Properties

Label 11.13.d.a.6.1
Level $11$
Weight $13$
Character 11.6
Analytic conductor $10.054$
Analytic rank $0$
Dimension $44$
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] = [11,13,Mod(2,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.2");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 11.d (of order \(10\), 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: \(10.0539319900\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 6.1
Character \(\chi\) \(=\) 11.6
Dual form 11.13.d.a.2.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-102.224 + 33.2144i) q^{2} +(-276.412 - 200.825i) q^{3} +(6032.72 - 4383.03i) q^{4} +(-6925.60 + 21314.8i) q^{5} +(34926.2 + 11348.2i) q^{6} +(128352. + 176662. i) q^{7} +(-212330. + 292248. i) q^{8} +(-128151. - 394409. i) q^{9} +O(q^{10})\) \(q+(-102.224 + 33.2144i) q^{2} +(-276.412 - 200.825i) q^{3} +(6032.72 - 4383.03i) q^{4} +(-6925.60 + 21314.8i) q^{5} +(34926.2 + 11348.2i) q^{6} +(128352. + 176662. i) q^{7} +(-212330. + 292248. i) q^{8} +(-128151. - 394409. i) q^{9} -2.40891e6i q^{10} +(-964895. + 1.48573e6i) q^{11} -2.54774e6 q^{12} +(2.85246e6 - 926820. i) q^{13} +(-1.89884e7 - 1.37959e7i) q^{14} +(6.19488e6 - 4.50084e6i) q^{15} +(2.55994e6 - 7.87867e6i) q^{16} +(-2.47333e7 - 8.03634e6i) q^{17} +(2.62002e7 + 3.60614e7i) q^{18} +(-1.37957e7 + 1.89881e7i) q^{19} +(5.16432e7 + 1.58941e8i) q^{20} -7.46080e7i q^{21} +(4.92871e7 - 1.83925e8i) q^{22} -2.03166e7 q^{23} +(1.17382e8 - 3.81396e7i) q^{24} +(-2.08843e8 - 1.51734e8i) q^{25} +(-2.60804e8 + 1.89486e8i) q^{26} +(-9.98944e7 + 3.07443e8i) q^{27} +(1.54863e9 + 5.03180e8i) q^{28} +(-2.97287e8 - 4.09181e8i) q^{29} +(-4.83769e8 + 6.65851e8i) q^{30} +(-3.09488e7 - 9.52506e7i) q^{31} -5.89219e8i q^{32} +(5.65082e8 - 2.16900e8i) q^{33} +2.79525e9 q^{34} +(-4.65444e9 + 1.51232e9i) q^{35} +(-2.50181e9 - 1.81767e9i) q^{36} +(3.00640e8 - 2.18427e8i) q^{37} +(7.79562e8 - 2.39925e9i) q^{38} +(-9.74583e8 - 3.16661e8i) q^{39} +(-4.75869e9 - 6.54977e9i) q^{40} +(5.62742e7 - 7.74548e7i) q^{41} +(2.47806e9 + 7.62669e9i) q^{42} -1.17244e10i q^{43} +(6.91074e8 + 1.31922e10i) q^{44} +9.29428e9 q^{45} +(2.07683e9 - 6.74803e8i) q^{46} +(3.70325e9 + 2.69057e9i) q^{47} +(-2.28984e9 + 1.66366e9i) q^{48} +(-1.04579e10 + 3.21862e10i) q^{49} +(2.63884e10 + 8.57413e9i) q^{50} +(5.22269e9 + 7.18842e9i) q^{51} +(1.31458e10 - 1.80936e10i) q^{52} +(1.37108e8 + 4.21975e8i) q^{53} -3.47459e10i q^{54} +(-2.49857e10 - 3.08562e10i) q^{55} -7.88822e10 q^{56} +(7.62659e9 - 2.47803e9i) q^{57} +(4.39804e10 + 3.19537e10i) q^{58} +(-1.02896e10 + 7.47584e9i) q^{59} +(1.76446e10 - 5.43046e10i) q^{60} +(-3.68200e10 - 1.19635e10i) q^{61} +(6.32739e9 + 8.70890e9i) q^{62} +(5.32286e10 - 7.32629e10i) q^{63} +(3.00561e10 + 9.25031e10i) q^{64} +6.72184e10i q^{65} +(-5.05605e10 + 4.09412e10i) q^{66} -1.66979e11 q^{67} +(-1.84432e11 + 5.99257e10i) q^{68} +(5.61575e9 + 4.08008e9i) q^{69} +(4.25562e11 - 3.09189e11i) q^{70} +(-1.67949e10 + 5.16894e10i) q^{71} +(1.42476e11 + 4.62931e10i) q^{72} +(-9.50064e10 - 1.30765e11i) q^{73} +(-2.34775e10 + 3.23140e10i) q^{74} +(2.72549e10 + 8.38821e10i) q^{75} +1.75017e11i q^{76} +(-3.86320e11 + 2.02374e10i) q^{77} +1.10143e11 q^{78} +(2.26473e11 - 7.35856e10i) q^{79} +(1.50203e11 + 1.09129e11i) q^{80} +(-8.89464e10 + 6.46233e10i) q^{81} +(-3.17993e9 + 9.78682e9i) q^{82} +(1.21293e11 + 3.94106e10i) q^{83} +(-3.27009e11 - 4.50089e11i) q^{84} +(3.42586e11 - 4.71529e11i) q^{85} +(3.89421e11 + 1.19851e12i) q^{86} +1.72805e11i q^{87} +(-2.29326e11 - 5.97455e11i) q^{88} +3.52477e11 q^{89} +(-9.50094e11 + 3.08704e11i) q^{90} +(5.29854e11 + 3.84961e11i) q^{91} +(-1.22564e11 + 8.90480e10i) q^{92} +(-1.05741e10 + 3.25437e10i) q^{93} +(-4.67925e11 - 1.52038e11i) q^{94} +(-3.09185e11 - 4.25556e11i) q^{95} +(-1.18330e11 + 1.62867e11i) q^{96} +(6.99748e10 + 2.15360e11i) q^{97} -3.63754e12i q^{98} +(7.09640e11 + 1.90165e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 5 q^{2} - 1083 q^{3} + 16247 q^{4} - 723 q^{5} + 147195 q^{6} - 219605 q^{7} + 921595 q^{8} - 3695582 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 5 q^{2} - 1083 q^{3} + 16247 q^{4} - 723 q^{5} + 147195 q^{6} - 219605 q^{7} + 921595 q^{8} - 3695582 q^{9} + 2565608 q^{11} + 7500402 q^{12} - 6670805 q^{13} - 249422 q^{14} + 31344279 q^{15} - 182249929 q^{16} - 7887605 q^{17} + 296147970 q^{18} - 59195705 q^{19} - 119854528 q^{20} + 615523885 q^{22} - 407959208 q^{23} + 217767665 q^{24} - 1102003838 q^{25} - 1289107598 q^{26} + 945406779 q^{27} + 5018997220 q^{28} - 541321205 q^{29} - 7192403540 q^{30} + 1789230381 q^{31} + 8868147617 q^{33} + 4668584258 q^{34} - 3628416965 q^{35} - 18485968210 q^{36} - 7637278083 q^{37} - 1555712420 q^{38} + 24275524235 q^{39} + 17352998460 q^{40} - 20307362045 q^{41} - 51939651970 q^{42} + 73504485716 q^{44} + 33796434396 q^{45} - 10698599530 q^{46} - 13177100523 q^{47} - 48055484488 q^{48} - 11538977128 q^{49} + 8631835695 q^{50} + 103295029335 q^{51} - 124762325930 q^{52} + 80932774677 q^{53} - 87742505883 q^{55} - 162644024476 q^{56} + 156654446895 q^{57} + 68439789940 q^{58} + 153452464089 q^{59} + 211654410344 q^{60} - 130004870645 q^{61} - 478111392680 q^{62} + 56162082000 q^{63} + 88053755815 q^{64} - 547107987930 q^{66} + 172356405472 q^{67} + 550428178040 q^{68} + 147718471202 q^{69} + 656066411580 q^{70} - 276485879307 q^{71} - 1923582671435 q^{72} + 401204208595 q^{73} + 668106311350 q^{74} + 545281450749 q^{75} - 431450680685 q^{77} + 349062971320 q^{78} + 454959862075 q^{79} + 732789378812 q^{80} + 681177766216 q^{81} + 455720922385 q^{82} - 1768304661305 q^{83} - 2152859747190 q^{84} - 2586009108005 q^{85} - 686286163053 q^{86} + 2647326267355 q^{88} + 587790027856 q^{89} + 6704158241200 q^{90} - 245650237373 q^{91} + 3006033812992 q^{92} + 794315205079 q^{93} - 1053727188680 q^{94} - 7101305012165 q^{95} - 13699998107060 q^{96} + 647608267617 q^{97} + 6944343091354 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{9}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −102.224 + 33.2144i −1.59724 + 0.518976i −0.966424 0.256954i \(-0.917281\pi\)
−0.630819 + 0.775930i \(0.717281\pi\)
\(3\) −276.412 200.825i −0.379167 0.275481i 0.381835 0.924230i \(-0.375292\pi\)
−0.761002 + 0.648750i \(0.775292\pi\)
\(4\) 6032.72 4383.03i 1.47283 1.07007i
\(5\) −6925.60 + 21314.8i −0.443239 + 1.36415i 0.441165 + 0.897426i \(0.354565\pi\)
−0.884404 + 0.466722i \(0.845435\pi\)
\(6\) 34926.2 + 11348.2i 0.748589 + 0.243231i
\(7\) 128352. + 176662.i 1.09098 + 1.50160i 0.846829 + 0.531865i \(0.178509\pi\)
0.244149 + 0.969738i \(0.421491\pi\)
\(8\) −212330. + 292248.i −0.809976 + 1.11484i
\(9\) −128151. 394409.i −0.241139 0.742150i
\(10\) 2.40891e6i 2.40891i
\(11\) −964895. + 1.48573e6i −0.544658 + 0.838658i
\(12\) −2.54774e6 −0.853233
\(13\) 2.85246e6 926820.i 0.590961 0.192015i 0.00175617 0.999998i \(-0.499441\pi\)
0.589205 + 0.807983i \(0.299441\pi\)
\(14\) −1.89884e7 1.37959e7i −2.52185 1.83223i
\(15\) 6.19488e6 4.50084e6i 0.543858 0.395136i
\(16\) 2.55994e6 7.87867e6i 0.152584 0.469606i
\(17\) −2.47333e7 8.03634e6i −1.02468 0.332939i −0.251995 0.967728i \(-0.581087\pi\)
−0.772685 + 0.634790i \(0.781087\pi\)
\(18\) 2.62002e7 + 3.60614e7i 0.770316 + 1.06025i
\(19\) −1.37957e7 + 1.89881e7i −0.293239 + 0.403608i −0.930063 0.367401i \(-0.880248\pi\)
0.636824 + 0.771009i \(0.280248\pi\)
\(20\) 5.16432e7 + 1.58941e8i 0.806925 + 2.48346i
\(21\) 7.46080e7i 0.869901i
\(22\) 4.92871e7 1.83925e8i 0.434708 1.62220i
\(23\) −2.03166e7 −0.137241 −0.0686204 0.997643i \(-0.521860\pi\)
−0.0686204 + 0.997643i \(0.521860\pi\)
\(24\) 1.17382e8 3.81396e7i 0.614232 0.199576i
\(25\) −2.08843e8 1.51734e8i −0.855422 0.621501i
\(26\) −2.60804e8 + 1.89486e8i −0.844258 + 0.613389i
\(27\) −9.98944e7 + 3.07443e8i −0.257845 + 0.793565i
\(28\) 1.54863e9 + 5.03180e8i 3.21365 + 1.04418i
\(29\) −2.97287e8 4.09181e8i −0.499791 0.687903i 0.482366 0.875970i \(-0.339778\pi\)
−0.982156 + 0.188067i \(0.939778\pi\)
\(30\) −4.83769e8 + 6.65851e8i −0.663607 + 0.913376i
\(31\) −3.09488e7 9.52506e7i −0.0348717 0.107324i 0.932106 0.362187i \(-0.117970\pi\)
−0.966977 + 0.254863i \(0.917970\pi\)
\(32\) 5.89219e8i 0.548753i
\(33\) 5.65082e8 2.16900e8i 0.437550 0.167948i
\(34\) 2.79525e9 1.80945
\(35\) −4.65444e9 + 1.51232e9i −2.53197 + 0.822687i
\(36\) −2.50181e9 1.81767e9i −1.14931 0.835025i
\(37\) 3.00640e8 2.18427e8i 0.117175 0.0851328i −0.527654 0.849459i \(-0.676928\pi\)
