0.358034 + 0.933709i \(0.616553\pi\)
\(174\) −1.89789 −0.143879
\(175\) −1.56569 −0.118355
\(176\) 4.50165 0.339325
\(177\) −5.53931 −0.416360
\(178\) 3.71243 0.278258
\(179\) 7.68557 0.574447 0.287223 0.957864i \(-0.407268\pi\)
0.287223 + 0.957864i \(0.407268\pi\)
\(180\) 5.26835 0.392680
\(181\) 10.6450 0.791235 0.395618 0.918415i \(-0.370531\pi\)
0.395618 + 0.918415i \(0.370531\pi\)
\(182\) 5.91310 0.438308
\(183\) −2.67353 −0.197633
\(184\) −4.63014 −0.341339
\(185\) −8.92354 −0.656072
\(186\) 0.873537 0.0640509
\(187\) −32.7439 −2.39447
\(188\) −2.59821 −0.189494
\(189\) −2.31618 −0.168478
\(190\) 15.4341 1.11970
\(191\) −13.7742 −0.996664 −0.498332 0.866986i \(-0.666054\pi\)
−0.498332 + 0.866986i \(0.666054\pi\)
\(192\) 0.396413 0.0286086
\(193\) −24.8018 −1.78527 −0.892637 0.450776i \(-0.851147\pi\)
−0.892637 + 0.450776i \(0.851147\pi\)
\(194\) 13.5994 0.976381
\(195\) 4.34393 0.311075
\(196\) 1.00000 0.0714286
\(197\) −14.4839 −1.03194 −0.515969 0.856607i \(-0.672568\pi\)
−0.515969 + 0.856607i \(0.672568\pi\)
\(198\) 12.7976 0.909483
\(199\) 2.67035 0.189296 0.0946482 0.995511i \(-0.469827\pi\)
0.0946482 + 0.995511i \(0.469827\pi\)
\(200\) 1.56569 0.110711
\(201\) 5.47475 0.386159
\(202\) −9.17375 −0.645462
\(203\) 4.78767 0.336028
\(204\) −2.88341 −0.201879
\(205\) −0.951366 −0.0664463
\(206\) −4.11643 −0.286805
\(207\) −13.1628 −0.914880
\(208\) −5.91310 −0.410000
\(209\) 37.4915 2.59334
\(210\) 0.734628 0.0506942
\(211\) 8.51835 0.586427 0.293214 0.956047i \(-0.405275\pi\)
0.293214 + 0.956047i \(0.405275\pi\)
\(212\) 0.359603 0.0246977
\(213\) 1.10894 0.0759833
\(214\) −0.279089 −0.0190781
\(215\) 18.0253 1.22931
\(216\) 2.31618 0.157596
\(217\) −2.20360 −0.149590
\(218\) −18.3186 −1.24069
\(219\) −3.08885 −0.208725
\(220\) −8.34241 −0.562445
\(221\) 43.0104 2.89319
\(222\) −1.90882 −0.128112
\(223\) −3.39491 −0.227340 −0.113670 0.993519i \(-0.536261\pi\)
−0.113670 + 0.993519i \(0.536261\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 4.45104 0.296736
\(226\) −0.364997 −0.0242792
\(227\) 17.3804 1.15358 0.576789 0.816893i \(-0.304306\pi\)
0.576789 + 0.816893i \(0.304306\pi\)
\(228\) 3.30148 0.218646
\(229\) −18.7849 −1.24134 −0.620670 0.784072i \(-0.713139\pi\)
−0.620670 + 0.784072i \(0.713139\pi\)
\(230\) 8.58053 0.565783
\(231\) 1.78451 0.117412
\(232\) −4.78767 −0.314326
\(233\) 15.2182 0.996976 0.498488 0.866897i \(-0.333889\pi\)
0.498488 + 0.866897i \(0.333889\pi\)
\(234\) −16.8101 −1.09891
\(235\) 4.81497 0.314094
\(236\) −13.9736 −0.909604
\(237\) −2.19887 −0.142832
\(238\) 7.27375 0.471487
\(239\) 24.4542 1.58181 0.790906 0.611937i \(-0.209610\pi\)
0.790906 + 0.611937i \(0.209610\pi\)
\(240\) −0.734628 −0.0474200
\(241\) 26.0041 1.67507 0.837536 0.546382i \(-0.183995\pi\)
0.837536 + 0.546382i \(0.183995\pi\)
\(242\) −9.26489 −0.595570
\(243\) 9.96542 0.639282
\(244\) −6.74430 −0.431759
\(245\) −1.85319 −0.118396
\(246\) −0.203505 −0.0129750
\(247\) −49.2465 −3.13348
\(248\) 2.20360 0.139929
\(249\) 6.41448 0.406501
\(250\) −12.1675 −0.769538
\(251\) 13.0731 0.825168 0.412584 0.910920i \(-0.364626\pi\)
0.412584 + 0.910920i \(0.364626\pi\)
\(252\) −2.84286 −0.179083
\(253\) 20.8433 1.31041
\(254\) 6.00997 0.377099
\(255\) 5.34350 0.334623
\(256\) 1.00000 0.0625000
\(257\) 3.55008 0.221448 0.110724 0.993851i \(-0.464683\pi\)
0.110724 + 0.993851i \(0.464683\pi\)
\(258\) 3.85576 0.240049
\(259\) 4.81524 0.299204
\(260\) 10.9581 0.679592
\(261\) −13.6107 −0.842478
\(262\) −20.2084 −1.24848
\(263\) 21.7902 1.34364 0.671820 0.740714i \(-0.265513\pi\)
0.671820 + 0.740714i \(0.265513\pi\)
\(264\) −1.78451 −0.109829
\(265\) −0.666413 −0.0409374
\(266\) −8.32838 −0.510646
\(267\) −1.47165 −0.0900638
\(268\) 13.8107 0.843624
\(269\) 25.2657 1.54048 0.770238 0.637756i \(-0.220137\pi\)
0.770238 + 0.637756i \(0.220137\pi\)
\(270\) −4.29233 −0.261223
\(271\) −25.3538 −1.54013 −0.770067 0.637963i \(-0.779777\pi\)
