LMFDB - Embedded newform 81.10.e.a.10.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,Mod(10,81)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not 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:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			10.5
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.21254 - 35.2331i) q^{2} +(-721.652 + 262.660i) q^{4} +(1770.10 + 1485.29i) q^{5} +(1506.43 + 548.294i) q^{7} +(4578.80 + 7930.71i) q^{8} +(41334.5 - 71593.4i) q^{10} +(-27997.7 + 23492.8i) q^{11} +(21795.3 - 123608. i) q^{13} +(9959.36 - 56482.3i) q^{14} +(-50230.1 + 42148.1i) q^{16} +(-224900. + 389539. i) q^{17} +(-27210.8 - 47130.6i) q^{19} +(-1.66752e6 - 606928. i) q^{20} +(1.00166e6 + 840494. i) q^{22} +(313324. - 114041. i) q^{23} +(588008. + 3.33476e6i) q^{25} -4.49048e6 q^{26} -1.23113e6 q^{28} +(564465. + 3.20124e6i) q^{29} +(-8.22217e6 + 2.99262e6i) q^{31} +(5.38881e6 + 4.52175e6i) q^{32} +(1.51218e7 + 5.50390e6i) q^{34} +(1.85215e6 + 3.20801e6i) q^{35} +(-8.86390e6 + 1.53527e7i) q^{37} +(-1.49151e6 + 1.25152e6i) q^{38} +(-3.67447e6 + 2.08390e7i) q^{40} +(-815267. + 4.62361e6i) q^{41} +(2.43510e7 - 2.04329e7i) q^{43} +(1.40340e7 - 2.43075e7i) q^{44} +(-5.96454e6 - 1.03309e7i) q^{46} +(-2.53795e7 - 9.23739e6i) q^{47} +(-2.89440e7 - 2.42869e7i) q^{49} +(1.13841e8 - 4.14347e7i) q^{50} +(1.67381e7 + 9.49264e7i) q^{52} -9.26556e7 q^{53} -8.44523e7 q^{55} +(2.54926e6 + 1.44576e7i) q^{56} +(1.09283e8 - 3.97757e7i) q^{58} +(6.23558e7 + 5.23227e7i) q^{59} +(1.19412e8 + 4.34624e7i) q^{61} +(1.56520e8 + 2.71100e8i) q^{62} +(1.09051e8 - 1.88882e8i) q^{64} +(2.22173e8 - 1.86425e8i) q^{65} +(-7.54148e6 + 4.27699e7i) q^{67} +(5.99835e7 - 3.40184e8i) q^{68} +(1.01522e8 - 8.51868e7i) q^{70} +(1.89260e7 - 3.27808e7i) q^{71} +(1.68954e8 + 2.92637e8i) q^{73} +(5.95992e8 + 2.16923e8i) q^{74} +(3.20161e7 + 2.68647e7i) q^{76} +(-5.50574e7 + 2.00393e7i) q^{77} +(6.04918e7 + 3.43066e8i) q^{79} -1.51514e8 q^{80} +1.67969e8 q^{82} +(1.22302e8 + 6.93609e8i) q^{83} +(-9.76672e8 + 3.55480e8i) q^{85} +(-8.71197e8 - 7.31021e8i) q^{86} +(-3.14511e8 - 1.14473e8i) q^{88} +(-3.09414e8 - 5.35921e8i) q^{89} +(1.00606e8 - 1.74255e8i) q^{91} +(-1.96157e8 + 1.64595e8i) q^{92} +(-1.67790e8 + 9.51587e8i) q^{94} +(2.18366e7 - 1.23842e8i) q^{95} +(4.97155e8 - 4.17163e8i) q^{97} +(-6.75886e8 + 1.17067e9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−6.21254	−	35.2331i	−0.274558	−	1.55710i	−0.740362	−	0.672209i	$-0.765346\pi$
$2$	−6.21254	−	35.2331i	−0.274558	−	1.55710i	0.465803	−	0.884888i	$-0.345765\pi$
$3$		0			0
$3$		0			0
$4$	−721.652	+	262.660i	−1.40948	+	0.513008i
$5$	1770.10	+	1485.29i	1.26658	+	1.06279i	0.994949	+	0.100384i	$0.0320072\pi$
$5$	1770.10	+	1485.29i	1.26658	+	1.06279i	0.271630	+	0.962402i	$0.412437\pi$
$6$		0			0
$7$	1506.43	+	548.294i	0.237141	+	0.0863123i	0.457857	−	0.889026i	$-0.348617\pi$
$7$	1506.43	+	548.294i	0.237141	+	0.0863123i	−0.220716	+	0.975338i	$0.570839\pi$
$8$	4578.80	+	7930.71i	0.395227	+	0.684553i
$9$		0			0
$10$	41334.5	−	71593.4i	1.30711	−	2.26398i
$11$	−27997.7	+	23492.8i	−0.576574	+	0.483803i	−0.883820	−	0.467827i	$-0.845037\pi$
$11$	−27997.7	+	23492.8i	−0.576574	+	0.483803i	0.307246	+	0.951630i	$0.400593\pi$
$12$		0			0
$13$	21795.3	−	123608.i	0.211650	−	1.20033i	−0.674976	−	0.737840i	$-0.735846\pi$
$13$	21795.3	−	123608.i	0.211650	−	1.20033i	0.886626	−	0.462488i	$-0.153043\pi$
$14$	9959.36	−	56482.3i	0.0692876	−	0.392949i
$15$		0			0
$16$	−50230.1	+	42148.1i	−0.191613	+	0.160782i
$17$	−224900.	+	389539.i	−0.653085	+	1.13118i	0.329285	+	0.944230i	$0.393192\pi$
$17$	−224900.	+	389539.i	−0.653085	+	1.13118i	−0.982370	+	0.186946i	$0.940141\pi$
$18$		0			0
$19$	−27210.8	−	47130.6i	−0.0479017	−	0.0829681i	0.841080	−	0.540910i	$-0.181920\pi$
$19$	−27210.8	−	47130.6i	−0.0479017	−	0.0829681i	−0.888982	+	0.457942i	$0.848587\pi$
$20$	−1.66752e6	−	606928.i	−2.33043	−	0.848207i
$21$		0			0
$22$	1.00166e6	+	840494.i	0.911631	+	0.764949i
$23$	313324.	−	114041.i	0.233463	−	0.0849736i	−0.222639	−	0.974901i	$-0.571467\pi$
$23$	313324.	−	114041.i	0.233463	−	0.0849736i	0.456103	+	0.889927i	$0.349245\pi$
$24$		0			0
$25$	588008.	+	3.33476e6i	0.301060	+	1.70740i
$26$	−4.49048e6			−1.92714
$27$		0			0
$28$	−1.23113e6			−0.378524
$29$	564465.	+	3.20124e6i	0.148199	+	0.840480i	0.964742	+	0.263196i	$0.0847765\pi$
$29$	564465.	+	3.20124e6i	0.148199	+	0.840480i	−0.816543	+	0.577284i	$0.804112\pi$
$30$		0			0
$31$	−8.22217e6	+	2.99262e6i	−1.59904	+	0.582002i	−0.979230	−	0.202752i	$-0.935011\pi$
$31$	−8.22217e6	+	2.99262e6i	−1.59904	+	0.582002i	−0.619807	+	0.784754i	$0.712789\pi$
$32$	5.38881e6	+	4.52175e6i	0.908485	+	0.762310i
$33$		0			0
$34$	1.51218e7	+	5.50390e6i	1.94066	+	0.706343i
$35$	1.85215e6	+	3.20801e6i	0.208626	+	0.361351i
$36$		0			0
$37$	−8.86390e6	+	1.53527e7i	−0.777530	+	1.34672i	0.155831	+	0.987784i	$0.450194\pi$
$37$	−8.86390e6	+	1.53527e7i	−0.777530	+	1.34672i	−0.933361	+	0.358938i	$0.883139\pi$
$38$	−1.49151e6	+	1.25152e6i	−0.116038	+	0.0973671i
$39$		0			0
$40$	−3.67447e6	+	2.08390e7i	−0.226947	+	1.28708i
$41$	−815267.	+	4.62361e6i	−0.0450581	+	0.255537i	−0.999013	−	0.0444120i	$-0.985859\pi$
$41$	−815267.	+	4.62361e6i	−0.0450581	+	0.255537i	0.953955	+	0.299949i	$0.0969697\pi$
$42$		0			0
$43$	2.43510e7	−	2.04329e7i	1.08620	−	0.911428i	0.0897774	−	0.995962i	$-0.471384\pi$
$43$	2.43510e7	−	2.04329e7i	1.08620	−	0.911428i	0.996421	+	0.0845335i	$0.0269400\pi$
$44$	1.40340e7	−	2.43075e7i	0.564473	−	0.977696i
$45$		0			0
$46$	−5.96454e6	−	1.03309e7i	−0.196411	−	0.340195i
$47$	−2.53795e7	−	9.23739e6i	−0.758653	−	0.276127i	−0.0664108	−	0.997792i	$-0.521155\pi$
$47$	−2.53795e7	−	9.23739e6i	−0.758653	−	0.276127i	−0.692242	+	0.721665i	$0.743377\pi$
$48$		0			0
$49$	−2.89440e7	−	2.42869e7i	−0.717258	−	0.601851i
$50$	1.13841e8	−	4.14347e7i	2.57592	−	0.937560i
$51$		0			0
$52$	1.67381e7	+	9.49264e7i	0.317461	+	1.80041i
$53$	−9.26556e7			−1.61298			−0.806492	−	0.591245i	$-0.798637\pi$
$53$	−9.26556e7			−1.61298			−0.806492	+	0.591245i	$0.798637\pi$
$54$		0			0
$55$	−8.44523e7			−1.24446
$56$	2.54926e6	+	1.44576e7i	0.0346392	+	0.196449i
$57$		0			0
$58$	1.09283e8	−	3.97757e7i	1.26802	−	0.461521i
$59$	6.23558e7	+	5.23227e7i	0.669950	+	0.562155i	0.913051	−	0.407846i	$-0.133720\pi$
$59$	6.23558e7	+	5.23227e7i	0.669950	+	0.562155i	−0.243100	+	0.970001i	$0.578164\pi$
$60$		0			0
$61$	1.19412e8	+	4.34624e7i	1.10424	+	0.401910i	0.828877	−	0.559431i	$-0.188980\pi$
$61$	1.19412e8	+	4.34624e7i	1.10424	+	0.401910i	0.275362	+	0.961341i	$0.411202\pi$
$62$	1.56520e8	+	2.71100e8i	1.34526	+	2.33006i
$63$		0			0
$64$	1.09051e8	−	1.88882e8i	0.812492	−	1.40728i
$65$	2.22173e8	−	1.86425e8i	1.54376	−	1.29537i
$66$		0			0
$67$	−7.54148e6	+	4.27699e7i	−0.0457215	+	0.259299i	−0.999097	−	0.0424871i	$-0.986472\pi$
$67$	−7.54148e6	+	4.27699e7i	−0.0457215	+	0.259299i	0.953376	+	0.301786i	$0.0975830\pi$
$68$	5.99835e7	−	3.40184e8i	0.340206	−	1.92940i
$69$		0			0
$70$	1.01522e8	−	8.51868e7i	0.505379	−	0.424063i
$71$	1.89260e7	−	3.27808e7i	0.0883885	−	0.153093i	−0.818442	−	0.574590i	$-0.805162\pi$
$71$	1.89260e7	−	3.27808e7i	0.0883885	−	0.153093i	0.906830	+	0.421496i	$0.138495\pi$
$72$		0			0
$73$	1.68954e8	+	2.92637e8i	0.696331	+	1.20608i	0.969730	+	0.244180i	$0.0785186\pi$
$73$	1.68954e8	+	2.92637e8i	0.696331	+	1.20608i	−0.273399	+	0.961901i	$0.588148\pi$
$74$	5.95992e8	+	2.16923e8i	2.31045	+	0.840937i
$75$		0			0
$76$	3.20161e7	+	2.68647e7i	0.110080	+	0.0923677i
$77$	−5.50574e7	+	2.00393e7i	−0.178487	+	0.0649641i
$78$		0			0
$79$	6.04918e7	+	3.43066e8i	0.174733	+	0.990959i	0.938452	+	0.345410i	$0.112260\pi$
$79$	6.04918e7	+	3.43066e8i	0.174733	+	0.990959i	−0.763719	+	0.645549i	$0.776629\pi$
$80$	−1.51514e8			−0.413570
$81$		0			0
$82$	1.67969e8			0.410267
$83$	1.22302e8	+	6.93609e8i	0.282867	+	1.60422i	0.712807	+	0.701360i	$0.247424\pi$
$83$	1.22302e8	+	6.93609e8i	0.282867	+	1.60422i	−0.429940	+	0.902857i	$0.641465\pi$
