Properties

Label 43.9.f.a.22.20
Level $43$
Weight $9$
Character 43.22
Analytic conductor $17.517$
Analytic rank $0$
Dimension $174$
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] = [43,9,Mod(2,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([9]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.2");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.f (of order \(14\), degree \(6\), 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: \(17.5172802326\)
Analytic rank: \(0\)
Dimension: \(174\)
Relative dimension: \(29\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 22.20
Character \(\chi\) \(=\) 43.22
Dual form 43.9.f.a.2.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.47023 - 9.28252i) q^{2} +(45.7755 + 95.0539i) q^{3} +(93.4311 + 117.159i) q^{4} +(498.592 - 113.800i) q^{5} +1086.97 q^{6} -1744.42i q^{7} +(4076.58 - 930.453i) q^{8} +(-2849.12 + 3572.69i) q^{9} +O(q^{10})\) \(q+(4.47023 - 9.28252i) q^{2} +(45.7755 + 95.0539i) q^{3} +(93.4311 + 117.159i) q^{4} +(498.592 - 113.800i) q^{5} +1086.97 q^{6} -1744.42i q^{7} +(4076.58 - 930.453i) q^{8} +(-2849.12 + 3572.69i) q^{9} +(1172.46 - 5136.90i) q^{10} +(10887.9 - 13653.0i) q^{11} +(-6859.55 + 14244.0i) q^{12} +(6288.43 + 27551.4i) q^{13} +(-16192.6 - 7797.94i) q^{14} +(33640.5 + 42183.8i) q^{15} +(1049.93 - 4600.05i) q^{16} +(-18570.6 + 81363.1i) q^{17} +(20427.3 + 42417.8i) q^{18} +(-30312.4 + 24173.3i) q^{19} +(59916.7 + 47782.0i) q^{20} +(165814. - 79851.6i) q^{21} +(-78062.9 - 162099. i) q^{22} +(-28506.6 + 35746.1i) q^{23} +(275051. + 344903. i) q^{24} +(-116298. + 56006.1i) q^{25} +(283857. + 64788.6i) q^{26} +(204825. + 46749.9i) q^{27} +(204374. - 162983. i) q^{28} +(543762. - 1.12913e6i) q^{29} +(541953. - 123697. i) q^{30} +(-1.02751e6 - 494824. i) q^{31} +(798900. + 637101. i) q^{32} +(1.79617e6 + 409964. i) q^{33} +(672240. + 536094. i) q^{34} +(-198515. - 869752. i) q^{35} -684769. q^{36} +3.13557e6i q^{37} +(88886.1 + 389436. i) q^{38} +(-2.33101e6 + 1.85892e6i) q^{39} +(1.92666e6 - 927833. i) q^{40} +(-2.18126e6 - 1.05044e6i) q^{41} -1.89612e6i q^{42} +(-3.40038e6 - 354389. i) q^{43} +2.61684e6 q^{44} +(-1.01398e6 + 2.10554e6i) q^{45} +(204383. + 424406. i) q^{46} +(207835. + 260617. i) q^{47} +(485314. - 110770. i) q^{48} +2.72181e6 q^{49} +1.32990e6i q^{50} +(-8.58396e6 + 1.95923e6i) q^{51} +(-2.64036e6 + 3.31090e6i) q^{52} +(-271064. + 1.18761e6i) q^{53} +(1.34957e6 - 1.69231e6i) q^{54} +(3.87490e6 - 8.04632e6i) q^{55} +(-1.62310e6 - 7.11126e6i) q^{56} +(-3.68533e6 - 1.77476e6i) q^{57} +(-8.05046e6 - 1.00950e7i) q^{58} +(1.33975e6 - 5.86984e6i) q^{59} +(-1.79914e6 + 7.88256e6i) q^{60} +(-9.99937e6 - 2.07639e7i) q^{61} +(-9.18644e6 + 7.32594e6i) q^{62} +(6.23226e6 + 4.97006e6i) q^{63} +(1.05734e7 - 5.09190e6i) q^{64} +(6.27072e6 + 1.30213e7i) q^{65} +(1.18348e7 - 1.48404e7i) q^{66} +(-5.54357e6 - 6.95141e6i) q^{67} +(-1.12675e7 + 5.42613e6i) q^{68} +(-4.70271e6 - 1.07336e6i) q^{69} +(-8.96090e6 - 2.04527e6i) q^{70} +(-3.42485e6 + 2.73122e6i) q^{71} +(-8.29047e6 + 1.72153e7i) q^{72} +(-3.77485e6 + 861585. i) q^{73} +(2.91060e7 + 1.40167e7i) q^{74} +(-1.06472e7 - 8.49085e6i) q^{75} +(-5.66424e6 - 1.29283e6i) q^{76} +(-2.38165e7 - 1.89931e7i) q^{77} +(6.83531e6 + 2.99475e7i) q^{78} -1.28272e7 q^{79} -2.41303e6i q^{80} +(1.16037e7 + 5.08391e7i) q^{81} +(-1.95014e7 + 1.55519e7i) q^{82} +(4.73617e7 - 2.28082e7i) q^{83} +(2.48475e7 + 1.19659e7i) q^{84} +4.26803e7i q^{85} +(-1.84901e7 + 2.99799e7i) q^{86} +1.32219e8 q^{87} +(3.16820e7 - 6.57883e7i) q^{88} +(5.91783e6 + 1.22885e7i) q^{89} +(1.50121e7 + 1.88245e7i) q^{90} +(4.80611e7 - 1.09696e7i) q^{91} -6.85137e6 q^{92} -1.20320e8i q^{93} +(3.34825e6 - 764217. i) q^{94} +(-1.23626e7 + 1.55022e7i) q^{95} +(-2.39889e7 + 1.05102e8i) q^{96} +(2.40915e7 - 3.02098e7i) q^{97} +(1.21671e7 - 2.52653e7i) q^{98} +(1.77569e7 + 7.77982e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174 q - 7 q^{2} - 7 q^{3} + 4021 q^{4} - 7 q^{5} + 1780 q^{6} - 5383 q^{8} + 56490 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 174 q - 7 q^{2} - 7 q^{3} + 4021 q^{4} - 7 q^{5} + 1780 q^{6} - 5383 q^{8} + 56490 q^{9} - 24989 q^{10} - 14864 q^{11} - 1799 q^{12} + 133078 q^{13} - 243363 q^{14} - 7457 q^{15} - 558511 q^{16} + 55162 q^{17} - 45934 q^{18} + 619745 q^{19} + 1207493 q^{20} + 307272 q^{21} + 432761 q^{22} + 473962 q^{23} + 179363 q^{24} + 2991984 q^{25} + 112889 q^{26} - 7 q^{27} + 458745 q^{28} + 1369823 q^{29} + 4208148 q^{30} + 608540 q^{31} - 15074437 q^{32} - 10988257 q^{33} + 1542905 q^{34} - 4078926 q^{35} + 53343072 q^{36} - 15207265 q^{38} - 16862587 q^{39} - 537581 q^{40} - 852935 q^{41} + 2982351 q^{43} - 10366284 q^{44} + 52423812 q^{45} + 51003036 q^{46} + 5828578 q^{47} - 32078599 q^{48} - 145853506 q^{49} - 30015937 q^{51} + 71975797 q^{52} - 7800770 q^{53} + 43151245 q^{54} - 53485957 q^{55} + 25379079 q^{56} - 21662515 q^{57} - 191329035 q^{58} + 69716890 q^{59} - 106388277 q^{60} - 49131775 q^{61} + 67656953 q^{62} + 355075 q^{63} + 227160853 q^{64} - 87064999 q^{65} + 146686057 q^{66} - 31581292 q^{67} + 200919430 q^{68} - 30179079 q^{69} + 86518670 q^{70} - 60255454 q^{71} - 438784346 q^{72} - 50897868 q^{73} + 5087868 q^{74} + 206284834 q^{75} + 461519674 q^{76} + 256281375 q^{77} - 182130842 q^{78} - 236682026 q^{79} - 488977844 q^{81} - 226181851 q^{82} - 429023996 q^{83} - 513228846 q^{84} + 336855461 q^{86} + 255103986 q^{87} + 977894029 q^{88} - 258201748 q^{89} + 1399550866 q^{90} + 246776320 q^{91} + 363749100 q^{92} - 637129955 q^{94} + 60088655 q^{95} - 1169196874 q^{96} + 218930393 q^{97} - 330217825 q^{98} + 459482633 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.47023 9.28252i 0.279389 0.580158i −0.713300 0.700859i \(-0.752800\pi\)
0.992689 + 0.120702i \(0.0385144\pi\)
\(3\) 45.7755 + 95.0539i 0.565130 + 1.17350i 0.966280 + 0.257492i \(0.0828962\pi\)
−0.401150 + 0.916012i \(0.631389\pi\)
\(4\) 93.4311 + 117.159i 0.364965 + 0.457652i
\(5\) 498.592 113.800i 0.797747 0.182080i 0.195828 0.980638i \(-0.437260\pi\)
0.601918 + 0.798558i \(0.294403\pi\)
\(6\) 1086.97 0.838709
\(7\) 1744.42i 0.726538i −0.931684 0.363269i \(-0.881661\pi\)
0.931684 0.363269i \(-0.118339\pi\)
\(8\) 4076.58 930.453i 0.995259 0.227161i
\(9\) −2849.12 + 3572.69i −0.434251 + 0.544534i
\(10\) 1172.46 5136.90i 0.117246 0.513690i
\(11\) 10887.9 13653.0i 0.743659 0.932518i −0.255756 0.966741i \(-0.582324\pi\)
0.999414 + 0.0342231i \(0.0108957\pi\)
\(12\) −6859.55 + 14244.0i −0.330804 + 0.686921i
\(13\) 6288.43 + 27551.4i 0.220175 + 0.964651i 0.957346 + 0.288944i \(0.0933043\pi\)
−0.737171 + 0.675707i \(0.763839\pi\)
\(14\) −16192.6 7797.94i −0.421506 0.202987i
\(15\) 33640.5 + 42183.8i 0.664503 + 0.833260i
\(16\) 1049.93 4600.05i 0.0160207 0.0701913i
\(17\) −18570.6 + 81363.1i −0.222347 + 0.974164i 0.733360 + 0.679841i \(0.237951\pi\)
−0.955706 + 0.294323i \(0.904906\pi\)
\(18\) 20427.3 + 42417.8i 0.194590 + 0.404071i
\(19\) −30312.4 + 24173.3i −0.232598 + 0.185491i −0.732852 0.680388i \(-0.761811\pi\)
0.500254 + 0.865879i \(0.333240\pi\)
\(20\) 59916.7 + 47782.0i 0.374479 + 0.298637i
\(21\) 165814. 79851.6i 0.852596 0.410588i
\(22\) −78062.9 162099.i −0.333237 0.691975i
\(23\) −28506.6 + 35746.1i −0.101867 + 0.127737i −0.830152 0.557537i \(-0.811746\pi\)
0.728285 + 0.685275i \(0.240318\pi\)
\(24\) 275051. + 344903.i 0.829026 + 1.03957i
\(25\) −116298. + 56006.1i −0.297722 + 0.143376i
\(26\) 283857. + 64788.6i 0.621164 + 0.141777i
\(27\) 204825. + 46749.9i 0.385414 + 0.0879682i
\(28\) 204374. 162983.i 0.332501 0.265161i
\(29\) 543762. 1.12913e6i 0.768806 1.59644i −0.0334349 0.999441i \(-0.510645\pi\)
0.802241 0.597001i \(-0.203641\pi\)
\(30\) 541953. 123697.i 0.669077 0.152713i
\(31\) −1.02751e6 494824.i −1.11260 0.535802i −0.215004 0.976613i \(-0.568977\pi\)
−0.897600 + 0.440811i \(0.854691\pi\)
\(32\) 798900. + 637101.i 0.761890 + 0.607587i
\(33\) 1.79617e6 + 409964.i 1.51458 + 0.345693i
\(34\) 672240. + 536094.i 0.503047 + 0.401167i
\(35\) −198515. 869752.i −0.132288 0.579593i
\(36\) −684769. −0.407694
\(37\) 3.13557e6i 1.67305i 0.547927 + 0.836526i \(0.315417\pi\)
−0.547927 + 0.836526i \(0.684583\pi\)
\(38\) 88886.1 + 389436.i 0.0426285 + 0.186767i
\(39\) −2.33101e6 + 1.85892e6i −1.00759 + 0.803530i
\(40\) 1.92666e6 927833.i 0.752603 0.362435i
\(41\) −2.18126e6 1.05044e6i −0.771918 0.371736i 0.00609710 0.999981i \(-0.498059\pi\)
−0.778015 + 0.628245i \(0.783774\pi\)
