Properties

Label 6029.2.a.a.1.10
Level $6029$
Weight $2$
Character 6029.1
Self dual yes
Analytic conductor $48.142$
Analytic rank $1$
Dimension $234$
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] = [6029,2,Mod(1,6029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6029, 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("6029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6029 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6029.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.1418073786\)
Analytic rank: \(1\)
Dimension: \(234\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 6029.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.59814 q^{2} +1.65321 q^{3} +4.75033 q^{4} +2.01329 q^{5} -4.29528 q^{6} +1.44236 q^{7} -7.14575 q^{8} -0.266887 q^{9} +O(q^{10})\) \(q-2.59814 q^{2} +1.65321 q^{3} +4.75033 q^{4} +2.01329 q^{5} -4.29528 q^{6} +1.44236 q^{7} -7.14575 q^{8} -0.266887 q^{9} -5.23080 q^{10} -3.73074 q^{11} +7.85331 q^{12} +3.40621 q^{13} -3.74746 q^{14} +3.32839 q^{15} +9.06499 q^{16} +5.43724 q^{17} +0.693410 q^{18} -4.75327 q^{19} +9.56378 q^{20} +2.38453 q^{21} +9.69297 q^{22} -8.10231 q^{23} -11.8134 q^{24} -0.946681 q^{25} -8.84981 q^{26} -5.40086 q^{27} +6.85170 q^{28} +9.42502 q^{29} -8.64762 q^{30} +0.0440374 q^{31} -9.26062 q^{32} -6.16770 q^{33} -14.1267 q^{34} +2.90389 q^{35} -1.26780 q^{36} -5.74024 q^{37} +12.3497 q^{38} +5.63119 q^{39} -14.3864 q^{40} -9.87971 q^{41} -6.19535 q^{42} -11.2891 q^{43} -17.7222 q^{44} -0.537320 q^{45} +21.0509 q^{46} -1.87232 q^{47} +14.9864 q^{48} -4.91959 q^{49} +2.45961 q^{50} +8.98891 q^{51} +16.1806 q^{52} +6.24789 q^{53} +14.0322 q^{54} -7.51104 q^{55} -10.3068 q^{56} -7.85816 q^{57} -24.4875 q^{58} +7.29466 q^{59} +15.8110 q^{60} -11.4330 q^{61} -0.114415 q^{62} -0.384948 q^{63} +5.93040 q^{64} +6.85767 q^{65} +16.0246 q^{66} -4.92399 q^{67} +25.8287 q^{68} -13.3948 q^{69} -7.54471 q^{70} -5.63361 q^{71} +1.90711 q^{72} +5.71738 q^{73} +14.9140 q^{74} -1.56506 q^{75} -22.5796 q^{76} -5.38107 q^{77} -14.6306 q^{78} -11.6224 q^{79} +18.2504 q^{80} -8.12811 q^{81} +25.6689 q^{82} -6.88507 q^{83} +11.3273 q^{84} +10.9467 q^{85} +29.3307 q^{86} +15.5816 q^{87} +26.6589 q^{88} +12.0708 q^{89} +1.39603 q^{90} +4.91299 q^{91} -38.4887 q^{92} +0.0728033 q^{93} +4.86456 q^{94} -9.56968 q^{95} -15.3098 q^{96} -4.48974 q^{97} +12.7818 q^{98} +0.995685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59814 −1.83716 −0.918581 0.395232i \(-0.870664\pi\)
−0.918581 + 0.395232i \(0.870664\pi\)
\(3\) 1.65321 0.954483 0.477241 0.878772i \(-0.341637\pi\)
0.477241 + 0.878772i \(0.341637\pi\)
\(4\) 4.75033 2.37517
\(5\) 2.01329 0.900369 0.450184 0.892936i \(-0.351358\pi\)
0.450184 + 0.892936i \(0.351358\pi\)
\(6\) −4.29528 −1.75354
\(7\) 1.44236 0.545162 0.272581 0.962133i \(-0.412123\pi\)
0.272581 + 0.962133i \(0.412123\pi\)
\(8\) −7.14575 −2.52640
\(9\) −0.266887 −0.0889624
\(10\) −5.23080 −1.65412
\(11\) −3.73074 −1.12486 −0.562430 0.826845i \(-0.690133\pi\)
−0.562430 + 0.826845i \(0.690133\pi\)
\(12\) 7.85331 2.26706
\(13\) 3.40621 0.944712 0.472356 0.881408i \(-0.343404\pi\)
0.472356 + 0.881408i \(0.343404\pi\)
\(14\) −3.74746 −1.00155
\(15\) 3.32839 0.859387
\(16\) 9.06499 2.26625
\(17\) 5.43724 1.31872 0.659362 0.751826i \(-0.270827\pi\)
0.659362 + 0.751826i \(0.270827\pi\)
\(18\) 0.693410 0.163438
\(19\) −4.75327 −1.09047 −0.545237 0.838282i \(-0.683560\pi\)
−0.545237 + 0.838282i \(0.683560\pi\)
\(20\) 9.56378 2.13853
\(21\) 2.38453 0.520348
\(22\) 9.69297 2.06655
\(23\) −8.10231 −1.68945 −0.844724 0.535202i \(-0.820235\pi\)
−0.844724 + 0.535202i \(0.820235\pi\)
\(24\) −11.8134 −2.41141
\(25\) −0.946681 −0.189336
\(26\) −8.84981 −1.73559
\(27\) −5.40086 −1.03940
\(28\) 6.85170 1.29485
\(29\) 9.42502 1.75018 0.875092 0.483957i \(-0.160801\pi\)
0.875092 + 0.483957i \(0.160801\pi\)
\(30\) −8.64762 −1.57883
\(31\) 0.0440374 0.00790936 0.00395468 0.999992i \(-0.498741\pi\)
0.00395468 + 0.999992i \(0.498741\pi\)
\(32\) −9.26062 −1.63706
\(33\) −6.16770 −1.07366
\(34\) −14.1267 −2.42271
\(35\) 2.90389 0.490847
\(36\) −1.26780 −0.211300
\(37\) −5.74024 −0.943690 −0.471845 0.881681i \(-0.656412\pi\)
−0.471845 + 0.881681i \(0.656412\pi\)
\(38\) 12.3497 2.00338
\(39\) 5.63119 0.901712
\(40\) −14.3864 −2.27469
\(41\) −9.87971 −1.54295 −0.771476 0.636258i \(-0.780481\pi\)
−0.771476 + 0.636258i \(0.780481\pi\)
\(42\) −6.19535 −0.955963
\(43\) −11.2891 −1.72157 −0.860786 0.508968i \(-0.830027\pi\)
−0.860786 + 0.508968i \(0.830027\pi\)
\(44\) −17.7222 −2.67173
\(45\) −0.537320 −0.0800989
\(46\) 21.0509 3.10379
\(47\) −1.87232 −0.273106 −0.136553 0.990633i \(-0.543602\pi\)
−0.136553 + 0.990633i \(0.543602\pi\)
\(48\) 14.9864 2.16309
\(49\) −4.91959 −0.702799
\(50\) 2.45961 0.347841
\(51\) 8.98891 1.25870
\(52\) 16.1806 2.24385
\(53\) 6.24789 0.858214 0.429107 0.903254i \(-0.358828\pi\)
0.429107 + 0.903254i \(0.358828\pi\)
\(54\) 14.0322 1.90954
\(55\) −7.51104 −1.01279
\(56\) −10.3068 −1.37730
\(57\) −7.85816 −1.04084
\(58\) −24.4875 −3.21537
\(59\) 7.29466 0.949684 0.474842 0.880071i \(-0.342505\pi\)
