Properties

Label 43.9.f.a.22.5
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 22.5
Character \(\chi\) \(=\) 43.22
Dual form 43.9.f.a.2.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.2670 + 21.3197i) q^{2} +(22.6641 + 47.0626i) q^{3} +(-189.504 - 237.631i) q^{4} +(67.6603 - 15.4430i) q^{5} -1236.05 q^{6} -643.549i q^{7} +(1106.00 - 252.436i) q^{8} +(2389.49 - 2996.33i) q^{9} +O(q^{10})\) \(q+(-10.2670 + 21.3197i) q^{2} +(22.6641 + 47.0626i) q^{3} +(-189.504 - 237.631i) q^{4} +(67.6603 - 15.4430i) q^{5} -1236.05 q^{6} -643.549i q^{7} +(1106.00 - 252.436i) q^{8} +(2389.49 - 2996.33i) q^{9} +(-365.429 + 1601.05i) q^{10} +(11042.0 - 13846.3i) q^{11} +(6888.57 - 14304.3i) q^{12} +(-6526.90 - 28596.2i) q^{13} +(13720.3 + 6607.34i) q^{14} +(2260.25 + 2834.26i) q^{15} +(11340.7 - 49686.9i) q^{16} +(17030.8 - 74617.0i) q^{17} +(39347.9 + 81706.7i) q^{18} +(-10677.6 + 8515.14i) q^{19} +(-16491.6 - 13151.6i) q^{20} +(30287.1 - 14585.5i) q^{21} +(181829. + 377573. i) q^{22} +(-116904. + 146593. i) q^{23} +(36946.8 + 46329.8i) q^{24} +(-347602. + 167396. i) q^{25} +(676674. + 154446. i) q^{26} +(529295. + 120808. i) q^{27} +(-152927. + 121955. i) q^{28} +(75415.4 - 156602. i) q^{29} +(-83631.7 + 19088.4i) q^{30} +(267614. + 128876. i) q^{31} +(1.16993e6 + 932988. i) q^{32} +(901899. + 205852. i) q^{33} +(1.41596e6 + 1.12919e6i) q^{34} +(-9938.34 - 43542.7i) q^{35} -1.16484e6 q^{36} -890909. i q^{37} +(-71912.5 - 315069. i) q^{38} +(1.19788e6 - 955281. i) q^{39} +(70933.6 - 34159.8i) q^{40} +(-1.32710e6 - 639096. i) q^{41} +795461. i q^{42} +(-3.41261e6 - 205732. i) q^{43} -5.38281e6 q^{44} +(115401. - 239634. i) q^{45} +(-1.92506e6 - 3.99743e6i) q^{46} +(-1.33626e6 - 1.67562e6i) q^{47} +(2.59542e6 - 592387. i) q^{48} +5.35065e6 q^{49} -9.12942e6i q^{50} +(3.89766e6 - 889614. i) q^{51} +(-5.55847e6 + 6.97010e6i) q^{52} +(2.62764e6 - 1.15124e7i) q^{53} +(-8.00988e6 + 1.00441e7i) q^{54} +(533278. - 1.10736e6i) q^{55} +(-162455. - 711763. i) q^{56} +(-642744. - 309529. i) q^{57} +(2.56441e6 + 3.21567e6i) q^{58} +(1.98217e6 - 8.68446e6i) q^{59} +(245181. - 1.07421e6i) q^{60} +(5.06023e6 + 1.05077e7i) q^{61} +(-5.49520e6 + 4.38227e6i) q^{62} +(-1.92829e6 - 1.53776e6i) q^{63} +(-2.01478e7 + 9.70269e6i) q^{64} +(-883223. - 1.83403e6i) q^{65} +(-1.36485e7 + 1.71147e7i) q^{66} +(-1.35377e6 - 1.69757e6i) q^{67} +(-2.09587e7 + 1.00932e7i) q^{68} +(-9.54856e6 - 2.17940e6i) q^{69} +(1.03035e6 + 235172. i) q^{70} +(7.25236e6 - 5.78357e6i) q^{71} +(1.88639e6 - 3.91713e6i) q^{72} +(1.00650e7 - 2.29728e6i) q^{73} +(1.89939e7 + 9.14699e6i) q^{74} +(-1.57562e7 - 1.25651e7i) q^{75} +(4.04692e6 + 923683. i) q^{76} +(-8.91075e6 - 7.10609e6i) q^{77} +(8.06759e6 + 3.53464e7i) q^{78} +5.41691e7 q^{79} -3.53696e6i q^{80} +(715255. + 3.13373e6i) q^{81} +(2.72507e7 - 2.17317e7i) q^{82} +(3.52591e7 - 1.69799e7i) q^{83} +(-9.20549e6 - 4.43313e6i) q^{84} -5.31161e6i q^{85} +(3.94234e7 - 7.06435e7i) q^{86} +9.07930e6 q^{87} +(8.71714e6 - 1.81013e7i) q^{88} +(-2.53778e7 - 5.26976e7i) q^{89} +(3.92408e6 + 4.92065e6i) q^{90} +(-1.84031e7 + 4.20038e6i) q^{91} +5.69887e7 q^{92} +1.55155e7i q^{93} +(4.94431e7 - 1.12851e7i) q^{94} +(-590953. + 741031. i) q^{95} +(-1.73934e7 + 7.62053e7i) q^{96} +(-8.26743e6 + 1.03670e7i) q^{97} +(-5.49352e7 + 1.14074e8i) q^{98} +(-1.51031e7 - 6.61711e7i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.2670 + 21.3197i −0.641689 + 1.33248i 0.285677 + 0.958326i \(0.407782\pi\)
−0.927366 + 0.374155i \(0.877933\pi\)
\(3\) 22.6641 + 47.0626i 0.279804 + 0.581019i 0.992750 0.120200i \(-0.0383536\pi\)
−0.712946 + 0.701219i \(0.752639\pi\)
\(4\) −189.504 237.631i −0.740251 0.928246i
\(5\) 67.6603 15.4430i 0.108256 0.0247088i −0.168050 0.985779i \(-0.553747\pi\)
0.276306 + 0.961070i \(0.410890\pi\)
\(6\) −1236.05 −0.953745
\(7\) 643.549i 0.268034i −0.990979 0.134017i \(-0.957212\pi\)
0.990979 0.134017i \(-0.0427876\pi\)
\(8\) 1106.00 252.436i 0.270019 0.0616300i
\(9\) 2389.49 2996.33i 0.364197 0.456688i
\(10\) −365.429 + 1601.05i −0.0365429 + 0.160105i
\(11\) 11042.0 13846.3i 0.754185 0.945718i −0.245535 0.969388i \(-0.578964\pi\)
0.999720 + 0.0236696i \(0.00753498\pi\)
\(12\) 6888.57 14304.3i 0.332203 0.689827i
\(13\) −6526.90 28596.2i −0.228525 1.00123i −0.950843 0.309672i \(-0.899781\pi\)
0.722319 0.691560i \(-0.243076\pi\)
\(14\) 13720.3 + 6607.34i 0.357150 + 0.171994i
\(15\) 2260.25 + 2834.26i 0.0446469 + 0.0559854i
\(16\) 11340.7 49686.9i 0.173045 0.758161i
\(17\) 17030.8 74617.0i 0.203911 0.893392i −0.764617 0.644485i \(-0.777072\pi\)
0.968528 0.248906i \(-0.0800712\pi\)
\(18\) 39347.9 + 81706.7i 0.374827 + 0.778337i
\(19\) −10677.6 + 8515.14i −0.0819334 + 0.0653397i −0.663600 0.748088i \(-0.730972\pi\)
0.581667 + 0.813427i \(0.302401\pi\)
\(20\) −16491.6 13151.6i −0.103073 0.0821978i
\(21\) 30287.1 14585.5i 0.155733 0.0749970i
\(22\) 181829. + 377573.i 0.776199 + 1.61179i
\(23\) −116904. + 146593.i −0.417751 + 0.523843i −0.945528 0.325540i \(-0.894454\pi\)
0.527778 + 0.849383i \(0.323025\pi\)
\(24\) 36946.8 + 46329.8i 0.111361 + 0.139642i
\(25\) −347602. + 167396.i −0.889860 + 0.428534i
\(26\) 676674. + 154446.i 1.48077 + 0.337975i
\(27\) 529295. + 120808.i 0.995963 + 0.227322i
\(28\) −152927. + 121955.i −0.248801 + 0.198412i
\(29\) 75415.4 156602.i 0.106627 0.221414i −0.840828 0.541303i \(-0.817931\pi\)
0.947455 + 0.319889i \(0.103646\pi\)
\(30\) −83631.7 + 19088.4i −0.103249 + 0.0235659i
\(31\) 267614. + 128876.i 0.289776 + 0.139549i 0.573124 0.819468i \(-0.305731\pi\)
−0.283349 + 0.959017i \(0.591445\pi\)
\(32\) 1.16993e6 + 932988.i 1.11573 + 0.889767i
\(33\) 901899. + 205852.i 0.760505 + 0.173580i
\(34\) 1.41596e6 + 1.12919e6i 1.05958 + 0.844987i
\(35\) −9938.34 43542.7i −0.00662280 0.0290164i
\(36\) −1.16484e6 −0.693516
\(37\) 890909.i 0.475364i −0.971343 0.237682i \(-0.923612\pi\)
0.971343 0.237682i \(-0.0763877\pi\)
\(38\) −71912.5 315069.i −0.0344882 0.151103i
\(39\) 1.19788e6 955281.i 0.517793 0.412926i
\(40\) 70933.6 34159.8i 0.0277084 0.0133437i
\(41\) −1.32710e6 639096.i −0.469642 0.226168i 0.184067 0.982914i \(-0.441074\pi\)
−0.653709 + 0.756746i \(0.726788\pi\)
\(42\) 795461.i 0.255636i
\(43\) −3.41261e6 205732.i −0.998188 0.0601766i
\(44\) −5.38281e6 −1.43615
\(45\) 115401. 239634.i 0.0281424 0.0584383i
\(46\) −1.92506e6 3.99743e6i −0.429945 0.892789i
\(47\) −1.33626e6 1.67562e6i −0.273842 0.343387i 0.625825 0.779963i \(-0.284762\pi\)
−0.899667 + 0.436577i \(0.856191\pi\)
\(48\) 2.59542e6 592387.i 0.488925 0.111594i
\(49\) 5.35065e6 0.928158
\(50\) 9.12942e6i 1.46071i
\(51\) 3.89766e6 889614.i 0.576133 0.131499i
\(52\) −5.55847e6 + 6.97010e6i −0.760224 + 0.953291i
\(53\) 2.62764e6 1.15124e7i 0.333014 1.45903i −0.480249 0.877132i \(-0.659454\pi\)
0.813263 0.581896i \(-0.197689\pi\)
\(54\) −8.00988e6 + 1.00441e7i −0.942001 + 1.18123i
\(55\) 533278. 1.10736e6i 0.0582778 0.121015i
\(56\) −162455. 711763.i −0.0165189 0.0723741i
\(57\) −642744. 309529.i −0.0608890 0.0293226i
\(58\) 2.56441e6 + 3.21567e6i 0.226608 + 0.284157i
\(59\) 1.98217e6 8.68446e6i 0.163581 0.716696i −0.824891 0.565292i \(-0.808763\pi\)
0.988472 0.151404i \(-0.0483794\pi\)
\(60\) 245181. 1.07421e6i 0.0189183 0.0828866i
\(61\) 5.06023e6 + 1.05077e7i 0.365469 + 0.758905i 0.999901 0.0140740i \(-0.00448005\pi\)
−0.634432 + 0.772979i \(0.718766\pi\)
\(62\) −5.49520e6 + 4.38227e6i −0.371892 + 0.296574i
\(63\) −1.92829e6 1.53776e6i −0.122408 0.0976170i
\(64\) −2.01478e7 + 9.70269e6i −1.20090 + 0.578325i
\(65\) −883223. 1.83403e6i −0.0494785 0.102743i
\(66\) −1.36485e7 + 1.71147e7i −0.719300 + 0.901974i
\(67\) −1.35377e6 1.69757e6i −0.0671808 0.0842421i 0.747106 0.664705i \(-0.231443\pi\)
−0.814286 + 0.580463i \(0.802871\pi\)
\(68\) −2.09587e7 + 1.00932e7i −0.980232 + 0.472055i
\(69\) −9.54856e6 2.17940e6i −0.421251 0.0961479i
\(70\) 1.03035e6 + 235172.i 0.0429136 + 0.00979474i
\(71\) 7.25236e6 5.78357e6i 0.285395 0.227595i −0.470319 0.882496i \(-0.655861\pi\)
0.755714 + 0.654901i \(0.227290\pi\)
\(72\) 1.88639e6 3.91713e6i 0.0701942 0.145760i
\(73\) 1.00650e7 2.29728e6i 0.354424 0.0808951i −0.0416017 0.999134i \(-0.513246\pi\)
0.396026 + 0.918239i \(0.370389\pi\)