0.644830 + 0.764326i \(0.276928\pi\)
\(38\) 7.79562e8 2.39925e9i 0.258910 0.796844i
\(39\) −9.74583e8 3.16661e8i −0.276969 0.0899927i
\(40\) −4.75869e9 6.54977e9i −1.16179 1.59907i
\(41\) 5.62742e7 7.74548e7i 0.0118469 0.0163059i −0.803052 0.595908i \(-0.796792\pi\)
0.814899 + 0.579602i \(0.196792\pi\)
\(42\) 2.47806e9 + 7.62669e9i 0.451457 + 1.38944i
\(43\) 1.17244e10i 1.85473i −0.374153 0.927367i \(-0.622066\pi\)
0.374153 0.927367i \(-0.377934\pi\)
\(44\) 6.91074e8 + 1.31922e10i 0.0952377 + 1.81803i
\(45\) 9.29428e9 1.11929
\(46\) 2.07683e9 6.74803e8i 0.219207 0.0712246i
\(47\) 3.70325e9 + 2.69057e9i 0.343555 + 0.249607i 0.746160 0.665766i \(-0.231895\pi\)
−0.402605 + 0.915374i \(0.631895\pi\)
\(48\) −2.28984e9 + 1.66366e9i −0.187222 + 0.136025i
\(49\) −1.04579e10 + 3.21862e10i −0.755560 + 2.32537i
\(50\) 2.63884e10 + 8.57413e9i 1.68886 + 0.548744i
\(51\) 5.22269e9 + 7.18842e9i 0.296806 + 0.408519i
\(52\) 1.31458e10 1.80936e10i 0.664916 0.915178i
\(53\) 1.37108e8 + 4.21975e8i 0.00618597 + 0.0190385i 0.954102 0.299482i \(-0.0968139\pi\)
−0.947916 + 0.318521i \(0.896814\pi\)
\(54\) 3.47459e10i 1.40133i
\(55\) −2.49857e10 3.08562e10i −0.902641 1.11472i
\(56\) −7.88822e10 −2.55771
\(57\) 7.62659e9 2.47803e9i 0.222372 0.0722532i
\(58\) 4.39804e10 + 3.19537e10i 1.15529 + 0.839369i
\(59\) −1.02896e10 + 7.47584e9i −0.243942 + 0.177234i −0.703038 0.711152i \(-0.748174\pi\)
0.459096 + 0.888387i \(0.348174\pi\)
\(60\) 1.76446e10 5.43046e10i 0.378186 1.16394i
\(61\) −3.68200e10 1.19635e10i −0.714668 0.232210i −0.0709580 0.997479i \(-0.522606\pi\)
−0.643710 + 0.765270i \(0.722606\pi\)
\(62\) 6.32739e9 + 8.70890e9i 0.111397 + 0.153325i
\(63\) 5.32286e10 7.32629e10i 0.851337 1.17177i
\(64\) 3.00561e10 + 9.25031e10i 0.437373 + 1.34610i
\(65\) 6.72184e10i 0.891267i
\(66\) −5.05605e10 + 4.09412e10i −0.611713 + 0.495332i
\(67\) −1.66979e11 −1.84592 −0.922962 0.384892i \(-0.874239\pi\)
−0.922962 + 0.384892i \(0.874239\pi\)
\(68\) −1.84432e11 + 5.99257e10i −1.86545 + 0.606122i
\(69\) 5.61575e9 + 4.08008e9i 0.0520371 + 0.0378072i
\(70\) 4.25562e11 3.09189e11i 3.61722 2.62806i
\(71\) −1.67949e10 + 5.16894e10i −0.131108 + 0.403508i −0.994964 0.100230i \(-0.968042\pi\)
0.863857 + 0.503738i \(0.168042\pi\)
\(72\) 1.42476e11 + 4.62931e10i 1.02269 + 0.332293i
\(73\) −9.50064e10 1.30765e11i −0.627792 0.864081i 0.370099 0.928992i \(-0.379324\pi\)
−0.997891 + 0.0649109i \(0.979324\pi\)
\(74\) −2.34775e10 + 3.23140e10i −0.142975 + 0.196789i
\(75\) 2.72549e10 + 8.38821e10i 0.153136 + 0.471304i
\(76\) 1.75017e11i 0.908234i
\(77\) −3.86320e11 + 2.02374e10i −1.85354 + 0.0970981i
\(78\) 1.10143e11 0.489091
\(79\) 2.26473e11 7.35856e10i 0.931653 0.302712i 0.196414 0.980521i \(-0.437070\pi\)
0.735238 + 0.677809i \(0.237070\pi\)
\(80\) 1.50203e11 + 1.09129e11i 0.572980 + 0.416295i
\(81\) −8.89464e10 + 6.46233e10i −0.314933 + 0.228812i
\(82\) −3.17993e9 + 9.78682e9i −0.0104601 + 0.0321928i
\(83\) 1.21293e11 + 3.94106e10i 0.370995 + 0.120544i 0.488580 0.872519i \(-0.337515\pi\)
−0.117585 + 0.993063i \(0.537515\pi\)
\(84\) −3.27009e11 4.50089e11i −0.930859 1.28122i
\(85\) 3.42586e11 4.71529e11i 0.908356 1.25024i
\(86\) 3.89421e11 + 1.19851e12i 0.962562 + 2.96246i
\(87\) 1.72805e11i 0.398512i
\(88\) −2.29326e11 5.97455e11i −0.493807 1.28650i
\(89\) 3.52477e11 0.709236 0.354618 0.935011i \(-0.384611\pi\)
0.354618 + 0.935011i \(0.384611\pi\)
\(90\) −9.50094e11 + 3.08704e11i −1.78777 + 0.580882i
\(91\) 5.29854e11 + 3.84961e11i 0.933056 + 0.677905i
\(92\) −1.22564e11 + 8.90480e10i −0.202132 + 0.146858i
\(93\) −1.05741e10 + 3.25437e10i −0.0163435 + 0.0503002i
\(94\) −4.67925e11 1.52038e11i −0.678281 0.220387i
\(95\) −3.09185e11 4.25556e11i −0.420607 0.578915i
\(96\) −1.18330e11 + 1.62867e11i −0.151171 + 0.208069i
\(97\) 6.99748e10 + 2.15360e11i 0.0840062 + 0.258544i 0.984233 0.176877i \(-0.0565994\pi\)
−0.900227 + 0.435421i \(0.856599\pi\)
\(98\) 3.63754e12i 4.10631i
\(99\) 7.09640e11 + 1.90165e11i 0.753749 + 0.201985i
\(100\) −1.92494e12 −1.92494
\(101\) −5.73087e11 + 1.86207e11i −0.539874 + 0.175416i −0.566245 0.824237i \(-0.691605\pi\)
0.0263719 + 0.999652i \(0.491605\pi\)
\(102\) −7.72641e11 5.61357e11i −0.686083 0.498469i
\(103\) 6.83345e11 4.96479e11i 0.572291 0.415793i −0.263646 0.964620i \(-0.584925\pi\)
0.835937 + 0.548826i \(0.184925\pi\)
\(104\) −3.34803e11 + 1.03042e12i −0.264599 + 0.814353i
\(105\) 1.59026e12 + 5.16705e11i 1.18667 + 0.385574i
\(106\) −2.80313e10 3.85818e10i −0.0197610 0.0271987i
\(107\) −1.60851e11 + 2.21392e11i −0.107182 + 0.147523i −0.859238 0.511576i \(-0.829062\pi\)
0.752057 + 0.659098i \(0.229062\pi\)
\(108\) 7.44897e11 + 2.29256e12i 0.469412 + 1.44470i
\(109\) 2.05500e12i 1.22533i 0.790343 + 0.612665i \(0.209902\pi\)
−0.790343 + 0.612665i \(0.790098\pi\)
\(110\) 3.57899e12 + 2.32434e12i 2.02025 + 1.31203i
\(111\) −1.26966e11 −0.0678814
\(112\) 1.72044e12 5.59004e11i 0.871627 0.283209i
\(113\) 2.07295e12 + 1.50608e12i 0.995675 + 0.723400i 0.961157 0.276004i \(-0.0890102\pi\)
0.0345185 + 0.999404i \(0.489010\pi\)
\(114\) −6.97310e11 + 5.06626e11i −0.317685 + 0.230812i
\(115\) 1.40704e11 4.33043e11i 0.0608304 0.187217i
\(116\) −3.58690e12 1.16545e12i −1.47221 0.478352i
\(117\) −7.31092e11 1.00626e12i −0.285008 0.392280i
\(118\) 8.03535e11 1.10597e12i 0.297655 0.409686i
\(119\) −1.75486e12 5.40092e12i −0.617962 1.90189i
\(120\) 2.76610e12i 0.926363i
\(121\) −1.27638e12 2.86715e12i −0.406695 0.913564i
\(122\) 4.16123e12 1.26201
\(123\) −3.11098e10 + 1.01082e10i −0.00898393 + 0.00291906i
\(124\) −6.04191e11 4.38970e11i −0.166205 0.120755i
\(125\) 2.53911e11 1.84477e11i 0.0665612 0.0483596i
\(126\) −3.00783e12 + 9.25715e12i −0.751675 + 2.31342i
\(127\) −2.26703e12 7.36603e11i −0.540300 0.175554i 0.0261380 0.999658i \(-0.491679\pi\)
−0.566438 + 0.824104i \(0.691679\pi\)
\(128\) −4.72629e12 6.50518e12i −1.07463 1.47911i
\(129\) −2.35457e12 + 3.24078e12i −0.510943 + 0.703253i
\(130\) −2.23262e12 6.87130e12i −0.462546 1.42357i
\(131\) 6.26574e12i 1.23978i 0.784689 + 0.619890i \(0.212823\pi\)
−0.784689 + 0.619890i \(0.787177\pi\)
\(132\) 2.45830e12 3.78527e12i 0.464720 0.715571i
\(133\) −5.12519e12 −0.925976
\(134\) 1.70692e13 5.54612e12i 2.94839 0.957989i
\(135\) −5.86127e12 4.25846e12i −0.968253 0.703477i
\(136\) 7.60023e12 5.52189e12i 1.20114 0.872679i
\(137\) 1.17473e12 3.61546e12i 0.177671 0.546815i −0.822074 0.569380i \(-0.807183\pi\)
0.999745 + 0.0225651i \(0.00718331\pi\)
\(138\) −7.09579e11 2.30556e11i −0.102737 0.0333812i
\(139\) 5.66062e12 + 7.79118e12i 0.784830 + 1.08023i 0.994733 + 0.102503i \(0.0326852\pi\)
−0.209903 + 0.977722i \(0.567315\pi\)
\(140\) −2.14504e13 + 2.95239e13i −2.84883 + 3.92108i
\(141\) −4.83290e11 1.48741e12i −0.0615026 0.189286i
\(142\) 5.84171e12i 0.712541i
\(143\) −1.37531e12 + 5.13228e12i −0.160837 + 0.600197i
\(144\) −3.43548e12 −0.385312
\(145\) 1.07805e13 3.50280e12i 1.15993 0.376883i
\(146\) 1.40552e13 + 1.02117e13i 1.45117 + 1.05434i
\(147\) 9.35450e12 6.79644e12i 0.927079 0.673562i
\(148\) 8.56301e11 2.63542e12i 0.0814809 0.250772i
\(149\) −1.95305e13 6.34586e12i −1.78483 0.579926i −0.785583 0.618756i \(-0.787637\pi\)
−0.999246 + 0.0388297i \(0.987637\pi\)
\(150\) −5.57219e12 7.66946e12i −0.489191 0.673314i
\(151\) −1.85380e12 + 2.55153e12i −0.156387 + 0.215248i −0.880020 0.474937i \(-0.842471\pi\)
0.723633 + 0.690185i \(0.242471\pi\)
\(152\) −2.61999e12 8.06350e12i −0.212441 0.653826i
\(153\) 1.07849e13i 0.840752i
\(154\) 3.88188e13 1.49001e13i 2.91016 1.11703i
\(155\) 2.24459e12 0.161863
\(156\) −7.26732e12 + 2.36130e12i −0.504228 + 0.163834i
\(157\) −1.13141e13 8.22021e12i −0.755482 0.548889i 0.142040 0.989861i \(-0.454634\pi\)
−0.897521 + 0.440972i \(0.854634\pi\)
\(158\) −2.07068e13 + 1.50444e13i −1.33098 + 0.967010i
\(159\) 4.68450e10 1.44174e11i 0.00289921 0.00892286i
\(160\) 1.25591e13 + 4.08069e12i 0.748580 + 0.243228i
\(161\) −2.60768e12 3.58916e12i −0.149727 0.206081i
\(162\) 6.94599e12 9.56033e12i 0.384277 0.528911i
\(163\) 7.90636e12 + 2.43333e13i 0.421552 + 1.29740i 0.906257 + 0.422726i \(0.138927\pi\)
−0.484706 + 0.874677i \(0.661073\pi\)
\(164\) 7.13914e11i 0.0366930i
\(165\) 7.09650e11 + 1.35468e13i 0.0351674 + 0.671324i
\(166\) −1.37080e13 −0.655129
\(167\) 2.28305e13 7.41809e12i 1.05249 0.341974i 0.268844 0.963184i \(-0.413358\pi\)
0.783644 + 0.621210i \(0.213358\pi\)
\(168\) 2.18040e13 + 1.58416e13i 0.969797 + 0.704599i
\(169\) −1.15710e13 + 8.40684e12i −0.496651 + 0.360838i
