Properties

Label 8029.2.a.h.1.4
Level $8029$
Weight $2$
Character 8029.1
Self dual yes
Analytic conductor $64.112$
Analytic rank $0$
Dimension $71$
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] = [8029,2,Mod(1,8029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8029, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8029 = 7 \cdot 31 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8029.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: \(64.1118877829\)
Analytic rank: \(0\)
Dimension: \(71\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 8029.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.63529 q^{2} -1.71677 q^{3} +4.94476 q^{4} -3.15507 q^{5} +4.52418 q^{6} -1.00000 q^{7} -7.76032 q^{8} -0.0527133 q^{9} +O(q^{10})\) \(q-2.63529 q^{2} -1.71677 q^{3} +4.94476 q^{4} -3.15507 q^{5} +4.52418 q^{6} -1.00000 q^{7} -7.76032 q^{8} -0.0527133 q^{9} +8.31452 q^{10} +2.91781 q^{11} -8.48901 q^{12} -0.0307174 q^{13} +2.63529 q^{14} +5.41651 q^{15} +10.5612 q^{16} -3.68205 q^{17} +0.138915 q^{18} -5.89519 q^{19} -15.6011 q^{20} +1.71677 q^{21} -7.68927 q^{22} +8.32560 q^{23} +13.3226 q^{24} +4.95444 q^{25} +0.0809495 q^{26} +5.24080 q^{27} -4.94476 q^{28} +4.04619 q^{29} -14.2741 q^{30} -1.00000 q^{31} -12.3111 q^{32} -5.00919 q^{33} +9.70328 q^{34} +3.15507 q^{35} -0.260655 q^{36} +1.00000 q^{37} +15.5355 q^{38} +0.0527347 q^{39} +24.4843 q^{40} -0.941963 q^{41} -4.52418 q^{42} -9.88190 q^{43} +14.4279 q^{44} +0.166314 q^{45} -21.9404 q^{46} +4.99629 q^{47} -18.1311 q^{48} +1.00000 q^{49} -13.0564 q^{50} +6.32122 q^{51} -0.151891 q^{52} -2.05341 q^{53} -13.8110 q^{54} -9.20588 q^{55} +7.76032 q^{56} +10.1207 q^{57} -10.6629 q^{58} -0.211513 q^{59} +26.7834 q^{60} -2.55588 q^{61} +2.63529 q^{62} +0.0527133 q^{63} +11.3211 q^{64} +0.0969156 q^{65} +13.2007 q^{66} +13.4224 q^{67} -18.2069 q^{68} -14.2931 q^{69} -8.31452 q^{70} +12.9686 q^{71} +0.409072 q^{72} -1.09398 q^{73} -2.63529 q^{74} -8.50562 q^{75} -29.1503 q^{76} -2.91781 q^{77} -0.138971 q^{78} +5.42088 q^{79} -33.3212 q^{80} -8.83908 q^{81} +2.48235 q^{82} -14.6631 q^{83} +8.48901 q^{84} +11.6171 q^{85} +26.0417 q^{86} -6.94636 q^{87} -22.6431 q^{88} +8.61286 q^{89} -0.438286 q^{90} +0.0307174 q^{91} +41.1681 q^{92} +1.71677 q^{93} -13.1667 q^{94} +18.5997 q^{95} +21.1353 q^{96} -8.08133 q^{97} -2.63529 q^{98} -0.153807 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63529 −1.86343 −0.931716 0.363186i \(-0.881689\pi\)
−0.931716 + 0.363186i \(0.881689\pi\)
\(3\) −1.71677 −0.991176 −0.495588 0.868558i \(-0.665047\pi\)
−0.495588 + 0.868558i \(0.665047\pi\)
\(4\) 4.94476 2.47238
\(5\) −3.15507 −1.41099 −0.705494 0.708716i \(-0.749275\pi\)
−0.705494 + 0.708716i \(0.749275\pi\)
\(6\) 4.52418 1.84699
\(7\) −1.00000 −0.377964
\(8\) −7.76032 −2.74369
\(9\) −0.0527133 −0.0175711
\(10\) 8.31452 2.62928
\(11\) 2.91781 0.879752 0.439876 0.898059i \(-0.355022\pi\)
0.439876 + 0.898059i \(0.355022\pi\)
\(12\) −8.48901 −2.45056
\(13\) −0.0307174 −0.00851949 −0.00425974 0.999991i \(-0.501356\pi\)
−0.00425974 + 0.999991i \(0.501356\pi\)
\(14\) 2.63529 0.704311
\(15\) 5.41651 1.39854
\(16\) 10.5612 2.64029
\(17\) −3.68205 −0.893029 −0.446514 0.894776i \(-0.647335\pi\)
−0.446514 + 0.894776i \(0.647335\pi\)
\(18\) 0.138915 0.0327426
\(19\) −5.89519 −1.35245 −0.676224 0.736696i \(-0.736385\pi\)
−0.676224 + 0.736696i \(0.736385\pi\)
\(20\) −15.6011 −3.48850
\(21\) 1.71677 0.374629
\(22\) −7.68927 −1.63936
\(23\) 8.32560 1.73601 0.868004 0.496557i \(-0.165403\pi\)
0.868004 + 0.496557i \(0.165403\pi\)
\(24\) 13.3226 2.71947
\(25\) 4.95444 0.990889
\(26\) 0.0809495 0.0158755
\(27\) 5.24080 1.00859
\(28\) −4.94476 −0.934473
\(29\) 4.04619 0.751358 0.375679 0.926750i \(-0.377409\pi\)
0.375679 + 0.926750i \(0.377409\pi\)
\(30\) −14.2741 −2.60608
\(31\) −1.00000 −0.179605
\(32\) −12.3111 −2.17632
\(33\) −5.00919 −0.871989
\(34\) 9.70328 1.66410
\(35\) 3.15507 0.533304
\(36\) −0.260655 −0.0434425
\(37\) 1.00000 0.164399
\(38\) 15.5355 2.52020
\(39\) 0.0527347 0.00844431
\(40\) 24.4843 3.87131
\(41\) −0.941963 −0.147110 −0.0735550 0.997291i \(-0.523434\pi\)
−0.0735550 + 0.997291i \(0.523434\pi\)
\(42\) −4.52418 −0.698096
\(43\) −9.88190 −1.50698 −0.753488 0.657461i \(-0.771630\pi\)
−0.753488 + 0.657461i \(0.771630\pi\)
\(44\) 14.4279 2.17508
\(45\) 0.166314 0.0247926
\(46\) −21.9404 −3.23493
\(47\) 4.99629 0.728784 0.364392 0.931246i \(-0.381277\pi\)
0.364392 + 0.931246i \(0.381277\pi\)
\(48\) −18.1311 −2.61699
\(49\) 1.00000 0.142857
\(50\) −13.0564 −1.84646
\(51\) 6.32122 0.885148
\(52\) −0.151891 −0.0210634
\(53\) −2.05341 −0.282058 −0.141029 0.990005i \(-0.545041\pi\)
−0.141029 + 0.990005i \(0.545041\pi\)
\(54\) −13.8110 −1.87944
\(55\) −9.20588 −1.24132
\(56\) 7.76032 1.03702
\(57\) 10.1207 1.34051
\(58\) −10.6629 −1.40011
\(59\) −0.211513 −0.0275367 −0.0137684 0.999905i \(-0.504383\pi\)
−0.0137684 + 0.999905i \(0.504383\pi\)
\(60\) 26.7834 3.45772
\(61\) −2.55588 −0.327247 −0.163623 0.986523i \(-0.552318\pi\)
−0.163623 + 0.986523i \(0.552318\pi\)
\(62\) 2.63529 0.334682
\(63\) 0.0527133 0.00664125
\(64\) 11.3211 1.41514
