Properties

Label 10.26.a.b.1.2
Level $10$
Weight $26$
Character 10.1
Self dual yes
Analytic conductor $39.600$
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] = [10,26,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, 26, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("10.1");
 
S:= CuspForms(chi, 26);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 26 \)
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: \(39.5996779952\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\mathbb{Q}[x]/(x^{2} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 6900880 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3}\cdot 5 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2626.45\) 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)
 
\(f(q)\) \(=\) \(q-4096.00 q^{2} +1.19926e6 q^{3} +1.67772e7 q^{4} +2.44141e8 q^{5} -4.91217e9 q^{6} -1.32210e10 q^{7} -6.87195e10 q^{8} +5.90937e11 q^{9} -1.00000e12 q^{10} +1.51986e13 q^{11} +2.01203e13 q^{12} +3.15848e12 q^{13} +5.41533e13 q^{14} +2.92788e14 q^{15} +2.81475e14 q^{16} +1.62591e15 q^{17} -2.42048e15 q^{18} +5.64080e15 q^{19} +4.09600e15 q^{20} -1.58554e16 q^{21} -6.22536e16 q^{22} -1.52235e17 q^{23} -8.24125e16 q^{24} +5.96046e16 q^{25} -1.29371e16 q^{26} -3.07432e17 q^{27} -2.21812e17 q^{28} +1.86158e17 q^{29} -1.19926e18 q^{30} +6.41559e18 q^{31} -1.15292e18 q^{32} +1.82271e19 q^{33} -6.65974e18 q^{34} -3.22779e18 q^{35} +9.91428e18 q^{36} +3.10993e19 q^{37} -2.31047e19 q^{38} +3.78784e18 q^{39} -1.67772e19 q^{40} -2.12615e19 q^{41} +6.49439e19 q^{42} +4.45949e20 q^{43} +2.54991e20 q^{44} +1.44272e20 q^{45} +6.23555e20 q^{46} +5.28278e19 q^{47} +3.37562e20 q^{48} -1.16627e21 q^{49} -2.44141e20 q^{50} +1.94989e21 q^{51} +5.29905e19 q^{52} +2.38642e21 q^{53} +1.25924e21 q^{54} +3.71060e21 q^{55} +9.08541e20 q^{56} +6.76479e21 q^{57} -7.62501e20 q^{58} +1.91973e22 q^{59} +4.91217e21 q^{60} +1.98905e21 q^{61} -2.62783e22 q^{62} -7.81279e21 q^{63} +4.72237e21 q^{64} +7.71113e20 q^{65} -7.46583e22 q^{66} -1.03138e23 q^{67} +2.72783e22 q^{68} -1.82570e23 q^{69} +1.32210e22 q^{70} -1.01960e23 q^{71} -4.06089e22 q^{72} +3.26795e23 q^{73} -1.27383e23 q^{74} +7.14815e22 q^{75} +9.46369e22 q^{76} -2.00941e23 q^{77} -1.55150e22 q^{78} +2.14410e23 q^{79} +6.87195e22 q^{80} -8.69386e23 q^{81} +8.70871e22 q^{82} +1.80482e24 q^{83} -2.66010e23 q^{84} +3.96951e23 q^{85} -1.82661e24 q^{86} +2.23251e23 q^{87} -1.04444e24 q^{88} +3.14740e24 q^{89} -5.90937e23 q^{90} -4.17583e22 q^{91} -2.55408e24 q^{92} +7.69396e24 q^{93} -2.16383e23 q^{94} +1.37715e24 q^{95} -1.38265e24 q^{96} +4.10993e24 q^{97} +4.77706e24 q^{98} +8.98144e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8192 q^{2} - 438588 q^{3} + 33554432 q^{4} + 488281250 q^{5} + 1796456448 q^{6} - 34008596636 q^{7} - 137438953472 q^{8} + 2426195859786 q^{9} - 2000000000000 q^{10} + 19344682791984 q^{11} - 7358285611008 q^{12}+ \cdots + 16\!\cdots\!12 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4096.00 −0.707107
\(3\) 1.19926e6 1.30286 0.651430 0.758709i \(-0.274169\pi\)
0.651430 + 0.758709i \(0.274169\pi\)
\(4\) 1.67772e7 0.500000
\(5\) 2.44141e8 0.447214
\(6\) −4.91217e9 −0.921261
\(7\) −1.32210e10 −0.361027 −0.180513 0.983573i \(-0.557776\pi\)
−0.180513 + 0.983573i \(0.557776\pi\)
\(8\) −6.87195e10 −0.353553
\(9\) 5.90937e11 0.697445
\(10\) −1.00000e12 −0.316228
\(11\) 1.51986e13 1.46015 0.730073 0.683370i \(-0.239486\pi\)
0.730073 + 0.683370i \(0.239486\pi\)
\(12\) 2.01203e13 0.651430
\(13\) 3.15848e12 0.0375999 0.0187999 0.999823i \(-0.494015\pi\)
0.0187999 + 0.999823i \(0.494015\pi\)
\(14\) 5.41533e13 0.255284
\(15\) 2.92788e14 0.582657
\(16\) 2.81475e14 0.250000
\(17\) 1.62591e15 0.676840 0.338420 0.940995i \(-0.390108\pi\)
0.338420 + 0.940995i \(0.390108\pi\)
\(18\) −2.42048e15 −0.493168
\(19\) 5.64080e15 0.584683 0.292342 0.956314i \(-0.405566\pi\)
0.292342 + 0.956314i \(0.405566\pi\)
\(20\) 4.09600e15 0.223607
\(21\) −1.58554e16 −0.470367
\(22\) −6.22536e16 −1.03248
\(23\) −1.52235e17 −1.44849 −0.724247 0.689540i \(-0.757813\pi\)
−0.724247 + 0.689540i \(0.757813\pi\)
\(24\) −8.24125e16 −0.460631
\(25\) 5.96046e16 0.200000
\(26\) −1.29371e16 −0.0265871
\(27\) −3.07432e17 −0.394187
\(28\) −2.21812e17 −0.180513
\(29\) 1.86158e17 0.0977025 0.0488512 0.998806i \(-0.484444\pi\)
0.0488512 + 0.998806i \(0.484444\pi\)
\(30\) −1.19926e18 −0.412001
\(31\) 6.41559e18 1.46290 0.731451 0.681894i \(-0.238843\pi\)
0.731451 + 0.681894i \(0.238843\pi\)
\(32\) −1.15292e18 −0.176777
\(33\) 1.82271e19 1.90236
\(34\) −6.65974e18 −0.478598
\(35\) −3.22779e18 −0.161456
\(36\) 9.91428e18 0.348722
\(37\) 3.10993e19 0.776657 0.388328 0.921521i \(-0.373053\pi\)
0.388328 + 0.921521i \(0.373053\pi\)
\(38\) −2.31047e19 −0.413434
\(39\) 3.78784e18 0.0489874
\(40\) −1.67772e19 −0.158114
\(41\) −2.12615e19 −0.147162 −0.0735810 0.997289i \(-0.523443\pi\)
−0.0735810 + 0.997289i \(0.523443\pi\)
\(42\) 6.49439e19 0.332600
\(43\) 4.45949e20 1.70188 0.850942 0.525260i \(-0.176032\pi\)
0.850942 + 0.525260i \(0.176032\pi\)
\(44\) 2.54991e20 0.730073
\(45\) 1.44272e20 0.311907
\(46\) 6.23555e20 1.02424
\(47\) 5.28278e19 0.0663192 0.0331596 0.999450i \(-0.489443\pi\)
0.0331596 + 0.999450i \(0.489443\pi\)
\(48\) 3.37562e20 0.325715
\(49\) −1.16627e21 −0.869660
\(50\) −2.44141e20 −0.141421
\(51\) 1.94989e21 0.881827
\(52\) 5.29905e19 0.0187999
\(53\) 2.38642e21 0.667266 0.333633 0.942703i \(-0.391725\pi\)
0.333633 + 0.942703i \(0.391725\pi\)
\(54\) 1.25924e21 0.278732
\(55\) 3.71060e21 0.652997
\(56\) 9.08541e20 0.127642
\(57\) 6.76479e21 0.761761
\(58\) −7.62501e20 −0.0690861
