Properties

Label 8026.2.a.a.1.10
Level $8026$
Weight $2$
Character 8026.1
Self dual yes
Analytic conductor $64.088$
Analytic rank $1$
Dimension $71$
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] = [8026,2,Mod(1,8026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8026.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: \(64.0879326623\)
Analytic rank: \(1\)
Dimension: \(71\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 8026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.46200 q^{3} +1.00000 q^{4} -1.19890 q^{5} -2.46200 q^{6} +2.88631 q^{7} +1.00000 q^{8} +3.06146 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.46200 q^{3} +1.00000 q^{4} -1.19890 q^{5} -2.46200 q^{6} +2.88631 q^{7} +1.00000 q^{8} +3.06146 q^{9} -1.19890 q^{10} -4.46025 q^{11} -2.46200 q^{12} +2.03184 q^{13} +2.88631 q^{14} +2.95169 q^{15} +1.00000 q^{16} -1.33298 q^{17} +3.06146 q^{18} +2.99427 q^{19} -1.19890 q^{20} -7.10610 q^{21} -4.46025 q^{22} -7.98056 q^{23} -2.46200 q^{24} -3.56264 q^{25} +2.03184 q^{26} -0.151315 q^{27} +2.88631 q^{28} +5.45001 q^{29} +2.95169 q^{30} +9.51670 q^{31} +1.00000 q^{32} +10.9812 q^{33} -1.33298 q^{34} -3.46039 q^{35} +3.06146 q^{36} +2.05789 q^{37} +2.99427 q^{38} -5.00238 q^{39} -1.19890 q^{40} -1.03166 q^{41} -7.10610 q^{42} -4.26974 q^{43} -4.46025 q^{44} -3.67038 q^{45} -7.98056 q^{46} -3.70023 q^{47} -2.46200 q^{48} +1.33077 q^{49} -3.56264 q^{50} +3.28179 q^{51} +2.03184 q^{52} -3.14181 q^{53} -0.151315 q^{54} +5.34739 q^{55} +2.88631 q^{56} -7.37191 q^{57} +5.45001 q^{58} -3.60466 q^{59} +2.95169 q^{60} -8.62323 q^{61} +9.51670 q^{62} +8.83632 q^{63} +1.00000 q^{64} -2.43596 q^{65} +10.9812 q^{66} +12.4646 q^{67} -1.33298 q^{68} +19.6482 q^{69} -3.46039 q^{70} -7.46589 q^{71} +3.06146 q^{72} +0.802939 q^{73} +2.05789 q^{74} +8.77124 q^{75} +2.99427 q^{76} -12.8737 q^{77} -5.00238 q^{78} +10.5744 q^{79} -1.19890 q^{80} -8.81184 q^{81} -1.03166 q^{82} -6.47728 q^{83} -7.10610 q^{84} +1.59810 q^{85} -4.26974 q^{86} -13.4179 q^{87} -4.46025 q^{88} -12.7695 q^{89} -3.67038 q^{90} +5.86450 q^{91} -7.98056 q^{92} -23.4301 q^{93} -3.70023 q^{94} -3.58983 q^{95} -2.46200 q^{96} +12.6583 q^{97} +1.33077 q^{98} -13.6549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 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
\(3\) −2.46200 −1.42144 −0.710719 0.703476i \(-0.751630\pi\)
−0.710719 + 0.703476i \(0.751630\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.19890 −0.536164 −0.268082 0.963396i \(-0.586390\pi\)
−0.268082 + 0.963396i \(0.586390\pi\)
\(6\) −2.46200 −1.00511
\(7\) 2.88631 1.09092 0.545461 0.838136i \(-0.316355\pi\)
0.545461 + 0.838136i \(0.316355\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.06146 1.02049
\(10\) −1.19890 −0.379125
\(11\) −4.46025 −1.34482 −0.672408 0.740181i \(-0.734740\pi\)
−0.672408 + 0.740181i \(0.734740\pi\)
\(12\) −2.46200 −0.710719
\(13\) 2.03184 0.563530 0.281765 0.959483i \(-0.409080\pi\)
0.281765 + 0.959483i \(0.409080\pi\)
\(14\) 2.88631 0.771398
\(15\) 2.95169 0.762123
\(16\) 1.00000 0.250000
\(17\) −1.33298 −0.323294 −0.161647 0.986849i \(-0.551681\pi\)
−0.161647 + 0.986849i \(0.551681\pi\)
\(18\) 3.06146 0.721593
\(19\) 2.99427 0.686934 0.343467 0.939165i \(-0.388399\pi\)
0.343467 + 0.939165i \(0.388399\pi\)
\(20\) −1.19890 −0.268082
\(21\) −7.10610 −1.55068
\(22\) −4.46025 −0.950929
\(23\) −7.98056 −1.66406 −0.832030 0.554730i \(-0.812822\pi\)
−0.832030 + 0.554730i \(0.812822\pi\)
\(24\) −2.46200 −0.502554
\(25\) −3.56264 −0.712529
\(26\) 2.03184 0.398476
\(27\) −0.151315 −0.0291206
\(28\) 2.88631 0.545461
\(29\) 5.45001 1.01204 0.506020 0.862521i \(-0.331116\pi\)
0.506020 + 0.862521i \(0.331116\pi\)
\(30\) 2.95169 0.538903
\(31\) 9.51670 1.70925 0.854625 0.519246i \(-0.173787\pi\)
0.854625 + 0.519246i \(0.173787\pi\)
\(32\) 1.00000 0.176777
\(33\) 10.9812 1.91157
\(34\) −1.33298 −0.228603
\(35\) −3.46039 −0.584912
\(36\) 3.06146 0.510243
\(37\) 2.05789 0.338316 0.169158 0.985589i \(-0.445895\pi\)
0.169158 + 0.985589i \(0.445895\pi\)
\(38\) 2.99427 0.485736
\(39\) −5.00238 −0.801023
\(40\) −1.19890 −0.189562
\(41\) −1.03166 −0.161118 −0.0805591 0.996750i \(-0.525671\pi\)
−0.0805591 + 0.996750i \(0.525671\pi\)
\(42\) −7.10610 −1.09649
\(43\) −4.26974 −0.651130 −0.325565 0.945520i \(-0.605554\pi\)
−0.325565 + 0.945520i \(0.605554\pi\)
\(44\) −4.46025 −0.672408
\(45\) −3.67038 −0.547148
\(46\) −7.98056 −1.17667
\(47\) −3.70023 −0.539733 −0.269867 0.962898i \(-0.586980\pi\)
−0.269867 + 0.962898i \(0.586980\pi\)
\(48\) −2.46200 −0.355360
\(49\) 1.33077 0.190110
\(50\) −3.56264 −0.503834
\(51\) 3.28179 0.459542
\(52\) 2.03184 0.281765
\(53\) −3.14181 −0.431561 −0.215780 0.976442i \(-0.569230\pi\)
−0.215780 + 0.976442i \(0.569230\pi\)
\(54\) −0.151315 −0.0205914
\(55\) 5.34739 0.721042
\(56\) 2.88631 0.385699
\(57\) −7.37191 −0.976434
\(58\) 5.45001 0.715621
\(59\) −3.60466 −0.469286 −0.234643 0.972082i \(-0.575392\pi\)
−0.234643 + 0.972082i \(0.575392\pi\)
\(60\) 2.95169 0.381062
\(61\) −8.62323 −1.10409 −0.552045 0.833814i \(-0.686153\pi\)
−0.552045 + 0.833814i \(0.686153\pi\)
\(62\) 9.51670 1.20862
