Properties

Label 22.14.c.b.5.2
Level $22$
Weight $14$
Character 22.5
Analytic conductor $23.591$
Analytic rank $0$
Dimension $28$
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] = [22,14,Mod(3,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.3");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 22.c (of order \(5\), degree \(4\), 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: \(23.5908043694\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 5.2
Character \(\chi\) \(=\) 22.5
Dual form 22.14.c.b.9.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(19.7771 + 60.8676i) q^{2} +(-1229.94 - 893.604i) q^{3} +(-3313.73 + 2407.57i) q^{4} +(-7708.37 + 23723.9i) q^{5} +(30066.9 - 92536.4i) q^{6} +(-267598. + 194422. i) q^{7} +(-212079. - 154084. i) q^{8} +(221552. + 681866. i) q^{9} +O(q^{10})\) \(q+(19.7771 + 60.8676i) q^{2} +(-1229.94 - 893.604i) q^{3} +(-3313.73 + 2407.57i) q^{4} +(-7708.37 + 23723.9i) q^{5} +(30066.9 - 92536.4i) q^{6} +(-267598. + 194422. i) q^{7} +(-212079. - 154084. i) q^{8} +(221552. + 681866. i) q^{9} -1.59647e6 q^{10} +(-5.21632e6 + 2.70420e6i) q^{11} +6.22711e6 q^{12} +(4.79624e6 + 1.47613e7i) q^{13} +(-1.71263e7 - 1.24430e7i) q^{14} +(3.06806e7 - 2.22908e7i) q^{15} +(5.18444e6 - 1.59561e7i) q^{16} +(5.28249e7 - 1.62578e8i) q^{17} +(-3.71219e7 + 2.69707e7i) q^{18} +(-1.95731e8 - 1.42207e8i) q^{19} +(-3.15735e7 - 9.71732e7i) q^{20} +5.02866e8 q^{21} +(-2.67762e8 - 2.64024e8i) q^{22} +1.15203e9 q^{23} +(1.23154e8 + 3.79029e8i) q^{24} +(4.84164e8 + 3.51765e8i) q^{25} +(-8.03630e8 + 5.83871e8i) q^{26} +(-4.12182e8 + 1.26857e9i) q^{27} +(4.18667e8 - 1.28852e9i) q^{28} +(1.85581e9 - 1.34832e9i) q^{29} +(1.96356e9 + 1.42661e9i) q^{30} +(-6.47809e8 - 1.99375e9i) q^{31} +1.07374e9 q^{32} +(8.83225e9 + 1.33532e9i) q^{33} +1.09405e10 q^{34} +(-2.54970e9 - 7.84716e9i) q^{35} +(-2.37580e9 - 1.72612e9i) q^{36} +(7.81308e9 - 5.67653e9i) q^{37} +(4.78481e9 - 1.47261e10i) q^{38} +(7.29167e9 - 2.24415e10i) q^{39} +(5.29027e9 - 3.84361e9i) q^{40} +(-2.65937e10 - 1.93215e10i) q^{41} +(9.94522e9 + 3.06082e10i) q^{42} -1.78290e10 q^{43} +(1.07749e10 - 2.15197e10i) q^{44} -1.78844e10 q^{45} +(2.27838e10 + 7.01215e10i) q^{46} +(7.52930e10 + 5.47036e10i) q^{47} +(-2.06350e10 + 1.49922e10i) q^{48} +(3.86880e9 - 1.19069e10i) q^{49} +(-1.18358e10 + 3.64268e10i) q^{50} +(-2.10252e11 + 1.52757e11i) q^{51} +(-5.14323e10 - 3.73678e10i) q^{52} +(-7.04618e10 - 2.16859e11i) q^{53} -8.53664e10 q^{54} +(-2.39450e10 - 1.44597e11i) q^{55} +8.67093e10 q^{56} +(1.13661e11 + 3.49812e11i) q^{57} +(1.18772e11 + 8.62928e10i) q^{58} +(-2.73551e11 + 1.98746e11i) q^{59} +(-4.80009e10 + 1.47731e11i) q^{60} +(9.09885e10 - 2.80034e11i) q^{61} +(1.08543e11 - 7.88612e10i) q^{62} +(-1.91857e11 - 1.39392e11i) q^{63} +(2.12355e10 + 6.53561e10i) q^{64} -3.87167e11 q^{65} +(9.33985e10 + 5.64006e11i) q^{66} -2.87516e11 q^{67} +(2.16371e11 + 6.65921e11i) q^{68} +(-1.41693e12 - 1.02946e12i) q^{69} +(4.27212e11 - 3.10388e11i) q^{70} +(-4.25237e10 + 1.30875e11i) q^{71} +(5.80785e10 - 1.78747e11i) q^{72} +(5.33049e11 - 3.87282e11i) q^{73} +(5.00037e11 + 3.63298e11i) q^{74} +(-2.81153e11 - 8.65301e11i) q^{75} +9.90974e11 q^{76} +(8.70124e11 - 1.73781e12i) q^{77} +1.51017e12 q^{78} +(4.76487e11 + 1.46648e12i) q^{79} +(3.38577e11 + 2.45991e11i) q^{80} +(2.56531e12 - 1.86381e12i) q^{81} +(6.50106e11 - 2.00082e12i) q^{82} +(-2.56950e11 + 7.90810e11i) q^{83} +(-1.66636e12 + 1.21068e12i) q^{84} +(3.44981e12 + 2.50643e12i) q^{85} +(-3.52606e11 - 1.08521e12i) q^{86} -3.48740e12 q^{87} +(1.52295e12 + 2.30249e11i) q^{88} +5.20758e12 q^{89} +(-3.53701e11 - 1.08858e12i) q^{90} +(-4.15338e12 - 3.01761e12i) q^{91} +(-3.81753e12 + 2.77360e12i) q^{92} +(-9.84857e11 + 3.03108e12i) q^{93} +(-1.84060e12 + 5.66479e12i) q^{94} +(4.88248e12 - 3.54733e12i) q^{95} +(-1.32064e12 - 9.59500e11i) q^{96} +(9.27788e11 + 2.85544e12i) q^{97} +8.01260e11 q^{98} +(-2.99959e12 - 2.95771e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 448 q^{2} - 1248 q^{3} - 28672 q^{4} + 71554 q^{5} + 99008 q^{6} + 361734 q^{7} - 1835008 q^{8} - 8615367 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 448 q^{2} - 1248 q^{3} - 28672 q^{4} + 71554 q^{5} + 99008 q^{6} + 361734 q^{7} - 1835008 q^{8} - 8615367 q^{9} + 2898176 q^{10} + 8699239 q^{11} - 2449408 q^{12} + 32373940 q^{13} + 23150976 q^{14} - 192099788 q^{15} - 117440512 q^{16} + 288881082 q^{17} - 275612928 q^{18} - 98588517 q^{19} + 293085184 q^{20} + 1362925660 q^{21} - 44352704 q^{22} - 233099500 q^{23} + 405536768 q^{24} + 1117600307 q^{25} - 2827224960 q^{26} + 3575804241 q^{27} - 1485029376 q^{28} - 16868227562 q^{29} - 12294386432 q^{30} - 10874790260 q^{31} + 30064771072 q^{32} + 53369498501 q^{33} + 6456111488 q^{34} + 18823205444 q^{35} - 17639227392 q^{36} + 47951509642 q^{37} + 14611374592 q^{38} - 161088016778 q^{39} - 24692916224 q^{40} - 155498856970 q^{41} - 47678239360 q^{42} + 156723459918 q^{43} + 31490678784 q^{44} + 75277819092 q^{45} + 46604369920 q^{46} + 394942115908 q^{47} - 20937965568 q^{48} - 10631171627 q^{49} - 421539129152 q^{50} - 468879528009 q^{51} - 180942397440 q^{52} + 608978721416 q^{53} + 286529794304 q^{54} + 82053078738 q^{55} + 430964736 q^{56} - 655027400217 q^{57} - 1079566563968 q^{58} + 381384884765 q^{59} + 528673062912 q^{60} + 1151615204532 q^{61} - 101484696320 q^{62} + 5117893076470 q^{63} - 481036337152 q^{64} - 5194662408432 q^{65} - 2892007512576 q^{66} + 833522448542 q^{67} + 1183256911872 q^{68} - 4423665001426 q^{69} + 835597274496 q^{70} + 3476544683262 q^{71} - 2258466766848 q^{72} - 3737607886538 q^{73} + 3068896617088 q^{74} + 9622942863695 q^{75} - 1062618816512 q^{76} - 4431389843152 q^{77} - 2335610564352 q^{78} + 7224103591056 q^{79} - 1580346638336 q^{80} - 9164585352662 q^{81} + 1269347381440 q^{82} + 9607066728079 q^{83} + 260135567360 q^{84} + 25585834186966 q^{85} - 3541381155008 q^{86} - 34193079605396 q^{87} - 4585813704704 q^{88} + 19963863911122 q^{89} + 15393877925888 q^{90} - 11356103019586 q^{91} - 2505291898880 q^{92} + 6475155937894 q^{93} - 39623598881408 q^{94} - 51625880722484 q^{95} - 1340029796352 q^{96} + 4169205798475 q^{97} + 38124564609792 q^{98} + 71382923151637 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).

\(n\) \(13\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 19.7771 + 60.8676i 0.218508 + 0.672499i
\(3\) −1229.94 893.604i −0.974083 0.707712i −0.0177042 0.999843i \(-0.505636\pi\)
−0.956378 + 0.292131i \(0.905636\pi\)
\(4\) −3313.73 + 2407.57i −0.404508 + 0.293893i
\(5\) −7708.37 + 23723.9i −0.220627 + 0.679019i 0.778080 + 0.628166i \(0.216194\pi\)
−0.998706 + 0.0508530i \(0.983806\pi\)
\(6\) 30066.9 92536.4i 0.263091 0.809710i
\(7\) −267598. + 194422.i −0.859699 + 0.624608i −0.927803 0.373070i \(-0.878305\pi\)
0.0681042 + 0.997678i \(0.478305\pi\)
\(8\) −212079. 154084.i −0.286031 0.207813i
\(9\) 221552. + 681866.i 0.138963 + 0.427684i
\(10\) −1.59647e6 −0.504848
\(11\) −5.21632e6 + 2.70420e6i −0.887793 + 0.460242i
\(12\) 6.22711e6 0.602016
\(13\) 4.79624e6 + 1.47613e7i 0.275594 + 0.848190i 0.989062 + 0.147502i \(0.0471233\pi\)
−0.713468 + 0.700688i \(0.752877\pi\)
\(14\) −1.71263e7 1.24430e7i −0.607899 0.441664i
\(15\) 3.06806e7 2.22908e7i 0.695458 0.505280i
\(16\) 5.18444e6 1.59561e7i 0.0772542 0.237764i
\(17\) 5.28249e7 1.62578e8i 0.530788 1.63360i −0.221790 0.975094i \(-0.571190\pi\)
0.752578 0.658503i \(-0.228810\pi\)
\(18\) −3.71219e7 + 2.69707e7i −0.257252 + 0.186905i
\(19\) −1.95731e8 1.42207e8i −0.954468 0.693462i −0.00260886 0.999997i \(-0.500830\pi\)
−0.951859 + 0.306535i \(0.900830\pi\)
\(20\) −3.15735e7 9.71732e7i −0.110313 0.339509i
\(21\) 5.02866e8 1.27946
\(22\) −2.67762e8 2.64024e8i −0.503502 0.496473i
\(23\) 1.15203e9 1.62268 0.811342 0.584572i \(-0.198738\pi\)
0.811342 + 0.584572i \(0.198738\pi\)
\(24\) 1.23154e8 + 3.79029e8i 0.131545 + 0.404855i
\(25\) 4.84164e8 + 3.51765e8i 0.396627 + 0.288166i
\(26\) −8.03630e8 + 5.83871e8i −0.510187 + 0.370672i
\(27\) −4.12182e8 + 1.26857e9i −0.204751 + 0.630157i
\(28\) 4.18667e8 1.28852e9i 0.164188 0.505318i
\(29\) 1.85581e9 1.34832e9i 0.579357 0.420928i −0.259135 0.965841i \(-0.583438\pi\)
0.838492 + 0.544913i \(0.183438\pi\)
\(30\) 1.96356e9 + 1.42661e9i 0.491763 + 0.357287i
\(31\) −6.47809e8 1.99375e9i −0.131098 0.403478i 0.863865 0.503724i \(-0.168037\pi\)
−0.994963 + 0.100246i \(0.968037\pi\)
\(32\) 1.07374e9 0.176777
\(33\) 8.83225e9 + 1.33532e9i 1.19050 + 0.179988i
