Properties

Label 8049.2.a.b.1.10
Level $8049$
Weight $2$
Character 8049.1
Self dual yes
Analytic conductor $64.272$
Analytic rank $1$
Dimension $104$
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: \(1\)
Dimension: \(104\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
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)
 
\(f(q)\) \(=\) \(q-2.49098 q^{2} -1.00000 q^{3} +4.20498 q^{4} -3.30007 q^{5} +2.49098 q^{6} -0.252788 q^{7} -5.49255 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.49098 q^{2} -1.00000 q^{3} +4.20498 q^{4} -3.30007 q^{5} +2.49098 q^{6} -0.252788 q^{7} -5.49255 q^{8} +1.00000 q^{9} +8.22041 q^{10} +0.866258 q^{11} -4.20498 q^{12} -1.69541 q^{13} +0.629689 q^{14} +3.30007 q^{15} +5.27188 q^{16} +6.53809 q^{17} -2.49098 q^{18} +8.58286 q^{19} -13.8767 q^{20} +0.252788 q^{21} -2.15783 q^{22} -0.330861 q^{23} +5.49255 q^{24} +5.89049 q^{25} +4.22323 q^{26} -1.00000 q^{27} -1.06297 q^{28} -6.30189 q^{29} -8.22041 q^{30} -0.392200 q^{31} -2.14704 q^{32} -0.866258 q^{33} -16.2862 q^{34} +0.834218 q^{35} +4.20498 q^{36} -4.11920 q^{37} -21.3797 q^{38} +1.69541 q^{39} +18.1258 q^{40} -5.47986 q^{41} -0.629689 q^{42} +3.91004 q^{43} +3.64259 q^{44} -3.30007 q^{45} +0.824169 q^{46} -5.33816 q^{47} -5.27188 q^{48} -6.93610 q^{49} -14.6731 q^{50} -6.53809 q^{51} -7.12916 q^{52} -5.15842 q^{53} +2.49098 q^{54} -2.85871 q^{55} +1.38845 q^{56} -8.58286 q^{57} +15.6979 q^{58} -9.03502 q^{59} +13.8767 q^{60} -2.97621 q^{61} +0.976961 q^{62} -0.252788 q^{63} -5.19553 q^{64} +5.59498 q^{65} +2.15783 q^{66} +15.5848 q^{67} +27.4925 q^{68} +0.330861 q^{69} -2.07802 q^{70} -12.4476 q^{71} -5.49255 q^{72} -3.53769 q^{73} +10.2608 q^{74} -5.89049 q^{75} +36.0908 q^{76} -0.218979 q^{77} -4.22323 q^{78} +10.0125 q^{79} -17.3976 q^{80} +1.00000 q^{81} +13.6502 q^{82} +0.830870 q^{83} +1.06297 q^{84} -21.5762 q^{85} -9.73983 q^{86} +6.30189 q^{87} -4.75797 q^{88} +9.43735 q^{89} +8.22041 q^{90} +0.428579 q^{91} -1.39126 q^{92} +0.392200 q^{93} +13.2973 q^{94} -28.3241 q^{95} +2.14704 q^{96} +4.48288 q^{97} +17.2777 q^{98} +0.866258 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9} + 8 q^{10} - 52 q^{11} - 87 q^{12} + 35 q^{13} - 23 q^{14} + 15 q^{15} + 53 q^{16} - 19 q^{17} - 9 q^{18} - 22 q^{19} - 35 q^{20} + 10 q^{21} - q^{22} - 70 q^{23} + 27 q^{24} + 79 q^{25} - 39 q^{26} - 104 q^{27} - 9 q^{28} - 37 q^{29} - 8 q^{30} - 47 q^{31} - 53 q^{32} + 52 q^{33} - 17 q^{34} - 54 q^{35} + 87 q^{36} + 65 q^{37} - 33 q^{38} - 35 q^{39} + 14 q^{40} - 47 q^{41} + 23 q^{42} - 30 q^{43} - 122 q^{44} - 15 q^{45} - 6 q^{46} - 101 q^{47} - 53 q^{48} + 78 q^{49} - 64 q^{50} + 19 q^{51} + 41 q^{52} - 48 q^{53} + 9 q^{54} - 29 q^{55} - 71 q^{56} + 22 q^{57} - 2 q^{58} - 86 q^{59} + 35 q^{60} + 34 q^{61} - 36 q^{62} - 10 q^{63} - 15 q^{64} - 64 q^{65} + q^{66} - 38 q^{67} - 33 q^{68} + 70 q^{69} - 29 q^{70} - 176 q^{71} - 27 q^{72} + 69 q^{73} - 86 q^{74} - 79 q^{75} - 54 q^{76} - 45 q^{77} + 39 q^{78} - 101 q^{79} - 76 q^{80} + 104 q^{81} + 38 q^{82} - 67 q^{83} + 9 q^{84} + 3 q^{85} - 90 q^{86} + 37 q^{87} + 7 q^{88} - 91 q^{89} + 8 q^{90} - 47 q^{91} - 136 q^{92} + 47 q^{93} - 20 q^{94} - 130 q^{95} + 53 q^{96} + 86 q^{97} - 44 q^{98} - 52 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49098 −1.76139 −0.880694 0.473685i \(-0.842923\pi\)
−0.880694 + 0.473685i \(0.842923\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.20498 2.10249
\(5\) −3.30007 −1.47584 −0.737919 0.674889i \(-0.764191\pi\)
−0.737919 + 0.674889i \(0.764191\pi\)
\(6\) 2.49098 1.01694
\(7\) −0.252788 −0.0955447 −0.0477724 0.998858i \(-0.515212\pi\)
−0.0477724 + 0.998858i \(0.515212\pi\)
\(8\) −5.49255 −1.94191
\(9\) 1.00000 0.333333
\(10\) 8.22041 2.59952
\(11\) 0.866258 0.261187 0.130593 0.991436i \(-0.458312\pi\)
0.130593 + 0.991436i \(0.458312\pi\)
\(12\) −4.20498 −1.21387
\(13\) −1.69541 −0.470222 −0.235111 0.971969i \(-0.575545\pi\)
−0.235111 + 0.971969i \(0.575545\pi\)
\(14\) 0.629689 0.168291
\(15\) 3.30007 0.852075
\(16\) 5.27188 1.31797
\(17\) 6.53809 1.58572 0.792860 0.609404i \(-0.208591\pi\)
0.792860 + 0.609404i \(0.208591\pi\)
\(18\) −2.49098 −0.587129
\(19\) 8.58286 1.96904 0.984522 0.175261i \(-0.0560768\pi\)
0.984522 + 0.175261i \(0.0560768\pi\)
\(20\) −13.8767 −3.10293
\(21\) 0.252788 0.0551628
\(22\) −2.15783 −0.460051
\(23\) −0.330861 −0.0689894 −0.0344947 0.999405i \(-0.510982\pi\)
−0.0344947 + 0.999405i \(0.510982\pi\)
\(24\) 5.49255 1.12116
\(25\) 5.89049 1.17810
\(26\) 4.22323 0.828244
\(27\) −1.00000 −0.192450
\(28\) −1.06297 −0.200882
\(29\) −6.30189 −1.17023 −0.585116 0.810950i \(-0.698951\pi\)
−0.585116 + 0.810950i \(0.698951\pi\)
\(30\) −8.22041 −1.50084
\(31\) −0.392200 −0.0704412 −0.0352206 0.999380i \(-0.511213\pi\)
−0.0352206 + 0.999380i \(0.511213\pi\)
\(32\) −2.14704 −0.379546
\(33\) −0.866258 −0.150796
\(34\) −16.2862 −2.79307
\(35\) 0.834218 0.141009
\(36\) 4.20498 0.700830
\(37\) −4.11920 −0.677193 −0.338596 0.940932i \(-0.609952\pi\)
−0.338596 + 0.940932i \(0.609952\pi\)
\(38\) −21.3797 −3.46825
\(39\) 1.69541 0.271483
\(40\) 18.1258 2.86595
\(41\) −5.47986 −0.855810 −0.427905 0.903824i \(-0.640748\pi\)
−0.427905 + 0.903824i \(0.640748\pi\)
\(42\) −0.629689 −0.0971631