\(65\) 0.0969156 0.0120209
\(66\) 13.2007 1.62489
\(67\) 13.4224 1.63981 0.819905 0.572500i \(-0.194026\pi\)
0.819905 + 0.572500i \(0.194026\pi\)
\(68\) −18.2069 −2.20791
\(69\) −14.2931 −1.72069
\(70\) −8.31452 −0.993775
\(71\) 12.9686 1.53909 0.769545 0.638592i \(-0.220483\pi\)
0.769545 + 0.638592i \(0.220483\pi\)
\(72\) 0.409072 0.0482096
\(73\) −1.09398 −0.128041 −0.0640206 0.997949i \(-0.520392\pi\)
−0.0640206 + 0.997949i \(0.520392\pi\)
\(74\) −2.63529 −0.306346
\(75\) −8.50562 −0.982145
\(76\) −29.1503 −3.34377
\(77\) −2.91781 −0.332515
\(78\) −0.138971 −0.0157354
\(79\) 5.42088 0.609897 0.304949 0.952369i \(-0.401361\pi\)
0.304949 + 0.952369i \(0.401361\pi\)
\(80\) −33.3212 −3.72542
\(81\) −8.83908 −0.982120
\(82\) 2.48235 0.274129
\(83\) −14.6631 −1.60948 −0.804740 0.593628i \(-0.797695\pi\)
−0.804740 + 0.593628i \(0.797695\pi\)
\(84\) 8.48901 0.926226
\(85\) 11.6171 1.26005
\(86\) 26.0417 2.80815
\(87\) −6.94636 −0.744728
\(88\) −22.6431 −2.41376
\(89\) 8.61286 0.912962 0.456481 0.889733i \(-0.349110\pi\)
0.456481 + 0.889733i \(0.349110\pi\)
\(90\) −0.438286 −0.0461994
\(91\) 0.0307174 0.00322006
\(92\) 41.1681 4.29207
\(93\) 1.71677 0.178020
\(94\) −13.1667 −1.35804
\(95\) 18.5997 1.90829
\(96\) 21.1353 2.15712
\(97\) −8.08133 −0.820535 −0.410267 0.911965i \(-0.634565\pi\)
−0.410267 + 0.911965i \(0.634565\pi\)
\(98\) −2.63529 −0.266205
\(99\) −0.153807 −0.0154582
\(100\) 24.4986 2.44986
\(101\) 16.3437 1.62626 0.813131 0.582080i \(-0.197761\pi\)
0.813131 + 0.582080i \(0.197761\pi\)
\(102\) −16.6583 −1.64941
\(103\) −20.0535 −1.97593 −0.987965 0.154679i \(-0.950566\pi\)
−0.987965 + 0.154679i \(0.950566\pi\)
\(104\) 0.238377 0.0233748
\(105\) −5.41651 −0.528597
\(106\) 5.41135 0.525596
\(107\) −5.23674 −0.506255 −0.253127 0.967433i \(-0.581459\pi\)
−0.253127 + 0.967433i \(0.581459\pi\)
\(108\) 25.9145 2.49362
\(109\) 6.44359 0.617184 0.308592 0.951194i \(-0.400142\pi\)
0.308592 + 0.951194i \(0.400142\pi\)
\(110\) 24.2602 2.31312
\(111\) −1.71677 −0.162948
\(112\) −10.5612 −0.997937
\(113\) −10.9113 −1.02645 −0.513225 0.858254i \(-0.671549\pi\)
−0.513225 + 0.858254i \(0.671549\pi\)
\(114\) −26.6709 −2.49796
\(115\) −26.2678 −2.44949
\(116\) 20.0075 1.85765
\(117\) 0.00161922 0.000149697 0
\(118\) 0.557400 0.0513128
\(119\) 3.68205 0.337533
\(120\) −42.0338 −3.83715
\(121\) −2.48640 −0.226037
\(122\) 6.73549 0.609802
\(123\) 1.61713 0.145812
\(124\) −4.94476 −0.444053
\(125\) 0.143730 0.0128556
\(126\) −0.138915 −0.0123755
\(127\) −2.59075 −0.229892 −0.114946 0.993372i \(-0.536670\pi\)
−0.114946 + 0.993372i \(0.536670\pi\)
\(128\) −5.21213 −0.460691
\(129\) 16.9649 1.49368
\(130\) −0.255401 −0.0224001
\(131\) 0.701835 0.0613196 0.0306598 0.999530i \(-0.490239\pi\)
0.0306598 + 0.999530i \(0.490239\pi\)
\(132\) −24.7693 −2.15589
\(133\) 5.89519 0.511177
\(134\) −35.3720 −3.05567
\(135\) −16.5351 −1.42311
\(136\) 28.5739 2.45019
\(137\) 2.14898 0.183600 0.0918001 0.995777i \(-0.470738\pi\)
0.0918001 + 0.995777i \(0.470738\pi\)
\(138\) 37.6665 3.20639
\(139\) −19.4665 −1.65113 −0.825564 0.564308i \(-0.809143\pi\)
−0.825564 + 0.564308i \(0.809143\pi\)
\(140\) 15.6011 1.31853
\(141\) −8.57747 −0.722353
\(142\) −34.1761 −2.86799
\(143\) −0.0896276 −0.00749504
\(144\) −0.556714 −0.0463928
\(145\) −12.7660 −1.06016
\(146\) 2.88297 0.238596
\(147\) −1.71677 −0.141597
\(148\) 4.94476 0.406457
\(149\) 16.6330 1.36262 0.681312 0.731993i \(-0.261410\pi\)
0.681312 + 0.731993i \(0.261410\pi\)
\(150\) 22.4148 1.83016
\(151\) −9.08362 −0.739214 −0.369607 0.929188i \(-0.620508\pi\)
−0.369607 + 0.929188i \(0.620508\pi\)
\(152\) 45.7485 3.71069
\(153\) 0.194093 0.0156915
\(154\) 7.68927 0.619619
\(155\) 3.15507 0.253421
\(156\) 0.260761 0.0208776
\(157\) 17.0886 1.36382 0.681908 0.731438i \(-0.261150\pi\)
0.681908 + 0.731438i \(0.261150\pi\)
\(158\) −14.2856 −1.13650
\(159\) 3.52523 0.279569
\(160\) 38.8424 3.07076
\(161\) −8.32560 −0.656149
\(162\) 23.2936 1.83012
\(163\) 7.49295 0.586893 0.293447 0.955975i \(-0.405198\pi\)
0.293447 + 0.955975i \(0.405198\pi\)
\(164\) −4.65779 −0.363712
\(165\) 15.8043 1.23037
\(166\) 38.6414 2.99916
\(167\) −23.7939 −1.84123 −0.920615 0.390472i \(-0.872312\pi\)
−0.920615 + 0.390472i \(0.872312\pi\)
\(168\) −13.3226 −1.02786
\(169\) −12.9991 −0.999927
\(170\) −30.6145 −2.34802
\(171\) 0.310755 0.0237640
\(172\) −48.8637 −3.72582
\(173\) 1.45358 0.110514 0.0552569 0.998472i \(-0.482402\pi\)
0.0552569 + 0.998472i \(0.482402\pi\)
\(174\) 18.3057 1.38775
\(175\) −4.95444 −0.374521
\(176\) 30.8155 2.32280
\(177\) 0.363119 0.0272937
\(178\) −22.6974 −1.70124
\(179\) −12.9025 −0.964379 −0.482189 0.876067i \(-0.660158\pi\)
−0.482189 + 0.876067i \(0.660158\pi\)
\(180\) 0.822383 0.0612968
\(181\) −5.47227 −0.406750 −0.203375 0.979101i \(-0.565191\pi\)
−0.203375 + 0.979101i \(0.565191\pi\)
\(182\) −0.0809495 −0.00600037
\(183\) 4.38785 0.324359
\(184\) −64.6093 −4.76306
\(185\) −3.15507 −0.231965
\(186\) −4.52418 −0.331729
\(187\) −10.7435 −0.785644
\(188\) 24.7055 1.80183
\(189\) −5.24080 −0.381212
\(190\) −49.0156 −3.55597
\(191\) 25.8131 1.86777 0.933886 0.357570i \(-0.116395\pi\)