\(74\) 1.89939e7 + 9.14699e6i 0.633414 + 0.305036i
\(75\) −1.57562e7 1.25651e7i −0.497973 0.397120i
\(76\) 4.04692e6 + 923683.i 0.121303 + 0.0276865i
\(77\) −8.91075e6 7.10609e6i −0.253484 0.202147i
\(78\) 8.06759e6 + 3.53464e7i 0.217954 + 0.954920i
\(79\) 5.41691e7 1.39073 0.695366 0.718656i \(-0.255242\pi\)
0.695366 + 0.718656i \(0.255242\pi\)
\(80\) 3.53696e6i 0.0863516i
\(81\) 715255. + 3.13373e6i 0.0166158 + 0.0727985i
\(82\) 2.72507e7 2.17317e7i 0.602728 0.480660i
\(83\) 3.52591e7 1.69799e7i 0.742949 0.357785i −0.0238136 0.999716i \(-0.507581\pi\)
0.766762 + 0.641931i \(0.221867\pi\)
\(84\) −9.20549e6 4.43313e6i −0.184897 0.0890417i
\(85\) 5.31161e6i 0.101754i
\(86\) 3.94234e7 7.06435e7i 0.720710 1.29145i
\(87\) 9.07930e6 0.158480
\(88\) 8.71714e6 1.81013e7i 0.145359 0.301842i
\(89\) −2.53778e7 5.26976e7i −0.404478 0.839906i −0.999349 0.0360853i \(-0.988511\pi\)
0.594871 0.803821i \(-0.297203\pi\)
\(90\) 3.92408e6 + 4.92065e6i 0.0598092 + 0.0749984i
\(91\) −1.84031e7 + 4.20038e6i −0.268364 + 0.0612524i
\(92\) 5.69887e7 0.795496
\(93\) 1.55155e7i 0.207411i
\(94\) 4.94431e7 1.12851e7i 0.633277 0.144541i
\(95\) −590953. + 741031.i −0.00725535 + 0.00909792i
\(96\) −1.73934e7 + 7.62053e7i −0.204785 + 0.897223i
\(97\) −8.26743e6 + 1.03670e7i −0.0933864 + 0.117103i −0.826329 0.563188i \(-0.809575\pi\)
0.732943 + 0.680290i \(0.238146\pi\)
\(98\) −5.49352e7 + 1.14074e8i −0.595589 + 1.23675i
\(99\) −1.51031e7 6.61711e7i −0.157227 0.688855i
\(100\) 1.05650e8 + 5.08786e7i 1.05650 + 0.508786i
\(101\) −4.16860e7 5.22726e7i −0.400594 0.502329i 0.540093 0.841606i \(-0.318389\pi\)
−0.940687 + 0.339277i \(0.889818\pi\)
\(102\) −2.10510e7 + 9.22305e7i −0.194479 + 0.852068i
\(103\) −3.22961e7 + 1.41499e8i −0.286947 + 1.25720i 0.601744 + 0.798689i \(0.294473\pi\)
−0.888691 + 0.458507i \(0.848384\pi\)
\(104\) −1.44374e7 2.99797e7i −0.123412 0.256267i
\(105\) 1.82399e6 1.45458e6i 0.0150060 0.0119669i
\(106\) 2.18464e8 + 1.74219e8i 1.73044 + 1.37998i
\(107\) −1.90599e8 + 9.17875e7i −1.45407 + 0.700242i −0.983296 0.182012i \(-0.941739\pi\)
−0.470772 + 0.882255i \(0.656025\pi\)
\(108\) −7.15960e7 1.48671e8i −0.526252 1.09277i
\(109\) 4.51038e7 5.65584e7i 0.319527 0.400674i −0.595965 0.803010i \(-0.703230\pi\)
0.915492 + 0.402336i \(0.131802\pi\)
\(110\) 1.81335e7 + 2.27387e7i 0.123854 + 0.155308i
\(111\) 4.19285e7 2.01917e7i 0.276196 0.133009i
\(112\) −3.19759e7 7.29830e6i −0.203213 0.0463820i
\(113\) −4.93356e7 1.12605e7i −0.302584 0.0690629i 0.0685331 0.997649i \(-0.478168\pi\)
−0.371117 + 0.928586i \(0.621025\pi\)
\(114\) 1.31981e7 1.05252e7i 0.0781436 0.0623174i
\(115\) −5.64591e6 + 1.17238e7i −0.0322807 + 0.0670315i
\(116\) −5.15049e7 + 1.17557e7i −0.284457 + 0.0649255i
\(117\) −1.01280e8 4.87737e7i −0.540479 0.260281i
\(118\) 1.64799e8 + 1.31423e8i 0.850016 + 0.677865i
\(119\) −4.80197e7 1.09602e7i −0.239459 0.0546550i
\(120\) 3.21530e6 + 2.56412e6i 0.0155059 + 0.0123655i
\(121\) −2.20933e7 9.67970e7i −0.103067 0.451565i
\(122\) −2.75974e8 −1.24574
\(123\) 7.69411e7i 0.336154i
\(124\) −2.00890e7 8.80159e7i −0.0849714 0.372284i
\(125\) −4.21288e7 + 3.35966e7i −0.172559 + 0.137612i
\(126\) 5.25823e7 2.53223e7i 0.208621 0.100466i
\(127\) −1.03599e8 4.98905e7i −0.398235 0.191780i 0.224037 0.974581i \(-0.428076\pi\)
−0.622273 + 0.782801i \(0.713791\pi\)
\(128\) 1.46086e8i 0.544212i
\(129\) −6.76615e7 1.65269e8i −0.244333 0.596804i
\(130\) 4.81691e7 0.168653
\(131\) 4.07419e7 8.46014e7i 0.138343 0.287271i −0.820274 0.571970i \(-0.806179\pi\)
0.958617 + 0.284699i \(0.0918936\pi\)
\(132\) −1.21997e8 2.53329e8i −0.401839 0.834428i
\(133\) 5.47991e6 + 6.87159e6i 0.0175133 + 0.0219609i
\(134\) 5.00909e7 1.14329e7i 0.155360 0.0354599i
\(135\) 3.76779e7 0.113436
\(136\) 8.68253e7i 0.253799i
\(137\) −3.65714e8 + 8.34719e7i −1.03815 + 0.236951i −0.707434 0.706780i \(-0.750147\pi\)
−0.330715 + 0.943731i \(0.607290\pi\)
\(138\) 1.44499e8 1.81196e8i 0.398428 0.499612i
\(139\) 6.90390e7 3.02480e8i 0.184942 0.810284i −0.794290 0.607539i \(-0.792157\pi\)
0.979232 0.202744i \(-0.0649861\pi\)
\(140\) −8.46373e6 + 1.06132e7i −0.0220318 + 0.0276270i
\(141\) 4.85737e7 1.00864e8i 0.122892 0.255188i
\(142\) 4.88437e7 + 2.13998e8i 0.120131 + 0.526328i
\(143\) −4.68021e8 2.25387e8i −1.11923 0.538995i
\(144\) −1.21780e8 1.52707e8i −0.283221 0.355148i
\(145\) 2.68422e6 1.17603e7i 0.00607221 0.0266041i
\(146\) −5.43607e7 + 2.38170e8i −0.119639 + 0.524173i
\(147\) 1.21268e8 + 2.51815e8i 0.259702 + 0.539278i
\(148\) −2.11708e8 + 1.68831e8i −0.441255 + 0.351889i
\(149\) 2.42201e8 + 1.93149e8i 0.491395 + 0.391874i 0.837600 0.546285i \(-0.183958\pi\)
−0.346205 + 0.938159i \(0.612530\pi\)
\(150\) 4.29654e8 2.06910e8i 0.848699 0.408712i
\(151\) 1.61841e8 + 3.36067e8i 0.311302 + 0.646425i 0.996649 0.0817911i \(-0.0260640\pi\)
−0.685348 + 0.728216i \(0.740350\pi\)
\(152\) −9.65991e6 + 1.21131e7i −0.0180967 + 0.0226925i
\(153\) −1.82882e8 2.29327e8i −0.333738 0.418494i
\(154\) 2.42986e8 1.17016e8i 0.432015 0.208048i
\(155\) 2.00971e7 + 4.58702e6i 0.0348181 + 0.00794701i
\(156\) −4.54008e8 1.03624e8i −0.766594 0.174970i
\(157\) 6.05723e8 4.83048e8i 0.996954 0.795044i 0.0181485 0.999835i \(-0.494223\pi\)
0.978806 + 0.204791i \(0.0656514\pi\)
\(158\) −5.56156e8 + 1.15487e9i −0.892417 + 1.85312i
\(159\) 6.01358e8 1.37256e8i 0.940902 0.214755i
\(160\) 9.35659e7 + 4.50590e7i 0.142770 + 0.0687545i
\(161\) 9.43396e7 + 7.52334e7i 0.140408 + 0.111971i
\(162\) −7.41538e7 1.69251e7i −0.107665 0.0245738i
\(163\) 7.95271e8 + 6.34207e8i 1.12659 + 0.898423i 0.995669 0.0929700i \(-0.0296361\pi\)
0.130918 + 0.991393i \(0.458207\pi\)
\(164\) 9.96216e7 + 4.36471e8i 0.137714 + 0.603364i
\(165\) 6.42017e7 0.0866185
\(166\) 9.26046e8i 1.21955i
\(167\) 1.23540e8 + 5.41263e8i 0.158833 + 0.695893i 0.990140 + 0.140080i \(0.0447360\pi\)
−0.831307 + 0.555813i \(0.812407\pi\)
\(168\) 2.98155e7 2.37771e7i 0.0374287 0.0298484i
\(169\) −4.01945e7 + 1.93567e7i −0.0492742 + 0.0237292i
\(170\) 1.13242e8 + 5.45344e7i 0.135585 + 0.0652943i
\(171\) 5.23406e7i 0.0612145i
\(172\) 5.97815e8 + 8.49927e8i 0.683051 + 0.971109i
\(173\) −5.78075e8 −0.645357 −0.322679 0.946509i \(-0.604583\pi\)
−0.322679 + 0.946509i \(0.604583\pi\)
\(174\) −9.32174e7 + 1.93568e8i −0.101695 + 0.211172i
\(175\) 1.07728e8 + 2.23699e8i 0.114862 + 0.238513i
\(176\) −5.62753e8 7.05670e8i −0.586499 0.735446i
\(177\) 4.53637e8 1.03540e8i 0.462185 0.105491i
\(178\) 1.38405e9 1.37871
\(179\) 9.47397e8i 0.922826i −0.887185 0.461413i \(-0.847343\pi\)
0.887185 0.461413i \(-0.152657\pi\)
\(180\) −7.88134e7 + 1.79886e7i −0.0750775 + 0.0171360i
\(181\) −9.98130e7 + 1.25162e8i −0.0929978 + 0.116616i −0.826153 0.563446i \(-0.809475\pi\)
0.733155 + 0.680061i \(0.238047\pi\)
\(182\) 9.93939e7 4.35473e8i 0.0905887 0.396895i
\(183\) −3.79833e8 + 4.76295e8i −0.338679 + 0.424690i
\(184\) −9.22898e7 + 1.91642e8i −0.0805161 + 0.167193i
\(185\) −1.37583e7 6.02792e7i −0.0117457 0.0514612i
\(186\) −3.30785e8 1.59298e8i −0.276372 0.133094i
\(187\) −8.45111e8 1.05974e9i −0.691110 0.866625i
\(188\) −1.44951e8 + 6.35073e8i −0.116035 + 0.508385i
\(189\) 7.77460e7 3.40628e8i 0.0609300 0.266952i
\(190\) −9.73124e6 2.02071e7i −0.00746713 0.0155057i
\(191\) 1.99586e9 1.59165e9i 1.49968 1.19595i 0.573302 0.819344i \(-0.305662\pi\)
0.926373 0.376607i \(-0.122909\pi\)
\(192\) −9.13267e8 7.28306e8i −0.672036 0.535931i
\(193\) −1.04727e9 + 5.04341e8i −0.754798 + 0.363492i −0.771383 0.636371i \(-0.780435\pi\)
0.0165849 + 0.999862i \(0.494721\pi\)
\(194\) −1.36140e8 2.82698e8i −0.0961122 0.199579i
\(195\) 6.62967e7 8.31335e7i 0.0458515 0.0574960i
\(196\) −1.01397e9 1.27148e9i −0.687070 0.861559i
\(197\) 6.19917e8 2.98536e8i 0.411593 0.198213i −0.216617 0.976257i \(-0.569502\pi\)
0.628210 + 0.778044i \(0.283788\pi\)
\(198\) 1.56581e9 + 3.57386e8i 1.01878 + 0.232529i
\(199\) 2.61932e9 + 5.97844e8i 1.67023 + 0.381220i 0.949936 0.312446i \(-0.101148\pi\)
0.720297 + 0.693666i \(0.244005\pi\)
\(200\) −3.42189e8 + 2.72887e8i −0.213868 + 0.170554i
\(201\) 4.92101e7 1.02186e8i 0.0301488 0.0626046i
\(202\) 1.54243e9 3.52049e8i 0.926401 0.211445i
\(203\) −1.00781e8 4.85335e7i −0.0593463 0.0285797i