\(63\) 8.83632 1.11327
\(64\) 1.00000 0.125000
\(65\) −2.43596 −0.302144
\(66\) 10.9812 1.35169
\(67\) 12.4646 1.52279 0.761396 0.648288i \(-0.224515\pi\)
0.761396 + 0.648288i \(0.224515\pi\)
\(68\) −1.33298 −0.161647
\(69\) 19.6482 2.36536
\(70\) −3.46039 −0.413596
\(71\) −7.46589 −0.886038 −0.443019 0.896512i \(-0.646093\pi\)
−0.443019 + 0.896512i \(0.646093\pi\)
\(72\) 3.06146 0.360797
\(73\) 0.802939 0.0939769 0.0469884 0.998895i \(-0.485038\pi\)
0.0469884 + 0.998895i \(0.485038\pi\)
\(74\) 2.05789 0.239225
\(75\) 8.77124 1.01282
\(76\) 2.99427 0.343467
\(77\) −12.8737 −1.46709
\(78\) −5.00238 −0.566409
\(79\) 10.5744 1.18972 0.594858 0.803831i \(-0.297208\pi\)
0.594858 + 0.803831i \(0.297208\pi\)
\(80\) −1.19890 −0.134041
\(81\) −8.81184 −0.979094
\(82\) −1.03166 −0.113928
\(83\) −6.47728 −0.710974 −0.355487 0.934681i \(-0.615685\pi\)
−0.355487 + 0.934681i \(0.615685\pi\)
\(84\) −7.10610 −0.775339
\(85\) 1.59810 0.173338
\(86\) −4.26974 −0.460418
\(87\) −13.4179 −1.43855
\(88\) −4.46025 −0.475464
\(89\) −12.7695 −1.35357 −0.676784 0.736182i \(-0.736627\pi\)
−0.676784 + 0.736182i \(0.736627\pi\)
\(90\) −3.67038 −0.386892
\(91\) 5.86450 0.614767
\(92\) −7.98056 −0.832030
\(93\) −23.4301 −2.42959
\(94\) −3.70023 −0.381649
\(95\) −3.58983 −0.368309
\(96\) −2.46200 −0.251277
\(97\) 12.6583 1.28526 0.642629 0.766178i \(-0.277844\pi\)
0.642629 + 0.766178i \(0.277844\pi\)
\(98\) 1.33077 0.134428
\(99\) −13.6549 −1.37237
\(100\) −3.56264 −0.356264
\(101\) 5.05589 0.503080 0.251540 0.967847i \(-0.419063\pi\)
0.251540 + 0.967847i \(0.419063\pi\)
\(102\) 3.28179 0.324946
\(103\) 10.9353 1.07748 0.538741 0.842471i \(-0.318900\pi\)
0.538741 + 0.842471i \(0.318900\pi\)
\(104\) 2.03184 0.199238
\(105\) 8.51949 0.831417
\(106\) −3.14181 −0.305160
\(107\) −9.24635 −0.893878 −0.446939 0.894564i \(-0.647486\pi\)
−0.446939 + 0.894564i \(0.647486\pi\)
\(108\) −0.151315 −0.0145603
\(109\) 4.09628 0.392352 0.196176 0.980569i \(-0.437148\pi\)
0.196176 + 0.980569i \(0.437148\pi\)
\(110\) 5.34739 0.509853
\(111\) −5.06654 −0.480895
\(112\) 2.88631 0.272730
\(113\) −6.43963 −0.605790 −0.302895 0.953024i \(-0.597953\pi\)
−0.302895 + 0.953024i \(0.597953\pi\)
\(114\) −7.37191 −0.690443
\(115\) 9.56787 0.892209
\(116\) 5.45001 0.506020
\(117\) 6.22038 0.575075
\(118\) −3.60466 −0.331836
\(119\) −3.84738 −0.352688
\(120\) 2.95169 0.269451
\(121\) 8.89384 0.808531
\(122\) −8.62323 −0.780710
\(123\) 2.53995 0.229019
\(124\) 9.51670 0.854625
\(125\) 10.2657 0.918195
\(126\) 8.83632 0.787202
\(127\) 9.74175 0.864441 0.432220 0.901768i \(-0.357730\pi\)
0.432220 + 0.901768i \(0.357730\pi\)
\(128\) 1.00000 0.0883883
\(129\) 10.5121 0.925540
\(130\) −2.43596 −0.213648
\(131\) 13.2358 1.15642 0.578209 0.815889i \(-0.303752\pi\)
0.578209 + 0.815889i \(0.303752\pi\)
\(132\) 10.9812 0.955787
\(133\) 8.64240 0.749391
\(134\) 12.4646 1.07678
\(135\) 0.181412 0.0156134
\(136\) −1.33298 −0.114302
\(137\) −5.10401 −0.436065 −0.218033 0.975941i \(-0.569964\pi\)
−0.218033 + 0.975941i \(0.569964\pi\)
\(138\) 19.6482 1.67256
\(139\) −12.3829 −1.05031 −0.525154 0.851007i \(-0.675992\pi\)
−0.525154 + 0.851007i \(0.675992\pi\)
\(140\) −3.46039 −0.292456
\(141\) 9.10997 0.767198
\(142\) −7.46589 −0.626524
\(143\) −9.06249 −0.757844
\(144\) 3.06146 0.255122
\(145\) −6.53400 −0.542619
\(146\) 0.802939 0.0664517
\(147\) −3.27636 −0.270230
\(148\) 2.05789 0.169158
\(149\) 0.709098 0.0580916 0.0290458 0.999578i \(-0.490753\pi\)
0.0290458 + 0.999578i \(0.490753\pi\)
\(150\) 8.77124 0.716169
\(151\) −19.9658 −1.62479 −0.812396 0.583106i \(-0.801837\pi\)
−0.812396 + 0.583106i \(0.801837\pi\)
\(152\) 2.99427 0.242868
\(153\) −4.08085 −0.329917
\(154\) −12.8737 −1.03739
\(155\) −11.4096 −0.916437
\(156\) −5.00238 −0.400511
\(157\) 0.989398 0.0789625 0.0394813 0.999220i \(-0.487429\pi\)
0.0394813 + 0.999220i \(0.487429\pi\)
\(158\) 10.5744 0.841256
\(159\) 7.73515 0.613437
\(160\) −1.19890 −0.0947812
\(161\) −23.0343 −1.81536
\(162\) −8.81184 −0.692324
\(163\) −17.9899 −1.40908 −0.704538 0.709666i \(-0.748846\pi\)
−0.704538 + 0.709666i \(0.748846\pi\)
\(164\) −1.03166 −0.0805591
\(165\) −13.1653 −1.02492
\(166\) −6.47728 −0.502735
\(167\) 3.32310 0.257149 0.128574 0.991700i \(-0.458960\pi\)
0.128574 + 0.991700i \(0.458960\pi\)
\(168\) −7.10610 −0.548247
\(169\) −8.87165 −0.682434
\(170\) 1.59810 0.122569
\(171\) 9.16685 0.701007
\(172\) −4.26974 −0.325565
\(173\) −0.654520 −0.0497623 −0.0248811 0.999690i \(-0.507921\pi\)
−0.0248811 + 0.999690i \(0.507921\pi\)
\(174\) −13.4179 −1.01721
\(175\) −10.2829 −0.777313
\(176\) −4.46025 −0.336204
\(177\) 8.87468 0.667062
\(178\) −12.7695 −0.957117
\(179\) 20.6354 1.54237 0.771183 0.636614i \(-0.219666\pi\)
0.771183 + 0.636614i \(0.219666\pi\)
\(180\) −3.67038 −0.273574
\(181\) −6.42961 −0.477909 −0.238955 0.971031i \(-0.576805\pi\)
−0.238955 + 0.971031i \(0.576805\pi\)
\(182\) 5.86450 0.434706
\(183\) 21.2304 1.56940
\(184\) −7.98056 −0.588334
\(185\) −2.46721 −0.181393
\(186\) −23.4301 −1.71798
\(187\) 5.94541 0.434771
\(188\) −3.70023 −0.269867
\(189\) −0.436743 −0.0317683
\(190\) −3.58983 −0.260434
