LMFDB - Embedded newform 42.12.f.a.5.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,12,Mod(5,42)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("42.5"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.2704135835$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-27.7128 - 16.0000i) q^{2} +(-296.285 - 298.935i) q^{3} +(512.000 + 886.810i) q^{4} +(-3221.21 + 5579.29i) q^{5} +(3427.95 + 13024.9i) q^{6} +(25344.2 + 36537.6i) q^{7} -32768.0i q^{8} +(-1576.82 + 177140. i) q^{9} +(178537. - 103079. i) q^{10} +(104738. - 60470.5i) q^{11} +(113400. - 415803. i) q^{12} -50908.1i q^{13} +(-117756. - 1.41807e6i) q^{14} +(2.62224e6 - 690133. i) q^{15} +(-524288. + 908093. i) q^{16} +(-4.53557e6 - 7.85584e6i) q^{17} +(2.87794e6 - 4.88382e6i) q^{18} +(8.06088e6 + 4.65395e6i) q^{19} -6.59703e6 q^{20} +(3.41326e6 - 1.84018e7i) q^{21} -3.87011e6 q^{22} +(2.27133e7 + 1.31135e7i) q^{23} +(-9.79549e6 + 9.70868e6i) q^{24} +(3.66173e6 + 6.34231e6i) q^{25} +(-814529. + 1.41081e6i) q^{26} +(5.34205e7 - 5.20126e7i) q^{27} +(-1.94257e7 + 4.11827e7i) q^{28} +6.87194e6i q^{29} +(-8.37118e7 - 2.28303e7i) q^{30} +(-2.29050e8 + 1.32242e8i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(-4.91090e7 - 1.33933e7i) q^{33} +2.90277e8i q^{34} +(-2.85493e8 + 2.37072e7i) q^{35} +(-1.57897e8 + 8.92973e7i) q^{36} +(1.04519e8 - 1.81032e8i) q^{37} +(-1.48927e8 - 2.57948e8i) q^{38} +(-1.52182e7 + 1.50833e7i) q^{39} +(1.82822e8 + 1.05552e8i) q^{40} +1.44633e8 q^{41} +(-3.89020e8 + 4.55354e8i) q^{42} -1.24766e9 q^{43} +(1.07252e8 + 6.19217e7i) q^{44} +(-9.83236e8 - 5.79402e8i) q^{45} +(-4.19632e8 - 7.26824e8i) q^{46} +(7.02288e7 - 1.21640e8i) q^{47} +(4.26800e8 - 1.12327e8i) q^{48} +(-6.92673e8 + 1.85203e9i) q^{49} -2.34351e8i q^{50} +(-1.00456e9 + 3.68341e9i) q^{51} +(4.51458e7 - 2.60649e7i) q^{52} +(-4.50048e9 + 2.59835e9i) q^{53} +(-2.31263e9 + 5.86689e8i) q^{54} +7.79151e8i q^{55} +(1.19727e9 - 8.30478e8i) q^{56} +(-9.97095e8 - 3.78858e9i) q^{57} +(1.09951e8 - 1.90441e8i) q^{58} +(-2.19074e9 - 3.79447e9i) q^{59} +(1.95460e9 + 1.97208e9i) q^{60} +(-2.62835e9 - 1.51748e9i) q^{61} +8.46349e9 q^{62} +(-6.51224e9 + 4.43185e9i) q^{63} -1.07374e9 q^{64} +(2.84031e8 + 1.63985e8i) q^{65} +(1.14666e9 + 1.15691e9i) q^{66} +(4.30716e9 + 7.46022e9i) q^{67} +(4.64443e9 - 8.04439e9i) q^{68} +(-2.80953e9 - 1.06751e10i) q^{69} +(8.29113e9 + 3.91089e9i) q^{70} -1.02508e10i q^{71} +(5.80452e9 + 5.16692e7i) q^{72} +(2.57319e10 - 1.48563e10i) q^{73} +(-5.79304e9 + 3.34461e9i) q^{74} +(8.11017e8 - 2.97375e9i) q^{75} +9.53130e9i q^{76} +(4.86394e9 + 2.29430e9i) q^{77} +(6.63072e8 - 1.74510e8i) q^{78} +(1.06233e10 - 1.84001e10i) q^{79} +(-3.37768e9 - 5.85031e9i) q^{80} +(-3.13761e10 - 5.58636e8i) q^{81} +(-4.00818e9 - 2.31412e9i) q^{82} -3.90065e10 q^{83} +(1.80665e10 - 6.39482e9i) q^{84} +5.84401e10 q^{85} +(3.45761e10 + 1.99625e10i) q^{86} +(2.05426e9 - 2.03606e9i) q^{87} +(-1.98150e9 - 3.43205e9i) q^{88} +(-4.37364e10 + 7.57537e10i) q^{89} +(1.79778e10 + 3.17886e10i) q^{90} +(1.86006e9 - 1.29022e9i) q^{91} +2.68565e10i q^{92} +(1.07396e11 + 2.92896e10i) q^{93} +(-3.89247e9 + 2.24732e9i) q^{94} +(-5.19315e10 + 2.99827e10i) q^{95} +(-1.36250e10 - 3.71589e9i) q^{96} -9.26196e10i q^{97} +(4.88284e10 - 4.02423e10i) q^{98} +(1.05466e10 + 1.86486e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) $ 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−27.7128	−	16.0000i	−0.612372	−	0.353553i
$2$	−27.7128	−	16.0000i	−0.612372	−	0.353553i
$3$	−296.285	−	298.935i	−0.703953	−	0.710247i
$3$	−296.285	−	298.935i	−0.703953	−	0.710247i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	−3221.21	+	5579.29i	−0.460981	+	0.798443i	−0.999010	−	0.0444833i	$-0.985836\pi$
$5$	−3221.21	+	5579.29i	−0.460981	+	0.798443i	0.538029	+	0.842926i	$0.319169\pi$
$6$	3427.95	+	13024.9i	0.179971	+	0.683820i
$7$	25344.2	+	36537.6i	0.569953	+	0.821677i
$7$	25344.2	+	36537.6i	0.569953	+	0.821677i
$8$		−	32768.0i		−	0.353553i
$9$	−1576.82	+	177140.i	−0.00890119	+	0.999960i
$10$	178537.	−	103079.i	0.564585	−	0.325963i
$11$	104738.	−	60470.5i	0.196085	−	0.113210i	−0.398743	−	0.917063i	$-0.630553\pi$
$11$	104738.	−	60470.5i	0.196085	−	0.113210i	0.594828	+	0.803853i	$0.297220\pi$
$12$	113400.	−	415803.i	0.131558	−	0.482382i
$13$		−	50908.1i		−	0.0380275i	−0.999819	−	0.0190138i	$-0.993947\pi$
$13$		−	50908.1i		−	0.0380275i	0.999819	−	0.0190138i	$-0.00605264\pi$
$14$	−117756.	−	1.41807e6i	−0.0585165	−	0.704681i
$15$	2.62224e6	−	690133.i	0.891601	−	0.234656i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−4.53557e6	−	7.85584e6i	−0.774753	−	1.34191i	−0.934933	−	0.354824i	$-0.884541\pi$
$17$	−4.53557e6	−	7.85584e6i	−0.774753	−	1.34191i	0.160180	−	0.987088i	$-0.448792\pi$
$18$	2.87794e6	−	4.88382e6i	0.358990	−	0.609201i
$19$	8.06088e6	+	4.65395e6i	0.746858	+	0.431198i	0.824557	−	0.565778i	$-0.191424\pi$
$19$	8.06088e6	+	4.65395e6i	0.746858	+	0.431198i	−0.0776997	+	0.996977i	$0.524758\pi$
$20$	−6.59703e6			−0.460981
$21$	3.41326e6	−	1.84018e7i	0.182374	−	0.983229i
$22$	−3.87011e6			−0.160103
$23$	2.27133e7	+	1.31135e7i	0.735828	+	0.424831i	0.820551	−	0.571574i	$-0.193667\pi$
$23$	2.27133e7	+	1.31135e7i	0.735828	+	0.424831i	−0.0847223	+	0.996405i	$0.527000\pi$
$24$	−9.79549e6	+	9.70868e6i	−0.251110	+	0.248885i
$25$	3.66173e6	+	6.34231e6i	0.0749923	+	0.129890i
$26$	−814529.	+	1.41081e6i	−0.0134448	+	0.0232870i
$27$	5.34205e7	−	5.20126e7i	0.716485	−	0.697603i
$28$	−1.94257e7	+	4.11827e7i	−0.213309	+	0.452216i
$29$			6.87194e6i			0.0622143i	0.999516	+	0.0311071i	$0.00990331\pi$
$29$			6.87194e6i			0.0622143i	−0.999516	+	0.0311071i	$0.990097\pi$
$30$	−8.37118e7	−	2.28303e7i	−0.628955	−	0.171532i
$31$	−2.29050e8	+	1.32242e8i	−1.43695	+	0.829622i	−0.997636	−	0.0687127i	$-0.978111\pi$
$31$	−2.29050e8	+	1.32242e8i	−1.43695	+	0.829622i	−0.439311	+	0.898335i	$0.644777\pi$
$32$	2.90590e7	−	1.67772e7i	0.153093	−	0.0883883i
$33$	−4.91090e7	−	1.33933e7i	−0.218441	−	0.0595744i
$34$			2.90277e8i			1.09567i
$35$	−2.85493e8	+	2.37072e7i	−0.918800	+	0.0762968i
$36$	−1.57897e8	+	8.92973e7i	−0.435221	+	0.246136i
$37$	1.04519e8	−	1.81032e8i	0.247791	−	0.429187i	−0.715121	−	0.699000i	$-0.753629\pi$
$37$	1.04519e8	−	1.81032e8i	0.247791	−	0.429187i	0.962913	+	0.269813i	$0.0869619\pi$
$38$	−1.48927e8	−	2.57948e8i	−0.304903	−	0.528108i
$39$	−1.52182e7	+	1.50833e7i	−0.0270089	+	0.0267696i
$40$	1.82822e8	+	1.05552e8i	0.282292	+	0.162982i
$41$	1.44633e8			0.194965			0.0974823	−	0.995237i	$-0.468921\pi$
$41$	1.44633e8			0.194965			0.0974823	+	0.995237i	$0.468921\pi$
$42$	−3.89020e8	+	4.55354e8i	−0.459305	+	0.537623i
$43$	−1.24766e9			−1.29425			−0.647126	−	0.762383i	$-0.724029\pi$
$43$	−1.24766e9			−1.29425			−0.647126	+	0.762383i	$0.724029\pi$
$44$	1.07252e8	+	6.19217e7i	0.0980424	+	0.0566048i
$45$	−9.83236e8	−	5.79402e8i	−0.794308	−	0.468070i
$46$	−4.19632e8	−	7.26824e8i	−0.300401	−	0.520309i
$47$	7.02288e7	−	1.21640e8i	0.0446660	−	0.0773637i	−0.842828	−	0.538183i	$-0.819111\pi$
$47$	7.02288e7	−	1.21640e8i	0.0446660	−	0.0773637i	0.887494	+	0.460819i	$0.152444\pi$
$48$	4.26800e8	−	1.12327e8i	0.241767	−	0.0636294i
$49$	−6.92673e8	+	1.85203e9i	−0.350308	+	0.936635i
$50$		−	2.34351e8i		−	0.106055i
$51$	−1.00456e9	+	3.68341e9i	−0.407699	+	1.49491i
$52$	4.51458e7	−	2.60649e7i	0.0164664	−	0.00950689i
$53$	−4.50048e9	+	2.59835e9i	−1.47823	+	0.853455i	−0.999697	−	0.0246152i	$-0.992164\pi$
$53$	−4.50048e9	+	2.59835e9i	−1.47823	+	0.853455i	−0.478531	+	0.878071i	$0.658831\pi$
$54$	−2.31263e9	+	5.86689e8i	−0.685395	+	0.173877i
$55$			7.79151e8i			0.208750i
$56$	1.19727e9	−	8.30478e8i	0.290507	−	0.201509i
$57$	−9.97095e8	−	3.78858e9i	−0.219495	−	0.833997i
$58$	1.09951e8	−	1.90441e8i	0.0219961	−	0.0380983i
$59$	−2.19074e9	−	3.79447e9i	−0.398937	−	0.690978i	0.594658	−	0.803978i	$-0.297287\pi$
$59$	−2.19074e9	−	3.79447e9i	−0.398937	−	0.690978i	−0.993595	+	0.113000i	$0.963954\pi$