$84$		0			0
$85$	−9.76672e8	+	3.55480e8i	−2.02938	+	0.738635i
$86$	−8.71197e8	−	7.31021e8i	−1.71741	−	1.44108i
$87$		0			0
$88$	−3.14511e8	−	1.14473e8i	−0.559067	−	0.203484i
$89$	−3.09414e8	−	5.35921e8i	−0.522739	−	0.905411i	−0.999650	−	0.0264590i	$-0.991577\pi$
$89$	−3.09414e8	−	5.35921e8i	−0.522739	−	0.905411i	0.476911	−	0.878952i	$-0.341756\pi$
$90$		0			0
$91$	1.00606e8	−	1.74255e8i	0.153794	−	0.266379i
$92$	−1.96157e8	+	1.64595e8i	−0.285469	+	0.239537i
$93$		0			0
$94$	−1.67790e8	+	9.51587e8i	−0.221662	+	1.25711i
$95$	2.18366e7	−	1.23842e8i	0.0275061	−	0.155995i
$96$		0			0
$97$	4.97155e8	−	4.17163e8i	0.570190	−	0.478446i	−0.311519	−	0.950240i	$-0.600838\pi$
$97$	4.97155e8	−	4.17163e8i	0.570190	−	0.478446i	0.881709	+	0.471794i	$0.156393\pi$
$98$	−6.75886e8	+	1.17067e9i	−0.740212	+	1.28208i
$99$		0			0
$100$	−1.30024e9	−	2.25209e9i	−1.30024	−	2.25209i
$101$	−7.78395e8	−	2.83313e8i	−0.744310	−	0.270907i	−0.0581007	−	0.998311i	$-0.518504\pi$
$101$	−7.78395e8	−	2.83313e8i	−0.744310	−	0.270907i	−0.686209	+	0.727404i	$0.740727\pi$
$102$		0			0
$103$	1.00555e9	+	8.43755e8i	0.880309	+	0.738667i	0.966243	−	0.257634i	$-0.0829428\pi$
$103$	1.00555e9	+	8.43755e8i	0.880309	+	0.738667i	−0.0859333	+	0.996301i	$0.527387\pi$
$104$	1.08009e9	−	3.93121e8i	0.905338	−	0.329516i
$105$		0			0
$106$	5.75627e8	+	3.26454e9i	0.442858	+	2.51157i
$107$	−1.37213e8			−0.101197			−0.0505984	−	0.998719i	$-0.516113\pi$
$107$	−1.37213e8			−0.101197			−0.0505984	+	0.998719i	$0.516113\pi$
$108$		0			0
$109$	−1.10795e9			−0.751797			−0.375899	−	0.926661i	$-0.622666\pi$
$109$	−1.10795e9			−0.751797			−0.375899	+	0.926661i	$0.622666\pi$
$110$	5.24664e8	+	2.97551e9i	0.341675	+	1.93774i
$111$		0			0
$112$	−9.87775e7	+	3.59521e7i	−0.0593167	+	0.0215895i
$113$	1.95291e8	+	1.63868e8i	0.112675	+	0.0945458i	0.697385	−	0.716697i	$-0.254347\pi$
$113$	1.95291e8	+	1.63868e8i	0.112675	+	0.0945458i	−0.584709	+	0.811243i	$0.698791\pi$
$114$		0			0
$115$	7.23997e8	+	2.63513e8i	0.386008	+	0.140496i
$116$	−1.24818e9	−	2.16192e9i	−0.640056	−	1.10861i
$117$		0			0
$118$	1.45610e9	−	2.52204e9i	0.691390	−	1.19752i
$119$	−5.52377e8	+	4.63500e8i	−0.252508	+	0.211879i
$120$		0			0
$121$	−1.77497e8	+	1.00663e9i	−0.0752760	+	0.426911i
$122$	7.89462e8	−	4.47726e9i	0.322635	−	1.82976i
$123$		0			0
$124$	5.14750e9	−	4.31927e9i	1.95523	−	1.64064i
$125$	−1.65571e9	+	2.86777e9i	−0.606580	+	1.05063i
$126$		0			0
$127$	−1.73158e9	−	2.99918e9i	−0.590644	−	1.02302i	−0.994146	−	0.108046i	$-0.965541\pi$
$127$	−1.73158e9	−	2.99918e9i	−0.590644	−	1.02302i	0.403502	−	0.914979i	$-0.367793\pi$
$128$	−3.94786e9	−	1.43690e9i	−1.29992	−	0.473133i
$129$		0			0
$130$	−7.94859e9	−	6.66966e9i	−2.44087	−	2.04813i
$131$	−8.94172e8	+	3.25452e8i	−0.265277	+	0.0965531i	−0.471235	−	0.882008i	$-0.656191\pi$
$131$	−8.94172e8	+	3.25452e8i	−0.265277	+	0.0965531i	0.205957	+	0.978561i	$0.433969\pi$
$132$		0			0
$133$	−1.51497e7	−	8.59182e7i	−0.00419828	−	0.0238096i
$134$	1.55377e9			0.416307
$135$		0			0
$136$	−4.11909e9			−1.03247
$137$	6.93712e8	+	3.93423e9i	0.168243	+	0.954152i	0.945658	+	0.325164i	$0.105419\pi$
$137$	6.93712e8	+	3.93423e9i	0.168243	+	0.954152i	−0.777415	+	0.628988i	$0.783469\pi$
$138$		0			0
$139$	3.34375e9	−	1.21703e9i	0.759744	−	0.276524i	0.0670437	−	0.997750i	$-0.478643\pi$
$139$	3.34375e9	−	1.21703e9i	0.759744	−	0.276524i	0.692700	+	0.721226i	$0.256421\pi$
$140$	−2.17922e9	−	1.82858e9i	−0.479430	−	0.402289i
$141$		0			0
$142$	−1.27255e9	−	4.63169e8i	−0.262649	−	0.0955964i
$143$	2.29367e9	+	3.97276e9i	0.458690	+	0.794475i
$144$		0			0
$145$	−3.75561e9	+	6.50490e9i	−0.705544	+	1.22204i
$146$	9.26087e9	−	7.77079e9i	1.68680	−	1.41539i
$147$		0			0
$148$	2.36411e9	−	1.34075e10i	0.405032	−	2.29705i
$149$	4.40515e7	−	2.49829e8i	0.00732188	−	0.0415245i	−0.980928	−	0.194372i	$-0.937733\pi$
$149$	4.40515e7	−	2.49829e8i	0.00732188	−	0.0415245i	0.988250	+	0.152847i	$0.0488443\pi$
$150$		0			0
$151$	−2.73163e9	+	2.29211e9i	−0.427589	+	0.358790i	−0.831041	−	0.556211i	$-0.812255\pi$
$151$	−2.73163e9	+	2.29211e9i	−0.427589	+	0.358790i	0.403452	+	0.915001i	$0.367810\pi$
$152$	2.49186e8	−	4.31603e8i	0.0378641	−	0.0655825i
$153$		0			0
$154$	1.04809e9	+	1.81535e9i	0.150161	+	0.260086i
$155$	−1.89989e10	−	6.91505e9i	−2.64385	−	0.962283i
$156$		0			0
$157$	3.49262e9	+	2.93066e9i	0.458778	+	0.384961i	0.842681	−	0.538413i	$-0.180976\pi$
$157$	3.49262e9	+	2.93066e9i	0.458778	+	0.384961i	−0.383903	+	0.923373i	$0.625420\pi$
$158$	1.17115e10	−	4.26262e9i	1.49505	−	0.544152i
$159$		0			0
$160$	2.82262e9	+	1.60079e10i	0.340496	+	1.93105i
$161$	5.34527e8			0.0626980
$162$		0			0
$163$	−1.97696e9			−0.219358			−0.109679	−	0.993967i	$-0.534982\pi$
$163$	−1.97696e9			−0.219358			−0.109679	+	0.993967i	$0.534982\pi$
$164$	−6.26098e8	−	3.55078e9i	−0.0675841	−	0.383289i
$165$		0			0
$166$	2.36782e10	−	8.61815e9i	2.42026	−	0.880902i
$167$	5.59234e9	+	4.69253e9i	0.556377	+	0.466856i	0.877094	−	0.480320i	$-0.159479\pi$
$167$	5.59234e9	+	4.69253e9i	0.556377	+	0.466856i	−0.320717	+	0.947175i	$0.603924\pi$
$168$		0			0
$169$	−4.83881e9	−	1.76118e9i	−0.456298	−	0.166079i
$170$	1.85923e10	+	3.22027e10i	1.70731	+	2.95715i
$171$		0			0
$172$	−1.22060e10	+	2.11415e10i	−1.06340	+	1.84186i
$173$	−1.18102e10	+	9.90995e9i	−1.00242	+	0.841132i	−0.987318	−	0.158754i	$-0.949252\pi$
$173$	−1.18102e10	+	9.90995e9i	−1.00242	+	0.841132i	−0.0151035	+	0.999886i	$0.504808\pi$
$174$		0			0
$175$	−9.42639e8	+	5.34597e9i	−0.0759756	+	0.430879i
$176$	4.16149e8	−	2.36010e9i	0.0326920	−	0.185406i
$177$		0			0
$178$	−1.69599e10	+	1.42310e10i	−1.26629	+	1.06254i
$179$	7.75125e9	−	1.34256e10i	0.564330	−	0.977448i	−0.432782	−	0.901499i	$-0.642468\pi$
$179$	7.75125e9	−	1.34256e10i	0.564330	−	0.977448i	0.997112	−	0.0759492i	$-0.0241987\pi$
$180$		0			0
$181$	7.67302e9	+	1.32901e10i	0.531389	+	0.920393i	0.999329	+	0.0366324i	$0.0116630\pi$
$181$	7.67302e9	+	1.32901e10i	0.531389	+	0.920393i	−0.467940	+	0.883760i	$0.655004\pi$
$182$	−6.76458e9	−	2.46210e9i	−0.457003	−	0.166336i
$183$		0			0
$184$	2.33907e9	+	1.96271e9i	0.150440	+	0.126234i
$185$	−3.84932e10	+	1.40104e10i	−2.41608	+	0.879381i
$186$		0			0
$187$	−2.85468e9	−	1.61897e10i	−0.170715	−	0.968171i
$188$	2.07415e10			1.21096
$189$		0			0
$190$	−4.49898e9			−0.250451
$191$	−3.29981e8	−	1.87142e9i	−0.0179407	−	0.101747i	0.974523	−	0.224290i	$-0.0720062\pi$
$191$	−3.29981e8	−	1.87142e9i	−0.0179407	−	0.101747i	−0.992463	+	0.122543i	$0.960895\pi$
$192$		0			0
$193$	2.57704e10	−	9.37966e9i	1.33694	−	0.486608i	0.428095	−	0.903734i	$-0.359185\pi$
$193$	2.57704e10	−	9.37966e9i	1.33694	−	0.486608i	0.908849	+	0.417126i	$0.136963\pi$
$194$	−1.77865e10	−	1.49247e10i	−0.901537	−	0.756480i
$195$		0			0
$196$	2.72667e10	+	9.92425e9i	1.31971	+	0.480336i
$197$	−1.12282e10	−	1.94478e10i	−0.531144	−	0.919968i	−0.999339	−	0.0363435i	$-0.988429\pi$
$197$	−1.12282e10	−	1.94478e10i	−0.531144	−	0.919968i	0.468195	−	0.883625i	$-0.344904\pi$
$198$		0			0
$199$	6.95778e9	−	1.20512e10i	0.314508	−	0.544744i	−0.664825	−	0.746999i	$-0.731494\pi$
$199$	6.95778e9	−	1.20512e10i	0.314508	−	0.544744i	0.979333	+	0.202255i	$0.0648271\pi$
$200$	−2.37546e10	+	1.99325e10i	−1.04982	+	0.880901i
$201$		0			0
$202$	−5.14617e9	+	2.91854e10i	−0.217472	+	1.23334i
$203$	−9.04897e8	+	5.13193e9i	−0.0373996	+	0.212104i
$204$		0			0
$205$	−8.31050e9	+	6.97334e9i	−0.328651	+	0.275771i
$206$	2.34811e10	−	4.06704e10i	0.908480	−	1.57353i
$207$		0			0
$208$	4.11504e9	+	7.12745e9i	0.152436	+	0.264028i
$209$	1.86907e9	+	6.80286e8i	0.0677591	+	0.0246623i
$210$		0			0
$211$	−4.03052e10	−	3.38201e10i	−1.39988	−	1.17464i	−0.961154	−	0.276013i	$-0.910987\pi$
$211$	−4.03052e10	−	3.38201e10i	−1.39988	−	1.17464i	−0.438723	−	0.898622i	$-0.644569\pi$
$212$	6.68651e10	−	2.43369e10i	2.27346	−	0.827473i
$213$		0			0
$214$	8.52439e8	+	4.83442e9i	0.0277844	+	0.157573i
$215$	7.34525e10			2.34441