0.933886 + 0.357570i \(0.116395\pi\)
\(192\) −19.4357 −1.40265
\(193\) −13.0934 −0.942486 −0.471243 0.882003i \(-0.656195\pi\)
−0.471243 + 0.882003i \(0.656195\pi\)
\(194\) 21.2967 1.52901
\(195\) −0.166381 −0.0119148
\(196\) 4.94476 0.353197
\(197\) −23.2418 −1.65591 −0.827956 0.560793i \(-0.810496\pi\)
−0.827956 + 0.560793i \(0.810496\pi\)
\(198\) 0.405327 0.0288053
\(199\) 3.19180 0.226261 0.113130 0.993580i \(-0.463912\pi\)
0.113130 + 0.993580i \(0.463912\pi\)
\(200\) −38.4481 −2.71869
\(201\) −23.0432 −1.62534
\(202\) −43.0705 −3.03043
\(203\) −4.04619 −0.283987
\(204\) 31.2570 2.18842
\(205\) 2.97196 0.207570
\(206\) 52.8468 3.68201
\(207\) −0.438870 −0.0305036
\(208\) −0.324412 −0.0224939
\(209\) −17.2010 −1.18982
\(210\) 14.2741 0.985006
\(211\) 10.9866 0.756350 0.378175 0.925734i \(-0.376552\pi\)
0.378175 + 0.925734i \(0.376552\pi\)
\(212\) −10.1537 −0.697356
\(213\) −22.2641 −1.52551
\(214\) 13.8003 0.943372
\(215\) 31.1781 2.12633
\(216\) −40.6702 −2.76726
\(217\) 1.00000 0.0678844
\(218\) −16.9808 −1.15008
\(219\) 1.87811 0.126911
\(220\) −45.5209 −3.06902
\(221\) 0.113103 0.00760815
\(222\) 4.52418 0.303643
\(223\) 3.69938 0.247729 0.123864 0.992299i \(-0.460471\pi\)
0.123864 + 0.992299i \(0.460471\pi\)
\(224\) 12.3111 0.822572
\(225\) −0.261165 −0.0174110
\(226\) 28.7545 1.91272
\(227\) −0.155384 −0.0103132 −0.00515661 0.999987i \(-0.501641\pi\)
−0.00515661 + 0.999987i \(0.501641\pi\)
\(228\) 50.0443 3.31426
\(229\) 28.5629 1.88749 0.943744 0.330676i \(-0.107277\pi\)
0.943744 + 0.330676i \(0.107277\pi\)
\(230\) 69.2234 4.56445
\(231\) 5.00919 0.329581
\(232\) −31.3997 −2.06149
\(233\) −2.73029 −0.178867 −0.0894337 0.995993i \(-0.528506\pi\)
−0.0894337 + 0.995993i \(0.528506\pi\)
\(234\) −0.00426711 −0.000278950 0
\(235\) −15.7636 −1.02831
\(236\) −1.04588 −0.0680813
\(237\) −9.30639 −0.604515
\(238\) −9.70328 −0.628970
\(239\) −6.23443 −0.403271 −0.201636 0.979461i \(-0.564626\pi\)
−0.201636 + 0.979461i \(0.564626\pi\)
\(240\) 57.2047 3.69255
\(241\) 3.34339 0.215367 0.107683 0.994185i \(-0.465657\pi\)
0.107683 + 0.994185i \(0.465657\pi\)
\(242\) 6.55239 0.421204
\(243\) −0.547749 −0.0351381
\(244\) −12.6382 −0.809079
\(245\) −3.15507 −0.201570
\(246\) −4.26161 −0.271710
\(247\) 0.181085 0.0115222
\(248\) 7.76032 0.492781
\(249\) 25.1730 1.59528
\(250\) −0.378772 −0.0239556
\(251\) −9.76237 −0.616196 −0.308098 0.951355i \(-0.599692\pi\)
−0.308098 + 0.951355i \(0.599692\pi\)
\(252\) 0.260655 0.0164197
\(253\) 24.2925 1.52726
\(254\) 6.82739 0.428388
\(255\) −19.9439 −1.24893
\(256\) −8.90671 −0.556669
\(257\) 1.76103 0.109850 0.0549249 0.998490i \(-0.482508\pi\)
0.0549249 + 0.998490i \(0.482508\pi\)
\(258\) −44.7075 −2.78337
\(259\) −1.00000 −0.0621370
\(260\) 0.479225 0.0297203
\(261\) −0.213288 −0.0132022
\(262\) −1.84954 −0.114265
\(263\) −25.5470 −1.57530 −0.787648 0.616125i \(-0.788701\pi\)
−0.787648 + 0.616125i \(0.788701\pi\)
\(264\) 38.8729 2.39246
\(265\) 6.47866 0.397981
\(266\) −15.5355 −0.952545
\(267\) −14.7863 −0.904905
\(268\) 66.3707 4.05424
\(269\) 22.0236 1.34281 0.671403 0.741093i \(-0.265692\pi\)
0.671403 + 0.741093i \(0.265692\pi\)
\(270\) 43.5747 2.65187
\(271\) −2.44701 −0.148645 −0.0743227 0.997234i \(-0.523679\pi\)
−0.0743227 + 0.997234i \(0.523679\pi\)
\(272\) −38.8868 −2.35786
\(273\) −0.0527347 −0.00319165
\(274\) −5.66320 −0.342127
\(275\) 14.4561 0.871736
\(276\) −70.6761 −4.25420
\(277\) 26.8285 1.61197 0.805985 0.591936i \(-0.201636\pi\)
0.805985 + 0.591936i \(0.201636\pi\)
\(278\) 51.3000 3.07677
\(279\) 0.0527133 0.00315586
\(280\) −24.4843 −1.46322
\(281\) −22.4358 −1.33841 −0.669205 0.743078i \(-0.733365\pi\)
−0.669205 + 0.743078i \(0.733365\pi\)
\(282\) 22.6041 1.34606
\(283\) −25.4290 −1.51160 −0.755798 0.654805i \(-0.772751\pi\)
−0.755798 + 0.654805i \(0.772751\pi\)
\(284\) 64.1267 3.80522
\(285\) −31.9313 −1.89145
\(286\) 0.236195 0.0139665
\(287\) 0.941963 0.0556023
\(288\) 0.648960 0.0382404
\(289\) −3.44250 −0.202500
\(290\) 33.6421 1.97553
\(291\) 13.8738 0.813294
\(292\) −5.40949 −0.316567
\(293\) 7.43809 0.434538 0.217269 0.976112i \(-0.430285\pi\)
0.217269 + 0.976112i \(0.430285\pi\)
\(294\) 4.52418 0.263856
\(295\) 0.667339 0.0388540
\(296\) −7.76032 −0.451059
\(297\) 15.2916 0.887310
\(298\) −43.8327 −2.53916
\(299\) −0.255741 −0.0147899
\(300\) −42.0583 −2.42824
\(301\) 9.88190 0.569584
\(302\) 23.9380 1.37748
\(303\) −28.0584 −1.61191
\(304\) −62.2600 −3.57086
\(305\) 8.06397 0.461741
\(306\) −0.511492 −0.0292400
\(307\) −27.6917 −1.58045 −0.790224 0.612818i \(-0.790036\pi\)
−0.790224 + 0.612818i \(0.790036\pi\)
\(308\) −14.4279 −0.822104
\(309\) 34.4272 1.95849
\(310\) −8.31452 −0.472233
\(311\) 7.38443 0.418733 0.209366 0.977837i \(-0.432860\pi\)
0.209366 + 0.977837i \(0.432860\pi\)
\(312\) −0.409238 −0.0231685
\(313\) −25.6010 −1.44705 −0.723527 0.690297i \(-0.757480\pi\)
−0.723527 + 0.690297i \(0.757480\pi\)
\(314\) −45.0334 −2.54138
\(315\) −0.166314 −0.00937073
\(316\) 26.8050 1.50790
\(317\) −20.8879 −1.17318 −0.586590 0.809884i \(-0.699530\pi\)
−0.586590 + 0.809884i \(0.699530\pi\)
\(318\) −9.29002 −0.520958
\(319\) 11.8060 0.661009