\(59\) 1.91973e22 1.40472 0.702361 0.711821i \(-0.252129\pi\)
0.702361 + 0.711821i \(0.252129\pi\)
\(60\) 4.91217e21 0.291328
\(61\) 1.98905e21 0.0959450 0.0479725 0.998849i \(-0.484724\pi\)
0.0479725 + 0.998849i \(0.484724\pi\)
\(62\) −2.62783e22 −1.03443
\(63\) −7.81279e21 −0.251796
\(64\) 4.72237e21 0.125000
\(65\) 7.71113e20 0.0168152
\(66\) −7.46583e22 −1.34518
\(67\) −1.03138e23 −1.53987 −0.769933 0.638125i \(-0.779710\pi\)
−0.769933 + 0.638125i \(0.779710\pi\)
\(68\) 2.72783e22 0.338420
\(69\) −1.82570e23 −1.88719
\(70\) 1.32210e22 0.114167
\(71\) −1.01960e23 −0.737393 −0.368697 0.929550i \(-0.620196\pi\)
−0.368697 + 0.929550i \(0.620196\pi\)
\(72\) −4.06089e22 −0.246584
\(73\) 3.26795e23 1.67009 0.835044 0.550183i \(-0.185442\pi\)
0.835044 + 0.550183i \(0.185442\pi\)
\(74\) −1.27383e23 −0.549179
\(75\) 7.14815e22 0.260572
\(76\) 9.46369e22 0.292342
\(77\) −2.00941e23 −0.527151
\(78\) −1.55150e22 −0.0346393
\(79\) 2.14410e23 0.408231 0.204115 0.978947i \(-0.434568\pi\)
0.204115 + 0.978947i \(0.434568\pi\)
\(80\) 6.87195e22 0.111803
\(81\) −8.69386e23 −1.21102
\(82\) 8.70871e22 0.104059
\(83\) 1.80482e24 1.85335 0.926674 0.375865i \(-0.122654\pi\)
0.926674 + 0.375865i \(0.122654\pi\)
\(84\) −2.66010e23 −0.235184
\(85\) 3.96951e23 0.302692
\(86\) −1.82661e24 −1.20341
\(87\) 2.23251e23 0.127293
\(88\) −1.04444e24 −0.516239
\(89\) 3.14740e24 1.35076 0.675378 0.737472i \(-0.263981\pi\)
0.675378 + 0.737472i \(0.263981\pi\)
\(90\) −5.90937e23 −0.220551
\(91\) −4.17583e22 −0.0135745
\(92\) −2.55408e24 −0.724247
\(93\) 7.69396e24 1.90596
\(94\) −2.16383e23 −0.0468948
\(95\) 1.37715e24 0.261478
\(96\) −1.38265e24 −0.230315
\(97\) 4.10993e24 0.601433 0.300717 0.953714i \(-0.402774\pi\)
0.300717 + 0.953714i \(0.402774\pi\)
\(98\) 4.77706e24 0.614942
\(99\) 8.98144e24 1.01837
\(100\) 1.00000e24 0.100000
\(101\) 7.38400e24 0.652040 0.326020 0.945363i \(-0.394292\pi\)
0.326020 + 0.945363i \(0.394292\pi\)
\(102\) −7.98676e24 −0.623546
\(103\) −1.77047e25 −1.22355 −0.611777 0.791030i \(-0.709545\pi\)
−0.611777 + 0.791030i \(0.709545\pi\)
\(104\) −2.17049e23 −0.0132936
\(105\) −3.87096e24 −0.210355
\(106\) −9.77478e24 −0.471828
\(107\) −3.05016e25 −1.30926 −0.654630 0.755949i \(-0.727176\pi\)
−0.654630 + 0.755949i \(0.727176\pi\)
\(108\) −5.15786e24 −0.197094
\(109\) −7.07393e23 −0.0240896 −0.0120448 0.999927i \(-0.503834\pi\)
−0.0120448 + 0.999927i \(0.503834\pi\)
\(110\) −1.51986e25 −0.461738
\(111\) 3.72962e25 1.01188
\(112\) −3.72138e24 −0.0902567
\(113\) −4.42998e24 −0.0961437 −0.0480719 0.998844i \(-0.515308\pi\)
−0.0480719 + 0.998844i \(0.515308\pi\)
\(114\) −2.77086e25 −0.538646
\(115\) −3.71668e25 −0.647786
\(116\) 3.12320e24 0.0488512
\(117\) 1.86646e24 0.0262238
\(118\) −7.86322e25 −0.993289
\(119\) −2.14962e25 −0.244357
\(120\) −2.01203e25 −0.206000
\(121\) 1.22651e26 1.13202
\(122\) −8.14714e24 −0.0678433
\(123\) −2.54981e25 −0.191732
\(124\) 1.07636e26 0.731451
\(125\) 1.45519e25 0.0894427
\(126\) 3.20012e25 0.178047
\(127\) −3.71403e26 −1.87197 −0.935985 0.352040i \(-0.885488\pi\)
−0.935985 + 0.352040i \(0.885488\pi\)
\(128\) −1.93428e25 −0.0883883
\(129\) 5.34810e26 2.21732
\(130\) −3.15848e24 −0.0118901
\(131\) 1.04713e26 0.358187 0.179093 0.983832i \(-0.442684\pi\)
0.179093 + 0.983832i \(0.442684\pi\)
\(132\) 3.05800e26 0.951182
\(133\) −7.45771e25 −0.211086
\(134\) 4.22452e26 1.08885
\(135\) −7.50567e25 −0.176286
\(136\) −1.11732e26 −0.239299
\(137\) 5.94307e25 0.116146 0.0580729 0.998312i \(-0.481504\pi\)
0.0580729 + 0.998312i \(0.481504\pi\)
\(138\) 7.47805e26 1.33444
\(139\) −4.16988e26 −0.679890 −0.339945 0.940445i \(-0.610408\pi\)
−0.339945 + 0.940445i \(0.610408\pi\)
\(140\) −5.41533e25 −0.0807280
\(141\) 6.33543e25 0.0864047
\(142\) 4.17627e26 0.521416
\(143\) 4.80046e25 0.0549012
\(144\) 1.66334e26 0.174361
\(145\) 4.54486e25 0.0436939
\(146\) −1.33855e27 −1.18093
\(147\) −1.39867e27 −1.13305
\(148\) 5.21760e26 0.388328
\(149\) −2.31720e27 −1.58539 −0.792693 0.609621i \(-0.791322\pi\)
−0.792693 + 0.609621i \(0.791322\pi\)
\(150\) −2.92788e26 −0.184252
\(151\) −1.72926e27 −1.00149 −0.500747 0.865593i \(-0.666941\pi\)
−0.500747 + 0.865593i \(0.666941\pi\)
\(152\) −3.87633e26 −0.206717
\(153\) 9.60812e26 0.472058
\(154\) 8.23056e26 0.372752
\(155\) 1.56631e27 0.654230
\(156\) 6.35494e25 0.0244937
\(157\) −1.99124e27 −0.708561 −0.354280 0.935139i \(-0.615274\pi\)
−0.354280 + 0.935139i \(0.615274\pi\)
\(158\) −8.78222e26 −0.288663
\(159\) 2.86194e27 0.869354
\(160\) −2.81475e26 −0.0790569
\(161\) 2.01270e27 0.522945
\(162\) 3.56100e27 0.856317
\(163\) 5.29799e26 0.117968 0.0589842 0.998259i \(-0.481214\pi\)
0.0589842 + 0.998259i \(0.481214\pi\)
\(164\) −3.56709e26 −0.0735810
\(165\) 4.44998e27 0.850763
\(166\) −7.39253e27 −1.31052
\(167\) −8.51848e27 −1.40090 −0.700449 0.713703i \(-0.747017\pi\)
−0.700449 + 0.713703i \(0.747017\pi\)
\(168\) 1.08958e27 0.166300
\(169\) −7.04643e27 −0.998586
\(170\) −1.62591e27 −0.214035
\(171\) 3.33336e27 0.407784
\(172\) 7.48179e27 0.850942
\(173\) −1.49682e28 −1.58341 −0.791705 0.610904i \(-0.790806\pi\)
−0.791705 + 0.610904i \(0.790806\pi\)
\(174\) −9.14437e26 −0.0900095
\(175\) −7.88034e26 −0.0722053
\(176\) 4.27804e27 0.365036
\(177\) 2.30226e28 1.83016
\(178\) −1.28917e28 −0.955128
\(179\) 1.97459e28 1.36400 0.681999 0.731353i \(-0.261111\pi\)
0.681999 + 0.731353i \(0.261111\pi\)
\(180\) 2.42048e27 0.155953
\(181\) 2.28995e28 1.37672 0.688358 0.725371i \(-0.258332\pi\)
0.688358 + 0.725371i \(0.258332\pi\)
\(182\) 1.71042e26 0.00959866
\(183\) 2.38539e27 0.125003
\(184\) 1.04615e28 0.512120
\(185\) 7.59261e27 0.347332