$216$		0			0
$217$	−1.40269e10			−0.429431
$218$	6.88319e9	+	3.90365e10i	0.206412	+	1.17062i
$219$		0			0
$220$	6.09452e10	−	2.21822e10i	1.75403	−	0.638415i
$221$	4.32481e10	+	3.62895e10i	1.21956	+	1.02333i
$222$		0			0
$223$	−5.34246e8	−	1.94450e8i	−0.0144667	−	0.00526545i	0.334777	−	0.942298i	$-0.391339\pi$
$223$	−5.34246e8	−	1.94450e8i	−0.0144667	−	0.00526545i	−0.349243	+	0.937032i	$0.613561\pi$
$224$	5.63859e9	+	9.76633e9i	0.149642	+	0.259188i
$225$		0			0
$226$	4.56034e9	−	7.89874e9i	0.116281	−	0.201405i
$227$	3.12318e10	−	2.62066e10i	0.780695	−	0.655081i	−0.162729	−	0.986671i	$-0.552030\pi$
$227$	3.12318e10	−	2.62066e10i	0.780695	−	0.655081i	0.943424	+	0.331590i	$0.107585\pi$
$228$		0			0
$229$	5.47423e9	−	3.10459e10i	0.131542	−	0.746010i	−0.845664	−	0.533715i	$-0.820795\pi$
$229$	5.47423e9	−	3.10459e10i	0.131542	−	0.746010i	0.977206	−	0.212294i	$-0.0680935\pi$
$230$	4.78653e9	−	2.71457e10i	0.112783	−	0.639627i
$231$		0			0
$232$	−2.28035e10	+	1.91344e10i	−0.516781	+	0.433631i
$233$	−3.33632e10	+	5.77867e10i	−0.741593	+	1.28448i	0.210177	+	0.977663i	$0.432596\pi$
$233$	−3.33632e10	+	5.77867e10i	−0.741593	+	1.28448i	−0.951770	+	0.306813i	$0.900737\pi$
$234$		0			0
$235$	−3.12041e10	−	5.40470e10i	−0.667430	−	1.15602i
$236$	−5.87423e10	−	2.13804e10i	−1.23267	−	0.448655i
$237$		0			0
$238$	1.97622e10	+	1.65824e10i	0.399244	+	0.335006i
$239$	4.43780e9	−	1.61523e9i	0.0879786	−	0.0320216i	−0.297656	−	0.954673i	$-0.596205\pi$
$239$	4.43780e9	−	1.61523e9i	0.0879786	−	0.0320216i	0.385635	+	0.922652i	$0.373983\pi$
$240$		0			0
$241$	−2.83407e9	−	1.60728e10i	−0.0541171	−	0.306913i	0.945720	−	0.324984i	$-0.105359\pi$
$241$	−2.83407e9	−	1.60728e10i	−0.0541171	−	0.306913i	−0.999837	+	0.0180703i	$0.994248\pi$
$242$	3.65696e10			0.685410
$243$		0			0
$244$	−9.75896e10			−1.76258
$245$	−1.51606e10	−	8.59803e10i	−0.268825	−	1.52458i
$246$		0			0
$247$	−6.41876e9	+	2.33624e9i	−0.109727	+	0.0399375i
$248$	−6.13813e10	−	5.15050e10i	−1.03039	−	0.864603i
$249$		0			0
$250$	1.11326e11	+	4.05195e10i	1.80247	+	0.656046i
$251$	−5.89048e9	−	1.02026e10i	−0.0936740	−	0.162248i	0.815380	−	0.578926i	$-0.196528\pi$
$251$	−5.89048e9	−	1.02026e10i	−0.0936740	−	0.162248i	−0.909054	+	0.416677i	$0.863194\pi$
$252$		0			0
$253$	−6.09321e9	+	1.05537e10i	−0.0934983	+	0.161944i
$254$	−9.49129e10	+	7.96414e10i	−1.43078	+	1.20057i
$255$		0			0
$256$	−6.70935e9	+	3.80506e10i	−0.0976339	+	0.553710i
$257$	1.09492e10	−	6.20960e10i	0.156561	−	0.887900i	−0.800784	−	0.598953i	$-0.795584\pi$
$257$	1.09492e10	−	6.20960e10i	0.156561	−	0.887900i	0.957345	−	0.288947i	$-0.0933053\pi$
$258$		0			0
$259$	−2.17706e10	+	1.82677e10i	−0.300623	+	0.252253i
$260$	−1.11365e11	+	1.92890e11i	−1.51136	+	2.61776i
$261$		0			0
$262$	1.70218e10	+	2.94826e10i	0.223177	+	0.386553i
$263$	5.15504e10	+	1.87628e10i	0.664402	+	0.241823i	0.652136	−	0.758102i	$-0.273873\pi$
$263$	5.15504e10	+	1.87628e10i	0.664402	+	0.241823i	0.0122665	+	0.999925i	$0.496095\pi$
$264$		0			0
$265$	−1.64009e11	−	1.37620e11i	−2.04297	−	1.71426i
$266$	−2.93305e9	+	1.06754e9i	−0.0359213	+	0.0130743i
$267$		0			0
$268$	−5.79160e9	−	3.28458e10i	−0.0685792	−	0.388932i
$269$	−1.43660e11			−1.67283			−0.836413	−	0.548100i	$-0.815351\pi$
$269$	−1.43660e11			−1.67283			−0.836413	+	0.548100i	$0.815351\pi$
$270$		0			0
$271$	4.30943e10			0.485353			0.242676	−	0.970107i	$-0.421975\pi$
$271$	4.30943e10			0.485353			0.242676	+	0.970107i	$0.421975\pi$
$272$	−5.12154e9	−	2.90457e10i	−0.0567336	−	0.321752i
$273$		0			0
$274$	1.34305e11	−	4.88832e10i	1.43951	−	0.523941i
$275$	−9.48058e10	−	7.95515e10i	−0.999627	−	0.838787i
$276$		0			0
$277$	5.48827e9	+	1.99757e9i	0.0560114	+	0.0203865i	0.369874	−	0.929082i	$-0.379401\pi$
$277$	5.48827e9	+	1.99757e9i	0.0560114	+	0.0203865i	−0.313863	+	0.949468i	$0.601623\pi$
$278$	−6.36527e10	−	1.10250e11i	−0.639169	−	1.10707i
$279$		0			0
$280$	−1.69612e10	+	2.93777e10i	−0.164910	+	0.285632i
$281$	−5.79159e10	+	4.85972e10i	−0.554139	+	0.464978i	−0.876340	−	0.481693i	$-0.840022\pi$
$281$	−5.79159e10	+	4.85972e10i	−0.554139	+	0.464978i	0.322200	+	0.946671i	$0.395578\pi$
$282$		0			0
$283$	−1.25055e10	+	7.09223e10i	−0.115894	+	0.657270i	0.870409	+	0.492329i	$0.163854\pi$
$283$	−1.25055e10	+	7.09223e10i	−0.115894	+	0.657270i	−0.986303	+	0.164941i	$0.947257\pi$
$284$	−5.04778e9	+	2.86274e10i	−0.0460435	+	0.261126i
$285$		0			0
$286$	1.25723e11	−	1.05494e11i	1.11114	−	0.932355i
$287$	−3.76324e9	+	6.51812e9i	−0.0327411	+	0.0567093i
$288$		0			0
$289$	−4.18662e10	−	7.25144e10i	−0.353040	−	0.611483i
$290$	2.52520e11	+	9.19097e10i	2.09655	+	0.763080i
$291$		0			0
$292$	−1.98790e11	−	1.66805e11i	−1.60019	−	1.34272i
$293$	−1.80961e11	+	6.58643e10i	−1.43443	+	0.522091i	−0.938198	−	0.346098i	$-0.887506\pi$
$293$	−1.80961e11	+	6.58643e10i	−1.43443	+	0.522091i	−0.496234	+	0.868189i	$0.665284\pi$
$294$		0			0
$295$	3.26615e10	+	1.85233e11i	0.251095	+	1.42403i
$296$	−1.62344e11			−1.22920
$297$		0			0
$298$	−9.07591e9			−0.0666679
$299$	−7.26727e9	−	4.12148e10i	−0.0525837	−	0.298217i
$300$		0			0
$301$	4.78863e10	−	1.74292e10i	0.336250	−	0.122385i
$302$	9.77286e10	+	8.20041e10i	0.676068	+	0.567289i
$303$		0			0
$304$	3.35327e9	+	1.22049e9i	0.0225184	+	0.00819601i
$305$	1.46817e11	+	2.54294e11i	0.971461	+	1.68262i
$306$		0			0
$307$	2.33740e10	−	4.04850e10i	0.150179	−	0.260118i	−0.781114	−	0.624389i	$-0.785348\pi$
$307$	2.33740e10	−	4.04850e10i	0.150179	−	0.260118i	0.931293	+	0.364270i	$0.118682\pi$
$308$	3.44688e10	−	2.89228e10i	0.218247	−	0.183131i
$309$		0			0
$310$	−1.25607e11	+	7.12352e11i	−0.772477	+	4.38093i
$311$	3.53529e10	−	2.00496e11i	0.214291	−	1.21530i	−0.667842	−	0.744303i	$-0.732782\pi$
$311$	3.53529e10	−	2.00496e11i	0.214291	−	1.21530i	0.882133	−	0.471001i	$-0.156107\pi$
$312$		0			0
$313$	−1.80712e11	+	1.51636e11i	−1.06424	+	0.893001i	−0.994518	−	0.104566i	$-0.966655\pi$
$313$	−1.80712e11	+	1.51636e11i	−1.06424	+	0.893001i	−0.0697191	+	0.997567i	$0.522210\pi$
$314$	8.15580e10	−	1.41263e11i	0.473460	−	0.820057i
$315$		0			0
$316$	−1.33764e11	−	2.31685e11i	−0.754651	−	1.30709i
$317$	1.07735e11	+	3.92125e10i	0.599227	+	0.218101i	0.623783	−	0.781598i	$-0.285595\pi$
$317$	1.07735e11	+	3.92125e10i	0.599227	+	0.218101i	−0.0245558	+	0.999698i	$0.507817\pi$
$318$		0			0
$319$	−9.10100e10	−	7.63664e10i	−0.492075	−	0.412900i
$320$	4.73574e11	−	1.72367e11i	2.52472	−	0.918923i
$321$		0			0
$322$	−3.32077e9	−	1.88330e10i	−0.0172142	−	0.0976268i
$323$	2.44789e10			0.125135
$324$		0			0
$325$	4.25017e11			2.11316
$326$	1.22820e10	+	6.96545e10i	0.0602266	+	0.341562i
$327$		0			0
$328$	−4.04015e10	+	1.47049e10i	−0.192737	+	0.0701505i
$329$	−3.31676e10	−	2.78309e10i	−0.156075	−	0.130962i
$330$		0			0
$331$	−1.71864e11	−	6.25534e10i	−0.786972	−	0.286434i	−0.0828952	−	0.996558i	$-0.526417\pi$
$331$	−1.71864e11	−	6.25534e10i	−0.786972	−	0.286434i	−0.704077	+	0.710124i	$0.748639\pi$
$332$	−2.70443e11	−	4.68421e11i	−1.22167	−	2.11599i
$333$		0			0
$334$	1.30590e11	−	2.26188e11i	0.574182	−	0.994512i
$335$	−7.68748e10	+	6.45056e10i	−0.333490	+	0.279831i
$336$		0			0
$337$	1.14090e9	−	6.47036e9i	0.00481851	−	0.0273271i	−0.982304	−	0.187295i	$-0.940028\pi$
$337$	1.14090e9	−	6.47036e9i	0.00481851	−	0.0273271i	0.987122	+	0.159968i	$0.0511391\pi$
$338$	−3.19906e10	+	1.81428e11i	−0.133321	+	0.756099i
$339$		0			0
$340$	6.11447e11	−	5.13065e11i	2.48144	−	2.08218i
$341$	1.59896e11	−	2.76949e11i	0.640389	−	1.10919i
$342$		0			0
$343$	−6.26311e10	−	1.08480e11i	−0.244324	−	0.423182i
$344$	2.73546e11	+	9.95626e10i	1.05322	+	0.383339i
$345$		0			0
$346$	4.22530e11	+	3.54544e11i	1.58495	+	1.32993i
$347$	−2.68610e11	+	9.77660e10i	−0.994579	+	0.361997i	−0.787492	−	0.616325i	$-0.788621\pi$
$347$	−2.68610e11	+	9.77660e10i	−0.994579	+	0.361997i	−0.207088	+	0.978322i	$0.566398\pi$
$348$		0			0
$349$	−1.79070e10	−	1.01555e11i	−0.0646112	−	0.366428i	−0.999921	−	0.0125974i	$-0.995990\pi$