\(43\) 3.91004 0.596275 0.298138 0.954523i \(-0.403635\pi\)
0.298138 + 0.954523i \(0.403635\pi\)
\(44\) 3.64259 0.549142
\(45\) −3.30007 −0.491946
\(46\) 0.824169 0.121517
\(47\) −5.33816 −0.778651 −0.389325 0.921100i \(-0.627292\pi\)
−0.389325 + 0.921100i \(0.627292\pi\)
\(48\) −5.27188 −0.760930
\(49\) −6.93610 −0.990871
\(50\) −14.6731 −2.07509
\(51\) −6.53809 −0.915516
\(52\) −7.12916 −0.988637
\(53\) −5.15842 −0.708564 −0.354282 0.935139i \(-0.615275\pi\)
−0.354282 + 0.935139i \(0.615275\pi\)
\(54\) 2.49098 0.338979
\(55\) −2.85871 −0.385469
\(56\) 1.38845 0.185539
\(57\) −8.58286 −1.13683
\(58\) 15.6979 2.06123
\(59\) −9.03502 −1.17626 −0.588129 0.808767i \(-0.700135\pi\)
−0.588129 + 0.808767i \(0.700135\pi\)
\(60\) 13.8767 1.79148
\(61\) −2.97621 −0.381064 −0.190532 0.981681i \(-0.561021\pi\)
−0.190532 + 0.981681i \(0.561021\pi\)
\(62\) 0.976961 0.124074
\(63\) −0.252788 −0.0318482
\(64\) −5.19553 −0.649442
\(65\) 5.59498 0.693972
\(66\) 2.15783 0.265610
\(67\) 15.5848 1.90398 0.951992 0.306122i \(-0.0990315\pi\)
0.951992 + 0.306122i \(0.0990315\pi\)
\(68\) 27.4925 3.33396
\(69\) 0.330861 0.0398310
\(70\) −2.07802 −0.248371
\(71\) −12.4476 −1.47725 −0.738627 0.674114i \(-0.764526\pi\)
−0.738627 + 0.674114i \(0.764526\pi\)
\(72\) −5.49255 −0.647304
\(73\) −3.53769 −0.414055 −0.207028 0.978335i \(-0.566379\pi\)
−0.207028 + 0.978335i \(0.566379\pi\)
\(74\) 10.2608 1.19280
\(75\) −5.89049 −0.680175
\(76\) 36.0908 4.13989
\(77\) −0.218979 −0.0249550
\(78\) −4.22323 −0.478187
\(79\) 10.0125 1.12650 0.563249 0.826287i \(-0.309551\pi\)
0.563249 + 0.826287i \(0.309551\pi\)
\(80\) −17.3976 −1.94511
\(81\) 1.00000 0.111111
\(82\) 13.6502 1.50741
\(83\) 0.830870 0.0911998 0.0455999 0.998960i \(-0.485480\pi\)
0.0455999 + 0.998960i \(0.485480\pi\)
\(84\) 1.06297 0.115979
\(85\) −21.5762 −2.34027
\(86\) −9.73983 −1.05027
\(87\) 6.30189 0.675634
\(88\) −4.75797 −0.507201
\(89\) 9.43735 1.00036 0.500178 0.865922i \(-0.333268\pi\)
0.500178 + 0.865922i \(0.333268\pi\)
\(90\) 8.22041 0.866508
\(91\) 0.428579 0.0449273
\(92\) −1.39126 −0.145049
\(93\) 0.392200 0.0406692
\(94\) 13.2973 1.37151
\(95\) −28.3241 −2.90599
\(96\) 2.14704 0.219131
\(97\) 4.48288 0.455167 0.227584 0.973759i \(-0.426918\pi\)
0.227584 + 0.973759i \(0.426918\pi\)
\(98\) 17.2777 1.74531
\(99\) 0.866258 0.0870622
\(100\) 24.7694 2.47694
\(101\) −9.49629 −0.944917 −0.472458 0.881353i \(-0.656633\pi\)
−0.472458 + 0.881353i \(0.656633\pi\)
\(102\) 16.2862 1.61258
\(103\) 5.02397 0.495026 0.247513 0.968885i \(-0.420387\pi\)
0.247513 + 0.968885i \(0.420387\pi\)
\(104\) 9.31213 0.913129
\(105\) −0.834218 −0.0814113
\(106\) 12.8495 1.24806
\(107\) 14.2898 1.38145 0.690725 0.723118i \(-0.257292\pi\)
0.690725 + 0.723118i \(0.257292\pi\)
\(108\) −4.20498 −0.404624
\(109\) 10.5485 1.01036 0.505182 0.863013i \(-0.331425\pi\)
0.505182 + 0.863013i \(0.331425\pi\)
\(110\) 7.12100 0.678960
\(111\) 4.11920 0.390977
\(112\) −1.33267 −0.125925
\(113\) 3.77217 0.354856 0.177428 0.984134i \(-0.443222\pi\)
0.177428 + 0.984134i \(0.443222\pi\)
\(114\) 21.3797 2.00240
\(115\) 1.09187 0.101817
\(116\) −26.4993 −2.46040
\(117\) −1.69541 −0.156741
\(118\) 22.5060 2.07185
\(119\) −1.65275 −0.151507
\(120\) −18.1258 −1.65465
\(121\) −10.2496 −0.931782
\(122\) 7.41367 0.671202
\(123\) 5.47986 0.494102
\(124\) −1.64919 −0.148102
\(125\) −2.93867 −0.262843
\(126\) 0.629689 0.0560971
\(127\) −1.64141 −0.145652 −0.0728258 0.997345i \(-0.523202\pi\)
−0.0728258 + 0.997345i \(0.523202\pi\)
\(128\) 17.2360 1.52347
\(129\) −3.91004 −0.344260
\(130\) −13.9370 −1.22235
\(131\) 11.2097 0.979400 0.489700 0.871891i \(-0.337106\pi\)
0.489700 + 0.871891i \(0.337106\pi\)
\(132\) −3.64259 −0.317047
\(133\) −2.16964 −0.188132
\(134\) −38.8214 −3.35366
\(135\) 3.30007 0.284025
\(136\) −35.9108 −3.07933
\(137\) −7.67703 −0.655893 −0.327947 0.944696i \(-0.606357\pi\)
−0.327947 + 0.944696i \(0.606357\pi\)
\(138\) −0.824169 −0.0701579
\(139\) −7.14740 −0.606234 −0.303117 0.952953i \(-0.598027\pi\)
−0.303117 + 0.952953i \(0.598027\pi\)
\(140\) 3.50787 0.296469
\(141\) 5.33816 0.449554
\(142\) 31.0066 2.60202
\(143\) −1.46866 −0.122816
\(144\) 5.27188 0.439323
\(145\) 20.7967 1.72707
\(146\) 8.81231 0.729312
\(147\) 6.93610 0.572080
\(148\) −17.3212 −1.42379
\(149\) −6.68129 −0.547352 −0.273676 0.961822i \(-0.588240\pi\)
−0.273676 + 0.961822i \(0.588240\pi\)
\(150\) 14.6731 1.19805
\(151\) −14.6051 −1.18855 −0.594273 0.804263i \(-0.702560\pi\)
−0.594273 + 0.804263i \(0.702560\pi\)
\(152\) −47.1418 −3.82371
\(153\) 6.53809 0.528573
\(154\) 0.545473 0.0439554
\(155\) 1.29429 0.103960
\(156\) 7.12916 0.570790
\(157\) 15.5162 1.23833 0.619166 0.785260i \(-0.287471\pi\)
0.619166 + 0.785260i \(0.287471\pi\)
\(158\) −24.9410 −1.98420
\(159\) 5.15842 0.409089
\(160\) 7.08538 0.560149
\(161\) 0.0836377 0.00659157
\(162\) −2.49098 −0.195710
\(163\) 24.1841 1.89425 0.947123 0.320870i \(-0.103975\pi\)
0.947123 + 0.320870i \(0.103975\pi\)
\(164\) −23.0427 −1.79933
\(165\) 2.85871 0.222551
\(166\) −2.06968 −0.160638
\(167\) 6.18236 0.478405 0.239203 0.970970i \(-0.423114\pi\)
0.239203 + 0.970970i \(0.423114\pi\)
\(168\) −1.38845 −0.107121
\(169\) −10.1256 −0.778891
\(170\) 53.7458 4.12212
\(171\) 8.58286 0.656348
\(172\) 16.4416 1.25366
