Properties

Label 5077.2.a.b.1.5
Level $5077$
Weight $2$
Character 5077.1
Self dual yes
Analytic conductor $40.540$
Analytic rank $1$
Dimension $205$
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] = [5077,2,Mod(1,5077)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5077, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5077.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5077 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5077.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: \(40.5400491062\)
Analytic rank: \(1\)
Dimension: \(205\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 5077.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.77001 q^{2} -0.453815 q^{3} +5.67294 q^{4} -2.74837 q^{5} +1.25707 q^{6} -3.66610 q^{7} -10.1741 q^{8} -2.79405 q^{9} +O(q^{10})\) \(q-2.77001 q^{2} -0.453815 q^{3} +5.67294 q^{4} -2.74837 q^{5} +1.25707 q^{6} -3.66610 q^{7} -10.1741 q^{8} -2.79405 q^{9} +7.61300 q^{10} -3.29970 q^{11} -2.57446 q^{12} -2.96983 q^{13} +10.1551 q^{14} +1.24725 q^{15} +16.8363 q^{16} +0.979742 q^{17} +7.73954 q^{18} -2.27616 q^{19} -15.5913 q^{20} +1.66373 q^{21} +9.14020 q^{22} -2.05068 q^{23} +4.61714 q^{24} +2.55352 q^{25} +8.22645 q^{26} +2.62943 q^{27} -20.7975 q^{28} +0.750007 q^{29} -3.45489 q^{30} +7.68000 q^{31} -26.2887 q^{32} +1.49745 q^{33} -2.71389 q^{34} +10.0758 q^{35} -15.8505 q^{36} -6.11894 q^{37} +6.30499 q^{38} +1.34775 q^{39} +27.9621 q^{40} +4.59256 q^{41} -4.60854 q^{42} +4.12047 q^{43} -18.7190 q^{44} +7.67908 q^{45} +5.68039 q^{46} -1.26549 q^{47} -7.64058 q^{48} +6.44027 q^{49} -7.07328 q^{50} -0.444622 q^{51} -16.8477 q^{52} -4.52493 q^{53} -7.28353 q^{54} +9.06880 q^{55} +37.2991 q^{56} +1.03296 q^{57} -2.07752 q^{58} +4.39496 q^{59} +7.07557 q^{60} +10.4117 q^{61} -21.2736 q^{62} +10.2433 q^{63} +39.1471 q^{64} +8.16219 q^{65} -4.14796 q^{66} +0.130613 q^{67} +5.55801 q^{68} +0.930627 q^{69} -27.9100 q^{70} -4.55199 q^{71} +28.4269 q^{72} +13.5446 q^{73} +16.9495 q^{74} -1.15883 q^{75} -12.9125 q^{76} +12.0970 q^{77} -3.73329 q^{78} +15.0185 q^{79} -46.2725 q^{80} +7.18888 q^{81} -12.7214 q^{82} +1.79303 q^{83} +9.43823 q^{84} -2.69269 q^{85} -11.4137 q^{86} -0.340364 q^{87} +33.5714 q^{88} -8.62803 q^{89} -21.2711 q^{90} +10.8877 q^{91} -11.6334 q^{92} -3.48530 q^{93} +3.50541 q^{94} +6.25573 q^{95} +11.9302 q^{96} -5.07395 q^{97} -17.8396 q^{98} +9.21954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77001 −1.95869 −0.979345 0.202195i \(-0.935192\pi\)
−0.979345 + 0.202195i \(0.935192\pi\)
\(3\) −0.453815 −0.262010 −0.131005 0.991382i \(-0.541820\pi\)
−0.131005 + 0.991382i \(0.541820\pi\)
\(4\) 5.67294 2.83647
\(5\) −2.74837 −1.22911 −0.614554 0.788875i \(-0.710664\pi\)
−0.614554 + 0.788875i \(0.710664\pi\)
\(6\) 1.25707 0.513197
\(7\) −3.66610 −1.38565 −0.692827 0.721104i \(-0.743635\pi\)
−0.692827 + 0.721104i \(0.743635\pi\)
\(8\) −10.1741 −3.59707
\(9\) −2.79405 −0.931351
\(10\) 7.61300 2.40744
\(11\) −3.29970 −0.994898 −0.497449 0.867493i \(-0.665730\pi\)
−0.497449 + 0.867493i \(0.665730\pi\)
\(12\) −2.57446 −0.743184
\(13\) −2.96983 −0.823683 −0.411841 0.911256i \(-0.635114\pi\)
−0.411841 + 0.911256i \(0.635114\pi\)
\(14\) 10.1551 2.71407
\(15\) 1.24725 0.322039
\(16\) 16.8363 4.20909
\(17\) 0.979742 0.237622 0.118811 0.992917i \(-0.462092\pi\)
0.118811 + 0.992917i \(0.462092\pi\)
\(18\) 7.73954 1.82423
\(19\) −2.27616 −0.522188 −0.261094 0.965313i \(-0.584083\pi\)
−0.261094 + 0.965313i \(0.584083\pi\)
\(20\) −15.5913 −3.48632
\(21\) 1.66373 0.363055
\(22\) 9.14020 1.94870
\(23\) −2.05068 −0.427596 −0.213798 0.976878i \(-0.568583\pi\)
−0.213798 + 0.976878i \(0.568583\pi\)
\(24\) 4.61714 0.942470
\(25\) 2.55352 0.510705
\(26\) 8.22645 1.61334
\(27\) 2.62943 0.506033
\(28\) −20.7975 −3.93036
\(29\) 0.750007 0.139273 0.0696364 0.997572i \(-0.477816\pi\)
0.0696364 + 0.997572i \(0.477816\pi\)
\(30\) −3.45489 −0.630774
\(31\) 7.68000 1.37937 0.689684 0.724110i \(-0.257749\pi\)
0.689684 + 0.724110i \(0.257749\pi\)
\(32\) −26.2887 −4.64722
\(33\) 1.49745 0.260673
\(34\) −2.71389 −0.465429
\(35\) 10.0758 1.70312
\(36\) −15.8505 −2.64175
\(37\) −6.11894 −1.00595 −0.502974 0.864302i \(-0.667761\pi\)
−0.502974 + 0.864302i \(0.667761\pi\)
\(38\) 6.30499 1.02280
\(39\) 1.34775 0.215813
\(40\) 27.9621 4.42119
\(41\) 4.59256 0.717238 0.358619 0.933484i \(-0.383248\pi\)
0.358619 + 0.933484i \(0.383248\pi\)
\(42\) −4.60854 −0.711113
\(43\) 4.12047 0.628366 0.314183 0.949363i \(-0.398270\pi\)
0.314183 + 0.949363i \(0.398270\pi\)
\(44\) −18.7190 −2.82200
\(45\) 7.67908 1.14473
\(46\) 5.68039 0.837527
\(47\) −1.26549 −0.184590 −0.0922952 0.995732i \(-0.529420\pi\)
−0.0922952 + 0.995732i \(0.529420\pi\)
\(48\) −7.64058 −1.10282
\(49\) 6.44027 0.920038
\(50\) −7.07328 −1.00031
\(51\) −0.444622 −0.0622595
\(52\) −16.8477 −2.33635
\(53\) −4.52493 −0.621546 −0.310773 0.950484i \(-0.600588\pi\)
−0.310773 + 0.950484i \(0.600588\pi\)
\(54\) −7.28353 −0.991163
\(55\) 9.06880 1.22284
\(56\) 37.2991 4.98430
\(57\) 1.03296 0.136818
\(58\) −2.07752 −0.272792
\(59\) 4.39496 0.572175 0.286087 0.958203i \(-0.407645\pi\)