\(34\) 1.09405e10 1.21457
\(35\) −2.54970e9 7.84716e9i −0.234448 0.721556i
\(36\) −2.37580e9 1.72612e9i −0.181905 0.132162i
\(37\) 7.81308e9 5.67653e9i 0.500623 0.363724i −0.308632 0.951182i \(-0.599871\pi\)
0.809255 + 0.587458i \(0.199871\pi\)
\(38\) 4.78481e9 1.47261e10i 0.257793 0.793405i
\(39\) 7.29167e9 2.24415e10i 0.331823 1.02125i
\(40\) 5.29027e9 3.84361e9i 0.204215 0.148371i
\(41\) −2.65937e10 1.93215e10i −0.874348 0.635251i 0.0574024 0.998351i \(-0.481718\pi\)
−0.931750 + 0.363100i \(0.881718\pi\)
\(42\) 9.94522e9 + 3.06082e10i 0.279572 + 0.860435i
\(43\) −1.78290e10 −0.430112 −0.215056 0.976602i \(-0.568993\pi\)
−0.215056 + 0.976602i \(0.568993\pi\)
\(44\) 1.07749e10 2.15197e10i 0.223858 0.447088i
\(45\) −1.78844e10 −0.321064
\(46\) 2.27838e10 + 7.01215e10i 0.354569 + 1.09125i
\(47\) 7.52930e10 + 5.47036e10i 1.01887 + 0.740252i 0.966051 0.258352i \(-0.0831794\pi\)
0.0528189 + 0.998604i \(0.483179\pi\)
\(48\) −2.06350e10 + 1.49922e10i −0.243521 + 0.176928i
\(49\) 3.86880e9 1.19069e10i 0.0399302 0.122892i
\(50\) −1.18358e10 + 3.64268e10i −0.107125 + 0.329698i
\(51\) −2.10252e11 + 1.52757e11i −1.67315 + 1.21561i
\(52\) −5.14323e10 3.73678e10i −0.360757 0.262105i
\(53\) −7.04618e10 2.16859e11i −0.436677 1.34395i −0.891358 0.453300i \(-0.850247\pi\)
0.454681 0.890654i \(-0.349753\pi\)
\(54\) −8.53664e10 −0.468520
\(55\) −2.39450e10 1.44597e11i −0.116642 0.704370i
\(56\) 8.67093e10 0.375702
\(57\) 1.13661e11 + 3.49812e11i 0.438959 + 1.35098i
\(58\) 1.18772e11 + 8.62928e10i 0.409667 + 0.297641i
\(59\) −2.73551e11 + 1.98746e11i −0.844306 + 0.613424i −0.923570 0.383430i \(-0.874743\pi\)
0.0792644 + 0.996854i \(0.474743\pi\)
\(60\) −4.80009e10 + 1.47731e11i −0.132821 + 0.408780i
\(61\) 9.09885e10 2.80034e11i 0.226122 0.695932i −0.772054 0.635557i \(-0.780770\pi\)
0.998176 0.0603747i \(-0.0192296\pi\)
\(62\) 1.08543e11 7.88612e10i 0.242692 0.176326i
\(63\) −1.91857e11 1.39392e11i −0.386601 0.280882i
\(64\) 2.12355e10 + 6.53561e10i 0.0386271 + 0.118882i
\(65\) −3.87167e11 −0.636740
\(66\) 9.33985e10 + 5.64006e11i 0.139093 + 0.839940i
\(67\) −2.87516e11 −0.388308 −0.194154 0.980971i \(-0.562196\pi\)
−0.194154 + 0.980971i \(0.562196\pi\)
\(68\) 2.16371e11 + 6.65921e11i 0.265394 + 0.816799i
\(69\) −1.41693e12 1.02946e12i −1.58063 1.14839i
\(70\) 4.27212e11 3.10388e11i 0.434017 0.315332i
\(71\) −4.25237e10 + 1.30875e11i −0.0393960 + 0.121248i −0.968820 0.247764i \(-0.920304\pi\)
0.929424 + 0.369013i \(0.120304\pi\)
\(72\) 5.80785e10 1.78747e11i 0.0491308 0.151209i
\(73\) 5.33049e11 3.87282e11i 0.412257 0.299522i −0.362258 0.932078i \(-0.617994\pi\)
0.774515 + 0.632556i \(0.217994\pi\)
\(74\) 5.00037e11 + 3.63298e11i 0.353994 + 0.257192i
\(75\) −2.81153e11 8.65301e11i −0.182408 0.561395i
\(76\) 9.90974e11 0.589894
\(77\) 8.70124e11 1.73781e12i 0.475764 0.950192i
\(78\) 1.51017e12 0.759294
\(79\) 4.76487e11 + 1.46648e12i 0.220534 + 0.678733i 0.998714 + 0.0506922i \(0.0161427\pi\)
−0.778181 + 0.628040i \(0.783857\pi\)
\(80\) 3.38577e11 + 2.45991e11i 0.144402 + 0.104914i
\(81\) 2.56531e12 1.86381e12i 1.00922 0.733244i
\(82\) 6.50106e11 2.00082e12i 0.236153 0.726805i
\(83\) −2.56950e11 + 7.90810e11i −0.0862662 + 0.265500i −0.984879 0.173242i \(-0.944576\pi\)
0.898613 + 0.438742i \(0.144576\pi\)
\(84\) −1.66636e12 + 1.21068e12i −0.517553 + 0.376024i
\(85\) 3.44981e12 + 2.50643e12i 0.992137 + 0.720830i
\(86\) −3.52606e11 1.08521e12i −0.0939830 0.289250i
\(87\) −3.48740e12 −0.862237
\(88\) 1.52295e12 + 2.30249e11i 0.349581 + 0.0528519i
\(89\) 5.20758e12 1.11071 0.555355 0.831613i \(-0.312582\pi\)
0.555355 + 0.831613i \(0.312582\pi\)
\(90\) −3.53701e11 1.08858e12i −0.0701551 0.215915i
\(91\) −4.15338e12 3.01761e12i −0.766713 0.557050i
\(92\) −3.81753e12 + 2.77360e12i −0.656389 + 0.476895i
\(93\) −9.84857e11 + 3.03108e12i −0.157846 + 0.485801i
\(94\) −1.84060e12 + 5.66479e12i −0.275187 + 0.846939i
\(95\) 4.88248e12 3.54733e12i 0.681455 0.495106i
\(96\) −1.32064e12 9.59500e11i −0.172195 0.125107i
\(97\) 9.27788e11 + 2.85544e12i 0.113092 + 0.348062i 0.991544 0.129768i \(-0.0414234\pi\)
−0.878452 + 0.477830i \(0.841423\pi\)
\(98\) 8.01260e11 0.0913701
\(99\) −2.99959e12 2.95771e12i −0.320209 0.315738i
\(100\) −2.45129e12 −0.245129
\(101\) 4.35997e11 + 1.34186e12i 0.0408690 + 0.125782i 0.969409 0.245450i \(-0.0789356\pi\)
−0.928540 + 0.371232i \(0.878936\pi\)
\(102\) −1.34561e13 9.77646e12i −1.18309 0.859569i
\(103\) −7.68769e12 + 5.58544e12i −0.634387 + 0.460909i −0.857917 0.513788i \(-0.828242\pi\)
0.223530 + 0.974697i \(0.428242\pi\)
\(104\) 1.25731e12 3.86959e12i 0.0974370 0.299880i
\(105\) −3.87628e12 + 1.19300e13i −0.282283 + 0.868777i
\(106\) 1.18062e13 8.57768e12i 0.808390 0.587329i
\(107\) −2.17196e12 1.57802e12i −0.139913 0.101653i 0.515627 0.856813i \(-0.327559\pi\)
−0.655540 + 0.755160i \(0.727559\pi\)
\(108\) −1.68830e12 5.19605e12i −0.102375 0.315079i
\(109\) 2.76454e13 1.57889 0.789443 0.613824i \(-0.210370\pi\)
0.789443 + 0.613824i \(0.210370\pi\)
\(110\) 8.32769e12 4.31717e12i 0.448200 0.232352i
\(111\) −1.46822e13 −0.745060
\(112\) 1.71486e12 + 5.27779e12i 0.0820939 + 0.252659i
\(113\) −3.19898e13 2.32419e13i −1.44544 1.05018i −0.986870 0.161520i \(-0.948360\pi\)
−0.458574 0.888656i \(-0.651640\pi\)
\(114\) −1.90444e13 + 1.38365e13i −0.812615 + 0.590399i
\(115\) −8.88030e12 + 2.73307e13i −0.358007 + 1.10183i
\(116\) −2.90347e12 + 8.93598e12i −0.110647 + 0.340538i
\(117\) −9.00262e12 + 6.54079e12i −0.324460 + 0.235734i
\(118\) −1.75072e13 1.27198e13i −0.597014 0.433756i
\(119\) 1.74729e13 + 5.37761e13i 0.564040 + 1.73594i
\(120\) −9.94138e12 −0.303926
\(121\) 1.98973e13 2.82120e13i 0.576354 0.817200i
\(122\) 1.88445e13 0.517423
\(123\) 1.54429e13 + 4.75285e13i 0.402112 + 1.23757i
\(124\) 6.94676e12 + 5.04712e12i 0.171609 + 0.124682i
\(125\) −3.67121e13 + 2.66729e13i −0.860784 + 0.625396i
\(126\) 4.69009e12 1.44346e13i 0.104417 0.321364i
\(127\) 2.51891e13 7.75241e13i 0.532707 1.63950i −0.215844 0.976428i \(-0.569250\pi\)
0.748551 0.663077i \(-0.230750\pi\)
\(128\) −3.55809e12 + 2.58511e12i −0.0715077 + 0.0519534i
\(129\) 2.19286e13 + 1.59321e13i 0.418965 + 0.304396i
\(130\) −7.65704e12 2.35660e13i −0.139133 0.428207i
\(131\) 7.64273e13 1.32125 0.660625 0.750716i \(-0.270291\pi\)
0.660625 + 0.750716i \(0.270291\pi\)
\(132\) −3.24826e13 + 1.68394e13i −0.534466 + 0.277073i
\(133\) 8.00255e13 1.25370
\(134\) −5.68623e12 1.75004e13i −0.0848484 0.261136i
\(135\) −2.69181e13 1.95572e13i −0.382715 0.278059i
\(136\) −3.62539e13 + 2.63400e13i −0.491305 + 0.356954i
\(137\) 8.24827e12 2.53856e13i 0.106581 0.328022i −0.883517 0.468398i \(-0.844831\pi\)
0.990098 + 0.140376i \(0.0448312\pi\)
\(138\) 3.46380e13 1.06605e14i 0.426913 1.31390i
\(139\) 1.05968e14 7.69902e13i 1.24617 0.905398i 0.248180 0.968714i \(-0.420168\pi\)
0.997994 + 0.0633163i \(0.0201677\pi\)
\(140\) 2.73416e13 + 1.98648e13i 0.306896 + 0.222973i
\(141\) −4.37226e13 1.34564e14i −0.468578 1.44213i
\(142\) −8.80702e12 −0.0901477
\(143\) −6.49363e13 6.40297e13i −0.635043 0.626177i
\(144\) 1.20285e13 0.112423
\(145\) 1.76823e13 + 5.44205e13i 0.157996 + 0.486262i
\(146\) 3.41151e13 + 2.47861e13i 0.291510 + 0.211794i
\(147\) −1.53985e13 + 1.11876e13i −0.125868 + 0.0914483i
\(148\) −1.22238e13 + 3.76210e13i −0.0956105 + 0.294259i
\(149\) −5.74850e13 + 1.76921e14i −0.430372 + 1.32455i 0.467383 + 0.884055i \(0.345197\pi\)
−0.897755 + 0.440494i \(0.854803\pi\)
\(150\) 4.71084e13 3.42263e13i 0.337680 0.245339i
\(151\) −1.14747e14 8.33684e13i −0.787754 0.572337i 0.119542 0.992829i \(-0.461857\pi\)
−0.907296 + 0.420493i \(0.861857\pi\)
\(152\) 1.95986e13 + 6.03182e13i 0.128897 + 0.396703i
\(153\) 1.22560e14 0.772423
\(154\) 1.22985e14 + 1.85936e13i 0.742961 + 0.112326i
\(155\) 5.22932e13 0.302893
\(156\) 2.98667e13 + 9.19202e13i 0.165912 + 0.510624i
\(157\) −1.52597e14 1.10868e14i −0.813200 0.590824i 0.101557 0.994830i \(-0.467618\pi\)
−0.914757 + 0.404005i \(0.867618\pi\)
\(158\) −7.98373e13 + 5.80052e13i −0.408258 + 0.296617i
\(159\) −1.07122e14 + 3.29689e14i −0.525773 + 1.61816i
\(160\) −8.27680e12 + 2.54734e13i −0.0390016 + 0.120035i
\(161\) −3.08282e14 + 2.23980e14i −1.39502 + 1.01354i
\(162\) 1.64180e14 + 1.19284e14i 0.713629 + 0.518482i
\(163\) −5.89584e13 1.81455e14i −0.246222 0.757792i −0.995433 0.0954614i \(-0.969567\pi\)
0.749212 0.662331i \(-0.230433\pi\)
\(164\) 1.34642e14 0.540377
\(165\) −9.97612e13 + 1.99243e14i −0.384872 + 0.768664i
\(166\) −5.32165e13 −0.197398
