Properties

Label 10.32.a.b.1.2
Level $10$
Weight $32$
Character 10.1
Self dual yes
Analytic conductor $60.877$
Analytic rank $0$
Dimension $2$
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] = [10,32,Mod(1,10)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(10, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 32, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("10.1");
 
S:= CuspForms(chi, 32);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 32 \)
Character orbit: \([\chi]\) \(=\) 10.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: \(60.8771328190\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{337159}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 337159 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3\cdot 5 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(580.654\) of defining polynomial
Character \(\chi\) \(=\) 10.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-32768.0 q^{2} +1.82748e7 q^{3} +1.07374e9 q^{4} -3.05176e10 q^{5} -5.98827e11 q^{6} -9.80486e12 q^{7} -3.51844e13 q^{8} -2.83707e14 q^{9} +1.00000e15 q^{10} -2.50417e16 q^{11} +1.96224e16 q^{12} -5.10202e16 q^{13} +3.21285e17 q^{14} -5.57701e17 q^{15} +1.15292e18 q^{16} +5.39972e17 q^{17} +9.29650e18 q^{18} +8.95940e19 q^{19} -3.27680e19 q^{20} -1.79181e20 q^{21} +8.20567e20 q^{22} +3.91328e20 q^{23} -6.42986e20 q^{24} +9.31323e20 q^{25} +1.67183e21 q^{26} -1.64725e22 q^{27} -1.05279e22 q^{28} +7.65729e22 q^{29} +1.82748e22 q^{30} -1.67730e23 q^{31} -3.77789e22 q^{32} -4.57632e23 q^{33} -1.76938e22 q^{34} +2.99220e23 q^{35} -3.04628e23 q^{36} -2.35029e24 q^{37} -2.93582e24 q^{38} -9.32383e23 q^{39} +1.07374e24 q^{40} +4.23536e24 q^{41} +5.87142e24 q^{42} +2.21121e25 q^{43} -2.68884e25 q^{44} +8.65804e24 q^{45} -1.28230e25 q^{46} +9.02140e25 q^{47} +2.10694e25 q^{48} -6.16402e25 q^{49} -3.05176e25 q^{50} +9.86786e24 q^{51} -5.47826e25 q^{52} +8.66817e25 q^{53} +5.39771e26 q^{54} +7.64213e26 q^{55} +3.44978e26 q^{56} +1.63731e27 q^{57} -2.50914e27 q^{58} +3.37162e27 q^{59} -5.98827e26 q^{60} -3.72439e27 q^{61} +5.49619e27 q^{62} +2.78170e27 q^{63} +1.23794e27 q^{64} +1.55701e27 q^{65} +1.49957e28 q^{66} -1.08156e28 q^{67} +5.79791e26 q^{68} +7.15142e27 q^{69} -9.80486e27 q^{70} +3.01084e28 q^{71} +9.98204e27 q^{72} +1.41961e29 q^{73} +7.70144e28 q^{74} +1.70197e28 q^{75} +9.62009e28 q^{76} +2.45531e29 q^{77} +3.05523e28 q^{78} +4.24928e29 q^{79} -3.51844e28 q^{80} -1.25793e29 q^{81} -1.38784e29 q^{82} -2.61223e29 q^{83} -1.92395e29 q^{84} -1.64786e28 q^{85} -7.24570e29 q^{86} +1.39935e30 q^{87} +8.81077e29 q^{88} -1.92566e30 q^{89} -2.83707e29 q^{90} +5.00246e29 q^{91} +4.20185e29 q^{92} -3.06523e30 q^{93} -2.95613e30 q^{94} -2.73419e30 q^{95} -6.90401e29 q^{96} -1.19769e30 q^{97} +2.01983e30 q^{98} +7.10450e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 65536 q^{2} + 29024244 q^{3} + 2147483648 q^{4} - 61035156250 q^{5} - 951066427392 q^{6} + 12795158105212 q^{7} - 70368744177664 q^{8} - 785828540134926 q^{9} + 20\!\cdots\!00 q^{10} - 500906012122176 q^{11}+ \cdots - 52\!\cdots\!12 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −32768.0 −0.707107
\(3\) 1.82748e7 0.735313 0.367656 0.929962i \(-0.380160\pi\)
0.367656 + 0.929962i \(0.380160\pi\)
\(4\) 1.07374e9 0.500000
\(5\) −3.05176e10 −0.447214
\(6\) −5.98827e11 −0.519945
\(7\) −9.80486e12 −0.780587 −0.390294 0.920690i \(-0.627627\pi\)
−0.390294 + 0.920690i \(0.627627\pi\)
\(8\) −3.51844e13 −0.353553
\(9\) −2.83707e14 −0.459315
\(10\) 1.00000e15 0.316228
\(11\) −2.50417e16 −1.80750 −0.903749 0.428063i \(-0.859196\pi\)
−0.903749 + 0.428063i \(0.859196\pi\)
\(12\) 1.96224e16 0.367656
\(13\) −5.10202e16 −0.276453 −0.138226 0.990401i \(-0.544140\pi\)
−0.138226 + 0.990401i \(0.544140\pi\)
\(14\) 3.21285e17 0.551959
\(15\) −5.57701e17 −0.328842
\(16\) 1.15292e18 0.250000
\(17\) 5.39972e17 0.0457523 0.0228762 0.999738i \(-0.492718\pi\)
0.0228762 + 0.999738i \(0.492718\pi\)
\(18\) 9.29650e18 0.324785
\(19\) 8.95940e19 1.35394 0.676968 0.736012i \(-0.263293\pi\)
0.676968 + 0.736012i \(0.263293\pi\)
\(20\) −3.27680e19 −0.223607
\(21\) −1.79181e20 −0.573976
\(22\) 8.20567e20 1.27809
\(23\) 3.91328e20 0.306026 0.153013 0.988224i \(-0.451102\pi\)
0.153013 + 0.988224i \(0.451102\pi\)
\(24\) −6.42986e20 −0.259972
\(25\) 9.31323e20 0.200000
\(26\) 1.67183e21 0.195481
\(27\) −1.64725e22 −1.07305
\(28\) −1.05279e22 −0.390294
\(29\) 7.65729e22 1.64781 0.823903 0.566731i \(-0.191792\pi\)
0.823903 + 0.566731i \(0.191792\pi\)
\(30\) 1.82748e22 0.232526
\(31\) −1.67730e23 −1.28382 −0.641912 0.766778i \(-0.721858\pi\)
−0.641912 + 0.766778i \(0.721858\pi\)
\(32\) −3.77789e22 −0.176777
\(33\) −4.57632e23 −1.32908
\(34\) −1.76938e22 −0.0323518
\(35\) 2.99220e23 0.349089
\(36\) −3.04628e23 −0.229657
\(37\) −2.35029e24 −1.15876 −0.579382 0.815056i \(-0.696706\pi\)
−0.579382 + 0.815056i \(0.696706\pi\)
\(38\) −2.93582e24 −0.957378
\(39\) −9.32383e23 −0.203279
\(40\) 1.07374e24 0.158114
\(41\) 4.23536e24 0.425344 0.212672 0.977124i \(-0.431783\pi\)
0.212672 + 0.977124i \(0.431783\pi\)
\(42\) 5.87142e24 0.405862
\(43\) 2.21121e25 1.06138 0.530688 0.847567i \(-0.321934\pi\)
0.530688 + 0.847567i \(0.321934\pi\)
\(44\) −2.68884e25 −0.903749
\(45\) 8.65804e24 0.205412
\(46\) −1.28230e25 −0.216393
\(47\) 9.02140e25 1.09083 0.545415 0.838166i \(-0.316372\pi\)
0.545415 + 0.838166i \(0.316372\pi\)
\(48\) 2.10694e25 0.183828
\(49\) −6.16402e25 −0.390683
\(50\) −3.05176e25 −0.141421
\(51\) 9.86786e24 0.0336423
\(52\) −5.47826e25 −0.138226
\(53\) 8.66817e25 0.162799 0.0813994 0.996682i \(-0.474061\pi\)