0.286087 + 0.958203i \(0.407645\pi\)
\(60\) 7.07557 0.913452
\(61\) 10.4117 1.33309 0.666543 0.745467i \(-0.267773\pi\)
0.666543 + 0.745467i \(0.267773\pi\)
\(62\) −21.2736 −2.70176
\(63\) 10.2433 1.29053
\(64\) 39.1471 4.89338
\(65\) 8.16219 1.01239
\(66\) −4.14796 −0.510578
\(67\) 0.130613 0.0159569 0.00797845 0.999968i \(-0.497460\pi\)
0.00797845 + 0.999968i \(0.497460\pi\)
\(68\) 5.55801 0.674008
\(69\) 0.930627 0.112034
\(70\) −27.9100 −3.33588
\(71\) −4.55199 −0.540222 −0.270111 0.962829i \(-0.587060\pi\)
−0.270111 + 0.962829i \(0.587060\pi\)
\(72\) 28.4269 3.35014
\(73\) 13.5446 1.58528 0.792638 0.609692i \(-0.208707\pi\)
0.792638 + 0.609692i \(0.208707\pi\)
\(74\) 16.9495 1.97034
\(75\) −1.15883 −0.133810
\(76\) −12.9125 −1.48117
\(77\) 12.0970 1.37858
\(78\) −3.73329 −0.422711
\(79\) 15.0185 1.68972 0.844859 0.534989i \(-0.179684\pi\)
0.844859 + 0.534989i \(0.179684\pi\)
\(80\) −46.2725 −5.17342
\(81\) 7.18888 0.798765
\(82\) −12.7214 −1.40485
\(83\) 1.79303 0.196811 0.0984055 0.995146i \(-0.468626\pi\)
0.0984055 + 0.995146i \(0.468626\pi\)
\(84\) 9.43823 1.02980
\(85\) −2.69269 −0.292063
\(86\) −11.4137 −1.23077
\(87\) −0.340364 −0.0364909
\(88\) 33.5714 3.57872
\(89\) −8.62803 −0.914569 −0.457285 0.889320i \(-0.651178\pi\)
−0.457285 + 0.889320i \(0.651178\pi\)
\(90\) −21.2711 −2.24217
\(91\) 10.8877 1.14134
\(92\) −11.6334 −1.21286
\(93\) −3.48530 −0.361408
\(94\) 3.50541 0.361555
\(95\) 6.25573 0.641825
\(96\) 11.9302 1.21762
\(97\) −5.07395 −0.515182 −0.257591 0.966254i \(-0.582929\pi\)
−0.257591 + 0.966254i \(0.582929\pi\)
\(98\) −17.8396 −1.80207
\(99\) 9.21954 0.926599
\(100\) 14.4860 1.44860
\(101\) −13.6434 −1.35757 −0.678784 0.734338i \(-0.737493\pi\)
−0.678784 + 0.734338i \(0.737493\pi\)
\(102\) 1.23160 0.121947
\(103\) 3.40598 0.335601 0.167801 0.985821i \(-0.446334\pi\)
0.167801 + 0.985821i \(0.446334\pi\)
\(104\) 30.2152 2.96285
\(105\) −4.57254 −0.446234
\(106\) 12.5341 1.21742
\(107\) −10.2554 −0.991431 −0.495715 0.868485i \(-0.665094\pi\)
−0.495715 + 0.868485i \(0.665094\pi\)
\(108\) 14.9166 1.43535
\(109\) 3.18609 0.305172 0.152586 0.988290i \(-0.451240\pi\)
0.152586 + 0.988290i \(0.451240\pi\)
\(110\) −25.1206 −2.39516
\(111\) 2.77687 0.263569
\(112\) −61.7237 −5.83234
\(113\) 10.0315 0.943689 0.471844 0.881682i \(-0.343588\pi\)
0.471844 + 0.881682i \(0.343588\pi\)
\(114\) −2.86130 −0.267985
\(115\) 5.63601 0.525561
\(116\) 4.25474 0.395043
\(117\) 8.29786 0.767138
\(118\) −12.1741 −1.12071
\(119\) −3.59183 −0.329262
\(120\) −12.6896 −1.15840
\(121\) −0.111956 −0.0101778
\(122\) −28.8406 −2.61110
\(123\) −2.08417 −0.187924
\(124\) 43.5681 3.91253
\(125\) 6.72381 0.601396
\(126\) −28.3739 −2.52775
\(127\) 4.03807 0.358321 0.179161 0.983820i \(-0.442662\pi\)
0.179161 + 0.983820i \(0.442662\pi\)
\(128\) −55.8603 −4.93740
\(129\) −1.86993 −0.164638
\(130\) −22.6093 −1.98297
\(131\) 14.6660 1.28138 0.640689 0.767800i \(-0.278649\pi\)
0.640689 + 0.767800i \(0.278649\pi\)
\(132\) 8.49497 0.739392
\(133\) 8.34463 0.723572
\(134\) −0.361799 −0.0312546
\(135\) −7.22663 −0.621969
\(136\) −9.96795 −0.854745
\(137\) −15.6534 −1.33736 −0.668681 0.743549i \(-0.733141\pi\)
−0.668681 + 0.743549i \(0.733141\pi\)
\(138\) −2.57784 −0.219441
\(139\) −23.0205 −1.95257 −0.976285 0.216490i \(-0.930539\pi\)
−0.976285 + 0.216490i \(0.930539\pi\)
\(140\) 57.1593 4.83084
\(141\) 0.574297 0.0483645
\(142\) 12.6091 1.05813
\(143\) 9.79956 0.819480
\(144\) −47.0416 −3.92013
\(145\) −2.06129 −0.171181
\(146\) −37.5187 −3.10507
\(147\) −2.92269 −0.241059
\(148\) −34.7124 −2.85334
\(149\) −16.9382 −1.38763 −0.693815 0.720153i \(-0.744072\pi\)
−0.693815 + 0.720153i \(0.744072\pi\)
\(150\) 3.20996 0.262092
\(151\) 0.822424 0.0669279 0.0334640 0.999440i \(-0.489346\pi\)
0.0334640 + 0.999440i \(0.489346\pi\)
\(152\) 23.1578 1.87835
\(153\) −2.73745 −0.221310
\(154\) −33.5089 −2.70022
\(155\) −21.1075 −1.69539
\(156\) 7.64572 0.612148
\(157\) 10.8646 0.867090 0.433545 0.901132i \(-0.357263\pi\)
0.433545 + 0.901132i \(0.357263\pi\)
\(158\) −41.6015 −3.30964
\(159\) 2.05348 0.162851
\(160\) 72.2509 5.71193
\(161\) 7.51798 0.592500
\(162\) −19.9133 −1.56453
\(163\) −10.8043 −0.846257 −0.423129 0.906070i \(-0.639068\pi\)
−0.423129 + 0.906070i \(0.639068\pi\)
\(164\) 26.0533 2.03442
\(165\) −4.11556 −0.320396
\(166\) −4.96671 −0.385492
\(167\) −12.3818 −0.958129 −0.479064 0.877780i \(-0.659024\pi\)
−0.479064 + 0.877780i \(0.659024\pi\)
\(168\) −16.9269 −1.30594
\(169\) −4.18011 −0.321547
\(170\) 7.45877 0.572062
\(171\) 6.35972 0.486340
\(172\) 23.3752 1.78234
\(173\) −10.7755 −0.819244 −0.409622 0.912255i \(-0.634339\pi\)
−0.409622 + 0.912255i \(0.634339\pi\)
\(174\) 0.942811 0.0714743
\(175\) −9.36147 −0.707660
\(176\) −55.5549 −4.18761
\(177\) −1.99450 −0.149916
\(178\) 23.8997 1.79136
\(179\) 16.5051 1.23365 0.616824 0.787101i \(-0.288419\pi\)
0.616824 + 0.787101i \(0.288419\pi\)
\(180\) 43.5629 3.24699
\(181\) 5.77800 0.429475 0.214738 0.976672i \(-0.431110\pi\)
0.214738 + 0.976672i \(0.431110\pi\)
\(182\) −30.1590 −2.23553
\(183\) −4.72500 −0.349282
\(184\) 20.8637 1.53809
\(185\) 16.8171 1.23642