\(167\) −1.12068e14 3.44910e14i −0.399784 1.23041i −0.925173 0.379546i \(-0.876080\pi\)
0.525389 0.850862i \(-0.323920\pi\)
\(168\) −1.06647e14 7.74838e13i −0.365965 0.265889i
\(169\) 5.01389e13 3.64280e13i 0.165543 0.120274i
\(170\) −8.43334e13 + 2.59551e14i −0.267967 + 0.824718i
\(171\) 5.36016e13 1.64969e14i 0.163947 0.504576i
\(172\) 5.90806e13 4.29245e13i 0.173984 0.126407i
\(173\) −1.40680e14 1.02210e14i −0.398964 0.289864i 0.370155 0.928970i \(-0.379305\pi\)
−0.769119 + 0.639106i \(0.779305\pi\)
\(174\) −6.89707e13 2.12270e14i −0.188406 0.579853i
\(175\) −1.97952e14 −0.520970
\(176\) 1.61047e13 + 9.72518e13i 0.0408434 + 0.246641i
\(177\) 5.14051e14 1.25655
\(178\) 1.02991e14 + 3.16973e14i 0.242699 + 0.746951i
\(179\) −4.12703e14 2.99847e14i −0.937764 0.681325i 0.0101177 0.999949i \(-0.496779\pi\)
−0.947881 + 0.318624i \(0.896779\pi\)
\(180\) 5.92640e13 4.30578e13i 0.129873 0.0943584i
\(181\) 5.35628e13 1.64849e14i 0.113228 0.348479i −0.878346 0.478026i \(-0.841352\pi\)
0.991573 + 0.129547i \(0.0413524\pi\)
\(182\) 1.01533e14 3.12486e14i 0.207082 0.637333i
\(183\) −3.62150e14 + 2.63117e14i −0.712781 + 0.517866i
\(184\) −2.44322e14 1.77510e14i −0.464137 0.337215i
\(185\) 7.44436e13 + 2.29114e14i 0.136525 + 0.420180i
\(186\) −2.03972e14 −0.361191
\(187\) 1.64093e14 + 9.90911e14i 0.280621 + 1.69459i
\(188\) −3.81204e14 −0.629696
\(189\) −1.36338e14 4.19604e14i −0.217577 0.669634i
\(190\) 3.12479e14 + 2.27029e14i 0.481861 + 0.350093i
\(191\) 1.05187e15 7.64228e14i 1.56763 1.13895i 0.638256 0.769824i \(-0.279656\pi\)
0.929378 0.369129i \(-0.120344\pi\)
\(192\) 3.22841e13 9.93602e13i 0.0465083 0.143138i
\(193\) 7.23823e13 2.22770e14i 0.100812 0.310266i −0.887913 0.460011i \(-0.847845\pi\)
0.988725 + 0.149745i \(0.0478454\pi\)
\(194\) −1.55455e14 + 1.12944e14i −0.209359 + 0.152109i
\(195\) 4.76193e14 + 3.45974e14i 0.620237 + 0.450629i
\(196\) 1.58466e13 + 4.87708e13i 0.0199651 + 0.0614462i
\(197\) 8.05582e14 0.981928 0.490964 0.871180i \(-0.336645\pi\)
0.490964 + 0.871180i \(0.336645\pi\)
\(198\) 1.20706e14 2.41073e14i 0.142365 0.284331i
\(199\) −1.07802e15 −1.23050 −0.615251 0.788331i \(-0.710945\pi\)
−0.615251 + 0.788331i \(0.710945\pi\)
\(200\) −4.84793e13 1.49204e14i −0.0535626 0.164849i
\(201\) 3.53628e14 + 2.56926e14i 0.378244 + 0.274810i
\(202\) −7.30531e13 + 5.30762e13i −0.0756579 + 0.0549687i
\(203\) −2.34468e14 + 7.21619e14i −0.235158 + 0.723742i
\(204\) 3.28947e14 1.01239e15i 0.319543 0.983452i
\(205\) 6.63376e14 4.81971e14i 0.624251 0.453545i
\(206\) −4.92012e14 3.57468e14i −0.448579 0.325912i
\(207\) 2.55235e14 + 7.85532e14i 0.225493 + 0.693996i
\(208\) 2.60398e14 0.222960
\(209\) 1.40555e15 + 2.12501e14i 1.16653 + 0.176364i
\(210\) −8.02810e14 −0.645932
\(211\) −5.19703e14 1.59948e15i −0.405433 1.24780i −0.920533 0.390665i \(-0.872245\pi\)
0.515099 0.857131i \(-0.327755\pi\)
\(212\) 7.55595e14 + 5.48972e14i 0.571618 + 0.415305i
\(213\) 1.69252e14 1.22968e14i 0.124184 0.0902249i
\(214\) 5.30954e13 1.63411e14i 0.0377892 0.116303i
\(215\) 1.37433e14 4.22974e14i 0.0948942 0.292054i
\(216\) 2.82882e14 2.05526e14i 0.189520 0.137694i
\(217\) 5.60981e14 + 4.07577e14i 0.364720 + 0.264985i
\(218\) 5.46746e14 + 1.68271e15i 0.344999 + 1.06180i
\(219\) −1.00169e15 −0.613548
\(220\) 4.27474e14 + 4.21506e14i 0.254192 + 0.250643i
\(221\) 2.65323e15 1.53188
\(222\) −2.90371e14 8.93670e14i −0.162802 0.501052i
\(223\) −1.03730e15 7.53643e14i −0.564837 0.410378i 0.268389 0.963311i \(-0.413509\pi\)
−0.833226 + 0.552933i \(0.813509\pi\)
\(224\) −2.87332e14 + 2.08759e14i −0.151975 + 0.110416i
\(225\) −1.32590e14 + 4.08069e14i −0.0681277 + 0.209675i
\(226\) 7.82016e14 2.40680e15i 0.390401 1.20153i
\(227\) −2.82461e15 + 2.05220e15i −1.37022 + 0.995525i −0.372502 + 0.928031i \(0.621500\pi\)
−0.997720 + 0.0674933i \(0.978500\pi\)
\(228\) −1.21884e15 8.85538e14i −0.574605 0.417475i
\(229\) −2.46222e14 7.57794e14i −0.112823 0.347232i 0.878664 0.477441i \(-0.158435\pi\)
−0.991487 + 0.130208i \(0.958435\pi\)
\(230\) −1.83918e15 −0.819208
\(231\) −2.62311e15 + 1.35985e15i −1.13590 + 0.588862i
\(232\) −6.01334e14 −0.253188
\(233\) 8.09770e14 + 2.49221e15i 0.331549 + 1.02040i 0.968397 + 0.249414i \(0.0802380\pi\)
−0.636848 + 0.770990i \(0.719762\pi\)
\(234\) −5.76168e14 4.18610e14i −0.229428 0.166689i
\(235\) −1.87817e15 + 1.36457e15i −0.727435 + 0.528512i
\(236\) 4.27979e14 1.31718e15i 0.161248 0.496270i
\(237\) 7.24398e14 2.22947e15i 0.265530 0.817216i
\(238\) −2.92766e15 + 2.12707e15i −1.04417 + 0.758632i
\(239\) 3.57390e15 + 2.59659e15i 1.24039 + 0.901192i 0.997624 0.0688936i \(-0.0219469\pi\)
0.242761 + 0.970086i \(0.421947\pi\)
\(240\) −1.96611e14 6.05108e14i −0.0664104 0.204390i
\(241\) 3.02081e14 0.0993144 0.0496572 0.998766i \(-0.484187\pi\)
0.0496572 + 0.998766i \(0.484187\pi\)
\(242\) 2.11071e15 + 6.53150e14i 0.675504 + 0.209032i
\(243\) −2.69410e15 −0.839407
\(244\) 3.72689e14 + 1.14702e15i 0.113061 + 0.347966i
\(245\) 2.52657e14 + 1.83566e14i 0.0746366 + 0.0542267i
\(246\) −2.58753e15 + 1.87995e15i −0.744402 + 0.540839i
\(247\) 1.16039e15 3.57131e15i 0.325142 1.00068i
\(248\) −1.69819e14 + 5.22650e14i −0.0463501 + 0.142651i
\(249\) 1.02270e15 7.43038e14i 0.271928 0.197567i
\(250\) −2.34958e15 1.70707e15i −0.608666 0.442222i
\(251\) 4.18273e14 + 1.28731e15i 0.105580 + 0.324941i 0.989866 0.142004i \(-0.0453546\pi\)
−0.884286 + 0.466945i \(0.845355\pi\)
\(252\) 9.71357e14 0.238933
\(253\) −6.00937e15 + 3.11533e15i −1.44061 + 0.746828i
\(254\) 5.21688e15 1.21897
\(255\) −2.00330e15 6.16552e15i −0.456283 1.40430i
\(256\) −2.27718e14 1.65447e14i −0.0505636 0.0367366i
\(257\) 6.51314e15 4.73208e15i 1.41002 1.02444i 0.416701 0.909044i \(-0.363186\pi\)
0.993320 0.115396i \(-0.0368137\pi\)
\(258\) −5.36063e14 + 1.64983e15i −0.113159 + 0.348266i
\(259\) −9.87127e14 + 3.03806e15i −0.203200 + 0.625386i
\(260\) 1.28297e15 9.32132e14i 0.257567 0.187133i
\(261\) 1.33054e15 + 9.66690e14i 0.260533 + 0.189288i
\(262\) 1.51151e15 + 4.65195e15i 0.288704 + 0.888539i
\(263\) −5.10930e15 −0.952027 −0.476013 0.879438i \(-0.657919\pi\)
−0.476013 + 0.879438i \(0.657919\pi\)
\(264\) −1.66738e15 1.64410e15i −0.303117 0.298885i
\(265\) 5.68790e15 1.00891
\(266\) 1.58267e15 + 4.87096e15i 0.273943 + 0.843109i
\(267\) −6.40501e15 4.65351e15i −1.08192 0.786063i
\(268\) 9.52752e14 6.92215e14i 0.157074 0.114121i
\(269\) −1.17360e15 + 3.61196e15i −0.188855 + 0.581237i −0.999993 0.00361754i \(-0.998848\pi\)
0.811138 + 0.584855i \(0.198848\pi\)
\(270\) 6.58036e14 2.02523e15i 0.103368 0.318133i
\(271\) 6.80863e15 4.94676e15i 1.04414 0.758613i 0.0730515 0.997328i \(-0.476726\pi\)
0.971090 + 0.238715i \(0.0767262\pi\)
\(272\) −2.32025e15 1.68576e15i −0.347405 0.252405i
\(273\) 2.41186e15 + 7.42296e15i 0.352611 + 1.08522i
\(274\) 1.70829e15 0.243883
\(275\) −3.47680e15 5.25645e14i −0.484749 0.0732875i
\(276\) 7.17383e15 0.976881
\(277\) 1.07218e15 + 3.29982e15i 0.142609 + 0.438906i 0.996696 0.0812248i \(-0.0258832\pi\)
−0.854087 + 0.520131i \(0.825883\pi\)
\(278\) 6.78195e15 + 4.92737e15i 0.881177 + 0.640213i
\(279\) 1.21595e15 8.83439e14i 0.154343 0.112137i
\(280\) −6.68388e14 + 2.05709e15i −0.0828899 + 0.255109i
\(281\) −1.32728e14 + 4.08494e14i −0.0160831 + 0.0494988i −0.958776 0.284163i \(-0.908284\pi\)
0.942693 + 0.333662i \(0.108284\pi\)
\(282\) 7.32590e15 5.32258e15i 0.867445 0.630235i
\(283\) −7.78953e15 5.65943e15i −0.901363 0.654878i 0.0374528 0.999298i \(-0.488076\pi\)
−0.938816 + 0.344420i \(0.888076\pi\)
\(284\) −1.74177e14 5.36062e14i −0.0196980 0.0606242i
\(285\) −9.17506e15 −1.01419
\(286\) 2.61308e15 5.21884e15i 0.282341 0.563890i
\(287\) 1.08730e16 1.14846
\(288\) 2.37889e14 + 7.32149e14i 0.0245654 + 0.0756046i
\(289\) −1.56283e16 1.13546e16i −1.57789 1.14640i
\(290\) −2.96274e15 + 2.15256e15i −0.292487 + 0.212504i
\(291\) 1.41051e15 4.34109e15i 0.136167 0.419078i
\(292\) −8.33972e14 + 2.56670e15i −0.0787341 + 0.242319i
\(293\) 1.71582e16 1.24661e16i 1.58428 1.15105i 0.672701 0.739914i \(-0.265134\pi\)
0.911576 0.411131i \(-0.134866\pi\)
\(294\) −9.85502e14 7.16009e14i −0.0890020 0.0646637i
\(295\) −2.60641e15 8.02171e15i −0.230250 0.708637i
\(296\) −2.53165e15 −0.218780
\(297\) −1.28039e15 7.73188e15i −0.108249 0.653684i
\(298\) −1.19056e16 −0.984797
\(299\) 5.52542e15 + 1.70055e16i 0.447201 + 1.37634i
\(300\) 3.01494e15 + 2.19048e15i 0.238776 + 0.173481i
\(301\) 4.77101e15 3.46634e15i 0.369767 0.268652i
\(302\) 2.80508e15 8.63315e15i 0.212765 0.654823i
\(303\) 6.62841e14 2.04002e15i 0.0492076 0.151445i
