Properties

Label 21.9.f.b.10.4
Level $21$
Weight $9$
Character 21.10
Analytic conductor $8.555$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [21,9,Mod(10,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.10");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 21.f (of order \(6\), degree \(2\), 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: \(8.55495081128\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 1331 x^{10} + 1482 x^{9} + 1359381 x^{8} + 1222227 x^{7} + 474169529 x^{6} + 1911324162 x^{5} + 121870629463 x^{4} + \cdots + 556282980265104 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{5}\cdot 7^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 10.4
Root \(-5.65790 + 9.79977i\) of defining polynomial
Character \(\chi\) \(=\) 21.10
Dual form 21.9.f.b.19.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(6.15790 + 10.6658i) q^{2} +(40.5000 + 23.3827i) q^{3} +(52.1605 - 90.3446i) q^{4} +(599.787 - 346.287i) q^{5} +575.953i q^{6} +(-419.022 - 2364.15i) q^{7} +4437.64 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\) \(q+(6.15790 + 10.6658i) q^{2} +(40.5000 + 23.3827i) q^{3} +(52.1605 - 90.3446i) q^{4} +(599.787 - 346.287i) q^{5} +575.953i q^{6} +(-419.022 - 2364.15i) q^{7} +4437.64 q^{8} +(1093.50 + 1894.00i) q^{9} +(7386.86 + 4264.81i) q^{10} +(-3938.27 + 6821.28i) q^{11} +(4225.00 - 2439.31i) q^{12} +17386.7i q^{13} +(22635.3 - 19027.4i) q^{14} +32388.5 q^{15} +(13973.5 + 24202.8i) q^{16} +(71270.0 + 41147.8i) q^{17} +(-13467.3 + 23326.1i) q^{18} +(-57863.8 + 33407.7i) q^{19} -72250.1i q^{20} +(38309.9 - 105546. i) q^{21} -97005.8 q^{22} +(-131172. - 227197. i) q^{23} +(179725. + 103764. i) q^{24} +(44517.2 - 77106.0i) q^{25} +(-185443. + 107065. i) q^{26} +102276. i q^{27} +(-235445. - 85459.0i) q^{28} -941711. q^{29} +(199445. + 345449. i) q^{30} +(-665638. - 384306. i) q^{31} +(395924. - 685760. i) q^{32} +(-319000. + 184174. i) q^{33} +1.01354e6i q^{34} +(-1.07000e6 - 1.27289e6i) q^{35} +228150. q^{36} +(1.75477e6 + 3.03936e6i) q^{37} +(-712640. - 411443. i) q^{38} +(-406547. + 704160. i) q^{39} +(2.66164e6 - 1.53670e6i) q^{40} -2.49329e6i q^{41} +(1.36164e6 - 241337. i) q^{42} +5.71816e6 q^{43} +(410844. + 711602. i) q^{44} +(1.31173e6 + 757330. i) q^{45} +(1.61549e6 - 2.79811e6i) q^{46} +(-3.24842e6 + 1.87548e6i) q^{47} +1.30695e6i q^{48} +(-5.41364e6 + 1.98127e6i) q^{49} +1.09653e6 q^{50} +(1.92429e6 + 3.33297e6i) q^{51} +(1.57079e6 + 906898. i) q^{52} +(-2.12611e6 + 3.68253e6i) q^{53} +(-1.09085e6 + 629805. i) q^{54} +5.45508e6i q^{55} +(-1.85947e6 - 1.04913e7i) q^{56} -3.12465e6 q^{57} +(-5.79897e6 - 1.00441e7i) q^{58} +(-8.47648e6 - 4.89390e6i) q^{59} +(1.68940e6 - 2.92613e6i) q^{60} +(-2.00337e7 + 1.15665e7i) q^{61} -9.46608e6i q^{62} +(4.01950e6 - 3.37883e6i) q^{63} +1.69067e7 q^{64} +(6.02078e6 + 1.04283e7i) q^{65} +(-3.92874e6 - 2.26826e6i) q^{66} +(-7.18931e6 + 1.24523e7i) q^{67} +(7.43496e6 - 4.29258e6i) q^{68} -1.22686e7i q^{69} +(6.98740e6 - 1.92507e7i) q^{70} +2.47374e7 q^{71} +(4.85256e6 + 8.40488e6i) q^{72} +(-4.43036e7 - 2.55787e7i) q^{73} +(-2.16114e7 + 3.74321e7i) q^{74} +(3.60589e6 - 2.08186e6i) q^{75} +6.97025e6i q^{76} +(1.77768e7 + 6.45240e6i) q^{77} -1.00139e7 q^{78} +(1.40231e6 + 2.42887e6i) q^{79} +(1.67622e7 + 9.67767e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(2.65930e7 - 1.53535e7i) q^{82} +3.15219e7i q^{83} +(-7.53726e6 - 8.96643e6i) q^{84} +5.69958e7 q^{85} +(3.52119e7 + 6.09888e7i) q^{86} +(-3.81393e7 - 2.20197e7i) q^{87} +(-1.74766e7 + 3.02704e7i) q^{88} +(9.41691e7 - 5.43685e7i) q^{89} +1.86543e7i q^{90} +(4.11048e7 - 7.28540e6i) q^{91} -2.73680e7 q^{92} +(-1.79722e7 - 3.11288e7i) q^{93} +(-4.00070e7 - 2.30980e7i) q^{94} +(-2.31373e7 + 4.00750e7i) q^{95} +(3.20698e7 - 1.85155e7i) q^{96} -4.54417e7i q^{97} +(-5.44684e7 - 4.55404e7i) q^{98} -1.72260e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.15790 + 10.6658i 0.384869 + 0.666612i 0.991751 0.128179i \(-0.0409133\pi\)
−0.606882 + 0.794792i \(0.707580\pi\)
\(3\) 40.5000 + 23.3827i 0.500000 + 0.288675i
\(4\) 52.1605 90.3446i 0.203752 0.352909i
\(5\) 599.787 346.287i 0.959659 0.554060i 0.0635911 0.997976i \(-0.479745\pi\)
0.896068 + 0.443916i \(0.146411\pi\)
\(6\) 575.953i 0.444408i
\(7\) −419.022 2364.15i −0.174520 0.984654i
\(8\) 4437.64 1.08341
\(9\) 1093.50 + 1894.00i 0.166667 + 0.288675i
\(10\) 7386.86 + 4264.81i 0.738686 + 0.426481i
\(11\) −3938.27 + 6821.28i −0.268989 + 0.465902i −0.968601 0.248620i \(-0.920023\pi\)
0.699612 + 0.714523i \(0.253356\pi\)
\(12\) 4225.00 2439.31i 0.203752 0.117636i
\(13\) 17386.7i 0.608756i 0.952551 + 0.304378i \(0.0984486\pi\)
−0.952551 + 0.304378i \(0.901551\pi\)
\(14\) 22635.3 19027.4i 0.589215 0.495300i
\(15\) 32388.5 0.639773
\(16\) 13973.5 + 24202.8i 0.213218 + 0.369305i
\(17\) 71270.0 + 41147.8i 0.853319 + 0.492664i 0.861769 0.507300i \(-0.169357\pi\)
−0.00845047 + 0.999964i \(0.502690\pi\)
\(18\) −13467.3 + 23326.1i −0.128290 + 0.222204i
\(19\) −57863.8 + 33407.7i −0.444010 + 0.256349i −0.705297 0.708912i \(-0.749186\pi\)
0.261287 + 0.965261i \(0.415853\pi\)
\(20\) 72250.1i 0.451563i
\(21\) 38309.9 105546.i 0.196985 0.542706i
\(22\) −97005.8 −0.414102
\(23\) −131172. 227197.i −0.468738 0.811878i 0.530624 0.847608i \(-0.321958\pi\)
−0.999361 + 0.0357297i \(0.988624\pi\)
\(24\) 179725. + 103764.i 0.541704 + 0.312753i
\(25\) 44517.2 77106.0i 0.113964 0.197391i
\(26\) −185443. + 107065.i −0.405804 + 0.234291i
\(27\) 102276.i 0.192450i
\(28\) −235445. 85459.0i −0.383052 0.139036i
\(29\) −941711. −1.33145 −0.665726 0.746196i \(-0.731878\pi\)
−0.665726 + 0.746196i \(0.731878\pi\)
\(30\) 199445. + 345449.i 0.246229 + 0.426481i
\(31\) −665638. 384306.i −0.720761 0.416131i 0.0942719 0.995546i \(-0.469948\pi\)
−0.815033 + 0.579415i \(0.803281\pi\)
\(32\) 395924. 685760.i 0.377582 0.653992i
\(33\) −319000. + 184174.i −0.268989 + 0.155301i
\(34\) 1.01354e6i 0.758444i
\(35\) −1.07000e6 1.27289e6i −0.713036 0.848238i
\(36\) 228150. 0.135835
\(37\) 1.75477e6 + 3.03936e6i 0.936298 + 1.62172i 0.772303 + 0.635255i \(0.219105\pi\)
0.163995 + 0.986461i \(0.447562\pi\)
\(38\) −712640. 411443.i −0.341771 0.197322i
\(39\) −406547. + 704160.i −0.175733 + 0.304378i
\(40\) 2.66164e6 1.53670e6i 1.03970 0.600273i
\(41\) 2.49329e6i 0.882345i −0.897422 0.441172i \(-0.854563\pi\)
0.897422 0.441172i \(-0.145437\pi\)
\(42\) 1.36164e6 241337.i 0.437588 0.0775581i
\(43\) 5.71816e6 1.67256 0.836282 0.548299i \(-0.184725\pi\)
0.836282 + 0.548299i \(0.184725\pi\)
\(44\) 410844. + 711602.i 0.109614 + 0.189857i
\(45\) 1.31173e6 + 757330.i 0.319886 + 0.184687i
\(46\) 1.61549e6 2.79811e6i 0.360805 0.624933i
\(47\) −3.24842e6 + 1.87548e6i −0.665704 + 0.384345i −0.794447 0.607333i \(-0.792239\pi\)
0.128743 + 0.991678i \(0.458906\pi\)
\(48\) 1.30695e6i 0.246203i
\(49\) −5.41364e6 + 1.98127e6i −0.939086 + 0.343683i
\(50\) 1.09653e6 0.175445
\(51\) 1.92429e6 + 3.33297e6i 0.284440 + 0.492664i
\(52\) 1.57079e6 + 906898.i 0.214835 + 0.124035i
\(53\) −2.12611e6 + 3.68253e6i −0.269452 + 0.466705i −0.968720 0.248154i \(-0.920176\pi\)
0.699268 + 0.714859i \(0.253509\pi\)
\(54\) −1.09085e6 + 629805.i −0.128290 + 0.0740680i
\(55\) 5.45508e6i 0.596143i
\(56\) −1.85947e6 1.04913e7i −0.189076 1.06678i
\(57\) −3.12465e6 −0.296007
\(58\) −5.79897e6 1.00441e7i −0.512435 0.887563i
\(59\) −8.47648e6 4.89390e6i −0.699532 0.403875i 0.107641 0.994190i \(-0.465670\pi\)
−0.807173 + 0.590315i \(0.799004\pi\)
\(60\) 1.68940e6 2.92613e6i 0.130355 0.225781i
\(61\) −2.00337e7 + 1.15665e7i −1.44691 + 0.835376i −0.998296 0.0583477i \(-0.981417\pi\)
−0.448618 + 0.893724i \(0.648083\pi\)
\(62\) 9.46608e6i 0.640624i
\(63\) 4.01950e6 3.37883e6i 0.255158 0.214488i
\(64\) 1.69067e7 1.00772
\(65\) 6.02078e6 + 1.04283e7i 0.337287 + 0.584198i
\(66\) −3.92874e6 2.26826e6i −0.207051 0.119541i