\(186\) −3.15145e28 −1.34772
\(187\) 2.47117e28 0.988284
\(188\) 8.86304e26 0.0331596
\(189\) 4.06457e27 0.142312
\(190\) −5.64080e27 −0.184893
\(191\) 6.00777e28 1.84415 0.922074 0.387013i \(-0.126493\pi\)
0.922074 + 0.387013i \(0.126493\pi\)
\(192\) 5.66335e27 0.162858
\(193\) −6.00445e28 −1.61810 −0.809052 0.587736i \(-0.800019\pi\)
−0.809052 + 0.587736i \(0.800019\pi\)
\(194\) −1.68343e28 −0.425277
\(195\) 9.24766e26 0.0219078
\(196\) −1.95668e28 −0.434830
\(197\) −3.69371e27 −0.0770255 −0.0385128 0.999258i \(-0.512262\pi\)
−0.0385128 + 0.999258i \(0.512262\pi\)
\(198\) −3.67880e28 −0.720097
\(199\) −1.22806e28 −0.225713 −0.112856 0.993611i \(-0.536000\pi\)
−0.112856 + 0.993611i \(0.536000\pi\)
\(200\) −4.09600e27 −0.0707107
\(201\) −1.23689e29 −2.00623
\(202\) −3.02448e28 −0.461062
\(203\) −2.46119e27 −0.0352732
\(204\) 3.27138e28 0.440914
\(205\) −5.19080e27 −0.0658129
\(206\) 7.25184e28 0.865183
\(207\) −8.99613e28 −1.01024
\(208\) 8.89033e26 0.00939996
\(209\) 8.57325e28 0.853723
\(210\) 1.58554e28 0.148743
\(211\) −2.20546e29 −1.94970 −0.974850 0.222861i \(-0.928460\pi\)
−0.974850 + 0.222861i \(0.928460\pi\)
\(212\) 4.00375e28 0.333633
\(213\) −1.22276e29 −0.960720
\(214\) 1.24935e29 0.925787
\(215\) 1.08874e29 0.761106
\(216\) 2.11266e28 0.139366
\(217\) −8.48206e28 −0.528147
\(218\) 2.89748e27 0.0170339
\(219\) 3.91912e29 2.17589
\(220\) 6.22536e28 0.326498
\(221\) 5.13541e27 0.0254491
\(222\) −1.52765e29 −0.715504
\(223\) −2.23533e27 −0.00989761 −0.00494880 0.999988i \(-0.501575\pi\)
−0.00494880 + 0.999988i \(0.501575\pi\)
\(224\) 1.52428e28 0.0638211
\(225\) 3.52226e28 0.139489
\(226\) 1.81452e28 0.0679839
\(227\) −2.34973e29 −0.833094 −0.416547 0.909114i \(-0.636760\pi\)
−0.416547 + 0.909114i \(0.636760\pi\)
\(228\) 1.13494e29 0.380880
\(229\) 3.37494e29 1.07232 0.536158 0.844118i \(-0.319875\pi\)
0.536158 + 0.844118i \(0.319875\pi\)
\(230\) 1.52235e29 0.458054
\(231\) −2.40981e29 −0.686804
\(232\) −1.27926e28 −0.0345430
\(233\) 2.45486e29 0.628172 0.314086 0.949395i \(-0.398302\pi\)
0.314086 + 0.949395i \(0.398302\pi\)
\(234\) −7.64503e27 −0.0185430
\(235\) 1.28974e28 0.0296589
\(236\) 3.22078e29 0.702361
\(237\) 2.57133e29 0.531868
\(238\) 8.80485e28 0.172787
\(239\) 2.75069e29 0.512234 0.256117 0.966646i \(-0.417557\pi\)
0.256117 + 0.966646i \(0.417557\pi\)
\(240\) 8.24125e28 0.145664
\(241\) −3.54884e29 −0.595489 −0.297744 0.954646i \(-0.596234\pi\)
−0.297744 + 0.954646i \(0.596234\pi\)
\(242\) −5.02380e29 −0.800462
\(243\) −7.82136e29 −1.18360
\(244\) 3.33707e28 0.0479725
\(245\) −2.84735e29 −0.388924
\(246\) 1.04440e29 0.135575
\(247\) 1.78164e28 0.0219840
\(248\) −4.40876e29 −0.517214
\(249\) 2.16445e30 2.41465
\(250\) −5.96046e28 −0.0632456
\(251\) −1.45056e30 −1.46425 −0.732124 0.681171i \(-0.761471\pi\)
−0.732124 + 0.681171i \(0.761471\pi\)
\(252\) −1.31077e29 −0.125898
\(253\) −2.31377e30 −2.11501
\(254\) 1.52127e30 1.32368
\(255\) 4.76048e29 0.394365
\(256\) 7.92282e28 0.0625000
\(257\) 2.49157e28 0.0187201 0.00936006 0.999956i \(-0.497021\pi\)
0.00936006 + 0.999956i \(0.497021\pi\)
\(258\) −2.19058e30 −1.56788
\(259\) −4.11164e29 −0.280394
\(260\) 1.29371e28 0.00840758
\(261\) 1.10007e29 0.0681421
\(262\) −4.28905e29 −0.253276
\(263\) −1.49953e30 −0.844325 −0.422162 0.906520i \(-0.638729\pi\)
−0.422162 + 0.906520i \(0.638729\pi\)
\(264\) −1.25256e30 −0.672588
\(265\) 5.82622e29 0.298410
\(266\) 3.05468e29 0.149261
\(267\) 3.77455e30 1.75985
\(268\) −1.73036e30 −0.769933
\(269\) 1.77042e30 0.751920 0.375960 0.926636i \(-0.377313\pi\)
0.375960 + 0.926636i \(0.377313\pi\)
\(270\) 3.07432e29 0.124653
\(271\) 2.89777e30 1.12188 0.560941 0.827855i \(-0.310439\pi\)
0.560941 + 0.827855i \(0.310439\pi\)
\(272\) 4.57654e29 0.169210
\(273\) −5.00791e28 −0.0176857
\(274\) −2.43428e29 −0.0821275
\(275\) 9.05909e29 0.292029
\(276\) −3.06301e30 −0.943593
\(277\) −1.66393e30 −0.489935 −0.244968 0.969531i \(-0.578777\pi\)
−0.244968 + 0.969531i \(0.578777\pi\)
\(278\) 1.70798e30 0.480755
\(279\) 3.79121e30 1.02029
\(280\) 2.21812e29 0.0570833
\(281\) −2.85222e30 −0.702027 −0.351013 0.936370i \(-0.614163\pi\)
−0.351013 + 0.936370i \(0.614163\pi\)
\(282\) −2.59499e29 −0.0610973
\(283\) −1.34367e30 −0.302665 −0.151333 0.988483i \(-0.548356\pi\)
−0.151333 + 0.988483i \(0.548356\pi\)
\(284\) −1.71060e30 −0.368697
\(285\) 1.65156e30 0.340670
\(286\) −1.96627e29 −0.0388210
\(287\) 2.81099e29 0.0531294
\(288\) −6.81304e29 −0.123292
\(289\) −3.12704e30 −0.541888
\(290\) −1.86158e29 −0.0308962
\(291\) 4.92887e30 0.783583
\(292\) 5.48271e30 0.835044
\(293\) 1.77083e30 0.258423 0.129212 0.991617i \(-0.458755\pi\)
0.129212 + 0.991617i \(0.458755\pi\)
\(294\) 5.72893e30 0.801184
\(295\) 4.68685e30 0.628211
\(296\) −2.13713e30 −0.274590
\(297\) −4.67255e30 −0.575571
\(298\) 9.49125e30 1.12104
\(299\) −4.80831e29 −0.0544632
\(300\) 1.19926e30 0.130286
\(301\) −5.89590e30 −0.614425
\(302\) 7.08305e30 0.708164
\(303\) 8.85533e30 0.849517
\(304\) 1.58774e30 0.146171
\(305\) 4.85607e29 0.0429079
\(306\) −3.93549e30 −0.333796
\(307\) −1.28750e31 −1.04838 −0.524189 0.851602i \(-0.675631\pi\)
−0.524189 + 0.851602i \(0.675631\pi\)
\(308\) −3.37124e30 −0.263576
\(309\) −2.12325e31 −1.59412
\(310\) −6.41559e30 −0.462610
\(311\) −4.08326e29 −0.0282815 −0.0141407 0.999900i \(-0.504501\pi\)
−0.0141407 + 0.999900i \(0.504501\pi\)
\(312\) −2.60298e29 −0.0173196
\(313\) −9.20841e30 −0.588682 −0.294341 0.955701i \(-0.595100\pi\)
−0.294341 + 0.955701i \(0.595100\pi\)
\(314\) 8.15610e30 0.501028
\(315\) −1.90742e30 −0.112607
\(316\) 3.59720e30 0.204115