\(204\) −9.50022e8 7.57618e8i −0.548546 0.437451i
\(205\) −9.96613e7 2.27470e7i −0.0564301 0.0128798i
\(206\) −2.68512e9 2.14131e9i −1.49106 1.18908i
\(207\) 1.59899e8 + 7.00565e8i 0.0870894 + 0.381564i
\(208\) −1.49488e9 −0.798641
\(209\) 2.41870e8i 0.126764i
\(210\) 1.22843e7 + 5.38211e7i 0.00631646 + 0.0276742i
\(211\) −1.54640e9 + 1.23321e9i −0.780175 + 0.622169i −0.930426 0.366479i \(-0.880563\pi\)
0.150251 + 0.988648i \(0.451992\pi\)
\(212\) −3.23366e9 + 1.55725e9i −1.60085 + 0.770929i
\(213\) 4.36558e8 + 2.10235e8i 0.212092 + 0.102138i
\(214\) 5.00589e9i 2.38686i
\(215\) −2.34075e8 + 3.87810e7i −0.109547 + 0.0181495i
\(216\) 6.15895e8 0.282938
\(217\) 8.29381e7 1.72223e8i 0.0374037 0.0776696i
\(218\) 7.42726e8 + 1.54229e9i 0.328854 + 0.682872i
\(219\) 3.36231e8 + 4.21620e8i 0.146171 + 0.183293i
\(220\) −3.64202e8 + 8.31268e7i −0.155472 + 0.0354855i
\(221\) −2.24492e9 −0.941092
\(222\) 1.10121e9i 0.453376i
\(223\) −4.25953e9 + 9.72209e8i −1.72243 + 0.393134i −0.965509 0.260371i \(-0.916155\pi\)
−0.756922 + 0.653505i \(0.773298\pi\)
\(224\) 6.00424e8 7.52908e8i 0.238488 0.299054i
\(225\) −3.29018e8 + 1.44152e9i −0.128378 + 0.562459i
\(226\) 7.46601e8 9.36208e8i 0.286190 0.358871i
\(227\) −1.33062e9 + 2.76307e9i −0.501132 + 1.04061i 0.484980 + 0.874525i \(0.338827\pi\)
−0.986111 + 0.166085i \(0.946887\pi\)
\(228\) 4.82491e7 + 2.11393e8i 0.0178546 + 0.0782260i
\(229\) −4.28395e8 2.06304e8i −0.155777 0.0750181i 0.354371 0.935105i \(-0.384695\pi\)
−0.510148 + 0.860087i \(0.670409\pi\)
\(230\) −1.91982e8 2.40738e8i −0.0686040 0.0860267i
\(231\) 1.32476e8 5.80416e8i 0.0465254 0.203841i
\(232\) 4.38772e7 1.92238e8i 0.0151456 0.0663572i
\(233\) 1.74253e9 + 3.61841e9i 0.591231 + 1.22770i 0.955108 + 0.296258i \(0.0957387\pi\)
−0.363877 + 0.931447i \(0.618547\pi\)
\(234\) 2.07968e9 1.65849e9i 0.693639 0.553159i
\(235\) −1.16288e8 9.27368e7i −0.0381298 0.0304075i
\(236\) −2.43933e9 + 1.17472e9i −0.786361 + 0.378692i
\(237\) 1.22770e9 + 2.54934e9i 0.389133 + 0.808042i
\(238\) 7.26687e8 9.11237e8i 0.226485 0.284003i
\(239\) 3.04871e8 + 3.82296e8i 0.0934382 + 0.117168i 0.826353 0.563153i \(-0.190412\pi\)
−0.732914 + 0.680321i \(0.761840\pi\)
\(240\) 1.66458e8 8.01622e7i 0.0501719 0.0241615i
\(241\) −1.03782e9 2.36876e8i −0.307648 0.0702187i 0.0659096 0.997826i \(-0.479005\pi\)
−0.373558 + 0.927607i \(0.621862\pi\)
\(242\) 2.29052e9 + 5.22795e8i 0.667839 + 0.152430i
\(243\) 2.65362e9 2.11619e9i 0.761052 0.606919i
\(244\) 1.53801e9 3.19372e9i 0.433911 0.901026i
\(245\) 3.62026e8 8.26301e7i 0.100479 0.0229337i
\(246\) 1.64036e9 + 7.89957e8i 0.447919 + 0.215706i
\(247\) 3.13193e8 + 2.49763e8i 0.0841441 + 0.0671027i
\(248\) 3.28513e8 + 7.49809e7i 0.0868452 + 0.0198218i
\(249\) 1.59823e9 + 1.27455e9i 0.415760 + 0.331558i
\(250\) −2.83732e8 1.24311e9i −0.0726353 0.318236i
\(251\) −4.42727e9 −1.11543 −0.557713 0.830034i \(-0.688321\pi\)
−0.557713 + 0.830034i \(0.688321\pi\)
\(252\) 7.49632e8i 0.185886i
\(253\) 7.38907e8 + 3.23736e9i 0.180346 + 0.790149i
\(254\) 2.12730e9 1.69647e9i 0.511086 0.407578i
\(255\) 2.49978e8 1.20383e8i 0.0591209 0.0284711i
\(256\) −2.04334e9 9.84021e8i −0.475752 0.229110i
\(257\) 4.21190e9i 0.965485i −0.875762 0.482742i \(-0.839641\pi\)
0.875762 0.482742i \(-0.160359\pi\)
\(258\) 4.21816e9 + 2.54295e8i 0.952016 + 0.0573931i
\(259\) −5.73344e8 −0.127414
\(260\) −2.68448e8 + 5.57438e8i −0.0587444 + 0.121984i
\(261\) −2.89026e8 6.00168e8i −0.0622837 0.129333i
\(262\) 1.38538e9 + 1.73721e9i 0.294011 + 0.368678i
\(263\) 5.48643e8 1.25224e8i 0.114674 0.0261737i −0.164799 0.986327i \(-0.552697\pi\)
0.279473 + 0.960154i \(0.409840\pi\)
\(264\) 1.04946e9 0.216048
\(265\) 8.19513e8i 0.166178i
\(266\) −2.02763e8 + 4.62792e7i −0.0405006 + 0.00924400i
\(267\) 1.90492e9 2.38869e9i 0.374827 0.470019i
\(268\) −1.46851e8 + 6.43395e8i −0.0284667 + 0.124721i
\(269\) −4.63085e9 + 5.80690e9i −0.884405 + 1.10901i 0.108964 + 0.994046i \(0.465247\pi\)
−0.993370 + 0.114964i \(0.963325\pi\)
\(270\) −3.86840e8 + 8.03282e8i −0.0727908 + 0.151152i
\(271\) −1.64403e9 7.20297e9i −0.304812 1.33547i −0.862768 0.505600i \(-0.831271\pi\)
0.557956 0.829871i \(-0.311586\pi\)
\(272\) −3.51434e9 1.69242e9i −0.642049 0.309195i
\(273\) −6.14770e8 7.70897e8i −0.110678 0.138786i
\(274\) 1.97520e9 8.65392e9i 0.350436 1.53536i
\(275\) −1.52041e9 + 6.66137e9i −0.265847 + 1.16475i
\(276\) 1.29160e9 + 2.68204e9i 0.222583 + 0.462198i
\(277\) −3.87938e9 + 3.09370e9i −0.658936 + 0.525484i −0.894894 0.446279i \(-0.852749\pi\)
0.235958 + 0.971763i \(0.424177\pi\)
\(278\) 5.73995e9 + 4.57746e9i 0.961012 + 0.766382i
\(279\) 1.02562e9 4.93911e8i 0.169265 0.0815140i
\(280\) −2.19835e7 4.56493e7i −0.00357656 0.00742680i
\(281\) −2.63153e9 + 3.29983e9i −0.422069 + 0.529257i −0.946719 0.322060i \(-0.895625\pi\)
0.524651 + 0.851318i \(0.324196\pi\)
\(282\) 1.65169e9 + 2.07115e9i 0.261175 + 0.327503i
\(283\) 9.03084e9 4.34902e9i 1.40793 0.678025i 0.433180 0.901307i \(-0.357391\pi\)
0.974754 + 0.223282i \(0.0716771\pi\)
\(284\) −2.74871e9 6.27375e8i −0.422528 0.0964392i
\(285\) −4.82683e7 1.10169e7i −0.00731615 0.00166986i
\(286\) 9.61036e9 7.66401e9i 1.43640 1.14549i
\(287\) −4.11290e8 + 8.54052e8i −0.0606206 + 0.125880i
\(288\) 5.59108e9 1.27613e9i 0.812692 0.185492i
\(289\) 1.00730e9 + 4.85089e8i 0.144400 + 0.0695393i
\(290\) 2.23168e8 + 1.77971e8i 0.0315530 + 0.0251626i
\(291\) −6.75273e8 1.54127e8i −0.0941689 0.0214934i
\(292\) −2.45327e9 1.95642e9i −0.337454 0.269110i
\(293\) 2.15531e9 + 9.44303e9i 0.292442 + 1.28127i 0.881116 + 0.472900i \(0.156793\pi\)
−0.588674 + 0.808370i \(0.700350\pi\)
\(294\) −6.61368e9 −0.885226
\(295\) 6.18204e8i 0.0816288i
\(296\) −2.24898e8 9.85343e8i −0.0292967 0.128357i
\(297\) 7.51723e9 5.99479e9i 0.966123 0.770457i
\(298\) −6.60456e9 + 3.18059e9i −0.837488 + 0.403313i
\(299\) 4.95502e9 + 2.38621e9i 0.619955 + 0.298555i
\(300\) 6.12530e9i 0.756210i
\(301\) −1.32399e8 + 2.19618e9i −0.0161294 + 0.267548i
\(302\) −8.82648e9 −1.06111
\(303\) 1.51530e9 3.14656e9i 0.179775 0.373307i
\(304\) 3.01999e8 + 6.27106e8i 0.0353599 + 0.0734255i
\(305\) 5.04647e8 + 6.32807e8i 0.0583160 + 0.0731260i
\(306\) 6.76683e9 1.54449e9i 0.771791 0.176156i
\(307\) 1.57298e9 0.177080 0.0885398 0.996073i \(-0.471780\pi\)
0.0885398 + 0.996073i \(0.471780\pi\)
\(308\) 3.46410e9i 0.384935i
\(309\) −7.39125e9 + 1.68700e9i −0.810744 + 0.185047i
\(310\) −3.04131e8 + 3.81368e8i −0.0329317 + 0.0412950i
\(311\) 2.27824e9 9.98160e9i 0.243533 1.06699i −0.694242 0.719742i \(-0.744260\pi\)
0.937775 0.347245i \(-0.112883\pi\)
\(312\) 1.08371e9 1.35893e9i 0.114365 0.143409i
\(313\) −6.13991e9 + 1.27497e10i −0.639712 + 1.32838i 0.288913 + 0.957356i \(0.406706\pi\)
−0.928625 + 0.371020i \(0.879008\pi\)
\(314\) 4.07946e9 + 1.78733e10i 0.419647 + 1.83859i
\(315\) −1.54216e8 7.42665e7i −0.0156634 0.00754311i
\(316\) −1.02653e10 1.28723e10i −1.02949 1.29094i
\(317\) 4.08668e9 1.79049e10i 0.404701 1.77311i −0.203243 0.979128i \(-0.565148\pi\)
0.607943 0.793981i \(-0.291995\pi\)
\(318\) −3.24790e9 + 1.42300e10i −0.317610 + 1.39154i
\(319\) −1.33561e9 2.77342e9i −0.128978 0.267826i
\(320\) −1.21337e9 + 9.67629e8i −0.115716 + 0.0922803i
\(321\) −8.63951e9 6.88978e9i −0.813709 0.648911i
\(322\) −2.57254e9 + 1.23887e9i −0.239298 + 0.115240i
\(323\) 4.53525e8 + 9.41753e8i 0.0416669 + 0.0865221i
\(324\) 6.09128e8 7.63823e8i 0.0552750 0.0693127i
\(325\) 7.05565e9 + 8.84751e9i 0.632417 + 0.793026i
\(326\) −2.16862e10 + 1.04435e10i −1.92005 + 0.924648i
\(327\) 3.68402e9 + 8.40854e8i 0.322204 + 0.0735410i
\(328\) −1.62910e9 3.71830e8i −0.140751 0.0321255i
\(329\) −1.07834e9 + 8.59949e8i −0.0920392 + 0.0733988i
\(330\) −6.59160e8 + 1.36876e9i −0.0555821 + 0.115417i
\(331\) 1.53457e10 3.50256e9i 1.27842 0.291792i 0.471194 0.882029i \(-0.343823\pi\)
0.807230 + 0.590237i \(0.200966\pi\)
\(332\) −1.07167e10 5.16089e9i −0.882081 0.424788i
\(333\) −2.66946e9 2.12882e9i −0.217093 0.173126i
\(334\) −1.28080e10 2.92333e9i −1.02919 0.234905i
\(335\) −1.17812e8 9.39519e7i −0.00935428 0.00745979i
\(336\) −3.81230e8 1.67028e9i −0.0299110 0.131049i
\(337\) −1.82421e10 −1.41435 −0.707173 0.707040i \(-0.750030\pi\)
−0.707173 + 0.707040i \(0.750030\pi\)