\(191\) 1.49819 0.108405 0.0542026 0.998530i \(-0.482738\pi\)
0.0542026 + 0.998530i \(0.482738\pi\)
\(192\) −2.46200 −0.177680
\(193\) −6.67653 −0.480587 −0.240293 0.970700i \(-0.577244\pi\)
−0.240293 + 0.970700i \(0.577244\pi\)
\(194\) 12.6583 0.908815
\(195\) 5.99735 0.429479
\(196\) 1.33077 0.0950551
\(197\) −3.38365 −0.241075 −0.120538 0.992709i \(-0.538462\pi\)
−0.120538 + 0.992709i \(0.538462\pi\)
\(198\) −13.6549 −0.970410
\(199\) −12.5763 −0.891509 −0.445755 0.895155i \(-0.647065\pi\)
−0.445755 + 0.895155i \(0.647065\pi\)
\(200\) −3.56264 −0.251917
\(201\) −30.6878 −2.16455
\(202\) 5.05589 0.355731
\(203\) 15.7304 1.10406
\(204\) 3.28179 0.229771
\(205\) 1.23685 0.0863857
\(206\) 10.9353 0.761895
\(207\) −24.4322 −1.69815
\(208\) 2.03184 0.140882
\(209\) −13.3552 −0.923800
\(210\) 8.51949 0.587901
\(211\) −20.9915 −1.44512 −0.722559 0.691310i \(-0.757034\pi\)
−0.722559 + 0.691310i \(0.757034\pi\)
\(212\) −3.14181 −0.215780
\(213\) 18.3811 1.25945
\(214\) −9.24635 −0.632067
\(215\) 5.11899 0.349112
\(216\) −0.151315 −0.0102957
\(217\) 27.4681 1.86466
\(218\) 4.09628 0.277435
\(219\) −1.97684 −0.133582
\(220\) 5.34739 0.360521
\(221\) −2.70839 −0.182186
\(222\) −5.06654 −0.340044
\(223\) 23.4488 1.57025 0.785123 0.619340i \(-0.212600\pi\)
0.785123 + 0.619340i \(0.212600\pi\)
\(224\) 2.88631 0.192850
\(225\) −10.9069 −0.727126
\(226\) −6.43963 −0.428358
\(227\) 4.39085 0.291431 0.145716 0.989327i \(-0.453452\pi\)
0.145716 + 0.989327i \(0.453452\pi\)
\(228\) −7.37191 −0.488217
\(229\) −7.91979 −0.523354 −0.261677 0.965155i \(-0.584276\pi\)
−0.261677 + 0.965155i \(0.584276\pi\)
\(230\) 9.56787 0.630887
\(231\) 31.6950 2.08538
\(232\) 5.45001 0.357810
\(233\) 13.8801 0.909316 0.454658 0.890666i \(-0.349761\pi\)
0.454658 + 0.890666i \(0.349761\pi\)
\(234\) 6.22038 0.406639
\(235\) 4.43619 0.289385
\(236\) −3.60466 −0.234643
\(237\) −26.0343 −1.69111
\(238\) −3.84738 −0.249388
\(239\) 0.655256 0.0423850 0.0211925 0.999775i \(-0.493254\pi\)
0.0211925 + 0.999775i \(0.493254\pi\)
\(240\) 2.95169 0.190531
\(241\) −26.3634 −1.69821 −0.849107 0.528221i \(-0.822859\pi\)
−0.849107 + 0.528221i \(0.822859\pi\)
\(242\) 8.89384 0.571718
\(243\) 22.1487 1.42084
\(244\) −8.62323 −0.552045
\(245\) −1.59546 −0.101930
\(246\) 2.53995 0.161941
\(247\) 6.08387 0.387108
\(248\) 9.51670 0.604311
\(249\) 15.9471 1.01061
\(250\) 10.2657 0.649262
\(251\) 20.6635 1.30427 0.652134 0.758103i \(-0.273874\pi\)
0.652134 + 0.758103i \(0.273874\pi\)
\(252\) 8.83632 0.556636
\(253\) 35.5953 2.23786
\(254\) 9.74175 0.611252
\(255\) −3.93453 −0.246390
\(256\) 1.00000 0.0625000
\(257\) −23.2413 −1.44975 −0.724876 0.688879i \(-0.758103\pi\)
−0.724876 + 0.688879i \(0.758103\pi\)
\(258\) 10.5121 0.654456
\(259\) 5.93971 0.369076
\(260\) −2.43596 −0.151072
\(261\) 16.6850 1.03277
\(262\) 13.2358 0.817711
\(263\) −12.1298 −0.747955 −0.373978 0.927438i \(-0.622006\pi\)
−0.373978 + 0.927438i \(0.622006\pi\)
\(264\) 10.9812 0.675843
\(265\) 3.76671 0.231387
\(266\) 8.64240 0.529899
\(267\) 31.4386 1.92401
\(268\) 12.4646 0.761396
\(269\) −15.8102 −0.963963 −0.481981 0.876181i \(-0.660083\pi\)
−0.481981 + 0.876181i \(0.660083\pi\)
\(270\) 0.181412 0.0110404
\(271\) −21.9603 −1.33399 −0.666996 0.745061i \(-0.732420\pi\)
−0.666996 + 0.745061i \(0.732420\pi\)
\(272\) −1.33298 −0.0808235
\(273\) −14.4384 −0.873853
\(274\) −5.10401 −0.308345
\(275\) 15.8903 0.958220
\(276\) 19.6482 1.18268
\(277\) 27.7483 1.66723 0.833616 0.552345i \(-0.186267\pi\)
0.833616 + 0.552345i \(0.186267\pi\)
\(278\) −12.3829 −0.742680
\(279\) 29.1350 1.74427
\(280\) −3.46039 −0.206798
\(281\) −1.99872 −0.119234 −0.0596168 0.998221i \(-0.518988\pi\)
−0.0596168 + 0.998221i \(0.518988\pi\)
\(282\) 9.10997 0.542491
\(283\) 16.1175 0.958087 0.479044 0.877791i \(-0.340984\pi\)
0.479044 + 0.877791i \(0.340984\pi\)
\(284\) −7.46589 −0.443019
\(285\) 8.83818 0.523528
\(286\) −9.06249 −0.535877
\(287\) −2.97769 −0.175767
\(288\) 3.06146 0.180398
\(289\) −15.2232 −0.895481
\(290\) −6.53400 −0.383690
\(291\) −31.1648 −1.82691
\(292\) 0.802939 0.0469884
\(293\) −26.0218 −1.52021 −0.760106 0.649799i \(-0.774853\pi\)
−0.760106 + 0.649799i \(0.774853\pi\)
\(294\) −3.27636 −0.191081
\(295\) 4.32162 0.251614
\(296\) 2.05789 0.119613
\(297\) 0.674904 0.0391619
\(298\) 0.709098 0.0410770
\(299\) −16.2152 −0.937748
\(300\) 8.77124 0.506408
\(301\) −12.3238 −0.710331
\(302\) −19.9658 −1.14890
\(303\) −12.4476 −0.715097
\(304\) 2.99427 0.171733
\(305\) 10.3384 0.591973
\(306\) −4.08085 −0.233287
\(307\) −27.2390 −1.55461 −0.777307 0.629122i \(-0.783415\pi\)
−0.777307 + 0.629122i \(0.783415\pi\)
\(308\) −12.8737 −0.733545
\(309\) −26.9226 −1.53157
\(310\) −11.4096 −0.648019
\(311\) −21.6769 −1.22918 −0.614592 0.788845i \(-0.710679\pi\)
−0.614592 + 0.788845i \(0.710679\pi\)
\(312\) −5.00238 −0.283204
\(313\) −1.30840 −0.0739553 −0.0369777 0.999316i \(-0.511773\pi\)
−0.0369777 + 0.999316i \(0.511773\pi\)
\(314\) 0.989398 0.0558350
\(315\) −10.5938 −0.596895
\(316\) 10.5744 0.594858
\(317\) −19.8519 −1.11499 −0.557496 0.830180i \(-0.688238\pi\)
−0.557496 + 0.830180i \(0.688238\pi\)
\(318\) 7.73515 0.433765