\(317\) −1.73757e31 −0.947764 −0.473882 0.880588i \(-0.657148\pi\)
−0.473882 + 0.880588i \(0.657148\pi\)
\(318\) −1.17225e31 −0.614726
\(319\) 2.82934e30 0.142660
\(320\) 1.15292e30 0.0559017
\(321\) −3.65794e31 −1.70578
\(322\) −8.24403e30 −0.369778
\(323\) 9.17145e30 0.395737
\(324\) −1.45859e31 −0.605508
\(325\) 1.88260e29 0.00751997
\(326\) −2.17006e30 −0.0834163
\(327\) −8.48349e29 −0.0313854
\(328\) 1.46108e30 0.0520296
\(329\) −6.98437e29 −0.0239430
\(330\) −1.82271e31 −0.601581
\(331\) 5.61759e31 1.78525 0.892627 0.450797i \(-0.148860\pi\)
0.892627 + 0.450797i \(0.148860\pi\)
\(332\) 3.02798e31 0.926674
\(333\) 1.83777e31 0.541675
\(334\) 3.48917e31 0.990584
\(335\) −2.51801e31 −0.688649
\(336\) −4.46291e30 −0.117592
\(337\) 4.19121e31 1.06406 0.532029 0.846726i \(-0.321430\pi\)
0.532029 + 0.846726i \(0.321430\pi\)
\(338\) 2.88622e31 0.706107
\(339\) −5.31270e30 −0.125262
\(340\) 6.65974e30 0.151346
\(341\) 9.75082e31 2.13605
\(342\) −1.36534e31 −0.288347
\(343\) 3.31496e31 0.674997
\(344\) −3.06454e31 −0.601707
\(345\) −4.45726e31 −0.843975
\(346\) 6.13098e31 1.11964
\(347\) −1.70880e31 −0.301004 −0.150502 0.988610i \(-0.548089\pi\)
−0.150502 + 0.988610i \(0.548089\pi\)
\(348\) 3.74554e30 0.0636463
\(349\) −8.15918e31 −1.33761 −0.668803 0.743439i \(-0.733193\pi\)
−0.668803 + 0.743439i \(0.733193\pi\)
\(350\) 3.22779e30 0.0510569
\(351\) −9.71019e29 −0.0148214
\(352\) −1.75228e31 −0.258120
\(353\) 5.64031e31 0.801899 0.400949 0.916100i \(-0.368680\pi\)
0.400949 + 0.916100i \(0.368680\pi\)
\(354\) −9.43005e31 −1.29412
\(355\) −2.48925e31 −0.329772
\(356\) 5.28046e31 0.675378
\(357\) −2.57796e31 −0.318363
\(358\) −8.08791e31 −0.964492
\(359\) 4.12655e31 0.475233 0.237616 0.971359i \(-0.423634\pi\)
0.237616 + 0.971359i \(0.423634\pi\)
\(360\) −9.91428e30 −0.110276
\(361\) −6.12579e31 −0.658145
\(362\) −9.37965e31 −0.973485
\(363\) 1.47091e32 1.47487
\(364\) −7.00588e29 −0.00678727
\(365\) 7.97839e31 0.746886
\(366\) −9.77054e30 −0.0883904
\(367\) 1.10522e32 0.966323 0.483161 0.875531i \(-0.339488\pi\)
0.483161 + 0.875531i \(0.339488\pi\)
\(368\) −4.28504e31 −0.362124
\(369\) −1.25642e31 −0.102637
\(370\) −3.10993e31 −0.245601
\(371\) −3.15509e31 −0.240901
\(372\) 1.29083e32 0.952979
\(373\) −1.60774e31 −0.114777 −0.0573885 0.998352i \(-0.518277\pi\)
−0.0573885 + 0.998352i \(0.518277\pi\)
\(374\) −1.01219e32 −0.698822
\(375\) 1.74515e31 0.116531
\(376\) −3.63030e30 −0.0234474
\(377\) 5.87975e29 0.00367360
\(378\) −1.66485e31 −0.100630
\(379\) −2.27403e32 −1.32986 −0.664930 0.746906i \(-0.731539\pi\)
−0.664930 + 0.746906i \(0.731539\pi\)
\(380\) 2.31047e31 0.130739
\(381\) −4.45409e32 −2.43892
\(382\) −2.46078e32 −1.30401
\(383\) 3.38623e32 1.73673 0.868363 0.495929i \(-0.165172\pi\)
0.868363 + 0.495929i \(0.165172\pi\)
\(384\) −2.31971e31 −0.115158
\(385\) −4.90579e31 −0.235749
\(386\) 2.45942e32 1.14417
\(387\) 2.63528e32 1.18697
\(388\) 6.89531e31 0.300717
\(389\) −3.10148e32 −1.30978 −0.654890 0.755724i \(-0.727285\pi\)
−0.654890 + 0.755724i \(0.727285\pi\)
\(390\) −3.78784e30 −0.0154912
\(391\) −2.47521e32 −0.980398
\(392\) 8.01457e31 0.307471
\(393\) 1.25578e32 0.466667
\(394\) 1.51294e31 0.0544653
\(395\) 5.23461e31 0.182566
\(396\) 1.50683e32 0.509185
\(397\) −3.84570e32 −1.25920 −0.629599 0.776920i \(-0.716781\pi\)
−0.629599 + 0.776920i \(0.716781\pi\)
\(398\) 5.03013e31 0.159603
\(399\) −8.94374e31 −0.275016
\(400\) 1.67772e31 0.0500000
\(401\) 3.65396e32 1.05550 0.527751 0.849399i \(-0.323035\pi\)
0.527751 + 0.849399i \(0.323035\pi\)
\(402\) 5.06630e32 1.41862
\(403\) 2.02635e31 0.0550049
\(404\) 1.23883e32 0.326020
\(405\) −2.12252e32 −0.541583
\(406\) 1.00810e31 0.0249419
\(407\) 4.72667e32 1.13403
\(408\) −1.33996e32 −0.311773
\(409\) −1.30167e31 −0.0293737 −0.0146868 0.999892i \(-0.504675\pi\)
−0.0146868 + 0.999892i \(0.504675\pi\)
\(410\) 2.12615e31 0.0465367
\(411\) 7.12729e31 0.151322
\(412\) −2.97036e32 −0.611777
\(413\) −2.53808e32 −0.507142
\(414\) 3.68482e32 0.714351
\(415\) 4.40629e32 0.828843
\(416\) −3.64148e30 −0.00664678
\(417\) −5.00077e32 −0.885802
\(418\) −3.51160e32 −0.603673
\(419\) 8.70006e32 1.45160 0.725800 0.687905i \(-0.241470\pi\)
0.725800 + 0.687905i \(0.241470\pi\)
\(420\) −6.49439e31 −0.105177
\(421\) −5.04763e32 −0.793527 −0.396763 0.917921i \(-0.629867\pi\)
−0.396763 + 0.917921i \(0.629867\pi\)
\(422\) 9.03355e32 1.37865
\(423\) 3.12179e31 0.0462540
\(424\) −1.63994e32 −0.235914
\(425\) 9.69120e31 0.135368
\(426\) 5.00843e32 0.679332
\(427\) −2.62972e31 −0.0346387
\(428\) −5.11733e32 −0.654630
\(429\) 5.75700e31 0.0715286
\(430\) −4.45949e32 −0.538183
\(431\) 8.61019e32 1.00936 0.504681 0.863306i \(-0.331610\pi\)
0.504681 + 0.863306i \(0.331610\pi\)
\(432\) −8.65345e31 −0.0985468
\(433\) −1.24809e33 −1.38085 −0.690427 0.723402i \(-0.742577\pi\)
−0.690427 + 0.723402i \(0.742577\pi\)
\(434\) 3.47425e32 0.373456
\(435\) 5.45047e31 0.0569270
\(436\) −1.18681e31 −0.0120448
\(437\) −8.58728e32 −0.846910
\(438\) −1.60527e33 −1.53859
\(439\) 3.66479e32 0.341384 0.170692 0.985324i \(-0.445400\pi\)
0.170692 + 0.985324i \(0.445400\pi\)
\(440\) −2.54991e32 −0.230869
\(441\) −6.89194e32 −0.606540
\(442\) −2.10346e31 −0.0179952
\(443\) 1.58140e33 1.31521 0.657606 0.753362i \(-0.271569\pi\)
0.657606 + 0.753362i \(0.271569\pi\)
\(444\) 6.25726e32 0.505938
\(445\) 7.68408e32 0.604076
\(446\) 9.15590e30 0.00699866
\(447\) −2.77892e33 −2.06554
\(448\) −6.24345e31 −0.0451283
\(449\) 2.03169e33 1.42817 0.714083 0.700061i \(-0.246844\pi\)
0.714083 + 0.700061i \(0.246844\pi\)
\(450\) −1.44272e32 −0.0986336
\(451\) −3.23146e32 −0.214878
\(452\) −7.43227e31 −0.0480719
