Properties

Label 6043.2.a.c.1.8
Level $6043$
Weight $2$
Character 6043.1
Self dual yes
Analytic conductor $48.254$
Analytic rank $0$
Dimension $259$
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] = [6043,2,Mod(1,6043)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6043, 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("6043.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6043 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6043.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: \(48.2535979415\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 6043.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.62452 q^{2} -2.36333 q^{3} +4.88811 q^{4} +3.68491 q^{5} +6.20260 q^{6} +1.44250 q^{7} -7.57990 q^{8} +2.58531 q^{9} +O(q^{10})\) \(q-2.62452 q^{2} -2.36333 q^{3} +4.88811 q^{4} +3.68491 q^{5} +6.20260 q^{6} +1.44250 q^{7} -7.57990 q^{8} +2.58531 q^{9} -9.67113 q^{10} -2.04225 q^{11} -11.5522 q^{12} +4.18689 q^{13} -3.78586 q^{14} -8.70865 q^{15} +10.1174 q^{16} +6.70285 q^{17} -6.78519 q^{18} +3.78984 q^{19} +18.0123 q^{20} -3.40909 q^{21} +5.35994 q^{22} -1.61930 q^{23} +17.9138 q^{24} +8.57859 q^{25} -10.9886 q^{26} +0.980053 q^{27} +7.05108 q^{28} +2.83106 q^{29} +22.8560 q^{30} +1.97280 q^{31} -11.3935 q^{32} +4.82651 q^{33} -17.5918 q^{34} +5.31548 q^{35} +12.6373 q^{36} -3.63001 q^{37} -9.94652 q^{38} -9.89498 q^{39} -27.9313 q^{40} +10.1067 q^{41} +8.94722 q^{42} -4.57801 q^{43} -9.98275 q^{44} +9.52664 q^{45} +4.24990 q^{46} +5.72661 q^{47} -23.9107 q^{48} -4.91920 q^{49} -22.5147 q^{50} -15.8410 q^{51} +20.4660 q^{52} +0.958172 q^{53} -2.57217 q^{54} -7.52553 q^{55} -10.9340 q^{56} -8.95664 q^{57} -7.43017 q^{58} +9.09821 q^{59} -42.5688 q^{60} -6.37699 q^{61} -5.17767 q^{62} +3.72930 q^{63} +9.66764 q^{64} +15.4283 q^{65} -12.6673 q^{66} +4.49415 q^{67} +32.7642 q^{68} +3.82694 q^{69} -13.9506 q^{70} -1.97391 q^{71} -19.5964 q^{72} +3.64190 q^{73} +9.52704 q^{74} -20.2740 q^{75} +18.5252 q^{76} -2.94594 q^{77} +25.9696 q^{78} -3.02288 q^{79} +37.2817 q^{80} -10.0721 q^{81} -26.5254 q^{82} -3.50471 q^{83} -16.6640 q^{84} +24.6994 q^{85} +12.0151 q^{86} -6.69072 q^{87} +15.4801 q^{88} +11.6591 q^{89} -25.0029 q^{90} +6.03957 q^{91} -7.91533 q^{92} -4.66238 q^{93} -15.0296 q^{94} +13.9653 q^{95} +26.9265 q^{96} +8.22875 q^{97} +12.9106 q^{98} -5.27985 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62452 −1.85582 −0.927908 0.372809i \(-0.878395\pi\)
−0.927908 + 0.372809i \(0.878395\pi\)
\(3\) −2.36333 −1.36447 −0.682233 0.731135i \(-0.738991\pi\)
−0.682233 + 0.731135i \(0.738991\pi\)
\(4\) 4.88811 2.44405
\(5\) 3.68491 1.64794 0.823972 0.566631i \(-0.191753\pi\)
0.823972 + 0.566631i \(0.191753\pi\)
\(6\) 6.20260 2.53220
\(7\) 1.44250 0.545212 0.272606 0.962126i \(-0.412114\pi\)
0.272606 + 0.962126i \(0.412114\pi\)
\(8\) −7.57990 −2.67990
\(9\) 2.58531 0.861769
\(10\) −9.67113 −3.05828
\(11\) −2.04225 −0.615763 −0.307881 0.951425i \(-0.599620\pi\)
−0.307881 + 0.951425i \(0.599620\pi\)
\(12\) −11.5522 −3.33483
\(13\) 4.18689 1.16123 0.580617 0.814177i \(-0.302811\pi\)
0.580617 + 0.814177i \(0.302811\pi\)
\(14\) −3.78586 −1.01181
\(15\) −8.70865 −2.24856
\(16\) 10.1174 2.52934
\(17\) 6.70285 1.62568 0.812840 0.582487i \(-0.197920\pi\)
0.812840 + 0.582487i \(0.197920\pi\)
\(18\) −6.78519 −1.59929
\(19\) 3.78984 0.869450 0.434725 0.900563i \(-0.356846\pi\)
0.434725 + 0.900563i \(0.356846\pi\)
\(20\) 18.0123 4.02766
\(21\) −3.40909 −0.743924
\(22\) 5.35994 1.14274
\(23\) −1.61930 −0.337648 −0.168824 0.985646i \(-0.553997\pi\)
−0.168824 + 0.985646i \(0.553997\pi\)
\(24\) 17.9138 3.65663
\(25\) 8.57859 1.71572
\(26\) −10.9886 −2.15504
\(27\) 0.980053 0.188611
\(28\) 7.05108 1.33253
\(29\) 2.83106 0.525715 0.262857 0.964835i \(-0.415335\pi\)
0.262857 + 0.964835i \(0.415335\pi\)
\(30\) 22.8560 4.17292
\(31\) 1.97280 0.354326 0.177163 0.984182i \(-0.443308\pi\)
0.177163 + 0.984182i \(0.443308\pi\)
\(32\) −11.3935 −2.01410
\(33\) 4.82651 0.840188
\(34\) −17.5918 −3.01696
\(35\) 5.31548 0.898479
\(36\) 12.6373 2.10621
\(37\) −3.63001 −0.596770 −0.298385 0.954446i \(-0.596448\pi\)
−0.298385 + 0.954446i \(0.596448\pi\)
\(38\) −9.94652 −1.61354
\(39\) −9.89498 −1.58446
\(40\) −27.9313 −4.41632
\(41\) 10.1067 1.57841 0.789204 0.614131i \(-0.210493\pi\)
0.789204 + 0.614131i \(0.210493\pi\)
\(42\) 8.94722 1.38059
\(43\) −4.57801 −0.698140 −0.349070 0.937097i \(-0.613502\pi\)
−0.349070 + 0.937097i \(0.613502\pi\)
\(44\) −9.98275 −1.50496
\(45\) 9.52664 1.42015
\(46\) 4.24990 0.626613
\(47\) 5.72661 0.835311 0.417656 0.908605i \(-0.362852\pi\)
0.417656 + 0.908605i \(0.362852\pi\)
\(48\) −23.9107 −3.45121
\(49\) −4.91920 −0.702743
\(50\) −22.5147 −3.18406
\(51\) −15.8410 −2.21819
\(52\) 20.4660 2.83812
\(53\) 0.958172 0.131615 0.0658075 0.997832i \(-0.479038\pi\)
0.0658075 + 0.997832i \(0.479038\pi\)
\(54\) −2.57217 −0.350028
\(55\) −7.52553 −1.01474
\(56\) −10.9340 −1.46111
\(57\) −8.95664 −1.18634
\(58\) −7.43017 −0.975630
\(59\) 9.09821 1.18449 0.592243 0.805759i \(-0.298242\pi\)
0.592243 + 0.805759i \(0.298242\pi\)