\(42\) 1.89612e6i 0.609354i
\(43\) −3.40038e6 354389.i −0.994613 0.103659i
\(44\) 2.61684e6 0.698178
\(45\) −1.01398e6 + 2.10554e6i −0.247274 + 0.513469i
\(46\) 204383. + 424406.i 0.0456472 + 0.0947873i
\(47\) 207835. + 260617.i 0.0425919 + 0.0534086i 0.802671 0.596422i \(-0.203411\pi\)
−0.760079 + 0.649830i \(0.774840\pi\)
\(48\) 485314. 110770.i 0.0914235 0.0208668i
\(49\) 2.72181e6 0.472143
\(50\) 1.32990e6i 0.212783i
\(51\) −8.58396e6 + 1.95923e6i −1.26884 + 0.289605i
\(52\) −2.64036e6 + 3.31090e6i −0.361118 + 0.452828i
\(53\) −271064. + 1.18761e6i −0.0343533 + 0.150512i −0.989196 0.146601i \(-0.953167\pi\)
0.954842 + 0.297113i \(0.0960238\pi\)
\(54\) 1.34957e6 1.69231e6i 0.158716 0.199023i
\(55\) 3.87490e6 8.04632e6i 0.423458 0.879319i
\(56\) −1.62310e6 7.11126e6i −0.165041 0.723094i
\(57\) −3.68533e6 1.77476e6i −0.349122 0.168128i
\(58\) −8.05046e6 1.00950e7i −0.711392 0.892057i
\(59\) 1.33975e6 5.86984e6i 0.110565 0.484416i −0.889080 0.457752i \(-0.848655\pi\)
0.999644 0.0266633i \(-0.00848821\pi\)
\(60\) −1.79914e6 + 7.88256e6i −0.138823 + 0.608222i
\(61\) −9.99937e6 2.07639e7i −0.722193 1.49965i −0.860604 0.509274i \(-0.829914\pi\)
0.138411 0.990375i \(-0.455800\pi\)
\(62\) −9.18644e6 + 7.32594e6i −0.621699 + 0.495789i
\(63\) 6.23226e6 + 4.97006e6i 0.395625 + 0.315500i
\(64\) 1.05734e7 5.09190e6i 0.630227 0.303501i
\(65\) 6.27072e6 + 1.30213e7i 0.351288 + 0.729458i
\(66\) 1.18348e7 1.48404e7i 0.623713 0.782112i
\(67\) −5.54357e6 6.95141e6i −0.275100 0.344964i 0.625018 0.780610i \(-0.285091\pi\)
−0.900118 + 0.435646i \(0.856520\pi\)
\(68\) −1.12675e7 + 5.42613e6i −0.526977 + 0.253779i
\(69\) −4.70271e6 1.07336e6i −0.207468 0.0473533i
\(70\) −8.96090e6 2.04527e6i −0.373215 0.0851840i
\(71\) −3.42485e6 + 2.73122e6i −0.134774 + 0.107479i −0.688557 0.725182i \(-0.741755\pi\)
0.553782 + 0.832661i \(0.313184\pi\)
\(72\) −8.29047e6 + 1.72153e7i −0.308496 + 0.640598i
\(73\) −3.77485e6 + 861585.i −0.132926 + 0.0303394i −0.288466 0.957490i \(-0.593145\pi\)
0.155540 + 0.987830i \(0.450288\pi\)
\(74\) 2.91060e7 + 1.40167e7i 0.970634 + 0.467433i
\(75\) −1.06472e7 8.49085e6i −0.336504 0.268353i
\(76\) −5.66424e6 1.29283e6i −0.169780 0.0387512i
\(77\) −2.38165e7 1.89931e7i −0.677510 0.540296i
\(78\) 6.83531e6 + 2.99475e7i 0.184663 + 0.809062i
\(79\) −1.28272e7 −0.329324 −0.164662 0.986350i \(-0.552653\pi\)
−0.164662 + 0.986350i \(0.552653\pi\)
\(80\) 2.41303e6i 0.0589119i
\(81\) 1.16037e7 + 5.08391e7i 0.269560 + 1.18102i
\(82\) −1.95014e7 + 1.55519e7i −0.431331 + 0.343975i
\(83\) 4.73617e7 2.28082e7i 0.997964 0.480594i 0.137717 0.990472i \(-0.456024\pi\)
0.860247 + 0.509878i \(0.170309\pi\)
\(84\) 2.48475e7 + 1.19659e7i 0.499074 + 0.240341i
\(85\) 4.26803e7i 0.817621i
\(86\) −1.84901e7 + 2.99799e7i −0.338023 + 0.548071i
\(87\) 1.32219e8 2.30791
\(88\) 3.16820e7 6.57883e7i 0.528301 1.09703i
\(89\) 5.91783e6 + 1.22885e7i 0.0943197 + 0.195857i 0.942791 0.333385i \(-0.108191\pi\)
−0.848471 + 0.529242i \(0.822477\pi\)
\(90\) 1.50121e7 + 1.88245e7i 0.228807 + 0.286915i
\(91\) 4.80611e7 1.09696e7i 0.700856 0.159966i
\(92\) −6.85137e6 −0.0956371
\(93\) 1.20320e8i 1.60844i
\(94\) 3.34825e6 764217.i 0.0428851 0.00978825i
\(95\) −1.23626e7 + 1.55022e7i −0.151780 + 0.190326i
\(96\) −2.39889e7 + 1.05102e8i −0.282439 + 1.23745i
\(97\) 2.40915e7 3.02098e7i 0.272130 0.341241i −0.626922 0.779082i \(-0.715685\pi\)
0.899052 + 0.437842i \(0.144257\pi\)
\(98\) 1.21671e7 2.52653e7i 0.131912 0.273917i
\(99\) 1.77569e7 + 7.77982e7i 0.184853 + 0.809895i
\(100\) −1.74274e7 8.39261e6i −0.174274 0.0839261i
\(101\) −1.02189e8 1.28141e8i −0.982017 1.23141i −0.972846 0.231453i \(-0.925652\pi\)
−0.00917121 0.999958i \(-0.502919\pi\)
\(102\) −2.01856e7 + 8.84390e7i −0.186484 + 0.817040i
\(103\) 1.71960e7 7.53407e7i 0.152784 0.669392i −0.839284 0.543693i \(-0.817026\pi\)
0.992068 0.125699i \(-0.0401174\pi\)
\(104\) 5.12706e7 + 1.06464e8i 0.438263 + 0.910063i
\(105\) 7.35862e7 5.86830e7i 0.605395 0.482787i
\(106\) 9.81230e6 + 7.82505e6i 0.0777226 + 0.0619817i
\(107\) 9.14622e7 4.40459e7i 0.697761 0.336024i −0.0511536 0.998691i \(-0.516290\pi\)
0.748914 + 0.662667i \(0.230576\pi\)
\(108\) 1.36598e7 + 2.83649e7i 0.100404 + 0.208491i
\(109\) −2.72115e7 + 3.41221e7i −0.192773 + 0.241730i −0.868819 0.495130i \(-0.835121\pi\)
0.676046 + 0.736859i \(0.263692\pi\)
\(110\) −5.73685e7 7.19378e7i −0.391834 0.491345i
\(111\) −2.98048e8 + 1.43532e8i −1.96334 + 0.945492i
\(112\) −8.02441e6 1.83152e6i −0.0509966 0.0116396i
\(113\) −1.50521e8 3.43555e7i −0.923174 0.210709i −0.265587 0.964087i \(-0.585566\pi\)
−0.657587 + 0.753378i \(0.728423\pi\)
\(114\) −3.29486e7 + 2.62756e7i −0.195082 + 0.155573i
\(115\) −1.01452e7 + 2.10668e7i −0.0580056 + 0.120450i
\(116\) 1.83092e8 4.17896e7i 1.01120 0.230800i
\(117\) −1.16349e8 5.60308e7i −0.620897 0.299008i
\(118\) −4.84979e7 3.86758e7i −0.250147 0.199485i
\(119\) 1.41931e8 + 3.23949e7i 0.707767 + 0.161543i
\(120\) 1.76388e8 + 1.40665e8i 0.850638 + 0.678361i
\(121\) −2.01586e7 8.83207e7i −0.0940415 0.412023i
\(122\) −2.37441e8 −1.07181
\(123\) 2.55421e8i 1.11593i
\(124\) −3.80286e7 1.66614e8i −0.160851 0.704735i
\(125\) −2.07799e8 + 1.65714e8i −0.851144 + 0.678765i
\(126\) 7.39943e7 3.56338e7i 0.293573 0.141377i
\(127\) −3.77691e8 1.81886e8i −1.45185 0.699174i −0.468935 0.883233i \(-0.655362\pi\)
−0.982915 + 0.184058i \(0.941076\pi\)
\(128\) 1.40679e8i 0.524068i
\(129\) −1.21968e8 3.39442e8i −0.440441 1.22576i
\(130\) 1.48902e8 0.521347
\(131\) 6.57803e7 1.36594e8i 0.223363 0.463817i −0.758930 0.651173i \(-0.774277\pi\)
0.982292 + 0.187355i \(0.0599916\pi\)
\(132\) 1.19787e8 + 2.48741e8i 0.394562 + 0.819316i
\(133\) 4.21684e7 + 5.28774e7i 0.134766 + 0.168991i
\(134\) −8.93077e7 + 2.03839e7i −0.276993 + 0.0632219i
\(135\) 1.07444e8 0.323480
\(136\) 3.48963e8i 1.02005i
\(137\) 5.33431e7 1.21752e7i 0.151425 0.0345617i −0.146137 0.989264i \(-0.546684\pi\)
0.297561 + 0.954703i \(0.403827\pi\)
\(138\) −3.09857e7 + 3.88548e7i −0.0854368 + 0.107134i
\(139\) 3.32920e7 1.45862e8i 0.0891828 0.390735i −0.910561 0.413375i \(-0.864350\pi\)
0.999744 + 0.0226396i \(0.00720702\pi\)
\(140\) 8.33517e7 1.04520e8i 0.216971 0.272073i
\(141\) −1.52589e7 + 3.16854e7i −0.0386053 + 0.0801646i
\(142\) 1.00428e7 + 4.40004e7i 0.0247003 + 0.108219i
\(143\) 4.44627e8 + 2.14121e8i 1.06329 + 0.512054i
\(144\) 1.34432e7 + 1.68572e7i 0.0312645 + 0.0392045i
\(145\) 1.42619e8 6.24857e8i 0.322631 1.41354i
\(146\) −8.87676e6 + 3.88916e7i −0.0195363 + 0.0855943i
\(147\) 1.24592e8 + 2.58719e8i 0.266822 + 0.554062i
\(148\) −3.67360e8 + 2.92960e8i −0.765676 + 0.610606i
\(149\) −3.54253e8 2.82507e8i −0.718734 0.573171i 0.194355 0.980931i \(-0.437739\pi\)
−0.913089 + 0.407760i \(0.866310\pi\)
\(150\) −1.26412e8 + 6.08767e7i −0.249702 + 0.120250i
\(151\) 3.46101e8 + 7.18685e8i 0.665724 + 1.38239i 0.910784 + 0.412883i \(0.135478\pi\)
−0.245060 + 0.969508i \(0.578808\pi\)
\(152\) −1.01079e8 + 1.26749e8i −0.189359 + 0.237449i
\(153\) −2.37775e8 2.98161e8i −0.433911 0.544107i
\(154\) −2.82769e8 + 1.36174e8i −0.502746 + 0.242110i
\(155\) −5.68621e8 1.29784e8i −0.985136 0.224851i
\(156\) −4.35578e8 9.94178e7i −0.735474 0.167867i
\(157\) 3.93482e7 3.13792e7i 0.0647629 0.0516467i −0.590573 0.806984i \(-0.701098\pi\)
0.655336 + 0.755337i \(0.272527\pi\)
\(158\) −5.73404e7 + 1.19069e8i −0.0920095 + 0.191060i
\(159\) −1.25295e8 + 2.85978e7i −0.196040 + 0.0447449i
\(160\) 4.70827e8 + 2.26738e8i 0.718425 + 0.345975i
\(161\) 6.23561e7 + 4.97274e7i 0.0928059 + 0.0740102i
\(162\) 5.23786e8 + 1.19551e8i 0.760491 + 0.173577i
\(163\) −2.03066e8 1.61940e8i −0.287665 0.229405i 0.469015 0.883190i \(-0.344609\pi\)
−0.756681 + 0.653785i \(0.773180\pi\)
\(164\) −8.07291e7 3.53697e8i −0.111598 0.488941i
\(165\) 9.42210e8 1.27119
\(166\) 5.41594e8i 0.713249i
\(167\) 3.30362e8 + 1.44741e9i 0.424741 + 1.86091i 0.503467 + 0.864014i \(0.332057\pi\)
−0.0787265 + 0.996896i \(0.525085\pi\)
\(168\) 6.01655e8 4.79804e8i 0.755284 0.602319i
\(169\) 1.54126e7 7.42230e6i 0.0188942 0.00909896i
\(170\) 3.96181e8 + 1.90791e8i 0.474349 + 0.228434i
\(171\) 1.77169e8i 0.207207i
\(172\) −2.76182e8 4.31496e8i −0.315559 0.493018i
\(173\) 2.79469e8 0.311996 0.155998 0.987757i \(-0.450141\pi\)
0.155998 + 0.987757i \(0.450141\pi\)
\(174\) 5.91051e8 1.22733e9i 0.644804 1.33895i
\(175\) 9.76979e7 + 2.02872e8i 0.104168 + 0.216307i
\(176\) −5.13730e7 6.44197e7i −0.0535407 0.0671379i
\(177\) 6.19279e8 1.41346e8i 0.630947 0.144010i
