Properties

Label 6026.2.a.m.1.12
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $0$
Dimension $41$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.1178522580\)
Analytic rank: \(0\)
Dimension: \(41\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.30065 q^{3} +1.00000 q^{4} +2.66833 q^{5} -1.30065 q^{6} -4.20545 q^{7} +1.00000 q^{8} -1.30832 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.30065 q^{3} +1.00000 q^{4} +2.66833 q^{5} -1.30065 q^{6} -4.20545 q^{7} +1.00000 q^{8} -1.30832 q^{9} +2.66833 q^{10} -2.85367 q^{11} -1.30065 q^{12} +5.25232 q^{13} -4.20545 q^{14} -3.47055 q^{15} +1.00000 q^{16} -3.66501 q^{17} -1.30832 q^{18} -2.56826 q^{19} +2.66833 q^{20} +5.46980 q^{21} -2.85367 q^{22} +1.00000 q^{23} -1.30065 q^{24} +2.11998 q^{25} +5.25232 q^{26} +5.60360 q^{27} -4.20545 q^{28} +1.86198 q^{29} -3.47055 q^{30} +9.92467 q^{31} +1.00000 q^{32} +3.71161 q^{33} -3.66501 q^{34} -11.2215 q^{35} -1.30832 q^{36} +0.702891 q^{37} -2.56826 q^{38} -6.83140 q^{39} +2.66833 q^{40} -1.57152 q^{41} +5.46980 q^{42} -3.65307 q^{43} -2.85367 q^{44} -3.49103 q^{45} +1.00000 q^{46} -9.81910 q^{47} -1.30065 q^{48} +10.6858 q^{49} +2.11998 q^{50} +4.76688 q^{51} +5.25232 q^{52} -1.81090 q^{53} +5.60360 q^{54} -7.61453 q^{55} -4.20545 q^{56} +3.34039 q^{57} +1.86198 q^{58} +7.25435 q^{59} -3.47055 q^{60} +12.6714 q^{61} +9.92467 q^{62} +5.50207 q^{63} +1.00000 q^{64} +14.0149 q^{65} +3.71161 q^{66} -15.7750 q^{67} -3.66501 q^{68} -1.30065 q^{69} -11.2215 q^{70} +0.378262 q^{71} -1.30832 q^{72} +11.9647 q^{73} +0.702891 q^{74} -2.75735 q^{75} -2.56826 q^{76} +12.0010 q^{77} -6.83140 q^{78} +12.9176 q^{79} +2.66833 q^{80} -3.36334 q^{81} -1.57152 q^{82} +8.73622 q^{83} +5.46980 q^{84} -9.77946 q^{85} -3.65307 q^{86} -2.42178 q^{87} -2.85367 q^{88} -4.30510 q^{89} -3.49103 q^{90} -22.0883 q^{91} +1.00000 q^{92} -12.9085 q^{93} -9.81910 q^{94} -6.85296 q^{95} -1.30065 q^{96} +17.8664 q^{97} +10.6858 q^{98} +3.73351 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 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
\(3\) −1.30065 −0.750928 −0.375464 0.926837i \(-0.622517\pi\)
−0.375464 + 0.926837i \(0.622517\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.66833 1.19331 0.596657 0.802497i \(-0.296495\pi\)
0.596657 + 0.802497i \(0.296495\pi\)
\(6\) −1.30065 −0.530986
\(7\) −4.20545 −1.58951 −0.794755 0.606931i \(-0.792401\pi\)
−0.794755 + 0.606931i \(0.792401\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.30832 −0.436107
\(10\) 2.66833 0.843800
\(11\) −2.85367 −0.860413 −0.430207 0.902730i \(-0.641559\pi\)
−0.430207 + 0.902730i \(0.641559\pi\)
\(12\) −1.30065 −0.375464
\(13\) 5.25232 1.45673 0.728365 0.685189i \(-0.240280\pi\)
0.728365 + 0.685189i \(0.240280\pi\)
\(14\) −4.20545 −1.12395
\(15\) −3.47055 −0.896093
\(16\) 1.00000 0.250000
\(17\) −3.66501 −0.888896 −0.444448 0.895805i \(-0.646600\pi\)
−0.444448 + 0.895805i \(0.646600\pi\)
\(18\) −1.30832 −0.308374
\(19\) −2.56826 −0.589199 −0.294599 0.955621i \(-0.595186\pi\)
−0.294599 + 0.955621i \(0.595186\pi\)
\(20\) 2.66833 0.596657
\(21\) 5.46980 1.19361
\(22\) −2.85367 −0.608404
\(23\) 1.00000 0.208514
\(24\) −1.30065 −0.265493
\(25\) 2.11998 0.423997
\(26\) 5.25232 1.03006
\(27\) 5.60360 1.07841
\(28\) −4.20545 −0.794755
\(29\) 1.86198 0.345761 0.172881 0.984943i \(-0.444692\pi\)
0.172881 + 0.984943i \(0.444692\pi\)
\(30\) −3.47055 −0.633633
\(31\) 9.92467 1.78252 0.891262 0.453489i \(-0.149821\pi\)
0.891262 + 0.453489i \(0.149821\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.71161 0.646109
\(34\) −3.66501 −0.628544
\(35\) −11.2215 −1.89678
\(36\) −1.30832 −0.218053
\(37\) 0.702891 0.115555 0.0577773 0.998329i \(-0.481599\pi\)
0.0577773 + 0.998329i \(0.481599\pi\)
\(38\) −2.56826 −0.416626
\(39\) −6.83140 −1.09390
\(40\) 2.66833 0.421900
\(41\) −1.57152 −0.245430 −0.122715 0.992442i \(-0.539160\pi\)
−0.122715 + 0.992442i \(0.539160\pi\)
\(42\) 5.46980 0.844008
\(43\) −3.65307 −0.557088 −0.278544 0.960424i \(-0.589852\pi\)
−0.278544 + 0.960424i \(0.589852\pi\)
\(44\) −2.85367 −0.430207
\(45\) −3.49103 −0.520412
\(46\) 1.00000 0.147442
\(47\) −9.81910 −1.43226 −0.716131 0.697966i \(-0.754089\pi\)
−0.716131 + 0.697966i \(0.754089\pi\)
\(48\) −1.30065 −0.187732
\(49\) 10.6858 1.52654
\(50\) 2.11998 0.299811
\(51\) 4.76688 0.667497
\(52\) 5.25232 0.728365
\(53\) −1.81090 −0.248746 −0.124373 0.992236i \(-0.539692\pi\)
−0.124373 + 0.992236i \(0.539692\pi\)
\(54\) 5.60360 0.762553
\(55\) −7.61453 −1.02674
\(56\) −4.20545 −0.561977
\(57\) 3.34039 0.442446
\(58\) 1.86198 0.244490
\(59\) 7.25435 0.944437 0.472218 0.881482i \(-0.343453\pi\)
0.472218 + 0.881482i \(0.343453\pi\)
\(60\) −3.47055 −0.448046
\(61\) 12.6714 1.62241 0.811205 0.584761i \(-0.198812\pi\)
0.811205 + 0.584761i \(0.198812\pi\)
\(62\) 9.92467 1.26043
\(63\) 5.50207 0.693196
\(64\) 1.00000 0.125000
\(65\) 14.0149 1.73834
\(66\) 3.71161 0.456868
\(67\) −15.7750 −1.92722 −0.963609 0.267316i \(-0.913863\pi\)
−0.963609 + 0.267316i \(0.913863\pi\)
\(68\) −3.66501 −0.444448
\(69\) −1.30065 −0.156579