0.0813994 + 0.996682i \(0.474061\pi\)
\(54\) 5.39771e26 0.758763
\(55\) 7.64213e26 0.808337
\(56\) 3.44978e26 0.275979
\(57\) 1.63731e27 0.995567
\(58\) −2.50914e27 −1.16517
\(59\) 3.37162e27 1.20125 0.600624 0.799532i \(-0.294919\pi\)
0.600624 + 0.799532i \(0.294919\pi\)
\(60\) −5.98827e26 −0.164421
\(61\) −3.72439e27 −0.791485 −0.395742 0.918362i \(-0.629513\pi\)
−0.395742 + 0.918362i \(0.629513\pi\)
\(62\) 5.49619e27 0.907800
\(63\) 2.78170e27 0.358535
\(64\) 1.23794e27 0.125000
\(65\) 1.55701e27 0.123633
\(66\) 1.49957e28 0.939799
\(67\) −1.08156e28 −0.536900 −0.268450 0.963294i \(-0.586511\pi\)
−0.268450 + 0.963294i \(0.586511\pi\)
\(68\) 5.79791e26 0.0228762
\(69\) 7.15142e27 0.225025
\(70\) −9.80486e27 −0.246843
\(71\) 3.01084e28 0.608393 0.304196 0.952609i \(-0.401612\pi\)
0.304196 + 0.952609i \(0.401612\pi\)
\(72\) 9.98204e27 0.162392
\(73\) 1.41961e29 1.86494 0.932471 0.361246i \(-0.117648\pi\)
0.932471 + 0.361246i \(0.117648\pi\)
\(74\) 7.70144e28 0.819370
\(75\) 1.70197e28 0.147063
\(76\) 9.62009e28 0.676968
\(77\) 2.45531e29 1.41091
\(78\) 3.05523e28 0.143740
\(79\) 4.24928e29 1.64095 0.820475 0.571682i \(-0.193709\pi\)
0.820475 + 0.571682i \(0.193709\pi\)
\(80\) −3.51844e28 −0.111803
\(81\) −1.25793e29 −0.329715
\(82\) −1.38784e29 −0.300764
\(83\) −2.61223e29 −0.469138 −0.234569 0.972099i \(-0.575368\pi\)
−0.234569 + 0.972099i \(0.575368\pi\)
\(84\) −1.92395e29 −0.286988
\(85\) −1.64786e28 −0.0204611
\(86\) −7.24570e29 −0.750506
\(87\) 1.39935e30 1.21165
\(88\) 8.81077e29 0.639047
\(89\) −1.92566e30 −1.17229 −0.586144 0.810207i \(-0.699355\pi\)
−0.586144 + 0.810207i \(0.699355\pi\)
\(90\) −2.83707e29 −0.145248
\(91\) 5.00246e29 0.215795
\(92\) 4.20185e29 0.153013
\(93\) −3.06523e30 −0.944012
\(94\) −2.95613e30 −0.771333
\(95\) −2.73419e30 −0.605499
\(96\) −6.90401e29 −0.129986
\(97\) −1.19769e30 −0.192035 −0.0960177 0.995380i \(-0.530611\pi\)
−0.0960177 + 0.995380i \(0.530611\pi\)
\(98\) 2.01983e30 0.276255
\(99\) 7.10450e30 0.830210
\(100\) 1.00000e30 0.100000
\(101\) −1.82554e30 −0.156462 −0.0782311 0.996935i \(-0.524927\pi\)
−0.0782311 + 0.996935i \(0.524927\pi\)
\(102\) −3.23350e29 −0.0237887
\(103\) −3.09796e31 −1.95929 −0.979644 0.200744i \(-0.935664\pi\)
−0.979644 + 0.200744i \(0.935664\pi\)
\(104\) 1.79512e30 0.0977407
\(105\) 5.46818e30 0.256690
\(106\) −2.84038e30 −0.115116
\(107\) −7.75249e30 −0.271639 −0.135820 0.990734i \(-0.543367\pi\)
−0.135820 + 0.990734i \(0.543367\pi\)
\(108\) −1.76872e31 −0.536527
\(109\) 2.74905e31 0.722890 0.361445 0.932393i \(-0.382284\pi\)
0.361445 + 0.932393i \(0.382284\pi\)
\(110\) −2.50417e31 −0.571581
\(111\) −4.29510e31 −0.852055
\(112\) −1.13042e31 −0.195147
\(113\) 3.04360e31 0.457796 0.228898 0.973450i \(-0.426488\pi\)
0.228898 + 0.973450i \(0.426488\pi\)
\(114\) −5.36514e31 −0.703972
\(115\) −1.19424e31 −0.136859
\(116\) 8.22195e31 0.823903
\(117\) 1.44748e31 0.126979
\(118\) −1.10481e32 −0.849410
\(119\) −5.29435e30 −0.0357137
\(120\) 1.96224e31 0.116263
\(121\) 4.35145e32 2.26705
\(122\) 1.22041e32 0.559664
\(123\) 7.74002e31 0.312761
\(124\) −1.80099e32 −0.641912
\(125\) −2.84217e31 −0.0894427
\(126\) −9.11508e31 −0.253523
\(127\) 5.99688e32 1.47560 0.737798 0.675021i \(-0.235865\pi\)
0.737798 + 0.675021i \(0.235865\pi\)
\(128\) −4.05648e31 −0.0883883
\(129\) 4.04094e32 0.780444
\(130\) −5.10202e31 −0.0874220
\(131\) 8.06361e32 1.22694 0.613471 0.789717i \(-0.289773\pi\)
0.613471 + 0.789717i \(0.289773\pi\)
\(132\) −4.91378e32 −0.664538
\(133\) −8.78457e32 −1.05687
\(134\) 3.54407e32 0.379645
\(135\) 5.02701e32 0.479884
\(136\) −1.89986e31 −0.0161759
\(137\) 1.25859e33 0.956566 0.478283 0.878206i \(-0.341259\pi\)
0.478283 + 0.878206i \(0.341259\pi\)
\(138\) −2.34338e32 −0.159117
\(139\) −1.28760e33 −0.781721 −0.390861 0.920450i \(-0.627823\pi\)
−0.390861 + 0.920450i \(0.627823\pi\)
\(140\) 3.21285e32 0.174545
\(141\) 1.64864e33 0.802102
\(142\) −9.86593e32 −0.430198
\(143\) 1.27764e33 0.499687
\(144\) −3.27091e32 −0.114829
\(145\) −2.33682e33 −0.736921
\(146\) −4.65178e33 −1.31871
\(147\) −1.12646e33 −0.287274
\(148\) −2.52361e33 −0.579382
\(149\) −4.23721e31 −0.00876380 −0.00438190 0.999990i \(-0.501395\pi\)
−0.00438190 + 0.999990i \(0.501395\pi\)
\(150\) −5.57701e32 −0.103989
\(151\) −7.07794e33 −1.19060 −0.595298 0.803505i \(-0.702966\pi\)
−0.595298 + 0.803505i \(0.702966\pi\)
\(152\) −3.15231e33 −0.478689
\(153\) −1.53194e32 −0.0210147
\(154\) −8.04554e33 −0.997664
\(155\) 5.11872e33 0.574143
\(156\) −1.00114e33 −0.101640
\(157\) 1.32372e34 1.21717 0.608583 0.793490i \(-0.291738\pi\)
0.608583 + 0.793490i \(0.291738\pi\)
\(158\) −1.39240e34 −1.16033
\(159\) 1.58409e33 0.119708
\(160\) 1.15292e33 0.0790569
\(161\) −3.83691e33 −0.238880
\(162\) 4.12199e33 0.233144
\(163\) 1.78685e34 0.918715 0.459358 0.888251i \(-0.348080\pi\)
0.459358 + 0.888251i \(0.348080\pi\)
\(164\) 4.54768e33 0.212672
\(165\) 1.39658e34 0.594381
\(166\) 8.55975e33 0.331731
\(167\) 1.88144e34 0.664331 0.332165 0.943221i \(-0.392221\pi\)
0.332165 + 0.943221i \(0.392221\pi\)
\(168\) 6.30438e33 0.202931
\(169\) −3.14569e34 −0.923574
\(170\) 5.39972e32 0.0144682
\(171\) −2.54184e34 −0.621883
\(172\) 2.37427e34 0.530688
\(173\) 3.38111e34 0.690789 0.345394 0.938458i \(-0.387745\pi\)
0.345394 + 0.938458i \(0.387745\pi\)
\(174\) −4.58539e34 −0.856768
\(175\) −9.13148e33 −0.156117
\(176\) −2.88711e34 −0.451874
\(177\) 6.16155e34 0.883293
\(178\) 6.31000e34 0.828932
\(179\) −2.41562e34 −0.290942 −0.145471 0.989362i \(-0.546470\pi\)
−0.145471 + 0.989362i \(0.546470\pi\)
\(180\) 9.29650e33 0.102706
\(181\) 3.12629e34 0.316965 0.158482 0.987362i \(-0.449340\pi\)