\(67\) −7.18931e6 + 1.24523e7i −0.356770 + 0.617944i −0.987419 0.158124i \(-0.949455\pi\)
0.630649 + 0.776068i \(0.282789\pi\)
\(68\) 7.43496e6 4.29258e6i 0.347731 0.200762i
\(69\) 1.22686e7i 0.541252i
\(70\) 6.98740e6 1.92507e7i 0.291020 0.801779i
\(71\) 2.47374e7 0.973464 0.486732 0.873551i \(-0.338189\pi\)
0.486732 + 0.873551i \(0.338189\pi\)
\(72\) 4.85256e6 + 8.40488e6i 0.180568 + 0.312753i
\(73\) −4.43036e7 2.55787e7i −1.56008 0.900715i −0.997247 0.0741458i \(-0.976377\pi\)
−0.562836 0.826569i \(-0.690290\pi\)
\(74\) −2.16114e7 + 3.74321e7i −0.720704 + 1.24830i
\(75\) 3.60589e6 2.08186e6i 0.113964 0.0657971i
\(76\) 6.97025e6i 0.208927i
\(77\) 1.77768e7 + 6.45240e6i 0.505696 + 0.183552i
\(78\) −1.00139e7 −0.270536
\(79\) 1.40231e6 + 2.42887e6i 0.0360028 + 0.0623586i 0.883465 0.468497i \(-0.155204\pi\)
−0.847463 + 0.530855i \(0.821871\pi\)
\(80\) 1.67622e7 + 9.67767e6i 0.409234 + 0.236271i
\(81\) −2.39148e6 + 4.14217e6i −0.0555556 + 0.0962250i
\(82\) 2.65930e7 1.53535e7i 0.588182 0.339587i
\(83\) 3.15219e7i 0.664201i 0.943244 + 0.332101i \(0.107757\pi\)
−0.943244 + 0.332101i \(0.892243\pi\)
\(84\) −7.53726e6 8.96643e6i −0.151390 0.180095i
\(85\) 5.69958e7 1.09186
\(86\) 3.52119e7 + 6.09888e7i 0.643718 + 1.11495i
\(87\) −3.81393e7 2.20197e7i −0.665726 0.384357i
\(88\) −1.74766e7 + 3.02704e7i −0.291425 + 0.504763i
\(89\) 9.41691e7 5.43685e7i 1.50089 0.866538i 0.500888 0.865512i \(-0.333007\pi\)
0.999999 0.00102619i \(-0.000326645\pi\)
\(90\) 1.86543e7i 0.284320i
\(91\) 4.11048e7 7.28540e6i 0.599414 0.106240i
\(92\) −2.73680e7 −0.382025
\(93\) −1.79722e7 3.11288e7i −0.240254 0.416131i
\(94\) −4.00070e7 2.30980e7i −0.512418 0.295844i
\(95\) −2.31373e7 + 4.00750e7i −0.284066 + 0.492016i
\(96\) 3.20698e7 1.85155e7i 0.377582 0.217997i
\(97\) 4.54417e7i 0.513296i −0.966505 0.256648i \(-0.917382\pi\)
0.966505 0.256648i \(-0.0826180\pi\)
\(98\) −5.44684e7 4.55404e7i −0.590528 0.493733i
\(99\) −1.72260e7 −0.179326
\(100\) −4.64408e6 8.04378e6i −0.0464408 0.0804378i
\(101\) −5.93288e7 3.42535e7i −0.570138 0.329169i 0.187066 0.982347i \(-0.440102\pi\)
−0.757204 + 0.653178i \(0.773435\pi\)
\(102\) −2.36992e7 + 4.10482e7i −0.218944 + 0.379222i
\(103\) 3.24315e7 1.87243e7i 0.288150 0.166363i −0.348958 0.937139i \(-0.613464\pi\)
0.637107 + 0.770775i \(0.280131\pi\)
\(104\) 7.71558e7i 0.659531i
\(105\) −1.35715e7 7.65714e7i −0.111653 0.629955i
\(106\) −5.23694e7 −0.414815
\(107\) −6.48143e7 1.12262e8i −0.494465 0.856438i 0.505515 0.862818i \(-0.331303\pi\)
−0.999980 + 0.00637956i \(0.997969\pi\)
\(108\) 9.24008e6 + 5.33476e6i 0.0679173 + 0.0392121i
\(109\) −1.05665e8 + 1.83016e8i −0.748554 + 1.29653i 0.199961 + 0.979804i \(0.435918\pi\)
−0.948516 + 0.316730i \(0.897415\pi\)
\(110\) −5.81828e7 + 3.35919e7i −0.397397 + 0.229437i
\(111\) 1.64125e8i 1.08114i
\(112\) 5.13639e7 4.31769e7i 0.326427 0.274397i
\(113\) 1.54451e8 0.947278 0.473639 0.880719i \(-0.342940\pi\)
0.473639 + 0.880719i \(0.342940\pi\)
\(114\) −1.92413e7 3.33269e7i −0.113924 0.197322i
\(115\) −1.57351e8 9.08464e7i −0.899657 0.519417i
\(116\) −4.91201e7 + 8.50786e7i −0.271286 + 0.469881i
\(117\) −3.29303e7 + 1.90123e7i −0.175733 + 0.101459i
\(118\) 1.20545e8i 0.621756i
\(119\) 6.74159e7 1.85735e8i 0.336182 0.926203i
\(120\) 1.43729e8 0.693136
\(121\) 7.61596e7 + 1.31912e8i 0.355290 + 0.615380i
\(122\) −2.46732e8 1.42451e8i −1.11374 0.643020i
\(123\) 5.82999e7 1.00978e8i 0.254711 0.441172i
\(124\) −6.94400e7 + 4.00912e7i −0.293713 + 0.169575i
\(125\) 2.08874e8i 0.855548i
\(126\) 6.07896e7 + 2.20647e7i 0.241183 + 0.0875418i
\(127\) 2.75296e8 1.05824 0.529120 0.848547i \(-0.322522\pi\)
0.529120 + 0.848547i \(0.322522\pi\)
\(128\) 2.75306e6 + 4.76845e6i 0.0102560 + 0.0177638i
\(129\) 2.31586e8 + 1.33706e8i 0.836282 + 0.482828i
\(130\) −7.41508e7 + 1.28433e8i −0.259622 + 0.449679i
\(131\) 2.88035e8 1.66297e8i 0.978047 0.564676i 0.0763670 0.997080i \(-0.475668\pi\)
0.901680 + 0.432404i \(0.142335\pi\)
\(132\) 3.84265e7i 0.126571i
\(133\) 1.03227e8 + 1.22800e8i 0.329904 + 0.392458i
\(134\) −1.77084e8 −0.549239
\(135\) 3.54168e7 + 6.13437e7i 0.106629 + 0.184687i
\(136\) 3.16271e8 + 1.82599e8i 0.924493 + 0.533756i
\(137\) 1.88426e8 3.26363e8i 0.534882 0.926442i −0.464287 0.885685i \(-0.653690\pi\)
0.999169 0.0407575i \(-0.0129771\pi\)
\(138\) 1.30855e8 7.55490e7i 0.360805 0.208311i
\(139\) 3.05080e8i 0.817250i −0.912702 0.408625i \(-0.866008\pi\)
0.912702 0.408625i \(-0.133992\pi\)
\(140\) −1.70810e8 + 3.02744e7i −0.444633 + 0.0788067i
\(141\) −1.75415e8 −0.443803
\(142\) 1.52330e8 + 2.63844e8i 0.374656 + 0.648923i
\(143\) −1.18599e8 6.84733e7i −0.283621 0.163749i
\(144\) −3.05600e7 + 5.29315e7i −0.0710728 + 0.123102i
\(145\) −5.64826e8 + 3.26103e8i −1.27774 + 0.737704i
\(146\) 6.30045e8i 1.38663i
\(147\) −2.65580e8 4.63442e7i −0.568756 0.0992491i
\(148\) 3.66119e8 0.763090
\(149\) 2.64372e8 + 4.57905e8i 0.536377 + 0.929032i 0.999095 + 0.0425269i \(0.0135408\pi\)
−0.462718 + 0.886505i \(0.653126\pi\)
\(150\) 4.44094e7 + 2.56398e7i 0.0877224 + 0.0506465i
\(151\) 1.17540e8 2.03585e8i 0.226088 0.391595i −0.730558 0.682851i \(-0.760740\pi\)
0.956645 + 0.291256i \(0.0940731\pi\)
\(152\) −2.56779e8 + 1.48251e8i −0.481044 + 0.277731i
\(153\) 1.79980e8i 0.328443i
\(154\) 4.06476e7 + 2.29337e8i 0.0722690 + 0.407747i
\(155\) −5.32321e8 −0.922246
\(156\) 4.24114e7 + 7.34587e7i 0.0716117 + 0.124035i
\(157\) −3.13489e8 1.80993e8i −0.515969 0.297895i 0.219315 0.975654i \(-0.429618\pi\)
−0.735284 + 0.677759i \(0.762951\pi\)
\(158\) −1.72706e7 + 2.99135e7i −0.0277127 + 0.0479998i
\(159\) −1.72215e8 + 9.94282e7i −0.269452 + 0.155568i
\(160\) 5.48413e8i 0.836812i
\(161\) −4.82164e8 + 4.05311e8i −0.717614 + 0.603233i
\(162\) −5.89061e7 −0.0855264
\(163\) −5.75962e8 9.97595e8i −0.815912 1.41320i −0.908671 0.417512i \(-0.862902\pi\)
0.0927592 0.995689i \(-0.470431\pi\)
\(164\) −2.25256e8 1.30051e8i −0.311387 0.179779i
\(165\) −1.27555e8 + 2.20931e8i −0.172092 + 0.298072i
\(166\) −3.36206e8 + 1.94109e8i −0.442765 + 0.255630i
\(167\) 3.43851e8i 0.442084i 0.975264 + 0.221042i \(0.0709458\pi\)
−0.975264 + 0.221042i \(0.929054\pi\)
\(168\) 1.70005e8 4.68376e8i 0.213415 0.587973i
\(169\) 5.13434e8 0.629416
\(170\) 3.50974e8 + 6.07906e8i 0.420223 + 0.727848i
\(171\) −1.26548e8 7.30626e7i −0.148003 0.0854498i
\(172\) 2.98262e8 5.16606e8i 0.340788 0.590263i
\(173\) 3.92504e8 2.26612e8i 0.438187 0.252988i −0.264641 0.964347i \(-0.585253\pi\)
0.702828 + 0.711359i \(0.251920\pi\)
\(174\) 5.42382e8i 0.591709i
\(175\) −2.00944e8 7.29363e7i −0.214251 0.0777663i
\(176\) −2.20125e8 −0.229413
\(177\) −2.28865e8 3.96406e8i −0.233177 0.403875i
\(178\) 1.15977e9 + 6.69592e8i 1.15529 + 0.667007i
\(179\) 7.05221e8 1.22148e9i 0.686931 1.18980i −0.285894 0.958261i \(-0.592291\pi\)
0.972826 0.231539i \(-0.0743760\pi\)
\(180\) 1.36841e8 7.90054e7i 0.130355 0.0752605i
\(181\) 1.66506e9i 1.55137i 0.631120 + 0.775685i \(0.282595\pi\)
−0.631120 + 0.775685i \(0.717405\pi\)
\(182\) 3.30824e8 + 3.93552e8i 0.301516 + 0.358688i
\(183\) −1.08182e9 −0.964609
\(184\) −5.82095e8 1.00822e9i −0.507835 0.879596i
\(185\) 2.10498e9 + 1.21531e9i 1.79705 + 1.03753i
\(186\) 2.21342e8 3.83376e8i 0.184932 0.320312i
\(187\) −5.61361e8 + 3.24102e8i −0.459066 + 0.265042i
\(188\) 3.91304e8i 0.313244i
\(189\) 2.41796e8 4.28559e7i 0.189497 0.0335864i
\(190\) −5.69909e8 −0.437312
\(191\) 3.07369e8 + 5.32378e8i 0.230954 + 0.400025i 0.958089 0.286470i \(-0.0924819\pi\)
−0.727135 + 0.686495i \(0.759149\pi\)
\(192\) 6.84720e8 + 3.95323e8i 0.503858 + 0.290902i
\(193\) 2.77018e7 4.79808e7i 0.0199654 0.0345811i −0.855870 0.517191i \(-0.826978\pi\)
0.875835 + 0.482610i \(0.160311\pi\)
\(194\) 4.84672e8 2.79825e8i 0.342169 0.197551i
\(195\) 5.63128e8i 0.389465i
\(196\) −1.03382e8 + 5.92437e8i −0.0700517 + 0.401438i