\(170\) −1.93588e13 + 5.95802e13i −0.802018 + 2.46836i
\(171\) 9.25702e12 + 3.00779e12i 0.370249 + 0.120301i
\(172\) −5.13886e13 7.07303e13i −1.98470 2.73171i
\(173\) 1.17680e13 1.61973e13i 0.438962 0.604179i −0.531019 0.847360i \(-0.678191\pi\)
0.969981 + 0.243180i \(0.0781907\pi\)
\(174\) −5.73963e12 1.76648e13i −0.206818 0.636521i
\(175\) 5.63701e13i 1.96255i
\(176\) 9.23555e12 + 1.14055e13i 0.310732 + 0.383740i
\(177\) 4.34552e12 0.141319
\(178\) −3.60314e13 + 1.17073e13i −1.13282 + 0.368076i
\(179\) −2.07194e13 1.50535e13i −0.629881 0.457635i 0.226478 0.974016i \(-0.427279\pi\)
−0.856359 + 0.516381i \(0.827279\pi\)
\(180\) 5.60698e13 4.07371e13i 1.64852 1.19772i
\(181\) −1.69303e13 + 5.21062e13i −0.481497 + 1.48190i 0.355494 + 0.934679i \(0.384313\pi\)
−0.836991 + 0.547217i \(0.815687\pi\)
\(182\) −6.69498e13 2.17533e13i −1.84213 0.598545i
\(183\) 7.77491e12 + 1.07012e13i 0.207009 + 0.284923i
\(184\) 4.31382e12 5.93747e12i 0.111162 0.153001i
\(185\) 2.57363e12 + 7.92082e12i 0.0641971 + 0.197578i
\(186\) 3.67795e12i 0.0888235i
\(187\) 3.58049e13 2.89929e13i 0.837322 0.678019i
\(188\) 3.41335e13 0.773097
\(189\) −6.71352e13 + 2.18136e13i −1.47292 + 0.478581i
\(190\) 4.57405e13 + 3.32325e13i 0.972254 + 0.706384i
\(191\) 2.18594e13 1.58818e13i 0.450234 0.327114i −0.339454 0.940623i \(-0.610242\pi\)
0.789688 + 0.613508i \(0.210242\pi\)
\(192\) 1.02691e13 3.16050e13i 0.204986 0.630883i
\(193\) −6.00557e11 1.95133e11i −0.0116201 0.00377560i 0.303201 0.952927i \(-0.401945\pi\)
−0.314821 + 0.949151i \(0.601945\pi\)
\(194\) −1.43061e13 1.96907e13i −0.268356 0.369361i
\(195\) 1.34992e13 1.85800e13i 0.245527 0.337939i
\(196\) 7.79832e13 + 2.40007e14i 1.37551 + 4.23339i
\(197\) 4.26153e13i 0.729068i 0.931190 + 0.364534i \(0.118772\pi\)
−0.931190 + 0.364534i \(0.881228\pi\)
\(198\) −7.88581e13 + 4.13100e12i −1.30875 + 0.0685589i
\(199\) −6.29059e13 −1.01291 −0.506457 0.862265i \(-0.669045\pi\)
−0.506457 + 0.862265i \(0.669045\pi\)
\(200\) 8.86876e13 2.88163e13i 1.38574 0.450255i
\(201\) 4.61551e13 + 3.35337e13i 0.699912 + 0.508516i
\(202\) 5.23982e13 3.80695e13i 0.771273 0.560362i
\(203\) 3.41291e13 1.05039e14i 0.487696 1.50097i
\(204\) 6.30140e13 + 2.04745e13i 0.874291 + 0.284075i
\(205\) 1.26120e12 + 1.73590e12i 0.0169927 + 0.0233884i
\(206\) −5.33636e13 + 7.34488e13i −0.698300 + 0.961128i
\(207\) 2.60359e12 + 8.01303e12i 0.0330941 + 0.101853i
\(208\) 2.48462e13i 0.306817i
\(209\) −1.48999e13 3.88182e13i −0.178775 0.465755i
\(210\) −1.79724e14 −2.09551
\(211\) −4.21413e13 + 1.36925e13i −0.477544 + 0.155163i −0.537891 0.843014i \(-0.680779\pi\)
0.0603479 + 0.998177i \(0.480779\pi\)
\(212\) 2.67666e12 + 1.94471e12i 0.0294835 + 0.0214210i
\(213\) 1.50229e13 1.09148e13i 0.160870 0.116879i
\(214\) 9.08931e12 2.79740e13i 0.0946342 0.291254i
\(215\) 2.49904e14 + 8.11989e13i 2.53013 + 0.822090i
\(216\) −6.86390e13 9.44735e13i −0.675847 0.930224i
\(217\) 1.28548e13 1.76931e13i 0.123114 0.169452i
\(218\) −6.82557e13 2.10069e14i −0.635916 1.95715i
\(219\) 5.52248e13i 0.500575i
\(220\) −2.85975e14 7.66336e13i −2.52227 0.675901i
\(221\) −7.79989e13 −0.669476
\(222\) 1.29789e13 4.21711e12i 0.108423 0.0352288i
\(223\) 2.63671e13 + 1.91568e13i 0.214404 + 0.155774i 0.689804 0.723996i \(-0.257697\pi\)
−0.475400 + 0.879770i \(0.657697\pi\)
\(224\) 1.04093e14 7.56277e13i 0.824008 0.598677i
\(225\) −3.30816e13 + 1.01815e14i −0.254971 + 0.784720i
\(226\) −2.61928e14 8.51055e13i −1.96576 0.638715i
\(227\) −8.36068e13 1.15075e14i −0.611063 0.841057i 0.385601 0.922666i \(-0.373994\pi\)
−0.996664 + 0.0816090i \(0.973994\pi\)
\(228\) 3.51478e13 4.83768e13i 0.250201 0.344372i
\(229\) 3.27365e13 + 1.00753e14i 0.226997 + 0.698625i 0.998083 + 0.0618934i \(0.0197139\pi\)
−0.771086 + 0.636731i \(0.780286\pi\)
\(230\) 4.89406e13i 0.330600i
\(231\) 1.10848e14 + 7.19889e13i 0.729550 + 0.473798i
\(232\) 1.82705e14 1.17172
\(233\) 9.28375e13 3.01647e13i 0.580214 0.188523i −0.00418255 0.999991i \(-0.501331\pi\)
0.584396 + 0.811468i \(0.301331\pi\)
\(234\) 1.08157e14 + 7.85809e13i 0.658811 + 0.478654i
\(235\) −8.29963e13 + 6.03003e13i −0.492778 + 0.358024i
\(236\) −2.93075e13 + 9.01993e13i −0.169632 + 0.522073i
\(237\) −7.73778e13 2.51416e13i −0.436643 0.141874i
\(238\) 3.58777e14 + 4.93814e14i 1.97407 + 2.71708i
\(239\) 1.79238e14 2.46700e14i 0.961707 1.32368i 0.0155802 0.999879i \(-0.495040\pi\)
0.946127 0.323797i \(-0.104960\pi\)
\(240\) −1.96022e13 6.03293e13i −0.102574 0.315690i
\(241\) 1.90416e14i 0.971854i 0.873999 + 0.485927i \(0.161518\pi\)
−0.873999 + 0.485927i \(0.838482\pi\)
\(242\) 2.25707e14 + 2.50696e14i 1.12371 + 1.24812i
\(243\) 2.09360e14 1.01685
\(244\) −2.74561e14 + 8.92102e13i −1.30107 + 0.422742i
\(245\) −6.13615e14 4.45817e14i −2.83726 2.06139i
\(246\) 2.84441e12 2.06659e12i 0.0128346 0.00932488i
\(247\) −2.17530e13 + 6.69488e13i −0.0957938 + 0.294823i
\(248\) 3.44081e13 + 1.11799e13i 0.147894 + 0.0480537i
\(249\) −2.56123e13 3.52524e13i −0.107462 0.147908i
\(250\) −1.98284e13 + 2.72914e13i −0.0812170 + 0.111786i
\(251\) −3.52455e13 1.08474e14i −0.140949 0.433795i 0.855519 0.517771i \(-0.173238\pi\)
−0.996468 + 0.0839759i \(0.973238\pi\)
\(252\) 6.75277e14i 2.63681i
\(253\) 1.96033e13 3.01850e13i 0.0747492 0.115098i
\(254\) 2.56210e14 0.954099
\(255\) −1.89390e14 + 6.15365e13i −0.688836 + 0.223816i
\(256\) 3.76899e14 + 2.73833e14i 1.33901 + 0.972850i
\(257\) −3.13685e14 + 2.27905e14i −1.08867 + 0.790962i −0.979173 0.203025i \(-0.934923\pi\)
−0.109493 + 0.993988i \(0.534923\pi\)
\(258\) 1.33051e14 4.09490e14i 0.451129 1.38843i
\(259\) 7.71757e13 + 2.50759e13i 0.255671 + 0.0830726i
\(260\) 2.94620e14 + 4.05509e14i 0.953722 + 1.31269i
\(261\) −1.23287e14 + 1.69690e14i −0.390008 + 0.536800i
\(262\) −2.08113e14 6.40506e14i −0.643416 1.98023i
\(263\) 2.37703e13i 0.0718290i −0.999355 0.0359145i \(-0.988566\pi\)
0.999355 0.0359145i \(-0.0114344\pi\)
\(264\) −5.65956e13 + 2.11198e14i −0.167170 + 0.623831i
\(265\) −9.94388e12 −0.0287131
\(266\) 5.23915e14 1.70230e14i 1.47901 0.480559i
\(267\) −9.74290e13 7.07863e13i −0.268918 0.195381i
\(268\) −1.00734e15 + 7.31874e14i −2.71873 + 1.97528i
\(269\) −1.35259e14 + 4.16283e14i −0.356986 + 1.09869i 0.597863 + 0.801599i \(0.296017\pi\)
−0.954849 + 0.297092i \(0.903983\pi\)
\(270\) 7.40602e14 + 2.40636e14i 1.91162 + 0.621124i
\(271\) −1.24463e14 1.71309e14i −0.314214 0.432479i 0.622475 0.782639i \(-0.286127\pi\)
−0.936690 + 0.350160i \(0.886127\pi\)
\(272\) −1.26631e14 + 1.74293e14i −0.312700 + 0.430394i
\(273\) −6.91482e13 2.12816e14i −0.167034 0.514078i
\(274\) 4.08603e14i 0.965603i
\(275\) 4.26948e14 1.63879e14i 0.987139 0.378902i
\(276\) 5.17613e13 0.117098
\(277\) 7.51972e13 2.44330e13i 0.166465 0.0540878i −0.224599 0.974451i \(-0.572107\pi\)
0.391064 + 0.920364i \(0.372107\pi\)
\(278\) −8.37429e14 6.08428e14i −1.81417 1.31807i
\(279\) −3.36016e13 + 2.44130e13i −0.0712417 + 0.0517601i
\(280\) 5.46307e14 1.68136e15i 1.13367 3.48909i
\(281\) −3.99999e14 1.29968e14i −0.812495 0.263996i −0.126841 0.991923i \(-0.540484\pi\)
−0.685654 + 0.727927i \(0.740484\pi\)
\(282\) 9.88073e13 + 1.35997e14i 0.196469 + 0.270417i
\(283\) 8.98193e13 1.23626e14i 0.174844 0.240652i −0.712597 0.701574i \(-0.752481\pi\)
0.887441 + 0.460922i \(0.152481\pi\)
\(284\) 1.25237e14 + 3.85440e14i 0.238684 + 0.734594i
\(285\) 1.79721e14i 0.335374i
\(286\) −2.98763e13 5.70320e14i −0.0545922 1.04213i
\(287\) 2.09063e13 0.0374098
\(288\) −2.32393e14 + 7.55091e13i −0.407257 + 0.132326i
\(289\) 7.58021e13 + 5.50734e13i 0.130105 + 0.0945268i
\(290\) −9.85677e14 + 7.16137e14i −1.65709 + 1.20395i
\(291\) 2.39079e13 7.35809e13i 0.0393716 0.121173i
\(292\) −1.14629e15 3.72453e14i −1.84926 0.600862i
\(293\) 7.34528e14 + 1.01099e15i 1.16092 + 1.59787i 0.707781 + 0.706432i \(0.249696\pi\)
0.453140 + 0.891439i \(0.350304\pi\)
\(294\) −7.30510e14 + 1.00546e15i −1.13121 + 1.55697i
\(295\) −8.80844e13 2.71096e14i −0.133649 0.411330i
\(296\) 1.34240e14i 0.199587i
\(297\) −3.60391e14 4.45067e14i −0.525092 0.648465i
\(298\) 2.20725e15 3.15177
\(299\) −5.79521e13 + 1.88298e13i −0.0811040 + 0.0263523i
\(300\) 5.32079e14 + 3.86578e14i 0.729875 + 0.530285i
\(301\) 2.07127e15 1.50486e15i 2.78507 2.02347i
\(302\) 1.04754e14 3.22399e14i 0.138079 0.424964i
\(303\) 1.95803e14 + 6.36204e13i 0.253026 + 0.0822130i
\(304\) 1.14285e14 + 1.57300e14i 0.144793 + 0.199291i
\(305\) 5.10001e14 7.01956e14i 0.633537 0.871988i
\(306\) −3.58215e14 1.10247e15i −0.436330 1.34288i
