Properties

Label 8049.2.a.d.1.1
Level $8049$
Weight $2$
Character 8049.1
Self dual yes
Analytic conductor $64.272$
Analytic rank $0$
Dimension $129$
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] = [8049,2,Mod(1,8049)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8049, 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("8049.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8049 = 3 \cdot 2683 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8049.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: \(64.2715885869\)
Analytic rank: \(0\)
Dimension: \(129\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 8049.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.82087 q^{2} +1.00000 q^{3} +5.95730 q^{4} +1.28710 q^{5} -2.82087 q^{6} +2.58338 q^{7} -11.1630 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.82087 q^{2} +1.00000 q^{3} +5.95730 q^{4} +1.28710 q^{5} -2.82087 q^{6} +2.58338 q^{7} -11.1630 q^{8} +1.00000 q^{9} -3.63075 q^{10} +5.50374 q^{11} +5.95730 q^{12} +5.71159 q^{13} -7.28738 q^{14} +1.28710 q^{15} +19.5748 q^{16} +4.87983 q^{17} -2.82087 q^{18} +5.71437 q^{19} +7.66766 q^{20} +2.58338 q^{21} -15.5253 q^{22} -3.55185 q^{23} -11.1630 q^{24} -3.34336 q^{25} -16.1116 q^{26} +1.00000 q^{27} +15.3900 q^{28} -8.92701 q^{29} -3.63075 q^{30} -7.74680 q^{31} -32.8918 q^{32} +5.50374 q^{33} -13.7654 q^{34} +3.32508 q^{35} +5.95730 q^{36} +8.26151 q^{37} -16.1195 q^{38} +5.71159 q^{39} -14.3680 q^{40} -5.39003 q^{41} -7.28738 q^{42} -8.03917 q^{43} +32.7874 q^{44} +1.28710 q^{45} +10.0193 q^{46} +7.41995 q^{47} +19.5748 q^{48} -0.326141 q^{49} +9.43118 q^{50} +4.87983 q^{51} +34.0256 q^{52} +1.41138 q^{53} -2.82087 q^{54} +7.08390 q^{55} -28.8383 q^{56} +5.71437 q^{57} +25.1819 q^{58} -1.88343 q^{59} +7.66766 q^{60} +4.49047 q^{61} +21.8527 q^{62} +2.58338 q^{63} +53.6340 q^{64} +7.35141 q^{65} -15.5253 q^{66} -3.11381 q^{67} +29.0706 q^{68} -3.55185 q^{69} -9.37962 q^{70} +4.39590 q^{71} -11.1630 q^{72} +5.03934 q^{73} -23.3046 q^{74} -3.34336 q^{75} +34.0422 q^{76} +14.2183 q^{77} -16.1116 q^{78} +17.2533 q^{79} +25.1948 q^{80} +1.00000 q^{81} +15.2046 q^{82} -8.55662 q^{83} +15.3900 q^{84} +6.28085 q^{85} +22.6774 q^{86} -8.92701 q^{87} -61.4383 q^{88} -12.1637 q^{89} -3.63075 q^{90} +14.7552 q^{91} -21.1594 q^{92} -7.74680 q^{93} -20.9307 q^{94} +7.35500 q^{95} -32.8918 q^{96} -0.748112 q^{97} +0.920002 q^{98} +5.50374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.82087 −1.99465 −0.997327 0.0730622i \(-0.976723\pi\)
−0.997327 + 0.0730622i \(0.976723\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.95730 2.97865
\(5\) 1.28710 0.575611 0.287805 0.957689i \(-0.407074\pi\)
0.287805 + 0.957689i \(0.407074\pi\)
\(6\) −2.82087 −1.15161
\(7\) 2.58338 0.976426 0.488213 0.872724i \(-0.337649\pi\)
0.488213 + 0.872724i \(0.337649\pi\)
\(8\) −11.1630 −3.94672
\(9\) 1.00000 0.333333
\(10\) −3.63075 −1.14814
\(11\) 5.50374 1.65944 0.829721 0.558179i \(-0.188500\pi\)
0.829721 + 0.558179i \(0.188500\pi\)
\(12\) 5.95730 1.71972
\(13\) 5.71159 1.58411 0.792054 0.610451i \(-0.209012\pi\)
0.792054 + 0.610451i \(0.209012\pi\)
\(14\) −7.28738 −1.94763
\(15\) 1.28710 0.332329
\(16\) 19.5748 4.89369
\(17\) 4.87983 1.18353 0.591766 0.806110i \(-0.298431\pi\)
0.591766 + 0.806110i \(0.298431\pi\)
\(18\) −2.82087 −0.664885
\(19\) 5.71437 1.31097 0.655484 0.755209i \(-0.272465\pi\)
0.655484 + 0.755209i \(0.272465\pi\)
\(20\) 7.66766 1.71454
\(21\) 2.58338 0.563740
\(22\) −15.5253 −3.31001
\(23\) −3.55185 −0.740613 −0.370306 0.928910i \(-0.620747\pi\)
−0.370306 + 0.928910i \(0.620747\pi\)
\(24\) −11.1630 −2.27864
\(25\) −3.34336 −0.668672
\(26\) −16.1116 −3.15975
\(27\) 1.00000 0.192450
\(28\) 15.3900 2.90843
\(29\) −8.92701 −1.65771 −0.828853 0.559467i \(-0.811006\pi\)
−0.828853 + 0.559467i \(0.811006\pi\)
\(30\) −3.63075 −0.662882
\(31\) −7.74680 −1.39137 −0.695683 0.718349i \(-0.744898\pi\)
−0.695683 + 0.718349i \(0.744898\pi\)
\(32\) −32.8918 −5.81451
\(33\) 5.50374 0.958079
\(34\) −13.7654 −2.36074
\(35\) 3.32508 0.562042
\(36\) 5.95730 0.992883
\(37\) 8.26151 1.35818 0.679092 0.734053i \(-0.262374\pi\)
0.679092 + 0.734053i \(0.262374\pi\)
\(38\) −16.1195 −2.61493
\(39\) 5.71159 0.914586
\(40\) −14.3680 −2.27177
\(41\) −5.39003 −0.841782 −0.420891 0.907111i \(-0.638282\pi\)
−0.420891 + 0.907111i \(0.638282\pi\)
\(42\) −7.28738 −1.12447
\(43\) −8.03917 −1.22596 −0.612981 0.790097i \(-0.710030\pi\)
−0.612981 + 0.790097i \(0.710030\pi\)
\(44\) 32.7874 4.94289
\(45\) 1.28710 0.191870
\(46\) 10.0193 1.47727
\(47\) 7.41995 1.08231 0.541155 0.840923i \(-0.317987\pi\)
0.541155 + 0.840923i \(0.317987\pi\)
\(48\) 19.5748 2.82538
\(49\) −0.326141 −0.0465916
\(50\) 9.43118 1.33377
\(51\) 4.87983 0.683313
\(52\) 34.0256 4.71850
\(53\) 1.41138 0.193869 0.0969343 0.995291i \(-0.469096\pi\)
0.0969343 + 0.995291i \(0.469096\pi\)
\(54\) −2.82087 −0.383871
\(55\) 7.08390 0.955192
\(56\) −28.8383 −3.85368
\(57\) 5.71437 0.756887
\(58\) 25.1819 3.30655
\(59\) −1.88343 −0.245201 −0.122601 0.992456i \(-0.539123\pi\)
−0.122601 + 0.992456i \(0.539123\pi\)