\(197\) −9.92633e8 −0.659058 −0.329529 0.944145i \(-0.606890\pi\)
−0.329529 + 0.944145i \(0.606890\pi\)
\(198\) −1.06076e8 1.83729e8i −0.0690170 0.119541i
\(199\) −3.82547e8 2.20864e8i −0.243934 0.140835i 0.373049 0.927811i \(-0.378312\pi\)
−0.616984 + 0.786976i \(0.711646\pi\)
\(200\) 1.97551e8 3.42169e8i 0.123470 0.213856i
\(201\) −5.82334e8 + 3.36211e8i −0.356770 + 0.205981i
\(202\) 8.43719e8i 0.506748i
\(203\) 3.94598e8 + 2.22635e9i 0.232365 + 1.31102i
\(204\) 4.01488e8 0.231820
\(205\) −8.63396e8 1.49545e9i −0.488871 0.846750i
\(206\) 3.99420e8 + 2.30605e8i 0.221800 + 0.128056i
\(207\) 2.86873e8 4.96879e8i 0.156246 0.270626i
\(208\) −4.20806e8 + 2.42952e8i −0.224817 + 0.129798i
\(209\) 5.26274e8i 0.275820i
\(210\) 7.33123e8 6.16270e8i 0.376964 0.316879i
\(211\) 9.54646e7 0.0481629 0.0240814 0.999710i \(-0.492334\pi\)
0.0240814 + 0.999710i \(0.492334\pi\)
\(212\) 2.21798e8 + 3.84165e8i 0.109803 + 0.190184i
\(213\) 1.00186e9 + 5.78426e8i 0.486732 + 0.281015i
\(214\) 7.98240e8 1.38259e9i 0.380608 0.659233i
\(215\) 3.42968e9 1.98013e9i 1.60509 0.926700i
\(216\) 4.53864e8i 0.208502i
\(217\) −6.29642e8 + 1.73470e9i −0.283958 + 0.782323i
\(218\) −2.60269e9 −1.15238
\(219\) −1.19620e9 2.07188e9i −0.520028 0.900715i
\(220\) 4.92838e8 + 2.84540e8i 0.210384 + 0.121465i
\(221\) −7.15423e8 + 1.23915e9i −0.299912 + 0.519463i
\(222\) −1.75053e9 + 1.01067e9i −0.720704 + 0.416099i
\(223\) 1.02921e9i 0.416183i −0.978109 0.208092i \(-0.933275\pi\)
0.978109 0.208092i \(-0.0667252\pi\)
\(224\) −1.78714e9 6.48676e8i −0.709851 0.257653i
\(225\) 1.94718e8 0.0759760
\(226\) 9.51095e8 + 1.64735e9i 0.364578 + 0.631467i
\(227\) −4.19700e9 2.42314e9i −1.58065 0.912587i −0.994765 0.102192i \(-0.967415\pi\)
−0.585883 0.810396i \(-0.699252\pi\)
\(228\) −1.62983e8 + 2.82295e8i −0.0603119 + 0.104463i
\(229\) 2.36871e9 1.36757e9i 0.861329 0.497289i −0.00312784 0.999995i \(-0.500996\pi\)
0.864457 + 0.502706i \(0.167662\pi\)
\(230\) 2.23769e9i 0.799630i
\(231\) 5.69085e8 + 6.76991e8i 0.199861 + 0.237758i
\(232\) −4.17898e9 −1.44251
\(233\) −6.07143e8 1.05160e9i −0.206000 0.356803i 0.744451 0.667677i \(-0.232711\pi\)
−0.950451 + 0.310875i \(0.899378\pi\)
\(234\) −4.05563e8 2.34152e8i −0.135268 0.0780970i
\(235\) −1.29891e9 + 2.24978e9i −0.425900 + 0.737680i
\(236\) −8.84275e8 + 5.10537e8i −0.285062 + 0.164581i
\(237\) 1.31159e8i 0.0415724i
\(238\) 2.39615e9 4.24694e8i 0.746804 0.132364i
\(239\) 1.57918e9 0.483996 0.241998 0.970277i \(-0.422197\pi\)
0.241998 + 0.970277i \(0.422197\pi\)
\(240\) 4.52580e8 + 7.83891e8i 0.136411 + 0.236271i
\(241\) 2.61845e9 + 1.51176e9i 0.776204 + 0.448142i 0.835083 0.550124i \(-0.185419\pi\)
−0.0588794 + 0.998265i \(0.518753\pi\)
\(242\) −9.37966e8 + 1.62461e9i −0.273480 + 0.473681i
\(243\) −1.93710e8 + 1.11839e8i −0.0555556 + 0.0320750i
\(244\) 2.41325e9i 0.680838i
\(245\) −2.56095e9 + 3.06301e9i −0.710781 + 0.850128i
\(246\) 1.43602e9 0.392121
\(247\) −5.80849e8 1.00606e9i −0.156054 0.270294i
\(248\) −2.95386e9 1.70541e9i −0.780878 0.450840i
\(249\) −7.37066e8 + 1.27664e9i −0.191738 + 0.332101i
\(250\) −2.22781e9 + 1.28623e9i −0.570319 + 0.329274i
\(251\) 5.42496e9i 1.36679i −0.730049 0.683394i \(-0.760503\pi\)
0.730049 0.683394i \(-0.239497\pi\)
\(252\) −9.55999e7 5.39382e8i −0.0237058 0.133750i
\(253\) 2.06636e9 0.504341
\(254\) 1.69524e9 + 2.93625e9i 0.407284 + 0.705436i
\(255\) 2.30833e9 + 1.33271e9i 0.545930 + 0.315193i
\(256\) 2.13015e9 3.68952e9i 0.495963 0.859033i
\(257\) 1.13951e9 6.57898e8i 0.261208 0.150809i −0.363677 0.931525i \(-0.618479\pi\)
0.624886 + 0.780716i \(0.285146\pi\)
\(258\) 3.29339e9i 0.743301i
\(259\) 6.45022e9 5.42211e9i 1.43343 1.20495i
\(260\) 1.25619e9 0.274891
\(261\) −1.02976e9 1.78360e9i −0.221909 0.384357i
\(262\) 3.54738e9 + 2.04808e9i 0.752840 + 0.434652i
\(263\) 3.07284e9 5.32231e9i 0.642269 1.11244i −0.342657 0.939461i \(-0.611327\pi\)
0.984925 0.172981i \(-0.0553400\pi\)
\(264\) −1.41561e9 + 8.17300e8i −0.291425 + 0.168254i
\(265\) 2.94498e9i 0.597170i
\(266\) −6.74102e8 + 1.85719e9i −0.134648 + 0.370963i
\(267\) 5.08513e9 1.00059
\(268\) 7.49996e8 + 1.29903e9i 0.145385 + 0.251814i
\(269\) −3.72246e8 2.14917e8i −0.0710921 0.0410451i 0.464033 0.885818i \(-0.346402\pi\)
−0.535125 + 0.844773i \(0.679735\pi\)
\(270\) −4.36187e8 + 7.55497e8i −0.0820762 + 0.142160i
\(271\) −4.12961e9 + 2.38423e9i −0.765653 + 0.442050i −0.831322 0.555791i \(-0.812415\pi\)
0.0656684 + 0.997841i \(0.479082\pi\)
\(272\) 2.29991e9i 0.420180i
\(273\) 1.83510e9 + 6.66081e8i 0.330376 + 0.119916i
\(274\) 4.64123e9 0.823437
\(275\) 3.50641e8 + 6.07328e8i 0.0613101 + 0.106192i
\(276\) −1.10840e9 6.39937e8i −0.191013 0.110281i
\(277\) −4.03571e9 + 6.99006e9i −0.685490 + 1.18730i 0.287793 + 0.957693i \(0.407079\pi\)
−0.973283 + 0.229611i \(0.926255\pi\)
\(278\) 3.25392e9 1.87865e9i 0.544789 0.314534i
\(279\) 1.68095e9i 0.277421i
\(280\) −4.74828e9 5.64862e9i −0.772510 0.918988i
\(281\) 2.68776e9 0.431087 0.215543 0.976494i \(-0.430848\pi\)
0.215543 + 0.976494i \(0.430848\pi\)
\(282\) −1.08019e9 1.87094e9i −0.170806 0.295844i
\(283\) −3.07841e9 1.77732e9i −0.479933 0.277089i 0.240456 0.970660i \(-0.422703\pi\)
−0.720388 + 0.693571i \(0.756036\pi\)
\(284\) 1.29031e9 2.23489e9i 0.198345 0.343544i
\(285\) −1.87412e9 + 1.08203e9i −0.284066 + 0.164005i
\(286\) 1.68661e9i 0.252087i
\(287\) −5.89453e9 + 1.04475e9i −0.868804 + 0.153987i
\(288\) 1.73177e9 0.251721
\(289\) −1.01600e8 1.75976e8i −0.0145647 0.0252268i
\(290\) −6.95629e9 4.01622e9i −0.983525 0.567839i
\(291\) 1.06255e9 1.84039e9i 0.148176 0.256648i
\(292\) −4.62180e9 + 2.66840e9i −0.635740 + 0.367045i
\(293\) 1.16597e9i 0.158203i −0.996867 0.0791016i \(-0.974795\pi\)
0.996867 0.0791016i \(-0.0252052\pi\)
\(294\) −1.14112e9 3.11800e9i −0.152736 0.417337i
\(295\) −6.77878e9 −0.895083
\(296\) 7.78706e9 + 1.34876e10i 1.01439 + 1.75698i
\(297\) −6.97652e8 4.02790e8i −0.0896629 0.0517669i
\(298\) −3.25595e9 + 5.63947e9i −0.412870 + 0.715111i
\(299\) 3.95019e9 2.28065e9i 0.494235 0.285347i
\(300\) 4.34364e8i 0.0536252i
\(301\) −2.39604e9 1.35186e10i −0.291896 1.64690i
\(302\) 2.89519e9 0.348056
\(303\) −1.60188e9 2.77453e9i −0.190046 0.329169i
\(304\) −1.61712e9 9.33643e8i −0.189342 0.109317i
\(305\) −8.01065e9 + 1.38749e10i −0.925696 + 1.60335i
\(306\) −1.91963e9 + 1.10830e9i −0.218944 + 0.126407i
\(307\) 1.55694e10i 1.75274i 0.481636 + 0.876372i \(0.340043\pi\)
−0.481636 + 0.876372i \(0.659957\pi\)
\(308\) 1.51018e9 1.26947e9i 0.167814 0.141066i
\(309\) 1.75130e9 0.192100
\(310\) −3.27798e9 5.67763e9i −0.354944 0.614781i
\(311\) −1.28785e10 7.43543e9i −1.37665 0.794812i −0.384899 0.922959i \(-0.625764\pi\)
−0.991755 + 0.128147i \(0.959097\pi\)
\(312\) −1.80411e9 + 3.12481e9i −0.190390 + 0.329766i
\(313\) 1.20730e10 6.97034e9i 1.25787 0.726234i 0.285213 0.958464i \(-0.407936\pi\)
0.972661 + 0.232230i \(0.0746023\pi\)
\(314\) 4.45815e9i 0.458602i
\(315\) 1.24080e9 3.41848e9i 0.126026 0.347209i
\(316\) 2.92581e8 0.0293425
\(317\) 8.43967e9 + 1.46179e10i 0.835773 + 1.44760i 0.893400 + 0.449263i \(0.148313\pi\)
−0.0576270 + 0.998338i \(0.518353\pi\)
\(318\) −2.12096e9 1.22454e9i −0.207408 0.119747i
\(319\) 3.70871e9 6.42367e9i 0.358146 0.620327i
\(320\) 1.01404e10 5.85456e9i 0.967063 0.558334i
\(321\) 6.06213e9i 0.570959i
\(322\) −7.29209e9 2.64679e9i −0.678310 0.246205i
\(323\) −5.49861e9 −0.505176
\(324\) 2.49482e8 + 4.32116e8i 0.0226391 + 0.0392121i
\(325\) 1.34062e9 + 7.74006e8i 0.120163 + 0.0693762i
\(326\) 7.09343e9 1.22862e10i 0.628038 1.08779i
\(327\) −8.55883e9 + 4.94144e9i −0.748554 + 0.432178i
\(328\) 1.10644e10i 0.955940i
\(329\) 5.79508e9 + 6.89391e9i 0.494625 + 0.588412i
\(330\) −3.14187e9 −0.264931
\(331\) 7.48921e8 + 1.29717e9i 0.0623913 + 0.108065i 0.895534 0.444993i \(-0.146794\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(332\) 2.84783e9 + 1.64420e9i 0.234402 + 0.135332i