\(60\) −42.5688 −5.49561
\(61\) −6.37699 −0.816490 −0.408245 0.912872i \(-0.633859\pi\)
−0.408245 + 0.912872i \(0.633859\pi\)
\(62\) −5.17767 −0.657564
\(63\) 3.72930 0.469847
\(64\) 9.66764 1.20846
\(65\) 15.4283 1.91365
\(66\) −12.6673 −1.55923
\(67\) 4.49415 0.549048 0.274524 0.961580i \(-0.411480\pi\)
0.274524 + 0.961580i \(0.411480\pi\)
\(68\) 32.7642 3.97325
\(69\) 3.82694 0.460710
\(70\) −13.9506 −1.66741
\(71\) −1.97391 −0.234259 −0.117130 0.993117i \(-0.537369\pi\)
−0.117130 + 0.993117i \(0.537369\pi\)
\(72\) −19.5964 −2.30945
\(73\) 3.64190 0.426252 0.213126 0.977025i \(-0.431635\pi\)
0.213126 + 0.977025i \(0.431635\pi\)
\(74\) 9.52704 1.10750
\(75\) −20.2740 −2.34104
\(76\) 18.5252 2.12498
\(77\) −2.94594 −0.335721
\(78\) 25.9696 2.94047
\(79\) −3.02288 −0.340100 −0.170050 0.985435i \(-0.554393\pi\)
−0.170050 + 0.985435i \(0.554393\pi\)
\(80\) 37.2817 4.16822
\(81\) −10.0721 −1.11912
\(82\) −26.5254 −2.92924
\(83\) −3.50471 −0.384691 −0.192346 0.981327i \(-0.561610\pi\)
−0.192346 + 0.981327i \(0.561610\pi\)
\(84\) −16.6640 −1.81819
\(85\) 24.6994 2.67903
\(86\) 12.0151 1.29562
\(87\) −6.69072 −0.717320
\(88\) 15.4801 1.65018
\(89\) 11.6591 1.23586 0.617932 0.786231i \(-0.287971\pi\)
0.617932 + 0.786231i \(0.287971\pi\)
\(90\) −25.0029 −2.63553
\(91\) 6.03957 0.633119
\(92\) −7.91533 −0.825230
\(93\) −4.66238 −0.483466
\(94\) −15.0296 −1.55018
\(95\) 13.9653 1.43280
\(96\) 26.9265 2.74817
\(97\) 8.22875 0.835503 0.417752 0.908561i \(-0.362818\pi\)
0.417752 + 0.908561i \(0.362818\pi\)
\(98\) 12.9106 1.30416
\(99\) −5.27985 −0.530645
\(100\) 41.9331 4.19331
\(101\) 12.3860 1.23245 0.616226 0.787569i \(-0.288661\pi\)
0.616226 + 0.787569i \(0.288661\pi\)
\(102\) 41.5751 4.11655
\(103\) 4.92656 0.485429 0.242714 0.970098i \(-0.421962\pi\)
0.242714 + 0.970098i \(0.421962\pi\)
\(104\) −31.7362 −3.11199
\(105\) −12.5622 −1.22595
\(106\) −2.51474 −0.244253
\(107\) −2.17911 −0.210663 −0.105331 0.994437i \(-0.533590\pi\)
−0.105331 + 0.994437i \(0.533590\pi\)
\(108\) 4.79060 0.460976
\(109\) −9.72180 −0.931180 −0.465590 0.885001i \(-0.654158\pi\)
−0.465590 + 0.885001i \(0.654158\pi\)
\(110\) 19.7509 1.88318
\(111\) 8.57890 0.814273
\(112\) 14.5943 1.37903
\(113\) 17.4592 1.64242 0.821211 0.570625i \(-0.193299\pi\)
0.821211 + 0.570625i \(0.193299\pi\)
\(114\) 23.5069 2.20162
\(115\) −5.96700 −0.556425
\(116\) 13.8385 1.28487
\(117\) 10.8244 1.00072
\(118\) −23.8784 −2.19819
\(119\) 9.66884 0.886341
\(120\) 66.0107 6.02592
\(121\) −6.82920 −0.620836
\(122\) 16.7365 1.51526
\(123\) −23.8855 −2.15369
\(124\) 9.64328 0.865992
\(125\) 13.1868 1.17946
\(126\) −9.78762 −0.871950
\(127\) 6.48617 0.575555 0.287777 0.957697i \(-0.407084\pi\)
0.287777 + 0.957697i \(0.407084\pi\)
\(128\) −2.58598 −0.228570
\(129\) 10.8193 0.952588
\(130\) −40.4919 −3.55138
\(131\) −0.598287 −0.0522726 −0.0261363 0.999658i \(-0.508320\pi\)
−0.0261363 + 0.999658i \(0.508320\pi\)
\(132\) 23.5925 2.05346
\(133\) 5.46684 0.474035
\(134\) −11.7950 −1.01893
\(135\) 3.61141 0.310821
\(136\) −50.8069 −4.35666
\(137\) 3.79200 0.323972 0.161986 0.986793i \(-0.448210\pi\)
0.161986 + 0.986793i \(0.448210\pi\)
\(138\) −10.0439 −0.854993
\(139\) 1.58937 0.134809 0.0674043 0.997726i \(-0.478528\pi\)
0.0674043 + 0.997726i \(0.478528\pi\)
\(140\) 25.9826 2.19593
\(141\) −13.5338 −1.13975
\(142\) 5.18056 0.434743
\(143\) −8.55069 −0.715044
\(144\) 26.1565 2.17971
\(145\) 10.4322 0.866348
\(146\) −9.55824 −0.791046
\(147\) 11.6257 0.958870
\(148\) −17.7439 −1.45854
\(149\) −6.76024 −0.553820 −0.276910 0.960896i \(-0.589310\pi\)
−0.276910 + 0.960896i \(0.589310\pi\)
\(150\) 53.2096 4.34454
\(151\) −19.3917 −1.57807 −0.789035 0.614348i \(-0.789419\pi\)
−0.789035 + 0.614348i \(0.789419\pi\)
\(152\) −28.7266 −2.33004
\(153\) 17.3289 1.40096
\(154\) 7.73169 0.623037
\(155\) 7.26962 0.583910
\(156\) −48.3677 −3.87252
\(157\) 14.9557 1.19359 0.596796 0.802393i \(-0.296440\pi\)
0.596796 + 0.802393i \(0.296440\pi\)
\(158\) 7.93360 0.631163
\(159\) −2.26447 −0.179584
\(160\) −41.9840 −3.31912
\(161\) −2.33584 −0.184090
\(162\) 26.4345 2.07689
\(163\) 16.0042 1.25354 0.626772 0.779202i \(-0.284376\pi\)
0.626772 + 0.779202i \(0.284376\pi\)
\(164\) 49.4029 3.85772
\(165\) 17.7853 1.38458
\(166\) 9.19817 0.713917
\(167\) −6.75575 −0.522776 −0.261388 0.965234i \(-0.584180\pi\)
−0.261388 + 0.965234i \(0.584180\pi\)
\(168\) 25.8405 1.99364
\(169\) 4.53002 0.348463
\(170\) −64.8242 −4.97179
\(171\) 9.79791 0.749265
\(172\) −22.3778 −1.70629
\(173\) −7.07484 −0.537890 −0.268945 0.963156i \(-0.586675\pi\)
−0.268945 + 0.963156i \(0.586675\pi\)
\(174\) 17.5599 1.33121
\(175\) 12.3746 0.935431
\(176\) −20.6623 −1.55748
\(177\) −21.5020 −1.61619
\(178\) −30.5996 −2.29354
\(179\) 5.34826 0.399748 0.199874 0.979822i \(-0.435947\pi\)
0.199874 + 0.979822i \(0.435947\pi\)
\(180\) 46.5672 3.47092
\(181\) 6.47765 0.481480 0.240740 0.970590i \(-0.422610\pi\)
0.240740 + 0.970590i \(0.422610\pi\)
\(182\) −15.8510 −1.17495
\(183\) 15.0709 1.11407
\(184\) 12.2742 0.904863
\(185\) −13.3763 −0.983444
\(186\) 12.2365 0.897224