\(70\) −11.2215 −1.34123
\(71\) 0.378262 0.0448914 0.0224457 0.999748i \(-0.492855\pi\)
0.0224457 + 0.999748i \(0.492855\pi\)
\(72\) −1.30832 −0.154187
\(73\) 11.9647 1.40037 0.700184 0.713963i \(-0.253101\pi\)
0.700184 + 0.713963i \(0.253101\pi\)
\(74\) 0.702891 0.0817094
\(75\) −2.75735 −0.318391
\(76\) −2.56826 −0.294599
\(77\) 12.0010 1.36764
\(78\) −6.83140 −0.773504
\(79\) 12.9176 1.45335 0.726673 0.686984i \(-0.241066\pi\)
0.726673 + 0.686984i \(0.241066\pi\)
\(80\) 2.66833 0.298328
\(81\) −3.36334 −0.373704
\(82\) −1.57152 −0.173545
\(83\) 8.73622 0.958925 0.479463 0.877562i \(-0.340832\pi\)
0.479463 + 0.877562i \(0.340832\pi\)
\(84\) 5.46980 0.596804
\(85\) −9.77946 −1.06073
\(86\) −3.65307 −0.393921
\(87\) −2.42178 −0.259642
\(88\) −2.85367 −0.304202
\(89\) −4.30510 −0.456339 −0.228170 0.973621i \(-0.573274\pi\)
−0.228170 + 0.973621i \(0.573274\pi\)
\(90\) −3.49103 −0.367987
\(91\) −22.0883 −2.31549
\(92\) 1.00000 0.104257
\(93\) −12.9085 −1.33855
\(94\) −9.81910 −1.01276
\(95\) −6.85296 −0.703099
\(96\) −1.30065 −0.132747
\(97\) 17.8664 1.81406 0.907031 0.421063i \(-0.138343\pi\)
0.907031 + 0.421063i \(0.138343\pi\)
\(98\) 10.6858 1.07943
\(99\) 3.73351 0.375232
\(100\) 2.11998 0.211998
\(101\) 10.4315 1.03798 0.518988 0.854782i \(-0.326309\pi\)
0.518988 + 0.854782i \(0.326309\pi\)
\(102\) 4.76688 0.471992
\(103\) 10.7732 1.06151 0.530757 0.847524i \(-0.321908\pi\)
0.530757 + 0.847524i \(0.321908\pi\)
\(104\) 5.25232 0.515032
\(105\) 14.5952 1.42435
\(106\) −1.81090 −0.175890
\(107\) −8.76351 −0.847200 −0.423600 0.905849i \(-0.639234\pi\)
−0.423600 + 0.905849i \(0.639234\pi\)
\(108\) 5.60360 0.539207
\(109\) 11.2050 1.07325 0.536624 0.843821i \(-0.319699\pi\)
0.536624 + 0.843821i \(0.319699\pi\)
\(110\) −7.61453 −0.726017
\(111\) −0.914212 −0.0867732
\(112\) −4.20545 −0.397377
\(113\) −8.86378 −0.833834 −0.416917 0.908945i \(-0.636889\pi\)
−0.416917 + 0.908945i \(0.636889\pi\)
\(114\) 3.34039 0.312856
\(115\) 2.66833 0.248823
\(116\) 1.86198 0.172881
\(117\) −6.87171 −0.635290
\(118\) 7.25435 0.667817
\(119\) 15.4130 1.41291
\(120\) −3.47055 −0.316817
\(121\) −2.85658 −0.259689
\(122\) 12.6714 1.14722
\(123\) 2.04399 0.184301
\(124\) 9.92467 0.891262
\(125\) −7.68483 −0.687352
\(126\) 5.50207 0.490163
\(127\) −6.68674 −0.593352 −0.296676 0.954978i \(-0.595878\pi\)
−0.296676 + 0.954978i \(0.595878\pi\)
\(128\) 1.00000 0.0883883
\(129\) 4.75135 0.418333
\(130\) 14.0149 1.22919
\(131\) 1.00000 0.0873704
\(132\) 3.71161 0.323054
\(133\) 10.8007 0.936537
\(134\) −15.7750 −1.36275
\(135\) 14.9523 1.28688
\(136\) −3.66501 −0.314272
\(137\) 18.7955 1.60581 0.802904 0.596109i \(-0.203287\pi\)
0.802904 + 0.596109i \(0.203287\pi\)
\(138\) −1.30065 −0.110718
\(139\) 13.2145 1.12084 0.560418 0.828210i \(-0.310640\pi\)
0.560418 + 0.828210i \(0.310640\pi\)
\(140\) −11.2215 −0.948392
\(141\) 12.7712 1.07553
\(142\) 0.378262 0.0317430
\(143\) −14.9884 −1.25339
\(144\) −1.30832 −0.109027
\(145\) 4.96838 0.412602
\(146\) 11.9647 0.990209
\(147\) −13.8984 −1.14632
\(148\) 0.702891 0.0577773
\(149\) −19.3153 −1.58237 −0.791186 0.611576i \(-0.790536\pi\)
−0.791186 + 0.611576i \(0.790536\pi\)
\(150\) −2.75735 −0.225137
\(151\) 12.8549 1.04612 0.523059 0.852296i \(-0.324791\pi\)
0.523059 + 0.852296i \(0.324791\pi\)
\(152\) −2.56826 −0.208313
\(153\) 4.79501 0.387654
\(154\) 12.0010 0.967064
\(155\) 26.4823 2.12711
\(156\) −6.83140 −0.546950
\(157\) 15.1710 1.21078 0.605390 0.795929i \(-0.293017\pi\)
0.605390 + 0.795929i \(0.293017\pi\)
\(158\) 12.9176 1.02767
\(159\) 2.35534 0.186790
\(160\) 2.66833 0.210950
\(161\) −4.20545 −0.331436
\(162\) −3.36334 −0.264249
\(163\) 23.0022 1.80167 0.900837 0.434158i \(-0.142954\pi\)
0.900837 + 0.434158i \(0.142954\pi\)
\(164\) −1.57152 −0.122715
\(165\) 9.90381 0.771010
\(166\) 8.73622 0.678063
\(167\) −10.1821 −0.787915 −0.393957 0.919129i \(-0.628894\pi\)
−0.393957 + 0.919129i \(0.628894\pi\)
\(168\) 5.46980 0.422004
\(169\) 14.5868 1.12206
\(170\) −9.77946 −0.750051
\(171\) 3.36010 0.256953
\(172\) −3.65307 −0.278544
\(173\) 15.3418 1.16641 0.583207 0.812324i \(-0.301798\pi\)
0.583207 + 0.812324i \(0.301798\pi\)
\(174\) −2.42178 −0.183595
\(175\) −8.91548 −0.673947
\(176\) −2.85367 −0.215103
\(177\) −9.43535 −0.709204
\(178\) −4.30510 −0.322681
\(179\) −3.34395 −0.249939 −0.124969 0.992161i \(-0.539883\pi\)
−0.124969 + 0.992161i \(0.539883\pi\)
\(180\) −3.49103 −0.260206
\(181\) −13.3129 −0.989540 −0.494770 0.869024i \(-0.664748\pi\)
−0.494770 + 0.869024i \(0.664748\pi\)
\(182\) −22.0883 −1.63730
\(183\) −16.4810 −1.21831
\(184\) 1.00000 0.0737210
\(185\) 1.87554 0.137893
\(186\) −12.9085 −0.946496
\(187\) 10.4587 0.764818
\(188\) −9.81910 −0.716131
\(189\) −23.5656 −1.71415
\(190\) −6.85296 −0.497166
\(191\) −16.8178 −1.21689 −0.608446 0.793595i \(-0.708207\pi\)
−0.608446 + 0.793595i \(0.708207\pi\)
\(192\) −1.30065 −0.0938660
\(193\) −14.2903 −1.02864 −0.514318 0.857599i \(-0.671955\pi\)
−0.514318 + 0.857599i \(0.671955\pi\)
\(194\) 17.8664 1.28274
\(195\) −18.2284 −1.30537
\(196\) 10.6858 0.763270