\(319\) −24.3084 −1.36101
\(320\) −1.19890 −0.0670204
\(321\) 22.7645 1.27059
\(322\) −23.0343 −1.28365
\(323\) −3.99129 −0.222082
\(324\) −8.81184 −0.489547
\(325\) −7.23870 −0.401531
\(326\) −17.9899 −0.996367
\(327\) −10.0850 −0.557704
\(328\) −1.03166 −0.0569639
\(329\) −10.6800 −0.588807
\(330\) −13.1653 −0.724725
\(331\) 2.23277 0.122724 0.0613620 0.998116i \(-0.480456\pi\)
0.0613620 + 0.998116i \(0.480456\pi\)
\(332\) −6.47728 −0.355487
\(333\) 6.30016 0.345247
\(334\) 3.32310 0.181832
\(335\) −14.9438 −0.816465
\(336\) −7.10610 −0.387669
\(337\) −17.2026 −0.937085 −0.468542 0.883441i \(-0.655221\pi\)
−0.468542 + 0.883441i \(0.655221\pi\)
\(338\) −8.87165 −0.482554
\(339\) 15.8544 0.861093
\(340\) 1.59810 0.0866692
\(341\) −42.4469 −2.29863
\(342\) 9.16685 0.495687
\(343\) −16.3631 −0.883526
\(344\) −4.26974 −0.230209
\(345\) −23.5561 −1.26822
\(346\) −0.654520 −0.0351872
\(347\) −10.1459 −0.544659 −0.272330 0.962204i \(-0.587794\pi\)
−0.272330 + 0.962204i \(0.587794\pi\)
\(348\) −13.4179 −0.719277
\(349\) 11.0457 0.591265 0.295633 0.955302i \(-0.404470\pi\)
0.295633 + 0.955302i \(0.404470\pi\)
\(350\) −10.2829 −0.549643
\(351\) −0.307448 −0.0164103
\(352\) −4.46025 −0.237732
\(353\) −28.5221 −1.51808 −0.759038 0.651046i \(-0.774330\pi\)
−0.759038 + 0.651046i \(0.774330\pi\)
\(354\) 8.87468 0.471684
\(355\) 8.95085 0.475062
\(356\) −12.7695 −0.676784
\(357\) 9.47225 0.501325
\(358\) 20.6354 1.09062
\(359\) 13.3587 0.705047 0.352523 0.935803i \(-0.385324\pi\)
0.352523 + 0.935803i \(0.385324\pi\)
\(360\) −3.67038 −0.193446
\(361\) −10.0343 −0.528122
\(362\) −6.42961 −0.337933
\(363\) −21.8967 −1.14928
\(364\) 5.86450 0.307383
\(365\) −0.962642 −0.0503870
\(366\) 21.2304 1.10973
\(367\) −4.65239 −0.242853 −0.121426 0.992600i \(-0.538747\pi\)
−0.121426 + 0.992600i \(0.538747\pi\)
\(368\) −7.98056 −0.416015
\(369\) −3.15838 −0.164419
\(370\) −2.46721 −0.128264
\(371\) −9.06823 −0.470799
\(372\) −23.4301 −1.21480
\(373\) 2.22264 0.115084 0.0575420 0.998343i \(-0.481674\pi\)
0.0575420 + 0.998343i \(0.481674\pi\)
\(374\) 5.94541 0.307430
\(375\) −25.2743 −1.30516
\(376\) −3.70023 −0.190825
\(377\) 11.0735 0.570315
\(378\) −0.436743 −0.0224636
\(379\) 6.43360 0.330472 0.165236 0.986254i \(-0.447161\pi\)
0.165236 + 0.986254i \(0.447161\pi\)
\(380\) −3.58983 −0.184154
\(381\) −23.9842 −1.22875
\(382\) 1.49819 0.0766541
\(383\) −13.0227 −0.665429 −0.332714 0.943028i \(-0.607965\pi\)
−0.332714 + 0.943028i \(0.607965\pi\)
\(384\) −2.46200 −0.125639
\(385\) 15.4342 0.786600
\(386\) −6.67653 −0.339826
\(387\) −13.0716 −0.664469
\(388\) 12.6583 0.642629
\(389\) 14.1203 0.715928 0.357964 0.933735i \(-0.383471\pi\)
0.357964 + 0.933735i \(0.383471\pi\)
\(390\) 5.99735 0.303688
\(391\) 10.6379 0.537981
\(392\) 1.33077 0.0672141
\(393\) −32.5866 −1.64378
\(394\) −3.38365 −0.170466
\(395\) −12.6777 −0.637882
\(396\) −13.6549 −0.686184
\(397\) −5.80414 −0.291302 −0.145651 0.989336i \(-0.546528\pi\)
−0.145651 + 0.989336i \(0.546528\pi\)
\(398\) −12.5763 −0.630392
\(399\) −21.2776 −1.06521
\(400\) −3.56264 −0.178132
\(401\) −13.0278 −0.650579 −0.325289 0.945614i \(-0.605462\pi\)
−0.325289 + 0.945614i \(0.605462\pi\)
\(402\) −30.6878 −1.53057
\(403\) 19.3364 0.963213
\(404\) 5.05589 0.251540
\(405\) 10.5645 0.524954
\(406\) 15.7304 0.780686
\(407\) −9.17872 −0.454972
\(408\) 3.28179 0.162473
\(409\) −11.9401 −0.590402 −0.295201 0.955435i \(-0.595387\pi\)
−0.295201 + 0.955435i \(0.595387\pi\)
\(410\) 1.23685 0.0610839
\(411\) 12.5661 0.619840
\(412\) 10.9353 0.538741
\(413\) −10.4041 −0.511955
\(414\) −24.4322 −1.20077
\(415\) 7.76560 0.381198
\(416\) 2.03184 0.0996189
\(417\) 30.4869 1.49295
\(418\) −13.3552 −0.653225
\(419\) 14.8690 0.726399 0.363199 0.931711i \(-0.381684\pi\)
0.363199 + 0.931711i \(0.381684\pi\)
\(420\) 8.51949 0.415708
\(421\) 1.29715 0.0632193 0.0316097 0.999500i \(-0.489937\pi\)
0.0316097 + 0.999500i \(0.489937\pi\)
\(422\) −20.9915 −1.02185
\(423\) −11.3281 −0.550791
\(424\) −3.14181 −0.152580
\(425\) 4.74892 0.230356
\(426\) 18.3811 0.890565
\(427\) −24.8893 −1.20448
\(428\) −9.24635 −0.446939
\(429\) 22.3119 1.07723
\(430\) 5.11899 0.246859
\(431\) −29.6509 −1.42823 −0.714116 0.700027i \(-0.753171\pi\)
−0.714116 + 0.700027i \(0.753171\pi\)
\(432\) −0.151315 −0.00728016
\(433\) −25.1200 −1.20719 −0.603595 0.797291i \(-0.706265\pi\)
−0.603595 + 0.797291i \(0.706265\pi\)
\(434\) 27.4681 1.31851
\(435\) 16.0867 0.771300
\(436\) 4.09628 0.196176
\(437\) −23.8960 −1.14310
\(438\) −1.97684 −0.0944570
\(439\) 8.97809 0.428501 0.214251 0.976779i \(-0.431269\pi\)
0.214251 + 0.976779i \(0.431269\pi\)
\(440\) 5.34739 0.254927
\(441\) 4.07410 0.194005
\(442\) −2.70839 −0.128825
\(443\) −14.8845 −0.707183 −0.353592 0.935400i \(-0.615040\pi\)
−0.353592 + 0.935400i \(0.615040\pi\)
\(444\) −5.06654 −0.240447
\(445\) 15.3094 0.725734
\(446\) 23.4488 1.11033
\(447\) −1.74580 −0.0825736
\(448\) 2.88631 0.136365
\(449\) 2.41434 0.113940 0.0569698 0.998376i \(-0.481856\pi\)
0.0569698 + 0.998376i \(0.481856\pi\)
\(450\) −10.9069 −0.514156
\(451\) 4.60146 0.216674
\(452\) −6.43963 −0.302895
\(453\) 49.1558 2.30954