$60$	1.95460e9	+	1.97208e9i	0.324509	+	0.327411i
$61$	−2.62835e9	−	1.51748e9i	−0.398446	−	0.230043i	0.287367	−	0.957821i	$-0.407220\pi$
$61$	−2.62835e9	−	1.51748e9i	−0.398446	−	0.230043i	−0.685813	+	0.727777i	$0.740553\pi$
$62$	8.46349e9			1.17326
$63$	−6.51224e9	+	4.43185e9i	−0.826718	+	0.562616i
$64$	−1.07374e9			−0.125000
$65$	2.84031e8	+	1.63985e8i	0.0303628	+	0.0175300i
$66$	1.14666e9	+	1.15691e9i	0.112705	+	0.113712i
$67$	4.30716e9	+	7.46022e9i	0.389744	+	0.675056i	0.992415	−	0.122933i	$-0.0392302\pi$
$67$	4.30716e9	+	7.46022e9i	0.389744	+	0.675056i	−0.602671	+	0.797990i	$0.705897\pi$
$68$	4.64443e9	−	8.04439e9i	0.387376	−	0.670956i
$69$	−2.80953e9	−	1.06751e10i	−0.216254	−	0.821680i
$70$	8.29113e9	+	3.91089e9i	0.589623	+	0.278123i
$71$		−	1.02508e10i		−	0.674274i	−0.941456	−	0.337137i	$-0.890541\pi$
$71$		−	1.02508e10i		−	0.674274i	0.941456	−	0.337137i	$-0.109459\pi$
$72$	5.80452e9	+	5.16692e7i	0.353539	+	0.00314705i
$73$	2.57319e10	−	1.48563e10i	1.45276	−	0.838754i	0.454127	−	0.890937i	$-0.349951\pi$
$73$	2.57319e10	−	1.48563e10i	1.45276	−	0.838754i	0.998638	+	0.0521826i	$0.0166178\pi$
$74$	−5.79304e9	+	3.34461e9i	−0.303481	+	0.175215i
$75$	8.11017e8	−	2.97375e9i	0.0394633	−	0.144700i
$76$			9.53130e9i			0.431198i
$77$	4.86394e9	+	2.29430e9i	0.204781	+	0.0965944i
$78$	6.63072e8	−	1.74510e8i	0.0260040	−	0.00684386i
$79$	1.06233e10	−	1.84001e10i	0.388427	−	0.672776i	−0.603811	−	0.797128i	$-0.706352\pi$
$79$	1.06233e10	−	1.84001e10i	0.388427	−	0.672776i	0.992238	+	0.124352i	$0.0396852\pi$
$80$	−3.37768e9	−	5.85031e9i	−0.115245	−	0.199611i
$81$	−3.13761e10	−	5.58636e8i	−0.999842	−	0.0178017i
$82$	−4.00818e9	−	2.31412e9i	−0.119391	−	0.0689304i
$83$	−3.90065e10			−1.08695			−0.543473	−	0.839427i	$-0.682891\pi$
$83$	−3.90065e10			−1.08695			−0.543473	+	0.839427i	$0.682891\pi$
$84$	1.80665e10	−	6.39482e9i	0.471344	−	0.166837i
$85$	5.84401e10			1.42859
$86$	3.45761e10	+	1.99625e10i	0.792564	+	0.457587i
$87$	2.05426e9	−	2.03606e9i	0.0441875	−	0.0437959i
$88$	−1.98150e9	−	3.43205e9i	−0.0400257	−	0.0693265i
$89$	−4.37364e10	+	7.57537e10i	−0.830229	+	1.43800i	0.0676269	+	0.997711i	$0.478457\pi$
$89$	−4.37364e10	+	7.57537e10i	−0.830229	+	1.43800i	−0.897856	+	0.440289i	$0.854876\pi$
$90$	1.79778e10	+	3.17886e10i	0.320925	+	0.567464i
$91$	1.86006e9	−	1.29022e9i	0.0312464	−	0.0216739i
$92$			2.68565e10i			0.424831i
$93$	1.07396e11	+	2.92896e10i	1.60078	+	0.436573i
$94$	−3.89247e9	+	2.24732e9i	−0.0547044	+	0.0315836i
$95$	−5.19315e10	+	2.99827e10i	−0.688575	+	0.397549i
$96$	−1.36250e10	−	3.71589e9i	−0.170548	−	0.0465127i
$97$		−	9.26196e10i		−	1.09511i	−0.836769	−	0.547556i	$-0.815558\pi$
$97$		−	9.26196e10i		−	1.09511i	0.836769	−	0.547556i	$-0.184442\pi$
$98$	4.88284e10	−	4.02423e10i	0.545669	−	0.449717i
$99$	1.05466e10	+	1.86486e10i	0.111460	+	0.197085i
$100$	−3.74962e9	+	6.49452e9i	−0.0374962	+	0.0649452i
$101$	−6.35841e10	−	1.10131e11i	−0.601978	−	1.04266i	−0.992521	−	0.122072i	$-0.961046\pi$
$101$	−6.35841e10	−	1.10131e11i	−0.601978	−	1.04266i	0.390543	−	0.920585i	$-0.372287\pi$
$102$	8.67738e10	−	8.60048e10i	0.778193	−	0.771297i
$103$	−9.96928e10	−	5.75577e10i	−0.847343	−	0.489214i	0.0124105	−	0.999923i	$-0.496050\pi$
$103$	−9.96928e10	−	5.75577e10i	−0.847343	−	0.489214i	−0.859753	+	0.510709i	$0.829383\pi$
$104$	−1.66816e9			−0.0134448
$105$	9.16743e10	+	7.83196e10i	0.700982	+	0.598866i
$106$	1.66295e11			1.20697
$107$	−1.62755e11	−	9.39667e10i	−1.12182	−	0.647684i	−0.179956	−	0.983675i	$-0.557596\pi$
$107$	−1.62755e11	−	9.39667e10i	−1.12182	−	0.647684i	−0.941865	+	0.335991i	$0.890929\pi$
$108$	7.34766e10	+	2.07433e10i	0.481192	+	0.135846i
$109$	3.16943e10	+	5.48961e10i	0.197303	+	0.341740i	0.947653	−	0.319301i	$-0.103448\pi$
$109$	3.16943e10	+	5.48961e10i	0.197303	+	0.341740i	−0.750350	+	0.661041i	$0.770115\pi$
$110$	1.24664e10	−	2.15925e10i	0.0738043	−	0.127833i
$111$	−8.50844e10	+	2.23929e10i	−0.479262	+	0.126135i
$112$	−4.64672e10	+	3.85862e9i	−0.249142	+	0.0206887i
$113$		−	1.53892e11i		−	0.785752i	−0.919591	−	0.392876i	$-0.871480\pi$
$113$		−	1.53892e11i		−	0.785752i	0.919591	−	0.392876i	$-0.128520\pi$
$114$	−3.29849e10	+	1.20946e11i	−0.160450	+	0.588320i
$115$	−1.46328e11	+	8.44826e10i	−0.678406	+	0.391678i
$116$	−6.09410e9	+	3.51843e9i	−0.0269396	+	0.0155536i
$117$	9.01786e9	+	8.02729e7i	0.0380260	+	0.000338491i
$118$			1.40207e11i			0.564182i
$119$	1.72084e11	−	3.64819e11i	0.661046	−	1.40142i
$120$	−2.26143e10	−	8.59256e10i	−0.0829633	−	0.315229i
$121$	−1.35342e11	+	2.34420e11i	−0.474367	+	0.821628i
$122$	4.85594e10	+	8.41073e10i	0.162665	+	0.281744i
$123$	−4.28526e10	−	4.32357e10i	−0.137246	−	0.138473i
$124$	−2.34547e11	−	1.35416e11i	−0.718474	−	0.414811i
$125$	−3.61752e11			−1.06024
$126$	2.51382e11	−	1.86232e10i	0.705174	−	0.0522416i
$127$	−5.94681e11			−1.59722			−0.798608	−	0.601851i	$-0.794430\pi$
$127$	−5.94681e11			−1.59722			−0.798608	+	0.601851i	$0.794430\pi$
$128$	2.97564e10	+	1.71799e10i	0.0765466	+	0.0441942i
$129$	3.69663e11	+	3.72968e11i	0.911092	+	0.919238i
$130$	−5.24753e9	−	9.08899e9i	−0.0123956	−	0.0214698i
$131$	−2.19837e11	+	3.80768e11i	−0.497861	+	0.862321i	−0.999997	−	0.00246806i	$-0.999214\pi$
$131$	−2.19837e11	+	3.80768e11i	−0.497861	+	0.862321i	0.502136	+	0.864789i	$0.332548\pi$
$132$	−1.32665e10	−	5.04077e10i	−0.0288138	−	0.109481i
$133$	3.42519e10	+	4.12476e11i	0.0713675	+	0.859439i
$134$		−	2.75658e11i		−	0.551181i
$135$	1.18115e11	+	4.65592e11i	0.226710	+	0.893654i
$136$	−2.57420e11	+	1.48622e11i	−0.474437	+	0.273917i
$137$	−6.10753e11	+	3.52618e11i	−1.08119	+	0.624226i	−0.931217	−	0.364464i	$-0.881252\pi$
$137$	−6.10753e11	+	3.52618e11i	−1.08119	+	0.624226i	−0.149974	+	0.988690i	$0.547919\pi$
$138$	−9.29420e10	+	3.40790e11i	−0.158080	+	0.579632i
$139$		−	5.03076e11i		−	0.822342i	−0.911558	−	0.411171i	$-0.865120\pi$
$139$		−	5.03076e11i		−	0.822342i	0.911558	−	0.411171i	$-0.134880\pi$
$140$	−1.67196e11	−	2.41040e11i	−0.262738	−	0.378778i
$141$	−5.71701e10	+	1.50463e10i	−0.0863901	+	0.0227365i
$142$	−1.64013e11	+	2.84078e11i	−0.238392	+	0.412907i
$143$	−3.07843e9	−	5.33201e9i	−0.00430509	−	0.00745663i
$144$	−1.60033e11	−	9.43043e10i	−0.215385	−	0.126922i
$145$	−3.83405e10	−	2.21359e10i	−0.0496746	−	0.0286796i
$146$	−9.50803e11			−1.18618
$147$	7.58866e11	−	3.41666e11i	0.911842	−	0.410541i
$148$	2.14055e11			0.247791
$149$	−3.38203e11	−	1.95261e11i	−0.377270	−	0.217817i	0.299360	−	0.954140i	$-0.403227\pi$
$149$	−3.38203e11	−	1.95261e11i	−0.377270	−	0.217817i	−0.676630	+	0.736323i	$0.736560\pi$
$150$	−7.00556e10	+	6.94348e10i	−0.0753253	+	0.0746578i
$151$	1.13993e11	+	1.97442e11i	0.118170	+	0.204676i	0.919042	−	0.394159i	$-0.128964\pi$
$151$	1.13993e11	+	1.97442e11i	0.118170	+	0.204676i	−0.800873	+	0.598835i	$0.795631\pi$
$152$	1.52501e11	−	2.64139e11i	0.152452	−	0.264054i
$153$	1.39874e12	−	7.91044e11i	1.34875	−	0.762778i
$154$	−9.80847e10	−	1.41405e11i	−0.0912509	−	0.131553i
$155$		−	1.70392e12i		−	1.52976i
$156$	−2.11678e10	−	5.77298e9i	−0.0183438	−	0.00500282i
$157$	2.21949e11	−	1.28142e11i	0.185697	−	0.107212i	−0.404270	−	0.914640i	$-0.632474\pi$
$157$	2.21949e11	−	1.28142e11i	0.185697	−	0.107212i	0.589967	+	0.807428i	$0.299141\pi$
$158$	−5.88802e11	+	3.39945e11i	−0.475724	+	0.274660i
$159$	2.11016e12	+	5.75495e11i	1.64677	+	0.449115i
$160$			2.16171e11i			0.162982i
$161$	9.65120e10	+	1.16224e12i	0.0703135	+	0.846747i
$162$	8.60581e11	+	5.17499e11i	0.605982	+	0.364399i
$163$	1.14815e12	−	1.98865e12i	0.781568	−	1.35371i	−0.149461	−	0.988768i	$-0.547754\pi$
$163$	1.14815e12	−	1.98865e12i	0.781568	−	1.35371i	0.931028	−	0.364947i	$-0.118913\pi$
$164$	7.40520e10	+	1.28262e11i	0.0487411	+	0.0844221i
$165$	2.32915e11	−	2.30851e11i	0.148264	−	0.146950i
$166$	1.08098e12	+	6.24104e11i	0.665615	+	0.384293i
$167$	1.67604e12			0.998491			0.499246	−	0.866461i	$-0.333611\pi$
$167$	1.67604e12			0.998491			0.499246	+	0.866461i	$0.333611\pi$