\(186\) 9.65430 0.707887
\(187\) −3.23286 −0.236410
\(188\) −7.17903 −0.523585
\(189\) −9.63973 −0.701187
\(190\) −17.3284 −1.25714
\(191\) 6.70763 0.485347 0.242674 0.970108i \(-0.421976\pi\)
0.242674 + 0.970108i \(0.421976\pi\)
\(192\) −17.7655 −1.28212
\(193\) 4.68338 0.337117 0.168558 0.985692i \(-0.446089\pi\)
0.168558 + 0.985692i \(0.446089\pi\)
\(194\) 14.0549 1.00908
\(195\) −3.70412 −0.265258
\(196\) 36.5352 2.60966
\(197\) 11.7303 0.835750 0.417875 0.908505i \(-0.362775\pi\)
0.417875 + 0.908505i \(0.362775\pi\)
\(198\) −25.5382 −1.81492
\(199\) 15.8724 1.12516 0.562582 0.826742i \(-0.309808\pi\)
0.562582 + 0.826742i \(0.309808\pi\)
\(200\) −25.9797 −1.83704
\(201\) −0.0592741 −0.00418087
\(202\) 37.7923 2.65905
\(203\) −2.74960 −0.192984
\(204\) −2.52231 −0.176597
\(205\) −12.6221 −0.881562
\(206\) −9.43459 −0.657339
\(207\) 5.72970 0.398241
\(208\) −50.0011 −3.46695
\(209\) 7.51066 0.519524
\(210\) 12.6660 0.874035
\(211\) −20.4531 −1.40805 −0.704026 0.710174i \(-0.748616\pi\)
−0.704026 + 0.710174i \(0.748616\pi\)
\(212\) −25.6696 −1.76300
\(213\) 2.06576 0.141544
\(214\) 28.4076 1.94191
\(215\) −11.3246 −0.772329
\(216\) −26.7519 −1.82024
\(217\) −28.1556 −1.91133
\(218\) −8.82549 −0.597738
\(219\) −6.14674 −0.415358
\(220\) 51.4467 3.46854
\(221\) −2.90967 −0.195725
\(222\) −7.69194 −0.516249
\(223\) −3.19195 −0.213749 −0.106874 0.994273i \(-0.534084\pi\)
−0.106874 + 0.994273i \(0.534084\pi\)
\(224\) 96.3768 6.43944
\(225\) −7.13468 −0.475645
\(226\) −27.7875 −1.84839
\(227\) −2.32334 −0.154205 −0.0771026 0.997023i \(-0.524567\pi\)
−0.0771026 + 0.997023i \(0.524567\pi\)
\(228\) 5.85990 0.388081
\(229\) 10.9869 0.726035 0.363017 0.931782i \(-0.381747\pi\)
0.363017 + 0.931782i \(0.381747\pi\)
\(230\) −15.6118 −1.02941
\(231\) −5.48981 −0.361203
\(232\) −7.63062 −0.500974
\(233\) −1.46796 −0.0961692 −0.0480846 0.998843i \(-0.515312\pi\)
−0.0480846 + 0.998843i \(0.515312\pi\)
\(234\) −22.9851 −1.50259
\(235\) 3.47803 0.226881
\(236\) 24.9323 1.62296
\(237\) −6.81564 −0.442723
\(238\) 9.94939 0.644923
\(239\) −15.6932 −1.01511 −0.507554 0.861620i \(-0.669450\pi\)
−0.507554 + 0.861620i \(0.669450\pi\)
\(240\) 20.9991 1.35549
\(241\) 20.4302 1.31602 0.658011 0.753008i \(-0.271398\pi\)
0.658011 + 0.753008i \(0.271398\pi\)
\(242\) 0.310118 0.0199352
\(243\) −11.1507 −0.715318
\(244\) 59.0651 3.78126
\(245\) −17.7002 −1.13083
\(246\) 5.77317 0.368084
\(247\) 6.75982 0.430117
\(248\) −78.1368 −4.96169
\(249\) −0.813705 −0.0515665
\(250\) −18.6250 −1.17795
\(251\) −15.3821 −0.970907 −0.485454 0.874262i \(-0.661346\pi\)
−0.485454 + 0.874262i \(0.661346\pi\)
\(252\) 58.1094 3.66055
\(253\) 6.76662 0.425414
\(254\) −11.1855 −0.701840
\(255\) 1.22198 0.0765236
\(256\) 76.4394 4.77746
\(257\) −6.93175 −0.432391 −0.216195 0.976350i \(-0.569365\pi\)
−0.216195 + 0.976350i \(0.569365\pi\)
\(258\) 5.17972 0.322475
\(259\) 22.4326 1.39390
\(260\) 46.3036 2.87163
\(261\) −2.09556 −0.129712
\(262\) −40.6250 −2.50982
\(263\) 14.4344 0.890064 0.445032 0.895515i \(-0.353192\pi\)
0.445032 + 0.895515i \(0.353192\pi\)
\(264\) −15.2352 −0.937661
\(265\) 12.4362 0.763947
\(266\) −23.1147 −1.41725
\(267\) 3.91553 0.239626
\(268\) 0.740959 0.0452613
\(269\) 7.75215 0.472657 0.236329 0.971673i \(-0.424056\pi\)
0.236329 + 0.971673i \(0.424056\pi\)
\(270\) 20.0178 1.21825
\(271\) 1.51990 0.0923272 0.0461636 0.998934i \(-0.485300\pi\)
0.0461636 + 0.998934i \(0.485300\pi\)
\(272\) 16.4953 1.00017
\(273\) −4.94099 −0.299043
\(274\) 43.3601 2.61948
\(275\) −8.42587 −0.508099
\(276\) 5.27939 0.317782
\(277\) 27.0614 1.62596 0.812982 0.582288i \(-0.197843\pi\)
0.812982 + 0.582288i \(0.197843\pi\)
\(278\) 63.7668 3.82448
\(279\) −21.4583 −1.28468
\(280\) −102.512 −6.12624
\(281\) 26.0726 1.55536 0.777682 0.628658i \(-0.216396\pi\)
0.777682 + 0.628658i \(0.216396\pi\)
\(282\) −1.59081 −0.0947312
\(283\) −21.5785 −1.28271 −0.641355 0.767244i \(-0.721627\pi\)
−0.641355 + 0.767244i \(0.721627\pi\)
\(284\) −25.8232 −1.53232
\(285\) −2.83895 −0.168165
\(286\) −27.1449 −1.60511
\(287\) −16.8368 −0.993844
\(288\) 73.4519 4.32819
\(289\) −16.0401 −0.943536
\(290\) 5.70980 0.335291
\(291\) 2.30264 0.134983
\(292\) 76.8377 4.49659
\(293\) −11.1908 −0.653771 −0.326885 0.945064i \(-0.605999\pi\)
−0.326885 + 0.945064i \(0.605999\pi\)
\(294\) 8.09587 0.472160
\(295\) −12.0790 −0.703264
\(296\) 62.2545 3.61847
\(297\) −8.67633 −0.503452
\(298\) 46.9189 2.71794
\(299\) 6.09016 0.352203
\(300\) −6.57396 −0.379547
\(301\) −15.1060 −0.870698
\(302\) −2.27812 −0.131091
\(303\) 6.19157 0.355696
\(304\) −38.3223 −2.19793
\(305\) −28.6153 −1.63851
\(306\) 7.58276 0.433477
\(307\) 30.7810 1.75677 0.878383 0.477957i \(-0.158623\pi\)
0.878383 + 0.477957i \(0.158623\pi\)
\(308\) 68.6257 3.91031
\(309\) −1.54568 −0.0879309
\(310\) 58.4678 3.32075
\(311\) 9.33936 0.529587 0.264793 0.964305i \(-0.414696\pi\)
0.264793 + 0.964305i \(0.414696\pi\)
\(312\) −13.7121 −0.776296
\(313\) 33.8024 1.91063 0.955313 0.295597i \(-0.0955186\pi\)
0.955313 + 0.295597i \(0.0955186\pi\)
\(314\) −30.0950 −1.69836
\(315\) −28.1523 −1.58620
\(316\) 85.1993 4.79283