$349$	−1.79070e10	−	1.01555e11i	−0.0646112	−	0.366428i	0.935309	−	0.353831i	$-0.115121\pi$
$350$	1.94211e11			0.691780
$351$		0			0
$352$	−2.57103e11			−0.892616
$353$	8.25985e9	+	4.68439e10i	0.0283130	+	0.160571i	0.995686	−	0.0927847i	$-0.0295768\pi$
$353$	8.25985e9	+	4.68439e10i	0.0283130	+	0.160571i	−0.967373	+	0.253356i	$0.918466\pi$
$354$		0			0
$355$	8.21897e10	−	2.99146e10i	0.274657	−	0.0999668i
$356$	3.64054e11	+	3.05478e11i	1.20127	+	1.00799i
$357$		0			0
$358$	−5.21179e11	−	1.89694e11i	−1.67692	−	0.610350i
$359$	1.99329e10	+	3.45248e10i	0.0633353	+	0.109700i	0.895954	−	0.444146i	$-0.146493\pi$
$359$	1.99329e10	+	3.45248e10i	0.0633353	+	0.109700i	−0.832619	+	0.553846i	$0.813160\pi$
$360$		0			0
$361$	1.59863e11	−	2.76891e11i	0.495411	−	0.858077i
$362$	4.20581e11	−	3.52909e11i	1.28724	−	1.08013i
$363$		0			0
$364$	−2.68329e10	+	1.52177e11i	−0.0801146	+	0.454352i
$365$	−1.35585e11	+	7.68941e11i	−0.399847	+	2.26765i
$366$		0			0
$367$	6.15238e8	−	5.16246e8i	0.00177029	−	0.00148545i	−0.641902	−	0.766787i	$-0.721854\pi$
$367$	6.15238e8	−	5.16246e8i	0.00177029	−	0.00148545i	0.643672	+	0.765301i	$0.277410\pi$
$368$	−1.09317e10	+	1.89343e10i	−0.0310723	+	0.0538187i
$369$		0			0
$370$	7.32770e11	+	1.26919e12i	2.03264	+	3.52063i
$371$	−1.39579e11	−	5.08025e10i	−0.382505	−	0.139220i
$372$		0			0
$373$	−3.19686e11	−	2.68248e11i	−0.855132	−	0.717541i	0.105782	−	0.994389i	$-0.466266\pi$
$373$	−3.19686e11	−	2.68248e11i	−0.855132	−	0.717541i	−0.960914	+	0.276848i	$0.910710\pi$
$374$	−5.52679e11	+	2.01159e11i	−1.46067	+	0.531639i
$375$		0			0
$376$	−4.29487e10	−	2.43574e11i	−0.110816	−	0.628471i
$377$	4.08000e11			1.04022
$378$		0			0
$379$	4.26116e11			1.06084			0.530422	−	0.847734i	$-0.322034\pi$
$379$	4.26116e11			1.06084			0.530422	+	0.847734i	$0.322034\pi$
$380$	1.67698e10	+	9.51062e10i	0.0412573	+	0.233982i
$381$		0			0
$382$	−6.38858e10	+	2.32525e10i	−0.153504	+	0.0558708i
$383$	−1.13545e11	−	9.52756e10i	−0.269633	−	0.226249i	0.497938	−	0.867213i	$-0.334091\pi$
$383$	−1.13545e11	−	9.52756e10i	−0.269633	−	0.226249i	−0.767572	+	0.640963i	$0.778535\pi$
$384$		0			0
$385$	−1.27221e11	−	4.63047e10i	−0.295111	−	0.107412i
$386$	−4.90574e11	−	8.49699e11i	−1.12476	−	1.94815i
$387$		0			0
$388$	−2.49201e11	+	4.31629e11i	−0.558223	+	0.966870i
$389$	2.01275e11	−	1.68890e11i	0.445674	−	0.373965i	−0.392154	−	0.919900i	$-0.628270\pi$
$389$	2.01275e11	−	1.68890e11i	0.445674	−	0.373965i	0.837828	+	0.545935i	$0.183825\pi$
$390$		0			0
$391$	−2.60434e10	+	1.47700e11i	−0.0563511	+	0.319583i
$392$	6.00836e10	−	3.40751e11i	0.128519	−	0.728870i
$393$		0			0
$394$	−6.15451e11	+	5.16425e11i	−1.28665	+	1.07963i
$395$	−4.02476e11	+	6.97108e11i	−0.831864	+	1.44083i
$396$		0			0
$397$	2.56781e11	+	4.44758e11i	0.518807	+	0.898600i	0.999761	+	0.0218543i	$0.00695701\pi$
$397$	2.56781e11	+	4.44758e11i	0.518807	+	0.898600i	−0.480954	+	0.876746i	$0.659710\pi$
$398$	−4.67827e11	−	1.70275e11i	−0.934570	−	0.340156i
$399$		0			0
$400$	−1.70089e11	−	1.42722e11i	−0.332206	−	0.278754i
$401$	−1.87326e11	+	6.81812e10i	−0.361784	+	0.131679i	−0.516515	−	0.856278i	$-0.672771\pi$
$401$	−1.87326e11	+	6.81812e10i	−0.361784	+	0.131679i	0.154731	+	0.987957i	$0.450549\pi$
$402$		0			0
$403$	1.90706e11	+	1.08155e12i	0.360157	+	2.04255i
$404$	6.36145e11			1.18807
$405$		0			0
$406$	1.86435e11			0.340534
$407$	−1.12511e11	−	6.38079e11i	−0.203244	−	1.15266i
$408$		0			0
$409$	6.99412e11	−	2.54565e11i	1.23589	−	0.449826i	0.360276	−	0.932846i	$-0.382682\pi$
$409$	6.99412e11	−	2.54565e11i	1.23589	−	0.449826i	0.875609	+	0.483020i	$0.160460\pi$
$410$	2.97322e11	+	2.49482e11i	0.519636	+	0.436026i
$411$		0			0
$412$	−9.47276e11	−	3.44780e11i	−1.61972	−	0.589529i
$413$	6.52461e10	+	1.13010e11i	0.110352	+	0.191135i
$414$		0			0
$415$	−8.13723e11	+	1.40941e12i	−1.34667	+	2.33250i
$416$	6.76373e11	−	5.67544e11i	1.10730	−	0.929137i
$417$		0			0
$418$	1.23569e10	−	7.00794e10i	0.0197978	−	0.112279i
$419$	−1.72124e11	+	9.76164e11i	−0.272821	+	1.54725i	0.472977	+	0.881075i	$0.343179\pi$
$419$	−1.72124e11	+	9.76164e11i	−0.272821	+	1.54725i	−0.745798	+	0.666172i	$0.767932\pi$
$420$		0			0
$421$	−1.96202e11	+	1.64633e11i	−0.304392	+	0.255415i	−0.782170	−	0.623065i	$-0.785887\pi$
$421$	−1.96202e11	+	1.64633e11i	−0.304392	+	0.255415i	0.477777	+	0.878481i	$0.341443\pi$
$422$	−9.41187e11	+	1.63018e12i	−1.44467	+	2.50225i
$423$		0			0
$424$	−4.24251e11	−	7.34825e11i	−0.637495	−	1.10417i
$425$	−1.43126e12	−	5.20936e11i	−2.12798	−	0.774523i
$426$		0			0
$427$	1.56055e11	+	1.30946e11i	0.227171	+	0.190619i
$428$	9.90197e10	−	3.60402e10i	0.142635	−	0.0519147i
$429$		0			0
$430$	−4.56327e11	−	2.58796e12i	−0.643677	−	3.65047i
$431$	6.89668e11			0.962703			0.481351	−	0.876528i	$-0.340146\pi$
$431$	6.89668e11			0.962703			0.481351	+	0.876528i	$0.340146\pi$
$432$		0			0
$433$	−1.44732e11			−0.197866			−0.0989328	−	0.995094i	$-0.531543\pi$
$433$	−1.44732e11			−0.197866			−0.0989328	+	0.995094i	$0.531543\pi$
$434$	8.71429e10	+	4.94212e11i	0.117904	+	0.668666i
$435$		0			0
$436$	7.99554e11	−	2.91014e11i	1.05964	−	0.385678i
$437$	−1.39006e10	−	1.16640e10i	−0.0182334	−	0.0152996i
$438$		0			0
$439$	3.38231e11	+	1.23106e11i	0.434633	+	0.158193i	0.550065	−	0.835122i	$-0.314603\pi$
$439$	3.38231e11	+	1.23106e11i	0.434633	+	0.158193i	−0.115432	+	0.993315i	$0.536825\pi$
$440$	−3.86690e11	−	6.69767e11i	−0.491842	−	0.851896i
$441$		0			0
$442$	1.00991e12	−	1.74921e12i	1.25858	−	2.17993i
$443$	6.27579e11	−	5.26601e11i	0.774197	−	0.649628i	−0.167583	−	0.985858i	$-0.553596\pi$
$443$	6.27579e11	−	5.26601e11i	0.774197	−	0.649628i	0.941780	+	0.336230i	$0.109152\pi$
$444$		0			0
$445$	2.48304e11	−	1.40820e12i	0.300167	−	1.70233i
$446$	−3.53203e9	+	2.00312e10i	−0.00422686	+	0.0239717i
$447$		0			0
$448$	2.67840e11	−	2.24744e11i	0.314140	−	0.263595i
$449$	5.50978e11	−	9.54322e11i	0.639773	−	1.10812i	−0.345709	−	0.938342i	$-0.612362\pi$
$449$	5.50978e11	−	9.54322e11i	0.639773	−	1.10812i	0.985482	−	0.169778i	$-0.0543049\pi$
$450$		0			0
$451$	−8.57962e10	−	1.48603e11i	−0.0976503	−	0.169135i
$452$	−1.83974e11	−	6.69609e10i	−0.207316	−	0.0754568i
$453$		0			0
$454$	−1.11737e12	−	9.37584e11i	−1.23437	−	1.03576i
$455$	4.36903e11	−	1.59020e11i	0.477896	−	0.173940i
$456$		0			0
$457$	−3.59519e10	−	2.03894e11i	−0.0385567	−	0.218666i	0.959442	−	0.281908i	$-0.0909672\pi$
$457$	−3.59519e10	−	2.03894e11i	−0.0385567	−	0.218666i	−0.997998	+	0.0632419i	$0.979856\pi$
$458$	−1.12785e12			−1.19773
$459$		0			0
$460$	−5.91689e11			−0.616145
$461$	−2.69174e10	−	1.52656e11i	−0.0277574	−	0.157420i	0.967779	−	0.251803i	$-0.0810234\pi$
$461$	−2.69174e10	−	1.52656e11i	−0.0277574	−	0.157420i	−0.995536	+	0.0943826i	$0.969912\pi$
$462$		0			0
$463$	−1.65833e12	+	6.03581e11i	−1.67709	+	0.610410i	−0.992906	−	0.118903i	$-0.962062\pi$
$463$	−1.65833e12	+	6.03581e11i	−1.67709	+	0.610410i	−0.684181	+	0.729312i	$0.739840\pi$
$464$	−1.63279e11	−	1.37008e11i	−0.163531	−	0.137219i
$465$		0			0
$466$	2.24327e12	+	8.16485e11i	2.20367	+	0.802069i
$467$	−8.73307e11	−	1.51261e12i	−0.849652	−	1.47164i	−0.881519	−	0.472149i	$-0.843479\pi$
$467$	−8.73307e11	−	1.51261e12i	−0.849652	−	1.47164i	0.0318667	−	0.999492i	$-0.489855\pi$
$468$		0			0
$469$	−3.48112e10	+	6.02947e10i	−0.0332231	+	0.0575442i
$470$	−1.71039e12	+	1.43518e12i	−1.61679	+	1.35665i
$471$		0			0
$472$	−1.29442e11	+	7.34101e11i	−0.120043	+	0.680796i
$473$	−2.01744e11	+	1.14415e12i	−0.185322	+	1.05101i
$474$		0			0
$475$	1.41169e11	−	1.18455e11i	0.127238	−	0.106766i
$476$	2.76881e11	−	4.79573e11i	0.247208	−	0.428177i
$477$		0			0
$478$	−8.44795e10	−	1.46323e11i	−0.0740160	−	0.128199i
$479$	1.32543e12	+	4.82417e11i	1.15039	+	0.418709i	0.845657	−	0.533727i	$-0.179209\pi$
$479$	1.32543e12	+	4.82417e11i	1.15039	+	0.418709i	0.304738	+	0.952436i	$0.401431\pi$
$480$		0			0
$481$	1.70452e12	+	1.43026e12i	1.45194	+	1.21833i
$482$	−5.48689e11	+	1.99706e11i	−0.463036	+	0.168531i