\(60\) 7.66766 0.989891
\(61\) 4.49047 0.574946 0.287473 0.957789i \(-0.407185\pi\)
0.287473 + 0.957789i \(0.407185\pi\)
\(62\) 21.8527 2.77529
\(63\) 2.58338 0.325475
\(64\) 53.6340 6.70425
\(65\) 7.35141 0.911830
\(66\) −15.5253 −1.91104
\(67\) −3.11381 −0.380412 −0.190206 0.981744i \(-0.560916\pi\)
−0.190206 + 0.981744i \(0.560916\pi\)
\(68\) 29.0706 3.52533
\(69\) −3.55185 −0.427593
\(70\) −9.37962 −1.12108
\(71\) 4.39590 0.521698 0.260849 0.965380i \(-0.415998\pi\)
0.260849 + 0.965380i \(0.415998\pi\)
\(72\) −11.1630 −1.31557
\(73\) 5.03934 0.589810 0.294905 0.955527i \(-0.404712\pi\)
0.294905 + 0.955527i \(0.404712\pi\)
\(74\) −23.3046 −2.70911
\(75\) −3.34336 −0.386058
\(76\) 34.0422 3.90491
\(77\) 14.2183 1.62032
\(78\) −16.1116 −1.82428
\(79\) 17.2533 1.94115 0.970575 0.240798i \(-0.0774091\pi\)
0.970575 + 0.240798i \(0.0774091\pi\)
\(80\) 25.1948 2.81686
\(81\) 1.00000 0.111111
\(82\) 15.2046 1.67906
\(83\) −8.55662 −0.939211 −0.469606 0.882876i \(-0.655604\pi\)
−0.469606 + 0.882876i \(0.655604\pi\)
\(84\) 15.3900 1.67918
\(85\) 6.28085 0.681254
\(86\) 22.6774 2.44537
\(87\) −8.92701 −0.957076
\(88\) −61.4383 −6.54935
\(89\) −12.1637 −1.28934 −0.644672 0.764459i \(-0.723006\pi\)
−0.644672 + 0.764459i \(0.723006\pi\)
\(90\) −3.63075 −0.382715
\(91\) 14.7552 1.54677
\(92\) −21.1594 −2.20602
\(93\) −7.74680 −0.803305
\(94\) −20.9307 −2.15884
\(95\) 7.35500 0.754607
\(96\) −32.8918 −3.35701
\(97\) −0.748112 −0.0759593 −0.0379796 0.999279i \(-0.512092\pi\)
−0.0379796 + 0.999279i \(0.512092\pi\)
\(98\) 0.920002 0.0929342
\(99\) 5.50374 0.553147
\(100\) −19.9174 −1.99174
\(101\) −0.176176 −0.0175302 −0.00876509 0.999962i \(-0.502790\pi\)
−0.00876509 + 0.999962i \(0.502790\pi\)
\(102\) −13.7654 −1.36297
\(103\) −8.81068 −0.868143 −0.434071 0.900879i \(-0.642923\pi\)
−0.434071 + 0.900879i \(0.642923\pi\)
\(104\) −63.7585 −6.25203
\(105\) 3.32508 0.324495
\(106\) −3.98133 −0.386701
\(107\) 13.0834 1.26482 0.632411 0.774633i \(-0.282065\pi\)
0.632411 + 0.774633i \(0.282065\pi\)
\(108\) 5.95730 0.573241
\(109\) 10.8167 1.03605 0.518025 0.855365i \(-0.326667\pi\)
0.518025 + 0.855365i \(0.326667\pi\)
\(110\) −19.9827 −1.90528
\(111\) 8.26151 0.784148
\(112\) 50.5691 4.77833
\(113\) 19.4323 1.82803 0.914016 0.405677i \(-0.132964\pi\)
0.914016 + 0.405677i \(0.132964\pi\)
\(114\) −16.1195 −1.50973
\(115\) −4.57161 −0.426305
\(116\) −53.1809 −4.93772
\(117\) 5.71159 0.528036
\(118\) 5.31289 0.489091
\(119\) 12.6065 1.15563
\(120\) −14.3680 −1.31161
\(121\) 19.2912 1.75375
\(122\) −12.6670 −1.14682
\(123\) −5.39003 −0.486003
\(124\) −46.1499 −4.14439
\(125\) −10.7388 −0.960506
\(126\) −7.28738 −0.649211
\(127\) −3.45101 −0.306228 −0.153114 0.988209i \(-0.548930\pi\)
−0.153114 + 0.988209i \(0.548930\pi\)
\(128\) −85.5107 −7.55815
\(129\) −8.03917 −0.707810
\(130\) −20.7374 −1.81879
\(131\) 6.18630 0.540500 0.270250 0.962790i \(-0.412894\pi\)
0.270250 + 0.962790i \(0.412894\pi\)
\(132\) 32.7874 2.85378
\(133\) 14.7624 1.28006
\(134\) 8.78364 0.758791
\(135\) 1.28710 0.110776
\(136\) −54.4736 −4.67107
\(137\) −7.63340 −0.652166 −0.326083 0.945341i \(-0.605729\pi\)
−0.326083 + 0.945341i \(0.605729\pi\)
\(138\) 10.0193 0.852900
\(139\) 12.4241 1.05379 0.526897 0.849929i \(-0.323355\pi\)
0.526897 + 0.849929i \(0.323355\pi\)
\(140\) 19.8085 1.67412
\(141\) 7.41995 0.624872
\(142\) −12.4003 −1.04061
\(143\) 31.4351 2.62874
\(144\) 19.5748 1.63123
\(145\) −11.4900 −0.954193
\(146\) −14.2153 −1.17647
\(147\) −0.326141 −0.0268997
\(148\) 49.2162 4.04555
\(149\) −8.42534 −0.690231 −0.345115 0.938560i \(-0.612160\pi\)
−0.345115 + 0.938560i \(0.612160\pi\)
\(150\) 9.43118 0.770053
\(151\) −11.2229 −0.913305 −0.456652 0.889645i \(-0.650952\pi\)
−0.456652 + 0.889645i \(0.650952\pi\)
\(152\) −63.7896 −5.17402
\(153\) 4.87983 0.394511
\(154\) −40.1079 −3.23198
\(155\) −9.97094 −0.800885
\(156\) 34.0256 2.72423
\(157\) −3.06391 −0.244527 −0.122263 0.992498i \(-0.539015\pi\)
−0.122263 + 0.992498i \(0.539015\pi\)
\(158\) −48.6693 −3.87193
\(159\) 1.41138 0.111930
\(160\) −42.3353 −3.34690
\(161\) −9.17579 −0.723154
\(162\) −2.82087 −0.221628
\(163\) −2.33880 −0.183189 −0.0915944 0.995796i \(-0.529196\pi\)
−0.0915944 + 0.995796i \(0.529196\pi\)
\(164\) −32.1100 −2.50737
\(165\) 7.08390 0.551481
\(166\) 24.1371 1.87340
\(167\) −15.7238 −1.21674 −0.608372 0.793652i \(-0.708177\pi\)
−0.608372 + 0.793652i \(0.708177\pi\)
\(168\) −28.8383 −2.22492
\(169\) 19.6222 1.50940
\(170\) −17.7175 −1.35887
\(171\) 5.71437 0.436989
\(172\) −47.8917 −3.65171
\(173\) −1.27131 −0.0966557 −0.0483279 0.998832i \(-0.515389\pi\)
−0.0483279 + 0.998832i \(0.515389\pi\)
\(174\) 25.1819 1.90904
\(175\) −8.63718 −0.652909
\(176\) 107.735 8.12080
\(177\) −1.88343 −0.141567
\(178\) 34.3121 2.57180
\(179\) 26.0073 1.94388 0.971938 0.235239i \(-0.0755872\pi\)
0.971938 + 0.235239i \(0.0755872\pi\)
\(180\) 7.66766 0.571514
\(181\) 3.15225 0.234305 0.117153 0.993114i \(-0.462623\pi\)
0.117153 + 0.993114i \(0.462623\pi\)
\(182\) −41.6225 −3.08526
\(183\) 4.49047 0.331945
\(184\) 39.6494 2.92299
\(185\) 10.6334 0.781785
