Properties

Label 8.12.b.a.5.5
Level $8$
Weight $12$
Character 8.5
Analytic conductor $6.147$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8,12,Mod(5,8)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8.5");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 8.b (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(6.14674544448\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} - 48 x^{8} + 8836 x^{7} - 92554 x^{6} - 2200342 x^{5} - 88894588 x^{4} + 2040335460 x^{3} + 7439251985 x^{2} - 747501940689 x + 34431558027300 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{45}\cdot 3^{2}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.5
Root \(7.36621 - 21.0240i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.12.b.a.5.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(16.7324 - 42.0479i) q^{2} +284.352i q^{3} +(-1488.05 - 1407.13i) q^{4} -10467.0i q^{5} +(11956.4 + 4757.90i) q^{6} -70503.2 q^{7} +(-84065.4 + 39024.9i) q^{8} +96290.8 q^{9} +O(q^{10})\) \(q+(16.7324 - 42.0479i) q^{2} +284.352i q^{3} +(-1488.05 - 1407.13i) q^{4} -10467.0i q^{5} +(11956.4 + 4757.90i) q^{6} -70503.2 q^{7} +(-84065.4 + 39024.9i) q^{8} +96290.8 q^{9} +(-440117. - 175139. i) q^{10} -177453. i q^{11} +(400120. - 423131. i) q^{12} -1.12148e6i q^{13} +(-1.17969e6 + 2.96451e6i) q^{14} +2.97633e6 q^{15} +(234297. + 4.18775e6i) q^{16} +6.79913e6 q^{17} +(1.61118e6 - 4.04882e6i) q^{18} -3.43350e6i q^{19} +(-1.47284e7 + 1.55755e7i) q^{20} -2.00477e7i q^{21} +(-7.46151e6 - 2.96921e6i) q^{22} +2.44952e7 q^{23} +(-1.10968e7 - 2.39042e7i) q^{24} -6.07308e7 q^{25} +(-4.71557e7 - 1.87650e7i) q^{26} +7.77527e7i q^{27} +(1.04912e8 + 9.92068e7i) q^{28} -6.35956e7i q^{29} +(4.98012e7 - 1.25148e8i) q^{30} -8.31656e7 q^{31} +(1.80007e8 + 6.02196e7i) q^{32} +5.04591e7 q^{33} +(1.13766e8 - 2.85889e8i) q^{34} +7.37960e8i q^{35} +(-1.43286e8 - 1.35493e8i) q^{36} -4.05150e8i q^{37} +(-1.44371e8 - 5.74507e7i) q^{38} +3.18895e8 q^{39} +(4.08475e8 + 8.79916e8i) q^{40} -1.21207e9 q^{41} +(-8.42965e8 - 3.35447e8i) q^{42} -8.44416e8i q^{43} +(-2.49698e8 + 2.64059e8i) q^{44} -1.00788e9i q^{45} +(4.09865e8 - 1.02997e9i) q^{46} +1.31838e9 q^{47} +(-1.19080e9 + 6.66229e7i) q^{48} +2.99337e9 q^{49} +(-1.01617e9 + 2.55360e9i) q^{50} +1.93335e9i q^{51} +(-1.57806e9 + 1.66882e9i) q^{52} -1.71718e8i q^{53} +(3.26934e9 + 1.30099e9i) q^{54} -1.85740e9 q^{55} +(5.92688e9 - 2.75138e9i) q^{56} +9.76323e8 q^{57} +(-2.67406e9 - 1.06411e9i) q^{58} -8.98489e9i q^{59} +(-4.42893e9 - 4.18807e9i) q^{60} +1.06321e10i q^{61} +(-1.39156e9 + 3.49694e9i) q^{62} -6.78880e9 q^{63} +(5.54405e9 - 6.56128e9i) q^{64} -1.17385e10 q^{65} +(8.44302e8 - 2.12170e9i) q^{66} +4.61172e9i q^{67} +(-1.01175e10 - 9.56724e9i) q^{68} +6.96528e9i q^{69} +(3.10297e10 + 1.23478e10i) q^{70} -3.76291e9 q^{71} +(-8.09472e9 + 3.75773e9i) q^{72} +2.35994e10 q^{73} +(-1.70357e10 - 6.77914e9i) q^{74} -1.72690e10i q^{75} +(-4.83137e9 + 5.10923e9i) q^{76} +1.25110e10i q^{77} +(5.33588e9 - 1.34088e10i) q^{78} +1.77494e10 q^{79} +(4.38334e10 - 2.45240e9i) q^{80} -5.05153e9 q^{81} +(-2.02808e10 + 5.09649e10i) q^{82} -4.42674e9i q^{83} +(-2.82097e10 + 2.98321e10i) q^{84} -7.11668e10i q^{85} +(-3.55059e10 - 1.41291e10i) q^{86} +1.80836e10 q^{87} +(6.92507e9 + 1.49176e10i) q^{88} -7.93798e9 q^{89} +(-4.23792e10 - 1.68643e10i) q^{90} +7.90677e10i q^{91} +(-3.64502e10 - 3.44679e10i) q^{92} -2.36483e10i q^{93} +(2.20597e10 - 5.54351e10i) q^{94} -3.59386e10 q^{95} +(-1.71236e10 + 5.11853e10i) q^{96} +1.20863e10 q^{97} +(5.00863e10 - 1.25865e11i) q^{98} -1.70870e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18} + 8296432 q^{20} - 24201892 q^{22} - 45357808 q^{23} + 10668944 q^{24} - 41502654 q^{25} - 101931080 q^{26} - 95722144 q^{28} + 261362768 q^{30} + 442035392 q^{31} + 343908512 q^{32} - 54732216 q^{33} - 187103796 q^{34} - 431195700 q^{36} + 375100844 q^{38} - 431459312 q^{39} + 1519138784 q^{40} - 654907964 q^{41} - 3697737056 q^{42} - 4127012952 q^{44} + 6028867440 q^{46} - 560226528 q^{47} + 9357606048 q^{48} + 1143661722 q^{49} - 9626584226 q^{50} - 11595427248 q^{52} + 20050494008 q^{54} + 5632783984 q^{55} + 18698733760 q^{56} - 783862360 q^{57} - 22828679464 q^{58} - 43681325472 q^{60} + 40774631744 q^{62} - 14483624624 q^{63} + 55266728512 q^{64} - 80291360 q^{65} - 83128448712 q^{66} - 83303223768 q^{68} + 100120831168 q^{70} - 11769460176 q^{71} + 112862051672 q^{72} + 32304890372 q^{73} - 102103996184 q^{74} - 97501928568 q^{76} + 144445560944 q^{78} + 57291670496 q^{79} + 128322038976 q^{80} - 23172996094 q^{81} - 123309929604 q^{82} - 199990865984 q^{84} + 130201908124 q^{86} - 73844404272 q^{87} + 169216119632 q^{88} - 108276011804 q^{89} - 228506434984 q^{90} - 141139403232 q^{92} + 145336130016 q^{94} + 70146835376 q^{95} + 109508068928 q^{96} + 60995282900 q^{97} - 6194726778 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 16.7324 42.0479i 0.369738 0.929136i
\(3\) 284.352i 0.675600i 0.941218 + 0.337800i \(0.109683\pi\)
−0.941218 + 0.337800i \(0.890317\pi\)
\(4\) −1488.05 1407.13i −0.726588 0.687073i
\(5\) 10467.0i 1.49792i −0.662615 0.748961i \(-0.730553\pi\)
0.662615 0.748961i \(-0.269447\pi\)
\(6\) 11956.4 + 4757.90i 0.627725 + 0.249795i
\(7\) −70503.2 −1.58551 −0.792756 0.609539i \(-0.791354\pi\)
−0.792756 + 0.609539i \(0.791354\pi\)
\(8\) −84065.4 + 39024.9i −0.907032 + 0.421063i
\(9\) 96290.8 0.543564
\(10\) −440117. 175139.i −1.39177 0.553838i
\(11\) 177453.i 0.332218i −0.986107 0.166109i \(-0.946880\pi\)
0.986107 0.166109i \(-0.0531203\pi\)
\(12\) 400120. 423131.i 0.464187 0.490883i
\(13\) 1.12148e6i 0.837726i −0.908050 0.418863i \(-0.862429\pi\)
0.908050 0.418863i \(-0.137571\pi\)
\(14\) −1.17969e6 + 2.96451e6i −0.586223 + 1.47316i
\(15\) 2.97633e6 1.01200
\(16\) 234297. + 4.18775e6i 0.0558607 + 0.998439i
\(17\) 6.79913e6 1.16141 0.580704 0.814115i \(-0.302778\pi\)
0.580704 + 0.814115i \(0.302778\pi\)
\(18\) 1.61118e6 4.04882e6i 0.200976 0.505045i
\(19\) 3.43350e6i 0.318121i −0.987269 0.159060i \(-0.949154\pi\)
0.987269 0.159060i \(-0.0508465\pi\)
\(20\) −1.47284e7 + 1.55755e7i −1.02918 + 1.08837i
\(21\) 2.00477e7i 1.07117i
\(22\) −7.46151e6 2.96921e6i −0.308675 0.122833i
\(23\) 2.44952e7 0.793558 0.396779 0.917914i \(-0.370128\pi\)
0.396779 + 0.917914i \(0.370128\pi\)
\(24\) −1.10968e7 2.39042e7i −0.284470 0.612791i
\(25\) −6.07308e7 −1.24377
\(26\) −4.71557e7 1.87650e7i −0.778361 0.309739i
\(27\) 7.77527e7i 1.04283i
\(28\) 1.04912e8 + 9.92068e7i 1.15201 + 1.08936i
\(29\) 6.35956e7i 0.575756i −0.957667 0.287878i \(-0.907050\pi\)
0.957667 0.287878i \(-0.0929497\pi\)
\(30\) 4.98012e7 1.25148e8i 0.374173 0.940282i
\(31\) −8.31656e7 −0.521740 −0.260870 0.965374i \(-0.584009\pi\)
−0.260870 + 0.965374i \(0.584009\pi\)
\(32\) 1.80007e8 + 6.02196e7i 0.948339 + 0.317258i
\(33\) 5.04591e7 0.224446
\(34\) 1.13766e8 2.85889e8i 0.429416 1.07911i
\(35\) 7.37960e8i 2.37497i
\(36\) −1.43286e8 1.35493e8i −0.394947 0.373468i
\(37\) 4.05150e8i 0.960520i −0.877126 0.480260i \(-0.840542\pi\)
0.877126 0.480260i \(-0.159458\pi\)
\(38\) −1.44371e8 5.74507e7i −0.295578 0.117621i
\(39\) 3.18895e8 0.565968
\(40\) 4.08475e8 + 8.79916e8i 0.630718 + 1.35866i
\(41\) −1.21207e9 −1.63386 −0.816931 0.576735i \(-0.804327\pi\)
−0.816931 + 0.576735i \(0.804327\pi\)
\(42\) −8.42965e8 3.35447e8i −0.995265 0.396053i
\(43\) 8.44416e8i 0.875951i −0.898987 0.437975i \(-0.855696\pi\)