\(187\) −13.6889 −1.00103
\(188\) 27.9923 2.04155
\(189\) 1.41372 0.102833
\(190\) −36.6521 −2.65902
\(191\) −18.6051 −1.34621 −0.673107 0.739545i \(-0.735041\pi\)
−0.673107 + 0.739545i \(0.735041\pi\)
\(192\) −22.8478 −1.64890
\(193\) −1.49834 −0.107853 −0.0539264 0.998545i \(-0.517174\pi\)
−0.0539264 + 0.998545i \(0.517174\pi\)
\(194\) −21.5965 −1.55054
\(195\) −36.4621 −2.61111
\(196\) −24.0456 −1.71754
\(197\) 10.5944 0.754821 0.377411 0.926046i \(-0.376815\pi\)
0.377411 + 0.926046i \(0.376815\pi\)
\(198\) 13.8571 0.984780
\(199\) −21.2696 −1.50776 −0.753882 0.657010i \(-0.771821\pi\)
−0.753882 + 0.657010i \(0.771821\pi\)
\(200\) −65.0248 −4.59795
\(201\) −10.6212 −0.749158
\(202\) −32.5073 −2.28721
\(203\) 4.08379 0.286626
\(204\) −77.4326 −5.42137
\(205\) 37.2425 2.60113
\(206\) −12.9299 −0.900866
\(207\) −4.18640 −0.290975
\(208\) 42.3603 2.93716
\(209\) −7.73982 −0.535375
\(210\) 32.9697 2.27513
\(211\) 15.4221 1.06170 0.530851 0.847465i \(-0.321872\pi\)
0.530851 + 0.847465i \(0.321872\pi\)
\(212\) 4.68365 0.321674
\(213\) 4.66498 0.319639
\(214\) 5.71913 0.390952
\(215\) −16.8696 −1.15049
\(216\) −7.42870 −0.505459
\(217\) 2.84576 0.193183
\(218\) 25.5151 1.72810
\(219\) −8.60700 −0.581607
\(220\) −36.7856 −2.48008
\(221\) 28.0641 1.88779
\(222\) −22.5155 −1.51114
\(223\) −24.0319 −1.60929 −0.804646 0.593755i \(-0.797645\pi\)
−0.804646 + 0.593755i \(0.797645\pi\)
\(224\) −16.4350 −1.09811
\(225\) 22.1783 1.47855
\(226\) −45.8220 −3.04803
\(227\) 20.0790 1.33269 0.666347 0.745642i \(-0.267857\pi\)
0.666347 + 0.745642i \(0.267857\pi\)
\(228\) −43.7810 −2.89947
\(229\) −23.9178 −1.58053 −0.790267 0.612763i \(-0.790058\pi\)
−0.790267 + 0.612763i \(0.790058\pi\)
\(230\) 15.6605 1.03262
\(231\) 6.96222 0.458081
\(232\) −21.4591 −1.40886
\(233\) −18.3749 −1.20378 −0.601890 0.798579i \(-0.705585\pi\)
−0.601890 + 0.798579i \(0.705585\pi\)
\(234\) −28.4088 −1.85714
\(235\) 21.1021 1.37655
\(236\) 44.4730 2.89495
\(237\) 7.14404 0.464055
\(238\) −25.3761 −1.64489
\(239\) −18.6664 −1.20743 −0.603716 0.797200i \(-0.706314\pi\)
−0.603716 + 0.797200i \(0.706314\pi\)
\(240\) −88.1087 −5.68739
\(241\) −12.6233 −0.813136 −0.406568 0.913621i \(-0.633275\pi\)
−0.406568 + 0.913621i \(0.633275\pi\)
\(242\) 17.9234 1.15216
\(243\) 20.8635 1.33839
\(244\) −31.1714 −1.99555
\(245\) −18.1268 −1.15808
\(246\) 62.6881 3.99685
\(247\) 15.8676 1.00963
\(248\) −14.9537 −0.949558
\(249\) 8.28276 0.524899
\(250\) −34.6091 −2.18887
\(251\) −21.4104 −1.35141 −0.675705 0.737172i \(-0.736161\pi\)
−0.675705 + 0.737172i \(0.736161\pi\)
\(252\) 18.2292 1.14833
\(253\) 3.30703 0.207911
\(254\) −17.0231 −1.06812
\(255\) −58.3728 −3.65545
\(256\) −12.5483 −0.784270
\(257\) 17.7172 1.10517 0.552585 0.833457i \(-0.313641\pi\)
0.552585 + 0.833457i \(0.313641\pi\)
\(258\) −28.3955 −1.76783
\(259\) −5.23628 −0.325367
\(260\) 75.4153 4.67706
\(261\) 7.31916 0.453045
\(262\) 1.57022 0.0970083
\(263\) −24.2460 −1.49507 −0.747537 0.664221i \(-0.768764\pi\)
−0.747537 + 0.664221i \(0.768764\pi\)
\(264\) −36.5844 −2.25162
\(265\) 3.53078 0.216894
\(266\) −14.3478 −0.879722
\(267\) −27.5543 −1.68630
\(268\) 21.9679 1.34190
\(269\) 12.8653 0.784410 0.392205 0.919878i \(-0.371712\pi\)
0.392205 + 0.919878i \(0.371712\pi\)
\(270\) −9.47822 −0.576826
\(271\) 5.28306 0.320923 0.160461 0.987042i \(-0.448702\pi\)
0.160461 + 0.987042i \(0.448702\pi\)
\(272\) 67.8153 4.11190
\(273\) −14.2735 −0.863870
\(274\) −9.95218 −0.601233
\(275\) −17.5197 −1.05648
\(276\) 18.7065 1.12600
\(277\) 17.1917 1.03295 0.516474 0.856303i \(-0.327244\pi\)
0.516474 + 0.856303i \(0.327244\pi\)
\(278\) −4.17134 −0.250180
\(279\) 5.10031 0.305347
\(280\) −40.2908 −2.40783
\(281\) 13.4915 0.804835 0.402418 0.915456i \(-0.368170\pi\)
0.402418 + 0.915456i \(0.368170\pi\)
\(282\) 35.5198 2.11517
\(283\) 15.9173 0.946183 0.473092 0.881013i \(-0.343138\pi\)
0.473092 + 0.881013i \(0.343138\pi\)
\(284\) −9.64866 −0.572543
\(285\) −33.0044 −1.95501
\(286\) 22.4414 1.32699
\(287\) 14.5789 0.860568
\(288\) −29.4556 −1.73569
\(289\) 27.9282 1.64284
\(290\) −27.3796 −1.60778
\(291\) −19.4472 −1.14002
\(292\) 17.8020 1.04178
\(293\) −30.4994 −1.78179 −0.890896 0.454207i \(-0.849923\pi\)
−0.890896 + 0.454207i \(0.849923\pi\)
\(294\) −30.5118 −1.77949
\(295\) 33.5261 1.95197
\(296\) 27.5151 1.59928
\(297\) −2.00152 −0.116140
\(298\) 17.7424 1.02779
\(299\) −6.77984 −0.392088
\(300\) −99.1015 −5.72163
\(301\) −6.60376 −0.380634
\(302\) 50.8938 2.92861
\(303\) −29.2721 −1.68164
\(304\) 38.3433 2.19914
\(305\) −23.4987 −1.34553
\(306\) −45.4801 −2.59993
\(307\) −25.1799 −1.43710 −0.718548 0.695478i \(-0.755193\pi\)
−0.718548 + 0.695478i \(0.755193\pi\)
\(308\) −14.4001 −0.820521
\(309\) −11.6431 −0.662351
\(310\) −19.0793 −1.08363
\(311\) −24.8377 −1.40841 −0.704207 0.709994i \(-0.748697\pi\)
−0.704207 + 0.709994i \(0.748697\pi\)
\(312\) 75.0029 4.24620
\(313\) −17.2778 −0.976599 −0.488300 0.872676i \(-0.662383\pi\)
−0.488300 + 0.872676i \(0.662383\pi\)
\(314\) −39.2515 −2.21509
\(315\) 13.7421 0.774282
\(316\) −14.7761 −0.831223