0.474842 + 0.880071i \(0.342505\pi\)
\(60\) 15.8110 2.04119
\(61\) −11.4330 −1.46385 −0.731925 0.681385i \(-0.761378\pi\)
−0.731925 + 0.681385i \(0.761378\pi\)
\(62\) −0.114415 −0.0145308
\(63\) −0.384948 −0.0484989
\(64\) 5.93040 0.741300
\(65\) 6.85767 0.850589
\(66\) 16.0246 1.97249
\(67\) −4.92399 −0.601561 −0.300780 0.953693i \(-0.597247\pi\)
−0.300780 + 0.953693i \(0.597247\pi\)
\(68\) 25.8287 3.13219
\(69\) −13.3948 −1.61255
\(70\) −7.54471 −0.901765
\(71\) −5.63361 −0.668587 −0.334293 0.942469i \(-0.608498\pi\)
−0.334293 + 0.942469i \(0.608498\pi\)
\(72\) 1.90711 0.224755
\(73\) 5.71738 0.669168 0.334584 0.942366i \(-0.391404\pi\)
0.334584 + 0.942366i \(0.391404\pi\)
\(74\) 14.9140 1.73371
\(75\) −1.56506 −0.180718
\(76\) −22.5796 −2.59006
\(77\) −5.38107 −0.613230
\(78\) −14.6306 −1.65659
\(79\) −11.6224 −1.30762 −0.653812 0.756657i \(-0.726831\pi\)
−0.653812 + 0.756657i \(0.726831\pi\)
\(80\) 18.2504 2.04046
\(81\) −8.12811 −0.903123
\(82\) 25.6689 2.83465
\(83\) −6.88507 −0.755735 −0.377867 0.925860i \(-0.623343\pi\)
−0.377867 + 0.925860i \(0.623343\pi\)
\(84\) 11.3273 1.23591
\(85\) 10.9467 1.18734
\(86\) 29.3307 3.16281
\(87\) 15.5816 1.67052
\(88\) 26.6589 2.84185
\(89\) 12.0708 1.27950 0.639752 0.768581i \(-0.279037\pi\)
0.639752 + 0.768581i \(0.279037\pi\)
\(90\) 1.39603 0.147155
\(91\) 4.91299 0.515021
\(92\) −38.4887 −4.01272
\(93\) 0.0728033 0.00754935
\(94\) 4.86456 0.501741
\(95\) −9.56968 −0.981829
\(96\) −15.3098 −1.56255
\(97\) −4.48974 −0.455864 −0.227932 0.973677i \(-0.573196\pi\)
−0.227932 + 0.973677i \(0.573196\pi\)
\(98\) 12.7818 1.29116
\(99\) 0.995685 0.100070
\(100\) −4.49705 −0.449705
\(101\) 15.7960 1.57176 0.785879 0.618380i \(-0.212211\pi\)
0.785879 + 0.618380i \(0.212211\pi\)
\(102\) −23.3544 −2.31243
\(103\) 5.34126 0.526290 0.263145 0.964756i \(-0.415240\pi\)
0.263145 + 0.964756i \(0.415240\pi\)
\(104\) −24.3399 −2.38672
\(105\) 4.80074 0.468505
\(106\) −16.2329 −1.57668
\(107\) 0.216064 0.0208876 0.0104438 0.999945i \(-0.496676\pi\)
0.0104438 + 0.999945i \(0.496676\pi\)
\(108\) −25.6559 −2.46874
\(109\) 15.4582 1.48063 0.740316 0.672259i \(-0.234676\pi\)
0.740316 + 0.672259i \(0.234676\pi\)
\(110\) 19.5147 1.86066
\(111\) −9.48985 −0.900736
\(112\) 13.0750 1.23547
\(113\) 9.77920 0.919950 0.459975 0.887932i \(-0.347858\pi\)
0.459975 + 0.887932i \(0.347858\pi\)
\(114\) 20.4166 1.91219
\(115\) −16.3123 −1.52113
\(116\) 44.7720 4.15698
\(117\) −0.909073 −0.0840438
\(118\) −18.9525 −1.74472
\(119\) 7.84247 0.718918
\(120\) −23.7838 −2.17116
\(121\) 2.91839 0.265308
\(122\) 29.7046 2.68933
\(123\) −16.3333 −1.47272
\(124\) 0.209192 0.0187860
\(125\) −11.9724 −1.07084
\(126\) 1.00015 0.0891003
\(127\) −20.6491 −1.83231 −0.916156 0.400822i \(-0.868725\pi\)
−0.916156 + 0.400822i \(0.868725\pi\)
\(128\) 3.11322 0.275172
\(129\) −18.6633 −1.64321
\(130\) −17.8172 −1.56267
\(131\) −7.97819 −0.697058 −0.348529 0.937298i \(-0.613319\pi\)
−0.348529 + 0.937298i \(0.613319\pi\)
\(132\) −29.2986 −2.55012
\(133\) −6.85593 −0.594485
\(134\) 12.7932 1.10516
\(135\) −10.8735 −0.935840
\(136\) −38.8531 −3.33163
\(137\) −12.9898 −1.10979 −0.554896 0.831920i \(-0.687242\pi\)
−0.554896 + 0.831920i \(0.687242\pi\)
\(138\) 34.8017 2.96252
\(139\) −14.2125 −1.20549 −0.602746 0.797933i \(-0.705927\pi\)
−0.602746 + 0.797933i \(0.705927\pi\)
\(140\) 13.7944 1.16584
\(141\) −3.09535 −0.260675
\(142\) 14.6369 1.22830
\(143\) −12.7077 −1.06267
\(144\) −2.41933 −0.201611
\(145\) 18.9753 1.57581
\(146\) −14.8545 −1.22937
\(147\) −8.13313 −0.670809
\(148\) −27.2681 −2.24142
\(149\) −4.89879 −0.401324 −0.200662 0.979661i \(-0.564309\pi\)
−0.200662 + 0.979661i \(0.564309\pi\)
\(150\) 4.06626 0.332009
\(151\) 24.1129 1.96228 0.981142 0.193290i \(-0.0619160\pi\)
0.981142 + 0.193290i \(0.0619160\pi\)
\(152\) 33.9656 2.75498
\(153\) −1.45113 −0.117317
\(154\) 13.9808 1.12660
\(155\) 0.0886600 0.00712134
\(156\) 26.7500 2.14172
\(157\) −11.2949 −0.901432 −0.450716 0.892667i \(-0.648831\pi\)
−0.450716 + 0.892667i \(0.648831\pi\)
\(158\) 30.1967 2.40232
\(159\) 10.3291 0.819151
\(160\) −18.6443 −1.47396
\(161\) −11.6865 −0.921023
\(162\) 21.1180 1.65918
\(163\) −9.78659 −0.766545 −0.383273 0.923635i \(-0.625203\pi\)
−0.383273 + 0.923635i \(0.625203\pi\)
\(164\) −46.9319 −3.66477
\(165\) −12.4173 −0.966689
\(166\) 17.8884 1.38841
\(167\) −7.34958 −0.568728 −0.284364 0.958716i \(-0.591782\pi\)
−0.284364 + 0.958716i \(0.591782\pi\)
\(168\) −17.0393 −1.31461
\(169\) −1.39774 −0.107519
\(170\) −28.4411 −2.18133
\(171\) 1.26859 0.0970112
\(172\) −53.6270 −4.08902
\(173\) −23.2959 −1.77116 −0.885579 0.464489i \(-0.846238\pi\)
−0.885579 + 0.464489i \(0.846238\pi\)
\(174\) −40.4831 −3.06902
\(175\) −1.36546 −0.103219
\(176\) −33.8191 −2.54921
\(177\) 12.0596 0.906457
\(178\) −31.3617 −2.35066
\(179\) 6.31476 0.471987 0.235994 0.971755i \(-0.424166\pi\)
0.235994 + 0.971755i \(0.424166\pi\)
\(180\) −2.55245 −0.190248
\(181\) −10.5959 −0.787588 −0.393794 0.919199i \(-0.628838\pi\)
−0.393794 + 0.919199i \(0.628838\pi\)
\(182\) −12.7646 −0.946177
\(183\) −18.9012 −1.39722
\(184\) 57.8970 4.26823