0.898987 0.437975i \(-0.144304\pi\)
\(44\) −2.49698e8 + 2.64059e8i −0.228258 + 0.241385i
\(45\) 1.00788e9i 0.814216i
\(46\) 4.09865e8 1.02997e9i 0.293408 0.737324i
\(47\) 1.31838e9 0.838498 0.419249 0.907871i \(-0.362293\pi\)
0.419249 + 0.907871i \(0.362293\pi\)
\(48\) −1.19080e9 + 6.66229e7i −0.674545 + 0.0377395i
\(49\) 2.99337e9 1.51385
\(50\) −1.01617e9 + 2.55360e9i −0.459868 + 1.15563i
\(51\) 1.93335e9i 0.784647i
\(52\) −1.57806e9 + 1.66882e9i −0.575579 + 0.608682i
\(53\) 1.71718e8i 0.0564025i −0.999602 0.0282013i \(-0.991022\pi\)
0.999602 0.0282013i \(-0.00897793\pi\)
\(54\) 3.26934e9 + 1.30099e9i 0.968933 + 0.385574i
\(55\) −1.85740e9 −0.497636
\(56\) 5.92688e9 2.75138e9i 1.43811 0.667600i
\(57\) 9.76323e8 0.214923
\(58\) −2.67406e9 1.06411e9i −0.534955 0.212879i
\(59\) 8.98489e9i 1.63616i −0.575102 0.818082i \(-0.695038\pi\)
0.575102 0.818082i \(-0.304962\pi\)
\(60\) −4.42893e9 4.18807e9i −0.735304 0.695315i
\(61\) 1.06321e10i 1.61178i 0.592068 + 0.805888i \(0.298312\pi\)
−0.592068 + 0.805888i \(0.701688\pi\)
\(62\) −1.39156e9 + 3.49694e9i −0.192907 + 0.484768i
\(63\) −6.78880e9 −0.861827
\(64\) 5.54405e9 6.56128e9i 0.645413 0.763834i
\(65\) −1.17385e10 −1.25485
\(66\) 8.44302e8 2.12170e9i 0.0829863 0.208541i
\(67\) 4.61172e9i 0.417303i 0.977990 + 0.208652i \(0.0669075\pi\)
−0.977990 + 0.208652i \(0.933093\pi\)
\(68\) −1.01175e10 9.56724e9i −0.843865 0.797972i
\(69\) 6.96528e9i 0.536128i
\(70\) 3.10297e10 + 1.23478e10i 2.20667 + 0.878116i
\(71\) −3.76291e9 −0.247516 −0.123758 0.992312i \(-0.539495\pi\)
−0.123758 + 0.992312i \(0.539495\pi\)
\(72\) −8.09472e9 + 3.75773e9i −0.493030 + 0.228874i
\(73\) 2.35994e10 1.33237 0.666186 0.745786i \(-0.267926\pi\)
0.666186 + 0.745786i \(0.267926\pi\)
\(74\) −1.70357e10 6.77914e9i −0.892454 0.355140i
\(75\) 1.72690e10i 0.840290i
\(76\) −4.83137e9 + 5.10923e9i −0.218572 + 0.231143i
\(77\) 1.25110e10i 0.526735i
\(78\) 5.33588e9 1.34088e10i 0.209260 0.525861i
\(79\) 1.77494e10 0.648986 0.324493 0.945888i \(-0.394806\pi\)
0.324493 + 0.945888i \(0.394806\pi\)
\(80\) 4.38334e10 2.45240e9i 1.49558 0.0836750i
\(81\) −5.05153e9 −0.160974
\(82\) −2.02808e10 + 5.09649e10i −0.604101 + 1.51808i
\(83\) 4.42674e9i 0.123354i −0.998096 0.0616772i \(-0.980355\pi\)
0.998096 0.0616772i \(-0.0196449\pi\)
\(84\) −2.82097e10 + 2.98321e10i −0.735974 + 0.778301i
\(85\) 7.11668e10i 1.73970i
\(86\) −3.55059e10 1.41291e10i −0.813878 0.323872i
\(87\) 1.80836e10 0.388981
\(88\) 6.92507e9 + 1.49176e10i 0.139884 + 0.301332i
\(89\) −7.93798e9 −0.150683 −0.0753416 0.997158i \(-0.524005\pi\)
−0.0753416 + 0.997158i \(0.524005\pi\)
\(90\) −4.23792e10 1.68643e10i −0.756518 0.301046i
\(91\) 7.90677e10i 1.32822i
\(92\) −3.64502e10 3.44679e10i −0.576590 0.545233i
\(93\) 2.36483e10i 0.352488i
\(94\) 2.20597e10 5.54351e10i 0.310024 0.779079i
\(95\) −3.59386e10 −0.476520
\(96\) −1.71236e10 + 5.11853e10i −0.214340 + 0.640698i
\(97\) 1.20863e10 0.142906 0.0714528 0.997444i \(-0.477236\pi\)
0.0714528 + 0.997444i \(0.477236\pi\)
\(98\) 5.00863e10 1.25865e11i 0.559726 1.40657i
\(99\) 1.70870e10i 0.180582i
\(100\) 9.03707e10 + 8.54559e10i 0.903707 + 0.854559i
\(101\) 3.06086e10i 0.289785i −0.989447 0.144892i \(-0.953716\pi\)
0.989447 0.144892i \(-0.0462836\pi\)
\(102\) 8.12933e10 + 3.23496e10i 0.729044 + 0.290114i
\(103\) 5.88636e10 0.500313 0.250157 0.968205i \(-0.419518\pi\)
0.250157 + 0.968205i \(0.419518\pi\)
\(104\) 4.37655e10 + 9.42774e10i 0.352735 + 0.759844i
\(105\) −2.09841e11 −1.60453
\(106\) −7.22038e9 2.87326e9i −0.0524056 0.0208541i
\(107\) 2.63056e11i 1.81316i 0.422032 + 0.906581i \(0.361317\pi\)
−0.422032 + 0.906581i \(0.638683\pi\)
\(108\) 1.09408e11 1.15700e11i 0.716502 0.757710i
\(109\) 1.30128e11i 0.810072i 0.914301 + 0.405036i \(0.132741\pi\)
−0.914301 + 0.405036i \(0.867259\pi\)
\(110\) −3.10789e10 + 7.81000e10i −0.183995 + 0.462371i
\(111\) 1.15205e11 0.648928
\(112\) −1.65187e10 2.95250e11i −0.0885679 1.58304i
\(113\) 9.59652e10 0.489985 0.244992 0.969525i \(-0.421215\pi\)
0.244992 + 0.969525i \(0.421215\pi\)
\(114\) 1.63362e10 4.10524e10i 0.0794650 0.199692i
\(115\) 2.56393e11i 1.18869i
\(116\) −8.94870e10 + 9.46336e10i −0.395586 + 0.418337i
\(117\) 1.07988e11i 0.455358i
\(118\) −3.77796e11 1.50339e11i −1.52022 0.604951i
\(119\) −4.79360e11 −1.84142
\(120\) −2.50206e11 + 1.16151e11i −0.917912 + 0.426114i
\(121\) 2.53822e11 0.889631
\(122\) 4.47057e11 + 1.77901e11i 1.49756 + 0.595934i
\(123\) 3.44654e11i 1.10384i
\(124\) 1.23755e11 + 1.17025e11i 0.379090 + 0.358474i
\(125\) 1.24586e11i 0.365145i
\(126\) −1.13593e11 + 2.85455e11i −0.318650 + 0.800755i
\(127\) 6.41966e10 0.172421 0.0862107 0.996277i \(-0.472524\pi\)
0.0862107 + 0.996277i \(0.472524\pi\)
\(128\) −1.83123e11 3.42902e11i −0.471073 0.882094i
\(129\) 2.40112e11 0.591793
\(130\) −1.96414e11 + 4.93581e11i −0.463964 + 1.16592i
\(131\) 5.61342e9i 0.0127126i −0.999980 0.00635631i \(-0.997977\pi\)
0.999980 0.00635631i \(-0.00202329\pi\)
\(132\) −7.50858e10 7.10023e10i −0.163080 0.154211i
\(133\) 2.42073e11i 0.504384i
\(134\) 1.93913e11 + 7.71652e10i 0.387731 + 0.154293i
\(135\) 8.13840e11 1.56208
\(136\) −5.71572e11 + 2.65335e11i −1.05343 + 0.489025i
\(137\) −1.10990e10 −0.0196482 −0.00982408 0.999952i \(-0.503127\pi\)
−0.00982408 + 0.999952i \(0.503127\pi\)
\(138\) 2.92875e11 + 1.16546e11i 0.498136 + 0.198227i
\(139\) 8.85833e11i 1.44801i −0.689797 0.724003i \(-0.742300\pi\)
0.689797 0.724003i \(-0.257700\pi\)
\(140\) 1.03840e12 1.09812e12i 1.63178 1.72563i
\(141\) 3.74884e11i 0.566490i
\(142\) −6.29626e10 + 1.58223e11i −0.0915159 + 0.229976i
\(143\) −1.99009e11 −0.278307
\(144\) 2.25606e10 + 4.03242e11i 0.0303639 + 0.542715i
\(145\) −6.65658e11 −0.862437
\(146\) 3.94875e11 9.92306e11i 0.492628 1.23796i
\(147\) 8.51172e11i 1.02276i
\(148\) −5.70097e11 + 6.02885e11i −0.659948 + 0.697903i
\(149\) 6.27189e11i 0.699639i 0.936817 + 0.349819i \(0.113757\pi\)
−0.936817 + 0.349819i \(0.886243\pi\)
\(150\) −7.26123e11 2.88951e11i −0.780744 0.310687i
\(151\) −1.68335e12 −1.74502 −0.872512 0.488592i \(-0.837511\pi\)
−0.872512 + 0.488592i \(0.837511\pi\)
\(152\) 1.33992e11 + 2.88638e11i 0.133949 + 0.288546i
\(153\) 6.54694e11 0.631299
\(154\) 5.26060e11 + 2.09339e11i 0.489409 + 0.194754i
\(155\) 8.70498e11i 0.781526i
\(156\) −4.74532e11 4.48725e11i −0.411226 0.388861i
\(157\) 2.01565e12i 1.68642i −0.537581 0.843212i \(-0.680662\pi\)
0.537581 0.843212i \(-0.319338\pi\)
\(158\) 2.96991e11 7.46326e11i 0.239954 0.602996i
\(159\) 4.88284e10 0.0381056
\(160\) 6.30321e11 1.88414e12i 0.475228 1.42054i
\(161\) −1.72699e12 −1.25820
\(162\) −8.45243e10 + 2.12406e11i −0.0595181 + 0.149567i
\(163\) 1.19891e12i 0.816121i 0.912955 + 0.408060i \(0.133795\pi\)
−0.912955 + 0.408060i \(0.866205\pi\)
\(164\) 1.80362e12 + 1.70553e12i 1.18715 + 1.12258i
\(165\) 5.28157e11i 0.336203i
\(166\) −1.86135e11 7.40700e10i −0.114613 0.0456087i
\(167\) 1.37067e12 0.816568 0.408284 0.912855i \(-0.366127\pi\)
0.408284 + 0.912855i \(0.366127\pi\)
\(168\) 7.82361e11 + 1.68532e12i 0.451031 + 0.971587i
\(169\) 5.34450e11 0.298216
\(170\) −2.99242e12 1.19079e12i −1.61641 0.643231i
\(171\) 3.30614e11i 0.172919i
\(172\) −1.18820e12 + 1.25653e12i −0.601842 + 0.636456i
\(173\) 2.93882e11i 0.144185i 0.997398 + 0.0720925i \(0.0229677\pi\)
−0.997398 + 0.0720925i \(0.977032\pi\)
\(174\) 3.02582e11 7.60376e11i 0.143821 0.361416i
\(175\) 4.28172e12 1.97201
\(176\) 7.43128e11 4.15766e10i 0.331699 0.0185579i