\(178\) 1.40522e8 0.139980
\(179\) 1.60353e9i 1.56194i 0.624569 + 0.780970i \(0.285275\pi\)
−0.624569 + 0.780970i \(0.714725\pi\)
\(180\) −3.41420e8 + 7.79269e7i −0.325236 + 0.0742331i
\(181\) 6.47914e8 8.12458e8i 0.603674 0.756984i −0.382271 0.924050i \(-0.624858\pi\)
0.985946 + 0.167066i \(0.0534294\pi\)
\(182\) 1.13018e8 4.95165e8i 0.103006 0.451299i
\(183\) 1.51596e9 1.90096e9i 1.35171 1.69499i
\(184\) −8.29493e7 + 1.72246e8i −0.0723671 + 0.150272i
\(185\) 3.56829e8 + 1.56337e9i 0.304630 + 1.33467i
\(186\) −1.11687e9 5.37858e8i −0.933151 0.449382i
\(187\) 9.08656e8 + 1.13942e9i 0.743076 + 0.931787i
\(188\) −1.11153e7 + 4.86994e7i −0.00889797 + 0.0389846i
\(189\) 8.15514e7 3.57300e8i 0.0639122 0.280018i
\(190\) 8.86358e7 + 1.84054e8i 0.0680134 + 0.141231i
\(191\) −5.40867e8 + 4.31327e8i −0.406403 + 0.324095i −0.805265 0.592916i \(-0.797977\pi\)
0.398862 + 0.917011i \(0.369405\pi\)
\(192\) 9.68011e8 + 7.71963e8i 0.712320 + 0.568056i
\(193\) −1.27434e9 + 6.13690e8i −0.918451 + 0.442303i −0.832518 0.553998i \(-0.813102\pi\)
−0.0859334 + 0.996301i \(0.527387\pi\)
\(194\) −1.72729e8 3.58674e8i −0.121943 0.253217i
\(195\) −9.50677e8 + 1.19211e9i −0.657498 + 0.824477i
\(196\) 2.54302e8 + 3.18884e8i 0.172316 + 0.216077i
\(197\) −2.10108e9 + 1.01183e9i −1.39501 + 0.671802i −0.972143 0.234389i \(-0.924691\pi\)
−0.422869 + 0.906191i \(0.638977\pi\)
\(198\) 8.01541e8 + 1.82946e8i 0.521513 + 0.119032i
\(199\) 6.38828e7 + 1.45808e7i 0.0407354 + 0.00929759i 0.242840 0.970066i \(-0.421921\pi\)
−0.202105 + 0.979364i \(0.564778\pi\)
\(200\) −4.21986e8 + 3.36523e8i −0.263742 + 0.210327i
\(201\) 4.06999e8 8.45142e8i 0.249350 0.517780i
\(202\) −1.64628e9 + 3.75753e8i −0.988777 + 0.225682i
\(203\) −1.96968e9 9.48547e8i −1.15988 0.558566i
\(204\) −1.03155e9 8.22634e8i −0.595621 0.474992i
\(205\) −1.20710e9 2.75512e8i −0.683481 0.156000i
\(206\) −6.22481e8 4.96412e8i −0.345667 0.275660i
\(207\) −4.64909e7 2.03690e8i −0.0253214 0.110940i
\(208\) 1.33340e8 0.0712374
\(209\) 6.77052e8i 0.354843i
\(210\) −2.15779e8 9.45392e8i −0.110951 0.486110i
\(211\) 1.84842e9 1.47407e9i 0.932548 0.743682i −0.0341992 0.999415i \(-0.510888\pi\)
0.966748 + 0.255733i \(0.0823166\pi\)
\(212\) −1.64465e8 + 7.92021e7i −0.0814198 + 0.0392097i
\(213\) −4.16387e8 2.00522e8i −0.202292 0.0974188i
\(214\) 1.04589e9i 0.498693i
\(215\) −1.73573e9 + 2.10269e8i −0.812323 + 0.0984060i
\(216\) 8.78484e8 0.403570
\(217\) −8.63180e8 + 1.79241e9i −0.389280 + 0.808349i
\(218\) 1.95098e8 + 4.05125e8i 0.0863827 + 0.179375i
\(219\) −2.54693e8 3.19375e8i −0.110724 0.138843i
\(220\) 1.30473e9 2.97797e8i 0.556970 0.127125i
\(221\) −2.35845e9 −0.988683
\(222\) 3.40826e9i 1.40320i
\(223\) 3.33183e9 7.60469e8i 1.34730 0.307512i 0.512793 0.858512i \(-0.328611\pi\)
0.834505 + 0.551000i \(0.185754\pi\)
\(224\) 1.11137e9 1.39361e9i 0.441435 0.553542i
\(225\) 1.31255e8 5.75064e8i 0.0512135 0.224381i
\(226\) −9.91769e8 + 1.24364e9i −0.380169 + 0.476717i
\(227\) −8.29421e8 + 1.72231e9i −0.312372 + 0.648646i −0.996757 0.0804745i \(-0.974356\pi\)
0.684385 + 0.729121i \(0.260071\pi\)
\(228\) −1.36395e8 5.97588e8i −0.0504732 0.221137i
\(229\) 6.92971e8 + 3.33717e8i 0.251984 + 0.121349i 0.555612 0.831441i \(-0.312484\pi\)
−0.303628 + 0.952791i \(0.598198\pi\)
\(230\) 1.50201e8 + 1.88346e8i 0.0536738 + 0.0673048i
\(231\) 7.15149e8 3.13327e9i 0.251159 1.10040i
\(232\) 1.16608e9 5.10895e9i 0.402511 1.76352i
\(233\) −1.05470e9 2.19010e9i −0.357852 0.743088i 0.641866 0.766817i \(-0.278161\pi\)
−0.999718 + 0.0237287i \(0.992446\pi\)
\(234\) −1.04021e9 + 8.29543e8i −0.346944 + 0.276678i
\(235\) 1.33283e8 + 1.06290e8i 0.0437022 + 0.0348514i
\(236\) 8.12878e8 3.91462e8i 0.262046 0.126195i
\(237\) −5.87171e8 1.21927e9i −0.186111 0.386463i
\(238\) 9.35171e8 1.17267e9i 0.291463 0.365483i
\(239\) −3.14061e9 3.93820e9i −0.962547 1.20700i −0.978315 0.207120i \(-0.933591\pi\)
0.0157681 0.999876i \(-0.494981\pi\)
\(240\) 2.29368e8 1.10458e8i 0.0691334 0.0332929i
\(241\) 5.04569e9 + 1.15165e9i 1.49573 + 0.341390i 0.890618 0.454752i \(-0.150272\pi\)
0.605110 + 0.796142i \(0.293129\pi\)
\(242\) −9.09953e8 2.07691e8i −0.265312 0.0605558i
\(243\) −3.22360e9 + 2.57074e9i −0.924519 + 0.737280i
\(244\) 1.49842e9 3.11151e9i 0.422742 0.877833i
\(245\) 1.35707e9 3.09743e8i 0.376650 0.0859680i
\(246\) −2.37095e9 1.14179e9i −0.647415 0.311779i
\(247\) −8.56626e8 6.83136e8i −0.230146 0.183535i
\(248\) −4.64915e9 1.06114e9i −1.22904 0.280521i
\(249\) 4.33601e9 + 3.45786e9i 1.12796 + 0.899517i
\(250\) 6.09337e8 + 2.66968e9i 0.155990 + 0.683438i
\(251\) −1.45337e9 −0.366168 −0.183084 0.983097i \(-0.558608\pi\)
−0.183084 + 0.983097i \(0.558608\pi\)
\(252\) 1.19452e9i 0.296205i
\(253\) 1.77665e8 + 7.78400e8i 0.0433630 + 0.189986i
\(254\) −3.37673e9 + 2.69285e9i −0.811263 + 0.646960i
\(255\) −4.05693e9 + 1.95371e9i −0.959482 + 0.462062i
\(256\) 4.01265e9 + 1.93239e9i 0.934269 + 0.449920i
\(257\) 3.87974e9i 0.889344i 0.895694 + 0.444672i \(0.146680\pi\)
−0.895694 + 0.444672i \(0.853320\pi\)
\(258\) −3.69610e9 3.85210e8i −0.834191 0.0869397i
\(259\) 5.46974e9 1.21554
\(260\) −9.39678e8 + 1.95126e9i −0.205630 + 0.426994i
\(261\) 2.48480e9 + 5.15973e9i 0.535462 + 1.11190i
\(262\) −9.73886e8 1.22121e9i −0.206682 0.259171i
\(263\) 8.65614e9 1.97571e9i 1.80926 0.412952i 0.821665 0.569971i \(-0.193046\pi\)
0.987596 + 0.157019i \(0.0501884\pi\)
\(264\) 7.70369e9 1.58593
\(265\) 6.22980e8i 0.126325i
\(266\) 6.79338e8 1.55054e8i 0.135694 0.0309712i
\(267\) −8.97177e8 + 1.12502e9i −0.176536 + 0.221369i
\(268\) 2.96478e8 1.29896e9i 0.0574717 0.251800i
\(269\) −2.74702e9 + 3.44465e9i −0.524629 + 0.657864i −0.971585 0.236692i \(-0.923937\pi\)
0.446955 + 0.894556i \(0.352508\pi\)
\(270\) 4.80299e8 9.97352e8i 0.0903768 0.187669i
\(271\) 6.73491e8 + 2.95076e9i 0.124869 + 0.547087i 0.998201 + 0.0599610i \(0.0190976\pi\)
−0.873332 + 0.487126i \(0.838045\pi\)
\(272\) 3.54777e8 + 1.70852e8i 0.0648156 + 0.0312136i
\(273\) 3.24273e9 + 4.06626e9i 0.583795 + 0.732056i
\(274\) 1.25439e8 5.49585e8i 0.0222552 0.0975062i
\(275\) −5.01588e8 + 2.19760e9i −0.0877035 + 0.384254i
\(276\) −3.13625e8 6.51250e8i −0.0540474 0.112231i
\(277\) −5.84083e9 + 4.65790e9i −0.992100 + 0.791173i −0.977974 0.208727i \(-0.933068\pi\)
−0.0141256 + 0.999900i \(0.504496\pi\)
\(278\) −1.20514e9 9.61070e8i −0.201771 0.160907i
\(279\) 4.69537e9 2.26117e9i 0.774913 0.373178i
\(280\) −1.61853e9 3.36091e9i −0.263322 0.546795i
\(281\) −9.10646e8 + 1.14191e9i −0.146058 + 0.183151i −0.849479 0.527623i \(-0.823083\pi\)
0.703421 + 0.710773i \(0.251655\pi\)
\(282\) 2.25910e8 + 2.83282e8i 0.0357222 + 0.0447943i
\(283\) 1.06199e10 5.11425e9i 1.65567 0.797327i 0.656595 0.754243i \(-0.271996\pi\)
0.999071 0.0430839i \(-0.0137183\pi\)
\(284\) −6.39974e8 1.46070e8i −0.0983760 0.0224537i
\(285\) −2.03945e9 4.65490e8i −0.309124 0.0705555i
\(286\) 3.97517e9 3.17009e9i 0.594144 0.473814i
\(287\) −1.83240e9 + 3.80502e9i −0.270080 + 0.560828i
\(288\) −4.55233e9 + 1.03904e9i −0.661704 + 0.151030i
\(289\) 9.84917e6 + 4.74311e6i 0.00141191 + 0.000679942i
\(290\) −5.16270e9 4.11712e9i −0.729937 0.582105i
\(291\) 3.97436e9 + 9.07121e8i 0.554236 + 0.126501i
\(292\) −4.53631e8 3.61759e8i −0.0623981 0.0497608i
\(293\) −3.17226e9 1.38986e10i −0.430426 1.88582i −0.463015 0.886350i \(-0.653232\pi\)
0.0325891 0.999469i \(-0.489625\pi\)
\(294\) 2.95852e9 0.395990
\(295\) 3.07912e9i 0.406573i
\(296\) 2.91750e9 + 1.27824e10i 0.380053 + 1.66512i
\(297\) 2.86839e9 2.28746e9i 0.368648 0.293987i
\(298\) −4.20597e9 + 2.02549e9i −0.533336 + 0.256841i
\(299\) −1.16412e9 5.60609e8i −0.145650 0.0701416i
\(300\) 2.04072e9i 0.251941i
\(301\) −6.18203e8 + 5.93169e9i −0.0753122 + 0.722624i
\(302\) 8.21836e9 0.988001
\(303\) 7.50255e9 1.55792e10i 0.890099 1.84831i
\(304\) 7.93726e7 + 1.64819e8i 0.00929344 + 0.0192980i
\(305\) −7.34854e9 9.21478e9i −0.849184 1.06484i
\(306\) −3.83059e9 + 8.74307e8i −0.436898 + 0.0997191i
\(307\) 2.96360e7 0.00333631 0.00166815 0.999999i \(-0.499469\pi\)
0.00166815 + 0.999999i \(0.499469\pi\)
\(308\) 4.56486e9i 0.507253i
\(309\) 7.94858e9 1.81421e9i 0.871878 0.199000i
\(310\) −3.74659e9 + 4.69807e9i −0.405685 + 0.508713i
\(311\) 7.70255e8 3.37471e9i 0.0823366 0.360740i −0.916929 0.399050i \(-0.869340\pi\)
0.999266 + 0.0383095i \(0.0121973\pi\)
\(312\) −7.77292e9 + 9.74694e9i −0.820287 + 1.02861i
\(313\) −6.78201e9 + 1.40830e10i −0.706612 + 1.46730i 0.169672 + 0.985501i \(0.445729\pi\)
−0.876284 + 0.481795i \(0.839985\pi\)