\(197\) 14.1738 1.00984 0.504922 0.863165i \(-0.331521\pi\)
0.504922 + 0.863165i \(0.331521\pi\)
\(198\) 3.73351 0.265329
\(199\) 10.1475 0.719334 0.359667 0.933081i \(-0.382890\pi\)
0.359667 + 0.933081i \(0.382890\pi\)
\(200\) 2.11998 0.149906
\(201\) 20.5176 1.44720
\(202\) 10.4315 0.733959
\(203\) −7.83047 −0.549591
\(204\) 4.76688 0.333749
\(205\) −4.19334 −0.292875
\(206\) 10.7732 0.750604
\(207\) −1.30832 −0.0909345
\(208\) 5.25232 0.364183
\(209\) 7.32895 0.506954
\(210\) 14.5952 1.00717
\(211\) 20.9748 1.44397 0.721984 0.691910i \(-0.243230\pi\)
0.721984 + 0.691910i \(0.243230\pi\)
\(212\) −1.81090 −0.124373
\(213\) −0.491985 −0.0337103
\(214\) −8.76351 −0.599061
\(215\) −9.74759 −0.664780
\(216\) 5.60360 0.381277
\(217\) −41.7377 −2.83334
\(218\) 11.2050 0.758901
\(219\) −15.5619 −1.05158
\(220\) −7.61453 −0.513371
\(221\) −19.2498 −1.29488
\(222\) −0.914212 −0.0613579
\(223\) 12.8028 0.857337 0.428669 0.903462i \(-0.358983\pi\)
0.428669 + 0.903462i \(0.358983\pi\)
\(224\) −4.20545 −0.280988
\(225\) −2.77362 −0.184908
\(226\) −8.86378 −0.589610
\(227\) −15.5102 −1.02945 −0.514724 0.857356i \(-0.672106\pi\)
−0.514724 + 0.857356i \(0.672106\pi\)
\(228\) 3.34039 0.221223
\(229\) 12.3368 0.815237 0.407619 0.913152i \(-0.366359\pi\)
0.407619 + 0.913152i \(0.366359\pi\)
\(230\) 2.66833 0.175944
\(231\) −15.6090 −1.02700
\(232\) 1.86198 0.122245
\(233\) −6.15840 −0.403450 −0.201725 0.979442i \(-0.564655\pi\)
−0.201725 + 0.979442i \(0.564655\pi\)
\(234\) −6.87171 −0.449218
\(235\) −26.2006 −1.70914
\(236\) 7.25435 0.472218
\(237\) −16.8012 −1.09136
\(238\) 15.4130 0.999077
\(239\) −11.3501 −0.734174 −0.367087 0.930187i \(-0.619645\pi\)
−0.367087 + 0.930187i \(0.619645\pi\)
\(240\) −3.47055 −0.224023
\(241\) −3.47734 −0.223995 −0.111998 0.993708i \(-0.535725\pi\)
−0.111998 + 0.993708i \(0.535725\pi\)
\(242\) −2.85658 −0.183628
\(243\) −12.4363 −0.797788
\(244\) 12.6714 0.811205
\(245\) 28.5132 1.82164
\(246\) 2.04399 0.130320
\(247\) −13.4893 −0.858303
\(248\) 9.92467 0.630217
\(249\) −11.3627 −0.720084
\(250\) −7.68483 −0.486031
\(251\) −3.32774 −0.210045 −0.105022 0.994470i \(-0.533491\pi\)
−0.105022 + 0.994470i \(0.533491\pi\)
\(252\) 5.50207 0.346598
\(253\) −2.85367 −0.179409
\(254\) −6.68674 −0.419564
\(255\) 12.7196 0.796533
\(256\) 1.00000 0.0625000
\(257\) −4.07096 −0.253939 −0.126970 0.991907i \(-0.540525\pi\)
−0.126970 + 0.991907i \(0.540525\pi\)
\(258\) 4.75135 0.295806
\(259\) −2.95597 −0.183675
\(260\) 14.0149 0.869168
\(261\) −2.43607 −0.150789
\(262\) 1.00000 0.0617802
\(263\) 3.14816 0.194124 0.0970621 0.995278i \(-0.469055\pi\)
0.0970621 + 0.995278i \(0.469055\pi\)
\(264\) 3.71161 0.228434
\(265\) −4.83207 −0.296832
\(266\) 10.8007 0.662232
\(267\) 5.59940 0.342678
\(268\) −15.7750 −0.963609
\(269\) 28.7046 1.75015 0.875075 0.483987i \(-0.160812\pi\)
0.875075 + 0.483987i \(0.160812\pi\)
\(270\) 14.9523 0.909965
\(271\) −14.4065 −0.875130 −0.437565 0.899187i \(-0.644159\pi\)
−0.437565 + 0.899187i \(0.644159\pi\)
\(272\) −3.66501 −0.222224
\(273\) 28.7291 1.73876
\(274\) 18.7955 1.13548
\(275\) −6.04973 −0.364813
\(276\) −1.30065 −0.0782897
\(277\) 17.3840 1.04450 0.522251 0.852792i \(-0.325092\pi\)
0.522251 + 0.852792i \(0.325092\pi\)
\(278\) 13.2145 0.792551
\(279\) −12.9846 −0.777371
\(280\) −11.2215 −0.670614
\(281\) 11.6114 0.692678 0.346339 0.938109i \(-0.387425\pi\)
0.346339 + 0.938109i \(0.387425\pi\)
\(282\) 12.7712 0.760512
\(283\) 12.2581 0.728669 0.364335 0.931268i \(-0.381296\pi\)
0.364335 + 0.931268i \(0.381296\pi\)
\(284\) 0.378262 0.0224457
\(285\) 8.91327 0.527977
\(286\) −14.9884 −0.886281
\(287\) 6.60895 0.390114
\(288\) −1.30832 −0.0770935
\(289\) −3.56768 −0.209864
\(290\) 4.96838 0.291753
\(291\) −23.2379 −1.36223
\(292\) 11.9647 0.700184
\(293\) 13.1720 0.769517 0.384759 0.923017i \(-0.374285\pi\)
0.384759 + 0.923017i \(0.374285\pi\)
\(294\) −13.8984 −0.810573
\(295\) 19.3570 1.12701
\(296\) 0.702891 0.0408547
\(297\) −15.9908 −0.927881
\(298\) −19.3153 −1.11891
\(299\) 5.25232 0.303749
\(300\) −2.75735 −0.159196
\(301\) 15.3628 0.885496
\(302\) 12.8549 0.739717
\(303\) −13.5677 −0.779445
\(304\) −2.56826 −0.147300
\(305\) 33.8116 1.93604
\(306\) 4.79501 0.274112
\(307\) −12.3317 −0.703805 −0.351902 0.936037i \(-0.614465\pi\)
−0.351902 + 0.936037i \(0.614465\pi\)
\(308\) 12.0010 0.683818
\(309\) −14.0121 −0.797121
\(310\) 26.4823 1.50409
\(311\) 1.57092 0.0890787 0.0445393 0.999008i \(-0.485818\pi\)
0.0445393 + 0.999008i \(0.485818\pi\)
\(312\) −6.83140 −0.386752
\(313\) 2.11509 0.119552 0.0597759 0.998212i \(-0.480961\pi\)
0.0597759 + 0.998212i \(0.480961\pi\)
\(314\) 15.1710 0.856151
\(315\) 14.6813 0.827200
\(316\) 12.9176 0.726673
\(317\) −17.5972 −0.988357 −0.494178 0.869361i \(-0.664531\pi\)
−0.494178 + 0.869361i \(0.664531\pi\)
\(318\) 2.35534 0.132081
\(319\) −5.31348 −0.297498
\(320\) 2.66833 0.149164
\(321\) 11.3982 0.636187
\(322\) −4.20545 −0.234360
\(323\) 9.41270 0.523736
\(324\) −3.36334 −0.186852
\(325\) 11.1348 0.617649
\(326\) 23.0022 1.27398
\(327\) −14.5738 −0.805932