\(453\) −2.07383e33 −1.30481
\(454\) 9.62448e32 0.589086
\(455\) −1.01949e31 −0.00607072
\(456\) −4.64873e32 −0.269323
\(457\) −1.28100e33 −0.722097 −0.361048 0.932547i \(-0.617581\pi\)
−0.361048 + 0.932547i \(0.617581\pi\)
\(458\) −1.38238e33 −0.758241
\(459\) −4.99858e32 −0.266801
\(460\) −6.23555e32 −0.323893
\(461\) −1.55893e33 −0.788071 −0.394036 0.919095i \(-0.628921\pi\)
−0.394036 + 0.919095i \(0.628921\pi\)
\(462\) 9.87058e32 0.485644
\(463\) 5.69235e32 0.272602 0.136301 0.990667i \(-0.456479\pi\)
0.136301 + 0.990667i \(0.456479\pi\)
\(464\) 5.23987e31 0.0244256
\(465\) 1.87841e33 0.852370
\(466\) −1.00551e33 −0.444185
\(467\) 2.08645e33 0.897321 0.448661 0.893702i \(-0.351901\pi\)
0.448661 + 0.893702i \(0.351901\pi\)
\(468\) 3.13140e31 0.0131119
\(469\) 1.36359e33 0.555932
\(470\) −5.28278e31 −0.0209720
\(471\) −2.38801e33 −0.923156
\(472\) −1.31923e33 −0.496644
\(473\) 6.77782e33 2.48500
\(474\) −1.05322e33 −0.376087
\(475\) 3.36218e32 0.116937
\(476\) −3.60647e32 −0.122179
\(477\) 1.41022e33 0.465381
\(478\) −1.12668e33 −0.362204
\(479\) 4.90036e33 1.53474 0.767368 0.641207i \(-0.221566\pi\)
0.767368 + 0.641207i \(0.221566\pi\)
\(480\) −3.37562e32 −0.103000
\(481\) 9.82265e31 0.0292022
\(482\) 1.45361e33 0.421074
\(483\) 2.41375e33 0.681324
\(484\) 2.05775e33 0.566012
\(485\) 1.00340e33 0.268969
\(486\) 3.20363e33 0.836929
\(487\) −1.04707e33 −0.266603 −0.133302 0.991076i \(-0.542558\pi\)
−0.133302 + 0.991076i \(0.542558\pi\)
\(488\) −1.36686e32 −0.0339217
\(489\) 6.35367e32 0.153696
\(490\) 1.16627e33 0.275011
\(491\) −2.78591e33 −0.640397 −0.320198 0.947351i \(-0.603750\pi\)
−0.320198 + 0.947351i \(0.603750\pi\)
\(492\) −4.27787e32 −0.0958658
\(493\) 3.02676e32 0.0661289
\(494\) −7.29758e31 −0.0155450
\(495\) 2.19273e33 0.455429
\(496\) 1.80583e33 0.365726
\(497\) 1.34801e33 0.266219
\(498\) −8.86557e33 −1.70742
\(499\) −2.70519e33 −0.508090 −0.254045 0.967192i \(-0.581761\pi\)
−0.254045 + 0.967192i \(0.581761\pi\)
\(500\) 2.44141e32 0.0447214
\(501\) −1.02159e34 −1.82517
\(502\) 5.94150e33 1.03538
\(503\) −6.75761e33 −1.14867 −0.574333 0.818622i \(-0.694738\pi\)
−0.574333 + 0.818622i \(0.694738\pi\)
\(504\) 5.36891e32 0.0890234
\(505\) 1.80273e33 0.291601
\(506\) 9.47718e33 1.49554
\(507\) −8.45051e33 −1.30102
\(508\) −6.23111e33 −0.935985
\(509\) −5.92051e33 −0.867734 −0.433867 0.900977i \(-0.642851\pi\)
−0.433867 + 0.900977i \(0.642851\pi\)
\(510\) −1.94989e33 −0.278858
\(511\) −4.32056e33 −0.602946
\(512\) −3.24519e32 −0.0441942
\(513\) −1.73416e33 −0.230475
\(514\) −1.02055e32 −0.0132371
\(515\) −4.32244e33 −0.547190
\(516\) 8.97261e33 1.10866
\(517\) 8.02911e32 0.0968357
\(518\) 1.68413e33 0.198268
\(519\) −1.79508e34 −2.06296
\(520\) −5.29905e31 −0.00594506
\(521\) 1.90773e33 0.208951 0.104476 0.994527i \(-0.466684\pi\)
0.104476 + 0.994527i \(0.466684\pi\)
\(522\) −4.50590e32 −0.0481837
\(523\) 7.03264e33 0.734255 0.367128 0.930171i \(-0.380341\pi\)
0.367128 + 0.930171i \(0.380341\pi\)
\(524\) 1.75679e33 0.179093
\(525\) −9.45058e32 −0.0940734
\(526\) 6.14209e33 0.597028
\(527\) 1.04312e34 0.990150
\(528\) 5.13048e33 0.475591
\(529\) 1.21298e34 1.09814
\(530\) −2.38642e33 −0.211008
\(531\) 1.13444e34 0.979716
\(532\) −1.25120e33 −0.105543
\(533\) −6.71540e31 −0.00553327
\(534\) −1.54606e34 −1.24440
\(535\) −7.44669e33 −0.585519
\(536\) 7.08757e33 0.544425
\(537\) 2.36805e34 1.77710
\(538\) −7.25162e33 −0.531688
\(539\) −1.77258e34 −1.26983
\(540\) −1.25924e33 −0.0881429
\(541\) −1.92351e34 −1.31561 −0.657806 0.753188i \(-0.728515\pi\)
−0.657806 + 0.753188i \(0.728515\pi\)
\(542\) −1.18693e34 −0.793291
\(543\) 2.74625e34 1.79367
\(544\) −1.87455e33 −0.119649
\(545\) −1.72703e32 −0.0107732
\(546\) 2.05124e32 0.0125057
\(547\) −2.85894e33 −0.170358 −0.0851791 0.996366i \(-0.527146\pi\)
−0.0851791 + 0.996366i \(0.527146\pi\)
\(548\) 9.97082e32 0.0580729
\(549\) 1.17540e33 0.0669163
\(550\) −3.71060e33 −0.206496
\(551\) 1.05008e33 0.0571250
\(552\) 1.25461e34 0.667221
\(553\) −2.83471e33 −0.147382
\(554\) 6.81547e33 0.346437
\(555\) 9.10551e33 0.452524
\(556\) −6.99590e33 −0.339945
\(557\) −3.74961e34 −1.78154 −0.890770 0.454454i \(-0.849834\pi\)
−0.890770 + 0.454454i \(0.849834\pi\)
\(558\) −1.55288e34 −0.721457
\(559\) 1.40852e33 0.0639906
\(560\) −9.08541e32 −0.0403640
\(561\) 2.96357e34 1.28760
\(562\) 1.16827e34 0.496408
\(563\) 3.46228e34 1.43882 0.719410 0.694585i \(-0.244412\pi\)
0.719410 + 0.694585i \(0.244412\pi\)
\(564\) 1.06291e33 0.0432023
\(565\) −1.08154e33 −0.0429968
\(566\) 5.50368e33 0.214017
\(567\) 1.14942e34 0.437209
\(568\) 7.00661e33 0.260708
\(569\) 3.03324e34 1.10409 0.552043 0.833816i \(-0.313848\pi\)
0.552043 + 0.833816i \(0.313848\pi\)
\(570\) −6.76479e33 −0.240890
\(571\) −2.05373e34 −0.715472 −0.357736 0.933823i \(-0.616451\pi\)
−0.357736 + 0.933823i \(0.616451\pi\)
\(572\) 8.05383e32 0.0274506
\(573\) 7.20488e34 2.40267
\(574\) −1.15138e33 −0.0375682
\(575\) −9.07392e33 −0.289699
\(576\) 2.79062e33 0.0871806
\(577\) −1.73765e34 −0.531209 −0.265604 0.964082i \(-0.585571\pi\)
−0.265604 + 0.964082i \(0.585571\pi\)
\(578\) 1.28083e34 0.383173
\(579\) −7.20090e34 −2.10816
\(580\) 7.62501e32 0.0218469
\(581\) −2.38615e34 −0.669108
\(582\) −2.01887e34 −0.554077
\(583\) 3.62703e34 0.974305
\(584\) −2.24572e34 −0.590465
\(585\) 4.55679e32 0.0117276
\(586\) −7.25332e33 −0.182733
\(587\) −4.89727e34 −1.20775 −0.603876 0.797078i \(-0.706378\pi\)
−0.603876 + 0.797078i \(0.706378\pi\)
\(588\) −2.34657e34 −0.566523
\(589\) 3.61891e34 0.855335
\(590\) −1.91973e34 −0.444212
\(591\) −4.42972e33 −0.100353
\(592\) 8.75368e33 0.194164
