Properties

Label 6026.2.a.g.1.18
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6026,2,Mod(1,6026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6026.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.1178522580\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 6026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.90172 q^{3} +1.00000 q^{4} -3.81206 q^{5} +1.90172 q^{6} +1.69979 q^{7} +1.00000 q^{8} +0.616557 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.90172 q^{3} +1.00000 q^{4} -3.81206 q^{5} +1.90172 q^{6} +1.69979 q^{7} +1.00000 q^{8} +0.616557 q^{9} -3.81206 q^{10} +3.78817 q^{11} +1.90172 q^{12} +0.0820802 q^{13} +1.69979 q^{14} -7.24948 q^{15} +1.00000 q^{16} -5.51688 q^{17} +0.616557 q^{18} -5.52339 q^{19} -3.81206 q^{20} +3.23253 q^{21} +3.78817 q^{22} -1.00000 q^{23} +1.90172 q^{24} +9.53177 q^{25} +0.0820802 q^{26} -4.53265 q^{27} +1.69979 q^{28} -7.55480 q^{29} -7.24948 q^{30} -4.11848 q^{31} +1.00000 q^{32} +7.20406 q^{33} -5.51688 q^{34} -6.47969 q^{35} +0.616557 q^{36} -7.13271 q^{37} -5.52339 q^{38} +0.156094 q^{39} -3.81206 q^{40} -0.552467 q^{41} +3.23253 q^{42} -2.03192 q^{43} +3.78817 q^{44} -2.35035 q^{45} -1.00000 q^{46} +10.9517 q^{47} +1.90172 q^{48} -4.11072 q^{49} +9.53177 q^{50} -10.4916 q^{51} +0.0820802 q^{52} -10.8669 q^{53} -4.53265 q^{54} -14.4407 q^{55} +1.69979 q^{56} -10.5040 q^{57} -7.55480 q^{58} +7.85858 q^{59} -7.24948 q^{60} +8.75538 q^{61} -4.11848 q^{62} +1.04802 q^{63} +1.00000 q^{64} -0.312894 q^{65} +7.20406 q^{66} +8.48643 q^{67} -5.51688 q^{68} -1.90172 q^{69} -6.47969 q^{70} +4.08933 q^{71} +0.616557 q^{72} -0.0747777 q^{73} -7.13271 q^{74} +18.1268 q^{75} -5.52339 q^{76} +6.43908 q^{77} +0.156094 q^{78} -13.0743 q^{79} -3.81206 q^{80} -10.4695 q^{81} -0.552467 q^{82} +8.10379 q^{83} +3.23253 q^{84} +21.0306 q^{85} -2.03192 q^{86} -14.3671 q^{87} +3.78817 q^{88} +8.42844 q^{89} -2.35035 q^{90} +0.139519 q^{91} -1.00000 q^{92} -7.83222 q^{93} +10.9517 q^{94} +21.0555 q^{95} +1.90172 q^{96} -8.84960 q^{97} -4.11072 q^{98} +2.33562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.90172 1.09796 0.548981 0.835835i \(-0.315016\pi\)
0.548981 + 0.835835i \(0.315016\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.81206 −1.70480 −0.852402 0.522888i \(-0.824855\pi\)
−0.852402 + 0.522888i \(0.824855\pi\)
\(6\) 1.90172 0.776376
\(7\) 1.69979 0.642459 0.321230 0.947001i \(-0.395904\pi\)
0.321230 + 0.947001i \(0.395904\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.616557 0.205519
\(10\) −3.81206 −1.20548
\(11\) 3.78817 1.14218 0.571088 0.820889i \(-0.306521\pi\)
0.571088 + 0.820889i \(0.306521\pi\)
\(12\) 1.90172 0.548981
\(13\) 0.0820802 0.0227650 0.0113825 0.999935i \(-0.496377\pi\)
0.0113825 + 0.999935i \(0.496377\pi\)
\(14\) 1.69979 0.454287
\(15\) −7.24948 −1.87181
\(16\) 1.00000 0.250000
\(17\) −5.51688 −1.33804 −0.669019 0.743245i \(-0.733286\pi\)
−0.669019 + 0.743245i \(0.733286\pi\)
\(18\) 0.616557 0.145324
\(19\) −5.52339 −1.26715 −0.633577 0.773680i \(-0.718414\pi\)
−0.633577 + 0.773680i \(0.718414\pi\)
\(20\) −3.81206 −0.852402
\(21\) 3.23253 0.705395
\(22\) 3.78817 0.807641
\(23\) −1.00000 −0.208514
\(24\) 1.90172 0.388188
\(25\) 9.53177 1.90635
\(26\) 0.0820802 0.0160973
\(27\) −4.53265 −0.872309
\(28\) 1.69979 0.321230
\(29\) −7.55480 −1.40289 −0.701445 0.712723i \(-0.747461\pi\)
−0.701445 + 0.712723i \(0.747461\pi\)
\(30\) −7.24948 −1.32357
\(31\) −4.11848 −0.739701 −0.369851 0.929091i \(-0.620591\pi\)
−0.369851 + 0.929091i \(0.620591\pi\)
\(32\) 1.00000 0.176777
\(33\) 7.20406 1.25407
\(34\) −5.51688 −0.946136
\(35\) −6.47969 −1.09527
\(36\) 0.616557 0.102759
\(37\) −7.13271 −1.17261 −0.586305 0.810090i \(-0.699418\pi\)
−0.586305 + 0.810090i \(0.699418\pi\)
\(38\) −5.52339 −0.896013
\(39\) 0.156094 0.0249950
\(40\) −3.81206 −0.602739
\(41\) −0.552467 −0.0862808 −0.0431404 0.999069i \(-0.513736\pi\)
−0.0431404 + 0.999069i \(0.513736\pi\)
\(42\) 3.23253 0.498790
\(43\) −2.03192 −0.309865 −0.154932 0.987925i \(-0.549516\pi\)
−0.154932 + 0.987925i \(0.549516\pi\)
\(44\) 3.78817 0.571088
\(45\) −2.35035 −0.350369
\(46\) −1.00000 −0.147442
\(47\) 10.9517 1.59747 0.798736 0.601682i \(-0.205502\pi\)
0.798736 + 0.601682i \(0.205502\pi\)
\(48\) 1.90172 0.274490
\(49\) −4.11072 −0.587246
\(50\) 9.53177 1.34800
\(51\) −10.4916 −1.46911
\(52\) 0.0820802 0.0113825
\(53\) −10.8669 −1.49268 −0.746341 0.665564i \(-0.768191\pi\)
−0.746341 + 0.665564i \(0.768191\pi\)
\(54\) −4.53265 −0.616816
\(55\) −14.4407 −1.94719
\(56\) 1.69979 0.227144
\(57\) −10.5040 −1.39129
\(58\) −7.55480 −0.991993
\(59\) 7.85858 1.02310 0.511550 0.859253i \(-0.329071\pi\)
0.511550 + 0.859253i \(0.329071\pi\)
\(60\) −7.24948 −0.935904
\(61\) 8.75538 1.12101 0.560506 0.828150i \(-0.310607\pi\)
0.560506 + 0.828150i \(0.310607\pi\)
\(62\) −4.11848 −0.523048
\(63\) 1.04802 0.132037
\(64\) 1.00000 0.125000
\(65\) −0.312894 −0.0388098
\(66\) 7.20406 0.886758
\(67\) 8.48643 1.03678 0.518391 0.855144i \(-0.326531\pi\)
0.518391 + 0.855144i \(0.326531\pi\)
\(68\) −5.51688 −0.669019
\(69\) −1.90172 −0.228941