\(173\) −11.3238 −0.860935 −0.430467 0.902606i \(-0.641651\pi\)
−0.430467 + 0.902606i \(0.641651\pi\)
\(174\) −15.6979 −1.19005
\(175\) −1.48904 −0.112561
\(176\) 4.56681 0.344236
\(177\) 9.03502 0.679113
\(178\) −23.5082 −1.76202
\(179\) −4.52948 −0.338549 −0.169274 0.985569i \(-0.554142\pi\)
−0.169274 + 0.985569i \(0.554142\pi\)
\(180\) −13.8767 −1.03431
\(181\) 5.61638 0.417462 0.208731 0.977973i \(-0.433067\pi\)
0.208731 + 0.977973i \(0.433067\pi\)
\(182\) −1.06758 −0.0791343
\(183\) 2.97621 0.220008
\(184\) 1.81727 0.133971
\(185\) 13.5937 0.999427
\(186\) −0.976961 −0.0716343
\(187\) 5.66367 0.414169
\(188\) −22.4469 −1.63710
\(189\) 0.252788 0.0183876
\(190\) 70.5547 5.11858
\(191\) 2.52502 0.182704 0.0913521 0.995819i \(-0.470881\pi\)
0.0913521 + 0.995819i \(0.470881\pi\)
\(192\) 5.19553 0.374955
\(193\) −2.24897 −0.161884 −0.0809420 0.996719i \(-0.525793\pi\)
−0.0809420 + 0.996719i \(0.525793\pi\)
\(194\) −11.1667 −0.801726
\(195\) −5.59498 −0.400665
\(196\) −29.1661 −2.08330
\(197\) 1.39271 0.0992266 0.0496133 0.998769i \(-0.484201\pi\)
0.0496133 + 0.998769i \(0.484201\pi\)
\(198\) −2.15783 −0.153350
\(199\) 10.1436 0.719063 0.359531 0.933133i \(-0.382937\pi\)
0.359531 + 0.933133i \(0.382937\pi\)
\(200\) −32.3538 −2.28776
\(201\) −15.5848 −1.09927
\(202\) 23.6551 1.66437
\(203\) 1.59304 0.111809
\(204\) −27.4925 −1.92486
\(205\) 18.0839 1.26304
\(206\) −12.5146 −0.871933
\(207\) −0.330861 −0.0229965
\(208\) −8.93800 −0.619739
\(209\) 7.43497 0.514288
\(210\) 2.07802 0.143397
\(211\) −1.50575 −0.103660 −0.0518302 0.998656i \(-0.516505\pi\)
−0.0518302 + 0.998656i \(0.516505\pi\)
\(212\) −21.6910 −1.48975
\(213\) 12.4476 0.852893
\(214\) −35.5957 −2.43327
\(215\) −12.9034 −0.880006
\(216\) 5.49255 0.373721
\(217\) 0.0991432 0.00673028
\(218\) −26.2761 −1.77964
\(219\) 3.53769 0.239055
\(220\) −12.0208 −0.810444
\(221\) −11.0847 −0.745641
\(222\) −10.2608 −0.688663
\(223\) 16.5754 1.10997 0.554984 0.831861i \(-0.312724\pi\)
0.554984 + 0.831861i \(0.312724\pi\)
\(224\) 0.542745 0.0362636
\(225\) 5.89049 0.392699
\(226\) −9.39641 −0.625040
\(227\) 2.28245 0.151491 0.0757457 0.997127i \(-0.475866\pi\)
0.0757457 + 0.997127i \(0.475866\pi\)
\(228\) −36.0908 −2.39017
\(229\) −0.491074 −0.0324511 −0.0162255 0.999868i \(-0.505165\pi\)
−0.0162255 + 0.999868i \(0.505165\pi\)
\(230\) −2.71982 −0.179339
\(231\) 0.218979 0.0144078
\(232\) 34.6135 2.27249
\(233\) 9.77908 0.640649 0.320325 0.947308i \(-0.396208\pi\)
0.320325 + 0.947308i \(0.396208\pi\)
\(234\) 4.22323 0.276081
\(235\) 17.6163 1.14916
\(236\) −37.9920 −2.47307
\(237\) −10.0125 −0.650384
\(238\) 4.11696 0.266863
\(239\) 13.0928 0.846901 0.423451 0.905919i \(-0.360819\pi\)
0.423451 + 0.905919i \(0.360819\pi\)
\(240\) 17.3976 1.12301
\(241\) −25.4302 −1.63810 −0.819052 0.573719i \(-0.805500\pi\)
−0.819052 + 0.573719i \(0.805500\pi\)
\(242\) 25.5315 1.64123
\(243\) −1.00000 −0.0641500
\(244\) −12.5149 −0.801184
\(245\) 22.8896 1.46237
\(246\) −13.6502 −0.870306
\(247\) −14.5515 −0.925888
\(248\) 2.15418 0.136790
\(249\) −0.830870 −0.0526543
\(250\) 7.32016 0.462968
\(251\) −24.2725 −1.53207 −0.766034 0.642801i \(-0.777772\pi\)
−0.766034 + 0.642801i \(0.777772\pi\)
\(252\) −1.06297 −0.0669606
\(253\) −0.286611 −0.0180191
\(254\) 4.08872 0.256549
\(255\) 21.5762 1.35115
\(256\) −32.5436 −2.03397
\(257\) −2.97237 −0.185411 −0.0927056 0.995694i \(-0.529552\pi\)
−0.0927056 + 0.995694i \(0.529552\pi\)
\(258\) 9.73983 0.606375
\(259\) 1.04128 0.0647022
\(260\) 23.5268 1.45907
\(261\) −6.30189 −0.390077
\(262\) −27.9232 −1.72510
\(263\) 13.7085 0.845300 0.422650 0.906293i \(-0.361100\pi\)
0.422650 + 0.906293i \(0.361100\pi\)
\(264\) 4.75797 0.292833
\(265\) 17.0232 1.04572
\(266\) 5.40453 0.331373
\(267\) −9.43735 −0.577556
\(268\) 65.5337 4.00311
\(269\) 11.7569 0.716833 0.358417 0.933562i \(-0.383317\pi\)
0.358417 + 0.933562i \(0.383317\pi\)
\(270\) −8.22041 −0.500279
\(271\) −12.4951 −0.759023 −0.379511 0.925187i \(-0.623908\pi\)
−0.379511 + 0.925187i \(0.623908\pi\)
\(272\) 34.4680 2.08993
\(273\) −0.428579 −0.0259388
\(274\) 19.1233 1.15528
\(275\) 5.10268 0.307703
\(276\) 1.39126 0.0837443
\(277\) −30.6336 −1.84059 −0.920297 0.391221i \(-0.872053\pi\)
−0.920297 + 0.391221i \(0.872053\pi\)
\(278\) 17.8040 1.06781
\(279\) −0.392200 −0.0234804
\(280\) −4.58198 −0.273826
\(281\) −12.9428 −0.772104 −0.386052 0.922477i \(-0.626162\pi\)
−0.386052 + 0.922477i \(0.626162\pi\)
\(282\) −13.2973 −0.791840
\(283\) 23.2299 1.38087 0.690436 0.723394i \(-0.257419\pi\)
0.690436 + 0.723394i \(0.257419\pi\)
\(284\) −52.3417 −3.10591
\(285\) 28.3241 1.67777
\(286\) 3.65841 0.216326
\(287\) 1.38524 0.0817682
\(288\) −2.14704 −0.126515
\(289\) 25.7466 1.51451
\(290\) −51.8042 −3.04205
\(291\) −4.48288 −0.262791
\(292\) −14.8759 −0.870547
\(293\) 16.3329 0.954177 0.477088 0.878855i \(-0.341692\pi\)
0.477088 + 0.878855i \(0.341692\pi\)
\(294\) −17.2777 −1.00765
\(295\) 29.8162 1.73597
\(296\) 22.6249 1.31505
\(297\) −0.866258 −0.0502654
\(298\) 16.6429 0.964100
\(299\) 0.560946 0.0324403
\(300\) −24.7694 −1.43006
\(301\) −0.988409 −0.0569710
\(302\) 36.3810 2.09349
\(303\) 9.49629 0.545548
\(304\) 45.2478 2.59514
\(305\) 9.82171 0.562389
\(306\) −16.2862 −0.931023