−0.770067 + 0.637963i \(0.779777\pi\)
\(272\) −7.27375 −0.441036
\(273\) −2.34403 −0.141867
\(274\) −12.4323 −0.751063
\(275\) −7.04820 −0.425023
\(276\) 1.83545 0.110481
\(277\) 18.4191 1.10670 0.553348 0.832950i \(-0.313350\pi\)
0.553348 + 0.832950i \(0.313350\pi\)
\(278\) −2.95241 −0.177074
\(279\) 6.26453 0.375048
\(280\) 1.85319 0.110749
\(281\) 18.5363 1.10578 0.552892 0.833253i \(-0.313524\pi\)
0.552892 + 0.833253i \(0.313524\pi\)
\(282\) 1.02996 0.0613334
\(283\) −25.6547 −1.52502 −0.762508 0.646979i \(-0.776032\pi\)
−0.762508 + 0.646979i \(0.776032\pi\)
\(284\) 2.79743 0.165997
\(285\) −6.11826 −0.362414
\(286\) 26.6187 1.57400
\(287\) 0.513367 0.0303031
\(288\) 2.84286 0.167517
\(289\) 35.9074 2.11220
\(290\) 8.87245 0.521008
\(291\) −5.39099 −0.316025
\(292\) −7.79200 −0.455992
\(293\) −14.1525 −0.826795 −0.413398 0.910551i \(-0.635658\pi\)
−0.413398 + 0.910551i \(0.635658\pi\)
\(294\) −0.396413 −0.0231193
\(295\) 25.8957 1.50771
\(296\) −4.81524 −0.279880
\(297\) −10.4267 −0.605016
\(298\) −2.62018 −0.151783
\(299\) −27.3785 −1.58334
\(300\) −0.620660 −0.0358339
\(301\) −9.72662 −0.560633
\(302\) 8.04927 0.463184
\(303\) 3.63659 0.208917
\(304\) 8.32838 0.477665
\(305\) 12.4985 0.715660
\(306\) −20.6782 −1.18209
\(307\) 19.9849 1.14060 0.570299 0.821437i \(-0.306827\pi\)
0.570299 + 0.821437i \(0.306827\pi\)
\(308\) 4.50165 0.256506
\(309\) 1.63181 0.0928302
\(310\) −4.08369 −0.231938
\(311\) 6.95173 0.394197 0.197098 0.980384i \(-0.436848\pi\)
0.197098 + 0.980384i \(0.436848\pi\)
\(312\) 2.34403 0.132704
\(313\) −34.7474 −1.96404 −0.982021 0.188773i \(-0.939549\pi\)
−0.982021 + 0.188773i \(0.939549\pi\)
\(314\) −12.2632 −0.692050
\(315\) 5.26835 0.296838
\(316\) −5.54692 −0.312039
\(317\) 12.2511 0.688089 0.344045 0.938953i \(-0.388203\pi\)
0.344045 + 0.938953i \(0.388203\pi\)
\(318\) −0.142551 −0.00799389
\(319\) 21.5524 1.20670
\(320\) −1.85319 −0.103596
\(321\) 0.110635 0.00617502
\(322\) −4.63014 −0.258028
\(323\) −60.5785 −3.37068
\(324\) 7.61040 0.422800
\(325\) 9.25809 0.513546
\(326\) −13.3927 −0.741750
\(327\) 7.26171 0.401574
\(328\) −0.513367 −0.0283460
\(329\) −2.59821 −0.143244
\(330\) 3.30704 0.182047
\(331\) −29.8082 −1.63841 −0.819203 0.573504i \(-0.805584\pi\)
−0.819203 + 0.573504i \(0.805584\pi\)
\(332\) 16.1813 0.888065
\(333\) −13.6890 −0.750154
\(334\) 11.5887 0.634106
\(335\) −25.5939 −1.39834
\(336\) 0.396413 0.0216261
\(337\) 19.7025 1.07326 0.536632 0.843817i \(-0.319697\pi\)
0.536632 + 0.843817i \(0.319697\pi\)
\(338\) −21.9647 −1.19472
\(339\) 0.144690 0.00785846
\(340\) 13.4796 0.731035
\(341\) −9.91986 −0.537191
\(342\) 23.6764 1.28027
\(343\) 1.00000 0.0539949
\(344\) 9.72662 0.524424
\(345\) −3.40143 −0.183127
\(346\) 9.41841 0.506337
\(347\) −22.8987 −1.22927 −0.614634 0.788812i \(-0.710696\pi\)
−0.614634 + 0.788812i \(0.710696\pi\)
\(348\) 1.89789 0.101738
\(349\) 18.5304 0.991907 0.495954 0.868349i \(-0.334819\pi\)
0.495954 + 0.868349i \(0.334819\pi\)
\(350\) 1.56569 0.0836897
\(351\) 13.6958 0.731029
\(352\) −4.50165 −0.239939
\(353\) 4.38016 0.233132 0.116566 0.993183i \(-0.462811\pi\)
0.116566 + 0.993183i \(0.462811\pi\)
\(354\) 5.53931 0.294411
\(355\) −5.18417 −0.275147
\(356\) −3.71243 −0.196758
\(357\) −2.88341 −0.152606
\(358\) −7.68557 −0.406195
\(359\) 7.23830 0.382023 0.191011 0.981588i \(-0.438823\pi\)
0.191011 + 0.981588i \(0.438823\pi\)
\(360\) −5.26835 −0.277666
\(361\) 50.3619 2.65062
\(362\) −10.6450 −0.559488
\(363\) 3.67272 0.192768
\(364\) −5.91310 −0.309931
\(365\) 14.4400 0.755826
\(366\) 2.67353 0.139748
\(367\) 30.9515 1.61566 0.807828 0.589418i \(-0.200643\pi\)
0.807828 + 0.589418i \(0.200643\pi\)
\(368\) 4.63014 0.241363
\(369\) −1.45943 −0.0759749
\(370\) 8.92354 0.463913
\(371\) 0.359603 0.0186697
\(372\) −0.873537 −0.0452908
\(373\) −6.41367 −0.332087 −0.166043 0.986118i \(-0.553099\pi\)
−0.166043 + 0.986118i \(0.553099\pi\)
\(374\) 32.7439 1.69315