\(338\) 1.05567e9i 0.0808838i
\(339\) −5.88199e8 2.57707e9i −0.0445375 0.195131i
\(340\) −1.26220e9 + 1.00657e9i −0.0944525 + 0.0753233i
\(341\) 4.73945e9 2.28240e9i 0.350518 0.168801i
\(342\) −1.11589e9 5.37383e8i −0.0815672 0.0392807i
\(343\) 7.15334e9i 0.516812i
\(344\) −3.82626e9 + 6.33927e8i −0.273238 + 0.0452695i
\(345\) −6.79714e8 −0.0479789
\(346\) 5.93512e9 1.23244e10i 0.414119 0.859926i
\(347\) −6.08936e9 1.26447e10i −0.420005 0.872148i −0.998408 0.0563978i \(-0.982038\pi\)
0.578404 0.815751i \(-0.303676\pi\)
\(348\) −1.72057e9 2.15752e9i −0.117315 0.147109i
\(349\) −2.52169e9 + 5.75560e8i −0.169977 + 0.0387962i −0.306662 0.951818i \(-0.599212\pi\)
0.136685 + 0.990615i \(0.456355\pi\)
\(350\) −5.87523e9 −0.391519
\(351\) 1.59243e10i 1.04914i
\(352\) 2.58368e10 5.89708e9i 1.68294 0.384120i
\(353\) 1.70163e10 2.13378e10i 1.09589 1.37420i 0.174916 0.984583i \(-0.444035\pi\)
0.920975 0.389621i \(-0.127394\pi\)
\(354\) −2.45007e9 + 1.07345e10i −0.156015 + 0.683545i
\(355\) 4.01381e8 5.03316e8i 0.0252722 0.0316904i
\(356\) −7.71337e9 + 1.60170e10i −0.480224 + 0.997196i
\(357\) −5.72511e8 2.50833e9i −0.0352461 0.154423i
\(358\) 2.01982e10 + 9.72695e9i 1.22965 + 0.592167i
\(359\) −1.25036e10 1.56790e10i −0.752759 0.943930i 0.246926 0.969034i \(-0.420580\pi\)
−0.999685 + 0.0251044i \(0.992008\pi\)
\(360\) 6.71413e7 2.94165e8i 0.00399742 0.0175138i
\(361\) −3.73769e9 + 1.63759e10i −0.220077 + 0.964221i
\(362\) −1.64362e9 3.41302e9i −0.0957123 0.198749i
\(363\) 4.05479e9 3.23359e9i 0.233530 0.186234i
\(364\) 4.48560e9 + 3.57715e9i 0.255514 + 0.203766i
\(365\) 6.45526e8 3.10869e8i 0.0363699 0.0175148i
\(366\) −6.25471e9 1.29880e10i −0.348564 0.723802i
\(367\) 9.01414e9 1.13034e10i 0.496890 0.623080i −0.468635 0.883392i \(-0.655254\pi\)
0.965525 + 0.260312i \(0.0838254\pi\)
\(368\) 5.95796e9 + 7.47105e9i 0.324868 + 0.407371i
\(369\) −5.08603e9 + 2.44930e9i −0.274330 + 0.132110i
\(370\) 1.42639e9 + 3.25564e8i 0.0761082 + 0.0173712i
\(371\) −7.40882e9 1.69101e9i −0.391069 0.0892589i
\(372\) 3.68695e9 2.94025e9i 0.192529 0.153537i
\(373\) 3.03309e9 6.29827e9i 0.156693 0.325376i −0.807812 0.589440i \(-0.799349\pi\)
0.964505 + 0.264064i \(0.0850629\pi\)
\(374\) 3.12700e10 7.13718e9i 1.59824 0.364788i
\(375\) −2.53595e9 1.22125e9i −0.128238 0.0617561i
\(376\) −1.90089e9 1.51591e9i −0.0951053 0.0758439i
\(377\) −4.97044e9 1.13447e9i −0.246054 0.0561601i
\(378\) 6.46386e9 + 5.15475e9i 0.316610 + 0.252488i
\(379\) 4.25774e9 + 1.86544e10i 0.206358 + 0.904115i 0.966966 + 0.254904i \(0.0820438\pi\)
−0.760608 + 0.649211i \(0.775099\pi\)
\(380\) 2.88080e8 0.0138159
\(381\) 6.00635e9i 0.285043i
\(382\) 1.34419e10 + 5.88927e10i 0.631257 + 2.76572i
\(383\) 1.75431e10 1.39902e10i 0.815288 0.650171i −0.124389 0.992234i \(-0.539697\pi\)
0.939677 + 0.342063i \(0.111126\pi\)
\(384\) 6.87518e9 3.31091e9i 0.316198 0.152273i
\(385\) −7.12643e8 3.43191e8i −0.0324361 0.0156204i
\(386\) 2.75056e10i 1.23900i
\(387\) −8.77084e9 + 9.73370e9i −0.391019 + 0.433944i
\(388\) 4.03024e9 0.177830
\(389\) −7.65121e9 + 1.58879e10i −0.334143 + 0.693854i −0.998568 0.0535005i \(-0.982962\pi\)
0.664425 + 0.747355i \(0.268676\pi\)
\(390\) 1.09171e9 + 2.26696e9i 0.0471899 + 0.0979908i
\(391\) 8.94734e9 + 1.12196e10i 0.382813 + 0.480032i
\(392\) 5.91779e9 1.35070e9i 0.250620 0.0572024i
\(393\) 4.90494e9 0.205619
\(394\) 1.62815e10i 0.675631i
\(395\) 3.66510e9 8.36534e8i 0.150556 0.0343633i
\(396\) −1.28622e10 + 1.61287e10i −0.523039 + 0.655871i
\(397\) −1.07498e10 + 4.70980e10i −0.432752 + 1.89601i 0.0111575 + 0.999938i \(0.496448\pi\)
−0.443909 + 0.896072i \(0.646409\pi\)
\(398\) −3.96385e10 + 4.97051e10i −1.57974 + 1.98093i
\(399\) −1.99197e8 + 4.13637e8i −0.00785944 + 0.0163203i
\(400\) 4.37534e9 + 1.91696e10i 0.170912 + 0.748813i
\(401\) 1.20084e9 + 5.78292e8i 0.0464415 + 0.0223651i 0.456960 0.889487i \(-0.348938\pi\)
−0.410519 + 0.911852i \(0.634652\pi\)
\(402\) 1.67333e9 + 2.09829e9i 0.0640733 + 0.0803454i
\(403\) 1.93868e9 8.49390e9i 0.0734997 0.322023i
\(404\) −4.52190e9 + 1.98118e10i −0.169745 + 0.743699i
\(405\) 9.67886e7 + 2.00984e8i 0.00359753 + 0.00747034i
\(406\) 2.06944e9 1.65032e9i 0.0761638 0.0607386i
\(407\) −1.23358e10 9.83744e9i −0.449561 0.358513i
\(408\) 4.08622e9 1.96782e9i 0.147462 0.0710141i
\(409\) 1.09354e10 + 2.27076e10i 0.390788 + 0.811480i 0.999832 + 0.0183435i \(0.00583925\pi\)
−0.609043 + 0.793137i \(0.708446\pi\)
\(410\) 1.50818e9 1.89120e9i 0.0533727 0.0669272i
\(411\) −1.22170e10 1.53196e10i −0.428151 0.536885i
\(412\) 3.97447e10 1.91400e10i 1.37940 0.664284i
\(413\) −5.58888e9 1.27563e9i −0.192099 0.0438453i
\(414\) −1.65775e10 3.78371e9i −0.564311 0.128800i
\(415\) 2.12342e9 1.69337e9i 0.0715885 0.0570899i
\(416\) 1.90439e10 3.95451e10i 0.635891 1.32044i
\(417\) 1.58002e10 3.60629e9i 0.522538 0.119266i
\(418\) −5.15659e9 2.48328e9i −0.168911 0.0813432i
\(419\) 2.15607e9 + 1.71941e9i 0.0699530 + 0.0557857i 0.657842 0.753156i \(-0.271469\pi\)
−0.587889 + 0.808942i \(0.700041\pi\)
\(420\) −6.91307e8 1.57786e8i −0.0222164 0.00507075i
\(421\) −3.13619e10 2.50102e10i −0.998328 0.796140i −0.0192896 0.999814i \(-0.506140\pi\)
−0.979039 + 0.203674i \(0.934712\pi\)
\(422\) −1.04148e10 4.56302e10i −0.328398 1.43881i
\(423\) −8.21369e9 −0.256553
\(424\) 1.33960e10i 0.414489i
\(425\) 6.57064e9 + 2.87879e10i 0.201397 + 0.882376i
\(426\) −8.96430e9 + 7.14879e9i −0.272194 + 0.217067i
\(427\) 6.76221e9 3.25651e9i 0.203412 0.0979582i
\(428\) 5.79308e10 + 2.78980e10i 1.72637 + 0.831377i
\(429\) 2.71345e10i 0.801110i
\(430\) 1.57645e9 5.38857e9i 0.0461113 0.157616i
\(431\) −2.74496e9 −0.0795477 −0.0397738 0.999209i \(-0.512664\pi\)
−0.0397738 + 0.999209i \(0.512664\pi\)
\(432\) 1.20052e10 2.49290e10i 0.344694 0.715763i
\(433\) 2.66435e10 + 5.53258e10i 0.757948 + 1.57390i 0.817674 + 0.575681i \(0.195263\pi\)
−0.0597261 + 0.998215i \(0.519023\pi\)
\(434\) 2.82021e9 + 3.53643e9i 0.0794918 + 0.0996795i
\(435\) 6.14308e8 1.40212e8i 0.0171565 0.00391586i
\(436\) −2.19874e10 −0.608454
\(437\) 2.56072e9i 0.0702160i
\(438\) −1.24409e10 + 2.83956e9i −0.338030 + 0.0771532i
\(439\) 9.14648e9 1.14693e10i 0.246261 0.308802i −0.643303 0.765611i \(-0.722437\pi\)
0.889564 + 0.456810i \(0.151008\pi\)
\(440\) 3.10265e8 1.35936e9i 0.00827793 0.0362680i
\(441\) 1.27853e10 1.60323e10i 0.338032 0.423879i
\(442\) 2.30487e10 4.78610e10i 0.603888 1.25399i
\(443\) 3.57958e9 + 1.56832e10i 0.0929431 + 0.407210i 0.999902 0.0140090i \(-0.00445935\pi\)
−0.906959 + 0.421219i \(0.861602\pi\)
\(444\) −1.27438e10 6.13709e9i −0.327919 0.157918i
\(445\) −2.53088e9 3.17362e9i −0.0645404 0.0809311i
\(446\) 2.30055e10 1.00794e11i 0.581422 2.54738i
\(447\) −3.60080e9 + 1.57762e10i −0.0901923 + 0.395158i
\(448\) 6.24416e9 + 1.29661e10i 0.155011 + 0.321883i
\(449\) −2.07707e10 + 1.65641e10i −0.511053 + 0.407551i −0.844776 0.535120i \(-0.820266\pi\)
0.333723 + 0.942671i \(0.391695\pi\)
\(450\) −2.73548e10 2.18147e10i −0.667088 0.531985i
\(451\) −2.35029e10 + 1.13184e10i −0.568088 + 0.273577i
\(452\) 6.67346e9 + 1.38576e10i 0.159881 + 0.331997i
\(453\) −1.21482e10 + 1.52333e10i −0.288482 + 0.361745i
\(454\) −4.52462e10 5.67370e10i −1.06502 1.33550i
\(455\) −1.18029e9 + 5.68397e8i −0.0275387 + 0.0132619i
\(456\) −7.89009e8 1.80086e8i −0.0182483 0.00416506i
\(457\) −6.08317e10 1.38844e10i −1.39465 0.318320i −0.541814 0.840498i \(-0.682262\pi\)
−0.852836 + 0.522178i \(0.825120\pi\)
\(458\) 8.79668e9 7.01512e9i 0.199920 0.159431i
\(459\) 1.80287e10 3.74370e10i 0.406175 0.843431i
\(460\) 3.85587e9 8.80078e8i 0.0861175 0.0196558i
\(461\) −4.54863e10 2.19051e10i −1.00711 0.484999i −0.143765 0.989612i \(-0.545921\pi\)
−0.863346 + 0.504613i \(0.831635\pi\)
\(462\) 1.10142e10 + 8.78350e9i 0.241759 + 0.192797i
\(463\) −3.53513e9 8.06871e8i −0.0769275 0.0175582i 0.183884 0.982948i \(-0.441133\pi\)
−0.260811 + 0.965390i \(0.583990\pi\)
\(464\) −6.92578e9 5.52313e9i −0.149416 0.119155i
\(465\) 2.39605e8 + 1.04978e9i 0.00512489 + 0.0224536i
\(466\) −9.50340e10 −2.01528
\(467\) 2.17382e10i 0.457042i −0.973539 0.228521i \(-0.926611\pi\)
0.973539 0.228521i \(-0.0733889\pi\)
\(468\) 7.60279e9 + 3.33100e10i 0.158486 + 0.694371i