\(70\) −6.47969 −0.774470
\(71\) 4.08933 0.485314 0.242657 0.970112i \(-0.421981\pi\)
0.242657 + 0.970112i \(0.421981\pi\)
\(72\) 0.616557 0.0726619
\(73\) −0.0747777 −0.00875206 −0.00437603 0.999990i \(-0.501393\pi\)
−0.00437603 + 0.999990i \(0.501393\pi\)
\(74\) −7.13271 −0.829161
\(75\) 18.1268 2.09310
\(76\) −5.52339 −0.633577
\(77\) 6.43908 0.733802
\(78\) 0.156094 0.0176742
\(79\) −13.0743 −1.47098 −0.735488 0.677538i \(-0.763047\pi\)
−0.735488 + 0.677538i \(0.763047\pi\)
\(80\) −3.81206 −0.426201
\(81\) −10.4695 −1.16328
\(82\) −0.552467 −0.0610097
\(83\) 8.10379 0.889506 0.444753 0.895653i \(-0.353291\pi\)
0.444753 + 0.895653i \(0.353291\pi\)
\(84\) 3.23253 0.352698
\(85\) 21.0306 2.28109
\(86\) −2.03192 −0.219107
\(87\) −14.3671 −1.54032
\(88\) 3.78817 0.403820
\(89\) 8.42844 0.893412 0.446706 0.894681i \(-0.352597\pi\)
0.446706 + 0.894681i \(0.352597\pi\)
\(90\) −2.35035 −0.247748
\(91\) 0.139519 0.0146256
\(92\) −1.00000 −0.104257
\(93\) −7.83222 −0.812163
\(94\) 10.9517 1.12958
\(95\) 21.0555 2.16025
\(96\) 1.90172 0.194094
\(97\) −8.84960 −0.898541 −0.449271 0.893396i \(-0.648316\pi\)
−0.449271 + 0.893396i \(0.648316\pi\)
\(98\) −4.11072 −0.415246
\(99\) 2.33562 0.234739
\(100\) 9.53177 0.953177
\(101\) −11.1586 −1.11032 −0.555161 0.831743i \(-0.687343\pi\)
−0.555161 + 0.831743i \(0.687343\pi\)
\(102\) −10.4916 −1.03882
\(103\) −5.58492 −0.550298 −0.275149 0.961402i \(-0.588727\pi\)
−0.275149 + 0.961402i \(0.588727\pi\)
\(104\) 0.0820802 0.00804863
\(105\) −12.3226 −1.20256
\(106\) −10.8669 −1.05549
\(107\) −5.15619 −0.498468 −0.249234 0.968443i \(-0.580179\pi\)
−0.249234 + 0.968443i \(0.580179\pi\)
\(108\) −4.53265 −0.436155
\(109\) −3.75229 −0.359404 −0.179702 0.983721i \(-0.557513\pi\)
−0.179702 + 0.983721i \(0.557513\pi\)
\(110\) −14.4407 −1.37687
\(111\) −13.5644 −1.28748
\(112\) 1.69979 0.160615
\(113\) −17.4683 −1.64328 −0.821640 0.570007i \(-0.806940\pi\)
−0.821640 + 0.570007i \(0.806940\pi\)
\(114\) −10.5040 −0.983787
\(115\) 3.81206 0.355476
\(116\) −7.55480 −0.701445
\(117\) 0.0506071 0.00467863
\(118\) 7.85858 0.723441
\(119\) −9.37752 −0.859635
\(120\) −7.24948 −0.661784
\(121\) 3.35024 0.304567
\(122\) 8.75538 0.792675
\(123\) −1.05064 −0.0947330
\(124\) −4.11848 −0.369851
\(125\) −17.2754 −1.54516
\(126\) 1.04802 0.0933646
\(127\) 7.83989 0.695678 0.347839 0.937554i \(-0.386916\pi\)
0.347839 + 0.937554i \(0.386916\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.86415 −0.340220
\(130\) −0.312894 −0.0274427
\(131\) 1.00000 0.0873704
\(132\) 7.20406 0.627033
\(133\) −9.38860 −0.814095
\(134\) 8.48643 0.733116
\(135\) 17.2787 1.48712
\(136\) −5.51688 −0.473068
\(137\) 6.68048 0.570752 0.285376 0.958416i \(-0.407882\pi\)
0.285376 + 0.958416i \(0.407882\pi\)
\(138\) −1.90172 −0.161886
\(139\) 4.62069 0.391922 0.195961 0.980612i \(-0.437217\pi\)
0.195961 + 0.980612i \(0.437217\pi\)
\(140\) −6.47969 −0.547633
\(141\) 20.8271 1.75396
\(142\) 4.08933 0.343169
\(143\) 0.310934 0.0260016
\(144\) 0.616557 0.0513797
\(145\) 28.7993 2.39165
\(146\) −0.0747777 −0.00618864
\(147\) −7.81746 −0.644773
\(148\) −7.13271 −0.586305
\(149\) 7.66899 0.628268 0.314134 0.949379i \(-0.398286\pi\)
0.314134 + 0.949379i \(0.398286\pi\)
\(150\) 18.1268 1.48005
\(151\) −15.1421 −1.23225 −0.616125 0.787648i \(-0.711299\pi\)
−0.616125 + 0.787648i \(0.711299\pi\)
\(152\) −5.52339 −0.448006
\(153\) −3.40147 −0.274992
\(154\) 6.43908 0.518876
\(155\) 15.6999 1.26104
\(156\) 0.156094 0.0124975
\(157\) −19.7962 −1.57991 −0.789956 0.613163i \(-0.789897\pi\)
−0.789956 + 0.613163i \(0.789897\pi\)
\(158\) −13.0743 −1.04014
\(159\) −20.6658 −1.63891
\(160\) −3.81206 −0.301369
\(161\) −1.69979 −0.133962
\(162\) −10.4695 −0.822564
\(163\) −24.5017 −1.91912 −0.959561 0.281501i \(-0.909168\pi\)
−0.959561 + 0.281501i \(0.909168\pi\)
\(164\) −0.552467 −0.0431404
\(165\) −27.4623 −2.13793
\(166\) 8.10379 0.628976
\(167\) 20.5000 1.58633 0.793167 0.609004i \(-0.208430\pi\)
0.793167 + 0.609004i \(0.208430\pi\)
\(168\) 3.23253 0.249395
\(169\) −12.9933 −0.999482
\(170\) 21.0306 1.61298
\(171\) −3.40549 −0.260424
\(172\) −2.03192 −0.154932
\(173\) 5.38601 0.409491 0.204745 0.978815i \(-0.434363\pi\)
0.204745 + 0.978815i \(0.434363\pi\)
\(174\) −14.3671 −1.08917
\(175\) 16.2020 1.22475
\(176\) 3.78817 0.285544
\(177\) 14.9449 1.12332
\(178\) 8.42844 0.631738
\(179\) 1.59431 0.119165 0.0595823 0.998223i \(-0.481023\pi\)
0.0595823 + 0.998223i \(0.481023\pi\)
\(180\) −2.35035 −0.175185
\(181\) 6.50617 0.483600 0.241800 0.970326i \(-0.422262\pi\)
0.241800 + 0.970326i \(0.422262\pi\)
\(182\) 0.139519 0.0103418
\(183\) 16.6503 1.23083
\(184\) −1.00000 −0.0737210
\(185\) 27.1903 1.99907
\(186\) −7.83222 −0.574286
\(187\) −20.8989 −1.52828
\(188\) 10.9517 0.798736
\(189\) −7.70455 −0.560423
\(190\) 21.0555 1.52753
\(191\) −20.6033 −1.49080 −0.745402 0.666615i \(-0.767743\pi\)
−0.745402 + 0.666615i \(0.767743\pi\)
\(192\) 1.90172 0.137245
\(193\) 1.60684 0.115663 0.0578315 0.998326i \(-0.481581\pi\)
0.0578315 + 0.998326i \(0.481581\pi\)
\(194\) −8.84960 −0.635365
\(195\) −0.595039 −0.0426116
\(196\) −4.11072 −0.293623