\(454\) 4.39085 0.206073
\(455\) −7.03094 −0.329616
\(456\) −7.37191 −0.345222
\(457\) −6.08220 −0.284513 −0.142257 0.989830i \(-0.545436\pi\)
−0.142257 + 0.989830i \(0.545436\pi\)
\(458\) −7.91979 −0.370067
\(459\) 0.201700 0.00941453
\(460\) 9.56787 0.446104
\(461\) −16.7137 −0.778435 −0.389218 0.921146i \(-0.627255\pi\)
−0.389218 + 0.921146i \(0.627255\pi\)
\(462\) 31.6950 1.47458
\(463\) −33.7225 −1.56722 −0.783609 0.621254i \(-0.786623\pi\)
−0.783609 + 0.621254i \(0.786623\pi\)
\(464\) 5.45001 0.253010
\(465\) 28.0904 1.30266
\(466\) 13.8801 0.642984
\(467\) −23.7353 −1.09834 −0.549169 0.835712i \(-0.685055\pi\)
−0.549169 + 0.835712i \(0.685055\pi\)
\(468\) 6.22038 0.287537
\(469\) 35.9766 1.66125
\(470\) 4.43619 0.204626
\(471\) −2.43590 −0.112240
\(472\) −3.60466 −0.165918
\(473\) 19.0441 0.875650
\(474\) −26.0343 −1.19579
\(475\) −10.6675 −0.489460
\(476\) −3.84738 −0.176344
\(477\) −9.61853 −0.440402
\(478\) 0.655256 0.0299707
\(479\) 14.8171 0.677008 0.338504 0.940965i \(-0.390079\pi\)
0.338504 + 0.940965i \(0.390079\pi\)
\(480\) 2.95169 0.134726
\(481\) 4.18130 0.190651
\(482\) −26.3634 −1.20082
\(483\) 56.7106 2.58042
\(484\) 8.89384 0.404266
\(485\) −15.1760 −0.689108
\(486\) 22.1487 1.00469
\(487\) −0.442777 −0.0200642 −0.0100321 0.999950i \(-0.503193\pi\)
−0.0100321 + 0.999950i \(0.503193\pi\)
\(488\) −8.62323 −0.390355
\(489\) 44.2911 2.00291
\(490\) −1.59546 −0.0720755
\(491\) 2.45714 0.110889 0.0554446 0.998462i \(-0.482342\pi\)
0.0554446 + 0.998462i \(0.482342\pi\)
\(492\) 2.53995 0.114510
\(493\) −7.26472 −0.327187
\(494\) 6.08387 0.273726
\(495\) 16.3708 0.735813
\(496\) 9.51670 0.427312
\(497\) −21.5489 −0.966599
\(498\) 15.9471 0.714606
\(499\) −32.6070 −1.45969 −0.729846 0.683612i \(-0.760408\pi\)
−0.729846 + 0.683612i \(0.760408\pi\)
\(500\) 10.2657 0.459098
\(501\) −8.18147 −0.365521
\(502\) 20.6635 0.922257
\(503\) 6.68801 0.298203 0.149102 0.988822i \(-0.452362\pi\)
0.149102 + 0.988822i \(0.452362\pi\)
\(504\) 8.83632 0.393601
\(505\) −6.06150 −0.269733
\(506\) 35.5953 1.58240
\(507\) 21.8420 0.970038
\(508\) 9.74175 0.432220
\(509\) −3.38887 −0.150209 −0.0751046 0.997176i \(-0.523929\pi\)
−0.0751046 + 0.997176i \(0.523929\pi\)
\(510\) −3.93453 −0.174224
\(511\) 2.31753 0.102521
\(512\) 1.00000 0.0441942
\(513\) −0.453080 −0.0200040
\(514\) −23.2413 −1.02513
\(515\) −13.1103 −0.577707
\(516\) 10.5121 0.462770
\(517\) 16.5039 0.725842
\(518\) 5.93971 0.260976
\(519\) 1.61143 0.0707340
\(520\) −2.43596 −0.106824
\(521\) −17.8376 −0.781479 −0.390740 0.920501i \(-0.627781\pi\)
−0.390740 + 0.920501i \(0.627781\pi\)
\(522\) 16.6850 0.730282
\(523\) −29.1636 −1.27524 −0.637618 0.770353i \(-0.720080\pi\)
−0.637618 + 0.770353i \(0.720080\pi\)
\(524\) 13.2358 0.578209
\(525\) 25.3165 1.10490
\(526\) −12.1298 −0.528884
\(527\) −12.6855 −0.552590
\(528\) 10.9812 0.477893
\(529\) 40.6893 1.76910
\(530\) 3.76671 0.163615
\(531\) −11.0355 −0.478901
\(532\) 8.64240 0.374695
\(533\) −2.09616 −0.0907948
\(534\) 31.4386 1.36048
\(535\) 11.0854 0.479265
\(536\) 12.4646 0.538388
\(537\) −50.8045 −2.19238
\(538\) −15.8102 −0.681625
\(539\) −5.93557 −0.255663
\(540\) 0.181412 0.00780671
\(541\) 7.34951 0.315980 0.157990 0.987441i \(-0.449499\pi\)
0.157990 + 0.987441i \(0.449499\pi\)
\(542\) −21.9603 −0.943275
\(543\) 15.8297 0.679318
\(544\) −1.33298 −0.0571508
\(545\) −4.91102 −0.210365
\(546\) −14.4384 −0.617907
\(547\) 17.1119 0.731653 0.365826 0.930683i \(-0.380786\pi\)
0.365826 + 0.930683i \(0.380786\pi\)
\(548\) −5.10401 −0.218033
\(549\) −26.3997 −1.12671
\(550\) 15.8903 0.677564
\(551\) 16.3188 0.695205
\(552\) 19.6482 0.836281
\(553\) 30.5210 1.29789
\(554\) 27.7483 1.17891
\(555\) 6.07427 0.257838
\(556\) −12.3829 −0.525154
\(557\) 1.30178 0.0551582 0.0275791 0.999620i \(-0.491220\pi\)
0.0275791 + 0.999620i \(0.491220\pi\)
\(558\) 29.1350 1.23338
\(559\) −8.67541 −0.366931
\(560\) −3.46039 −0.146228
\(561\) −14.6376 −0.618000
\(562\) −1.99872 −0.0843109
\(563\) −6.06187 −0.255477 −0.127739 0.991808i \(-0.540772\pi\)
−0.127739 + 0.991808i \(0.540772\pi\)
\(564\) 9.10997 0.383599
\(565\) 7.72046 0.324802
\(566\) 16.1175 0.677470
\(567\) −25.4337 −1.06811
\(568\) −7.46589 −0.313262
\(569\) 34.0114 1.42583 0.712916 0.701250i \(-0.247374\pi\)
0.712916 + 0.701250i \(0.247374\pi\)
\(570\) 8.83818 0.370190
\(571\) −11.5520 −0.483435 −0.241718 0.970347i \(-0.577711\pi\)
−0.241718 + 0.970347i \(0.577711\pi\)
\(572\) −9.06249 −0.378922
\(573\) −3.68855 −0.154091
\(574\) −2.97769 −0.124286
\(575\) 28.4319 1.18569
\(576\) 3.06146 0.127561
\(577\) −44.1970 −1.83995 −0.919973 0.391981i \(-0.871790\pi\)
−0.919973 + 0.391981i \(0.871790\pi\)
\(578\) −15.2232 −0.633201
\(579\) 16.4376 0.683125
\(580\) −6.53400 −0.271310
\(581\) −18.6954 −0.775617
\(582\) −31.1648 −1.29182
\(583\) 14.0133 0.580370
\(584\) 0.802939 0.0332258
\(585\) −7.45760 −0.308334
\(586\) −26.0218 −1.07495
\(587\) 26.0799 1.07643 0.538216 0.842807i \(-0.319098\pi\)
0.538216 + 0.842807i \(0.319098\pi\)
\(588\) −3.27636 −0.135115
\(589\) 28.4956 1.17414
\(590\) 4.32162 0.177918
\(591\) 8.33056 0.342673
\(592\) 2.05789 0.0845789