\(185\) −11.5568 −0.849669
\(186\) −0.189153 −0.0138694
\(187\) −20.2849 −1.48338
\(188\) −8.89415 −0.648673
\(189\) −7.79000 −0.566639
\(190\) 24.8634 1.80378
\(191\) 7.65742 0.554071 0.277036 0.960860i \(-0.410648\pi\)
0.277036 + 0.960860i \(0.410648\pi\)
\(192\) 9.80422 0.707558
\(193\) 26.6124 1.91560 0.957800 0.287435i \(-0.0928025\pi\)
0.957800 + 0.287435i \(0.0928025\pi\)
\(194\) 11.6650 0.837497
\(195\) 11.3372 0.811873
\(196\) −23.3697 −1.66926
\(197\) 5.71918 0.407475 0.203738 0.979026i \(-0.434691\pi\)
0.203738 + 0.979026i \(0.434691\pi\)
\(198\) −2.58693 −0.183845
\(199\) −1.80996 −0.128305 −0.0641523 0.997940i \(-0.520434\pi\)
−0.0641523 + 0.997940i \(0.520434\pi\)
\(200\) 6.76474 0.478339
\(201\) −8.14040 −0.574179
\(202\) −41.0401 −2.88757
\(203\) 13.5943 0.954133
\(204\) 42.7003 2.98962
\(205\) −19.8907 −1.38923
\(206\) −13.8773 −0.966880
\(207\) 2.16240 0.150297
\(208\) 30.8772 2.14095
\(209\) 17.7332 1.22663
\(210\) −12.4730 −0.860719
\(211\) −11.1067 −0.764615 −0.382307 0.924035i \(-0.624870\pi\)
−0.382307 + 0.924035i \(0.624870\pi\)
\(212\) 29.6796 2.03840
\(213\) −9.31356 −0.638155
\(214\) −0.561363 −0.0383740
\(215\) −22.7282 −1.55005
\(216\) 38.5932 2.62593
\(217\) 0.0635180 0.00431188
\(218\) −40.1627 −2.72016
\(219\) 9.45204 0.638710
\(220\) −35.6799 −2.40554
\(221\) 18.5204 1.24581
\(222\) 24.6559 1.65480
\(223\) 0.644839 0.0431816 0.0215908 0.999767i \(-0.493127\pi\)
0.0215908 + 0.999767i \(0.493127\pi\)
\(224\) −13.3572 −0.892463
\(225\) 0.252657 0.0168438
\(226\) −25.4077 −1.69010
\(227\) −3.40110 −0.225739 −0.112869 0.993610i \(-0.536004\pi\)
−0.112869 + 0.993610i \(0.536004\pi\)
\(228\) −37.3289 −2.47217
\(229\) −16.8934 −1.11635 −0.558175 0.829723i \(-0.688498\pi\)
−0.558175 + 0.829723i \(0.688498\pi\)
\(230\) 42.3815 2.79456
\(231\) −8.89606 −0.585318
\(232\) −67.3488 −4.42167
\(233\) 14.6392 0.959048 0.479524 0.877529i \(-0.340809\pi\)
0.479524 + 0.877529i \(0.340809\pi\)
\(234\) 2.36190 0.154402
\(235\) −3.76952 −0.245896
\(236\) 34.6521 2.25566
\(237\) −19.2143 −1.24811
\(238\) −20.3758 −1.32077
\(239\) 19.5254 1.26299 0.631496 0.775379i \(-0.282441\pi\)
0.631496 + 0.775379i \(0.282441\pi\)
\(240\) 30.1718 1.94758
\(241\) −20.4738 −1.31883 −0.659417 0.751778i \(-0.729197\pi\)
−0.659417 + 0.751778i \(0.729197\pi\)
\(242\) −7.58239 −0.487414
\(243\) 2.76508 0.177380
\(244\) −54.3107 −3.47689
\(245\) −9.90454 −0.632778
\(246\) 42.4361 2.70563
\(247\) −16.1906 −1.03018
\(248\) −0.314680 −0.0199822
\(249\) −11.3825 −0.721336
\(250\) 31.1059 1.96731
\(251\) 19.9618 1.25998 0.629989 0.776604i \(-0.283059\pi\)
0.629989 + 0.776604i \(0.283059\pi\)
\(252\) −1.82863 −0.115193
\(253\) 30.2276 1.90039
\(254\) 53.6493 3.36626
\(255\) 18.0972 1.13329
\(256\) −19.9494 −1.24684
\(257\) 6.07861 0.379173 0.189587 0.981864i \(-0.439285\pi\)
0.189587 + 0.981864i \(0.439285\pi\)
\(258\) 48.4898 3.01884
\(259\) −8.27951 −0.514464
\(260\) 32.5762 2.02029
\(261\) −2.51542 −0.155700
\(262\) 20.7285 1.28061
\(263\) −12.1575 −0.749663 −0.374832 0.927093i \(-0.622299\pi\)
−0.374832 + 0.927093i \(0.622299\pi\)
\(264\) 44.0728 2.71250
\(265\) 12.5788 0.772709
\(266\) 17.8127 1.09217
\(267\) 19.9556 1.22127
\(268\) −23.3906 −1.42881
\(269\) 27.5734 1.68118 0.840588 0.541674i \(-0.182209\pi\)
0.840588 + 0.541674i \(0.182209\pi\)
\(270\) 28.2508 1.71929
\(271\) −15.1120 −0.917986 −0.458993 0.888440i \(-0.651790\pi\)
−0.458993 + 0.888440i \(0.651790\pi\)
\(272\) 49.2885 2.98855
\(273\) 8.12222 0.491579
\(274\) 33.7493 2.03887
\(275\) 3.53182 0.212977
\(276\) −63.6299 −3.83007
\(277\) 27.7426 1.66689 0.833446 0.552600i \(-0.186364\pi\)
0.833446 + 0.552600i \(0.186364\pi\)
\(278\) 36.9261 2.21468
\(279\) −0.0117530 −0.000703635 0
\(280\) −20.7504 −1.24008
\(281\) 4.26997 0.254725 0.127362 0.991856i \(-0.459349\pi\)
0.127362 + 0.991856i \(0.459349\pi\)
\(282\) 8.04215 0.478903
\(283\) 26.9329 1.60100 0.800498 0.599335i \(-0.204568\pi\)
0.800498 + 0.599335i \(0.204568\pi\)
\(284\) −26.7615 −1.58800
\(285\) −15.8207 −0.937139
\(286\) 33.0163 1.95229
\(287\) −14.2501 −0.841159
\(288\) 2.47154 0.145637
\(289\) 12.5635 0.739031
\(290\) −49.3004 −2.89502
\(291\) −7.42250 −0.435115
\(292\) 27.1594 1.58939
\(293\) 5.84367 0.341391 0.170695 0.985324i \(-0.445399\pi\)
0.170695 + 0.985324i \(0.445399\pi\)
\(294\) 21.1310 1.23239
\(295\) 14.6862 0.855066
\(296\) 41.0183 2.38414
\(297\) 20.1492 1.16917
\(298\) 12.7277 0.737298
\(299\) −27.5982 −1.59604
\(300\) −7.43458 −0.429236
\(301\) −16.2830 −0.938535
\(302\) −62.6488 −3.60503
\(303\) 26.1141 1.50022
\(304\) −43.0883 −2.47128
\(305\) −23.0180 −1.31801
\(306\) 3.77023 0.215530
\(307\) −12.6475 −0.721830 −0.360915 0.932599i \(-0.617536\pi\)
−0.360915 + 0.932599i \(0.617536\pi\)
\(308\) −25.5619 −1.45652
\(309\) 8.83024 0.502335
\(310\) −0.230351 −0.0130831
\(311\) −16.5795 −0.940138 −0.470069 0.882630i \(-0.655771\pi\)
−0.470069 + 0.882630i \(0.655771\pi\)
\(312\) −40.2391 −2.27809
\(313\) 18.9024 1.06842 0.534212 0.845350i \(-0.320608\pi\)
0.534212 + 0.845350i \(0.320608\pi\)
\(314\) 29.3458 1.65608
\(315\) −0.775010 −0.0436669