\(197\) 17.9324 1.27763 0.638815 0.769360i \(-0.279425\pi\)
0.638815 + 0.769360i \(0.279425\pi\)
\(198\) 2.33562 0.165985
\(199\) −11.7766 −0.834820 −0.417410 0.908718i \(-0.637062\pi\)
−0.417410 + 0.908718i \(0.637062\pi\)
\(200\) 9.53177 0.673998
\(201\) 16.1388 1.13835
\(202\) −11.1586 −0.785116
\(203\) −12.8415 −0.901300
\(204\) −10.4916 −0.734557
\(205\) 2.10603 0.147092
\(206\) −5.58492 −0.389120
\(207\) −0.616557 −0.0428536
\(208\) 0.0820802 0.00569124
\(209\) −20.9236 −1.44731
\(210\) −12.3226 −0.850339
\(211\) 15.5611 1.07127 0.535635 0.844450i \(-0.320072\pi\)
0.535635 + 0.844450i \(0.320072\pi\)
\(212\) −10.8669 −0.746341
\(213\) 7.77678 0.532856
\(214\) −5.15619 −0.352470
\(215\) 7.74579 0.528259
\(216\) −4.53265 −0.308408
\(217\) −7.00054 −0.475228
\(218\) −3.75229 −0.254137
\(219\) −0.142207 −0.00960943
\(220\) −14.4407 −0.973593
\(221\) −0.452826 −0.0304604
\(222\) −13.5644 −0.910386
\(223\) −3.02774 −0.202753 −0.101376 0.994848i \(-0.532325\pi\)
−0.101376 + 0.994848i \(0.532325\pi\)
\(224\) 1.69979 0.113572
\(225\) 5.87688 0.391792
\(226\) −17.4683 −1.16197
\(227\) 7.21767 0.479054 0.239527 0.970890i \(-0.423008\pi\)
0.239527 + 0.970890i \(0.423008\pi\)
\(228\) −10.5040 −0.695643
\(229\) −7.54120 −0.498337 −0.249168 0.968460i \(-0.580157\pi\)
−0.249168 + 0.968460i \(0.580157\pi\)
\(230\) 3.81206 0.251360
\(231\) 12.2454 0.805686
\(232\) −7.55480 −0.495997
\(233\) −15.3177 −1.00349 −0.501747 0.865014i \(-0.667309\pi\)
−0.501747 + 0.865014i \(0.667309\pi\)
\(234\) 0.0506071 0.00330829
\(235\) −41.7486 −2.72338
\(236\) 7.85858 0.511550
\(237\) −24.8638 −1.61507
\(238\) −9.37752 −0.607854
\(239\) 4.33818 0.280614 0.140307 0.990108i \(-0.455191\pi\)
0.140307 + 0.990108i \(0.455191\pi\)
\(240\) −7.24948 −0.467952
\(241\) 7.00632 0.451316 0.225658 0.974207i \(-0.427547\pi\)
0.225658 + 0.974207i \(0.427547\pi\)
\(242\) 3.35024 0.215361
\(243\) −6.31220 −0.404928
\(244\) 8.75538 0.560506
\(245\) 15.6703 1.00114
\(246\) −1.05064 −0.0669863
\(247\) −0.453361 −0.0288467
\(248\) −4.11848 −0.261524
\(249\) 15.4112 0.976643
\(250\) −17.2754 −1.09259
\(251\) −1.97249 −0.124503 −0.0622513 0.998061i \(-0.519828\pi\)
−0.0622513 + 0.998061i \(0.519828\pi\)
\(252\) 1.04802 0.0660187
\(253\) −3.78817 −0.238160
\(254\) 7.83989 0.491918
\(255\) 39.9945 2.50455
\(256\) 1.00000 0.0625000
\(257\) 25.3693 1.58249 0.791245 0.611499i \(-0.209433\pi\)
0.791245 + 0.611499i \(0.209433\pi\)
\(258\) −3.86415 −0.240572
\(259\) −12.1241 −0.753354
\(260\) −0.312894 −0.0194049
\(261\) −4.65796 −0.288320
\(262\) 1.00000 0.0617802
\(263\) −7.48012 −0.461244 −0.230622 0.973043i \(-0.574076\pi\)
−0.230622 + 0.973043i \(0.574076\pi\)
\(264\) 7.20406 0.443379
\(265\) 41.4252 2.54473
\(266\) −9.38860 −0.575652
\(267\) 16.0286 0.980932
\(268\) 8.48643 0.518391
\(269\) 17.7556 1.08258 0.541290 0.840836i \(-0.317936\pi\)
0.541290 + 0.840836i \(0.317936\pi\)
\(270\) 17.2787 1.05155
\(271\) −17.8908 −1.08679 −0.543394 0.839478i \(-0.682861\pi\)
−0.543394 + 0.839478i \(0.682861\pi\)
\(272\) −5.51688 −0.334510
\(273\) 0.265327 0.0160583
\(274\) 6.68048 0.403582
\(275\) 36.1080 2.17739
\(276\) −1.90172 −0.114470
\(277\) −8.98310 −0.539742 −0.269871 0.962896i \(-0.586981\pi\)
−0.269871 + 0.962896i \(0.586981\pi\)
\(278\) 4.62069 0.277131
\(279\) −2.53928 −0.152023
\(280\) −6.47969 −0.387235
\(281\) 26.4602 1.57848 0.789241 0.614084i \(-0.210474\pi\)
0.789241 + 0.614084i \(0.210474\pi\)
\(282\) 20.8271 1.24024
\(283\) −12.7482 −0.757803 −0.378902 0.925437i \(-0.623698\pi\)
−0.378902 + 0.925437i \(0.623698\pi\)
\(284\) 4.08933 0.242657
\(285\) 40.0417 2.37187
\(286\) 0.310934 0.0183859
\(287\) −0.939076 −0.0554319
\(288\) 0.616557 0.0363309
\(289\) 13.4359 0.790348
\(290\) 28.7993 1.69115
\(291\) −16.8295 −0.986563
\(292\) −0.0747777 −0.00437603
\(293\) −20.2959 −1.18570 −0.592850 0.805313i \(-0.701997\pi\)
−0.592850 + 0.805313i \(0.701997\pi\)
\(294\) −7.81746 −0.455924
\(295\) −29.9574 −1.74419
\(296\) −7.13271 −0.414580
\(297\) −17.1705 −0.996331
\(298\) 7.66899 0.444253
\(299\) −0.0820802 −0.00474682
\(300\) 18.1268 1.04655
\(301\) −3.45383 −0.199076
\(302\) −15.1421 −0.871333
\(303\) −21.2206 −1.21909
\(304\) −5.52339 −0.316788
\(305\) −33.3760 −1.91111
\(306\) −3.40147 −0.194449
\(307\) 18.9836 1.08345 0.541725 0.840556i \(-0.317771\pi\)
0.541725 + 0.840556i \(0.317771\pi\)
\(308\) 6.43908 0.366901
\(309\) −10.6210 −0.604206
\(310\) 15.6999 0.891693
\(311\) −12.9589 −0.734834 −0.367417 0.930056i \(-0.619758\pi\)
−0.367417 + 0.930056i \(0.619758\pi\)
\(312\) 0.156094 0.00883708
\(313\) −16.8440 −0.952076 −0.476038 0.879425i \(-0.657928\pi\)
−0.476038 + 0.879425i \(0.657928\pi\)
\(314\) −19.7962 −1.11717
\(315\) −3.99509 −0.225098
\(316\) −13.0743 −0.735488
\(317\) −9.34656 −0.524955 −0.262478 0.964938i \(-0.584540\pi\)
−0.262478 + 0.964938i \(0.584540\pi\)
\(318\) −20.6658 −1.15888
\(319\) −28.6189 −1.60235
\(320\) −3.81206 −0.213100
\(321\) −9.80566 −0.547298
\(322\) −1.69979 −0.0947255
\(323\) 30.4719 1.69550
\(324\) −10.4695 −0.581640
\(325\) 0.782370 0.0433981
\(326\) −24.5017 −1.35702