\(307\) 1.39643e15i 1.66798i 0.551783 + 0.833988i \(0.313948\pi\)
−0.551783 + 0.833988i \(0.686052\pi\)
\(308\) −2.24186e15 + 1.81534e15i −2.62605 + 2.12644i
\(309\) −2.88591e14 −0.331536
\(310\) −2.29450e14 + 7.45527e13i −0.258534 + 0.0840027i
\(311\) −7.78957e14 5.65945e14i −0.860897 0.625478i 0.0672319 0.997737i \(-0.478583\pi\)
−0.928129 + 0.372259i \(0.878583\pi\)
\(312\) 2.99477e14 2.17583e14i 0.324666 0.235883i
\(313\) −4.71514e14 + 1.45117e15i −0.501451 + 1.54331i 0.305204 + 0.952287i \(0.401275\pi\)
−0.806656 + 0.591022i \(0.798725\pi\)
\(314\) 1.42960e15 + 4.64506e14i 1.49155 + 0.484633i
\(315\) 1.19294e15 + 1.64195e15i 1.22112 + 1.68072i
\(316\) 1.04372e15 1.43656e15i 1.04824 1.44278i
\(317\) 2.74578e14 + 8.45064e14i 0.270589 + 0.832787i 0.990353 + 0.138568i \(0.0442500\pi\)
−0.719764 + 0.694219i \(0.755750\pi\)
\(318\) 1.62939e13i 0.0157566i
\(319\) 8.94784e14 4.68734e13i 0.849130 0.0444818i
\(320\) −2.17984e15 −2.03014
\(321\) 8.89222e13 2.88926e13i 0.0812793 0.0264092i
\(322\) 3.85778e14 + 2.80284e14i 0.346101 + 0.251457i
\(323\) 4.93807e14 3.58772e14i 0.434853 0.315939i
\(324\) −2.53343e14 + 7.79709e14i −0.218997 + 0.674004i
\(325\) −7.36346e14 2.39253e14i −0.624859 0.203029i
\(326\) −1.61643e15 2.22483e15i −1.34664 1.85349i
\(327\) 4.12696e14 5.68028e14i 0.337555 0.464604i
\(328\) 1.06873e13 + 3.28920e13i 0.00858269 + 0.0264148i
\(329\) 9.99566e14i 0.788199i
\(330\) −5.22492e14 1.36123e15i −0.404572 1.05402i
\(331\) −1.38523e15 −1.05331 −0.526653 0.850081i \(-0.676553\pi\)
−0.526653 + 0.850081i \(0.676553\pi\)
\(332\) 9.04466e14 2.93879e14i 0.675404 0.219452i
\(333\) −1.24677e14 9.05832e13i −0.0914369 0.0664328i
\(334\) −2.08743e15 + 1.51661e15i −1.50360 + 1.09243i
\(335\) 1.15643e15 3.55913e15i 0.818184 2.51811i
\(336\) −5.87812e14 1.90992e14i −0.408510 0.132733i
\(337\) −9.40557e14 1.29457e15i −0.642105 0.883781i 0.356621 0.934249i \(-0.383929\pi\)
−0.998726 + 0.0504678i \(0.983929\pi\)
\(338\) 9.03603e14 1.24370e15i 0.606007 0.834097i
\(339\) −2.70528e14 8.32601e14i −0.178244 0.548578i
\(340\) 4.34617e15i 2.81341i
\(341\) 1.71379e14 + 4.59251e13i 0.109001 + 0.0292095i
\(342\) −1.04619e15 −0.653812
\(343\) −4.15384e15 + 1.34966e15i −2.55085 + 0.828821i
\(344\) 3.42644e15 + 2.48946e15i 2.06773 + 1.50229i
\(345\) −1.25859e14 + 9.14416e13i −0.0746394 + 0.0542287i
\(346\) −6.64985e14 + 2.04661e15i −0.387575 + 1.19283i
\(347\) 2.54553e15 + 8.27092e14i 1.45815 + 0.473780i 0.927503 0.373816i \(-0.121951\pi\)
0.530642 + 0.847596i \(0.321951\pi\)
\(348\) 7.57410e14 + 1.04249e15i 0.426438 + 0.586941i
\(349\) 5.38227e14 7.40806e14i 0.297861 0.409970i −0.633687 0.773590i \(-0.718459\pi\)
0.931547 + 0.363620i \(0.118459\pi\)
\(350\) 1.87230e15 + 5.76235e15i 1.01851 + 3.13466i
\(351\) 9.69553e14i 0.518476i
\(352\) 8.75422e14 + 5.68534e14i 0.460216 + 0.298882i
\(353\) −2.35674e15 −1.21805 −0.609023 0.793152i \(-0.708438\pi\)
−0.609023 + 0.793152i \(0.708438\pi\)
\(354\) −4.44214e14 + 1.44334e14i −0.225721 + 0.0733413i
\(355\) −9.85436e14 7.15961e14i −0.492332 0.357700i
\(356\) 2.12639e15 1.54492e15i 1.04458 0.758935i
\(357\) −5.99575e14 + 1.84530e15i −0.289624 + 0.891370i
\(358\) 2.61800e15 + 8.50640e14i 1.24357 + 0.404062i
\(359\) −1.15459e15 1.58916e15i −0.539338 0.742335i 0.449180 0.893441i \(-0.351716\pi\)
−0.988517 + 0.151107i \(0.951716\pi\)
\(360\) −1.97346e15 + 2.71623e15i −0.906595 + 1.24782i
\(361\) 5.13724e14 + 1.58108e15i 0.232106 + 0.714350i
\(362\) 5.88881e15i 2.61683i
\(363\) −2.22989e14 + 1.04885e15i −0.0974638 + 0.458430i
\(364\) 4.88375e15 2.09964
\(365\) 3.44521e15 1.11942e15i 1.45700 0.473407i
\(366\) −1.15021e15 8.35680e14i −0.478512 0.347659i
\(367\) −4.24145e14 + 3.08159e14i −0.173587 + 0.126119i −0.671186 0.741289i \(-0.734215\pi\)
0.497599 + 0.867407i \(0.334215\pi\)
\(368\) −5.20091e13 + 1.60067e14i −0.0209407 + 0.0644490i
\(369\) −3.77605e13 1.22691e13i −0.0149582 0.00486022i
\(370\) −5.26171e14 7.24212e14i −0.205077 0.282264i
\(371\) −5.69489e13 + 7.83834e13i −0.0218394 + 0.0300594i
\(372\) 7.88495e13 + 2.42674e14i 0.0297537 + 0.0915725i
\(373\) 1.76039e15i 0.653664i −0.945082 0.326832i \(-0.894019\pi\)
0.945082 0.326832i \(-0.105981\pi\)
\(374\) −2.69712e15 + 4.15300e15i −0.985532 + 1.51751i
\(375\) −1.07232e14 −0.0385599
\(376\) −1.57263e15 + 5.10977e14i −0.556543 + 0.180832i
\(377\) −1.22724e15 8.91639e14i −0.427445 0.310557i
\(378\) 6.13828e15 4.45972e15i 2.10424 1.52882i
\(379\) −5.63690e14 + 1.73486e15i −0.190198 + 0.585368i −0.999999 0.00133589i \(-0.999575\pi\)
0.809801 + 0.586704i \(0.199575\pi\)
\(380\) −3.73045e15 1.21210e15i −1.23897 0.402564i
\(381\) 4.78707e14 + 6.58884e14i 0.156502 + 0.215407i
\(382\) −1.70704e15 + 2.34954e15i −0.549369 + 0.756141i
\(383\) 7.22011e14 + 2.22212e15i 0.228745 + 0.704004i 0.997890 + 0.0649298i \(0.0206823\pi\)
−0.769145 + 0.639074i \(0.779318\pi\)
\(384\) 2.74727e15i 0.856869i
\(385\) 2.24414e15 8.37448e15i 0.689105 2.57154i
\(386\) 6.78723e13 0.0205196
\(387\) −4.62423e15 + 1.50250e15i −1.37649 + 0.447249i
\(388\) 1.36607e15 + 9.92506e14i 0.400389 + 0.290899i
\(389\) −2.53150e15 + 1.83924e15i −0.730602 + 0.530813i −0.889754 0.456441i \(-0.849124\pi\)
0.159152 + 0.987254i \(0.449124\pi\)
\(390\) −7.62807e14 + 2.34768e15i −0.216784 + 0.667192i
\(391\) 5.02495e14 + 1.63271e14i 0.140628 + 0.0456928i
\(392\) −7.18580e15 9.89041e15i −1.98043 2.72582i
\(393\) 1.25832e15 1.73193e15i 0.341535 0.470083i
\(394\) −1.41544e15 4.35629e15i −0.378369 1.16450i
\(395\) 5.33686e15i 1.40509i
\(396\) 5.11455e15 1.96316e15i 1.32628 0.509078i
\(397\) 4.69291e15 1.19867 0.599335 0.800499i \(-0.295432\pi\)
0.599335 + 0.800499i \(0.295432\pi\)
\(398\) 6.43046e15 2.08938e15i 1.61787 0.525678i
\(399\) 1.41666e15 + 1.02927e15i 0.351099 + 0.255088i
\(400\) −1.73008e15 + 1.25698e15i −0.422384 + 0.306880i
\(401\) −1.12068e15 + 3.44909e15i −0.269535 + 0.829542i 0.721079 + 0.692853i \(0.243646\pi\)
−0.990614 + 0.136690i \(0.956354\pi\)
\(402\) −5.83194e15 1.89491e15i −1.38184 0.448986i
\(403\) −1.76560e14 2.43014e14i −0.0412157 0.0567285i
\(404\) −2.64112e15 + 3.63519e15i −0.607435 + 0.836063i
\(405\) −7.61427e14 2.34343e15i −0.172543 0.531034i
\(406\) 1.18710e16i 2.65052i
\(407\) 3.44396e13 + 6.57430e14i 0.00757690 + 0.144638i
\(408\) −3.20973e15 −0.695838
\(409\) 4.23349e15 1.37554e15i 0.904395 0.293856i 0.180345 0.983603i \(-0.442278\pi\)
0.724050 + 0.689747i \(0.242278\pi\)
\(410\) −1.86581e14 1.35559e14i −0.0392794 0.0285382i
\(411\) −1.05079e15 + 7.63442e14i −0.218004 + 0.158389i
\(412\) 1.94635e15 5.99024e15i 0.397958 1.22479i
\(413\) −2.64140e15 8.58241e14i −0.532271 0.172945i
\(414\) −5.32297e14 7.32644e14i −0.105719 0.145509i
\(415\) −1.68006e15 + 2.31240e15i −0.328879 + 0.452663i
\(416\) −5.46099e14 1.68072e15i −0.105369 0.324292i
\(417\) 3.29038e15i 0.625791i
\(418\) 2.81245e15 + 3.47324e15i 0.527262 + 0.651145i
\(419\) −2.85199e15 −0.527064 −0.263532 0.964651i \(-0.584887\pi\)
−0.263532 + 0.964651i \(0.584887\pi\)
\(420\) 1.18583e16 3.85299e15i 2.16036 0.701944i
\(421\) 1.68739e15 + 1.22596e15i 0.303055 + 0.220182i 0.728911 0.684609i \(-0.240027\pi\)
−0.425856 + 0.904791i \(0.640027\pi\)
\(422\) 3.85304e15 2.79940e15i 0.682227 0.495667i
\(423\) 5.86609e14 1.80540e15i 0.102402 0.315160i
\(424\) −1.52434e14 4.95287e13i −0.0262353 0.00852435i
\(425\) 3.94600e15 + 5.43121e15i 0.669613 + 0.921643i
\(426\) −1.17316e15 + 1.61472e15i −0.196291 + 0.270172i
\(427\) −2.61243e15 8.04024e15i −0.431000 1.32648i
\(428\) 2.04061e15i 0.331968i
\(429\) 1.41085e15 1.14243e15i 0.226327 0.183267i
\(430\) −2.82431e16 −4.46788
\(431\) −5.34248e15 + 1.73588e15i −0.833450 + 0.270804i −0.694498 0.719495i \(-0.744373\pi\)
−0.138952 + 0.990299i \(0.544373\pi\)
\(432\) 2.16652e15 + 1.57407e15i 0.333319 + 0.242171i
\(433\) 5.60853e15 4.07484e15i 0.850985 0.618276i −0.0744328 0.997226i \(-0.523715\pi\)
0.925417 + 0.378950i \(0.123715\pi\)
\(434\) −7.26397e14 + 2.23562e15i −0.108701 + 0.334549i
\(435\) −3.68331e15 1.19678e15i −0.543630 0.176636i
\(436\) 9.00712e15 + 1.23972e16i 1.31119 + 1.80470i
\(437\) 2.80280e14 3.85773e14i 0.0402443 0.0553915i
\(438\) −1.83426e15 5.64527e15i −0.259786 0.799540i
\(439\) 2.84904e15i 0.398026i −0.979997 0.199013i \(-0.936226\pi\)
0.979997 0.199013i \(-0.0637736\pi\)
\(440\) 1.43229e16 7.50306e14i 1.97385 0.103400i
\(441\) 1.40347e16 1.90797
\(442\) 7.97332e15 2.59069e15i 1.06932 0.347442i
\(443\) −4.44518e15 3.22961e15i −0.588122 0.427296i 0.253521 0.967330i \(-0.418411\pi\)