\(328\) −1.57152 −0.0867727
\(329\) 41.2937 2.27660
\(330\) 9.90381 0.545187
\(331\) −18.0421 −0.991681 −0.495840 0.868414i \(-0.665140\pi\)
−0.495840 + 0.868414i \(0.665140\pi\)
\(332\) 8.73622 0.479463
\(333\) −0.919606 −0.0503941
\(334\) −10.1821 −0.557140
\(335\) −42.0928 −2.29978
\(336\) 5.46980 0.298402
\(337\) −21.5947 −1.17634 −0.588168 0.808739i \(-0.700151\pi\)
−0.588168 + 0.808739i \(0.700151\pi\)
\(338\) 14.5868 0.793419
\(339\) 11.5286 0.626150
\(340\) −9.77946 −0.530366
\(341\) −28.3217 −1.53371
\(342\) 3.36010 0.181694
\(343\) −15.5004 −0.836942
\(344\) −3.65307 −0.196960
\(345\) −3.47055 −0.186848
\(346\) 15.3418 0.824779
\(347\) 13.8264 0.742240 0.371120 0.928585i \(-0.378974\pi\)
0.371120 + 0.928585i \(0.378974\pi\)
\(348\) −2.42178 −0.129821
\(349\) 5.65619 0.302769 0.151384 0.988475i \(-0.451627\pi\)
0.151384 + 0.988475i \(0.451627\pi\)
\(350\) −8.91548 −0.476553
\(351\) 29.4319 1.57096
\(352\) −2.85367 −0.152101
\(353\) 20.0562 1.06749 0.533743 0.845647i \(-0.320785\pi\)
0.533743 + 0.845647i \(0.320785\pi\)
\(354\) −9.43535 −0.501483
\(355\) 1.00933 0.0535696
\(356\) −4.30510 −0.228170
\(357\) −20.0469 −1.06099
\(358\) −3.34395 −0.176733
\(359\) −11.6364 −0.614145 −0.307073 0.951686i \(-0.599349\pi\)
−0.307073 + 0.951686i \(0.599349\pi\)
\(360\) −3.49103 −0.183993
\(361\) −12.4041 −0.652845
\(362\) −13.3129 −0.699710
\(363\) 3.71539 0.195008
\(364\) −22.0883 −1.15774
\(365\) 31.9259 1.67108
\(366\) −16.4810 −0.861478
\(367\) −27.0101 −1.40991 −0.704957 0.709250i \(-0.749034\pi\)
−0.704957 + 0.709250i \(0.749034\pi\)
\(368\) 1.00000 0.0521286
\(369\) 2.05605 0.107034
\(370\) 1.87554 0.0975049
\(371\) 7.61563 0.395384
\(372\) −12.9085 −0.669274
\(373\) −1.84894 −0.0957345 −0.0478672 0.998854i \(-0.515242\pi\)
−0.0478672 + 0.998854i \(0.515242\pi\)
\(374\) 10.4587 0.540808
\(375\) 9.99524 0.516152
\(376\) −9.81910 −0.506381
\(377\) 9.77972 0.503681
\(378\) −23.5656 −1.21209
\(379\) 10.7898 0.554234 0.277117 0.960836i \(-0.410621\pi\)
0.277117 + 0.960836i \(0.410621\pi\)
\(380\) −6.85296 −0.351549
\(381\) 8.69708 0.445565
\(382\) −16.8178 −0.860472
\(383\) 10.4496 0.533952 0.266976 0.963703i \(-0.413976\pi\)
0.266976 + 0.963703i \(0.413976\pi\)
\(384\) −1.30065 −0.0663733
\(385\) 32.0225 1.63202
\(386\) −14.2903 −0.727356
\(387\) 4.77938 0.242950
\(388\) 17.8664 0.907031
\(389\) −2.54826 −0.129202 −0.0646010 0.997911i \(-0.520577\pi\)
−0.0646010 + 0.997911i \(0.520577\pi\)
\(390\) −18.2284 −0.923033
\(391\) −3.66501 −0.185348
\(392\) 10.6858 0.539714
\(393\) −1.30065 −0.0656089
\(394\) 14.1738 0.714068
\(395\) 34.4685 1.73430
\(396\) 3.73351 0.187616
\(397\) 11.9449 0.599499 0.299750 0.954018i \(-0.403097\pi\)
0.299750 + 0.954018i \(0.403097\pi\)
\(398\) 10.1475 0.508646
\(399\) −14.0478 −0.703272
\(400\) 2.11998 0.105999
\(401\) 26.9570 1.34617 0.673083 0.739567i \(-0.264970\pi\)
0.673083 + 0.739567i \(0.264970\pi\)
\(402\) 20.5176 1.02333
\(403\) 52.1275 2.59666
\(404\) 10.4315 0.518988
\(405\) −8.97449 −0.445946
\(406\) −7.83047 −0.388620
\(407\) −2.00582 −0.0994247
\(408\) 4.76688 0.235996
\(409\) 29.9678 1.48181 0.740907 0.671607i \(-0.234396\pi\)
0.740907 + 0.671607i \(0.234396\pi\)
\(410\) −4.19334 −0.207094
\(411\) −24.4463 −1.20585
\(412\) 10.7732 0.530757
\(413\) −30.5078 −1.50119
\(414\) −1.30832 −0.0643004
\(415\) 23.3111 1.14430
\(416\) 5.25232 0.257516
\(417\) −17.1873 −0.841668
\(418\) 7.32895 0.358471
\(419\) −18.6662 −0.911902 −0.455951 0.890005i \(-0.650701\pi\)
−0.455951 + 0.890005i \(0.650701\pi\)
\(420\) 14.5952 0.712174
\(421\) −3.04689 −0.148496 −0.0742481 0.997240i \(-0.523656\pi\)
−0.0742481 + 0.997240i \(0.523656\pi\)
\(422\) 20.9748 1.02104
\(423\) 12.8465 0.624619
\(424\) −1.81090 −0.0879449
\(425\) −7.76977 −0.376889
\(426\) −0.491985 −0.0238367
\(427\) −53.2890 −2.57884
\(428\) −8.76351 −0.423600
\(429\) 19.4946 0.941206
\(430\) −9.74759 −0.470071
\(431\) 2.00453 0.0965547 0.0482774 0.998834i \(-0.484627\pi\)
0.0482774 + 0.998834i \(0.484627\pi\)
\(432\) 5.60360 0.269603
\(433\) 9.17585 0.440963 0.220482 0.975391i \(-0.429237\pi\)
0.220482 + 0.975391i \(0.429237\pi\)
\(434\) −41.7377 −2.00347
\(435\) −6.46211 −0.309834
\(436\) 11.2050 0.536624
\(437\) −2.56826 −0.122856
\(438\) −15.5619 −0.743576
\(439\) −21.4540 −1.02394 −0.511972 0.859002i \(-0.671085\pi\)
−0.511972 + 0.859002i \(0.671085\pi\)
\(440\) −7.61453 −0.363008
\(441\) −13.9804 −0.665735
\(442\) −19.2498 −0.915620
\(443\) 38.1606 1.81306 0.906531 0.422139i \(-0.138720\pi\)
0.906531 + 0.422139i \(0.138720\pi\)
\(444\) −0.914212 −0.0433866
\(445\) −11.4874 −0.544556
\(446\) 12.8028 0.606229
\(447\) 25.1224 1.18825
\(448\) −4.20545 −0.198689
\(449\) −11.8880 −0.561029 −0.280515 0.959850i \(-0.590505\pi\)
−0.280515 + 0.959850i \(0.590505\pi\)
\(450\) −2.77362 −0.130750
\(451\) 4.48460 0.211171
\(452\) −8.86378 −0.416917
\(453\) −16.7197 −0.785560
\(454\) −15.5102 −0.727930
\(455\) −58.9390 −2.76310
\(456\) 3.34039 0.156428
\(457\) −20.4974 −0.958828 −0.479414 0.877589i \(-0.659151\pi\)
−0.479414 + 0.877589i \(0.659151\pi\)