\(316\) −55.2104 −3.10583
\(317\) 5.05382 0.283851 0.141925 0.989877i \(-0.454671\pi\)
0.141925 + 0.989877i \(0.454671\pi\)
\(318\) −26.8364 −1.50491
\(319\) −35.1623 −1.96871
\(320\) 11.9396 0.667443
\(321\) 0.357199 0.0199369
\(322\) 30.3631 1.69207
\(323\) −25.8446 −1.43803
\(324\) −38.6112 −2.14507
\(325\) −3.22459 −0.178868
\(326\) 25.4269 1.40827
\(327\) 25.5558 1.41324
\(328\) 70.5979 3.89812
\(329\) −2.70057 −0.148887
\(330\) 32.2620 1.77596
\(331\) 27.3204 1.50167 0.750833 0.660492i \(-0.229652\pi\)
0.750833 + 0.660492i \(0.229652\pi\)
\(332\) −32.7064 −1.79500
\(333\) 1.53200 0.0839529
\(334\) 19.0953 1.04485
\(335\) −9.91339 −0.541627
\(336\) 21.6158 1.17924
\(337\) −0.593491 −0.0323295 −0.0161648 0.999869i \(-0.505146\pi\)
−0.0161648 + 0.999869i \(0.505146\pi\)
\(338\) 3.63153 0.197529
\(339\) 16.1671 0.878076
\(340\) 52.0005 2.82012
\(341\) −0.164292 −0.00889692
\(342\) −3.29596 −0.178225
\(343\) −17.1924 −0.928301
\(344\) 80.6690 4.34938
\(345\) −26.9676 −1.45189
\(346\) 60.5261 3.25390
\(347\) −30.2804 −1.62554 −0.812769 0.582586i \(-0.802041\pi\)
−0.812769 + 0.582586i \(0.802041\pi\)
\(348\) 74.0176 3.96776
\(349\) 19.4498 1.04113 0.520563 0.853823i \(-0.325722\pi\)
0.520563 + 0.853823i \(0.325722\pi\)
\(350\) 3.54765 0.189630
\(351\) −18.3965 −0.981930
\(352\) 34.5489 1.84146
\(353\) 3.44548 0.183385 0.0916923 0.995787i \(-0.470772\pi\)
0.0916923 + 0.995787i \(0.470772\pi\)
\(354\) −31.3326 −1.66531
\(355\) −11.3421 −0.601975
\(356\) 57.3404 3.03904
\(357\) 12.9653 0.686195
\(358\) −16.4066 −0.867118
\(359\) −34.9173 −1.84286 −0.921431 0.388541i \(-0.872979\pi\)
−0.921431 + 0.388541i \(0.872979\pi\)
\(360\) 3.83955 0.202362
\(361\) 3.59355 0.189134
\(362\) 27.5297 1.44693
\(363\) 4.82472 0.253232
\(364\) 23.3383 1.22326
\(365\) 11.5107 0.602498
\(366\) 49.1081 2.56692
\(367\) −6.84534 −0.357324 −0.178662 0.983911i \(-0.557177\pi\)
−0.178662 + 0.983911i \(0.557177\pi\)
\(368\) −73.4473 −3.82871
\(369\) 2.63677 0.137265
\(370\) 30.0261 1.56098
\(371\) 9.01173 0.467866
\(372\) 0.345840 0.0179310
\(373\) −15.6257 −0.809066 −0.404533 0.914523i \(-0.632566\pi\)
−0.404533 + 0.914523i \(0.632566\pi\)
\(374\) 52.7030 2.72521
\(375\) −19.7929 −1.02210
\(376\) 13.3791 0.689977
\(377\) 32.1036 1.65342
\(378\) 20.2395 1.04101
\(379\) 35.1845 1.80731 0.903654 0.428264i \(-0.140875\pi\)
0.903654 + 0.428264i \(0.140875\pi\)
\(380\) −45.4592 −2.33201
\(381\) −34.1374 −1.74891
\(382\) −19.8950 −1.01792
\(383\) −7.91595 −0.404486 −0.202243 0.979335i \(-0.564823\pi\)
−0.202243 + 0.979335i \(0.564823\pi\)
\(384\) 5.14682 0.262647
\(385\) −10.8336 −0.552133
\(386\) −69.1427 −3.51927
\(387\) 3.01291 0.153155
\(388\) −21.3278 −1.08275
\(389\) −0.603547 −0.0306010 −0.0153005 0.999883i \(-0.504870\pi\)
−0.0153005 + 0.999883i \(0.504870\pi\)
\(390\) −29.4556 −1.49154
\(391\) −44.0542 −2.22791
\(392\) 35.1541 1.77555
\(393\) −13.1896 −0.665330
\(394\) −14.8592 −0.748598
\(395\) −23.3993 −1.17734
\(396\) 4.72983 0.237683
\(397\) 6.97307 0.349968 0.174984 0.984571i \(-0.444013\pi\)
0.174984 + 0.984571i \(0.444013\pi\)
\(398\) 4.70253 0.235716
\(399\) −11.3343 −0.567426
\(400\) −8.58165 −0.429083
\(401\) −12.9048 −0.644437 −0.322219 0.946665i \(-0.604429\pi\)
−0.322219 + 0.946665i \(0.604429\pi\)
\(402\) 21.1499 1.05486
\(403\) 0.150001 0.00747207
\(404\) 75.0361 3.73319
\(405\) −16.3642 −0.813144
\(406\) −35.3199 −1.75290
\(407\) 21.4153 1.06152
\(408\) −64.2325 −3.17998
\(409\) 10.0890 0.498870 0.249435 0.968392i \(-0.419755\pi\)
0.249435 + 0.968392i \(0.419755\pi\)
\(410\) 51.6788 2.55223
\(411\) −21.4749 −1.05928
\(412\) 25.3727 1.25003
\(413\) 10.5215 0.517731
\(414\) −5.61822 −0.276121
\(415\) −13.8616 −0.680440
\(416\) −31.5436 −1.54655
\(417\) −23.4963 −1.15062
\(418\) −46.0733 −2.25352
\(419\) −4.22807 −0.206555 −0.103277 0.994653i \(-0.532933\pi\)
−0.103277 + 0.994653i \(0.532933\pi\)
\(420\) 22.8051 1.11278
\(421\) 13.8674 0.675857 0.337929 0.941172i \(-0.390274\pi\)
0.337929 + 0.941172i \(0.390274\pi\)
\(422\) 28.8567 1.40472
\(423\) 0.499699 0.0242962
\(424\) −44.6459 −2.16820
\(425\) −5.14733 −0.249682
\(426\) 24.1979 1.17239
\(427\) −16.4906 −0.798035
\(428\) 1.02637 0.0496116
\(429\) −21.0085 −1.01430
\(430\) 59.0510 2.84769
\(431\) −8.73912 −0.420948 −0.210474 0.977599i \(-0.567501\pi\)
−0.210474 + 0.977599i \(0.567501\pi\)
\(432\) −48.9587 −2.35553
\(433\) −15.7443 −0.756625 −0.378312 0.925678i \(-0.623495\pi\)
−0.378312 + 0.925678i \(0.623495\pi\)
\(434\) −0.165029 −0.00792163
\(435\) 31.3702 1.50408
\(436\) 73.4318 3.51675
\(437\) 38.5124 1.84230
\(438\) −24.5577 −1.17341
\(439\) 29.7230 1.41860 0.709300 0.704907i \(-0.249011\pi\)
0.709300 + 0.704907i \(0.249011\pi\)
\(440\) 53.6720 2.55871
\(441\) 1.31297 0.0625226
\(442\) −48.1185 −2.28876
\(443\) 21.6471 1.02849 0.514243 0.857645i \(-0.328073\pi\)
0.514243 + 0.857645i \(0.328073\pi\)
\(444\) −45.0799 −2.13940
\(445\) 24.3020 1.15203
\(446\) −1.67538 −0.0793317
\(447\) −8.09874 −0.383057
\(448\) 8.55379 0.404128
\(449\) 11.2403 0.530463 0.265232 0.964185i \(-0.414552\pi\)
0.265232 + 0.964185i \(0.414552\pi\)
\(450\) −0.656438 −0.0309448