−0.841643 + 0.540034i \(0.818411\pi\)
\(444\) −7.65952e14 + 5.56496e14i −0.0999778 + 0.0726381i
\(445\) −2.44111e15 + 7.51298e15i −0.314361 + 0.967502i
\(446\) −3.33162e15 1.08251e15i −0.423298 0.137538i
\(447\) 4.12407e15 + 5.67630e15i 0.516989 + 0.711574i
\(448\) −1.24840e16 + 1.71828e16i −1.54414 + 2.12532i
\(449\) 2.89333e15 + 8.90474e15i 0.353118 + 1.08678i 0.957093 + 0.289781i \(0.0935825\pi\)
−0.603975 + 0.797003i \(0.706418\pi\)
\(450\) 1.15066e16i 1.38571i
\(451\) 6.07786e13 + 1.58344e14i 0.00722256 + 0.0188167i
\(452\) 1.91067e16 2.24055
\(453\) 1.02482e15 3.32986e14i 0.118593 0.0385333i
\(454\) 1.23687e16 + 8.98640e15i 1.41250 + 1.02624i
\(455\) −1.18749e16 + 8.62765e15i −1.33833 + 0.972353i
\(456\) −8.95158e14 + 2.75501e15i −0.0995659 + 0.306432i
\(457\) −1.04136e16 3.38357e15i −1.14315 0.371431i −0.324589 0.945855i \(-0.605226\pi\)
−0.818557 + 0.574425i \(0.805226\pi\)
\(458\) −6.69289e15 9.21197e15i −0.725138 0.998067i
\(459\) 4.94143e15 6.80130e15i 0.528417 0.727304i
\(460\) −1.04921e15 3.22914e15i −0.110743 0.340832i
\(461\) 4.15162e15i 0.432526i 0.976335 + 0.216263i \(0.0693869\pi\)
−0.976335 + 0.216263i \(0.930613\pi\)
\(462\) −1.37223e16 3.67721e15i −1.41116 0.378153i
\(463\) 4.37955e15 0.444574 0.222287 0.974981i \(-0.428648\pi\)
0.222287 + 0.974981i \(0.428648\pi\)
\(464\) −3.98484e15 + 1.29475e15i −0.399303 + 0.129741i
\(465\) −6.20432e14 4.50770e14i −0.0613728 0.0445900i
\(466\) −8.48828e15 + 6.16709e15i −0.828903 + 0.602234i
\(467\) 5.19900e15 1.60009e16i 0.501209 1.54256i −0.305843 0.952082i \(-0.598938\pi\)
0.807052 0.590480i \(-0.201062\pi\)
\(468\) −8.82095e15 2.86610e15i −0.839537 0.272782i
\(469\) −2.14322e16 2.94989e16i −2.01386 2.77184i
\(470\) 6.48133e15 8.92079e15i 0.601280 0.827592i
\(471\) 1.47654e15 + 4.54433e15i 0.135245 + 0.416241i
\(472\) 4.59447e15i 0.415511i
\(473\) 1.74194e16 + 1.13129e16i 1.55549 + 1.01020i
\(474\) 8.74490e15 0.771054
\(475\) 5.76226e15 1.87227e15i 0.501685 0.163007i
\(476\) −3.42590e16 2.48906e16i −2.94532 2.13990i
\(477\) 1.48860e14 1.08153e14i 0.0126377 0.00918184i
\(478\) −1.01283e16 + 3.11718e16i −0.849124 + 2.61333i
\(479\) 1.07469e16 + 3.49186e15i 0.889750 + 0.289097i 0.718000 0.696043i \(-0.245058\pi\)
0.171750 + 0.985141i \(0.445058\pi\)
\(480\) −2.65198e15 3.65014e15i −0.216832 0.298443i
\(481\) 6.55119e14 9.01694e14i 0.0528993 0.0728096i
\(482\) −6.32456e15 1.94650e16i −0.504368 1.55229i
\(483\) 1.51578e15i 0.119386i
\(484\) −2.02669e16 1.17023e16i −1.57658 0.910331i
\(485\) −5.07498e15 −0.389927
\(486\) −2.14015e16 + 6.95378e15i −1.62415 + 0.527720i
\(487\) 9.81236e15 + 7.12910e15i 0.735529 + 0.534393i 0.891308 0.453399i \(-0.149789\pi\)
−0.155779 + 0.987792i \(0.549789\pi\)
\(488\) 1.13143e16 8.22033e15i 0.837740 0.608654i
\(489\) 2.70132e15 8.31382e15i 0.197571 0.608061i
\(490\) 7.75335e16 + 2.51921e16i 5.60161 + 1.82007i
\(491\) 1.22086e16 + 1.68037e16i 0.871320 + 1.19927i 0.978750 + 0.205056i \(0.0657376\pi\)
−0.107431 + 0.994213i \(0.534262\pi\)
\(492\) −1.43372e14 + 1.97335e14i −0.0101082 + 0.0139128i
\(493\) 4.06458e15 + 1.25095e16i 0.283096 + 0.871280i
\(494\) 7.56626e15i 0.520619i
\(495\) −8.96800e15 + 1.38088e16i −0.609628 + 0.938698i
\(496\) −8.29675e14 −0.0557209
\(497\) −1.12872e16 + 3.66744e15i −0.748944 + 0.243347i
\(498\) 3.78907e15 + 2.75292e15i 0.248403 + 0.180475i
\(499\) −8.37139e15 + 6.08217e15i −0.542244 + 0.393963i −0.824918 0.565253i \(-0.808779\pi\)
0.282674 + 0.959216i \(0.408779\pi\)
\(500\) 7.23205e14 2.22580e15i 0.0462851 0.142451i
\(501\) −7.80038e15 2.53450e15i −0.493276 0.160275i
\(502\) 7.20583e15 + 9.91798e15i 0.450258 + 0.619727i
\(503\) −5.00222e15 + 6.88496e15i −0.308855 + 0.425102i −0.935024 0.354585i \(-0.884622\pi\)
0.626169 + 0.779688i \(0.284622\pi\)
\(504\) 1.01089e16 + 3.11119e16i 0.616764 + 1.89820i
\(505\) 1.35048e16i 0.814218i
\(506\) −1.00134e15 + 3.73673e15i −0.0596596 + 0.222633i
\(507\) 4.88668e15 0.287718
\(508\) −1.69049e16 + 5.49274e15i −0.983627 + 0.319600i
\(509\) 1.09826e16 + 7.97929e15i 0.631534 + 0.458836i 0.856931 0.515431i \(-0.172368\pi\)
−0.225397 + 0.974267i \(0.572368\pi\)
\(510\) 1.73162e16 1.25810e16i 0.984083 0.714978i
\(511\) 1.09069e16 3.35680e16i 0.612600 1.88539i
\(512\) −1.62998e16 5.29612e15i −0.904820 0.293994i
\(513\) −4.45966e15 6.13819e15i −0.244679 0.336772i
\(514\) 2.44962e16 3.37162e16i 1.32837 1.82835i
\(515\) 5.84978e15 + 1.80038e16i 0.313543 + 0.964985i
\(516\) 2.98709e16i 1.58252i
\(517\) −7.57072e15 + 2.90593e15i −0.396455 + 0.152175i
\(518\) −8.72205e15 −0.451482
\(519\) −6.50566e15 + 2.11382e15i −0.332879 + 0.108159i
\(520\) −1.96444e16 1.42725e16i −0.993617 0.721905i
\(521\) 1.89764e16 1.37872e16i 0.948829 0.689365i −0.00170024 0.999999i \(-0.500541\pi\)
0.950530 + 0.310634i \(0.100541\pi\)
\(522\) 6.96667e15 2.14412e16i 0.344352 1.05980i
\(523\) −2.44893e16 7.95706e15i −1.19665 0.388815i −0.358121 0.933675i \(-0.616583\pi\)
−0.838527 + 0.544861i \(0.816583\pi\)
\(524\) 2.74629e16 + 3.77994e16i 1.32666 + 1.82599i
\(525\) −1.13205e16 + 1.55814e16i −0.540644 + 0.744132i
\(526\) 7.89516e14 + 2.42988e15i 0.0372775 + 0.114728i
\(527\) 2.60458e15i 0.121583i
\(528\) −2.62311e14 5.00735e15i −0.0121063 0.231102i
\(529\) −2.15019e16 −0.981165
\(530\) 1.01650e15 3.30280e14i 0.0458618 0.0149014i
\(531\) 4.26717e15 + 3.10028e15i 0.190359 + 0.138304i
\(532\) −3.09188e16 + 2.24638e16i −1.36381 + 0.990863i
\(533\) 8.87332e13 2.73093e14i 0.00387011 0.0119110i
\(534\) 1.23107e16 + 3.99998e15i 0.530926 + 0.172508i
\(535\) −3.60494e15 4.96177e15i −0.153736 0.211599i
\(536\) 3.54548e16 4.87993e16i 1.49515 2.05790i
\(537\) 2.70397e15 + 8.32195e15i 0.112760 + 0.347040i
\(538\) 4.70465e16i 1.94014i
\(539\) −3.77293e16 4.65940e16i −1.53867 1.90019i
\(540\) −5.40243e16 −2.17885
\(541\) 2.95935e14 9.61552e13i 0.0118036 0.00383521i −0.303109 0.952956i \(-0.598025\pi\)
0.314913 + 0.949121i \(0.398025\pi\)
\(542\) 1.84130e16 + 1.33779e16i 0.726323 + 0.527704i
\(543\) 1.51440e16 1.10028e16i 0.590801 0.429242i
\(544\) −4.73516e15 + 1.45733e16i −0.182701 + 0.562296i
\(545\) −4.38019e16 1.42321e16i −1.67153 0.543113i
\(546\) 1.41371e16 + 1.94581e16i 0.533588 + 0.734420i
\(547\) 1.43870e16 1.98020e16i 0.537088 0.739238i −0.451102 0.892472i \(-0.648969\pi\)
0.988190 + 0.153235i \(0.0489690\pi\)
\(548\) −8.75982e15 2.69600e16i −0.323453 0.995487i
\(549\) 1.60553e16i 0.586386i
\(550\) −3.82009e16 + 3.09331e16i −1.38006 + 1.11750i
\(551\) 1.18708e16 0.424201
\(552\) −2.38479e15 + 7.74865e14i −0.0842976 + 0.0273900i
\(553\) 4.20682e16 + 3.05643e16i 1.47097 + 1.06872i
\(554\) −6.87539e15 + 4.99527e15i −0.237815 + 0.172783i
\(555\) 8.79318e14 2.70626e15i 0.0300876 0.0926002i
\(556\) 6.82979e16 + 2.21913e16i 2.31184 + 0.751164i
\(557\) 1.04608e16 + 1.43981e16i 0.350296 + 0.482142i 0.947413 0.320013i \(-0.103687\pi\)
−0.597117 + 0.802154i \(0.703687\pi\)
\(558\) 2.62401e15 3.61164e15i 0.0869281 0.119646i
\(559\) −1.08664e16 3.34435e16i −0.356137 1.09608i
\(560\) 4.05422e16i 1.31456i
\(561\) −1.57194e16 + 8.23465e14i −0.504266 + 0.0264160i
\(562\) 4.52061e16 1.43476
\(563\) 1.94297e16 6.31308e15i 0.610119 0.198240i 0.0123708 0.999923i \(-0.496062\pi\)
0.597748 + 0.801684i \(0.296062\pi\)
\(564\) −9.43493e15 6.85488e15i −0.293133 0.212973i
\(565\) −4.64583e16 + 3.37539e16i −1.42815 + 1.03761i
\(566\) −5.07549e15 + 1.56207e16i −0.154376 + 0.475120i
\(567\) −2.28330e16 7.41889e15i −0.687170 0.223275i
\(568\) −1.15401e16 1.58835e16i −0.343651 0.472995i
\(569\) −1.86539e16 + 2.56749e16i −0.549663 + 0.756546i −0.989966 0.141303i \(-0.954871\pi\)
0.440304 + 0.897849i \(0.354871\pi\)
\(570\) −5.96933e15 1.83717e16i −0.174051 0.535674i
\(571\) 2.73045e16i 0.787802i 0.919153 + 0.393901i \(0.128875\pi\)
−0.919153 + 0.393901i \(0.871125\pi\)
\(572\) 1.41980e16 + 3.69896e16i 0.405370 + 1.05610i
\(573\) −9.23168e15 −0.260827
\(574\) −2.13711e15 + 6.94390e14i −0.0597525 + 0.0194148i
\(575\) 4.24298e15 + 3.08270e15i 0.117399 + 0.0852952i
\(576\) 3.26323e16 2.37088e16i 0.893538 0.649194i
\(577\) 6.07423e15 1.86946e16i 0.164603 0.506595i −0.834404 0.551153i \(-0.814188\pi\)
0.999007 + 0.0445583i \(0.0141881\pi\)
\(578\) −9.57799e15 3.11208e15i −0.256866 0.0834609i
\(579\) 1.26814e14 + 1.74544e14i 0.00336585 + 0.00463270i
\(580\) 4.96829e16 6.83826e16i 1.30508 1.79629i
\(581\) 8.60594e15 + 2.64864e16i 0.223739 + 0.688598i
\(582\) 8.31579e15i 0.213976i
\(583\) −7.59238e14 2.03456e14i −0.0193360 0.00518153i