\(320\) −35.7188 −1.99674
\(321\) 8.99026 0.501787
\(322\) 21.9404 1.22269
\(323\) 21.7064 1.20777
\(324\) −43.7072 −2.42818
\(325\) −0.152188 −0.00844187
\(326\) −19.7461 −1.09364
\(327\) −11.0621 −0.611738
\(328\) 7.30993 0.403623
\(329\) −4.99629 −0.275455
\(330\) −41.6490 −2.29270
\(331\) −24.3817 −1.34014 −0.670069 0.742299i \(-0.733735\pi\)
−0.670069 + 0.742299i \(0.733735\pi\)
\(332\) −72.5053 −3.97925
\(333\) −0.0527133 −0.00288867
\(334\) 62.7040 3.43101
\(335\) −42.3486 −2.31375
\(336\) 18.1311 0.989130
\(337\) −10.5971 −0.577261 −0.288630 0.957441i \(-0.593200\pi\)
−0.288630 + 0.957441i \(0.593200\pi\)
\(338\) 34.2563 1.86330
\(339\) 18.7322 1.01739
\(340\) 57.4439 3.11533
\(341\) −2.91781 −0.158008
\(342\) −0.818929 −0.0442826
\(343\) −1.00000 −0.0539949
\(344\) 76.6867 4.13467
\(345\) 45.0957 2.42787
\(346\) −3.83061 −0.205935
\(347\) 12.1532 0.652416 0.326208 0.945298i \(-0.394229\pi\)
0.326208 + 0.945298i \(0.394229\pi\)
\(348\) −34.3481 −1.84125
\(349\) −2.61459 −0.139956 −0.0699778 0.997549i \(-0.522293\pi\)
−0.0699778 + 0.997549i \(0.522293\pi\)
\(350\) 13.0564 0.697894
\(351\) −0.160984 −0.00859268
\(352\) −35.9215 −1.91462
\(353\) −20.6057 −1.09673 −0.548366 0.836239i \(-0.684750\pi\)
−0.548366 + 0.836239i \(0.684750\pi\)
\(354\) −0.956925 −0.0508600
\(355\) −40.9168 −2.17164
\(356\) 42.5886 2.25719
\(357\) −6.32122 −0.334555
\(358\) 34.0019 1.79705
\(359\) 24.5795 1.29726 0.648629 0.761105i \(-0.275343\pi\)
0.648629 + 0.761105i \(0.275343\pi\)
\(360\) −1.29065 −0.0680232
\(361\) 15.7532 0.829116
\(362\) 14.4210 0.757952
\(363\) 4.26857 0.224042
\(364\) 0.151891 0.00796123
\(365\) 3.45159 0.180665
\(366\) −11.5633 −0.604421
\(367\) −1.27829 −0.0667263 −0.0333632 0.999443i \(-0.510622\pi\)
−0.0333632 + 0.999443i \(0.510622\pi\)
\(368\) 87.9281 4.58357
\(369\) 0.0496540 0.00258488
\(370\) 8.31452 0.432251
\(371\) 2.05341 0.106608
\(372\) 8.48901 0.440134
\(373\) −28.2010 −1.46019 −0.730096 0.683345i \(-0.760525\pi\)
−0.730096 + 0.683345i \(0.760525\pi\)
\(374\) 28.3123 1.46399
\(375\) −0.246752 −0.0127422
\(376\) −38.7728 −1.99956
\(377\) −0.124289 −0.00640119
\(378\) 13.8110 0.710363
\(379\) 20.5998 1.05814 0.529071 0.848578i \(-0.322541\pi\)
0.529071 + 0.848578i \(0.322541\pi\)
\(380\) 91.9711 4.71802
\(381\) 4.44772 0.227863
\(382\) −68.0251 −3.48047
\(383\) 22.6238 1.15602 0.578011 0.816029i \(-0.303829\pi\)
0.578011 + 0.816029i \(0.303829\pi\)
\(384\) 8.94801 0.456626
\(385\) 9.20588 0.469175
\(386\) 34.5050 1.75626
\(387\) 0.520908 0.0264792
\(388\) −39.9603 −2.02868
\(389\) 4.52612 0.229483 0.114742 0.993395i \(-0.463396\pi\)
0.114742 + 0.993395i \(0.463396\pi\)
\(390\) 0.438464 0.0222025
\(391\) −30.6553 −1.55030
\(392\) −7.76032 −0.391955
\(393\) −1.20489 −0.0607785
\(394\) 61.2490 3.08568
\(395\) −17.1032 −0.860558
\(396\) −0.760540 −0.0382186
\(397\) −13.4606 −0.675568 −0.337784 0.941224i \(-0.609677\pi\)
−0.337784 + 0.941224i \(0.609677\pi\)
\(398\) −8.41132 −0.421621
\(399\) −10.1207 −0.506667
\(400\) 52.3247 2.61624
\(401\) 6.90612 0.344875 0.172438 0.985020i \(-0.444836\pi\)
0.172438 + 0.985020i \(0.444836\pi\)
\(402\) 60.7254 3.02871
\(403\) 0.0307174 0.00153015
\(404\) 80.8159 4.02074
\(405\) 27.8879 1.38576
\(406\) 10.6629 0.529190
\(407\) 2.91781 0.144630
\(408\) −49.0547 −2.42857
\(409\) −3.56735 −0.176394 −0.0881971 0.996103i \(-0.528111\pi\)
−0.0881971 + 0.996103i \(0.528111\pi\)
\(410\) −7.83197 −0.386794
\(411\) −3.68930 −0.181980
\(412\) −99.1598 −4.88525
\(413\) 0.211513 0.0104079
\(414\) 1.15655 0.0568413
\(415\) 46.2629 2.27096
\(416\) 0.378167 0.0185411
\(417\) 33.4195 1.63656
\(418\) 45.3297 2.21715
\(419\) 0.534638 0.0261188 0.0130594 0.999915i \(-0.495843\pi\)
0.0130594 + 0.999915i \(0.495843\pi\)
\(420\) −26.7834 −1.30689
\(421\) −29.8011 −1.45242 −0.726209 0.687474i \(-0.758720\pi\)
−0.726209 + 0.687474i \(0.758720\pi\)
\(422\) −28.9529 −1.40941
\(423\) −0.263371 −0.0128055
\(424\) 15.9351 0.773879
\(425\) −18.2425 −0.884892
\(426\) 58.6723 2.84268
\(427\) 2.55588 0.123688
\(428\) −25.8945 −1.25166
\(429\) 0.153870 0.00742890
\(430\) −82.1633 −3.96227
\(431\) −2.06961 −0.0996897 −0.0498449 0.998757i \(-0.515873\pi\)
−0.0498449 + 0.998757i \(0.515873\pi\)
\(432\) 55.3489 2.66298
\(433\) 22.4412 1.07846 0.539228 0.842160i \(-0.318716\pi\)
0.539228 + 0.842160i \(0.318716\pi\)
\(434\) −2.63529 −0.126498
\(435\) 21.9162 1.05080
\(436\) 31.8621 1.52592
\(437\) −49.0810 −2.34786
\(438\) −4.94938 −0.236491
\(439\) 18.3921 0.877808 0.438904 0.898534i \(-0.355367\pi\)
0.438904 + 0.898534i \(0.355367\pi\)
\(440\) 71.4405 3.40579
\(441\) −0.0527133 −0.00251016
\(442\) −0.298060 −0.0141773
\(443\) −19.2915 −0.916568 −0.458284 0.888806i \(-0.651536\pi\)
−0.458284 + 0.888806i \(0.651536\pi\)
\(444\) −8.48901 −0.402870
\(445\) −27.1742 −1.28818
\(446\) −9.74895 −0.461626
\(447\) −28.5549 −1.35060
\(448\) −11.3211 −0.534871
\(449\) −6.25959 −0.295408 −0.147704 0.989032i \(-0.547188\pi\)
−0.147704 + 0.989032i \(0.547188\pi\)
\(450\) 0.688246 0.0324442
\(451\) −2.74847 −0.129420
\(452\) −53.9539 −2.53778
\(453\) 15.5945 0.732691
\(454\) 0.409483 0.0192180