\(186\) 21.8527 1.60232
\(187\) 26.8573 1.96400
\(188\) 44.2028 3.22382
\(189\) 2.58338 0.187913
\(190\) −20.7475 −1.50518
\(191\) −14.0165 −1.01420 −0.507099 0.861888i \(-0.669282\pi\)
−0.507099 + 0.861888i \(0.669282\pi\)
\(192\) 53.6340 3.87070
\(193\) −3.72039 −0.267800 −0.133900 0.990995i \(-0.542750\pi\)
−0.133900 + 0.990995i \(0.542750\pi\)
\(194\) 2.11033 0.151513
\(195\) 7.35141 0.526445
\(196\) −1.94292 −0.138780
\(197\) 16.7597 1.19408 0.597039 0.802212i \(-0.296344\pi\)
0.597039 + 0.802212i \(0.296344\pi\)
\(198\) −15.5253 −1.10334
\(199\) 14.6221 1.03653 0.518267 0.855219i \(-0.326577\pi\)
0.518267 + 0.855219i \(0.326577\pi\)
\(200\) 37.3220 2.63906
\(201\) −3.11381 −0.219631
\(202\) 0.496970 0.0349667
\(203\) −23.0619 −1.61863
\(204\) 29.0706 2.03535
\(205\) −6.93754 −0.484539
\(206\) 24.8538 1.73164
\(207\) −3.55185 −0.246871
\(208\) 111.803 7.75214
\(209\) 31.4505 2.17547
\(210\) −9.37962 −0.647255
\(211\) −18.1465 −1.24925 −0.624627 0.780923i \(-0.714749\pi\)
−0.624627 + 0.780923i \(0.714749\pi\)
\(212\) 8.40804 0.577466
\(213\) 4.39590 0.301202
\(214\) −36.9066 −2.52288
\(215\) −10.3473 −0.705677
\(216\) −11.1630 −0.759546
\(217\) −20.0129 −1.35857
\(218\) −30.5125 −2.06656
\(219\) 5.03934 0.340527
\(220\) 42.2009 2.84518
\(221\) 27.8716 1.87484
\(222\) −23.3046 −1.56410
\(223\) −12.0369 −0.806050 −0.403025 0.915189i \(-0.632041\pi\)
−0.403025 + 0.915189i \(0.632041\pi\)
\(224\) −84.9722 −5.67744
\(225\) −3.34336 −0.222891
\(226\) −54.8158 −3.64629
\(227\) 21.6411 1.43637 0.718184 0.695853i \(-0.244973\pi\)
0.718184 + 0.695853i \(0.244973\pi\)
\(228\) 34.0422 2.25450
\(229\) 0.382159 0.0252538 0.0126269 0.999920i \(-0.495981\pi\)
0.0126269 + 0.999920i \(0.495981\pi\)
\(230\) 12.8959 0.850330
\(231\) 14.2183 0.935494
\(232\) 99.6523 6.54250
\(233\) −23.4617 −1.53703 −0.768513 0.639834i \(-0.779003\pi\)
−0.768513 + 0.639834i \(0.779003\pi\)
\(234\) −16.1116 −1.05325
\(235\) 9.55025 0.622990
\(236\) −11.2201 −0.730368
\(237\) 17.2533 1.12072
\(238\) −35.5612 −2.30509
\(239\) 7.62569 0.493265 0.246633 0.969109i \(-0.420676\pi\)
0.246633 + 0.969109i \(0.420676\pi\)
\(240\) 25.1948 1.62632
\(241\) −13.1669 −0.848152 −0.424076 0.905627i \(-0.639401\pi\)
−0.424076 + 0.905627i \(0.639401\pi\)
\(242\) −54.4179 −3.49812
\(243\) 1.00000 0.0641500
\(244\) 26.7511 1.71256
\(245\) −0.419778 −0.0268186
\(246\) 15.2046 0.969408
\(247\) 32.6381 2.07671
\(248\) 86.4775 5.49133
\(249\) −8.55662 −0.542254
\(250\) 30.2927 1.91588
\(251\) 9.18538 0.579776 0.289888 0.957061i \(-0.406382\pi\)
0.289888 + 0.957061i \(0.406382\pi\)
\(252\) 15.3900 0.969477
\(253\) −19.5485 −1.22900
\(254\) 9.73485 0.610819
\(255\) 6.28085 0.393322
\(256\) 133.946 8.37165
\(257\) −18.4091 −1.14833 −0.574164 0.818740i \(-0.694673\pi\)
−0.574164 + 0.818740i \(0.694673\pi\)
\(258\) 22.6774 1.41184
\(259\) 21.3426 1.32617
\(260\) 43.7945 2.71602
\(261\) −8.92701 −0.552568
\(262\) −17.4507 −1.07811
\(263\) −28.5947 −1.76322 −0.881611 0.471976i \(-0.843541\pi\)
−0.881611 + 0.471976i \(0.843541\pi\)
\(264\) −61.4383 −3.78127
\(265\) 1.81660 0.111593
\(266\) −41.6428 −2.55328
\(267\) −12.1637 −0.744403
\(268\) −18.5499 −1.13311
\(269\) −7.31009 −0.445704 −0.222852 0.974852i \(-0.571537\pi\)
−0.222852 + 0.974852i \(0.571537\pi\)
\(270\) −3.63075 −0.220961
\(271\) 3.50290 0.212786 0.106393 0.994324i \(-0.466070\pi\)
0.106393 + 0.994324i \(0.466070\pi\)
\(272\) 95.5216 5.79185
\(273\) 14.7552 0.893025
\(274\) 21.5328 1.30085
\(275\) −18.4010 −1.10962
\(276\) −21.1594 −1.27365
\(277\) −1.50911 −0.0906738 −0.0453369 0.998972i \(-0.514436\pi\)
−0.0453369 + 0.998972i \(0.514436\pi\)
\(278\) −35.0466 −2.10196
\(279\) −7.74680 −0.463788
\(280\) −37.1179 −2.21822
\(281\) 17.4136 1.03881 0.519405 0.854528i \(-0.326154\pi\)
0.519405 + 0.854528i \(0.326154\pi\)
\(282\) −20.9307 −1.24640
\(283\) −17.7691 −1.05627 −0.528133 0.849162i \(-0.677108\pi\)
−0.528133 + 0.849162i \(0.677108\pi\)
\(284\) 26.1877 1.55395
\(285\) 7.35500 0.435672
\(286\) −88.6743 −5.24342
\(287\) −13.9245 −0.821938
\(288\) −32.8918 −1.93817
\(289\) 6.81275 0.400750
\(290\) 32.4118 1.90329
\(291\) −0.748112 −0.0438551
\(292\) 30.0208 1.75684
\(293\) −15.8907 −0.928346 −0.464173 0.885745i \(-0.653648\pi\)
−0.464173 + 0.885745i \(0.653648\pi\)
\(294\) 0.920002 0.0536556
\(295\) −2.42417 −0.141140
\(296\) −92.2233 −5.36037
\(297\) 5.50374 0.319360
\(298\) 23.7668 1.37677
\(299\) −20.2867 −1.17321
\(300\) −19.9174 −1.14993
\(301\) −20.7682 −1.19706
\(302\) 31.6583 1.82173
\(303\) −0.176176 −0.0101211
\(304\) 111.858 6.41547
\(305\) 5.77971 0.330945
\(306\) −13.7654 −0.786913
\(307\) −28.3786 −1.61965 −0.809825 0.586672i \(-0.800438\pi\)
−0.809825 + 0.586672i \(0.800438\pi\)
\(308\) 84.7024 4.82637
\(309\) −8.81068 −0.501222
\(310\) 28.1267 1.59749
\(311\) −12.8537 −0.728869 −0.364435 0.931229i \(-0.618738\pi\)
−0.364435 + 0.931229i \(0.618738\pi\)
\(312\) −63.7585 −3.60961
\(313\) 26.4270 1.49374 0.746872 0.664967i \(-0.231555\pi\)
0.746872 + 0.664967i \(0.231555\pi\)
\(314\) 8.64288 0.487746
\(315\) 3.32508 0.187347
\(316\) 102.783 5.78200