\(584\) 5.83885e16 1.47181
\(585\) 2.65115e16 8.61412e15i 0.661454 0.214920i
\(586\) −1.08666e17 7.89502e16i −2.68353 1.94970i
\(587\) −3.61882e16 + 2.62922e16i −0.884581 + 0.642686i −0.934460 0.356069i \(-0.884117\pi\)
0.0498781 + 0.998755i \(0.484117\pi\)
\(588\) 2.66441e16 8.20020e16i 0.644669 1.98409i
\(589\) 2.23559e15 + 7.26386e14i 0.0535426 + 0.0173971i
\(590\) 1.80086e16 + 2.47867e16i 0.426941 + 0.587634i
\(591\) 8.55823e15 1.17794e16i 0.200844 0.276438i
\(592\) −9.51300e14 2.92780e15i −0.0220998 0.0680160i
\(593\) 4.00771e16i 0.921654i −0.887490 0.460827i \(-0.847553\pi\)
0.887490 0.460827i \(-0.152447\pi\)
\(594\) 5.16231e16 + 3.35261e16i 1.17524 + 0.763246i
\(595\) 1.27273e17 2.86837
\(596\) −1.45636e17 + 4.73201e16i −3.24932 + 1.05577i
\(597\) 1.73880e16 + 1.26331e16i 0.384063 + 0.279038i
\(598\) 5.29865e15 3.84969e15i 0.115867 0.0841819i
\(599\) 1.15800e16 3.56396e16i 0.250697 0.771565i −0.743951 0.668235i \(-0.767050\pi\)
0.994647 0.103330i \(-0.0329498\pi\)
\(600\) −3.03014e16 9.84552e15i −0.649464 0.211024i
\(601\) −3.51227e16 4.83423e16i −0.745318 1.02584i −0.998295 0.0583697i \(-0.981410\pi\)
0.252977 0.967472i \(-0.418590\pi\)
\(602\) −1.61749e17 + 2.22628e17i −3.39830 + 4.67737i
\(603\) 2.13986e16 + 6.58581e16i 0.445125 + 1.36995i
\(604\) 2.35179e16i 0.484370i
\(605\) 6.99526e16 7.34913e15i 1.42650 0.149866i
\(606\) −2.21288e16 −0.446810
\(607\) 7.25675e16 2.35786e16i 1.45081 0.471396i 0.525560 0.850757i \(-0.323856\pi\)
0.925249 + 0.379360i \(0.123856\pi\)
\(608\) 1.11881e16 + 8.12866e15i 0.221481 + 0.160915i
\(609\) −3.05282e16 + 2.21800e16i −0.598407 + 0.434768i
\(610\) −2.88190e16 + 8.86958e16i −0.559371 + 1.72157i
\(611\) 1.30570e16 + 4.24249e15i 0.250956 + 0.0815406i
\(612\) 4.72705e16 + 6.50623e16i 0.899667 + 1.23829i
\(613\) 1.22794e16 1.69012e16i 0.231428 0.318533i −0.677471 0.735549i \(-0.736924\pi\)
0.908899 + 0.417016i \(0.136924\pi\)
\(614\) −4.63817e16 1.42748e17i −0.865638 2.66416i
\(615\) 7.33104e14i 0.0135492i
\(616\) 7.61130e16 1.17198e17i 1.39308 2.14504i
\(617\) −4.17104e16 −0.756021 −0.378010 0.925801i \(-0.623392\pi\)
−0.378010 + 0.925801i \(0.623392\pi\)
\(618\) 2.95007e16 9.58537e15i 0.529544 0.172059i
\(619\) −1.13529e16 8.24833e15i −0.201819 0.146630i 0.482286 0.876014i \(-0.339807\pi\)
−0.684104 + 0.729384i \(0.739807\pi\)
\(620\) 1.35410e16 9.83808e15i 0.238396 0.173205i
\(621\) 2.02951e15 6.24619e15i 0.0353868 0.108909i
\(622\) 9.84253e16 + 3.19803e16i 1.69967 + 0.552256i
\(623\) 4.52413e16 + 6.22693e16i 0.773761 + 1.06499i
\(624\) −4.98974e15 + 6.86779e15i −0.0845222 + 0.116335i
\(625\) −1.73017e16 5.32493e16i −0.290275 0.893375i
\(626\) 1.64005e17i 2.72528i
\(627\) −3.67716e15 + 1.37221e16i −0.0605212 + 0.225848i
\(628\) −1.04284e17 −1.70005
\(629\) −9.19116e15 + 2.98639e15i −0.148411 + 0.0482217i
\(630\) −1.76483e17 1.28223e17i −2.82267 2.05079i
\(631\) −6.25124e16 + 4.54179e16i −0.990353 + 0.719534i −0.959998 0.280006i \(-0.909664\pi\)
−0.0303547 + 0.999539i \(0.509664\pi\)
\(632\) −2.65819e16 + 8.18107e16i −0.417142 + 1.28383i
\(633\) 1.43982e16 + 4.67825e15i 0.223813 + 0.0727213i
\(634\) −5.61366e16 7.72655e16i −0.864392 1.18973i
\(635\) 3.14011e16 4.32199e16i 0.478964 0.659237i
\(636\) −3.49316e14 1.07508e15i −0.00527808 0.0162442i
\(637\) 1.01502e17i 1.51929i
\(638\) −8.99112e16 + 3.45113e16i −1.33318 + 0.511726i
\(639\) 2.25391e16 0.331079
\(640\) 1.71389e17 5.56877e16i 2.49404 0.810363i
\(641\) 4.12727e16 + 2.99864e16i 0.594998 + 0.432291i 0.844100 0.536186i \(-0.180135\pi\)
−0.249102 + 0.968477i \(0.580135\pi\)
\(642\) −8.13029e15 + 5.90700e15i −0.116117 + 0.0843639i
\(643\) −6.10319e15 + 1.87837e16i −0.0863557 + 0.265775i −0.984905 0.173098i \(-0.944622\pi\)
0.898549 + 0.438873i \(0.144622\pi\)
\(644\) −3.14628e16 1.02229e16i −0.441044 0.143304i
\(645\) −5.27699e16 7.26315e16i −0.732872 1.00871i
\(646\) −3.85623e16 + 5.30764e16i −0.530601 + 0.730309i
\(647\) 1.97052e16 + 6.06464e16i 0.268631 + 0.826760i 0.990835 + 0.135080i \(0.0431292\pi\)
−0.722204 + 0.691680i \(0.756871\pi\)
\(648\) 3.97159e16i 0.536431i
\(649\) −1.17872e15 2.25010e16i −0.0157740 0.301116i
\(650\) 8.32186e16 1.10342
\(651\) −7.10646e15 + 2.30903e15i −0.0933614 + 0.0303349i
\(652\) 1.54350e17 + 1.12142e17i 2.00919 + 1.45976i
\(653\) 4.18564e15 3.04104e15i 0.0539862 0.0392233i −0.560465 0.828178i \(-0.689378\pi\)
0.614451 + 0.788955i \(0.289378\pi\)
\(654\) −2.33205e16 + 7.17733e16i −0.298038 + 0.917268i
\(655\) −1.33553e17 4.33940e16i −1.69124 0.549518i
\(656\) −4.66183e14 6.41646e14i −0.00584970 0.00805142i
\(657\) −3.93998e16 + 5.42291e16i −0.489893 + 0.674280i
\(658\) −3.32000e16 1.02179e17i −0.409056 1.25895i
\(659\) 1.34808e17i 1.64590i −0.568114 0.822950i \(-0.692327\pi\)
0.568114 0.822950i \(-0.307673\pi\)
\(660\) 6.36570e16 + 7.86135e16i 0.770163 + 0.951116i
\(661\) −1.35647e16 −0.162631 −0.0813154 0.996688i \(-0.525912\pi\)
−0.0813154 + 0.996688i \(0.525912\pi\)
\(662\) 1.41603e17 4.60097e16i 1.68238 0.546640i
\(663\) 2.15599e16 + 1.56642e16i 0.253843 + 0.184428i
\(664\) −3.72719e16 + 2.70796e16i −0.434884 + 0.315962i
\(665\) 3.54950e16 1.09242e17i 0.410428 1.26317i
\(666\) 1.57536e16 + 5.11866e15i 0.180524 + 0.0586558i
\(667\) 6.03985e15 + 8.31314e15i 0.0685916 + 0.0944083i
\(668\) 1.05216e17 1.44818e17i 1.18420 1.62991i
\(669\) −3.44101e15 1.05904e16i −0.0383822 0.118128i
\(670\) 4.02237e17i 4.44665i
\(671\) 5.33020e16 4.31611e16i 0.583994 0.472887i
\(672\) −4.39604e16 −0.477360
\(673\) −1.55625e17 + 5.05655e16i −1.67490 + 0.544207i −0.983911 0.178660i \(-0.942824\pi\)
−0.690987 + 0.722867i \(0.742824\pi\)
\(674\) 1.39145e17 + 1.01095e17i 1.48426 + 1.07838i
\(675\) 6.75117e16 4.90501e16i 0.713767 0.518582i
\(676\) −3.29573e16 + 1.01432e17i −0.345360 + 1.06291i
\(677\) −1.31124e17 4.26048e16i −1.36192 0.442514i −0.465235 0.885187i \(-0.654030\pi\)
−0.896683 + 0.442674i \(0.854030\pi\)
\(678\) 5.53087e16 + 7.61259e16i 0.569398 + 0.783708i
\(679\) −2.90645e16 + 4.00039e16i −0.296582 + 0.408210i
\(680\) 6.50619e16 + 2.00240e17i 0.658072 + 2.02534i
\(681\) 4.85985e16i 0.487237i
\(682\) −1.90444e16 + 9.97643e14i −0.189261 + 0.00991446i
\(683\) −3.06836e16 −0.302261 −0.151131 0.988514i \(-0.548291\pi\)
−0.151131 + 0.988514i \(0.548291\pi\)
\(684\) 6.90282e16 2.24286e16i 0.674046 0.219011i
\(685\) 6.89271e16 + 5.00785e16i 0.667186 + 0.484739i
\(686\) 3.79792e17 2.75935e17i 3.64419 2.64766i
\(687\) 1.11849e16 3.44236e16i 0.106388 0.327428i
\(688\) −9.23731e16 3.00138e16i −0.870993 0.283003i
\(689\) 7.82190e14 + 1.07659e15i 0.00731134 + 0.0100632i
\(690\) 9.82852e15 1.35278e16i 0.0910739 0.125352i
\(691\) −1.03531e16 3.18635e16i −0.0951046 0.292702i 0.892176 0.451687i \(-0.149178\pi\)
−0.987281 + 0.158985i \(0.949178\pi\)
\(692\) 1.49293e17i 1.35958i
\(693\) 5.74892e16 + 1.49775e17i 0.519023 + 1.35219i
\(694\) −2.87684e17 −2.57489
\(695\) −2.05271e17 + 6.66965e16i −1.82145 + 0.591826i
\(696\) −5.05020e16 3.66918e16i −0.444276 0.322786i
\(697\) −2.01430e15 + 1.46347e15i −0.0175682 + 0.0127641i
\(698\) −3.04140e16 + 9.36047e16i −0.262991 + 0.809404i
\(699\) −3.17193e16 1.03062e16i −0.271932 0.0883561i
\(700\) −2.47071e17 3.40065e17i −2.10007 2.89050i
\(701\) −1.39276e16 + 1.91697e16i −0.117373 + 0.161550i −0.863661 0.504073i \(-0.831834\pi\)
0.746288 + 0.665623i \(0.231834\pi\)
\(702\) −3.22032e16 9.91111e16i −0.269076 0.828132i
\(703\) 8.72193e15i 0.0722571i
\(704\) −1.66436e17 4.46004e16i −1.36713 0.366355i
\(705\) 3.50510e16 0.285474
\(706\) 2.40915e17 7.82779e16i 1.94552 0.632137i
\(707\) −1.06453e17 7.73425e16i −0.852395 0.619301i
\(708\) 2.62153e16 1.90465e16i 0.208140 0.151222i
\(709\) 2.76241e16 8.50181e16i 0.217475 0.669320i −0.781493 0.623914i \(-0.785542\pi\)
0.998969 0.0454066i \(-0.0144583\pi\)
\(710\) 1.24515e17 + 4.04574e16i 0.972012 + 0.315826i
\(711\) −5.80456e16 7.98930e16i −0.449316 0.618431i
\(712\) −7.48416e16 + 1.03011e17i −0.574464 + 0.790682i
\(713\) 6.28773e14 + 1.93516e15i 0.00478582 + 0.0147292i
\(714\) 2.08548e17i 1.57404i
\(715\) −9.98686e16 6.48587e16i −0.747468 0.485436i
\(716\) −1.90974e17 −1.41741
\(717\) −9.90872e16 + 3.21954e16i −0.729294 + 0.236962i
\(718\) 1.70809e17 + 1.24100e17i 1.24671 + 0.905786i
\(719\) 1.70437e17 1.23830e17i 1.23365 0.896297i 0.236489 0.971634i \(-0.424003\pi\)
0.997158 + 0.0753375i \(0.0240034\pi\)
\(720\) 2.37928e16 7.32266e16i 0.170785 0.525623i
\(721\) 1.75418e17 + 5.69968e16i 1.24871 + 0.405731i