\(455\) −0.0969156 −0.00454347
\(456\) −78.5395 −3.67795
\(457\) 11.8843 0.555926 0.277963 0.960592i \(-0.410341\pi\)
0.277963 + 0.960592i \(0.410341\pi\)
\(458\) −75.2715 −3.51721
\(459\) −19.2969 −0.900701
\(460\) −129.888 −6.05607
\(461\) −9.98204 −0.464910 −0.232455 0.972607i \(-0.574676\pi\)
−0.232455 + 0.972607i \(0.574676\pi\)
\(462\) −13.2007 −0.614152
\(463\) −19.7536 −0.918029 −0.459014 0.888429i \(-0.651797\pi\)
−0.459014 + 0.888429i \(0.651797\pi\)
\(464\) 42.7325 1.98381
\(465\) −5.41651 −0.251185
\(466\) 7.19512 0.333307
\(467\) 1.23145 0.0569849 0.0284924 0.999594i \(-0.490929\pi\)
0.0284924 + 0.999594i \(0.490929\pi\)
\(468\) 0.00800665 0.000370108 0
\(469\) −13.4224 −0.619790
\(470\) 41.5418 1.91618
\(471\) −29.3371 −1.35178
\(472\) 1.64141 0.0755521
\(473\) −28.8335 −1.32577
\(474\) 24.5251 1.12647
\(475\) −29.2074 −1.34013
\(476\) 18.2069 0.834511
\(477\) 0.108242 0.00495607
\(478\) 16.4295 0.751469
\(479\) −23.4862 −1.07311 −0.536556 0.843865i \(-0.680275\pi\)
−0.536556 + 0.843865i \(0.680275\pi\)
\(480\) −66.6834 −3.04367
\(481\) −0.0307174 −0.00140060
\(482\) −8.81082 −0.401322
\(483\) 14.2931 0.650359
\(484\) −12.2947 −0.558849
\(485\) 25.4971 1.15776
\(486\) 1.44348 0.0654775
\(487\) 15.3945 0.697592 0.348796 0.937199i \(-0.386591\pi\)
0.348796 + 0.937199i \(0.386591\pi\)
\(488\) 19.8344 0.897862
\(489\) −12.8636 −0.581714
\(490\) 8.31452 0.375612
\(491\) −29.8889 −1.34887 −0.674434 0.738336i \(-0.735612\pi\)
−0.674434 + 0.738336i \(0.735612\pi\)
\(492\) 7.99633 0.360502
\(493\) −14.8983 −0.670985
\(494\) −0.477212 −0.0214708
\(495\) 0.485272 0.0218114
\(496\) −10.5612 −0.474210
\(497\) −12.9686 −0.581722
\(498\) −66.3383 −2.97269
\(499\) 29.9586 1.34113 0.670566 0.741850i \(-0.266051\pi\)
0.670566 + 0.741850i \(0.266051\pi\)
\(500\) 0.710713 0.0317841
\(501\) 40.8486 1.82498
\(502\) 25.7267 1.14824
\(503\) −1.48938 −0.0664083 −0.0332042 0.999449i \(-0.510571\pi\)
−0.0332042 + 0.999449i \(0.510571\pi\)
\(504\) −0.409072 −0.0182215
\(505\) −51.5656 −2.29464
\(506\) −64.0178 −2.84594
\(507\) 22.3163 0.991104
\(508\) −12.8107 −0.568381
\(509\) −9.82058 −0.435289 −0.217645 0.976028i \(-0.569837\pi\)
−0.217645 + 0.976028i \(0.569837\pi\)
\(510\) 52.5579 2.32730
\(511\) 1.09398 0.0483950
\(512\) 33.8960 1.49801
\(513\) −30.8955 −1.36407
\(514\) −4.64082 −0.204698
\(515\) 63.2701 2.78801
\(516\) 83.8875 3.69294
\(517\) 14.5782 0.641149
\(518\) 2.63529 0.115788
\(519\) −2.49546 −0.109539
\(520\) −0.752096 −0.0329816
\(521\) −3.83043 −0.167814 −0.0839071 0.996474i \(-0.526740\pi\)
−0.0839071 + 0.996474i \(0.526740\pi\)
\(522\) 0.562076 0.0246014
\(523\) −14.4193 −0.630514 −0.315257 0.949006i \(-0.602091\pi\)
−0.315257 + 0.949006i \(0.602091\pi\)
\(524\) 3.47041 0.151606
\(525\) 8.50562 0.371216
\(526\) 67.3238 2.93546
\(527\) 3.68205 0.160393
\(528\) −52.9029 −2.30230
\(529\) 46.3156 2.01372
\(530\) −17.0732 −0.741611
\(531\) 0.0111496 0.000483850 0
\(532\) 29.1503 1.26383
\(533\) 0.0289347 0.00125330
\(534\) 38.9662 1.68623
\(535\) 16.5223 0.714320
\(536\) −104.162 −4.49912
\(537\) 22.1506 0.955868
\(538\) −58.0387 −2.50223
\(539\) 2.91781 0.125679
\(540\) −81.7620 −3.51848
\(541\) −27.4267 −1.17916 −0.589582 0.807708i \(-0.700708\pi\)
−0.589582 + 0.807708i \(0.700708\pi\)
\(542\) 6.44859 0.276991
\(543\) 9.39460 0.403161
\(544\) 45.3302 1.94352
\(545\) −20.3300 −0.870840
\(546\) 0.138971 0.00594742
\(547\) −17.9831 −0.768901 −0.384450 0.923146i \(-0.625609\pi\)
−0.384450 + 0.923146i \(0.625609\pi\)
\(548\) 10.6262 0.453930
\(549\) 0.134729 0.00575008
\(550\) −38.0961 −1.62442
\(551\) −23.8530 −1.01617
\(552\) 110.919 4.72103
\(553\) −5.42088 −0.230519
\(554\) −70.7010 −3.00380
\(555\) 5.41651 0.229918
\(556\) −96.2574 −4.08222
\(557\) 11.3799 0.482180 0.241090 0.970503i \(-0.422495\pi\)
0.241090 + 0.970503i \(0.422495\pi\)
\(558\) −0.138915 −0.00588074
\(559\) 0.303547 0.0128387
\(560\) 33.3212 1.40808
\(561\) 18.4441 0.778711
\(562\) 59.1250 2.49404
\(563\) 22.6930 0.956396 0.478198 0.878252i \(-0.341290\pi\)
0.478198 + 0.878252i \(0.341290\pi\)
\(564\) −42.4136 −1.78593
\(565\) 34.4259 1.44831
\(566\) 67.0128 2.81676
\(567\) 8.83908 0.371207
\(568\) −100.640 −4.22278
\(569\) −42.2509 −1.77125 −0.885624 0.464402i \(-0.846269\pi\)
−0.885624 + 0.464402i \(0.846269\pi\)
\(570\) 84.1484 3.52459
\(571\) −32.6900 −1.36803 −0.684017 0.729466i \(-0.739769\pi\)
−0.684017 + 0.729466i \(0.739769\pi\)
\(572\) −0.443187 −0.0185306
\(573\) −44.3151 −1.85129
\(574\) −2.48235 −0.103611
\(575\) 41.2487 1.72019
\(576\) −0.596772 −0.0248655
\(577\) −1.97451 −0.0821999 −0.0411000 0.999155i \(-0.513086\pi\)
−0.0411000 + 0.999155i \(0.513086\pi\)
\(578\) 9.07199 0.377345
\(579\) 22.4784 0.934169
\(580\) −63.1248 −2.62112
\(581\) 14.6631 0.608326
\(582\) −36.5614 −1.51552
\(583\) −5.99147 −0.248141
\(584\) 8.48966 0.351305
\(585\) −0.00510874 −0.000211220 0
\(586\) −19.6015 −0.809732
\(587\) 35.4273 1.46224 0.731122 0.682247i \(-0.238997\pi\)
0.731122 + 0.682247i \(0.238997\pi\)
\(588\) −8.48901 −0.350081
\(589\) 5.89519 0.242907
\(590\) −1.75863 −0.0724018
\(591\) 39.9008 1.64130
\(592\) 10.5612 0.434061