\(333\) −3.83769e9 + 6.64707e9i −0.312099 + 0.540572i
\(334\) −3.66745e9 + 2.11740e9i −0.294699 + 0.170144i
\(335\) 9.95827e9i 0.790687i
\(336\) 3.08983e9 5.47641e8i 0.242425 0.0429674i
\(337\) 3.31551e9 0.257058 0.128529 0.991706i \(-0.458974\pi\)
0.128529 + 0.991706i \(0.458974\pi\)
\(338\) 3.16168e9 + 5.47619e9i 0.242243 + 0.419577i
\(339\) 6.25527e9 + 3.61148e9i 0.473639 + 0.273456i
\(340\) 2.97293e9 5.14926e9i 0.222469 0.385327i
\(341\) 5.24292e9 3.02700e9i 0.387753 0.223869i
\(342\) 1.79965e9i 0.131548i
\(343\) 6.95245e9 + 1.19685e10i 0.502298 + 0.864695i
\(344\) 2.53752e10 1.81207
\(345\) −4.24847e9 7.35856e9i −0.299886 0.519417i
\(346\) 4.83400e9 + 2.79091e9i 0.337289 + 0.194734i
\(347\) −1.16207e10 + 2.01277e10i −0.801522 + 1.38828i 0.117092 + 0.993121i \(0.462643\pi\)
−0.918614 + 0.395156i \(0.870691\pi\)
\(348\) −3.97873e9 + 2.29712e9i −0.271286 + 0.156627i
\(349\) 6.14767e9i 0.414390i 0.978300 + 0.207195i \(0.0664334\pi\)
−0.978300 + 0.207195i \(0.933567\pi\)
\(350\) −4.59470e8 2.59236e9i −0.0306186 0.172752i
\(351\) −1.77824e9 −0.117155
\(352\) 3.11851e9 + 5.40141e9i 0.203131 + 0.351833i
\(353\) −7.32923e9 4.23153e9i −0.472019 0.272520i 0.245065 0.969507i \(-0.421191\pi\)
−0.717085 + 0.696986i \(0.754524\pi\)
\(354\) 2.81866e9 4.88206e9i 0.179485 0.310878i
\(355\) 1.48371e10 8.56623e9i 0.934194 0.539357i
\(356\) 1.13436e10i 0.706235i
\(357\) 7.07333e9 5.94591e9i 0.435463 0.366054i
\(358\) 1.73707e10 1.05751
\(359\) −3.60495e9 6.24396e9i −0.217031 0.375909i 0.736868 0.676037i \(-0.236304\pi\)
−0.953899 + 0.300128i \(0.902971\pi\)
\(360\) 5.82101e9 + 3.36076e9i 0.346568 + 0.200091i
\(361\) −6.25963e9 + 1.08420e10i −0.368570 + 0.638382i
\(362\) −1.77592e10 + 1.02533e10i −1.03416 + 0.597074i
\(363\) 7.12326e9i 0.410254i
\(364\) 1.48585e9 4.09360e9i 0.0846387 0.233185i
\(365\) −3.54303e10 −1.99620
\(366\) −6.66175e9 1.15385e10i −0.371248 0.643020i
\(367\) −9.98844e9 5.76683e9i −0.550596 0.317887i 0.198766 0.980047i \(-0.436307\pi\)
−0.749362 + 0.662160i \(0.769640\pi\)
\(368\) 3.66586e9 6.34946e9i 0.199887 0.346214i
\(369\) 4.72229e9 2.72642e9i 0.254711 0.147057i
\(370\) 2.99351e10i 1.59725i
\(371\) 9.59694e9 + 3.48338e9i 0.506567 + 0.183868i
\(372\) −3.74976e9 −0.195809
\(373\) −1.73249e10 3.00077e10i −0.895028 1.55023i −0.833770 0.552112i \(-0.813822\pi\)
−0.0612579 0.998122i \(-0.519511\pi\)
\(374\) −6.91361e9 3.99157e9i −0.353361 0.204013i
\(375\) −4.88403e9 + 8.45940e9i −0.246975 + 0.427774i
\(376\) −1.44153e10 + 8.32270e9i −0.721230 + 0.416402i
\(377\) 1.63732e10i 0.810530i
\(378\) 1.94605e9 + 2.31504e9i 0.0953205 + 0.113394i
\(379\) −8.00514e9 −0.387982 −0.193991 0.981003i \(-0.562143\pi\)
−0.193991 + 0.981003i \(0.562143\pi\)
\(380\) 2.41371e9 + 4.18067e9i 0.115758 + 0.200498i
\(381\) 1.11495e10 + 6.43715e9i 0.529120 + 0.305488i
\(382\) −3.78549e9 + 6.55666e9i −0.177774 + 0.307914i
\(383\) 3.01500e10 1.74071e10i 1.40118 0.808970i 0.406663 0.913578i \(-0.366692\pi\)
0.994513 + 0.104609i \(0.0333590\pi\)
\(384\) 2.57496e8i 0.0118426i
\(385\) 1.28967e10 2.28580e9i 0.586995 0.104039i
\(386\) 6.82339e8 0.0307362
\(387\) 6.25281e9 + 1.08302e10i 0.278761 + 0.482828i
\(388\) −4.10541e9 2.37026e9i −0.181146 0.104585i
\(389\) 5.42166e9 9.39059e9i 0.236774 0.410105i −0.723013 0.690835i \(-0.757243\pi\)
0.959787 + 0.280730i \(0.0905766\pi\)
\(390\) −6.00621e9 + 3.46769e9i −0.259622 + 0.149893i
\(391\) 2.15898e10i 0.923721i
\(392\) −2.40238e10 + 8.79215e9i −1.01741 + 0.372349i
\(393\) 1.55539e10 0.652031
\(394\) −6.11254e9 1.05872e10i −0.253651 0.439337i
\(395\) 1.68218e9 + 9.71205e8i 0.0691008 + 0.0398954i
\(396\) −8.98515e8 + 1.55627e9i −0.0365380 + 0.0632857i
\(397\) −2.22969e10 + 1.28731e10i −0.897598 + 0.518228i −0.876420 0.481547i \(-0.840075\pi\)
−0.0211778 + 0.999776i \(0.506742\pi\)
\(398\) 5.44023e9i 0.216813i
\(399\) 1.30930e9 + 7.38715e9i 0.0516590 + 0.291464i
\(400\) 2.48824e9 0.0971968
\(401\) −2.16690e10 3.75319e10i −0.838035 1.45152i −0.891536 0.452951i \(-0.850371\pi\)
0.0535008 0.998568i \(-0.482962\pi\)
\(402\) −7.17192e9 4.14071e9i −0.274619 0.158552i
\(403\) 6.68180e9 1.15732e10i 0.253322 0.438767i
\(404\) −6.18924e9 + 3.57336e9i −0.232333 + 0.134138i
\(405\) 3.31256e9i 0.123124i
\(406\) −2.13159e10 + 1.79183e10i −0.784512 + 0.659468i
\(407\) −2.76431e10 −1.00741
\(408\) 8.53932e9 + 1.47905e10i 0.308164 + 0.533756i
\(409\) 2.07477e10 + 1.19787e10i 0.741441 + 0.428071i 0.822593 0.568631i \(-0.192527\pi\)
−0.0811522 + 0.996702i \(0.525860\pi\)
\(410\) 1.06334e10 1.84176e10i 0.376303 0.651775i
\(411\) 1.52625e10 8.81179e9i 0.534882 0.308814i
\(412\) 3.90668e9i 0.135587i
\(413\) −8.01810e9 + 2.20904e10i −0.275595 + 0.759281i
\(414\) 7.06615e9 0.240537
\(415\) 1.09156e10 + 1.89064e10i 0.368007 + 0.637407i
\(416\) 1.19231e10 + 6.88379e9i 0.398121 + 0.229855i
\(417\) 7.13359e9 1.23557e10i 0.235920 0.408625i
\(418\) 5.61313e9 3.24074e9i 0.183865 0.106155i
\(419\) 2.38523e9i 0.0773882i −0.999251 0.0386941i \(-0.987680\pi\)
0.999251 0.0386941i \(-0.0123198\pi\)
\(420\) −7.62571e9 2.76789e9i −0.245066 0.0889512i
\(421\) −7.22610e9 −0.230025 −0.115013 0.993364i \(-0.536691\pi\)
−0.115013 + 0.993364i \(0.536691\pi\)
\(422\) 5.87861e8 + 1.01821e9i 0.0185364 + 0.0321060i
\(423\) −7.10430e9 4.10167e9i −0.221901 0.128115i
\(424\) −9.43490e9 + 1.63417e10i −0.291927 + 0.505632i
\(425\) 6.34548e9 3.66357e9i 0.194495 0.112292i
\(426\) 1.42476e10i 0.432615i
\(427\) 3.57395e10 + 4.25162e10i 1.07507 + 1.27892i
\(428\) −1.35230e10 −0.402993
\(429\) −3.20218e9 5.54634e9i −0.0945402 0.163749i
\(430\) 4.22393e10 + 2.43869e10i 1.23550 + 0.713316i
\(431\) 1.24772e10 2.16112e10i 0.361584 0.626282i −0.626638 0.779311i \(-0.715569\pi\)
0.988222 + 0.153029i \(0.0489027\pi\)
\(432\) −2.47536e9 + 1.42915e9i −0.0710728 + 0.0410339i
\(433\) 2.44690e10i 0.696089i −0.937478 0.348044i \(-0.886846\pi\)
0.937478 0.348044i \(-0.113154\pi\)
\(434\) −2.23793e10 + 3.96650e9i −0.630793 + 0.111802i
\(435\) −3.05006e10 −0.851827
\(436\) 1.10230e10 + 1.90925e10i 0.305039 + 0.528343i
\(437\) 1.51802e10 + 8.76432e9i 0.416249 + 0.240321i
\(438\) 1.47321e10 2.55168e10i 0.400285 0.693314i
\(439\) −1.55993e10 + 9.00624e9i −0.419997 + 0.242485i −0.695076 0.718936i \(-0.744629\pi\)
0.275079 + 0.961422i \(0.411296\pi\)
\(440\) 2.42077e10i 0.645867i
\(441\) −9.67233e9 8.08691e9i −0.255727 0.213810i
\(442\) −1.76220e10 −0.461707
\(443\) 2.64552e10 + 4.58217e10i 0.686904 + 1.18975i 0.972834 + 0.231502i \(0.0743639\pi\)
−0.285931 + 0.958250i \(0.592303\pi\)
\(444\) 1.48278e10 + 8.56086e9i 0.381545 + 0.220285i
\(445\) 3.76543e10 6.52191e10i 0.960227 1.66316i
\(446\) 1.09773e10 6.33777e9i 0.277433 0.160176i
\(447\) 2.47269e10i 0.619355i
\(448\) −7.08426e9 3.99699e10i −0.175866 0.992250i
\(449\) 2.18030e10 0.536451 0.268226 0.963356i \(-0.413563\pi\)
0.268226 + 0.963356i \(0.413563\pi\)
\(450\) 1.19906e9 + 2.07682e9i 0.0292408 + 0.0506465i
\(451\) 1.70075e10 + 9.81926e9i 0.411086 + 0.237341i
\(452\) 8.05625e9 1.39538e10i 0.193010 0.334303i
\(453\) 9.52071e9 5.49679e9i 0.226088 0.130532i
\(454\) 5.96857e10i 1.40491i
\(455\) 2.21313e10 1.86037e10i 0.516370 0.434065i
\(456\) −1.38661e10 −0.320696
\(457\) −6.11374e9 1.05893e10i −0.140166 0.242774i 0.787393 0.616451i \(-0.211430\pi\)
−0.927559 + 0.373677i \(0.878097\pi\)
\(458\) 2.91725e10 + 1.68428e10i 0.662998 + 0.382782i
\(459\) −4.20842e9 + 7.28920e9i −0.0948132 + 0.164221i
\(460\) −1.64150e10 + 9.47719e9i −0.366614 + 0.211665i
\(461\) 2.03062e10i 0.449599i 0.974405 + 0.224799i \(0.0721727\pi\)
−0.974405 + 0.224799i \(0.927827\pi\)
\(462\) −3.71628e9 + 1.02386e10i −0.0815719 + 0.224736i
\(463\) −6.13108e9 −0.133418 −0.0667088 0.997772i \(-0.521250\pi\)
−0.0667088 + 0.997772i \(0.521250\pi\)
\(464\) −1.31590e10 2.27920e10i −0.283890 0.491712i
\(465\) −2.15590e10 1.24471e10i −0.461123 0.266230i