\(375\) 4.82334 0.249076
\(376\) 2.59821 0.133992
\(377\) −28.3099 −1.45804
\(378\) 2.31618 0.119132
\(379\) 33.8537 1.73895 0.869474 0.493979i \(-0.164458\pi\)
0.869474 + 0.493979i \(0.164458\pi\)
\(380\) −15.4341 −0.791750
\(381\) −2.38243 −0.122056
\(382\) 13.7742 0.704748
\(383\) 31.4277 1.60588 0.802941 0.596059i \(-0.203268\pi\)
0.802941 + 0.596059i \(0.203268\pi\)
\(384\) −0.396413 −0.0202294
\(385\) −8.34241 −0.425169
\(386\) 24.8018 1.26238
\(387\) 27.6514 1.40560
\(388\) −13.5994 −0.690406
\(389\) 16.4239 0.832723 0.416362 0.909199i \(-0.363305\pi\)
0.416362 + 0.909199i \(0.363305\pi\)
\(390\) −4.34393 −0.219963
\(391\) −33.6785 −1.70319
\(392\) −1.00000 −0.0505076
\(393\) 8.01087 0.404095
\(394\) 14.4839 0.729691
\(395\) 10.2795 0.517217
\(396\) −12.7976 −0.643101
\(397\) −13.5998 −0.682553 −0.341277 0.939963i \(-0.610859\pi\)
−0.341277 + 0.939963i \(0.610859\pi\)
\(398\) −2.67035 −0.133853
\(399\) 3.30148 0.165281
\(400\) −1.56569 −0.0782846
\(401\) 10.9174 0.545188 0.272594 0.962129i \(-0.412118\pi\)
0.272594 + 0.962129i \(0.412118\pi\)
\(402\) −5.47475 −0.273056
\(403\) 13.0301 0.649077
\(404\) 9.17375 0.456411
\(405\) −14.1035 −0.700809
\(406\) −4.78767 −0.237608
\(407\) 21.6765 1.07447
\(408\) 2.88341 0.142750
\(409\) 3.69620 0.182765 0.0913827 0.995816i \(-0.470871\pi\)
0.0913827 + 0.995816i \(0.470871\pi\)
\(410\) 0.951366 0.0469846
\(411\) 4.92833 0.243097
\(412\) 4.11643 0.202802
\(413\) −13.9736 −0.687596
\(414\) 13.1628 0.646918
\(415\) −29.9870 −1.47200
\(416\) 5.91310 0.289913
\(417\) 1.17037 0.0573134
\(418\) −37.4915 −1.83377
\(419\) 15.6733 0.765692 0.382846 0.923812i \(-0.374944\pi\)
0.382846 + 0.923812i \(0.374944\pi\)
\(420\) −0.734628 −0.0358462
\(421\) −8.12216 −0.395850 −0.197925 0.980217i \(-0.563420\pi\)
−0.197925 + 0.980217i \(0.563420\pi\)
\(422\) −8.51835 −0.414667
\(423\) 7.38633 0.359136
\(424\) −0.359603 −0.0174639
\(425\) 11.3884 0.552421
\(426\) −1.10894 −0.0537283
\(427\) −6.74430 −0.326379
\(428\) 0.279089 0.0134903
\(429\) −10.5520 −0.509456
\(430\) −18.0253 −0.869256
\(431\) −1.00000 −0.0481683
\(432\) −2.31618 −0.111437
\(433\) 22.6687 1.08939 0.544693 0.838635i \(-0.316646\pi\)
0.544693 + 0.838635i \(0.316646\pi\)
\(434\) 2.20360 0.105776
\(435\) −3.51716 −0.168635
\(436\) 18.3186 0.877300
\(437\) 38.5616 1.84465
\(438\) 3.08885 0.147591
\(439\) −9.28641 −0.443216 −0.221608 0.975136i \(-0.571131\pi\)
−0.221608 + 0.975136i \(0.571131\pi\)
\(440\) 8.34241 0.397709
\(441\) −2.84286 −0.135374
\(442\) −43.0104 −2.04579
\(443\) −34.2337 −1.62649 −0.813245 0.581922i \(-0.802301\pi\)
−0.813245 + 0.581922i \(0.802301\pi\)
\(444\) 1.90882 0.0905887
\(445\) 6.87983 0.326135
\(446\) 3.39491 0.160754
\(447\) 1.03867 0.0491275
\(448\) 1.00000 0.0472456
\(449\) −16.4904 −0.778231 −0.389116 0.921189i \(-0.627219\pi\)
−0.389116 + 0.921189i \(0.627219\pi\)
\(450\) −4.45104 −0.209824
\(451\) 2.31100 0.108821
\(452\) 0.364997 0.0171680
\(453\) −3.19084 −0.149919
\(454\) −17.3804 −0.815702
\(455\) 10.9581 0.513723
\(456\) −3.30148 −0.154606
\(457\) −28.1687 −1.31768 −0.658838 0.752284i \(-0.728952\pi\)
−0.658838 + 0.752284i \(0.728952\pi\)
\(458\) 18.7849 0.877760
\(459\) 16.8473 0.786366
\(460\) −8.58053 −0.400069
\(461\) −16.2469 −0.756692 −0.378346 0.925664i \(-0.623507\pi\)
−0.378346 + 0.925664i \(0.623507\pi\)
\(462\) −1.78451 −0.0830231
\(463\) 28.9035 1.34326 0.671629 0.740888i \(-0.265595\pi\)
0.671629 + 0.740888i \(0.265595\pi\)
\(464\) 4.78767 0.222262
\(465\) 1.61883 0.0750714
\(466\) −15.2182 −0.704969
\(467\) −6.68344 −0.309273 −0.154636 0.987971i \(-0.549421\pi\)
−0.154636 + 0.987971i \(0.549421\pi\)
\(468\) 16.8101 0.777047
\(469\) 13.8107 0.637720
\(470\) −4.81497 −0.222098
\(471\) 4.86128 0.223996
\(472\) 13.9736 0.643187
\(473\) −43.7859 −2.01328
\(474\) 2.19887 0.100998
\(475\) −13.0397 −0.598301
\(476\) −7.27375 −0.333392
\(477\) −1.02230 −0.0468079
\(478\) −24.4542 −1.11851