0.158482 + 0.987362i \(0.449340\pi\)
\(182\) −1.63921e34 −0.152590
\(183\) −6.80623e34 −0.581989
\(184\) −1.37686e34 −0.108197
\(185\) 7.17253e34 0.518215
\(186\) 1.00442e35 0.667517
\(187\) −1.35218e34 −0.0826972
\(188\) 9.68666e34 0.545415
\(189\) 1.61510e35 0.837612
\(190\) 8.95940e34 0.428152
\(191\) −5.87939e33 −0.0259009 −0.0129504 0.999916i \(-0.504122\pi\)
−0.0129504 + 0.999916i \(0.504122\pi\)
\(192\) 2.26231e34 0.0919141
\(193\) −2.74156e35 −1.02768 −0.513841 0.857885i \(-0.671778\pi\)
−0.513841 + 0.857885i \(0.671778\pi\)
\(194\) 3.92458e34 0.135790
\(195\) 2.84541e34 0.0909092
\(196\) −6.61857e34 −0.195342
\(197\) 2.83335e35 0.772812 0.386406 0.922329i \(-0.373716\pi\)
0.386406 + 0.922329i \(0.373716\pi\)
\(198\) −2.32800e35 −0.587047
\(199\) −5.63487e35 −1.31420 −0.657100 0.753803i \(-0.728217\pi\)
−0.657100 + 0.753803i \(0.728217\pi\)
\(200\) −3.27680e34 −0.0707107
\(201\) −1.97653e35 −0.394789
\(202\) 5.98192e34 0.110636
\(203\) −7.50786e35 −1.28626
\(204\) 1.05955e34 0.0168211
\(205\) −1.29253e35 −0.190220
\(206\) 1.01514e36 1.38543
\(207\) −1.11022e35 −0.140562
\(208\) −5.88223e34 −0.0691131
\(209\) −2.24359e36 −2.44724
\(210\) −1.79181e35 −0.181507
\(211\) −1.37274e36 −1.29184 −0.645920 0.763405i \(-0.723526\pi\)
−0.645920 + 0.763405i \(0.723526\pi\)
\(212\) 9.30737e34 0.0813994
\(213\) 5.50225e35 0.447359
\(214\) 2.54034e35 0.192078
\(215\) −6.74809e35 −0.474662
\(216\) 5.79575e35 0.379382
\(217\) 1.64457e36 1.00214
\(218\) −9.00809e35 −0.511160
\(219\) 2.59431e36 1.37132
\(220\) 8.20567e35 0.404169
\(221\) −2.75495e34 −0.0126483
\(222\) 1.40742e36 0.602494
\(223\) 5.24242e34 0.0209318 0.0104659 0.999945i \(-0.496669\pi\)
0.0104659 + 0.999945i \(0.496669\pi\)
\(224\) 3.70417e35 0.137990
\(225\) −2.64222e35 −0.0918630
\(226\) −9.97327e35 −0.323710
\(227\) −2.30435e36 −0.698471 −0.349235 0.937035i \(-0.613559\pi\)
−0.349235 + 0.937035i \(0.613559\pi\)
\(228\) 1.75805e36 0.497784
\(229\) 3.22039e36 0.852037 0.426019 0.904714i \(-0.359916\pi\)
0.426019 + 0.904714i \(0.359916\pi\)
\(230\) 3.91328e35 0.0967740
\(231\) 4.48701e36 1.03746
\(232\) −2.69417e36 −0.582587
\(233\) 3.35115e36 0.677917 0.338959 0.940801i \(-0.389925\pi\)
0.338959 + 0.940801i \(0.389925\pi\)
\(234\) −4.74310e35 −0.0897875
\(235\) −2.75311e36 −0.487834
\(236\) 3.62025e36 0.600624
\(237\) 7.76546e36 1.20661
\(238\) 1.73485e35 0.0252534
\(239\) 5.41220e36 0.738255 0.369127 0.929379i \(-0.379657\pi\)
0.369127 + 0.929379i \(0.379657\pi\)
\(240\) −6.42986e35 −0.0822105
\(241\) −3.64065e36 −0.436430 −0.218215 0.975901i \(-0.570023\pi\)
−0.218215 + 0.975901i \(0.570023\pi\)
\(242\) −1.42588e37 −1.60304
\(243\) 7.87579e36 0.830609
\(244\) −3.99903e36 −0.395742
\(245\) 1.88111e36 0.174719
\(246\) −2.53625e36 −0.221155
\(247\) −4.57111e36 −0.374299
\(248\) 5.90149e36 0.453900
\(249\) −4.77379e36 −0.344963
\(250\) 9.31323e35 0.0632456
\(251\) −6.60375e36 −0.421549 −0.210774 0.977535i \(-0.567599\pi\)
−0.210774 + 0.977535i \(0.567599\pi\)
\(252\) 2.98683e36 0.179268
\(253\) −9.79952e36 −0.553142
\(254\) −1.96506e37 −1.04340
\(255\) −3.01143e35 −0.0150453
\(256\) 1.32923e36 0.0625000
\(257\) −1.70943e37 −0.756638 −0.378319 0.925675i \(-0.623498\pi\)
−0.378319 + 0.925675i \(0.623498\pi\)
\(258\) −1.32413e37 −0.551857
\(259\) 2.30443e37 0.904517
\(260\) 1.67183e36 0.0618167
\(261\) −2.17242e37 −0.756862
\(262\) −2.64228e37 −0.867580
\(263\) 6.06914e37 1.87851 0.939254 0.343224i \(-0.111519\pi\)
0.939254 + 0.343224i \(0.111519\pi\)
\(264\) 1.61015e37 0.469899
\(265\) −2.64531e36 −0.0728058
\(266\) 2.87853e37 0.747317
\(267\) −3.51909e37 −0.861998
\(268\) −1.16132e37 −0.268450
\(269\) −4.69833e37 −1.02514 −0.512570 0.858646i \(-0.671306\pi\)
−0.512570 + 0.858646i \(0.671306\pi\)
\(270\) −1.64725e37 −0.339329
\(271\) −2.99460e37 −0.582526 −0.291263 0.956643i \(-0.594075\pi\)
−0.291263 + 0.956643i \(0.594075\pi\)
\(272\) 6.22546e35 0.0114381
\(273\) 9.14188e36 0.158677
\(274\) −4.12414e37 −0.676394
\(275\) −2.33219e37 −0.361499
\(276\) 7.67877e36 0.112513
\(277\) 7.82408e37 1.08392 0.541960 0.840404i \(-0.317682\pi\)
0.541960 + 0.840404i \(0.317682\pi\)
\(278\) 4.21921e37 0.552760
\(279\) 4.75862e37 0.589679
\(280\) −1.05279e37 −0.123422
\(281\) 1.79861e38 1.99522 0.997608 0.0691186i \(-0.0220187\pi\)
0.997608 + 0.0691186i \(0.0220187\pi\)
\(282\) −5.40226e37 −0.567172
\(283\) 1.02428e38 1.01796 0.508979 0.860779i \(-0.330023\pi\)
0.508979 + 0.860779i \(0.330023\pi\)
\(284\) 3.23287e37 0.304196
\(285\) −4.99667e37 −0.445231
\(286\) −4.18655e37 −0.353332
\(287\) −4.15271e37 −0.332018
\(288\) 1.07181e37 0.0811962
\(289\) −1.38997e38 −0.997907
\(290\) 7.65729e37 0.521082
\(291\) −2.18874e37 −0.141206
\(292\) 1.52430e38 0.932471
\(293\) −2.65665e38 −1.54129 −0.770647 0.637262i \(-0.780067\pi\)
−0.770647 + 0.637262i \(0.780067\pi\)
\(294\) 3.69118e37 0.203134
\(295\) −1.02894e38 −0.537214
\(296\) 8.26936e37 0.409685
\(297\) 4.12500e38 1.93954
\(298\) 1.38845e36 0.00619694
\(299\) −1.99656e37 −0.0846018
\(300\) 1.82748e37 0.0735313
\(301\) −2.16806e38 −0.828497
\(302\) 2.31930e38 0.841879
\(303\) −3.33613e37 −0.115049
\(304\) 1.03295e38 0.338484
\(305\) 1.13659e38 0.353963
\(306\) 5.01985e36 0.0148597
\(307\) −1.23731e38 −0.348204 −0.174102 0.984728i \(-0.555702\pi\)
−0.174102 + 0.984728i \(0.555702\pi\)
\(308\) 2.63636e38 0.705455
\(309\) −5.66144e38 −1.44069
\(310\) −1.67730e38 −0.405981
\(311\) 7.02325e38 1.61716 0.808579 0.588388i \(-0.200237\pi\)
0.808579 + 0.588388i \(0.200237\pi\)
\(312\) 3.28053e37 0.0718700
\(313\) 6.10426e38 1.27261 0.636306 0.771437i \(-0.280462\pi\)