\(593\) 34.6176 1.42157 0.710786 0.703408i \(-0.248339\pi\)
0.710786 + 0.703408i \(0.248339\pi\)
\(594\) −40.2979 −1.65344
\(595\) −11.6171 −0.476255
\(596\) 82.2461 3.36893
\(597\) −5.47957 −0.224264
\(598\) 0.673953 0.0275600
\(599\) 43.6696 1.78429 0.892146 0.451748i \(-0.149199\pi\)
0.892146 + 0.451748i \(0.149199\pi\)
\(600\) 66.0063 2.69470
\(601\) 3.28076 0.133825 0.0669124 0.997759i \(-0.478685\pi\)
0.0669124 + 0.997759i \(0.478685\pi\)
\(602\) −26.0417 −1.06138
\(603\) −0.707540 −0.0288133
\(604\) −44.9164 −1.82762
\(605\) 7.84476 0.318935
\(606\) 73.9420 3.00369
\(607\) −41.9500 −1.70270 −0.851348 0.524601i \(-0.824214\pi\)
−0.851348 + 0.524601i \(0.824214\pi\)
\(608\) 72.5764 2.94336
\(609\) 6.94636 0.281481
\(610\) −21.2509 −0.860424
\(611\) −0.153473 −0.00620887
\(612\) 0.959744 0.0387954
\(613\) 37.0642 1.49701 0.748505 0.663130i \(-0.230772\pi\)
0.748505 + 0.663130i \(0.230772\pi\)
\(614\) 72.9757 2.94506
\(615\) −5.10215 −0.205739
\(616\) 22.6431 0.912317
\(617\) 7.59001 0.305562 0.152781 0.988260i \(-0.451177\pi\)
0.152781 + 0.988260i \(0.451177\pi\)
\(618\) −90.7256 −3.64952
\(619\) 47.5164 1.90985 0.954923 0.296853i \(-0.0959373\pi\)
0.954923 + 0.296853i \(0.0959373\pi\)
\(620\) 15.6011 0.626554
\(621\) 43.6328 1.75092
\(622\) −19.4601 −0.780280
\(623\) −8.61286 −0.345067
\(624\) 0.556940 0.0222954
\(625\) −25.2257 −1.00903
\(626\) 67.4661 2.69649
\(627\) 29.5301 1.17932
\(628\) 84.4990 3.37188
\(629\) −3.68205 −0.146813
\(630\) 0.438286 0.0174617
\(631\) 35.2433 1.40301 0.701506 0.712664i \(-0.252511\pi\)
0.701506 + 0.712664i \(0.252511\pi\)
\(632\) −42.0678 −1.67337
\(633\) −18.8614 −0.749675
\(634\) 55.0456 2.18614
\(635\) 8.17399 0.324375
\(636\) 17.4314 0.691202
\(637\) −0.0307174 −0.00121707
\(638\) −31.1123 −1.23175
\(639\) −0.683618 −0.0270435
\(640\) 16.4446 0.650030
\(641\) −19.6869 −0.777586 −0.388793 0.921325i \(-0.627108\pi\)
−0.388793 + 0.921325i \(0.627108\pi\)
\(642\) −23.6920 −0.935047
\(643\) 39.3743 1.55277 0.776386 0.630257i \(-0.217051\pi\)
0.776386 + 0.630257i \(0.217051\pi\)
\(644\) −41.1681 −1.62225
\(645\) −53.5255 −2.10756
\(646\) −57.2026 −2.25061
\(647\) −26.6643 −1.04828 −0.524141 0.851631i \(-0.675614\pi\)
−0.524141 + 0.851631i \(0.675614\pi\)
\(648\) 68.5941 2.69463
\(649\) −0.617155 −0.0242255
\(650\) 0.401060 0.0157309
\(651\) −1.71677 −0.0672854
\(652\) 37.0509 1.45102
\(653\) −0.346561 −0.0135620 −0.00678099 0.999977i \(-0.502158\pi\)
−0.00678099 + 0.999977i \(0.502158\pi\)
\(654\) 29.1520 1.13993
\(655\) −2.21434 −0.0865213
\(656\) −9.94823 −0.388413
\(657\) 0.0576675 0.00224982
\(658\) 13.1667 0.513291
\(659\) −15.8594 −0.617795 −0.308898 0.951095i \(-0.599960\pi\)
−0.308898 + 0.951095i \(0.599960\pi\)
\(660\) 78.1487 3.04194
\(661\) −6.31293 −0.245545 −0.122772 0.992435i \(-0.539178\pi\)
−0.122772 + 0.992435i \(0.539178\pi\)
\(662\) 64.2528 2.49726
\(663\) −0.194172 −0.00754101
\(664\) 113.790 4.41590
\(665\) −18.5997 −0.721265
\(666\) 0.138915 0.00538284
\(667\) 33.6870 1.30436
\(668\) −117.655 −4.55222
\(669\) −6.35097 −0.245543
\(670\) 111.601 4.31152
\(671\) −7.45756 −0.287896
\(672\) −21.1353 −0.815313
\(673\) 5.93953 0.228952 0.114476 0.993426i \(-0.463481\pi\)
0.114476 + 0.993426i \(0.463481\pi\)
\(674\) 27.9265 1.07569
\(675\) 25.9652 0.999402
\(676\) −64.2773 −2.47220
\(677\) 36.8244 1.41528 0.707638 0.706575i \(-0.249761\pi\)
0.707638 + 0.706575i \(0.249761\pi\)
\(678\) −49.3648 −1.89584
\(679\) 8.08133 0.310133
\(680\) −90.1525 −3.45719
\(681\) 0.266759 0.0102222
\(682\) 7.68927 0.294438
\(683\) 30.5136 1.16757 0.583785 0.811908i \(-0.301571\pi\)
0.583785 + 0.811908i \(0.301571\pi\)
\(684\) 1.53661 0.0587537
\(685\) −6.78019 −0.259058
\(686\) 2.63529 0.100616
\(687\) −49.0358 −1.87083
\(688\) −104.364 −3.97886
\(689\) 0.0630756 0.00240299
\(690\) −118.840 −4.52418
\(691\) −7.84131 −0.298297 −0.149149 0.988815i \(-0.547653\pi\)
−0.149149 + 0.988815i \(0.547653\pi\)
\(692\) 7.18762 0.273232
\(693\) 0.153807 0.00584265
\(694\) −32.0271 −1.21573
\(695\) 61.4182 2.32972
\(696\) 53.9059 2.04330
\(697\) 3.46836 0.131373
\(698\) 6.89020 0.260798
\(699\) 4.68728 0.177289
\(700\) −24.4986 −0.925959
\(701\) 36.5833 1.38173 0.690866 0.722983i \(-0.257229\pi\)
0.690866 + 0.722983i \(0.257229\pi\)
\(702\) 0.424240 0.0160119
\(703\) −5.89519 −0.222341
\(704\) 33.0328 1.24497
\(705\) 27.0625 1.01923
\(706\) 54.3021 2.04368
\(707\) −16.3437 −0.614669
\(708\) 1.79554 0.0674805
\(709\) 4.67072 0.175412 0.0877062 0.996146i \(-0.472046\pi\)
0.0877062 + 0.996146i \(0.472046\pi\)
\(710\) 107.828 4.04670
\(711\) −0.285753 −0.0107166
\(712\) −66.8385 −2.50488
\(713\) −8.32560 −0.311796
\(714\) 16.6583 0.623420
\(715\) 0.282781 0.0105754
\(716\) −63.7999 −2.38431
\(717\) 10.7031 0.399713
\(718\) −64.7743 −2.41735
\(719\) −1.94794 −0.0726461 −0.0363230 0.999340i \(-0.511565\pi\)
−0.0363230 + 0.999340i \(0.511565\pi\)
\(720\) 1.75647 0.0654598
\(721\) 20.0535 0.746831
\(722\) −41.5143 −1.54500
\(723\) −5.73983 −0.213466
\(724\) −27.0591 −1.00564
\(725\) 20.0466 0.744513
\(726\) −11.2489 −0.417487
\(727\) 0.410968 0.0152420 0.00762098 0.999971i \(-0.497574\pi\)