\(304\) −3.28382e15 + 2.38584e15i −0.238617 + 0.173365i
\(305\) 5.94213e15 + 4.31721e15i 0.422662 + 0.307082i
\(306\) 2.42389e15 + 7.45995e15i 0.168781 + 0.519454i
\(307\) −8.32249e15 −0.567353 −0.283677 0.958920i \(-0.591554\pi\)
−0.283677 + 0.958920i \(0.591554\pi\)
\(308\) 1.30053e15 + 7.85351e15i 0.0868041 + 0.524184i
\(309\) 1.44466e16 0.944136
\(310\) 1.03421e15 + 3.18296e15i 0.0661845 + 0.203695i
\(311\) 2.21842e15 + 1.61178e15i 0.139028 + 0.101010i 0.655125 0.755520i \(-0.272616\pi\)
−0.516098 + 0.856530i \(0.672616\pi\)
\(312\) −5.00429e15 + 3.63583e15i −0.307141 + 0.223151i
\(313\) −7.43967e15 + 2.28970e16i −0.447214 + 1.37638i 0.432823 + 0.901479i \(0.357517\pi\)
−0.880037 + 0.474905i \(0.842483\pi\)
\(314\) 3.73035e15 1.14808e16i 0.219638 0.675976i
\(315\) 4.78583e15 3.47711e15i 0.276019 0.200539i
\(316\) −5.10959e15 3.71233e15i −0.288682 0.209740i
\(317\) 9.79797e15 + 3.01550e16i 0.542314 + 1.66907i 0.727292 + 0.686328i \(0.240778\pi\)
−0.184978 + 0.982743i \(0.559222\pi\)
\(318\) −2.21859e16 −1.20310
\(319\) −6.03436e15 + 1.20518e16i −0.320621 + 0.640341i
\(320\) −1.71419e15 −0.0892453
\(321\) 1.26126e15 + 3.88175e15i 0.0643458 + 0.198036i
\(322\) −1.97301e16 1.43347e16i −0.986427 0.716681i
\(323\) −3.34593e16 + 2.43096e16i −1.63946 + 1.19114i
\(324\) −4.01351e15 + 1.23523e16i −0.192745 + 0.593207i
\(325\) −2.87035e15 + 8.83404e15i −0.135112 + 0.415831i
\(326\) 9.87872e15 7.17731e15i 0.455813 0.331167i
\(327\) −3.40022e16 2.47040e16i −1.53797 1.11740i
\(328\) 2.66283e15 + 8.19536e15i 0.118077 + 0.363402i
\(329\) −3.07839e16 −1.33829
\(330\) −1.41004e16 2.13179e15i −0.601023 0.0908666i
\(331\) 2.13748e16 0.893348 0.446674 0.894697i \(-0.352608\pi\)
0.446674 + 0.894697i \(0.352608\pi\)
\(332\) −1.05247e15 3.23916e15i −0.0431331 0.132750i
\(333\) 5.60164e15 + 4.06983e15i 0.225127 + 0.163564i
\(334\) 1.87775e16 1.36426e16i 0.740092 0.537708i
\(335\) 2.21628e15 6.82102e15i 0.0856710 0.263668i
\(336\) 2.60708e15 8.02377e15i 0.0988437 0.304210i
\(337\) 2.49455e16 1.81240e16i 0.927679 0.673998i −0.0177443 0.999843i \(-0.505648\pi\)
0.945424 + 0.325844i \(0.105648\pi\)
\(338\) 3.20889e15 + 2.33140e15i 0.117057 + 0.0850467i
\(339\) 1.85764e16 + 5.71723e16i 0.664758 + 2.04592i
\(340\) −1.74661e16 −0.613174
\(341\) 8.77069e15 + 8.64824e15i 0.302086 + 0.297868i
\(342\) 1.11013e16 0.375151
\(343\) −8.62368e15 2.65410e16i −0.285944 0.880045i
\(344\) 3.78116e15 + 2.74717e15i 0.123025 + 0.0893832i
\(345\) 3.53451e16 2.56797e16i 1.12851 0.819909i
\(346\) 3.43904e15 1.05843e16i 0.107756 0.331640i
\(347\) 5.72429e15 1.76176e16i 0.176027 0.541757i −0.823652 0.567096i \(-0.808067\pi\)
0.999679 + 0.0253397i \(0.00806673\pi\)
\(348\) 1.15563e16 8.39616e15i 0.348782 0.253405i
\(349\) −1.29302e16 9.39432e15i −0.383035 0.278292i 0.379560 0.925167i \(-0.376075\pi\)
−0.762596 + 0.646876i \(0.776075\pi\)
\(350\) −3.91492e15 1.20489e16i −0.113836 0.350352i
\(351\) −2.07026e16 −0.590921
\(352\) −5.60098e15 + 2.90361e15i −0.156941 + 0.0813601i
\(353\) 1.47826e16 0.406645 0.203323 0.979112i \(-0.434826\pi\)
0.203323 + 0.979112i \(0.434826\pi\)
\(354\) 1.01664e16 + 3.12891e16i 0.274567 + 0.845029i
\(355\) −2.77707e15 2.01766e15i −0.0736381 0.0535012i
\(356\) −1.72565e16 + 1.25376e16i −0.449292 + 0.326429i
\(357\) 2.65639e16 8.17552e16i 0.679122 2.09012i
\(358\) 1.00889e16 3.10504e16i 0.253281 0.779520i
\(359\) −3.61227e14 + 2.62447e14i −0.00890567 + 0.00647035i −0.592229 0.805770i \(-0.701752\pi\)
0.583324 + 0.812240i \(0.301752\pi\)
\(360\) 3.79290e15 + 2.75570e15i 0.0918343 + 0.0667215i
\(361\) 5.09276e15 + 1.56739e16i 0.121103 + 0.372718i
\(362\) 1.10933e16 0.259093
\(363\) −4.96828e16 + 1.69187e16i −1.13976 + 0.388128i
\(364\) 2.10283e16 0.473855
\(365\) 5.07893e15 + 1.56313e16i 0.112426 + 0.346013i
\(366\) −2.31776e16 1.68395e16i −0.504012 0.366186i
\(367\) 1.22550e16 8.90380e15i 0.261809 0.190215i −0.449135 0.893464i \(-0.648268\pi\)
0.710944 + 0.703248i \(0.248268\pi\)
\(368\) 5.97265e15 1.83819e16i 0.125359 0.385816i
\(369\) 7.28278e15 2.24141e16i 0.150185 0.462221i
\(370\) −1.24733e16 + 9.06241e15i −0.252738 + 0.183625i
\(371\) 6.10176e16 + 4.43318e16i 1.21485 + 0.882644i
\(372\) −4.03398e15 1.24153e16i −0.0789231 0.242900i
\(373\) −1.45128e16 −0.279025 −0.139512 0.990220i \(-0.544554\pi\)
−0.139512 + 0.990220i \(0.544554\pi\)
\(374\) −5.70691e16 + 2.95853e16i −1.07829 + 0.558998i
\(375\) 6.89887e16 1.28108
\(376\) −7.53910e15 2.32030e16i −0.137594 0.423470i
\(377\) 2.88039e16 + 2.09273e16i 0.516693 + 0.375400i
\(378\) 2.28439e16 1.65971e16i 0.402786 0.292641i
\(379\) −6.30688e15 + 1.94106e16i −0.109310 + 0.336422i −0.990718 0.135934i \(-0.956596\pi\)
0.881408 + 0.472356i \(0.156596\pi\)
\(380\) −7.63880e15 + 2.35098e16i −0.130146 + 0.400549i
\(381\) −1.00257e17 + 7.28409e16i −1.67920 + 1.22001i
\(382\) 6.73196e16 + 4.89106e16i 1.10848 + 0.805361i
\(383\) 2.40083e16 + 7.38898e16i 0.388659 + 1.19617i 0.933791 + 0.357819i \(0.116479\pi\)
−0.545132 + 0.838350i \(0.683521\pi\)
\(384\) 6.68630e15 0.106422
\(385\) 3.45204e16 + 3.40384e16i 0.540232 + 0.532690i
\(386\) 1.49910e16 0.230682
\(387\) −3.95005e15 1.21570e16i −0.0597697 0.183952i
\(388\) −9.94910e15 7.22844e15i −0.148039 0.107557i
\(389\) 6.69172e16 4.86182e16i 0.979187 0.711421i 0.0216601 0.999765i \(-0.493105\pi\)
0.957527 + 0.288344i \(0.0931048\pi\)
\(390\) −1.16409e16 + 3.58271e16i −0.167520 + 0.515574i
\(391\) 6.08560e16 1.87296e17i 0.861301 2.65081i
\(392\) −2.65516e15 + 1.92909e15i −0.0369600 + 0.0268530i
\(393\) −9.40010e16 6.82957e16i −1.28701 0.935065i
\(394\) 1.59321e16 + 4.90339e16i 0.214559 + 0.660345i
\(395\) −3.84635e16 −0.509528
\(396\) 1.70607e16 + 2.57936e15i 0.222320 + 0.0336119i
\(397\) −2.50759e16 −0.321454 −0.160727 0.986999i \(-0.551384\pi\)
−0.160727 + 0.986999i \(0.551384\pi\)
\(398\) −2.13201e16 6.56166e16i −0.268874 0.827510i
\(399\) −9.84265e16 7.15111e16i −1.22120 0.887257i
\(400\) 8.12292e15 5.90164e15i 0.0991567 0.0720416i
\(401\) −2.62565e16 + 8.08092e16i −0.315354 + 0.970560i 0.660254 + 0.751042i \(0.270449\pi\)
−0.975608 + 0.219518i \(0.929551\pi\)
\(402\) −8.64472e15 + 2.66057e16i −0.102160 + 0.314417i
\(403\) 2.63233e16 1.91250e16i 0.306096 0.222392i
\(404\) −4.67540e15 3.39687e15i −0.0534982 0.0388688i
\(405\) 2.44425e16 + 7.52262e16i 0.275225 + 0.847055i
\(406\) −4.85603e16 −0.538099
\(407\) −2.54050e16 + 5.07388e16i −0.277049 + 0.553320i
\(408\) 6.81276e16 0.731193
\(409\) −2.89637e16 8.91412e16i −0.305952 0.941623i −0.979320 0.202316i \(-0.935153\pi\)
0.673368 0.739307i \(-0.264847\pi\)
\(410\) 4.24560e16 + 3.08461e16i 0.441412 + 0.320705i
\(411\) −3.28295e16 + 2.38520e16i −0.335964 + 0.244092i
\(412\) 1.20276e16 3.70173e16i 0.121157 0.372883i
\(413\) 3.45612e16 1.06368e17i 0.342699 1.05472i
\(414\) −4.27657e16 + 3.10711e16i −0.417439 + 0.303287i
\(415\) −1.67805e16 1.21917e16i −0.161247 0.117153i
\(416\) 5.14992e15 + 1.58498e16i 0.0487185 + 0.149940i
\(417\) −1.99133e17 −1.85464
\(418\) 1.48633e16 + 8.97553e16i 0.136292 + 0.823027i
\(419\) −1.56654e17 −1.41433 −0.707163 0.707050i \(-0.750025\pi\)
−0.707163 + 0.707050i \(0.750025\pi\)
\(420\) −1.58772e16 4.88651e16i −0.141141 0.434389i
\(421\) −1.60951e16 1.16938e16i −0.140884 0.102358i 0.515111 0.857123i \(-0.327751\pi\)
−0.655995 + 0.754765i \(0.727751\pi\)
\(422\) 8.70785e16 6.32662e16i 0.750550 0.545307i
\(423\) −2.06192e16 + 6.34595e16i −0.175009 + 0.538622i
\(424\) −1.84711e16 + 5.68483e16i −0.154389 + 0.475160i
\(425\) 8.27654e16 6.01326e16i 0.681272 0.494973i
\(426\) 1.08321e16 + 7.86998e15i 0.0878113 + 0.0637986i
\(427\) 3.00963e16 + 9.26268e16i 0.240288 + 0.739529i
\(428\) 1.09965e16 0.0864709
\(429\) 2.26505e16 + 1.36780e17i 0.175431 + 1.05938i
\(430\) 2.84634e16 0.217141
\(431\) 1.43166e16 + 4.40621e16i 0.107582 + 0.331103i 0.990328 0.138748i \(-0.0443077\pi\)
−0.882746 + 0.469851i \(0.844308\pi\)
\(432\) 1.81044e16 + 1.31536e16i 0.134011 + 0.0973647i
\(433\) −1.81457e17 + 1.31836e17i −1.32313 + 0.961310i −0.323242 + 0.946316i \(0.604773\pi\)
−0.999888 + 0.0149940i \(0.995227\pi\)
\(434\) −1.37136e16 + 4.22063e16i −0.0985076 + 0.303175i
\(435\) 2.68822e16 8.27349e16i 0.190232 0.585475i
\(436\) −9.16095e16 + 6.65582e16i −0.638673 + 0.464023i
\(437\) −2.25489e17 1.63827e17i −1.54880 1.12527i
\(438\) −1.98106e16 6.09708e16i −0.134065 0.412610i
\(439\) 2.20796e17 1.47222 0.736110 0.676862i \(-0.236661\pi\)
0.736110 + 0.676862i \(0.236661\pi\)
\(440\) −1.72019e16 + 3.43555e16i −0.113014 + 0.225711i