\(466\) 7.47745e9 1.29513e10i 0.158566 0.274644i
\(467\) −1.81078e10 + 1.04546e10i −0.380714 + 0.219805i −0.678129 0.734943i \(-0.737209\pi\)
0.297415 + 0.954748i \(0.403875\pi\)
\(468\) 3.96677e9i 0.0826901i
\(469\) 3.24515e10 + 1.17789e10i 0.670724 + 0.243451i
\(470\) −3.19942e10 −0.655662
\(471\) −8.46420e9 1.46604e10i −0.171990 0.297895i
\(472\) −3.76156e10 2.17174e10i −0.757879 0.437562i
\(473\) −2.25197e10 + 3.90052e10i −0.449901 + 0.779252i
\(474\) −1.39892e9 + 8.07665e8i −0.0277127 + 0.0159999i
\(475\) 5.94887e9i 0.116858i
\(476\) −1.32637e10 1.57787e10i −0.258367 0.307357i
\(477\) −9.29959e9 −0.179635
\(478\) 9.72447e9 + 1.68433e10i 0.186275 + 0.322637i
\(479\) 4.68705e10 + 2.70607e10i 0.890343 + 0.514040i 0.874055 0.485827i \(-0.161482\pi\)
0.0162884 + 0.999867i \(0.494815\pi\)
\(480\) 1.28234e10 2.22107e10i 0.241567 0.418406i
\(481\) −5.28443e10 + 3.05097e10i −0.987229 + 0.569977i
\(482\) 3.72371e10i 0.689903i
\(483\) −2.90049e10 + 5.14082e9i −0.532946 + 0.0944592i
\(484\) 1.58901e10 0.289564
\(485\) −1.57359e10 2.72553e10i −0.284396 0.492589i
\(486\) −2.38570e9 1.37738e9i −0.0427632 0.0246893i
\(487\) −3.39854e10 + 5.88645e10i −0.604195 + 1.04650i 0.387984 + 0.921666i \(0.373172\pi\)
−0.992178 + 0.124829i \(0.960162\pi\)
\(488\) −8.89026e10 + 5.13279e10i −1.56760 + 0.905054i
\(489\) 5.38701e10i 0.942134i
\(490\) −4.84395e10 8.45280e9i −0.840264 0.146628i
\(491\) 4.32393e10 0.743965 0.371982 0.928240i \(-0.378678\pi\)
0.371982 + 0.928240i \(0.378678\pi\)
\(492\) −6.08191e9 1.05342e10i −0.103796 0.179779i
\(493\) −6.71158e10 3.87493e10i −1.13615 0.655959i
\(494\) 7.15362e9 1.23904e10i 0.120121 0.208055i
\(495\) −1.03319e10 + 5.96513e9i −0.172092 + 0.0993572i
\(496\) 2.14804e10i 0.354907i
\(497\) −1.03655e10 5.84829e10i −0.169889 0.958525i
\(498\) −1.81551e10 −0.295177
\(499\) −1.58775e10 2.75007e10i −0.256083 0.443549i 0.709106 0.705102i \(-0.249099\pi\)
−0.965189 + 0.261553i \(0.915765\pi\)
\(500\) 1.88706e10 + 1.08950e10i 0.301930 + 0.174320i
\(501\) −8.04017e9 + 1.39260e10i −0.127619 + 0.221042i
\(502\) 5.78615e10 3.34063e10i 0.911118 0.526034i
\(503\) 8.94883e8i 0.0139796i −0.999976 0.00698979i \(-0.997775\pi\)
0.999976 0.00698979i \(-0.00222494\pi\)
\(504\) 1.78371e10 1.49940e10i 0.276441 0.232379i
\(505\) −4.74462e10 −0.729518
\(506\) 1.27245e10 + 2.20394e10i 0.194105 + 0.336200i
\(507\) 2.07941e10 + 1.20055e10i 0.314708 + 0.181697i
\(508\) 1.43596e10 2.48715e10i 0.215619 0.373462i
\(509\) 2.33944e10 1.35068e10i 0.348530 0.201224i −0.315508 0.948923i \(-0.602175\pi\)
0.664038 + 0.747699i \(0.268841\pi\)
\(510\) 3.28269e10i 0.485232i
\(511\) −4.19078e10 + 1.15459e11i −0.614626 + 1.69333i
\(512\) 5.38785e10 0.784035
\(513\) −3.41680e9 5.91807e9i −0.0493345 0.0854498i
\(514\) 1.40340e10 + 8.10255e9i 0.201062 + 0.116083i
\(515\) 1.29680e10 2.24612e10i 0.184350 0.319304i
\(516\) 2.41592e10 1.39483e10i 0.340788 0.196754i
\(517\) 2.95445e10i 0.413538i
\(518\) 9.75509e10 + 3.54079e10i 1.35492 + 0.491791i
\(519\) 2.11952e10 0.292125
\(520\) 2.67181e10 + 4.62771e10i 0.365420 + 0.632925i
\(521\) 5.11210e10 + 2.95147e10i 0.693822 + 0.400578i 0.805042 0.593217i \(-0.202143\pi\)
−0.111220 + 0.993796i \(0.535476\pi\)
\(522\) 1.26823e10 2.19665e10i 0.170812 0.295854i
\(523\) 1.78755e10 1.03205e10i 0.238920 0.137941i −0.375760 0.926717i \(-0.622618\pi\)
0.614680 + 0.788776i \(0.289285\pi\)
\(524\) 3.46965e10i 0.460215i
\(525\) −6.43279e9 7.65253e9i −0.0846764 0.100732i
\(526\) 7.56889e10 0.988757
\(527\) −3.16267e10 5.47790e10i −0.410026 0.710185i
\(528\) −8.91506e9 5.14712e9i −0.114707 0.0662259i
\(529\) 4.74326e9 8.21557e9i 0.0605696 0.104910i
\(530\) −3.14105e10 + 1.81349e10i −0.398081 + 0.229832i
\(531\) 2.14059e10i 0.269250i
\(532\) 1.64787e10 2.92069e9i 0.205720 0.0364619i
\(533\) 4.33501e10 0.537132
\(534\) 3.13137e10 + 5.42370e10i 0.385097 + 0.667007i
\(535\) −7.77495e10 4.48887e10i −0.949036 0.547926i
\(536\) −3.19036e10 + 5.52587e10i −0.386528 + 0.669486i
\(537\) 5.71229e10 3.29799e10i 0.686931 0.396600i
\(538\) 5.29374e9i 0.0631878i
\(539\) 7.80560e9 4.47307e10i 0.0924807 0.529969i
\(540\) 7.38944e9 0.0869033
\(541\) 6.80843e9 + 1.17926e10i 0.0794800 + 0.137663i 0.903026 0.429587i \(-0.141341\pi\)
−0.823546 + 0.567250i \(0.808007\pi\)
\(542\) −5.08595e10 2.93637e10i −0.589352 0.340263i
\(543\) −3.89335e10 + 6.74349e10i −0.447842 + 0.775685i
\(544\) 5.64350e10 3.25828e10i 0.644396 0.372042i
\(545\) 1.46361e11i 1.65897i
\(546\) 4.19605e9 + 2.36744e10i 0.0472139 + 0.266384i
\(547\) 5.06240e10 0.565467 0.282734 0.959198i \(-0.408759\pi\)
0.282734 + 0.959198i \(0.408759\pi\)
\(548\) −1.96567e10 3.40465e10i −0.217966 0.377529i
\(549\) −4.38138e10 2.52959e10i −0.482305 0.278459i
\(550\) −4.31842e9 + 7.47973e9i −0.0471927 + 0.0817401i
\(551\) 5.44910e10 3.14604e10i 0.591179 0.341317i
\(552\) 5.44438e10i 0.586397i
\(553\) 5.15463e9 4.33303e9i 0.0551185 0.0463331i
\(554\) −9.94061e10 −1.05529
\(555\) 5.68345e10 + 9.84402e10i 0.599018 + 1.03753i
\(556\) −2.75624e10 1.59131e10i −0.288415 0.166516i
\(557\) −4.04371e10 + 7.00392e10i −0.420107 + 0.727646i −0.995950 0.0899142i \(-0.971341\pi\)
0.575843 + 0.817560i \(0.304674\pi\)
\(558\) 1.79287e10 1.03512e10i 0.184932 0.106771i
\(559\) 9.94199e10i 1.01818i
\(560\) 1.58558e10 4.36836e10i 0.161226 0.444188i
\(561\) −3.03135e10 −0.306044
\(562\) 1.65509e10 + 2.86671e10i 0.165912 + 0.287368i
\(563\) −4.93301e10 2.84808e10i −0.490997 0.283477i 0.233991 0.972239i \(-0.424821\pi\)
−0.724988 + 0.688762i \(0.758155\pi\)
\(564\) −9.14973e9 + 1.58478e10i −0.0904257 + 0.156622i
\(565\) 9.26378e10 5.34845e10i 0.909064 0.524848i
\(566\) 4.37782e10i 0.426572i
\(567\) 1.07948e10 + 3.91817e9i 0.104444 + 0.0379098i
\(568\) 1.09776e11 1.05466
\(569\) −4.64899e10 8.05228e10i −0.443516 0.768192i 0.554432 0.832229i \(-0.312936\pi\)
−0.997948 + 0.0640371i \(0.979602\pi\)
\(570\) −2.30813e10 1.33260e10i −0.218656 0.126241i
\(571\) −8.15655e10 + 1.41276e11i −0.767294 + 1.32899i 0.171731 + 0.985144i \(0.445064\pi\)
−0.939025 + 0.343849i \(0.888269\pi\)
\(572\) −1.23724e10 + 7.14321e9i −0.115577 + 0.0667282i
\(573\) 2.87484e10i 0.266683i
\(574\) −4.74410e10 5.64364e10i −0.437025 0.519891i
\(575\) −2.33576e10 −0.213677
\(576\) 1.84874e10 + 3.20212e10i 0.167953 + 0.290902i
\(577\) −2.74753e10 1.58629e10i −0.247879 0.143113i 0.370914 0.928667i \(-0.379044\pi\)
−0.618792 + 0.785554i \(0.712378\pi\)
\(578\) 1.25128e9 2.16729e9i 0.0112110 0.0194180i
\(579\) 2.24384e9 1.29548e9i 0.0199654 0.0115270i
\(580\) 6.80387e10i 0.601235i
\(581\) 7.45226e10 1.32084e10i 0.654008 0.115916i
\(582\) 2.61723e10 0.228113
\(583\) −1.67464e10 2.90055e10i −0.144959 0.251077i
\(584\) −1.96604e11 1.13509e11i −1.69021 0.975842i
\(585\) −1.31675e10 + 2.28067e10i −0.112429 + 0.194733i
\(586\) 1.24360e10 7.17990e9i 0.105460 0.0608875i
\(587\) 1.86947e11i 1.57458i −0.616582 0.787291i \(-0.711483\pi\)
0.616582 0.787291i \(-0.288517\pi\)
\(588\) −1.80397e10 + 2.15764e10i −0.150911 + 0.180497i
\(589\) 5.13551e10 0.426700
\(590\) −4.17431e10 7.23011e10i −0.344490 0.596674i
\(591\) −4.02017e10 2.32104e10i −0.329529 0.190254i
\(592\) −4.90406e10 + 8.49408e10i −0.399272 + 0.691559i
\(593\) −1.78206e11 + 1.02887e11i −1.44113 + 0.832039i −0.997926 0.0643792i \(-0.979493\pi\)
−0.443209 + 0.896418i \(0.646160\pi\)
\(594\) 9.92135e9i 0.0796939i
\(595\) −2.38825e10 1.34747e11i −0.190551 1.07510i
\(596\) 5.51591e10 0.437151
\(597\) −1.03288e10 1.78900e10i −0.0813114 0.140835i
\(598\) 4.86498e10 + 2.80880e10i 0.380432 + 0.219642i
\(599\) −1.95751e10 + 3.39051e10i −0.152054 + 0.263364i −0.931982 0.362504i \(-0.881922\pi\)
0.779929 + 0.625868i \(0.215255\pi\)
\(600\) 1.60017e10 9.23856e9i 0.123470 0.0712852i
\(601\) 1.52677e11i 1.17024i 0.810946 + 0.585121i \(0.198953\pi\)
−0.810946 + 0.585121i \(0.801047\pi\)