\(317\) −24.0540 −1.35101 −0.675503 0.737357i \(-0.736074\pi\)
−0.675503 + 0.737357i \(0.736074\pi\)
\(318\) −3.98133 −0.223262
\(319\) −49.1320 −2.75086
\(320\) 69.0326 3.85904
\(321\) 13.0834 0.730246
\(322\) 25.8837 1.44244
\(323\) 27.8852 1.55157
\(324\) 5.95730 0.330961
\(325\) −19.0959 −1.05925
\(326\) 6.59744 0.365398
\(327\) 10.8167 0.598164
\(328\) 60.1690 3.32228
\(329\) 19.1686 1.05680
\(330\) −19.9827 −1.10001
\(331\) 11.7313 0.644811 0.322405 0.946602i \(-0.395509\pi\)
0.322405 + 0.946602i \(0.395509\pi\)
\(332\) −50.9743 −2.79758
\(333\) 8.26151 0.452728
\(334\) 44.3547 2.42698
\(335\) −4.00780 −0.218969
\(336\) 50.5691 2.75877
\(337\) −8.12339 −0.442509 −0.221255 0.975216i \(-0.571015\pi\)
−0.221255 + 0.975216i \(0.571015\pi\)
\(338\) −55.3516 −3.01073
\(339\) 19.4323 1.05542
\(340\) 37.4169 2.02922
\(341\) −42.6364 −2.30889
\(342\) −16.1195 −0.871642
\(343\) −18.9262 −1.02192
\(344\) 89.7413 4.83853
\(345\) −4.57161 −0.246127
\(346\) 3.58619 0.192795
\(347\) 13.7414 0.737678 0.368839 0.929493i \(-0.379755\pi\)
0.368839 + 0.929493i \(0.379755\pi\)
\(348\) −53.1809 −2.85079
\(349\) 22.7269 1.21654 0.608271 0.793729i \(-0.291863\pi\)
0.608271 + 0.793729i \(0.291863\pi\)
\(350\) 24.3643 1.30233
\(351\) 5.71159 0.304862
\(352\) −181.028 −9.64884
\(353\) 4.28109 0.227859 0.113930 0.993489i \(-0.463656\pi\)
0.113930 + 0.993489i \(0.463656\pi\)
\(354\) 5.31289 0.282377
\(355\) 5.65799 0.300295
\(356\) −72.4625 −3.84050
\(357\) 12.6065 0.667205
\(358\) −73.3631 −3.87736
\(359\) 27.7077 1.46236 0.731178 0.682186i \(-0.238971\pi\)
0.731178 + 0.682186i \(0.238971\pi\)
\(360\) −14.3680 −0.757258
\(361\) 13.6541 0.718635
\(362\) −8.89209 −0.467358
\(363\) 19.2912 1.01253
\(364\) 87.9011 4.60727
\(365\) 6.48616 0.339501
\(366\) −12.6670 −0.662116
\(367\) 4.00823 0.209228 0.104614 0.994513i \(-0.466639\pi\)
0.104614 + 0.994513i \(0.466639\pi\)
\(368\) −69.5267 −3.62433
\(369\) −5.39003 −0.280594
\(370\) −29.9955 −1.55939
\(371\) 3.64615 0.189298
\(372\) −46.1499 −2.39276
\(373\) −33.8094 −1.75059 −0.875293 0.483593i \(-0.839332\pi\)
−0.875293 + 0.483593i \(0.839332\pi\)
\(374\) −75.7610 −3.91751
\(375\) −10.7388 −0.554548
\(376\) −82.8289 −4.27158
\(377\) −50.9874 −2.62598
\(378\) −7.28738 −0.374822
\(379\) −9.95169 −0.511184 −0.255592 0.966785i \(-0.582270\pi\)
−0.255592 + 0.966785i \(0.582270\pi\)
\(380\) 43.8159 2.24771
\(381\) −3.45101 −0.176801
\(382\) 39.5387 2.02298
\(383\) −33.6597 −1.71993 −0.859965 0.510354i \(-0.829515\pi\)
−0.859965 + 0.510354i \(0.829515\pi\)
\(384\) −85.5107 −4.36370
\(385\) 18.3004 0.932675
\(386\) 10.4947 0.534168
\(387\) −8.03917 −0.408654
\(388\) −4.45673 −0.226256
\(389\) 16.1923 0.820980 0.410490 0.911865i \(-0.365358\pi\)
0.410490 + 0.911865i \(0.365358\pi\)
\(390\) −20.7374 −1.05008
\(391\) −17.3324 −0.876539
\(392\) 3.64072 0.183884
\(393\) 6.18630 0.312058
\(394\) −47.2768 −2.38177
\(395\) 22.2068 1.11735
\(396\) 32.7874 1.64763
\(397\) 25.1385 1.26166 0.630832 0.775920i \(-0.282714\pi\)
0.630832 + 0.775920i \(0.282714\pi\)
\(398\) −41.2470 −2.06753
\(399\) 14.7624 0.739045
\(400\) −65.4455 −3.27228
\(401\) −8.75459 −0.437184 −0.218592 0.975816i \(-0.570146\pi\)
−0.218592 + 0.975816i \(0.570146\pi\)
\(402\) 8.78364 0.438088
\(403\) −44.2465 −2.20407
\(404\) −1.04953 −0.0522162
\(405\) 1.28710 0.0639568
\(406\) 65.0545 3.22860
\(407\) 45.4692 2.25383
\(408\) −54.4736 −2.69684
\(409\) −5.87867 −0.290682 −0.145341 0.989382i \(-0.546428\pi\)
−0.145341 + 0.989382i \(0.546428\pi\)
\(410\) 19.5699 0.966487
\(411\) −7.63340 −0.376528
\(412\) −52.4878 −2.58589
\(413\) −4.86561 −0.239421
\(414\) 10.0193 0.492422
\(415\) −11.0133 −0.540620
\(416\) −187.865 −9.21082
\(417\) 12.4241 0.608409
\(418\) −88.7176 −4.33932
\(419\) −7.24945 −0.354159 −0.177079 0.984197i \(-0.556665\pi\)
−0.177079 + 0.984197i \(0.556665\pi\)
\(420\) 19.8085 0.966556
\(421\) 36.9107 1.79892 0.899459 0.437005i \(-0.143961\pi\)
0.899459 + 0.437005i \(0.143961\pi\)
\(422\) 51.1888 2.49183
\(423\) 7.41995 0.360770
\(424\) −15.7553 −0.765145
\(425\) −16.3150 −0.791395
\(426\) −12.4003 −0.600794
\(427\) 11.6006 0.561393
\(428\) 77.9418 3.76746
\(429\) 31.4351 1.51770
\(430\) 29.1882 1.40758
\(431\) 28.2983 1.36308 0.681540 0.731781i \(-0.261311\pi\)
0.681540 + 0.731781i \(0.261311\pi\)
\(432\) 19.5748 0.941792
\(433\) 21.7269 1.04413 0.522065 0.852906i \(-0.325162\pi\)
0.522065 + 0.852906i \(0.325162\pi\)
\(434\) 56.4538 2.70987
\(435\) −11.4900 −0.550904
\(436\) 64.4382 3.08603
\(437\) −20.2966 −0.970919
\(438\) −14.2153 −0.679233
\(439\) −12.1015 −0.577574 −0.288787 0.957393i \(-0.593252\pi\)
−0.288787 + 0.957393i \(0.593252\pi\)
\(440\) −79.0776 −3.76988
\(441\) −0.326141 −0.0155305
\(442\) −78.6220 −3.73967
\(443\) 11.0435 0.524694 0.262347 0.964974i \(-0.415504\pi\)
0.262347 + 0.964974i \(0.415504\pi\)
\(444\) 49.2162 2.33570
\(445\) −15.6559 −0.742161
\(446\) 33.9545 1.60779
\(447\) −8.42534 −0.398505
\(448\) 138.557 6.54621
\(449\) 6.23074 0.294047 0.147023 0.989133i \(-0.453031\pi\)
0.147023 + 0.989133i \(0.453031\pi\)
\(450\) 9.43118 0.444590
\(451\) −29.6654 −1.39689