\(177\) 2.55487e12 1.10539
\(178\) −1.32822e11 + 3.33775e11i −0.0557133 + 0.140005i
\(179\) 7.29331e11i 0.296642i 0.988939 + 0.148321i \(0.0473869\pi\)
−0.988939 + 0.148321i \(0.952613\pi\)
\(180\) −1.41821e12 + 1.49978e12i −0.559426 + 0.591600i
\(181\) 9.65669e11i 0.369484i −0.982787 0.184742i \(-0.940855\pi\)
0.982787 0.184742i \(-0.0591450\pi\)
\(182\) 3.32463e12 + 1.32299e12i 1.23410 + 0.491094i
\(183\) −3.02326e12 −1.08892
\(184\) −2.05920e12 + 9.55924e11i −0.719782 + 0.334138i
\(185\) −4.24072e12 −1.43878
\(186\) −9.94363e11 3.95694e11i −0.327509 0.130328i
\(187\) 1.20652e12i 0.385840i
\(188\) −1.96182e12 1.85513e12i −0.609243 0.576110i
\(189\) 5.48181e12i 1.65342i
\(190\) −6.01339e11 + 1.51114e12i −0.176187 + 0.442752i
\(191\) −6.96835e11 −0.198357 −0.0991783 0.995070i \(-0.531621\pi\)
−0.0991783 + 0.995070i \(0.531621\pi\)
\(192\) 1.86572e12 + 1.57646e12i 0.516047 + 0.436041i
\(193\) 3.70530e12 0.995997 0.497999 0.867178i \(-0.334068\pi\)
0.497999 + 0.867178i \(0.334068\pi\)
\(194\) 2.02233e11 5.08204e11i 0.0528376 0.132779i
\(195\) 3.33788e12i 0.847775i
\(196\) −4.45429e12 4.21205e12i −1.09994 1.04012i
\(197\) 5.75699e12i 1.38239i 0.722667 + 0.691196i \(0.242916\pi\)
−0.722667 + 0.691196i \(0.757084\pi\)
\(198\) −7.18475e11 2.85908e11i −0.167785 0.0667678i
\(199\) −2.74148e12 −0.622720 −0.311360 0.950292i \(-0.600784\pi\)
−0.311360 + 0.950292i \(0.600784\pi\)
\(200\) 5.10536e12 2.37001e12i 1.12814 0.523704i
\(201\) −1.31135e12 −0.281930
\(202\) −1.28703e12 5.12155e11i −0.269250 0.107144i
\(203\) 4.48369e12i 0.912867i
\(204\) 2.72047e12 2.87693e12i 0.539110 0.570115i
\(205\) 1.26868e13i 2.44740i
\(206\) 9.84930e11 2.47509e12i 0.184985 0.464859i
\(207\) 2.35867e12 0.431350
\(208\) 4.69647e12 2.62759e11i 0.836418 0.0467960i
\(209\) −6.09283e11 −0.105685
\(210\) −3.51114e12 + 8.82335e12i −0.593256 + 1.49083i
\(211\) 9.16702e12i 1.50895i −0.656329 0.754475i \(-0.727892\pi\)
0.656329 0.754475i \(-0.272108\pi\)
\(212\) −2.41629e11 + 2.55525e11i −0.0387527 + 0.0409814i
\(213\) 1.06999e12i 0.167222i
\(214\) 1.10609e13 + 4.40155e12i 1.68467 + 0.670394i
\(215\) −8.83853e12 −1.31211
\(216\) −3.03429e12 6.53631e12i −0.439098 0.945882i
\(217\) 5.86344e12 0.827226
\(218\) 5.47159e12 + 2.17735e12i 0.752667 + 0.299514i
\(219\) 6.71055e12i 0.900151i
\(220\) 2.76392e12 + 2.61360e12i 0.361576 + 0.341912i
\(221\) 7.62507e12i 0.972941i
\(222\) 1.92766e12 4.84414e12i 0.239933 0.602942i
\(223\) 4.37572e12 0.531340 0.265670 0.964064i \(-0.414407\pi\)
0.265670 + 0.964064i \(0.414407\pi\)
\(224\) −1.26910e13 4.24567e12i −1.50360 0.503016i
\(225\) −5.84782e12 −0.676067
\(226\) 1.60573e12 4.03514e12i 0.181166 0.455263i
\(227\) 3.94488e12i 0.434402i −0.976127 0.217201i \(-0.930307\pi\)
0.976127 0.217201i \(-0.0696927\pi\)
\(228\) −1.45282e12 1.37381e12i −0.156160 0.147668i
\(229\) 6.68785e12i 0.701764i 0.936420 + 0.350882i \(0.114118\pi\)
−0.936420 + 0.350882i \(0.885882\pi\)
\(230\) −1.07808e13 4.29007e12i −1.10445 0.439502i
\(231\) −3.55752e12 −0.355862
\(232\) 2.48181e12 + 5.34619e12i 0.242429 + 0.522229i
\(233\) 6.20865e12 0.592298 0.296149 0.955142i \(-0.404298\pi\)
0.296149 + 0.955142i \(0.404298\pi\)
\(234\) −4.54066e12 1.80690e12i −0.423089 0.168363i
\(235\) 1.37995e13i 1.25600i
\(236\) −1.26429e13 + 1.33700e13i −1.12416 + 1.18882i
\(237\) 5.04709e12i 0.438455i
\(238\) −8.02086e12 + 2.01561e13i −0.680844 + 1.71093i
\(239\) 1.79550e13 1.48935 0.744676 0.667426i \(-0.232604\pi\)
0.744676 + 0.667426i \(0.232604\pi\)
\(240\) 6.97344e11 + 1.24641e13i 0.0565309 + 1.01042i
\(241\) −9.94501e12 −0.787973 −0.393987 0.919116i \(-0.628904\pi\)
−0.393987 + 0.919116i \(0.628904\pi\)
\(242\) 4.24706e12 1.06727e13i 0.328930 0.826589i
\(243\) 1.23372e13i 0.934078i
\(244\) 1.49607e13 1.58211e13i 1.10741 1.17110i
\(245\) 3.13317e13i 2.26762i
\(246\) −1.44920e13 5.76690e12i −1.02562 0.408131i
\(247\) −3.85059e12 −0.266498
\(248\) 6.99135e12 3.24553e12i 0.473235 0.219685i
\(249\) 1.25875e12 0.0833382
\(250\) 5.23859e12 + 2.08463e12i 0.339269 + 0.135008i
\(251\) 8.09796e12i 0.513062i 0.966536 + 0.256531i \(0.0825796\pi\)
−0.966536 + 0.256531i \(0.917420\pi\)
\(252\) 1.01021e13 + 9.55270e12i 0.626193 + 0.592138i
\(253\) 4.34675e12i 0.263634i
\(254\) 1.07416e12 2.69933e12i 0.0637507 0.160203i
\(255\) 2.02364e13 1.17534
\(256\) −1.74824e13 + 1.96236e12i −0.993759 + 0.111547i
\(257\) 1.44416e13 0.803494 0.401747 0.915751i \(-0.368403\pi\)
0.401747 + 0.915751i \(0.368403\pi\)
\(258\) 4.01765e12 1.00962e13i 0.218808 0.549856i
\(259\) 2.85644e13i 1.52292i
\(260\) 1.74676e13 + 1.65176e13i 0.911757 + 0.862172i
\(261\) 6.12367e12i 0.312960i
\(262\) −2.36032e11 9.39260e10i −0.0118118 0.00470034i
\(263\) −3.40203e13 −1.66717 −0.833587 0.552388i \(-0.813717\pi\)
−0.833587 + 0.552388i \(0.813717\pi\)
\(264\) −4.24186e12 + 1.96916e12i −0.203580 + 0.0945060i
\(265\) −1.79738e12 −0.0844865
\(266\) 1.01786e13 + 4.05046e12i 0.468642 + 0.186490i
\(267\) 2.25718e12i 0.101802i
\(268\) 6.48927e12 6.86248e12i 0.286718 0.303207i
\(269\) 1.44957e13i 0.627484i 0.949508 + 0.313742i \(0.101583\pi\)
−0.949508 + 0.313742i \(0.898417\pi\)
\(270\) 1.36175e13 3.42203e13i 0.577560 1.45139i
\(271\) −6.60502e12 −0.274501 −0.137250 0.990536i \(-0.543826\pi\)
−0.137250 + 0.990536i \(0.543826\pi\)
\(272\) 1.59302e12 + 2.84731e13i 0.0648771 + 1.15959i
\(273\) −2.24831e13 −0.897348
\(274\) −1.85713e11 + 4.66691e11i −0.00726466 + 0.0182558i
\(275\) 1.07768e13i 0.413202i
\(276\) 9.80103e12 1.03647e13i 0.368359 0.389544i
\(277\) 1.55779e13i 0.573945i 0.957939 + 0.286973i \(0.0926489\pi\)
−0.957939 + 0.286973i \(0.907351\pi\)
\(278\) −3.72474e13 1.48221e13i −1.34539 0.535382i
\(279\) −8.00808e12 −0.283599
\(280\) −2.87988e13 6.20369e13i −1.00001 2.15417i
\(281\) −4.02464e13 −1.37038 −0.685192 0.728363i \(-0.740282\pi\)
−0.685192 + 0.728363i \(0.740282\pi\)
\(282\) 1.57631e13 + 6.27272e12i 0.526346 + 0.209453i
\(283\) 2.95788e13i 0.968623i −0.874896 0.484312i \(-0.839070\pi\)
0.874896 0.484312i \(-0.160930\pi\)
\(284\) 5.59941e12 + 5.29489e12i 0.179842 + 0.170062i
\(285\) 1.02192e13i 0.321937i
\(286\) −3.32990e12 + 8.36791e12i −0.102901 + 0.258585i
\(287\) 8.54546e13 2.59051
\(288\) 1.73330e13 + 5.79859e12i 0.515483 + 0.172450i
\(289\) 1.19563e13 0.348866
\(290\) −1.11381e13 + 2.79895e13i −0.318875 + 0.801321i
\(291\) 3.43677e12i 0.0965471i
\(292\) −3.51172e13 3.32074e13i −0.968086 0.915437i
\(293\) 6.87067e12i 0.185878i −0.995672 0.0929388i \(-0.970374\pi\)
0.995672 0.0929388i \(-0.0296261\pi\)
\(294\) 3.57900e13 + 1.42422e13i 0.950279 + 0.378151i
\(295\) −9.40452e13 −2.45084
\(296\) 1.58109e13 + 3.40591e13i 0.404439 + 0.871222i
\(297\) 1.37974e13 0.346447
\(298\) 2.63720e13 + 1.04944e13i 0.650060 + 0.258683i
\(299\) 2.74708e13i 0.664784i
\(300\) −2.42996e13 + 2.56971e13i −0.577341 + 0.610545i
\(301\) 5.95340e13i 1.38883i
\(302\) −2.81665e13 + 7.07814e13i −0.645201 + 1.62137i
\(303\) 8.70362e12 0.195779
\(304\) 1.43787e13 8.04458e11i 0.317624 0.0177705i
\(305\) 1.11287e14 2.41431
\(306\) 1.09546e13 2.75285e13i 0.233415 0.586563i
\(307\) 9.07345e13i 1.89894i −0.313856 0.949471i \(-0.601621\pi\)
0.313856 0.949471i \(-0.398379\pi\)
\(308\) 1.76045e13 1.86170e13i 0.361905 0.382719i
\(309\) 1.67380e13i 0.338012i
\(310\) 3.66026e13 + 1.45655e13i 0.726144 + 0.288960i
\(311\) 3.13492e13 0.611005 0.305503 0.952191i \(-0.401176\pi\)
0.305503 + 0.952191i \(0.401176\pi\)