\(479\) −27.5978 −1.26098 −0.630488 0.776199i \(-0.717145\pi\)
−0.630488 + 0.776199i \(0.717145\pi\)
\(480\) 0.734628 0.0335310
\(481\) −28.4730 −1.29826
\(482\) −26.0041 −1.18445
\(483\) 1.83545 0.0835158
\(484\) 9.26489 0.421131
\(485\) 25.2023 1.14438
\(486\) −9.96542 −0.452040
\(487\) −20.2647 −0.918281 −0.459140 0.888364i \(-0.651843\pi\)
−0.459140 + 0.888364i \(0.651843\pi\)
\(488\) 6.74430 0.305300
\(489\) 5.30902 0.240082
\(490\) 1.85319 0.0837185
\(491\) 28.2429 1.27458 0.637291 0.770623i \(-0.280055\pi\)
0.637291 + 0.770623i \(0.280055\pi\)
\(492\) 0.203505 0.00917473
\(493\) −34.8243 −1.56841
\(494\) 49.2465 2.21570
\(495\) 23.7163 1.06597
\(496\) −2.20360 −0.0989448
\(497\) 2.79743 0.125482
\(498\) −6.41448 −0.287440
\(499\) 20.0006 0.895351 0.447675 0.894196i \(-0.352252\pi\)
0.447675 + 0.894196i \(0.352252\pi\)
\(500\) 12.1675 0.544146
\(501\) −4.59391 −0.205241
\(502\) −13.0731 −0.583482
\(503\) 33.7244 1.50370 0.751848 0.659337i \(-0.229163\pi\)
0.751848 + 0.659337i \(0.229163\pi\)
\(504\) 2.84286 0.126631
\(505\) −17.0007 −0.756520
\(506\) −20.8433 −0.926597
\(507\) 8.70710 0.386696
\(508\) −6.00997 −0.266649
\(509\) 22.5708 1.00043 0.500217 0.865900i \(-0.333253\pi\)
0.500217 + 0.865900i \(0.333253\pi\)
\(510\) −5.34350 −0.236614
\(511\) −7.79200 −0.344698
\(512\) −1.00000 −0.0441942
\(513\) −19.2901 −0.851677
\(514\) −3.55008 −0.156587
\(515\) −7.62852 −0.336153
\(516\) −3.85576 −0.169740
\(517\) −11.6962 −0.514399
\(518\) −4.81524 −0.211569
\(519\) −3.73358 −0.163886
\(520\) −10.9581 −0.480544
\(521\) −9.29541 −0.407239 −0.203620 0.979050i \(-0.565271\pi\)
−0.203620 + 0.979050i \(0.565271\pi\)
\(522\) 13.6107 0.595722
\(523\) −2.04093 −0.0892437 −0.0446219 0.999004i \(-0.514208\pi\)
−0.0446219 + 0.999004i \(0.514208\pi\)
\(524\) 20.2084 0.882808
\(525\) −0.620660 −0.0270878
\(526\) −21.7902 −0.950097
\(527\) 16.0285 0.698211
\(528\) 1.78451 0.0776610
\(529\) −1.56179 −0.0679040
\(530\) 0.666413 0.0289471
\(531\) 39.7249 1.72392
\(532\) 8.32838 0.361081
\(533\) −3.03559 −0.131486
\(534\) 1.47165 0.0636847
\(535\) −0.517205 −0.0223607
\(536\) −13.8107 −0.596532
\(537\) 3.04666 0.131473
\(538\) −25.2657 −1.08928
\(539\) 4.50165 0.193900
\(540\) 4.29233 0.184712
\(541\) 9.48686 0.407872 0.203936 0.978984i \(-0.434627\pi\)
0.203936 + 0.978984i \(0.434627\pi\)
\(542\) 25.3538 1.08904
\(543\) 4.21981 0.181089
\(544\) 7.27375 0.311859
\(545\) −33.9477 −1.45416
\(546\) 2.34403 0.100315
\(547\) 14.6635 0.626964 0.313482 0.949594i \(-0.398504\pi\)
0.313482 + 0.949594i \(0.398504\pi\)
\(548\) 12.4323 0.531082
\(549\) 19.1731 0.818287
\(550\) 7.04820 0.300536
\(551\) 39.8735 1.69867
\(552\) −1.83545 −0.0781219
\(553\) −5.54692 −0.235879
\(554\) −18.4191 −0.782553
\(555\) −3.53741 −0.150155
\(556\) 2.95241 0.125210
\(557\) −15.3489 −0.650353 −0.325176 0.945653i \(-0.605424\pi\)
−0.325176 + 0.945653i \(0.605424\pi\)
\(558\) −6.26453 −0.265199
\(559\) 57.5145 2.43260
\(560\) −1.85319 −0.0783115
\(561\) −12.9801 −0.548020
\(562\) −18.5363 −0.781907
\(563\) 34.7976 1.46654 0.733271 0.679936i \(-0.237993\pi\)
0.733271 + 0.679936i \(0.237993\pi\)
\(564\) −1.02996 −0.0433693
\(565\) −0.676408 −0.0284567
\(566\) 25.6547 1.07835
\(567\) 7.61040 0.319607
\(568\) −2.79743 −0.117378
\(569\) −22.8252 −0.956881 −0.478441 0.878120i \(-0.658798\pi\)
−0.478441 + 0.878120i \(0.658798\pi\)
\(570\) 6.11826 0.256266
\(571\) −18.6595 −0.780875 −0.390437 0.920630i \(-0.627676\pi\)
−0.390437 + 0.920630i \(0.627676\pi\)
\(572\) −26.6187 −1.11298
\(573\) −5.46026 −0.228106
\(574\) −0.513367 −0.0214275
\(575\) −7.24937 −0.302320
\(576\) −2.84286 −0.118452
\(577\) −24.7924 −1.03212 −0.516061 0.856552i \(-0.672602\pi\)
−0.516061 + 0.856552i \(0.672602\pi\)
\(578\) −35.9074 −1.49355
\(579\) −9.83176 −0.408594
\(580\) −8.87245 −0.368409
\(581\) 16.1813 0.671314
\(582\) 5.39099 0.223464
\(583\) 1.61881 0.0670442
\(584\) 7.79200 0.322435
\(585\) −31.1523 −1.28799