$483$		0			0
$484$	−1.36312e11	−	7.73061e11i	−0.112909	−	0.640339i
$485$	1.49962e12			1.23068
$486$		0			0
$487$	1.38869e12			1.11873			0.559364	−	0.828922i	$-0.311045\pi$
$487$	1.38869e12			1.11873			0.559364	+	0.828922i	$0.311045\pi$
$488$	2.02075e11	+	1.14603e12i	0.161296	+	0.914756i
$489$		0			0
$490$	−2.93516e12	+	1.06831e12i	−2.30012	+	0.837174i
$491$	−6.70416e11	−	5.62546e11i	−0.520569	−	0.436809i	0.344261	−	0.938874i	$-0.388129\pi$
$491$	−6.70416e11	−	5.62546e11i	−0.520569	−	0.436809i	−0.864830	+	0.502065i	$0.832574\pi$
$492$		0			0
$493$	−1.37395e12	−	5.00079e11i	−1.04752	−	0.381265i
$494$	1.22190e11	+	2.11639e11i	0.0923131	+	0.159891i
$495$		0			0
$496$	2.86867e11	−	4.96868e11i	0.212820	−	0.368616i
$497$	4.64841e10	−	3.90048e10i	0.0341744	−	0.0286757i
$498$		0			0
$499$	2.97697e9	−	1.68832e10i	0.00214942	−	0.0121900i	−0.983714	−	0.179740i	$-0.942474\pi$
$499$	2.97697e9	−	1.68832e10i	0.00214942	−	0.0121900i	0.985864	+	0.167550i	$0.0535855\pi$
$500$	4.41596e11	−	2.50442e12i	0.315981	−	1.79202i
$501$		0			0
$502$	−3.22875e11	+	2.70924e11i	−0.226917	+	0.190406i
$503$	9.25971e11	−	1.60383e12i	0.644973	−	1.11713i	−0.339335	−	0.940666i	$-0.610202\pi$
$503$	9.25971e11	−	1.60383e12i	0.644973	−	1.11713i	0.984308	−	0.176460i	$-0.0564646\pi$
$504$		0			0
$505$	−9.57035e11	−	1.65763e12i	−0.654812	−	1.13417i
$506$	4.09695e11	+	1.49117e11i	0.277833	+	0.101123i
$507$		0			0
$508$	2.03736e12	+	1.70955e12i	1.35732	+	1.13892i
$509$	1.12381e12	−	4.09035e11i	0.742103	−	0.270104i	0.0568244	−	0.998384i	$-0.481902\pi$
$509$	1.12381e12	−	4.09035e11i	0.742103	−	0.270104i	0.685279	+	0.728281i	$0.259680\pi$
$510$		0			0
$511$	9.40656e10	+	5.33472e11i	0.0610291	+	0.346113i
$512$	−7.68704e11			−0.494361
$513$		0			0
$514$	−2.25585e12			−1.42553
$515$	5.26699e11	+	2.98706e12i	0.329936	+	1.87116i
$516$		0			0
$517$	9.27581e11	−	3.37612e11i	0.571011	−	0.207831i
$518$	7.78879e11	+	6.53557e11i	0.475320	+	0.398841i
$519$		0			0
$520$	2.49577e12	+	9.08385e11i	1.49689	+	0.544823i
$521$	1.15462e12	+	1.99985e12i	0.686544	+	1.18913i	0.972949	+	0.231020i	$0.0742062\pi$
$521$	1.15462e12	+	1.99985e12i	0.686544	+	1.18913i	−0.286406	+	0.958108i	$0.592460\pi$
$522$		0			0
$523$	1.17646e12	−	2.03769e12i	0.687574	−	1.19091i	−0.285047	−	0.958514i	$-0.592009\pi$
$523$	1.17646e12	−	2.03769e12i	0.687574	−	1.19091i	0.972621	−	0.232399i	$-0.0746574\pi$
$524$	5.59798e11	−	4.69726e11i	0.324370	−	0.272179i
$525$		0			0
$526$	3.40813e11	−	1.93284e12i	0.194124	−	1.10093i
$527$	6.83424e11	−	3.87589e12i	0.385960	−	2.18889i
$528$		0			0
$529$	−1.29460e12	+	1.08630e12i	−0.718760	+	0.603111i
$530$	−3.82987e12	+	6.63353e12i	−2.10835	+	3.65177i
$531$		0			0
$532$	3.35001e10	+	5.80239e10i	0.0181319	+	0.0314054i
$533$	5.53744e11	+	2.01546e11i	0.297192	+	0.108169i
$534$		0			0
$535$	−2.42880e11	−	2.03800e11i	−0.128174	−	0.107551i
$536$	−3.73727e11	+	1.36025e11i	−0.195575	+	0.0711833i
$537$		0			0
$538$	8.92494e11	+	5.06159e12i	0.459288	+	2.60475i
$539$	1.38093e12			0.704730
$540$		0			0
$541$	9.16468e11			0.459970			0.229985	−	0.973194i	$-0.426132\pi$
$541$	9.16468e11			0.459970			0.229985	+	0.973194i	$0.426132\pi$
$542$	−2.67725e11	−	1.51834e12i	−0.133258	−	0.755742i
$543$		0			0
$544$	−2.97334e12	+	1.08221e12i	−1.45562	+	0.529804i
$545$	−1.96118e12	−	1.64562e12i	−0.952211	−	0.799000i
$546$		0			0
$547$	2.66271e12	+	9.69146e11i	1.27169	+	0.462856i	0.887675	−	0.460471i	$-0.152320\pi$
$547$	2.66271e12	+	9.69146e11i	1.27169	+	0.462856i	0.384013	+	0.923328i	$0.374542\pi$
$548$	−1.53398e12	−	2.65694e12i	−0.726621	−	1.25855i
$549$		0			0
$550$	−2.21386e12	+	3.83452e12i	−1.03162	+	1.78681i
$551$	1.35517e11	−	1.13712e11i	0.0626341	−	0.0525562i
$552$		0			0
$553$	−9.69747e10	+	5.49971e11i	−0.0440956	+	0.250079i
$554$	3.62843e10	−	2.05779e11i	0.0163653	−	0.0928125i
$555$		0			0
$556$	−2.09336e12	+	1.75654e12i	−0.928982	+	0.779508i
$557$	−4.19856e11	+	7.27212e11i	−0.184821	+	0.320120i	−0.943516	−	0.331326i	$-0.892504\pi$
$557$	−4.19856e11	+	7.27212e11i	−0.184821	+	0.320120i	0.758695	+	0.651446i	$0.225837\pi$
$558$		0			0
$559$	−1.99493e12	−	3.45531e12i	−0.864119	−	1.49670i
$560$	−2.28245e11	−	8.30744e10i	−0.0980743	−	0.0356961i
$561$		0			0
$562$	2.07203e12	+	1.73864e12i	0.876160	+	0.735185i
$563$	2.09958e10	−	7.64184e9i	0.00880733	−	0.00320561i	−0.337613	−	0.941285i	$-0.609619\pi$
$563$	2.09958e10	−	7.64184e9i	0.00880733	−	0.00320561i	0.346420	+	0.938079i	$0.387397\pi$
$564$		0			0
$565$	1.02292e11	+	5.80126e11i	0.0422302	+	0.239500i
$566$	2.57650e12			1.05525
$567$		0			0
$568$	3.46633e11			0.139734
$569$	−4.20191e11	−	2.38302e12i	−0.168051	−	0.953065i	−0.945863	−	0.324567i	$-0.894781\pi$
$569$	−4.20191e11	−	2.38302e12i	−0.168051	−	0.953065i	0.777812	−	0.628497i	$-0.216330\pi$
$570$		0			0
$571$	1.43334e12	−	5.21692e11i	0.564268	−	0.205377i	−0.0441063	−	0.999027i	$-0.514044\pi$
$571$	1.43334e12	−	5.21692e11i	0.564268	−	0.205377i	0.608375	+	0.793650i	$0.291822\pi$
$572$	−2.69872e12	−	2.26449e12i	−1.05408	−	0.884482i
$573$		0			0
$574$	2.53033e11	+	9.20964e10i	0.0972912	+	0.0354111i
$575$	5.64535e11	+	9.77803e11i	0.215370	+	0.373032i
$576$		0			0
$577$	−2.13078e12	+	3.69061e12i	−0.800289	+	1.38614i	0.119137	+	0.992878i	$0.461987\pi$
$577$	−2.13078e12	+	3.69061e12i	−0.800289	+	1.38614i	−0.919426	+	0.393263i	$0.871346\pi$
$578$	−2.29481e12	+	1.92558e12i	−0.855208	+	0.717605i
$579$		0			0
$580$	1.00166e12	−	5.68072e12i	0.367533	−	2.08438i
$581$	−1.96063e11	+	1.11193e12i	−0.0713843	+	0.404841i
$582$		0			0
$583$	2.59414e12	−	2.17674e12i	0.930004	−	0.780366i
$584$	−1.54721e12	+	2.67985e12i	−0.550417	+	0.953351i
$585$		0			0
$586$	3.44483e12	+	5.96662e12i	1.20678	+	2.09021i
$587$	2.90560e12	+	1.05755e12i	1.01010	+	0.367646i	0.793471	−	0.608608i	$-0.208272\pi$
$587$	2.90560e12	+	1.05755e12i	1.01010	+	0.367646i	0.216628	+	0.976254i	$0.430494\pi$
$588$		0			0
$589$	3.64776e11	+	3.06083e11i	0.124884	+	0.104790i
$590$	6.32341e12	−	2.30153e12i	2.14841	−	0.781957i
$591$		0			0
$592$	−2.01853e11	−	1.14477e12i	−0.0675442	−	0.383062i
$593$	3.07187e12			1.02013			0.510067	−	0.860135i	$-0.329621\pi$
$593$	3.07187e12			1.02013			0.510067	+	0.860135i	$0.329621\pi$
$594$		0			0
$595$	−1.66619e12			−0.545003
$596$	3.38301e10	+	1.91860e11i	0.0109823	+	0.0622839i
$597$		0			0
$598$	−1.40697e12	+	5.12097e11i	−0.449916	+	0.163756i
$599$	2.64849e12	+	2.22235e12i	0.840577	+	0.705328i	0.957693	−	0.287790i	$-0.0929206\pi$
$599$	2.64849e12	+	2.22235e12i	0.840577	+	0.705328i	−0.117116	+	0.993118i	$0.537365\pi$
$600$		0			0
$601$	4.26406e11	+	1.55199e11i	0.133318	+	0.0485237i	0.407817	−	0.913063i	$-0.366290\pi$
$601$	4.26406e11	+	1.55199e11i	0.133318	+	0.0485237i	−0.274500	+	0.961587i	$0.588512\pi$
$602$	−9.11579e11	−	1.57890e12i	−0.282885	−	0.489971i
$603$		0			0
$604$	1.36924e12	−	2.37160e12i	0.418615	−	0.725062i
$605$	−1.80933e12	+	1.51821e12i	−0.549059	+	0.460715i
$606$		0			0
$607$	1.02906e12	−	5.83607e12i	0.307673	−	1.74490i	−0.302974	−	0.952999i	$-0.597979\pi$
$607$	1.02906e12	−	5.83607e12i	0.307673	−	1.74490i	0.610647	−	0.791903i	$-0.290909\pi$
$608$	6.64785e10	−	3.77018e11i	0.0197294	−	0.111891i
$609$		0			0
$610$	8.04745e12	−	6.75261e12i	2.35328	−	1.97464i
$611$	−1.69497e12	+	2.93577e12i	−0.492012	+	0.852190i
$612$		0			0
$613$	8.01686e11	+	1.38856e12i	0.229315	+	0.397185i	0.957605	−	0.288084i	$-0.0930181\pi$
$613$	8.01686e11	+	1.38856e12i	0.229315	+	0.397185i	−0.728290	+	0.685269i	$0.759685\pi$
$614$	−1.57162e12	−	5.72024e11i	−0.446263	−	0.162426i
$615$		0			0
$616$	−4.11023e11	−	3.44889e11i	−0.115014	−	0.0965086i
$617$	−1.97987e12	+	7.20615e11i	−0.549990	+	0.200180i	−0.602042	−	0.798465i	$-0.705646\pi$
$617$	−1.97987e12	+	7.20615e11i	−0.549990	+	0.200180i	0.0520523	+	0.998644i	$0.483424\pi$
$618$		0			0
$619$	1.13726e12	+	6.44970e12i	0.311351	+	1.76576i	0.591988	+	0.805947i	$0.298343\pi$
$619$	1.13726e12	+	6.44970e12i	0.311351	+	1.76576i	−0.280637	+	0.959814i	$0.590546\pi$