\(593\) −16.2881 −0.668874 −0.334437 0.942418i \(-0.608546\pi\)
−0.334437 + 0.942418i \(0.608546\pi\)
\(594\) 0.674904 0.0276917
\(595\) 4.61261 0.189099
\(596\) 0.709098 0.0290458
\(597\) 30.9629 1.26723
\(598\) −16.2152 −0.663088
\(599\) 15.9106 0.650090 0.325045 0.945699i \(-0.394621\pi\)
0.325045 + 0.945699i \(0.394621\pi\)
\(600\) 8.77124 0.358084
\(601\) −31.0357 −1.26597 −0.632985 0.774164i \(-0.718171\pi\)
−0.632985 + 0.774164i \(0.718171\pi\)
\(602\) −12.3238 −0.502280
\(603\) 38.1598 1.55399
\(604\) −19.9658 −0.812396
\(605\) −10.6628 −0.433505
\(606\) −12.4476 −0.505650
\(607\) −10.8182 −0.439096 −0.219548 0.975602i \(-0.570458\pi\)
−0.219548 + 0.975602i \(0.570458\pi\)
\(608\) 2.99427 0.121434
\(609\) −38.7283 −1.56935
\(610\) 10.3384 0.418588
\(611\) −7.51825 −0.304156
\(612\) −4.08085 −0.164959
\(613\) 1.33415 0.0538859 0.0269429 0.999637i \(-0.491423\pi\)
0.0269429 + 0.999637i \(0.491423\pi\)
\(614\) −27.2390 −1.09928
\(615\) −3.04514 −0.122792
\(616\) −12.8737 −0.518694
\(617\) 19.0417 0.766590 0.383295 0.923626i \(-0.374789\pi\)
0.383295 + 0.923626i \(0.374789\pi\)
\(618\) −26.9226 −1.08299
\(619\) −24.3086 −0.977047 −0.488523 0.872551i \(-0.662464\pi\)
−0.488523 + 0.872551i \(0.662464\pi\)
\(620\) −11.4096 −0.458219
\(621\) 1.20758 0.0484585
\(622\) −21.6769 −0.869165
\(623\) −36.8568 −1.47664
\(624\) −5.00238 −0.200256
\(625\) 5.50564 0.220226
\(626\) −1.30840 −0.0522943
\(627\) 32.8806 1.31312
\(628\) 0.989398 0.0394813
\(629\) −2.74312 −0.109375
\(630\) −10.5938 −0.422069
\(631\) 19.2026 0.764445 0.382222 0.924070i \(-0.375159\pi\)
0.382222 + 0.924070i \(0.375159\pi\)
\(632\) 10.5744 0.420628
\(633\) 51.6812 2.05415
\(634\) −19.8519 −0.788418
\(635\) −11.6794 −0.463482
\(636\) 7.73515 0.306718
\(637\) 2.70391 0.107133
\(638\) −24.3084 −0.962379
\(639\) −22.8565 −0.904191
\(640\) −1.19890 −0.0473906
\(641\) −17.4940 −0.690970 −0.345485 0.938424i \(-0.612286\pi\)
−0.345485 + 0.938424i \(0.612286\pi\)
\(642\) 22.7645 0.898445
\(643\) 20.5920 0.812069 0.406035 0.913858i \(-0.366911\pi\)
0.406035 + 0.913858i \(0.366911\pi\)
\(644\) −23.0343 −0.907680
\(645\) −12.6030 −0.496241
\(646\) −3.99129 −0.157035
\(647\) 36.8988 1.45064 0.725321 0.688411i \(-0.241691\pi\)
0.725321 + 0.688411i \(0.241691\pi\)
\(648\) −8.81184 −0.346162
\(649\) 16.0777 0.631104
\(650\) −7.23870 −0.283925
\(651\) −67.6266 −2.65050
\(652\) −17.9899 −0.704538
\(653\) 38.3135 1.49932 0.749662 0.661821i \(-0.230216\pi\)
0.749662 + 0.661821i \(0.230216\pi\)
\(654\) −10.0850 −0.394357
\(655\) −15.8684 −0.620029
\(656\) −1.03166 −0.0402795
\(657\) 2.45817 0.0959022
\(658\) −10.6800 −0.416349
\(659\) 16.3406 0.636538 0.318269 0.948000i \(-0.396898\pi\)
0.318269 + 0.948000i \(0.396898\pi\)
\(660\) −13.1653 −0.512458
\(661\) 13.8754 0.539689 0.269844 0.962904i \(-0.413028\pi\)
0.269844 + 0.962904i \(0.413028\pi\)
\(662\) 2.23277 0.0867790
\(663\) 6.66806 0.258966
\(664\) −6.47728 −0.251367
\(665\) −10.3614 −0.401796
\(666\) 6.30016 0.244126
\(667\) −43.4941 −1.68410
\(668\) 3.32310 0.128574
\(669\) −57.7309 −2.23201
\(670\) −14.9438 −0.577328
\(671\) 38.4618 1.48480
\(672\) −7.10610 −0.274124
\(673\) 11.7096 0.451372 0.225686 0.974200i \(-0.427538\pi\)
0.225686 + 0.974200i \(0.427538\pi\)
\(674\) −17.2026 −0.662619
\(675\) 0.539082 0.0207493
\(676\) −8.87165 −0.341217
\(677\) 15.4219 0.592713 0.296356 0.955077i \(-0.404228\pi\)
0.296356 + 0.955077i \(0.404228\pi\)
\(678\) 15.8544 0.608884
\(679\) 36.5358 1.40212
\(680\) 1.59810 0.0612844
\(681\) −10.8103 −0.414252
\(682\) −42.4469 −1.62537
\(683\) 13.7023 0.524306 0.262153 0.965026i \(-0.415568\pi\)
0.262153 + 0.965026i \(0.415568\pi\)
\(684\) 9.16685 0.350503
\(685\) 6.11919 0.233802
\(686\) −16.3631 −0.624748
\(687\) 19.4985 0.743916
\(688\) −4.26974 −0.162782
\(689\) −6.38364 −0.243197
\(690\) −23.5561 −0.896767
\(691\) 40.9967 1.55959 0.779793 0.626037i \(-0.215324\pi\)
0.779793 + 0.626037i \(0.215324\pi\)
\(692\) −0.654520 −0.0248811
\(693\) −39.4122 −1.49715
\(694\) −10.1459 −0.385132
\(695\) 14.8459 0.563137
\(696\) −13.4179 −0.508606
\(697\) 1.37518 0.0520885
\(698\) 11.0457 0.418088
\(699\) −34.1729 −1.29254
\(700\) −10.2829 −0.388656
\(701\) −1.49858 −0.0566007 −0.0283003 0.999599i \(-0.509009\pi\)
−0.0283003 + 0.999599i \(0.509009\pi\)
\(702\) −0.307448 −0.0116039
\(703\) 6.16190 0.232400
\(704\) −4.46025 −0.168102
\(705\) −10.9219 −0.411343
\(706\) −28.5221 −1.07344
\(707\) 14.5929 0.548821
\(708\) 8.87468 0.333531
\(709\) 31.0293 1.16533 0.582665 0.812712i \(-0.302010\pi\)
0.582665 + 0.812712i \(0.302010\pi\)
\(710\) 8.95085 0.335919
\(711\) 32.3732 1.21409
\(712\) −12.7695 −0.478559
\(713\) −75.9486 −2.84430
\(714\) 9.47225 0.354490
\(715\) 10.8650 0.406328
\(716\) 20.6354 0.771183
\(717\) −1.61324 −0.0602477
\(718\) 13.3587 0.498543
\(719\) 43.3963 1.61841 0.809204 0.587528i \(-0.199899\pi\)
0.809204 + 0.587528i \(0.199899\pi\)
\(720\) −3.67038 −0.136787
\(721\) 31.5625 1.17545
\(722\) −10.0343 −0.373439
\(723\) 64.9067 2.41391
\(724\) −6.42961 −0.238955
\(725\) −19.4164 −0.721108
\(726\) −21.8967 −0.812662
\(727\) −42.4453 −1.57421 −0.787104 0.616820i \(-0.788421\pi\)