\(317\) 13.0245 0.731530 0.365765 0.930707i \(-0.380807\pi\)
0.365765 + 0.930707i \(0.380807\pi\)
\(318\) −5.68815 −0.318976
\(319\) −2.47480 −0.138562
\(320\) −107.591 −6.01449
\(321\) 4.65407 0.259765
\(322\) −20.8248 −1.16052
\(323\) −2.23005 −0.124083
\(324\) 40.7821 2.26567
\(325\) −7.58354 −0.420659
\(326\) 29.9280 1.65756
\(327\) −1.44589 −0.0799582
\(328\) −46.7250 −2.57996
\(329\) 4.63940 0.255778
\(330\) 11.4001 0.627556
\(331\) 17.5961 0.967172 0.483586 0.875297i \(-0.339334\pi\)
0.483586 + 0.875297i \(0.339334\pi\)
\(332\) 10.1718 0.558248
\(333\) 17.0966 0.936890
\(334\) 34.2975 1.87668
\(335\) −0.358972 −0.0196127
\(336\) 28.0111 1.52813
\(337\) −0.723998 −0.0394387 −0.0197193 0.999806i \(-0.506277\pi\)
−0.0197193 + 0.999806i \(0.506277\pi\)
\(338\) 11.5789 0.629810
\(339\) −4.55247 −0.247256
\(340\) −15.2755 −0.828429
\(341\) −25.3417 −1.37233
\(342\) −17.6165 −0.952589
\(343\) 2.05204 0.110800
\(344\) −41.9219 −2.26028
\(345\) −2.55771 −0.137702
\(346\) 29.8481 1.60465
\(347\) 4.95238 0.265858 0.132929 0.991126i \(-0.457562\pi\)
0.132929 + 0.991126i \(0.457562\pi\)
\(348\) −1.93087 −0.103505
\(349\) 12.1255 0.649064 0.324532 0.945875i \(-0.394793\pi\)
0.324532 + 0.945875i \(0.394793\pi\)
\(350\) 25.9313 1.38609
\(351\) −7.80895 −0.416811
\(352\) 86.7448 4.62351
\(353\) −22.4537 −1.19509 −0.597546 0.801835i \(-0.703857\pi\)
−0.597546 + 0.801835i \(0.703857\pi\)
\(354\) 5.52477 0.293638
\(355\) 12.5106 0.663991
\(356\) −48.9463 −2.59415
\(357\) 1.63003 0.0862701
\(358\) −45.7192 −2.41634
\(359\) 18.3685 0.969450 0.484725 0.874667i \(-0.338920\pi\)
0.484725 + 0.874667i \(0.338920\pi\)
\(360\) −78.1274 −4.11768
\(361\) −13.8191 −0.727320
\(362\) −16.0051 −0.841209
\(363\) 0.0508072 0.00266669
\(364\) 61.7652 3.23737
\(365\) −37.2256 −1.94847
\(366\) 13.0883 0.684136
\(367\) 24.7449 1.29167 0.645836 0.763476i \(-0.276509\pi\)
0.645836 + 0.763476i \(0.276509\pi\)
\(368\) −34.5259 −1.79979
\(369\) −12.8319 −0.668000
\(370\) −46.5835 −2.42176
\(371\) 16.5888 0.861248
\(372\) −19.7719 −1.02512
\(373\) −20.4524 −1.05899 −0.529494 0.848314i \(-0.677618\pi\)
−0.529494 + 0.848314i \(0.677618\pi\)
\(374\) 8.95504 0.463054
\(375\) −3.05137 −0.157572
\(376\) 12.8751 0.663985
\(377\) −2.22739 −0.114717
\(378\) 26.7021 1.37341
\(379\) −14.8428 −0.762425 −0.381212 0.924488i \(-0.624493\pi\)
−0.381212 + 0.924488i \(0.624493\pi\)
\(380\) 35.4884 1.82052
\(381\) −1.83254 −0.0938838
\(382\) −18.5802 −0.950645
\(383\) −12.5466 −0.641103 −0.320551 0.947231i \(-0.603868\pi\)
−0.320551 + 0.947231i \(0.603868\pi\)
\(384\) 25.3503 1.29365
\(385\) −33.2471 −1.69443
\(386\) −12.9730 −0.660308
\(387\) −11.5128 −0.585229
\(388\) −28.7842 −1.46130
\(389\) 25.5944 1.29769 0.648845 0.760921i \(-0.275253\pi\)
0.648845 + 0.760921i \(0.275253\pi\)
\(390\) 10.2604 0.519558
\(391\) −2.00913 −0.101606
\(392\) −65.5236 −3.30944
\(393\) −6.65567 −0.335734
\(394\) −32.4930 −1.63697
\(395\) −41.2765 −2.07685
\(396\) 52.3019 2.62827
\(397\) −22.0990 −1.10912 −0.554558 0.832145i \(-0.687113\pi\)
−0.554558 + 0.832145i \(0.687113\pi\)
\(398\) −43.9666 −2.20385
\(399\) −3.78692 −0.189583
\(400\) 42.9920 2.14960
\(401\) 5.48851 0.274083 0.137041 0.990565i \(-0.456241\pi\)
0.137041 + 0.990565i \(0.456241\pi\)
\(402\) 0.164190 0.00818903
\(403\) −22.8083 −1.13616
\(404\) −77.3980 −3.85070
\(405\) −19.7577 −0.981768
\(406\) 7.61640 0.377996
\(407\) 20.1907 1.00082
\(408\) 4.52361 0.223952
\(409\) −25.4927 −1.26053 −0.630267 0.776378i \(-0.717055\pi\)
−0.630267 + 0.776378i \(0.717055\pi\)
\(410\) 34.9632 1.72671
\(411\) 7.10376 0.350402
\(412\) 19.3219 0.951922
\(413\) −16.1123 −0.792837
\(414\) −15.8713 −0.780032
\(415\) −4.92791 −0.241902
\(416\) 78.0729 3.82784
\(417\) 10.4470 0.511593
\(418\) −20.8046 −1.01759
\(419\) −22.2973 −1.08929 −0.544647 0.838665i \(-0.683336\pi\)
−0.544647 + 0.838665i \(0.683336\pi\)
\(420\) −25.9397 −1.26573
\(421\) −23.9500 −1.16725 −0.583626 0.812023i \(-0.698366\pi\)
−0.583626 + 0.812023i \(0.698366\pi\)
\(422\) 56.6553 2.75794
\(423\) 3.53584 0.171918
\(424\) 46.0369 2.23575
\(425\) 2.50180 0.121355
\(426\) −5.72218 −0.277240
\(427\) −38.1704 −1.84720
\(428\) −58.1785 −2.81216
\(429\) −4.44719 −0.214712
\(430\) 31.3691 1.51275
\(431\) 4.42706 0.213244 0.106622 0.994300i \(-0.465997\pi\)
0.106622 + 0.994300i \(0.465997\pi\)
\(432\) 44.2699 2.12994
\(433\) −6.81306 −0.327415 −0.163707 0.986509i \(-0.552345\pi\)
−0.163707 + 0.986509i \(0.552345\pi\)
\(434\) 77.9912 3.74370
\(435\) 0.935446 0.0448512
\(436\) 18.0745 0.865611
\(437\) 4.66767 0.223285
\(438\) 17.0265 0.813559
\(439\) 26.0996 1.24567 0.622833 0.782355i \(-0.285982\pi\)
0.622833 + 0.782355i \(0.285982\pi\)
\(440\) −92.2665 −4.39863
\(441\) −17.9944 −0.856878
\(442\) 8.05980 0.383366
\(443\) −26.9424 −1.28007 −0.640037 0.768344i \(-0.721081\pi\)
−0.640037 + 0.768344i \(0.721081\pi\)
\(444\) 15.7530 0.747604
\(445\) 23.7130 1.12410
\(446\) 8.84172 0.418668
\(447\) 7.68680 0.363573
\(448\) −143.517 −6.78054
\(449\) 22.0242 1.03939 0.519693 0.854353i \(-0.326046\pi\)
0.519693 + 0.854353i \(0.326046\pi\)
\(450\) 19.7631 0.931642