\(458\) 12.3368 0.576460
\(459\) −20.5373 −0.958597
\(460\) 2.66833 0.124412
\(461\) 18.5868 0.865673 0.432837 0.901472i \(-0.357513\pi\)
0.432837 + 0.901472i \(0.357513\pi\)
\(462\) −15.6090 −0.726196
\(463\) −32.0652 −1.49020 −0.745099 0.666954i \(-0.767598\pi\)
−0.745099 + 0.666954i \(0.767598\pi\)
\(464\) 1.86198 0.0864403
\(465\) −34.4441 −1.59731
\(466\) −6.15840 −0.285282
\(467\) −22.3931 −1.03623 −0.518115 0.855311i \(-0.673366\pi\)
−0.518115 + 0.855311i \(0.673366\pi\)
\(468\) −6.87171 −0.317645
\(469\) 66.3408 3.06333
\(470\) −26.2006 −1.20854
\(471\) −19.7321 −0.909209
\(472\) 7.25435 0.333909
\(473\) 10.4246 0.479326
\(474\) −16.8012 −0.771707
\(475\) −5.44467 −0.249818
\(476\) 15.4130 0.706454
\(477\) 2.36923 0.108480
\(478\) −11.3501 −0.519140
\(479\) −35.9014 −1.64037 −0.820187 0.572095i \(-0.806131\pi\)
−0.820187 + 0.572095i \(0.806131\pi\)
\(480\) −3.47055 −0.158408
\(481\) 3.69180 0.168332
\(482\) −3.47734 −0.158388
\(483\) 5.46980 0.248884
\(484\) −2.85658 −0.129844
\(485\) 47.6736 2.16475
\(486\) −12.4363 −0.564121
\(487\) −16.9582 −0.768449 −0.384225 0.923240i \(-0.625531\pi\)
−0.384225 + 0.923240i \(0.625531\pi\)
\(488\) 12.6714 0.573609
\(489\) −29.9178 −1.35293
\(490\) 28.5132 1.28810
\(491\) 35.5842 1.60589 0.802947 0.596051i \(-0.203264\pi\)
0.802947 + 0.596051i \(0.203264\pi\)
\(492\) 2.04399 0.0921503
\(493\) −6.82419 −0.307346
\(494\) −13.4893 −0.606912
\(495\) 9.96224 0.447769
\(496\) 9.92467 0.445631
\(497\) −1.59076 −0.0713554
\(498\) −11.3627 −0.509176
\(499\) 14.9594 0.669676 0.334838 0.942276i \(-0.391318\pi\)
0.334838 + 0.942276i \(0.391318\pi\)
\(500\) −7.68483 −0.343676
\(501\) 13.2433 0.591667
\(502\) −3.32774 −0.148524
\(503\) −4.93850 −0.220197 −0.110098 0.993921i \(-0.535117\pi\)
−0.110098 + 0.993921i \(0.535117\pi\)
\(504\) 5.50207 0.245082
\(505\) 27.8347 1.23863
\(506\) −2.85367 −0.126861
\(507\) −18.9723 −0.842589
\(508\) −6.68674 −0.296676
\(509\) 38.1329 1.69021 0.845106 0.534599i \(-0.179537\pi\)
0.845106 + 0.534599i \(0.179537\pi\)
\(510\) 12.7196 0.563234
\(511\) −50.3171 −2.22590
\(512\) 1.00000 0.0441942
\(513\) −14.3915 −0.635400
\(514\) −4.07096 −0.179562
\(515\) 28.7464 1.26672
\(516\) 4.75135 0.209166
\(517\) 28.0204 1.23234
\(518\) −2.95597 −0.129878
\(519\) −19.9542 −0.875893
\(520\) 14.0149 0.614595
\(521\) 16.9751 0.743693 0.371846 0.928294i \(-0.378725\pi\)
0.371846 + 0.928294i \(0.378725\pi\)
\(522\) −2.43607 −0.106624
\(523\) 35.9553 1.57222 0.786109 0.618088i \(-0.212093\pi\)
0.786109 + 0.618088i \(0.212093\pi\)
\(524\) 1.00000 0.0436852
\(525\) 11.5959 0.506086
\(526\) 3.14816 0.137267
\(527\) −36.3740 −1.58448
\(528\) 3.71161 0.161527
\(529\) 1.00000 0.0434783
\(530\) −4.83207 −0.209892
\(531\) −9.49102 −0.411875
\(532\) 10.8007 0.468268
\(533\) −8.25412 −0.357526
\(534\) 5.59940 0.242310
\(535\) −23.3839 −1.01098
\(536\) −15.7750 −0.681374
\(537\) 4.34930 0.187686
\(538\) 28.7046 1.23754
\(539\) −30.4937 −1.31346
\(540\) 14.9523 0.643442
\(541\) −32.1060 −1.38035 −0.690173 0.723644i \(-0.742466\pi\)
−0.690173 + 0.723644i \(0.742466\pi\)
\(542\) −14.4065 −0.618811
\(543\) 17.3154 0.743074
\(544\) −3.66501 −0.157136
\(545\) 29.8987 1.28072
\(546\) 28.7291 1.22949
\(547\) 27.7705 1.18738 0.593690 0.804694i \(-0.297670\pi\)
0.593690 + 0.804694i \(0.297670\pi\)
\(548\) 18.7955 0.802904
\(549\) −16.5783 −0.707544
\(550\) −6.04973 −0.257962
\(551\) −4.78205 −0.203722
\(552\) −1.30065 −0.0553592
\(553\) −54.3243 −2.31011
\(554\) 17.3840 0.738574
\(555\) −2.43942 −0.103548
\(556\) 13.2145 0.560418
\(557\) −5.14927 −0.218181 −0.109091 0.994032i \(-0.534794\pi\)
−0.109091 + 0.994032i \(0.534794\pi\)
\(558\) −12.9846 −0.549684
\(559\) −19.1871 −0.811527
\(560\) −11.2215 −0.474196
\(561\) −13.6031 −0.574324
\(562\) 11.6114 0.489797
\(563\) −38.5209 −1.62346 −0.811731 0.584031i \(-0.801475\pi\)
−0.811731 + 0.584031i \(0.801475\pi\)
\(564\) 12.7712 0.537763
\(565\) −23.6515 −0.995026
\(566\) 12.2581 0.515247
\(567\) 14.1443 0.594006
\(568\) 0.378262 0.0158715
\(569\) 10.8903 0.456546 0.228273 0.973597i \(-0.426692\pi\)
0.228273 + 0.973597i \(0.426692\pi\)
\(570\) 8.91327 0.373336
\(571\) −6.01142 −0.251570 −0.125785 0.992058i \(-0.540145\pi\)
−0.125785 + 0.992058i \(0.540145\pi\)
\(572\) −14.9884 −0.626695
\(573\) 21.8740 0.913798
\(574\) 6.60895 0.275852
\(575\) 2.11998 0.0884095
\(576\) −1.30832 −0.0545133
\(577\) −12.9805 −0.540387 −0.270194 0.962806i \(-0.587088\pi\)
−0.270194 + 0.962806i \(0.587088\pi\)
\(578\) −3.56768 −0.148396
\(579\) 18.5866 0.772432
\(580\) 4.96838 0.206301
\(581\) −36.7397 −1.52422
\(582\) −23.2379 −0.963243
\(583\) 5.16770 0.214024
\(584\) 11.9647 0.495105
\(585\) −18.3360 −0.758100
\(586\) 13.1720 0.544131
\(587\) 2.20337 0.0909427 0.0454714 0.998966i \(-0.485521\pi\)
0.0454714 + 0.998966i \(0.485521\pi\)
\(588\) −13.8984 −0.573161
\(589\) −25.4891 −1.05026
\(590\) 19.3570 0.796916
\(591\) −18.4352 −0.758321
\(592\) 0.702891 0.0288886
\(593\) 31.9688 1.31280 0.656401 0.754412i \(-0.272078\pi\)
0.656401 + 0.754412i \(0.272078\pi\)
\(594\) −15.9908 −0.656111