$168$	−6.02991e11	−	1.11846e11i	−0.347624	−	0.0644790i
$169$	1.78957e12			0.998554
$170$	−1.61954e12	−	9.35041e11i	−0.874827	−	0.505082i
$171$	−8.37112e11	+	1.42057e12i	−0.437829	+	0.742990i
$172$	−6.38800e11	−	1.10643e12i	−0.323563	−	0.560427i
$173$	1.01491e12	−	1.75788e12i	0.497937	−	0.862452i	−0.502060	−	0.864833i	$-0.667424\pi$
$173$	1.01491e12	−	1.75788e12i	0.497937	−	0.862452i	0.999997	+	0.00238076i	$0.000757822\pi$
$174$	−8.95062e10	+	2.35567e10i	−0.0425434	+	0.0111968i
$175$	−1.38929e11	+	2.94532e11i	−0.0639860	+	0.135651i
$176$			1.26816e11i			0.0566048i
$177$	−4.85214e11	+	1.77913e12i	−0.209933	+	0.769760i
$178$	2.42412e12	−	1.39957e12i	1.01682	−	0.587061i
$179$	−2.05515e12	+	1.18654e12i	−0.835894	+	0.482603i	−0.855866	−	0.517197i	$-0.826975\pi$
$179$	−2.05515e12	+	1.18654e12i	−0.835894	+	0.482603i	0.0199727	+	0.999801i	$0.493642\pi$
$180$	1.04023e10	−	1.16860e12i	0.00410328	−	0.460963i
$181$		−	1.80880e12i		−	0.692085i	−0.938219	−	0.346042i	$-0.887525\pi$
$181$		−	1.80880e12i		−	0.692085i	0.938219	−	0.346042i	$-0.112475\pi$
$182$	−7.21911e10	+	5.99472e9i	−0.0267973	+	0.00222524i
$183$	3.25116e11	+	1.23531e12i	0.117100	+	0.444935i
$184$	4.29703e11	−	7.44268e11i	0.150200	−	0.260155i
$185$	6.73355e11	+	1.16629e12i	0.228455	+	0.395695i
$186$	−2.50761e12	−	2.53003e12i	−0.825922	−	0.833306i
$187$	−9.50093e11	−	5.48536e11i	−0.303835	−	0.175419i
$188$	1.43828e11			0.0446660
$189$	3.25432e12	+	6.33641e11i	0.981567	+	0.191119i
$190$	1.91889e12			0.562219
$191$	−9.20403e11	−	5.31395e11i	−0.261996	−	0.151263i	0.363249	−	0.931692i	$-0.381667\pi$
$191$	−9.20403e11	−	5.31395e11i	−0.261996	−	0.151263i	−0.625245	+	0.780429i	$0.715001\pi$
$192$	3.18134e11	+	3.20979e11i	0.0879941	+	0.0887809i
$193$	1.99091e12	+	3.44835e12i	0.535163	+	0.926929i	0.999155	+	0.0410900i	$0.0130830\pi$
$193$	1.99091e12	+	3.44835e12i	0.535163	+	0.926929i	−0.463993	+	0.885839i	$0.653584\pi$
$194$	−1.48191e12	+	2.56675e12i	−0.387180	+	0.670616i
$195$	−3.51334e10	−	1.33493e11i	−0.00892338	−	0.0339054i
$196$	−1.99705e12	+	3.33971e11i	−0.493152	+	0.0824709i
$197$		−	4.44591e11i		−	0.106757i	−0.998574	−	0.0533785i	$-0.983001\pi$
$197$		−	4.44591e11i		−	0.106757i	0.998574	−	0.0533785i	$-0.0169990\pi$
$198$	6.10246e9	−	6.85551e11i	0.00142510	−	0.160096i
$199$	−5.19502e12	+	2.99934e12i	−1.18004	+	0.681294i	−0.956023	−	0.293292i	$-0.905249\pi$
$199$	−5.19502e12	+	2.99934e12i	−1.18004	+	0.681294i	−0.224013	+	0.974586i	$0.571916\pi$
$200$	2.07825e11	−	1.19988e11i	0.0459232	−	0.0265138i
$201$	9.53969e11	−	3.49791e12i	0.205095	−	0.752022i
$202$			4.06938e12i			0.851326i
$203$	−2.51084e11	+	1.74164e11i	−0.0511201	+	0.0354592i
$204$	−3.78082e12	+	9.95054e11i	−0.749239	+	0.197188i
$205$	−4.65892e11	+	8.06948e11i	−0.0898750	+	0.155668i
$206$	1.84185e12	+	3.19017e12i	0.345926	+	0.599162i
$207$	−2.35874e12	+	4.00275e12i	−0.431364	+	0.732018i
$208$	4.62293e10	+	2.66905e10i	0.00823320	+	0.00475344i
$209$	1.12571e12			0.195263
$210$	−1.28744e12	−	3.63725e12i	−0.217531	−	0.614563i
$211$	7.80379e12			1.28455			0.642277	−	0.766473i	$-0.277990\pi$
$211$	7.80379e12			1.28455			0.642277	+	0.766473i	$0.277990\pi$
$212$	−4.60849e12	−	2.66071e12i	−0.739114	−	0.426728i
$213$	−3.06431e12	+	3.03716e12i	−0.478901	+	0.474657i
$214$	3.00693e12	+	5.20816e12i	0.457982	+	0.793247i
$215$	4.01896e12	−	6.96104e12i	0.596626	−	1.03339i
$216$	−1.70435e12	−	1.75048e12i	−0.246640	−	0.253316i
$217$	−1.06369e13	−	5.01738e12i	−1.50067	−	0.707862i
$218$		−	2.02843e12i		−	0.279029i
$219$	−1.20650e13	−	3.29044e12i	−1.61840	−	0.441378i
$220$	−6.90959e11	+	3.98925e11i	−0.0903915	+	0.0521875i
$221$	−3.99926e11	+	2.30897e11i	−0.0510296	+	0.0294619i
$222$	2.71621e12	+	7.40780e11i	0.338082	+	0.0922036i
$223$		−	6.64946e12i		−	0.807439i	−0.914883	−	0.403719i	$-0.867717\pi$
$223$		−	6.64946e12i		−	0.807439i	0.914883	−	0.403719i	$-0.132283\pi$
$224$	1.34948e12	+	6.36543e11i	0.159883	+	0.0754160i
$225$	−1.12925e12	+	6.38639e11i	−0.130553	+	0.0738332i
$226$	−2.46228e12	+	4.26479e12i	−0.277805	+	0.481173i
$227$	3.32433e12	+	5.75790e12i	0.366068	+	0.634048i	0.988947	−	0.148270i	$-0.0473705\pi$
$227$	3.32433e12	+	5.75790e12i	0.366068	+	0.634048i	−0.622879	+	0.782318i	$0.714037\pi$
$228$	2.84923e12	−	2.82398e12i	0.306257	−	0.303543i
$229$	−8.88140e12	−	5.12768e12i	−0.931937	−	0.538054i	−0.0445130	−	0.999009i	$-0.514174\pi$
$229$	−8.88140e12	−	5.12768e12i	−0.931937	−	0.538054i	−0.887424	+	0.460955i	$0.847507\pi$
$230$	5.40689e12			0.553916
$231$	−7.55269e11	−	2.13377e12i	−0.0755502	−	0.213443i
$232$	2.25180e11			0.0219961
$233$	4.97741e12	+	2.87371e12i	0.474838	+	0.274148i	0.718263	−	0.695772i	$-0.244938\pi$
$233$	4.97741e12	+	2.87371e12i	0.474838	+	0.274148i	−0.243425	+	0.969920i	$0.578271\pi$
$234$	−2.48626e11	−	1.46510e11i	−0.0231664	−	0.0136515i
$235$	4.52442e11	+	7.83653e11i	0.0411804	+	0.0713265i
$236$	2.24331e12	−	3.88553e12i	0.199468	−	0.345489i
$237$	−8.64794e12	+	2.27600e12i	−0.751271	+	0.197723i
$238$	−1.06060e13	+	7.35682e12i	−0.900284	+	0.624478i
$239$			4.62568e12i			0.383695i	0.981425	+	0.191848i	$0.0614480\pi$
$239$			4.62568e12i			0.383695i	−0.981425	+	0.191848i	$0.938552\pi$
$240$	−7.48103e11	+	2.74307e12i	−0.0606457	+	0.222369i
$241$	−7.15594e12	+	4.13149e12i	−0.566987	+	0.327350i	−0.755945	−	0.654635i	$-0.772822\pi$
$241$	−7.15594e12	+	4.13149e12i	−0.566987	+	0.327350i	0.188958	+	0.981985i	$0.439489\pi$
$242$	7.50144e12	−	4.33096e12i	0.580979	−	0.335428i
$243$	9.12928e12	+	9.54491e12i	0.691198	+	0.722666i
$244$		−	3.10780e12i		−	0.230043i
$245$	−8.10179e12	−	9.83040e12i	−0.586364	−	0.711472i
$246$	4.95794e11	+	1.88383e12i	0.0350880	+	0.133321i
$247$	2.36924e11	−	4.10364e11i	0.0163974	−	0.0284012i
$248$	4.33331e12	+	7.50551e12i	0.293316	+	0.508038i
$249$	1.15571e13	+	1.16604e13i	0.765158	+	0.771999i
$250$	1.00252e13	+	5.78803e12i	0.649264	+	0.374853i
$251$	9.21617e12			0.583909			0.291954	−	0.956432i	$-0.405694\pi$
$251$	9.21617e12			0.583909			0.291954	+	0.956432i	$0.405694\pi$
$252$	−7.26448e12	−	3.50601e12i	−0.450300	−	0.217325i
$253$	3.17192e12			0.192380
$254$	1.64803e13	+	9.51490e12i	0.978091	+	0.564701i
$255$	−1.73149e13	−	1.74698e13i	−1.00566	−	1.01465i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−1.75644e13	+	3.04224e13i	−0.977238	+	1.69263i	−0.304895	+	0.952386i	$0.598621\pi$
$257$	−1.75644e13	+	3.04224e13i	−0.977238	+	1.69263i	−0.672343	+	0.740240i	$0.734712\pi$
$258$	−4.27691e12	−	1.62506e13i	−0.232928	−	0.885035i
$259$	9.26345e12	−	7.69233e11i	0.493883	−	0.0410119i
$260$			3.35842e11i			0.0175300i
$261$	−1.21729e12	−	1.08358e10i	−0.0622118	−	0.000553781i
$262$	1.21846e13	−	7.03478e12i	0.609753	−	0.352041i
$263$	3.22586e11	−	1.86245e11i	0.0158085	−	0.00912702i	−0.492075	−	0.870553i	$-0.663761\pi$
$263$	3.22586e11	−	1.86245e11i	0.0158085	−	0.00912702i	0.507883	+	0.861426i	$0.330428\pi$
$264$	−4.38871e11	+	1.60920e12i	−0.0210627	+	0.0772307i
$265$		−	3.34793e13i		−	1.57371i
$266$	5.65041e12	−	1.19789e13i	0.260154	−	0.551529i
$267$	3.56039e13	−	9.37039e12i	1.60578	−	0.422616i
$268$	−4.41053e12	+	7.63926e12i	−0.194872	+	0.337528i
$269$	−9.79631e12	−	1.69677e13i	−0.424058	−	0.734490i	0.572274	−	0.820062i	$-0.306061\pi$
$269$	−9.79631e12	−	1.69677e13i	−0.424058	−	0.734490i	−0.996332	+	0.0855726i	$0.972728\pi$
$270$	4.17616e12	−	1.47927e13i	0.177124	−	0.627403i
$271$	−2.52272e13	−	1.45649e13i	−1.04843	−	0.605308i	−0.126217	−	0.992003i	$-0.540284\pi$
$271$	−2.52272e13	−	1.45649e13i	−1.04843	−	0.605308i	−0.922208	+	0.386694i	$0.873617\pi$
$272$	9.51179e12			0.387376
$273$	−9.36802e11	−	1.73762e11i	−0.0373898	−	0.00693524i
$274$	2.25676e13			0.882789
$275$	7.67045e11	+	4.42853e11i	0.0294097	+	0.0169797i
$276$	8.02833e12	−	7.95718e12i	0.301735	−	0.299061i
$277$	3.83146e12	+	6.63629e12i	0.141165	+	0.244504i	0.927935	−	0.372741i	$-0.121582\pi$
$277$	3.83146e12	+	6.63629e12i	0.141165	+	0.244504i	−0.786771	+	0.617245i	$0.788249\pi$