\(451\) −15.1541 −0.713579
\(452\) 56.9084 2.67674
\(453\) −0.373228 −0.0175358
\(454\) 6.43566 0.302040
\(455\) −29.9234 −1.40283
\(456\) −10.5094 −0.492146
\(457\) −10.9497 −0.512205 −0.256102 0.966650i \(-0.582438\pi\)
−0.256102 + 0.966650i \(0.582438\pi\)
\(458\) −30.4338 −1.42208
\(459\) 2.57616 0.120245
\(460\) 31.9727 1.49074
\(461\) 16.2581 0.757215 0.378607 0.925557i \(-0.376403\pi\)
0.378607 + 0.925557i \(0.376403\pi\)
\(462\) 15.2068 0.707485
\(463\) −19.5275 −0.907522 −0.453761 0.891123i \(-0.649918\pi\)
−0.453761 + 0.891123i \(0.649918\pi\)
\(464\) 12.6274 0.586211
\(465\) 9.57888 0.444210
\(466\) 4.06626 0.188366
\(467\) 37.0618 1.71502 0.857508 0.514471i \(-0.172012\pi\)
0.857508 + 0.514471i \(0.172012\pi\)
\(468\) 47.0732 2.17596
\(469\) −0.478839 −0.0221108
\(470\) −9.63415 −0.444390
\(471\) −4.93052 −0.227186
\(472\) −44.7146 −2.05816
\(473\) −13.5963 −0.625160
\(474\) 18.8794 0.867158
\(475\) −5.81224 −0.266684
\(476\) −20.3762 −0.933943
\(477\) 12.6429 0.578878
\(478\) 43.4703 1.98828
\(479\) −27.8668 −1.27327 −0.636634 0.771166i \(-0.719674\pi\)
−0.636634 + 0.771166i \(0.719674\pi\)
\(480\) −32.7885 −1.49658
\(481\) 18.1722 0.828582
\(482\) −56.5917 −2.57768
\(483\) −3.41177 −0.155241
\(484\) −0.635118 −0.0288690
\(485\) 13.9451 0.633214
\(486\) 30.8875 1.40109
\(487\) −21.4182 −0.970553 −0.485277 0.874361i \(-0.661281\pi\)
−0.485277 + 0.874361i \(0.661281\pi\)
\(488\) −105.930 −4.79521
\(489\) 4.90315 0.221728
\(490\) 49.0297 2.21494
\(491\) 15.9681 0.720629 0.360314 0.932831i \(-0.382669\pi\)
0.360314 + 0.932831i \(0.382669\pi\)
\(492\) −11.8234 −0.533039
\(493\) 0.734813 0.0330943
\(494\) −18.7247 −0.842466
\(495\) −25.3387 −1.13889
\(496\) 129.303 5.80588
\(497\) 16.6881 0.748561
\(498\) 2.25397 0.101003
\(499\) −25.3815 −1.13623 −0.568116 0.822949i \(-0.692327\pi\)
−0.568116 + 0.822949i \(0.692327\pi\)
\(500\) 38.1438 1.70584
\(501\) 5.61902 0.251039
\(502\) 42.6084 1.90171
\(503\) 38.5387 1.71836 0.859178 0.511677i \(-0.170976\pi\)
0.859178 + 0.511677i \(0.170976\pi\)
\(504\) −104.216 −4.64213
\(505\) 37.4970 1.66860
\(506\) −18.7436 −0.833254
\(507\) 1.89699 0.0842485
\(508\) 22.9077 1.01637
\(509\) 16.2262 0.719214 0.359607 0.933104i \(-0.382911\pi\)
0.359607 + 0.933104i \(0.382911\pi\)
\(510\) −3.38490 −0.149886
\(511\) −49.6558 −2.19664
\(512\) −100.017 −4.42016
\(513\) −5.98501 −0.264244
\(514\) 19.2010 0.846919
\(515\) −9.36088 −0.412490
\(516\) −10.6080 −0.466991
\(517\) 4.17573 0.183649
\(518\) −62.1386 −2.73021
\(519\) 4.89007 0.214650
\(520\) −83.0426 −3.64166
\(521\) 34.2941 1.50245 0.751227 0.660044i \(-0.229462\pi\)
0.751227 + 0.660044i \(0.229462\pi\)
\(522\) 5.80471 0.254065
\(523\) −32.3929 −1.41644 −0.708222 0.705990i \(-0.750502\pi\)
−0.708222 + 0.705990i \(0.750502\pi\)
\(524\) 83.1995 3.63459
\(525\) 4.24837 0.185414
\(526\) −39.9834 −1.74336
\(527\) 7.52442 0.327769
\(528\) 25.2117 1.09720
\(529\) −18.7947 −0.817162
\(530\) −34.4482 −1.49634
\(531\) −12.2797 −0.532896
\(532\) 47.3386 2.05239
\(533\) −13.6391 −0.590777
\(534\) −10.8460 −0.469354
\(535\) 28.1857 1.21857
\(536\) −1.32886 −0.0573982
\(537\) −7.49025 −0.323228
\(538\) −21.4735 −0.925789
\(539\) −21.2510 −0.915344
\(540\) −40.9962 −1.76420
\(541\) 25.1036 1.07929 0.539645 0.841893i \(-0.318559\pi\)
0.539645 + 0.841893i \(0.318559\pi\)
\(542\) −4.21013 −0.180840
\(543\) −2.62214 −0.112527
\(544\) −25.7561 −1.10428
\(545\) −8.75655 −0.375089
\(546\) 13.6866 0.585732
\(547\) −30.6241 −1.30939 −0.654697 0.755892i \(-0.727204\pi\)
−0.654697 + 0.755892i \(0.727204\pi\)
\(548\) −88.8009 −3.79339
\(549\) −29.0909 −1.24157
\(550\) 23.3397 0.995209
\(551\) −1.70714 −0.0727265
\(552\) −9.46826 −0.402996
\(553\) −55.0594 −2.34137
\(554\) −74.9604 −3.18476
\(555\) −7.63185 −0.323954
\(556\) −130.594 −5.53840
\(557\) −21.4771 −0.910015 −0.455007 0.890488i \(-0.650363\pi\)
−0.455007 + 0.890488i \(0.650363\pi\)
\(558\) 59.4397 2.51628
\(559\) −12.2371 −0.517574
\(560\) 169.639 7.16857
\(561\) 1.46712 0.0619418
\(562\) −72.2214 −3.04648
\(563\) 46.7467 1.97014 0.985070 0.172156i \(-0.0550732\pi\)
0.985070 + 0.172156i \(0.0550732\pi\)
\(564\) 3.25795 0.137185
\(565\) −27.5704 −1.15989
\(566\) 59.7727 2.51243
\(567\) −26.3551 −1.10681
\(568\) 46.3123 1.94322
\(569\) 17.5040 0.733804 0.366902 0.930260i \(-0.380418\pi\)
0.366902 + 0.930260i \(0.380418\pi\)
\(570\) 7.86390 0.329382
\(571\) −32.3897 −1.35547 −0.677733 0.735308i \(-0.737037\pi\)
−0.677733 + 0.735308i \(0.737037\pi\)
\(572\) 55.5923 2.32443
\(573\) −3.04402 −0.127166
\(574\) 46.6380 1.94663
\(575\) −5.23645 −0.218375
\(576\) −109.379 −4.55746
\(577\) −17.3114 −0.720681 −0.360341 0.932821i \(-0.617340\pi\)
−0.360341 + 0.932821i \(0.617340\pi\)
\(578\) 44.4312 1.84809
\(579\) −2.12539 −0.0883280
\(580\) −11.6936 −0.485550
\(581\) −6.57343 −0.272712
\(582\) −6.37832 −0.264390
\(583\) 14.9309 0.618375
\(584\) −137.804 −5.70236
\(585\) −22.8056 −0.942894
\(586\) 30.9985 1.28053
\(587\) −15.4541 −0.637858 −0.318929 0.947779i \(-0.603323\pi\)
−0.318929 + 0.947779i \(0.603323\pi\)
\(588\) −16.5802 −0.683757
\(589\) −17.4809 −0.720289