\(595\) 41.1270 1.68604
\(596\) −19.3153 −0.791186
\(597\) −13.1983 −0.540169
\(598\) 5.25232 0.214783
\(599\) 12.5338 0.512117 0.256058 0.966661i \(-0.417576\pi\)
0.256058 + 0.966661i \(0.417576\pi\)
\(600\) −2.75735 −0.112568
\(601\) 15.9943 0.652421 0.326211 0.945297i \(-0.394228\pi\)
0.326211 + 0.945297i \(0.394228\pi\)
\(602\) 15.3628 0.626140
\(603\) 20.6387 0.840473
\(604\) 12.8549 0.523059
\(605\) −7.62229 −0.309890
\(606\) −13.5677 −0.551151
\(607\) −29.5180 −1.19810 −0.599049 0.800712i \(-0.704454\pi\)
−0.599049 + 0.800712i \(0.704454\pi\)
\(608\) −2.56826 −0.104157
\(609\) 10.1847 0.412703
\(610\) 33.8116 1.36899
\(611\) −51.5730 −2.08642
\(612\) 4.79501 0.193827
\(613\) −5.06021 −0.204380 −0.102190 0.994765i \(-0.532585\pi\)
−0.102190 + 0.994765i \(0.532585\pi\)
\(614\) −12.3317 −0.497665
\(615\) 5.45404 0.219928
\(616\) 12.0010 0.483532
\(617\) −34.3285 −1.38201 −0.691006 0.722849i \(-0.742832\pi\)
−0.691006 + 0.722849i \(0.742832\pi\)
\(618\) −14.0121 −0.563650
\(619\) 37.8126 1.51982 0.759909 0.650030i \(-0.225244\pi\)
0.759909 + 0.650030i \(0.225244\pi\)
\(620\) 26.4823 1.06355
\(621\) 5.60360 0.224865
\(622\) 1.57092 0.0629881
\(623\) 18.1048 0.725355
\(624\) −6.83140 −0.273475
\(625\) −31.1056 −1.24422
\(626\) 2.11509 0.0845360
\(627\) −9.53238 −0.380686
\(628\) 15.1710 0.605390
\(629\) −2.57610 −0.102716
\(630\) 14.6813 0.584919
\(631\) 29.9115 1.19076 0.595378 0.803446i \(-0.297002\pi\)
0.595378 + 0.803446i \(0.297002\pi\)
\(632\) 12.9176 0.513835
\(633\) −27.2809 −1.08432
\(634\) −17.5972 −0.698874
\(635\) −17.8424 −0.708055
\(636\) 2.35534 0.0933951
\(637\) 56.1251 2.22376
\(638\) −5.31348 −0.210363
\(639\) −0.494888 −0.0195775
\(640\) 2.66833 0.105475
\(641\) 10.0568 0.397221 0.198610 0.980079i \(-0.436357\pi\)
0.198610 + 0.980079i \(0.436357\pi\)
\(642\) 11.3982 0.449852
\(643\) 27.2073 1.07295 0.536476 0.843915i \(-0.319755\pi\)
0.536476 + 0.843915i \(0.319755\pi\)
\(644\) −4.20545 −0.165718
\(645\) 12.6782 0.499202
\(646\) 9.41270 0.370338
\(647\) 38.3899 1.50926 0.754632 0.656148i \(-0.227815\pi\)
0.754632 + 0.656148i \(0.227815\pi\)
\(648\) −3.36334 −0.132124
\(649\) −20.7015 −0.812606
\(650\) 11.1348 0.436744
\(651\) 54.2859 2.12763
\(652\) 23.0022 0.900837
\(653\) −17.8023 −0.696658 −0.348329 0.937372i \(-0.613251\pi\)
−0.348329 + 0.937372i \(0.613251\pi\)
\(654\) −14.5738 −0.569880
\(655\) 2.66833 0.104260
\(656\) −1.57152 −0.0613576
\(657\) −15.6537 −0.610710
\(658\) 41.2937 1.60980
\(659\) −2.86094 −0.111446 −0.0557232 0.998446i \(-0.517746\pi\)
−0.0557232 + 0.998446i \(0.517746\pi\)
\(660\) 9.90381 0.385505
\(661\) 30.1564 1.17295 0.586473 0.809969i \(-0.300516\pi\)
0.586473 + 0.809969i \(0.300516\pi\)
\(662\) −18.0421 −0.701224
\(663\) 25.0372 0.972363
\(664\) 8.73622 0.339031
\(665\) 28.8198 1.11758
\(666\) −0.919606 −0.0356340
\(667\) 1.86198 0.0720962
\(668\) −10.1821 −0.393957
\(669\) −16.6519 −0.643799
\(670\) −42.0928 −1.62619
\(671\) −36.1601 −1.39594
\(672\) 5.46980 0.211002
\(673\) −42.1563 −1.62500 −0.812502 0.582958i \(-0.801895\pi\)
−0.812502 + 0.582958i \(0.801895\pi\)
\(674\) −21.5947 −0.831796
\(675\) 11.8795 0.457244
\(676\) 14.5868 0.561032
\(677\) 14.4134 0.553953 0.276977 0.960877i \(-0.410668\pi\)
0.276977 + 0.960877i \(0.410668\pi\)
\(678\) 11.5286 0.442755
\(679\) −75.1364 −2.88347
\(680\) −9.77946 −0.375025
\(681\) 20.1733 0.773042
\(682\) −28.3217 −1.08449
\(683\) −18.0549 −0.690852 −0.345426 0.938446i \(-0.612266\pi\)
−0.345426 + 0.938446i \(0.612266\pi\)
\(684\) 3.36010 0.128477
\(685\) 50.1526 1.91623
\(686\) −15.5004 −0.591807
\(687\) −16.0458 −0.612185
\(688\) −3.65307 −0.139272
\(689\) −9.51140 −0.362356
\(690\) −3.47055 −0.132122
\(691\) 7.78487 0.296150 0.148075 0.988976i \(-0.452692\pi\)
0.148075 + 0.988976i \(0.452692\pi\)
\(692\) 15.3418 0.583207
\(693\) −15.7011 −0.596435
\(694\) 13.8264 0.524843
\(695\) 35.2606 1.33751
\(696\) −2.42178 −0.0917973
\(697\) 5.75964 0.218162
\(698\) 5.65619 0.214090
\(699\) 8.00990 0.302962
\(700\) −8.91548 −0.336974
\(701\) 21.2195 0.801451 0.400726 0.916198i \(-0.368758\pi\)
0.400726 + 0.916198i \(0.368758\pi\)
\(702\) 29.4319 1.11083
\(703\) −1.80520 −0.0680846
\(704\) −2.85367 −0.107552
\(705\) 34.0777 1.28344
\(706\) 20.0562 0.754826
\(707\) −43.8692 −1.64987
\(708\) −9.43535 −0.354602
\(709\) −17.7505 −0.666635 −0.333318 0.942815i \(-0.608168\pi\)
−0.333318 + 0.942815i \(0.608168\pi\)
\(710\) 1.00933 0.0378794
\(711\) −16.9004 −0.633814
\(712\) −4.30510 −0.161340
\(713\) 9.92467 0.371682
\(714\) −20.0469 −0.750236
\(715\) −39.9939 −1.49569
\(716\) −3.34395 −0.124969
\(717\) 14.7624 0.551312
\(718\) −11.6364 −0.434266
\(719\) −35.6917 −1.33108 −0.665538 0.746364i \(-0.731798\pi\)
−0.665538 + 0.746364i \(0.731798\pi\)
\(720\) −3.49103 −0.130103
\(721\) −45.3061 −1.68729
\(722\) −12.4041 −0.461631
\(723\) 4.52279 0.168204
\(724\) −13.3129 −0.494770
\(725\) 3.94737 0.146602
\(726\) 3.71539 0.137891
\(727\) 35.9271 1.33246 0.666232 0.745745i \(-0.267906\pi\)
0.666232 + 0.745745i \(0.267906\pi\)
\(728\) −22.0883 −0.818648