$278$	−8.04922e12	+	1.39417e13i	−0.290742	+	0.503579i
$279$	−2.30642e13	−	4.07824e13i	−0.816799	−	1.44428i
$280$	7.76838e11	+	9.35503e12i	0.0269750	+	0.324845i
$281$			5.40056e13i			1.83888i	0.393226	+	0.919442i	$0.371359\pi$
$281$			5.40056e13i			1.83888i	−0.393226	+	0.919442i	$0.628641\pi$
$282$	1.82509e12	+	4.97747e11i	0.0609415	+	0.0166203i
$283$	1.66859e13	−	9.63361e12i	0.546417	−	0.315474i	−0.201259	−	0.979538i	$-0.564503\pi$
$283$	1.66859e13	−	9.63361e12i	0.546417	−	0.315474i	0.747676	+	0.664064i	$0.231170\pi$
$284$	9.09050e12	−	5.24840e12i	0.291969	−	0.168568i
$285$	2.43494e13	+	6.64070e12i	0.767082	+	0.209203i
$286$			1.97020e11i			0.00608831i
$287$	3.66560e12	+	5.28454e12i	0.111121	+	0.160198i
$288$	2.92609e12	+	5.17396e12i	0.0870221	+	0.153874i
$289$	−2.40069e13	+	4.15812e13i	−0.700484	+	1.21327i
$290$	7.08349e11	+	1.22690e12i	0.0202796	+	0.0351252i
$291$	−2.76872e13	+	2.74418e13i	−0.777799	+	0.770907i
$292$	2.63494e13	+	1.52128e13i	0.726382	+	0.419377i
$293$	6.76028e13			1.82891			0.914457	−	0.404684i	$-0.132618\pi$
$293$	6.76028e13			1.82891			0.914457	+	0.404684i	$0.132618\pi$
$294$	−2.64970e13	−	2.67331e12i	−0.703535	−	0.0709805i
$295$	2.82272e13			0.735609
$296$	−5.93207e12	−	3.42488e12i	−0.151741	−	0.0876075i
$297$	2.44992e12	−	8.67805e12i	0.0615165	−	0.217902i
$298$	6.24836e12	+	1.08225e13i	0.154020	+	0.266770i
$299$	6.67584e11	−	1.15629e12i	0.0161553	−	0.0279817i
$300$	3.05240e12	−	8.03344e11i	0.0725227	−	0.0190869i
$301$	−3.16208e13	−	4.55864e13i	−0.737662	−	1.06346i
$302$		−	7.29558e12i		−	0.167117i
$303$	−1.40829e13	+	5.16377e13i	−0.316780	+	1.16153i
$304$	−8.45245e12	+	4.88002e12i	−0.186714	+	0.107800i
$305$	1.69329e13	−	9.77623e12i	0.367353	−	0.212091i
$306$	−5.14196e13	−	4.57714e11i	−1.09562	−	0.00975274i
$307$		−	7.52333e13i		−	1.57452i	−0.616619	−	0.787261i	$-0.711498\pi$
$307$		−	7.52333e13i		−	1.57452i	0.616619	−	0.787261i	$-0.288502\pi$
$308$	4.55728e11	+	5.48808e12i	0.00936864	+	0.112821i
$309$	1.23316e13	+	4.68551e13i	0.249027	+	0.946206i
$310$	−2.72626e13	+	4.72203e13i	−0.540852	+	0.936784i
$311$	−4.22459e13	−	7.31720e13i	−0.823384	−	1.42614i	−0.903148	−	0.429329i	$-0.858750\pi$
$311$	−4.22459e13	−	7.31720e13i	−0.823384	−	1.42614i	0.0797640	−	0.996814i	$-0.474583\pi$
$312$	4.94250e11	+	4.98670e11i	0.00946448	+	0.00954910i
$313$	2.62298e13	+	1.51438e13i	0.493516	+	0.284932i	0.726032	−	0.687661i	$-0.241362\pi$
$313$	2.62298e13	+	1.51438e13i	0.493516	+	0.284932i	−0.232516	+	0.972593i	$0.574696\pi$
$314$	−8.20110e12			−0.151621
$315$	−3.74933e12	−	5.06096e13i	−0.0681154	−	0.919443i
$316$	2.17565e13			0.388427
$317$	6.61046e13	+	3.81655e13i	1.15986	+	0.669645i	0.951270	−	0.308358i	$-0.0997795\pi$
$317$	6.61046e13	+	3.81655e13i	1.15986	+	0.669645i	0.208589	+	0.978003i	$0.433113\pi$
$318$	−4.92707e13	−	4.97112e13i	−0.849649	−	0.857245i
$319$	4.15549e11	+	7.19752e11i	0.00704326	+	0.0121993i
$320$	3.45874e12	−	5.99072e12i	0.0576227	−	0.0998054i
$321$	2.01321e13	+	7.64941e13i	0.329694	+	1.25271i
$322$	1.59212e13	−	3.37531e13i	0.256312	−	0.543384i
$323$		−	8.44334e13i		−	1.33629i
$324$	−1.55692e13	−	2.81106e13i	−0.242252	−	0.437395i
$325$	3.22875e11	−	1.86412e11i	0.00493942	−	0.00285177i
$326$	−6.36369e13	+	3.67408e13i	−0.957221	+	0.552652i
$327$	7.01978e12	−	2.57394e13i	0.103827	−	0.380703i
$328$		−	4.73933e12i		−	0.0689304i
$329$	6.22432e12	−	5.16865e11i	0.0890255	−	0.00739265i
$330$	−1.01484e13	+	2.67089e12i	−0.142748	+	0.0375690i
$331$	−6.65071e13	+	1.15194e14i	−0.920055	+	1.59358i	−0.120729	+	0.992685i	$0.538523\pi$
$331$	−6.65071e13	+	1.15194e14i	−0.920055	+	1.59358i	−0.799326	+	0.600897i	$0.794810\pi$
$332$	−1.99713e13	−	3.45914e13i	−0.271736	−	0.470661i
$333$	3.19033e13	+	1.88000e13i	0.426965	+	0.251602i
$334$	−4.64478e13	−	2.68167e13i	−0.611448	−	0.353020i
$335$	−5.54970e13			−0.718659
$336$	1.49210e13	+	1.27474e13i	0.190079	+	0.162389i
$337$	6.59253e13			0.826205			0.413102	−	0.910685i	$-0.364445\pi$
$337$	6.59253e13			0.826205			0.413102	+	0.910685i	$0.364445\pi$
$338$	−4.95940e13	−	2.86331e13i	−0.611487	−	0.353042i
$339$	−4.60037e13	+	4.55961e13i	−0.558078	+	0.553132i
$340$	2.99213e13	+	5.18252e13i	0.357147	+	0.618596i
$341$	−1.59935e13	+	2.77015e13i	−0.187842	+	0.325353i
$342$	4.59278e13	−	2.59741e13i	0.530801	−	0.300191i
$343$	−8.52241e13	+	2.16296e13i	−0.969270	+	0.245997i
$344$			4.08832e13i			0.457587i
$345$	6.86097e13	+	1.87116e13i	0.755754	+	0.206113i
$346$	−5.62521e13	+	3.24771e13i	−0.609846	+	0.352094i
$347$	5.88757e13	−	3.39919e13i	0.628238	−	0.362713i	−0.151831	−	0.988406i	$-0.548517\pi$
$347$	5.88757e13	−	3.39919e13i	0.628238	−	0.362713i	0.780069	+	0.625693i	$0.215184\pi$
$348$	2.85737e12	+	7.79278e11i	0.0300111	+	0.00818477i
$349$		−	1.54262e14i		−	1.59484i	−0.603423	−	0.797422i	$-0.706197\pi$
$349$		−	1.54262e14i		−	1.59484i	0.603423	−	0.797422i	$-0.293803\pi$
$350$	8.56263e12	−	5.93943e12i	0.0871431	−	0.0604464i
$351$	−2.64786e12	−	2.71953e12i	−0.0265281	−	0.0272462i
$352$	2.02905e12	−	3.51442e12i	0.0200128	−	0.0346632i
$353$	1.30253e13	+	2.25604e13i	0.126481	+	0.219071i	0.922311	−	0.386449i	$-0.126298\pi$
$353$	1.30253e13	+	2.25604e13i	0.126481	+	0.219071i	−0.795830	+	0.605520i	$0.792965\pi$
$354$	4.19128e13	−	4.15413e13i	0.400708	−	0.397157i
$355$	5.71921e13	+	3.30199e13i	0.538369	+	0.310828i
$356$	−8.95722e13			−0.830229
$357$	−1.60043e14	+	5.66488e13i	−1.46070	+	0.517030i
$358$	7.59385e13			0.682504
$359$	−1.09426e14	−	6.31769e13i	−0.968499	−	0.559163i	−0.0697208	−	0.997567i	$-0.522211\pi$
$359$	−1.09426e14	−	6.31769e13i	−0.968499	−	0.559163i	−0.898778	+	0.438403i	$0.855544\pi$
$360$	−1.89858e13	+	3.22187e13i	−0.165488	+	0.280830i
$361$	−1.49266e13	−	2.58536e13i	−0.128136	−	0.221938i
$362$	−2.89409e13	+	5.01270e13i	−0.244689	+	0.423814i
$363$	1.10176e14	−	2.89967e13i	0.917491	−	0.241469i
$364$	2.09653e12	+	9.88927e11i	0.0171967	+	0.00811160i
$365$			1.91421e14i			1.54660i
$366$	1.07551e13	−	3.94359e13i	0.0855993	−	0.313867i
$367$	−9.09957e13	+	5.25364e13i	−0.713440	+	0.411905i	−0.812333	−	0.583193i	$-0.801803\pi$
$367$	−9.09957e13	+	5.25364e13i	−0.713440	+	0.411905i	0.0988935	+	0.995098i	$0.468470\pi$
$368$	−2.38166e13	+	1.37505e13i	−0.183957	+	0.106208i
$369$	−2.28060e11	+	2.56203e13i	−0.00173542	+	0.194957i
$370$		−	4.30947e13i		−	0.323083i
$371$	−2.08999e14	−	9.85838e13i	−1.54379	−	0.728198i
$372$	2.90124e13	+	1.10236e14i	0.211153	+	0.802301i
$373$	−9.92170e13	+	1.71849e14i	−0.711521	+	1.23239i	0.252765	+	0.967528i	$0.418660\pi$
$373$	−9.92170e13	+	1.71849e14i	−0.711521	+	1.23239i	−0.964286	+	0.264863i	$0.914673\pi$
$374$	1.75532e13	+	3.04030e13i	0.124040	+	0.214844i
$375$	1.07182e14	+	1.08140e14i	0.746361	+	0.753034i
$376$	−3.98589e12	−	2.30126e12i	−0.0273522	−	0.0157918i
$377$	3.49837e11			0.00236586
$378$	−8.00480e13	−	6.96290e13i	−0.533514	−	0.464072i
$379$	1.57834e14			1.03677			0.518387	−	0.855146i	$-0.326533\pi$
$379$	1.57834e14			1.03677			0.518387	+	0.855146i	$0.326533\pi$
$380$	−5.31779e13	−	3.07023e13i	−0.344288	−	0.198774i
$381$	1.76195e14	+	1.77771e14i	1.12436	+	1.13442i
$382$	1.70046e13	+	2.94529e13i	0.106959	+	0.185259i
$383$	8.52988e13	−	1.47742e14i	0.528871	−	0.916032i	−0.470562	−	0.882367i	$-0.655949\pi$
$383$	8.52988e13	−	1.47742e14i	0.528871	−	0.916032i	0.999433	−	0.0336648i	$-0.0107179\pi$
$384$	−3.68073e12	−	1.39854e13i	−0.0224964	−	0.0854776i
$385$	−2.84683e13	+	1.97469e13i	−0.171525	+	0.118978i
$386$		−	1.27418e14i		−	0.756834i
$387$	1.96733e12	−	2.21010e14i	0.0115204	−	1.29420i
$388$	8.21360e13	−	4.74212e13i	0.474197	−	0.273778i
$389$	1.97095e13	−	1.13793e13i	0.112190	−	0.0647729i	−0.442855	−	0.896593i	$-0.646034\pi$
$389$	1.97095e13	−	1.13793e13i	0.112190	−	0.0647729i	0.555045	+	0.831820i	$0.312701\pi$
$390$	−1.16225e12	+	4.26161e12i	−0.00652293	+	0.0239176i
$391$		−	2.37909e14i		−	1.31656i
$392$	6.06874e13	+	2.26975e13i	0.331150	+	0.123853i