\(602\) 1.29432e11 1.08802e11i 0.985500 0.828421i
\(603\) −3.14461e10 −0.237847
\(604\) −1.22619e10 2.12382e10i −0.0921316 0.159577i
\(605\) 9.13590e10 + 5.27462e10i 0.681915 + 0.393704i
\(606\) 1.97284e10 3.41706e10i 0.146286 0.253374i
\(607\) 9.72972e10 5.61746e10i 0.716713 0.413795i −0.0968285 0.995301i \(-0.530870\pi\)
0.813542 + 0.581506i \(0.197536\pi\)
\(608\) 5.29076e10i 0.387172i
\(609\) −3.60768e10 + 9.93939e10i −0.262276 + 0.722588i
\(610\) −1.97315e11 −1.42509
\(611\) −3.26083e10 5.64793e10i −0.233972 0.405251i
\(612\) 1.62603e10 + 9.38787e9i 0.115910 + 0.0669208i
\(613\) 1.13358e11 1.96341e11i 0.802803 1.39050i −0.114961 0.993370i \(-0.536674\pi\)
0.917764 0.397126i \(-0.129992\pi\)
\(614\) −1.66060e11 + 9.58748e10i −1.16840 + 0.674576i
\(615\) 8.07541e10i 0.564500i
\(616\) 7.88869e10 + 2.86334e10i 0.547876 + 0.198861i
\(617\) 3.86668e10 0.266807 0.133403 0.991062i \(-0.457409\pi\)
0.133403 + 0.991062i \(0.457409\pi\)
\(618\) 1.07843e10 + 1.86790e10i 0.0739332 + 0.128056i
\(619\) 1.89244e10 + 1.09260e10i 0.128902 + 0.0744216i 0.563064 0.826413i \(-0.309622\pi\)
−0.434162 + 0.900835i \(0.642956\pi\)
\(620\) −2.77661e10 + 4.80924e10i −0.187909 + 0.325469i
\(621\) 2.32367e10 1.34157e10i 0.156246 0.0902086i
\(622\) 1.83146e11i 1.22359i
\(623\) −1.67994e11 1.99849e11i −1.11517 1.32663i
\(624\) −2.27235e10 −0.149878
\(625\) 8.97199e10 + 1.55399e11i 0.587988 + 1.01843i
\(626\) 1.48688e11 + 8.58453e10i 0.968233 + 0.559010i
\(627\) 1.23057e10 2.13141e10i 0.0796225 0.137910i
\(628\) −3.27035e10 + 1.88814e10i −0.210259 + 0.121393i
\(629\) 2.88820e11i 1.84512i
\(630\) 4.41015e10 7.81655e9i 0.279957 0.0496195i
\(631\) −1.04547e11 −0.659469 −0.329735 0.944074i \(-0.606959\pi\)
−0.329735 + 0.944074i \(0.606959\pi\)
\(632\) 6.22296e9 + 1.07785e10i 0.0390057 + 0.0675599i
\(633\) 3.86631e9 + 2.23222e9i 0.0240814 + 0.0139034i
\(634\) −1.03941e11 + 1.80032e11i −0.643326 + 1.11427i
\(635\) 1.65119e11 9.53314e10i 1.01555 0.586328i
\(636\) 2.07449e10i 0.126789i
\(637\) −3.44476e10 9.41252e10i −0.209219 0.571674i
\(638\) 9.13515e10 0.551357
\(639\) 2.70503e10 + 4.68525e10i 0.162244 + 0.281015i
\(640\) 3.30250e9 + 1.90670e9i 0.0196845 + 0.0113648i
\(641\) −3.72418e10 + 6.45048e10i −0.220597 + 0.382085i −0.954989 0.296640i \(-0.904134\pi\)
0.734393 + 0.678725i \(0.237467\pi\)
\(642\) 6.46574e10 3.73300e10i 0.380608 0.219744i
\(643\) 8.61211e9i 0.0503809i 0.999683 + 0.0251904i \(0.00801921\pi\)
−0.999683 + 0.0251904i \(0.991981\pi\)
\(644\) 1.14678e10 + 6.47022e10i 0.0666710 + 0.376162i
\(645\) 1.85203e11 1.07006
\(646\) −3.38599e10 5.86471e10i −0.194427 0.336757i
\(647\) 1.13712e11 + 6.56517e10i 0.648917 + 0.374653i 0.788041 0.615622i \(-0.211095\pi\)
−0.139124 + 0.990275i \(0.544429\pi\)
\(648\) −1.06126e10 + 1.83815e10i −0.0601894 + 0.104251i
\(649\) 6.67653e10 3.85470e10i 0.376333 0.217276i
\(650\) 1.90650e10i 0.106803i
\(651\) −6.60625e10 + 5.55327e10i −0.367816 + 0.309190i
\(652\) −1.20170e11 −0.664975
\(653\) 6.27850e10 + 1.08747e11i 0.345305 + 0.598086i 0.985409 0.170202i \(-0.0544421\pi\)
−0.640104 + 0.768288i \(0.721109\pi\)
\(654\) −1.05409e11 6.08578e10i −0.576190 0.332664i
\(655\) 1.15173e11 1.99485e11i 0.625728 1.08379i
\(656\) 6.03446e10 3.48400e10i 0.325854 0.188132i
\(657\) 1.11881e11i 0.600476i
\(658\) −3.78435e10 + 1.04261e11i −0.201877 + 0.556185i
\(659\) 3.01394e11 1.59806 0.799029 0.601292i \(-0.205347\pi\)
0.799029 + 0.601292i \(0.205347\pi\)
\(660\) 1.33066e10 + 2.30477e10i 0.0701281 + 0.121465i
\(661\) −1.35322e11 7.81282e10i −0.708863 0.409262i 0.101777 0.994807i \(-0.467547\pi\)
−0.810640 + 0.585545i \(0.800881\pi\)
\(662\) −9.22356e9 + 1.59757e10i −0.0480249 + 0.0831816i
\(663\) −5.79493e10 + 3.34570e10i −0.299912 + 0.173154i
\(664\) 1.39883e11i 0.719602i
\(665\) 1.04439e11 + 3.79079e10i 0.534040 + 0.193840i
\(666\) −9.45285e10 −0.480469
\(667\) 1.23526e11 + 2.13954e11i 0.624102 + 1.08098i
\(668\) 3.10651e10 + 1.79355e10i 0.156015 + 0.0900755i
\(669\) 2.40657e10 4.16830e10i 0.120142 0.208092i
\(670\) −1.06213e11 + 6.13220e10i −0.527082 + 0.304311i
\(671\) 1.82208e11i 0.898827i
\(672\) −5.72115e10 6.80596e10i −0.280547 0.333743i
\(673\) 1.83722e10 0.0895575 0.0447787 0.998997i \(-0.485742\pi\)
0.0447787 + 0.998997i \(0.485742\pi\)
\(674\) 2.04166e10 + 3.53626e10i 0.0989337 + 0.171358i
\(675\) 7.88608e9 + 4.55303e9i 0.0379880 + 0.0219324i
\(676\) 2.67810e10 4.63860e10i 0.128245 0.222127i
\(677\) −2.19669e11 + 1.26826e11i −1.04572 + 0.603745i −0.921447 0.388503i \(-0.872992\pi\)
−0.124270 + 0.992248i \(0.539659\pi\)
\(678\) 8.89566e10i 0.420978i
\(679\) −1.07431e11 + 1.90411e10i −0.505418 + 0.0895803i
\(680\) 2.52927e11 1.18293
\(681\) −1.13319e11 1.96274e11i −0.526883 0.912587i
\(682\) 6.45707e10 + 3.72799e10i 0.298468 + 0.172321i
\(683\) 1.33944e11 2.31998e11i 0.615519 1.06611i −0.374774 0.927116i \(-0.622280\pi\)
0.990293 0.138994i \(-0.0443869\pi\)
\(684\) −1.32016e10 + 7.62197e9i −0.0603119 + 0.0348211i
\(685\) 2.60998e11i 1.18542i
\(686\) −8.48409e10 + 1.47854e11i −0.383097 + 0.667632i
\(687\) 1.27910e11 0.574220
\(688\) 7.99026e10 + 1.38395e11i 0.356621 + 0.617686i
\(689\) −6.40269e10 3.69659e10i −0.284109 0.164031i
\(690\) 5.23233e10 9.06266e10i 0.230833 0.399815i
\(691\) −3.41080e10 + 1.96922e10i −0.149604 + 0.0863740i −0.572933 0.819602i \(-0.694195\pi\)
0.423329 + 0.905976i \(0.360861\pi\)
\(692\) 4.72809e10i 0.206187i
\(693\) 7.21807e9 + 4.07248e10i 0.0312959 + 0.176574i
\(694\) −2.86237e11 −1.23392
\(695\) −1.05645e11 1.82983e11i −0.452805 0.784281i
\(696\) −1.69249e11 9.77157e10i −0.721254 0.416416i
\(697\) 1.02594e11 1.77697e11i 0.434699 0.752921i
\(698\) −6.55698e10 + 3.78568e10i −0.276237 + 0.159486i
\(699\) 5.67865e10i 0.237868i
\(700\) −1.70708e10 + 1.43498e10i −0.0710985 + 0.0597661i
\(701\) −1.69041e11 −0.700036 −0.350018 0.936743i \(-0.613825\pi\)
−0.350018 + 0.936743i \(0.613825\pi\)
\(702\) −1.09502e10 1.89663e10i −0.0450893 0.0780970i
\(703\) −2.03076e11 1.17246e11i −0.831452 0.480039i
\(704\) −6.65829e10 + 1.15325e11i −0.271064 + 0.469497i
\(705\) −1.05212e11 + 6.07439e10i −0.425900 + 0.245893i
\(706\) 1.04229e11i 0.419539i
\(707\) −5.61204e10 + 1.54615e11i −0.224617 + 0.618835i
\(708\) −4.77509e10 −0.190041
\(709\) 1.06387e11 + 1.84268e11i 0.421021 + 0.729229i 0.996040 0.0889111i \(-0.0283387\pi\)
−0.575019 + 0.818140i \(0.695005\pi\)
\(710\) 1.82731e11 + 1.05500e11i 0.719084 + 0.415163i
\(711\) −3.06685e9 + 5.31195e9i −0.0120009 + 0.0207862i
\(712\) 4.17889e11 2.41268e11i 1.62608 0.938815i
\(713\) 2.01641e11i 0.780226i
\(714\) 1.06975e11 + 3.88284e10i 0.411612 + 0.149402i
\(715\) −9.48458e10 −0.362906
\(716\) −7.35694e10 1.27426e11i −0.279927 0.484848i
\(717\) 6.39570e10 + 3.69256e10i 0.241998 + 0.139717i
\(718\) 4.43979e10 7.68994e10i 0.167057 0.289351i
\(719\) −3.83519e11 + 2.21425e11i −1.43507 + 0.828535i −0.997501 0.0706518i \(-0.977492\pi\)
−0.437564 + 0.899187i \(0.644159\pi\)
\(720\) 4.23301e10i 0.157514i
\(721\) −5.78567e10 6.88271e10i −0.214098 0.254694i
\(722\) −1.54185e11 −0.567404
\(723\) 7.06981e10 + 1.22453e11i 0.258735 + 0.448142i
\(724\) 1.50429e11 + 8.68503e10i 0.547492 + 0.316095i
\(725\) −4.19223e10 + 7.26116e10i −0.151738 + 0.262817i
\(726\) −7.59753e10 + 4.38643e10i −0.273480 + 0.157894i
\(727\) 8.87622e10i 0.317754i −0.987298 0.158877i \(-0.949213\pi\)
0.987298 0.158877i \(-0.0507873\pi\)
\(728\) 1.82408e11 3.23300e10i 0.649410 0.115101i
\(729\) −1.04604e10 −0.0370370
\(730\) −2.18176e11 3.77893e11i −0.768274 1.33069i
\(731\) 4.07534e11 + 2.35290e11i 1.42723 + 0.824012i
\(732\) −5.64284e10 + 9.77368e10i −0.196541 + 0.340419i
\(733\) −4.76316e11 + 2.75001e11i −1.64998 + 0.952619i −0.672908 + 0.739726i \(0.734955\pi\)
−0.977076 + 0.212893i \(0.931711\pi\)
\(734\) 1.42046e11i 0.489379i
\(735\) −1.75340e11 + 6.41702e10i −0.600802 + 0.219879i