0.00762098 + 0.999971i \(0.497574\pi\)
\(728\) −0.238377 −0.00883484
\(729\) 27.4576 1.01695
\(730\) −9.09595 −0.336656
\(731\) 36.3857 1.34577
\(732\) 21.6969 0.801939
\(733\) −23.5920 −0.871391 −0.435695 0.900094i \(-0.643498\pi\)
−0.435695 + 0.900094i \(0.643498\pi\)
\(734\) 3.36867 0.124340
\(735\) 5.41651 0.199791
\(736\) −102.498 −3.77811
\(737\) 39.1640 1.44263
\(738\) −0.130853 −0.00481676
\(739\) 33.1133 1.21809 0.609046 0.793135i \(-0.291553\pi\)
0.609046 + 0.793135i \(0.291553\pi\)
\(740\) −15.6011 −0.573506
\(741\) −0.310881 −0.0114205
\(742\) −5.41135 −0.198657
\(743\) 43.8621 1.60915 0.804573 0.593854i \(-0.202394\pi\)
0.804573 + 0.593854i \(0.202394\pi\)
\(744\) −13.3226 −0.488432
\(745\) −52.4781 −1.92265
\(746\) 74.3178 2.72097
\(747\) 0.772938 0.0282803
\(748\) −53.1242 −1.94241
\(749\) 5.23674 0.191346
\(750\) 0.650262 0.0237442
\(751\) −37.0041 −1.35030 −0.675149 0.737681i \(-0.735921\pi\)
−0.675149 + 0.737681i \(0.735921\pi\)
\(752\) 52.7667 1.92420
\(753\) 16.7597 0.610758
\(754\) 0.327537 0.0119282
\(755\) 28.6594 1.04302
\(756\) −25.9145 −0.942501
\(757\) −9.15847 −0.332870 −0.166435 0.986052i \(-0.553226\pi\)
−0.166435 + 0.986052i \(0.553226\pi\)
\(758\) −54.2865 −1.97178
\(759\) −41.7045 −1.51378
\(760\) −144.340 −5.23575
\(761\) −19.0128 −0.689214 −0.344607 0.938747i \(-0.611988\pi\)
−0.344607 + 0.938747i \(0.611988\pi\)
\(762\) −11.7210 −0.424608
\(763\) −6.44359 −0.233274
\(764\) 127.640 4.61785
\(765\) −0.612376 −0.0221405
\(766\) −59.6203 −2.15417
\(767\) 0.00649715 0.000234599 0
\(768\) 15.2907 0.551757
\(769\) 27.3612 0.986670 0.493335 0.869839i \(-0.335778\pi\)
0.493335 + 0.869839i \(0.335778\pi\)
\(770\) −24.2602 −0.874276
\(771\) −3.02327 −0.108880
\(772\) −64.7439 −2.33019
\(773\) −29.3331 −1.05504 −0.527519 0.849543i \(-0.676878\pi\)
−0.527519 + 0.849543i \(0.676878\pi\)
\(774\) −1.37274 −0.0493423
\(775\) −4.95444 −0.177969
\(776\) 62.7137 2.25129
\(777\) 1.71677 0.0615886
\(778\) −11.9276 −0.427627
\(779\) 5.55305 0.198959
\(780\) −0.822717 −0.0294580
\(781\) 37.8399 1.35402
\(782\) 80.7856 2.88889
\(783\) 21.2052 0.757814
\(784\) 10.5612 0.377185
\(785\) −53.9156 −1.92433
\(786\) 3.17523 0.113257
\(787\) −18.4009 −0.655922 −0.327961 0.944691i \(-0.606361\pi\)
−0.327961 + 0.944691i \(0.606361\pi\)
\(788\) −114.925 −4.09405
\(789\) 43.8582 1.56139
\(790\) 45.0721 1.60359
\(791\) 10.9113 0.387962
\(792\) 1.19359 0.0424125
\(793\) 0.0785101 0.00278797
\(794\) 35.4726 1.25888
\(795\) −11.1223 −0.394469
\(796\) 15.7827 0.559403
\(797\) 8.85858 0.313787 0.156893 0.987616i \(-0.449852\pi\)
0.156893 + 0.987616i \(0.449852\pi\)
\(798\) 26.6709 0.944139
\(799\) −18.3966 −0.650825
\(800\) −60.9948 −2.15649
\(801\) −0.454012 −0.0160417
\(802\) −18.1996 −0.642652
\(803\) −3.19203 −0.112644
\(804\) −113.943 −4.01846
\(805\) 26.2678 0.925819
\(806\) −0.0809495 −0.00285132
\(807\) −37.8095 −1.33096
\(808\) −126.833 −4.46195
\(809\) 3.73318 0.131252 0.0656259 0.997844i \(-0.479096\pi\)
0.0656259 + 0.997844i \(0.479096\pi\)
\(810\) −73.4927 −2.58227
\(811\) 14.7047 0.516352 0.258176 0.966098i \(-0.416878\pi\)
0.258176 + 0.966098i \(0.416878\pi\)
\(812\) −20.0075 −0.702124
\(813\) 4.20095 0.147334
\(814\) −7.68927 −0.269509
\(815\) −23.6408 −0.828100
\(816\) 66.7595 2.33705
\(817\) 58.2557 2.03811
\(818\) 9.40101 0.328699
\(819\) −0.00161922 −5.65800e−5 0
\(820\) 14.6956 0.513193
\(821\) 30.9000 1.07842 0.539208 0.842173i \(-0.318724\pi\)
0.539208 + 0.842173i \(0.318724\pi\)
\(822\) 9.72239 0.339107
\(823\) −0.903887 −0.0315075 −0.0157538 0.999876i \(-0.505015\pi\)
−0.0157538 + 0.999876i \(0.505015\pi\)
\(824\) 155.621 5.42133
\(825\) −24.8178 −0.864044
\(826\) −0.557400 −0.0193944
\(827\) 26.8039 0.932062 0.466031 0.884768i \(-0.345684\pi\)
0.466031 + 0.884768i \(0.345684\pi\)
\(828\) −2.17011 −0.0754165
\(829\) 29.8044 1.03515 0.517574 0.855638i \(-0.326835\pi\)
0.517574 + 0.855638i \(0.326835\pi\)
\(830\) −121.916 −4.23178
\(831\) −46.0583 −1.59775
\(832\) −0.347755 −0.0120562
\(833\) −3.68205 −0.127576
\(834\) −88.0701 −3.04962
\(835\) 75.0714 2.59795
\(836\) −85.0550 −2.94169
\(837\) −5.24080 −0.181148
\(838\) −1.40893 −0.0486706
\(839\) −25.2381 −0.871317 −0.435659 0.900112i \(-0.643484\pi\)
−0.435659 + 0.900112i \(0.643484\pi\)
\(840\) 42.0338 1.45031
\(841\) −12.6284 −0.435461
\(842\) 78.5347 2.70648
\(843\) 38.5171 1.32660
\(844\) 54.3262 1.86999
\(845\) 41.0129 1.41089
\(846\) 0.694060 0.0238623
\(847\) 2.48640 0.0854338
\(848\) −21.6865 −0.744716
\(849\) 43.6556 1.49826
\(850\) 48.0744 1.64894
\(851\) 8.32560 0.285398
\(852\) −110.091 −3.77164
\(853\) 56.0810 1.92018 0.960089 0.279694i \(-0.0902331\pi\)
0.960089 + 0.279694i \(0.0902331\pi\)
\(854\) −6.73549 −0.230484
\(855\) −0.980451 −0.0335307
\(856\) 40.6388 1.38900
\(857\) −3.81599 −0.130352 −0.0651759 0.997874i \(-0.520761\pi\)
−0.0651759 + 0.997874i \(0.520761\pi\)
\(858\) −0.405491 −0.0138432
\(859\) 26.6296 0.908590 0.454295 0.890851i \(-0.349891\pi\)
0.454295 + 0.890851i \(0.349891\pi\)
\(860\) 154.168 5.25709
\(861\) −1.61713 −0.0551117
\(862\) 5.45403 0.185765