\(722\) −1.05029e17 1.44561e17i −0.741460 1.02053i
\(723\) 3.82403e16 5.26333e16i 0.267727 0.368494i
\(724\) 1.26247e17 + 3.88548e17i 0.876575 + 2.69782i
\(725\) 1.30563e17i 0.899067i
\(726\) −1.20422e16 1.14623e17i −0.0822404 0.782805i
\(727\) 2.12386e17 1.43853 0.719267 0.694734i \(-0.244478\pi\)
0.719267 + 0.694734i \(0.244478\pi\)
\(728\) −2.25008e17 + 7.31096e16i −1.51151 + 0.491118i
\(729\) −1.06000e16 7.70134e15i −0.0706220 0.0513099i
\(730\) −3.15001e17 + 2.28861e17i −2.08149 + 1.51229i
\(731\) −9.42216e16 + 2.89984e17i −0.617513 + 1.90051i
\(732\) 9.38077e16 + 3.04800e16i 0.609778 + 0.198129i
\(733\) 1.51817e17 + 2.08958e17i 0.978806 + 1.34721i 0.937470 + 0.348065i \(0.113161\pi\)
0.0413354 + 0.999145i \(0.486839\pi\)
\(734\) 3.31222e16 4.55889e16i 0.211809 0.291529i
\(735\) 8.00793e16 + 2.46459e17i 0.507921 + 1.56322i
\(736\) 1.19709e16i 0.0753112i
\(737\) 1.61117e17 2.48087e17i 1.00540 1.54810i
\(738\) 4.26752e15 0.0264142
\(739\) −8.84457e16 + 2.87377e16i −0.543013 + 0.176435i −0.567664 0.823261i \(-0.692153\pi\)
0.0246510 + 0.999696i \(0.492153\pi\)
\(740\) 5.02431e16 + 3.65038e16i 0.305975 + 0.222304i
\(741\) 1.94578e16 1.41369e16i 0.117540 0.0853977i
\(742\) 3.21805e15 9.90415e15i 0.0192828 0.0593463i
\(743\) 5.10858e15 + 1.65988e15i 0.0303646 + 0.00986605i 0.324160 0.946002i \(-0.394918\pi\)
−0.293795 + 0.955868i \(0.594918\pi\)
\(744\) −7.26563e15 1.00003e16i −0.0428387 0.0589623i
\(745\) 2.70522e17 3.72341e17i 1.58221 2.17773i
\(746\) 5.84702e16 + 1.79953e17i 0.339236 + 1.04406i
\(747\) 5.28897e16i 0.304402i
\(748\) 8.89242e16 3.31840e17i 0.507704 1.89461i
\(749\) −5.97571e16 −0.338453
\(750\) 1.09616e16 3.56165e15i 0.0615895 0.0200117i
\(751\) −9.39708e16 6.82738e16i −0.523786 0.380552i 0.294243 0.955731i \(-0.404933\pi\)
−0.818028 + 0.575178i \(0.804933\pi\)
\(752\) 3.06782e16 2.22890e16i 0.169638 0.123249i
\(753\) −1.20421e16 + 3.70618e16i −0.0660592 + 0.203309i
\(754\) 1.55068e17 + 5.03845e16i 0.843904 + 0.274201i
\(755\) −4.15468e16 5.71842e16i −0.224314 0.308741i
\(756\) −3.09399e17 + 4.25851e17i −1.65725 + 2.28101i
\(757\) 8.20171e16 + 2.52423e17i 0.435842 + 1.34138i 0.892221 + 0.451598i \(0.149146\pi\)
−0.456380 + 0.889785i \(0.650854\pi\)
\(758\) 1.96066e17i 1.03368i
\(759\) −1.14805e16 + 4.40666e15i −0.0600497 + 0.0230494i
\(760\) 1.90017e17 0.986078
\(761\) 1.58514e17 5.15042e16i 0.816129 0.265176i 0.128937 0.991653i \(-0.458843\pi\)
0.687191 + 0.726476i \(0.258843\pi\)
\(762\) −7.08196e16 5.14534e16i −0.361762 0.262836i
\(763\) −3.63041e17 + 2.63764e17i −1.83996 + 1.33681i
\(764\) 6.22614e16 1.91621e17i 0.313082 0.963568i
\(765\) −2.29878e17 7.46920e16i −1.14691 0.372654i
\(766\) −1.47613e17 2.03172e17i −0.730722 1.00575i
\(767\) −2.24219e16 + 3.08611e16i −0.110129 + 0.151579i
\(768\) −4.91869e16 1.51382e17i −0.239708 0.737744i
\(769\) 2.19475e17i 1.06127i −0.847600 0.530636i \(-0.821953\pi\)
0.847600 0.530636i \(-0.178047\pi\)
\(770\) 4.87500e16 + 9.30607e17i 0.233900 + 4.46501i
\(771\) 1.32476e17 0.630681
\(772\) −4.47826e15 + 1.45508e15i −0.0211546 + 0.00687356i
\(773\) −2.51323e17 1.82597e17i −1.17803 0.855886i −0.186079 0.982535i \(-0.559578\pi\)
−0.991948 + 0.126649i \(0.959578\pi\)
\(774\) 4.22800e17 3.07182e17i 1.96648 1.42873i
\(775\) −7.98926e15 + 2.45884e16i −0.0368720 + 0.113480i
\(776\) −7.77963e16 2.52776e16i −0.356278 0.115762i
\(777\) −1.62964e16 2.24301e16i −0.0740571 0.101931i
\(778\) 1.97690e17 2.72096e17i 0.891469 1.22700i
\(779\) 6.94380e14 + 2.13708e15i 0.00310722 + 0.00956305i
\(780\) 1.71255e17i 0.760459i
\(781\) −6.05915e16 7.48277e16i −0.266996 0.329728i
\(782\) −5.67898e16 −0.248330
\(783\) 1.55497e17 5.05241e16i 0.674764 0.219244i
\(784\) 2.26813e17 + 1.64789e17i 0.976722 + 0.709630i
\(785\) 2.53569e17 1.84229e17i 1.08362 0.787300i
\(786\) −7.11048e16 + 2.18838e17i −0.301553 + 0.928085i
\(787\) 1.63409e17 + 5.30948e16i 0.687745 + 0.223462i 0.631983 0.774982i \(-0.282241\pi\)
0.0557618 + 0.998444i \(0.482241\pi\)
\(788\) 1.86784e17 + 2.57086e17i 0.780158 + 1.07379i
\(789\) −4.77367e15 + 6.57040e15i −0.0197875 + 0.0272351i
\(790\) −1.77261e17 5.45552e17i −0.729205 2.24426i
\(791\) 5.59521e17i 2.28432i
\(792\) −2.06253e17 + 1.67013e17i −0.835699 + 0.676704i
\(793\) −1.16115e17 −0.466929
\(794\) −4.79726e17 + 1.55872e17i −1.91457 + 0.622080i
\(795\) 2.74861e15 + 1.99698e15i 0.0108871 + 0.00790991i
\(796\) −3.79493e17 + 2.75718e17i −1.49185 + 1.08389i
\(797\) −1.66641e16 + 5.12870e16i −0.0650179 + 0.200105i −0.978288 0.207250i \(-0.933549\pi\)
0.913270 + 0.407355i \(0.133549\pi\)
\(798\) −1.79003e17 5.81616e16i −0.693175 0.225226i
\(799\) −6.99713e16 9.63073e16i −0.268930 0.370151i
\(800\) −8.94042e16 + 1.23054e17i −0.341050 + 0.469415i
\(801\) −4.51704e16 1.39020e17i −0.171025 0.526360i
\(802\) 3.89801e17i 1.46486i
\(803\) 2.85953e17 1.49797e16i 1.06660 0.0558741i
\(804\) 4.25420e17 1.57500
\(805\) 9.45621e16 3.07251e16i 0.347490 0.112906i
\(806\) 2.61202e16 + 1.89774e16i 0.0952722 + 0.0692193i
\(807\) 1.20987e17 8.79025e16i 0.438025 0.318244i
\(808\) 6.72651e16 2.07021e17i 0.241725 0.743953i
\(809\) −3.73073e16 1.21219e16i −0.133077 0.0432394i 0.241721 0.970346i \(-0.422288\pi\)
−0.374798 + 0.927106i \(0.622288\pi\)
\(810\) 1.55671e17 + 2.14263e17i 0.551187 + 0.758644i
\(811\) −2.32130e17 + 3.19499e17i −0.815841 + 1.12291i 0.174555 + 0.984647i \(0.444151\pi\)
−0.990396 + 0.138261i \(0.955849\pi\)
\(812\) −2.54496e17 7.83258e17i −0.887860 2.73255i
\(813\) 7.23474e16i 0.250542i
\(814\) −2.53567e16 6.60609e16i −0.0871659 0.227090i
\(815\) −5.73416e17 −1.95670
\(816\) 7.00049e16 2.27460e16i 0.237131 0.0770484i
\(817\) 2.22625e17 + 1.61747e17i 0.748586 + 0.543880i
\(818\) −3.87074e17 + 2.81226e17i −1.29203 + 0.938718i
\(819\) 8.39308e16 2.58313e17i 0.278111 0.855938i
\(820\) 1.52170e16 + 4.94429e15i 0.0500547 + 0.0162637i
\(821\) 2.28545e17 + 3.14566e17i 0.746300 + 1.02719i 0.998231 + 0.0594489i \(0.0189343\pi\)
−0.251931 + 0.967745i \(0.581066\pi\)
\(822\) 8.20579e16 1.12943e17i 0.266005 0.366124i
\(823\) −1.18376e17 3.64324e17i −0.380947 1.17243i −0.939378 0.342883i \(-0.888596\pi\)
0.558431 0.829551i \(-0.311404\pi\)
\(824\) 3.05124e17i 0.974793i
\(825\) −1.50925e17 4.04438e16i −0.478670 0.128271i
\(826\) 2.98519e17 0.939921
\(827\) 1.34808e17 4.38016e16i 0.421387 0.136917i −0.0906450 0.995883i \(-0.528893\pi\)
0.512032 + 0.858966i \(0.328893\pi\)
\(828\) 5.08281e16 + 3.69288e16i 0.157733 + 0.114599i
\(829\) −1.74425e17 + 1.26727e17i −0.537381 + 0.390430i −0.823111 0.567880i \(-0.807764\pi\)
0.285731 + 0.958310i \(0.407764\pi\)
\(830\) 9.49364e16 2.92184e17i 0.290378 0.893692i
\(831\) −2.56922e16 8.34791e15i −0.0780181 0.0253496i
\(832\) 1.71467e17 + 2.36004e17i 0.516941 + 0.711509i
\(833\) 5.17318e17 7.12027e17i 1.54842 2.13121i
\(834\) 1.09288e17 + 3.36354e17i 0.324770 + 0.999540i
\(835\) 5.38003e17i 1.58733i
\(836\) −2.60028e17 1.68873e17i −0.761698 0.494677i
\(837\) 3.23758e16 0.0941602
\(838\) 2.91540e17 9.47271e16i 0.841849 0.273533i
\(839\) −2.41871e17 1.75730e17i −0.693446 0.503818i 0.184345 0.982862i \(-0.440984\pi\)
−0.877791 + 0.479044i \(0.840984\pi\)
\(840\) −4.88666e17 + 3.55036e17i −1.39103 + 1.01064i
\(841\) 3.02856e16 9.32096e16i 0.0855974 0.263442i
\(842\) −2.13210e17 6.92761e16i −0.598322 0.194407i
\(843\) 8.44639e16 + 1.16255e17i 0.235345 + 0.323925i
\(844\) −1.94212e17 + 2.67310e17i −0.537305 + 0.739537i
\(845\) −9.90540e16 3.04857e17i −0.272102 0.837444i
\(846\) 2.04038e17i 0.556530i
\(847\) 3.42690e17 5.93495e17i 0.928114 1.60737i
\(848\) 3.67559e15 0.00988445
\(849\) −4.96543e16 + 1.61337e16i −0.132590 + 0.0430811i
\(850\) −5.83769e17 4.24133e17i −1.54784 1.12457i
\(851\) −6.10796e15 + 4.43769e15i −0.0160812 + 0.0116837i
\(852\) 4.27891e16 1.31691e17i 0.111865 0.344286i
\(853\) 1.37510e17 + 4.46797e16i 0.356977 + 0.115989i 0.482015 0.876163i \(-0.339905\pi\)
−0.125038 + 0.992152i \(0.539905\pi\)
\(854\) 5.34104e17 + 7.35131e17i 1.37682 + 1.89504i
\(855\) −1.28221e17 + 1.76481e17i −0.328218 + 0.451753i
\(856\) −3.05478e16 9.40164e16i −0.0776493 0.238980i
\(857\) 5.39655e17i 1.36217i 0.732205 + 0.681085i \(0.238491\pi\)
−0.732205 + 0.681085i \(0.761509\pi\)
\(858\) −1.06276e17 + 1.63643e17i −0.266387 + 0.410180i
\(859\) −3.66949e17 −0.913370 −0.456685 0.889628i \(-0.650963\pi\)
−0.456685 + 0.889628i \(0.650963\pi\)
\(860\) 1.86350e18 6.05488e17i 4.60616 1.49663i
\(861\) −5.77875e15 4.19851e15i −0.0141845 0.0103057i
\(862\) 4.88471e17 3.54895e17i 1.19068 0.865080i