\(736\) −2.07737e11 −0.707948
\(737\) −5.66269e10 9.80806e10i −0.191934 0.332440i
\(738\) 5.81588e10 + 3.35780e10i 0.196061 + 0.113196i
\(739\) 7.88531e9 1.36578e10i 0.0264388 0.0457933i −0.852503 0.522722i \(-0.824917\pi\)
0.878942 + 0.476929i \(0.158250\pi\)
\(740\) 2.19594e11 1.26782e11i 0.732307 0.422797i
\(741\) 5.43272e10i 0.180196i
\(742\) 2.19440e10 + 1.23809e11i 0.0723935 + 0.408449i
\(743\) −5.11592e11 −1.67868 −0.839342 0.543604i \(-0.817059\pi\)
−0.839342 + 0.543604i \(0.817059\pi\)
\(744\) −7.97543e10 1.38138e11i −0.260293 0.450840i
\(745\) 3.17134e11 + 1.83097e11i 1.02948 + 0.594370i
\(746\) 2.13371e11 3.69569e11i 0.688937 1.19327i
\(747\) −5.97024e10 + 3.44692e10i −0.191738 + 0.110700i
\(748\) 6.76212e10i 0.216011i
\(749\) −2.38245e11 + 2.00271e11i −0.757001 + 0.636342i
\(750\) −1.20302e11 −0.380213
\(751\) −1.11780e11 1.93609e11i −0.351402 0.608646i 0.635093 0.772435i \(-0.280962\pi\)
−0.986495 + 0.163789i \(0.947628\pi\)
\(752\) −9.07836e10 5.24139e10i −0.283881 0.163899i
\(753\) 1.26850e11 2.19711e11i 0.394558 0.683394i
\(754\) 1.74634e11 1.00825e11i 0.540309 0.311948i
\(755\) 1.62810e11i 0.501064i
\(756\) 8.74040e9 2.40803e10i 0.0267574 0.0737183i
\(757\) 6.02473e11 1.83465 0.917326 0.398136i \(-0.130343\pi\)
0.917326 + 0.398136i \(0.130343\pi\)
\(758\) −4.92948e10 8.53812e10i −0.149322 0.258634i
\(759\) 8.36877e10 + 4.83171e10i 0.252171 + 0.145591i
\(760\) −1.02675e11 + 1.77839e11i −0.307759 + 0.533055i
\(761\) 8.77901e10 5.06856e10i 0.261762 0.151128i −0.363376 0.931643i \(-0.618376\pi\)
0.625138 + 0.780514i \(0.285043\pi\)
\(762\) 1.58557e11i 0.470291i
\(763\) 4.76955e11 + 1.73119e11i 1.40727 + 0.510796i
\(764\) 6.41300e10 0.188230
\(765\) 6.23249e10 + 1.07950e11i 0.181977 + 0.315193i
\(766\) 3.71322e11 + 2.14383e11i 1.07854 + 0.622694i
\(767\) 8.50886e10 1.47378e11i 0.245861 0.425844i
\(768\) 1.72542e11 9.96171e10i 0.495963 0.286344i
\(769\) 4.58024e11i 1.30973i 0.755744 + 0.654867i \(0.227275\pi\)
−0.755744 + 0.654867i \(0.772725\pi\)
\(770\) 1.03796e11 + 1.23477e11i 0.295270 + 0.351257i
\(771\) 6.15337e10 0.174139
\(772\) −2.88987e9 5.00541e9i −0.00813598 0.0140919i
\(773\) −9.04927e9 5.22460e9i −0.0253452 0.0146330i 0.487274 0.873249i \(-0.337991\pi\)
−0.512619 + 0.858616i \(0.671325\pi\)
\(774\) −7.70084e10 + 1.33382e11i −0.214573 + 0.371651i
\(775\) −5.92646e10 + 3.42164e10i −0.164282 + 0.0948480i
\(776\) 2.01654e11i 0.556109i
\(777\) 3.88017e11 6.87721e10i 1.06455 0.188681i
\(778\) 1.33544e11 0.364508
\(779\) 8.32952e10 + 1.44272e11i 0.226188 + 0.391770i
\(780\) 5.08756e10 + 2.93731e10i 0.137446 + 0.0793543i
\(781\) −9.74223e10 + 1.68740e11i −0.261851 + 0.453539i
\(782\) 2.30272e11 1.32948e11i 0.615764 0.355511i
\(783\) 9.63143e10i 0.256238i
\(784\) −1.23600e11 1.03340e11i −0.327154 0.273529i
\(785\) −2.50702e11 −0.660206
\(786\) 9.57792e10 + 1.65894e11i 0.250947 + 0.434652i
\(787\) 2.09662e11 + 1.21048e11i 0.546539 + 0.315544i 0.747725 0.664009i \(-0.231146\pi\)
−0.201186 + 0.979553i \(0.564480\pi\)
\(788\) −5.17763e10 + 8.96791e10i −0.134284 + 0.232587i
\(789\) 2.48900e11 1.43702e11i 0.642269 0.370814i
\(790\) 2.39223e10i 0.0614179i
\(791\) −6.47185e10 3.65146e11i −0.165319 0.932741i
\(792\) −7.64427e10 −0.194283
\(793\) −2.01103e11 3.48320e11i −0.508540 0.880817i
\(794\) −2.74604e11 1.58543e11i −0.690915 0.398900i
\(795\) −6.88614e10 + 1.19272e11i −0.172388 + 0.298585i
\(796\) −3.99077e10 + 2.30407e10i −0.0994041 + 0.0573910i
\(797\) 6.17249e10i 0.152977i −0.997070 0.0764887i \(-0.975629\pi\)
0.997070 0.0764887i \(-0.0243709\pi\)
\(798\) −7.07273e10 + 5.94540e10i −0.174412 + 0.146612i
\(799\) −3.08687e11 −0.757411
\(800\) −3.52508e10 6.10562e10i −0.0860615 0.149063i
\(801\) 2.05948e11 + 1.18904e11i 0.500296 + 0.288846i
\(802\) 2.66872e11 4.62235e11i 0.645067 1.11729i
\(803\) 3.48959e11 2.01471e11i 0.839290 0.484564i
\(804\) 7.01477e10i 0.167876i
\(805\) −1.48841e11 + 4.10068e11i −0.354438 + 0.976500i
\(806\) 1.64584e11 0.389984
\(807\) −1.00507e10 1.74082e10i −0.0236974 0.0410451i
\(808\) −2.63280e11 1.52005e11i −0.617693 0.356625i
\(809\) −4.81158e10 + 8.33390e10i −0.112329 + 0.194560i −0.916709 0.399555i \(-0.869165\pi\)
0.804380 + 0.594116i \(0.202498\pi\)
\(810\) −3.53311e10 + 2.03984e10i −0.0820762 + 0.0473867i
\(811\) 3.79647e9i 0.00877599i 0.999990 + 0.00438800i \(0.00139675\pi\)
−0.999990 + 0.00438800i \(0.998603\pi\)
\(812\) 2.21721e11 + 8.04777e10i 0.510015 + 0.185119i
\(813\) −2.22999e11 −0.510436
\(814\) −1.70223e11 2.94835e11i −0.387723 0.671555i
\(815\) −6.90909e11 3.98896e11i −1.56600 0.904128i
\(816\) −5.37781e10 + 9.31464e10i −0.121295 + 0.210090i
\(817\) −3.30875e11 + 1.91031e11i −0.742635 + 0.428761i
\(818\) 2.95054e11i 0.659005i
\(819\) 5.87466e10 + 6.98857e10i 0.130571 + 0.155329i
\(820\) −1.80141e11 −0.398434
\(821\) 3.66956e11 + 6.35586e11i 0.807683 + 1.39895i 0.914464 + 0.404666i \(0.132612\pi\)
−0.106781 + 0.994283i \(0.534054\pi\)
\(822\) 1.87970e11 + 1.08524e11i 0.411718 + 0.237706i
\(823\) −1.45630e11 + 2.52238e11i −0.317432 + 0.549809i −0.979952 0.199236i \(-0.936154\pi\)
0.662519 + 0.749045i \(0.269487\pi\)
\(824\) 1.43919e11 8.30919e10i 0.312184 0.180239i
\(825\) 3.27957e10i 0.0707948i
\(826\) −2.84986e11 + 5.05109e10i −0.612214 + 0.108509i
\(827\) −7.82523e11 −1.67292 −0.836460 0.548029i \(-0.815379\pi\)
−0.836460 + 0.548029i \(0.815379\pi\)
\(828\) −2.99269e10 5.18349e10i −0.0636708 0.110281i
\(829\) −3.16706e11 1.82850e11i −0.670560 0.387148i 0.125729 0.992065i \(-0.459873\pi\)
−0.796289 + 0.604916i \(0.793206\pi\)
\(830\) −1.34435e11 + 2.32848e11i −0.283269 + 0.490636i
\(831\) −3.26893e11 + 1.88732e11i −0.685490 + 0.395768i
\(832\) 2.93950e11i 0.613452i
\(833\) −4.67355e11 8.15545e10i −0.970660 0.169382i
\(834\) 1.75712e11 0.363193
\(835\) 1.19071e11 + 2.06238e11i 0.244941 + 0.424250i
\(836\) −4.75460e10 2.74507e10i −0.0973394 0.0561990i
\(837\) 3.93052e10 6.80787e10i 0.0800845 0.138710i
\(838\) 2.54404e10 1.46880e10i 0.0515879 0.0297843i
\(839\) 7.98985e10i 0.161247i −0.996745 0.0806233i \(-0.974309\pi\)
0.996745 0.0806233i \(-0.0256911\pi\)
\(840\) −6.02255e10 3.39796e11i −0.120966 0.682498i
\(841\) 3.86574e11 0.772767
\(842\) −4.44976e10 7.70721e10i −0.0885296 0.153338i
\(843\) 1.08854e11 + 6.28470e10i 0.215543 + 0.124444i
\(844\) 4.97948e9 8.62471e9i 0.00981328 0.0169971i
\(845\) 3.07951e11 1.77796e11i 0.604025 0.348734i
\(846\) 1.01031e11i 0.197230i
\(847\) 2.79948e11 2.35327e11i 0.543931 0.457234i
\(848\) −1.18836e11 −0.229809
\(849\) −8.31170e10 1.43963e11i −0.159978 0.277089i
\(850\) 7.81497e10 + 4.51198e10i 0.149710 + 0.0864353i
\(851\) 4.60355e11 7.97357e11i 0.877757 1.52032i
\(852\) 1.04515e11 6.03419e10i 0.198345 0.114515i
\(853\) 3.15788e11i 0.596485i −0.954490 0.298242i \(-0.903600\pi\)
0.954490 0.298242i \(-0.0964004\pi\)
\(854\) −2.33389e11 + 6.43001e11i −0.438782 + 1.20887i
\(855\) −1.01203e11 −0.189377
\(856\) −2.87623e11 4.98177e11i −0.535708 0.927873i
\(857\) −4.63397e10 2.67542e10i −0.0859072 0.0495986i 0.456431 0.889759i \(-0.349128\pi\)
−0.542338 + 0.840160i \(0.682461\pi\)
\(858\) 3.94374e10 6.83076e10i 0.0727712 0.126043i
\(859\) 9.50570e9 5.48812e9i 0.0174587 0.0100798i −0.491245 0.871021i \(-0.663458\pi\)
0.508704 + 0.860942i \(0.330125\pi\)
\(860\) 4.13138e11i 0.755268i
\(861\) −2.63157e11 9.55178e10i −0.478854 0.173809i
\(862\) 3.07334e11 0.556650
\(863\) 1.41661e11 + 2.45363e11i 0.255391 + 0.442350i 0.965002 0.262244i \(-0.0844625\pi\)
−0.709611 + 0.704594i \(0.751129\pi\)
\(864\) 7.01367e10 + 4.04934e10i 0.125861 + 0.0726657i
\(865\) 1.56946e11 2.71838e11i 0.280340 0.485564i
\(866\) 2.60981e11 1.50678e11i 0.464022 0.267903i
\(867\) 9.50271e9i 0.0168179i
\(868\) 1.23879e11 + 1.47368e11i 0.218232 + 0.259611i
\(869\) −2.20907e10 −0.0387374
\(870\) −1.87820e11 3.25313e11i −0.327842 0.567839i
\(871\) −2.16503e11 1.24998e11i −0.376177 0.217186i