0.636306 + 0.771437i \(0.280462\pi\)
\(314\) −4.33755e38 −0.860667
\(315\) −8.48908e37 −0.160342
\(316\) 4.56263e38 0.820475
\(317\) −5.90092e38 −1.01042 −0.505209 0.862997i \(-0.668585\pi\)
−0.505209 + 0.862997i \(0.668585\pi\)
\(318\) −5.19073e37 −0.0846464
\(319\) −1.91752e39 −2.97840
\(320\) −3.77789e37 −0.0559017
\(321\) −1.41675e38 −0.199740
\(322\) 1.25728e38 0.168914
\(323\) 4.83783e37 0.0619457
\(324\) −1.35069e38 −0.164858
\(325\) −4.75163e37 −0.0552905
\(326\) −5.85516e38 −0.649630
\(327\) 5.02383e38 0.531550
\(328\) −1.49018e38 −0.150382
\(329\) −8.84535e38 −0.851488
\(330\) −4.57632e38 −0.420291
\(331\) −1.26563e39 −1.10910 −0.554552 0.832149i \(-0.687110\pi\)
−0.554552 + 0.832149i \(0.687110\pi\)
\(332\) −2.80486e38 −0.234569
\(333\) 6.66794e38 0.532238
\(334\) −6.16509e38 −0.469753
\(335\) 3.30067e38 0.240109
\(336\) −2.06582e38 −0.143494
\(337\) −1.15260e39 −0.764565 −0.382283 0.924045i \(-0.624862\pi\)
−0.382283 + 0.924045i \(0.624862\pi\)
\(338\) 1.03078e39 0.653065
\(339\) 5.56211e38 0.336623
\(340\) −1.76938e37 −0.0102305
\(341\) 4.20026e39 2.32051
\(342\) 8.32911e38 0.439738
\(343\) 2.15134e39 1.08555
\(344\) −7.78001e38 −0.375253
\(345\) −2.18244e38 −0.100634
\(346\) −1.10792e39 −0.488461
\(347\) 3.25921e39 1.37406 0.687029 0.726630i \(-0.258914\pi\)
0.687029 + 0.726630i \(0.258914\pi\)
\(348\) 1.50254e39 0.605826
\(349\) 6.30486e37 0.0243154 0.0121577 0.999926i \(-0.496130\pi\)
0.0121577 + 0.999926i \(0.496130\pi\)
\(350\) 2.99220e38 0.110392
\(351\) 8.40431e38 0.296648
\(352\) 9.46050e38 0.319523
\(353\) 4.15083e39 1.34161 0.670807 0.741632i \(-0.265948\pi\)
0.670807 + 0.741632i \(0.265948\pi\)
\(354\) −2.01902e39 −0.624582
\(355\) −9.18837e38 −0.272081
\(356\) −2.06766e39 −0.586144
\(357\) −9.67530e37 −0.0262607
\(358\) 7.91551e38 0.205727
\(359\) −7.62845e39 −1.89877 −0.949385 0.314114i \(-0.898293\pi\)
−0.949385 + 0.314114i \(0.898293\pi\)
\(360\) −3.04628e38 −0.0726241
\(361\) 3.64823e39 0.833144
\(362\) −1.02442e39 −0.224128
\(363\) 7.95217e39 1.66699
\(364\) 5.37135e38 0.107898
\(365\) −4.33231e39 −0.834027
\(366\) 2.23027e39 0.411528
\(367\) −4.70956e38 −0.0833021 −0.0416510 0.999132i \(-0.513262\pi\)
−0.0416510 + 0.999132i \(0.513262\pi\)
\(368\) 4.51170e38 0.0765066
\(369\) −1.20160e39 −0.195367
\(370\) −2.35029e39 −0.366434
\(371\) −8.49901e38 −0.127079
\(372\) −3.29127e39 −0.472006
\(373\) 5.24767e38 0.0721904 0.0360952 0.999348i \(-0.488508\pi\)
0.0360952 + 0.999348i \(0.488508\pi\)
\(374\) 4.43084e38 0.0584757
\(375\) −5.19400e38 −0.0657684
\(376\) −3.17412e39 −0.385667
\(377\) −3.90677e39 −0.455540
\(378\) −5.29238e39 −0.592281
\(379\) −4.30594e39 −0.462551 −0.231276 0.972888i \(-0.574290\pi\)
−0.231276 + 0.972888i \(0.574290\pi\)
\(380\) −2.93582e39 −0.302749
\(381\) 1.09592e40 1.08503
\(382\) 1.92656e38 0.0183147
\(383\) 2.43638e39 0.222415 0.111208 0.993797i \(-0.464528\pi\)
0.111208 + 0.993797i \(0.464528\pi\)
\(384\) −7.41312e38 −0.0649931
\(385\) −7.49300e39 −0.630978
\(386\) 8.98354e39 0.726682
\(387\) −6.27336e39 −0.487506
\(388\) −1.28601e39 −0.0960177
\(389\) −1.05964e40 −0.760219 −0.380110 0.924941i \(-0.624114\pi\)
−0.380110 + 0.924941i \(0.624114\pi\)
\(390\) −9.32383e38 −0.0642825
\(391\) 2.11306e38 0.0140014
\(392\) 2.16877e39 0.138127
\(393\) 1.47361e40 0.902187
\(394\) −9.28432e39 −0.546461
\(395\) −1.29678e40 −0.733855
\(396\) 7.62840e39 0.415105
\(397\) −2.43442e40 −1.27392 −0.636962 0.770896i \(-0.719809\pi\)
−0.636962 + 0.770896i \(0.719809\pi\)
\(398\) 1.84644e40 0.929280
\(399\) −1.60536e40 −0.777127
\(400\) 1.07374e39 0.0500000
\(401\) −1.19933e40 −0.537279 −0.268639 0.963241i \(-0.586574\pi\)
−0.268639 + 0.963241i \(0.586574\pi\)
\(402\) 6.47670e39 0.279158
\(403\) 8.55764e39 0.354916
\(404\) −1.96016e39 −0.0782311
\(405\) 3.83890e39 0.147453
\(406\) 2.46018e40 0.909521
\(407\) 5.88554e40 2.09446
\(408\) −3.47195e38 −0.0118943
\(409\) −5.19301e40 −1.71281 −0.856403 0.516308i \(-0.827306\pi\)
−0.856403 + 0.516308i \(0.827306\pi\)
\(410\) 4.23536e39 0.134506
\(411\) 2.30004e40 0.703376
\(412\) −3.32640e40 −0.979644
\(413\) −3.30582e40 −0.937678
\(414\) 3.63797e39 0.0993927
\(415\) 7.97189e39 0.209805
\(416\) 1.92749e39 0.0488704
\(417\) −2.35306e40 −0.574810
\(418\) 7.35179e40 1.73046
\(419\) 5.00033e40 1.13418 0.567089 0.823656i \(-0.308069\pi\)
0.567089 + 0.823656i \(0.308069\pi\)
\(420\) 5.87142e39 0.128345
\(421\) −9.66156e39 −0.203552 −0.101776 0.994807i \(-0.532452\pi\)
−0.101776 + 0.994807i \(0.532452\pi\)
\(422\) 4.49818e40 0.913469
\(423\) −2.55943e40 −0.501035
\(424\) −3.04984e39 −0.0575581
\(425\) 5.02888e38 0.00915046
\(426\) −1.80298e40 −0.316331
\(427\) 3.65171e40 0.617823
\(428\) −8.32417e39 −0.135820
\(429\) 2.33485e40 0.367427
\(430\) 2.21121e40 0.335637
\(431\) −6.30614e40 −0.923350 −0.461675 0.887049i \(-0.652751\pi\)
−0.461675 + 0.887049i \(0.652751\pi\)
\(432\) −1.89915e40 −0.268263
\(433\) 1.25919e41 1.71605 0.858026 0.513606i \(-0.171691\pi\)
0.858026 + 0.513606i \(0.171691\pi\)
\(434\) −5.38893e40 −0.708618
\(435\) −4.27048e40 −0.541868
\(436\) 2.95177e40 0.361445
\(437\) 3.50606e40 0.414340
\(438\) −8.50102e40 −0.969667
\(439\) −8.26623e39 −0.0910138 −0.0455069 0.998964i \(-0.514490\pi\)
−0.0455069 + 0.998964i \(0.514490\pi\)
\(440\) −2.68884e40 −0.285790
\(441\) 1.74877e40 0.179447
\(442\) 9.02742e38 0.00894373
\(443\) 1.43030e41 1.36826 0.684132 0.729358i \(-0.260181\pi\)
0.684132 + 0.729358i \(0.260181\pi\)
\(444\) −4.61183e40 −0.426027
\(445\) 5.87664e40 0.524263
\(446\) −1.71784e39 −0.0148010
\(447\) −7.74339e38 −0.00644414
\(448\) −1.21378e40 −0.0975734