\(317\) −4.17294 −0.234376 −0.117188 0.993110i \(-0.537388\pi\)
−0.117188 + 0.993110i \(0.537388\pi\)
\(318\) 5.94316 0.333276
\(319\) −5.78174 −0.323715
\(320\) 35.6244 1.99147
\(321\) 5.14996 0.287443
\(322\) 6.13046 0.341637
\(323\) 25.4028 1.41345
\(324\) −49.2335 −2.73520
\(325\) 35.9176 1.99235
\(326\) −42.0033 −2.32635
\(327\) 22.9758 1.27056
\(328\) −76.6081 −4.22997
\(329\) 8.26061 0.455422
\(330\) −46.6778 −2.56953
\(331\) −14.8212 −0.814647 −0.407323 0.913284i \(-0.633538\pi\)
−0.407323 + 0.913284i \(0.633538\pi\)
\(332\) −17.1314 −0.940207
\(333\) −9.38470 −0.514278
\(334\) 17.7306 0.970175
\(335\) 16.5606 0.904801
\(336\) −34.4910 −1.88164
\(337\) 3.36606 0.183361 0.0916805 0.995788i \(-0.470776\pi\)
0.0916805 + 0.995788i \(0.470776\pi\)
\(338\) −11.8891 −0.646684
\(339\) −41.2617 −2.24103
\(340\) 120.733 6.54769
\(341\) −4.02897 −0.218181
\(342\) −25.7148 −1.39050
\(343\) −17.1934 −0.928357
\(344\) 34.7008 1.87094
\(345\) 14.1020 0.759224
\(346\) 18.5681 0.998225
\(347\) 8.88548 0.476997 0.238499 0.971143i \(-0.423345\pi\)
0.238499 + 0.971143i \(0.423345\pi\)
\(348\) −32.7049 −1.75317
\(349\) −29.2784 −1.56724 −0.783619 0.621242i \(-0.786628\pi\)
−0.783619 + 0.621242i \(0.786628\pi\)
\(350\) −32.4774 −1.73599
\(351\) 4.10337 0.219022
\(352\) 23.2684 1.24021
\(353\) −3.25932 −0.173476 −0.0867381 0.996231i \(-0.527644\pi\)
−0.0867381 + 0.996231i \(0.527644\pi\)
\(354\) 56.4325 2.99936
\(355\) −7.27367 −0.386046
\(356\) 56.9910 3.02052
\(357\) −22.8506 −1.20938
\(358\) −14.0366 −0.741859
\(359\) 18.9364 0.999427 0.499713 0.866191i \(-0.333439\pi\)
0.499713 + 0.866191i \(0.333439\pi\)
\(360\) −72.2109 −3.80585
\(361\) −4.63708 −0.244057
\(362\) −17.0007 −0.893538
\(363\) 16.1396 0.847111
\(364\) 29.5221 1.54738
\(365\) 13.4201 0.702440
\(366\) −39.5539 −2.06752
\(367\) 16.0713 0.838914 0.419457 0.907775i \(-0.362220\pi\)
0.419457 + 0.907775i \(0.362220\pi\)
\(368\) −16.3831 −0.854029
\(369\) 26.1291 1.36022
\(370\) 35.1063 1.82509
\(371\) 1.38216 0.0717582
\(372\) −22.7902 −1.18162
\(373\) 30.3065 1.56921 0.784605 0.619996i \(-0.212866\pi\)
0.784605 + 0.619996i \(0.212866\pi\)
\(374\) 35.9269 1.85773
\(375\) −31.1647 −1.60934
\(376\) −43.4071 −2.23855
\(377\) 11.8533 0.610477
\(378\) −3.71034 −0.190840
\(379\) −21.7825 −1.11889 −0.559445 0.828867i \(-0.688986\pi\)
−0.559445 + 0.828867i \(0.688986\pi\)
\(380\) 68.2636 3.50185
\(381\) −15.3289 −0.785325
\(382\) 48.8293 2.49833
\(383\) 22.1758 1.13313 0.566565 0.824017i \(-0.308272\pi\)
0.566565 + 0.824017i \(0.308272\pi\)
\(384\) 6.11151 0.311877
\(385\) −10.8555 −0.553250
\(386\) 3.93242 0.200155
\(387\) −11.8356 −0.601635
\(388\) 40.2230 2.04201
\(389\) 10.6234 0.538627 0.269314 0.963053i \(-0.413203\pi\)
0.269314 + 0.963053i \(0.413203\pi\)
\(390\) 95.6956 4.84574
\(391\) −10.8540 −0.548908
\(392\) 37.2871 1.88328
\(393\) 1.41395 0.0713242
\(394\) −27.8053 −1.40081
\(395\) −11.1390 −0.560466
\(396\) −25.8085 −1.29693
\(397\) 23.8991 1.19946 0.599730 0.800203i \(-0.295275\pi\)
0.599730 + 0.800203i \(0.295275\pi\)
\(398\) 55.8226 2.79813
\(399\) −12.9199 −0.646805
\(400\) 86.7929 4.33964
\(401\) −6.67423 −0.333295 −0.166648 0.986017i \(-0.553294\pi\)
−0.166648 + 0.986017i \(0.553294\pi\)
\(402\) 27.8754 1.39030
\(403\) 8.25991 0.411455
\(404\) 60.5441 3.01218
\(405\) −37.1149 −1.84425
\(406\) −10.7180 −0.531925
\(407\) 7.41341 0.367469
\(408\) 120.073 5.94451
\(409\) −1.66836 −0.0824952 −0.0412476 0.999149i \(-0.513133\pi\)
−0.0412476 + 0.999149i \(0.513133\pi\)
\(410\) −97.7437 −4.82722
\(411\) −8.96173 −0.442049
\(412\) 24.0816 1.18641
\(413\) 13.1241 0.645797
\(414\) 10.9873 0.539996
\(415\) −12.9145 −0.633950
\(416\) −47.7032 −2.33884
\(417\) −3.75620 −0.183942
\(418\) 20.3133 0.993557
\(419\) 30.0850 1.46975 0.734875 0.678202i \(-0.237241\pi\)
0.734875 + 0.678202i \(0.237241\pi\)
\(420\) −61.4054 −2.99628
\(421\) 4.66050 0.227139 0.113569 0.993530i \(-0.463772\pi\)
0.113569 + 0.993530i \(0.463772\pi\)
\(422\) −40.4757 −1.97032
\(423\) 14.8050 0.719846
\(424\) −7.26285 −0.352715
\(425\) 57.5010 2.78921
\(426\) −12.2433 −0.593192
\(427\) −9.19879 −0.445161
\(428\) −10.6517 −0.514871
\(429\) 20.2081 0.975654
\(430\) 44.2745 2.13511
\(431\) 17.1602 0.826578 0.413289 0.910600i \(-0.364380\pi\)
0.413289 + 0.910600i \(0.364380\pi\)
\(432\) 9.91556 0.477063
\(433\) −6.26900 −0.301269 −0.150634 0.988590i \(-0.548132\pi\)
−0.150634 + 0.988590i \(0.548132\pi\)
\(434\) −7.46876 −0.358512
\(435\) −24.6547 −1.18210
\(436\) −47.5212 −2.27585
\(437\) −6.13691 −0.293568
\(438\) 22.5892 1.07936
\(439\) −18.8050 −0.897515 −0.448757 0.893654i \(-0.648133\pi\)
−0.448757 + 0.893654i \(0.648133\pi\)
\(440\) 57.0427 2.71941
\(441\) −12.7177 −0.605603
\(442\) −73.6547 −3.50340
\(443\) −33.3164 −1.58291 −0.791456 0.611227i \(-0.790676\pi\)
−0.791456 + 0.611227i \(0.790676\pi\)
\(444\) 41.9346 1.99013
\(445\) 42.9629 2.03664
\(446\) 63.0721 2.98655
\(447\) 15.9766 0.755669
\(448\) 13.9455 0.658865
\(449\) −36.1979 −1.70828 −0.854141 0.520041i \(-0.825917\pi\)
−0.854141 + 0.520041i \(0.825917\pi\)
\(450\) −58.2074 −2.74392