\(451\) 36.8586 1.73560
\(452\) 46.4544 2.18503
\(453\) 39.8638 1.87297
\(454\) 8.83653 0.414719
\(455\) 9.89125 0.463709
\(456\) 56.1524 2.62958
\(457\) 27.7369 1.29748 0.648740 0.761010i \(-0.275296\pi\)
0.648740 + 0.761010i \(0.275296\pi\)
\(458\) 43.8915 2.05092
\(459\) −29.3657 −1.37068
\(460\) −77.4887 −3.61293
\(461\) 6.30503 0.293655 0.146827 0.989162i \(-0.453094\pi\)
0.146827 + 0.989162i \(0.453094\pi\)
\(462\) 23.1132 1.07532
\(463\) −4.82972 −0.224456 −0.112228 0.993682i \(-0.535799\pi\)
−0.112228 + 0.993682i \(0.535799\pi\)
\(464\) 85.4377 3.96635
\(465\) 0.146574 0.00679720
\(466\) −38.0348 −1.76193
\(467\) −34.0684 −1.57650 −0.788248 0.615358i \(-0.789012\pi\)
−0.788248 + 0.615358i \(0.789012\pi\)
\(468\) −4.31840 −0.199618
\(469\) −7.10217 −0.327948
\(470\) 9.79374 0.451752
\(471\) −18.6729 −0.860402
\(472\) −52.1258 −2.39928
\(473\) 42.1166 1.93653
\(474\) 49.9215 2.29297
\(475\) 4.49983 0.206466
\(476\) 37.2543 1.70755
\(477\) −1.66748 −0.0763488
\(478\) −50.7297 −2.32032
\(479\) −9.65667 −0.441225 −0.220612 0.975362i \(-0.570806\pi\)
−0.220612 + 0.975362i \(0.570806\pi\)
\(480\) −30.8229 −1.40687
\(481\) −19.5525 −0.891516
\(482\) 53.1938 2.42291
\(483\) −19.3202 −0.879100
\(484\) 13.8633 0.630151
\(485\) −9.03914 −0.410446
\(486\) −7.18407 −0.325876
\(487\) 14.6484 0.663784 0.331892 0.943317i \(-0.392313\pi\)
0.331892 + 0.943317i \(0.392313\pi\)
\(488\) 81.6976 3.69828
\(489\) −16.1793 −0.731654
\(490\) 25.7334 1.16252
\(491\) −9.90530 −0.447020 −0.223510 0.974702i \(-0.571751\pi\)
−0.223510 + 0.974702i \(0.571751\pi\)
\(492\) −77.5885 −3.49796
\(493\) 51.2461 2.30801
\(494\) 42.0655 1.89262
\(495\) 2.00460 0.0901000
\(496\) 0.399199 0.0179246
\(497\) −8.12571 −0.364488
\(498\) 29.5733 1.32521
\(499\) 24.2703 1.08649 0.543243 0.839575i \(-0.317196\pi\)
0.543243 + 0.839575i \(0.317196\pi\)
\(500\) −56.8727 −2.54343
\(501\) −12.1504 −0.542841
\(502\) −51.8636 −2.31479
\(503\) 4.80596 0.214287 0.107144 0.994244i \(-0.465830\pi\)
0.107144 + 0.994244i \(0.465830\pi\)
\(504\) 2.75074 0.122528
\(505\) 31.8018 1.41516
\(506\) −78.5355 −3.49133
\(507\) −2.31076 −0.102625
\(508\) −98.0901 −4.35205
\(509\) 12.3833 0.548881 0.274441 0.961604i \(-0.411507\pi\)
0.274441 + 0.961604i \(0.411507\pi\)
\(510\) −47.0192 −2.08204
\(511\) 8.24653 0.364805
\(512\) 45.6049 2.01547
\(513\) 25.6717 1.13343
\(514\) −15.7931 −0.696603
\(515\) 10.7535 0.473855
\(516\) −88.6568 −3.90290
\(517\) 6.98514 0.307206
\(518\) 21.5113 0.945154
\(519\) −38.5131 −1.69054
\(520\) −49.0032 −2.14893
\(521\) −22.6313 −0.991497 −0.495749 0.868466i \(-0.665106\pi\)
−0.495749 + 0.868466i \(0.665106\pi\)
\(522\) 6.53541 0.286047
\(523\) −24.4574 −1.06945 −0.534723 0.845027i \(-0.679584\pi\)
−0.534723 + 0.845027i \(0.679584\pi\)
\(524\) −37.8990 −1.65563
\(525\) −2.25739 −0.0985206
\(526\) 31.5869 1.37725
\(527\) 0.239442 0.0104303
\(528\) −55.9101 −2.43318
\(529\) 42.6474 1.85423
\(530\) −32.6815 −1.41959
\(531\) −1.94685 −0.0844861
\(532\) −32.5680 −1.41200
\(533\) −33.6524 −1.45765
\(534\) −51.8475 −2.24366
\(535\) 0.434998 0.0188066
\(536\) 35.1856 1.51979
\(537\) 10.4396 0.450504
\(538\) −71.6394 −3.08860
\(539\) 18.3537 0.790549
\(540\) −51.6526 −2.22277
\(541\) 7.63310 0.328172 0.164086 0.986446i \(-0.447532\pi\)
0.164086 + 0.986446i \(0.447532\pi\)
\(542\) 39.2630 1.68649
\(543\) −17.5173 −0.751739
\(544\) −50.3522 −2.15883
\(545\) 31.1219 1.33311
\(546\) −21.1027 −0.903110
\(547\) 26.3335 1.12594 0.562970 0.826478i \(-0.309659\pi\)
0.562970 + 0.826478i \(0.309659\pi\)
\(548\) −61.7058 −2.63594
\(549\) 3.05133 0.130228
\(550\) −9.17615 −0.391272
\(551\) −44.7997 −1.90853
\(552\) 95.7161 4.07395
\(553\) −16.7637 −0.712867
\(554\) −72.0792 −3.06235
\(555\) −19.1058 −0.810995
\(556\) −67.5142 −2.86324
\(557\) −29.0926 −1.23269 −0.616347 0.787475i \(-0.711388\pi\)
−0.616347 + 0.787475i \(0.711388\pi\)
\(558\) 0.0305360 0.00129269
\(559\) −38.4530 −1.62639
\(560\) 26.3237 1.11238
\(561\) −33.5352 −1.41586
\(562\) −11.0940 −0.467971
\(563\) −5.25239 −0.221362 −0.110681 0.993856i \(-0.535303\pi\)
−0.110681 + 0.993856i \(0.535303\pi\)
\(564\) −14.7039 −0.619147
\(565\) 19.6883 0.828294
\(566\) −69.9755 −2.94129
\(567\) −11.7237 −0.492348
\(568\) 40.2564 1.68912
\(569\) −28.7723 −1.20620 −0.603099 0.797666i \(-0.706068\pi\)
−0.603099 + 0.797666i \(0.706068\pi\)
\(570\) 41.1045 1.72168
\(571\) −11.0364 −0.461859 −0.230930 0.972970i \(-0.574177\pi\)
−0.230930 + 0.972970i \(0.574177\pi\)
\(572\) −60.3656 −2.52401
\(573\) 12.6593 0.528852
\(574\) 37.0238 1.54534
\(575\) 7.67030 0.319874
\(576\) −1.58275 −0.0659478
\(577\) 3.05554 0.127204 0.0636019 0.997975i \(-0.479741\pi\)
0.0636019 + 0.997975i \(0.479741\pi\)
\(578\) −32.6418 −1.35772
\(579\) 43.9959 1.82841
\(580\) 90.1388 3.74281
\(581\) −9.93077 −0.411998
\(582\) 19.2847 0.799376
\(583\) −23.3092 −0.965370
\(584\) −40.8549 −1.69059
\(585\) −1.83022 −0.0756704
\(586\) −15.1827 −0.627190
\(587\) 26.1743 1.08033 0.540164 0.841560i \(-0.318362\pi\)
0.540164 + 0.841560i \(0.318362\pi\)
\(588\) −38.6351 −1.59328
\(589\) −0.209322 −0.00862495