\(327\) −7.13582 −0.394612
\(328\) −0.552467 −0.0305049
\(329\) 18.6156 1.02631
\(330\) −27.4623 −1.51175
\(331\) −16.0184 −0.880454 −0.440227 0.897887i \(-0.645102\pi\)
−0.440227 + 0.897887i \(0.645102\pi\)
\(332\) 8.10379 0.444753
\(333\) −4.39772 −0.240994
\(334\) 20.5000 1.12171
\(335\) −32.3507 −1.76751
\(336\) 3.23253 0.176349
\(337\) 33.5475 1.82745 0.913724 0.406336i \(-0.133194\pi\)
0.913724 + 0.406336i \(0.133194\pi\)
\(338\) −12.9933 −0.706740
\(339\) −33.2199 −1.80426
\(340\) 21.0306 1.14055
\(341\) −15.6015 −0.844869
\(342\) −3.40549 −0.184148
\(343\) −18.8859 −1.01974
\(344\) −2.03192 −0.109554
\(345\) 7.24948 0.390299
\(346\) 5.38601 0.289554
\(347\) −7.08623 −0.380409 −0.190204 0.981745i \(-0.560915\pi\)
−0.190204 + 0.981745i \(0.560915\pi\)
\(348\) −14.3671 −0.770160
\(349\) 22.0543 1.18054 0.590269 0.807207i \(-0.299022\pi\)
0.590269 + 0.807207i \(0.299022\pi\)
\(350\) 16.2020 0.866033
\(351\) −0.372041 −0.0198581
\(352\) 3.78817 0.201910
\(353\) −8.76815 −0.466681 −0.233341 0.972395i \(-0.574966\pi\)
−0.233341 + 0.972395i \(0.574966\pi\)
\(354\) 14.9449 0.794311
\(355\) −15.5888 −0.827366
\(356\) 8.42844 0.446706
\(357\) −17.8335 −0.943846
\(358\) 1.59431 0.0842621
\(359\) −11.0981 −0.585735 −0.292867 0.956153i \(-0.594609\pi\)
−0.292867 + 0.956153i \(0.594609\pi\)
\(360\) −2.35035 −0.123874
\(361\) 11.5079 0.605678
\(362\) 6.50617 0.341957
\(363\) 6.37123 0.334403
\(364\) 0.139519 0.00731278
\(365\) 0.285057 0.0149205
\(366\) 16.6503 0.870327
\(367\) 11.0724 0.577972 0.288986 0.957333i \(-0.406682\pi\)
0.288986 + 0.957333i \(0.406682\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −0.340627 −0.0177323
\(370\) 27.1903 1.41356
\(371\) −18.4714 −0.958988
\(372\) −7.83222 −0.406082
\(373\) −8.10125 −0.419467 −0.209733 0.977759i \(-0.567260\pi\)
−0.209733 + 0.977759i \(0.567260\pi\)
\(374\) −20.8989 −1.08065
\(375\) −32.8530 −1.69652
\(376\) 10.9517 0.564792
\(377\) −0.620099 −0.0319367
\(378\) −7.70455 −0.396279
\(379\) 2.20636 0.113333 0.0566666 0.998393i \(-0.481953\pi\)
0.0566666 + 0.998393i \(0.481953\pi\)
\(380\) 21.0555 1.08012
\(381\) 14.9093 0.763827
\(382\) −20.6033 −1.05416
\(383\) −23.0649 −1.17856 −0.589281 0.807928i \(-0.700589\pi\)
−0.589281 + 0.807928i \(0.700589\pi\)
\(384\) 1.90172 0.0970470
\(385\) −24.5462 −1.25099
\(386\) 1.60684 0.0817861
\(387\) −1.25279 −0.0636831
\(388\) −8.84960 −0.449271
\(389\) 3.60124 0.182590 0.0912951 0.995824i \(-0.470899\pi\)
0.0912951 + 0.995824i \(0.470899\pi\)
\(390\) −0.595039 −0.0301310
\(391\) 5.51688 0.279000
\(392\) −4.11072 −0.207623
\(393\) 1.90172 0.0959293
\(394\) 17.9324 0.903422
\(395\) 49.8400 2.50772
\(396\) 2.33562 0.117369
\(397\) 24.0232 1.20569 0.602844 0.797859i \(-0.294034\pi\)
0.602844 + 0.797859i \(0.294034\pi\)
\(398\) −11.7766 −0.590307
\(399\) −17.8545 −0.893844
\(400\) 9.53177 0.476589
\(401\) −12.1290 −0.605694 −0.302847 0.953039i \(-0.597937\pi\)
−0.302847 + 0.953039i \(0.597937\pi\)
\(402\) 16.1388 0.804932
\(403\) −0.338046 −0.0168393
\(404\) −11.1586 −0.555161
\(405\) 39.9104 1.98317
\(406\) −12.8415 −0.637315
\(407\) −27.0199 −1.33933
\(408\) −10.4916 −0.519411
\(409\) −18.2638 −0.903085 −0.451542 0.892250i \(-0.649126\pi\)
−0.451542 + 0.892250i \(0.649126\pi\)
\(410\) 2.10603 0.104010
\(411\) 12.7044 0.626663
\(412\) −5.58492 −0.275149
\(413\) 13.3579 0.657300
\(414\) −0.616557 −0.0303021
\(415\) −30.8921 −1.51643
\(416\) 0.0820802 0.00402431
\(417\) 8.78728 0.430315
\(418\) −20.9236 −1.02340
\(419\) 33.0384 1.61403 0.807016 0.590529i \(-0.201081\pi\)
0.807016 + 0.590529i \(0.201081\pi\)
\(420\) −12.3226 −0.601280
\(421\) 33.6532 1.64016 0.820079 0.572250i \(-0.193929\pi\)
0.820079 + 0.572250i \(0.193929\pi\)
\(422\) 15.5611 0.757502
\(423\) 6.75235 0.328311
\(424\) −10.8669 −0.527743
\(425\) −52.5856 −2.55078
\(426\) 7.77678 0.376786
\(427\) 14.8823 0.720205
\(428\) −5.15619 −0.249234
\(429\) 0.591311 0.0285487
\(430\) 7.74579 0.373535
\(431\) −11.5779 −0.557690 −0.278845 0.960336i \(-0.589951\pi\)
−0.278845 + 0.960336i \(0.589951\pi\)
\(432\) −4.53265 −0.218077
\(433\) 2.98800 0.143594 0.0717970 0.997419i \(-0.477127\pi\)
0.0717970 + 0.997419i \(0.477127\pi\)
\(434\) −7.00054 −0.336037
\(435\) 54.7683 2.62594
\(436\) −3.75229 −0.179702
\(437\) 5.52339 0.264220
\(438\) −0.142207 −0.00679489
\(439\) −23.7476 −1.13341 −0.566706 0.823920i \(-0.691783\pi\)
−0.566706 + 0.823920i \(0.691783\pi\)
\(440\) −14.4407 −0.688434
\(441\) −2.53449 −0.120690
\(442\) −0.452826 −0.0215388
\(443\) −18.6889 −0.887935 −0.443967 0.896043i \(-0.646429\pi\)
−0.443967 + 0.896043i \(0.646429\pi\)
\(444\) −13.5644 −0.643740
\(445\) −32.1297 −1.52309
\(446\) −3.02774 −0.143368
\(447\) 14.5843 0.689814
\(448\) 1.69979 0.0803074
\(449\) 0.368707 0.0174004 0.00870018 0.999962i \(-0.497231\pi\)
0.00870018 + 0.999962i \(0.497231\pi\)
\(450\) 5.87688 0.277039
\(451\) −2.09284 −0.0985479
\(452\) −17.4683 −0.821640
\(453\) −28.7962 −1.35296
\(454\) 7.21767 0.338742
\(455\) −0.531854 −0.0249337
\(456\) −10.5040 −0.491894
\(457\) 10.4175 0.487311 0.243656 0.969862i \(-0.421653\pi\)