\(312\) −2.68080e13 + 1.24448e13i −0.513351 + 0.238308i
\(313\) 5.53280e13 1.04100 0.520501 0.853861i \(-0.325745\pi\)
0.520501 + 0.853861i \(0.325745\pi\)
\(314\) −8.47538e13 3.37267e13i −1.56692 0.623535i
\(315\) 7.10587e13i 1.29095i
\(316\) −2.64121e13 2.49757e13i −0.471545 0.445901i
\(317\) 7.13159e13i 1.25130i −0.780105 0.625648i \(-0.784834\pi\)
0.780105 0.625648i \(-0.215166\pi\)
\(318\) 8.17017e11 2.05313e12i 0.0140891 0.0354053i
\(319\) −1.12852e13 −0.191276
\(320\) −6.86772e13 5.80298e13i −1.14416 0.966777i
\(321\) −7.48004e13 −1.22497
\(322\) −2.88968e13 + 7.26164e13i −0.465202 + 1.16904i
\(323\) 2.33448e13i 0.369468i
\(324\) 7.51695e12 + 7.10814e12i 0.116962 + 0.110601i
\(325\) 6.81082e13i 1.04194i
\(326\) 5.04116e13 + 2.00606e13i 0.758287 + 0.301751i
\(327\) −3.70021e13 −0.547285
\(328\) 1.01893e14 4.73008e13i 1.48197 0.687958i
\(329\) −9.29499e13 −1.32945
\(330\) −2.22079e13 8.83735e12i −0.312378 0.124307i
\(331\) 5.31188e13i 0.734843i −0.930055 0.367421i \(-0.880241\pi\)
0.930055 0.367421i \(-0.119759\pi\)
\(332\) −6.22898e12 + 6.58722e12i −0.0847535 + 0.0896278i
\(333\) 3.90122e13i 0.522104i
\(334\) 2.29346e13 5.76338e13i 0.301916 0.758703i
\(335\) 4.82711e13 0.625087
\(336\) 8.39550e13 4.69712e12i 1.06950 0.0598365i
\(337\) −7.86684e13 −0.985907 −0.492953 0.870056i \(-0.664083\pi\)
−0.492953 + 0.870056i \(0.664083\pi\)
\(338\) 8.94265e12 2.24725e13i 0.110262 0.277083i
\(339\) 2.72879e13i 0.331034i
\(340\) −1.00141e14 + 1.05900e14i −1.19530 + 1.26404i
\(341\) 1.47580e13i 0.173331i
\(342\) −1.39016e13 5.53197e12i −0.160665 0.0639347i
\(343\) −7.16343e13 −0.814710
\(344\) 3.29532e13 + 7.09862e13i 0.368830 + 0.794515i
\(345\) 7.29059e13 0.803078
\(346\) 1.23571e13 + 4.91736e12i 0.133967 + 0.0533106i
\(347\) 1.76592e14i 1.88434i 0.335140 + 0.942168i \(0.391216\pi\)
−0.335140 + 0.942168i \(0.608784\pi\)
\(348\) −2.69093e13 2.54459e13i −0.282629 0.267258i
\(349\) 9.38942e13i 0.970731i 0.874311 + 0.485365i \(0.161313\pi\)
−0.874311 + 0.485365i \(0.838687\pi\)
\(350\) 7.16435e13 1.80037e14i 0.729126 1.83226i
\(351\) 8.71978e13 0.873608
\(352\) 1.06861e13 3.19427e13i 0.105399 0.315055i
\(353\) −1.67481e13 −0.162631 −0.0813157 0.996688i \(-0.525912\pi\)
−0.0813157 + 0.996688i \(0.525912\pi\)
\(354\) 4.27492e13 1.07427e14i 0.408705 1.02706i
\(355\) 3.93865e13i 0.370759i
\(356\) 1.18121e13 + 1.11697e13i 0.109485 + 0.103530i
\(357\) 1.36307e14i 1.24407i
\(358\) 3.06668e13 + 1.22035e13i 0.275621 + 0.109680i
\(359\) −9.36639e13 −0.828996 −0.414498 0.910050i \(-0.636043\pi\)
−0.414498 + 0.910050i \(0.636043\pi\)
\(360\) 3.93324e13 + 8.47278e13i 0.342836 + 0.738520i
\(361\) 1.04701e14 0.898799
\(362\) −4.06043e13 1.61580e13i −0.343301 0.136612i
\(363\) 7.21749e13i 0.601035i
\(364\) 1.11258e14 1.17657e14i 0.912587 0.965072i
\(365\) 2.47016e14i 1.99579i
\(366\) −5.05865e13 + 1.27122e14i −0.402613 + 1.01175i
\(367\) 1.95745e14 1.53471 0.767356 0.641221i \(-0.221572\pi\)
0.767356 + 0.641221i \(0.221572\pi\)
\(368\) 5.73916e12 + 1.02580e14i 0.0443287 + 0.792319i
\(369\) −1.16711e14 −0.888109
\(370\) −7.09575e13 + 1.78314e14i −0.531972 + 1.33683i
\(371\) 1.21067e13i 0.0894269i
\(372\) −3.32762e13 + 3.51900e13i −0.242185 + 0.256114i
\(373\) 8.96613e13i 0.642993i 0.946911 + 0.321497i \(0.104186\pi\)
−0.946911 + 0.321497i \(0.895814\pi\)
\(374\) −5.07318e13 2.01881e13i −0.358498 0.142660i
\(375\) −3.54264e13 −0.246692
\(376\) −1.10830e14 + 5.14496e13i −0.760544 + 0.353060i
\(377\) −7.13210e13 −0.482325
\(378\) −2.30499e14 9.17239e13i −1.53626 0.611333i
\(379\) 1.15327e14i 0.757560i −0.925487 0.378780i \(-0.876344\pi\)
0.925487 0.378780i \(-0.123656\pi\)
\(380\) 5.34785e13 + 5.05701e13i 0.346234 + 0.327404i
\(381\) 1.82544e13i 0.116488i
\(382\) −1.16597e13 + 2.93005e13i −0.0733399 + 0.184300i
\(383\) −1.11809e14 −0.693241 −0.346620 0.938006i \(-0.612671\pi\)
−0.346620 + 0.938006i \(0.612671\pi\)
\(384\) 9.75050e13 5.20714e13i 0.595943 0.318257i
\(385\) 1.30953e14 0.789007
\(386\) 6.19986e13 1.55800e14i 0.368258 0.925417i
\(387\) 8.13094e13i 0.476136i
\(388\) −1.79851e13 1.70070e13i −0.103834 0.0981867i
\(389\) 1.78296e12i 0.0101489i −0.999987 0.00507445i \(-0.998385\pi\)
0.999987 0.00507445i \(-0.00161525\pi\)
\(390\) −1.40351e14 5.58508e13i −0.787699 0.313454i
\(391\) 1.66546e14 0.921644
\(392\) −2.51639e14 + 1.16816e14i −1.37311 + 0.637424i
\(393\) 1.59619e12 0.00858865
\(394\) 2.42069e14 + 9.63284e13i 1.28443 + 0.511122i
\(395\) 1.85784e14i 0.972129i
\(396\) −2.40436e13 + 2.54264e13i −0.124073 + 0.131208i
\(397\) 1.20974e14i 0.615666i −0.951440 0.307833i \(-0.900396\pi\)
0.951440 0.307833i \(-0.0996037\pi\)
\(398\) −4.58715e13 + 1.15273e14i −0.230243 + 0.578591i
\(399\) −6.88339e13 −0.340762
\(400\) −1.42291e13 2.54326e14i −0.0694778 1.24183i
\(401\) 1.71934e14 0.828072 0.414036 0.910260i \(-0.364119\pi\)
0.414036 + 0.910260i \(0.364119\pi\)
\(402\) −2.19421e13 + 5.51397e13i −0.104240 + 0.261951i
\(403\) 9.32683e13i 0.437075i
\(404\) −4.30701e13 + 4.55472e13i −0.199103 + 0.210554i
\(405\) 5.28746e13i 0.241126i
\(406\) 1.88530e14 + 7.50230e13i 0.848178 + 0.337521i
\(407\) −7.18950e13 −0.319102
\(408\) −7.54487e13 1.62528e14i −0.330386 0.711700i
\(409\) −1.44862e14 −0.625861 −0.312930 0.949776i \(-0.601311\pi\)
−0.312930 + 0.949776i \(0.601311\pi\)
\(410\) 5.33452e14 + 2.12280e14i 2.27397 + 0.904895i
\(411\) 3.15603e12i 0.0132743i
\(412\) −8.75921e13 8.28285e13i −0.363522 0.343752i
\(413\) 6.33463e14i 2.59416i
\(414\) 3.94662e13 9.91770e13i 0.159486 0.400783i
\(415\) −4.63349e13 −0.184775
\(416\) 6.75348e13 2.01873e14i 0.265775 0.794448i
\(417\) 2.51889e14 0.978273
\(418\) −1.01948e13 + 2.56191e13i −0.0390759 + 0.0981961i
\(419\) 3.35193e14i 1.26799i 0.773336 + 0.633997i \(0.218587\pi\)
−0.773336 + 0.633997i \(0.781413\pi\)
\(420\) 3.12254e14 + 2.95272e14i 1.16583 + 1.10243i
\(421\) 1.42923e14i 0.526686i 0.964702 + 0.263343i \(0.0848250\pi\)
−0.964702 + 0.263343i \(0.915175\pi\)
\(422\) −3.85454e14 1.53386e14i −1.40202 0.557915i
\(423\) 1.26948e14 0.455777
\(424\) 6.70128e12 + 1.44355e13i 0.0237490 + 0.0511589i
\(425\) −4.12917e14 −1.44452
\(426\) −4.49909e13 1.79036e13i −0.155372 0.0618282i
\(427\) 7.49596e14i 2.55549i
\(428\) 3.70152e14 3.91440e14i 1.24578 1.31742i
\(429\) 5.65887e13i 0.188025i
\(430\) −1.47890e14 + 3.71642e14i −0.485135 + 1.21912i
\(431\) −2.65512e14 −0.859924 −0.429962 0.902847i \(-0.641473\pi\)
−0.429962 + 0.902847i \(0.641473\pi\)
\(432\) −3.25609e14 + 1.82172e13i −1.04120 + 0.0582534i
\(433\) −1.09976e14 −0.347227 −0.173614 0.984814i \(-0.555544\pi\)
−0.173614 + 0.984814i \(0.555544\pi\)
\(434\) 9.81095e13 2.46545e14i 0.305856 0.768605i
\(435\) 1.89281e14i 0.582662i
\(436\) 1.83106e14 1.93637e14i 0.556579 0.588589i
\(437\) 8.41044e13i 0.252447i
\(438\) 2.82165e14 + 1.12284e14i 0.836363 + 0.332820i
\(439\) −4.19854e14 −1.22897 −0.614487 0.788927i \(-0.710637\pi\)
−0.614487 + 0.788927i \(0.710637\pi\)
\(440\) 1.56143e14 7.24850e13i 0.451371 0.209536i
\(441\) 2.88234e14 0.822873
\(442\) −3.20618e14 1.27586e14i −0.903994 0.359733i
\(443\) 4.39100e14i 1.22277i 0.791335 + 0.611383i \(0.209386\pi\)
−0.791335 + 0.611383i \(0.790614\pi\)
\(444\) −1.71432e14 1.62108e14i −0.471503 0.445861i
\(445\) 8.30872e13i 0.225712i
\(446\) 7.32163e13 1.83990e14i 0.196456 0.493687i
\(447\) −1.78343e14 −0.472676
\(448\) −3.90873e14 + 4.62591e14i −1.02331 + 1.21107i
\(449\) −2.29397e14 −0.593242 −0.296621 0.954995i \(-0.595860\pi\)