\(590\) −38.1569 −1.57089
\(591\) 9.45503 0.388928
\(592\) −52.0352 −2.13864
\(593\) −22.7743 −0.935229 −0.467615 0.883932i \(-0.654887\pi\)
−0.467615 + 0.883932i \(0.654887\pi\)
\(594\) −52.3504 −2.14796
\(595\) 15.7891 0.647291
\(596\) −23.2709 −0.953212
\(597\) −2.99225 −0.122465
\(598\) 71.7039 2.93219
\(599\) −37.8063 −1.54472 −0.772361 0.635183i \(-0.780925\pi\)
−0.772361 + 0.635183i \(0.780925\pi\)
\(600\) 11.1836 0.456567
\(601\) −34.3589 −1.40153 −0.700764 0.713393i \(-0.747157\pi\)
−0.700764 + 0.713393i \(0.747157\pi\)
\(602\) 42.3054 1.72424
\(603\) 1.31415 0.0535163
\(604\) 114.544 4.66075
\(605\) 5.87555 0.238875
\(606\) −67.8481 −2.75614
\(607\) −44.5187 −1.80696 −0.903480 0.428630i \(-0.858996\pi\)
−0.903480 + 0.428630i \(0.858996\pi\)
\(608\) 44.0182 1.78517
\(609\) 22.4743 0.910704
\(610\) 59.8039 2.42139
\(611\) −6.37752 −0.258007
\(612\) −6.89334 −0.278647
\(613\) −16.9501 −0.684609 −0.342305 0.939589i \(-0.611207\pi\)
−0.342305 + 0.939589i \(0.611207\pi\)
\(614\) 32.8599 1.32612
\(615\) −32.8835 −1.32599
\(616\) 38.4518 1.54927
\(617\) 17.8366 0.718073 0.359036 0.933324i \(-0.383105\pi\)
0.359036 + 0.933324i \(0.383105\pi\)
\(618\) −22.9422 −0.922870
\(619\) 15.2259 0.611982 0.305991 0.952034i \(-0.401012\pi\)
0.305991 + 0.952034i \(0.401012\pi\)
\(620\) 0.421164 0.0169144
\(621\) 43.7594 1.75601
\(622\) 43.0759 1.72719
\(623\) 17.4105 0.697537
\(624\) 51.0467 2.04350
\(625\) −19.3704 −0.774816
\(626\) −49.1110 −1.96287
\(627\) 29.3167 1.17080
\(628\) −53.6546 −2.14105
\(629\) −31.2111 −1.24447
\(630\) 2.01358 0.0802231
\(631\) 31.5181 1.25472 0.627359 0.778731i \(-0.284136\pi\)
0.627359 + 0.778731i \(0.284136\pi\)
\(632\) 83.0509 3.30359
\(633\) −18.3617 −0.729812
\(634\) −13.1305 −0.521480
\(635\) −41.5726 −1.64976
\(636\) 49.0666 1.94562
\(637\) −16.7572 −0.663943
\(638\) 91.3565 3.61684
\(639\) 1.50354 0.0594790
\(640\) 6.26780 0.247757
\(641\) 24.8029 0.979655 0.489828 0.871819i \(-0.337060\pi\)
0.489828 + 0.871819i \(0.337060\pi\)
\(642\) −0.928053 −0.0366273
\(643\) −1.70507 −0.0672412 −0.0336206 0.999435i \(-0.510704\pi\)
−0.0336206 + 0.999435i \(0.510704\pi\)
\(644\) −55.5146 −2.18758
\(645\) −37.5745 −1.47950
\(646\) 67.1480 2.64190
\(647\) 20.8917 0.821339 0.410669 0.911784i \(-0.365295\pi\)
0.410669 + 0.911784i \(0.365295\pi\)
\(648\) 58.0814 2.28165
\(649\) −27.2145 −1.06826
\(650\) 8.37794 0.328610
\(651\) 0.105009 0.00411562
\(652\) −46.4896 −1.82067
\(653\) −30.2909 −1.18538 −0.592688 0.805432i \(-0.701933\pi\)
−0.592688 + 0.805432i \(0.701933\pi\)
\(654\) −66.3975 −2.59635
\(655\) −16.0624 −0.627609
\(656\) −89.5595 −3.49671
\(657\) −1.52589 −0.0595308
\(658\) 7.01645 0.273530
\(659\) 33.6408 1.31046 0.655229 0.755430i \(-0.272572\pi\)
0.655229 + 0.755430i \(0.272572\pi\)
\(660\) −58.9865 −2.29605
\(661\) −19.7038 −0.766389 −0.383195 0.923668i \(-0.625176\pi\)
−0.383195 + 0.923668i \(0.625176\pi\)
\(662\) −70.9823 −2.75881
\(663\) 30.6181 1.18911
\(664\) 49.1990 1.90929
\(665\) −13.8030 −0.535256
\(666\) −3.98034 −0.154235
\(667\) −76.3645 −2.95684
\(668\) −34.9130 −1.35082
\(669\) 1.06606 0.0412161
\(670\) 25.7564 0.995056
\(671\) 42.6536 1.64663
\(672\) −22.0822 −0.851841
\(673\) 42.6013 1.64216 0.821080 0.570813i \(-0.193372\pi\)
0.821080 + 0.570813i \(0.193372\pi\)
\(674\) 1.54197 0.0593946
\(675\) 5.11289 0.196795
\(676\) −6.63973 −0.255374
\(677\) 5.88371 0.226129 0.113065 0.993588i \(-0.463933\pi\)
0.113065 + 0.993588i \(0.463933\pi\)
\(678\) −42.0044 −1.61317
\(679\) −6.47584 −0.248520
\(680\) −78.2224 −2.99969
\(681\) −5.62274 −0.215464
\(682\) 0.426854 0.0163451
\(683\) 30.9349 1.18369 0.591846 0.806051i \(-0.298399\pi\)
0.591846 + 0.806051i \(0.298399\pi\)
\(684\) 6.02620 0.230418
\(685\) −26.1522 −0.999222
\(686\) 44.6682 1.70544
\(687\) −27.9284 −1.06554
\(688\) −102.336 −3.90151
\(689\) 21.2816 0.810766
\(690\) 70.0657 2.66736
\(691\) 25.4504 0.968180 0.484090 0.875018i \(-0.339151\pi\)
0.484090 + 0.875018i \(0.339151\pi\)
\(692\) −110.663 −4.20679
\(693\) 1.43614 0.0545544
\(694\) 78.6728 2.98638
\(695\) −28.6139 −1.08539
\(696\) −111.342 −4.22041
\(697\) −53.7183 −2.03473
\(698\) −50.5334 −1.91272
\(699\) 24.2018 0.915395
\(700\) −6.48637 −0.245162
\(701\) −39.6667 −1.49819 −0.749094 0.662463i \(-0.769511\pi\)
−0.749094 + 0.662463i \(0.769511\pi\)
\(702\) 47.7966 1.80397
\(703\) 27.2849 1.02907
\(704\) −22.1248 −0.833858
\(705\) −6.23182 −0.234704
\(706\) −8.95185 −0.336907
\(707\) 22.7835 0.856862
\(708\) 57.2872 2.15299
\(709\) −13.9802 −0.525037 −0.262519 0.964927i \(-0.584553\pi\)
−0.262519 + 0.964927i \(0.584553\pi\)
\(710\) 29.4683 1.10593
\(711\) 3.10187 0.116329
\(712\) −86.2550 −3.23254
\(713\) −0.356805 −0.0133625
\(714\) −33.6856 −1.26065
\(715\) −25.5842 −0.956793
\(716\) 29.9972 1.12105
\(717\) 32.2796 1.20550
\(718\) 90.7199 3.38564
\(719\) −16.6240 −0.619972 −0.309986 0.950741i \(-0.600324\pi\)
−0.309986 + 0.950741i \(0.600324\pi\)
\(720\) −4.87080 −0.181524
\(721\) 7.70403 0.286913
\(722\) −9.33654 −0.347470
\(723\) −33.8475 −1.25880
\(724\) −50.3341 −1.87065
\(725\) −8.92249 −0.331373
\(726\) −12.5353 −0.465229