0.243656 + 0.969862i \(0.421653\pi\)
\(458\) −7.54120 −0.352377
\(459\) 25.0061 1.16718
\(460\) 3.81206 0.177738
\(461\) 16.8127 0.783044 0.391522 0.920169i \(-0.371949\pi\)
0.391522 + 0.920169i \(0.371949\pi\)
\(462\) 12.2454 0.569706
\(463\) 26.7192 1.24175 0.620874 0.783911i \(-0.286778\pi\)
0.620874 + 0.783911i \(0.286778\pi\)
\(464\) −7.55480 −0.350723
\(465\) 29.8569 1.38458
\(466\) −15.3177 −0.709578
\(467\) 40.8350 1.88962 0.944809 0.327622i \(-0.106247\pi\)
0.944809 + 0.327622i \(0.106247\pi\)
\(468\) 0.0506071 0.00233931
\(469\) 14.4251 0.666090
\(470\) −41.7486 −1.92572
\(471\) −37.6470 −1.73468
\(472\) 7.85858 0.361721
\(473\) −7.69726 −0.353920
\(474\) −24.8638 −1.14203
\(475\) −52.6477 −2.41564
\(476\) −9.37752 −0.429818
\(477\) −6.70005 −0.306774
\(478\) 4.33818 0.198424
\(479\) 21.7109 0.991998 0.495999 0.868323i \(-0.334802\pi\)
0.495999 + 0.868323i \(0.334802\pi\)
\(480\) −7.24948 −0.330892
\(481\) −0.585454 −0.0266944
\(482\) 7.00632 0.319129
\(483\) −3.23253 −0.147085
\(484\) 3.35024 0.152283
\(485\) 33.7352 1.53184
\(486\) −6.31220 −0.286327
\(487\) 11.7332 0.531684 0.265842 0.964017i \(-0.414350\pi\)
0.265842 + 0.964017i \(0.414350\pi\)
\(488\) 8.75538 0.396338
\(489\) −46.5955 −2.10712
\(490\) 15.6703 0.707912
\(491\) 6.44619 0.290912 0.145456 0.989365i \(-0.453535\pi\)
0.145456 + 0.989365i \(0.453535\pi\)
\(492\) −1.05064 −0.0473665
\(493\) 41.6789 1.87712
\(494\) −0.453361 −0.0203977
\(495\) −8.90352 −0.400183
\(496\) −4.11848 −0.184925
\(497\) 6.95099 0.311795
\(498\) 15.4112 0.690591
\(499\) 12.0858 0.541033 0.270516 0.962715i \(-0.412806\pi\)
0.270516 + 0.962715i \(0.412806\pi\)
\(500\) −17.2754 −0.772578
\(501\) 38.9853 1.74173
\(502\) −1.97249 −0.0880366
\(503\) −25.2036 −1.12377 −0.561887 0.827214i \(-0.689924\pi\)
−0.561887 + 0.827214i \(0.689924\pi\)
\(504\) 1.04802 0.0466823
\(505\) 42.5372 1.89288
\(506\) −3.78817 −0.168405
\(507\) −24.7096 −1.09739
\(508\) 7.83989 0.347839
\(509\) 22.6801 1.00528 0.502639 0.864496i \(-0.332362\pi\)
0.502639 + 0.864496i \(0.332362\pi\)
\(510\) 39.9945 1.77099
\(511\) −0.127106 −0.00562284
\(512\) 1.00000 0.0441942
\(513\) 25.0356 1.10535
\(514\) 25.3693 1.11899
\(515\) 21.2900 0.938150
\(516\) −3.86415 −0.170110
\(517\) 41.4870 1.82459
\(518\) −12.1241 −0.532702
\(519\) 10.2427 0.449605
\(520\) −0.312894 −0.0137213
\(521\) 41.6078 1.82287 0.911434 0.411445i \(-0.134976\pi\)
0.911434 + 0.411445i \(0.134976\pi\)
\(522\) −4.65796 −0.203873
\(523\) −18.1236 −0.792489 −0.396244 0.918145i \(-0.629687\pi\)
−0.396244 + 0.918145i \(0.629687\pi\)
\(524\) 1.00000 0.0436852
\(525\) 30.8117 1.34473
\(526\) −7.48012 −0.326149
\(527\) 22.7212 0.989749
\(528\) 7.20406 0.313516
\(529\) 1.00000 0.0434783
\(530\) 41.4252 1.79940
\(531\) 4.84526 0.210266
\(532\) −9.38860 −0.407047
\(533\) −0.0453466 −0.00196418
\(534\) 16.0286 0.693624
\(535\) 19.6557 0.849790
\(536\) 8.48643 0.366558
\(537\) 3.03195 0.130838
\(538\) 17.7556 0.765499
\(539\) −15.5721 −0.670739
\(540\) 17.2787 0.743558
\(541\) 39.1108 1.68150 0.840752 0.541421i \(-0.182113\pi\)
0.840752 + 0.541421i \(0.182113\pi\)
\(542\) −17.8908 −0.768476
\(543\) 12.3730 0.530974
\(544\) −5.51688 −0.236534
\(545\) 14.3039 0.612714
\(546\) 0.265327 0.0113549
\(547\) −26.1251 −1.11703 −0.558515 0.829495i \(-0.688629\pi\)
−0.558515 + 0.829495i \(0.688629\pi\)
\(548\) 6.68048 0.285376
\(549\) 5.39819 0.230389
\(550\) 36.1080 1.53965
\(551\) 41.7281 1.77768
\(552\) −1.90172 −0.0809428
\(553\) −22.2236 −0.945042
\(554\) −8.98310 −0.381655
\(555\) 51.7084 2.19490
\(556\) 4.62069 0.195961
\(557\) 16.4895 0.698683 0.349342 0.936995i \(-0.386405\pi\)
0.349342 + 0.936995i \(0.386405\pi\)
\(558\) −2.53928 −0.107496
\(559\) −0.166780 −0.00705406
\(560\) −6.47969 −0.273817
\(561\) −39.7439 −1.67799
\(562\) 26.4602 1.11615
\(563\) −18.2186 −0.767821 −0.383910 0.923370i \(-0.625423\pi\)
−0.383910 + 0.923370i \(0.625423\pi\)
\(564\) 20.8271 0.876981
\(565\) 66.5901 2.80147
\(566\) −12.7482 −0.535848
\(567\) −17.7960 −0.747361
\(568\) 4.08933 0.171585
\(569\) −13.2476 −0.555368 −0.277684 0.960672i \(-0.589567\pi\)
−0.277684 + 0.960672i \(0.589567\pi\)
\(570\) 40.0417 1.67716
\(571\) 16.5933 0.694408 0.347204 0.937790i \(-0.387131\pi\)
0.347204 + 0.937790i \(0.387131\pi\)
\(572\) 0.310934 0.0130008
\(573\) −39.1819 −1.63685
\(574\) −0.939076 −0.0391963
\(575\) −9.53177 −0.397502
\(576\) 0.616557 0.0256899
\(577\) 12.2119 0.508390 0.254195 0.967153i \(-0.418189\pi\)
0.254195 + 0.967153i \(0.418189\pi\)
\(578\) 13.4359 0.558860
\(579\) 3.05577 0.126994
\(580\) 28.7993 1.19583
\(581\) 13.7747 0.571472
\(582\) −16.8295 −0.697606
\(583\) −41.1656 −1.70491
\(584\) −0.0747777 −0.00309432
\(585\) −0.192917 −0.00797614
\(586\) −20.2959 −0.838416
\(587\) 20.2571 0.836101 0.418050 0.908424i \(-0.362714\pi\)
0.418050 + 0.908424i \(0.362714\pi\)
\(588\) −7.81746 −0.322387
\(589\) 22.7480 0.937315
\(590\) −29.9574 −1.23333
\(591\) 34.1025 1.40279
\(592\) −7.13271 −0.293153
\(593\) 1.22700 0.0503870 0.0251935 0.999683i \(-0.491980\pi\)
0.0251935 + 0.999683i \(0.491980\pi\)
\(594\) −17.1705 −0.704513