\(590\) 33.4588 1.37748
\(591\) −5.32339 −0.218975
\(592\) −103.021 −4.23412
\(593\) 20.9145 0.858855 0.429428 0.903101i \(-0.358715\pi\)
0.429428 + 0.903101i \(0.358715\pi\)
\(594\) 24.0335 0.986106
\(595\) 9.87167 0.404699
\(596\) −96.0893 −3.93597
\(597\) −7.20312 −0.294804
\(598\) −16.8698 −0.689857
\(599\) 7.93391 0.324171 0.162085 0.986777i \(-0.448178\pi\)
0.162085 + 0.986777i \(0.448178\pi\)
\(600\) 11.7900 0.481324
\(601\) 9.93108 0.405097 0.202549 0.979272i \(-0.435078\pi\)
0.202549 + 0.979272i \(0.435078\pi\)
\(602\) 41.8438 1.70543
\(603\) −0.364939 −0.0148615
\(604\) 4.66556 0.189839
\(605\) 0.307696 0.0125096
\(606\) −17.1507 −0.696699
\(607\) 15.9424 0.647081 0.323540 0.946214i \(-0.395127\pi\)
0.323540 + 0.946214i \(0.395127\pi\)
\(608\) 59.8373 2.42672
\(609\) 1.24781 0.0505637
\(610\) 79.2645 3.20933
\(611\) 3.75828 0.152044
\(612\) −15.5294 −0.627738
\(613\) 24.3333 0.982811 0.491406 0.870931i \(-0.336483\pi\)
0.491406 + 0.870931i \(0.336483\pi\)
\(614\) −85.2637 −3.44096
\(615\) 5.72808 0.230978
\(616\) −123.076 −4.95887
\(617\) −42.2289 −1.70007 −0.850036 0.526724i \(-0.823420\pi\)
−0.850036 + 0.526724i \(0.823420\pi\)
\(618\) 4.28156 0.172229
\(619\) 19.9759 0.802898 0.401449 0.915881i \(-0.368507\pi\)
0.401449 + 0.915881i \(0.368507\pi\)
\(620\) −119.741 −4.80893
\(621\) −5.39210 −0.216378
\(622\) −25.8701 −1.03730
\(623\) 31.6312 1.26728
\(624\) 22.6912 0.908376
\(625\) −31.2471 −1.24989
\(626\) −93.6329 −3.74232
\(627\) −3.40845 −0.136120
\(628\) 61.6342 2.45947
\(629\) −5.99499 −0.239036
\(630\) 77.9819 3.10687
\(631\) 19.1345 0.761734 0.380867 0.924630i \(-0.375626\pi\)
0.380867 + 0.924630i \(0.375626\pi\)
\(632\) −152.800 −6.07804
\(633\) 9.28194 0.368924
\(634\) −36.0780 −1.43284
\(635\) −11.0981 −0.440415
\(636\) 11.6493 0.461923
\(637\) −19.1265 −0.757819
\(638\) 6.85521 0.271401
\(639\) 12.7185 0.503136
\(640\) 153.525 6.06860
\(641\) −3.24092 −0.128008 −0.0640042 0.997950i \(-0.520387\pi\)
−0.0640042 + 0.997950i \(0.520387\pi\)
\(642\) −12.8918 −0.508799
\(643\) 19.7549 0.779059 0.389530 0.921014i \(-0.372638\pi\)
0.389530 + 0.921014i \(0.372638\pi\)
\(644\) 42.6490 1.68061
\(645\) 5.13926 0.202358
\(646\) 6.17726 0.243041
\(647\) −21.3018 −0.837458 −0.418729 0.908111i \(-0.637524\pi\)
−0.418729 + 0.908111i \(0.637524\pi\)
\(648\) −73.1401 −2.87322
\(649\) −14.5021 −0.569256
\(650\) 21.0064 0.823941
\(651\) 12.7774 0.500787
\(652\) −61.2921 −2.40038
\(653\) 45.6267 1.78551 0.892755 0.450542i \(-0.148769\pi\)
0.892755 + 0.450542i \(0.148769\pi\)
\(654\) 4.00514 0.156613
\(655\) −40.3077 −1.57495
\(656\) 77.3220 3.01892
\(657\) −37.8443 −1.47645
\(658\) −12.8512 −0.500991
\(659\) −2.38239 −0.0928047 −0.0464024 0.998923i \(-0.514776\pi\)
−0.0464024 + 0.998923i \(0.514776\pi\)
\(660\) −23.3473 −0.908792
\(661\) 12.0865 0.470112 0.235056 0.971982i \(-0.424473\pi\)
0.235056 + 0.971982i \(0.424473\pi\)
\(662\) −48.7414 −1.89439
\(663\) 1.32045 0.0512821
\(664\) −18.2424 −0.707943
\(665\) −22.9341 −0.889347
\(666\) −47.3578 −1.83508
\(667\) −1.53802 −0.0595524
\(668\) −70.2409 −2.71770
\(669\) 1.44855 0.0560043
\(670\) 0.994355 0.0384153
\(671\) −34.3556 −1.32628
\(672\) −43.7372 −1.68720
\(673\) 43.3388 1.67059 0.835295 0.549803i \(-0.185297\pi\)
0.835295 + 0.549803i \(0.185297\pi\)
\(674\) 2.00548 0.0772482
\(675\) 6.71431 0.258434
\(676\) −23.7135 −0.912057
\(677\) 14.4629 0.555856 0.277928 0.960602i \(-0.410352\pi\)
0.277928 + 0.960602i \(0.410352\pi\)
\(678\) 12.6104 0.484298
\(679\) 18.6016 0.713864
\(680\) 27.3956 1.05057
\(681\) 1.05436 0.0404034
\(682\) 70.1967 2.68797
\(683\) −24.2843 −0.929215 −0.464607 0.885517i \(-0.653805\pi\)
−0.464607 + 0.885517i \(0.653805\pi\)
\(684\) 36.0783 1.37949
\(685\) 43.0214 1.64376
\(686\) −5.68417 −0.217023
\(687\) −4.98602 −0.190228
\(688\) 69.3736 2.64484
\(689\) 13.4383 0.511957
\(690\) 7.08486 0.269716
\(691\) 8.52572 0.324334 0.162167 0.986763i \(-0.448152\pi\)
0.162167 + 0.986763i \(0.448152\pi\)
\(692\) −61.1286 −2.32376
\(693\) −33.7997 −1.28395
\(694\) −13.7181 −0.520733
\(695\) 63.2687 2.39992
\(696\) 3.46289 0.131260
\(697\) 4.49953 0.170432
\(698\) −33.5878 −1.27132
\(699\) 0.666182 0.0251973
\(700\) −53.1070 −2.00726
\(701\) −29.1666 −1.10161 −0.550804 0.834635i \(-0.685679\pi\)
−0.550804 + 0.834635i \(0.685679\pi\)
\(702\) 21.6309 0.816404
\(703\) 13.9277 0.525294
\(704\) −129.174 −4.86842
\(705\) −1.57838 −0.0594452
\(706\) 62.1970 2.34081
\(707\) 50.0180 1.88112
\(708\) −11.3147 −0.425231
\(709\) 8.89435 0.334034 0.167017 0.985954i \(-0.446586\pi\)
0.167017 + 0.985954i \(0.446586\pi\)
\(710\) −34.6543 −1.30055
\(711\) −41.9626 −1.57372
\(712\) 87.7821 3.28977
\(713\) −15.7492 −0.589812
\(714\) −4.51518 −0.168976
\(715\) −26.9328 −1.00723
\(716\) 93.6323 3.49920
\(717\) 7.12181 0.265969
\(718\) −50.8808 −1.89885
\(719\) −20.1059 −0.749822 −0.374911 0.927061i \(-0.622327\pi\)
−0.374911 + 0.927061i \(0.622327\pi\)
\(720\) 129.288 4.81827
\(721\) −12.4866 −0.465027
\(722\) 38.2789 1.42459
\(723\) −9.27151 −0.344811
\(724\) 32.7782 1.21819
\(725\) 1.91516 0.0711273
\(726\) −0.140736 −0.00522321