\(593\) 1.10421e34 0.239810 0.119905 0.992785i \(-0.461741\pi\)
0.119905 + 0.992785i \(0.461741\pi\)
\(594\) 1.91388e34 0.406990
\(595\) −5.24810e33 −0.109280
\(596\) −3.88761e34 −0.792693
\(597\) −1.47276e34 −0.294072
\(598\) 1.96949e33 0.0385113
\(599\) −1.03520e35 −1.98240 −0.991198 0.132391i \(-0.957735\pi\)
−0.991198 + 0.132391i \(0.957735\pi\)
\(600\) −4.91217e33 −0.0921261
\(601\) 9.90327e34 1.81906 0.909532 0.415635i \(-0.136441\pi\)
0.909532 + 0.415635i \(0.136441\pi\)
\(602\) 2.41496e34 0.434464
\(603\) −6.09479e34 −1.07397
\(604\) −2.90122e34 −0.500747
\(605\) 2.99442e34 0.506256
\(606\) −3.62714e34 −0.600699
\(607\) −6.59371e34 −1.06972 −0.534862 0.844940i \(-0.679636\pi\)
−0.534862 + 0.844940i \(0.679636\pi\)
\(608\) −6.50340e33 −0.103358
\(609\) −2.95161e33 −0.0459560
\(610\) −1.98905e33 −0.0303405
\(611\) 1.66856e32 0.00249359
\(612\) 1.61198e34 0.236029
\(613\) −7.31630e34 −1.04963 −0.524814 0.851217i \(-0.675865\pi\)
−0.524814 + 0.851217i \(0.675865\pi\)
\(614\) 5.27360e34 0.741315
\(615\) −6.22512e33 −0.0857450
\(616\) 1.38086e34 0.186376
\(617\) 9.91183e34 1.31096 0.655480 0.755213i \(-0.272466\pi\)
0.655480 + 0.755213i \(0.272466\pi\)
\(618\) 8.69685e34 1.12721
\(619\) 4.22193e34 0.536263 0.268131 0.963382i \(-0.413594\pi\)
0.268131 + 0.963382i \(0.413594\pi\)
\(620\) 2.62783e34 0.327115
\(621\) 4.68020e34 0.570978
\(622\) 1.67250e33 0.0199980
\(623\) −4.16118e34 −0.487659
\(624\) 1.06618e33 0.0122468
\(625\) 3.55271e33 0.0400000
\(626\) 3.77177e34 0.416261
\(627\) 1.02816e35 1.11228
\(628\) −3.34074e34 −0.354280
\(629\) 5.05648e34 0.525672
\(630\) 7.81279e33 0.0796249
\(631\) 8.43792e34 0.843080 0.421540 0.906810i \(-0.361490\pi\)
0.421540 + 0.906810i \(0.361490\pi\)
\(632\) −1.47341e34 −0.144331
\(633\) −2.64492e35 −2.54019
\(634\) 7.11707e34 0.670171
\(635\) −9.06746e34 −0.837170
\(636\) 4.80154e34 0.434677
\(637\) −3.68365e33 −0.0326991
\(638\) −1.15890e34 −0.100876
\(639\) −6.02517e34 −0.514291
\(640\) −4.72237e33 −0.0395285
\(641\) −1.28702e35 −1.05647 −0.528236 0.849097i \(-0.677147\pi\)
−0.528236 + 0.849097i \(0.677147\pi\)
\(642\) 1.49829e35 1.20617
\(643\) 8.92172e34 0.704387 0.352194 0.935927i \(-0.385436\pi\)
0.352194 + 0.935927i \(0.385436\pi\)
\(644\) 3.37675e34 0.261473
\(645\) 1.30569e35 0.991614
\(646\) −3.75663e34 −0.279828
\(647\) 1.63366e33 0.0119360 0.00596800 0.999982i \(-0.498100\pi\)
0.00596800 + 0.999982i \(0.498100\pi\)
\(648\) 5.97437e34 0.428159
\(649\) 2.91773e35 2.05110
\(650\) −7.71113e32 −0.00531742
\(651\) −1.01722e35 −0.688101
\(652\) 8.88855e33 0.0589842
\(653\) −1.93507e35 −1.25974 −0.629871 0.776700i \(-0.716892\pi\)
−0.629871 + 0.776700i \(0.716892\pi\)
\(654\) 3.47484e33 0.0221928
\(655\) 2.55647e34 0.160186
\(656\) −5.98458e33 −0.0367905
\(657\) 1.93115e35 1.16479
\(658\) 2.86080e33 0.0169303
\(659\) 1.10886e35 0.643889 0.321944 0.946759i \(-0.395664\pi\)
0.321944 + 0.946759i \(0.395664\pi\)
\(660\) 7.46583e34 0.425382
\(661\) −1.40626e35 −0.786224 −0.393112 0.919490i \(-0.628602\pi\)
−0.393112 + 0.919490i \(0.628602\pi\)
\(662\) −2.30096e35 −1.26236
\(663\) 6.15870e33 0.0331566
\(664\) −1.24026e35 −0.655258
\(665\) −1.82073e34 −0.0944006
\(666\) −7.52752e34 −0.383022
\(667\) −2.83397e34 −0.141521
\(668\) −1.42916e35 −0.700449
\(669\) −2.68074e33 −0.0128952
\(670\) 1.03138e35 0.486948
\(671\) 3.02308e34 0.140094
\(672\) 1.82801e34 0.0831500
\(673\) −1.02658e35 −0.458358 −0.229179 0.973384i \(-0.573604\pi\)
−0.229179 + 0.973384i \(0.573604\pi\)
\(674\) −1.71672e35 −0.752403
\(675\) −1.83244e34 −0.0788374
\(676\) −1.18220e35 −0.499293
\(677\) −3.50696e35 −1.45403 −0.727014 0.686622i \(-0.759093\pi\)
−0.727014 + 0.686622i \(0.759093\pi\)
\(678\) 2.17608e34 0.0885735
\(679\) −5.43374e34 −0.217133
\(680\) −2.72783e34 −0.107018
\(681\) −2.81793e35 −1.08540
\(682\) −3.99394e35 −1.51042
\(683\) 1.09953e35 0.408270 0.204135 0.978943i \(-0.434562\pi\)
0.204135 + 0.978943i \(0.434562\pi\)
\(684\) 5.59245e34 0.203892
\(685\) 1.45094e34 0.0519420
\(686\) −1.35781e35 −0.477295
\(687\) 4.04743e35 1.39708
\(688\) 1.25524e35 0.425471
\(689\) 7.53746e33 0.0250891
\(690\) 1.82570e35 0.596780
\(691\) 4.88341e35 1.56764 0.783822 0.620985i \(-0.213267\pi\)
0.783822 + 0.620985i \(0.213267\pi\)
\(692\) −2.51125e35 −0.791705
\(693\) −1.18744e35 −0.367659
\(694\) 6.99924e34 0.212842
\(695\) −1.01804e35 −0.304056
\(696\) −1.53417e34 −0.0450048
\(697\) −3.45694e34 −0.0996051
\(698\) 3.34200e35 0.945831
\(699\) 2.94402e35 0.818420
\(700\) −1.32210e34 −0.0361027
\(701\) −1.82400e35 −0.489270 −0.244635 0.969615i \(-0.578668\pi\)
−0.244635 + 0.969615i \(0.578668\pi\)
\(702\) 3.97729e33 0.0104803
\(703\) 1.75425e35 0.454098
\(704\) 7.17735e34 0.182518
\(705\) 1.54674e34 0.0386413
\(706\) −2.31027e35 −0.567028
\(707\) −9.76239e34 −0.235404
\(708\) 3.86255e35 0.915079
\(709\) 7.70973e35 1.79457 0.897287 0.441447i \(-0.145535\pi\)
0.897287 + 0.441447i \(0.145535\pi\)
\(710\) 1.01960e35 0.233184
\(711\) 1.26703e35 0.284718
\(712\) −2.16288e35 −0.477564
\(713\) −9.76678e35 −2.11901
\(714\) 1.05593e35 0.225117
\(715\) 1.17199e34 0.0245526
\(716\) 3.31281e35 0.681999
\(717\) 3.29880e35 0.667370
\(718\) −1.69023e35 −0.336040
\(719\) 3.81081e35 0.744570 0.372285 0.928118i \(-0.378574\pi\)
0.372285 + 0.928118i \(0.378574\pi\)
\(720\) 4.06089e34 0.0779767
\(721\) 2.34074e35 0.441736
\(722\) 2.50912e35 0.465379
\(723\) −4.25598e35 −0.775838
\(724\) 3.84190e35 0.688358
\(725\) 1.10959e34 0.0195405
\(726\) −6.02485e35 −1.04289
\(727\) 2.79252e35 0.475133 0.237567 0.971371i \(-0.423650\pi\)
0.237567 + 0.971371i \(0.423650\pi\)