\(449\) −1.81047e41 −1.40596 −0.702980 0.711210i \(-0.748148\pi\)
−0.702980 + 0.711210i \(0.748148\pi\)
\(450\) 8.65804e39 0.0649569
\(451\) −1.06061e41 −0.768808
\(452\) 3.26804e40 0.228898
\(453\) −1.29348e41 −0.875461
\(454\) 7.55091e40 0.493893
\(455\) −1.52663e40 −0.0965066
\(456\) −5.76077e40 −0.351986
\(457\) 1.94398e41 1.14813 0.574064 0.818810i \(-0.305366\pi\)
0.574064 + 0.818810i \(0.305366\pi\)
\(458\) −1.05526e41 −0.602481
\(459\) −8.89469e39 −0.0490947
\(460\) −1.28230e40 −0.0684296
\(461\) −1.15427e41 −0.595582 −0.297791 0.954631i \(-0.596250\pi\)
−0.297791 + 0.954631i \(0.596250\pi\)
\(462\) −1.47030e41 −0.733595
\(463\) −1.83772e41 −0.886694 −0.443347 0.896350i \(-0.646209\pi\)
−0.443347 + 0.896350i \(0.646209\pi\)
\(464\) 8.82825e40 0.411951
\(465\) 9.35434e40 0.422175
\(466\) −1.09810e41 −0.479360
\(467\) −1.32162e41 −0.558078 −0.279039 0.960280i \(-0.590016\pi\)
−0.279039 + 0.960280i \(0.590016\pi\)
\(468\) 1.55422e40 0.0634894
\(469\) 1.06046e41 0.419097
\(470\) 9.02140e40 0.344951
\(471\) 2.41906e41 0.894998
\(472\) −1.18628e41 −0.424705
\(473\) −5.53726e41 −1.91844
\(474\) −2.54458e41 −0.853203
\(475\) 8.34410e40 0.270787
\(476\) −5.68476e39 −0.0178568
\(477\) −2.45922e40 −0.0747759
\(478\) −1.77347e41 −0.522025
\(479\) 6.48535e41 1.84813 0.924066 0.382233i \(-0.124845\pi\)
0.924066 + 0.382233i \(0.124845\pi\)
\(480\) 2.10694e40 0.0581316
\(481\) 1.19913e41 0.320343
\(482\) 1.19297e41 0.308603
\(483\) −7.01186e40 −0.175652
\(484\) 4.67233e41 1.13352
\(485\) 3.65505e40 0.0858809
\(486\) −2.58074e41 −0.587330
\(487\) 1.77648e41 0.391617 0.195808 0.980642i \(-0.437267\pi\)
0.195808 + 0.980642i \(0.437267\pi\)
\(488\) 1.31040e41 0.279832
\(489\) 3.26543e41 0.675543
\(490\) −6.16402e40 −0.123545
\(491\) 7.79527e41 1.51380 0.756900 0.653531i \(-0.226713\pi\)
0.756900 + 0.653531i \(0.226713\pi\)
\(492\) 8.31078e40 0.156381
\(493\) 4.13472e40 0.0753909
\(494\) 1.49786e41 0.264669
\(495\) −2.16812e41 −0.371281
\(496\) −1.93380e41 −0.320956
\(497\) −2.95209e41 −0.474904
\(498\) 1.56427e41 0.243926
\(499\) 8.45266e41 1.27772 0.638859 0.769324i \(-0.279407\pi\)
0.638859 + 0.769324i \(0.279407\pi\)
\(500\) −3.05176e40 −0.0447214
\(501\) 3.43828e41 0.488491
\(502\) 2.16392e41 0.298080
\(503\) −2.43928e41 −0.325805 −0.162903 0.986642i \(-0.552086\pi\)
−0.162903 + 0.986642i \(0.552086\pi\)
\(504\) −9.78724e40 −0.126761
\(505\) 5.57110e40 0.0699720
\(506\) 3.21111e41 0.391130
\(507\) −5.74867e41 −0.679116
\(508\) 6.43910e41 0.737798
\(509\) 9.04219e41 1.00496 0.502479 0.864589i \(-0.332421\pi\)
0.502479 + 0.864589i \(0.332421\pi\)
\(510\) 9.86786e39 0.0106386
\(511\) −1.39191e42 −1.45575
\(512\) −4.35561e40 −0.0441942
\(513\) −1.47584e42 −1.45285
\(514\) 5.60146e41 0.535024
\(515\) 9.45421e41 0.876220
\(516\) 4.33892e41 0.390222
\(517\) −2.25911e42 −1.97167
\(518\) −7.55115e41 −0.639590
\(519\) 6.17890e41 0.507946
\(520\) −5.47826e40 −0.0437110
\(521\) −1.32797e42 −1.02850 −0.514249 0.857641i \(-0.671929\pi\)
−0.514249 + 0.857641i \(0.671929\pi\)
\(522\) 7.11859e41 0.535182
\(523\) −6.64786e41 −0.485183 −0.242591 0.970129i \(-0.577997\pi\)
−0.242591 + 0.970129i \(0.577997\pi\)
\(524\) 8.65823e41 0.613471
\(525\) −1.66876e41 −0.114795
\(526\) −1.98874e42 −1.32831
\(527\) −9.05697e40 −0.0587379
\(528\) −5.27613e41 −0.332269
\(529\) −1.48203e42 −0.906348
\(530\) 8.66817e40 0.0514815
\(531\) −9.56551e41 −0.551751
\(532\) −9.43236e41 −0.528433
\(533\) −2.16089e41 −0.117587
\(534\) 1.15314e42 0.609525
\(535\) 2.36587e41 0.121481
\(536\) 3.80542e41 0.189823
\(537\) −4.41449e41 −0.213934
\(538\) 1.53955e42 0.724883
\(539\) 1.54358e42 0.706159
\(540\) 5.39771e41 0.239942
\(541\) −3.24428e42 −1.40140 −0.700699 0.713457i \(-0.747128\pi\)
−0.700699 + 0.713457i \(0.747128\pi\)
\(542\) 9.81271e41 0.411908
\(543\) 5.71322e41 0.233068
\(544\) −2.03996e40 −0.00808794
\(545\) −8.38944e41 −0.323286
\(546\) −2.99561e41 −0.112202
\(547\) 4.67015e42 1.70031 0.850153 0.526536i \(-0.176510\pi\)
0.850153 + 0.526536i \(0.176510\pi\)
\(548\) 1.35140e42 0.478283
\(549\) 1.05663e42 0.363541
\(550\) 7.64213e41 0.255619
\(551\) 6.86047e42 2.23102
\(552\) −2.51618e41 −0.0795584
\(553\) −4.16636e42 −1.28091
\(554\) −2.56380e42 −0.766447
\(555\) 1.31076e42 0.381050
\(556\) −1.38255e42 −0.390861
\(557\) −3.04905e42 −0.838320 −0.419160 0.907912i \(-0.637675\pi\)
−0.419160 + 0.907912i \(0.637675\pi\)
\(558\) −1.55930e42 −0.416966
\(559\) −1.12817e42 −0.293420
\(560\) 3.44978e41 0.0872723
\(561\) −2.47108e41 −0.0608083
\(562\) −5.89370e42 −1.41083
\(563\) 6.25531e41 0.145669 0.0728347 0.997344i \(-0.476795\pi\)
0.0728347 + 0.997344i \(0.476795\pi\)
\(564\) 1.77021e42 0.401051
\(565\) −9.28833e41 −0.204732
\(566\) −3.35637e42 −0.719805
\(567\) 1.23338e42 0.257371
\(568\) −1.05935e42 −0.215099
\(569\) 6.38935e42 1.26246 0.631228 0.775597i \(-0.282551\pi\)
0.631228 + 0.775597i \(0.282551\pi\)
\(570\) 1.63731e42 0.314826
\(571\) 4.53027e42 0.847744 0.423872 0.905722i \(-0.360671\pi\)
0.423872 + 0.905722i \(0.360671\pi\)
\(572\) 1.37185e42 0.249844
\(573\) −1.07444e41 −0.0190453
\(574\) 1.36076e42 0.234772
\(575\) 3.64452e41 0.0612053
\(576\) −3.51212e41 −0.0574144
\(577\) 9.48731e42 1.50980 0.754898 0.655843i \(-0.227687\pi\)
0.754898 + 0.655843i \(0.227687\pi\)
\(578\) 4.55467e42 0.705627
\(579\) −5.01013e42 −0.755669
\(580\) −2.50914e42 −0.368461
\(581\) 2.56125e42 0.366203
\(582\) 7.17208e41 0.0998478
\(583\) −2.17066e42 −0.294258
\(584\) −4.99481e42 −0.659356
\(585\) −4.41735e41 −0.0567866
\(586\) 8.70530e42 1.08986
\(587\) 1.48304e43 1.80827 0.904134 0.427250i \(-0.140518\pi\)