\(469\) −1.09247e9 + 8.71217e8i −0.0225797 + 0.0180067i
\(470\) 3.17105e9 1.52710e9i 0.0649849 0.0312951i
\(471\) 3.64616e10 + 1.75590e10i 0.740888 + 0.356793i
\(472\) 1.01054e10i 0.203603i
\(473\) −4.05307e10 + 4.49801e10i −0.809728 + 0.898620i
\(474\) −6.69559e10 −1.32640
\(475\) 2.28617e9 4.74727e9i 0.0449090 0.0932545i
\(476\) 6.49546e9 + 1.34880e10i 0.126527 + 0.262735i
\(477\) −2.82163e10 3.53822e10i −0.545039 0.683457i
\(478\) −1.12806e10 + 2.57471e9i −0.216082 + 0.0493194i
\(479\) 4.67791e10 0.888607 0.444304 0.895876i \(-0.353451\pi\)
0.444304 + 0.895876i \(0.353451\pi\)
\(480\) 5.42468e9i 0.102190i
\(481\) −2.54766e10 + 5.81487e9i −0.475950 + 0.108633i
\(482\) 1.57055e10 1.96940e10i 0.290980 0.364877i
\(483\) −1.40255e9 + 6.14497e9i −0.0257709 + 0.112910i
\(484\) −1.88152e10 + 2.35935e10i −0.342868 + 0.429943i
\(485\) −3.99278e8 + 8.29110e8i −0.00721620 + 0.0149846i
\(486\) 1.78718e10 + 7.83015e10i 0.320349 + 1.40354i
\(487\) 9.36417e10 + 4.50955e10i 1.66477 + 0.801710i 0.998427 + 0.0560617i \(0.0178543\pi\)
0.666340 + 0.745648i \(0.267860\pi\)
\(488\) 8.24912e9 + 1.03441e10i 0.145455 + 0.182395i
\(489\) −1.18233e10 + 5.18013e10i −0.206778 + 0.905951i
\(490\) −1.95528e9 + 8.56665e9i −0.0339176 + 0.148603i
\(491\) 2.25200e10 + 4.67634e10i 0.387475 + 0.804600i 0.999901 + 0.0140718i \(0.00447935\pi\)
−0.612426 + 0.790528i \(0.709806\pi\)
\(492\) −1.82836e10 + 1.45807e10i −0.312033 + 0.248838i
\(493\) −1.04008e10 8.29432e9i −0.176067 0.140408i
\(494\) −8.54042e9 + 4.11285e9i −0.143407 + 0.0690614i
\(495\) −2.04376e9 4.24392e9i −0.0340416 0.0706881i
\(496\) 9.43837e9 1.18353e10i 0.155945 0.195548i
\(497\) −3.72201e9 4.66725e9i −0.0610031 0.0764955i
\(498\) −4.35821e10 + 2.09880e10i −0.708583 + 0.341236i
\(499\) 4.57830e10 + 1.04497e10i 0.738418 + 0.168539i 0.575156 0.818044i \(-0.304941\pi\)
0.163262 + 0.986583i \(0.447799\pi\)
\(500\) 1.59672e10 + 3.64440e9i 0.255475 + 0.0583104i
\(501\) −2.26733e10 + 1.80814e10i −0.359885 + 0.286999i
\(502\) 4.54548e10 9.43880e10i 0.715757 1.48628i
\(503\) 7.68579e10 1.75423e10i 1.20065 0.274041i 0.424995 0.905196i \(-0.360276\pi\)
0.775657 + 0.631155i \(0.217419\pi\)
\(504\) −2.52086e9 1.21398e9i −0.0390685 0.0188144i
\(505\) −3.62773e9 2.89302e9i −0.0557788 0.0444821i
\(506\) −7.66059e10 1.74848e10i −1.16859 0.266722i
\(507\) −1.82195e9 1.45295e9i −0.0275743 0.0219898i
\(508\) 7.77688e9 + 3.40727e10i 0.116775 + 0.511626i
\(509\) 9.85840e10 1.46871 0.734354 0.678767i \(-0.237485\pi\)
0.734354 + 0.678767i \(0.237485\pi\)
\(510\) 6.56543e9i 0.0970471i
\(511\) −1.47841e9 6.47734e9i −0.0216826 0.0949977i
\(512\) 7.11970e10 5.67777e10i 1.03605 0.826224i
\(513\) −6.68033e9 + 3.21708e9i −0.0964558 + 0.0464507i
\(514\) 8.97964e10 + 4.32437e10i 1.28649 + 0.619541i
\(515\) 1.00726e10i 0.143190i
\(516\) −2.64508e10 + 4.73976e10i −0.373113 + 0.668586i
\(517\) −3.79560e10 −0.531274
\(518\) 5.88654e9 1.22235e10i 0.0817600 0.169776i
\(519\) −1.31016e10 2.72057e10i −0.180574 0.374965i
\(520\) −1.43982e9 1.80547e9i −0.0196922 0.0246932i
\(521\) −8.71449e10 + 1.98903e10i −1.18274 + 0.269954i −0.768281 0.640112i \(-0.778888\pi\)
−0.414463 + 0.910066i \(0.636031\pi\)
\(522\) 1.57628e10 0.212301
\(523\) 5.02686e10i 0.671878i 0.941884 + 0.335939i \(0.109054\pi\)
−0.941884 + 0.335939i \(0.890946\pi\)
\(524\) −2.78247e10 + 6.35080e9i −0.369067 + 0.0842370i
\(525\) −8.08628e9 + 1.01399e10i −0.106442 + 0.133474i
\(526\) −2.96319e9 + 1.29826e10i −0.0387094 + 0.169597i
\(527\) 1.41740e10 1.77737e10i 0.183760 0.230428i
\(528\) 2.04563e10 4.24780e10i 0.263204 0.546548i
\(529\) 9.60290e9 + 4.20731e10i 0.122625 + 0.537256i
\(530\) 1.74718e10 + 8.41396e9i 0.221428 + 0.106634i
\(531\) −2.12851e10 2.66907e10i −0.267731 0.335724i
\(532\) 5.94435e8 2.60439e9i 0.00742093 0.0325132i
\(533\) −9.61390e9 + 4.21212e10i −0.119122 + 0.521906i
\(534\) 3.13683e10 + 6.51370e10i 0.385768 + 0.801056i
\(535\) −1.14785e10 + 9.15378e9i −0.140110 + 0.111734i
\(536\) −1.92579e9 1.53577e9i −0.0233319 0.0186066i
\(537\) 4.45869e10 2.14719e10i 0.536180 0.258211i
\(538\) −7.62563e10 1.58348e11i −0.910221 1.89009i
\(539\) 5.90820e10 7.40864e10i 0.700003 0.877776i
\(540\) −7.14013e9 8.95343e9i −0.0839713 0.105297i
\(541\) −4.01628e10 + 1.93414e10i −0.468851 + 0.225787i −0.653365 0.757043i \(-0.726643\pi\)
0.184514 + 0.982830i \(0.440929\pi\)
\(542\) 1.70444e11 + 3.89028e10i 1.97508 + 0.450800i
\(543\) −8.15260e9 1.86078e9i −0.0937771 0.0214040i
\(544\) 8.95416e10 7.14071e10i 1.02242 0.815353i
\(545\) 2.17830e9 4.52330e9i 0.0246907 0.0512707i
\(546\) 2.27472e10 5.19189e9i 0.255951 0.0584191i
\(547\) −8.43976e10 4.06438e10i −0.942716 0.453988i −0.101590 0.994826i \(-0.532393\pi\)
−0.841127 + 0.540838i \(0.818107\pi\)
\(548\) 8.91399e10 + 7.10867e10i 0.988439 + 0.788254i
\(549\) 4.35759e10 + 9.94591e9i 0.479686 + 0.109485i
\(550\) −1.26408e11 1.00807e11i −1.38142 1.10164i
\(551\) 5.28226e8 + 2.31431e9i 0.00573078 + 0.0251082i
\(552\) −1.11108e10 −0.119671
\(553\) 3.48605e10i 0.372763i
\(554\) −2.61271e10 1.14470e11i −0.277365 1.21522i
\(555\) 2.52507e9 2.01368e9i 0.0266135 0.0212235i
\(556\) −8.49617e10 + 4.09154e10i −0.889046 + 0.428142i
\(557\) 1.35190e11 + 6.51041e10i 1.40451 + 0.676375i 0.974070 0.226245i \(-0.0726451\pi\)
0.430437 + 0.902621i \(0.358359\pi\)
\(558\) 2.69368e10i 0.277850i
\(559\) 1.63906e10 + 9.89303e10i 0.167860 + 1.01317i
\(560\) −2.27621e9 −0.0231451
\(561\) 3.07202e10 6.37911e10i 0.310150 0.644034i
\(562\) −4.33335e10 8.99829e10i −0.434389 0.902017i
\(563\) −1.65824e9 2.07937e9i −0.0165050 0.0206966i 0.773511 0.633783i \(-0.218499\pi\)
−0.790015 + 0.613087i \(0.789928\pi\)
\(564\) −3.31734e10 + 7.57161e9i −0.327849 + 0.0748293i
\(565\) −3.51195e9 −0.0344632
\(566\) 2.37186e11i 2.31113i
\(567\) 2.01671e9 4.60301e8i 0.0195124 0.00445359i
\(568\) 6.56110e9 8.22736e9i 0.0630353 0.0790437i
\(569\) 3.90427e10 1.71057e11i 0.372470 1.63190i −0.347351 0.937735i \(-0.612919\pi\)
0.719820 0.694161i \(-0.244224\pi\)
\(570\) 7.30449e8 9.15954e8i 0.00691975 0.00867709i
\(571\) 2.37518e10 4.93211e10i 0.223435 0.463968i −0.758873 0.651239i \(-0.774250\pi\)
0.982308 + 0.187270i \(0.0599640\pi\)
\(572\) 3.51330e10 + 1.53928e11i 0.328195 + 1.43792i
\(573\) 1.20142e11 + 5.78571e10i 1.11449 + 0.536708i
\(574\) −1.39854e10 1.75371e10i −0.128833 0.161552i
\(575\) 1.60969e10 7.05251e10i 0.147255 0.645167i
\(576\) −1.90707e10 + 8.35541e10i −0.173251 + 0.759063i
\(577\) 7.87786e10 + 1.63585e11i 0.710731 + 1.47585i 0.872292 + 0.488985i \(0.162633\pi\)
−0.161562 + 0.986863i \(0.551653\pi\)
\(578\) −2.06839e10 + 1.64949e10i −0.185320 + 0.147787i
\(579\) −4.74711e10 3.78570e10i −0.422392 0.336846i
\(580\) −3.30329e9 + 1.59078e9i −0.0291901 + 0.0140572i
\(581\) −1.09274e10 2.26910e10i −0.0958985 0.199135i
\(582\) 1.02190e10 1.28142e10i 0.0890667 0.111686i
\(583\) −1.30390e11 1.63504e11i −1.12868 1.41531i
\(584\) 1.05520e10 5.08156e9i 0.0907157 0.0436864i
\(585\) −7.60582e9 1.73598e9i −0.0649416 0.0148225i
\(586\) −2.23451e11 5.10013e10i −1.89493 0.432504i
\(587\) 4.22838e10 3.37202e10i 0.356140 0.284012i −0.429033 0.903289i \(-0.641145\pi\)
0.785173 + 0.619277i \(0.212574\pi\)
\(588\) 3.68583e10 7.65370e10i 0.308337 0.640269i
\(589\) −3.95488e9 + 9.02676e8i −0.0328604 + 0.00750017i
\(590\) 1.31799e10 + 6.34711e9i 0.108769 + 0.0523803i
\(591\) 2.80998e10 + 2.24088e10i 0.230331 + 0.183683i
\(592\) −4.42665e10 1.01035e10i −0.360403 0.0822596i
\(593\) −1.79555e11 1.43190e11i −1.45204 1.15796i −0.957365 0.288880i \(-0.906717\pi\)
−0.494671 0.869080i \(-0.664712\pi\)
\(594\) 5.06276e10 + 2.21814e11i 0.406669 + 1.78173i
\(595\) −3.41828e9 −0.0272734
\(596\) 9.41570e10i 0.746221i
\(597\) 3.12287e10 + 1.36822e11i 0.245842 + 1.07710i
\(598\) −1.01747e11 + 8.11402e10i −0.795637 + 0.634499i
\(599\) 1.58763e11 7.64561e10i 1.23322 0.593888i 0.300258 0.953858i \(-0.402927\pi\)
0.932964 + 0.359970i \(0.117213\pi\)
\(600\) −2.05982e10 9.91956e9i −0.158937 0.0765398i
\(601\) 8.66023e10i 0.663791i 0.943316 + 0.331896i \(0.107688\pi\)
−0.943316 + 0.331896i \(0.892312\pi\)
\(602\) −4.54625e10 2.53709e10i −0.346153 0.193175i
\(603\) −8.32131e9 −0.0629394
\(604\) 4.91903e10 1.02145e11i 0.369600 0.767481i