\(595\) 35.7476 1.46551
\(596\) 7.66899 0.314134
\(597\) −22.3958 −0.916599
\(598\) −0.0820802 −0.00335651
\(599\) −30.1500 −1.23189 −0.615947 0.787787i \(-0.711227\pi\)
−0.615947 + 0.787787i \(0.711227\pi\)
\(600\) 18.1268 0.740024
\(601\) 33.6219 1.37146 0.685732 0.727854i \(-0.259482\pi\)
0.685732 + 0.727854i \(0.259482\pi\)
\(602\) −3.45383 −0.140768
\(603\) 5.23236 0.213078
\(604\) −15.1421 −0.616125
\(605\) −12.7713 −0.519227
\(606\) −21.2206 −0.862027
\(607\) 14.6986 0.596596 0.298298 0.954473i \(-0.403581\pi\)
0.298298 + 0.954473i \(0.403581\pi\)
\(608\) −5.52339 −0.224003
\(609\) −24.4211 −0.989592
\(610\) −33.3760 −1.35136
\(611\) 0.898919 0.0363664
\(612\) −3.40147 −0.137496
\(613\) −45.8172 −1.85054 −0.925270 0.379309i \(-0.876162\pi\)
−0.925270 + 0.379309i \(0.876162\pi\)
\(614\) 18.9836 0.766115
\(615\) 4.00510 0.161501
\(616\) 6.43908 0.259438
\(617\) 41.5817 1.67402 0.837008 0.547191i \(-0.184303\pi\)
0.837008 + 0.547191i \(0.184303\pi\)
\(618\) −10.6210 −0.427238
\(619\) 8.25007 0.331598 0.165799 0.986160i \(-0.446980\pi\)
0.165799 + 0.986160i \(0.446980\pi\)
\(620\) 15.6999 0.630522
\(621\) 4.53265 0.181889
\(622\) −12.9589 −0.519606
\(623\) 14.3266 0.573981
\(624\) 0.156094 0.00624876
\(625\) 18.1958 0.727832
\(626\) −16.8440 −0.673220
\(627\) −39.7908 −1.58909
\(628\) −19.7962 −0.789956
\(629\) 39.3503 1.56900
\(630\) −3.99509 −0.159168
\(631\) −42.9920 −1.71149 −0.855743 0.517402i \(-0.826899\pi\)
−0.855743 + 0.517402i \(0.826899\pi\)
\(632\) −13.0743 −0.520068
\(633\) 29.5929 1.17621
\(634\) −9.34656 −0.371200
\(635\) −29.8861 −1.18599
\(636\) −20.6658 −0.819454
\(637\) −0.337409 −0.0133686
\(638\) −28.6189 −1.13303
\(639\) 2.52130 0.0997413
\(640\) −3.81206 −0.150685
\(641\) −13.7923 −0.544764 −0.272382 0.962189i \(-0.587811\pi\)
−0.272382 + 0.962189i \(0.587811\pi\)
\(642\) −9.80566 −0.386998
\(643\) 50.2295 1.98086 0.990429 0.138021i \(-0.0440741\pi\)
0.990429 + 0.138021i \(0.0440741\pi\)
\(644\) −1.69979 −0.0669810
\(645\) 14.7304 0.580007
\(646\) 30.4719 1.19890
\(647\) 20.1171 0.790886 0.395443 0.918490i \(-0.370591\pi\)
0.395443 + 0.918490i \(0.370591\pi\)
\(648\) −10.4695 −0.411282
\(649\) 29.7697 1.16856
\(650\) 0.782370 0.0306871
\(651\) −13.3131 −0.521782
\(652\) −24.5017 −0.959561
\(653\) −0.300068 −0.0117426 −0.00587128 0.999983i \(-0.501869\pi\)
−0.00587128 + 0.999983i \(0.501869\pi\)
\(654\) −7.13582 −0.279033
\(655\) −3.81206 −0.148949
\(656\) −0.552467 −0.0215702
\(657\) −0.0461047 −0.00179871
\(658\) 18.6156 0.725711
\(659\) −6.02316 −0.234629 −0.117314 0.993095i \(-0.537429\pi\)
−0.117314 + 0.993095i \(0.537429\pi\)
\(660\) −27.4623 −1.06897
\(661\) −37.6291 −1.46360 −0.731802 0.681517i \(-0.761320\pi\)
−0.731802 + 0.681517i \(0.761320\pi\)
\(662\) −16.0184 −0.622575
\(663\) −0.861151 −0.0334443
\(664\) 8.10379 0.314488
\(665\) 35.7899 1.38787
\(666\) −4.39772 −0.170408
\(667\) 7.55480 0.292523
\(668\) 20.5000 0.793167
\(669\) −5.75793 −0.222614
\(670\) −32.3507 −1.24982
\(671\) 33.1669 1.28039
\(672\) 3.23253 0.124697
\(673\) 41.8784 1.61429 0.807146 0.590352i \(-0.201011\pi\)
0.807146 + 0.590352i \(0.201011\pi\)
\(674\) 33.5475 1.29220
\(675\) −43.2042 −1.66293
\(676\) −12.9933 −0.499741
\(677\) −45.9654 −1.76659 −0.883296 0.468815i \(-0.844681\pi\)
−0.883296 + 0.468815i \(0.844681\pi\)
\(678\) −33.2199 −1.27580
\(679\) −15.0424 −0.577276
\(680\) 21.0306 0.806488
\(681\) 13.7260 0.525982
\(682\) −15.6015 −0.597413
\(683\) 11.9940 0.458936 0.229468 0.973316i \(-0.426301\pi\)
0.229468 + 0.973316i \(0.426301\pi\)
\(684\) −3.40549 −0.130212
\(685\) −25.4664 −0.973019
\(686\) −18.8859 −0.721066
\(687\) −14.3413 −0.547155
\(688\) −2.03192 −0.0774662
\(689\) −0.891957 −0.0339808
\(690\) 7.24948 0.275983
\(691\) 0.814765 0.0309951 0.0154976 0.999880i \(-0.495067\pi\)
0.0154976 + 0.999880i \(0.495067\pi\)
\(692\) 5.38601 0.204745
\(693\) 3.97006 0.150810
\(694\) −7.08623 −0.268990
\(695\) −17.6143 −0.668150
\(696\) −14.3671 −0.544585
\(697\) 3.04789 0.115447
\(698\) 22.0543 0.834767
\(699\) −29.1300 −1.10180
\(700\) 16.2020 0.612377
\(701\) 1.72387 0.0651098 0.0325549 0.999470i \(-0.489636\pi\)
0.0325549 + 0.999470i \(0.489636\pi\)
\(702\) −0.372041 −0.0140418
\(703\) 39.3968 1.48588
\(704\) 3.78817 0.142772
\(705\) −79.3943 −2.99016
\(706\) −8.76815 −0.329994
\(707\) −18.9672 −0.713336
\(708\) 14.9449 0.561662
\(709\) −23.4873 −0.882084 −0.441042 0.897486i \(-0.645391\pi\)
−0.441042 + 0.897486i \(0.645391\pi\)
\(710\) −15.5888 −0.585036
\(711\) −8.06106 −0.302313
\(712\) 8.42844 0.315869
\(713\) 4.11848 0.154238
\(714\) −17.8335 −0.667400
\(715\) −1.18530 −0.0443276
\(716\) 1.59431 0.0595823
\(717\) 8.25003 0.308103
\(718\) −11.0981 −0.414177
\(719\) 23.5350 0.877709 0.438855 0.898558i \(-0.355384\pi\)
0.438855 + 0.898558i \(0.355384\pi\)
\(720\) −2.35035 −0.0875923
\(721\) −9.49317 −0.353544
\(722\) 11.5079 0.428279
\(723\) 13.3241 0.495528
\(724\) 6.50617 0.241800
\(725\) −72.0106 −2.67441
\(726\) 6.37123 0.236458
\(727\) −24.0772 −0.892973 −0.446486 0.894790i \(-0.647325\pi\)
−0.446486 + 0.894790i \(0.647325\pi\)
\(728\) 0.139519 0.00517092