\(729\) 26.2652 0.972786
\(730\) 31.9259 1.18163
\(731\) 13.3885 0.495193
\(732\) −16.4810 −0.609157
\(733\) −11.7726 −0.434829 −0.217415 0.976079i \(-0.569762\pi\)
−0.217415 + 0.976079i \(0.569762\pi\)
\(734\) −27.0101 −0.996960
\(735\) −37.0856 −1.36792
\(736\) 1.00000 0.0368605
\(737\) 45.0165 1.65820
\(738\) 2.05605 0.0756843
\(739\) −20.5475 −0.755853 −0.377926 0.925836i \(-0.623363\pi\)
−0.377926 + 0.925836i \(0.623363\pi\)
\(740\) 1.87554 0.0689464
\(741\) 17.5448 0.644524
\(742\) 7.61563 0.279579
\(743\) −18.8448 −0.691348 −0.345674 0.938355i \(-0.612350\pi\)
−0.345674 + 0.938355i \(0.612350\pi\)
\(744\) −12.9085 −0.473248
\(745\) −51.5396 −1.88827
\(746\) −1.84894 −0.0676945
\(747\) −11.4298 −0.418194
\(748\) 10.4587 0.382409
\(749\) 36.8545 1.34663
\(750\) 9.99524 0.364975
\(751\) −15.1990 −0.554619 −0.277310 0.960781i \(-0.589443\pi\)
−0.277310 + 0.960781i \(0.589443\pi\)
\(752\) −9.81910 −0.358066
\(753\) 4.32821 0.157729
\(754\) 9.77972 0.356156
\(755\) 34.3012 1.24835
\(756\) −23.5656 −0.857074
\(757\) −44.6561 −1.62305 −0.811527 0.584315i \(-0.801363\pi\)
−0.811527 + 0.584315i \(0.801363\pi\)
\(758\) 10.7898 0.391903
\(759\) 3.71161 0.134723
\(760\) −6.85296 −0.248583
\(761\) −19.1290 −0.693427 −0.346714 0.937971i \(-0.612702\pi\)
−0.346714 + 0.937971i \(0.612702\pi\)
\(762\) 8.69708 0.315062
\(763\) −47.1222 −1.70594
\(764\) −16.8178 −0.608446
\(765\) 12.7947 0.462592
\(766\) 10.4496 0.377561
\(767\) 38.1022 1.37579
\(768\) −1.30065 −0.0469330
\(769\) 9.53986 0.344016 0.172008 0.985096i \(-0.444974\pi\)
0.172008 + 0.985096i \(0.444974\pi\)
\(770\) 32.0225 1.15401
\(771\) 5.29488 0.190690
\(772\) −14.2903 −0.514318
\(773\) −30.7760 −1.10694 −0.553468 0.832871i \(-0.686696\pi\)
−0.553468 + 0.832871i \(0.686696\pi\)
\(774\) 4.77938 0.171791
\(775\) 21.0402 0.755785
\(776\) 17.8664 0.641368
\(777\) 3.84467 0.137927
\(778\) −2.54826 −0.0913596
\(779\) 4.03607 0.144607
\(780\) −18.2284 −0.652683
\(781\) −1.07943 −0.0386252
\(782\) −3.66501 −0.131061
\(783\) 10.4338 0.372874
\(784\) 10.6858 0.381635
\(785\) 40.4813 1.44484
\(786\) −1.30065 −0.0463925
\(787\) 28.9575 1.03222 0.516112 0.856521i \(-0.327379\pi\)
0.516112 + 0.856521i \(0.327379\pi\)
\(788\) 14.1738 0.504922
\(789\) −4.09465 −0.145773
\(790\) 34.4685 1.22633
\(791\) 37.2762 1.32539
\(792\) 3.73351 0.132665
\(793\) 66.5544 2.36342
\(794\) 11.9449 0.423910
\(795\) 6.28481 0.222899
\(796\) 10.1475 0.359667
\(797\) −20.3463 −0.720704 −0.360352 0.932816i \(-0.617343\pi\)
−0.360352 + 0.932816i \(0.617343\pi\)
\(798\) −14.0478 −0.497288
\(799\) 35.9871 1.27313
\(800\) 2.11998 0.0749528
\(801\) 5.63244 0.199013
\(802\) 26.9570 0.951883
\(803\) −34.1434 −1.20489
\(804\) 20.5176 0.723601
\(805\) −11.2215 −0.395507
\(806\) 52.1275 1.83611
\(807\) −37.3345 −1.31424
\(808\) 10.4315 0.366980
\(809\) −42.6845 −1.50071 −0.750353 0.661037i \(-0.770116\pi\)
−0.750353 + 0.661037i \(0.770116\pi\)
\(810\) −8.97449 −0.315332
\(811\) 17.5640 0.616755 0.308377 0.951264i \(-0.400214\pi\)
0.308377 + 0.951264i \(0.400214\pi\)
\(812\) −7.83047 −0.274796
\(813\) 18.7377 0.657160
\(814\) −2.00582 −0.0703039
\(815\) 61.3775 2.14996
\(816\) 4.76688 0.166874
\(817\) 9.38202 0.328235
\(818\) 29.9678 1.04780
\(819\) 28.8986 1.00980
\(820\) −4.19334 −0.146438
\(821\) −38.2203 −1.33390 −0.666949 0.745104i \(-0.732400\pi\)
−0.666949 + 0.745104i \(0.732400\pi\)
\(822\) −24.4463 −0.852662
\(823\) 42.2945 1.47429 0.737146 0.675733i \(-0.236173\pi\)
0.737146 + 0.675733i \(0.236173\pi\)
\(824\) 10.7732 0.375302
\(825\) 7.86856 0.273948
\(826\) −30.5078 −1.06150
\(827\) 47.3573 1.64677 0.823387 0.567481i \(-0.192082\pi\)
0.823387 + 0.567481i \(0.192082\pi\)
\(828\) −1.30832 −0.0454673
\(829\) −39.9784 −1.38851 −0.694254 0.719731i \(-0.744265\pi\)
−0.694254 + 0.719731i \(0.744265\pi\)
\(830\) 23.3111 0.809141
\(831\) −22.6104 −0.784346
\(832\) 5.25232 0.182091
\(833\) −39.1635 −1.35694
\(834\) −17.1873 −0.595149
\(835\) −27.1692 −0.940229
\(836\) 7.32895 0.253477
\(837\) 55.6139 1.92230
\(838\) −18.6662 −0.644812
\(839\) 23.1644 0.799722 0.399861 0.916576i \(-0.369058\pi\)
0.399861 + 0.916576i \(0.369058\pi\)
\(840\) 14.5952 0.503583
\(841\) −25.5330 −0.880449
\(842\) −3.04689 −0.105003
\(843\) −15.1023 −0.520151
\(844\) 20.9748 0.721984
\(845\) 38.9225 1.33897
\(846\) 12.8465 0.441673
\(847\) 12.0132 0.412778
\(848\) −1.81090 −0.0621865
\(849\) −15.9435 −0.547179
\(850\) −7.76977 −0.266501
\(851\) 0.702891 0.0240948
\(852\) −0.491985 −0.0168551
\(853\) −7.34019 −0.251323 −0.125662 0.992073i \(-0.540105\pi\)
−0.125662 + 0.992073i \(0.540105\pi\)
\(854\) −53.2890 −1.82351
\(855\) 8.96586 0.306626
\(856\) −8.76351 −0.299531
\(857\) 29.2763 1.00006 0.500030 0.866008i \(-0.333322\pi\)
0.500030 + 0.866008i \(0.333322\pi\)
\(858\) 19.4946 0.665533
\(859\) 22.8807 0.780680 0.390340 0.920671i \(-0.372357\pi\)
0.390340 + 0.920671i \(0.372357\pi\)
\(860\) −9.74759 −0.332390
\(861\) −8.59590 −0.292947
\(862\) 2.00453 0.0682745
\(863\) −19.3138 −0.657450 −0.328725 0.944426i \(-0.606619\pi\)
−0.328725 + 0.944426i \(0.606619\pi\)