\(586\) 14.1525 0.584633
\(587\) 31.6830 1.30770 0.653849 0.756625i \(-0.273153\pi\)
0.653849 + 0.756625i \(0.273153\pi\)
\(588\) 0.396413 0.0163478
\(589\) −18.3524 −0.756199
\(590\) −25.8957 −1.06611
\(591\) −5.74163 −0.236179
\(592\) 4.81524 0.197905
\(593\) 11.0718 0.454665 0.227332 0.973817i \(-0.427000\pi\)
0.227332 + 0.973817i \(0.427000\pi\)
\(594\) 10.4267 0.427811
\(595\) 13.4796 0.552611
\(596\) 2.62018 0.107327
\(597\) 1.05856 0.0433241
\(598\) 27.3785 1.11959
\(599\) 7.47933 0.305597 0.152799 0.988257i \(-0.451171\pi\)
0.152799 + 0.988257i \(0.451171\pi\)
\(600\) 0.620660 0.0253384
\(601\) 4.47727 0.182632 0.0913158 0.995822i \(-0.470893\pi\)
0.0913158 + 0.995822i \(0.470893\pi\)
\(602\) 9.72662 0.396428
\(603\) −39.2619 −1.59887
\(604\) −8.04927 −0.327520
\(605\) −17.1696 −0.698043
\(606\) −3.63659 −0.147726
\(607\) 21.2494 0.862488 0.431244 0.902235i \(-0.358075\pi\)
0.431244 + 0.902235i \(0.358075\pi\)
\(608\) −8.32838 −0.337760
\(609\) 1.89789 0.0769065
\(610\) −12.4985 −0.506048
\(611\) 15.3634 0.621539
\(612\) 20.6782 0.835867
\(613\) 18.3626 0.741657 0.370828 0.928701i \(-0.379074\pi\)
0.370828 + 0.928701i \(0.379074\pi\)
\(614\) −19.9849 −0.806525
\(615\) −0.377134 −0.0152075
\(616\) −4.50165 −0.181377
\(617\) 13.3137 0.535988 0.267994 0.963421i \(-0.413639\pi\)
0.267994 + 0.963421i \(0.413639\pi\)
\(618\) −1.63181 −0.0656409
\(619\) −30.6216 −1.23078 −0.615392 0.788221i \(-0.711002\pi\)
−0.615392 + 0.788221i \(0.711002\pi\)
\(620\) 4.08369 0.164005
\(621\) −10.7243 −0.430350
\(622\) −6.95173 −0.278739
\(623\) −3.71243 −0.148735
\(624\) −2.34403 −0.0938362
\(625\) −14.7202 −0.588806
\(626\) 34.7474 1.38879
\(627\) 14.8621 0.593535
\(628\) 12.2632 0.489354
\(629\) −35.0248 −1.39653
\(630\) −5.26835 −0.209896
\(631\) −15.3971 −0.612948 −0.306474 0.951879i \(-0.599149\pi\)
−0.306474 + 0.951879i \(0.599149\pi\)
\(632\) 5.54692 0.220645
\(633\) 3.37678 0.134215
\(634\) −12.2511 −0.486552
\(635\) 11.1376 0.441983
\(636\) 0.142551 0.00565253
\(637\) −5.91310 −0.234285
\(638\) −21.5524 −0.853269
\(639\) −7.95270 −0.314604
\(640\) 1.85319 0.0732537
\(641\) −22.8879 −0.904016 −0.452008 0.892014i \(-0.649292\pi\)
−0.452008 + 0.892014i \(0.649292\pi\)
\(642\) −0.110635 −0.00436640
\(643\) −1.91750 −0.0756189 −0.0378095 0.999285i \(-0.512038\pi\)
−0.0378095 + 0.999285i \(0.512038\pi\)
\(644\) 4.63014 0.182453
\(645\) 7.14545 0.281352
\(646\) 60.5785 2.38343
\(647\) −2.59839 −0.102153 −0.0510767 0.998695i \(-0.516265\pi\)
−0.0510767 + 0.998695i \(0.516265\pi\)
\(648\) −7.61040 −0.298965
\(649\) −62.9043 −2.46921
\(650\) −9.25809 −0.363132
\(651\) −0.873537 −0.0342366
\(652\) 13.3927 0.524497
\(653\) 5.61564 0.219757 0.109878 0.993945i \(-0.464954\pi\)
0.109878 + 0.993945i \(0.464954\pi\)
\(654\) −7.26171 −0.283955
\(655\) −37.4500 −1.46329
\(656\) 0.513367 0.0200436
\(657\) 22.1515 0.864214
\(658\) 2.59821 0.101289
\(659\) 12.4802 0.486160 0.243080 0.970006i \(-0.421842\pi\)
0.243080 + 0.970006i \(0.421842\pi\)
\(660\) −3.30704 −0.128726
\(661\) 49.7759 1.93606 0.968028 0.250842i \(-0.0807074\pi\)
0.968028 + 0.250842i \(0.0807074\pi\)
\(662\) 29.8082 1.15853
\(663\) 17.0499 0.662162
\(664\) −16.1813 −0.627957
\(665\) −15.4341 −0.598507
\(666\) 13.6890 0.530439
\(667\) 22.1676 0.858332
\(668\) −11.5887 −0.448380
\(669\) −1.34579 −0.0520311
\(670\) 25.5939 0.988777
\(671\) −30.3605 −1.17205
\(672\) −0.396413 −0.0152920
\(673\) 11.8038 0.455002 0.227501 0.973778i \(-0.426945\pi\)
0.227501 + 0.973778i \(0.426945\pi\)
\(674\) −19.7025 −0.758912
\(675\) 3.62643 0.139581
\(676\) 21.9647 0.844797
\(677\) 30.0895 1.15643 0.578217 0.815883i \(-0.303749\pi\)
0.578217 + 0.815883i \(0.303749\pi\)
\(678\) −0.144690 −0.00555677
\(679\) −13.5994 −0.521898
\(680\) −13.4796 −0.516920
\(681\) 6.88981 0.264018
\(682\) 9.91986 0.379851
\(683\) −11.1270 −0.425763 −0.212881 0.977078i \(-0.568285\pi\)
−0.212881 + 0.977078i \(0.568285\pi\)