\(863\) −1.12294e17 + 3.45605e17i −0.271826 + 0.836596i 0.718215 + 0.695821i \(0.244959\pi\)
−0.990042 + 0.140775i \(0.955041\pi\)
\(864\) 1.81151e17 + 5.88596e16i 0.435471 + 0.141493i
\(865\) 2.63742e17 + 3.63009e17i 0.629625 + 0.866605i
\(866\) −4.37980e17 + 6.02828e17i −1.03836 + 1.42918i
\(867\) −9.89249e15 3.04460e16i −0.0232912 0.0716828i
\(868\) 1.63081e17i 0.381315i
\(869\) −1.09194e17 + 4.07481e17i −0.253560 + 0.946213i
\(870\) 4.16272e17 0.959978
\(871\) −4.76301e17 + 1.54760e17i −1.09087 + 0.354445i
\(872\) −6.00569e17 4.36339e17i −1.36604 0.992488i
\(873\) 7.59727e16 5.51974e16i 0.171622 0.124690i
\(874\) −1.58380e16 + 4.87444e16i −0.0355330 + 0.109359i
\(875\) 6.51802e16 + 2.11783e16i 0.145234 + 0.0471893i
\(876\) 2.42052e17 + 3.33155e17i 0.535653 + 0.737263i
\(877\) −1.92741e17 + 2.65286e17i −0.423621 + 0.583064i −0.966474 0.256763i \(-0.917344\pi\)
0.542853 + 0.839828i \(0.317344\pi\)
\(878\) 9.46292e16 + 2.91239e17i 0.206566 + 0.635744i
\(879\) 4.26962e17i 0.925671i
\(880\) −3.07067e17 + 1.17864e17i −0.661207 + 0.253797i
\(881\) 8.50950e17 1.81990 0.909952 0.414714i \(-0.136118\pi\)
0.909952 + 0.414714i \(0.136118\pi\)
\(882\) −1.43468e18 + 4.66155e17i −3.04750 + 0.990192i
\(883\) 7.33100e17 + 5.32628e17i 1.54667 + 1.12372i 0.945970 + 0.324254i \(0.105113\pi\)
0.600704 + 0.799471i \(0.294887\pi\)
\(884\) −4.70545e17 + 3.41871e17i −0.986025 + 0.716389i
\(885\) −3.00953e16 + 9.26238e16i −0.0626382 + 0.192781i
\(886\) 5.61672e17 + 1.82498e17i 1.16113 + 0.377274i
\(887\) −3.72972e17 5.13352e17i −0.765834 1.05408i −0.996706 0.0810955i \(-0.974158\pi\)
0.230873 0.972984i \(-0.425842\pi\)
\(888\) 2.69588e16 3.71056e16i 0.0549823 0.0756766i
\(889\) −1.60849e17 4.95043e17i −0.325843 1.00284i
\(890\) 8.49083e17i 1.70848i
\(891\) −1.01892e16 1.94505e17i −0.0203645 0.388746i
\(892\) 2.43030e17 0.482470
\(893\) −1.02178e17 + 3.31995e16i −0.201487 + 0.0654671i
\(894\) −6.10113e17 4.43273e17i −1.19505 0.868252i
\(895\) 4.64357e17 3.37375e17i 0.903470 0.656409i
\(896\) 5.42587e17 1.66991e18i 1.04863 3.22735i
\(897\) 1.98002e16 + 6.43347e15i 0.0380114 + 0.0123507i
\(898\) −5.91532e17 8.14174e17i −1.12803 1.55260i
\(899\) −2.97740e16 + 4.09804e16i −0.0564000 + 0.0776280i
\(900\) 2.46684e17 + 7.59216e17i 0.464180 + 1.42860i
\(901\) 1.15387e16i 0.0215679i
\(902\) −1.14723e16 1.41678e16i −0.0213016 0.0263065i
\(903\) −8.74738e17 −1.61343
\(904\) −8.80300e17 + 2.86027e17i −1.61295 + 0.524078i
\(905\) −9.93380e17 7.21733e17i −1.80811 1.31367i
\(906\) −9.37012e16 + 6.80779e16i −0.169424 + 0.123094i
\(907\) 1.13563e17 3.49510e17i 0.203982 0.627792i −0.795772 0.605597i \(-0.792935\pi\)
0.999754 0.0221950i \(-0.00706548\pi\)
\(908\) −1.00875e18 3.27763e17i −1.79999 0.584851i
\(909\) 1.46884e17 + 2.02168e17i 0.260369 + 0.358368i
\(910\) 9.27335e17 1.27637e18i 1.63301 2.24764i
\(911\) 1.90380e17 + 5.85929e17i 0.333051 + 1.02503i 0.967674 + 0.252204i \(0.0811554\pi\)
−0.634623 + 0.772822i \(0.718845\pi\)
\(912\) 6.64310e16i 0.115452i
\(913\) −1.75589e17 + 1.42183e17i −0.303160 + 0.245483i
\(914\) 1.17689e18 2.01865
\(915\) −2.81941e17 + 9.16082e16i −0.480432 + 0.156102i
\(916\) 6.39092e17 + 4.64328e17i 1.08191 + 0.786053i
\(917\) −1.10692e18 + 8.04223e17i −1.86166 + 1.35257i
\(918\) −2.79229e17 + 8.59380e17i −0.466558 + 1.43592i
\(919\) 2.38127e17 + 7.73722e16i 0.395290 + 0.128437i 0.499915 0.866074i \(-0.333364\pi\)
−0.104626 + 0.994512i \(0.533364\pi\)
\(920\) 9.66802e16 + 1.33069e17i 0.159445 + 0.219457i
\(921\) 2.80439e17 3.85991e17i 0.459495 0.632440i
\(922\) −1.37894e17 4.24394e17i −0.224471 0.690849i
\(923\) 1.63008e17i 0.263632i
\(924\) 9.84242e17 5.15597e16i 1.58150 0.0828473i
\(925\) −9.59293e16 −0.153144
\(926\) −4.47693e17 + 1.45464e17i −0.710092 + 0.230723i
\(927\) −2.83387e17 2.05893e17i −0.446583 0.324462i
\(928\) −2.41097e17 + 1.75167e17i −0.377488 + 0.274261i
\(929\) −3.71964e16 + 1.14479e17i −0.0578637 + 0.178086i −0.975811 0.218617i \(-0.929846\pi\)
0.917947 + 0.396703i \(0.129846\pi\)
\(930\) 7.83948e16 + 2.54720e16i 0.121168 + 0.0393700i
\(931\) −4.66881e17 6.42606e17i −0.716981 0.986840i
\(932\) 4.27850e17 5.88885e17i 0.652824 0.898535i
\(933\) 1.01657e17 + 3.12869e17i 0.154116 + 0.474321i
\(934\) 1.80835e18i 2.72396i
\(935\) 3.70008e17 + 9.63968e17i 0.553785 + 1.44276i
\(936\) 4.49311e17 0.668178
\(937\) −1.27696e17 + 4.14909e16i −0.188686 + 0.0613078i −0.401836 0.915712i \(-0.631628\pi\)
0.213150 + 0.977020i \(0.431628\pi\)
\(938\) 3.17066e18 + 2.30362e18i 4.65514 + 3.38216i
\(939\) 4.21764e17 3.06430e17i 0.615285 0.447031i
\(940\) −2.36395e17 + 7.27550e17i −0.342666 + 1.05462i
\(941\) 2.11305e17 + 6.86570e16i 0.304348 + 0.0988888i 0.457210 0.889359i \(-0.348849\pi\)
−0.152861 + 0.988248i \(0.548849\pi\)
\(942\) −3.01875e17 4.15495e17i −0.432038 0.594649i
\(943\) −1.14330e15 + 1.57361e15i −0.00162588 + 0.00223784i
\(944\) 3.25590e16 + 1.00206e17i 0.0460086 + 0.141600i
\(945\) 1.58205e18i 2.22141i
\(946\) −2.15642e18 5.77864e17i −3.00876 0.806267i
\(947\) 3.87774e17 0.537624 0.268812 0.963193i \(-0.413369\pi\)
0.268812 + 0.963193i \(0.413369\pi\)
\(948\) −5.76995e17 + 1.87477e17i −0.794917 + 0.258284i
\(949\) −3.92197e17 2.84948e17i −0.536917 0.390093i
\(950\) −5.26853e17 + 3.82781e17i −0.716717 + 0.520725i
\(951\) 9.38135e16 2.88728e17i 0.126818 0.390307i
\(952\) 1.95102e18 + 6.33924e17i 2.62083 + 0.851561i
\(953\) −2.50792e17 3.45186e17i −0.334778 0.460782i 0.608129 0.793838i \(-0.291920\pi\)
−0.942907 + 0.333056i \(0.891920\pi\)
\(954\) −1.16248e16 + 1.60001e16i −0.0154204 + 0.0212243i
\(955\) 1.87128e17 + 5.75920e17i 0.246671 + 0.759175i
\(956\) 2.27388e18i 2.97865i
\(957\) −2.56743e17 1.66739e17i −0.334216 0.217053i
\(958\) −1.21456e18 −1.57118
\(959\) 7.89495e17 2.56522e17i 1.01493 0.329772i
\(960\) 6.02535e17 + 4.37767e17i 0.769759 + 0.559263i
\(961\) 6.29118e17 4.57081e17i 0.798715 0.580300i
\(962\) −3.70193e16 + 1.13934e17i −0.0467066 + 0.143748i
\(963\) 1.07932e17 + 3.50693e16i 0.135330 + 0.0439713i
\(964\) 8.34598e17 + 1.14873e18i 1.03996 + 1.43138i
\(965\) 8.31844e15 1.14493e16i 0.0103010 0.0141781i
\(966\) −5.03457e16 1.54948e17i −0.0619583 0.190688i
\(967\) 3.26609e17i 0.399456i −0.979851 0.199728i \(-0.935994\pi\)
0.979851 0.199728i \(-0.0640058\pi\)
\(968\) 1.10893e18 + 2.35764e17i 1.34789 + 0.286566i
\(969\) −2.08545e17 −0.251917
\(970\) 5.18782e17 1.68563e17i 0.622809 0.202363i
\(971\) −8.44931e17 6.13878e17i −1.00810 0.732431i −0.0442941 0.999019i \(-0.514104\pi\)
−0.963811 + 0.266587i \(0.914104\pi\)
\(972\) 1.26301e18 9.17631e17i 1.49765 1.08810i
\(973\) −6.49851e17 + 2.00003e18i −0.765837 + 2.35701i
\(974\) −1.23984e18 4.02850e17i −1.45216 0.471834i
\(975\) 1.55487e17 + 2.14010e17i 0.180995 + 0.249118i
\(976\) −1.88513e17 + 2.59467e17i −0.218094 + 0.300180i
\(977\) 5.36677e17 + 1.65172e18i 0.617086 + 1.89919i 0.361210 + 0.932484i \(0.382364\pi\)
0.255875 + 0.966710i \(0.417636\pi\)
\(978\) 9.39591e17i 1.07376i
\(979\) −3.40103e17 + 5.23687e17i −0.386291 + 0.594806i
\(980\) −5.65579e18 −6.38465
\(981\) 8.10511e17 2.63351e17i 0.909379 0.295475i
\(982\) −1.80613e18 1.31223e18i −2.01410 1.46333i
\(983\) 1.16421e18 8.45849e17i 1.29036 0.937500i 0.290546 0.956861i \(-0.406163\pi\)
0.999813 + 0.0193605i \(0.00616302\pi\)
\(984\) 3.65146e15 1.12380e16i 0.00402250 0.0123800i
\(985\) −9.08337e17 2.95137e17i −0.994557 0.323151i
\(986\) −8.30991e17 1.14376e18i −0.904347 1.24473i
\(987\) 2.00738e17 2.76292e17i 0.217134 0.298859i
\(988\) 1.62209e17 + 4.99227e17i 0.174395 + 0.536731i
\(989\) 2.38200e17i 0.254545i
\(990\) 4.58088e17 1.70946e18i 0.486562 1.81571i
\(991\) 1.77928e18 1.87846 0.939232 0.343284i \(-0.111539\pi\)
0.939232 + 0.343284i \(0.111539\pi\)
\(992\) −5.61234e16 + 1.82356e16i −0.0588944 + 0.0191360i
\(993\) 3.82895e17 + 2.78190e17i 0.399378 + 0.290165i
\(994\) 1.03201e18 7.49798e17i 1.06995 0.777367i
\(995\) 4.35661e17 1.34083e18i 0.448963 1.38176i
\(996\) −3.09024e17 1.00408e17i −0.316545 0.102852i
\(997\) 6.12116e17 + 8.42505e17i 0.623251 + 0.857831i 0.997585 0.0694630i \(-0.0221286\pi\)
−0.374334 + 0.927294i \(0.622129\pi\)
\(998\) 6.53737e17 8.99792e17i 0.661637 0.910666i
\(999\) 3.71218e16 + 1.14249e17i 0.0373454 + 0.114937i
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 11.13.d.a.6.1 yes 44
11.2 odd 10 inner 11.13.d.a.2.1 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.13.d.a.2.1 44 11.2 odd 10 inner
11.13.d.a.6.1 yes 44 1.1 even 1 trivial