\(729\) 19.4045 0.718686
\(730\) 0.285057 0.0105504
\(731\) 11.2098 0.414611
\(732\) 16.6503 0.615414
\(733\) 32.1388 1.18707 0.593536 0.804807i \(-0.297731\pi\)
0.593536 + 0.804807i \(0.297731\pi\)
\(734\) 11.0724 0.408688
\(735\) 29.8006 1.09921
\(736\) −1.00000 −0.0368605
\(737\) 32.1480 1.18419
\(738\) −0.340627 −0.0125386
\(739\) 9.88353 0.363572 0.181786 0.983338i \(-0.441812\pi\)
0.181786 + 0.983338i \(0.441812\pi\)
\(740\) 27.1903 0.999535
\(741\) −0.862169 −0.0316726
\(742\) −18.4714 −0.678107
\(743\) 9.05882 0.332336 0.166168 0.986097i \(-0.446861\pi\)
0.166168 + 0.986097i \(0.446861\pi\)
\(744\) −7.83222 −0.287143
\(745\) −29.2346 −1.07107
\(746\) −8.10125 −0.296608
\(747\) 4.99644 0.182810
\(748\) −20.8989 −0.764138
\(749\) −8.76443 −0.320245
\(750\) −32.8530 −1.19962
\(751\) −44.0372 −1.60694 −0.803470 0.595345i \(-0.797015\pi\)
−0.803470 + 0.595345i \(0.797015\pi\)
\(752\) 10.9517 0.399368
\(753\) −3.75114 −0.136699
\(754\) −0.620099 −0.0225827
\(755\) 57.7227 2.10074
\(756\) −7.70455 −0.280212
\(757\) −8.98333 −0.326505 −0.163252 0.986584i \(-0.552198\pi\)
−0.163252 + 0.986584i \(0.552198\pi\)
\(758\) 2.20636 0.0801387
\(759\) −7.20406 −0.261491
\(760\) 21.0555 0.763763
\(761\) −48.8188 −1.76968 −0.884841 0.465893i \(-0.845733\pi\)
−0.884841 + 0.465893i \(0.845733\pi\)
\(762\) 14.9093 0.540107
\(763\) −6.37810 −0.230903
\(764\) −20.6033 −0.745402
\(765\) 12.9666 0.468808
\(766\) −23.0649 −0.833369
\(767\) 0.645034 0.0232908
\(768\) 1.90172 0.0686226
\(769\) −13.4763 −0.485967 −0.242984 0.970030i \(-0.578126\pi\)
−0.242984 + 0.970030i \(0.578126\pi\)
\(770\) −24.5462 −0.884582
\(771\) 48.2453 1.73751
\(772\) 1.60684 0.0578315
\(773\) −0.981471 −0.0353011 −0.0176505 0.999844i \(-0.505619\pi\)
−0.0176505 + 0.999844i \(0.505619\pi\)
\(774\) −1.25279 −0.0450307
\(775\) −39.2564 −1.41013
\(776\) −8.84960 −0.317682
\(777\) −23.0567 −0.827154
\(778\) 3.60124 0.129111
\(779\) 3.05149 0.109331
\(780\) −0.595039 −0.0213058
\(781\) 15.4911 0.554315
\(782\) 5.51688 0.197283
\(783\) 34.2433 1.22375
\(784\) −4.11072 −0.146812
\(785\) 75.4644 2.69344
\(786\) 1.90172 0.0678323
\(787\) −31.0430 −1.10656 −0.553281 0.832995i \(-0.686624\pi\)
−0.553281 + 0.832995i \(0.686624\pi\)
\(788\) 17.9324 0.638815
\(789\) −14.2251 −0.506428
\(790\) 49.8400 1.77323
\(791\) −29.6924 −1.05574
\(792\) 2.33562 0.0829927
\(793\) 0.718644 0.0255198
\(794\) 24.0232 0.852551
\(795\) 78.7793 2.79401
\(796\) −11.7766 −0.417410
\(797\) −4.27674 −0.151490 −0.0757450 0.997127i \(-0.524133\pi\)
−0.0757450 + 0.997127i \(0.524133\pi\)
\(798\) −17.8545 −0.632043
\(799\) −60.4193 −2.13748
\(800\) 9.53177 0.336999
\(801\) 5.19661 0.183613
\(802\) −12.1290 −0.428291
\(803\) −0.283271 −0.00999640
\(804\) 16.1388 0.569173
\(805\) 6.47969 0.228379
\(806\) −0.338046 −0.0119072
\(807\) 33.7663 1.18863
\(808\) −11.1586 −0.392558
\(809\) 7.29946 0.256635 0.128318 0.991733i \(-0.459042\pi\)
0.128318 + 0.991733i \(0.459042\pi\)
\(810\) 39.9104 1.40231
\(811\) 18.9530 0.665530 0.332765 0.943010i \(-0.392018\pi\)
0.332765 + 0.943010i \(0.392018\pi\)
\(812\) −12.8415 −0.450650
\(813\) −34.0234 −1.19325
\(814\) −27.0199 −0.947048
\(815\) 93.4019 3.27173
\(816\) −10.4916 −0.367279
\(817\) 11.2231 0.392646
\(818\) −18.2638 −0.638577
\(819\) 0.0860213 0.00300583
\(820\) 2.10603 0.0735459
\(821\) −6.97547 −0.243446 −0.121723 0.992564i \(-0.538842\pi\)
−0.121723 + 0.992564i \(0.538842\pi\)
\(822\) 12.7044 0.443118
\(823\) −13.0591 −0.455211 −0.227606 0.973753i \(-0.573090\pi\)
−0.227606 + 0.973753i \(0.573090\pi\)
\(824\) −5.58492 −0.194560
\(825\) 68.6674 2.39069
\(826\) 13.3579 0.464782
\(827\) 24.1786 0.840771 0.420386 0.907346i \(-0.361895\pi\)
0.420386 + 0.907346i \(0.361895\pi\)
\(828\) −0.616557 −0.0214268
\(829\) −47.8361 −1.66142 −0.830709 0.556707i \(-0.812065\pi\)
−0.830709 + 0.556707i \(0.812065\pi\)
\(830\) −30.8921 −1.07228
\(831\) −17.0834 −0.592616
\(832\) 0.0820802 0.00284562
\(833\) 22.6783 0.785758
\(834\) 8.78728 0.304279
\(835\) −78.1470 −2.70439
\(836\) −20.9236 −0.723656
\(837\) 18.6676 0.645248
\(838\) 33.0384 1.14129
\(839\) 26.9570 0.930659 0.465330 0.885137i \(-0.345936\pi\)
0.465330 + 0.885137i \(0.345936\pi\)
\(840\) −12.3226 −0.425169
\(841\) 28.0749 0.968101
\(842\) 33.6532 1.15977
\(843\) 50.3200 1.73311
\(844\) 15.5611 0.535635
\(845\) 49.5310 1.70392
\(846\) 6.75235 0.232151
\(847\) 5.69469 0.195672
\(848\) −10.8669 −0.373171
\(849\) −24.2436 −0.832038
\(850\) −52.5856 −1.80367
\(851\) 7.13271 0.244506
\(852\) 7.77678 0.266428
\(853\) 47.7188 1.63386 0.816931 0.576736i \(-0.195674\pi\)
0.816931 + 0.576736i \(0.195674\pi\)
\(854\) 14.8823 0.509262
\(855\) 12.9819 0.443972
\(856\) −5.15619 −0.176235
\(857\) 25.3827 0.867057 0.433528 0.901140i \(-0.357268\pi\)
0.433528 + 0.901140i \(0.357268\pi\)
\(858\) 0.591311 0.0201870
\(859\) 32.2608 1.10072 0.550362 0.834926i \(-0.314490\pi\)
0.550362 + 0.834926i \(0.314490\pi\)
\(860\) 7.74579 0.264129
\(861\) −1.78586 −0.0608621
\(862\) −11.5779 −0.394346
\(863\) 3.87368 0.131862 0.0659308 0.997824i \(-0.478998\pi\)
0.0659308 + 0.997824i \(0.478998\pi\)