\(684\) −23.6764 −0.905289
\(685\) −23.0394 −0.880291
\(686\) −1.00000 −0.0381802
\(687\) −7.44658 −0.284105
\(688\) −9.72662 −0.370824
\(689\) −2.12637 −0.0810082
\(690\) 3.40143 0.129490
\(691\) −16.2487 −0.618128 −0.309064 0.951041i \(-0.600016\pi\)
−0.309064 + 0.951041i \(0.600016\pi\)
\(692\) −9.41841 −0.358034
\(693\) −12.7976 −0.486139
\(694\) 22.8987 0.869224
\(695\) −5.47137 −0.207541
\(696\) −1.89789 −0.0719395
\(697\) −3.73410 −0.141439
\(698\) −18.5304 −0.701384
\(699\) 6.03268 0.228177
\(700\) −1.56569 −0.0591776
\(701\) −4.16286 −0.157229 −0.0786146 0.996905i \(-0.525050\pi\)
−0.0786146 + 0.996905i \(0.525050\pi\)
\(702\) −13.6958 −0.516916
\(703\) 40.1031 1.51252
\(704\) 4.50165 0.169662
\(705\) 1.90872 0.0718864
\(706\) −4.38016 −0.164849
\(707\) 9.17375 0.345014
\(708\) −5.53931 −0.208180
\(709\) −18.9149 −0.710365 −0.355183 0.934797i \(-0.615581\pi\)
−0.355183 + 0.934797i \(0.615581\pi\)
\(710\) 5.18417 0.194559
\(711\) 15.7691 0.591388
\(712\) 3.71243 0.139129
\(713\) −10.2030 −0.382105
\(714\) 2.88341 0.107909
\(715\) 49.3295 1.84482
\(716\) 7.68557 0.287223
\(717\) 9.69397 0.362028
\(718\) −7.23830 −0.270131
\(719\) −21.3952 −0.797906 −0.398953 0.916971i \(-0.630626\pi\)
−0.398953 + 0.916971i \(0.630626\pi\)
\(720\) 5.26835 0.196340
\(721\) 4.11643 0.153304
\(722\) −50.3619 −1.87427
\(723\) 10.3084 0.383372
\(724\) 10.6450 0.395618
\(725\) −7.49601 −0.278395
\(726\) −3.67272 −0.136307
\(727\) 22.7888 0.845190 0.422595 0.906319i \(-0.361119\pi\)
0.422595 + 0.906319i \(0.361119\pi\)
\(728\) 5.91310 0.219154
\(729\) −18.8808 −0.699289
\(730\) −14.4400 −0.534450
\(731\) 70.7490 2.61675
\(732\) −2.67353 −0.0988164
\(733\) 7.70908 0.284741 0.142371 0.989813i \(-0.454527\pi\)
0.142371 + 0.989813i \(0.454527\pi\)
\(734\) −30.9515 −1.14244
\(735\) −0.734628 −0.0270972
\(736\) −4.63014 −0.170669
\(737\) 62.1711 2.29010
\(738\) 1.45943 0.0537223
\(739\) 15.0538 0.553762 0.276881 0.960904i \(-0.410699\pi\)
0.276881 + 0.960904i \(0.410699\pi\)
\(740\) −8.92354 −0.328036
\(741\) −19.5220 −0.717157
\(742\) −0.359603 −0.0132015
\(743\) 26.2891 0.964454 0.482227 0.876046i \(-0.339828\pi\)
0.482227 + 0.876046i \(0.339828\pi\)
\(744\) 0.873537 0.0320254
\(745\) −4.85568 −0.177898
\(746\) 6.41367 0.234821
\(747\) −46.0011 −1.68309
\(748\) −32.7439 −1.19723
\(749\) 0.279089 0.0101977
\(750\) −4.82334 −0.176124
\(751\) 38.5238 1.40575 0.702877 0.711311i \(-0.251898\pi\)
0.702877 + 0.711311i \(0.251898\pi\)
\(752\) −2.59821 −0.0947468
\(753\) 5.18235 0.188855
\(754\) 28.3099 1.03099
\(755\) 14.9168 0.542879
\(756\) −2.31618 −0.0842388
\(757\) −13.8897 −0.504828 −0.252414 0.967619i \(-0.581225\pi\)
−0.252414 + 0.967619i \(0.581225\pi\)
\(758\) −33.8537 −1.22962
\(759\) 8.26255 0.299912
\(760\) 15.4341 0.559852
\(761\) −33.8042 −1.22540 −0.612701 0.790315i \(-0.709917\pi\)
−0.612701 + 0.790315i \(0.709917\pi\)
\(762\) 2.38243 0.0863063
\(763\) 18.3186 0.663176
\(764\) −13.7742 −0.498332
\(765\) −38.3206 −1.38549
\(766\) −31.4277 −1.13553
\(767\) 82.6272 2.98350
\(768\) 0.396413 0.0143043
\(769\) −42.6134 −1.53668 −0.768340 0.640042i \(-0.778917\pi\)
−0.768340 + 0.640042i \(0.778917\pi\)
\(770\) 8.34241 0.300640
\(771\) 1.40730 0.0506826
\(772\) −24.8018 −0.892637
\(773\) 33.6637 1.21080 0.605399 0.795922i \(-0.293013\pi\)
0.605399 + 0.795922i \(0.293013\pi\)
\(774\) −27.6514 −0.993909
\(775\) 3.45017 0.123934
\(776\) 13.5994 0.488191
\(777\) 1.90882 0.0684786
\(778\) −16.4239 −0.588824
\(779\) 4.27552 0.153186
\(780\) 4.34393 0.155538
\(781\) 12.5931 0.450616
\(782\) 33.6785 1.20434
\(783\) −11.0891 −0.396293
\(784\) 1.00000 0.0357143
\(785\) −22.7260 −0.811124
\(786\) −8.01087 −0.285738
\(787\) 8.08015 0.288026 0.144013 0.989576i \(-0.453999\pi\)
0.144013 + 0.989576i \(0.453999\pi\)
\(788\) −14.4839 −0.515969
\(789\) 8.63791 0.307518
\(790\) −10.2795 −0.365728
\(791\) 0.364997 0.0129778
\(792\) 12.7976 0.454741