\(307\) −5.52388 −0.315264 −0.157632 0.987498i \(-0.550386\pi\)
−0.157632 + 0.987498i \(0.550386\pi\)
\(308\) −0.920803 −0.0524676
\(309\) −5.02397 −0.285803
\(310\) −3.22404 −0.183113
\(311\) 0.610266 0.0346050 0.0173025 0.999850i \(-0.494492\pi\)
0.0173025 + 0.999850i \(0.494492\pi\)
\(312\) −9.31213 −0.527196
\(313\) 24.6675 1.39429 0.697146 0.716929i \(-0.254453\pi\)
0.697146 + 0.716929i \(0.254453\pi\)
\(314\) −38.6506 −2.18118
\(315\) 0.834218 0.0470028
\(316\) 42.1025 2.36845
\(317\) −29.2000 −1.64003 −0.820016 0.572340i \(-0.806036\pi\)
−0.820016 + 0.572340i \(0.806036\pi\)
\(318\) −12.8495 −0.720565
\(319\) −5.45906 −0.305649
\(320\) 17.1456 0.958471
\(321\) −14.2898 −0.797580
\(322\) −0.208340 −0.0116103
\(323\) 56.1155 3.12235
\(324\) 4.20498 0.233610
\(325\) −9.98679 −0.553967
\(326\) −60.2421 −3.33650
\(327\) −10.5485 −0.583334
\(328\) 30.0984 1.66191
\(329\) 1.34942 0.0743960
\(330\) −7.12100 −0.391998
\(331\) −21.1649 −1.16333 −0.581665 0.813429i \(-0.697598\pi\)
−0.581665 + 0.813429i \(0.697598\pi\)
\(332\) 3.49379 0.191747
\(333\) −4.11920 −0.225731
\(334\) −15.4001 −0.842657
\(335\) −51.4309 −2.80997
\(336\) 1.33267 0.0727029
\(337\) −33.1359 −1.80503 −0.902513 0.430662i \(-0.858280\pi\)
−0.902513 + 0.430662i \(0.858280\pi\)
\(338\) 25.2226 1.37193
\(339\) −3.77217 −0.204876
\(340\) −90.7273 −4.92038
\(341\) −0.339746 −0.0183983
\(342\) −21.3797 −1.15608
\(343\) 3.52287 0.190217
\(344\) −21.4761 −1.15791
\(345\) −1.09187 −0.0587841
\(346\) 28.2074 1.51644
\(347\) 10.1332 0.543980 0.271990 0.962300i \(-0.412318\pi\)
0.271990 + 0.962300i \(0.412318\pi\)
\(348\) 26.4993 1.42051
\(349\) −22.4799 −1.20332 −0.601660 0.798752i \(-0.705494\pi\)
−0.601660 + 0.798752i \(0.705494\pi\)
\(350\) 3.70917 0.198264
\(351\) 1.69541 0.0904943
\(352\) −1.85989 −0.0991324
\(353\) −32.6651 −1.73859 −0.869293 0.494297i \(-0.835425\pi\)
−0.869293 + 0.494297i \(0.835425\pi\)
\(354\) −22.5060 −1.19618
\(355\) 41.0779 2.18019
\(356\) 39.6838 2.10324
\(357\) 1.65275 0.0874727
\(358\) 11.2828 0.596316
\(359\) 6.08836 0.321331 0.160666 0.987009i \(-0.448636\pi\)
0.160666 + 0.987009i \(0.448636\pi\)
\(360\) 18.1258 0.955315
\(361\) 54.6656 2.87713
\(362\) −13.9903 −0.735313
\(363\) 10.2496 0.537964
\(364\) 1.80216 0.0944590
\(365\) 11.6746 0.611078
\(366\) −7.41367 −0.387519
\(367\) −8.13070 −0.424419 −0.212210 0.977224i \(-0.568066\pi\)
−0.212210 + 0.977224i \(0.568066\pi\)
\(368\) −1.74426 −0.0909259
\(369\) −5.47986 −0.285270
\(370\) −33.8616 −1.76038
\(371\) 1.30398 0.0676995
\(372\) 1.64919 0.0855066
\(373\) −16.8537 −0.872651 −0.436326 0.899789i \(-0.643720\pi\)
−0.436326 + 0.899789i \(0.643720\pi\)
\(374\) −14.1081 −0.729512
\(375\) 2.93867 0.151752
\(376\) 29.3201 1.51207
\(377\) 10.6843 0.550269
\(378\) −0.629689 −0.0323877
\(379\) −12.4834 −0.641229 −0.320614 0.947210i \(-0.603889\pi\)
−0.320614 + 0.947210i \(0.603889\pi\)
\(380\) −119.102 −6.10981
\(381\) 1.64141 0.0840919
\(382\) −6.28978 −0.321813
\(383\) −7.27147 −0.371555 −0.185777 0.982592i \(-0.559480\pi\)
−0.185777 + 0.982592i \(0.559480\pi\)
\(384\) −17.2360 −0.879573
\(385\) 0.722648 0.0368295
\(386\) 5.60213 0.285141
\(387\) 3.91004 0.198758
\(388\) 18.8504 0.956983
\(389\) 12.4577 0.631633 0.315816 0.948820i \(-0.397722\pi\)
0.315816 + 0.948820i \(0.397722\pi\)
\(390\) 13.9370 0.705726
\(391\) −2.16320 −0.109398
\(392\) 38.0969 1.92418
\(393\) −11.2097 −0.565457
\(394\) −3.46922 −0.174777
\(395\) −33.0421 −1.66253
\(396\) 3.64259 0.183047
\(397\) −28.0490 −1.40774 −0.703870 0.710329i \(-0.748546\pi\)
−0.703870 + 0.710329i \(0.748546\pi\)
\(398\) −25.2676 −1.26655
\(399\) 2.16964 0.108618
\(400\) 31.0539 1.55270
\(401\) 28.9364 1.44502 0.722509 0.691362i \(-0.242989\pi\)
0.722509 + 0.691362i \(0.242989\pi\)
\(402\) 38.8214 1.93623
\(403\) 0.664939 0.0331230
\(404\) −39.9317 −1.98668
\(405\) −3.30007 −0.163982
\(406\) −3.96823 −0.196940
\(407\) −3.56829 −0.176874
\(408\) 35.9108 1.77785
\(409\) 15.1959 0.751387 0.375694 0.926744i \(-0.377405\pi\)
0.375694 + 0.926744i \(0.377405\pi\)
\(410\) −45.0467 −2.22470
\(411\) 7.67703 0.378680
\(412\) 21.1257 1.04079
\(413\) 2.28394 0.112385
\(414\) 0.824169 0.0405057
\(415\) −2.74193 −0.134596
\(416\) 3.64011 0.178471
\(417\) 7.14740 0.350010
\(418\) −18.5204 −0.905860
\(419\) −13.6956 −0.669076 −0.334538 0.942382i \(-0.608580\pi\)
−0.334538 + 0.942382i \(0.608580\pi\)
\(420\) −3.50787 −0.171166
\(421\) 29.3738 1.43159 0.715796 0.698310i \(-0.246064\pi\)
0.715796 + 0.698310i \(0.246064\pi\)
\(422\) 3.75080 0.182586
\(423\) −5.33816 −0.259550
\(424\) 28.3329 1.37597
\(425\) 38.5125 1.86813
\(426\) −31.0066 −1.50228
\(427\) 0.752349 0.0364087
\(428\) 60.0884 2.90448
\(429\) 1.46866 0.0709077
\(430\) 32.1421 1.55003
\(431\) 0.295952 0.0142555 0.00712776 0.999975i \(-0.497731\pi\)
0.00712776 + 0.999975i \(0.497731\pi\)
\(432\) −5.27188 −0.253643
\(433\) 13.6064 0.653882 0.326941 0.945045i \(-0.393982\pi\)
0.326941 + 0.945045i \(0.393982\pi\)
\(434\) −0.246964 −0.0118546
\(435\) −20.7967 −0.997126
\(436\) 44.3563 2.12428
\(437\) −2.83974 −0.135843
\(438\) −8.81231 −0.421069
\(439\) −10.0809 −0.481136 −0.240568 0.970632i \(-0.577334\pi\)
−0.240568 + 0.970632i \(0.577334\pi\)
\(440\) 15.7016 0.748546
\(441\) −6.93610 −0.330290