\(452\) 115.764 5.44507
\(453\) −11.2229 −0.527297
\(454\) −61.0466 −2.86506
\(455\) 18.9915 0.890335
\(456\) −63.7896 −2.98722
\(457\) −21.6536 −1.01291 −0.506455 0.862266i \(-0.669044\pi\)
−0.506455 + 0.862266i \(0.669044\pi\)
\(458\) −1.07802 −0.0503726
\(459\) 4.87983 0.227771
\(460\) −27.2344 −1.26981
\(461\) 39.4092 1.83547 0.917735 0.397193i \(-0.130016\pi\)
0.917735 + 0.397193i \(0.130016\pi\)
\(462\) −40.1079 −1.86599
\(463\) 21.3620 0.992776 0.496388 0.868101i \(-0.334659\pi\)
0.496388 + 0.868101i \(0.334659\pi\)
\(464\) −174.744 −8.11230
\(465\) −9.97094 −0.462391
\(466\) 66.1823 3.06584
\(467\) 20.9324 0.968636 0.484318 0.874892i \(-0.339068\pi\)
0.484318 + 0.874892i \(0.339068\pi\)
\(468\) 34.0256 1.57283
\(469\) −8.04416 −0.371445
\(470\) −26.9400 −1.24265
\(471\) −3.06391 −0.141177
\(472\) 21.0247 0.967740
\(473\) −44.2456 −2.03441
\(474\) −48.6693 −2.23546
\(475\) −19.1052 −0.876607
\(476\) 75.1004 3.44222
\(477\) 1.41138 0.0646229
\(478\) −21.5111 −0.983894
\(479\) 10.9268 0.499259 0.249629 0.968341i \(-0.419691\pi\)
0.249629 + 0.968341i \(0.419691\pi\)
\(480\) −42.3353 −1.93233
\(481\) 47.1863 2.15151
\(482\) 37.1420 1.69177
\(483\) −9.17579 −0.417513
\(484\) 114.923 5.22379
\(485\) −0.962899 −0.0437230
\(486\) −2.82087 −0.127957
\(487\) −9.62579 −0.436186 −0.218093 0.975928i \(-0.569984\pi\)
−0.218093 + 0.975928i \(0.569984\pi\)
\(488\) −50.1272 −2.26915
\(489\) −2.33880 −0.105764
\(490\) 1.18414 0.0534939
\(491\) −8.64578 −0.390179 −0.195089 0.980785i \(-0.562500\pi\)
−0.195089 + 0.980785i \(0.562500\pi\)
\(492\) −32.1100 −1.44763
\(493\) −43.5623 −1.96195
\(494\) −92.0679 −4.14233
\(495\) 7.08390 0.318397
\(496\) −151.642 −6.80892
\(497\) 11.3563 0.509399
\(498\) 24.1371 1.08161
\(499\) 12.4016 0.555171 0.277585 0.960701i \(-0.410466\pi\)
0.277585 + 0.960701i \(0.410466\pi\)
\(500\) −63.9741 −2.86101
\(501\) −15.7238 −0.702487
\(502\) −25.9108 −1.15645
\(503\) 13.2869 0.592432 0.296216 0.955121i \(-0.404275\pi\)
0.296216 + 0.955121i \(0.404275\pi\)
\(504\) −28.8383 −1.28456
\(505\) −0.226757 −0.0100906
\(506\) 55.1437 2.45144
\(507\) 19.6222 0.871453
\(508\) −20.5587 −0.912145
\(509\) 11.9148 0.528116 0.264058 0.964507i \(-0.414939\pi\)
0.264058 + 0.964507i \(0.414939\pi\)
\(510\) −17.7175 −0.784542
\(511\) 13.0185 0.575906
\(512\) −206.824 −9.14041
\(513\) 5.71437 0.252296
\(514\) 51.9297 2.29052
\(515\) −11.3403 −0.499712
\(516\) −47.8917 −2.10832
\(517\) 40.8375 1.79603
\(518\) −60.2047 −2.64524
\(519\) −1.27131 −0.0558042
\(520\) −82.0638 −3.59874
\(521\) −32.6972 −1.43249 −0.716246 0.697848i \(-0.754141\pi\)
−0.716246 + 0.697848i \(0.754141\pi\)
\(522\) 25.1819 1.10218
\(523\) −25.9663 −1.13543 −0.567715 0.823225i \(-0.692172\pi\)
−0.567715 + 0.823225i \(0.692172\pi\)
\(524\) 36.8536 1.60996
\(525\) −8.63718 −0.376957
\(526\) 80.6618 3.51702
\(527\) −37.8030 −1.64673
\(528\) 107.735 4.68855
\(529\) −10.3843 −0.451493
\(530\) −5.12439 −0.222589
\(531\) −1.88343 −0.0817337
\(532\) 87.9440 3.81286
\(533\) −30.7856 −1.33347
\(534\) 34.3121 1.48483
\(535\) 16.8397 0.728046
\(536\) 34.7595 1.50138
\(537\) 26.0073 1.12230
\(538\) 20.6208 0.889025
\(539\) −1.79500 −0.0773161
\(540\) 7.66766 0.329964
\(541\) 20.8169 0.894990 0.447495 0.894286i \(-0.352316\pi\)
0.447495 + 0.894286i \(0.352316\pi\)
\(542\) −9.88121 −0.424434
\(543\) 3.15225 0.135276
\(544\) −160.507 −6.88166
\(545\) 13.9222 0.596362
\(546\) −41.6225 −1.78128
\(547\) 25.3777 1.08507 0.542536 0.840032i \(-0.317464\pi\)
0.542536 + 0.840032i \(0.317464\pi\)
\(548\) −45.4744 −1.94257
\(549\) 4.49047 0.191649
\(550\) 51.9068 2.21331
\(551\) −51.0123 −2.17320
\(552\) 39.6494 1.68759
\(553\) 44.5719 1.89539
\(554\) 4.25701 0.180863
\(555\) 10.6334 0.451364
\(556\) 74.0138 3.13888
\(557\) −30.3107 −1.28431 −0.642153 0.766576i \(-0.721959\pi\)
−0.642153 + 0.766576i \(0.721959\pi\)
\(558\) 21.8527 0.925098
\(559\) −45.9164 −1.94206
\(560\) 65.0877 2.75046
\(561\) 26.8573 1.13392
\(562\) −49.1215 −2.07207
\(563\) −18.6293 −0.785132 −0.392566 0.919724i \(-0.628413\pi\)
−0.392566 + 0.919724i \(0.628413\pi\)
\(564\) 44.2028 1.86127
\(565\) 25.0113 1.05224
\(566\) 50.1244 2.10688
\(567\) 2.58338 0.108492
\(568\) −49.0715 −2.05899
\(569\) 27.6394 1.15870 0.579352 0.815078i \(-0.303306\pi\)
0.579352 + 0.815078i \(0.303306\pi\)
\(570\) −20.7475 −0.869016
\(571\) −19.6999 −0.824417 −0.412208 0.911090i \(-0.635242\pi\)
−0.412208 + 0.911090i \(0.635242\pi\)
\(572\) 187.268 7.83008
\(573\) −14.0165 −0.585548
\(574\) 39.2792 1.63948
\(575\) 11.8751 0.495227
\(576\) 53.6340 2.23475
\(577\) 5.90951 0.246016 0.123008 0.992406i \(-0.460746\pi\)
0.123008 + 0.992406i \(0.460746\pi\)
\(578\) −19.2179 −0.799358
\(579\) −3.72039 −0.154614
\(580\) −68.4493 −2.84220
\(581\) −22.1050 −0.917071
\(582\) 2.11033 0.0874758
\(583\) 7.76790 0.321714
\(584\) −56.2542 −2.32781
\(585\) 7.35141 0.303943
\(586\) 44.8256 1.85173
\(587\) −1.94760 −0.0803860 −0.0401930 0.999192i \(-0.512797\pi\)
−0.0401930 + 0.999192i \(0.512797\pi\)
\(588\) −1.94292 −0.0801247
\(589\) −44.2681 −1.82403
\(590\) 6.83825 0.281526
\(591\) 16.7597 0.689401