\(793\) 39.8797 1.41617
\(794\) 13.5998 0.482638
\(795\) −0.264175 −0.00936931
\(796\) 2.67035 0.0946482
\(797\) 46.4614 1.64575 0.822873 0.568225i \(-0.192370\pi\)
0.822873 + 0.568225i \(0.192370\pi\)
\(798\) −3.30148 −0.116871
\(799\) 18.8987 0.668588
\(800\) 1.56569 0.0553556
\(801\) 10.5539 0.372904
\(802\) −10.9174 −0.385506
\(803\) −35.0769 −1.23784
\(804\) 5.47475 0.193079
\(805\) −8.58053 −0.302424
\(806\) −13.0301 −0.458967
\(807\) 10.0157 0.352568
\(808\) −9.17375 −0.322731
\(809\) 36.1851 1.27220 0.636100 0.771607i \(-0.280547\pi\)
0.636100 + 0.771607i \(0.280547\pi\)
\(810\) 14.1035 0.495547
\(811\) −42.5480 −1.49406 −0.747031 0.664790i \(-0.768521\pi\)
−0.747031 + 0.664790i \(0.768521\pi\)
\(812\) 4.78767 0.168014
\(813\) −10.0506 −0.352489
\(814\) −21.6765 −0.759762
\(815\) −24.8191 −0.869375
\(816\) −2.88341 −0.100939
\(817\) −81.0070 −2.83408
\(818\) −3.69620 −0.129235
\(819\) 16.8101 0.587392
\(820\) −0.951366 −0.0332232
\(821\) 43.5049 1.51833 0.759166 0.650897i \(-0.225607\pi\)
0.759166 + 0.650897i \(0.225607\pi\)
\(822\) −4.92833 −0.171895
\(823\) −32.9144 −1.14732 −0.573661 0.819093i \(-0.694477\pi\)
−0.573661 + 0.819093i \(0.694477\pi\)
\(824\) −4.11643 −0.143403
\(825\) −2.79400 −0.0972745
\(826\) 13.9736 0.486204
\(827\) −3.23098 −0.112352 −0.0561761 0.998421i \(-0.517891\pi\)
−0.0561761 + 0.998421i \(0.517891\pi\)
\(828\) −13.1628 −0.457440
\(829\) −6.72134 −0.233442 −0.116721 0.993165i \(-0.537238\pi\)
−0.116721 + 0.993165i \(0.537238\pi\)
\(830\) 29.9870 1.04086
\(831\) 7.30157 0.253289
\(832\) −5.91310 −0.205000
\(833\) −7.27375 −0.252020
\(834\) −1.17037 −0.0405267
\(835\) 21.4761 0.743210
\(836\) 37.4915 1.29667
\(837\) 5.10395 0.176418
\(838\) −15.6733 −0.541426
\(839\) 38.7657 1.33834 0.669170 0.743110i \(-0.266650\pi\)
0.669170 + 0.743110i \(0.266650\pi\)
\(840\) 0.734628 0.0253471
\(841\) −6.07823 −0.209594
\(842\) 8.12216 0.279908
\(843\) 7.34803 0.253080
\(844\) 8.51835 0.293214
\(845\) −40.7048 −1.40029
\(846\) −7.38633 −0.253947
\(847\) 9.26489 0.318345
\(848\) 0.359603 0.0123488
\(849\) −10.1699 −0.349029
\(850\) −11.3884 −0.390620
\(851\) 22.2952 0.764270
\(852\) 1.10894 0.0379916
\(853\) −10.3735 −0.355182 −0.177591 0.984104i \(-0.556830\pi\)
−0.177591 + 0.984104i \(0.556830\pi\)
\(854\) 6.74430 0.230785
\(855\) 43.8768 1.50055
\(856\) −0.279089 −0.00953907
\(857\) −31.0956 −1.06221 −0.531103 0.847307i \(-0.678222\pi\)
−0.531103 + 0.847307i \(0.678222\pi\)
\(858\) 10.5520 0.360240
\(859\) 13.8503 0.472567 0.236284 0.971684i \(-0.424071\pi\)
0.236284 + 0.971684i \(0.424071\pi\)
\(860\) 18.0253 0.614657
\(861\) 0.203505 0.00693545
\(862\) 1.00000 0.0340601
\(863\) −43.7122 −1.48798 −0.743990 0.668191i \(-0.767069\pi\)
−0.743990 + 0.668191i \(0.767069\pi\)
\(864\) 2.31618 0.0787982
\(865\) 17.4541 0.593457
\(866\) −22.6687 −0.770312
\(867\) 14.2341 0.483417
\(868\) −2.20360 −0.0747952
\(869\) −24.9703 −0.847060
\(870\) 3.51716 0.119243
\(871\) −81.6641 −2.76708
\(872\) −18.3186 −0.620345
\(873\) 38.6612 1.30848
\(874\) −38.5616 −1.30436
\(875\) 12.1675 0.411335
\(876\) −3.08885 −0.104363
\(877\) 37.6783 1.27231 0.636153 0.771563i \(-0.280525\pi\)
0.636153 + 0.771563i \(0.280525\pi\)
\(878\) 9.28641 0.313401
\(879\) −5.61022 −0.189228
\(880\) −8.34241 −0.281223
\(881\) 34.8598 1.17446 0.587228 0.809421i \(-0.300219\pi\)
0.587228 + 0.809421i \(0.300219\pi\)
\(882\) 2.84286 0.0957240
\(883\) −27.9868 −0.941830 −0.470915 0.882178i \(-0.656076\pi\)
−0.470915 + 0.882178i \(0.656076\pi\)
\(884\) 43.0104 1.44660
\(885\) 10.2654 0.345067
\(886\) 34.2337 1.15010
\(887\) 37.6784 1.26512 0.632558 0.774513i \(-0.282005\pi\)
0.632558 + 0.774513i \(0.282005\pi\)
\(888\) −1.90882 −0.0640559
\(889\) −6.00997 −0.201568
\(890\) −6.87983 −0.230612
\(891\) 34.2594 1.14773
\(892\) −3.39491 −0.113670
\(893\) −21.6388 −0.724116
\(894\) −1.03867 −0.0347384
\(895\) −14.2428 −0.476085
\(896\) −1.00000 −0.0334077