\(451\) −20.6405 −0.971925
\(452\) 85.3423 4.01417
\(453\) 45.8288 2.15322
\(454\) −52.6979 −2.47323
\(455\) 22.2553 1.04334
\(456\) 67.8904 3.17926
\(457\) −21.0418 −0.984295 −0.492147 0.870512i \(-0.663788\pi\)
−0.492147 + 0.870512i \(0.663788\pi\)
\(458\) 62.7728 2.93318
\(459\) 6.56915 0.306622
\(460\) −29.1673 −1.35993
\(461\) −27.4626 −1.27906 −0.639531 0.768766i \(-0.720871\pi\)
−0.639531 + 0.768766i \(0.720871\pi\)
\(462\) −18.2725 −0.850114
\(463\) 0.965338 0.0448630 0.0224315 0.999748i \(-0.492859\pi\)
0.0224315 + 0.999748i \(0.492859\pi\)
\(464\) 28.6429 1.32971
\(465\) −17.1805 −0.796725
\(466\) 48.2253 2.23399
\(467\) −39.0325 −1.80621 −0.903104 0.429423i \(-0.858717\pi\)
−0.903104 + 0.429423i \(0.858717\pi\)
\(468\) 52.9108 2.44580
\(469\) 6.48280 0.299348
\(470\) −55.3828 −2.55462
\(471\) −35.3451 −1.62862
\(472\) −68.9635 −3.17430
\(473\) 9.34945 0.429888
\(474\) −18.7497 −0.861201
\(475\) 32.5115 1.49173
\(476\) 47.2623 2.16626
\(477\) 2.47717 0.113422
\(478\) 48.9904 2.24077
\(479\) 10.4600 0.477930 0.238965 0.971028i \(-0.423192\pi\)
0.238965 + 0.971028i \(0.423192\pi\)
\(480\) 99.2218 4.52883
\(481\) −15.1985 −0.692990
\(482\) 33.1300 1.50903
\(483\) 5.52035 0.251185
\(484\) −33.3819 −1.51736
\(485\) 30.3222 1.37686
\(486\) −54.7567 −2.48381
\(487\) 9.88739 0.448040 0.224020 0.974584i \(-0.428082\pi\)
0.224020 + 0.974584i \(0.428082\pi\)
\(488\) 48.3369 2.18811
\(489\) −37.8231 −1.71042
\(490\) 47.5743 2.14919
\(491\) 31.7982 1.43503 0.717516 0.696542i \(-0.245279\pi\)
0.717516 + 0.696542i \(0.245279\pi\)
\(492\) −116.755 −5.26372
\(493\) 18.9762 0.854644
\(494\) −41.6450 −1.87370
\(495\) −19.4558 −0.874474
\(496\) 19.9596 0.896213
\(497\) −2.84735 −0.127721
\(498\) −21.7383 −0.974115
\(499\) 1.93556 0.0866474 0.0433237 0.999061i \(-0.486205\pi\)
0.0433237 + 0.999061i \(0.486205\pi\)
\(500\) 64.4585 2.88267
\(501\) 15.9660 0.713310
\(502\) 56.1919 2.50797
\(503\) −14.0918 −0.628323 −0.314162 0.949369i \(-0.601723\pi\)
−0.314162 + 0.949369i \(0.601723\pi\)
\(504\) −28.2677 −1.25914
\(505\) 45.6413 2.03101
\(506\) −8.67937 −0.385845
\(507\) −10.7059 −0.475466
\(508\) 31.7051 1.40669
\(509\) 22.8242 1.01167 0.505833 0.862631i \(-0.331185\pi\)
0.505833 + 0.862631i \(0.331185\pi\)
\(510\) 153.201 6.78384
\(511\) 5.25343 0.232398
\(512\) 38.1053 1.68403
\(513\) 3.71425 0.163988
\(514\) −46.4992 −2.05099
\(515\) 18.1540 0.799959
\(516\) 52.8860 2.32818
\(517\) −11.6952 −0.514354
\(518\) 13.7427 0.603821
\(519\) 16.7201 0.733933
\(520\) −116.945 −5.12838
\(521\) −19.0370 −0.834024 −0.417012 0.908901i \(-0.636923\pi\)
−0.417012 + 0.908901i \(0.636923\pi\)
\(522\) −19.2093 −0.840768
\(523\) −34.8911 −1.52568 −0.762841 0.646587i \(-0.776196\pi\)
−0.762841 + 0.646587i \(0.776196\pi\)
\(524\) −2.92449 −0.127757
\(525\) −29.2452 −1.27636
\(526\) 63.6342 2.77458
\(527\) 13.2234 0.576021
\(528\) 48.8316 2.12512
\(529\) −20.3779 −0.885994
\(530\) −9.26661 −0.402516
\(531\) 23.5217 1.02075
\(532\) 26.7225 1.15857
\(533\) 42.3158 1.83290
\(534\) 72.3168 3.12946
\(535\) −8.02985 −0.347161
\(536\) −34.0652 −1.47139
\(537\) −12.6397 −0.545443
\(538\) −33.7652 −1.45572
\(539\) 10.0463 0.432723
\(540\) 17.6530 0.759663
\(541\) 10.1093 0.434634 0.217317 0.976101i \(-0.430269\pi\)
0.217317 + 0.976101i \(0.430269\pi\)
\(542\) −13.8655 −0.595574
\(543\) −15.3088 −0.656963
\(544\) −76.3687 −3.27428
\(545\) −35.8240 −1.53453
\(546\) 37.4610 1.60318
\(547\) 4.39700 0.188002 0.0940010 0.995572i \(-0.470034\pi\)
0.0940010 + 0.995572i \(0.470034\pi\)
\(548\) 18.5357 0.791806
\(549\) −16.4865 −0.703626
\(550\) 45.9807 1.96062
\(551\) 10.7293 0.457082
\(552\) −29.0078 −1.23466
\(553\) −4.36049 −0.185427
\(554\) −45.1199 −1.91696
\(555\) 31.6125 1.34188
\(556\) 7.76901 0.329480
\(557\) −12.8064 −0.542625 −0.271312 0.962491i \(-0.587458\pi\)
−0.271312 + 0.962491i \(0.587458\pi\)
\(558\) −13.3859 −0.566669
\(559\) −19.1676 −0.810703
\(560\) 53.7787 2.27256
\(561\) 32.3514 1.36588
\(562\) −35.4087 −1.49363
\(563\) −6.63051 −0.279443 −0.139721 0.990191i \(-0.544621\pi\)
−0.139721 + 0.990191i \(0.544621\pi\)
\(564\) −66.1548 −2.78562
\(565\) 64.3356 2.70662
\(566\) −41.7752 −1.75594
\(567\) −14.5290 −0.610160
\(568\) 14.9620 0.627791
\(569\) 41.1452 1.72490 0.862448 0.506146i \(-0.168930\pi\)
0.862448 + 0.506146i \(0.168930\pi\)
\(570\) 86.6208 3.62815
\(571\) 16.2718 0.680952 0.340476 0.940253i \(-0.389412\pi\)
0.340476 + 0.940253i \(0.389412\pi\)
\(572\) −41.7967 −1.74761
\(573\) 43.9698 1.83686
\(574\) −38.2627 −1.59706
\(575\) −13.8914 −0.579309
\(576\) 24.9938 1.04141
\(577\) 4.69143 0.195307 0.0976535 0.995220i \(-0.468866\pi\)
0.0976535 + 0.995220i \(0.468866\pi\)
\(578\) −73.2981 −3.04880
\(579\) 3.54106 0.147162
\(580\) 50.9938 2.11740
\(581\) −5.05553 −0.209739
\(582\) 51.0396 2.11566
\(583\) −1.95683 −0.0810436
\(584\) −27.6052 −1.14231
\(585\) 39.8870 1.64912
\(586\) 80.0462 3.30668
\(587\) −10.8228 −0.446704 −0.223352 0.974738i \(-0.571700\pi\)
−0.223352 + 0.974738i \(0.571700\pi\)
\(588\) 56.8276 2.34353
\(589\) 7.47662 0.308069