\(441\) 8.97608e15 0.0581080
\(442\) 5.24732e16 + 1.61496e17i 0.334729 + 1.03019i
\(443\) 6.46494e16 + 4.69706e16i 0.406388 + 0.295258i 0.772138 0.635455i \(-0.219188\pi\)
−0.365750 + 0.930713i \(0.619188\pi\)
\(444\) 4.86529e16 3.53484e16i 0.301383 0.218968i
\(445\) −4.01420e16 + 1.23544e17i −0.245052 + 0.754193i
\(446\) 2.53577e16 7.80429e16i 0.152557 0.469523i
\(447\) 2.28800e17 1.66233e17i 1.35662 0.985641i
\(448\) −1.83892e16 1.33606e16i −0.107462 0.0780760i
\(449\) −2.92942e16 9.01583e16i −0.168725 0.519284i 0.830566 0.556920i \(-0.188017\pi\)
−0.999291 + 0.0376365i \(0.988017\pi\)
\(450\) −2.74604e16 −0.155893
\(451\) 1.90971e17 + 2.88722e16i 1.06861 + 0.161559i
\(452\) 1.61962e17 0.893333
\(453\) 6.66333e16 + 2.05076e17i 0.362287 + 1.11501i
\(454\) −1.80775e17 1.31341e17i −0.968893 0.703942i
\(455\) 1.03605e17 7.52737e16i 0.547404 0.397713i
\(456\) 2.97955e16 9.17012e16i 0.155196 0.477643i
\(457\) 4.42183e16 1.36090e17i 0.227063 0.698828i −0.771013 0.636820i \(-0.780250\pi\)
0.998076 0.0620081i \(-0.0197505\pi\)
\(458\) 4.12555e16 2.99739e16i 0.208861 0.151746i
\(459\) 1.84468e17 + 1.34024e17i 0.920744 + 0.668960i
\(460\) −3.63737e16 1.11947e17i −0.179003 0.550916i
\(461\) −2.71671e17 −1.31822 −0.659109 0.752047i \(-0.729067\pi\)
−0.659109 + 0.752047i \(0.729067\pi\)
\(462\) −1.34648e17 1.32769e17i −0.644211 0.635217i
\(463\) 1.97663e17 0.932500 0.466250 0.884653i \(-0.345605\pi\)
0.466250 + 0.884653i \(0.345605\pi\)
\(464\) −1.18926e16 3.66018e16i −0.0553237 0.170269i
\(465\) −6.43175e16 4.67294e16i −0.295043 0.214361i
\(466\) −1.35680e17 + 9.85775e16i −0.613774 + 0.445933i
\(467\) 3.79255e16 1.16723e17i 0.169189 0.520709i −0.830132 0.557567i \(-0.811735\pi\)
0.999321 + 0.0368578i \(0.0117349\pi\)
\(468\) 1.40849e16 4.33489e16i 0.0619663 0.190713i
\(469\) 7.69389e16 5.58994e16i 0.333828 0.242540i
\(470\) −1.20203e17 8.73326e16i −0.514374 0.373715i
\(471\) 8.86127e16 + 2.72722e17i 0.373990 + 1.15102i
\(472\) 8.86380e16 0.368975
\(473\) 9.30018e16 4.82132e16i 0.381851 0.197956i
\(474\) 1.50029e17 0.607597
\(475\) −4.47424e16 1.37703e17i −0.178735 0.550091i
\(476\) −1.87370e17 1.36132e17i −0.738338 0.536434i
\(477\) 1.32258e17 9.60911e16i 0.514106 0.373520i
\(478\) −8.73670e16 + 2.68888e17i −0.335017 + 1.03107i
\(479\) 2.52044e15 7.75711e15i 0.00953443 0.0293440i −0.946176 0.323652i \(-0.895089\pi\)
0.955711 + 0.294308i \(0.0950892\pi\)
\(480\) 3.29431e16 2.39345e16i 0.122941 0.0893217i
\(481\) 1.21266e17 + 8.81052e16i 0.446475 + 0.324383i
\(482\) 5.97428e15 + 1.83869e16i 0.0217010 + 0.0667888i
\(483\) 5.79318e17 2.07616
\(484\) 1.98792e15 + 1.41391e17i 0.00702918 + 0.499951i
\(485\) −7.48939e16 −0.261292
\(486\) −5.32814e16 1.63983e17i −0.183417 0.564500i
\(487\) −1.17034e17 8.50303e16i −0.397534 0.288826i 0.371002 0.928632i \(-0.379014\pi\)
−0.768536 + 0.639807i \(0.779014\pi\)
\(488\) −6.24456e16 + 4.53694e16i −0.209302 + 0.152067i
\(489\) −8.96338e16 + 2.75864e17i −0.296459 + 0.912406i
\(490\) −6.17641e15 + 1.90090e16i −0.0201587 + 0.0620420i
\(491\) −1.75898e17 + 1.27798e17i −0.566542 + 0.411617i −0.833848 0.551995i \(-0.813867\pi\)
0.267305 + 0.963612i \(0.413867\pi\)
\(492\) −1.65602e17 1.20317e17i −0.526371 0.382431i
\(493\) −1.21175e17 3.72940e17i −0.380110 1.16986i
\(494\) 2.40326e17 0.744004
\(495\) 9.32906e16 4.83629e16i 0.285039 0.147767i
\(496\) −3.51710e16 −0.106061
\(497\) −1.40656e16 4.32893e16i −0.0418640 0.128844i
\(498\) 6.54531e16 + 4.75544e16i 0.192282 + 0.139701i
\(499\) −3.62935e17 + 2.63688e17i −1.05239 + 0.764604i −0.972665 0.232213i \(-0.925403\pi\)
−0.0797220 + 0.996817i \(0.525403\pi\)
\(500\) 5.74373e16 1.76774e17i 0.164395 0.505956i
\(501\) −1.70376e17 + 5.24364e17i −0.481353 + 1.48145i
\(502\) −7.00834e16 + 5.09185e16i −0.195452 + 0.142004i
\(503\) −1.33451e17 9.69577e16i −0.367392 0.266926i 0.388737 0.921349i \(-0.372912\pi\)
−0.756129 + 0.654423i \(0.772912\pi\)
\(504\) 1.92106e16 + 5.91242e16i 0.0522087 + 0.160682i
\(505\) −3.51950e16 −0.0944251
\(506\) −3.08470e17 3.04164e17i −0.817025 0.805618i
\(507\) −9.42201e16 −0.246372
\(508\) 1.03175e17 + 3.17539e17i 0.266354 + 0.819752i
\(509\) −2.06572e17 1.50083e17i −0.526509 0.382531i 0.292541 0.956253i \(-0.405499\pi\)
−0.819050 + 0.573722i \(0.805499\pi\)
\(510\) 3.35661e17 2.43872e17i 0.844685 0.613700i
\(511\) −6.73469e16 + 2.07272e17i −0.167333 + 0.514998i
\(512\) 5.56676e15 1.71327e16i 0.0136568 0.0420312i
\(513\) 2.61076e17 1.89683e17i 0.632418 0.459479i
\(514\) 4.16841e17 + 3.02853e17i 0.997035 + 0.724388i
\(515\) −7.32489e16 2.25437e17i −0.173003 0.532449i
\(516\) −1.11023e17 −0.258935
\(517\) −5.40682e17 8.17439e16i −1.24524 0.188264i
\(518\) −2.04442e17 −0.464972
\(519\) 8.16928e16 + 2.51425e17i 0.183483 + 0.564703i
\(520\) 8.21101e16 + 5.96564e16i 0.182127 + 0.132323i
\(521\) −4.33815e17 + 3.15185e17i −0.950298 + 0.690432i −0.950877 0.309568i \(-0.899816\pi\)
0.000579489 1.00000i \(0.499816\pi\)
\(522\) −3.25260e16 + 1.00105e17i −0.0703676 + 0.216569i
\(523\) −1.42876e16 + 4.39728e16i −0.0305280 + 0.0939556i −0.965160 0.261662i \(-0.915729\pi\)
0.934632 + 0.355618i \(0.115729\pi\)
\(524\) −2.53260e17 + 1.84004e17i −0.534457 + 0.388306i
\(525\) 2.43469e17 + 1.76891e17i 0.507468 + 0.368697i
\(526\) −1.01047e17 3.10991e17i −0.208025 0.640236i
\(527\) −3.58362e17 −0.728706
\(528\) 6.70967e16 1.34005e17i 0.134766 0.269154i
\(529\) 8.23142e17 1.63310
\(530\) 1.12490e17 + 3.46209e17i 0.220455 + 0.678492i
\(531\) −1.96124e17 1.42492e17i −0.379679 0.275853i
\(532\) −2.65183e17 + 1.92667e17i −0.507131 + 0.368452i
\(533\) 1.57660e17 4.85229e17i 0.297849 0.916684i
\(534\) 1.56576e17 4.81890e17i 0.292217 0.899353i
\(535\) 5.41792e16 3.93635e16i 0.0998925 0.0725762i
\(536\) 6.09761e16 + 4.43018e16i 0.111068 + 0.0806956i
\(537\) 2.39656e17 + 7.37587e17i 0.431277 + 1.32733i
\(538\) −2.43062e17 −0.432148
\(539\) 1.20179e16 + 7.25724e16i 0.0211106 + 0.127481i
\(540\) 1.36285e17 0.236531
\(541\) −6.63081e16 2.04075e17i −0.113706 0.349952i 0.877969 0.478718i \(-0.158898\pi\)
−0.991675 + 0.128766i \(0.958898\pi\)
\(542\) 4.35752e17 + 3.16592e17i 0.738319 + 0.536420i
\(543\) −2.13189e17 + 1.54891e17i −0.356916 + 0.259315i
\(544\) 5.67204e16 1.74567e17i 0.0938309 0.288782i
\(545\) −2.13101e17 + 6.55858e17i −0.348344 + 1.07209i
\(546\) −4.04118e17 + 2.93609e17i −0.652764 + 0.474261i
\(547\) −2.49653e17 1.81383e17i −0.398491 0.289521i 0.370435 0.928858i \(-0.379209\pi\)
−0.768926 + 0.639338i \(0.779209\pi\)
\(548\) 3.37849e16 + 1.03979e17i 0.0532905 + 0.164011i
\(549\) 2.11104e17 0.329062
\(550\) −3.67662e16 2.22020e17i −0.0566358 0.342007i
\(551\) −5.54981e17 −0.844875
\(552\) 1.41877e17 + 4.36654e17i 0.213456 + 0.656951i
\(553\) −4.12622e17 2.99787e17i −0.613534 0.445759i
\(554\) −1.79648e17 + 1.30522e17i −0.264002 + 0.191809i
\(555\) 1.13176e17 3.48319e17i 0.164380 0.505910i
\(556\) −1.65790e17 + 5.10250e17i −0.237998 + 0.732482i
\(557\) 3.16112e17 2.29669e17i 0.448521 0.325870i −0.340491 0.940248i \(-0.610593\pi\)
0.789012 + 0.614378i \(0.210593\pi\)
\(558\) 7.78207e16 + 5.65401e16i 0.109137 + 0.0792929i
\(559\) −8.55121e16 2.63179e17i −0.118536 0.364817i
\(560\) −1.38429e17 −0.189672
\(561\) 6.83657e17 1.36540e18i 0.925933 1.84927i
\(562\) −2.74890e16 −0.0368021
\(563\) −4.40393e17 1.35539e18i −0.582822 1.79374i −0.607847 0.794054i \(-0.707967\pi\)
0.0250253 0.999687i \(-0.492033\pi\)
\(564\) 4.68858e17 + 3.40645e17i 0.613376 + 0.445644i
\(565\) 7.97979e17 5.79765e17i 1.03199 0.749786i
\(566\) 1.90422e17 5.86057e17i 0.243450 0.749261i
\(567\) −3.24109e17 + 9.97504e17i −0.409639 + 1.26074i
\(568\) 2.91841e16 2.12035e16i 0.0364655 0.0264937i
\(569\) 4.99795e17 + 3.63123e17i 0.617394 + 0.448563i 0.852010 0.523525i \(-0.175383\pi\)
−0.234616 + 0.972088i \(0.575383\pi\)
\(570\) −1.81456e17 5.58464e17i −0.221608 0.682038i
\(571\) 1.57981e18 1.90753 0.953764 0.300558i \(-0.0971727\pi\)
0.953764 + 0.300558i \(0.0971727\pi\)
\(572\) 3.69337e17 + 5.58389e16i 0.440909 + 0.0666595i
\(573\) −1.97665e18 −2.33306
\(574\) 2.15035e17 + 6.61811e17i 0.250947 + 0.772336i
\(575\) 5.57772e17 + 4.05245e17i 0.643600 + 0.467602i
\(576\) −3.98594e16 + 2.89595e16i −0.0454762 + 0.0330404i
\(577\) 3.47679e17 1.07005e18i 0.392226 1.20715i −0.538875 0.842386i \(-0.681151\pi\)
0.931101 0.364761i \(-0.118849\pi\)
\(578\) 3.82047e17 1.17582e18i 0.426173 1.31163i
\(579\) −2.88094e17 + 2.09313e17i −0.317778 + 0.230879i
\(580\) −1.89615e17 1.37764e17i −0.206820 0.150263i
\(581\) −8.49913e16 2.61576e17i −0.0916705 0.282133i