\(314\) −1.15382e8 5.05523e8i −0.0118692 0.0520022i
\(315\) 3.67295e9 + 1.76880e9i 0.373055 + 0.179654i
\(316\) −1.19846e9 1.50282e9i −0.120192 0.150716i
\(317\) −2.18168e9 + 9.55857e9i −0.216050 + 0.946576i 0.744315 + 0.667829i \(0.232776\pi\)
−0.960364 + 0.278747i \(0.910081\pi\)
\(318\) −2.94638e8 + 1.29089e9i −0.0288124 + 0.126236i
\(319\) −9.49563e9 1.97179e10i −0.916982 1.90413i
\(320\) 4.69237e9 3.74204e9i 0.447500 0.356869i
\(321\) 8.37346e9 + 6.67761e9i 0.788651 + 0.628928i
\(322\) 7.40341e8 3.56530e8i 0.0688666 0.0331644i
\(323\) −1.40390e9 2.91522e9i −0.128981 0.267832i
\(324\) −4.87211e9 + 6.10943e9i −0.442117 + 0.554397i
\(325\) −2.27438e9 2.85198e9i −0.203858 0.255630i
\(326\) −2.41096e9 + 1.16106e9i −0.213462 + 0.102798i
\(327\) −4.48906e9 1.02460e9i −0.392613 0.0896113i
\(328\) −9.86946e9 2.25264e9i −0.852703 0.194624i
\(329\) 4.54625e8 3.62551e8i 0.0388034 0.0309446i
\(330\) 4.21189e9 8.74608e9i 0.355158 0.737493i
\(331\) −1.92657e10 + 4.39726e9i −1.60499 + 0.366328i −0.928853 0.370449i \(-0.879204\pi\)
−0.676135 + 0.736777i \(0.736347\pi\)
\(332\) 7.09724e9 + 3.41785e9i 0.584167 + 0.281320i
\(333\) −1.12024e10 8.93363e9i −0.911034 0.726526i
\(334\) 1.49124e10 + 3.40366e9i 1.19829 + 0.273502i
\(335\) −3.55505e9 2.83506e9i −0.282271 0.225104i
\(336\) −1.93229e8 8.46590e8i −0.0151605 0.0664227i
\(337\) −1.20558e10 −0.934710 −0.467355 0.884070i \(-0.654793\pi\)
−0.467355 + 0.884070i \(0.654793\pi\)
\(338\) 1.76247e8i 0.0135038i
\(339\) −3.62457e9 1.58803e10i −0.274446 1.20243i
\(340\) −5.00038e9 + 3.98767e9i −0.374186 + 0.298403i
\(341\) −1.79433e10 + 8.64104e9i −1.32704 + 0.639070i
\(342\) −1.64458e9 7.91988e8i −0.120213 0.0578914i
\(343\) 1.48042e10i 1.06957i
\(344\) −1.41917e10 + 1.71920e9i −1.01345 + 0.122770i
\(345\) −2.46688e9 −0.174129
\(346\) 1.24929e9 2.59418e9i 0.0871684 0.181007i
\(347\) 6.83732e9 + 1.41978e10i 0.471594 + 0.979274i 0.992104 + 0.125419i \(0.0400275\pi\)
−0.520510 + 0.853855i \(0.674258\pi\)
\(348\) 1.23534e10 + 1.54907e10i 0.842306 + 1.05622i
\(349\) 2.33134e10 5.32114e9i 1.57146 0.358676i 0.654000 0.756495i \(-0.273090\pi\)
0.917464 + 0.397818i \(0.130232\pi\)
\(350\) 2.31989e9 0.154595
\(351\) 5.93719e9i 0.391158i
\(352\) 1.73967e10 3.97068e9i 1.13317 0.258639i
\(353\) −1.69400e10 + 2.12421e10i −1.09098 + 1.36804i −0.166837 + 0.985984i \(0.553355\pi\)
−0.924139 + 0.382056i \(0.875216\pi\)
\(354\) 1.45627e9 6.38032e9i 0.0927316 0.406284i
\(355\) −1.39679e9 + 1.75151e9i −0.0879460 + 0.110281i
\(356\) −8.86797e8 + 1.84145e9i −0.0552108 + 0.114647i
\(357\) 3.41772e9 + 1.49740e10i 0.210409 + 0.921861i
\(358\) 1.48848e10 + 7.16813e9i 0.906171 + 0.436389i
\(359\) −1.07206e10 1.34432e10i −0.645416 0.809327i 0.346252 0.938141i \(-0.387454\pi\)
−0.991669 + 0.128815i \(0.958883\pi\)
\(360\) −2.17445e9 + 9.52688e9i −0.129461 + 0.567206i
\(361\) −3.44471e9 + 1.50922e10i −0.202826 + 0.888639i
\(362\) −4.64534e9 9.64614e9i −0.270510 0.561719i
\(363\) 7.47246e9 5.95908e9i 0.430365 0.343205i
\(364\) 5.77560e9 + 4.60588e9i 0.328997 + 0.262366i
\(365\) −1.78406e9 + 8.59158e8i −0.100517 + 0.0484063i
\(366\) −1.08690e10 2.25697e10i −0.605710 1.25777i
\(367\) 1.10322e10 1.38339e10i 0.608132 0.762573i −0.378489 0.925606i \(-0.623556\pi\)
0.986621 + 0.163033i \(0.0521276\pi\)
\(368\) 1.34504e8 + 1.68663e8i 0.00733405 + 0.00919661i
\(369\) 9.96756e9 4.80012e9i 0.537630 0.258909i
\(370\) 1.61071e10 + 3.67634e9i 0.859431 + 0.196159i
\(371\) 2.07169e9 + 4.72849e8i 0.109352 + 0.0249590i
\(372\) 1.40966e10 1.12416e10i 0.736108 0.587026i
\(373\) −6.19920e9 + 1.28728e10i −0.320258 + 0.665024i −0.997495 0.0707422i \(-0.977463\pi\)
0.677236 + 0.735766i \(0.263178\pi\)
\(374\) 1.46386e10 3.34116e9i 0.748191 0.170770i
\(375\) −2.52639e10 1.21664e10i −1.27754 0.615231i
\(376\) 1.08975e9 + 8.69046e8i 0.0545224 + 0.0434802i
\(377\) 3.45286e10 + 7.88093e9i 1.70928 + 0.390132i
\(378\) −2.95209e9 2.35421e9i −0.144598 0.115313i
\(379\) 4.19756e9 + 1.83907e10i 0.203442 + 0.891336i 0.968822 + 0.247758i \(0.0796937\pi\)
−0.765380 + 0.643578i \(0.777449\pi\)
\(380\) −2.97127e9 −0.142497
\(381\) 4.42270e10i 2.09888i
\(382\) 1.58600e9 + 6.94873e9i 0.0744819 + 0.326326i
\(383\) 2.41510e9 1.92598e9i 0.112238 0.0895069i −0.565762 0.824568i \(-0.691418\pi\)
0.678001 + 0.735061i \(0.262847\pi\)
\(384\) −1.33720e10 + 6.43963e9i −0.614997 + 0.296167i
\(385\) −1.40361e10 6.75945e9i −0.638859 0.307658i
\(386\) 1.45724e10i 0.656421i
\(387\) 1.09542e10 1.11388e10i 0.488358 0.496587i
\(388\) 5.79024e9 0.255487
\(389\) −1.26404e10 + 2.62480e10i −0.552028 + 1.14630i 0.419144 + 0.907920i \(0.362330\pi\)
−0.971172 + 0.238379i \(0.923384\pi\)
\(390\) 6.81606e9 + 1.41537e10i 0.294629 + 0.611803i
\(391\) −2.37903e9 2.98321e9i −0.101787 0.127637i
\(392\) 1.10957e10 2.53252e9i 0.469905 0.107253i
\(393\) 1.59949e10 0.670521
\(394\) 2.40264e10i 0.997021i
\(395\) −6.39553e9 + 1.45974e9i −0.262717 + 0.0599634i
\(396\) −7.45570e9 + 9.34915e9i −0.303185 + 0.380182i
\(397\) 6.80530e9 2.98160e10i 0.273959 1.20029i −0.631336 0.775509i \(-0.717493\pi\)
0.905295 0.424783i \(-0.139650\pi\)
\(398\) 4.20918e8 5.27814e8i 0.0167751 0.0210353i
\(399\) −3.09593e9 + 6.42876e9i −0.122152 + 0.253650i
\(400\) 1.35526e8 + 5.93779e8i 0.00529399 + 0.0231945i
\(401\) 4.00666e9 + 1.92951e9i 0.154955 + 0.0746223i 0.509754 0.860320i \(-0.329736\pi\)
−0.354799 + 0.934943i \(0.615451\pi\)
\(402\) −6.02567e9 7.55596e9i −0.230729 0.289324i
\(403\) 7.17166e9 3.14211e10i 0.271894 1.19125i
\(404\) 5.46523e9 2.39447e10i 0.205155 0.898844i
\(405\) 1.15710e10 + 2.40274e10i 0.430082 + 0.893074i
\(406\) −1.76098e10 + 1.40434e10i −0.648113 + 0.516853i
\(407\) 4.28099e10 + 3.41398e10i 1.56015 + 1.24418i
\(408\) −3.31702e10 + 1.59739e10i −1.19704 + 0.576463i
\(409\) −7.71469e9 1.60197e10i −0.275693 0.572482i 0.716443 0.697645i \(-0.245769\pi\)
−0.992136 + 0.125163i \(0.960054\pi\)
\(410\) −7.95344e9 + 9.97330e9i −0.281462 + 0.352942i
\(411\) 3.59911e9 + 4.51314e9i 0.126133 + 0.158166i
\(412\) 1.04335e10 5.02450e9i 0.362110 0.174383i
\(413\) −1.02394e10 2.33709e9i −0.351946 0.0803294i
\(414\) −2.09858e9 4.78988e8i −0.0714373 0.0163051i
\(415\) 2.10186e10 1.67617e10i 0.708616 0.565102i
\(416\) −1.25292e10 + 2.60172e10i −0.418360 + 0.868734i
\(417\) 1.53887e10 3.51237e9i 0.508930 0.116160i
\(418\) 6.28475e9 + 3.02658e9i 0.205865 + 0.0991394i
\(419\) −5.82296e9 4.64366e9i −0.188924 0.150662i 0.524460 0.851435i \(-0.324267\pi\)
−0.713384 + 0.700773i \(0.752839\pi\)
\(420\) 1.37505e10 + 3.13846e9i 0.441896 + 0.100860i
\(421\) −3.67423e10 2.93010e10i −1.16960 0.932726i −0.170983 0.985274i \(-0.554694\pi\)
−0.998618 + 0.0525475i \(0.983266\pi\)
\(422\) −5.42020e9 2.37474e10i −0.170909 0.748802i
\(423\) −1.52325e9 −0.0475784
\(424\) 5.09360e9i 0.157602i
\(425\) −2.39711e9 1.05024e10i −0.0734737 0.321909i
\(426\) −3.72269e9 + 2.96875e9i −0.113037 + 0.0901436i
\(427\) −3.62209e10 + 1.74431e10i −1.08955 + 0.524700i
\(428\) 1.37058e10 + 6.60035e9i 0.408440 + 0.196694i
\(429\) 5.20650e10i 1.53715i
\(430\) −5.80729e9 + 1.70519e10i −0.169863 + 0.498769i
\(431\) 5.16650e10 1.49723 0.748614 0.663006i \(-0.230720\pi\)
0.748614 + 0.663006i \(0.230720\pi\)
\(432\) 4.30104e8 8.93121e8i 0.0123492 0.0256434i
\(433\) −2.62302e10 5.44676e10i −0.746192 1.54948i −0.833009 0.553259i \(-0.813384\pi\)
0.0868176 0.996224i \(-0.472330\pi\)
\(434\) 1.27795e10 + 1.60250e10i 0.360209 + 0.451688i
\(435\) 6.59235e10 1.50466e10i 1.84113 0.420225i
\(436\) −6.54011e9 −0.180984
\(437\) 1.77265e9i 0.0486068i
\(438\) −4.10314e9 + 9.36514e8i −0.111486 + 0.0254459i
\(439\) −2.54162e10 + 3.18709e10i −0.684309 + 0.858097i −0.995743 0.0921710i \(-0.970619\pi\)
0.311434 + 0.950268i \(0.399191\pi\)
\(440\) 8.30964e9 3.64069e10i 0.221703 0.971344i
\(441\) −7.75477e9 + 9.72418e9i −0.205029 + 0.257098i
\(442\) −1.05428e10 + 2.18923e10i −0.276227 + 0.573592i
\(443\) 5.49599e9 + 2.40795e10i 0.142702 + 0.625219i 0.994801 + 0.101838i \(0.0324724\pi\)
−0.852099 + 0.523381i \(0.824670\pi\)
\(444\) −4.46631e10 2.15086e10i −1.14926 0.553452i
\(445\) 4.34901e9 + 5.45349e9i 0.110905 + 0.139070i
\(446\) 7.83498e9 3.43273e10i 0.198015 0.867561i
\(447\) 1.06373e10 4.66050e10i 0.266441 1.16735i
\(448\) −8.88241e9 1.84445e10i −0.220505 0.457883i
\(449\) 1.85939e10 1.48281e10i 0.457493 0.364838i −0.367461 0.930039i \(-0.619773\pi\)
0.824953 + 0.565201i \(0.191201\pi\)
\(450\) −4.75131e9 3.78904e9i −0.115868 0.0924015i