\(590\) −87.9900 −3.62249
\(591\) −25.0381 −1.02993
\(592\) −36.7262 −1.50944
\(593\) 44.7931 1.83943 0.919717 0.392582i \(-0.128418\pi\)
0.919717 + 0.392582i \(0.128418\pi\)
\(594\) 5.25302 0.215534
\(595\) 35.6288 1.46064
\(596\) −33.0448 −1.35357
\(597\) 50.2670 2.05729
\(598\) 17.7938 0.727644
\(599\) 7.30926 0.298648 0.149324 0.988788i \(-0.452290\pi\)
0.149324 + 0.988788i \(0.452290\pi\)
\(600\) 153.675 6.27375
\(601\) 4.12192 0.168137 0.0840684 0.996460i \(-0.473209\pi\)
0.0840684 + 0.996460i \(0.473209\pi\)
\(602\) 17.3317 0.706387
\(603\) 11.6188 0.473153
\(604\) −94.7885 −3.85689
\(605\) −25.1650 −1.02310
\(606\) 76.8253 3.12082
\(607\) 47.8930 1.94392 0.971958 0.235154i \(-0.0755595\pi\)
0.971958 + 0.235154i \(0.0755595\pi\)
\(608\) −43.1795 −1.75116
\(609\) −9.65133 −0.391092
\(610\) 61.6727 2.49706
\(611\) 23.9767 0.969992
\(612\) 84.7057 3.42402
\(613\) −36.4591 −1.47257 −0.736284 0.676673i \(-0.763421\pi\)
−0.736284 + 0.676673i \(0.763421\pi\)
\(614\) 66.0853 2.66699
\(615\) −88.0162 −3.54915
\(616\) 22.3299 0.899699
\(617\) 11.3157 0.455552 0.227776 0.973714i \(-0.426855\pi\)
0.227776 + 0.973714i \(0.426855\pi\)
\(618\) 30.5575 1.22920
\(619\) −19.2107 −0.772145 −0.386073 0.922468i \(-0.626169\pi\)
−0.386073 + 0.922468i \(0.626169\pi\)
\(620\) 35.5347 1.42711
\(621\) −1.58700 −0.0636843
\(622\) 65.1870 2.61376
\(623\) 16.8182 0.673809
\(624\) −100.111 −4.00766
\(625\) 5.69930 0.227972
\(626\) 45.3460 1.81239
\(627\) 18.2917 0.730501
\(628\) 73.1049 2.91720
\(629\) −24.3314 −0.970158
\(630\) −36.0665 −1.43692
\(631\) −40.2222 −1.60122 −0.800609 0.599187i \(-0.795491\pi\)
−0.800609 + 0.599187i \(0.795491\pi\)
\(632\) 22.9131 0.911434
\(633\) −36.4475 −1.44866
\(634\) 10.9520 0.434958
\(635\) 23.9010 0.948482
\(636\) −11.0690 −0.438914
\(637\) −20.5962 −0.816049
\(638\) 15.1743 0.600756
\(639\) −5.10315 −0.201878
\(640\) −9.52911 −0.376671
\(641\) 2.68531 0.106063 0.0530316 0.998593i \(-0.483112\pi\)
0.0530316 + 0.998593i \(0.483112\pi\)
\(642\) −13.5162 −0.533440
\(643\) −42.3765 −1.67117 −0.835583 0.549364i \(-0.814870\pi\)
−0.835583 + 0.549364i \(0.814870\pi\)
\(644\) −11.4178 −0.449926
\(645\) 39.8683 1.56981
\(646\) −66.6701 −2.62310
\(647\) 10.8181 0.425304 0.212652 0.977128i \(-0.431790\pi\)
0.212652 + 0.977128i \(0.431790\pi\)
\(648\) 76.3455 2.99914
\(649\) −18.5809 −0.729363
\(650\) −94.2665 −3.69744
\(651\) −6.72547 −0.263592
\(652\) 78.2302 3.06373
\(653\) 15.3427 0.600407 0.300203 0.953875i \(-0.402945\pi\)
0.300203 + 0.953875i \(0.402945\pi\)
\(654\) −60.3004 −2.35793
\(655\) −2.20464 −0.0861422
\(656\) 102.254 3.99234
\(657\) 9.41544 0.367331
\(658\) −21.6801 −0.845180
\(659\) −22.6007 −0.880397 −0.440199 0.897900i \(-0.645092\pi\)
−0.440199 + 0.897900i \(0.645092\pi\)
\(660\) 86.9363 3.38399
\(661\) 6.82214 0.265350 0.132675 0.991160i \(-0.457643\pi\)
0.132675 + 0.991160i \(0.457643\pi\)
\(662\) 38.8985 1.51183
\(663\) −66.3245 −2.57583
\(664\) 26.5653 1.03093
\(665\) 20.1448 0.781183
\(666\) 24.6303 0.954406
\(667\) −4.58435 −0.177507
\(668\) −33.0228 −1.27769
\(669\) 56.7951 2.19583
\(670\) −43.4636 −1.67914
\(671\) 13.0234 0.502764
\(672\) 38.8413 1.49834
\(673\) −32.1276 −1.23843 −0.619213 0.785223i \(-0.712548\pi\)
−0.619213 + 0.785223i \(0.712548\pi\)
\(674\) −8.83429 −0.340284
\(675\) 8.40748 0.323604
\(676\) 22.1432 0.851663
\(677\) −17.3343 −0.666210 −0.333105 0.942890i \(-0.608096\pi\)
−0.333105 + 0.942890i \(0.608096\pi\)
\(678\) 108.292 4.15894
\(679\) 11.8699 0.455527
\(680\) −187.219 −7.17952
\(681\) −47.4533 −1.81842
\(682\) 10.5741 0.404903
\(683\) −5.50702 −0.210720 −0.105360 0.994434i \(-0.533600\pi\)
−0.105360 + 0.994434i \(0.533600\pi\)
\(684\) 47.8932 1.83124
\(685\) 13.9732 0.533888
\(686\) 45.1245 1.72286
\(687\) 56.5256 2.15658
\(688\) −46.3174 −1.76584
\(689\) 4.01176 0.152836
\(690\) −37.0109 −1.40898
\(691\) −18.6106 −0.707981 −0.353990 0.935249i \(-0.615175\pi\)
−0.353990 + 0.935249i \(0.615175\pi\)
\(692\) −34.5826 −1.31463
\(693\) −7.61617 −0.289314
\(694\) −23.3201 −0.885219
\(695\) 5.85670 0.222157
\(696\) 50.7149 1.92234
\(697\) 67.7440 2.56599
\(698\) 76.8418 2.90851
\(699\) 43.4259 1.64252
\(700\) 60.4883 2.28624
\(701\) −15.5127 −0.585907 −0.292954 0.956127i \(-0.594638\pi\)
−0.292954 + 0.956127i \(0.594638\pi\)
\(702\) −10.7694 −0.406464
\(703\) −13.7572 −0.518862
\(704\) −19.7438 −0.744121
\(705\) −49.8710 −1.87825
\(706\) 8.55416 0.321940
\(707\) 17.8668 0.671949
\(708\) −105.104 −3.95006
\(709\) 21.7783 0.817900 0.408950 0.912557i \(-0.365895\pi\)
0.408950 + 0.912557i \(0.365895\pi\)
\(710\) 19.0899 0.716431
\(711\) −7.81507 −0.293088
\(712\) −88.3749 −3.31199
\(713\) −3.19457 −0.119638
\(714\) 59.9719 2.24439
\(715\) −31.5085 −1.17835
\(716\) 26.1429 0.977006
\(717\) 44.1149 1.64750
\(718\) −49.6990 −1.85475
\(719\) −10.3831 −0.387226 −0.193613 0.981078i \(-0.562021\pi\)
−0.193613 + 0.981078i \(0.562021\pi\)
\(720\) 96.3846 3.59204
\(721\) 7.10655 0.264662
\(722\) 12.1701 0.452925
\(723\) 29.8329 1.10950
\(724\) 31.6634 1.17676
\(725\) 24.2865 0.901978
\(726\) −42.3588 −1.57208