\(582\) 2.92128e17 0.311582
\(583\) 9.53982e17 + 9.40664e17i 1.00622 + 0.992176i
\(584\) −1.72723e17 −0.180163
\(585\) −8.57777e16 2.63996e17i −0.0884832 0.272323i
\(586\) 1.09812e18 + 7.97833e17i 1.12025 + 0.813912i
\(587\) 7.99555e17 5.80910e17i 0.806679 0.586086i −0.106187 0.994346i \(-0.533864\pi\)
0.912866 + 0.408260i \(0.133864\pi\)
\(588\) 2.40914e16 7.41457e16i 0.0240386 0.0739832i
\(589\) −1.56729e17 + 4.82362e17i −0.154668 + 0.476019i
\(590\) 4.36715e17 3.17292e17i 0.426246 0.309686i
\(591\) −9.90818e17 7.19871e17i −0.956479 0.694922i
\(592\) −5.00688e16 1.54096e17i −0.0478053 0.147129i
\(593\) −8.72116e17 −0.823605 −0.411802 0.911273i \(-0.635101\pi\)
−0.411802 + 0.911273i \(0.635101\pi\)
\(594\) 4.45299e17 2.30848e17i 0.415948 0.215633i
\(595\) −1.41047e18 −1.30317
\(596\) −2.35459e17 7.24667e17i −0.215186 0.662275i
\(597\) 1.32590e18 + 9.63323e17i 1.19861 + 0.870841i
\(598\) −9.25807e17 + 6.72639e17i −0.827872 + 0.601484i
\(599\) −1.57407e17 + 4.84448e17i −0.139235 + 0.428522i −0.996225 0.0868120i \(-0.972332\pi\)
0.856990 + 0.515334i \(0.172332\pi\)
\(600\) −7.37026e16 + 2.26833e17i −0.0644911 + 0.198483i
\(601\) 4.66236e17 3.38740e17i 0.403573 0.293213i −0.367422 0.930054i \(-0.619760\pi\)
0.770995 + 0.636842i \(0.219760\pi\)
\(602\) 3.05345e17 + 2.21846e17i 0.261465 + 0.189965i
\(603\) −6.36998e16 1.96048e17i −0.0539604 0.166073i
\(604\) 5.80956e17 0.486859
\(605\) 5.15923e17 + 6.89510e17i 0.427735 + 0.571651i
\(606\) 1.37280e17 0.112599
\(607\) −2.06425e15 6.35312e15i −0.00167508 0.00515538i 0.950215 0.311594i \(-0.100863\pi\)
−0.951891 + 0.306438i \(0.900863\pi\)
\(608\) −2.10165e17 1.52694e17i −0.168728 0.122588i
\(609\) 9.33223e17 6.78026e17i 0.741264 0.538560i
\(610\) −1.45260e17 + 4.47065e17i −0.114157 + 0.351340i
\(611\) −4.46373e17 + 1.37379e18i −0.347080 + 1.06820i
\(612\) −4.06132e17 + 2.95072e17i −0.312452 + 0.227010i
\(613\) 1.01319e18 + 7.36128e17i 0.771257 + 0.560351i 0.902342 0.431020i \(-0.141846\pi\)
−0.131085 + 0.991371i \(0.541846\pi\)
\(614\) −1.64595e17 5.06570e17i −0.123971 0.381544i
\(615\) −1.24660e18 −0.929052
\(616\) −4.52304e17 + 2.34480e17i −0.333546 + 0.172914i
\(617\) −1.75128e18 −1.27791 −0.638957 0.769242i \(-0.720634\pi\)
−0.638957 + 0.769242i \(0.720634\pi\)
\(618\) 2.85711e17 + 8.79328e17i 0.206301 + 0.634930i
\(619\) 2.23325e17 + 1.62255e17i 0.159569 + 0.115934i 0.664704 0.747106i \(-0.268557\pi\)
−0.505135 + 0.863040i \(0.668557\pi\)
\(620\) −1.73286e17 + 1.25899e17i −0.122523 + 0.0890180i
\(621\) −4.74848e17 + 1.46143e18i −0.332245 + 1.02255i
\(622\) −5.42312e16 + 1.66906e17i −0.0375501 + 0.115567i
\(623\) −1.39354e18 + 1.01247e18i −0.954876 + 0.693758i
\(624\) −3.20274e17 2.32693e17i −0.217181 0.157791i
\(625\) −1.24046e17 3.81775e17i −0.0832460 0.256205i
\(626\) −1.54082e18 −1.02334
\(627\) −1.53885e18 1.51737e18i −1.01148 0.997361i
\(628\) 7.72587e17 0.502585
\(629\) −5.10157e17 1.57010e18i −0.328454 1.01088i
\(630\) 3.06293e17 + 2.22535e17i 0.195175 + 0.141803i
\(631\) 1.99594e18 1.45014e18i 1.25880 0.914573i 0.260104 0.965581i \(-0.416243\pi\)
0.998698 + 0.0510075i \(0.0162432\pi\)
\(632\) 1.24908e17 3.84428e17i 0.0779704 0.239968i
\(633\) −7.90100e17 + 2.43168e18i −0.488155 + 1.50239i
\(634\) −1.64169e18 + 1.19276e18i −1.00395 + 0.729411i
\(635\) 1.64501e18 + 1.19517e18i 0.995725 + 0.723436i
\(636\) −4.38773e17 1.35040e18i −0.262887 0.809082i
\(637\) 1.94317e17 0.115241
\(638\) −8.52905e17 1.28948e17i −0.500687 0.0756971i
\(639\) −9.86602e16 −0.0573306
\(640\) −3.39018e16 1.04339e17i −0.0195008 0.0600173i
\(641\) 2.80424e18 + 2.03740e18i 1.59676 + 1.16011i 0.893390 + 0.449282i \(0.148320\pi\)
0.703365 + 0.710829i \(0.251680\pi\)
\(642\) −2.11329e17 + 1.53539e17i −0.119119 + 0.0865450i
\(643\) 1.02486e17 3.15420e17i 0.0571865 0.176002i −0.918383 0.395692i \(-0.870505\pi\)
0.975570 + 0.219690i \(0.0705047\pi\)
\(644\) 4.82317e17 1.48442e18i 0.266425 0.819971i
\(645\) −5.47005e17 + 3.97422e17i −0.299125 + 0.217327i
\(646\) −2.14139e18 1.55581e18i −1.15927 0.842260i
\(647\) −3.48729e17 1.07328e18i −0.186900 0.575220i 0.813075 0.582158i \(-0.197792\pi\)
−0.999976 + 0.00693786i \(0.997792\pi\)
\(648\) −8.31232e17 −0.441047
\(649\) 8.89478e17 1.77646e18i 0.467245 0.933179i
\(650\) −5.94474e17 −0.309169
\(651\) −3.25761e17 1.00259e18i −0.167735 0.516234i
\(652\) 6.32238e17 + 4.59348e17i 0.322308 + 0.234171i
\(653\) 2.79032e16 2.02728e16i 0.0140837 0.0102324i −0.580721 0.814103i \(-0.697229\pi\)
0.594805 + 0.803870i \(0.297229\pi\)
\(654\) 8.31212e17 2.55821e18i 0.415390 1.27844i
\(655\) −5.89130e17 + 1.81316e18i −0.291503 + 0.897153i
\(656\) −4.46169e17 + 3.24161e17i −0.218587 + 0.158813i
\(657\) 3.82173e17 + 2.77665e17i 0.185389 + 0.134693i
\(658\) −6.08815e17 1.87374e18i −0.292427 0.899997i
\(659\) 3.57478e18 1.70018 0.850089 0.526639i \(-0.176548\pi\)
0.850089 + 0.526639i \(0.176548\pi\)
\(660\) −1.49108e17 9.00419e17i −0.0702206 0.424042i
\(661\) −7.08247e17 −0.330275 −0.165137 0.986271i \(-0.552807\pi\)
−0.165137 + 0.986271i \(0.552807\pi\)
\(662\) 4.22732e17 + 1.30103e18i 0.195204 + 0.600775i
\(663\) −3.26332e18 2.37094e18i −1.49218 1.08413i
\(664\) 1.76345e17 1.28122e17i 0.0798493 0.0580139i
\(665\) −6.16866e17 + 1.89852e18i −0.276599 + 0.851283i
\(666\) −1.36937e17 + 4.21448e17i −0.0608047 + 0.187138i
\(667\) 2.13795e18 1.55331e18i 0.940113 0.683032i
\(668\) 1.20176e18 + 8.73130e17i 0.523324 + 0.380217i
\(669\) 6.02359e17 + 1.85387e18i 0.259768 + 0.799484i
\(670\) 4.59011e17 0.196036
\(671\) 2.82643e17 + 1.70680e18i 0.119548 + 0.721915i
\(672\) 5.39948e17 0.226179
\(673\) −6.33196e17 1.94878e18i −0.262688 0.808470i −0.992217 0.124520i \(-0.960261\pi\)
0.729529 0.683950i \(-0.239739\pi\)
\(674\) 1.59651e18 + 1.15993e18i 0.655968 + 0.476589i
\(675\) −6.45802e17 + 4.69202e17i −0.262800 + 0.190935i
\(676\) −7.84440e16 + 2.41426e17i −0.0316159 + 0.0973038i
\(677\) −7.72203e17 + 2.37660e18i −0.308251 + 0.948700i 0.670192 + 0.742187i \(0.266212\pi\)
−0.978444 + 0.206513i \(0.933788\pi\)
\(678\) −3.11256e18 + 2.26140e18i −1.23062 + 0.894098i
\(679\) −8.03433e17 5.83728e17i −0.314627 0.228590i
\(680\) −3.45429e17 1.06312e18i −0.133984 0.412359i
\(681\) 5.30796e18 2.03925
\(682\) −3.52939e17 + 7.04888e17i −0.134308 + 0.268239i
\(683\) −3.97353e18 −1.49776 −0.748879 0.662707i \(-0.769407\pi\)
−0.748879 + 0.662707i \(0.769407\pi\)
\(684\) 2.19552e17 + 6.75712e17i 0.0819734 + 0.252288i
\(685\) 5.38665e17 + 3.91363e17i 0.199219 + 0.144741i
\(686\) 1.44493e18 1.04981e18i 0.529348 0.384594i
\(687\) −3.74329e17 + 1.15207e18i −0.135842 + 0.418079i
\(688\) −9.24335e16 + 2.84481e17i −0.0332280 + 0.102265i
\(689\) 2.86317e18 2.08022e18i 1.01958 0.740770i
\(690\) 2.26209e18 + 1.64350e18i 0.797976 + 0.579764i
\(691\) −6.93455e17 2.13424e18i −0.242332 0.745822i −0.996064 0.0886395i \(-0.971748\pi\)
0.753732 0.657182i \(-0.228252\pi\)
\(692\) 7.12255e17 0.246573
\(693\) 1.37773e18 + 2.08294e17i 0.472496 + 0.0714350i
\(694\) 1.18555e18 0.402794
\(695\) 1.00967e18 + 3.10745e18i 0.339843 + 1.04593i
\(696\) 7.39605e17 + 5.37354e17i 0.246626 + 0.179185i
\(697\) −4.54607e18 + 3.30291e18i −1.50184 + 1.09115i
\(698\) 3.16089e17 9.72821e17i 0.103454 0.318400i
\(699\) 1.23108e18 3.78889e18i 0.399196 1.22860i
\(700\) 6.55961e17 4.76584e17i 0.210737 0.153109i
\(701\) 6.24384e17 + 4.53642e17i 0.198740 + 0.144393i 0.682704 0.730695i \(-0.260804\pi\)
−0.483965 + 0.875088i \(0.660804\pi\)
\(702\) −4.09438e17 1.26012e18i −0.129121 0.397393i
\(703\) −2.33651e18 −0.730058
\(704\) −2.87507e17 2.83493e17i −0.0890075 0.0877649i
\(705\) 3.52942e18 1.08262
\(706\) 2.92357e17 + 8.99783e17i 0.0888552 + 0.273468i
\(707\) −3.77559e17 2.74312e17i −0.113699 0.0826075i
\(708\) −1.70343e18 + 1.23761e18i −0.508286 + 0.369291i
\(709\) 1.28489e18 3.95448e18i 0.379896 1.16920i −0.560220 0.828344i \(-0.689283\pi\)
0.940116 0.340856i \(-0.110717\pi\)
\(710\) 6.78878e16 2.08937e17i 0.0198890 0.0612119i
\(711\) −8.94374e17 + 6.49801e17i −0.259637 + 0.188637i
\(712\) −1.10442e18 8.02406e17i −0.317697 0.230821i
\(713\) −7.46297e17 2.29687e18i −0.212730 0.654717i
\(714\) 5.50160e18 1.55400
\(715\) 2.01959e18 1.04698e18i 0.565293 0.293055i
\(716\) 2.08949e18 0.579570
\(717\) −2.07536e18 6.38731e18i −0.570452 1.75567i
\(718\) −2.31185e16 1.67966e16i −0.00629726 0.00457523i
\(719\) 3.82551e17 2.77939e17i 0.103265 0.0750261i −0.534955 0.844881i \(-0.679671\pi\)
0.638219 + 0.769855i \(0.279671\pi\)
\(720\) −9.27205e16 + 2.85364e17i −0.0248036 + 0.0763376i