\(728\) 2.86961e33 0.00479933
\(729\) −2.01364e35 −0.331046
\(730\) −3.26795e35 −0.528128
\(731\) 7.25075e35 1.15190
\(732\) 4.00201e34 0.0625015
\(733\) 9.44086e35 1.44948 0.724739 0.689023i \(-0.241960\pi\)
0.724739 + 0.689023i \(0.241960\pi\)
\(734\) −4.52697e35 −0.683293
\(735\) −3.41471e35 −0.506713
\(736\) 1.75515e35 0.256060
\(737\) −1.56755e36 −2.24843
\(738\) 5.14630e34 0.0725756
\(739\) −9.13826e35 −1.26709 −0.633546 0.773705i \(-0.718401\pi\)
−0.633546 + 0.773705i \(0.718401\pi\)
\(740\) 1.27383e35 0.173666
\(741\) 2.13664e34 0.0286421
\(742\) 1.29233e35 0.170342
\(743\) 3.11791e35 0.404114 0.202057 0.979374i \(-0.435237\pi\)
0.202057 + 0.979374i \(0.435237\pi\)
\(744\) −5.28725e35 −0.673858
\(745\) −5.65722e35 −0.709006
\(746\) 6.58530e34 0.0811597
\(747\) 1.06653e36 1.29261
\(748\) 4.14593e35 0.494142
\(749\) 4.03263e35 0.472678
\(750\) −7.14815e34 −0.0824001
\(751\) 6.99901e35 0.793482 0.396741 0.917930i \(-0.370141\pi\)
0.396741 + 0.917930i \(0.370141\pi\)
\(752\) 1.48697e34 0.0165798
\(753\) −1.73960e36 −1.90771
\(754\) −2.40834e33 −0.00259763
\(755\) −4.22183e35 −0.447882
\(756\) 6.81921e34 0.0711560
\(757\) 5.56975e35 0.571660 0.285830 0.958280i \(-0.407731\pi\)
0.285830 + 0.958280i \(0.407731\pi\)
\(758\) 9.31442e35 0.940353
\(759\) −2.77481e36 −2.75556
\(760\) −9.46369e34 −0.0924466
\(761\) 1.53099e36 1.47117 0.735586 0.677431i \(-0.236907\pi\)
0.735586 + 0.677431i \(0.236907\pi\)
\(762\) 1.82440e36 1.72457
\(763\) 9.35246e33 0.00869699
\(764\) 1.00794e36 0.922074
\(765\) 2.34573e35 0.211111
\(766\) −1.38700e36 −1.22805
\(767\) 6.06344e34 0.0528174
\(768\) 9.50152e34 0.0814288
\(769\) −1.03936e36 −0.876371 −0.438185 0.898885i \(-0.644379\pi\)
−0.438185 + 0.898885i \(0.644379\pi\)
\(770\) 2.00941e35 0.166700
\(771\) 2.98804e34 0.0243897
\(772\) −1.00738e36 −0.809052
\(773\) −6.50514e34 −0.0514059 −0.0257030 0.999670i \(-0.508182\pi\)
−0.0257030 + 0.999670i \(0.508182\pi\)
\(774\) −1.07941e36 −0.839315
\(775\) 3.82399e35 0.292580
\(776\) −2.82432e35 −0.212639
\(777\) −4.93093e35 −0.365314
\(778\) 1.27036e36 0.926154
\(779\) −1.19932e35 −0.0860432
\(780\) 1.55150e34 0.0109539
\(781\) −1.54965e36 −1.07670
\(782\) 1.01385e36 0.693246
\(783\) −5.72308e34 −0.0385131
\(784\) −3.28277e35 −0.217415
\(785\) −4.86142e35 −0.316878
\(786\) −5.14368e35 −0.329984
\(787\) −2.59764e36 −1.64019 −0.820097 0.572224i \(-0.806081\pi\)
−0.820097 + 0.572224i \(0.806081\pi\)
\(788\) −6.19701e34 −0.0385128
\(789\) −1.79833e36 −1.10004
\(790\) −2.14410e35 −0.129094
\(791\) 5.85688e34 0.0347104
\(792\) −6.17200e35 −0.360048
\(793\) 6.28237e33 0.00360752
\(794\) 1.57520e36 0.890388
\(795\) 6.98716e35 0.388787
\(796\) −2.06034e35 −0.112856
\(797\) 2.04990e36 1.10536 0.552680 0.833394i \(-0.313605\pi\)
0.552680 + 0.833394i \(0.313605\pi\)
\(798\) 3.66335e35 0.194466
\(799\) 8.58934e34 0.0448875
\(800\) −6.87195e34 −0.0353553
\(801\) 1.85991e36 0.942077
\(802\) −1.49666e36 −0.746352
\(803\) 4.96684e36 2.43857
\(804\) −2.07516e36 −1.00311
\(805\) 4.91382e35 0.233868
\(806\) −8.29993e34 −0.0388944
\(807\) 2.12319e36 0.979647
\(808\) −5.07424e35 −0.230531
\(809\) 3.73106e35 0.166907 0.0834537 0.996512i \(-0.473405\pi\)
0.0834537 + 0.996512i \(0.473405\pi\)
\(810\) 8.69386e35 0.382957
\(811\) 2.01608e36 0.874474 0.437237 0.899346i \(-0.355957\pi\)
0.437237 + 0.899346i \(0.355957\pi\)
\(812\) −4.12919e34 −0.0176366
\(813\) 3.47518e36 1.46166
\(814\) −1.93604e36 −0.801882
\(815\) 1.29345e35 0.0527571
\(816\) 5.48846e35 0.220457
\(817\) 2.51551e36 0.995063
\(818\) 5.33163e34 0.0207703
\(819\) −2.46765e34 −0.00946750
\(820\) −8.70871e34 −0.0329064
\(821\) −5.48657e35 −0.204179 −0.102090 0.994775i \(-0.532553\pi\)
−0.102090 + 0.994775i \(0.532553\pi\)
\(822\) −2.91934e35 −0.107001
\(823\) 1.67463e36 0.604535 0.302267 0.953223i \(-0.402256\pi\)
0.302267 + 0.953223i \(0.402256\pi\)
\(824\) 1.21666e36 0.432592
\(825\) 1.08642e36 0.380473
\(826\) 1.03960e36 0.358604
\(827\) −2.91183e35 −0.0989345 −0.0494673 0.998776i \(-0.515752\pi\)
−0.0494673 + 0.998776i \(0.515752\pi\)
\(828\) −1.50930e36 −0.505122
\(829\) −5.85863e35 −0.193136 −0.0965682 0.995326i \(-0.530787\pi\)
−0.0965682 + 0.995326i \(0.530787\pi\)
\(830\) −1.80482e36 −0.586080
\(831\) −1.99549e36 −0.638317
\(832\) 1.49155e34 0.00469998
\(833\) −1.89626e36 −0.588620
\(834\) 2.04832e36 0.626356
\(835\) −2.07971e36 −0.626500
\(836\) 1.43835e36 0.426861
\(837\) −1.97236e36 −0.576657
\(838\) −3.56355e36 −1.02644
\(839\) 3.47157e36 0.985147 0.492574 0.870271i \(-0.336056\pi\)
0.492574 + 0.870271i \(0.336056\pi\)
\(840\) 2.66010e35 0.0743716
\(841\) −3.59571e36 −0.990454
\(842\) 2.06751e36 0.561108
\(843\) −3.42055e36 −0.914643
\(844\) −3.70014e36 −0.974850
\(845\) −1.72032e36 −0.446581
\(846\) −1.27869e35 −0.0327065
\(847\) −1.62158e36 −0.408691
\(848\) 6.71718e35 0.166816
\(849\) −1.61141e36 −0.394331
\(850\) −3.96951e35 −0.0957196
\(851\) −4.73441e36 −1.12498
\(852\) −2.05145e36 −0.480360
\(853\) 3.68459e35 0.0850210 0.0425105 0.999096i \(-0.486464\pi\)
0.0425105 + 0.999096i \(0.486464\pi\)
\(854\) 1.07713e35 0.0244933
\(855\) 8.13808e35 0.182367
\(856\) 2.09606e36 0.462893
\(857\) 2.02730e36 0.441222 0.220611 0.975362i \(-0.429195\pi\)
0.220611 + 0.975362i \(0.429195\pi\)
\(858\) −2.35807e35 −0.0505784
\(859\) 7.42092e36 1.56871 0.784356 0.620311i \(-0.212994\pi\)
0.784356 + 0.620311i \(0.212994\pi\)
\(860\) 1.82661e36 0.380553
\(861\) 3.37111e35 0.0692202
\(862\) −3.52673e36 −0.713726
\(863\) −9.61540e36 −1.91793 −0.958965 0.283526i \(-0.908496\pi\)
−0.958965 + 0.283526i \(0.908496\pi\)
\(864\) 3.54445e35 0.0696831
\(865\) −3.65435e36 −0.708123