$620$	1.55269e13			4.22010
$621$		0			0
$622$	−7.28374e12			−1.95118
$623$	−1.72267e11	−	9.76975e11i	−0.0458148	−	0.259829i
$624$		0			0
$625$	−9.75399e11	+	3.55016e11i	−0.255695	+	0.0930654i
$626$	6.46528e12	+	5.42501e12i	1.68268	+	1.41194i
$627$		0			0
$628$	−3.29022e12	−	1.19754e12i	−0.844125	−	0.307236i
$629$	−3.98699e12	−	6.90566e12i	−1.01559	−	1.75905i
$630$		0			0
$631$	3.09557e12	−	5.36168e12i	0.777335	−	1.34638i	−0.156138	−	0.987735i	$-0.549905\pi$
$631$	3.09557e12	−	5.36168e12i	0.777335	−	1.34638i	0.933473	−	0.358648i	$-0.116762\pi$
$632$	−2.44378e12	+	2.05057e12i	−0.609305	+	0.511268i
$633$		0			0
$634$	7.12265e11	−	4.03946e12i	0.175081	−	0.992936i
$635$	1.38959e12	−	7.88074e12i	0.339159	−	1.92347i
$636$		0			0
$637$	−3.63288e12	+	3.04835e12i	−0.874227	+	0.733563i
$638$	−2.12522e12	+	3.68099e12i	−0.507822	+	0.879573i
$639$		0			0
$640$	−4.85388e12	−	8.40717e12i	−1.14361	−	1.98080i
$641$	−2.14078e12	−	7.79179e11i	−0.500853	−	0.182296i	0.0792246	−	0.996857i	$-0.474756\pi$
$641$	−2.14078e12	−	7.79179e11i	−0.500853	−	0.182296i	−0.580078	+	0.814561i	$0.696978\pi$
$642$		0			0
$643$	2.03473e12	+	1.70734e12i	0.469416	+	0.393887i	0.846582	−	0.532259i	$-0.178657\pi$
$643$	2.03473e12	+	1.70734e12i	0.469416	+	0.393887i	−0.377165	+	0.926146i	$0.623101\pi$
$644$	−3.85743e11	+	1.40399e11i	−0.0883713	+	0.0321645i
$645$		0			0
$646$	−1.52076e11	−	8.62467e11i	−0.0343570	−	0.194848i
$647$	−5.48535e12			−1.23065			−0.615325	−	0.788273i	$-0.710975\pi$
$647$	−5.48535e12			−1.23065			−0.615325	+	0.788273i	$0.710975\pi$
$648$		0			0
$649$	−2.97503e12			−0.658248
$650$	−2.64044e12	−	1.49747e13i	−0.580184	−	3.29039i
$651$		0			0
$652$	1.42668e12	−	5.19268e11i	0.309180	−	0.112532i
$653$	−1.85150e12	−	1.55359e12i	−0.398486	−	0.334370i	0.421422	−	0.906865i	$-0.361531\pi$
$653$	−1.85150e12	−	1.55359e12i	−0.398486	−	0.334370i	−0.819908	+	0.572495i	$0.805976\pi$
$654$		0			0
$655$	−2.06616e12	−	7.52021e11i	−0.438610	−	0.159641i
$656$	−1.53925e11	−	2.66606e11i	−0.0324521	−	0.0562087i
$657$		0			0
$658$	−7.74513e11	+	1.34150e12i	−0.161069	+	0.278980i
$659$	−4.63443e12	+	3.88875e12i	−0.957221	+	0.803204i	−0.980499	−	0.196525i	$-0.937034\pi$
$659$	−4.63443e12	+	3.88875e12i	−0.957221	+	0.803204i	0.0232778	+	0.999729i	$0.492590\pi$
$660$		0			0
$661$	2.40374e11	−	1.36323e12i	0.0489758	−	0.277755i	−0.950478	−	0.310791i	$-0.899406\pi$
$661$	2.40374e11	−	1.36323e12i	0.0489758	−	0.277755i	0.999454	+	0.0330352i	$0.0105173\pi$
$662$	−1.13624e12	+	6.44392e12i	−0.229936	+	1.30403i
$663$		0			0
$664$	−4.94082e12	+	4.14584e12i	−0.986376	+	0.827668i
$665$	1.00797e11	−	1.74585e11i	0.0199871	−	0.0346187i
$666$		0			0
$667$	5.41932e11	+	9.38654e11i	0.106018	+	0.183628i
$668$	−5.26826e12	−	1.91749e12i	−1.02370	−	0.372597i
$669$		0			0
$670$	2.75032e12	+	2.30779e12i	0.527286	+	0.442446i
$671$	−4.36431e12	+	1.58848e12i	−0.831121	+	0.302503i
$672$		0			0
$673$	−2.07864e11	−	1.17886e12i	−0.0390582	−	0.221510i	0.959031	−	0.283301i	$-0.0914297\pi$
$673$	−2.07864e11	−	1.17886e12i	−0.0390582	−	0.221510i	−0.998089	+	0.0617916i	$0.980319\pi$
$674$	−2.35059e11			−0.0438739
$675$		0			0
$676$	3.95453e12			0.728342
$677$	7.18714e11	+	4.07603e12i	0.131494	+	0.745741i	0.977237	+	0.212150i	$0.0680467\pi$
$677$	7.18714e11	+	4.07603e12i	0.131494	+	0.745741i	−0.845743	+	0.533591i	$0.820842\pi$
$678$		0			0
$679$	9.77656e11	−	3.55838e11i	0.176511	−	0.0642448i
$680$	−7.29119e12	−	6.11804e12i	−1.30770	−	1.09729i
$681$		0			0
$682$	−1.07511e13	−	3.91309e12i	−1.90293	−	0.692612i
$683$	1.02786e12	+	1.78031e12i	0.180735	+	0.313042i	0.942131	−	0.335245i	$-0.108819\pi$
$683$	1.02786e12	+	1.78031e12i	0.180735	+	0.313042i	−0.761396	+	0.648287i	$0.775486\pi$
$684$		0			0
$685$	−4.61553e12	+	7.99434e12i	−0.800967	+	1.38731i
$686$	−3.43300e12	+	2.88063e12i	−0.591854	+	0.496625i
$687$		0			0
$688$	−3.61946e11	+	2.05270e12i	−0.0615879	+	0.349282i
$689$	−2.01946e12	+	1.14529e13i	−0.341388	+	1.93611i
$690$		0			0
$691$	2.83791e12	−	2.38129e12i	0.473530	−	0.397339i	−0.374550	−	0.927207i	$-0.622203\pi$
$691$	2.83791e12	−	2.38129e12i	0.473530	−	0.397339i	0.848080	+	0.529868i	$0.177758\pi$
$692$	5.91992e12	−	1.02536e13i	0.981383	−	1.69981i
$693$		0			0
$694$	5.11335e12	+	8.85658e12i	0.836735	+	1.44927i
$695$	7.72640e12	+	2.81218e12i	1.25616	+	0.457205i
$696$		0			0
$697$	−1.61772e12	−	1.35743e12i	−0.259631	−	0.217856i
$698$	−3.46686e12	+	1.26184e12i	−0.552825	+	0.201212i
$699$		0			0
$700$	−7.23915e11	−	4.10552e12i	−0.113958	−	0.646290i
$701$	2.09874e12			0.328267			0.164134	−	0.986438i	$-0.447517\pi$
$701$	2.09874e12			0.328267			0.164134	+	0.986438i	$0.447517\pi$
$702$		0			0
$703$	9.64777e11			0.148980
$704$	1.38419e12	+	7.85016e12i	0.212383	+	1.20449i
$705$		0			0
$706$	1.59914e12	−	5.82040e11i	0.242251	−	0.0881722i
$707$	−1.01726e12	−	8.53579e11i	−0.153124	−	0.128486i
$708$		0			0
$709$	−6.35854e12	−	2.31432e12i	−0.945038	−	0.343966i	−0.176885	−	0.984232i	$-0.556602\pi$
$709$	−6.35854e12	−	2.31432e12i	−0.945038	−	0.343966i	−0.768153	+	0.640266i	$0.778824\pi$
$710$	−1.56459e12	−	2.70995e12i	−0.231067	−	0.400220i
$711$		0			0
$712$	2.83349e12	−	4.90775e12i	0.413201	−	0.715686i
$713$	−2.23492e12	+	1.87532e12i	−0.323861	+	0.271752i
$714$		0			0
$715$	−1.84067e12	+	1.04389e13i	−0.263389	+	1.49375i
$716$	−2.06735e12	+	1.17245e13i	−0.293972	+	1.66720i
$717$		0			0
$718$	1.09258e12	−	9.16786e11i	0.153424	−	0.128738i
$719$	2.85974e12	−	4.95321e12i	0.399067	−	0.691204i	−0.594544	−	0.804063i	$-0.702667\pi$
$719$	2.85974e12	−	4.95321e12i	0.399067	−	0.691204i	0.993611	+	0.112859i	$0.0360007\pi$
$720$		0			0
$721$	1.05216e12	+	1.82239e12i	0.145001	+	0.251150i
$722$	−1.07489e13	−	3.91227e12i	−1.47213	−	0.535811i
$723$		0			0
$724$	−9.02801e12	−	7.57540e12i	−1.22115	−	1.02467i
$725$	−1.03435e13	+	3.76471e12i	−1.39042	+	0.506070i
$726$		0			0
$727$	−8.26875e10	−	4.68944e11i	−0.0109783	−	0.0622610i	0.978826	−	0.204692i	$-0.0656192\pi$
$727$	−8.26875e10	−	4.68944e11i	−0.0109783	−	0.0622610i	−0.989805	+	0.142431i	$0.954508\pi$
$728$	1.84263e12			0.243134
$729$		0			0
$730$	2.79345e13			3.64073
$731$	2.48286e12	+	1.40810e13i	0.321607	+	1.82392i
$732$		0			0
$733$	5.14486e12	−	1.87258e12i	0.658273	−	0.239592i	0.00878244	−	0.999961i	$-0.497204\pi$
$733$	5.14486e12	−	1.87258e12i	0.658273	−	0.239592i	0.649491	+	0.760370i	$0.274982\pi$
$734$	−2.20111e10	−	1.84695e10i	−0.00279904	−	0.00234868i
$735$		0			0
$736$	2.20411e12	+	8.02229e11i	0.276874	+	0.100774i
$737$	−7.93642e11	−	1.37463e12i	−0.0990880	−	0.171625i
$738$		0			0
$739$	−2.67157e12	+	4.62729e12i	−0.329508	+	0.570725i	−0.982414	−	0.186714i	$-0.940216\pi$
$739$	−2.67157e12	+	4.62729e12i	−0.329508	+	0.570725i	0.652906	+	0.757439i	$0.273550\pi$
$740$	2.40987e13	−	2.02212e13i	2.95428	−	2.47894i
$741$		0			0
$742$	−9.22790e11	+	5.23340e12i	−0.111760	+	0.633821i
$743$	2.53767e12	−	1.43918e13i	0.305481	−	1.73247i	−0.315749	−	0.948843i	$-0.602256\pi$
$743$	2.53767e12	−	1.43918e13i	0.305481	−	1.73247i	0.621230	−	0.783628i	$-0.286633\pi$
$744$		0			0
$745$	4.49043e11	−	3.76792e11i	0.0534054	−	0.0448124i
$746$	−7.46514e12	+	1.29300e13i	−0.882498	+	1.52853i
$747$		0			0
$748$	6.31248e12	+	1.09335e13i	0.737297	+	1.27704i
$749$	−2.06701e11	−	7.52328e10i	−0.0239979	−	0.00873452i
$750$		0			0
$751$	1.19906e13	+	1.00613e13i	1.37550	+	1.15418i	0.970845	+	0.239710i	$0.0770523\pi$
$751$	1.19906e13	+	1.00613e13i	1.37550	+	1.15418i	0.404654	+	0.914470i	$0.367392\pi$
$752$	1.66415e12	−	6.05703e11i	0.189764	−	0.0690684i
$753$		0			0
$754$	−2.53472e12	−	1.43751e13i	−0.285600	−	1.61972i
$755$	−8.23971e12			−0.922892
$756$		0			0
$757$	−1.63526e13			−1.80990			−0.904951	−	0.425517i	$-0.860092\pi$
$757$	−1.63526e13			−1.80990			−0.904951	+	0.425517i	$0.860092\pi$
$758$	−2.64726e12	−	1.50134e13i	−0.291263	−	1.65184i
$759$		0			0
$760$	1.08214e12	−	3.93866e11i	0.117658	−	0.0428240i