−0.296621 + 0.954995i \(0.595860\pi\)
\(450\) −9.78481e13 + 2.45889e14i −0.249968 + 0.628159i
\(451\) 2.15085e14i 0.542798i
\(452\) −1.42801e14 1.35035e14i −0.356017 0.336655i
\(453\) 4.78665e14i 1.17894i
\(454\) −1.65874e14 6.60074e13i −0.403619 0.160615i
\(455\) 8.27605e14 1.98957
\(456\) −8.20750e13 + 3.81009e13i −0.194942 + 0.0904958i
\(457\) 7.94851e14 1.86529 0.932646 0.360794i \(-0.117494\pi\)
0.932646 + 0.360794i \(0.117494\pi\)
\(458\) 2.81210e14 + 1.11904e14i 0.652035 + 0.259469i
\(459\) 5.28651e14i 1.21115i
\(460\) −3.60777e14 + 3.81526e14i −0.816715 + 0.863686i
\(461\) 1.44773e14i 0.323841i −0.986804 0.161920i \(-0.948231\pi\)
0.986804 0.161920i \(-0.0517688\pi\)
\(462\) −5.95260e13 + 1.49586e14i −0.131576 + 0.330645i
\(463\) −5.29259e13 −0.115604 −0.0578020 0.998328i \(-0.518409\pi\)
−0.0578020 + 0.998328i \(0.518409\pi\)
\(464\) 2.66323e14 1.49003e13i 0.574857 0.0321621i
\(465\) −2.47528e14 −0.527999
\(466\) 1.03886e14 2.61061e14i 0.218995 0.550325i
\(467\) 6.96522e14i 1.45108i −0.688179 0.725541i \(-0.741590\pi\)
0.688179 0.725541i \(-0.258410\pi\)
\(468\) −1.51952e14 + 1.60692e14i −0.312864 + 0.330857i
\(469\) 3.25141e14i 0.661639i
\(470\) −5.80241e14 2.30899e14i −1.16700 0.464392i
\(471\) 5.73155e14 1.13935
\(472\) 3.50634e14 + 7.55319e14i 0.688927 + 1.48405i
\(473\) −1.49844e14 −0.291006
\(474\) 2.12219e14 + 8.44500e13i 0.407384 + 0.162113i
\(475\) 2.08519e14i 0.395668i
\(476\) 7.13314e14 + 6.74521e14i 1.33796 + 1.26519i
\(477\) 1.65349e13i 0.0306584i
\(478\) 3.00431e14 7.54971e14i 0.550670 1.38381i
\(479\) −7.63619e12 −0.0138367 −0.00691833 0.999976i \(-0.502202\pi\)
−0.00691833 + 0.999976i \(0.502202\pi\)
\(480\) 5.35759e14 + 1.79233e14i 0.959716 + 0.321064i
\(481\) −4.54366e14 −0.804652
\(482\) −1.66404e14 + 4.18167e14i −0.291343 + 0.732134i
\(483\) 4.91074e14i 0.850037i
\(484\) −3.77701e14 3.57160e14i −0.646396 0.611242i
\(485\) 1.26508e14i 0.214061i
\(486\) 5.18755e14 + 2.06432e14i 0.867886 + 0.345364i
\(487\) 6.21942e14 1.02882 0.514411 0.857544i \(-0.328010\pi\)
0.514411 + 0.857544i \(0.328010\pi\)
\(488\) −4.14916e14 8.93791e14i −0.678659 1.46193i
\(489\) −3.40913e14 −0.551372
\(490\) −1.31743e15 5.24255e14i −2.10693 0.838426i
\(491\) 7.67233e14i 1.21333i 0.794957 + 0.606665i \(0.207493\pi\)
−0.794957 + 0.606665i \(0.792507\pi\)
\(492\) −4.84972e14 + 5.12864e14i −0.758418 + 0.802036i
\(493\) 4.32395e14i 0.668687i
\(494\) −6.44297e13 + 1.61909e14i −0.0985343 + 0.247613i
\(495\) −1.78851e14 −0.270497
\(496\) −1.94855e13 3.48277e14i −0.0291448 0.520926i
\(497\) 2.65297e14 0.392439
\(498\) 2.10620e13 5.29280e13i 0.0308133 0.0774326i
\(499\) 1.22133e15i 1.76717i 0.468268 + 0.883586i \(0.344878\pi\)
−0.468268 + 0.883586i \(0.655122\pi\)
\(500\) 1.75309e14 1.85391e14i 0.250881 0.265310i
\(501\) 3.89753e14i 0.551674i
\(502\) 3.40502e14 + 1.35498e14i 0.476705 + 0.189698i
\(503\) −6.20160e14 −0.858776 −0.429388 0.903120i \(-0.641271\pi\)
−0.429388 + 0.903120i \(0.641271\pi\)
\(504\) 5.70704e14 2.64932e14i 0.781704 0.362883i
\(505\) −3.20381e14 −0.434075
\(506\) −1.82772e14 7.27316e13i −0.244952 0.0974754i
\(507\) 1.51972e14i 0.201475i
\(508\) −9.55278e13 9.03326e13i −0.125279 0.118466i
\(509\) 1.04994e14i 0.136213i −0.997678 0.0681065i \(-0.978304\pi\)
0.997678 0.0681065i \(-0.0216958\pi\)
\(510\) 3.38605e14 8.50900e14i 0.434567 1.09205i
\(511\) −1.66383e15 −2.11249
\(512\) −2.10010e14 + 7.67933e14i −0.263788 + 0.964581i
\(513\) 2.66964e14 0.331747
\(514\) 2.41643e14 6.07238e14i 0.297082 0.746555i
\(515\) 6.16128e14i 0.749430i
\(516\) −3.57299e14 3.37867e14i −0.429990 0.406605i
\(517\) 2.33950e14i 0.278564i
\(518\) 1.20107e15 + 4.77951e14i 1.41500 + 0.563079i
\(519\) −8.35661e13 −0.0974114
\(520\) 9.86806e14 4.58095e14i 1.13819 0.528369i
\(521\) 5.40389e14 0.616736 0.308368 0.951267i \(-0.400217\pi\)
0.308368 + 0.951267i \(0.400217\pi\)
\(522\) −2.57487e14 1.02464e14i −0.290783 0.115713i
\(523\) 6.71719e14i 0.750634i −0.926897 0.375317i \(-0.877534\pi\)
0.926897 0.375317i \(-0.122466\pi\)
\(524\) −7.89879e12 + 8.35306e12i −0.00873450 + 0.00923684i
\(525\) 1.21752e15i 1.33229i
\(526\) −5.69241e14 + 1.43048e15i −0.616417 + 1.54903i
\(527\) −5.65454e14 −0.605953
\(528\) 1.18224e13 + 2.11310e14i 0.0125377 + 0.224096i
\(529\) −3.52793e14 −0.370266
\(530\) −3.00745e13 + 7.55761e13i −0.0312379 + 0.0784995i
\(531\) 8.65162e14i 0.889360i
\(532\) 3.40627e14 3.60217e14i 0.346549 0.366480i
\(533\) 1.35931e15i 1.36873i
\(534\) −9.49098e13 3.77681e13i −0.0945876 0.0376399i
\(535\) 2.75341e15 2.71597
\(536\) −1.79972e14 3.87686e14i −0.175711 0.378507i
\(537\) −2.07387e14 −0.200412
\(538\) 6.09515e14 + 2.42549e14i 0.583018 + 0.232005i
\(539\) 5.31181e14i 0.502927i
\(540\) −1.21104e15 1.14518e15i −1.13499 1.07326i
\(541\) 8.46704e14i 0.785501i −0.919645 0.392750i \(-0.871524\pi\)
0.919645 0.392750i \(-0.128476\pi\)
\(542\) −1.10518e14 + 2.77727e14i −0.101493 + 0.255048i
\(543\) 2.74590e14 0.249624
\(544\) 1.22389e15 + 4.09441e14i 1.10141 + 0.368466i
\(545\) 1.36205e15 1.21342
\(546\) −3.76196e14 + 9.45366e14i −0.331783 + 0.833759i
\(547\) 1.21824e15i 1.06366i 0.846850 + 0.531832i \(0.178496\pi\)
−0.846850 + 0.531832i \(0.821504\pi\)
\(548\) 1.65159e13 + 1.56177e13i 0.0142761 + 0.0134997i
\(549\) 1.02377e15i 0.876104i
\(550\) 4.53144e14 + 1.80323e14i 0.383921 + 0.152776i
\(551\) −2.18355e14 −0.183160
\(552\) −2.71819e14 5.85539e14i −0.225743 0.486285i
\(553\) −1.25139e15 −1.02897
\(554\) 6.55019e14 + 2.60656e14i 0.533273 + 0.212209i
\(555\) 1.20586e15i 0.972043i
\(556\) −1.24648e15 + 1.31817e15i −0.994886 + 1.05210i
\(557\) 2.98945e14i 0.236259i −0.992998 0.118129i \(-0.962310\pi\)
0.992998 0.118129i \(-0.0376898\pi\)
\(558\) −1.33995e14 + 3.36723e14i −0.104857 + 0.263502i
\(559\) −9.46993e14 −0.733807
\(560\) −3.09039e15 + 1.72902e14i −2.37126 + 0.132668i
\(561\) 3.43078e14 0.260674
\(562\) −6.73419e14 + 1.69228e15i −0.506682 + 1.27327i
\(563\) 1.79792e15i 1.33960i −0.742542 0.669799i \(-0.766380\pi\)
0.742542 0.669799i \(-0.233620\pi\)
\(564\) 5.27509e14 5.57847e14i 0.389220 0.411605i
\(565\) 1.00447e15i 0.733958i
\(566\) −1.24373e15 4.94925e14i −0.899983 0.358137i
\(567\) 3.56149e14 0.255226
\(568\) 3.16331e14 1.46847e14i 0.224505 0.104220i
\(569\) 1.49115e15 1.04810 0.524051 0.851687i \(-0.324420\pi\)
0.524051 + 0.851687i \(0.324420\pi\)
\(570\) −4.29697e14 1.70992e14i −0.299123 0.119032i
\(571\) 1.07492e15i 0.741098i −0.928813 0.370549i \(-0.879169\pi\)
0.928813 0.370549i \(-0.120831\pi\)
\(572\) 2.96136e14 + 2.80031e14i 0.202215 + 0.191217i
\(573\) 1.98147e14i 0.134010i
\(574\) 1.42986e15 3.59319e15i 0.957808 2.40693i
\(575\) −1.48762e15 −0.987002
\(576\) 5.33841e14 6.31791e14i 0.350823 0.415193i
\(577\) 1.22495e15 0.797352 0.398676 0.917092i \(-0.369470\pi\)
0.398676 + 0.917092i \(0.369470\pi\)
\(578\) 2.00058e14 5.02738e14i 0.128989 0.324144i
\(579\) 1.05361e15i 0.672896i
\(580\) 9.90534e14 + 9.36665e14i 0.626636 + 0.592557i
\(581\) 3.12099e14i 0.195580i
\(582\) 1.44509e14 + 5.75055e13i 0.0897054 + 0.0356971i
\(583\) −3.04718e13 −0.0187379
\(584\) −1.98389e15 + 9.20964e14i −1.20850 + 0.561012i
\(585\) −1.13031e15 −0.682090
\(586\) −2.88897e14 1.14963e14i −0.172706 0.0687259i
\(587\) 3.42431e14i 0.202798i 0.994846 + 0.101399i \(0.0323319\pi\)
−0.994846 + 0.101399i \(0.967668\pi\)
\(588\) 1.19771e15 1.26659e15i 0.702708 0.743122i
\(589\) 2.85549e14i 0.165977i
\(590\) −1.57360e15 + 3.95441e15i −0.906169 + 2.27717i