$393$	1.78959e14	−	4.70993e13i	0.962931	−	0.253429i
$394$	−7.11345e12	+	1.23209e13i	−0.0377443	+	0.0653750i
$395$	6.84395e13	+	1.18541e14i	0.358115	+	0.620274i
$396$	−1.11379e13	+	1.89009e13i	−0.0574753	+	0.0975347i
$397$	6.36468e13	+	3.67465e13i	0.323913	+	0.187011i	0.653135	−	0.757241i	$-0.273453\pi$
$397$	6.36468e13	+	3.67465e13i	0.323913	+	0.187011i	−0.329222	+	0.944252i	$0.606787\pi$
$398$	1.91958e14			0.963495
$399$	1.13155e14	−	1.32450e14i	0.560174	−	0.655693i
$400$	−7.67921e12			−0.0374962
$401$	−5.70677e13	−	3.29480e13i	−0.274850	−	0.158685i	0.356240	−	0.934395i	$-0.384059\pi$
$401$	−5.70677e13	−	3.29480e13i	−0.274850	−	0.158685i	−0.631090	+	0.775710i	$0.717392\pi$
$402$	−8.24038e13	+	8.16735e13i	−0.391475	+	0.388006i
$403$	6.73219e12	+	1.16605e13i	0.0315485	+	0.0546436i
$404$	6.51101e13	−	1.12774e14i	0.300989	−	0.521329i
$405$	1.04186e14	−	1.73257e14i	0.475122	−	0.790110i
$406$	9.74487e12	−	8.09210e11i	0.0438412	−	0.00364056i
$407$		−	2.52813e13i		−	0.112210i
$408$	1.20698e14	+	3.29174e13i	0.528530	+	0.144143i
$409$	2.28700e14	−	1.32040e14i	0.988071	−	0.570463i	0.0833742	−	0.996518i	$-0.473430\pi$
$409$	2.28700e14	−	1.32040e14i	0.988071	−	0.570463i	0.904697	+	0.426055i	$0.140097\pi$
$410$	2.58224e13	−	1.49085e13i	0.110074	−	0.0635512i
$411$	2.86367e14	+	7.80995e13i	1.20446	+	0.328487i
$412$		−	1.17878e14i		−	0.489214i
$413$	8.31185e13	−	1.76212e14i	0.340386	−	0.721622i
$414$	1.29411e14	−	7.31876e13i	0.522962	−	0.295757i
$415$	1.25648e14	−	2.17629e14i	0.501061	−	0.867864i
$416$	−8.54096e11	−	1.47934e12i	−0.00336119	−	0.00582175i
$417$	−1.50387e14	+	1.49054e14i	−0.584066	+	0.578890i
$418$	−3.11965e13	−	1.80113e13i	−0.119574	−	0.0690360i
$419$	−3.46229e14			−1.30974			−0.654871	−	0.755741i	$-0.727277\pi$
$419$	−3.46229e14			−1.30974			−0.654871	+	0.755741i	$0.727277\pi$
$420$	−2.25174e13	+	1.21397e14i	−0.0840711	+	0.453250i
$421$	−1.52531e14			−0.562090			−0.281045	−	0.959695i	$-0.590681\pi$
$421$	−1.52531e14			−0.562090			−0.281045	+	0.959695i	$0.590681\pi$
$422$	−2.16265e14	−	1.24861e14i	−0.786625	−	0.454158i
$423$	2.14365e13	+	1.26321e13i	0.0769631	+	0.0453528i
$424$	8.51428e13	+	1.47472e14i	0.301742	+	0.522633i
$425$	3.32161e13	−	5.75320e13i	0.116201	−	0.201266i
$426$	1.33515e14	−	3.51392e13i	0.461082	−	0.121350i
$427$	−1.11683e13	−	1.34493e14i	−0.0380743	−	0.458508i
$428$		−	1.92444e14i		−	0.647684i
$429$	−6.81825e11	+	2.50005e12i	−0.00226547	+	0.00830679i
$430$	−2.22753e14	+	1.28607e14i	−0.730714	+	0.421878i
$431$	−3.53153e14	+	2.03893e14i	−1.14377	+	0.660355i	−0.947361	−	0.320168i	$-0.896261\pi$
$431$	−3.53153e14	+	2.03893e14i	−1.14377	+	0.660355i	−0.196407	+	0.980523i	$0.562927\pi$
$432$	1.92246e13	+	7.57804e13i	0.0614748	+	0.242324i
$433$			4.84121e14i			1.52852i	0.644910	+	0.764259i	$0.276895\pi$
$433$			4.84121e14i			1.52852i	−0.644910	+	0.764259i	$0.723105\pi$
$434$	2.14500e14	+	3.09236e14i	0.668704	+	0.964044i
$435$	4.74255e12	+	1.80199e13i	0.0145989	+	0.0554703i
$436$	−3.24549e13	+	5.62136e13i	−0.0986517	+	0.170870i
$437$	1.22059e14	+	2.11413e14i	0.366373	+	0.634576i
$438$	2.81709e14	+	2.84228e14i	0.835013	+	0.842479i
$439$	−1.58341e14	−	9.14185e13i	−0.463489	−	0.267596i	0.250021	−	0.968240i	$-0.419562\pi$
$439$	−1.58341e14	−	9.14185e13i	−0.463489	−	0.267596i	−0.713510	+	0.700645i	$0.752896\pi$
$440$	2.55312e13			0.0738043
$441$	−3.26977e14	−	1.25620e14i	−0.933479	−	0.358631i
$442$	1.47774e13			0.0416655
$443$	−2.02304e14	−	1.16800e14i	−0.563357	−	0.325254i	0.191135	−	0.981564i	$-0.438783\pi$
$443$	−2.02304e14	−	1.16800e14i	−0.563357	−	0.325254i	−0.754492	+	0.656310i	$0.772117\pi$
$444$	−6.34215e13	−	6.39885e13i	−0.174433	−	0.175993i
$445$	−2.81768e14	−	4.88036e14i	−0.765441	−	1.32578i
$446$	−1.06391e14	+	1.84275e14i	−0.285473	+	0.494453i
$447$	4.18341e13	+	1.58954e14i	0.110877	+	0.421288i
$448$	−2.72131e13	−	3.92320e13i	−0.0712441	−	0.102710i
$449$			3.69553e14i			0.955700i	0.878441	+	0.477850i	$0.158584\pi$
$449$			3.69553e14i			0.955700i	−0.878441	+	0.477850i	$0.841416\pi$
$450$	4.15129e13	+	3.69529e11i	0.106051	+	0.000944017i
$451$	1.51485e13	−	8.74601e12i	0.0382296	−	0.0220719i
$452$	1.36473e14	−	7.87929e13i	0.340241	−	0.196438i
$453$	2.52478e13	−	9.25759e13i	0.0621846	−	0.228012i
$454$		−	2.12757e14i		−	0.517698i
$455$	1.20689e12	+	1.45339e13i	0.00290138	+	0.0349397i
$456$	−1.24144e14	+	3.26728e13i	−0.294862	+	0.0776032i
$457$	−3.88192e14	+	6.72368e14i	−0.910976	+	1.57786i	−0.0982887	+	0.995158i	$0.531337\pi$
$457$	−3.88192e14	+	6.72368e14i	−0.910976	+	1.57786i	−0.812688	+	0.582699i	$0.801996\pi$
$458$	1.64086e14	+	2.84205e14i	0.380461	+	0.658979i
$459$	−6.50896e14	−	1.83756e14i	−1.49122	−	0.420989i
$460$	−1.49840e14	−	8.65102e13i	−0.339203	−	0.195839i
$461$	7.50947e13			0.167979			0.0839893	−	0.996467i	$-0.473234\pi$
$461$	7.50947e13			0.167979			0.0839893	+	0.996467i	$0.473234\pi$
$462$	−1.32097e13	+	7.12171e13i	−0.0291986	+	0.157418i
$463$	4.48992e14			0.980715			0.490357	−	0.871521i	$-0.336866\pi$
$463$	4.48992e14			0.980715			0.490357	+	0.871521i	$0.336866\pi$
$464$	−6.24036e12	−	3.60287e12i	−0.0134698	−	0.00777679i
$465$	−5.09359e14	+	5.04845e14i	−1.08651	+	1.07688i
$466$	−9.19586e13	−	1.59277e14i	−0.193852	−	0.335761i
$467$	1.51249e14	−	2.61971e14i	0.315101	−	0.545771i	−0.664358	−	0.747415i	$-0.731295\pi$
$467$	1.51249e14	−	2.61971e14i	0.315101	−	0.545771i	0.979459	+	0.201644i	$0.0646282\pi$
$468$	4.54596e12	+	8.03822e12i	0.00935994	+	0.0165504i
$469$	−1.63417e14	+	3.46446e14i	−0.332543	+	0.704994i
$470$		−	2.89563e13i		−	0.0582378i
$471$	−1.04066e14	−	2.83815e13i	−0.206869	−	0.0564183i
$472$	−1.24337e14	+	7.17860e13i	−0.244298	+	0.141045i
$473$	−1.30677e14	+	7.54464e13i	−0.253783	+	0.146522i
$474$	2.76075e14	+	7.52925e13i	0.529963	+	0.144534i
$475$			6.81662e13i			0.129346i
$476$	4.11632e14	−	3.41818e13i	0.772095	−	0.0641145i
$477$	−4.53176e14	−	8.01312e14i	−0.840264	−	1.48577i
$478$	7.40108e13	−	1.28190e14i	0.135657	−	0.234965i
$479$	−3.92365e14	−	6.79595e14i	−0.710959	−	1.23142i	−0.964498	−	0.264092i	$-0.914928\pi$
$479$	−3.92365e14	−	6.79595e14i	−0.710959	−	1.23142i	0.253539	−	0.967325i	$-0.418405\pi$
$480$	6.46211e13	−	6.40485e13i	0.115757	−	0.114731i
$481$	−9.21602e12	−	5.32087e12i	−0.0163209	−	0.00942290i
$482$	2.64415e14			0.462943
$483$	3.18839e14	−	3.73206e14i	0.551902	−	0.646010i
$484$	−2.77181e14			−0.474367
$485$	5.16752e14	+	2.98347e14i	0.874384	+	0.504826i
$486$	−1.00280e14	−	4.10585e14i	−0.167769	−	0.686916i
$487$	3.72678e14	+	6.45498e14i	0.616489	+	1.06779i	0.990121	+	0.140213i	$0.0447787\pi$
$487$	3.72678e14	+	6.45498e14i	0.616489	+	1.06779i	−0.373633	+	0.927577i	$0.621888\pi$
$488$	−4.97248e13	+	8.61259e13i	−0.0813325	+	0.140872i
$489$	−9.34657e14	+	2.45987e14i	−1.51166	+	0.397845i
$490$	6.72369e13	+	4.02057e14i	0.107530	+	0.642997i
$491$			4.35501e13i			0.0688718i	0.999407	+	0.0344359i	$0.0109635\pi$
$491$			4.35501e13i			0.0688718i	−0.999407	+	0.0344359i	$0.989037\pi$
$492$	1.64014e13	−	6.01388e13i	0.0256491	−	0.0940474i
$493$	5.39849e13	−	3.11682e13i	0.0834861	−	0.0482007i
$494$	−1.31317e13	+	7.58156e12i	−0.0200827	+	0.0115947i
$495$	−1.38019e14	−	1.22858e12i	−0.208742	−	0.00185813i
$496$		−	2.77332e14i		−	0.414811i
$497$	3.74540e14	−	2.59798e14i	0.554036	−	0.384304i
$498$	−1.33712e14	−	5.08055e14i	−0.195619	−	0.743275i
$499$	−4.28214e14	+	7.41689e14i	−0.619595	+	1.07317i	0.369964	+	0.929046i	$0.379370\pi$
$499$	−4.28214e14	+	7.41689e14i	−0.619595	+	1.07317i	−0.989560	+	0.144125i	$0.953963\pi$
$500$	−1.85217e14	−	3.20805e14i	−0.265061	−	0.459099i
$501$	−4.96587e14	−	5.01027e14i	−0.702891	−	0.709175i
$502$	−2.55406e14	−	1.47459e14i	−0.357570	−	0.206443i
$503$	−1.46656e13			−0.0203084			−0.0101542	−	0.999948i	$-0.503232\pi$
$503$	−1.46656e13			−0.0203084			−0.0101542	+	0.999948i	$0.503232\pi$
$504$	1.45223e14	+	2.13393e14i	0.198915	+	0.292289i
$505$	8.19270e14			1.11000