\(451\) −3.80909e10 + 1.83436e10i −0.920695 + 0.443383i
\(452\) −1.00383e10 2.08448e10i −0.240495 0.499394i
\(453\) −5.24709e10 + 6.57964e10i −1.24602 + 1.56246i
\(454\) 1.22797e10 + 1.53982e10i 0.289044 + 0.362449i
\(455\) 2.27145e10 1.09387e10i 0.529979 0.255224i
\(456\) −1.66749e10 3.80594e9i −0.385659 0.0880242i
\(457\) 5.71053e10 + 1.30339e10i 1.30922 + 0.298820i 0.819509 0.573066i \(-0.194246\pi\)
0.489709 + 0.871886i \(0.337103\pi\)
\(458\) 6.19548e9 4.94073e9i 0.140803 0.112287i
\(459\) −7.60744e9 + 1.57970e10i −0.171391 + 0.355897i
\(460\) −3.41604e9 + 7.79688e8i −0.0762942 + 0.0174136i
\(461\) 1.45236e10 + 6.99418e9i 0.321566 + 0.154858i 0.587702 0.809078i \(-0.300033\pi\)
−0.266136 + 0.963935i \(0.585747\pi\)
\(462\) −2.58878e10 2.06448e10i −0.568234 0.453151i
\(463\) −3.04487e9 6.94971e8i −0.0662589 0.0151232i 0.189263 0.981926i \(-0.439390\pi\)
−0.255522 + 0.966803i \(0.582247\pi\)
\(464\) −4.62316e9 3.68685e9i −0.0997394 0.0795395i
\(465\) −1.36925e10 5.99906e10i −0.292866 1.28313i
\(466\) −2.50444e10 −0.531088
\(467\) 2.54196e10i 0.534444i −0.963635 0.267222i \(-0.913894\pi\)
0.963635 0.267222i \(-0.0861056\pi\)
\(468\) −4.30612e9 1.88663e10i −0.0897641 0.393282i
\(469\) −1.21262e10 + 9.67029e9i −0.250629 + 0.199870i
\(470\) 1.58244e9 7.62064e8i 0.0324292 0.0156171i
\(471\) 4.78390e9 + 2.30380e9i 0.0972071 + 0.0468125i
\(472\) 2.51755e10i 0.507235i
\(473\) −4.18615e10 + 4.25669e10i −0.836316 + 0.850408i
\(474\) −1.39427e10 −0.276207
\(475\) 2.17141e9 4.50898e9i 0.0426548 0.0885735i
\(476\) 9.46544e9 + 1.96552e10i 0.184380 + 0.382868i
\(477\) −3.47066e9 4.35208e9i −0.0670408 0.0840665i
\(478\) −5.05956e10 + 1.15481e10i −0.969173 + 0.221208i
\(479\) 3.36124e10 0.638494 0.319247 0.947672i \(-0.396570\pi\)
0.319247 + 0.947672i \(0.396570\pi\)
\(480\) 5.51330e10i 1.03860i
\(481\) −8.63893e10 + 1.97178e10i −1.61391 + 0.368365i
\(482\) 3.32456e10 4.16886e10i 0.615950 0.772377i
\(483\) −1.87239e9 + 8.20349e9i −0.0344040 + 0.150734i
\(484\) 8.46412e9 1.06137e10i 0.154241 0.193412i
\(485\) 8.57394e9 1.78040e10i 0.154958 0.321773i
\(486\) 9.45268e9 + 4.14149e10i 0.169438 + 0.742355i
\(487\) −2.58847e10 1.24654e10i −0.460179 0.221610i 0.189407 0.981899i \(-0.439343\pi\)
−0.649586 + 0.760288i \(0.725058\pi\)
\(488\) −6.00831e10 7.53418e10i −1.05943 1.32849i
\(489\) 6.09755e9 2.67151e10i 0.106640 0.467220i
\(490\) 3.19122e9 1.39817e10i 0.0553571 0.242535i
\(491\) −4.82878e9 1.00271e10i −0.0830828 0.172523i 0.855288 0.518152i \(-0.173380\pi\)
−0.938371 + 0.345629i \(0.887666\pi\)
\(492\) 2.99249e10 2.38643e10i 0.510707 0.407275i
\(493\) 8.17718e10 + 6.52108e10i 1.38425 + 1.10391i
\(494\) −1.01705e10 + 4.89787e9i −0.170780 + 0.0822432i
\(495\) 1.77069e10 + 3.67688e10i 0.294932 + 0.612433i
\(496\) −3.35504e9 + 4.20709e9i −0.0554333 + 0.0695112i
\(497\) 4.76439e9 + 5.97436e9i 0.0780876 + 0.0979187i
\(498\) 5.14806e10 2.47917e10i 0.837001 0.403079i
\(499\) 3.00751e10 + 6.86445e9i 0.485071 + 0.110714i 0.458061 0.888921i \(-0.348544\pi\)
0.0270102 + 0.999635i \(0.491401\pi\)
\(500\) −3.88298e10 8.86264e9i −0.621276 0.141802i
\(501\) −1.22459e11 + 9.76581e10i −1.94375 + 1.55009i
\(502\) −6.49689e9 + 1.34909e10i −0.102304 + 0.212435i
\(503\) 2.10004e10 4.79321e9i 0.328062 0.0748780i −0.0553179 0.998469i \(-0.517617\pi\)
0.383380 + 0.923591i \(0.374760\pi\)
\(504\) 3.00307e10 + 1.44620e10i 0.465419 + 0.224134i
\(505\) −6.55331e10 5.22609e10i −1.00762 0.803548i
\(506\) 8.01972e9 + 1.83045e9i 0.122337 + 0.0279226i
\(507\) 1.41104e9 + 1.12526e9i 0.0213554 + 0.0170303i
\(508\) −1.39785e10 6.12437e10i −0.209896 0.919616i
\(509\) −5.35598e10 −0.797936 −0.398968 0.916965i \(-0.630632\pi\)
−0.398968 + 0.916965i \(0.630632\pi\)
\(510\) 4.63921e10i 0.685746i
\(511\) 1.50296e9 + 6.58492e9i 0.0220427 + 0.0965754i
\(512\) 7.71831e9 6.15515e9i 0.112316 0.0895692i
\(513\) −7.33883e9 + 3.53419e9i −0.105964 + 0.0510294i
\(514\) 3.60137e10 + 1.73433e10i 0.515960 + 0.248473i
\(515\) 3.95212e10i 0.561825i
\(516\) 2.83730e10 4.60041e10i 0.400227 0.648930i
\(517\) 5.82109e9 0.0814784
\(518\) 2.44510e10 5.07730e10i 0.339608 0.705202i
\(519\) 1.27928e10 + 2.65646e10i 0.176318 + 0.366129i
\(520\) 3.76788e10 + 4.72477e10i 0.515328 + 0.646200i
\(521\) 1.21545e11 2.77419e10i 1.64963 0.376518i 0.706183 0.708029i \(-0.250416\pi\)
0.943451 + 0.331511i \(0.107558\pi\)
\(522\) 5.90029e10 0.794678
\(523\) 6.39792e10i 0.855130i 0.903985 + 0.427565i \(0.140629\pi\)
−0.903985 + 0.427565i \(0.859371\pi\)
\(524\) 2.21491e10 5.05540e9i 0.293787 0.0670549i
\(525\) −1.48116e10 + 1.85731e10i −0.194968 + 0.244483i
\(526\) 2.03554e10 8.91826e10i 0.265911 1.16503i
\(527\) 5.93420e10 7.44125e10i 0.769343 0.964725i
\(528\) 3.77171e9 7.83205e9i 0.0485292 0.100772i
\(529\) 1.69607e10 + 7.43096e10i 0.216581 + 0.948903i
\(530\) 5.78282e9 + 2.78486e9i 0.0732886 + 0.0352939i
\(531\) 1.71540e10 + 2.15104e10i 0.215768 + 0.270564i
\(532\) −2.25523e9 + 9.88079e9i −0.0281542 + 0.123352i
\(533\) 1.52244e10 6.67023e10i 0.188638 0.826479i
\(534\) 6.43248e9 + 1.33572e10i 0.0791068 + 0.164267i
\(535\) 4.05899e10 3.23693e10i 0.495453 0.395110i
\(536\) −2.90668e10 2.31800e10i −0.352158 0.280837i
\(537\) −1.52421e11 + 7.34023e10i −1.83294 + 0.882699i
\(538\) 1.96953e10 + 4.08977e10i 0.235089 + 0.488168i
\(539\) 2.96348e10 3.71609e10i 0.351113 0.440282i
\(540\) 1.00386e10 + 1.25880e10i 0.118059 + 0.148041i
\(541\) 1.11965e11 5.39195e10i 1.30705 0.629444i 0.354854 0.934922i \(-0.384531\pi\)
0.952199 + 0.305478i \(0.0988163\pi\)
\(542\) 3.04011e10 + 6.93886e9i 0.352284 + 0.0804065i
\(543\) 1.06886e11 + 2.43960e10i 1.22948 + 0.280620i
\(544\) −6.66726e10 + 5.31696e10i −0.761293 + 0.607111i
\(545\) −9.68431e9 + 2.01097e10i −0.109770 + 0.227939i
\(546\) 5.22409e10 1.19236e10i 0.587814 0.134165i
\(547\) −1.45508e10 7.00730e9i −0.162532 0.0782711i 0.350849 0.936432i \(-0.385893\pi\)
−0.513381 + 0.858161i \(0.671607\pi\)
\(548\) 6.41034e9 + 5.11208e9i 0.0710819 + 0.0566859i
\(549\) 1.02672e11 + 2.34343e10i 1.13022 + 0.257966i
\(550\) 1.81571e10 + 1.44798e10i 0.198424 + 0.158238i
\(551\) 1.08122e10 + 4.73712e10i 0.117302 + 0.513935i
\(552\) −2.01697e10 −0.217242
\(553\) 2.23760e10i 0.239266i
\(554\) 1.71273e10 + 7.50395e10i 0.181823 + 0.796619i
\(555\) −1.32270e11 + 1.05482e11i −1.39409 + 1.11175i
\(556\) 2.01995e10 9.72758e9i 0.211369 0.101790i
\(557\) −5.77246e10 2.77987e10i −0.599708 0.288804i 0.109295 0.994009i \(-0.465141\pi\)
−0.709003 + 0.705205i \(0.750855\pi\)
\(558\) 5.36928e10i 0.553833i
\(559\) −1.16191e10 9.59139e10i −0.118994 0.982278i
\(560\) −4.20933e9 −0.0428017
\(561\) −6.67119e10 + 1.38529e11i −0.673522 + 1.39858i
\(562\) 6.52905e9 + 1.35577e10i 0.0654493 + 0.135907i
\(563\) 5.77171e10 + 7.23749e10i 0.574475 + 0.720368i 0.981159 0.193200i \(-0.0618867\pi\)
−0.406685 + 0.913569i \(0.633315\pi\)
\(564\) −5.13788e9 + 1.17269e9i −0.0507771 + 0.0115895i
\(565\) −7.89583e10 −0.774825
\(566\) 1.21441e11i 1.18331i
\(567\) 8.86846e10 2.02417e10i 0.858057 0.195846i
\(568\) −1.14204e10 + 1.43207e10i −0.109720 + 0.137585i
\(569\) −3.61647e10 + 1.58448e11i −0.345013 + 1.51160i 0.443326 + 0.896361i \(0.353798\pi\)
−0.788339 + 0.615241i \(0.789059\pi\)
\(570\) −1.34377e10 + 1.68503e10i −0.127299 + 0.159628i
\(571\) −5.69324e10 + 1.18221e11i −0.535569 + 1.11212i 0.441117 + 0.897449i \(0.354582\pi\)
−0.976686 + 0.214671i \(0.931132\pi\)
\(572\) 1.64558e10 + 7.20976e10i 0.153722 + 0.673499i
\(573\) −6.57577e10 3.16673e10i −0.609998 0.293760i
\(574\) 2.71289e10 + 3.40186e10i 0.249911 + 0.313379i
\(575\) 1.31325e9 5.75373e9i 0.0120137 0.0526354i
\(576\) −1.19333e10 + 5.22831e10i −0.108410 + 0.474976i
\(577\) −3.69040e10 7.66320e10i −0.332943 0.691364i 0.665543 0.746359i \(-0.268200\pi\)
−0.998487 + 0.0549952i \(0.982486\pi\)
\(578\) 8.80560e7 7.02223e7i 0.000788947 0.000629164i
\(579\) −1.16667e11 9.30390e10i −1.03809 0.827848i
\(580\) 8.65326e10 4.16719e10i 0.764659 0.368240i
\(581\) −3.97870e10 8.26186e10i −0.349170 0.725059i
\(582\) 2.61867e10 3.28370e10i 0.228238 0.286202i
\(583\) 1.32631e10 + 1.66314e10i 0.114808 + 0.143964i
\(584\) −1.45868e10 + 7.02465e9i −0.125403 + 0.0603911i
\(585\) −6.43870e10 1.46959e10i −0.549762 0.125480i
\(586\) −1.43195e11 3.26832e10i −1.21433 0.277163i
\(587\) 5.03608e10 4.01614e10i 0.424171 0.338265i −0.388026 0.921648i \(-0.626843\pi\)
0.812197 + 0.583384i \(0.198272\pi\)
\(588\) −1.86704e10 + 3.87694e10i −0.156187 + 0.324325i
\(589\) 4.31079e10 9.83910e9i 0.358176 0.0817512i