\(721\) 9.71285e17 2.98931e18i 0.257494 0.792486i
\(722\) −8.53314e17 + 6.19969e17i −0.224190 + 0.162884i
\(723\) −3.71541e17 2.69941e17i −0.0967404 0.0702861i
\(724\) 2.19393e17 + 6.75223e17i 0.0566138 + 0.174239i
\(725\) 1.37281e18 0.351086
\(726\) −2.01238e18 2.68947e18i −0.510062 0.681677i
\(727\) −3.54753e18 −0.891153 −0.445577 0.895244i \(-0.647001\pi\)
−0.445577 + 0.895244i \(0.647001\pi\)
\(728\) 4.15879e17 + 1.27994e18i 0.103541 + 0.318667i
\(729\) −7.76358e17 5.64057e17i −0.191573 0.139186i
\(730\) −8.50995e17 + 6.18284e17i −0.208127 + 0.151213i
\(731\) −9.41816e17 + 2.89861e18i −0.228299 + 0.702631i
\(732\) 5.66595e17 1.74380e18i 0.136129 0.418962i
\(733\) −1.25164e17 + 9.09371e16i −0.0298060 + 0.0216553i −0.602589 0.798052i \(-0.705864\pi\)
0.572782 + 0.819707i \(0.305864\pi\)
\(734\) 7.84322e17 + 5.69843e17i 0.185127 + 0.134503i
\(735\) −1.46718e17 4.51551e17i −0.0343253 0.105643i
\(736\) 1.23699e18 0.286853
\(737\) 1.49978e18 7.77502e17i 0.344737 0.178716i
\(738\) 1.50832e18 0.343659
\(739\) 1.56606e18 + 4.81983e18i 0.353687 + 1.08854i 0.956767 + 0.290856i \(0.0939401\pi\)
−0.603080 + 0.797681i \(0.706060\pi\)
\(740\) −7.98293e17 5.79994e17i −0.178713 0.129843i
\(741\) −4.61854e18 + 3.35556e18i −1.02491 + 0.744642i
\(742\) −1.49162e18 + 4.59075e18i −0.328121 + 1.00985i
\(743\) −9.28268e17 + 2.85691e18i −0.202417 + 0.622974i 0.797393 + 0.603460i \(0.206212\pi\)
−0.999810 + 0.0195138i \(0.993788\pi\)
\(744\) 6.75909e17 4.91077e17i 0.146105 0.106151i
\(745\) −3.75414e18 2.72754e18i −0.804442 0.584461i
\(746\) −2.87020e17 8.83358e17i −0.0609692 0.187644i
\(747\) −5.96155e17 −0.125538
\(748\) −2.92945e18 2.88855e18i −0.611540 0.603003i
\(749\) 8.88015e17 0.183776
\(750\) 1.36440e18 + 4.19918e18i 0.279925 + 0.861522i
\(751\) −4.82000e18 3.50194e18i −0.980364 0.712276i −0.0225743 0.999745i \(-0.507186\pi\)
−0.957790 + 0.287469i \(0.907186\pi\)
\(752\) 1.26321e18 9.17774e17i 0.254717 0.185063i
\(753\) 6.35896e17 1.95709e18i 0.127121 0.391239i
\(754\) −7.04136e17 + 2.16711e18i −0.139554 + 0.429503i
\(755\) 2.86234e18 2.07961e18i 0.562426 0.408627i
\(756\) 1.46201e18 + 1.06221e18i 0.284812 + 0.206928i
\(757\) 2.38499e18 + 7.34025e18i 0.460642 + 1.41771i 0.864381 + 0.502837i \(0.167711\pi\)
−0.403739 + 0.914874i \(0.632289\pi\)
\(758\) −1.30621e18 −0.250128
\(759\) 1.01750e19 + 1.53833e18i 1.93181 + 0.292064i
\(760\) −1.58206e18 −0.297807
\(761\) −5.28921e17 1.62785e18i −0.0987166 0.303819i 0.889488 0.456959i \(-0.151061\pi\)
−0.988204 + 0.153140i \(0.951061\pi\)
\(762\) −6.41644e18 4.66182e18i −1.18737 0.862677i
\(763\) −7.39787e18 + 5.37486e18i −1.35737 + 0.986184i
\(764\) −1.64568e18 + 5.06489e18i −0.299392 + 0.921432i
\(765\) −9.44740e17 + 2.90761e18i −0.170417 + 0.524490i
\(766\) −4.02268e18 + 2.92265e18i −0.719497 + 0.522745i
\(767\) −4.24577e18 3.08473e18i −0.752985 0.547076i
\(768\) 1.32236e17 + 4.06979e17i 0.0232542 + 0.0715689i
\(769\) −6.17110e18 −1.07607 −0.538036 0.842922i \(-0.680834\pi\)
−0.538036 + 0.842922i \(0.680834\pi\)
\(770\) −1.38913e18 + 2.77435e18i −0.240188 + 0.479702i
\(771\) −1.22394e19 −2.09848
\(772\) 2.96478e17 + 9.12466e17i 0.0504058 + 0.155133i
\(773\) −4.21810e18 3.06463e18i −0.711133 0.516668i 0.172406 0.985026i \(-0.444846\pi\)
−0.883539 + 0.468358i \(0.844846\pi\)
\(774\) 6.61847e17 4.80860e17i 0.110647 0.0803901i
\(775\) 3.87687e17 1.19318e18i 0.0642718 0.197808i
\(776\) 2.43214e17 7.48536e17i 0.0399841 0.123058i
\(777\) 3.92893e18 2.85454e18i 0.640528 0.465370i
\(778\) 4.28270e18 + 3.11157e18i 0.692390 + 0.503051i
\(779\) 2.45757e18 + 7.56363e18i 0.394015 + 1.21265i
\(780\) −2.41093e18 −0.383328
\(781\) −1.32094e17 7.97676e17i −0.0208282 0.125775i
\(782\) 1.26038e19 1.97087
\(783\) 9.45508e17 + 2.90997e18i 0.146627 + 0.451271i
\(784\) −1.69930e17 1.23462e17i −0.0261346 0.0189879i
\(785\) 3.80650e18 2.76558e18i 0.580594 0.421826i
\(786\) 2.29793e18 7.07231e18i 0.347609 1.06983i
\(787\) −1.24625e18 + 3.83558e18i −0.186970 + 0.575433i −0.999977 0.00682046i \(-0.997829\pi\)
0.813007 + 0.582254i \(0.197829\pi\)
\(788\) −2.66949e18 + 1.93949e18i −0.397198 + 0.288581i
\(789\) 6.28413e18 + 4.56569e18i 0.927352 + 0.673761i
\(790\) −7.60696e17 2.34118e18i −0.111336 0.342657i
\(791\) 1.30791e19 1.89859
\(792\) 1.80413e17 + 1.08946e18i 0.0259749 + 0.156855i
\(793\) 4.57007e18 0.652600
\(794\) −4.95928e17 1.52631e18i −0.0702402 0.216177i
\(795\) −6.99577e18 5.08272e18i −0.982764 0.714020i
\(796\) 3.57227e18 2.59541e18i 0.497748 0.361635i
\(797\) −4.40852e18 + 1.35680e19i −0.609275 + 1.87516i −0.145088 + 0.989419i \(0.546347\pi\)
−0.464187 + 0.885737i \(0.653653\pi\)
\(798\) 2.40612e18 7.40527e18i 0.329836 1.01513i
\(799\) 1.28710e19 9.35131e18i 1.75008 1.27151i
\(800\) 5.19867e17 + 3.77705e17i 0.0701144 + 0.0509411i
\(801\) 1.15375e18 + 3.55087e18i 0.154348 + 0.475033i
\(802\) −5.43794e18 −0.721608
\(803\) −1.73326e18 + 3.46166e18i −0.228146 + 0.455652i
\(804\) −1.79039e18 −0.233768
\(805\) −2.93733e18 9.04018e18i −0.380435 1.17086i
\(806\) 1.68469e18 + 1.22400e18i 0.216443 + 0.157255i
\(807\) 4.67112e18 3.39377e18i 0.595310 0.432518i
\(808\) 1.14294e17 3.51761e17i 0.0144494 0.0444706i
\(809\) 3.69972e18 1.13866e19i 0.463985 1.42800i −0.396270 0.918134i \(-0.629696\pi\)
0.860255 0.509864i \(-0.170304\pi\)
\(810\) −4.09544e18 + 2.97551e18i −0.509504 + 0.370177i
\(811\) −5.76320e18 4.18721e18i −0.711259 0.516760i 0.172320 0.985041i \(-0.444874\pi\)
−0.883580 + 0.468281i \(0.844874\pi\)
\(812\) −9.60382e17 2.95575e18i −0.117579 0.361871i
\(813\) −1.27946e19 −1.55396
\(814\) −3.59079e18 5.42879e17i −0.432644 0.0654100i
\(815\) 4.75931e18 0.568878
\(816\) 1.34736e18 + 4.14676e18i 0.159771 + 0.491726i
\(817\) 3.48969e18 + 2.53541e18i 0.410529 + 0.298267i
\(818\) 4.85300e18 3.52591e18i 0.566387 0.411504i
\(819\) 1.13742e18 3.50061e18i 0.131697 0.405320i
\(820\) −1.03787e18 + 3.19424e18i −0.119221 + 0.366926i
\(821\) −1.07599e19 + 7.81752e18i −1.22625 + 0.890920i −0.996603 0.0823551i \(-0.973756\pi\)
−0.229643 + 0.973275i \(0.573756\pi\)
\(822\) −2.10109e18 1.52653e18i −0.237562 0.172599i
\(823\) −2.78458e18 8.57006e18i −0.312364 0.961358i −0.976826 0.214036i \(-0.931339\pi\)
0.664462 0.747322i \(-0.268661\pi\)
\(824\) 2.49103e18 0.277237
\(825\) 3.80653e18 + 3.75339e18i 0.420319 + 0.414451i
\(826\) 7.15791e18 0.784180
\(827\) 5.32627e17 + 1.63926e18i 0.0578946 + 0.178181i 0.975822 0.218568i \(-0.0701384\pi\)
−0.917927 + 0.396749i \(0.870138\pi\)
\(828\) −2.73700e18 1.98855e18i −0.295174 0.214456i
\(829\) 3.07154e18 2.23161e18i 0.328664 0.238788i −0.411200 0.911545i \(-0.634890\pi\)
0.739863 + 0.672757i \(0.234890\pi\)
\(830\) 4.10212e17 1.26250e18i 0.0435513 0.134037i
\(831\) 1.63002e18 5.01668e18i 0.171706 0.528457i
\(832\) −8.62891e17 + 6.26927e17i −0.0901891 + 0.0655263i
\(833\) −1.73144e18 1.25797e18i −0.179562 0.130460i
\(834\) −3.93827e18 1.21208e19i −0.405253 1.24724i
\(835\) 9.04650e18 0.923673
\(836\) −5.16924e18 + 2.67979e18i −0.523704 + 0.271494i
\(837\) 2.79622e18 0.281097
\(838\) −3.09815e18 9.53514e18i −0.309042 0.951132i
\(839\) 1.39010e19 + 1.00997e19i 1.37592 + 0.999664i 0.997248 + 0.0741320i \(0.0236186\pi\)
0.378670 + 0.925532i \(0.376381\pi\)
\(840\) 2.66030e18 1.93282e18i 0.261285 0.189835i
\(841\) −1.54466e18 + 4.75397e18i −0.150542 + 0.463322i
\(842\) 3.93459e17 1.21094e18i 0.0380514 0.117110i
\(843\) 5.28279e17 3.83817e17i 0.0506972 0.0368337i
\(844\) 5.57302e18 + 4.04904e18i 0.530719 + 0.385590i
\(845\) 4.77727e17 + 1.47029e18i 0.0451452 + 0.138943i
\(846\) −4.27042e18 −0.400463
\(847\) 1.60533e17 + 1.14179e19i 0.0149391 + 1.06254i
\(848\) −3.82553e18 −0.353279
\(849\) 4.52337e18 + 1.39215e19i 0.414536 + 1.27581i
\(850\) 5.29699e18 + 3.84849e18i 0.481732 + 0.349999i
\(851\) 9.00092e18 6.53955e18i 0.812353 0.590209i
\(852\) −2.64800e17 + 8.14969e17i −0.0237170 + 0.0729935i
\(853\) −5.99591e17 + 1.84535e18i −0.0532950 + 0.164025i −0.974161 0.225853i \(-0.927483\pi\)
0.920866 + 0.389878i \(0.127483\pi\)
\(854\) −5.04275e18 + 3.66378e18i −0.444828 + 0.323186i
\(855\) 3.50053e18 + 2.54328e18i 0.306446 + 0.222646i
\(856\) 2.17479e17 + 6.69331e17i 0.0188946 + 0.0581515i
\(857\) 1.33759e18 0.115331 0.0576657 0.998336i \(-0.481634\pi\)
0.0576657 + 0.998336i \(0.481634\pi\)
\(858\) −7.87751e18 + 4.08379e18i −0.674096 + 0.349459i
\(859\) 2.10304e19 1.78604 0.893021 0.450016i \(-0.148582\pi\)
0.893021 + 0.450016i \(0.148582\pi\)
\(860\) 5.62924e17 + 1.73250e18i 0.0474471 + 0.146027i