$506$	−8.79028e13	−	5.07507e13i	−0.117808	−	0.0680165i
$507$	−5.30223e14	−	5.34964e14i	−0.702935	−	0.709220i
$508$	−3.04477e14	−	5.27369e14i	−0.399304	−	0.691615i
$509$	2.41682e13	−	4.18605e13i	0.0313542	−	0.0543071i	−0.849922	−	0.526908i	$-0.823351\pi$
$509$	2.41682e13	−	4.18605e13i	0.0313542	−	0.0543071i	0.881277	+	0.472601i	$0.156685\pi$
$510$	2.00330e14	+	7.61175e14i	0.257104	+	0.976897i
$511$	1.19497e15	+	5.63661e14i	1.51719	+	0.715654i
$512$			3.51844e13i			0.0441942i
$513$	6.72681e14	−	1.70652e14i	0.835917	−	0.212063i
$514$	9.73516e14	−	5.62060e14i	1.19687	−	0.691012i
$515$	6.42262e14	−	3.70810e14i	0.781219	−	0.451037i
$516$	−1.41484e14	+	5.18780e14i	−0.170269	+	0.624324i
$517$		−	1.69871e13i		−	0.0202265i
$518$	−2.69024e14	−	1.26898e14i	−0.316940	−	0.149500i
$519$	−8.26193e14	+	2.17441e14i	−0.963078	+	0.253467i
$520$	5.37347e12	−	9.30713e12i	0.00619779	−	0.0107349i
$521$	3.87655e14	+	6.71438e14i	0.442423	+	0.766299i	0.997869	−	0.0652539i	$-0.0207857\pi$
$521$	3.87655e14	+	6.71438e14i	0.442423	+	0.766299i	−0.555446	+	0.831553i	$0.687452\pi$
$522$	3.35613e13	+	1.97770e13i	0.0379010	+	0.0223343i
$523$	−1.06756e15	−	6.16358e14i	−1.19298	−	0.688769i	−0.234002	−	0.972236i	$-0.575182\pi$
$523$	−1.06756e15	−	6.16358e14i	−1.19298	−	0.688769i	−0.958982	+	0.283467i	$0.908515\pi$
$524$	−4.50226e14			−0.497861
$525$	1.29209e14	−	4.57346e13i	0.141389	−	0.0500460i
$526$	−1.19197e13			−0.0129076
$527$	2.07775e15	+	1.19959e15i	2.22656	+	1.28550i
$528$	3.79096e13	−	3.75737e13i	0.0402034	−	0.0398471i
$529$	−1.32477e14	−	2.29456e14i	−0.139038	−	0.240821i
$530$	−5.35669e14	+	9.27806e14i	−0.556390	+	0.963696i
$531$	6.75606e14	−	3.82084e14i	0.694502	−	0.392770i
$532$	−3.48251e14	+	2.41563e14i	−0.354306	+	0.245763i
$533$		−	7.36298e12i		−	0.00741402i
$534$	−1.13661e15	−	3.09982e14i	−1.13275	−	0.308930i
$535$	1.04853e15	−	6.05372e14i	1.03428	−	0.597140i
$536$	2.44456e14	−	1.41137e14i	0.238668	−	0.137795i
$537$	9.63608e14	+	2.62800e14i	0.931197	+	0.253961i
$538$			6.26964e14i			0.599708i
$539$	3.94441e13	+	2.35864e14i	0.0373460	+	0.223318i
$540$	−3.52416e14	+	3.43129e14i	−0.330286	+	0.321582i
$541$	1.07424e15	−	1.86064e15i	0.996591	−	1.72615i	0.426846	−	0.904325i	$-0.359625\pi$
$541$	1.07424e15	−	1.86064e15i	0.996591	−	1.72615i	0.569745	−	0.821821i	$-0.307042\pi$
$542$	4.66077e14	+	8.07269e14i	0.428018	+	0.741348i
$543$	−5.40714e14	+	5.35922e14i	−0.491551	+	0.487195i
$544$	−2.63598e14	−	1.52189e14i	−0.237219	−	0.136958i
$545$	−4.08375e14			−0.363813
$546$	2.31812e13	+	1.98043e13i	0.0204445	+	0.0174662i
$547$	−1.60383e15			−1.40032			−0.700160	−	0.713986i	$-0.746888\pi$
$547$	−1.60383e15			−1.40032			−0.700160	+	0.713986i	$0.746888\pi$
$548$	−6.25411e14	−	3.61081e14i	−0.540596	−	0.312113i
$549$	2.72951e14	−	4.63194e14i	0.233581	−	0.396383i
$550$	−1.41713e13	−	2.45454e13i	−0.0120065	−	0.0207958i
$551$	−3.19817e13	+	5.53939e13i	−0.0268267	+	0.0464652i
$552$	−3.49802e14	+	9.20626e13i	−0.290508	+	0.0764572i
$553$	9.41533e14	−	7.81846e13i	0.774190	−	0.0642884i
$554$		−	2.45214e14i		−	0.199637i
$555$	1.49138e14	−	5.46843e14i	0.120220	−	0.440810i
$556$	4.46133e14	−	2.57575e14i	0.356084	−	0.205585i
$557$	2.68302e14	−	1.54904e14i	0.212041	−	0.122422i	−0.390219	−	0.920722i	$-0.627601\pi$
$557$	2.68302e14	−	1.54904e14i	0.212041	−	0.122422i	0.602260	+	0.798300i	$0.294267\pi$
$558$	−1.33454e13	+	1.49922e15i	−0.0104434	+	1.17322i
$559$			6.35158e13i			0.0492172i
$560$	1.28152e14	−	2.71684e14i	0.0983313	−	0.208463i
$561$	1.17522e14	+	4.46539e14i	0.0892944	+	0.339284i
$562$	8.64090e14	−	1.49665e15i	0.650144	−	1.12608i
$563$	8.25955e14	+	1.43060e15i	0.615404	+	1.06591i	0.990314	+	0.138849i	$0.0443403\pi$
$563$	8.25955e14	+	1.43060e15i	0.615404	+	1.06591i	−0.374910	+	0.927061i	$0.622326\pi$
$564$	−4.26143e13	−	4.29953e13i	−0.0314427	−	0.0317239i
$565$	8.58610e14	+	4.95719e14i	0.627378	+	0.362217i
$566$	−6.16551e14			−0.446148
$567$	−7.74790e14	−	1.16057e15i	−0.555235	−	0.831693i
$568$	−3.35898e14			−0.238392
$569$	4.60776e14	+	2.66029e14i	0.323871	+	0.186987i	0.653117	−	0.757257i	$-0.273461\pi$
$569$	4.60776e14	+	2.66029e14i	0.323871	+	0.186987i	−0.329246	+	0.944244i	$0.606794\pi$
$570$	−5.68540e14	−	5.73623e14i	−0.395776	−	0.399314i
$571$	7.73728e14	+	1.34014e15i	0.533445	+	0.923954i	0.999237	+	0.0390597i	$0.0124363\pi$
$571$	7.73728e14	+	1.34014e15i	0.533445	+	0.923954i	−0.465792	+	0.884894i	$0.654230\pi$
$572$	3.15232e12	−	5.45997e12i	0.00215254	−	0.00372831i
$573$	1.13850e14	+	4.32585e14i	0.0769984	+	0.292564i
$574$	−1.70314e13	−	2.05099e14i	−0.0114086	−	0.137388i
$575$			1.92073e14i			0.127436i
$576$	1.69310e12	−	1.90203e14i	0.00111265	−	0.124995i
$577$	3.68443e14	−	2.12721e14i	0.239830	−	0.138466i	−0.375269	−	0.926916i	$-0.622450\pi$
$577$	3.68443e14	−	2.12721e14i	0.239830	−	0.138466i	0.615099	+	0.788450i	$0.289116\pi$
$578$	1.33060e15	−	7.68221e14i	0.857914	−	0.495317i
$579$	4.40955e14	−	1.61685e15i	0.281619	−	1.03261i
$580$		−	4.53344e13i		−	0.0286796i
$581$	−9.88588e14	−	1.42521e15i	−0.619507	−	0.893118i
$582$	1.20636e15	−	3.17495e14i	0.748859	−	0.197088i
$583$	−3.14247e14	+	5.44292e14i	−0.193239	+	0.334699i
$584$	−4.86811e14	−	8.43181e14i	−0.296544	−	0.513630i
$585$	−2.94962e13	+	5.00547e13i	−0.0177996	+	0.0302056i
$586$	−1.87347e15	−	1.08165e15i	−1.11998	−	0.646618i
$587$	−2.93512e14			−0.173827			−0.0869133	−	0.996216i	$-0.527700\pi$
$587$	−2.93512e14			−0.173827			−0.0869133	+	0.996216i	$0.527700\pi$
$588$	6.91532e14	+	4.98036e14i	0.405730	+	0.292204i
$589$	−2.46179e15			−1.43093
$590$	−7.82256e14	−	4.51636e14i	−0.450467	−	0.260077i
$591$	−1.32904e14	+	1.31726e14i	−0.0758238	+	0.0751518i
$592$	1.09596e14	+	1.89826e14i	0.0619479	+	0.107297i
$593$	2.41806e12	−	4.18820e12i	0.00135415	−	0.00234545i	−0.865348	−	0.501172i	$-0.832902\pi$
$593$	2.41806e12	−	4.18820e12i	0.00135415	−	0.00234545i	0.866702	+	0.498827i	$0.166236\pi$
$594$	−2.06743e14	+	2.01295e14i	−0.114711	+	0.111688i
$595$	1.48111e15	+	2.13526e15i	0.814227	+	1.17384i
$596$		−	3.99895e14i		−	0.217817i
$597$	2.43582e15	+	6.64308e14i	1.31458	+	0.358518i
$598$	−3.70012e13	+	2.13627e13i	−0.0197861	+	0.0114235i
$599$	1.15539e15	−	6.67064e14i	0.612182	−	0.353443i	−0.161637	−	0.986850i	$-0.551677\pi$
$599$	1.15539e15	−	6.67064e14i	0.612182	−	0.353443i	0.773819	+	0.633407i	$0.218344\pi$
$600$	−9.74439e13	−	2.65754e13i	−0.0511591	−	0.0139524i
$601$			3.47430e15i			1.80741i	0.428151	+	0.903707i	$0.359165\pi$
$601$			3.47430e15i			1.80741i	−0.428151	+	0.903707i	$0.640835\pi$
$602$	1.46919e14	+	1.76926e15i	0.0757350	+	0.912035i
$603$	−1.32829e15	+	7.51207e14i	−0.678499	+	0.383720i
$604$	−1.16729e14	+	2.02181e14i	−0.0590849	+	0.102338i
$605$	−8.71932e14	−	1.51023e15i	−0.437349	−	0.757510i
$606$	1.21648e15	−	1.20570e15i	0.604652	−	0.599293i
$607$	−2.06798e15	−	1.19395e15i	−1.01861	−	0.588096i	−0.104910	−	0.994482i	$-0.533456\pi$
$607$	−2.06798e15	−	1.19395e15i	−1.01861	−	0.588096i	−0.913702	+	0.406386i	$0.866789\pi$
$608$	3.12322e14			0.152452
$609$	1.26456e14	+	2.34557e13i	0.0611709	+	0.0113463i
$610$	−6.25679e14			−0.299942
$611$	−6.19245e12	−	3.57521e12i	−0.00294195	−	0.00169854i
$612$	1.41766e15	+	8.35398e14i	0.667481	+	0.393333i
$613$	−5.24528e14	−	9.08509e14i	−0.244757	−	0.423932i	0.717306	−	0.696758i	$-0.245375\pi$
$613$	−5.24528e14	−	9.08509e14i	−0.244757	−	0.423932i	−0.962063	+	0.272826i	$0.912042\pi$
$614$	−1.20373e15	+	2.08493e15i	−0.556678	+	0.964194i
$615$	3.79262e14	−	9.98159e13i	0.173831	−	0.0457495i
$616$	7.51797e13	−	1.59382e14i	0.0341513	−	0.0724010i
$617$			3.58079e14i			0.161217i	0.996746	+	0.0806084i	$0.0256863\pi$
$617$			3.58079e14i			0.161217i	−0.996746	+	0.0806084i	$0.974314\pi$
$618$	4.07940e14	−	1.49579e15i	0.182037	−	0.667475i
$619$	−2.08818e15	+	1.20561e15i	−0.923567	+	0.533222i	−0.884771	−	0.466025i	$-0.845686\pi$
$619$	−2.08818e15	+	1.20561e15i	−0.923567	+	0.533222i	−0.0387958	+	0.999247i	$0.512352\pi$