\(590\) −2.85820e10 1.37644e10i −0.235876 0.113592i
\(591\) −1.92356e11 1.53399e11i −1.57673 1.25740i
\(592\) 1.44238e10 + 3.29214e9i 0.117434 + 0.0268035i
\(593\) 1.56463e11 + 1.24775e11i 1.26530 + 1.00904i 0.998980 + 0.0451547i \(0.0143781\pi\)
0.266317 + 0.963886i \(0.414193\pi\)
\(594\) −8.41108e9 3.68514e10i −0.0675626 0.296011i
\(595\) 7.44523e10 0.594032
\(596\) 6.78988e10i 0.538118i
\(597\) 1.53831e9 + 6.73976e9i 0.0121100 + 0.0530575i
\(598\) −1.04077e10 + 8.29989e9i −0.0813863 + 0.0649034i
\(599\) 1.17764e10 5.67123e9i 0.0914758 0.0440524i −0.387586 0.921833i \(-0.626691\pi\)
0.479062 + 0.877781i \(0.340977\pi\)
\(600\) −5.13045e10 2.47069e10i −0.395868 0.190640i
\(601\) 4.73275e9i 0.0362757i −0.999835 0.0181378i \(-0.994226\pi\)
0.999835 0.0181378i \(-0.00577377\pi\)
\(602\) 5.22975e10 + 3.22545e10i 0.398194 + 0.245586i
\(603\) 4.06295e10 0.307307
\(604\) −5.18638e10 + 1.07696e11i −0.389688 + 0.809195i
\(605\) −2.01019e10 4.17419e10i −0.150043 0.311567i
\(606\) −1.11076e11 1.39285e11i −0.823627 1.03280i
\(607\) 2.57954e11 5.88762e10i 1.90015 0.433696i 0.900147 0.435586i \(-0.143459\pi\)
0.999998 + 0.00189002i \(0.000601612\pi\)
\(608\) −3.96174e10 −0.289916
\(609\) 2.30646e11i 1.67678i
\(610\) −1.18386e11 + 2.70208e10i −0.855030 + 0.195155i
\(611\) −5.87341e9 + 7.36502e9i −0.0421430 + 0.0528456i
\(612\) 1.27166e10 5.57149e10i 0.0906493 0.397160i
\(613\) 7.91629e10 9.92671e10i 0.560634 0.703013i −0.418041 0.908428i \(-0.637283\pi\)
0.978675 + 0.205415i \(0.0658544\pi\)
\(614\) 1.32480e8 2.75097e8i 0.000932129 0.00193559i
\(615\) −2.90670e10 1.27351e11i −0.203189 0.890229i
\(616\) −1.14762e11 5.52666e10i −0.797033 0.383831i
\(617\) 1.54022e11 + 1.93138e11i 1.06278 + 1.33268i 0.940351 + 0.340206i \(0.110497\pi\)
0.122428 + 0.992477i \(0.460932\pi\)
\(618\) 1.86915e10 8.18928e10i 0.128142 0.561425i
\(619\) 1.78875e10 7.83701e10i 0.121839 0.533811i −0.876762 0.480925i \(-0.840301\pi\)
0.998601 0.0528859i \(-0.0168420\pi\)
\(620\) −3.79215e10 7.87449e10i −0.256637 0.532912i
\(621\) −7.50998e9 + 5.98901e9i −0.0504978 + 0.0402706i
\(622\) −2.78826e10 2.22356e10i −0.186282 0.148555i
\(623\) 2.14363e10 1.03232e10i 0.142297 0.0685268i
\(624\) 6.10373e9 + 1.26745e10i 0.0402584 + 0.0835975i
\(625\) −5.33108e10 + 6.68496e10i −0.349378 + 0.438106i
\(626\) 1.00409e11 + 1.25908e11i 0.653843 + 0.819893i
\(627\) −6.43564e10 + 3.09924e10i −0.416410 + 0.200533i
\(628\) 7.35269e9 + 1.67820e9i 0.0472724 + 0.0107896i
\(629\) −2.55120e11 5.82294e10i −1.62983 0.371997i
\(630\) 3.28378e10 2.61873e10i 0.208455 0.166237i
\(631\) −6.78633e10 + 1.40920e11i −0.428073 + 0.888902i 0.569678 + 0.821868i \(0.307068\pi\)
−0.997751 + 0.0670341i \(0.978646\pi\)
\(632\) −5.22911e10 + 1.19351e10i −0.327763 + 0.0748097i
\(633\) 2.24728e11 + 1.08223e11i 1.39973 + 0.674073i
\(634\) 7.89750e10 + 6.29805e10i 0.488802 + 0.389806i
\(635\) −2.09012e11 4.77057e10i −1.28551 0.293410i
\(636\) −1.50569e10 1.20075e10i −0.0920255 0.0733879i
\(637\) 1.71159e10 + 7.49897e10i 0.103954 + 0.455453i
\(638\) −2.25479e11 −1.36089
\(639\) 2.00175e10i 0.120062i
\(640\) 1.60093e10 + 7.01411e10i 0.0954226 + 0.418074i
\(641\) 2.38436e10 1.90146e10i 0.141234 0.112630i −0.550324 0.834951i \(-0.685496\pi\)
0.691558 + 0.722321i \(0.256924\pi\)
\(642\) 9.94164e10 4.78764e10i 0.585218 0.281826i
\(643\) 1.88886e9 + 9.09629e8i 0.0110499 + 0.00532133i 0.439401 0.898291i \(-0.355191\pi\)
−0.428351 + 0.903613i \(0.640905\pi\)
\(644\) 1.19517e10i 0.0694840i
\(645\) −9.94410e10 1.55363e11i −0.574548 0.897653i
\(646\) −3.33364e10 −0.191420
\(647\) 1.31543e11 2.73153e11i 0.750675 1.55879i −0.0766417 0.997059i \(-0.524420\pi\)
0.827317 0.561735i \(-0.189866\pi\)
\(648\) 9.46068e10 + 1.96453e11i 0.536565 + 1.11419i
\(649\) −6.55538e10 8.22019e10i −0.369504 0.463343i
\(650\) −3.66405e10 + 8.36296e9i −0.205262 + 0.0468497i
\(651\) −2.09888e11 −1.16860
\(652\) 3.89213e10i 0.215376i
\(653\) 1.59238e11 3.63451e10i 0.875779 0.199891i 0.239077 0.971001i \(-0.423155\pi\)
0.636702 + 0.771110i \(0.280298\pi\)
\(654\) −2.95780e10 + 3.70896e10i −0.161680 + 0.202741i
\(655\) 1.72530e10 7.55905e10i 0.0937347 0.410679i
\(656\) −7.12224e9 + 8.93101e9i −0.0384593 + 0.0482264i
\(657\) 7.67684e9 1.59411e10i 0.0412023 0.0855574i
\(658\) −1.33311e9 5.84075e9i −0.00711153 0.0311577i
\(659\) 2.56388e11 + 1.23470e11i 1.35943 + 0.654665i 0.964508 0.264052i \(-0.0850591\pi\)
0.394917 + 0.918717i \(0.370773\pi\)
\(660\) 8.80317e10 + 1.10388e11i 0.463942 + 0.581764i
\(661\) −6.29259e10 + 2.75696e11i −0.329628 + 1.44419i 0.490214 + 0.871602i \(0.336919\pi\)
−0.819841 + 0.572591i \(0.805938\pi\)
\(662\) −4.53042e10 + 1.98491e11i −0.235888 + 1.03349i
\(663\) −1.07959e11 2.24180e11i −0.558735 1.16022i
\(664\) 1.71852e11 1.37047e11i 0.884061 0.705015i
\(665\) 2.70423e10 + 2.15655e10i 0.138279 + 0.110274i
\(666\) −1.33004e11 + 6.40513e10i −0.676032 + 0.325560i
\(667\) 2.48613e10 + 5.16251e10i 0.125609 + 0.260830i
\(668\) −1.38711e11 + 1.73938e11i −0.696634 + 0.873551i
\(669\) 2.24802e11 + 2.81893e11i 1.12227 + 1.40728i
\(670\) −4.22084e10 + 2.03265e10i −0.209459 + 0.100870i
\(671\) −3.92362e11 8.95540e10i −1.93552 0.441769i
\(672\) 1.83342e11 + 4.18466e10i 0.899052 + 0.205203i
\(673\) −9.01647e10 + 7.19040e10i −0.439518 + 0.350504i −0.818112 0.575059i \(-0.804979\pi\)
0.378594 + 0.925563i \(0.376408\pi\)
\(674\) −5.38922e10 + 1.11908e11i −0.261148 + 0.542279i
\(675\) −2.64389e10 + 6.03452e9i −0.127359 + 0.0290688i
\(676\) 2.30960e9 + 1.11225e9i 0.0110599 + 0.00532616i
\(677\) 3.17905e11 + 2.53521e11i 1.51336 + 1.20687i 0.913551 + 0.406725i \(0.133329\pi\)
0.599811 + 0.800141i \(0.295242\pi\)
\(678\) −1.63612e11 3.73433e10i −0.774275 0.176723i
\(679\) −5.26985e10 4.20256e10i −0.247924 0.197713i
\(680\) 3.97120e10 + 1.73990e11i 0.185732 + 0.813745i
\(681\) −2.01679e11 −0.937720
\(682\) 2.05187e11i 0.948443i
\(683\) −6.44482e10 2.82366e11i −0.296161 1.29757i −0.875793 0.482687i \(-0.839661\pi\)
0.579632 0.814879i \(-0.303196\pi\)
\(684\) 2.07570e10 1.65531e10i 0.0948287 0.0756233i
\(685\) 2.52109e10 1.21409e10i 0.114505 0.0551429i
\(686\) −1.37420e11 6.61781e10i −0.620518 0.298826i
\(687\) 8.11457e10i 0.364283i
\(688\) −5.20038e9 + 1.52699e10i −0.0232103 + 0.0681524i
\(689\) −3.44249e10 −0.152755
\(690\) −1.10275e10 + 2.28989e10i −0.0486498 + 0.101022i
\(691\) −5.01932e10 1.04227e11i −0.220157 0.457161i 0.761412 0.648268i \(-0.224507\pi\)
−0.981569 + 0.191107i \(0.938792\pi\)
\(692\) 2.61111e10 + 3.27423e10i 0.113868 + 0.142786i
\(693\) 1.35712e11 3.09755e10i 0.588419 0.134303i
\(694\) 1.62356e11 0.699892
\(695\) 7.65142e10i 0.327946i
\(696\) 5.39003e11 1.23024e11i 2.29697 0.524268i
\(697\) 1.25974e11 1.57967e11i 0.533765 0.669321i
\(698\) 5.48228e10 2.40194e11i 0.230961 1.01191i
\(699\) 1.59898e11 2.00506e11i 0.669784 0.839883i
\(700\) −1.46402e10 + 3.04007e10i −0.0609755 + 0.126617i
\(701\) −3.63357e10 1.59197e11i −0.150474 0.659270i −0.992747 0.120219i \(-0.961640\pi\)
0.842273 0.539051i \(-0.181217\pi\)
\(702\) 5.51121e10 + 2.65406e10i 0.226934 + 0.109285i
\(703\) −7.57971e10 9.50466e10i −0.310335 0.389148i
\(704\) 4.56029e10 1.99799e11i 0.185653 0.813399i
\(705\) −4.00215e9 + 1.75345e10i −0.0162008 + 0.0709803i
\(706\) 1.21455e11 + 2.52203e11i 0.488872 + 1.01515i
\(707\) −2.23532e11 + 1.78260e11i −0.894666 + 0.713473i
\(708\) 7.44199e10 + 5.93479e10i 0.296180 + 0.236196i
\(709\) 2.52279e11 1.21491e11i 0.998381 0.480795i 0.137992 0.990433i \(-0.455935\pi\)
0.860389 + 0.509638i \(0.170221\pi\)
\(710\) 1.00145e10 + 2.07954e10i 0.0394091 + 0.0818338i
\(711\) 3.65462e10 4.58275e10i 0.143009 0.179328i
\(712\) 3.55584e10 + 4.45888e10i 0.138364 + 0.173503i
\(713\) 4.69789e10 2.26239e10i 0.181780 0.0875404i
\(714\) 1.54275e11 + 3.52122e10i 0.593610 + 0.135488i
\(715\) 2.46054e11 + 5.61603e10i 0.941471 + 0.214885i
\(716\) −1.87867e11 + 1.49819e11i −0.714825 + 0.570054i
\(717\) 2.30578e11 4.78800e11i 0.872451 1.81166i
\(718\) −1.72710e11 + 3.94199e10i −0.649859 + 0.148326i
\(719\) 3.03254e11 + 1.46039e11i 1.13473 + 0.546455i 0.904411 0.426661i \(-0.140310\pi\)
0.230314 + 0.973116i \(0.426025\pi\)
\(720\) 8.62101e9 + 6.87502e9i 0.0320795 + 0.0255826i
\(721\) −1.31426e11 2.99970e10i −0.486339 0.111004i
\(722\) 1.24696e11 + 9.94414e10i 0.458883 + 0.365947i
\(723\) 1.21501e11 + 5.32330e11i 0.444658 + 1.94817i
\(724\) 1.55722e11 0.566755
\(725\) 1.61770e11i 0.585524i
\(726\) −2.19118e10 9.60017e10i −0.0788734 0.345567i