\(861\) −1.33731e19 9.71611e18i −1.11869 0.812778i
\(862\) −2.39881e18 + 1.74284e18i −0.199159 + 0.144697i
\(863\) 5.03959e18 1.55103e19i 0.415265 1.27805i −0.496749 0.867894i \(-0.665473\pi\)
0.912014 0.410160i \(-0.134527\pi\)
\(864\) −4.42578e17 + 1.36211e18i −0.0361951 + 0.111397i
\(865\) 3.50924e18 2.54961e18i 0.284845 0.206952i
\(866\) −1.16133e19 8.43752e18i −0.935594 0.679749i
\(867\) 9.07534e18 + 2.79310e19i 0.725670 + 2.23338i
\(868\) −2.84021e18 −0.225410
\(869\) −6.45115e18 6.36109e18i −0.508170 0.501075i
\(870\) 5.56753e18 0.435299
\(871\) −1.37900e18 4.24412e18i −0.107015 0.329359i
\(872\) −5.86301e18 4.25972e18i −0.451610 0.328114i
\(873\) −1.74147e18 + 1.26525e18i −0.133145 + 0.0967354i
\(874\) 5.51225e18 1.69650e19i 0.418316 1.28745i
\(875\) 4.63831e18 1.42753e19i 0.349388 1.07531i
\(876\) 3.31935e18 2.41165e18i 0.248185 0.180317i
\(877\) −1.15255e19 8.37376e18i −0.855386 0.621474i 0.0712401 0.997459i \(-0.477304\pi\)
−0.926626 + 0.375985i \(0.877304\pi\)
\(878\) 4.36671e18 + 1.34394e19i 0.321692 + 0.990066i
\(879\) −3.22433e19 −2.35783
\(880\) −2.43134e18 3.67586e17i −0.176485 0.0266822i
\(881\) −2.54134e19 −1.83113 −0.915565 0.402170i \(-0.868256\pi\)
−0.915565 + 0.402170i \(0.868256\pi\)
\(882\) 1.77521e17 + 5.46352e17i 0.0126971 + 0.0390775i
\(883\) 1.39876e19 + 1.01626e19i 0.993114 + 0.721540i 0.960601 0.277932i \(-0.0896488\pi\)
0.0325134 + 0.999471i \(0.489649\pi\)
\(884\) −8.79210e18 + 6.38784e18i −0.619659 + 0.450209i
\(885\) −3.96250e18 + 1.21953e19i −0.277229 + 0.853222i
\(886\) −1.58041e18 + 4.86400e18i −0.109762 + 0.337811i
\(887\) 8.96368e18 6.51250e18i 0.617992 0.448997i −0.234228 0.972182i \(-0.575256\pi\)
0.852220 + 0.523184i \(0.175256\pi\)
\(888\) 3.11378e18 + 2.26230e18i 0.213110 + 0.154834i
\(889\) 8.33180e18 + 2.56426e19i 0.566079 + 1.74221i
\(890\) −8.31373e18 −0.560739
\(891\) −8.34137e18 + 1.66593e19i −0.558512 + 1.11546i
\(892\) 5.25178e18 0.349088
\(893\) −6.95796e18 2.14144e19i −0.459142 1.41309i
\(894\) 1.46432e19 + 1.06389e19i 0.959274 + 0.696953i
\(895\) 1.02948e19 7.47962e18i 0.669528 0.486441i
\(896\) 4.49540e17 1.38354e18i 0.0290246 0.0893285i
\(897\) 8.40024e18 2.58533e19i 0.538444 1.65716i
\(898\) 4.90837e18 3.56614e18i 0.312350 0.226935i
\(899\) −3.89043e18 2.82657e18i −0.245788 0.178575i
\(900\) −5.43087e17 1.67145e18i −0.0340638 0.104838i
\(901\) −3.89788e19 −2.42726
\(902\) 2.01946e18 + 1.21949e19i 0.124851 + 0.753940i
\(903\) −8.96560e18 −0.550312
\(904\) 3.20314e18 + 9.85824e18i 0.195200 + 0.600765i
\(905\) 3.49799e18 + 2.54144e18i 0.211643 + 0.153767i
\(906\) −1.11647e19 + 8.11162e18i −0.670677 + 0.487275i
\(907\) −3.34469e18 + 1.02939e19i −0.199484 + 0.613950i 0.800410 + 0.599452i \(0.204615\pi\)
−0.999895 + 0.0144977i \(0.995385\pi\)
\(908\) 4.41920e18 1.36009e19i 0.261689 0.805396i
\(909\) −8.18373e17 + 5.94583e17i −0.0481156 + 0.0349581i
\(910\) 6.63075e18 + 4.81752e18i 0.387073 + 0.281225i
\(911\) 4.59694e18 + 1.41479e19i 0.266440 + 0.820019i 0.991358 + 0.131183i \(0.0418777\pi\)
−0.724918 + 0.688835i \(0.758122\pi\)
\(912\) 6.17090e18 0.355126
\(913\) −7.98178e17 4.81997e18i −0.0456079 0.275413i
\(914\) 9.15797e18 0.519576
\(915\) −3.45059e18 1.06198e19i −0.194382 0.598247i
\(916\) 2.64035e18 + 1.91833e18i 0.147687 + 0.107301i
\(917\) −2.04518e19 + 1.48591e19i −1.13588 + 0.825263i
\(918\) −4.50948e18 + 1.38787e19i −0.248685 + 0.765372i
\(919\) −5.64992e18 + 1.73887e19i −0.309379 + 0.952172i 0.668627 + 0.743598i \(0.266882\pi\)
−0.978007 + 0.208574i \(0.933118\pi\)
\(920\) 6.09456e18 4.42796e18i 0.331377 0.240759i
\(921\) 1.02362e19 + 7.43701e18i 0.552649 + 0.401523i
\(922\) −5.37286e18 1.65360e19i −0.288041 0.886500i
\(923\) −2.13583e18 −0.113699
\(924\) 5.41835e18 1.08215e19i 0.286417 0.572031i
\(925\) 5.77962e18 0.303374
\(926\) 3.90920e18 + 1.20313e19i 0.203759 + 0.627105i
\(927\) −5.51174e18 4.00452e18i −0.285280 0.207268i
\(928\) 1.99266e18 1.44775e18i 0.102417 0.0744102i
\(929\) −8.46427e17 + 2.60504e18i −0.0432004 + 0.132957i −0.970330 0.241783i \(-0.922268\pi\)
0.927130 + 0.374740i \(0.122268\pi\)
\(930\) 1.57229e18 4.83902e18i 0.0796883 0.245255i
\(931\) −2.45049e18 + 1.78039e18i −0.123333 + 0.0896069i
\(932\) −8.68354e18 6.30896e18i −0.434004 0.315322i
\(933\) −1.28824e18 3.96478e18i −0.0639388 0.196784i
\(934\) 7.85469e18 0.387145
\(935\) −2.47732e19 3.74537e18i −1.21257 0.183324i
\(936\) 2.91710e18 0.141794
\(937\) −1.01336e19 3.11880e19i −0.489165 1.50550i −0.825856 0.563881i \(-0.809308\pi\)
0.336691 0.941615i \(-0.390692\pi\)
\(938\) 4.92409e18 + 3.57756e18i 0.236052 + 0.171502i
\(939\) 2.96111e19 2.15138e19i 1.40971 1.02421i
\(940\) 2.93846e18 9.04365e18i 0.138928 0.427575i
\(941\) −3.02972e18 + 9.32453e18i −0.142256 + 0.437819i −0.996648 0.0818103i \(-0.973930\pi\)
0.854392 + 0.519629i \(0.173930\pi\)
\(942\) −1.48474e19 + 1.07873e19i −0.692342 + 0.503016i
\(943\) −3.06368e19 2.22590e19i −1.41879 1.03081i
\(944\) 1.75300e18 + 5.39519e18i 0.0806240 + 0.248135i
\(945\) 1.10056e19 0.502697
\(946\) 4.77393e18 + 4.70728e18i 0.216563 + 0.213539i
\(947\) −2.08413e19 −0.938966 −0.469483 0.882941i \(-0.655560\pi\)
−0.469483 + 0.882941i \(0.655560\pi\)
\(948\) 2.96713e18 + 9.13190e18i 0.132765 + 0.408608i
\(949\) 8.27342e18 + 6.01099e18i 0.367667 + 0.267126i
\(950\) 7.49677e18 5.44672e18i 0.330880 0.240399i
\(951\) 1.48957e19 4.58444e19i 0.652963 2.00961i
\(952\) 4.58042e18 1.40971e19i 0.199418 0.613746i
\(953\) 2.33815e19 1.69876e19i 1.01104 0.734562i 0.0466117 0.998913i \(-0.485158\pi\)
0.964427 + 0.264351i \(0.0851576\pi\)
\(954\) 8.46451e18 + 6.14983e18i 0.363528 + 0.264118i
\(955\) 1.00223e19 + 3.08454e19i 0.427509 + 1.31574i
\(956\) −1.80944e19 −0.766600
\(957\) 1.81914e19 9.43064e18i 0.765489 0.396838i
\(958\) 5.22003e17 0.0218171
\(959\) 2.72828e18 + 8.39678e18i 0.113258 + 0.348572i
\(960\) 2.10836e18 + 1.53181e18i 0.0869323 + 0.0631600i
\(961\) 1.61988e19 1.17691e19i 0.663409 0.481995i
\(962\) −2.96446e18 + 9.12366e18i −0.120589 + 0.371134i
\(963\) 5.94799e17 1.83060e18i 0.0240325 0.0739644i
\(964\) −1.00102e18 + 7.27280e17i −0.0401735 + 0.0291878i
\(965\) 4.72703e18 + 3.43439e18i 0.188435 + 0.136906i
\(966\) 1.14572e19 + 3.52617e19i 0.453657 + 1.39621i
\(967\) 4.55874e19 1.79297 0.896484 0.443076i \(-0.146113\pi\)
0.896484 + 0.443076i \(0.146113\pi\)
\(968\) −8.56682e18 + 2.91730e18i −0.334680 + 0.113970i
\(969\) 6.28760e19 2.43995
\(970\) −1.48118e18 4.55861e18i −0.0570943 0.175718i
\(971\) −3.53661e19 2.56950e19i −1.35414 0.983838i −0.998794 0.0491014i \(-0.984364\pi\)
−0.355343 0.934736i \(-0.615636\pi\)
\(972\) 8.92752e18 6.48622e18i 0.339547 0.246695i
\(973\) −1.33883e19 + 4.12049e19i −0.505815 + 1.55674i
\(974\) 2.86100e18 8.80524e18i 0.107370 0.330452i
\(975\) 1.14245e19 8.30038e18i 0.425899 0.309434i
\(976\) −3.99652e18 2.90364e18i −0.147999 0.107527i
\(977\) −1.09114e19 3.35817e19i −0.401388 1.23535i −0.923874 0.382697i \(-0.874995\pi\)
0.522486 0.852648i \(-0.325005\pi\)
\(978\) −1.85639e19 −0.678370
\(979\) −2.71644e19 + 1.40823e19i −0.986081 + 0.511196i
\(980\) −1.27919e18 −0.0461280
\(981\) 6.12489e18 + 1.88505e19i 0.219407 + 0.675264i
\(982\) −1.12575e19 8.17905e18i −0.400606 0.291057i
\(983\) −1.18247e19 + 8.59111e18i −0.418014 + 0.303705i −0.776838 0.629700i \(-0.783178\pi\)
0.358824 + 0.933405i \(0.383178\pi\)
\(984\) 4.04828e18 1.24593e19i 0.142168 0.437548i
\(985\) −6.20973e18 + 1.91116e19i −0.216639 + 0.666747i
\(986\) 2.03035e19 1.47513e19i 0.703672 0.511247i
\(987\) 3.78623e19 + 2.75086e19i 1.30360 + 0.947123i
\(988\) 4.75295e18 + 1.46281e19i 0.162571 + 0.500342i
\(989\) −2.05396e19 −0.697936
\(990\) 4.78875e18 + 4.72190e18i 0.161657 + 0.159400i
\(991\) 9.80576e18 0.328853 0.164427 0.986389i \(-0.447423\pi\)
0.164427 + 0.986389i \(0.447423\pi\)
\(992\) −6.95580e17 2.14077e18i −0.0231751 0.0713255i
\(993\) −2.62898e19 1.91006e19i −0.870195 0.632233i
\(994\) 2.35674e18 1.71227e18i 0.0774998 0.0563069i
\(995\) 8.30979e18 2.55749e19i 0.271481 0.835533i
\(996\) −1.60005e18 + 4.92446e18i −0.0519337 + 0.159835i
\(997\) 1.30637e19 9.49135e18i 0.421258 0.306062i −0.356886 0.934148i \(-0.616161\pi\)
0.778144 + 0.628086i \(0.216161\pi\)
\(998\) −2.32278e19 1.68760e19i −0.744150 0.540657i
\(999\) 3.98065e18 + 1.22512e19i 0.126701 + 0.389944i
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 22.14.c.b.5.2 28
11.9 even 5 inner 22.14.c.b.9.2 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.14.c.b.5.2 28 1.1 even 1 trivial
22.14.c.b.9.2 yes 28 11.9 even 5 inner