$761$	4.02816e12	+	3.38003e12i	0.435388	+	0.365334i	0.833980	−	0.551794i	$-0.186057\pi$
$761$	4.02816e12	+	3.38003e12i	0.435388	+	0.365334i	−0.398592	+	0.917128i	$0.630501\pi$
$762$		0			0
$763$	−1.66904e12	−	6.07482e11i	−0.178282	−	0.0648893i
$764$	7.29678e11	+	1.26384e12i	0.0774838	+	0.134206i
$765$		0			0
$766$	−2.65145e12	+	4.59245e12i	−0.278262	+	0.481964i
$767$	7.82655e12	−	6.56725e12i	0.816566	−	0.685180i
$768$		0			0
$769$	1.68291e12	−	9.54424e12i	0.173537	−	0.984176i	−0.766282	−	0.642504i	$-0.777896\pi$
$769$	1.68291e12	−	9.54424e12i	0.173537	−	0.984176i	0.939819	−	0.341672i	$-0.110993\pi$
$770$	−8.41091e11	+	4.77006e12i	−0.0862253	+	0.489008i
$771$		0			0
$772$	−1.61336e13	+	1.35377e13i	−1.63476	+	1.37172i
$773$	2.53754e12	−	4.39516e12i	0.255627	−	0.442758i	−0.709439	−	0.704767i	$-0.751052\pi$
$773$	2.53754e12	−	4.39516e12i	0.255627	−	0.442758i	0.965066	+	0.262009i	$0.0843849\pi$
$774$		0			0
$775$	−1.48144e13	−	2.56593e13i	−1.47511	−	2.55497i
$776$	5.58477e12	+	2.03269e12i	0.552876	+	0.201230i
$777$		0			0
$778$	−7.20095e12	−	6.04231e12i	−0.704663	−	0.591282i
$779$	2.40097e11	−	8.73883e10i	0.0233598	−	0.00850227i
$780$		0			0
$781$	2.40230e11	+	1.36241e12i	0.0231045	+	0.131032i
$782$	5.36571e12			0.513093
$783$		0			0
$784$	2.47750e12			0.234203
$785$	1.82941e12	+	1.03751e13i	0.171948	+	0.975166i
$786$		0			0
$787$	−1.25621e12	+	4.57222e11i	−0.116728	+	0.0424855i	−0.399724	−	0.916636i	$-0.630894\pi$
$787$	−1.25621e12	+	4.57222e11i	−0.116728	+	0.0424855i	0.282996	+	0.959121i	$0.408672\pi$
$788$	1.32110e13	+	1.10854e13i	1.22059	+	1.02419i
$789$		0			0
$790$	2.70617e13	+	9.84964e12i	2.47191	+	0.899702i
$791$	2.04343e11	+	3.53933e11i	0.0185595	+	0.0321460i
$792$		0			0
$793$	7.97490e12	−	1.38129e13i	0.716136	−	1.24038i
$794$	1.40749e13	−	1.18103e13i	1.25676	−	1.05455i
$795$		0			0
$796$	−1.85572e12	+	1.05243e13i	−0.163834	+	0.929149i
$797$	2.97134e12	−	1.68513e13i	0.260850	−	1.47935i	−0.519748	−	0.854319i	$-0.673974\pi$
$797$	2.97134e12	−	1.68513e13i	0.260850	−	1.47935i	0.780598	−	0.625033i	$-0.214915\pi$
$798$		0			0
$799$	9.30618e12	−	7.80881e12i	0.807813	−	0.677836i
$800$	−1.19103e13	+	2.06292e13i	−1.02806	+	1.78065i
$801$		0			0
$802$	3.56601e12	+	6.17651e12i	0.304367	+	0.527179i
$803$	−1.16052e13	−	4.22394e12i	−0.984991	−	0.358508i
$804$		0			0
$805$	9.46166e11	+	7.93927e11i	0.0794119	+	0.0666345i
$806$	3.69215e13	−	1.34383e13i	3.08156	−	1.12160i
$807$		0			0
$808$	−1.31724e12	−	7.47046e12i	−0.108721	−	0.616590i
$809$	−4.01160e12			−0.329268			−0.164634	−	0.986355i	$-0.552644\pi$
$809$	−4.01160e12			−0.329268			−0.164634	+	0.986355i	$0.552644\pi$
$810$		0			0
$811$	−4.68406e12			−0.380215			−0.190107	−	0.981763i	$-0.560884\pi$
$811$	−4.68406e12			−0.380215			−0.190107	+	0.981763i	$0.560884\pi$
$812$	−6.94930e11	−	3.94114e12i	−0.0560969	−	0.318141i
$813$		0			0
$814$	−2.17825e13	+	7.92819e12i	−1.73900	+	0.632942i
$815$	−3.49942e12	−	2.93636e12i	−0.277835	−	0.233131i
$816$		0			0
$817$	−1.62563e12	−	5.91680e11i	−0.127650	−	0.0464609i
$818$	−1.33142e13	−	2.30610e13i	−1.03974	−	1.80089i
$819$		0			0
$820$	4.16567e12	−	7.21516e12i	0.321753	−	0.557293i
$821$	−9.75166e12	+	8.18261e12i	−0.749091	+	0.628562i	−0.935262	−	0.353956i	$-0.884836\pi$
$821$	−9.75166e12	+	8.18261e12i	−0.749091	+	0.628562i	0.186172	+	0.982517i	$0.440392\pi$
$822$		0			0
$823$	−2.14203e12	+	1.21481e13i	−0.162752	+	0.923013i	0.788600	+	0.614907i	$0.210806\pi$
$823$	−2.14203e12	+	1.21481e13i	−0.162752	+	0.923013i	−0.951352	+	0.308107i	$0.900305\pi$
$824$	−2.08738e12	+	1.18381e13i	−0.157735	+	0.894560i
$825$		0			0
$826$	3.57633e12	−	3.00090e12i	0.267318	−	0.224306i
$827$	−1.63634e12	+	2.83423e12i	−0.121646	+	0.210698i	−0.920417	−	0.390938i	$-0.872151\pi$
$827$	−1.63634e12	+	2.83423e12i	−0.121646	+	0.210698i	0.798771	+	0.601636i	$0.205484\pi$
$828$		0			0
$829$	1.59813e12	+	2.76804e12i	0.117521	+	0.203553i	0.918785	−	0.394759i	$-0.129172\pi$
$829$	1.59813e12	+	2.76804e12i	0.117521	+	0.203553i	−0.801264	+	0.598312i	$0.795838\pi$
$830$	5.47131e13	+	1.99140e13i	4.00166	+	1.45649i
$831$		0			0
$832$	−2.09704e13	−	1.75962e13i	−1.51723	−	1.27311i
$833$	1.59702e13	−	5.81267e12i	1.14923	−	0.418286i
$834$		0			0
$835$	2.92923e12	+	1.66125e13i	0.208528	+	1.18262i
$836$	−1.52750e12			−0.108157
$837$		0			0
$838$	3.54626e13			2.48412
$839$	4.01100e12	+	2.27475e13i	0.279463	+	1.58491i	0.724418	+	0.689360i	$0.242108\pi$
$839$	4.01100e12	+	2.27475e13i	0.279463	+	1.58491i	−0.444956	+	0.895553i	$0.646781\pi$
$840$		0			0
$841$	3.70294e12	−	1.34776e12i	0.255249	−	0.0929031i
$842$	7.01944e12	+	5.89001e12i	0.481280	+	0.403842i
$843$		0			0
$844$	3.79695e13	+	1.38198e13i	2.57569	+	0.937475i
$845$	−5.94931e12	−	1.03045e13i	−0.401431	−	0.695300i
$846$		0			0
$847$	−8.19318e11	+	1.41910e12i	−0.0546987	+	0.0947410i
$848$	4.65410e12	−	3.90525e12i	0.309068	−	0.259339i
$849$		0			0
$850$	−9.46242e12	+	5.36641e13i	−0.621752	+	3.52613i
$851$	−1.02644e12	+	5.82122e12i	−0.0670888	+	0.380480i
$852$		0			0
$853$	1.13053e12	−	9.48625e11i	0.0731156	−	0.0613513i	−0.605497	−	0.795847i	$-0.707026\pi$
$853$	1.13053e12	−	9.48625e11i	0.0731156	−	0.0613513i	0.678613	+	0.734496i	$0.262581\pi$
$854$	3.64412e12	−	6.31180e12i	0.234440	−	0.406063i
$855$		0			0
$856$	−6.28269e11	−	1.08819e12i	−0.0399957	−	0.0692746i
$857$	−1.24331e13	−	4.52528e12i	−0.787346	−	0.286570i	−0.0831136	−	0.996540i	$-0.526486\pi$
$857$	−1.24331e13	−	4.52528e12i	−0.787346	−	0.286570i	−0.704232	+	0.709970i	$0.748709\pi$
$858$		0			0
$859$	−8.22964e10	−	6.90549e10i	−0.00515717	−	0.00432738i	0.640205	−	0.768204i	$-0.278849\pi$
$859$	−8.22964e10	−	6.90549e10i	−0.00515717	−	0.00432738i	−0.645363	+	0.763876i	$0.723294\pi$
$860$	−5.30071e13	+	1.92930e13i	−3.30439	+	1.20270i
$861$		0			0
$862$	−4.28459e12	−	2.42991e13i	−0.264318	−	1.49902i
$863$	1.25905e13			0.772670			0.386335	−	0.922358i	$-0.373741\pi$
$863$	1.25905e13			0.772670			0.386335	+	0.922358i	$0.373741\pi$
$864$		0			0
$865$	−3.56244e13			−2.16359
$866$	8.99156e11	+	5.09937e12i	0.0543256	+	0.308096i
$867$		0			0
$868$	1.01226e13	−	3.68431e12i	0.605273	−	0.220301i
$869$	−9.75323e12	−	8.18393e12i	−0.580175	−	0.486825i
$870$		0			0
$871$	5.12231e12	+	1.86437e12i	0.301567	+	0.109761i
$872$	−5.07308e12	−	8.78683e12i	−0.297131	−	0.514645i
$873$		0			0
$874$	−3.24600e11	+	5.62224e11i	−0.0188169	+	0.0325918i
$875$	−4.06658e12	+	3.41227e12i	−0.234527	+	0.196792i
$876$		0			0
$877$	−5.15279e12	+	2.92229e13i	−0.294133	+	1.66811i	0.376571	+	0.926388i	$0.377103\pi$
$877$	−5.15279e12	+	2.92229e13i	−0.294133	+	1.66811i	−0.670705	+	0.741725i	$0.734008\pi$
$878$	2.23613e12	−	1.26817e13i	0.126991	−	0.720199i
$879$		0			0
$880$	4.24205e12	−	3.55950e12i	0.238453	−	0.200086i
$881$	−1.25156e12	+	2.16776e12i	−0.0699936	+	0.121233i	−0.898898	−	0.438157i	$-0.855631\pi$
$881$	−1.25156e12	+	2.16776e12i	−0.0699936	+	0.121233i	0.828905	+	0.559390i	$0.188965\pi$
$882$		0			0
$883$	9.03816e12	+	1.56546e13i	0.500330	+	0.866598i	1.00000		0.000381660i	$0.000121486\pi$
$883$	9.03816e12	+	1.56546e13i	0.500330	+	0.866598i	−0.499669	+	0.866216i	$0.666545\pi$
$884$	−4.07419e13	−	1.48288e13i	−2.24391	−	0.816717i
$885$		0			0
$886$	−2.24526e13	−	1.88400e13i	−1.22410	−	1.02714i
$887$	−3.61702e11	+	1.31649e11i	−0.0196198	+	0.00714103i	−0.351811	−	0.936071i	$-0.614434\pi$
$887$	−3.61702e11	+	1.31649e11i	−0.0196198	+	0.00714103i	0.332192	+	0.943212i	$0.392212\pi$
$888$		0			0
$889$	−9.64061e11	−	5.46746e12i	−0.0517662	−	0.293581i
$890$	−5.11579e13			−2.73311
$891$		0			0
$892$	4.36614e11			0.0230917
$893$	2.55235e11	+	1.44751e12i	0.0134310	+	0.0761710i
$894$		0			0
$895$	3.36613e13	−	1.22517e13i	1.75359	−	0.638253i
$896$	−5.15931e12	−	4.32918e12i	−0.267427	−	0.224398i
$897$		0			0
$898$	−3.70467e13	−	1.34839e13i	−1.90110	−	0.691945i
$899$	−1.42212e13	−	2.46319e13i	−0.726137	−	1.25771i
$900$		0			0
$901$	2.08383e13	−	3.60929e13i	1.05342	−	1.82457i
$902$	−4.70274e12	+	3.94607e12i	−0.236549	+	0.198488i