\(727\) −1.32817e11 + 1.05918e11i −0.475464 + 0.379170i −0.831699 0.555227i \(-0.812632\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(728\) 1.85718e11 8.94373e10i 0.661195 0.318415i
\(729\) −8.36689e10 4.02928e10i −0.296247 0.142665i
\(730\) 2.04012e10i 0.0718397i
\(731\) 9.19814e10 2.70085e11i 0.322130 0.945868i
\(732\) 3.64352e11 1.26905
\(733\) 9.28717e10 1.92850e11i 0.321712 0.668042i −0.675908 0.736986i \(-0.736248\pi\)
0.997621 + 0.0689433i \(0.0219628\pi\)
\(734\) −7.90974e10 1.64247e11i −0.272507 0.565867i
\(735\) 9.15629e10 + 1.14816e11i 0.313740 + 0.393418i
\(736\) −4.55478e10 + 1.03960e10i −0.155223 + 0.0354286i
\(737\) −1.55265e11 −0.526266
\(738\) 1.13982e11i 0.384246i
\(739\) −4.53263e11 + 1.03454e11i −1.51975 + 0.346873i −0.899286 0.437362i \(-0.855913\pi\)
−0.620464 + 0.784235i \(0.713056\pi\)
\(740\) −1.49824e11 + 1.87873e11i −0.499636 + 0.626524i
\(741\) 2.57223e10 1.12697e11i 0.0853171 0.373799i
\(742\) 1.36501e10 1.71167e10i 0.0450320 0.0564684i
\(743\) −4.84388e10 + 1.00584e11i −0.158942 + 0.330046i −0.965198 0.261521i \(-0.915776\pi\)
0.806256 + 0.591567i \(0.201490\pi\)
\(744\) −1.11952e11 4.90494e11i −0.365377 1.60082i
\(745\) −2.08777e11 1.00542e11i −0.677731 0.326378i
\(746\) 9.17800e10 + 1.15089e11i 0.296342 + 0.371601i
\(747\) −5.34528e10 + 2.34192e11i −0.171667 + 0.752124i
\(748\) −4.85963e10 + 2.12914e11i −0.155238 + 0.680140i
\(749\) −7.68344e10 1.59548e11i −0.244134 0.506949i
\(750\) −2.25871e11 + 1.80126e11i −0.713862 + 0.569286i
\(751\) −4.86958e11 3.88336e11i −1.53085 1.22081i −0.892489 0.451069i \(-0.851043\pi\)
−0.638358 0.769740i \(-0.720386\pi\)
\(752\) 1.41706e9 6.82422e8i 0.00443117 0.00213394i
\(753\) −6.65287e10 1.38148e11i −0.206933 0.429700i
\(754\) 2.27506e11 2.85283e11i 0.703893 0.882654i
\(755\) 2.54349e11 + 3.18944e11i 0.782786 + 0.981583i
\(756\) 4.94803e10 2.38284e10i 0.151476 0.0729472i
\(757\) −2.77779e11 6.34013e10i −0.845895 0.193070i −0.222457 0.974943i \(-0.571408\pi\)
−0.623438 + 0.781873i \(0.714265\pi\)
\(758\) 1.89476e11 + 4.32467e10i 0.573955 + 0.131001i
\(759\) −6.58573e10 + 5.25194e10i −0.198443 + 0.158253i
\(760\) −3.59730e10 + 7.46987e10i −0.107826 + 0.223902i
\(761\) −4.82925e11 + 1.10224e11i −1.43993 + 0.328654i −0.870005 0.493043i \(-0.835884\pi\)
−0.569924 + 0.821698i \(0.693027\pi\)
\(762\) −4.10538e11 1.97705e11i −1.21768 0.586404i
\(763\) 5.95232e10 + 4.74682e10i 0.175626 + 0.140057i
\(764\) −1.01068e11 2.30680e10i −0.296646 0.0677075i
\(765\) −1.52483e11 1.21602e11i −0.445222 0.355053i
\(766\) −7.08189e9 3.10278e10i −0.0205700 0.0901231i
\(767\) 1.70147e11 0.491636
\(768\) 4.69875e11i 1.35063i
\(769\) −1.16630e11 5.10991e11i −0.333508 1.46120i −0.812286 0.583259i \(-0.801777\pi\)
0.478778 0.877936i \(-0.341080\pi\)
\(770\) −1.25489e11 + 1.00075e11i −0.356980 + 0.284682i
\(771\) −3.68784e11 + 1.77597e11i −1.04365 + 0.502595i
\(772\) −1.90962e11 9.19626e10i −0.537624 0.258906i
\(773\) 5.01601e11i 1.40488i 0.711741 + 0.702442i \(0.247907\pi\)
−0.711741 + 0.702442i \(0.752093\pi\)
\(774\) −5.44283e10 1.51476e11i −0.151657 0.422066i
\(775\) 1.47211e11 0.408068
\(776\) 7.01022e10 1.45569e11i 0.193324 0.401440i
\(777\) 2.50380e11 + 5.19920e11i 0.686936 + 1.42644i
\(778\) 1.87142e11 + 2.34669e11i 0.510803 + 0.640527i
\(779\) 9.15117e10 2.08869e10i 0.248500 0.0567185i
\(780\) −2.28489e11 −0.617288
\(781\) 7.64967e10i 0.205607i
\(782\) −3.83265e10 + 8.74778e9i −0.102488 + 0.0233922i
\(783\) 1.64163e11 2.05854e11i 0.436745 0.547660i
\(784\) 2.85772e9 1.25205e10i 0.00756406 0.0331403i
\(785\) 1.60477e10 2.01232e10i 0.0422606 0.0529931i
\(786\) 7.15010e10 1.48473e11i 0.187336 0.389008i
\(787\) 1.14732e10 + 5.02675e10i 0.0299080 + 0.131035i 0.987678 0.156500i \(-0.0500212\pi\)
−0.957770 + 0.287536i \(0.907164\pi\)
\(788\) −3.14851e11 1.51624e11i −0.816582 0.393245i
\(789\) 5.84038e11 + 7.32360e11i 1.50707 + 1.88980i
\(790\) −1.50394e10 + 6.58920e10i −0.0386120 + 0.169170i
\(791\) −5.99303e10 + 2.62572e11i −0.153088 + 0.670721i
\(792\) 1.44775e11 + 3.00629e11i 0.367954 + 0.764064i
\(793\) 5.09194e11 4.06069e11i 1.28763 1.02685i
\(794\) −2.46346e11 1.96455e11i −0.619818 0.494288i
\(795\) −5.92166e10 + 2.85172e10i −0.148243 + 0.0713902i
\(796\) 4.26037e9 + 8.84675e9i 0.0106119 + 0.0220359i
\(797\) 2.16374e11 2.71325e11i 0.536257 0.672445i −0.437715 0.899114i \(-0.644212\pi\)
0.973972 + 0.226669i \(0.0727836\pi\)
\(798\) 4.58356e10 + 5.74760e10i 0.113029 + 0.141734i
\(799\) −2.50642e10 + 1.20703e10i −0.0614989 + 0.0296163i
\(800\) −1.28592e11 2.93502e10i −0.313945 0.0716558i
\(801\) −6.07636e10 1.38689e10i −0.147609 0.0336908i
\(802\) 3.58214e10 2.85666e10i 0.0865854 0.0690496i
\(803\) −2.93370e10 + 6.09189e10i −0.0705592 + 0.146518i
\(804\) 1.37042e11 3.12790e10i 0.327967 0.0748564i
\(805\) 3.67492e10 + 1.76975e10i 0.0875114 + 0.0421433i
\(806\) −2.59608e11 2.07031e11i −0.615146 0.490562i
\(807\) −4.53174e11 1.03434e11i −1.06849 0.243876i
\(808\) −5.35812e11 4.27296e11i −1.25709 1.00250i
\(809\) −1.11574e11 4.88837e11i −0.260477 1.14122i −0.920736 0.390185i \(-0.872411\pi\)
0.660260 0.751037i \(-0.270446\pi\)
\(810\) 2.74760e11 0.638284
\(811\) 1.00476e11i 0.232262i 0.993234 + 0.116131i \(0.0370493\pi\)
−0.993234 + 0.116131i \(0.962951\pi\)
\(812\) −7.28985e10 3.19389e11i −0.167685 0.734676i
\(813\) −2.49652e11 + 1.99091e11i −0.571442 + 0.455710i
\(814\) 5.08274e11 2.44772e11i 1.15771 0.557524i
\(815\) −1.19676e11 5.76329e10i −0.271254 0.130629i
\(816\) 4.15437e10i 0.0937012i
\(817\) 1.11640e11 7.14562e10i 0.250573 0.160380i
\(818\) −1.83190e11 −0.409155
\(819\) −9.77410e10 + 2.02961e11i −0.217241 + 0.451105i
\(820\) −8.05017e10 1.67163e11i −0.178053 0.369731i
\(821\) 1.51683e11 + 1.90205e11i 0.333861 + 0.418648i 0.920219 0.391404i \(-0.128010\pi\)
−0.586358 + 0.810052i \(0.699439\pi\)
\(822\) 5.79822e10 1.32341e10i 0.127001 0.0289872i
\(823\) 5.99324e11 1.30636 0.653179 0.757204i \(-0.273435\pi\)
0.653179 + 0.757204i \(0.273435\pi\)
\(824\) 3.23133e11i 0.700926i
\(825\) −2.31851e11 + 5.29185e10i −0.500488 + 0.114233i
\(826\) −6.74667e10 + 8.46006e10i −0.144934 + 0.181741i
\(827\) −5.07117e10 + 2.22183e11i −0.108414 + 0.474994i 0.891351 + 0.453314i \(0.149758\pi\)
−0.999765 + 0.0216795i \(0.993099\pi\)
\(828\) 1.95204e10 2.44778e10i 0.0415305 0.0520777i
\(829\) 9.53839e10 1.98067e11i 0.201956 0.419366i −0.775251 0.631653i \(-0.782377\pi\)
0.977207 + 0.212287i \(0.0680911\pi\)
\(830\) −6.16335e10 2.70034e11i −0.129869 0.568992i
\(831\) −7.10119e11 3.41975e11i −1.48911 0.717118i
\(832\) 2.06779e11 + 2.59293e11i 0.431533 + 0.541125i
\(833\) −5.05456e10 + 2.21455e11i −0.104979 + 0.459944i
\(834\) 3.61873e10 1.58547e11i 0.0747984 0.327713i
\(835\) 3.29431e11 + 6.84071e11i 0.677671 + 1.40720i
\(836\) −7.93226e10 + 6.32577e10i −0.162395 + 0.129506i
\(837\) −1.87327e11 1.49388e11i −0.381680 0.304379i
\(838\) −6.91348e10 + 3.32936e10i −0.140191 + 0.0675125i
\(839\) 4.86656e9 + 1.01055e10i 0.00982141 + 0.0203944i 0.905822 0.423659i \(-0.139254\pi\)
−0.896000 + 0.444053i \(0.853540\pi\)
\(840\) 2.45378e11 3.07695e11i 0.492855 0.618020i
\(841\) −6.67366e11 8.36850e11i −1.33407 1.67288i
\(842\) −4.36234e11 + 2.10079e11i −0.867903 + 0.417960i
\(843\) −1.50229e11 3.42887e10i −0.297470 0.0678955i
\(844\) 3.45400e11 + 7.88353e10i 0.680695 + 0.155364i
\(845\) 6.83992e9 5.45465e9i 0.0134160 0.0106989i
\(846\) −6.80928e9 + 1.41396e10i −0.0132929 + 0.0276030i
\(847\) −1.54068e11 + 3.51651e10i −0.299350 + 0.0683247i
\(848\) 5.17847e9 + 2.49382e9i 0.0100142 + 0.00482261i
\(849\) 9.72259e11 + 7.75351e11i 1.87133 + 1.49234i
\(850\) −1.08205e11 2.46970e10i −0.207286 0.0473117i
\(851\) −1.12084e11 8.93843e10i −0.213711 0.170429i
\(852\) −1.54106e10 6.75185e10i −0.0292457 0.128134i
\(853\) 3.68649e11 0.696332 0.348166 0.937433i \(-0.386805\pi\)
0.348166 + 0.937433i \(0.386805\pi\)
\(854\) 4.14196e11i 0.778707i
\(855\) −2.01619e10 8.83352e10i −0.0377284 0.165299i
\(856\) 3.31871e11 2.64658e11i 0.618121 0.492935i
\(857\) 1.24835e11 6.01173e10i 0.231426 0.111449i −0.314577 0.949232i \(-0.601863\pi\)
0.546004 + 0.837783i \(0.316149\pi\)
\(858\) 4.83295e11 + 2.32743e11i 0.891791 + 0.429464i
\(859\) 2.14830e11i 0.394568i 0.980346 + 0.197284i \(0.0632121\pi\)
−0.980346 + 0.197284i \(0.936788\pi\)
\(860\) −1.86806e11 1.83711e11i −0.341506 0.335847i
\(861\) −4.45561e11 −0.810765
\(862\) 2.30955e11 4.79582e11i 0.418309 0.868628i
\(863\) 2.00100e11 + 4.15513e11i 0.360749 + 0.749102i 0.999799 0.0200628i \(-0.00638660\pi\)