\(592\) 161.717 6.64653
\(593\) −18.2732 −0.750390 −0.375195 0.926946i \(-0.622424\pi\)
−0.375195 + 0.926946i \(0.622424\pi\)
\(594\) −15.5253 −0.637012
\(595\) 16.2258 0.665195
\(596\) −50.1922 −2.05595
\(597\) 14.6221 0.598443
\(598\) 57.2261 2.34015
\(599\) −29.1238 −1.18997 −0.594984 0.803738i \(-0.702842\pi\)
−0.594984 + 0.803738i \(0.702842\pi\)
\(600\) 37.3220 1.52366
\(601\) −12.9892 −0.529842 −0.264921 0.964270i \(-0.585346\pi\)
−0.264921 + 0.964270i \(0.585346\pi\)
\(602\) 58.5845 2.38773
\(603\) −3.11381 −0.126804
\(604\) −66.8580 −2.72041
\(605\) 24.8298 1.00948
\(606\) 0.496970 0.0201880
\(607\) 23.1816 0.940911 0.470455 0.882424i \(-0.344090\pi\)
0.470455 + 0.882424i \(0.344090\pi\)
\(608\) −187.956 −7.62263
\(609\) −23.0619 −0.934515
\(610\) −16.3038 −0.660121
\(611\) 42.3797 1.71450
\(612\) 29.0706 1.17511
\(613\) −28.6397 −1.15675 −0.578373 0.815772i \(-0.696312\pi\)
−0.578373 + 0.815772i \(0.696312\pi\)
\(614\) 80.0522 3.23064
\(615\) −6.93754 −0.279748
\(616\) −158.719 −6.39496
\(617\) −21.5718 −0.868448 −0.434224 0.900805i \(-0.642977\pi\)
−0.434224 + 0.900805i \(0.642977\pi\)
\(618\) 24.8538 0.999765
\(619\) −23.8229 −0.957521 −0.478761 0.877945i \(-0.658914\pi\)
−0.478761 + 0.877945i \(0.658914\pi\)
\(620\) −59.3998 −2.38555
\(621\) −3.55185 −0.142531
\(622\) 36.2587 1.45384
\(623\) −31.4234 −1.25895
\(624\) 111.803 4.47570
\(625\) 2.89487 0.115795
\(626\) −74.5472 −2.97951
\(627\) 31.4505 1.25601
\(628\) −18.2526 −0.728358
\(629\) 40.3148 1.60745
\(630\) −9.37962 −0.373693
\(631\) −5.22326 −0.207935 −0.103967 0.994581i \(-0.533154\pi\)
−0.103967 + 0.994581i \(0.533154\pi\)
\(632\) −192.599 −7.66118
\(633\) −18.1465 −0.721257
\(634\) 67.8531 2.69479
\(635\) −4.44182 −0.176268
\(636\) 8.40804 0.333400
\(637\) −1.86278 −0.0738062
\(638\) 138.595 5.48702
\(639\) 4.39590 0.173899
\(640\) −110.061 −4.35055
\(641\) −34.6595 −1.36897 −0.684484 0.729028i \(-0.739972\pi\)
−0.684484 + 0.729028i \(0.739972\pi\)
\(642\) −36.9066 −1.45659
\(643\) −1.52388 −0.0600958 −0.0300479 0.999548i \(-0.509566\pi\)
−0.0300479 + 0.999548i \(0.509566\pi\)
\(644\) −54.6629 −2.15402
\(645\) −10.3473 −0.407423
\(646\) −78.6604 −3.09485
\(647\) 13.7841 0.541910 0.270955 0.962592i \(-0.412661\pi\)
0.270955 + 0.962592i \(0.412661\pi\)
\(648\) −11.1630 −0.438524
\(649\) −10.3659 −0.406897
\(650\) 53.8670 2.11284
\(651\) −20.0129 −0.784368
\(652\) −13.9329 −0.545655
\(653\) 42.4086 1.65958 0.829789 0.558077i \(-0.188461\pi\)
0.829789 + 0.558077i \(0.188461\pi\)
\(654\) −30.5125 −1.19313
\(655\) 7.96242 0.311118
\(656\) −105.509 −4.11942
\(657\) 5.03934 0.196603
\(658\) −54.0720 −2.10794
\(659\) 42.1578 1.64223 0.821117 0.570760i \(-0.193351\pi\)
0.821117 + 0.570760i \(0.193351\pi\)
\(660\) 42.2009 1.64267
\(661\) −1.19785 −0.0465909 −0.0232954 0.999729i \(-0.507416\pi\)
−0.0232954 + 0.999729i \(0.507416\pi\)
\(662\) −33.0925 −1.28618
\(663\) 27.8716 1.08244
\(664\) 95.5176 3.70680
\(665\) 19.0008 0.736818
\(666\) −23.3046 −0.903036
\(667\) 31.7074 1.22772
\(668\) −93.6712 −3.62425
\(669\) −12.0369 −0.465373
\(670\) 11.3055 0.436768
\(671\) 24.7144 0.954090
\(672\) −84.9722 −3.27787
\(673\) 48.3967 1.86556 0.932779 0.360450i \(-0.117377\pi\)
0.932779 + 0.360450i \(0.117377\pi\)
\(674\) 22.9150 0.882653
\(675\) −3.34336 −0.128686
\(676\) 116.895 4.49597
\(677\) −11.9473 −0.459173 −0.229586 0.973288i \(-0.573737\pi\)
−0.229586 + 0.973288i \(0.573737\pi\)
\(678\) −54.8158 −2.10519
\(679\) −1.93266 −0.0741686
\(680\) −70.1132 −2.68872
\(681\) 21.6411 0.829288
\(682\) 120.272 4.60544
\(683\) −34.8749 −1.33445 −0.667225 0.744857i \(-0.732518\pi\)
−0.667225 + 0.744857i \(0.732518\pi\)
\(684\) 34.0422 1.30164
\(685\) −9.82499 −0.375393
\(686\) 53.3884 2.03838
\(687\) 0.382159 0.0145803
\(688\) −157.365 −5.99949
\(689\) 8.06124 0.307109
\(690\) 12.8959 0.490938
\(691\) 11.2587 0.428302 0.214151 0.976801i \(-0.431302\pi\)
0.214151 + 0.976801i \(0.431302\pi\)
\(692\) −7.57355 −0.287903
\(693\) 14.2183 0.540107
\(694\) −38.7627 −1.47141
\(695\) 15.9911 0.606576
\(696\) 99.6523 3.77731
\(697\) −26.3024 −0.996276
\(698\) −64.1096 −2.42658
\(699\) −23.4617 −0.887402
\(700\) −51.4542 −1.94479
\(701\) 13.2909 0.501992 0.250996 0.967988i \(-0.419242\pi\)
0.250996 + 0.967988i \(0.419242\pi\)
\(702\) −16.1116 −0.608094
\(703\) 47.2093 1.78053
\(704\) 295.188 11.1253
\(705\) 9.55025 0.359683
\(706\) −12.0764 −0.454501
\(707\) −0.455130 −0.0171169
\(708\) −11.2201 −0.421678
\(709\) −16.8315 −0.632119 −0.316060 0.948739i \(-0.602360\pi\)
−0.316060 + 0.948739i \(0.602360\pi\)
\(710\) −15.9604 −0.598984
\(711\) 17.2533 0.647050
\(712\) 135.783 5.08868
\(713\) 27.5155 1.03046
\(714\) −35.5612 −1.33084
\(715\) 40.4603 1.51313
\(716\) 154.933 5.79012
\(717\) 7.62569 0.284787
\(718\) −78.1598 −2.91690
\(719\) 4.34534 0.162054 0.0810269 0.996712i \(-0.474180\pi\)
0.0810269 + 0.996712i \(0.474180\pi\)
\(720\) 25.1948 0.938954
\(721\) −22.7614 −0.847677
\(722\) −38.5163 −1.43343
\(723\) −13.1669 −0.489681
\(724\) 18.7789 0.697913
\(725\) 29.8462 1.10846
\(726\) −54.4179 −2.01964