0.904134 + 0.427250i \(0.140518\pi\)
\(588\) −1.20953e42 −0.143637
\(589\) −1.50276e43 −1.73822
\(590\) 3.37162e42 0.379868
\(591\) 5.17788e42 0.568259
\(592\) −2.70970e42 −0.289691
\(593\) 6.85391e42 0.713823 0.356912 0.934138i \(-0.383830\pi\)
0.356912 + 0.934138i \(0.383830\pi\)
\(594\) −1.35168e43 −1.37146
\(595\) 1.61571e41 0.0159716
\(596\) −4.54967e40 −0.00438190
\(597\) −1.02976e43 −0.966349
\(598\) 6.54234e41 0.0598225
\(599\) 1.05394e43 0.939078 0.469539 0.882912i \(-0.344420\pi\)
0.469539 + 0.882912i \(0.344420\pi\)
\(600\) −5.98827e41 −0.0519945
\(601\) −4.18011e42 −0.353698 −0.176849 0.984238i \(-0.556591\pi\)
−0.176849 + 0.984238i \(0.556591\pi\)
\(602\) 7.10431e42 0.585836
\(603\) 3.06847e42 0.246606
\(604\) −7.59988e42 −0.595298
\(605\) −1.32796e43 −1.01385
\(606\) 1.09318e42 0.0813517
\(607\) 4.39468e40 0.00318788 0.00159394 0.999999i \(-0.499493\pi\)
0.00159394 + 0.999999i \(0.499493\pi\)
\(608\) −3.38477e42 −0.239344
\(609\) −1.37204e43 −0.945801
\(610\) −3.72439e42 −0.250289
\(611\) −4.60274e42 −0.301563
\(612\) −1.64490e41 −0.0105074
\(613\) −2.74553e43 −1.70997 −0.854985 0.518653i \(-0.826434\pi\)
−0.854985 + 0.518653i \(0.826434\pi\)
\(614\) 4.05442e42 0.246217
\(615\) −2.36207e42 −0.139871
\(616\) −8.63884e42 −0.498832
\(617\) 2.93144e43 1.65067 0.825336 0.564641i \(-0.190986\pi\)
0.825336 + 0.564641i \(0.190986\pi\)
\(618\) 1.85514e43 1.01872
\(619\) −5.48823e42 −0.293919 −0.146959 0.989143i \(-0.546949\pi\)
−0.146959 + 0.989143i \(0.546949\pi\)
\(620\) 5.49619e42 0.287072
\(621\) −6.44614e42 −0.328383
\(622\) −2.30138e43 −1.14350
\(623\) 1.88808e43 0.915073
\(624\) −1.07496e42 −0.0508198
\(625\) 8.67362e41 0.0400000
\(626\) −2.00024e43 −0.899873
\(627\) −4.10011e43 −1.79948
\(628\) 1.42133e43 0.608583
\(629\) −1.26909e42 −0.0530162
\(630\) 2.78170e42 0.113379
\(631\) 2.48327e43 0.987572 0.493786 0.869583i \(-0.335613\pi\)
0.493786 + 0.869583i \(0.335613\pi\)
\(632\) −1.49508e43 −0.580163
\(633\) −2.50864e43 −0.949907
\(634\) 1.93361e43 0.714474
\(635\) −1.83010e43 −0.659907
\(636\) 1.70090e42 0.0598540
\(637\) 3.14490e42 0.108005
\(638\) 6.28332e43 2.10605
\(639\) −8.54196e42 −0.279444
\(640\) 1.23794e42 0.0395285
\(641\) 2.55989e43 0.797850 0.398925 0.916984i \(-0.369383\pi\)
0.398925 + 0.916984i \(0.369383\pi\)
\(642\) 4.64240e42 0.141237
\(643\) 4.50652e43 1.33836 0.669178 0.743103i \(-0.266647\pi\)
0.669178 + 0.743103i \(0.266647\pi\)
\(644\) −4.11985e42 −0.119440
\(645\) −1.23320e43 −0.349025
\(646\) −1.58526e42 −0.0438022
\(647\) 7.99244e42 0.215607 0.107804 0.994172i \(-0.465618\pi\)
0.107804 + 0.994172i \(0.465618\pi\)
\(648\) 4.42595e42 0.116572
\(649\) −8.44312e43 −2.17125
\(650\) 1.55701e42 0.0390963
\(651\) 3.00542e43 0.736884
\(652\) 1.91862e43 0.459358
\(653\) 6.70562e43 1.56778 0.783890 0.620900i \(-0.213233\pi\)
0.783890 + 0.620900i \(0.213233\pi\)
\(654\) −1.64621e43 −0.375863
\(655\) −2.46082e43 −0.548706
\(656\) 4.88304e42 0.106336
\(657\) −4.02753e43 −0.856595
\(658\) 2.89845e43 0.602093
\(659\) 2.04703e43 0.415337 0.207668 0.978199i \(-0.433412\pi\)
0.207668 + 0.978199i \(0.433412\pi\)
\(660\) 1.49957e43 0.297190
\(661\) 1.02079e43 0.197611 0.0988057 0.995107i \(-0.468498\pi\)
0.0988057 + 0.995107i \(0.468498\pi\)
\(662\) 4.14721e43 0.784254
\(663\) −5.03461e41 −0.00930049
\(664\) 9.19096e42 0.165865
\(665\) 2.68084e43 0.472645
\(666\) −2.18495e43 −0.376349
\(667\) 2.99651e43 0.504272
\(668\) 2.02018e43 0.332165
\(669\) 9.58040e41 0.0153914
\(670\) −1.08156e43 −0.169783
\(671\) 9.32651e43 1.43061
\(672\) 6.76928e42 0.101466
\(673\) −1.16828e43 −0.171125 −0.0855623 0.996333i \(-0.527269\pi\)
−0.0855623 + 0.996333i \(0.527269\pi\)
\(674\) 3.77683e43 0.540629
\(675\) −1.53412e43 −0.214611
\(676\) −3.37766e43 −0.461787
\(677\) −5.20282e43 −0.695208 −0.347604 0.937641i \(-0.613005\pi\)
−0.347604 + 0.937641i \(0.613005\pi\)
\(678\) −1.82259e43 −0.238029
\(679\) 1.17431e43 0.149900
\(680\) 5.79791e41 0.00723408
\(681\) −4.21115e43 −0.513595
\(682\) −1.37634e44 −1.64085
\(683\) −1.36522e44 −1.59104 −0.795521 0.605926i \(-0.792803\pi\)
−0.795521 + 0.605926i \(0.792803\pi\)
\(684\) −2.72928e43 −0.310942
\(685\) −3.84091e43 −0.427789
\(686\) −7.04950e43 −0.767600
\(687\) 5.88519e43 0.626514
\(688\) 2.54935e43 0.265344
\(689\) −4.42252e42 −0.0450061
\(690\) 7.15142e42 0.0711592
\(691\) 1.03195e44 1.00404 0.502020 0.864856i \(-0.332590\pi\)
0.502020 + 0.864856i \(0.332590\pi\)
\(692\) 3.63044e43 0.345394
\(693\) −6.96586e43 −0.648052
\(694\) −1.06798e44 −0.971606
\(695\) 3.92945e43 0.349596
\(696\) −4.92353e43 −0.428384
\(697\) 2.28698e42 0.0194605
\(698\) −2.06598e42 −0.0171936
\(699\) 6.12414e43 0.498482
\(700\) −9.80486e42 −0.0780587
\(701\) 1.21223e44 0.943967 0.471983 0.881607i \(-0.343538\pi\)
0.471983 + 0.881607i \(0.343538\pi\)
\(702\) −2.75392e43 −0.209762
\(703\) −2.10572e44 −1.56889
\(704\) −3.10002e43 −0.225937
\(705\) −5.03125e43 −0.358711
\(706\) −1.36015e44 −0.948664
\(707\) 1.78991e43 0.122132
\(708\) 6.61592e43 0.441646
\(709\) −2.19198e43 −0.143159 −0.0715797 0.997435i \(-0.522804\pi\)
−0.0715797 + 0.997435i \(0.522804\pi\)
\(710\) 3.01084e43 0.192391
\(711\) −1.20555e44 −0.753713
\(712\) 6.77531e43 0.414466
\(713\) −6.56375e43 −0.392884
\(714\) 3.17040e42 0.0185691
\(715\) −3.89903e43 −0.223467
\(716\) −2.59375e43 −0.145471
\(717\) 9.89066e43 0.542848
\(718\) 2.49969e44 1.34263
\(719\) 9.40579e43 0.494422 0.247211 0.968962i \(-0.420486\pi\)
0.247211 + 0.968962i \(0.420486\pi\)
\(720\) 9.98204e42 0.0513530
\(721\) 3.03750e44 1.52940
\(722\) −1.19545e44 −0.589122
\(723\) −6.65320e43 −0.320913
\(724\) 3.35683e43 0.158482