\(897\) −10.8532 −0.362377
\(898\) 16.4904 0.550293
\(899\) −10.5501 −0.351866
\(900\) 4.45104 0.148368
\(901\) −2.61566 −0.0871404
\(902\) −2.31100 −0.0769479
\(903\) −3.85576 −0.128312
\(904\) −0.364997 −0.0121396
\(905\) −19.7272 −0.655753
\(906\) 3.19084 0.106008
\(907\) −16.3508 −0.542920 −0.271460 0.962450i \(-0.587506\pi\)
−0.271460 + 0.962450i \(0.587506\pi\)
\(908\) 17.3804 0.576789
\(909\) −26.0796 −0.865007
\(910\) −10.9581 −0.363257
\(911\) −30.0717 −0.996320 −0.498160 0.867085i \(-0.665991\pi\)
−0.498160 + 0.867085i \(0.665991\pi\)
\(912\) 3.30148 0.109323
\(913\) 72.8427 2.41074
\(914\) 28.1687 0.931738
\(915\) 4.95455 0.163792
\(916\) −18.7849 −0.620670
\(917\) 20.2084 0.667340
\(918\) −16.8473 −0.556045
\(919\) −0.935366 −0.0308549 −0.0154274 0.999881i \(-0.504911\pi\)
−0.0154274 + 0.999881i \(0.504911\pi\)
\(920\) 8.58053 0.282892
\(921\) 7.92227 0.261048
\(922\) 16.2469 0.535062
\(923\) −16.5415 −0.544470
\(924\) 1.78451 0.0587062
\(925\) −7.53918 −0.247887
\(926\) −28.9035 −0.949827
\(927\) −11.7024 −0.384358
\(928\) −4.78767 −0.157163
\(929\) 45.6012 1.49613 0.748063 0.663628i \(-0.230984\pi\)
0.748063 + 0.663628i \(0.230984\pi\)
\(930\) −1.61883 −0.0530835
\(931\) 8.32838 0.272952
\(932\) 15.2182 0.498488
\(933\) 2.75576 0.0902194
\(934\) 6.68344 0.218689
\(935\) 60.6806 1.98447
\(936\) −16.8101 −0.549455
\(937\) 4.53867 0.148272 0.0741359 0.997248i \(-0.476380\pi\)
0.0741359 + 0.997248i \(0.476380\pi\)
\(938\) −13.8107 −0.450936
\(939\) −13.7743 −0.449509
\(940\) 4.81497 0.157047
\(941\) −8.02901 −0.261738 −0.130869 0.991400i \(-0.541777\pi\)
−0.130869 + 0.991400i \(0.541777\pi\)
\(942\) −4.86128 −0.158389
\(943\) 2.37696 0.0774046
\(944\) −13.9736 −0.454802
\(945\) 4.29233 0.139629
\(946\) 43.7859 1.42360
\(947\) −32.5271 −1.05699 −0.528494 0.848937i \(-0.677243\pi\)
−0.528494 + 0.848937i \(0.677243\pi\)
\(948\) −2.19887 −0.0714160
\(949\) 46.0748 1.49565
\(950\) 13.0397 0.423063
\(951\) 4.85649 0.157482
\(952\) 7.27375 0.235743
\(953\) −10.7839 −0.349326 −0.174663 0.984628i \(-0.555884\pi\)
−0.174663 + 0.984628i \(0.555884\pi\)
\(954\) 1.02230 0.0330982
\(955\) 25.5261 0.826006
\(956\) 24.4542 0.790906
\(957\) 8.54366 0.276177
\(958\) 27.5978 0.891645
\(959\) 12.4323 0.401460
\(960\) −0.734628 −0.0237100
\(961\) −26.1441 −0.843359
\(962\) 28.4730 0.918005
\(963\) −0.793410 −0.0255673
\(964\) 26.0041 0.837536
\(965\) 45.9624 1.47958
\(966\) −1.83545 −0.0590546
\(967\) 42.1615 1.35582 0.677911 0.735144i \(-0.262886\pi\)
0.677911 + 0.735144i \(0.262886\pi\)
\(968\) −9.26489 −0.297785
\(969\) −24.0141 −0.771444
\(970\) −25.2023 −0.809197
\(971\) 32.8473 1.05412 0.527060 0.849828i \(-0.323294\pi\)
0.527060 + 0.849828i \(0.323294\pi\)
\(972\) 9.96542 0.319641
\(973\) 2.95241 0.0946498
\(974\) 20.2647 0.649323
\(975\) 3.67003 0.117535
\(976\) −6.74430 −0.215880
\(977\) 25.7780 0.824713 0.412356 0.911023i \(-0.364706\pi\)
0.412356 + 0.911023i \(0.364706\pi\)
\(978\) −5.30902 −0.169764
\(979\) −16.7121 −0.534120
\(980\) −1.85319 −0.0591979
\(981\) −52.0770 −1.66269
\(982\) −28.2429 −0.901266
\(983\) −60.6238 −1.93360 −0.966799 0.255539i \(-0.917747\pi\)
−0.966799 + 0.255539i \(0.917747\pi\)
\(984\) −0.203505 −0.00648752
\(985\) 26.8415 0.855241
\(986\) 34.8243 1.10903
\(987\) −1.02996 −0.0327841
\(988\) −49.2465 −1.56674
\(989\) −45.0356 −1.43205
\(990\) −23.7163 −0.753753
\(991\) −52.1518 −1.65666 −0.828328 0.560243i \(-0.810708\pi\)
−0.828328 + 0.560243i \(0.810708\pi\)
\(992\) 2.20360 0.0699645
\(993\) −11.8163 −0.374980
\(994\) −2.79743 −0.0887292
\(995\) −4.94867 −0.156883
\(996\) 6.41448 0.203251
\(997\) −19.0242 −0.602503 −0.301252 0.953545i \(-0.597404\pi\)
−0.301252 + 0.953545i \(0.597404\pi\)
\(998\) −20.0006 −0.633109
\(999\) −11.1530 −0.352864
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 6034.2.a.p.1.15 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6034.2.a.p.1.15 27 1.1 even 1 trivial