−0.787104 + 0.616820i \(0.788421\pi\)
\(728\) 5.86450 0.217353
\(729\) −28.0947 −1.04055
\(730\) −0.962642 −0.0356290
\(731\) 5.69146 0.210506
\(732\) 21.2304 0.784698
\(733\) 40.3517 1.49042 0.745212 0.666828i \(-0.232348\pi\)
0.745212 + 0.666828i \(0.232348\pi\)
\(734\) −4.65239 −0.171723
\(735\) 3.92802 0.144887
\(736\) −7.98056 −0.294167
\(737\) −55.5952 −2.04787
\(738\) −3.15838 −0.116262
\(739\) 43.9563 1.61696 0.808479 0.588525i \(-0.200291\pi\)
0.808479 + 0.588525i \(0.200291\pi\)
\(740\) −2.46721 −0.0906963
\(741\) −14.9785 −0.550249
\(742\) −9.06823 −0.332905
\(743\) 40.3937 1.48190 0.740950 0.671560i \(-0.234376\pi\)
0.740950 + 0.671560i \(0.234376\pi\)
\(744\) −23.4301 −0.858991
\(745\) −0.850137 −0.0311466
\(746\) 2.22264 0.0813767
\(747\) −19.8299 −0.725540
\(748\) 5.94541 0.217386
\(749\) −26.6878 −0.975151
\(750\) −25.2743 −0.922886
\(751\) −35.7969 −1.30625 −0.653124 0.757251i \(-0.726542\pi\)
−0.653124 + 0.757251i \(0.726542\pi\)
\(752\) −3.70023 −0.134933
\(753\) −50.8736 −1.85394
\(754\) 11.0735 0.403274
\(755\) 23.9369 0.871154
\(756\) −0.436743 −0.0158842
\(757\) 13.5904 0.493951 0.246976 0.969022i \(-0.420563\pi\)
0.246976 + 0.969022i \(0.420563\pi\)
\(758\) 6.43360 0.233679
\(759\) −87.6357 −3.18097
\(760\) −3.58983 −0.130217
\(761\) 2.53674 0.0919569 0.0459784 0.998942i \(-0.485359\pi\)
0.0459784 + 0.998942i \(0.485359\pi\)
\(762\) −23.9842 −0.868857
\(763\) 11.8231 0.428026
\(764\) 1.49819 0.0542026
\(765\) 4.89252 0.176890
\(766\) −13.0227 −0.470529
\(767\) −7.32407 −0.264457
\(768\) −2.46200 −0.0888399
\(769\) −17.9429 −0.647038 −0.323519 0.946222i \(-0.604866\pi\)
−0.323519 + 0.946222i \(0.604866\pi\)
\(770\) 15.4342 0.556210
\(771\) 57.2201 2.06073
\(772\) −6.67653 −0.240293
\(773\) −31.9596 −1.14951 −0.574754 0.818326i \(-0.694902\pi\)
−0.574754 + 0.818326i \(0.694902\pi\)
\(774\) −13.0716 −0.469851
\(775\) −33.9046 −1.21789
\(776\) 12.6583 0.454407
\(777\) −14.6236 −0.524619
\(778\) 14.1203 0.506238
\(779\) −3.08907 −0.110677
\(780\) 5.99735 0.214740
\(781\) 33.2998 1.19156
\(782\) 10.6379 0.380410
\(783\) −0.824670 −0.0294713
\(784\) 1.33077 0.0475275
\(785\) −1.18619 −0.0423368
\(786\) −32.5866 −1.16233
\(787\) −39.5577 −1.41008 −0.705041 0.709167i \(-0.749071\pi\)
−0.705041 + 0.709167i \(0.749071\pi\)
\(788\) −3.38365 −0.120538
\(789\) 29.8636 1.06317
\(790\) −12.6777 −0.451051
\(791\) −18.5868 −0.660869
\(792\) −13.6549 −0.485205
\(793\) −17.5210 −0.622188
\(794\) −5.80414 −0.205981
\(795\) −9.27365 −0.328903
\(796\) −12.5763 −0.445755
\(797\) −22.4510 −0.795256 −0.397628 0.917547i \(-0.630167\pi\)
−0.397628 + 0.917547i \(0.630167\pi\)
\(798\) −21.2776 −0.753219
\(799\) 4.93231 0.174493
\(800\) −3.56264 −0.125958
\(801\) −39.0934 −1.38130
\(802\) −13.0278 −0.460029
\(803\) −3.58131 −0.126382
\(804\) −30.6878 −1.08228
\(805\) 27.6158 0.973330
\(806\) 19.3364 0.681094
\(807\) 38.9247 1.37021
\(808\) 5.05589 0.177866
\(809\) 46.5502 1.63662 0.818308 0.574780i \(-0.194912\pi\)
0.818308 + 0.574780i \(0.194912\pi\)
\(810\) 10.5645 0.371199
\(811\) 10.6732 0.374787 0.187393 0.982285i \(-0.439996\pi\)
0.187393 + 0.982285i \(0.439996\pi\)
\(812\) 15.7304 0.552029
\(813\) 54.0663 1.89619
\(814\) −9.17872 −0.321714
\(815\) 21.5680 0.755495
\(816\) 3.28179 0.114886
\(817\) −12.7848 −0.447283
\(818\) −11.9401 −0.417477
\(819\) 17.9539 0.627361
\(820\) 1.23685 0.0431928
\(821\) −40.3487 −1.40818 −0.704090 0.710111i \(-0.748645\pi\)
−0.704090 + 0.710111i \(0.748645\pi\)
\(822\) 12.5661 0.438293
\(823\) −28.6414 −0.998375 −0.499187 0.866494i \(-0.666368\pi\)
−0.499187 + 0.866494i \(0.666368\pi\)
\(824\) 10.9353 0.380947
\(825\) −39.1219 −1.36205
\(826\) −10.4041 −0.362007
\(827\) −38.0531 −1.32323 −0.661617 0.749842i \(-0.730130\pi\)
−0.661617 + 0.749842i \(0.730130\pi\)
\(828\) −24.4322 −0.849076
\(829\) −17.0035 −0.590556 −0.295278 0.955411i \(-0.595412\pi\)
−0.295278 + 0.955411i \(0.595412\pi\)
\(830\) 7.76560 0.269548
\(831\) −68.3163 −2.36987
\(832\) 2.03184 0.0704412
\(833\) −1.77388 −0.0614615
\(834\) 30.4869 1.05567
\(835\) −3.98405 −0.137874
\(836\) −13.3552 −0.461900
\(837\) −1.44002 −0.0497745
\(838\) 14.8690 0.513641
\(839\) −9.60081 −0.331457 −0.165728 0.986171i \(-0.552998\pi\)
−0.165728 + 0.986171i \(0.552998\pi\)
\(840\) 8.51949 0.293950
\(841\) 0.702575 0.0242267
\(842\) 1.29715 0.0447028
\(843\) 4.92085 0.169483
\(844\) −20.9915 −0.722559
\(845\) 10.6362 0.365896
\(846\) −11.3281 −0.389468
\(847\) 25.6704 0.882044
\(848\) −3.14181 −0.107890
\(849\) −39.6814 −1.36186
\(850\) 4.74892 0.162886
\(851\) −16.4231 −0.562978
\(852\) 18.3811 0.629724
\(853\) −28.2713 −0.967990 −0.483995 0.875071i \(-0.660815\pi\)
−0.483995 + 0.875071i \(0.660815\pi\)
\(854\) −24.8893 −0.851694
\(855\) −10.9901 −0.375854
\(856\) −9.24635 −0.316034
\(857\) −36.5633 −1.24898 −0.624489 0.781034i \(-0.714693\pi\)
−0.624489 + 0.781034i \(0.714693\pi\)
\(858\) 22.3119 0.761715
\(859\) −15.0619 −0.513906 −0.256953 0.966424i \(-0.582719\pi\)
−0.256953 + 0.966424i \(0.582719\pi\)
\(860\) 5.11899 0.174556
\(861\) 7.33107 0.249842
\(862\) −29.6509 −1.00991