\(725\) 7.13140e43 0.329561
\(726\) −2.60577e44 −1.17874
\(727\) 4.09641e44 1.81393 0.906965 0.421207i \(-0.138393\pi\)
0.906965 + 0.421207i \(0.138393\pi\)
\(728\) −1.76008e43 −0.0762952
\(729\) 2.21627e44 0.940473
\(730\) 1.41961e44 0.589746
\(731\) 1.19399e43 0.0485604
\(732\) −7.30813e43 −0.290994
\(733\) −4.57092e44 −1.78194 −0.890968 0.454067i \(-0.849973\pi\)
−0.890968 + 0.454067i \(0.849973\pi\)
\(734\) 1.54323e43 0.0589035
\(735\) 3.43768e43 0.128473
\(736\) −1.47839e43 −0.0540983
\(737\) 2.70842e44 0.970445
\(738\) 3.93740e43 0.138145
\(739\) 1.00404e44 0.344957 0.172478 0.985013i \(-0.444823\pi\)
0.172478 + 0.985013i \(0.444823\pi\)
\(740\) 7.70144e43 0.259108
\(741\) −8.35359e43 −0.275227
\(742\) 2.78496e43 0.0898582
\(743\) −7.43485e43 −0.234934 −0.117467 0.993077i \(-0.537477\pi\)
−0.117467 + 0.993077i \(0.537477\pi\)
\(744\) 1.07848e44 0.333759
\(745\) 1.29309e42 0.00391929
\(746\) −1.71956e43 −0.0510463
\(747\) 7.41106e43 0.215482
\(748\) −1.45190e43 −0.0413486
\(749\) 7.60121e43 0.212038
\(750\) 1.70197e43 0.0465053
\(751\) −5.97546e44 −1.59938 −0.799691 0.600411i \(-0.795003\pi\)
−0.799691 + 0.600411i \(0.795003\pi\)
\(752\) 1.04010e44 0.272708
\(753\) −1.20682e44 −0.309970
\(754\) 1.28017e44 0.322115
\(755\) 2.16002e44 0.532451
\(756\) 1.73421e44 0.418806
\(757\) −6.25091e44 −1.47896 −0.739481 0.673177i \(-0.764929\pi\)
−0.739481 + 0.673177i \(0.764929\pi\)
\(758\) 1.41097e44 0.327073
\(759\) −1.79084e44 −0.406732
\(760\) 9.62009e43 0.214076
\(761\) 8.11145e44 1.76863 0.884314 0.466892i \(-0.154626\pi\)
0.884314 + 0.466892i \(0.154626\pi\)
\(762\) −3.59110e44 −0.767229
\(763\) −2.69541e44 −0.564279
\(764\) −6.31294e42 −0.0129504
\(765\) 4.67510e42 0.00939807
\(766\) −7.98354e43 −0.157271
\(767\) −1.72021e44 −0.332088
\(768\) 2.42913e43 0.0459571
\(769\) 4.74855e44 0.880446 0.440223 0.897888i \(-0.354899\pi\)
0.440223 + 0.897888i \(0.354899\pi\)
\(770\) 2.45531e44 0.446169
\(771\) −3.12394e44 −0.556366
\(772\) −2.94373e44 −0.513841
\(773\) 3.40400e44 0.582380 0.291190 0.956665i \(-0.405949\pi\)
0.291190 + 0.956665i \(0.405949\pi\)
\(774\) 2.05565e44 0.344719
\(775\) −1.56211e44 −0.256765
\(776\) 4.21399e43 0.0678948
\(777\) 4.21129e44 0.665103
\(778\) 3.47222e44 0.537556
\(779\) 3.79463e44 0.575889
\(780\) 3.05523e43 0.0454546
\(781\) −7.53967e44 −1.09967
\(782\) −6.92407e42 −0.00990050
\(783\) −1.26135e45 −1.76818
\(784\) −7.10663e43 −0.0976708
\(785\) −4.03966e44 −0.544334
\(786\) −4.82871e44 −0.637943
\(787\) −1.06793e45 −1.38336 −0.691678 0.722206i \(-0.743128\pi\)
−0.691678 + 0.722206i \(0.743128\pi\)
\(788\) 3.04229e44 0.386406
\(789\) 1.10912e45 1.38129
\(790\) 4.24928e44 0.518914
\(791\) −2.98421e44 −0.357350
\(792\) −2.49967e44 −0.293524
\(793\) 1.90019e44 0.218808
\(794\) 7.97712e44 0.900800
\(795\) −4.83425e43 −0.0535351
\(796\) −6.05040e44 −0.657100
\(797\) −9.48957e43 −0.101075 −0.0505374 0.998722i \(-0.516093\pi\)
−0.0505374 + 0.998722i \(0.516093\pi\)
\(798\) 5.26044e44 0.549512
\(799\) 4.87131e43 0.0499080
\(800\) −3.51844e43 −0.0353553
\(801\) 5.46322e44 0.538449
\(802\) 3.92995e44 0.379913
\(803\) −3.55495e45 −3.37088
\(804\) −2.12229e44 −0.197395
\(805\) 1.17093e44 0.106831
\(806\) −2.80417e44 −0.250964
\(807\) −8.58608e44 −0.753798
\(808\) 6.42304e43 0.0553178
\(809\) 5.97219e44 0.504582 0.252291 0.967651i \(-0.418816\pi\)
0.252291 + 0.967651i \(0.418816\pi\)
\(810\) −1.25793e44 −0.104265
\(811\) 9.30989e44 0.757045 0.378522 0.925592i \(-0.376432\pi\)
0.378522 + 0.925592i \(0.376432\pi\)
\(812\) −8.06150e44 −0.643128
\(813\) −5.47256e44 −0.428339
\(814\) −1.92857e45 −1.48101
\(815\) −5.45304e44 −0.410862
\(816\) 1.13769e43 0.00841057
\(817\) 1.98111e45 1.43704
\(818\) 1.70165e45 1.21114
\(819\) −1.41923e44 −0.0991180
\(820\) −1.38784e44 −0.0951098
\(821\) 4.88604e44 0.328578 0.164289 0.986412i \(-0.447467\pi\)
0.164289 + 0.986412i \(0.447467\pi\)
\(822\) −7.53677e44 −0.497362
\(823\) 2.61589e45 1.69403 0.847017 0.531566i \(-0.178396\pi\)
0.847017 + 0.531566i \(0.178396\pi\)
\(824\) 1.09000e45 0.692713
\(825\) −4.26203e44 −0.265815
\(826\) 1.08325e45 0.663039
\(827\) 2.59698e45 1.56003 0.780015 0.625761i \(-0.215211\pi\)
0.780015 + 0.625761i \(0.215211\pi\)
\(828\) −1.19209e44 −0.0702812
\(829\) −2.36709e45 −1.36968 −0.684842 0.728692i \(-0.740129\pi\)
−0.684842 + 0.728692i \(0.740129\pi\)
\(830\) −2.61223e44 −0.148355
\(831\) 1.42983e45 0.797020
\(832\) −6.31600e43 −0.0345566
\(833\) −3.32840e43 −0.0178747
\(834\) 7.71051e44 0.406452
\(835\) −5.74169e44 −0.297098
\(836\) −2.40904e45 −1.22362
\(837\) 2.76294e45 1.37761
\(838\) −1.63851e45 −0.801985
\(839\) 2.59287e45 1.24586 0.622930 0.782277i \(-0.285942\pi\)
0.622930 + 0.782277i \(0.285942\pi\)
\(840\) −1.92395e44 −0.0907536
\(841\) 3.70398e45 1.71526
\(842\) 3.16590e44 0.143933
\(843\) 3.28692e45 1.46711
\(844\) −1.47396e45 −0.645920
\(845\) 9.59988e44 0.413035
\(846\) 8.38674e44 0.354285
\(847\) −4.26653e45 −1.76963
\(848\) 9.99371e43 0.0406997
\(849\) 1.87185e45 0.748518
\(850\) −1.64786e43 −0.00647035
\(851\) −9.19734e44 −0.354613
\(852\) 5.90799e44 0.223679
\(853\) 1.97911e45 0.735799 0.367900 0.929866i \(-0.380077\pi\)
0.367900 + 0.929866i \(0.380077\pi\)
\(854\) −1.19659e45 −0.436867
\(855\) 7.75709e44 0.278115
\(856\) 2.72767e44 0.0960390
\(857\) −2.57732e45 −0.891181 −0.445591 0.895237i \(-0.647006\pi\)
−0.445591 + 0.895237i \(0.647006\pi\)
\(858\) −7.65083e44 −0.259810
\(859\) 5.92532e44 0.197614 0.0988069 0.995107i \(-0.468497\pi\)
0.0988069 + 0.995107i \(0.468497\pi\)
\(860\) −7.24570e44 −0.237331
\(861\) −7.58897e44 −0.244137
\(862\) 2.06640e45 0.652907