\(605\) −2.98967e9 6.20812e9i −0.0223153 0.0463382i
\(606\) 5.15261e10 + 6.46117e10i 0.382064 + 0.479094i
\(607\) −1.91063e11 + 4.36089e10i −1.40742 + 0.321233i −0.857714 0.514127i \(-0.828116\pi\)
−0.549702 + 0.835361i \(0.685259\pi\)
\(608\) −2.04366e10 −0.149553
\(609\) 5.84298e9i 0.0424781i
\(610\) −1.86725e10 + 4.26187e9i −0.134860 + 0.0307809i
\(611\) −3.91947e10 + 4.91485e10i −0.281230 + 0.352652i
\(612\) −1.98382e10 + 8.69168e10i −0.141415 + 0.619581i
\(613\) −1.40918e11 + 1.76706e11i −0.997988 + 1.25144i −0.0302331 + 0.999543i \(0.509625\pi\)
−0.967755 + 0.251894i \(0.918946\pi\)
\(614\) −1.61498e10 + 3.35354e10i −0.113630 + 0.235955i
\(615\) −1.18820e9 5.20586e9i −0.00830597 0.0363908i
\(616\) −1.16491e10 5.60991e9i −0.0809039 0.0389612i
\(617\) 1.18686e11 + 1.48827e11i 0.818950 + 1.02693i 0.999063 + 0.0432844i \(0.0137822\pi\)
−0.180113 + 0.983646i \(0.557646\pi\)
\(618\) 3.99197e10 1.74900e11i 0.273674 1.19904i
\(619\) −3.61718e10 + 1.58479e11i −0.246381 + 1.07947i 0.688703 + 0.725043i \(0.258180\pi\)
−0.935085 + 0.354424i \(0.884677\pi\)
\(620\) −2.71846e9 5.64494e9i −0.0183974 0.0382026i
\(621\) −7.95863e10 + 6.34679e10i −0.535145 + 0.426764i
\(622\) 1.89414e11 + 1.51053e11i 1.26547 + 1.00918i
\(623\) −3.39135e10 + 1.63319e10i −0.225123 + 0.108414i
\(624\) −3.38801e10 7.03527e10i −0.223463 0.464026i
\(625\) 9.16323e10 1.14903e11i 0.600522 0.753030i
\(626\) −2.08780e11 2.61802e11i −1.35954 1.70481i
\(627\) −1.13830e10 + 5.48177e9i −0.0736524 + 0.0354691i
\(628\) −2.29574e11 5.23988e10i −1.47599 0.336886i
\(629\) −6.64770e10 1.51729e10i −0.424687 0.0969320i
\(630\) 3.16668e9 2.52534e9i 0.0201021 0.0160309i
\(631\) 5.66890e10 1.17716e11i 0.357587 0.742536i −0.642124 0.766601i \(-0.721946\pi\)
0.999710 + 0.0240646i \(0.00766075\pi\)
\(632\) 5.99108e10 1.36743e10i 0.375523 0.0857108i
\(633\) −9.30860e10 4.48279e10i −0.579788 0.279211i
\(634\) 3.39769e11 + 2.70957e11i 2.10294 + 1.67704i
\(635\) −7.77998e9 1.77573e9i −0.0478502 0.0109215i
\(636\) −1.46576e11 1.16891e11i −0.895849 0.714416i
\(637\) −3.49231e10 1.53008e11i −0.212107 0.929302i
\(638\) 7.28412e10 0.439637
\(639\) 3.55503e10i 0.213226i
\(640\) −2.25601e9 9.88421e9i −0.0134468 0.0589145i
\(641\) −9.16788e10 + 7.31114e10i −0.543046 + 0.433065i −0.856205 0.516636i \(-0.827184\pi\)
0.313159 + 0.949701i \(0.398613\pi\)
\(642\) 2.35590e11 1.13454e11i 1.38681 0.667852i
\(643\) 9.46155e10 + 4.55644e10i 0.553501 + 0.266552i 0.689658 0.724135i \(-0.257761\pi\)
−0.136157 + 0.990687i \(0.543475\pi\)
\(644\) 3.66751e10i 0.213220i
\(645\) −7.13024e9 1.01372e10i −0.0411970 0.0585707i
\(646\) −2.47342e10 −0.142026
\(647\) 5.47646e10 1.13720e11i 0.312523 0.648962i −0.684248 0.729249i \(-0.739870\pi\)
0.996772 + 0.0802876i \(0.0255839\pi\)
\(648\) 1.58214e9 + 3.28534e9i 0.00897314 + 0.0186329i
\(649\) −9.83602e10 1.23340e11i −0.554422 0.695223i
\(650\) −2.61067e11 + 5.95868e10i −1.46251 + 0.333808i
\(651\) 9.98496e9 0.0555933
\(652\) 3.09166e11i 1.71081i
\(653\) 1.09231e11 2.49313e10i 0.600750 0.137117i 0.0886790 0.996060i \(-0.471735\pi\)
0.512071 + 0.858943i \(0.328878\pi\)
\(654\) −5.57507e10 + 6.99092e10i −0.304747 + 0.382141i
\(655\) 1.45011e9 6.35333e9i 0.00787833 0.0345172i
\(656\) −4.68049e10 + 5.86915e10i −0.252741 + 0.316927i
\(657\) 1.71669e10 3.56475e10i 0.0921364 0.191323i
\(658\) −7.26249e9 3.18190e10i −0.0387420 0.169740i
\(659\) 3.68448e10 + 1.77435e10i 0.195359 + 0.0940801i 0.529006 0.848618i \(-0.322565\pi\)
−0.333647 + 0.942698i \(0.608279\pi\)
\(660\) −1.21665e10 1.52563e10i −0.0641194 0.0804032i
\(661\) −3.60332e10 + 1.57872e11i −0.188754 + 0.826986i 0.788520 + 0.615009i \(0.210847\pi\)
−0.977275 + 0.211977i \(0.932010\pi\)
\(662\) −8.28813e10 + 3.63127e11i −0.431544 + 1.89072i
\(663\) −5.08792e10 1.05652e11i −0.263321 0.546792i
\(664\) 3.47101e10 2.76804e10i 0.178560 0.142397i
\(665\) 4.76890e8 + 3.80307e8i 0.00243855 + 0.00194468i
\(666\) 7.27933e10 3.50554e10i 0.369994 0.178180i
\(667\) 1.41403e10 + 2.93627e10i 0.0714424 + 0.148352i
\(668\) 1.05210e11 1.31929e11i 0.528384 0.662572i
\(669\) −1.42293e11 1.78430e11i −0.710362 0.890765i
\(670\) 3.21260e9 1.54711e9i 0.0159426 0.00767753i
\(671\) 2.01367e11 + 4.59608e10i 0.993342 + 0.226724i
\(672\) 4.90419e10 + 1.11935e10i 0.240486 + 0.0548894i
\(673\) 2.23963e11 1.78604e11i 1.09173 0.870626i 0.0995003 0.995038i \(-0.468276\pi\)
0.992231 + 0.124411i \(0.0397041\pi\)
\(674\) 1.87292e11 3.88917e11i 0.907571 1.88459i
\(675\) −2.04207e11 + 4.66089e10i −0.983683 + 0.224519i
\(676\) 1.22168e10 + 5.88329e9i 0.0585019 + 0.0281730i
\(677\) 1.27180e11 + 1.01422e11i 0.605428 + 0.482813i 0.877573 0.479444i \(-0.159161\pi\)
−0.272145 + 0.962256i \(0.587733\pi\)
\(678\) 6.09814e10 + 1.39186e10i 0.288588 + 0.0658684i
\(679\) 6.67169e9 + 5.32050e9i 0.0313875 + 0.0250307i
\(680\) −1.34084e9 5.87462e9i −0.00627108 0.0274754i
\(681\) −1.60195e11 −0.744834
\(682\) 1.24477e11i 0.575376i
\(683\) −1.49391e10 6.54526e10i −0.0686503 0.300776i 0.928934 0.370246i \(-0.120727\pi\)
−0.997584 + 0.0694694i \(0.977869\pi\)
\(684\) 1.24378e10 9.91878e9i 0.0568221 0.0453141i
\(685\) −2.34553e10 + 1.12955e10i −0.106531 + 0.0513029i
\(686\) 1.52507e11 + 7.34435e10i 0.688642 + 0.331632i
\(687\) 2.48371e10i 0.111500i
\(688\) −4.89235e10 + 1.67229e11i −0.218355 + 0.746374i
\(689\) −3.46362e11 −1.53693
\(690\) 6.97864e9 1.44913e10i 0.0307875 0.0639309i
\(691\) −3.50442e10 7.27701e10i −0.153711 0.319184i 0.809866 0.586615i \(-0.199540\pi\)
−0.963577 + 0.267431i \(0.913825\pi\)
\(692\) 1.09548e11 + 1.37369e11i 0.477726 + 0.599050i
\(693\) −4.25844e10 + 9.71960e9i −0.184636 + 0.0421420i
\(694\) 3.32101e11 1.43163
\(695\) 2.15320e10i 0.0922881i
\(696\) 1.00417e10 2.29195e9i 0.0427926 0.00976714i
\(697\) −7.02890e10 + 8.81396e10i −0.297821 + 0.373456i
\(698\) 1.36195e10 5.96711e10i 0.0573773 0.251387i
\(699\) −1.30799e11 + 1.64016e11i −0.547891 + 0.687034i
\(700\) 3.27429e10 6.79913e10i 0.136372 0.283179i
\(701\) 9.93553e9 + 4.35304e10i 0.0411452 + 0.180269i 0.991325 0.131433i \(-0.0419580\pi\)
−0.950180 + 0.311702i \(0.899101\pi\)
\(702\) 3.39502e11 + 1.63496e11i 1.39796 + 0.673221i
\(703\) 7.58622e9 + 9.51282e9i 0.0310602 + 0.0389482i
\(704\) −8.81270e10 + 3.86109e11i −0.358772 + 1.57188i
\(705\) 1.72886e9 7.57462e9i 0.00699847 0.0306623i
\(706\) 2.80209e11 + 5.81859e11i 1.12788 + 2.34207i
\(707\) −3.36400e10 + 2.68270e10i −0.134641 + 0.107373i
\(708\) −1.10570e11 8.81770e10i −0.440054 0.350932i
\(709\) 1.49652e11 7.20687e10i 0.592240 0.285208i −0.113659 0.993520i \(-0.536257\pi\)
0.705900 + 0.708312i \(0.250543\pi\)
\(710\) 6.60955e9 + 1.37249e10i 0.0260099 + 0.0540101i
\(711\) 1.29437e11 1.62309e11i 0.506500 0.635131i
\(712\) −4.13706e10 5.18771e10i −0.160980 0.201862i
\(713\) −5.01774e10 + 2.41641e10i −0.194156 + 0.0935004i
\(714\) 5.93549e10 + 1.35474e10i 0.228383 + 0.0521269i
\(715\) −3.51470e10 8.02208e9i −0.134482 0.0306947i
\(716\) −2.25131e11 + 1.79536e11i −0.856609 + 0.683123i
\(717\) −1.10822e10 + 2.30124e10i −0.0419324 + 0.0870735i
\(718\) 4.62645e11 1.05596e11i 1.74081 0.397328i
\(719\) −5.36259e10 2.58249e10i −0.200659 0.0966323i 0.330856 0.943681i \(-0.392663\pi\)
−0.531515 + 0.847049i \(0.678377\pi\)
\(720\) −1.05979e10 8.45155e9i −0.0394357 0.0314490i
\(721\) 9.10613e10 + 2.07841e10i 0.336971 + 0.0769115i
\(722\) −3.10754e11 2.47818e11i −1.14359 0.911979i
\(723\) −1.23733e10 5.42111e10i −0.0452828 0.198397i
\(724\) 4.86572e10 0.177090
\(725\) 6.70592e10i 0.242721i
\(726\) 2.73085e10 + 1.19646e11i 0.0982994 + 0.430678i
\(727\) −1.75576e11 + 1.40017e11i −0.628531 + 0.501237i −0.885168 0.465271i \(-0.845957\pi\)
0.256637 + 0.966508i \(0.417386\pi\)
\(728\) −1.92934e10 + 9.29121e9i −0.0686884 + 0.0330786i
\(729\) 1.78736e11 + 8.60749e10i 0.632853 + 0.304766i
\(730\) 1.69541e10i 0.0597013i
\(731\) −7.34706e10 + 2.51134e11i −0.257303 + 0.879502i
\(732\) 1.85162e11 0.644924
\(733\) 1.53697e11 3.19156e11i 0.532415 1.10557i −0.445251 0.895406i \(-0.646886\pi\)
0.977666 0.210165i \(-0.0674001\pi\)
\(734\) 1.48436e11 + 3.08231e11i 0.511394 + 1.06192i
\(735\) 1.20938e10 + 1.51651e10i 0.0414394 + 0.0519633i
\(736\) −2.73539e11 + 6.24334e10i −0.932196 + 0.212768i