\(442\) 27.6119 1.31336
\(443\) 4.17952 0.198575 0.0992874 0.995059i \(-0.468344\pi\)
0.0992874 + 0.995059i \(0.468344\pi\)
\(444\) 17.3212 0.822026
\(445\) −31.1439 −1.47636
\(446\) −41.2889 −1.95508
\(447\) 6.68129 0.316014
\(448\) 1.31337 0.0620507
\(449\) 36.3050 1.71334 0.856669 0.515866i \(-0.172530\pi\)
0.856669 + 0.515866i \(0.172530\pi\)
\(450\) −14.6731 −0.691696
\(451\) −4.74697 −0.223526
\(452\) 15.8619 0.746081
\(453\) 14.6051 0.686207
\(454\) −5.68553 −0.266835
\(455\) −1.41434 −0.0663053
\(456\) 47.1418 2.20762
\(457\) −8.42188 −0.393959 −0.196980 0.980408i \(-0.563113\pi\)
−0.196980 + 0.980408i \(0.563113\pi\)
\(458\) 1.22325 0.0571589
\(459\) −6.53809 −0.305172
\(460\) 4.59128 0.214069
\(461\) 16.6185 0.774000 0.387000 0.922080i \(-0.373511\pi\)
0.387000 + 0.922080i \(0.373511\pi\)
\(462\) −0.545473 −0.0253777
\(463\) −12.3387 −0.573429 −0.286715 0.958016i \(-0.592563\pi\)
−0.286715 + 0.958016i \(0.592563\pi\)
\(464\) −33.2228 −1.54233
\(465\) −1.29429 −0.0600212
\(466\) −24.3595 −1.12843
\(467\) 6.44956 0.298450 0.149225 0.988803i \(-0.452322\pi\)
0.149225 + 0.988803i \(0.452322\pi\)
\(468\) −7.12916 −0.329546
\(469\) −3.93964 −0.181916
\(470\) −43.8819 −2.02412
\(471\) −15.5162 −0.714951
\(472\) 49.6253 2.28419
\(473\) 3.38710 0.155739
\(474\) 24.9410 1.14558
\(475\) 50.5572 2.31973
\(476\) −6.94977 −0.318542
\(477\) −5.15842 −0.236188
\(478\) −32.6138 −1.49172
\(479\) −3.46978 −0.158539 −0.0792693 0.996853i \(-0.525259\pi\)
−0.0792693 + 0.996853i \(0.525259\pi\)
\(480\) −7.08538 −0.323402
\(481\) 6.98374 0.318431
\(482\) 63.3462 2.88534
\(483\) −0.0836377 −0.00380565
\(484\) −43.0993 −1.95906
\(485\) −14.7938 −0.671753
\(486\) 2.49098 0.112993
\(487\) 33.8636 1.53451 0.767254 0.641343i \(-0.221623\pi\)
0.767254 + 0.641343i \(0.221623\pi\)
\(488\) 16.3470 0.739993
\(489\) −24.1841 −1.09364
\(490\) −57.0176 −2.57579
\(491\) 25.5921 1.15495 0.577477 0.816407i \(-0.304037\pi\)
0.577477 + 0.816407i \(0.304037\pi\)
\(492\) 23.0427 1.03884
\(493\) −41.2023 −1.85566
\(494\) 36.2474 1.63085
\(495\) −2.85871 −0.128490
\(496\) −2.06763 −0.0928393
\(497\) 3.14659 0.141144
\(498\) 2.06968 0.0927446
\(499\) −0.369851 −0.0165568 −0.00827841 0.999966i \(-0.502635\pi\)
−0.00827841 + 0.999966i \(0.502635\pi\)
\(500\) −12.3570 −0.552623
\(501\) −6.18236 −0.276207
\(502\) 60.4623 2.69857
\(503\) −5.14909 −0.229587 −0.114793 0.993389i \(-0.536621\pi\)
−0.114793 + 0.993389i \(0.536621\pi\)
\(504\) 1.38845 0.0618464
\(505\) 31.3385 1.39454
\(506\) 0.713943 0.0317386
\(507\) 10.1256 0.449693
\(508\) −6.90209 −0.306231
\(509\) 38.5337 1.70798 0.853988 0.520293i \(-0.174177\pi\)
0.853988 + 0.520293i \(0.174177\pi\)
\(510\) −53.7458 −2.37990
\(511\) 0.894284 0.0395608
\(512\) 46.5932 2.05915
\(513\) −8.58286 −0.378943
\(514\) 7.40410 0.326581
\(515\) −16.5795 −0.730578
\(516\) −16.4416 −0.723802
\(517\) −4.62422 −0.203373
\(518\) −2.59382 −0.113966
\(519\) 11.3238 0.497061
\(520\) −30.7307 −1.34763
\(521\) 5.61476 0.245987 0.122993 0.992407i \(-0.460751\pi\)
0.122993 + 0.992407i \(0.460751\pi\)
\(522\) 15.6979 0.687078
\(523\) −24.0678 −1.05241 −0.526205 0.850358i \(-0.676386\pi\)
−0.526205 + 0.850358i \(0.676386\pi\)
\(524\) 47.1367 2.05918
\(525\) 1.48904 0.0649871
\(526\) −34.1475 −1.48890
\(527\) −2.56424 −0.111700
\(528\) −4.56681 −0.198745
\(529\) −22.8905 −0.995240
\(530\) −42.4044 −1.84193
\(531\) −9.03502 −0.392086
\(532\) −9.12329 −0.395545
\(533\) 9.29061 0.402421
\(534\) 23.5082 1.01730
\(535\) −47.1575 −2.03880
\(536\) −85.6003 −3.69737
\(537\) 4.52948 0.195461
\(538\) −29.2863 −1.26262
\(539\) −6.00845 −0.258802
\(540\) 13.8767 0.597160
\(541\) −4.40018 −0.189179 −0.0945893 0.995516i \(-0.530154\pi\)
−0.0945893 + 0.995516i \(0.530154\pi\)
\(542\) 31.1250 1.33693
\(543\) −5.61638 −0.241022
\(544\) −14.0375 −0.601854
\(545\) −34.8109 −1.49113
\(546\) 1.06758 0.0456882
\(547\) 38.0465 1.62675 0.813375 0.581740i \(-0.197628\pi\)
0.813375 + 0.581740i \(0.197628\pi\)
\(548\) −32.2817 −1.37901
\(549\) −2.97621 −0.127021
\(550\) −12.7107 −0.541985
\(551\) −54.0883 −2.30424
\(552\) −1.81727 −0.0773483
\(553\) −2.53104 −0.107631
\(554\) 76.3076 3.24200
\(555\) −13.5937 −0.577019
\(556\) −30.0546 −1.27460
\(557\) −7.37486 −0.312483 −0.156241 0.987719i \(-0.549938\pi\)
−0.156241 + 0.987719i \(0.549938\pi\)
\(558\) 0.976961 0.0413581
\(559\) −6.62912 −0.280382
\(560\) 4.39790 0.185845
\(561\) −5.66367 −0.239120
\(562\) 32.2403 1.35998
\(563\) −13.1356 −0.553600 −0.276800 0.960928i \(-0.589274\pi\)
−0.276800 + 0.960928i \(0.589274\pi\)
\(564\) 22.4469 0.945183
\(565\) −12.4485 −0.523710
\(566\) −57.8651 −2.43225
\(567\) −0.252788 −0.0106161
\(568\) 68.3689 2.86870
\(569\) 27.5793 1.15618 0.578092 0.815972i \(-0.303797\pi\)
0.578092 + 0.815972i \(0.303797\pi\)
\(570\) −70.5547 −2.95521
\(571\) 36.0366 1.50808 0.754042 0.656826i \(-0.228102\pi\)
0.754042 + 0.656826i \(0.228102\pi\)
\(572\) −6.17569 −0.258219
\(573\) −2.52502 −0.105484
\(574\) −3.45061 −0.144026
\(575\) −1.94893 −0.0812762
\(576\) −5.19553 −0.216481
\(577\) −26.5890 −1.10691 −0.553457 0.832878i \(-0.686692\pi\)
−0.553457 + 0.832878i \(0.686692\pi\)
\(578\) −64.1343 −2.66763
\(579\) 2.24897 0.0934638
\(580\) 87.4497 3.63115
\(581\) −0.210034 −0.00871367