\(727\) −20.2989 −0.752846 −0.376423 0.926448i \(-0.622846\pi\)
−0.376423 + 0.926448i \(0.622846\pi\)
\(728\) −110.772 −4.10548
\(729\) −16.5063 −0.611344
\(730\) 103.115 3.81646
\(731\) 4.03700 0.149314
\(732\) −26.8046 −0.990728
\(733\) −6.33091 −0.233837 −0.116919 0.993141i \(-0.537302\pi\)
−0.116919 + 0.993141i \(0.537302\pi\)
\(734\) −68.5435 −2.52999
\(735\) 8.03262 0.296288
\(736\) 53.9095 1.98713
\(737\) −0.430984 −0.0158755
\(738\) 35.5443 1.30841
\(739\) −48.6350 −1.78907 −0.894534 0.447000i \(-0.852492\pi\)
−0.894534 + 0.447000i \(0.852492\pi\)
\(740\) 95.4024 3.50706
\(741\) −3.06771 −0.112695
\(742\) −45.9511 −1.68692
\(743\) 26.2443 0.962812 0.481406 0.876498i \(-0.340126\pi\)
0.481406 + 0.876498i \(0.340126\pi\)
\(744\) 35.4596 1.30001
\(745\) 46.5524 1.70555
\(746\) 56.6534 2.07423
\(747\) −5.00983 −0.183300
\(748\) −18.3398 −0.670570
\(749\) 37.5974 1.37378
\(750\) 8.45231 0.308635
\(751\) −2.70661 −0.0987657 −0.0493829 0.998780i \(-0.515725\pi\)
−0.0493829 + 0.998780i \(0.515725\pi\)
\(752\) −21.3062 −0.776956
\(753\) 6.98061 0.254388
\(754\) 6.16989 0.224694
\(755\) −2.26032 −0.0822616
\(756\) −54.6856 −1.98890
\(757\) −7.60354 −0.276356 −0.138178 0.990407i \(-0.544125\pi\)
−0.138178 + 0.990407i \(0.544125\pi\)
\(758\) 41.1147 1.49335
\(759\) −3.07079 −0.111463
\(760\) −63.6462 −2.30869
\(761\) 36.5550 1.32512 0.662558 0.749010i \(-0.269471\pi\)
0.662558 + 0.749010i \(0.269471\pi\)
\(762\) 5.07614 0.183889
\(763\) −11.6805 −0.422863
\(764\) 38.0520 1.37667
\(765\) 7.52352 0.272013
\(766\) 34.7542 1.25572
\(767\) −13.0523 −0.471291
\(768\) −34.6893 −1.25174
\(769\) 21.4810 0.774625 0.387312 0.921949i \(-0.373404\pi\)
0.387312 + 0.921949i \(0.373404\pi\)
\(770\) 92.0947 3.31886
\(771\) 3.14573 0.113291
\(772\) 26.5685 0.956221
\(773\) −15.8644 −0.570602 −0.285301 0.958438i \(-0.592093\pi\)
−0.285301 + 0.958438i \(0.592093\pi\)
\(774\) 31.8905 1.14628
\(775\) 19.6111 0.704450
\(776\) 51.6227 1.85315
\(777\) −10.1803 −0.365215
\(778\) −70.8967 −2.54177
\(779\) −10.4534 −0.374533
\(780\) −21.0132 −0.752395
\(781\) 15.0202 0.537466
\(782\) 5.56531 0.199015
\(783\) 1.97209 0.0704767
\(784\) 108.430 3.87252
\(785\) −29.8599 −1.06575
\(786\) 18.4362 0.657599
\(787\) 6.71771 0.239460 0.119730 0.992806i \(-0.461797\pi\)
0.119730 + 0.992806i \(0.461797\pi\)
\(788\) 66.5453 2.37058
\(789\) −6.55055 −0.233206
\(790\) 114.336 4.06790
\(791\) −36.7766 −1.30763
\(792\) −93.8002 −3.33304
\(793\) −30.9211 −1.09804
\(794\) 61.2143 2.17242
\(795\) −5.64371 −0.200162
\(796\) 90.0430 3.19149
\(797\) 5.48198 0.194182 0.0970908 0.995276i \(-0.469046\pi\)
0.0970908 + 0.995276i \(0.469046\pi\)
\(798\) 10.4898 0.371335
\(799\) −1.23985 −0.0438628
\(800\) −67.1287 −2.37336
\(801\) 24.1072 0.851785
\(802\) −15.2032 −0.536844
\(803\) −44.6932 −1.57719
\(804\) −0.336258 −0.0118589
\(805\) −20.6622 −0.728246
\(806\) 63.1791 2.22539
\(807\) −3.51804 −0.123841
\(808\) 138.809 4.88327
\(809\) 31.6107 1.11137 0.555687 0.831392i \(-0.312455\pi\)
0.555687 + 0.831392i \(0.312455\pi\)
\(810\) 54.7289 1.92298
\(811\) 10.8681 0.381629 0.190815 0.981626i \(-0.438887\pi\)
0.190815 + 0.981626i \(0.438887\pi\)
\(812\) −15.5983 −0.547393
\(813\) −0.689752 −0.0241907
\(814\) −55.9284 −1.96029
\(815\) 29.6942 1.04014
\(816\) −7.48580 −0.262055
\(817\) −9.37886 −0.328125
\(818\) 70.6150 2.46900
\(819\) −30.4208 −1.06299
\(820\) −71.6041 −2.50052
\(821\) 9.80523 0.342205 0.171102 0.985253i \(-0.445267\pi\)
0.171102 + 0.985253i \(0.445267\pi\)
\(822\) −19.6775 −0.686330
\(823\) −5.53124 −0.192807 −0.0964035 0.995342i \(-0.530734\pi\)
−0.0964035 + 0.995342i \(0.530734\pi\)
\(824\) −34.6526 −1.20718
\(825\) 3.82379 0.133127
\(826\) 44.6313 1.55292
\(827\) −23.5441 −0.818708 −0.409354 0.912376i \(-0.634246\pi\)
−0.409354 + 0.912376i \(0.634246\pi\)
\(828\) 32.5042 1.12960
\(829\) 50.4382 1.75179 0.875895 0.482502i \(-0.160272\pi\)
0.875895 + 0.482502i \(0.160272\pi\)
\(830\) 13.6504 0.473811
\(831\) −12.2809 −0.426019
\(832\) −116.260 −4.03060
\(833\) 6.30980 0.218622
\(834\) −28.9383 −1.00205
\(835\) 34.0296 1.17764
\(836\) 42.6075 1.47361
\(837\) 20.1940 0.698007
\(838\) 61.7636 2.13359
\(839\) −39.2420 −1.35478 −0.677392 0.735623i \(-0.736890\pi\)
−0.677392 + 0.735623i \(0.736890\pi\)
\(840\) 46.5213 1.60514
\(841\) −28.4375 −0.980603
\(842\) 66.3416 2.28628
\(843\) −11.8322 −0.407521
\(844\) −116.029 −3.99390
\(845\) 11.4885 0.395215
\(846\) −9.79430 −0.336735
\(847\) 0.410441 0.0141029
\(848\) −76.1832 −2.61614
\(849\) 9.79266 0.336083
\(850\) −6.92999 −0.237697
\(851\) 12.5480 0.430139
\(852\) 11.7189 0.401484
\(853\) −32.2363 −1.10375 −0.551874 0.833927i \(-0.686087\pi\)
−0.551874 + 0.833927i \(0.686087\pi\)
\(854\) 105.732 3.61809
\(855\) −17.4788 −0.597764
\(856\) 104.339 3.56625
\(857\) −1.95981 −0.0669458 −0.0334729 0.999440i \(-0.510657\pi\)
−0.0334729 + 0.999440i \(0.510657\pi\)
\(858\) 12.3187 0.420555
\(859\) 13.2145 0.450874 0.225437 0.974258i \(-0.427619\pi\)
0.225437 + 0.974258i \(0.427619\pi\)
\(860\) −64.2435 −2.19069
\(861\) 7.64078 0.260397
\(862\) −12.2630 −0.417679