\(863\) −3.98009e45 −1.23517 −0.617583 0.786506i \(-0.711888\pi\)
−0.617583 + 0.786506i \(0.711888\pi\)
\(864\) 6.22314e44 0.189691
\(865\) −1.03183e45 −0.308930
\(866\) −4.12613e45 −1.21343
\(867\) −2.54014e45 −0.733774
\(868\) 1.76585e45 0.501068
\(869\) −1.06409e46 −2.96601
\(870\) 1.39935e45 0.383158
\(871\) 5.51817e44 0.148427
\(872\) −9.67237e44 −0.255580
\(873\) 3.39792e44 0.0882047
\(874\) −1.14887e45 −0.292983
\(875\) 2.78671e44 0.0698179
\(876\) 2.78561e45 0.685658
\(877\) 6.85482e45 1.65769 0.828844 0.559480i \(-0.188999\pi\)
0.828844 + 0.559480i \(0.188999\pi\)
\(878\) 2.70868e44 0.0643565
\(879\) −4.85496e45 −1.13333
\(880\) 8.81077e44 0.202084
\(881\) −1.78938e44 −0.0403251 −0.0201625 0.999797i \(-0.506418\pi\)
−0.0201625 + 0.999797i \(0.506418\pi\)
\(882\) −5.73038e44 −0.126888
\(883\) 1.67939e45 0.365393 0.182696 0.983169i \(-0.441518\pi\)
0.182696 + 0.983169i \(0.441518\pi\)
\(884\) −2.95811e43 −0.00632417
\(885\) −1.88036e45 −0.395020
\(886\) −4.68681e45 −0.967509
\(887\) 9.72650e43 0.0197306 0.00986530 0.999951i \(-0.496860\pi\)
0.00986530 + 0.999951i \(0.496860\pi\)
\(888\) 1.51121e45 0.301247
\(889\) −5.87986e45 −1.15183
\(890\) −1.92566e45 −0.370710
\(891\) 3.15007e45 0.595959
\(892\) 5.62901e43 0.0104659
\(893\) 8.08264e45 1.47691
\(894\) 2.53736e43 0.00455669
\(895\) 7.37189e44 0.130113
\(896\) 3.97732e44 0.0689948
\(897\) −3.64867e44 −0.0622088
\(898\) 5.93255e45 0.994164
\(899\) −1.28436e46 −2.11549
\(900\) −2.83707e44 −0.0459315
\(901\) 4.68057e43 0.00744842
\(902\) 3.47540e45 0.543630
\(903\) −3.96208e45 −0.609205
\(904\) −1.07087e45 −0.161855
\(905\) −9.54068e44 −0.141751
\(906\) 4.23847e45 0.619044
\(907\) 5.07003e44 0.0727943 0.0363972 0.999337i \(-0.488412\pi\)
0.0363972 + 0.999337i \(0.488412\pi\)
\(908\) −2.47428e45 −0.349235
\(909\) 5.17917e44 0.0718654
\(910\) 5.00246e44 0.0682405
\(911\) −8.33096e44 −0.111728 −0.0558638 0.998438i \(-0.517791\pi\)
−0.0558638 + 0.998438i \(0.517791\pi\)
\(912\) 1.88769e45 0.248892
\(913\) 6.54147e45 0.847966
\(914\) −6.37003e45 −0.811850
\(915\) 2.07710e45 0.260273
\(916\) 3.45787e45 0.426019
\(917\) −7.90625e45 −0.957736
\(918\) 2.91461e44 0.0347152
\(919\) 7.80049e45 0.913549 0.456774 0.889583i \(-0.349005\pi\)
0.456774 + 0.889583i \(0.349005\pi\)
\(920\) 4.20185e44 0.0483870
\(921\) −2.26115e45 −0.256039
\(922\) 3.78230e45 0.421140
\(923\) −1.53614e45 −0.168192
\(924\) 4.81789e45 0.518730
\(925\) −2.18888e45 −0.231753
\(926\) 6.02184e45 0.626987
\(927\) 8.78910e45 0.899930
\(928\) −2.89284e45 −0.291294
\(929\) 9.20353e45 0.911404 0.455702 0.890133i \(-0.349388\pi\)
0.455702 + 0.890133i \(0.349388\pi\)
\(930\) −3.06523e45 −0.298523
\(931\) −5.52259e45 −0.528960
\(932\) 3.59827e45 0.338959
\(933\) 1.28348e46 1.18912
\(934\) 4.33068e45 0.394621
\(935\) 4.12654e44 0.0369833
\(936\) −5.09286e44 −0.0448938
\(937\) 1.17829e46 1.02162 0.510808 0.859695i \(-0.329346\pi\)
0.510808 + 0.859695i \(0.329346\pi\)
\(938\) −3.47491e45 −0.296346
\(939\) 1.11554e46 0.935768
\(940\) −2.95613e45 −0.243917
\(941\) −6.87236e45 −0.557785 −0.278892 0.960322i \(-0.589967\pi\)
−0.278892 + 0.960322i \(0.589967\pi\)
\(942\) −7.92677e45 −0.632859
\(943\) 1.65741e45 0.130167
\(944\) 3.88721e45 0.300312
\(945\) −4.92891e45 −0.374591
\(946\) 1.81445e46 1.35654
\(947\) −8.94323e45 −0.657763 −0.328882 0.944371i \(-0.606672\pi\)
−0.328882 + 0.944371i \(0.606672\pi\)
\(948\) 8.33810e45 0.603306
\(949\) −7.24289e45 −0.515568
\(950\) −2.73419e45 −0.191476
\(951\) −1.07838e46 −0.742974
\(952\) 1.86278e44 0.0126267
\(953\) −7.57551e45 −0.505210 −0.252605 0.967569i \(-0.581287\pi\)
−0.252605 + 0.967569i \(0.581287\pi\)
\(954\) 8.05836e44 0.0528746
\(955\) 1.79425e44 0.0115832
\(956\) 5.81130e45 0.369127
\(957\) −3.50422e46 −2.19006
\(958\) −2.12512e46 −1.30683
\(959\) −1.23403e46 −0.746684
\(960\) −6.90401e44 −0.0411052
\(961\) 1.10643e46 0.648203
\(962\) −3.92929e45 −0.226517
\(963\) 2.19943e45 0.124768
\(964\) −3.90912e45 −0.218215
\(965\) 8.36657e45 0.459594
\(966\) 2.29765e45 0.124205
\(967\) 3.23805e46 1.72255 0.861277 0.508136i \(-0.169665\pi\)
0.861277 + 0.508136i \(0.169665\pi\)
\(968\) −1.53103e46 −0.801522
\(969\) 8.84102e44 0.0455495
\(970\) −1.19769e45 −0.0607270
\(971\) −9.38917e44 −0.0468521 −0.0234260 0.999726i \(-0.507457\pi\)
−0.0234260 + 0.999726i \(0.507457\pi\)
\(972\) 8.45656e45 0.415305
\(973\) 1.26247e46 0.610202
\(974\) −5.82117e45 −0.276915
\(975\) −8.68349e44 −0.0406558
\(976\) −4.29393e45 −0.197871
\(977\) −2.21995e46 −1.00688 −0.503441 0.864030i \(-0.667933\pi\)
−0.503441 + 0.864030i \(0.667933\pi\)
\(978\) −1.07002e46 −0.477681
\(979\) 4.82218e46 2.11891
\(980\) 2.01983e45 0.0873594
\(981\) −7.79924e45 −0.332034
\(982\) −2.55436e46 −1.07042
\(983\) −9.42127e45 −0.388624 −0.194312 0.980940i \(-0.562247\pi\)
−0.194312 + 0.980940i \(0.562247\pi\)
\(984\) −2.72328e45 −0.110578
\(985\) −8.64670e45 −0.345612
\(986\) −1.35487e45 −0.0533094
\(987\) −1.61647e46 −0.626110
\(988\) −4.90819e45 −0.187150
\(989\) 8.65308e45 0.324809
\(990\) 7.10450e45 0.262536
\(991\) −5.11507e44 −0.0186084 −0.00930422 0.999957i \(-0.502962\pi\)
−0.00930422 + 0.999957i \(0.502962\pi\)
\(992\) 6.33667e45 0.226950
\(993\) −2.31290e46 −0.815538
\(994\) 9.67341e45 0.335808
\(995\) 1.71963e46 0.587728
\(996\) −5.12581e45 −0.172482
\(997\) 9.34514e45 0.309607 0.154804 0.987945i \(-0.450526\pi\)
0.154804 + 0.987945i \(0.450526\pi\)
\(998\) −2.76977e46 −0.903483
\(999\) 3.87152e46 1.24342
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 10.32.a.b.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.32.a.b.1.2 2 1.1 even 1 trivial