\(582\) 11.1667 0.462877
\(583\) −4.46852 −0.185067
\(584\) 19.4309 0.804058
\(585\) 5.59498 0.231324
\(586\) −40.6849 −1.68068
\(587\) 9.91669 0.409306 0.204653 0.978835i \(-0.434393\pi\)
0.204653 + 0.978835i \(0.434393\pi\)
\(588\) 29.1661 1.20279
\(589\) −3.36620 −0.138702
\(590\) −74.2716 −3.05771
\(591\) −1.39271 −0.0572885
\(592\) −21.7159 −0.892520
\(593\) −46.1857 −1.89662 −0.948310 0.317344i \(-0.897209\pi\)
−0.948310 + 0.317344i \(0.897209\pi\)
\(594\) 2.15783 0.0885368
\(595\) 5.45419 0.223600
\(596\) −28.0947 −1.15080
\(597\) −10.1436 −0.415151
\(598\) −1.39730 −0.0571400
\(599\) 23.0878 0.943342 0.471671 0.881775i \(-0.343651\pi\)
0.471671 + 0.881775i \(0.343651\pi\)
\(600\) 32.3538 1.32084
\(601\) −13.2257 −0.539488 −0.269744 0.962932i \(-0.586939\pi\)
−0.269744 + 0.962932i \(0.586939\pi\)
\(602\) 2.46211 0.100348
\(603\) 15.5848 0.634662
\(604\) −61.4141 −2.49890
\(605\) 33.8244 1.37516
\(606\) −23.6551 −0.960922
\(607\) −38.3276 −1.55567 −0.777834 0.628470i \(-0.783682\pi\)
−0.777834 + 0.628470i \(0.783682\pi\)
\(608\) −18.4277 −0.747343
\(609\) −1.59304 −0.0645532
\(610\) −24.4657 −0.990586
\(611\) 9.05037 0.366139
\(612\) 27.4925 1.11132
\(613\) −36.9493 −1.49237 −0.746184 0.665740i \(-0.768116\pi\)
−0.746184 + 0.665740i \(0.768116\pi\)
\(614\) 13.7599 0.555303
\(615\) −18.0839 −0.729215
\(616\) 1.20275 0.0484604
\(617\) −34.6841 −1.39633 −0.698164 0.715938i \(-0.745999\pi\)
−0.698164 + 0.715938i \(0.745999\pi\)
\(618\) 12.5146 0.503411
\(619\) −18.4086 −0.739906 −0.369953 0.929050i \(-0.620626\pi\)
−0.369953 + 0.929050i \(0.620626\pi\)
\(620\) 5.44245 0.218574
\(621\) 0.330861 0.0132770
\(622\) −1.52016 −0.0609529
\(623\) −2.38564 −0.0955788
\(624\) 8.93800 0.357806
\(625\) −19.7546 −0.790184
\(626\) −61.4463 −2.45589
\(627\) −7.43497 −0.296924
\(628\) 65.2455 2.60358
\(629\) −26.9317 −1.07384
\(630\) −2.07802 −0.0827903
\(631\) 5.93731 0.236360 0.118180 0.992992i \(-0.462294\pi\)
0.118180 + 0.992992i \(0.462294\pi\)
\(632\) −54.9943 −2.18756
\(633\) 1.50575 0.0598483
\(634\) 72.7365 2.88873
\(635\) 5.41677 0.214958
\(636\) 21.6910 0.860106
\(637\) 11.7595 0.465930
\(638\) 13.5984 0.538366
\(639\) −12.4476 −0.492418
\(640\) −56.8802 −2.24839
\(641\) −15.1781 −0.599498 −0.299749 0.954018i \(-0.596903\pi\)
−0.299749 + 0.954018i \(0.596903\pi\)
\(642\) 35.5957 1.40485
\(643\) 2.38802 0.0941745 0.0470873 0.998891i \(-0.485006\pi\)
0.0470873 + 0.998891i \(0.485006\pi\)
\(644\) 0.351694 0.0138587
\(645\) 12.9034 0.508072
\(646\) −139.783 −5.49967
\(647\) 19.6234 0.771475 0.385737 0.922609i \(-0.373947\pi\)
0.385737 + 0.922609i \(0.373947\pi\)
\(648\) −5.49255 −0.215768
\(649\) −7.82665 −0.307223
\(650\) 24.8769 0.975752
\(651\) −0.0991432 −0.00388573
\(652\) 101.694 3.98263
\(653\) −0.817489 −0.0319908 −0.0159954 0.999872i \(-0.505092\pi\)
−0.0159954 + 0.999872i \(0.505092\pi\)
\(654\) 26.2761 1.02748
\(655\) −36.9930 −1.44544
\(656\) −28.8892 −1.12793
\(657\) −3.53769 −0.138018
\(658\) −3.36138 −0.131040
\(659\) −20.6687 −0.805138 −0.402569 0.915390i \(-0.631883\pi\)
−0.402569 + 0.915390i \(0.631883\pi\)
\(660\) 12.0208 0.467910
\(661\) 3.44613 0.134039 0.0670195 0.997752i \(-0.478651\pi\)
0.0670195 + 0.997752i \(0.478651\pi\)
\(662\) 52.7214 2.04907
\(663\) 11.0847 0.430496
\(664\) −4.56360 −0.177102
\(665\) 7.15998 0.277652
\(666\) 10.2608 0.397600
\(667\) 2.08505 0.0807336
\(668\) 25.9967 1.00584
\(669\) −16.5754 −0.640840
\(670\) 128.113 4.94945
\(671\) −2.57816 −0.0995289
\(672\) −0.542745 −0.0209368
\(673\) 40.1017 1.54581 0.772903 0.634524i \(-0.218804\pi\)
0.772903 + 0.634524i \(0.218804\pi\)
\(674\) 82.5408 3.17935
\(675\) −5.89049 −0.226725
\(676\) −42.5779 −1.63761
\(677\) 23.4290 0.900450 0.450225 0.892915i \(-0.351344\pi\)
0.450225 + 0.892915i \(0.351344\pi\)
\(678\) 9.39641 0.360867
\(679\) −1.13322 −0.0434888
\(680\) 118.508 4.54459
\(681\) −2.28245 −0.0874636
\(682\) 0.846300 0.0324065
\(683\) 25.6193 0.980294 0.490147 0.871640i \(-0.336943\pi\)
0.490147 + 0.871640i \(0.336943\pi\)
\(684\) 36.0908 1.37996
\(685\) 25.3348 0.967992
\(686\) −8.77540 −0.335046
\(687\) 0.491074 0.0187356
\(688\) 20.6133 0.785873
\(689\) 8.74564 0.333182
\(690\) 2.71982 0.103542
\(691\) 1.82421 0.0693962 0.0346981 0.999398i \(-0.488953\pi\)
0.0346981 + 0.999398i \(0.488953\pi\)
\(692\) −47.6164 −1.81011
\(693\) −0.218979 −0.00831833
\(694\) −25.2416 −0.958159
\(695\) 23.5869 0.894704
\(696\) −34.6135 −1.31202
\(697\) −35.8278 −1.35708
\(698\) 55.9969 2.11951
\(699\) −9.77908 −0.369879
\(700\) −6.26139 −0.236658
\(701\) −26.8568 −1.01437 −0.507184 0.861838i \(-0.669314\pi\)
−0.507184 + 0.861838i \(0.669314\pi\)
\(702\) −4.22323 −0.159396
\(703\) −35.3546 −1.33342
\(704\) −4.50067 −0.169625
\(705\) −17.6163 −0.663469
\(706\) 81.3680 3.06232
\(707\) 2.40055 0.0902818
\(708\) 37.9920 1.42783
\(709\) 15.1296 0.568205 0.284102 0.958794i \(-0.408304\pi\)
0.284102 + 0.958794i \(0.408304\pi\)
\(710\) −102.324 −3.84016
\(711\) 10.0125 0.375499
\(712\) −51.8351 −1.94260
\(713\) 0.129764 0.00485969
\(714\) −4.11696 −0.154073
\(715\) 4.84669 0.181256
\(716\) −19.0463 −0.711795
\(717\) −13.0928 −0.488959
\(718\) −15.1660 −0.565989
\(719\) −6.29821 −0.234884 −0.117442 0.993080i \(-0.537469\pi\)