\(863\) −20.9152 −0.711960 −0.355980 0.934494i \(-0.615853\pi\)
−0.355980 + 0.934494i \(0.615853\pi\)
\(864\) −69.1241 −2.35165
\(865\) 29.6150 1.00694
\(866\) 18.8722 0.641304
\(867\) 7.27924 0.247216
\(868\) −159.725 −5.42142
\(869\) −49.5567 −1.68110
\(870\) −2.59119 −0.0878496
\(871\) −0.387898 −0.0131434
\(872\) −32.4155 −1.09773
\(873\) 14.1769 0.479815
\(874\) −12.9295 −0.437346
\(875\) −24.6502 −0.833327
\(876\) −34.8701 −1.17815
\(877\) −14.3841 −0.485716 −0.242858 0.970062i \(-0.578085\pi\)
−0.242858 + 0.970062i \(0.578085\pi\)
\(878\) −72.2961 −2.43987
\(879\) 5.07853 0.171295
\(880\) 152.685 5.14702
\(881\) −32.5760 −1.09751 −0.548756 0.835983i \(-0.684898\pi\)
−0.548756 + 0.835983i \(0.684898\pi\)
\(882\) 49.8447 1.67836
\(883\) −56.0790 −1.88721 −0.943604 0.331076i \(-0.892588\pi\)
−0.943604 + 0.331076i \(0.892588\pi\)
\(884\) −16.5064 −0.555169
\(885\) 5.48161 0.184262
\(886\) 74.6308 2.50727
\(887\) 14.8633 0.499059 0.249530 0.968367i \(-0.419724\pi\)
0.249530 + 0.968367i \(0.419724\pi\)
\(888\) −28.2520 −0.948076
\(889\) −14.8040 −0.496509
\(890\) −65.6852 −2.20177
\(891\) −23.7212 −0.794690
\(892\) −18.1077 −0.606292
\(893\) 2.88046 0.0963908
\(894\) −21.2925 −0.712127
\(895\) −45.3620 −1.51629
\(896\) 204.789 6.84153
\(897\) −2.76381 −0.0922808
\(898\) −61.0072 −2.03584
\(899\) 5.76005 0.192108
\(900\) −40.4746 −1.34915
\(901\) −4.43326 −0.147693
\(902\) 41.9770 1.39768
\(903\) 6.85534 0.228132
\(904\) −102.062 −3.39452
\(905\) −15.8801 −0.527871
\(906\) 1.03384 0.0343472
\(907\) −5.30131 −0.176027 −0.0880136 0.996119i \(-0.528052\pi\)
−0.0880136 + 0.996119i \(0.528052\pi\)
\(908\) −13.1801 −0.437398
\(909\) 38.1203 1.26437
\(910\) 82.8879 2.74771
\(911\) −42.6404 −1.41274 −0.706370 0.707843i \(-0.749668\pi\)
−0.706370 + 0.707843i \(0.749668\pi\)
\(912\) 17.3912 0.575881
\(913\) −5.91648 −0.195807
\(914\) 30.3307 1.00325
\(915\) 12.9860 0.429305
\(916\) 62.3280 2.05937
\(917\) −53.7671 −1.77555
\(918\) −7.13598 −0.235522
\(919\) 52.4702 1.73083 0.865416 0.501054i \(-0.167054\pi\)
0.865416 + 0.501054i \(0.167054\pi\)
\(920\) −57.3411 −1.89048
\(921\) −13.9689 −0.460291
\(922\) −45.0350 −1.48315
\(923\) 13.5187 0.444972
\(924\) −31.1434 −1.02454
\(925\) −15.6249 −0.513743
\(926\) 54.0914 1.77755
\(927\) −9.51648 −0.312562
\(928\) −19.7167 −0.647231
\(929\) 40.3864 1.32503 0.662517 0.749047i \(-0.269488\pi\)
0.662517 + 0.749047i \(0.269488\pi\)
\(930\) −26.5336 −0.870070
\(931\) −14.6591 −0.480432
\(932\) −8.32764 −0.272781
\(933\) −4.23834 −0.138757
\(934\) −102.661 −3.35918
\(935\) 8.88508 0.290573
\(936\) −84.4229 −2.75945
\(937\) 31.9884 1.04501 0.522507 0.852635i \(-0.324997\pi\)
0.522507 + 0.852635i \(0.324997\pi\)
\(938\) 1.32639 0.0433081
\(939\) −15.3400 −0.500603
\(940\) 19.7306 0.643542
\(941\) 46.6973 1.52229 0.761143 0.648584i \(-0.224638\pi\)
0.761143 + 0.648584i \(0.224638\pi\)
\(942\) 13.6576 0.444988
\(943\) −9.41786 −0.306688
\(944\) 73.9950 2.40833
\(945\) 26.4935 0.861835
\(946\) 37.6619 1.22449
\(947\) 6.98863 0.227100 0.113550 0.993532i \(-0.463778\pi\)
0.113550 + 0.993532i \(0.463778\pi\)
\(948\) −38.6647 −1.25577
\(949\) −40.2252 −1.30576
\(950\) 16.0999 0.522351
\(951\) −5.91072 −0.191668
\(952\) 36.5435 1.18438
\(953\) 16.5590 0.536399 0.268199 0.963363i \(-0.413571\pi\)
0.268199 + 0.963363i \(0.413571\pi\)
\(954\) −35.0209 −1.13384
\(955\) −18.4350 −0.596544
\(956\) −89.0265 −2.87932
\(957\) 1.12310 0.0363047
\(958\) 77.1913 2.49394
\(959\) 57.3870 1.85312
\(960\) 48.8262 1.57586
\(961\) 27.9824 0.902657
\(962\) −50.3372 −1.62294
\(963\) 28.6542 0.923370
\(964\) 115.899 3.73286
\(965\) −12.8716 −0.414353
\(966\) 9.45062 0.304069
\(967\) 30.3934 0.977387 0.488693 0.872456i \(-0.337474\pi\)
0.488693 + 0.872456i \(0.337474\pi\)
\(968\) 1.13905 0.0366103
\(969\) 1.01203 0.0325111
\(970\) −38.6280 −1.24027
\(971\) −11.9447 −0.383323 −0.191662 0.981461i \(-0.561388\pi\)
−0.191662 + 0.981461i \(0.561388\pi\)
\(972\) −63.2572 −2.02898
\(973\) 84.3952 2.70559
\(974\) 59.3287 1.90101
\(975\) 3.44152 0.110217
\(976\) 175.296 5.61107
\(977\) −38.2074 −1.22236 −0.611181 0.791491i \(-0.709305\pi\)
−0.611181 + 0.791491i \(0.709305\pi\)
\(978\) −13.5818 −0.434297
\(979\) 28.4699 0.909903
\(980\) −100.412 −3.20755
\(981\) −8.90210 −0.284222
\(982\) −44.2317 −1.41149
\(983\) 22.3415 0.712583 0.356292 0.934375i \(-0.384041\pi\)
0.356292 + 0.934375i \(0.384041\pi\)
\(984\) 21.2045 0.675975
\(985\) −32.2392 −1.02723
\(986\) −2.03544 −0.0648215
\(987\) −2.10543 −0.0670165
\(988\) 38.3480 1.22001
\(989\) −8.44975 −0.268686
\(990\) 70.1884 2.23073
\(991\) −21.0809 −0.669657 −0.334829 0.942279i \(-0.608678\pi\)
−0.334829 + 0.942279i \(0.608678\pi\)
\(992\) −201.897 −6.41023
\(993\) −7.98539 −0.253409
\(994\) −46.2260 −1.46620
\(995\) −43.6231 −1.38295
\(996\) −4.61610 −0.146267
\(997\) −12.8127 −0.405781 −0.202890 0.979201i \(-0.565034\pi\)
−0.202890 + 0.979201i \(0.565034\pi\)
\(998\) 70.3069 2.22553
\(999\) −16.0893 −0.509043
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 5077.2.a.b.1.5 205
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5077.2.a.b.1.5 205 1.1 even 1 trivial