−0.639050 + 0.769165i \(0.720672\pi\)
\(864\) 1.33850e11 + 1.67843e11i 0.240195 + 0.301195i
\(865\) 1.39341e11 3.18037e10i 0.248894 0.0568084i
\(866\) −6.22852e11 −1.10742
\(867\) 1.15332e9i 0.00204114i
\(868\) −2.90645e11 + 6.63378e10i −0.512016 + 0.116864i
\(869\) −1.39661e11 + 1.75130e11i −0.244904 + 0.307101i
\(870\) 1.55023e11 6.79198e11i 0.270594 1.18555i
\(871\) 1.56661e11 1.96447e11i 0.272200 0.341328i
\(872\) −7.91808e10 + 1.64421e11i −0.136948 + 0.284374i
\(873\) 3.92905e10 + 1.72143e11i 0.0676442 + 0.296368i
\(874\) −1.64546e10 7.92414e9i −0.0281996 0.0135802i
\(875\) 2.89075e11 + 3.62488e11i 0.493148 + 0.618389i
\(876\) 1.36214e10 5.96791e10i 0.0231315 0.101346i
\(877\) 2.58446e10 1.13233e11i 0.0436890 0.191414i −0.948374 0.317153i \(-0.897273\pi\)
0.992063 + 0.125739i \(0.0401303\pi\)
\(878\) 1.82226e11 + 3.78397e11i 0.306643 + 0.636750i
\(879\) 1.17590e12 9.37751e11i 1.96977 1.57084i
\(880\) −3.29451e10 2.62729e10i −0.0549364 0.0438103i
\(881\) −8.10418e10 + 3.90277e10i −0.134526 + 0.0647842i −0.499936 0.866062i \(-0.666643\pi\)
0.365410 + 0.930847i \(0.380929\pi\)
\(882\) 5.55993e10 + 1.15453e11i 0.0918745 + 0.190779i
\(883\) 1.62365e11 2.03599e11i 0.267084 0.334913i −0.630145 0.776477i \(-0.717005\pi\)
0.897230 + 0.441564i \(0.145576\pi\)
\(884\) −2.20352e11 2.76313e11i −0.360835 0.452473i
\(885\) 2.92682e11 1.40948e11i 0.477115 0.229766i
\(886\) 2.48087e11 + 5.66242e10i 0.402595 + 0.0918897i
\(887\) 5.56930e11 + 1.27116e11i 0.899717 + 0.205355i 0.647274 0.762257i \(-0.275909\pi\)
0.252443 + 0.967612i \(0.418766\pi\)
\(888\) −1.08147e12 + 8.62442e11i −1.73925 + 1.38700i
\(889\) −3.17286e11 + 6.58851e11i −0.507977 + 1.05482i
\(890\) 7.00632e10 1.59915e10i 0.111668 0.0254876i
\(891\) 8.20446e11 + 3.95106e11i 1.30179 + 0.626907i
\(892\) 4.00392e11 + 3.19302e11i 0.632450 + 0.504362i
\(893\) −1.25999e10 2.87586e9i −0.0198136 0.00452232i
\(894\) −3.85061e11 3.07076e11i −0.602809 0.480724i
\(895\) 1.82482e11 + 7.99505e11i 0.284399 + 1.24603i
\(896\) 2.45402e11 0.380755
\(897\) 1.36316e11i 0.210561i
\(898\) −5.45235e10 2.38883e11i −0.0838452 0.367350i
\(899\) −1.11744e12 + 8.91133e11i −1.71075 + 1.36428i
\(900\) 7.96371e10 3.83512e10i 0.121380 0.0584533i
\(901\) −9.15938e10 4.41093e10i −0.138985 0.0669315i
\(902\) 4.35580e11i 0.658025i
\(903\) −5.92129e11 + 2.12764e11i −0.890564 + 0.319997i
\(904\) −6.45578e11 −0.966663
\(905\) 2.30586e11 4.78818e11i 0.343747 0.713799i
\(906\) 3.76200e11 + 7.81187e11i 0.558349 + 1.15942i
\(907\) −1.24147e10 1.55675e10i −0.0183445 0.0230033i 0.772575 0.634924i \(-0.218969\pi\)
−0.790919 + 0.611921i \(0.790397\pi\)
\(908\) −2.79278e11 + 6.37433e10i −0.410859 + 0.0937759i
\(909\) 7.48958e11 1.09699
\(910\) 2.59747e11i 0.378778i
\(911\) 5.89439e11 1.34536e11i 0.855787 0.195328i 0.227950 0.973673i \(-0.426798\pi\)
0.627837 + 0.778345i \(0.283941\pi\)
\(912\) −1.20334e10 + 1.50893e10i −0.0173943 + 0.0218118i
\(913\) 2.04269e11 8.94963e11i 0.293982 1.28802i
\(914\) 3.76262e11 4.71817e11i 0.539144 0.676066i
\(915\) 5.39517e11 1.12032e12i 0.769699 1.59830i
\(916\) 2.56471e10 + 1.12367e11i 0.0364298 + 0.159609i
\(917\) −2.38277e11 1.14748e11i −0.336981 0.162281i
\(918\) 1.12629e11 + 1.41232e11i 0.158591 + 0.198867i
\(919\) −2.92473e11 + 1.28141e12i −0.410038 + 1.79649i 0.173974 + 0.984750i \(0.444339\pi\)
−0.584013 + 0.811745i \(0.698518\pi\)
\(920\) −2.17562e10 + 9.53201e10i −0.0303691 + 0.133056i
\(921\) 1.35660e9 + 2.81702e9i 0.00188545 + 0.00391517i
\(922\) 1.29847e11 1.03550e11i 0.179684 0.143293i
\(923\) −9.67859e10 7.71842e10i −0.133354 0.106346i
\(924\) 4.33908e11 2.08959e11i 0.595264 0.286664i
\(925\) −1.75611e11 3.64660e11i −0.239875 0.498105i
\(926\) −2.00623e10 + 2.51574e10i −0.0272858 + 0.0342154i
\(927\) 2.20175e11 + 2.76091e11i 0.298160 + 0.373881i
\(928\) 1.15378e12 5.55633e11i 1.55572 0.749197i
\(929\) −6.89166e11 1.57298e11i −0.925254 0.211183i −0.266755 0.963764i \(-0.585951\pi\)
−0.658499 + 0.752581i \(0.728808\pi\)
\(930\) −6.18072e11 1.41071e11i −0.826242 0.188584i
\(931\) −8.25045e10 + 6.57952e10i −0.109819 + 0.0875780i
\(932\) 1.58048e11 3.28191e11i 0.209472 0.434973i
\(933\) 3.56038e11 8.12633e10i 0.469861 0.107243i
\(934\) −2.35958e11 1.13632e11i −0.310062 0.149318i
\(935\) 5.82714e11 + 4.64699e11i 0.762447 + 0.608031i
\(936\) −5.26441e11 1.20157e11i −0.685877 0.156547i
\(937\) −4.55709e9 3.63416e9i −0.00591192 0.00471460i 0.620529 0.784183i \(-0.286918\pi\)
−0.626441 + 0.779469i \(0.715489\pi\)
\(938\) 3.55580e10 + 1.55790e11i 0.0459331 + 0.201246i
\(939\) −1.64909e12 −2.12121
\(940\) 2.55461e10i 0.0327200i
\(941\) 2.53923e11 + 1.11251e12i 0.323849 + 1.41888i 0.830641 + 0.556808i \(0.187974\pi\)
−0.506791 + 0.862069i \(0.669169\pi\)
\(942\) 4.27702e10 3.41081e10i 0.0543172 0.0433166i
\(943\) 9.97292e10 4.80271e10i 0.126118 0.0607350i
\(944\) −2.55949e10 1.23259e10i −0.0322304 0.0155214i
\(945\) 1.87427e11i 0.235020i
\(946\) 2.07997e11 + 5.78864e11i 0.259713 + 0.722790i
\(947\) 2.09245e11 0.260169 0.130084 0.991503i \(-0.458475\pi\)
0.130084 + 0.991503i \(0.458475\pi\)
\(948\) 8.79887e10 1.82710e11i 0.108942 0.226220i
\(949\) −4.74758e10 9.85844e10i −0.0585338 0.121547i
\(950\) −3.21480e10 4.03123e10i −0.0394693 0.0494930i
\(951\) −1.00845e12 + 2.30171e11i −1.23291 + 0.281403i
\(952\) 6.08736e11 0.741108
\(953\) 6.84339e11i 0.829659i −0.909899 0.414830i \(-0.863841\pi\)
0.909899 0.414830i \(-0.136159\pi\)
\(954\) −5.59129e10 + 1.27618e10i −0.0675023 + 0.0154070i
\(955\) −2.20586e11 + 2.76607e11i −0.265195 + 0.332544i
\(956\) 1.67964e11 7.35900e11i 0.201088 0.881023i
\(957\) 1.43959e12 1.80519e12i 1.71629 2.15217i
\(958\) 1.50255e11 3.12007e11i 0.178388 0.370427i
\(959\) −2.12387e10 9.30527e10i −0.0251104 0.110016i
\(960\) 5.70492e11 + 2.74734e11i 0.671683 + 0.323465i
\(961\) 2.79164e11 + 3.50060e11i 0.327315 + 0.410440i
\(962\) −2.03149e11 + 8.90054e11i −0.237200 + 1.03924i
\(963\) −1.03225e11 + 4.52258e11i −0.120027 + 0.525873i
\(964\) 3.36499e11 + 6.98747e11i 0.389651 + 0.809118i
\(965\) −5.65537e11 + 4.51001e11i −0.652157 + 0.520078i
\(966\) 6.77790e10 + 5.40520e10i 0.0778371 + 0.0620731i
\(967\) −1.22932e12 + 5.92010e11i −1.40592 + 0.677054i −0.974352 0.225028i \(-0.927753\pi\)
−0.431565 + 0.902082i \(0.642038\pi\)
\(968\) −1.64357e11 3.41290e11i −0.187191 0.388707i
\(969\) 2.12839e11 2.66892e11i 0.241411 0.302719i
\(970\) −1.26938e11 1.59176e11i −0.143386 0.179800i
\(971\) −4.89455e11 + 2.35709e11i −0.550600 + 0.265155i −0.688432 0.725301i \(-0.741701\pi\)
0.137833 + 0.990456i \(0.455986\pi\)
\(972\) −6.02369e11 1.37487e11i −0.674835 0.154027i
\(973\) −2.54444e11 5.80752e10i −0.283884 0.0647947i
\(974\) −2.31421e11 + 1.84552e11i −0.257138 + 0.205061i
\(975\) 1.66981e11 3.46739e11i 0.184777 0.383693i
\(976\) −1.06014e11 + 2.41969e10i −0.116832 + 0.0266662i
\(977\) −4.60498e11 2.21764e11i −0.505417 0.243396i 0.163759 0.986500i \(-0.447638\pi\)
−0.669175 + 0.743105i \(0.733352\pi\)
\(978\) −2.20726e11 1.76023e11i −0.241267 0.192404i
\(979\) 2.32208e11 + 5.29999e10i 0.252782 + 0.0576958i
\(980\) 1.63082e11 + 1.30053e11i 0.176808 + 0.140999i
\(981\) −4.43788e10 1.94436e11i −0.0479181 0.209943i
\(982\) −1.14662e11 −0.123303
\(983\) 1.22345e11i 0.131030i 0.997852 + 0.0655152i \(0.0208691\pi\)
−0.997852 + 0.0655152i \(0.979131\pi\)
\(984\) −2.37658e11 1.04125e12i −0.253496 1.11064i
\(985\) −9.32435e11 + 7.43592e11i −0.990544 + 0.789933i
\(986\) 9.70860e11 4.67541e11i 1.02719 0.494666i
\(987\) 5.52726e10 + 2.66179e10i 0.0582426 + 0.0280482i
\(988\) 1.64188e11i 0.172311i
\(989\) 1.09601e11 1.11448e11i 0.114559 0.116490i
\(990\) 4.20461e11 0.437708
\(991\) −4.16880e11 + 8.65660e11i −0.432232 + 0.897538i 0.565134 + 0.824999i \(0.308824\pi\)
−0.997366 + 0.0725390i \(0.976890\pi\)
\(992\) −5.05627e11 1.04995e12i −0.522136 1.08423i
\(993\) −1.29987e12 1.62999e12i −1.33691 1.67644i
\(994\) 7.67550e10 1.75188e10i 0.0786251 0.0179457i
\(995\) 3.35108e10 0.0341894
\(996\) 8.31074e11i 0.844505i
\(997\) −4.93799e11 + 1.12706e11i −0.499769 + 0.114069i −0.464972 0.885325i \(-0.653936\pi\)
−0.0347972 + 0.999394i \(0.511079\pi\)
\(998\) 1.98162e11 2.48487e11i 0.199755 0.250485i
\(999\) −1.46588e11 + 6.42242e11i −0.147175 + 0.644818i
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 43.9.f.a.22.20 yes 174
43.2 odd 14 inner 43.9.f.a.2.20 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.9.f.a.2.20 174 43.2 odd 14 inner
43.9.f.a.22.20 yes 174 1.1 even 1 trivial