\(737\) −3.84534e10 −0.130336
\(738\) 1.33580e11i 0.450314i
\(739\) 1.54236e11 3.52034e10i 0.517140 0.118034i 0.0440180 0.999031i \(-0.485984\pi\)
0.473122 + 0.880997i \(0.343127\pi\)
\(740\) −1.17169e10 + 1.46926e10i −0.0390739 + 0.0489971i
\(741\) −4.65624e9 + 2.04003e10i −0.0154441 + 0.0676650i
\(742\) 1.12118e11 1.40592e11i 0.369881 0.463816i
\(743\) 1.36542e11 2.83532e11i 0.448034 0.930352i −0.547576 0.836756i \(-0.684449\pi\)
0.995610 0.0935961i \(-0.0298362\pi\)
\(744\) 3.91667e9 + 1.71600e10i 0.0127828 + 0.0560050i
\(745\) 1.93702e10 + 9.32819e9i 0.0628794 + 0.0302811i
\(746\) 1.03136e11 + 1.29329e11i 0.333009 + 0.417581i
\(747\) 3.33741e10 1.46221e11i 0.107183 0.469600i
\(748\) −9.16738e10 + 4.01649e11i −0.292846 + 1.28304i
\(749\) 5.90698e10 + 1.22660e11i 0.187689 + 0.389739i
\(750\) 5.20734e10 4.15271e10i 0.164578 0.131246i
\(751\) −2.13722e11 1.70437e11i −0.671875 0.535802i 0.227062 0.973880i \(-0.427088\pi\)
−0.898937 + 0.438078i \(0.855659\pi\)
\(752\) −9.84103e10 + 4.73919e10i −0.307729 + 0.148195i
\(753\) −1.00340e11 2.08358e11i −0.312101 0.648084i
\(754\) 7.52182e10 9.43207e10i 0.232722 0.291824i
\(755\) 1.61401e10 + 2.02391e10i 0.0496728 + 0.0622877i
\(756\) −9.56769e10 + 4.60755e10i −0.292900 + 0.141053i
\(757\) 3.21886e11 + 7.34685e10i 0.980210 + 0.223726i 0.682464 0.730919i \(-0.260908\pi\)
0.297745 + 0.954645i \(0.403765\pi\)
\(758\) −4.41420e11 1.00751e11i −1.33713 0.305192i
\(759\) −1.35612e11 + 1.08147e11i −0.408630 + 0.325872i
\(760\) −4.66528e8 + 9.68756e8i −0.00139838 + 0.00290376i
\(761\) 2.76111e11 6.30205e10i 0.823275 0.187907i 0.209924 0.977718i \(-0.432678\pi\)
0.613351 + 0.789810i \(0.289821\pi\)
\(762\) 1.28054e11 + 6.16674e10i 0.379815 + 0.182909i
\(763\) −3.63981e10 2.90265e10i −0.107394 0.0856440i
\(764\) −7.56449e11 1.72655e11i −2.22027 0.506763i
\(765\) −1.59153e10 1.26921e10i −0.0464697 0.0370584i
\(766\) 1.18150e11 + 5.17651e11i 0.343179 + 1.50356i
\(767\) −2.61280e11 −0.754962
\(768\) 1.18467e11i 0.340527i
\(769\) −8.94179e9 3.91765e10i −0.0255693 0.112026i 0.960533 0.278167i \(-0.0897267\pi\)
−0.986102 + 0.166140i \(0.946870\pi\)
\(770\) 1.46334e10 1.16698e10i 0.0416278 0.0331971i
\(771\) 1.98223e11 9.54591e10i 0.560965 0.270147i
\(772\) 3.18310e11 + 1.53290e11i 0.896150 + 0.431563i
\(773\) 4.89235e10i 0.137025i 0.997650 + 0.0685124i \(0.0218253\pi\)
−0.997650 + 0.0685124i \(0.978175\pi\)
\(774\) −1.17469e11 2.86928e11i −0.327310 0.799482i
\(775\) −1.14596e11 −0.317661
\(776\) −6.52673e9 + 1.35529e10i −0.0179990 + 0.0373753i
\(777\) −1.29943e10 2.69830e10i −0.0356509 0.0740299i
\(778\) −2.60170e11 3.26243e11i −0.710132 0.890477i
\(779\) 1.96123e10 4.47637e9i 0.0532571 0.0121556i
\(780\) −3.23186e10 −0.0873120
\(781\) 1.64280e11i 0.441552i
\(782\) −3.31061e11 + 7.55625e10i −0.885281 + 0.202060i
\(783\) 5.88358e10 7.37777e10i 0.156529 0.196281i
\(784\) 6.06801e10 2.65857e11i 0.160613 0.703693i
\(785\) 3.35236e10 4.20373e10i 0.0882821 0.110702i
\(786\) −5.03591e10 + 1.04572e11i −0.131943 + 0.273983i
\(787\) 5.32324e10 + 2.33227e11i 0.138764 + 0.607966i 0.995708 + 0.0925551i \(0.0295034\pi\)
−0.856943 + 0.515411i \(0.827639\pi\)
\(788\) −1.88418e11 9.07375e10i −0.488673 0.235332i
\(789\) 1.83279e10 + 2.29824e10i 0.0472938 + 0.0593046i
\(790\) −1.97950e10 + 8.67274e10i −0.0508214 + 0.222663i
\(791\) −7.24670e9 + 3.17499e10i −0.0185112 + 0.0811029i
\(792\) −3.34080e10 6.93724e10i −0.0849082 0.176314i
\(793\) 2.67452e11 2.13286e11i 0.676322 0.539348i
\(794\) −8.93747e11 7.12739e11i −2.24870 1.79328i
\(795\) 3.85684e10 1.85736e10i 0.0965524 0.0464972i
\(796\) −3.54307e11 7.35726e11i −0.882526 1.83258i
\(797\) 2.86025e11 3.58664e11i 0.708876 0.888903i −0.288775 0.957397i \(-0.593248\pi\)
0.997652 + 0.0684940i \(0.0218194\pi\)
\(798\) −6.77346e9 8.49365e9i −0.0167032 0.0209451i
\(799\) −1.47787e11 + 7.11705e10i −0.362618 + 0.174628i
\(800\) −5.62848e11 1.28466e11i −1.37414 0.313639i
\(801\) −2.18540e11 4.98803e10i −0.530885 0.121171i
\(802\) −2.46580e10 + 1.96641e10i −0.0596020 + 0.0475310i
\(803\) 7.93296e10 1.64730e11i 0.190798 0.396196i
\(804\) −3.36080e10 + 7.67082e9i −0.0804302 + 0.0183577i
\(805\) 7.54487e9 + 3.63342e9i 0.0179667 + 0.00865231i
\(806\) 1.61183e11 + 1.28539e11i 0.381926 + 0.304576i
\(807\) −3.78242e11 8.63312e10i −0.891816 0.203551i
\(808\) −5.93000e10 4.72902e10i −0.139126 0.110950i
\(809\) 1.35154e11 + 5.92149e11i 0.315526 + 1.38241i 0.845310 + 0.534277i \(0.179416\pi\)
−0.529784 + 0.848133i \(0.677727\pi\)
\(810\) −5.27864e9 −0.0122626
\(811\) 3.91067e11i 0.903998i 0.892018 + 0.451999i \(0.149289\pi\)
−0.892018 + 0.451999i \(0.850711\pi\)
\(812\) 7.56535e9 + 3.31460e10i 0.0174022 + 0.0762441i
\(813\) 3.01730e11 2.40621e11i 0.690646 0.550772i
\(814\) 3.36383e11 1.61993e11i 0.766190 0.368978i
\(815\) 6.36023e10 + 3.06293e10i 0.144159 + 0.0694234i
\(816\) 2.03751e11i 0.459557i
\(817\) 3.81904e10 2.68621e10i 0.0857169 0.0602908i
\(818\) −5.96393e11 −1.33205
\(819\) −3.13883e10 + 6.51785e10i −0.0697641 + 0.144867i
\(820\) 1.34808e10 + 2.79933e10i 0.0298168 + 0.0619153i
\(821\) −1.30554e11 1.63710e11i −0.287355 0.360331i 0.617112 0.786875i \(-0.288302\pi\)
−0.904467 + 0.426544i \(0.859731\pi\)
\(822\) 4.52042e11 1.03176e11i 0.990129 0.225990i
\(823\) 4.91157e11 1.07058 0.535292 0.844667i \(-0.320201\pi\)
0.535292 + 0.844667i \(0.320201\pi\)
\(824\) 1.64650e11i 0.357151i
\(825\) −3.47960e11 + 7.94196e10i −0.751128 + 0.171440i
\(826\) 8.45771e10 1.06056e11i 0.181691 0.227833i
\(827\) −1.22242e11 + 5.35575e11i −0.261335 + 1.14498i 0.658471 + 0.752606i \(0.271204\pi\)
−0.919805 + 0.392375i \(0.871653\pi\)
\(828\) 1.36174e11 1.70757e11i 0.289717 0.363293i
\(829\) 2.06093e11 4.27957e11i 0.436360 0.906112i −0.560591 0.828093i \(-0.689426\pi\)
0.996952 0.0780192i \(-0.0248595\pi\)
\(830\) 1.43009e10 + 6.26565e10i 0.0301337 + 0.132024i
\(831\) −2.33520e11 1.12458e11i −0.489690 0.235822i
\(832\) 4.08963e11 + 5.12823e11i 0.853474 + 1.07022i
\(833\) 9.11260e10 3.99249e11i 0.189261 0.829209i
\(834\) −8.53359e10 + 3.73881e11i −0.176387 + 0.772804i
\(835\) 1.67175e10 + 3.47142e10i 0.0343894 + 0.0714103i
\(836\) 5.74757e10 4.58354e10i 0.117668 0.0938373i
\(837\) 1.26077e11 + 1.00543e11i 0.256883 + 0.204858i
\(838\) −5.87937e10 + 2.83135e10i −0.119221 + 0.0574140i
\(839\) 2.99384e11 + 6.21677e11i 0.604200 + 1.25463i 0.948798 + 0.315884i \(0.102301\pi\)
−0.344598 + 0.938750i \(0.611985\pi\)
\(840\) 1.65013e9 2.06920e9i 0.00331438 0.00415610i
\(841\) 2.93062e11 + 3.67488e11i 0.585835 + 0.734614i
\(842\) 8.55204e11 4.11845e11i 1.70146 0.819379i
\(843\) −2.14940e11 4.90587e10i −0.425605 0.0971416i
\(844\) 5.86099e11 + 1.33773e11i 1.15505 + 0.263633i
\(845\) −2.42065e9 + 1.93040e9i −0.00474793 + 0.00378635i
\(846\) 8.43301e10 1.75113e11i 0.164627 0.341852i
\(847\) −6.22936e10 + 1.42181e10i −0.121035 + 0.0276254i
\(848\) −5.42218e11 2.61118e11i −1.04855 0.504956i
\(849\) 4.09352e11 + 3.26448e11i 0.787892 + 0.628323i
\(850\) −6.81210e11 1.55482e11i −1.30498 0.297854i
\(851\) 1.30601e11 + 1.04151e11i 0.249016 + 0.198584i
\(852\) −3.27712e10 1.43580e11i −0.0621920 0.272481i
\(853\) −2.48957e11 −0.470250 −0.235125 0.971965i \(-0.575550\pi\)
−0.235125 + 0.971965i \(0.575550\pi\)
\(854\) 1.77603e11i 0.333902i
\(855\) 8.08297e8 + 3.54138e9i 0.00151254 + 0.00662687i
\(856\) −1.87631e11 + 1.49631e11i −0.349470 + 0.278693i
\(857\) −2.09091e11 + 1.00693e11i −0.387626 + 0.186671i −0.617539 0.786540i \(-0.711870\pi\)
0.229913 + 0.973211i \(0.426156\pi\)
\(858\) 5.78498e11 + 2.78590e11i 1.06746 + 0.514063i
\(859\) 3.29096e11i 0.604436i 0.953239 + 0.302218i \(0.0977271\pi\)
−0.953239 + 0.302218i \(0.902273\pi\)
\(860\) 5.35738e10 + 4.82742e10i 0.0979396 + 0.0882514i
\(861\) −4.95154e10 −0.0901006
\(862\) 2.81826e10 5.85218e10i 0.0510449 0.105996i
\(863\) 3.05010e11 + 6.33359e11i 0.549883 + 1.14184i 0.971930 + 0.235270i \(0.0755975\pi\)
−0.422047 + 0.906574i \(0.638688\pi\)
\(864\) 5.06526e11 + 6.35164e11i 0.908964 + 1.13981i
\(865\) −3.91127e10 + 8.92723e9i −0.0698640 + 0.0159460i
\(866\) −1.45308e12 −2.58355
\(867\) 5.84002e10i 0.103356i
\(868\) −5.66425e10 + 1.29283e10i −0.0997847 + 0.0227752i