\(591\) −1.63701e15 −0.933945
\(592\) 1.69667e15 9.49254e13i 0.959020 0.0536554i
\(593\) −2.01818e15 −1.13021 −0.565105 0.825019i \(-0.691164\pi\)
−0.565105 + 0.825019i \(0.691164\pi\)
\(594\) 2.30864e14 5.80152e14i 0.128095 0.321897i
\(595\) 5.01749e15i 2.75831i
\(596\) 8.82534e14 9.33290e14i 0.480703 0.508349i
\(597\) 7.79545e14i 0.420710i
\(598\) −1.15509e15 4.59654e14i −0.617675 0.245796i
\(599\) 3.55347e15 1.88280 0.941402 0.337287i \(-0.109509\pi\)
0.941402 + 0.337287i \(0.109509\pi\)
\(600\) 6.73919e14 + 1.45172e15i 0.353815 + 0.762169i
\(601\) −3.15707e14 −0.164238 −0.0821192 0.996623i \(-0.526169\pi\)
−0.0821192 + 0.996623i \(0.526169\pi\)
\(602\) 2.50328e15 + 9.96147e14i 1.29041 + 0.513503i
\(603\) 4.44066e14i 0.226831i
\(604\) 2.50492e15 + 2.36869e15i 1.26791 + 1.19896i
\(605\) 2.65677e15i 1.33260i
\(606\) 1.45633e14 3.65969e14i 0.0723868 0.181905i
\(607\) 3.02066e15 1.48787 0.743934 0.668253i \(-0.232957\pi\)
0.743934 + 0.668253i \(0.232957\pi\)
\(608\) 2.06764e14 6.18053e14i 0.100926 0.301686i
\(609\) −1.27495e15 −0.616733
\(610\) 1.86209e15 4.67937e15i 0.892663 2.24323i
\(611\) 1.47853e15i 0.702431i
\(612\) −9.74219e14 9.21236e14i −0.458695 0.433749i
\(613\) 2.56623e15i 1.19746i 0.800949 + 0.598732i \(0.204329\pi\)
−0.800949 + 0.598732i \(0.795671\pi\)
\(614\) −3.81520e15 1.51821e15i −1.76437 0.702110i
\(615\) −3.60751e15 −1.65346
\(616\) −4.88239e14 1.05174e15i −0.221788 0.477765i
\(617\) 9.15832e14 0.412332 0.206166 0.978517i \(-0.433901\pi\)
0.206166 + 0.978517i \(0.433901\pi\)
\(618\) 7.03798e14 + 2.80067e14i 0.314059 + 0.124976i
\(619\) 2.56124e15i 1.13280i 0.824131 + 0.566399i \(0.191664\pi\)
−0.824131 + 0.566399i \(0.808336\pi\)
\(620\) 1.22490e15 1.29535e15i 0.536966 0.567848i
\(621\) 1.90457e15i 0.827548i
\(622\) 5.24549e14 1.31817e15i 0.225912 0.567707i
\(623\) 5.59653e14 0.238910
\(624\) 7.47160e13 + 1.33545e15i 0.0316154 + 0.565084i
\(625\) −1.66132e15 −0.696810
\(626\) 9.25771e14 2.32643e15i 0.384897 0.967232i
\(627\) 1.73251e14i 0.0714011i
\(628\) −2.83627e15 + 2.99939e15i −1.15870 + 1.22534i
\(629\) 2.75467e15i 1.11555i
\(630\) 2.98787e15 + 1.18898e15i 1.19947 + 0.477312i
\(631\) −1.75943e15 −0.700179 −0.350090 0.936716i \(-0.613849\pi\)
−0.350090 + 0.936716i \(0.613849\pi\)
\(632\) −1.49211e15 + 6.92669e14i −0.588650 + 0.273264i
\(633\) 2.60666e15 1.01945
\(634\) −2.99868e15 1.19329e15i −1.16263 0.462651i
\(635\) 6.71948e14i 0.258274i
\(636\) −7.26593e13 6.87077e13i −0.0276871 0.0261813i
\(637\) 3.35699e15i 1.26819i
\(638\) −1.88829e14 + 4.74519e14i −0.0707220 + 0.177722i
\(639\) −3.62334e14 −0.134541
\(640\) −3.58917e15 + 1.91675e15i −1.32131 + 0.705630i
\(641\) −2.71995e15 −0.992755 −0.496377 0.868107i \(-0.665337\pi\)
−0.496377 + 0.868107i \(0.665337\pi\)
\(642\) −1.25159e15 + 3.14520e15i −0.452919 + 1.13817i
\(643\) 1.66231e15i 0.596419i −0.954500 0.298210i \(-0.903611\pi\)
0.954500 0.298210i \(-0.0963895\pi\)
\(644\) 2.56986e15 + 2.43010e15i 0.914190 + 0.864472i
\(645\) 2.51326e15i 0.886459i
\(646\) −9.81601e14 3.90615e14i −0.343286 0.136606i
\(647\) 2.35217e15 0.815635 0.407817 0.913063i \(-0.366290\pi\)
0.407817 + 0.913063i \(0.366290\pi\)
\(648\) 4.24659e14 1.97135e14i 0.146008 0.0677801i
\(649\) −1.59439e15 −0.543563
\(650\) 2.86381e15 + 1.13962e15i 0.968101 + 0.385243i
\(651\) 1.66728e15i 0.558874i
\(652\) 1.68702e15 1.78404e15i 0.560735 0.592984i
\(653\) 4.70527e15i 1.55082i 0.631457 + 0.775411i \(0.282457\pi\)
−0.631457 + 0.775411i \(0.717543\pi\)
\(654\) −6.19134e14 + 1.55586e15i −0.202352 + 0.508502i
\(655\) −5.87559e13 −0.0190425
\(656\) −2.83984e14 5.07584e15i −0.0912688 1.63131i
\(657\) 2.27241e15 0.724230
\(658\) −1.55528e15 + 3.90835e15i −0.491547 + 1.23524i
\(659\) 1.75566e15i 0.550262i −0.961407 0.275131i \(-0.911279\pi\)
0.961407 0.275131i \(-0.0887212\pi\)
\(660\) −7.43184e14 + 7.85926e14i −0.230996 + 0.244281i
\(661\) 2.25236e15i 0.694271i −0.937815 0.347135i \(-0.887154\pi\)
0.937815 0.347135i \(-0.112846\pi\)
\(662\) −2.23354e15 8.88806e14i −0.682769 0.271699i
\(663\) 2.16821e15 0.657319
\(664\) 1.72753e14 + 3.72136e14i 0.0519399 + 0.111886i
\(665\) 2.53378e15 0.755528
\(666\) −1.64038e15 6.52768e14i −0.485106 0.193042i
\(667\) 1.55779e15i 0.456896i
\(668\) −2.03963e15 1.92871e15i −0.593309 0.561042i
\(669\) 1.24425e15i 0.358974i
\(670\) 8.07692e14 2.02970e15i 0.231118 0.580791i
\(671\) 1.88669e15 0.535461
\(672\) 1.20727e15 3.60873e15i 0.339838 1.01583i
\(673\) 5.61222e15 1.56694 0.783470 0.621430i \(-0.213448\pi\)
0.783470 + 0.621430i \(0.213448\pi\)
\(674\) −1.31631e15 + 3.30784e15i −0.364527 + 0.916042i
\(675\) 4.72198e15i 1.29704i
\(676\) −7.95290e14 7.52039e14i −0.216680 0.204896i
\(677\) 5.99957e15i 1.62137i 0.585482 + 0.810685i \(0.300905\pi\)
−0.585482 + 0.810685i \(0.699095\pi\)
\(678\) 1.14740e15 + 4.56593e14i 0.307576 + 0.122396i
\(679\) −8.52124e14 −0.226579
\(680\) 2.77728e15 + 5.98267e15i 0.732521 + 1.57796i
\(681\) 1.12174e15 0.293482
\(682\) 6.20541e14 + 2.46936e14i 0.161048 + 0.0640871i
\(683\) 1.11579e15i 0.287255i 0.989632 + 0.143627i \(0.0458767\pi\)
−0.989632 + 0.143627i \(0.954123\pi\)
\(684\) −4.65216e14 + 4.91971e14i −0.118808 + 0.125641i
\(685\) 1.16174e14i 0.0294314i
\(686\) −1.19861e15 + 3.01207e15i −0.301229 + 0.756977i
\(687\) −1.90171e15 −0.474112
\(688\) 3.53621e15 1.97844e14i 0.874583 0.0489313i
\(689\) −1.92578e14 −0.0472499
\(690\) 1.21989e15 3.06554e15i 0.296928 0.746169i
\(691\) 2.73412e15i 0.660221i −0.943942 0.330110i \(-0.892914\pi\)
0.943942 0.330110i \(-0.107086\pi\)
\(692\) 4.13530e14 4.37312e14i 0.0990656 0.104763i
\(693\) 1.20469e15i 0.286314i
\(694\) 7.42532e15 + 2.95481e15i 1.75081 + 0.696710i
\(695\) −9.27205e15 −2.16900
\(696\) −1.52020e15 + 7.05709e14i −0.352818 + 0.163785i
\(697\) −8.24101e15 −1.89758
\(698\) 3.94805e15 + 1.57108e15i 0.901941 + 0.358916i
\(699\) 1.76545e15i 0.400156i
\(700\) −6.37142e15 6.02491e15i −1.43284 1.35491i
\(701\) 3.90980e15i 0.872380i 0.899855 + 0.436190i \(0.143672\pi\)
−0.899855 + 0.436190i \(0.856328\pi\)
\(702\) 1.45903e15 3.66648e15i 0.323006 0.811700i
\(703\) −1.39108e15 −0.305561
\(704\) −1.16432e15 9.83807e14i −0.253759 0.214417i
\(705\) 3.92393e15 0.848557
\(706\) −2.80236e14 + 7.04222e14i −0.0601310 + 0.151107i
\(707\) 2.15800e15i 0.459457i
\(708\) −3.80179e15 3.59503e15i −0.803165 0.759486i
\(709\) 7.61120e15i 1.59551i −0.602983 0.797754i \(-0.706021\pi\)
0.602983 0.797754i \(-0.293979\pi\)
\(710\) 1.65612e15 + 6.59032e14i 0.344486 + 0.137084i
\(711\) 1.70910e15 0.352765
\(712\) 6.67310e14 3.09779e14i 0.136674 0.0634471i
\(713\) −2.03716e15 −0.414031
\(714\) −5.73143e15 2.28075e15i −1.15591 0.459978i
\(715\) 2.08304e15i 0.416882i
\(716\) 1.02626e15 1.08528e15i 0.203815 0.215537i
\(717\) 5.10555e15i 1.00621i
\(718\) −1.56722e15 + 3.93837e15i −0.306511 + 0.770251i
\(719\) 6.49581e15 1.26074 0.630368 0.776296i \(-0.282904\pi\)
0.630368 + 0.776296i \(0.282904\pi\)
\(720\) 4.22075e15 2.36143e14i 0.812945 0.0454827i
\(721\) −4.15007e15 −0.793252
\(722\) 1.75191e15 4.40247e15i 0.332320 0.835107i
\(723\) 2.82789e15i 0.532355i
\(724\) −1.35882e15 + 1.43697e15i −0.253863 + 0.268463i
\(725\) 3.86222e15i 0.716106i
\(726\) 3.03481e15 + 1.20766e15i 0.558444 + 0.222225i
\(727\) −6.35413e15 −1.16043 −0.580213 0.814465i \(-0.697031\pi\)
−0.580213 + 0.814465i \(0.697031\pi\)
\(728\) −3.08561e15 6.64686e15i −0.559265 1.20474i
\(729\) −4.40299e15 −0.792038
\(730\) −1.03865e16 4.13318e15i −1.85436 0.737918i