\(727\) −29.4021 −1.09046 −0.545231 0.838286i \(-0.683558\pi\)
−0.545231 + 0.838286i \(0.683558\pi\)
\(728\) −164.712 −6.10465
\(729\) 1.00000 0.0370370
\(730\) −18.2966 −0.677187
\(731\) −39.2298 −1.45097
\(732\) 26.7511 0.988748
\(733\) −18.4629 −0.681943 −0.340971 0.940074i \(-0.610756\pi\)
−0.340971 + 0.940074i \(0.610756\pi\)
\(734\) −11.3067 −0.417337
\(735\) −0.419778 −0.0154837
\(736\) 116.827 4.30630
\(737\) −17.1376 −0.631272
\(738\) 15.2046 0.559688
\(739\) −35.8149 −1.31747 −0.658737 0.752374i \(-0.728909\pi\)
−0.658737 + 0.752374i \(0.728909\pi\)
\(740\) 63.3465 2.32866
\(741\) 32.6381 1.19899
\(742\) −10.2853 −0.377585
\(743\) −8.56045 −0.314052 −0.157026 0.987594i \(-0.550191\pi\)
−0.157026 + 0.987594i \(0.550191\pi\)
\(744\) 86.4775 3.17042
\(745\) −10.8443 −0.397304
\(746\) 95.3720 3.49182
\(747\) −8.55662 −0.313070
\(748\) 159.997 5.85007
\(749\) 33.7995 1.23501
\(750\) 30.2927 1.10613
\(751\) −16.7520 −0.611290 −0.305645 0.952146i \(-0.598872\pi\)
−0.305645 + 0.952146i \(0.598872\pi\)
\(752\) 145.244 5.29650
\(753\) 9.18538 0.334734
\(754\) 143.829 5.23793
\(755\) −14.4450 −0.525708
\(756\) 15.3900 0.559728
\(757\) −41.1103 −1.49418 −0.747090 0.664723i \(-0.768550\pi\)
−0.747090 + 0.664723i \(0.768550\pi\)
\(758\) 28.0724 1.01964
\(759\) −19.5485 −0.709565
\(760\) −82.1039 −2.97822
\(761\) 0.542636 0.0196706 0.00983528 0.999952i \(-0.496869\pi\)
0.00983528 + 0.999952i \(0.496869\pi\)
\(762\) 9.73485 0.352656
\(763\) 27.9436 1.01163
\(764\) −83.5004 −3.02094
\(765\) 6.28085 0.227085
\(766\) 94.9495 3.43067
\(767\) −10.7573 −0.388425
\(768\) 133.946 4.83338
\(769\) −49.6287 −1.78966 −0.894829 0.446410i \(-0.852702\pi\)
−0.894829 + 0.446410i \(0.852702\pi\)
\(770\) −51.6230 −1.86036
\(771\) −18.4091 −0.662988
\(772\) −22.1635 −0.797681
\(773\) −25.5809 −0.920080 −0.460040 0.887898i \(-0.652165\pi\)
−0.460040 + 0.887898i \(0.652165\pi\)
\(774\) 22.6774 0.815124
\(775\) 25.9003 0.930367
\(776\) 8.35118 0.299790
\(777\) 21.3426 0.765662
\(778\) −45.6762 −1.63757
\(779\) −30.8007 −1.10355
\(780\) 43.7945 1.56810
\(781\) 24.1939 0.865727
\(782\) 48.8925 1.74839
\(783\) −8.92701 −0.319025
\(784\) −6.38414 −0.228005
\(785\) −3.94357 −0.140752
\(786\) −17.4507 −0.622447
\(787\) −42.1706 −1.50322 −0.751610 0.659608i \(-0.770722\pi\)
−0.751610 + 0.659608i \(0.770722\pi\)
\(788\) 99.8423 3.55674
\(789\) −28.5947 −1.01800
\(790\) −62.6425 −2.22872
\(791\) 50.2009 1.78494
\(792\) −61.4383 −2.18312
\(793\) 25.6477 0.910777
\(794\) −70.9123 −2.51658
\(795\) 1.81660 0.0644282
\(796\) 87.1082 3.08747
\(797\) 38.7306 1.37191 0.685954 0.727645i \(-0.259385\pi\)
0.685954 + 0.727645i \(0.259385\pi\)
\(798\) −41.6428 −1.47414
\(799\) 36.2081 1.28095
\(800\) 109.969 3.88800
\(801\) −12.1637 −0.429782
\(802\) 24.6956 0.872030
\(803\) 27.7352 0.978755
\(804\) −18.5499 −0.654204
\(805\) −11.8102 −0.416255
\(806\) 124.813 4.39637
\(807\) −7.31009 −0.257327
\(808\) 1.96666 0.0691867
\(809\) 37.4145 1.31542 0.657712 0.753270i \(-0.271524\pi\)
0.657712 + 0.753270i \(0.271524\pi\)
\(810\) −3.63075 −0.127572
\(811\) −1.78602 −0.0627156 −0.0313578 0.999508i \(-0.509983\pi\)
−0.0313578 + 0.999508i \(0.509983\pi\)
\(812\) −137.386 −4.82132
\(813\) 3.50290 0.122852
\(814\) −128.263 −4.49560
\(815\) −3.01028 −0.105445
\(816\) 95.5216 3.34392
\(817\) −45.9388 −1.60720
\(818\) 16.5830 0.579809
\(819\) 14.7552 0.515588
\(820\) −41.3289 −1.44327
\(821\) 43.1268 1.50514 0.752568 0.658515i \(-0.228815\pi\)
0.752568 + 0.658515i \(0.228815\pi\)
\(822\) 21.5328 0.751043
\(823\) 8.97231 0.312755 0.156377 0.987697i \(-0.450018\pi\)
0.156377 + 0.987697i \(0.450018\pi\)
\(824\) 98.3537 3.42631
\(825\) −18.4010 −0.640641
\(826\) 13.7252 0.477562
\(827\) −0.268351 −0.00933148 −0.00466574 0.999989i \(-0.501485\pi\)
−0.00466574 + 0.999989i \(0.501485\pi\)
\(828\) −21.1594 −0.735341
\(829\) 3.22766 0.112101 0.0560507 0.998428i \(-0.482149\pi\)
0.0560507 + 0.998428i \(0.482149\pi\)
\(830\) 31.0670 1.07835
\(831\) −1.50911 −0.0523505
\(832\) 306.335 10.6203
\(833\) −1.59151 −0.0551427
\(834\) −35.0466 −1.21357
\(835\) −20.2382 −0.700371
\(836\) 187.360 6.47997
\(837\) −7.74680 −0.267768
\(838\) 20.4497 0.706424
\(839\) 23.5753 0.813910 0.406955 0.913448i \(-0.366591\pi\)
0.406955 + 0.913448i \(0.366591\pi\)
\(840\) −37.1179 −1.28069
\(841\) 50.6916 1.74799
\(842\) −104.120 −3.58822
\(843\) 17.4136 0.599757
\(844\) −108.104 −3.72109
\(845\) 25.2558 0.868827
\(846\) −20.9307 −0.719612
\(847\) 49.8365 1.71240
\(848\) 27.6275 0.948734
\(849\) −17.7691 −0.609835
\(850\) 46.0226 1.57856
\(851\) −29.3437 −1.00589
\(852\) 26.1877 0.897175
\(853\) 10.2631 0.351401 0.175700 0.984444i \(-0.443781\pi\)
0.175700 + 0.984444i \(0.443781\pi\)
\(854\) −32.7238 −1.11978
\(855\) 7.35500 0.251536
\(856\) −146.050 −4.99190
\(857\) −49.1576 −1.67919 −0.839597 0.543211i \(-0.817209\pi\)
−0.839597 + 0.543211i \(0.817209\pi\)
\(858\) −88.6743 −3.02729
\(859\) 11.5065 0.392595 0.196298 0.980544i \(-0.437108\pi\)
0.196298 + 0.980544i \(0.437108\pi\)
\(860\) −61.6417 −2.10196
\(861\) −13.9245 −0.474546
\(862\) −79.8257 −2.71887