\(727\) −8.27682 −0.306970 −0.153485 0.988151i \(-0.549050\pi\)
−0.153485 + 0.988151i \(0.549050\pi\)
\(728\) −45.7793 −1.69669
\(729\) −19.0909 −0.707072
\(730\) −35.2213 −1.30360
\(731\) −30.6857 −1.13495
\(732\) 73.6682 2.72286
\(733\) −33.6508 −1.24292 −0.621461 0.783445i \(-0.713460\pi\)
−0.621461 + 0.783445i \(0.713460\pi\)
\(734\) −42.1794 −1.55687
\(735\) 42.8396 1.58016
\(736\) 18.4495 0.680057
\(737\) −9.17820 −0.338084
\(738\) −68.5762 −2.52433
\(739\) −16.8784 −0.620882 −0.310441 0.950593i \(-0.600477\pi\)
−0.310441 + 0.950593i \(0.600477\pi\)
\(740\) −65.3847 −2.40359
\(741\) −37.5004 −1.37761
\(742\) −3.62751 −0.133170
\(743\) 20.7718 0.762044 0.381022 0.924566i \(-0.375572\pi\)
0.381022 + 0.924566i \(0.375572\pi\)
\(744\) 35.3404 1.29564
\(745\) −24.9109 −0.912664
\(746\) −79.5400 −2.91217
\(747\) −9.06074 −0.331515
\(748\) −66.9129 −2.44658
\(749\) −3.14336 −0.114856
\(750\) 81.7925 2.98664
\(751\) 28.2718 1.03165 0.515826 0.856693i \(-0.327485\pi\)
0.515826 + 0.856693i \(0.327485\pi\)
\(752\) 57.9382 2.11279
\(753\) 50.5997 1.84395
\(754\) −31.1093 −1.13293
\(755\) −71.4566 −2.60057
\(756\) 6.91043 0.251330
\(757\) 43.2007 1.57016 0.785078 0.619397i \(-0.212623\pi\)
0.785078 + 0.619397i \(0.212623\pi\)
\(758\) 57.1686 2.07646
\(759\) −7.81559 −0.283688
\(760\) −105.855 −3.83977
\(761\) −1.39520 −0.0505758 −0.0252879 0.999680i \(-0.508050\pi\)
−0.0252879 + 0.999680i \(0.508050\pi\)
\(762\) 40.2311 1.45742
\(763\) −14.0237 −0.507691
\(764\) −90.9435 −3.29022
\(765\) 63.8556 2.30870
\(766\) −58.2008 −2.10288
\(767\) 38.0932 1.37547
\(768\) 29.6558 1.07011
\(769\) 39.3227 1.41801 0.709006 0.705203i \(-0.249144\pi\)
0.709006 + 0.705203i \(0.249144\pi\)
\(770\) 28.4906 1.02673
\(771\) −41.8716 −1.50797
\(772\) −7.32405 −0.263598
\(773\) 45.8371 1.64864 0.824322 0.566121i \(-0.191557\pi\)
0.824322 + 0.566121i \(0.191557\pi\)
\(774\) 31.0627 1.11652
\(775\) 16.9239 0.607924
\(776\) −62.3731 −2.23906
\(777\) 12.3750 0.443952
\(778\) −27.8813 −0.999593
\(779\) 38.3030 1.37235
\(780\) −178.231 −6.38169
\(781\) 4.03122 0.144248
\(782\) 28.4864 1.01867
\(783\) 2.77459 0.0991557
\(784\) −49.7694 −1.77748
\(785\) 55.1104 1.96697
\(786\) −3.71093 −0.132365
\(787\) 1.56296 0.0557134 0.0278567 0.999612i \(-0.491132\pi\)
0.0278567 + 0.999612i \(0.491132\pi\)
\(788\) 51.7867 1.84482
\(789\) 57.3012 2.03998
\(790\) 29.2346 1.04012
\(791\) 25.1848 0.895469
\(792\) 40.0207 1.42208
\(793\) −26.6997 −0.948136
\(794\) −62.7236 −2.22598
\(795\) −8.34439 −0.295945
\(796\) −103.968 −3.68505
\(797\) −25.7735 −0.912945 −0.456472 0.889738i \(-0.650887\pi\)
−0.456472 + 0.889738i \(0.650887\pi\)
\(798\) 33.9086 1.20035
\(799\) 38.3846 1.35795
\(800\) −97.7400 −3.45563
\(801\) 30.1424 1.06503
\(802\) 17.5167 0.618535
\(803\) −7.43769 −0.262470
\(804\) −51.9173 −1.83098
\(805\) −8.60737 −0.303370
\(806\) −21.6783 −0.763586
\(807\) −30.4049 −1.07030
\(808\) −93.8846 −3.30285
\(809\) −39.1604 −1.37681 −0.688403 0.725329i \(-0.741688\pi\)
−0.688403 + 0.725329i \(0.741688\pi\)
\(810\) 97.4087 3.42259
\(811\) −36.4710 −1.28067 −0.640335 0.768095i \(-0.721205\pi\)
−0.640335 + 0.768095i \(0.721205\pi\)
\(812\) 19.9620 0.700530
\(813\) −12.4856 −0.437889
\(814\) −19.4566 −0.681955
\(815\) 58.9741 2.06577
\(816\) −160.270 −5.61056
\(817\) −17.3499 −0.606997
\(818\) 4.37865 0.153096
\(819\) 15.6141 0.545602
\(820\) 182.045 6.35730
\(821\) 10.7306 0.374501 0.187250 0.982312i \(-0.440042\pi\)
0.187250 + 0.982312i \(0.440042\pi\)
\(822\) 23.5202 0.820362
\(823\) 53.4014 1.86146 0.930728 0.365712i \(-0.119174\pi\)
0.930728 + 0.365712i \(0.119174\pi\)
\(824\) −37.3428 −1.30090
\(825\) 41.4047 1.44153
\(826\) −34.4446 −1.19848
\(827\) −43.0751 −1.49787 −0.748934 0.662645i \(-0.769434\pi\)
−0.748934 + 0.662645i \(0.769434\pi\)
\(828\) −20.4636 −0.711158
\(829\) −56.2030 −1.95201 −0.976005 0.217747i \(-0.930129\pi\)
−0.976005 + 0.217747i \(0.930129\pi\)
\(830\) 33.8945 1.17649
\(831\) −40.6295 −1.40942
\(832\) 40.4773 1.40330
\(833\) −32.9727 −1.14244
\(834\) 9.85822 0.341362
\(835\) −24.8944 −0.861505
\(836\) −37.8331 −1.30848
\(837\) 1.93345 0.0668299
\(838\) −78.9588 −2.72759
\(839\) 4.98207 0.172000 0.0860001 0.996295i \(-0.472591\pi\)
0.0860001 + 0.996295i \(0.472591\pi\)
\(840\) 95.2202 3.28541
\(841\) −20.9851 −0.723624
\(842\) −12.2316 −0.421528
\(843\) −31.8848 −1.09817
\(844\) 75.3849 2.59486
\(845\) 16.6927 0.574248
\(846\) −38.8561 −1.33590
\(847\) −9.85110 −0.338488
\(848\) 9.69419 0.332900
\(849\) −37.6177 −1.29104
\(850\) −150.913 −5.17626
\(851\) 5.87809 0.201498
\(852\) 22.8029 0.781215
\(853\) −24.7630 −0.847870 −0.423935 0.905693i \(-0.639351\pi\)
−0.423935 + 0.905693i \(0.639351\pi\)
\(854\) 24.1424 0.826136
\(855\) 36.1045 1.23475
\(856\) 16.5175 0.564555
\(857\) −7.91151 −0.270252 −0.135126 0.990828i \(-0.543144\pi\)
−0.135126 + 0.990828i \(0.543144\pi\)
\(858\) −53.0364 −1.81063
\(859\) 12.0684 0.411769 0.205884 0.978576i \(-0.433993\pi\)
0.205884 + 0.978576i \(0.433993\pi\)
\(860\) −82.4602 −2.81187
\(861\) −34.4548 −1.17422
\(862\) −45.0373 −1.53398