$903$		0			0
$904$	−4.05396e11	+	2.29912e12i	−0.0201893	+	0.114499i
$905$	−6.15757e12	+	3.49213e13i	−0.305134	+	1.73050i
$906$		0			0
$907$	8.24405e12	−	6.91758e12i	0.404490	−	0.339407i	−0.417736	−	0.908568i	$-0.637176\pi$
$907$	8.24405e12	−	6.91758e12i	0.404490	−	0.339407i	0.822226	+	0.569161i	$0.192732\pi$
$908$	−1.56551e13	+	2.71154e13i	−0.764310	+	1.32382i
$909$		0			0
$910$	−8.31703e12	−	1.44055e13i	−0.402052	−	0.696374i
$911$	9.04663e12	+	3.29270e12i	0.435165	+	0.158387i	0.550308	−	0.834962i	$-0.314510\pi$
$911$	9.04663e12	+	3.29270e12i	0.435165	+	0.158387i	−0.115143	+	0.993349i	$0.536733\pi$
$912$		0			0
$913$	−1.97190e13	−	1.65462e13i	−0.939219	−	0.788098i
$914$	−6.96045e12	+	2.53340e12i	−0.329898	+	0.120073i
$915$		0			0
$916$	4.20402e12	+	2.38422e13i	0.197304	+	1.11896i
$917$	−1.52545e12			−0.0712419
$918$		0			0
$919$	−1.65093e13			−0.763499			−0.381750	−	0.924266i	$-0.624678\pi$
$919$	−1.65093e13			−0.763499			−0.381750	+	0.924266i	$0.624678\pi$
$920$	1.22519e12	+	6.94839e12i	0.0563842	+	0.319771i
$921$		0			0
$922$	−5.21132e12	+	1.89677e12i	−0.237497	+	0.0864420i
$923$	−3.63945e12	−	3.05386e12i	−0.165055	−	0.138497i
$924$		0			0
$925$	−5.64097e13	−	2.05315e13i	−2.53347	−	0.922108i
$926$	3.15685e13	+	5.46782e13i	1.41093	+	2.44379i
$927$		0			0
$928$	−1.14334e13	+	1.98032e13i	−0.506069	+	0.876537i
$929$	−3.98546e12	+	3.34420e12i	−0.175553	+	0.147306i	−0.726330	−	0.687346i	$-0.758776\pi$
$929$	−3.98546e12	+	3.34420e12i	−0.175553	+	0.147306i	0.550778	+	0.834652i	$0.314331\pi$
$930$		0			0
$931$	−3.57064e11	+	2.02501e12i	−0.0155766	+	0.0883393i
$932$	8.89835e12	−	5.04650e13i	0.386312	−	2.19088i
$933$		0			0
$934$	−4.78686e13	+	4.01665e13i	−2.05821	+	1.72704i
$935$	1.89933e13	−	3.28974e13i	0.812735	−	1.40770i
$936$		0			0
$937$	−1.08049e13	−	1.87146e13i	−0.457923	−	0.793146i	0.540928	−	0.841069i	$-0.318073\pi$
$937$	−1.08049e13	−	1.87146e13i	−0.457923	−	0.793146i	−0.998851	+	0.0479228i	$0.984740\pi$
$938$	2.34063e12	+	8.51921e11i	0.0987236	+	0.0359324i
$939$		0			0
$940$	3.67145e13	+	3.08071e13i	1.53378	+	1.28699i
$941$	−9.95662e12	+	3.62391e12i	−0.413960	+	0.150669i	−0.540600	−	0.841280i	$-0.681803\pi$
$941$	−9.95662e12	+	3.62391e12i	−0.413960	+	0.150669i	0.126640	+	0.991949i	$0.459581\pi$
$942$		0			0
$943$	2.71837e11	+	1.54166e12i	0.0111945	+	0.0634873i
$944$	−5.33744e12			−0.218756
$945$		0			0
$946$	4.15653e13			1.68741
$947$	−6.24492e12	−	3.54167e13i	−0.252320	−	1.43098i	−0.802859	−	0.596169i	$-0.796689\pi$
$947$	−6.24492e12	−	3.54167e13i	−0.252320	−	1.43098i	0.550539	−	0.834809i	$-0.314422\pi$
$948$		0			0
$949$	3.98545e13	−	1.45059e13i	1.59507	−	0.580558i
$950$	−5.05054e12	−	4.23791e12i	−0.201179	−	0.168809i
$951$		0			0
$952$	−6.20511e12	−	2.25847e12i	−0.244840	−	0.0891146i
$953$	1.75493e13	+	3.03963e13i	0.689195	+	1.19372i	0.972099	+	0.234572i	$0.0753688\pi$
$953$	1.75493e13	+	3.03963e13i	0.689195	+	1.19372i	−0.282904	+	0.959148i	$0.591298\pi$
$954$		0			0
$955$	2.19549e12	−	3.80271e12i	0.0854117	−	0.147937i
$956$	−2.77829e12	+	2.33126e12i	−0.107577	+	0.0902674i
$957$		0			0
$958$	8.76275e12	−	4.96960e13i	0.336121	−	1.90624i
$959$	−1.11209e12	+	6.30699e12i	−0.0424578	+	0.240790i
$960$		0			0
$961$	3.83943e13	−	3.22166e13i	1.45215	−	1.21850i
$962$	3.98032e13	−	6.89411e13i	1.49841	−	2.59532i
$963$		0			0
$964$	6.26691e12	+	1.08546e13i	0.233726	+	0.404825i
$965$	5.95476e13	+	2.16736e13i	2.21050	+	0.804558i
$966$		0			0
$967$	−1.80056e13	−	1.51085e13i	−0.662200	−	0.555652i	0.248545	−	0.968620i	$-0.420047\pi$
$967$	−1.80056e13	−	1.51085e13i	−0.662200	−	0.555652i	−0.910745	+	0.412969i	$0.864492\pi$
$968$	−8.79606e12	+	3.20150e12i	−0.321995	+	0.117197i
$969$		0			0
$970$	−9.31646e12	−	5.28363e13i	−0.337892	−	1.91628i
$971$	2.59501e13			0.936811			0.468405	−	0.883514i	$-0.344829\pi$
$971$	2.59501e13			0.936811			0.468405	+	0.883514i	$0.344829\pi$
$972$		0			0
$973$	5.70440e12			0.204034
$974$	−8.62729e12	−	4.89278e13i	−0.307156	−	1.74197i
$975$		0			0
$976$	−7.82992e12	+	2.84986e12i	−0.276206	+	0.100531i
$977$	−1.35675e13	−	1.13845e13i	−0.476404	−	0.399750i	0.372720	−	0.927944i	$-0.378425\pi$
$977$	−1.35675e13	−	1.13845e13i	−0.476404	−	0.399750i	−0.849124	+	0.528194i	$0.822870\pi$
$978$		0			0
$979$	2.12532e13	+	7.73553e12i	0.739438	+	0.269133i
$980$	3.35243e13	+	5.80657e13i	1.16103	+	2.01096i
$981$		0			0
$982$	−1.56552e13	+	2.71157e13i	−0.537227	+	0.930505i
$983$	1.29947e13	−	1.09038e13i	0.443889	−	0.372467i	−0.393273	−	0.919422i	$-0.628657\pi$
$983$	1.29947e13	−	1.09038e13i	0.443889	−	0.372467i	0.837162	+	0.546954i	$0.184213\pi$
$984$		0			0
$985$	9.01060e12	−	5.11017e13i	0.304994	−	1.72971i
$986$	−9.08356e12	+	5.15154e13i	−0.306062	+	1.73577i
$987$		0			0
$988$	4.01848e12	−	3.37190e12i	0.134170	−	0.112582i
$989$	5.29957e12	−	9.17913e12i	0.176140	−	0.305083i
$990$		0			0
$991$	2.76904e13	+	4.79612e13i	0.912007	+	1.57964i	0.811225	+	0.584733i	$0.198801\pi$
$991$	2.76904e13	+	4.79612e13i	0.912007	+	1.57964i	0.100781	+	0.994909i	$0.467866\pi$
$992$	−5.78396e13	−	2.10519e13i	−1.89637	−	0.690221i
$993$		0			0
$994$	−1.66304e12	−	1.39546e12i	−0.0540337	−	0.0453397i
$995$	3.02155e13	−	1.09975e13i	0.977295	−	0.355706i
$996$		0			0
$997$	7.98790e12	+	4.53016e13i	0.256038	+	1.45206i	0.793394	+	0.608708i	$0.208312\pi$
$997$	7.98790e12	+	4.53016e13i	0.256038	+	1.45206i	−0.537357	+	0.843355i	$0.680577\pi$
$998$	−6.13343e11			−0.0195711
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.5		156
3.2	odd	2		27.10.e.a.13.22	✓	156
27.2	odd	18		27.10.e.a.25.22	yes	156
27.25	even	9	inner	81.10.e.a.73.5		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.22	✓	156	3.2	odd	2
27.10.e.a.25.22	yes	156	27.2	odd	18
81.10.e.a.10.5		156	1.1	even	1	trivial
81.10.e.a.73.5		156	27.25	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.21254 - 35.2331i) q^{2} +(-721.652 + 262.660i) q^{4} +(1770.10 + 1485.29i) q^{5} +(1506.43 + 548.294i) q^{7} +(4578.80 + 7930.71i) q^{8} +(41334.5 - 71593.4i) q^{10} +(-27997.7 + 23492.8i) q^{11} +(21795.3 - 123608. i) q^{13} +(9959.36 - 56482.3i) q^{14} +(-50230.1 + 42148.1i) q^{16} +(-224900. + 389539. i) q^{17} +(-27210.8 - 47130.6i) q^{19} +(-1.66752e6 - 606928. i) q^{20} +(1.00166e6 + 840494. i) q^{22} +(313324. - 114041. i) q^{23} +(588008. + 3.33476e6i) q^{25} -4.49048e6 q^{26} -1.23113e6 q^{28} +(564465. + 3.20124e6i) q^{29} +(-8.22217e6 + 2.99262e6i) q^{31} +(5.38881e6 + 4.52175e6i) q^{32} +(1.51218e7 + 5.50390e6i) q^{34} +(1.85215e6 + 3.20801e6i) q^{35} +(-8.86390e6 + 1.53527e7i) q^{37} +(-1.49151e6 + 1.25152e6i) q^{38} +(-3.67447e6 + 2.08390e7i) q^{40} +(-815267. + 4.62361e6i) q^{41} +(2.43510e7 - 2.04329e7i) q^{43} +(1.40340e7 - 2.43075e7i) q^{44} +(-5.96454e6 - 1.03309e7i) q^{46} +(-2.53795e7 - 9.23739e6i) q^{47} +(-2.89440e7 - 2.42869e7i) q^{49} +(1.13841e8 - 4.14347e7i) q^{50} +(1.67381e7 + 9.49264e7i) q^{52} -9.26556e7 q^{53} -8.44523e7 q^{55} +(2.54926e6 + 1.44576e7i) q^{56} +(1.09283e8 - 3.97757e7i) q^{58} +(6.23558e7 + 5.23227e7i) q^{59} +(1.19412e8 + 4.34624e7i) q^{61} +(1.56520e8 + 2.71100e8i) q^{62} +(1.09051e8 - 1.88882e8i) q^{64} +(2.22173e8 - 1.86425e8i) q^{65} +(-7.54148e6 + 4.27699e7i) q^{67} +(5.99835e7 - 3.40184e8i) q^{68} +(1.01522e8 - 8.51868e7i) q^{70} +(1.89260e7 - 3.27808e7i) q^{71} +(1.68954e8 + 2.92637e8i) q^{73} +(5.95992e8 + 2.16923e8i) q^{74} +(3.20161e7 + 2.68647e7i) q^{76} +(-5.50574e7 + 2.00393e7i) q^{77} +(6.04918e7 + 3.43066e8i) q^{79} -1.51514e8 q^{80} +1.67969e8 q^{82} +(1.22302e8 + 6.93609e8i) q^{83} +(-9.76672e8 + 3.55480e8i) q^{85} +(-8.71197e8 - 7.31021e8i) q^{86} +(-3.14511e8 - 1.14473e8i) q^{88} +(-3.09414e8 - 5.35921e8i) q^{89} +(1.00606e8 - 1.74255e8i) q^{91} +(-1.96157e8 + 1.64595e8i) q^{92} +(-1.67790e8 + 9.51587e8i) q^{94} +(2.18366e7 - 1.23842e8i) q^{95} +(4.97155e8 - 4.17163e8i) q^{97} +(-6.75886e8 + 1.17067e9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more