\(863\) 16.3316 0.555935 0.277967 0.960590i \(-0.410339\pi\)
0.277967 + 0.960590i \(0.410339\pi\)
\(864\) −32.8918 −1.11900
\(865\) −1.63631 −0.0556361
\(866\) −61.2888 −2.08268
\(867\) 6.81275 0.231373
\(868\) −119.223 −4.04669
\(869\) 94.9579 3.22123
\(870\) 32.4118 1.09886
\(871\) −17.7848 −0.602614
\(872\) −120.747 −4.08900
\(873\) −0.748112 −0.0253198
\(874\) 57.2541 1.93665
\(875\) −27.7424 −0.937863
\(876\) 30.0208 1.01431
\(877\) −5.31796 −0.179575 −0.0897874 0.995961i \(-0.528619\pi\)
−0.0897874 + 0.995961i \(0.528619\pi\)
\(878\) 34.1368 1.15206
\(879\) −15.8907 −0.535981
\(880\) 138.666 4.67442
\(881\) 8.19563 0.276118 0.138059 0.990424i \(-0.455914\pi\)
0.138059 + 0.990424i \(0.455914\pi\)
\(882\) 0.920002 0.0309781
\(883\) −0.839517 −0.0282520 −0.0141260 0.999900i \(-0.504497\pi\)
−0.0141260 + 0.999900i \(0.504497\pi\)
\(884\) 166.039 5.58450
\(885\) −2.42417 −0.0814874
\(886\) −31.1523 −1.04658
\(887\) −21.6898 −0.728271 −0.364135 0.931346i \(-0.618635\pi\)
−0.364135 + 0.931346i \(0.618635\pi\)
\(888\) −92.2233 −3.09481
\(889\) −8.91528 −0.299009
\(890\) 44.1632 1.48035
\(891\) 5.50374 0.184382
\(892\) −71.7074 −2.40094
\(893\) 42.4004 1.41887
\(894\) 23.7668 0.794880
\(895\) 33.4741 1.11892
\(896\) −220.907 −7.37998
\(897\) −20.2867 −0.677354
\(898\) −17.5761 −0.586522
\(899\) 69.1558 2.30647
\(900\) −19.9174 −0.663913
\(901\) 6.88732 0.229450
\(902\) 83.6821 2.78631
\(903\) −20.7682 −0.691124
\(904\) −216.922 −7.21473
\(905\) 4.05728 0.134869
\(906\) 31.6583 1.05177
\(907\) 25.8657 0.858856 0.429428 0.903101i \(-0.358715\pi\)
0.429428 + 0.903101i \(0.358715\pi\)
\(908\) 128.922 4.27844
\(909\) −0.176176 −0.00584340
\(910\) −53.5725 −1.77591
\(911\) −15.9196 −0.527439 −0.263720 0.964599i \(-0.584949\pi\)
−0.263720 + 0.964599i \(0.584949\pi\)
\(912\) 111.858 3.70397
\(913\) −47.0935 −1.55857
\(914\) 61.0818 2.02041
\(915\) 5.77971 0.191071
\(916\) 2.27663 0.0752221
\(917\) 15.9816 0.527758
\(918\) −13.7654 −0.454324
\(919\) −33.8725 −1.11735 −0.558675 0.829386i \(-0.688690\pi\)
−0.558675 + 0.829386i \(0.688690\pi\)
\(920\) 51.0329 1.68250
\(921\) −28.3786 −0.935105
\(922\) −111.168 −3.66113
\(923\) 25.1076 0.826426
\(924\) 84.7024 2.78651
\(925\) −27.6212 −0.908180
\(926\) −60.2593 −1.98024
\(927\) −8.81068 −0.289381
\(928\) 293.626 9.63874
\(929\) 16.5466 0.542876 0.271438 0.962456i \(-0.412501\pi\)
0.271438 + 0.962456i \(0.412501\pi\)
\(930\) 28.1267 0.922311
\(931\) −1.86369 −0.0610801
\(932\) −139.768 −4.57826
\(933\) −12.8537 −0.420813
\(934\) −59.0475 −1.93209
\(935\) 34.5682 1.13050
\(936\) −63.7585 −2.08401
\(937\) −40.8563 −1.33472 −0.667359 0.744736i \(-0.732575\pi\)
−0.667359 + 0.744736i \(0.732575\pi\)
\(938\) 22.6915 0.740904
\(939\) 26.4270 0.862414
\(940\) 56.8937 1.85567
\(941\) 20.7293 0.675755 0.337878 0.941190i \(-0.390291\pi\)
0.337878 + 0.941190i \(0.390291\pi\)
\(942\) 8.64288 0.281600
\(943\) 19.1446 0.623434
\(944\) −36.8676 −1.19994
\(945\) 3.32508 0.108165
\(946\) 124.811 4.05795
\(947\) 45.1600 1.46750 0.733751 0.679419i \(-0.237768\pi\)
0.733751 + 0.679419i \(0.237768\pi\)
\(948\) 102.783 3.33824
\(949\) 28.7826 0.934323
\(950\) 53.8933 1.74853
\(951\) −24.0540 −0.780004
\(952\) −140.726 −4.56096
\(953\) −14.8596 −0.481351 −0.240675 0.970606i \(-0.577369\pi\)
−0.240675 + 0.970606i \(0.577369\pi\)
\(954\) −3.98133 −0.128900
\(955\) −18.0407 −0.583784
\(956\) 45.4285 1.46926
\(957\) −49.1320 −1.58821
\(958\) −30.8231 −0.995849
\(959\) −19.7200 −0.636792
\(960\) 69.0326 2.22802
\(961\) 29.0128 0.935898
\(962\) −133.106 −4.29152
\(963\) 13.0834 0.421608
\(964\) −78.4389 −2.52635
\(965\) −4.78854 −0.154148
\(966\) 25.8837 0.832794
\(967\) −43.2454 −1.39068 −0.695339 0.718682i \(-0.744746\pi\)
−0.695339 + 0.718682i \(0.744746\pi\)
\(968\) −215.348 −6.92154
\(969\) 27.8852 0.895801
\(970\) 2.71621 0.0872123
\(971\) 5.66898 0.181926 0.0909632 0.995854i \(-0.471005\pi\)
0.0909632 + 0.995854i \(0.471005\pi\)
\(972\) 5.95730 0.191080
\(973\) 32.0961 1.02895
\(974\) 27.1531 0.870041
\(975\) −19.0959 −0.611558
\(976\) 87.9000 2.81361
\(977\) −9.55493 −0.305689 −0.152845 0.988250i \(-0.548843\pi\)
−0.152845 + 0.988250i \(0.548843\pi\)
\(978\) 6.59744 0.210963
\(979\) −66.9456 −2.13959
\(980\) −2.50074 −0.0798833
\(981\) 10.8167 0.345350
\(982\) 24.3886 0.778272
\(983\) −16.4872 −0.525858 −0.262929 0.964815i \(-0.584689\pi\)
−0.262929 + 0.964815i \(0.584689\pi\)
\(984\) 60.1690 1.91812
\(985\) 21.5715 0.687324
\(986\) 122.884 3.91341
\(987\) 19.1686 0.610142
\(988\) 194.435 6.18580
\(989\) 28.5540 0.907963
\(990\) −19.9827 −0.635093
\(991\) 19.5328 0.620481 0.310240 0.950658i \(-0.399590\pi\)
0.310240 + 0.950658i \(0.399590\pi\)
\(992\) 254.806 8.09011
\(993\) 11.7313 0.372282
\(994\) −32.0346 −1.01608
\(995\) 18.8202 0.596640
\(996\) −50.9743 −1.61518
\(997\) −13.3657 −0.423297 −0.211649 0.977346i \(-0.567883\pi\)
−0.211649 + 0.977346i \(0.567883\pi\)
\(998\) −34.9832 −1.10737
\(999\) 8.26151 0.261383
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 8049.2.a.d.1.1 129
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8049.2.a.d.1.1 129 1.1 even 1 trivial