$620$	1.51105e15	−	8.72405e14i	0.662406	−	0.382440i
$621$	1.89542e15	−	4.80847e14i	0.823573	−	0.208931i
$622$			2.70374e15i			1.16444i
$623$	−3.87632e15	+	3.21888e14i	−1.65476	+	0.137411i
$624$	−5.71836e12	−	2.17275e13i	−0.00241967	−	0.00919381i
$625$	9.86481e14	−	1.70863e15i	0.413760	−	0.716653i
$626$	−4.84601e14	−	8.39354e14i	−0.201477	−	0.348968i
$627$	−3.33531e14	−	3.36513e14i	−0.137456	−	0.138685i
$628$	2.27276e14	+	1.31218e14i	0.0928484	+	0.0536061i
$629$	−1.89622e15			−0.767909
$630$	−7.05849e14	+	1.46252e15i	−0.283360	+	0.587124i
$631$	−2.36463e15			−0.941028			−0.470514	−	0.882393i	$-0.655931\pi$
$631$	−2.36463e15			−0.941028			−0.470514	+	0.882393i	$0.655931\pi$
$632$	−6.02933e14	−	3.48104e14i	−0.237862	−	0.137330i
$633$	−2.31215e15	−	2.33282e15i	−0.904265	−	0.912350i
$634$	−1.22130e15	−	2.11535e15i	−0.473511	−	0.820145i
$635$	1.91559e15	−	3.31790e15i	0.736287	−	1.27529i
$636$	5.70050e14	+	2.16597e15i	0.217219	+	0.825350i
$637$	9.42834e13	+	3.52627e13i	0.0356179	+	0.0133213i
$638$		−	2.65951e13i		−	0.00996067i
$639$	1.81582e15	+	1.61636e13i	0.674247	+	0.00600184i
$640$	−1.91703e14	+	1.10680e14i	−0.0705731	+	0.0407454i
$641$	−2.28339e15	+	1.31831e15i	−0.833413	+	0.481171i	−0.855020	−	0.518595i	$-0.826455\pi$
$641$	−2.28339e15	+	1.31831e15i	−0.833413	+	0.481171i	0.0216069	+	0.999767i	$0.493122\pi$
$642$	6.65989e14	−	2.44198e15i	0.241004	−	0.883689i
$643$			2.28595e14i			0.0820173i	0.999159	+	0.0410087i	$0.0130571\pi$
$643$			2.28595e14i			0.0820173i	−0.999159	+	0.0410087i	$0.986943\pi$
$644$	−9.81272e14	+	6.80655e14i	−0.349074	+	0.242133i
$645$	−3.27166e15	+	8.61049e14i	−1.15396	+	0.303703i
$646$	−1.35093e15	+	2.33989e15i	−0.472450	+	0.818307i
$647$	7.55679e14	+	1.30888e15i	0.262038	+	0.453863i	0.966783	−	0.255597i	$-0.0822721\pi$
$647$	7.55679e14	+	1.30888e15i	0.262038	+	0.453863i	−0.704745	+	0.709460i	$0.748939\pi$
$648$	−1.83054e13	+	1.02813e15i	−0.00629384	+	0.353497i
$649$	−4.58906e14	−	2.64950e14i	−0.156451	−	0.0903270i
$650$	−1.19304e13			−0.00403302
$651$	1.65169e15	+	4.66631e15i	0.553647	+	1.56415i
$652$	2.35141e15			0.781568
$653$	−2.88975e15	−	1.66840e15i	−0.952440	−	0.549892i	−0.0586020	−	0.998281i	$-0.518664\pi$
$653$	−2.88975e15	−	1.66840e15i	−0.952440	−	0.549892i	−0.893838	+	0.448390i	$0.851998\pi$
$654$	−6.06369e14	+	6.00995e14i	−0.198180	+	0.196423i
$655$	−1.41628e15	−	2.45307e15i	−0.459009	−	0.795028i
$656$	−7.58292e13	+	1.31340e14i	−0.0243706	+	0.0422111i
$657$	2.59107e15	+	4.58157e15i	0.825790	+	1.46017i
$658$	−1.80763e14	−	8.52653e13i	−0.0571305	−	0.0269482i
$659$			8.58039e14i			0.268929i	0.990918	+	0.134464i	$0.0429314\pi$
$659$			8.58039e14i			0.268929i	−0.990918	+	0.134464i	$0.957069\pi$
$660$	3.23974e14	+	8.83558e13i	0.100697	+	0.0274627i
$661$	1.14074e15	−	6.58609e14i	0.351625	−	0.203011i	−0.313776	−	0.949497i	$-0.601594\pi$
$661$	1.14074e15	−	6.58609e14i	0.351625	−	0.203011i	0.665401	+	0.746486i	$0.268261\pi$
$662$	3.68620e15	−	2.12823e15i	1.12683	−	0.650577i
$663$	1.87515e14	+	5.11402e13i	0.0568477	+	0.0155038i
$664$			1.27817e15i			0.384293i
$665$	−2.41166e15	−	1.13757e15i	−0.719112	−	0.339202i
$666$	−5.83330e14	−	1.03145e15i	−0.172507	−	0.305029i
$667$	−9.01152e13	+	1.56084e14i	−0.0264305	+	0.0457790i
$668$	8.58133e14	+	1.48633e15i	0.249623	+	0.432359i
$669$	−1.98775e15	+	1.97014e15i	−0.573481	+	0.568399i
$670$	1.53798e15	+	8.87951e14i	0.440087	+	0.254084i
$671$	−3.67051e14			−0.104172
$672$	−2.09546e14	−	5.92003e14i	−0.0589858	−	0.166645i
$673$	−2.60116e13			−0.00726246			−0.00363123	−	0.999993i	$-0.501156\pi$
$673$	−2.60116e13			−0.00726246			−0.00363123	+	0.999993i	$0.501156\pi$
$674$	−1.82698e15	−	1.05480e15i	−0.505945	−	0.292107i
$675$	5.25492e14	+	1.48353e14i	0.144343	+	0.0407497i
$676$	9.16259e14	+	1.58701e15i	0.249638	+	0.432387i
$677$	1.94152e15	−	3.36280e15i	0.524691	−	0.908791i	−0.474896	−	0.880042i	$-0.657514\pi$
$677$	1.94152e15	−	3.36280e15i	0.524691	−	0.908791i	0.999587	−	0.0287489i	$-0.00915232\pi$
$678$	2.00443e15	−	5.27535e14i	0.537313	−	0.141413i
$679$	3.38410e15	−	2.34737e15i	0.899828	−	0.624162i
$680$		−	1.91496e15i		−	0.505082i
$681$	7.36287e14	−	2.69974e15i	0.192636	−	0.706338i
$682$	8.86449e14	−	5.11791e14i	0.230059	−	0.132825i
$683$	−4.49772e15	+	2.59676e15i	−1.15792	+	0.668525i	−0.950804	−	0.309792i	$-0.899741\pi$
$683$	−4.49772e15	+	2.59676e15i	−1.15792	+	0.668525i	−0.207115	+	0.978317i	$0.566407\pi$
$684$	−1.68837e15	−	1.50291e13i	−0.431181	−	0.00383818i
$685$		−	4.54343e15i		−	1.15103i
$686$	2.70787e15	+	7.64170e14i	0.680528	+	0.192047i
$687$	1.09859e15	+	4.17422e15i	0.273888	+	1.04067i
$688$	6.54131e14	−	1.13299e15i	0.161781	−	0.280214i
$689$	1.32277e14	+	2.29111e14i	0.0324548	+	0.0562134i
$690$	−1.60198e15	−	1.61631e15i	−0.389931	−	0.393417i
$691$	3.85121e15	+	2.22350e15i	0.929968	+	0.536918i	0.886802	−	0.462150i	$-0.152922\pi$
$691$	3.85121e15	+	2.22350e15i	0.929968	+	0.536918i	0.0431669	+	0.999068i	$0.486255\pi$
$692$	2.07854e15			0.497937
$693$	−4.14082e14	+	8.57981e14i	−0.0984133	+	0.203913i
$694$	−2.17548e15			−0.512954
$695$	2.80681e15	+	1.62051e15i	0.656593	+	0.379084i
$696$	−6.67175e13	−	6.73140e13i	−0.0154842	−	0.0156226i
$697$	−6.55993e14	−	1.13621e15i	−0.151049	−	0.261625i
$698$	−2.46819e15	+	4.27502e15i	−0.563862	+	0.976638i
$699$	−6.15683e14	−	2.33936e15i	−0.139551	−	0.530239i
$700$	−3.32326e14	+	2.75962e13i	−0.0747351	+	0.00620597i
$701$		−	4.22211e15i		−	0.942064i	−0.882116	−	0.471032i	$-0.843882\pi$
$701$		−	4.22211e15i		−	0.942064i	0.882116	−	0.471032i	$-0.156118\pi$
$702$	2.98672e13	+	1.17732e14i	0.00661212	+	0.0260639i
$703$	1.68503e15	−	9.72854e14i	0.370130	−	0.213695i
$704$	−1.12461e14	+	6.49297e13i	−0.0245106	+	0.0141512i
$705$	1.00209e14	−	3.67436e14i	0.0216704	−	0.0794587i
$706$		−	8.33616e14i		−	0.178871i
$707$	2.41244e15	−	5.11439e15i	0.513629	−	1.08890i
$708$	−1.82618e15	+	4.80623e14i	−0.385799	+	0.101536i
$709$	−7.07511e13	+	1.22545e14i	−0.0148313	+	0.0256886i	−0.873346	−	0.487101i	$-0.838054\pi$
$709$	−7.07511e13	+	1.22545e14i	−0.0148313	+	0.0256886i	0.858515	+	0.512789i	$0.171388\pi$
$710$	−1.05664e15	−	1.83015e15i	−0.219788	−	0.380685i
$711$	3.24264e15	+	1.91082e15i	0.669292	+	0.394400i
$712$	2.48230e15	+	1.43315e15i	0.508410	+	0.293530i
$713$	−6.93663e15			−1.40980
$714$	5.34162e15	+	9.90790e14i	1.07729	+	0.199821i
$715$	3.96651e13			0.00793826
$716$	−2.10447e15	−	1.21502e15i	−0.417947	−	0.241302i
$717$	1.38277e15	−	1.37052e15i	0.272519	−	0.270103i
$718$	2.02166e15	+	3.50162e15i	0.395388	+	0.684832i
$719$	−2.92451e15	+	5.06540e15i	−0.567603	+	0.983117i	0.429199	+	0.903210i	$0.358796\pi$
$719$	−2.92451e15	+	5.06540e15i	−0.567603	+	0.983117i	−0.996802	+	0.0799073i	$0.974538\pi$
$720$	1.04165e15	−	5.89097e14i	0.200629	−	0.113464i
$721$	−4.23609e14	−	5.10129e15i	−0.0809695	−	0.975071i
$722$			9.55300e14i			0.181211i
$723$	3.35525e15	+	9.15060e14i	0.631632	+	0.172262i
$724$	1.60406e15	−	9.26107e14i	0.299681	−	0.173021i
$725$	−4.35839e13	+	2.51632e13i	−0.00808104	+	0.00466559i
$726$	−3.51724e15	−	9.59240e14i	−0.647218	−	0.176513i
$727$			3.20154e15i			0.584682i	0.956314	+	0.292341i	$0.0944342\pi$
$727$			3.20154e15i			0.584682i	−0.956314	+	0.292341i	$0.905566\pi$
$728$	−4.22780e13	−	6.09505e13i	−0.00766288	−	0.0110473i
$729$	1.48431e14	−	5.55708e15i	0.0267008	−	0.999643i
$730$	3.06273e15	−	5.30481e15i	0.546806	−	0.947095i
$731$	5.65884e15	+	9.80140e15i	1.00272	+	1.73677i
$732$	−9.29029e14	+	9.20796e14i	−0.163387	+	0.161939i
$733$	5.38978e15	+	3.11179e15i	0.940805	+	0.543174i	0.890213	−	0.455545i	$-0.150556\pi$
$733$	5.38978e15	+	3.11179e15i	0.940805	+	0.543174i	0.0505924	+	0.998719i	$0.483889\pi$
$734$	3.36233e15			0.582521
$735$	−5.38205e14	+	5.33451e15i	−0.0925481	+	0.917306i
$736$	8.80033e14			0.150200
$737$	9.02245e14	+	5.20912e14i	0.152846	+	0.0882456i
$738$	4.16244e14	−	7.06360e14i	0.0699904	−	0.118773i