\(727\) −9.36085 −0.347175 −0.173587 0.984818i \(-0.555536\pi\)
−0.173587 + 0.984818i \(0.555536\pi\)
\(728\) −35.1070 −1.30115
\(729\) 28.9556 1.07243
\(730\) −29.9064 −1.10689
\(731\) −61.3815 −2.27028
\(732\) −89.7872 −3.31863
\(733\) −37.8108 −1.39657 −0.698286 0.715819i \(-0.746054\pi\)
−0.698286 + 0.715819i \(0.746054\pi\)
\(734\) 17.7851 0.656462
\(735\) −16.3743 −0.603976
\(736\) 75.0324 2.76573
\(737\) 18.3701 0.676671
\(738\) −6.85069 −0.252177
\(739\) 7.41914 0.272917 0.136459 0.990646i \(-0.456428\pi\)
0.136459 + 0.990646i \(0.456428\pi\)
\(740\) −54.8984 −2.01811
\(741\) −26.7665 −0.983293
\(742\) −23.4137 −0.859545
\(743\) 22.9086 0.840435 0.420217 0.907424i \(-0.361954\pi\)
0.420217 + 0.907424i \(0.361954\pi\)
\(744\) −0.520234 −0.0190727
\(745\) −9.86266 −0.361340
\(746\) 40.5976 1.48639
\(747\) 1.83754 0.0672320
\(748\) −96.3600 −3.52327
\(749\) 0.311642 0.0113871
\(750\) 51.4247 1.87776
\(751\) 22.8724 0.834624 0.417312 0.908763i \(-0.362972\pi\)
0.417312 + 0.908763i \(0.362972\pi\)
\(752\) −16.9726 −0.618927
\(753\) 33.0011 1.20263
\(754\) −83.4097 −3.03760
\(755\) 48.5462 1.76678
\(756\) −37.0051 −1.34586
\(757\) −15.9748 −0.580615 −0.290308 0.956933i \(-0.593758\pi\)
−0.290308 + 0.956933i \(0.593758\pi\)
\(758\) −91.4143 −3.32032
\(759\) 49.9726 1.81389
\(760\) 68.3825 2.48050
\(761\) −13.0772 −0.474047 −0.237024 0.971504i \(-0.576172\pi\)
−0.237024 + 0.971504i \(0.576172\pi\)
\(762\) 88.6937 3.21303
\(763\) 22.2964 0.807184
\(764\) 36.3753 1.31601
\(765\) −2.92153 −0.105628
\(766\) 20.5667 0.743107
\(767\) 24.8471 0.897178
\(768\) −32.9806 −1.19008
\(769\) −50.0321 −1.80420 −0.902102 0.431523i \(-0.857976\pi\)
−0.902102 + 0.431523i \(0.857976\pi\)
\(770\) 28.1473 1.01436
\(771\) 10.0492 0.361914
\(772\) 126.418 4.54987
\(773\) 12.5643 0.451906 0.225953 0.974138i \(-0.427450\pi\)
0.225953 + 0.974138i \(0.427450\pi\)
\(774\) −7.82797 −0.281371
\(775\) −0.0416894 −0.00149753
\(776\) 32.0826 1.15170
\(777\) −13.6878 −0.491047
\(778\) 1.56810 0.0562191
\(779\) 46.9609 1.68255
\(780\) 53.8554 1.92833
\(781\) 21.0175 0.752066
\(782\) 114.459 4.09304
\(783\) −50.9032 −1.81913
\(784\) −44.5960 −1.59272
\(785\) −22.7399 −0.811621
\(786\) 34.2685 1.22232
\(787\) −9.97149 −0.355445 −0.177723 0.984081i \(-0.556873\pi\)
−0.177723 + 0.984081i \(0.556873\pi\)
\(788\) 27.1680 0.967821
\(789\) −20.0989 −0.715541
\(790\) 60.7945 2.16297
\(791\) 14.1051 0.501521
\(792\) −7.11491 −0.252817
\(793\) −38.9433 −1.38292
\(794\) −18.1170 −0.642949
\(795\) 20.7954 0.737538
\(796\) −8.59791 −0.304745
\(797\) 39.0682 1.38387 0.691934 0.721961i \(-0.256759\pi\)
0.691934 + 0.721961i \(0.256759\pi\)
\(798\) 29.4481 1.04245
\(799\) −10.1803 −0.360152
\(800\) 8.76685 0.309955
\(801\) −3.22155 −0.113828
\(802\) 33.5286 1.18394
\(803\) −21.3300 −0.752720
\(804\) −38.6696 −1.36377
\(805\) −23.5282 −0.829260
\(806\) −0.389723 −0.0137274
\(807\) 45.5846 1.60465
\(808\) −112.874 −3.97089
\(809\) −39.8743 −1.40190 −0.700952 0.713208i \(-0.747242\pi\)
−0.700952 + 0.713208i \(0.747242\pi\)
\(810\) 42.5165 1.49388
\(811\) −21.7849 −0.764970 −0.382485 0.923962i \(-0.624932\pi\)
−0.382485 + 0.923962i \(0.624932\pi\)
\(812\) 64.5774 2.26622
\(813\) −24.9833 −0.876202
\(814\) −55.6400 −1.95018
\(815\) −19.7032 −0.690173
\(816\) 81.4844 2.85252
\(817\) 53.6601 1.87733
\(818\) −26.2127 −0.916505
\(819\) −1.31121 −0.0458175
\(820\) −94.4874 −3.29964
\(821\) −17.3108 −0.604150 −0.302075 0.953284i \(-0.597679\pi\)
−0.302075 + 0.953284i \(0.597679\pi\)
\(822\) 55.7948 1.94607
\(823\) −26.9088 −0.937980 −0.468990 0.883203i \(-0.655382\pi\)
−0.468990 + 0.883203i \(0.655382\pi\)
\(824\) −38.1673 −1.32962
\(825\) 5.83884 0.203282
\(826\) −27.3364 −0.951157
\(827\) 21.1406 0.735130 0.367565 0.929998i \(-0.380192\pi\)
0.367565 + 0.929998i \(0.380192\pi\)
\(828\) 10.2721 0.356981
\(829\) −44.5496 −1.54727 −0.773635 0.633631i \(-0.781564\pi\)
−0.773635 + 0.633631i \(0.781564\pi\)
\(830\) 36.0144 1.25008
\(831\) 45.8645 1.59102
\(832\) 20.2002 0.700315
\(833\) −26.7490 −0.926797
\(834\) 61.0468 2.11388
\(835\) −14.7968 −0.512065
\(836\) 84.2385 2.91345
\(837\) −0.237840 −0.00822096
\(838\) 10.9851 0.379475
\(839\) 25.7015 0.887315 0.443658 0.896196i \(-0.353681\pi\)
0.443658 + 0.896196i \(0.353681\pi\)
\(840\) −34.3049 −1.18363
\(841\) 59.8311 2.06314
\(842\) −36.0295 −1.24166
\(843\) 7.05917 0.243131
\(844\) −52.7604 −1.81609
\(845\) −2.81405 −0.0968063
\(846\) −1.29829 −0.0446360
\(847\) 4.20938 0.144636
\(848\) 56.6371 1.94493
\(849\) 44.5259 1.52812
\(850\) 13.3735 0.458706
\(851\) 46.5092 1.59432
\(852\) −44.2425 −1.51572
\(853\) 31.3102 1.07204 0.536021 0.844205i \(-0.319927\pi\)
0.536021 + 0.844205i \(0.319927\pi\)
\(854\) 42.8449 1.46612
\(855\) 2.55402 0.0873458
\(856\) −1.54394 −0.0527706
\(857\) 25.5767 0.873684 0.436842 0.899538i \(-0.356097\pi\)
0.436842 + 0.899538i \(0.356097\pi\)
\(858\) 54.5830 1.86343
\(859\) −55.5478 −1.89527 −0.947633 0.319361i \(-0.896532\pi\)
−0.947633 + 0.319361i \(0.896532\pi\)
\(860\) −107.966 −3.68162
\(861\) −23.5585 −0.802872
\(862\) 22.7055 0.773351