−0.117442 + 0.993080i \(0.537469\pi\)
\(720\) −17.3976 −0.648370
\(721\) −1.27000 −0.0472971
\(722\) −136.171 −5.06775
\(723\) 25.4302 0.945760
\(724\) 23.6168 0.877710
\(725\) −37.1212 −1.37865
\(726\) −25.5315 −0.947564
\(727\) −15.4988 −0.574819 −0.287410 0.957808i \(-0.592794\pi\)
−0.287410 + 0.957808i \(0.592794\pi\)
\(728\) −2.35399 −0.0872447
\(729\) 1.00000 0.0370370
\(730\) −29.0813 −1.07635
\(731\) 25.5642 0.945526
\(732\) 12.5149 0.462564
\(733\) −14.8320 −0.547831 −0.273915 0.961754i \(-0.588319\pi\)
−0.273915 + 0.961754i \(0.588319\pi\)
\(734\) 20.2534 0.747567
\(735\) −22.8896 −0.844297
\(736\) 0.710372 0.0261847
\(737\) 13.5004 0.497295
\(738\) 13.6502 0.502471
\(739\) −32.7803 −1.20584 −0.602922 0.797800i \(-0.705997\pi\)
−0.602922 + 0.797800i \(0.705997\pi\)
\(740\) 57.1611 2.10128
\(741\) 14.5515 0.534562
\(742\) −3.24820 −0.119245
\(743\) −48.3011 −1.77199 −0.885997 0.463691i \(-0.846525\pi\)
−0.885997 + 0.463691i \(0.846525\pi\)
\(744\) −2.15418 −0.0789760
\(745\) 22.0487 0.807803
\(746\) 41.9822 1.53708
\(747\) 0.830870 0.0303999
\(748\) 23.8156 0.870785
\(749\) −3.61229 −0.131990
\(750\) −7.32016 −0.267295
\(751\) −48.0579 −1.75366 −0.876830 0.480801i \(-0.840346\pi\)
−0.876830 + 0.480801i \(0.840346\pi\)
\(752\) −28.1422 −1.02624
\(753\) 24.2725 0.884539
\(754\) −26.6143 −0.969237
\(755\) 48.1979 1.75410
\(756\) 1.06297 0.0386597
\(757\) 47.1476 1.71361 0.856805 0.515640i \(-0.172446\pi\)
0.856805 + 0.515640i \(0.172446\pi\)
\(758\) 31.0959 1.12945
\(759\) 0.286611 0.0104033
\(760\) 155.572 5.64317
\(761\) −12.6815 −0.459703 −0.229852 0.973226i \(-0.573824\pi\)
−0.229852 + 0.973226i \(0.573824\pi\)
\(762\) −4.08872 −0.148119
\(763\) −2.66653 −0.0965350
\(764\) 10.6177 0.384134
\(765\) −21.5762 −0.780088
\(766\) 18.1131 0.654452
\(767\) 15.3181 0.553103
\(768\) 32.5436 1.17431
\(769\) −52.7162 −1.90100 −0.950498 0.310730i \(-0.899427\pi\)
−0.950498 + 0.310730i \(0.899427\pi\)
\(770\) −1.80010 −0.0648711
\(771\) 2.97237 0.107047
\(772\) −9.45685 −0.340359
\(773\) 9.27871 0.333732 0.166866 0.985980i \(-0.446635\pi\)
0.166866 + 0.985980i \(0.446635\pi\)
\(774\) −9.73983 −0.350091
\(775\) −2.31025 −0.0829865
\(776\) −24.6224 −0.883894
\(777\) −1.04128 −0.0373558
\(778\) −31.0320 −1.11255
\(779\) −47.0329 −1.68513
\(780\) −23.5268 −0.842393
\(781\) −10.7828 −0.385839
\(782\) 5.38849 0.192692
\(783\) 6.30189 0.225211
\(784\) −36.5663 −1.30594
\(785\) −51.2047 −1.82758
\(786\) 27.9232 0.995989
\(787\) 40.2522 1.43483 0.717417 0.696644i \(-0.245324\pi\)
0.717417 + 0.696644i \(0.245324\pi\)
\(788\) 5.85632 0.208623
\(789\) −13.7085 −0.488034
\(790\) 82.3071 2.92836
\(791\) −0.953559 −0.0339047
\(792\) −4.75797 −0.169067
\(793\) 5.04589 0.179185
\(794\) 69.8695 2.47958
\(795\) −17.0232 −0.603750
\(796\) 42.6537 1.51182
\(797\) 7.09151 0.251194 0.125597 0.992081i \(-0.459915\pi\)
0.125597 + 0.992081i \(0.459915\pi\)
\(798\) −5.40453 −0.191318
\(799\) −34.9014 −1.23472
\(800\) −12.6471 −0.447142
\(801\) 9.43735 0.333452
\(802\) −72.0801 −2.54524
\(803\) −3.06455 −0.108146
\(804\) −65.5337 −2.31119
\(805\) −0.276010 −0.00972809
\(806\) −1.65635 −0.0583425
\(807\) −11.7569 −0.413864
\(808\) 52.1589 1.83494
\(809\) −27.8915 −0.980614 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(810\) 8.22041 0.288836
\(811\) −13.8111 −0.484972 −0.242486 0.970155i \(-0.577963\pi\)
−0.242486 + 0.970155i \(0.577963\pi\)
\(812\) 6.69870 0.235078
\(813\) 12.4951 0.438222
\(814\) 8.88854 0.311543
\(815\) −79.8094 −2.79560
\(816\) −34.4680 −1.20662
\(817\) 33.5593 1.17409
\(818\) −37.8526 −1.32348
\(819\) 0.428579 0.0149758
\(820\) 76.0426 2.65552
\(821\) −11.3110 −0.394757 −0.197378 0.980327i \(-0.563243\pi\)
−0.197378 + 0.980327i \(0.563243\pi\)
\(822\) −19.1233 −0.667003
\(823\) −5.22466 −0.182120 −0.0910602 0.995845i \(-0.529026\pi\)
−0.0910602 + 0.995845i \(0.529026\pi\)
\(824\) −27.5944 −0.961296
\(825\) −5.10268 −0.177652
\(826\) −5.68925 −0.197954
\(827\) 4.38009 0.152311 0.0761553 0.997096i \(-0.475736\pi\)
0.0761553 + 0.997096i \(0.475736\pi\)
\(828\) −1.39126 −0.0483498
\(829\) −8.16601 −0.283617 −0.141809 0.989894i \(-0.545292\pi\)
−0.141809 + 0.989894i \(0.545292\pi\)
\(830\) 6.83010 0.237076
\(831\) 30.6336 1.06267
\(832\) 8.80856 0.305382
\(833\) −45.3488 −1.57124
\(834\) −17.8040 −0.616503
\(835\) −20.4022 −0.706048
\(836\) 31.2639 1.08128
\(837\) 0.392200 0.0135564
\(838\) 34.1156 1.17850
\(839\) 2.42446 0.0837015 0.0418508 0.999124i \(-0.486675\pi\)
0.0418508 + 0.999124i \(0.486675\pi\)
\(840\) 4.58198 0.158094
\(841\) 10.7138 0.369443
\(842\) −73.1695 −2.52159
\(843\) 12.9428 0.445775
\(844\) −6.33166 −0.217945
\(845\) 33.4152 1.14952
\(846\) 13.2973 0.457169
\(847\) 2.59097 0.0890268
\(848\) −27.1946 −0.933866
\(849\) −23.2299 −0.797246
\(850\) −95.9339 −3.29051
\(851\) 1.36289 0.0467191
\(852\) 52.3417 1.79320
\(853\) 3.56887 0.122196 0.0610978 0.998132i \(-0.480540\pi\)
0.0610978 + 0.998132i \(0.480540\pi\)
\(854\) −1.87408 −0.0641299
\(855\) −28.3241 −0.968663
\(856\) −78.4876 −2.68265
\(857\) 22.7608 0.777494 0.388747 0.921345i \(-0.372908\pi\)
0.388747 + 0.921345i \(0.372908\pi\)
\(858\) −3.65841 −0.124896
\(859\) −11.2838 −0.384998 −0.192499 0.981297i \(-0.561659\pi\)
−0.192499 + 0.981297i \(0.561659\pi\)