\(731\) 5.74129e15i 1.01734i
\(732\) 4.49877e15 + 4.25411e15i 0.791194 + 0.748165i
\(733\) 3.12820e15i 0.546038i 0.962009 + 0.273019i \(0.0880222\pi\)
−0.962009 + 0.273019i \(0.911978\pi\)
\(734\) 3.27528e15 8.23066e15i 0.567441 1.42596i
\(735\) 8.90925e15 1.53201
\(736\) 4.40931e15 + 1.47509e15i 0.752562 + 0.251763i
\(737\) 8.18362e14 0.138635
\(738\) −1.95285e15 + 4.90745e15i −0.328367 + 0.825174i
\(739\) 5.30842e15i 0.885973i 0.896528 + 0.442987i \(0.146081\pi\)
−0.896528 + 0.442987i \(0.853919\pi\)
\(740\) 6.31042e15 + 5.96723e15i 1.04540 + 0.988549i
\(741\) 1.09492e15i 0.180046i
\(742\) 5.09060e14 + 2.02574e14i 0.0830897 + 0.0330645i
\(743\) −7.29953e15 −1.18265 −0.591326 0.806433i \(-0.701395\pi\)
−0.591326 + 0.806433i \(0.701395\pi\)
\(744\) 9.22874e14 + 1.98801e15i 0.148420 + 0.319718i
\(745\) 6.56481e15 1.04800
\(746\) 3.77007e15 + 1.50025e15i 0.597428 + 0.237739i
\(747\) 4.26254e14i 0.0670510i
\(748\) −1.69773e15 + 1.79537e15i −0.265100 + 0.280347i
\(749\) 1.85462e16i 2.87479i
\(750\) −5.92769e14 + 1.48961e15i −0.0912113 + 0.229210i
\(751\) 1.15655e16 1.76663 0.883313 0.468784i \(-0.155308\pi\)
0.883313 + 0.468784i \(0.155308\pi\)
\(752\) 3.08892e14 + 5.52105e15i 0.0468391 + 0.837189i
\(753\) −2.30267e15 −0.346625
\(754\) −1.19337e15 + 2.99890e15i −0.178334 + 0.448146i
\(755\) 1.76197e16i 2.61391i
\(756\) −7.71360e15 + 8.15722e15i −1.13602 + 1.20136i
\(757\) 5.46519e15i 0.799057i 0.916721 + 0.399529i \(0.130826\pi\)
−0.916721 + 0.399529i \(0.869174\pi\)
\(758\) −4.84928e15 1.92971e15i −0.703876 0.280098i
\(759\) 1.23601e15 0.178111
\(760\) 3.02119e15 1.40250e15i 0.432219 0.200645i
\(761\) 1.25601e16 1.78393 0.891965 0.452105i \(-0.149327\pi\)
0.891965 + 0.452105i \(0.149327\pi\)
\(762\) 7.67561e14 + 3.05441e14i 0.108233 + 0.0430700i
\(763\) 9.17441e15i 1.28438i
\(764\) 1.03693e15 + 9.80535e14i 0.144124 + 0.136286i
\(765\) 6.85271e15i 0.945636i
\(766\) −1.87084e15 + 4.70134e15i −0.256317 + 0.644115i
\(767\) −1.00763e16 −1.37066
\(768\) −5.58001e14 4.97116e15i −0.0753612 0.671384i
\(769\) 6.63595e15 0.889832 0.444916 0.895572i \(-0.353234\pi\)
0.444916 + 0.895572i \(0.353234\pi\)
\(770\) 2.19116e15 5.50629e15i 0.291726 0.733095i
\(771\) 4.10650e15i 0.542841i
\(772\) −5.51368e15 5.21382e15i −0.723680 0.684323i
\(773\) 1.04365e16i 1.36009i −0.733170 0.680045i \(-0.761960\pi\)
0.733170 0.680045i \(-0.238040\pi\)
\(774\) −3.41889e15 1.36050e15i −0.442395 0.176045i
\(775\) 5.05072e15 0.648924
\(776\) −1.01604e15 + 4.71667e14i −0.129620 + 0.0601722i
\(777\) −8.12234e15 −1.02888
\(778\) −7.49697e13 2.98332e13i −0.00942970 0.00375243i
\(779\) 4.16163e15i 0.519766i
\(780\) −4.69682e15 + 4.96694e15i −0.582484 + 0.615983i
\(781\) 6.67739e14i 0.0822291i
\(782\) 2.78672e15 7.00293e15i 0.340766 0.856333i
\(783\) 4.94473e15 0.600417
\(784\) 7.01337e14 + 1.25355e16i 0.0845646 + 1.51148i
\(785\) −2.10979e16 −2.52613
\(786\) 2.67081e13 6.71164e13i 0.00317555 0.00798003i
\(787\) 8.64759e15i 1.02102i −0.859872 0.510510i \(-0.829457\pi\)
0.859872 0.510510i \(-0.170543\pi\)
\(788\) 8.10081e15 8.56671e15i 0.949805 1.00443i
\(789\) 9.67374e15i 1.12634i
\(790\) −7.81182e15 3.10861e15i −0.903240 0.359433i
\(791\) −6.76585e15 −0.776876
\(792\) 6.66820e14 + 1.43643e15i 0.0760362 + 0.163793i
\(793\) 1.19236e16 1.35023
\(794\) −5.08671e15 2.02419e15i −0.572037 0.227635i
\(795\) 5.11089e14i 0.0570791i
\(796\) 4.07946e15 + 3.85760e15i 0.452461 + 0.427854i
\(797\) 1.23890e16i 1.36463i 0.731056 + 0.682317i \(0.239028\pi\)
−0.731056 + 0.682317i \(0.760972\pi\)
\(798\) −1.15176e15 + 2.89432e15i −0.125993 + 0.316614i
\(799\) 8.96383e15 0.973838
\(800\) −1.09320e16 3.65718e15i −1.17951 0.394595i
\(801\) −7.64354e14 −0.0819060
\(802\) 2.87687e15 7.22947e15i 0.306169 0.769392i
\(803\) 4.18778e15i 0.442638i
\(804\) 1.95136e15 + 1.84524e15i 0.204847 + 0.193707i
\(805\) 1.80765e16i 1.88468i
\(806\) 3.92174e15 + 1.56060e15i 0.406103 + 0.161603i
\(807\) −4.12190e15 −0.423929
\(808\) 1.19450e15 + 2.57312e15i 0.122018 + 0.262844i
\(809\) −1.18494e16 −1.20221 −0.601104 0.799171i \(-0.705272\pi\)
−0.601104 + 0.799171i \(0.705272\pi\)
\(810\) 2.22327e15 + 8.84720e14i 0.224039 + 0.0891535i
\(811\) 2.92755e15i 0.293014i 0.989210 + 0.146507i \(0.0468032\pi\)
−0.989210 + 0.146507i \(0.953197\pi\)
\(812\) 6.30912e15 6.67197e15i 0.627207 0.663279i
\(813\) 1.87815e15i 0.185453i
\(814\) −1.20298e15 + 3.02303e15i −0.117984 + 0.296489i
\(815\) 1.25490e16 1.22248
\(816\) −8.09639e15 + 4.52978e14i −0.783422 + 0.0438310i
\(817\) −2.89930e15 −0.278658
\(818\) −2.42390e15 + 6.09116e15i −0.231404 + 0.581510i
\(819\) 7.61348e15i 0.721975i
\(820\) 1.78519e16 1.88786e16i 1.68154 1.77825i
\(821\) 1.19987e16i 1.12265i 0.827594 + 0.561326i \(0.189709\pi\)
−0.827594 + 0.561326i \(0.810291\pi\)
\(822\) −1.32705e14 5.28081e13i −0.0123336 0.00490801i
\(823\) −2.06230e16 −1.90393 −0.951967 0.306202i \(-0.900942\pi\)
−0.951967 + 0.306202i \(0.900942\pi\)
\(824\) −4.94839e15 + 2.29714e15i −0.453800 + 0.210663i
\(825\) −3.06442e15 −0.279159
\(826\) 2.66358e16 + 1.05994e16i 2.41032 + 0.959157i
\(827\) 9.90088e15i 0.890007i 0.895529 + 0.445004i \(0.146798\pi\)
−0.895529 + 0.445004i \(0.853202\pi\)
\(828\) −3.50982e15 3.31894e15i −0.313414 0.296369i
\(829\) 7.04297e15i 0.624749i −0.949959 0.312375i \(-0.898876\pi\)
0.949959 0.312375i \(-0.101124\pi\)
\(830\) −7.75294e14 + 1.94828e15i −0.0683183 + 0.171681i
\(831\) −4.42962e15 −0.387758
\(832\) −7.35833e15 6.21753e15i −0.639883 0.540679i
\(833\) 2.03523e16 1.75819
\(834\) 4.21470e15 1.05914e16i 0.361704 0.908949i
\(835\) 1.43469e16i 1.22315i
\(836\) 9.06646e14 + 8.57339e14i 0.0767897 + 0.0726136i
\(837\) 6.46635e15i 0.544088i
\(838\) 1.40941e16 + 5.60858e15i 1.17814 + 0.468825i
\(839\) 3.44381e15 0.285988 0.142994 0.989724i \(-0.454327\pi\)
0.142994 + 0.989724i \(0.454327\pi\)
\(840\) 1.76403e16 8.18900e15i 1.45536 0.675608i
\(841\) 8.15611e15 0.668505
\(842\) 6.00963e15 + 2.39145e15i 0.489363 + 0.194736i
\(843\) 1.14442e16i 0.925832i
\(844\) −1.28992e16 + 1.36410e16i −1.03676 + 1.09638i
\(845\) 5.59411e15i 0.446704i
\(846\) 2.12414e15 5.33788e15i 0.168518 0.423479i
\(847\) −1.78953e16 −1.41052
\(848\) 7.19113e14 4.02330e13i 0.0563145 0.00315069i
\(849\) 8.41080e15 0.654402
\(850\) −6.90910e15 + 1.73623e16i −0.534094 + 1.34216i
\(851\) 9.92425e15i 0.762228i
\(852\) −1.50561e15 + 1.59221e15i −0.114894 + 0.121501i
\(853\) 2.35072e16i 1.78231i 0.453704 + 0.891153i \(0.350102\pi\)
−0.453704 + 0.891153i \(0.649898\pi\)
\(854\) −3.15190e16 1.25426e16i −2.37440 0.944861i
\(855\) −3.46055e15 −0.259019
\(856\) −1.02657e16 2.21139e16i −0.763455 1.64460i
\(857\) −7.74414e15 −0.572240 −0.286120 0.958194i \(-0.592366\pi\)
−0.286120 + 0.958194i \(0.592366\pi\)
\(858\) −2.37944e15 9.46865e14i −0.174700 0.0695197i
\(859\) 6.93775e15i 0.506123i 0.967450 + 0.253061i \(0.0814375\pi\)
−0.967450 + 0.253061i \(0.918563\pi\)
\(860\) 1.31522e16 + 1.24369e16i 0.953360 + 0.901513i
\(861\) 2.42992e16i 1.75015i
\(862\) −4.44266e15 + 1.11642e16i −0.317946 + 0.798986i
\(863\) 1.06340e16 0.756201 0.378101 0.925765i \(-0.376577\pi\)
0.378101 + 0.925765i \(0.376577\pi\)
\(864\) −4.68223e15 + 1.39960e16i −0.330847 + 0.988959i
\(865\) 3.07608e15 0.215978
\(866\) −1.84016e15 + 4.62425e15i −0.128383 + 0.322621i
\(867\) 3.39981e15i 0.235694i
\(868\) −8.72511e15 8.25060e15i −0.601052 0.568365i
\(869\) 3.14968e15i 0.215604i