\(863\) 39.5856 1.34751 0.673754 0.738955i \(-0.264681\pi\)
0.673754 + 0.738955i \(0.264681\pi\)
\(864\) 50.0153 1.70155
\(865\) −46.9014 −1.59469
\(866\) 40.9060 1.39004
\(867\) 20.7702 0.705393
\(868\) 0.301731 0.0102414
\(869\) 43.3602 1.47089
\(870\) −81.5041 −2.76325
\(871\) −16.7721 −0.568302
\(872\) −110.461 −3.74067
\(873\) 1.19825 0.0405548
\(874\) −100.061 −3.38460
\(875\) −17.2685 −0.583782
\(876\) 44.9003 1.51704
\(877\) −38.2386 −1.29123 −0.645613 0.763665i \(-0.723398\pi\)
−0.645613 + 0.763665i \(0.723398\pi\)
\(878\) −77.2244 −2.60620
\(879\) 9.66083 0.325852
\(880\) −68.0875 −2.29523
\(881\) −25.7037 −0.865979 −0.432990 0.901399i \(-0.642541\pi\)
−0.432990 + 0.901399i \(0.642541\pi\)
\(882\) −3.41129 −0.114864
\(883\) −19.9929 −0.672816 −0.336408 0.941716i \(-0.609212\pi\)
−0.336408 + 0.941716i \(0.609212\pi\)
\(884\) 87.9779 2.95902
\(885\) 24.2795 0.816146
\(886\) −56.2423 −1.88950
\(887\) 23.8844 0.801960 0.400980 0.916087i \(-0.368670\pi\)
0.400980 + 0.916087i \(0.368670\pi\)
\(888\) 67.8120 2.27562
\(889\) −29.7835 −0.998907
\(890\) −63.1400 −2.11646
\(891\) 30.3238 1.01589
\(892\) 3.06320 0.102564
\(893\) 8.89965 0.297815
\(894\) 21.0417 0.703738
\(895\) 12.7134 0.424963
\(896\) 4.49039 0.150014
\(897\) −45.6256 −1.52340
\(898\) −29.2039 −0.974547
\(899\) 0.415054 0.0138428
\(900\) 1.20020 0.0400068
\(901\) 33.9713 1.13175
\(902\) −95.7638 −3.18859
\(903\) −26.9192 −0.895816
\(904\) −69.8797 −2.32416
\(905\) −21.3326 −0.709119
\(906\) −103.572 −3.44094
\(907\) 9.87344 0.327842 0.163921 0.986473i \(-0.447586\pi\)
0.163921 + 0.986473i \(0.447586\pi\)
\(908\) −16.1564 −0.536167
\(909\) −4.21574 −0.139827
\(910\) −25.6988 −0.851909
\(911\) −53.4567 −1.77110 −0.885550 0.464544i \(-0.846218\pi\)
−0.885550 + 0.464544i \(0.846218\pi\)
\(912\) −71.2342 −2.35880
\(913\) 25.6864 0.850095
\(914\) −72.0645 −2.38368
\(915\) −38.0536 −1.25801
\(916\) −80.2494 −2.65152
\(917\) −11.5074 −0.380009
\(918\) 76.2963 2.51815
\(919\) 17.3223 0.571410 0.285705 0.958318i \(-0.407772\pi\)
0.285705 + 0.958318i \(0.407772\pi\)
\(920\) 116.563 3.84298
\(921\) −20.9090 −0.688974
\(922\) −16.3814 −0.539491
\(923\) −19.1893 −0.631622
\(924\) −42.2592 −1.39023
\(925\) 5.43418 0.178675
\(926\) 12.5483 0.412362
\(927\) −1.42551 −0.0468200
\(928\) −87.2815 −2.86516
\(929\) 7.81347 0.256352 0.128176 0.991751i \(-0.459088\pi\)
0.128176 + 0.991751i \(0.459088\pi\)
\(930\) −0.380819 −0.0124876
\(931\) 23.3841 0.766384
\(932\) 69.5412 2.27790
\(933\) −27.4095 −0.897346
\(934\) 88.5144 2.89628
\(935\) −40.8393 −1.33559
\(936\) 6.49601 0.212329
\(937\) −40.7916 −1.33260 −0.666301 0.745683i \(-0.732123\pi\)
−0.666301 + 0.745683i \(0.732123\pi\)
\(938\) 18.4524 0.602494
\(939\) 31.2496 1.01979
\(940\) −17.9065 −0.584045
\(941\) −26.1953 −0.853941 −0.426971 0.904266i \(-0.640419\pi\)
−0.426971 + 0.904266i \(0.640419\pi\)
\(942\) 48.5148 1.58070
\(943\) 80.0485 2.60674
\(944\) 66.1260 2.15222
\(945\) −15.6835 −0.510184
\(946\) −109.425 −3.55771
\(947\) −45.8628 −1.49034 −0.745171 0.666873i \(-0.767632\pi\)
−0.745171 + 0.666873i \(0.767632\pi\)
\(948\) −91.2745 −2.96446
\(949\) 19.4746 0.632171
\(950\) −11.6912 −0.379312
\(951\) 8.35503 0.270931
\(952\) −56.0403 −1.81628
\(953\) 24.0684 0.779652 0.389826 0.920888i \(-0.372535\pi\)
0.389826 + 0.920888i \(0.372535\pi\)
\(954\) 4.33235 0.140265
\(955\) 15.4166 0.498868
\(956\) 92.7520 2.99982
\(957\) −58.1307 −1.87910
\(958\) 25.0894 0.810601
\(959\) −18.7360 −0.605016
\(960\) 19.7387 0.637063
\(961\) −30.9981 −0.999937
\(962\) 50.8001 1.63786
\(963\) −0.0576646 −0.00185821
\(964\) −97.2573 −3.13245
\(965\) 53.5783 1.72475
\(966\) 50.1966 1.61505
\(967\) 48.7240 1.56686 0.783429 0.621481i \(-0.213469\pi\)
0.783429 + 0.621481i \(0.213469\pi\)
\(968\) −20.8541 −0.670276
\(969\) −42.7267 −1.37258
\(970\) 23.4849 0.754056
\(971\) 13.3886 0.429661 0.214830 0.976651i \(-0.431080\pi\)
0.214830 + 0.976651i \(0.431080\pi\)
\(972\) 13.1351 0.421307
\(973\) −20.4996 −0.657188
\(974\) −38.0587 −1.21948
\(975\) −5.33094 −0.170727
\(976\) −103.640 −3.31745
\(977\) 55.7634 1.78403 0.892015 0.452006i \(-0.149291\pi\)
0.892015 + 0.452006i \(0.149291\pi\)
\(978\) 42.0362 1.34417
\(979\) −45.0330 −1.43926
\(980\) −47.0499 −1.50295
\(981\) −4.12561 −0.131720
\(982\) 25.7353 0.821248
\(983\) 26.5135 0.845648 0.422824 0.906212i \(-0.361039\pi\)
0.422824 + 0.906212i \(0.361039\pi\)
\(984\) 116.713 3.72069
\(985\) 11.5144 0.366878
\(986\) −133.145 −4.24018
\(987\) −4.46461 −0.142110
\(988\) −76.9108 −2.44686
\(989\) 91.4677 2.90851
\(990\) −5.20823 −0.165528
\(991\) 56.1775 1.78454 0.892268 0.451506i \(-0.149113\pi\)
0.892268 + 0.451506i \(0.149113\pi\)
\(992\) −0.407814 −0.0129481
\(993\) 45.1665 1.43332
\(994\) 21.1117 0.669624
\(995\) −3.64397 −0.115521
\(996\) −54.0706 −1.71329
\(997\) −8.72525 −0.276331 −0.138166 0.990409i \(-0.544121\pi\)
−0.138166 + 0.990409i \(0.544121\pi\)
\(998\) −63.0576 −1.99605
\(999\) 31.0023 0.980868
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 6029.2.a.a.1.10 234
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6029.2.a.a.1.10 234 1.1 even 1 trivial