\(860\) −54.2586 −1.85020
\(861\) −1.38524 −0.0472089
\(862\) −0.737211 −0.0251095
\(863\) 0.930016 0.0316581 0.0158291 0.999875i \(-0.494961\pi\)
0.0158291 + 0.999875i \(0.494961\pi\)
\(864\) 2.14704 0.0730437
\(865\) 37.3695 1.27060
\(866\) −33.8932 −1.15174
\(867\) −25.7466 −0.874401
\(868\) 0.416895 0.0141503
\(869\) 8.67343 0.294226
\(870\) 51.8042 1.75633
\(871\) −26.4226 −0.895296
\(872\) −57.9383 −1.96204
\(873\) 4.48288 0.151722
\(874\) 7.07373 0.239272
\(875\) 0.742859 0.0251132
\(876\) 14.8759 0.502610
\(877\) 35.3390 1.19331 0.596656 0.802497i \(-0.296496\pi\)
0.596656 + 0.802497i \(0.296496\pi\)
\(878\) 25.1114 0.847468
\(879\) −16.3329 −0.550894
\(880\) −15.0708 −0.508036
\(881\) 1.24826 0.0420549 0.0210274 0.999779i \(-0.493306\pi\)
0.0210274 + 0.999779i \(0.493306\pi\)
\(882\) 17.2777 0.581770
\(883\) 10.2014 0.343305 0.171652 0.985158i \(-0.445089\pi\)
0.171652 + 0.985158i \(0.445089\pi\)
\(884\) −46.6111 −1.56770
\(885\) −29.8162 −1.00226
\(886\) −10.4111 −0.349767
\(887\) 32.0112 1.07483 0.537416 0.843317i \(-0.319401\pi\)
0.537416 + 0.843317i \(0.319401\pi\)
\(888\) −22.6249 −0.759243
\(889\) 0.414928 0.0139162
\(890\) 77.5789 2.60045
\(891\) 0.866258 0.0290207
\(892\) 69.6990 2.33370
\(893\) −45.8167 −1.53320
\(894\) −16.6429 −0.556623
\(895\) 14.9476 0.499643
\(896\) −4.35706 −0.145559
\(897\) −0.560946 −0.0187294
\(898\) −90.4350 −3.01785
\(899\) 2.47160 0.0824325
\(900\) 24.7694 0.825645
\(901\) −33.7262 −1.12358
\(902\) 11.8246 0.393716
\(903\) 0.988409 0.0328922
\(904\) −20.7189 −0.689099
\(905\) −18.5345 −0.616107
\(906\) −36.3810 −1.20868
\(907\) 29.3494 0.974531 0.487266 0.873254i \(-0.337994\pi\)
0.487266 + 0.873254i \(0.337994\pi\)
\(908\) 9.59764 0.318509
\(909\) −9.49629 −0.314972
\(910\) 3.52309 0.116789
\(911\) −18.3068 −0.606532 −0.303266 0.952906i \(-0.598077\pi\)
−0.303266 + 0.952906i \(0.598077\pi\)
\(912\) −45.2478 −1.49831
\(913\) 0.719748 0.0238202
\(914\) 20.9787 0.693915
\(915\) −9.82171 −0.324696
\(916\) −2.06495 −0.0682280
\(917\) −2.83368 −0.0935765
\(918\) 16.2862 0.537526
\(919\) −29.3278 −0.967436 −0.483718 0.875224i \(-0.660714\pi\)
−0.483718 + 0.875224i \(0.660714\pi\)
\(920\) −5.99714 −0.197720
\(921\) 5.52388 0.182018
\(922\) −41.3963 −1.36331
\(923\) 21.1037 0.694638
\(924\) 0.920803 0.0302922
\(925\) −24.2641 −0.797799
\(926\) 30.7355 1.01003
\(927\) 5.02397 0.165009
\(928\) 13.5304 0.444157
\(929\) 24.8575 0.815547 0.407773 0.913083i \(-0.366305\pi\)
0.407773 + 0.913083i \(0.366305\pi\)
\(930\) 3.22404 0.105721
\(931\) −59.5316 −1.95107
\(932\) 41.1208 1.34696
\(933\) −0.610266 −0.0199792
\(934\) −16.0657 −0.525686
\(935\) −18.6905 −0.611246
\(936\) 9.31213 0.304376
\(937\) 36.9219 1.20619 0.603093 0.797671i \(-0.293935\pi\)
0.603093 + 0.797671i \(0.293935\pi\)
\(938\) 9.81356 0.320424
\(939\) −24.6675 −0.804995
\(940\) 74.0763 2.41610
\(941\) 4.92014 0.160392 0.0801959 0.996779i \(-0.474445\pi\)
0.0801959 + 0.996779i \(0.474445\pi\)
\(942\) 38.6506 1.25931
\(943\) 1.81307 0.0590418
\(944\) −47.6315 −1.55027
\(945\) −0.834218 −0.0271371
\(946\) −8.43720 −0.274317
\(947\) −37.9354 −1.23274 −0.616368 0.787458i \(-0.711397\pi\)
−0.616368 + 0.787458i \(0.711397\pi\)
\(948\) −42.1025 −1.36742
\(949\) 5.99784 0.194698
\(950\) −125.937 −4.08594
\(951\) 29.2000 0.946873
\(952\) 9.07781 0.294213
\(953\) 53.1225 1.72081 0.860404 0.509612i \(-0.170211\pi\)
0.860404 + 0.509612i \(0.170211\pi\)
\(954\) 12.8495 0.416019
\(955\) −8.33276 −0.269642
\(956\) 55.0548 1.78060
\(957\) 5.45906 0.176466
\(958\) 8.64316 0.279248
\(959\) 1.94066 0.0626671
\(960\) −17.1456 −0.553373
\(961\) −30.8462 −0.995038
\(962\) −17.3963 −0.560881
\(963\) 14.2898 0.460483
\(964\) −106.934 −3.44410
\(965\) 7.42175 0.238915
\(966\) 0.208340 0.00670322
\(967\) −46.1959 −1.48556 −0.742780 0.669535i \(-0.766493\pi\)
−0.742780 + 0.669535i \(0.766493\pi\)
\(968\) 56.2965 1.80944
\(969\) −56.1155 −1.80269
\(970\) 36.8511 1.18322
\(971\) −50.4578 −1.61927 −0.809633 0.586936i \(-0.800334\pi\)
−0.809633 + 0.586936i \(0.800334\pi\)
\(972\) −4.20498 −0.134875
\(973\) 1.80677 0.0579225
\(974\) −84.3536 −2.70286
\(975\) 9.98679 0.319833
\(976\) −15.6902 −0.502231
\(977\) −56.3159 −1.80170 −0.900852 0.434125i \(-0.857057\pi\)
−0.900852 + 0.434125i \(0.857057\pi\)
\(978\) 60.2421 1.92633
\(979\) 8.17518 0.261280
\(980\) 96.2504 3.07461
\(981\) 10.5485 0.336788
\(982\) −63.7493 −2.03432
\(983\) 18.2181 0.581067 0.290534 0.956865i \(-0.406167\pi\)
0.290534 + 0.956865i \(0.406167\pi\)
\(984\) −30.0984 −0.959503
\(985\) −4.59605 −0.146442
\(986\) 102.634 3.26854
\(987\) −1.34942 −0.0429526
\(988\) −61.1886 −1.94667
\(989\) −1.29368 −0.0411367
\(990\) 7.12100 0.226320
\(991\) −18.2555 −0.579906 −0.289953 0.957041i \(-0.593640\pi\)
−0.289953 + 0.957041i \(0.593640\pi\)
\(992\) 0.842068 0.0267357
\(993\) 21.1649 0.671648
\(994\) −7.83809 −0.248609
\(995\) −33.4747 −1.06122
\(996\) −3.49379 −0.110705
\(997\) −23.0943 −0.731403 −0.365701 0.930732i \(-0.619171\pi\)
−0.365701 + 0.930732i \(0.619171\pi\)
\(998\) 0.921292 0.0291630
\(999\) 4.11920 0.130326
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.b.1.10 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8049.2.a.b.1.10 104 1.1 even 1 trivial