\(870\) −7.95889e15 3.16714e15i −0.541373 0.215432i
\(871\) 5.17194e15 0.349586
\(872\) −5.07821e15 1.09392e16i −0.341091 0.734761i
\(873\) 1.16380e15 0.0776784
\(874\) −3.53641e15 1.40727e15i −0.234558 0.0933393i
\(875\) 8.78372e15i 0.578941i
\(876\) 9.44259e15 9.98565e15i 0.618470 0.654039i
\(877\) 1.60338e16i 1.04361i −0.853064 0.521807i \(-0.825258\pi\)
0.853064 0.521807i \(-0.174742\pi\)
\(878\) −7.02516e15 + 1.76540e16i −0.454398 + 1.14189i
\(879\) 1.95369e15 0.125579
\(880\) −4.35184e14 7.77835e15i −0.0277983 0.496859i
\(881\) −1.14261e16 −0.725319 −0.362659 0.931922i \(-0.618131\pi\)
−0.362659 + 0.931922i \(0.618131\pi\)
\(882\) 4.82285e15 1.21196e16i 0.304247 0.764561i
\(883\) 2.92988e16i 1.83682i −0.395631 0.918409i \(-0.629474\pi\)
0.395631 0.918409i \(-0.370526\pi\)
\(884\) −1.07294e16 + 1.13465e16i −0.668481 + 0.706927i
\(885\) 2.67420e16i 1.65579i
\(886\) 1.84633e16 + 7.34721e15i 1.13612 + 0.452103i
\(887\) 1.75093e16 1.07075 0.535375 0.844614i \(-0.320170\pi\)
0.535375 + 0.844614i \(0.320170\pi\)
\(888\) −9.68479e15 + 4.49588e15i −0.588598 + 0.273239i
\(889\) −4.52606e15 −0.273376
\(890\) 3.49364e15 + 1.39025e15i 0.209717 + 0.0834541i
\(891\) 8.96408e14i 0.0534784i
\(892\) −6.51130e15 6.15719e15i −0.386065 0.365070i
\(893\) 4.52665e15i 0.266744i
\(894\) −2.98410e15 + 7.49893e15i −0.174766 + 0.439181i
\(895\) 7.63394e15 0.444347
\(896\) 1.29107e16 + 2.41757e16i 0.746891 + 1.39857i
\(897\) 7.81140e15 0.449128
\(898\) −3.83836e15 + 9.64565e15i −0.219344 + 0.551203i
\(899\) 5.28897e15i 0.300395i
\(900\) 8.70186e15 + 8.22862e15i 0.491223 + 0.464508i
\(901\) 1.16753e15i 0.0655063i
\(902\) 9.04386e15 + 3.59888e15i 0.504333 + 0.200693i
\(903\) −1.69286e16 −0.938294
\(904\) −8.06736e15 + 3.74503e15i −0.444432 + 0.206314i
\(905\) −1.01077e16 −0.553458
\(906\) −2.01269e16 8.00922e15i −1.09540 0.435898i
\(907\) 2.44390e16i 1.32204i 0.750370 + 0.661018i \(0.229875\pi\)
−0.750370 + 0.661018i \(0.770125\pi\)
\(908\) −5.55095e15 + 5.87019e15i −0.298466 + 0.315631i
\(909\) 2.94732e15i 0.157517i
\(910\) 1.38478e16 3.47990e16i 0.735620 1.84859i
\(911\) 1.21506e15 0.0641576 0.0320788 0.999485i \(-0.489787\pi\)
0.0320788 + 0.999485i \(0.489787\pi\)
\(912\) 2.28750e14 + 4.08860e15i 0.0120057 + 0.214587i
\(913\) −7.85537e14 −0.0409805
\(914\) 1.32998e16 3.34218e16i 0.689668 1.73311i
\(915\) 3.16446e16i 1.63111i
\(916\) 9.41064e15 9.95187e15i 0.482163 0.509894i
\(917\) 3.95764e14i 0.0201560i
\(918\) 2.22287e16 + 8.84560e15i 1.12533 + 0.447809i
\(919\) 1.48461e16 0.747095 0.373548 0.927611i \(-0.378141\pi\)
0.373548 + 0.927611i \(0.378141\pi\)
\(920\) 1.00057e16 + 2.15538e16i 0.500512 + 1.07818i
\(921\) 2.58006e16 1.28293
\(922\) −6.08739e15 2.42240e15i −0.300892 0.119736i
\(923\) 4.22002e15i 0.207350i
\(924\) 5.29378e15 + 5.00589e15i 0.258565 + 0.244503i
\(925\) 2.46051e16i 1.19466i
\(926\) −8.85578e14 + 2.22542e15i −0.0427432 + 0.107412i
\(927\) 5.66802e15 0.271952
\(928\) 3.82970e15 1.14476e16i 0.182663 0.546012i
\(929\) 2.85016e16 1.35140 0.675698 0.737179i \(-0.263843\pi\)
0.675698 + 0.737179i \(0.263843\pi\)
\(930\) −4.14174e15 + 1.04080e16i −0.195221 + 0.490583i
\(931\) 1.02777e16i 0.481586i
\(932\) −9.23880e15 8.73636e15i −0.430356 0.406952i
\(933\) 8.91423e15i 0.412795i
\(934\) −2.92873e16 1.16545e16i −1.34825 0.536520i
\(935\) −1.26287e16 −0.577958
\(936\) 4.21421e15 + 9.07804e15i 0.191734 + 0.413024i
\(937\) −3.85184e16 −1.74221 −0.871106 0.491096i \(-0.836597\pi\)
−0.871106 + 0.491096i \(0.836597\pi\)
\(938\) −1.36715e16 5.44039e15i −0.614753 0.244633i
\(939\) 1.57327e16i 0.703301i
\(940\) −1.94177e16 + 2.05344e16i −0.862967 + 0.912598i
\(941\) 2.94192e16i 1.29983i −0.760005 0.649917i \(-0.774804\pi\)
0.760005 0.649917i \(-0.225196\pi\)
\(942\) 9.59026e15 2.40999e16i 0.421260 1.05861i
\(943\) −2.96899e16 −1.29657
\(944\) 3.76265e16 2.10513e15i 1.63361 0.0913973i
\(945\) −5.73783e16 −2.47670
\(946\) −2.50725e15 + 6.30062e15i −0.107596 + 0.270385i
\(947\) 1.23589e16i 0.527297i 0.964619 + 0.263649i \(0.0849259\pi\)
−0.964619 + 0.263649i \(0.915074\pi\)
\(948\) 7.10189e15 7.51033e15i 0.301251 0.318576i
\(949\) 2.64662e16i 1.11616i
\(950\) 8.76780e15 + 3.48903e15i 0.367630 + 0.146293i
\(951\) 2.02788e16 0.845377
\(952\) 4.02976e16 1.87070e16i 1.67023 0.775355i
\(953\) 3.43202e15 0.141429 0.0707145 0.997497i \(-0.477472\pi\)
0.0707145 + 0.997497i \(0.477472\pi\)
\(954\) −6.95256e14 2.76668e14i −0.0284858 0.0113356i
\(955\) 7.29380e15i 0.297123i
\(956\) −2.67180e16 2.52650e16i −1.08215 1.02329i
\(957\) 3.20898e15i 0.129226i
\(958\) −1.27772e14 + 3.21086e14i −0.00511594 + 0.0128562i
\(959\) 7.82516e14 0.0311524
\(960\) 1.65009e16 1.95285e16i 0.653155 0.772997i
\(961\) −1.84920e16 −0.727787
\(962\) −7.60265e15 + 1.91052e16i −0.297510 + 0.747632i
\(963\) 2.53298e16i 0.985570i
\(964\) 1.47987e16 + 1.39939e16i 0.572532 + 0.541395i
\(965\) 3.87835e16i 1.49193i
\(966\) −2.06486e16 8.21686e15i −0.789801 0.314291i
\(967\) −1.06675e16 −0.405712 −0.202856 0.979209i \(-0.565022\pi\)
−0.202856 + 0.979209i \(0.565022\pi\)
\(968\) −2.13377e16 + 9.90538e15i −0.806924 + 0.374590i
\(969\) 6.63815e15 0.249613
\(970\) −5.31940e15 2.11678e15i −0.198892 0.0791466i
\(971\) 4.21885e16i 1.56851i −0.620437 0.784256i \(-0.713045\pi\)
0.620437 0.784256i \(-0.286955\pi\)
\(972\) 1.73600e16 1.83585e16i 0.641780 0.678690i
\(973\) 6.24540e16i 2.29583i
\(974\) 1.04066e16 2.61514e16i 0.380395 0.955917i
\(975\) −1.93667e16 −0.703932
\(976\) −4.45246e16 + 2.49107e15i −1.60926 + 0.0900350i
\(977\) 1.40324e16 0.504326 0.252163 0.967685i \(-0.418858\pi\)
0.252163 + 0.967685i \(0.418858\pi\)
\(978\) −5.70429e15 + 1.43347e16i −0.203863 + 0.512299i
\(979\) 1.40862e15i 0.0500596i
\(980\) −4.40877e16 + 4.66233e16i −1.55802 + 1.64763i
\(981\) 1.25301e16i 0.440326i
\(982\) 3.22605e16 + 1.28377e16i 1.12735 + 0.448614i
\(983\) 4.61601e16 1.60407 0.802033 0.597280i \(-0.203752\pi\)
0.802033 + 0.597280i \(0.203752\pi\)
\(984\) 1.34501e16 + 2.89735e16i 0.464785 + 1.00122i
\(985\) 6.02587e16 2.07071
\(986\) −1.81813e16 7.23501e15i −0.621301 0.247239i
\(987\) 2.64305e16i 0.898176i
\(988\) 5.72988e15 + 5.41826e15i 0.193634 + 0.183104i
\(989\) 2.06842e16i 0.695118i
\(990\) −2.99261e15 + 7.52030e15i −0.100013 + 0.251329i
\(991\) −4.19157e16 −1.39307 −0.696534 0.717524i \(-0.745275\pi\)
−0.696534 + 0.717524i \(0.745275\pi\)
\(992\) −1.49704e16 5.00820e15i −0.494787 0.165526i
\(993\) 1.51045e16 0.496460
\(994\) 4.43906e15 1.11552e16i 0.145100 0.364630i
\(995\) 2.86952e16i 0.932785i
\(996\) −1.87309e15 1.77123e15i −0.0605526 0.0572595i
\(997\) 2.51325e16i 0.808002i 0.914759 + 0.404001i \(0.132381\pi\)
−0.914759 + 0.404001i \(0.867619\pi\)
\(998\) 5.13542e16 + 2.04358e16i 1.64194 + 0.653390i
\(999\) 3.15015e16 1.00166
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 8.12.b.a.5.5 10
3.2 odd 2 72.12.d.b.37.6 10
4.3 odd 2 32.12.b.a.17.4 10
8.3 odd 2 32.12.b.a.17.7 10
8.5 even 2 inner 8.12.b.a.5.6 yes 10
16.3 odd 4 256.12.a.o.1.7 10
16.5 even 4 256.12.a.p.1.7 10
16.11 odd 4 256.12.a.o.1.4 10
16.13 even 4 256.12.a.p.1.4 10
24.5 odd 2 72.12.d.b.37.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.12.b.a.5.5 10 1.1 even 1 trivial
8.12.b.a.5.6 yes 10 8.5 even 2 inner
32.12.b.a.17.4 10 4.3 odd 2
32.12.b.a.17.7 10 8.3 odd 2
72.12.d.b.37.5 10 24.5 odd 2
72.12.d.b.37.6 10 3.2 odd 2
256.12.a.o.1.4 10 16.11 odd 4
256.12.a.o.1.7 10 16.3 odd 4
256.12.a.p.1.4 10 16.13 even 4
256.12.a.p.1.7 10 16.5 even 4