\(872\) −4.68902e11 + 8.12161e11i −0.810990 + 1.40468i
\(873\) 8.60664e10 4.96905e10i 0.148176 0.0855493i
\(874\) 2.15879e11i 0.369969i
\(875\) 4.93810e11 8.75228e10i 0.842418 0.149310i
\(876\) −2.49577e11 −0.423827
\(877\) 1.86985e11 + 3.23867e11i 0.316088 + 0.547480i 0.979668 0.200625i \(-0.0642972\pi\)
−0.663580 + 0.748105i \(0.730964\pi\)
\(878\) −1.92117e11 1.10919e11i −0.323287 0.186650i
\(879\) 2.72634e10 4.72216e10i 0.0456693 0.0791016i
\(880\) −1.32028e11 + 7.62265e10i −0.220159 + 0.127109i
\(881\) 4.89938e11i 0.813276i 0.913589 + 0.406638i \(0.133299\pi\)
−0.913589 + 0.406638i \(0.866701\pi\)
\(882\) 2.66921e10 1.52962e11i 0.0441071 0.252760i
\(883\) 9.67505e11 1.59151 0.795757 0.605616i \(-0.207073\pi\)
0.795757 + 0.605616i \(0.207073\pi\)
\(884\) 7.46336e10 + 1.29269e11i 0.122215 + 0.211683i
\(885\) −2.74541e11 1.58506e11i −0.447542 0.258388i
\(886\) −3.25817e11 + 5.64331e11i −0.528736 + 0.915797i
\(887\) −1.80919e11 + 1.04454e11i −0.292273 + 0.168744i −0.638967 0.769234i \(-0.720638\pi\)
0.346693 + 0.937979i \(0.387304\pi\)
\(888\) 7.28329e11i 1.17132i
\(889\) −1.15355e11 6.50841e11i −0.184684 1.04200i
\(890\) 9.27485e11 1.47825
\(891\) −1.88366e10 3.26260e10i −0.0298876 0.0517669i
\(892\) −9.29836e10 5.36841e10i −0.146875 0.0847981i
\(893\) 1.25311e11 2.17045e11i 0.197053 0.341306i
\(894\) −2.63732e11 + 1.52266e11i −0.412870 + 0.238370i
\(895\) 9.76836e11i 1.52240i
\(896\) 1.01197e10 8.50675e9i 0.0157014 0.0131987i
\(897\) 2.13311e11 0.329490
\(898\) 1.34261e11 + 2.32546e11i 0.206463 + 0.357605i
\(899\) 6.26838e11 + 3.61905e11i 0.959659 + 0.554059i
\(900\) 1.01566e10 1.75917e10i 0.0154803 0.0268126i
\(901\) −3.03056e11 + 1.74969e11i −0.459857 + 0.265499i
\(902\) 2.41864e11i 0.365380i
\(903\) 2.19062e11 6.03530e11i 0.329470 0.907711i
\(904\) 6.85399e11 1.02629
\(905\) 5.76589e11 + 9.98681e11i 0.859551 + 1.48879i
\(906\) 1.17255e11 + 6.76973e10i 0.174028 + 0.100475i
\(907\) −4.20962e11 + 7.29128e11i −0.622034 + 1.07739i 0.367073 + 0.930192i \(0.380360\pi\)
−0.989107 + 0.147202i \(0.952973\pi\)
\(908\) −4.37835e11 + 2.52784e11i −0.644120 + 0.371883i
\(909\) 1.49825e11i 0.219446i
\(910\) 3.34706e11 + 1.21488e11i 0.488088 + 0.177160i
\(911\) 6.67597e11 0.969262 0.484631 0.874719i \(-0.338954\pi\)
0.484631 + 0.874719i \(0.338954\pi\)
\(912\) −4.36622e10 7.56251e10i −0.0631141 0.109317i
\(913\) −2.15019e11 1.24142e11i −0.309453 0.178663i
\(914\) 7.52956e10 1.30416e11i 0.107891 0.186872i
\(915\) −6.48863e11 + 3.74621e11i −0.925696 + 0.534451i
\(916\) 2.85333e11i 0.405294i
\(917\) −5.13844e11 6.11276e11i −0.726699 0.864490i
\(918\) −1.03660e11 −0.145963
\(919\) 9.12059e10 + 1.57973e11i 0.127868 + 0.221473i 0.922850 0.385159i \(-0.125853\pi\)
−0.794983 + 0.606632i \(0.792520\pi\)
\(920\) −6.98266e11 4.03144e11i −0.974697 0.562741i
\(921\) −3.64054e11 + 6.30561e11i −0.505973 + 0.876372i
\(922\) −2.16582e11 + 1.25044e11i −0.299708 + 0.173037i
\(923\) 4.30100e11i 0.592602i
\(924\) 9.08462e10 1.61016e10i 0.124629 0.0220892i
\(925\) 3.12470e11 0.426817
\(926\) −3.77546e10 6.53929e10i −0.0513483 0.0889379i
\(927\) 7.09277e10 + 4.09501e10i 0.0960498 + 0.0554544i
\(928\) −3.72846e11 + 6.45788e11i −0.502733 + 0.870759i
\(929\) 1.12132e12 6.47394e11i 1.50545 0.869172i 0.505470 0.862844i \(-0.331319\pi\)
0.999980 0.00632801i \(-0.00201428\pi\)
\(930\) 3.06592e11i 0.409854i
\(931\) 2.47065e11 2.95501e11i 0.328861 0.393333i
\(932\) −1.26676e11 −0.167892
\(933\) −3.47720e11 6.02270e11i −0.458885 0.794812i
\(934\) −2.23012e11 1.28756e11i −0.293050 0.169192i
\(935\) −2.24465e11 + 3.88784e11i −0.293698 + 0.508700i
\(936\) −1.46133e11 + 8.43699e10i −0.190390 + 0.109922i
\(937\) 1.31158e12i 1.70152i −0.525555 0.850760i \(-0.676142\pi\)
0.525555 0.850760i \(-0.323858\pi\)
\(938\) 7.42023e10 + 4.18655e11i 0.0958530 + 0.540810i
\(939\) 6.51941e11 0.838583
\(940\) 1.35503e11 + 2.34699e11i 0.173556 + 0.300607i
\(941\) 1.24935e11 + 7.21311e10i 0.159340 + 0.0919949i 0.577550 0.816356i \(-0.304009\pi\)
−0.418210 + 0.908350i \(0.637342\pi\)
\(942\) 1.04243e11 1.80555e11i 0.132387 0.229301i
\(943\) −5.66468e11 + 3.27051e11i −0.716356 + 0.413588i
\(944\) 2.73539e11i 0.344454i
\(945\) 1.30186e11 1.09435e11i 0.163243 0.137224i
\(946\) −5.54695e11 −0.692612
\(947\) 6.96706e11 + 1.20673e12i 0.866263 + 1.50041i 0.865788 + 0.500411i \(0.166818\pi\)
0.000475192 1.00000i \(0.499849\pi\)
\(948\) 1.18495e10 + 6.84133e9i 0.0146713 + 0.00847046i
\(949\) 4.44729e11 7.70293e11i 0.548315 0.949710i
\(950\) −6.34494e10 + 3.66325e10i −0.0778992 + 0.0449751i
\(951\) 7.89368e11i 0.965067i
\(952\) 2.99168e11 8.24226e11i 0.364223 1.00346i
\(953\) 3.36931e11 0.408479 0.204240 0.978921i \(-0.434528\pi\)
0.204240 + 0.978921i \(0.434528\pi\)
\(954\) −5.72660e10 9.91876e10i −0.0691358 0.119747i
\(955\) 3.68711e11 + 2.12876e11i 0.443275 + 0.255925i
\(956\) 8.23711e10 1.42671e11i 0.0986150 0.170806i
\(957\) 3.00405e11 1.73439e11i 0.358146 0.206776i
\(958\) 6.66548e11i 0.791352i
\(959\) −8.50526e11 3.08714e11i −1.00557 0.364991i
\(960\) 5.47581e11 0.644709
\(961\) −1.31063e11 2.27008e11i −0.153669 0.266163i
\(962\) −6.50820e11 3.75751e11i −0.759907 0.438733i
\(963\) 1.41749e11 2.45516e11i 0.164822 0.285479i
\(964\) 2.73159e11 1.57708e11i 0.316306 0.182619i
\(965\) 3.83711e10i 0.0442481i
\(966\) −2.33440e11 2.77704e11i −0.268082 0.318914i
\(967\) −1.61449e12 −1.84642 −0.923208 0.384300i \(-0.874443\pi\)
−0.923208 + 0.384300i \(0.874443\pi\)
\(968\) 3.37969e11 + 5.85379e11i 0.384924 + 0.666708i
\(969\) −2.22694e11 1.28572e11i −0.252588 0.145832i
\(970\) 1.93800e11 3.35671e11i 0.218911 0.379164i
\(971\) 6.08052e11 3.51059e11i 0.684012 0.394915i −0.117353 0.993090i \(-0.537441\pi\)
0.801365 + 0.598176i \(0.204107\pi\)
\(972\) 2.33342e10i 0.0261414i
\(973\) −7.21256e11 + 1.27835e11i −0.804708 + 0.142626i
\(974\) −8.37116e11 −0.930143
\(975\) 3.61967e10 + 6.26945e10i 0.0400544 + 0.0693762i
\(976\) −5.59882e11 3.23248e11i −0.617017 0.356235i
\(977\) 5.35565e9 9.27626e9i 0.00587806 0.0101811i −0.863071 0.505082i \(-0.831462\pi\)
0.868949 + 0.494901i \(0.164796\pi\)
\(978\) 5.74568e11 3.31727e11i 0.628038 0.362598i
\(979\) 8.56471e11i 0.932356i
\(980\) 1.43147e11 + 3.91136e11i 0.155195 + 0.424056i
\(981\) −4.62177e11 −0.499036
\(982\) 2.66263e11 + 4.61181e11i 0.286329 + 0.495936i
\(983\) −9.94085e11 5.73935e11i −1.06466 0.614680i −0.137940 0.990441i \(-0.544048\pi\)
−0.926717 + 0.375761i \(0.877381\pi\)
\(984\) 2.58714e11 4.48106e11i 0.275956 0.477970i
\(985\) −5.95369e11 + 3.43736e11i −0.632472 + 0.365158i
\(986\) 9.54458e11i 1.00983i
\(987\) 7.35027e10 + 4.14708e11i 0.0774524 + 0.436992i
\(988\) −1.21189e11 −0.127185
\(989\) −7.50064e11 1.29915e12i −0.783994 1.35792i
\(990\) −1.27246e11 7.34654e10i −0.132466 0.0764790i
\(991\) −6.49257e11 + 1.12455e12i −0.673166 + 1.16596i 0.303836 + 0.952724i \(0.401733\pi\)
−0.977001 + 0.213233i \(0.931601\pi\)
\(992\) −5.27083e11 + 3.04312e11i −0.544293 + 0.314248i
\(993\) 7.00471e10i 0.0720432i
\(994\) 5.59937e11 4.70688e11i 0.573580 0.482156i
\(995\) −3.05929e11 −0.312125
\(996\) 7.68915e10 + 1.33180e11i 0.0781342 + 0.135332i
\(997\) 2.89707e11 + 1.67263e11i 0.293210 + 0.169285i 0.639389 0.768884i \(-0.279188\pi\)
−0.346179 + 0.938169i \(0.612521\pi\)
\(998\) 1.95544e11 3.38693e11i 0.197117 0.341416i
\(999\) −3.10853e11 + 1.79471e11i −0.312099 + 0.180191i
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 21.9.f.b.10.4 12
3.2 odd 2 63.9.m.d.10.3 12
7.3 odd 6 147.9.d.b.97.6 12
7.4 even 3 147.9.d.b.97.5 12
7.5 odd 6 inner 21.9.f.b.19.4 yes 12
21.5 even 6 63.9.m.d.19.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.9.f.b.10.4 12 1.1 even 1 trivial
21.9.f.b.19.4 yes 12 7.5 odd 6 inner
63.9.m.d.10.3 12 3.2 odd 2
63.9.m.d.19.3 12 21.5 even 6
147.9.d.b.97.5 12 7.4 even 3
147.9.d.b.97.6 12 7.3 odd 6