\(869\) 5.98137e11 7.50040e11i 1.04887 1.31524i
\(870\) −3.31784e9 + 1.45364e10i −0.00579133 + 0.0253735i
\(871\) −3.97082e10 + 4.97925e10i −0.0689934 + 0.0865150i
\(872\) 3.56073e10 7.39393e10i 0.0615847 0.127882i
\(873\) 1.13081e10 + 4.95439e10i 0.0194685 + 0.0852969i
\(874\) 5.45937e10 + 2.62910e10i 0.0935615 + 0.0450568i
\(875\) 2.16210e10 + 2.71119e10i 0.0368845 + 0.0462517i
\(876\) 3.64728e10 1.59798e11i 0.0619374 0.271365i
\(877\) −2.11543e10 + 9.26831e10i −0.0357603 + 0.156676i −0.989656 0.143463i \(-0.954176\pi\)
0.953895 + 0.300139i \(0.0970332\pi\)
\(878\) 1.50615e11 + 3.12756e11i 0.253449 + 0.526293i
\(879\) −3.95565e11 + 3.15453e11i −0.662617 + 0.528419i
\(880\) −4.89737e10 3.90552e10i −0.0816642 0.0651251i
\(881\) −5.36826e11 + 2.58522e11i −0.891107 + 0.429135i −0.822669 0.568521i \(-0.807516\pi\)
−0.0684383 + 0.997655i \(0.521802\pi\)
\(882\) 2.10537e11 + 4.37184e11i 0.347899 + 0.722420i
\(883\) −3.82564e11 + 4.79720e11i −0.629305 + 0.789124i −0.989620 0.143707i \(-0.954098\pi\)
0.360315 + 0.932831i \(0.382669\pi\)
\(884\) 4.25422e11 + 5.33462e11i 0.696644 + 0.873564i
\(885\) 2.90943e10 1.40111e10i 0.0474279 0.0228401i
\(886\) −3.71112e11 8.47039e10i −0.602241 0.137458i
\(887\) 9.99824e10 + 2.28203e10i 0.161521 + 0.0368661i 0.302517 0.953144i \(-0.402173\pi\)
−0.140996 + 0.990010i \(0.545030\pi\)
\(888\) 4.12756e10 3.29162e10i 0.0663807 0.0529369i
\(889\) −3.21070e10 + 6.66709e10i −0.0514035 + 0.106741i
\(890\) 9.36453e10 2.13739e10i 0.149254 0.0340663i
\(891\) 5.12884e10 + 2.46992e10i 0.0813782 + 0.0391897i
\(892\) 1.03823e12 + 8.27957e11i 1.63996 + 1.30782i
\(893\) 2.85362e10 + 6.51321e9i 0.0448736 + 0.0102421i
\(894\) −2.99373e11 2.38742e11i −0.468665 0.373748i
\(895\) −1.46307e10 6.41011e10i −0.0228019 0.0999018i
\(896\) −9.40134e10 −0.145867
\(897\) 2.87277e11i 0.443743i
\(898\) −1.39888e11 6.12889e11i −0.215117 0.942489i
\(899\) 4.03644e10 3.21895e10i 0.0617959 0.0492806i
\(900\) 4.04900e11 1.94990e11i 0.617132 0.297195i
\(901\) −8.14272e11 3.92133e11i −1.23558 0.595023i
\(902\) 6.17282e11i 0.932518i
\(903\) −1.06359e11 + 4.35435e10i −0.159964 + 0.0654896i
\(904\) −5.74075e10 −0.0859598
\(905\) −4.82050e9 + 1.00099e10i −0.00718618 + 0.0149222i
\(906\) −2.00045e11 4.15397e11i −0.296902 0.616524i
\(907\) 3.32462e11 + 4.16895e11i 0.491262 + 0.616023i 0.964233 0.265054i \(-0.0853899\pi\)
−0.472971 + 0.881078i \(0.656819\pi\)
\(908\) 9.08749e11 2.07416e11i 1.33691 0.305140i
\(909\) −2.56234e11 −0.375303
\(910\) 3.09992e10i 0.0452048i
\(911\) −2.44729e11 + 5.58579e10i −0.355314 + 0.0810982i −0.396452 0.918055i \(-0.629759\pi\)
0.0411380 + 0.999153i \(0.486902\pi\)
\(912\) −2.26687e10 + 2.84257e10i −0.0327678 + 0.0410895i
\(913\) 1.54224e11 6.75699e11i 0.221957 0.972456i
\(914\) 9.20573e11 1.15436e12i 1.31909 1.65408i
\(915\) −1.83441e10 + 3.80920e10i −0.0261706 + 0.0543437i
\(916\) 3.21584e10 + 1.40895e11i 0.0456786 + 0.200131i
\(917\) −5.44451e10 2.62194e10i −0.0769984 0.0370805i
\(918\) 6.13044e11 + 7.68732e11i 0.863218 + 1.08244i
\(919\) 1.66005e11 7.27317e11i 0.232734 1.01967i −0.714627 0.699506i \(-0.753403\pi\)
0.947361 0.320169i \(-0.103740\pi\)
\(920\) −3.28483e9 + 1.43918e10i −0.00458523 + 0.0200892i
\(921\) 3.56501e10 + 7.40283e10i 0.0495476 + 0.102887i
\(922\) 9.34019e11 7.44855e11i 1.29250 1.03074i
\(923\) −2.12723e11 1.69641e11i −0.293095 0.233736i
\(924\) −1.63030e11 + 7.85109e10i −0.223655 + 0.107707i
\(925\) 1.49135e11 + 3.09682e11i 0.203710 + 0.423008i
\(926\) 5.34975e10 6.70838e10i 0.0727595 0.0912376i
\(927\) 3.46805e11 + 4.34880e11i 0.469642 + 0.588912i
\(928\) 2.34338e11 1.12851e11i 0.315974 0.152165i
\(929\) −1.51632e11 3.46090e10i −0.203577 0.0464650i 0.119517 0.992832i \(-0.461866\pi\)
−0.323093 + 0.946367i \(0.604723\pi\)
\(930\) −2.48410e10 5.66980e9i −0.0332076 0.00757942i
\(931\) −5.71323e10 + 4.55615e10i −0.0760472 + 0.0606456i
\(932\) 5.29628e11 1.09978e12i 0.701952 1.45762i
\(933\) 5.21394e11 1.19005e11i 0.688081 0.157050i
\(934\) 4.63452e11 + 2.23187e11i 0.608999 + 0.293279i
\(935\) −7.35459e10 5.86509e10i −0.0962304 0.0767412i
\(936\) −1.24327e11 2.83769e10i −0.161981 0.0369710i
\(937\) −6.53385e11 5.21057e11i −0.847639 0.675969i 0.100114 0.994976i \(-0.468079\pi\)
−0.947752 + 0.319007i \(0.896651\pi\)
\(938\) −7.35765e9 3.22360e10i −0.00950447 0.0416418i
\(939\) −7.39187e11 −0.950806
\(940\) 4.52077e10i 0.0579030i
\(941\) 2.52265e11 + 1.10524e12i 0.321735 + 1.40961i 0.834464 + 0.551062i \(0.185777\pi\)
−0.512729 + 0.858550i \(0.671365\pi\)
\(942\) −7.48705e11 + 5.97073e11i −0.950840 + 0.758269i
\(943\) 2.48829e11 1.19830e11i 0.314670 0.151537i
\(944\) −4.09025e11 1.96976e11i −0.515064 0.248042i
\(945\) 2.42476e10i 0.0304047i
\(946\) −5.42833e11 1.32591e12i −0.677800 1.65558i
\(947\) 1.16727e11 0.145135 0.0725675 0.997364i \(-0.476881\pi\)
0.0725675 + 0.997364i \(0.476881\pi\)
\(948\) 3.73148e11 7.74849e11i 0.462006 0.959365i
\(949\) −1.31387e11 2.72828e11i −0.161990 0.336375i
\(950\) 7.77383e10 + 9.74807e10i 0.0954422 + 0.119681i
\(951\) 9.35273e11 2.13470e11i 1.14345 0.260984i
\(952\) −5.58763e10 −0.0680268
\(953\) 6.43444e11i 0.780080i −0.920798 0.390040i \(-0.872461\pi\)
0.920798 0.390040i \(-0.127539\pi\)
\(954\) 1.04404e12 2.38294e11i 1.26044 0.287687i
\(955\) 1.10461e11 1.38513e11i 0.132799 0.166525i
\(956\) 3.30710e10 1.44894e11i 0.0395928 0.173467i
\(957\) 1.00254e11 1.25714e11i 0.119524 0.149878i
\(958\) −4.80282e11 + 9.97316e11i −0.570209 + 1.18405i
\(959\) 5.37183e10 + 2.35355e11i 0.0635108 + 0.278259i
\(960\) −7.30391e10 3.51738e10i −0.0859945 0.0414127i
\(961\) −4.76761e11 5.97839e11i −0.558994 0.700956i
\(962\) 1.37598e11 6.02855e11i 0.160661 0.703903i
\(963\) −1.80409e11 + 7.90423e11i −0.209774 + 0.919082i
\(964\) 1.40383e11 + 2.91507e11i 0.162557 + 0.337553i
\(965\) −6.30703e10 + 5.02969e10i −0.0727303 + 0.0580005i
\(966\) −1.16609e11 9.29924e10i −0.133913 0.106792i
\(967\) −1.53225e12 + 7.37894e11i −1.75237 + 0.843895i −0.775110 + 0.631826i \(0.782306\pi\)
−0.977255 + 0.212069i \(0.931980\pi\)
\(968\) −4.88702e10 1.01480e11i −0.0556599 0.115579i
\(969\) −3.40426e10 + 4.26881e10i −0.0386125 + 0.0484185i
\(970\) −1.35770e10 1.70250e10i −0.0153361 0.0192309i
\(971\) −6.54284e11 + 3.15087e11i −0.736020 + 0.354449i −0.764049 0.645159i \(-0.776791\pi\)
0.0280287 + 0.999607i \(0.491077\pi\)
\(972\) −1.00575e12 2.29555e11i −1.12674 0.257171i
\(973\) −1.94661e11 4.44300e10i −0.217183 0.0495707i
\(974\) −1.92284e12 + 1.53342e12i −2.13653 + 1.70382i
\(975\) −2.56476e11 + 5.32578e11i −0.283811 + 0.589339i
\(976\) 5.79480e11 1.32263e11i 0.638615 0.145760i
\(977\) 1.07327e12 + 5.16858e11i 1.17796 + 0.567274i 0.917315 0.398161i \(-0.130352\pi\)
0.260642 + 0.965436i \(0.416066\pi\)
\(978\) −9.82997e11 7.83914e11i −1.07448 0.856866i
\(979\) −1.00989e12 2.30500e11i −1.09937 0.250923i
\(980\) −8.82410e10 7.03698e10i −0.0956678 0.0762925i
\(981\) −6.16924e10 2.70292e11i −0.0666125 0.291848i
\(982\) −1.22819e12 −1.32075
\(983\) 1.51360e12i 1.62106i 0.585699 + 0.810529i \(0.300820\pi\)
−0.585699 + 0.810529i \(0.699180\pi\)
\(984\) −1.94227e10 8.50966e10i −0.0207172 0.0907678i
\(985\) 3.73334e10 2.97724e10i 0.0396600 0.0316278i
\(986\) 2.83617e11 1.36583e11i 0.300072 0.144507i
\(987\) −6.49111e10 3.12595e10i −0.0683991 0.0329393i
\(988\) 1.21755e11i 0.127779i
\(989\) 4.29105e11 4.76212e11i 0.448517 0.497755i
\(990\) 1.11462e11 0.116035
\(991\) −1.53102e11 + 3.17919e11i −0.158740 + 0.329627i −0.965136 0.261749i \(-0.915701\pi\)
0.806396 + 0.591376i \(0.201415\pi\)
\(992\) 1.92850e11 + 4.00457e11i 0.199146 + 0.413532i
\(993\) 5.12637e11 + 6.42826e11i 0.527245 + 0.661145i
\(994\) 1.37718e11 3.14333e10i 0.141074 0.0321992i
\(995\) 1.86457e11 0.190233
\(996\) 6.21322e11i 0.631364i
\(997\) 6.98765e11 1.59488e11i 0.707213 0.161417i 0.146238 0.989249i \(-0.453283\pi\)
0.560975 + 0.827833i \(0.310426\pi\)
\(998\) −6.92839e11 + 8.68793e11i −0.698410 + 0.875778i
\(999\) 1.07629e11 4.71554e11i 0.108061 0.473445i
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.22.5 yes 174
43.2 odd 14 inner 43.9.f.a.2.5 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.9.f.a.2.5 174 43.2 odd 14 inner
43.9.f.a.22.5 yes 174 1.1 even 1 trivial