\(864\) 5.60360 0.190638
\(865\) 40.9369 1.39190
\(866\) 9.17585 0.311808
\(867\) 4.64029 0.157593
\(868\) −41.7377 −1.41667
\(869\) −36.8626 −1.25048
\(870\) −6.46211 −0.219086
\(871\) −82.8551 −2.80744
\(872\) 11.2050 0.379450
\(873\) −23.3750 −0.791125
\(874\) −2.56826 −0.0868726
\(875\) 32.3181 1.09255
\(876\) −15.5619 −0.525788
\(877\) −40.2715 −1.35987 −0.679936 0.733272i \(-0.737992\pi\)
−0.679936 + 0.733272i \(0.737992\pi\)
\(878\) −21.4540 −0.724038
\(879\) −17.1321 −0.577852
\(880\) −7.61453 −0.256686
\(881\) −19.1517 −0.645238 −0.322619 0.946529i \(-0.604563\pi\)
−0.322619 + 0.946529i \(0.604563\pi\)
\(882\) −13.9804 −0.470746
\(883\) 9.21070 0.309965 0.154982 0.987917i \(-0.450468\pi\)
0.154982 + 0.987917i \(0.450468\pi\)
\(884\) −19.2498 −0.647441
\(885\) −25.1766 −0.846303
\(886\) 38.1606 1.28203
\(887\) 7.91081 0.265619 0.132810 0.991142i \(-0.457600\pi\)
0.132810 + 0.991142i \(0.457600\pi\)
\(888\) −0.914212 −0.0306789
\(889\) 28.1207 0.943139
\(890\) −11.4874 −0.385059
\(891\) 9.59785 0.321540
\(892\) 12.8028 0.428669
\(893\) 25.2180 0.843887
\(894\) 25.1224 0.840218
\(895\) −8.92276 −0.298255
\(896\) −4.20545 −0.140494
\(897\) −6.83140 −0.228094
\(898\) −11.8880 −0.396707
\(899\) 18.4796 0.616328
\(900\) −2.77362 −0.0924540
\(901\) 6.63696 0.221109
\(902\) 4.48460 0.149321
\(903\) −19.9815 −0.664944
\(904\) −8.86378 −0.294805
\(905\) −35.5232 −1.18083
\(906\) −16.7197 −0.555475
\(907\) −47.8891 −1.59013 −0.795065 0.606524i \(-0.792563\pi\)
−0.795065 + 0.606524i \(0.792563\pi\)
\(908\) −15.5102 −0.514724
\(909\) −13.6478 −0.452668
\(910\) −58.9390 −1.95381
\(911\) 5.14648 0.170510 0.0852552 0.996359i \(-0.472829\pi\)
0.0852552 + 0.996359i \(0.472829\pi\)
\(912\) 3.34039 0.110611
\(913\) −24.9303 −0.825072
\(914\) −20.4974 −0.677994
\(915\) −43.9769 −1.45383
\(916\) 12.3368 0.407619
\(917\) −4.20545 −0.138876
\(918\) −20.5373 −0.677831
\(919\) −51.2148 −1.68942 −0.844710 0.535224i \(-0.820227\pi\)
−0.844710 + 0.535224i \(0.820227\pi\)
\(920\) 2.66833 0.0879722
\(921\) 16.0391 0.528507
\(922\) 18.5868 0.612124
\(923\) 1.98675 0.0653947
\(924\) −15.6090 −0.513498
\(925\) 1.49012 0.0489948
\(926\) −32.0652 −1.05373
\(927\) −14.0948 −0.462934
\(928\) 1.86198 0.0611226
\(929\) −32.2420 −1.05782 −0.528912 0.848676i \(-0.677400\pi\)
−0.528912 + 0.848676i \(0.677400\pi\)
\(930\) −34.4441 −1.12947
\(931\) −27.4438 −0.899436
\(932\) −6.15840 −0.201725
\(933\) −2.04321 −0.0668917
\(934\) −22.3931 −0.732725
\(935\) 27.9073 0.912668
\(936\) −6.87171 −0.224609
\(937\) 33.8640 1.10629 0.553144 0.833086i \(-0.313428\pi\)
0.553144 + 0.833086i \(0.313428\pi\)
\(938\) 66.3408 2.16610
\(939\) −2.75098 −0.0897749
\(940\) −26.2006 −0.854569
\(941\) 16.6715 0.543475 0.271737 0.962371i \(-0.412402\pi\)
0.271737 + 0.962371i \(0.412402\pi\)
\(942\) −19.7321 −0.642908
\(943\) −1.57152 −0.0511757
\(944\) 7.25435 0.236109
\(945\) −62.8809 −2.04552
\(946\) 10.4246 0.338935
\(947\) 2.48133 0.0806324 0.0403162 0.999187i \(-0.487163\pi\)
0.0403162 + 0.999187i \(0.487163\pi\)
\(948\) −16.8012 −0.545679
\(949\) 62.8426 2.03996
\(950\) −5.44467 −0.176648
\(951\) 22.8877 0.742185
\(952\) 15.4130 0.499539
\(953\) 17.6732 0.572491 0.286246 0.958156i \(-0.407593\pi\)
0.286246 + 0.958156i \(0.407593\pi\)
\(954\) 2.36923 0.0767068
\(955\) −44.8754 −1.45213
\(956\) −11.3501 −0.367087
\(957\) 6.91096 0.223399
\(958\) −35.9014 −1.15992
\(959\) −79.0434 −2.55245
\(960\) −3.47055 −0.112012
\(961\) 67.4991 2.17739
\(962\) 3.69180 0.119029
\(963\) 11.4655 0.369470
\(964\) −3.47734 −0.111998
\(965\) −38.1312 −1.22749
\(966\) 5.46980 0.175988
\(967\) 28.4718 0.915590 0.457795 0.889058i \(-0.348639\pi\)
0.457795 + 0.889058i \(0.348639\pi\)
\(968\) −2.85658 −0.0918138
\(969\) −12.2426 −0.393288
\(970\) 47.6736 1.53071
\(971\) 59.6041 1.91279 0.956394 0.292081i \(-0.0943477\pi\)
0.956394 + 0.292081i \(0.0943477\pi\)
\(972\) −12.4363 −0.398894
\(973\) −55.5728 −1.78158
\(974\) −16.9582 −0.543376
\(975\) −14.4825 −0.463810
\(976\) 12.6714 0.405603
\(977\) 56.0328 1.79265 0.896323 0.443401i \(-0.146228\pi\)
0.896323 + 0.443401i \(0.146228\pi\)
\(978\) −29.9178 −0.956664
\(979\) 12.2853 0.392640
\(980\) 28.5132 0.910821
\(981\) −14.6598 −0.468051
\(982\) 35.5842 1.13554
\(983\) 52.4652 1.67338 0.836689 0.547678i \(-0.184488\pi\)
0.836689 + 0.547678i \(0.184488\pi\)
\(984\) 2.04399 0.0651601
\(985\) 37.8205 1.20506
\(986\) −6.82419 −0.217326
\(987\) −53.7085 −1.70956
\(988\) −13.4893 −0.429152
\(989\) −3.65307 −0.116161
\(990\) 9.96224 0.316621
\(991\) −15.2415 −0.484161 −0.242081 0.970256i \(-0.577830\pi\)
−0.242081 + 0.970256i \(0.577830\pi\)
\(992\) 9.92467 0.315109
\(993\) 23.4663 0.744681
\(994\) −1.59076 −0.0504559
\(995\) 27.0768 0.858392
\(996\) −11.3627 −0.360042
\(997\) −4.36515 −0.138246 −0.0691228 0.997608i \(-0.522020\pi\)
−0.0691228 + 0.997608i \(0.522020\pi\)
\(998\) 14.9594 0.473532
\(999\) 3.93872 0.124616
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.m.1.12 41
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.m.1.12 41 1.1 even 1 trivial