\(864\) −4.53265 −0.154204
\(865\) −20.5318 −0.698101
\(866\) 2.98800 0.101536
\(867\) 25.5514 0.867772
\(868\) −7.00054 −0.237614
\(869\) −49.5277 −1.68011
\(870\) 54.7683 1.85682
\(871\) 0.696568 0.0236023
\(872\) −3.75229 −0.127069
\(873\) −5.45628 −0.184667
\(874\) 5.52339 0.186832
\(875\) −29.3645 −0.992700
\(876\) −0.142207 −0.00480471
\(877\) −15.0557 −0.508394 −0.254197 0.967152i \(-0.581811\pi\)
−0.254197 + 0.967152i \(0.581811\pi\)
\(878\) −23.7476 −0.801444
\(879\) −38.5972 −1.30185
\(880\) −14.4407 −0.486797
\(881\) 27.1079 0.913289 0.456645 0.889649i \(-0.349051\pi\)
0.456645 + 0.889649i \(0.349051\pi\)
\(882\) −2.53449 −0.0853408
\(883\) −2.43104 −0.0818111 −0.0409056 0.999163i \(-0.513024\pi\)
−0.0409056 + 0.999163i \(0.513024\pi\)
\(884\) −0.452826 −0.0152302
\(885\) −56.9707 −1.91505
\(886\) −18.6889 −0.627865
\(887\) 3.03543 0.101920 0.0509598 0.998701i \(-0.483772\pi\)
0.0509598 + 0.998701i \(0.483772\pi\)
\(888\) −13.5644 −0.455193
\(889\) 13.3261 0.446945
\(890\) −32.1297 −1.07699
\(891\) −39.6604 −1.32867
\(892\) −3.02774 −0.101376
\(893\) −60.4906 −2.02424
\(894\) 14.5843 0.487772
\(895\) −6.07761 −0.203152
\(896\) 1.69979 0.0567859
\(897\) −0.156094 −0.00521183
\(898\) 0.368707 0.0123039
\(899\) 31.1143 1.03772
\(900\) 5.87688 0.195896
\(901\) 59.9513 1.99727
\(902\) −2.09284 −0.0696839
\(903\) −6.56824 −0.218577
\(904\) −17.4683 −0.580987
\(905\) −24.8019 −0.824443
\(906\) −28.7962 −0.956690
\(907\) −24.0127 −0.797330 −0.398665 0.917097i \(-0.630526\pi\)
−0.398665 + 0.917097i \(0.630526\pi\)
\(908\) 7.21767 0.239527
\(909\) −6.87991 −0.228192
\(910\) −0.531854 −0.0176308
\(911\) −19.7543 −0.654491 −0.327245 0.944939i \(-0.606120\pi\)
−0.327245 + 0.944939i \(0.606120\pi\)
\(912\) −10.5040 −0.347821
\(913\) 30.6985 1.01597
\(914\) 10.4175 0.344581
\(915\) −63.4720 −2.09832
\(916\) −7.54120 −0.249168
\(917\) 1.69979 0.0561319
\(918\) 25.0061 0.825324
\(919\) 50.2839 1.65871 0.829356 0.558720i \(-0.188707\pi\)
0.829356 + 0.558720i \(0.188707\pi\)
\(920\) 3.81206 0.125680
\(921\) 36.1016 1.18959
\(922\) 16.8127 0.553695
\(923\) 0.335653 0.0110482
\(924\) 12.2454 0.402843
\(925\) −67.9874 −2.23541
\(926\) 26.7192 0.878048
\(927\) −3.44342 −0.113097
\(928\) −7.55480 −0.247998
\(929\) −49.4977 −1.62397 −0.811983 0.583681i \(-0.801612\pi\)
−0.811983 + 0.583681i \(0.801612\pi\)
\(930\) 29.8569 0.979045
\(931\) 22.7051 0.744131
\(932\) −15.3177 −0.501747
\(933\) −24.6443 −0.806819
\(934\) 40.8350 1.33616
\(935\) 79.6676 2.60541
\(936\) 0.0506071 0.00165414
\(937\) −34.1441 −1.11544 −0.557719 0.830030i \(-0.688323\pi\)
−0.557719 + 0.830030i \(0.688323\pi\)
\(938\) 14.4251 0.470997
\(939\) −32.0326 −1.04534
\(940\) −41.7486 −1.36169
\(941\) −39.0998 −1.27462 −0.637309 0.770609i \(-0.719952\pi\)
−0.637309 + 0.770609i \(0.719952\pi\)
\(942\) −37.6470 −1.22661
\(943\) 0.552467 0.0179908
\(944\) 7.85858 0.255775
\(945\) 29.3702 0.955412
\(946\) −7.69726 −0.250259
\(947\) 0.739702 0.0240371 0.0120185 0.999928i \(-0.496174\pi\)
0.0120185 + 0.999928i \(0.496174\pi\)
\(948\) −24.8638 −0.807537
\(949\) −0.00613777 −0.000199240 0
\(950\) −52.6477 −1.70812
\(951\) −17.7746 −0.576381
\(952\) −9.37752 −0.303927
\(953\) 3.22958 0.104616 0.0523081 0.998631i \(-0.483342\pi\)
0.0523081 + 0.998631i \(0.483342\pi\)
\(954\) −6.70005 −0.216922
\(955\) 78.5411 2.54153
\(956\) 4.33818 0.140307
\(957\) −54.4252 −1.75932
\(958\) 21.7109 0.701448
\(959\) 11.3554 0.366685
\(960\) −7.24948 −0.233976
\(961\) −14.0381 −0.452842
\(962\) −0.585454 −0.0188758
\(963\) −3.17908 −0.102445
\(964\) 7.00632 0.225658
\(965\) −6.12537 −0.197183
\(966\) −3.23253 −0.104005
\(967\) −48.5822 −1.56230 −0.781150 0.624344i \(-0.785366\pi\)
−0.781150 + 0.624344i \(0.785366\pi\)
\(968\) 3.35024 0.107681
\(969\) 57.9491 1.86159
\(970\) 33.7352 1.08317
\(971\) −42.7600 −1.37223 −0.686117 0.727491i \(-0.740686\pi\)
−0.686117 + 0.727491i \(0.740686\pi\)
\(972\) −6.31220 −0.202464
\(973\) 7.85419 0.251794
\(974\) 11.7332 0.375958
\(975\) 1.48785 0.0476494
\(976\) 8.75538 0.280253
\(977\) 24.6400 0.788302 0.394151 0.919046i \(-0.371039\pi\)
0.394151 + 0.919046i \(0.371039\pi\)
\(978\) −46.5955 −1.48996
\(979\) 31.9284 1.02043
\(980\) 15.6703 0.500570
\(981\) −2.31350 −0.0738644
\(982\) 6.44619 0.205706
\(983\) 12.9428 0.412811 0.206406 0.978467i \(-0.433823\pi\)
0.206406 + 0.978467i \(0.433823\pi\)
\(984\) −1.05064 −0.0334932
\(985\) −68.3593 −2.17811
\(986\) 41.6789 1.32733
\(987\) 35.4017 1.12685
\(988\) −0.453361 −0.0144233
\(989\) 2.03192 0.0646113
\(990\) −8.90352 −0.282972
\(991\) 43.3100 1.37579 0.687894 0.725811i \(-0.258535\pi\)
0.687894 + 0.725811i \(0.258535\pi\)
\(992\) −4.11848 −0.130762
\(993\) −30.4627 −0.966704
\(994\) 6.95099 0.220472
\(995\) 44.8930 1.42320
\(996\) 15.4112 0.488322
\(997\) −17.5067 −0.554444 −0.277222 0.960806i \(-0.589414\pi\)
−0.277222 + 0.960806i \(0.589414\pi\)
\(998\) 12.0858 0.382568
\(999\) 32.3301 1.02288
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6026.2.a.g.1.18 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.g.1.18 21 1.1 even 1 trivial