\(863\) 13.7822 0.469152 0.234576 0.972098i \(-0.424630\pi\)
0.234576 + 0.972098i \(0.424630\pi\)
\(864\) −64.5201 −2.19502
\(865\) −4.58615 −0.155934
\(866\) −59.1391 −2.00963
\(867\) 5.90996 0.200713
\(868\) 4.94476 0.167836
\(869\) 15.8171 0.536558
\(870\) −57.7557 −1.95810
\(871\) −0.412302 −0.0139703
\(872\) −50.0043 −1.69336
\(873\) 0.425993 0.0144177
\(874\) 129.343 4.37508
\(875\) −0.143730 −0.00485897
\(876\) 9.28684 0.313773
\(877\) 22.7788 0.769184 0.384592 0.923087i \(-0.374342\pi\)
0.384592 + 0.923087i \(0.374342\pi\)
\(878\) −48.4686 −1.63574
\(879\) −12.7695 −0.430703
\(880\) −97.2248 −3.27745
\(881\) 22.0245 0.742024 0.371012 0.928628i \(-0.379011\pi\)
0.371012 + 0.928628i \(0.379011\pi\)
\(882\) 0.138915 0.00467751
\(883\) 20.6836 0.696057 0.348029 0.937484i \(-0.386851\pi\)
0.348029 + 0.937484i \(0.386851\pi\)
\(884\) 0.559269 0.0188102
\(885\) −1.14567 −0.0385111
\(886\) 50.8388 1.70796
\(887\) 32.4413 1.08927 0.544636 0.838673i \(-0.316668\pi\)
0.544636 + 0.838673i \(0.316668\pi\)
\(888\) 13.3226 0.447079
\(889\) 2.59075 0.0868910
\(890\) 71.6119 2.40043
\(891\) −25.7907 −0.864022
\(892\) 18.2926 0.612480
\(893\) −29.4541 −0.985643
\(894\) 75.2505 2.51675
\(895\) 40.7083 1.36073
\(896\) 5.21213 0.174125
\(897\) 0.439048 0.0146594
\(898\) 16.4958 0.550473
\(899\) −4.04619 −0.134948
\(900\) −1.29140 −0.0430467
\(901\) 7.56078 0.251886
\(902\) 7.24301 0.241166
\(903\) −16.9649 −0.564557
\(904\) 84.6753 2.81626
\(905\) 17.2654 0.573920
\(906\) −41.0959 −1.36532
\(907\) 37.0471 1.23013 0.615065 0.788476i \(-0.289130\pi\)
0.615065 + 0.788476i \(0.289130\pi\)
\(908\) −0.768339 −0.0254982
\(909\) −0.861532 −0.0285752
\(910\) 0.255401 0.00846646
\(911\) 10.1122 0.335033 0.167517 0.985869i \(-0.446425\pi\)
0.167517 + 0.985869i \(0.446425\pi\)
\(912\) 106.886 3.53935
\(913\) −42.7840 −1.41594
\(914\) −31.3187 −1.03593
\(915\) −13.8439 −0.457667
\(916\) 141.237 4.66659
\(917\) −0.701835 −0.0231766
\(918\) 50.8529 1.67840
\(919\) 14.4004 0.475027 0.237513 0.971384i \(-0.423668\pi\)
0.237513 + 0.971384i \(0.423668\pi\)
\(920\) 203.847 6.72062
\(921\) 47.5401 1.56650
\(922\) 26.3056 0.866328
\(923\) −0.398363 −0.0131123
\(924\) 24.7693 0.814850
\(925\) 4.95444 0.162901
\(926\) 52.0566 1.71068
\(927\) 1.05709 0.0347192
\(928\) −49.8132 −1.63520
\(929\) 2.76064 0.0905737 0.0452869 0.998974i \(-0.485580\pi\)
0.0452869 + 0.998974i \(0.485580\pi\)
\(930\) 14.2741 0.468066
\(931\) −5.89519 −0.193207
\(932\) −13.5007 −0.442229
\(933\) −12.6773 −0.415038
\(934\) −3.24524 −0.106187
\(935\) 33.8965 1.10853
\(936\) −0.0125656 −0.000410721 0
\(937\) 50.1341 1.63781 0.818905 0.573929i \(-0.194581\pi\)
0.818905 + 0.573929i \(0.194581\pi\)
\(938\) 35.3720 1.15494
\(939\) 43.9509 1.43428
\(940\) −77.9475 −2.54237
\(941\) 10.5373 0.343506 0.171753 0.985140i \(-0.445057\pi\)
0.171753 + 0.985140i \(0.445057\pi\)
\(942\) 77.3118 2.51895
\(943\) −7.84241 −0.255384
\(944\) −2.23383 −0.0727049
\(945\) 16.5351 0.537885
\(946\) 75.9847 2.47047
\(947\) 3.20529 0.104158 0.0520790 0.998643i \(-0.483415\pi\)
0.0520790 + 0.998643i \(0.483415\pi\)
\(948\) −46.0179 −1.49459
\(949\) 0.0336044 0.00109084
\(950\) 76.9699 2.49723
\(951\) 35.8596 1.16283
\(952\) −28.5739 −0.926085
\(953\) 34.9760 1.13298 0.566492 0.824067i \(-0.308300\pi\)
0.566492 + 0.824067i \(0.308300\pi\)
\(954\) −0.285250 −0.00923531
\(955\) −81.4421 −2.63541
\(956\) −30.8278 −0.997041
\(957\) −20.2681 −0.655176
\(958\) 61.8930 1.99967
\(959\) −2.14898 −0.0693943
\(960\) 61.3209 1.97912
\(961\) 1.00000 0.0322581
\(962\) 0.0809495 0.00260992
\(963\) 0.276046 0.00889545
\(964\) 16.5323 0.532469
\(965\) 41.3107 1.32984
\(966\) −37.6665 −1.21190
\(967\) −6.39790 −0.205743 −0.102871 0.994695i \(-0.532803\pi\)
−0.102871 + 0.994695i \(0.532803\pi\)
\(968\) 19.2953 0.620173
\(969\) −37.2648 −1.19712
\(970\) −67.1924 −2.15742
\(971\) −57.8957 −1.85796 −0.928980 0.370130i \(-0.879313\pi\)
−0.928980 + 0.370130i \(0.879313\pi\)
\(972\) −2.70849 −0.0868748
\(973\) 19.4665 0.624068
\(974\) −40.5690 −1.29992
\(975\) 0.261271 0.00836737
\(976\) −26.9931 −0.864027
\(977\) 58.5842 1.87428 0.937138 0.348959i \(-0.113465\pi\)
0.937138 + 0.348959i \(0.113465\pi\)
\(978\) 33.8995 1.08399
\(979\) 25.1307 0.803180
\(980\) −15.6011 −0.498358
\(981\) −0.339663 −0.0108446
\(982\) 78.7660 2.51352
\(983\) 2.21812 0.0707469 0.0353735 0.999374i \(-0.488738\pi\)
0.0353735 + 0.999374i \(0.488738\pi\)
\(984\) −12.5494 −0.400062
\(985\) 73.3295 2.33647
\(986\) 39.2613 1.25033
\(987\) 8.57747 0.273024
\(988\) 0.895423 0.0284872
\(989\) −82.2728 −2.61612
\(990\) −1.27883 −0.0406440
\(991\) −25.6608 −0.815141 −0.407571 0.913174i \(-0.633624\pi\)
−0.407571 + 0.913174i \(0.633624\pi\)
\(992\) 12.3111 0.390879
\(993\) 41.8576 1.32831
\(994\) 34.1761 1.08400
\(995\) −10.0703 −0.319251
\(996\) 124.475 3.94413
\(997\) 14.0269 0.444235 0.222118 0.975020i \(-0.428703\pi\)
0.222118 + 0.975020i \(0.428703\pi\)
\(998\) −78.9497 −2.49911
\(999\) 5.24080 0.165811
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 8029.2.a.h.1.4 71
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8029.2.a.h.1.4 71 1.1 even 1 trivial