\(863\) −37.3672 −1.27199 −0.635997 0.771691i \(-0.719411\pi\)
−0.635997 + 0.771691i \(0.719411\pi\)
\(864\) −11.1662 −0.379882
\(865\) −26.0702 −0.886412
\(866\) 16.4531 0.559100
\(867\) −66.0034 −2.24159
\(868\) 13.9104 0.472150
\(869\) 6.17348 0.209421
\(870\) 64.7068 2.19377
\(871\) 18.8165 0.637573
\(872\) 73.6903 2.49547
\(873\) 21.2739 0.720011
\(874\) 16.1064 0.544809
\(875\) 19.0219 0.643059
\(876\) −42.0719 −1.42148
\(877\) −6.53901 −0.220807 −0.110403 0.993887i \(-0.535214\pi\)
−0.110403 + 0.993887i \(0.535214\pi\)
\(878\) 49.3542 1.66562
\(879\) 72.0799 2.43120
\(880\) −76.1386 −2.56663
\(881\) 18.1282 0.610756 0.305378 0.952231i \(-0.401217\pi\)
0.305378 + 0.952231i \(0.401217\pi\)
\(882\) 33.3777 1.12389
\(883\) 43.8052 1.47416 0.737081 0.675804i \(-0.236204\pi\)
0.737081 + 0.675804i \(0.236204\pi\)
\(884\) 137.180 4.61387
\(885\) −79.2332 −2.66339
\(886\) 87.4396 2.93759
\(887\) 33.2280 1.11569 0.557844 0.829946i \(-0.311629\pi\)
0.557844 + 0.829946i \(0.311629\pi\)
\(888\) −65.0272 −2.18217
\(889\) 9.35628 0.313800
\(890\) −112.757 −3.77962
\(891\) 20.5698 0.689114
\(892\) −117.470 −3.93320
\(893\) 21.7029 0.726261
\(894\) −41.9310 −1.40238
\(895\) 19.7079 0.658762
\(896\) −3.73026 −0.124619
\(897\) 16.0230 0.534992
\(898\) 95.0020 3.17026
\(899\) 5.58513 0.186274
\(900\) 108.410 3.61366
\(901\) 6.42248 0.213964
\(902\) 54.1715 1.80371
\(903\) 15.6068 0.519363
\(904\) −132.339 −4.40152
\(905\) 23.8696 0.793452
\(906\) −120.279 −3.99599
\(907\) 16.7223 0.555255 0.277628 0.960689i \(-0.410452\pi\)
0.277628 + 0.960689i \(0.410452\pi\)
\(908\) 98.1485 3.25717
\(909\) 32.0216 1.06209
\(910\) −58.4095 −1.93626
\(911\) 0.157192 0.00520800 0.00260400 0.999997i \(-0.499171\pi\)
0.00260400 + 0.999997i \(0.499171\pi\)
\(912\) −90.6177 −3.00065
\(913\) 7.15750 0.236879
\(914\) 55.2247 1.82667
\(915\) 55.5350 1.83593
\(916\) −116.913 −3.86291
\(917\) −0.863027 −0.0284997
\(918\) −17.2409 −0.569033
\(919\) 21.1490 0.697642 0.348821 0.937189i \(-0.386582\pi\)
0.348821 + 0.937189i \(0.386582\pi\)
\(920\) 45.2292 1.49116
\(921\) 59.5084 1.96087
\(922\) 72.0762 2.37370
\(923\) −8.26452 −0.272030
\(924\) 34.0321 1.11957
\(925\) −31.1404 −1.02389
\(926\) −2.53355 −0.0832576
\(927\) 12.7367 0.418328
\(928\) −32.2556 −1.05884
\(929\) 35.0599 1.15028 0.575139 0.818056i \(-0.304948\pi\)
0.575139 + 0.818056i \(0.304948\pi\)
\(930\) 45.0905 1.47858
\(931\) −18.6430 −0.611000
\(932\) −89.8185 −2.94210
\(933\) 58.6995 1.92173
\(934\) 102.442 3.35199
\(935\) −50.4425 −1.64965
\(936\) −82.0478 −2.68181
\(937\) −17.9980 −0.587969 −0.293984 0.955810i \(-0.594981\pi\)
−0.293984 + 0.955810i \(0.594981\pi\)
\(938\) −17.0142 −0.555535
\(939\) 40.8331 1.33254
\(940\) 103.149 3.36435
\(941\) 27.5627 0.898518 0.449259 0.893402i \(-0.351688\pi\)
0.449259 + 0.893402i \(0.351688\pi\)
\(942\) 92.7640 3.02241
\(943\) −16.3659 −0.532947
\(944\) 92.0500 2.99597
\(945\) 5.20945 0.169463
\(946\) −24.5378 −0.797794
\(947\) −21.2393 −0.690183 −0.345092 0.938569i \(-0.612152\pi\)
−0.345092 + 0.938569i \(0.612152\pi\)
\(948\) 34.9208 1.13418
\(949\) 15.2482 0.494978
\(950\) −85.3272 −2.76838
\(951\) 9.86202 0.319798
\(952\) −73.2888 −2.37530
\(953\) −28.5794 −0.925779 −0.462889 0.886416i \(-0.653187\pi\)
−0.462889 + 0.886416i \(0.653187\pi\)
\(954\) −6.50138 −0.210490
\(955\) −68.5580 −2.21849
\(956\) −91.2435 −2.95103
\(957\) 13.6641 0.441699
\(958\) −27.4525 −0.886951
\(959\) 5.46994 0.176634
\(960\) −84.1921 −2.71729
\(961\) −27.1080 −0.874453
\(962\) 39.8887 1.28606
\(963\) −5.63368 −0.181543
\(964\) −61.7038 −1.98735
\(965\) −5.52125 −0.177735
\(966\) −14.4883 −0.466153
\(967\) 45.1205 1.45098 0.725489 0.688234i \(-0.241614\pi\)
0.725489 + 0.688234i \(0.241614\pi\)
\(968\) 51.7646 1.66378
\(969\) −60.0350 −1.92860
\(970\) −79.5813 −2.55520
\(971\) 36.6463 1.17604 0.588018 0.808848i \(-0.299909\pi\)
0.588018 + 0.808848i \(0.299909\pi\)
\(972\) 101.983 3.27111
\(973\) 2.29266 0.0734994
\(974\) −25.9497 −0.831481
\(975\) −84.8850 −2.71850
\(976\) −64.5184 −2.06518
\(977\) −31.8335 −1.01844 −0.509221 0.860636i \(-0.670066\pi\)
−0.509221 + 0.860636i \(0.670066\pi\)
\(978\) 99.2675 3.17423
\(979\) −23.8109 −0.760999
\(980\) −88.6060 −2.83041
\(981\) −25.1339 −0.802462
\(982\) −83.4550 −2.66316
\(983\) 12.9485 0.412992 0.206496 0.978447i \(-0.433794\pi\)
0.206496 + 0.978447i \(0.433794\pi\)
\(984\) 181.050 5.77166
\(985\) 39.0395 1.24390
\(986\) −49.8033 −1.58606
\(987\) −19.5225 −0.621408
\(988\) 77.5628 2.46760
\(989\) 7.41319 0.235726
\(990\) 51.0622 1.62286
\(991\) 25.2059 0.800692 0.400346 0.916364i \(-0.368890\pi\)
0.400346 + 0.916364i \(0.368890\pi\)
\(992\) −22.4771 −0.713648
\(993\) 35.0273 1.11156
\(994\) 7.47293 0.237027
\(995\) −78.3767 −2.48471
\(996\) 40.4870 1.28288
\(997\) 12.2848 0.389063 0.194532 0.980896i \(-0.437681\pi\)
0.194532 + 0.980896i \(0.437681\pi\)
\(998\) −5.07991 −0.160802
\(999\) −3.55760 −0.112558
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 6043.2.a.c.1.8 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6043.2.a.c.1.8 259 1.1 even 1 trivial