\(863\) 9.07086 0.308776 0.154388 0.988010i \(-0.450659\pi\)
0.154388 + 0.988010i \(0.450659\pi\)
\(864\) −0.151315 −0.00514785
\(865\) 0.784703 0.0266807
\(866\) −25.1200 −0.853612
\(867\) 37.4795 1.27287
\(868\) 27.4681 0.932329
\(869\) −47.1646 −1.59995
\(870\) 16.0867 0.545391
\(871\) 25.3260 0.858138
\(872\) 4.09628 0.138717
\(873\) 38.7530 1.31159
\(874\) −23.8960 −0.808294
\(875\) 29.6301 1.00168
\(876\) −1.97684 −0.0667912
\(877\) 19.4837 0.657917 0.328958 0.944344i \(-0.393302\pi\)
0.328958 + 0.944344i \(0.393302\pi\)
\(878\) 8.97809 0.302996
\(879\) 64.0659 2.16089
\(880\) 5.34739 0.180260
\(881\) 3.50048 0.117934 0.0589671 0.998260i \(-0.481219\pi\)
0.0589671 + 0.998260i \(0.481219\pi\)
\(882\) 4.07410 0.137182
\(883\) 51.7781 1.74247 0.871236 0.490864i \(-0.163319\pi\)
0.871236 + 0.490864i \(0.163319\pi\)
\(884\) −2.70839 −0.0910929
\(885\) −10.6398 −0.357654
\(886\) −14.8845 −0.500054
\(887\) 40.4064 1.35671 0.678357 0.734733i \(-0.262692\pi\)
0.678357 + 0.734733i \(0.262692\pi\)
\(888\) −5.06654 −0.170022
\(889\) 28.1177 0.943037
\(890\) 15.3094 0.513171
\(891\) 39.3030 1.31670
\(892\) 23.4488 0.785123
\(893\) −11.0795 −0.370761
\(894\) −1.74580 −0.0583884
\(895\) −24.7398 −0.826960
\(896\) 2.88631 0.0964248
\(897\) 39.9218 1.33295
\(898\) 2.41434 0.0805675
\(899\) 51.8661 1.72983
\(900\) −10.9069 −0.363563
\(901\) 4.18795 0.139521
\(902\) 4.60146 0.153212
\(903\) 30.3412 1.00969
\(904\) −6.43963 −0.214179
\(905\) 7.70845 0.256237
\(906\) 49.1558 1.63309
\(907\) −1.34959 −0.0448124 −0.0224062 0.999749i \(-0.507133\pi\)
−0.0224062 + 0.999749i \(0.507133\pi\)
\(908\) 4.39085 0.145716
\(909\) 15.4784 0.513386
\(910\) −7.03094 −0.233073
\(911\) 14.2620 0.472520 0.236260 0.971690i \(-0.424078\pi\)
0.236260 + 0.971690i \(0.424078\pi\)
\(912\) −7.37191 −0.244108
\(913\) 28.8903 0.956130
\(914\) −6.08220 −0.201181
\(915\) −25.4531 −0.841453
\(916\) −7.91979 −0.261677
\(917\) 38.2026 1.26156
\(918\) 0.201700 0.00665708
\(919\) −19.8407 −0.654483 −0.327242 0.944941i \(-0.606119\pi\)
−0.327242 + 0.944941i \(0.606119\pi\)
\(920\) 9.56787 0.315443
\(921\) 67.0626 2.20979
\(922\) −16.7137 −0.550437
\(923\) −15.1695 −0.499309
\(924\) 31.6950 1.04269
\(925\) −7.33154 −0.241060
\(926\) −33.7225 −1.10819
\(927\) 33.4778 1.09956
\(928\) 5.45001 0.178905
\(929\) −41.6358 −1.36603 −0.683013 0.730406i \(-0.739331\pi\)
−0.683013 + 0.730406i \(0.739331\pi\)
\(930\) 28.0904 0.921119
\(931\) 3.98469 0.130593
\(932\) 13.8801 0.454658
\(933\) 53.3686 1.74721
\(934\) −23.7353 −0.776642
\(935\) −7.12794 −0.233108
\(936\) 6.22038 0.203320
\(937\) 2.68119 0.0875905 0.0437953 0.999041i \(-0.486055\pi\)
0.0437953 + 0.999041i \(0.486055\pi\)
\(938\) 35.9766 1.17468
\(939\) 3.22129 0.105123
\(940\) 4.43619 0.144693
\(941\) −33.2694 −1.08455 −0.542276 0.840200i \(-0.682437\pi\)
−0.542276 + 0.840200i \(0.682437\pi\)
\(942\) −2.43590 −0.0793659
\(943\) 8.23322 0.268110
\(944\) −3.60466 −0.117322
\(945\) 0.523610 0.0170330
\(946\) 19.0441 0.619178
\(947\) −21.4682 −0.697622 −0.348811 0.937193i \(-0.613414\pi\)
−0.348811 + 0.937193i \(0.613414\pi\)
\(948\) −26.0343 −0.845553
\(949\) 1.63144 0.0529588
\(950\) −10.6675 −0.346100
\(951\) 48.8754 1.58489
\(952\) −3.84738 −0.124694
\(953\) 51.7762 1.67720 0.838598 0.544751i \(-0.183376\pi\)
0.838598 + 0.544751i \(0.183376\pi\)
\(954\) −9.61853 −0.311411
\(955\) −1.79618 −0.0581229
\(956\) 0.655256 0.0211925
\(957\) 59.8474 1.93459
\(958\) 14.8171 0.478717
\(959\) −14.7317 −0.475713
\(960\) 2.95169 0.0952654
\(961\) 59.5676 1.92153
\(962\) 4.18130 0.134811
\(963\) −28.3073 −0.912191
\(964\) −26.3634 −0.849107
\(965\) 8.00448 0.257673
\(966\) 56.7106 1.82463
\(967\) 25.6049 0.823397 0.411699 0.911320i \(-0.364936\pi\)
0.411699 + 0.911320i \(0.364936\pi\)
\(968\) 8.89384 0.285859
\(969\) 9.82658 0.315675
\(970\) −15.1760 −0.487273
\(971\) 5.32845 0.170998 0.0854991 0.996338i \(-0.472752\pi\)
0.0854991 + 0.996338i \(0.472752\pi\)
\(972\) 22.1487 0.710421
\(973\) −35.7410 −1.14580
\(974\) −0.442777 −0.0141875
\(975\) 17.8217 0.570752
\(976\) −8.62323 −0.276023
\(977\) −33.6344 −1.07606 −0.538030 0.842926i \(-0.680831\pi\)
−0.538030 + 0.842926i \(0.680831\pi\)
\(978\) 44.2911 1.41627
\(979\) 56.9553 1.82030
\(980\) −1.59546 −0.0509651
\(981\) 12.5406 0.400390
\(982\) 2.45714 0.0784105
\(983\) 19.9849 0.637418 0.318709 0.947853i \(-0.396751\pi\)
0.318709 + 0.947853i \(0.396751\pi\)
\(984\) 2.53995 0.0809706
\(985\) 4.05665 0.129256
\(986\) −7.26472 −0.231356
\(987\) 26.2942 0.836952
\(988\) 6.08387 0.193554
\(989\) 34.0749 1.08352
\(990\) 16.3708 0.520299
\(991\) 31.3951 0.997298 0.498649 0.866804i \(-0.333830\pi\)
0.498649 + 0.866804i \(0.333830\pi\)
\(992\) 9.51670 0.302156
\(993\) −5.49708 −0.174445
\(994\) −21.5489 −0.683488
\(995\) 15.0777 0.477995
\(996\) 15.9471 0.505303
\(997\) −33.9670 −1.07574 −0.537872 0.843026i \(-0.680772\pi\)
−0.537872 + 0.843026i \(0.680772\pi\)
\(998\) −32.6070 −1.03216
\(999\) −0.311391 −0.00985197
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 8026.2.a.a.1.10 71
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8026.2.a.a.1.10 71 1.1 even 1 trivial