\(866\) 5.11218e36 0.976411
\(867\) −3.75013e36 −0.706005
\(868\) −1.42305e36 −0.264073
\(869\) 3.25873e36 0.596076
\(870\) −2.23251e35 −0.0402535
\(871\) −3.25759e35 −0.0578987
\(872\) 4.86117e34 0.00851696
\(873\) 2.42871e36 0.419466
\(874\) 3.51735e36 0.598856
\(875\) −1.92391e35 −0.0322912
\(876\) 6.57519e36 1.08795
\(877\) −4.33793e36 −0.707600 −0.353800 0.935321i \(-0.615111\pi\)
−0.353800 + 0.935321i \(0.615111\pi\)
\(878\) −1.50110e36 −0.241395
\(879\) 2.12369e36 0.336690
\(880\) 1.04444e36 0.163249
\(881\) 3.45165e36 0.531898 0.265949 0.963987i \(-0.414315\pi\)
0.265949 + 0.963987i \(0.414315\pi\)
\(882\) 2.82294e36 0.428888
\(883\) −1.53217e36 −0.229509 −0.114754 0.993394i \(-0.536608\pi\)
−0.114754 + 0.993394i \(0.536608\pi\)
\(884\) 8.61579e34 0.0127245
\(885\) 5.62075e36 0.818471
\(886\) −6.47742e36 −0.929995
\(887\) −1.76030e35 −0.0249196 −0.0124598 0.999922i \(-0.503966\pi\)
−0.0124598 + 0.999922i \(0.503966\pi\)
\(888\) −2.56297e36 −0.357752
\(889\) 4.91032e36 0.675831
\(890\) −3.14740e36 −0.427146
\(891\) −1.32135e37 −1.76826
\(892\) −3.75026e34 −0.00494880
\(893\) 2.97991e35 0.0387757
\(894\) 1.13825e37 1.46055
\(895\) 4.82077e36 0.609998
\(896\) 2.55732e35 0.0319105
\(897\) −5.76642e35 −0.0709579
\(898\) −8.32181e36 −1.00987
\(899\) 1.19431e36 0.142929
\(900\) 5.90937e35 0.0697445
\(901\) 3.88011e36 0.451632
\(902\) 1.32361e36 0.151942
\(903\) −7.07072e36 −0.800510
\(904\) 3.04426e35 0.0339919
\(905\) 5.59071e36 0.615686
\(906\) 8.49443e36 0.922638
\(907\) 4.42056e36 0.473572 0.236786 0.971562i \(-0.423906\pi\)
0.236786 + 0.971562i \(0.423906\pi\)
\(908\) −3.94219e36 −0.416547
\(909\) 4.36348e36 0.454762
\(910\) 4.17583e34 0.00429265
\(911\) −4.66761e36 −0.473277 −0.236638 0.971598i \(-0.576046\pi\)
−0.236638 + 0.971598i \(0.576046\pi\)
\(912\) 1.90412e36 0.190440
\(913\) 2.74308e37 2.70616
\(914\) 5.24696e36 0.510600
\(915\) 5.82370e35 0.0559030
\(916\) 5.66221e36 0.536158
\(917\) −1.38441e36 −0.129315
\(918\) 2.04742e36 0.188657
\(919\) −1.51994e36 −0.138160 −0.0690801 0.997611i \(-0.522006\pi\)
−0.0690801 + 0.997611i \(0.522006\pi\)
\(920\) 2.55408e36 0.229027
\(921\) −1.54405e37 −1.36589
\(922\) 6.38538e36 0.557251
\(923\) −3.22038e35 −0.0277259
\(924\) −4.04299e36 −0.343402
\(925\) 1.85366e36 0.155331
\(926\) −2.33159e36 −0.192759
\(927\) −1.04624e37 −0.853361
\(928\) −2.14625e35 −0.0172715
\(929\) −1.16057e37 −0.921460 −0.460730 0.887540i \(-0.652412\pi\)
−0.460730 + 0.887540i \(0.652412\pi\)
\(930\) −7.69396e36 −0.602717
\(931\) −6.57872e36 −0.508476
\(932\) 4.11858e36 0.314086
\(933\) −4.89689e35 −0.0368468
\(934\) −8.54612e36 −0.634502
\(935\) 6.03312e36 0.441974
\(936\) −1.28262e35 −0.00927152
\(937\) 1.23945e36 0.0884062 0.0442031 0.999023i \(-0.485925\pi\)
0.0442031 + 0.999023i \(0.485925\pi\)
\(938\) −5.58525e36 −0.393104
\(939\) −1.10433e37 −0.766970
\(940\) 2.16383e35 0.0148294
\(941\) 1.07673e37 0.728176 0.364088 0.931365i \(-0.381381\pi\)
0.364088 + 0.931365i \(0.381381\pi\)
\(942\) 9.78129e36 0.652770
\(943\) 3.23675e36 0.213163
\(944\) 5.40357e36 0.351181
\(945\) 9.92326e35 0.0636439
\(946\) −2.77620e37 −1.75716
\(947\) −2.09189e37 −1.30667 −0.653333 0.757071i \(-0.726630\pi\)
−0.653333 + 0.757071i \(0.726630\pi\)
\(948\) 4.31398e36 0.265934
\(949\) 1.03217e36 0.0627951
\(950\) −1.37715e36 −0.0826867
\(951\) −2.08379e37 −1.23480
\(952\) 1.47721e36 0.0863933
\(953\) 7.62955e36 0.440390 0.220195 0.975456i \(-0.429331\pi\)
0.220195 + 0.975456i \(0.429331\pi\)
\(954\) −5.77628e36 −0.329074
\(955\) 1.46674e37 0.824728
\(956\) 4.61490e36 0.256117
\(957\) 3.39312e36 0.185866
\(958\) −2.00719e37 −1.08522
\(959\) −7.85734e35 −0.0419317
\(960\) 1.38265e36 0.0728321
\(961\) 2.19270e37 1.14008
\(962\) −4.02336e35 −0.0206491
\(963\) −1.80245e37 −0.913137
\(964\) −5.95397e36 −0.297744
\(965\) −1.46593e37 −0.723639
\(966\) −9.88674e36 −0.481769
\(967\) 2.91319e37 1.40132 0.700661 0.713495i \(-0.252889\pi\)
0.700661 + 0.713495i \(0.252889\pi\)
\(968\) −8.42854e36 −0.400231
\(969\) 1.09990e37 0.515590
\(970\) −4.10993e36 −0.190190
\(971\) 2.71465e37 1.24015 0.620073 0.784544i \(-0.287103\pi\)
0.620073 + 0.784544i \(0.287103\pi\)
\(972\) −1.31221e37 −0.591798
\(973\) 5.51300e36 0.245458
\(974\) 4.28882e36 0.188517
\(975\) 2.25773e35 0.00979747
\(976\) 5.59867e35 0.0239862
\(977\) 1.23101e37 0.520689 0.260344 0.965516i \(-0.416164\pi\)
0.260344 + 0.965516i \(0.416164\pi\)
\(978\) −2.60246e36 −0.108680
\(979\) 4.78362e37 1.97230
\(980\) −4.77706e36 −0.194462
\(981\) −4.18025e35 −0.0168012
\(982\) 1.14111e37 0.452829
\(983\) −3.87996e37 −1.52023 −0.760114 0.649790i \(-0.774857\pi\)
−0.760114 + 0.649790i \(0.774857\pi\)
\(984\) 1.75222e36 0.0677874
\(985\) −9.01784e35 −0.0344469
\(986\) −1.23976e36 −0.0467602
\(987\) −8.37608e35 −0.0311944
\(988\) 2.98909e35 0.0109920
\(989\) −6.78891e37 −2.46517
\(990\) −8.98144e36 −0.322037
\(991\) 2.23853e35 0.00792577 0.00396288 0.999992i \(-0.498739\pi\)
0.00396288 + 0.999992i \(0.498739\pi\)
\(992\) −7.39667e36 −0.258607
\(993\) 6.73695e37 2.32594
\(994\) −5.52145e36 −0.188245
\(995\) −2.99819e36 −0.100942
\(996\) 3.63134e37 1.20733
\(997\) −2.76187e37 −0.906806 −0.453403 0.891306i \(-0.649790\pi\)
−0.453403 + 0.891306i \(0.649790\pi\)
\(998\) 1.10805e37 0.359274
\(999\) −9.56094e36 −0.306148
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 10.26.a.b.1.2 2
5.2 odd 4 50.26.b.f.49.1 4
5.3 odd 4 50.26.b.f.49.4 4
5.4 even 2 50.26.a.f.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.26.a.b.1.2 2 1.1 even 1 trivial
50.26.a.f.1.1 2 5.4 even 2
50.26.b.f.49.1 4 5.2 odd 4
50.26.b.f.49.4 4 5.3 odd 4