$739$	−3.78337e15	−	6.55299e15i	−0.631444	−	1.09369i	−0.987257	−	0.159136i	$-0.949129\pi$
$739$	−3.78337e15	−	6.55299e15i	−0.631444	−	1.09369i	0.355813	−	0.934557i	$-0.384204\pi$
$740$	−6.89516e14	+	1.19428e15i	−0.114227	+	0.197847i
$741$	−1.92869e14	+	5.07602e13i	−0.0317148	+	0.00834686i
$742$	4.21460e15	+	6.07601e15i	0.687915	+	0.991739i
$743$			2.66450e15i			0.431695i	0.976427	+	0.215848i	$0.0692514\pi$
$743$			2.66450e15i			0.431695i	−0.976427	+	0.215848i	$0.930749\pi$
$744$	9.59761e14	−	3.51915e15i	0.154352	−	0.565961i
$745$	2.17884e15	−	1.25795e15i	0.347829	−	0.200819i
$746$	5.49917e15	−	3.17494e15i	0.871432	−	0.503121i
$747$	6.15062e13	−	6.90961e15i	0.00967511	−	1.08690i
$748$		−	1.12340e15i		−	0.175419i
$749$	−6.91570e14	−	8.32819e15i	−0.107198	−	1.29092i
$750$	−1.24007e15	−	4.71177e15i	−0.190813	−	0.725016i
$751$	−3.54975e15	+	6.14835e15i	−0.542223	+	0.939158i	0.456553	+	0.889696i	$0.349084\pi$
$751$	−3.54975e15	+	6.14835e15i	−0.542223	+	0.939158i	−0.998776	+	0.0494618i	$0.984249\pi$
$752$	7.36402e13	+	1.27549e14i	0.0111665	+	0.0193409i
$753$	−2.73062e15	−	2.75503e15i	−0.411044	−	0.414719i
$754$	−9.69497e12	−	5.59739e12i	−0.00144879	−	0.000836457i
$755$	−1.46879e15			−0.217896
$756$	1.10429e15	+	3.21038e15i	0.162635	+	0.472811i
$757$	8.44083e14			0.123412			0.0617061	−	0.998094i	$-0.480346\pi$
$757$	8.44083e14			0.123412			0.0617061	+	0.998094i	$0.480346\pi$
$758$	−4.37402e15	−	2.52534e15i	−0.634892	−	0.366555i
$759$	−9.39794e14	−	9.48197e14i	−0.135426	−	0.136637i
$760$	9.82472e14	+	1.70169e15i	0.140555	+	0.243448i
$761$	8.90473e14	−	1.54234e15i	0.126475	−	0.219061i	−0.795833	−	0.605516i	$-0.792967\pi$
$761$	8.90473e14	−	1.54234e15i	0.126475	−	0.219061i	0.922309	+	0.386454i	$0.126300\pi$
$762$	−2.03854e15	−	7.74566e15i	−0.287453	−	1.09221i
$763$	−1.20251e15	+	2.54933e15i	−0.168346	+	0.356895i
$764$		−	1.08830e15i		−	0.151263i
$765$	−9.21494e13	+	1.03521e16i	−0.0127161	+	1.42853i
$766$	−4.72774e15	+	2.72956e15i	−0.647732	+	0.373968i
$767$	−1.93169e14	+	1.11526e14i	−0.0262762	+	0.0151706i
$768$	−1.21762e14	+	4.46466e14i	−0.0164447	+	0.0602978i
$769$		−	2.71335e15i		−	0.363841i	−0.983313	−	0.181920i	$-0.941769\pi$
$769$		−	2.71335e15i		−	0.363841i	0.983313	−	0.181920i	$-0.0582313\pi$
$770$	1.10489e15	−	9.17496e13i	0.147102	−	0.0122153i
$771$	1.42984e16	−	3.76311e15i	1.89011	−	0.497448i
$772$	−2.03869e15	+	3.53111e15i	−0.267581	+	0.463465i
$773$	2.63341e15	+	4.56119e15i	0.343187	+	0.594417i	0.985023	−	0.172425i	$-0.0551603\pi$
$773$	2.63341e15	+	4.56119e15i	0.343187	+	0.594417i	−0.641836	+	0.766842i	$0.721827\pi$
$774$	−3.59068e15	+	6.09333e15i	−0.464624	+	0.788459i
$775$	−1.67744e15	−	9.68471e14i	−0.215520	−	0.124431i
$776$	−3.03496e15			−0.387180
$777$	−2.97458e15	−	2.54125e15i	−0.376799	−	0.321908i
$778$	−7.28276e14			−0.0916027
$779$	1.16587e15	+	6.73114e14i	0.145611	+	0.0840684i
$780$	1.00395e14	−	9.95051e13i	0.0124506	−	0.0123403i
$781$	−6.19870e14	−	1.07365e15i	−0.0763343	−	0.132215i
$782$	−3.80655e15	+	6.59313e15i	−0.465473	+	0.806222i
$783$	3.57428e14	+	3.67102e14i	0.0434009	+	0.0445756i
$784$	−1.31866e15	−	1.60001e15i	−0.158999	−	0.192923i
$785$			1.65109e15i			0.197691i
$786$	−5.71306e15	−	1.55809e15i	−0.679273	−	0.185255i
$787$	−4.19434e15	+	2.42160e15i	−0.495225	+	0.285918i	−0.726739	−	0.686913i	$-0.758965\pi$
$787$	−4.19434e15	+	2.42160e15i	−0.495225	+	0.285918i	0.231515	+	0.972831i	$0.425632\pi$
$788$	3.94267e14	−	2.27630e14i	0.0462271	−	0.0266892i
$789$	−1.51253e14	−	4.12505e13i	−0.0176108	−	0.00480292i
$790$		−	4.38013e15i		−	0.506452i
$791$	5.62286e15	−	3.90027e15i	0.645635	−	0.447841i
$792$	6.11078e14	−	3.45590e14i	0.0696800	−	0.0394070i
$793$	−7.72520e13	+	1.33804e14i	−0.00874797	+	0.0151519i
$794$	−1.17589e15	−	2.03670e15i	−0.132237	−	0.229041i
$795$	−1.00081e16	+	9.91943e15i	−1.11772	+	1.10782i
$796$	−5.31970e15	−	3.07133e15i	−0.590018	−	0.340647i
$797$	−5.77447e15			−0.636050			−0.318025	−	0.948082i	$-0.603020\pi$
$797$	−5.77447e15			−0.636050			−0.318025	+	0.948082i	$0.603020\pi$
$798$	−5.25504e15	+	1.86008e15i	−0.574858	+	0.203477i
$799$	−1.27411e15			−0.138420
$800$	2.12813e14	+	1.22867e14i	0.0229616	+	0.0132569i
$801$	−1.33500e16	−	7.86692e15i	−1.43055	−	0.842996i
$802$	1.05434e15	+	1.82617e15i	0.112207	+	0.194348i
$803$	1.79673e15	−	3.11203e15i	0.189910	−	0.328934i
$804$	3.59042e15	−	9.44942e14i	0.376909	−	0.0991967i
$805$	−6.79536e15	−	3.20535e15i	−0.708493	−	0.334193i
$806$		−	4.30860e14i		−	0.0446163i
$807$	−2.16973e15	+	7.95574e15i	−0.223152	+	0.818232i
$808$	−3.60877e15	+	2.08352e15i	−0.368635	+	0.212832i
$809$	1.41977e16	−	8.19706e15i	1.44046	−	0.831651i	0.442581	−	0.896728i	$-0.354063\pi$
$809$	1.41977e16	−	8.19706e15i	1.44046	−	0.831651i	0.997880	+	0.0650776i	$0.0207295\pi$
$810$	−5.65939e15	+	3.13446e15i	−0.570298	+	0.315861i
$811$		−	2.49306e15i		−	0.249527i	−0.992187	−	0.124764i	$-0.960183\pi$
$811$		−	2.49306e15i		−	0.249527i	0.992187	−	0.124764i	$-0.0398172\pi$
$812$	−2.83005e14	−	1.33492e14i	−0.0281343	−	0.0132708i
$813$	3.12049e15	+	1.18566e16i	0.308123	+	1.17075i
$814$	−4.04501e14	+	7.00615e14i	−0.0396721	+	0.0687140i
$815$	7.39685e15	+	1.28117e16i	0.720576	+	1.24807i
$816$	−2.81820e15	−	2.84340e15i	−0.272695	−	0.275133i
$817$	−1.00572e16	−	5.80654e15i	−0.966622	−	0.558079i
$818$	−8.45057e15			−0.806757
$819$	2.25617e14	+	3.31526e14i	0.0213949	+	0.0314381i
$820$	−9.54147e14			−0.0898750
$821$	1.42794e16	+	8.24421e15i	1.33605	+	0.771368i	0.986219	−	0.165445i	$-0.0529060\pi$
$821$	1.42794e16	+	8.24421e15i	1.33605	+	0.771368i	0.349830	+	0.936813i	$0.386239\pi$
$822$	−6.68645e15	−	6.74623e15i	−0.621442	−	0.626998i
$823$	−1.81011e15	−	3.13520e15i	−0.167111	−	0.289445i	0.770292	−	0.637692i	$-0.220111\pi$
$823$	−1.81011e15	−	3.13520e15i	−0.167111	−	0.289445i	−0.937403	+	0.348247i	$0.886777\pi$
$824$	−1.88605e15	+	3.26673e15i	−0.172963	+	0.299581i
$825$	−9.48800e13	−	3.60507e14i	−0.00864327	−	0.0328411i
$826$	−5.12284e15	+	3.55343e15i	−0.463575	+	0.321557i
$827$			2.76850e15i			0.248865i	0.992228	+	0.124432i	$0.0397110\pi$
$827$			2.76850e15i			0.248865i	−0.992228	+	0.124432i	$0.960289\pi$
$828$	−4.75735e15	−	4.23478e13i	−0.424814	−	0.00378150i
$829$	−1.08020e16	+	6.23655e15i	−0.958198	+	0.553216i	−0.895618	−	0.444824i	$-0.853266\pi$
$829$	−1.08020e16	+	6.23655e15i	−0.958198	+	0.553216i	−0.0625798	+	0.998040i	$0.519933\pi$
$830$	−6.96412e15	+	4.02074e15i	−0.613672	+	0.354304i
$831$	8.48610e14	−	3.11159e15i	0.0742852	−	0.272381i
$832$			5.46621e13i			0.00475344i
$833$	1.76910e16	−	2.95850e15i	1.52828	−	0.255578i
$834$	6.55251e15	−	1.72452e15i	0.562334	−	0.147998i
$835$	−5.39887e15	+	9.35113e15i	−0.460286	+	0.797238i
$836$	5.76362e14	+	9.98288e14i	0.0488158	+	0.0845515i
$837$	−5.35770e15	+	1.89779e16i	−0.450804	+	1.59683i
$838$	9.59497e15	+	5.53966e15i	0.802050	+	0.463064i
$839$	6.58933e14			0.0547205			0.0273603	−	0.999626i	$-0.491290\pi$
$839$	6.58933e14			0.0547205			0.0273603	+	0.999626i	$0.491290\pi$
$840$	2.56638e15	−	3.00398e15i	0.211731	−	0.247834i
$841$	1.21533e16			0.996129
$842$	4.22706e15	+	2.44049e15i	0.344209	+	0.198729i
$843$	1.61442e16	−	1.60011e16i	1.30606	−	1.29449i
$844$	3.99554e15	+	6.92048e15i	0.321138	+	0.556228i
$845$	−5.76457e15	+	9.98453e15i	−0.460315	+	0.797289i
$846$	−3.91953e14	−	6.93056e14i	−0.0310954	−	0.0549834i
$847$	−1.19953e16	+	9.96085e14i	−0.945480	+	0.0785123i
$848$		−	5.44914e15i		−	0.426728i
$849$	−7.82361e15	−	2.13369e15i	−0.608716	−	0.166012i
$850$	−1.84102e15	+	1.06292e15i	−0.142317	+	0.0821665i
$851$	4.74794e15	−	2.74123e15i	0.364664	−	0.210539i
$852$	−4.26231e15	−	1.16244e15i	−0.325258	−	0.0887059i
$853$			4.28445e15i			0.324844i	0.986721	+	0.162422i	$0.0519306\pi$
$853$			4.28445e15i			0.324844i	−0.986721	+	0.162422i	$0.948069\pi$
$854$	−1.84239e15	+	3.90588e15i	−0.138791	+	0.294239i
$855$	−5.22924e15	−	9.24643e15i	−0.391404	−	0.692086i
$856$	−3.07910e15	+	5.33316e15i	−0.228991	+	0.396624i
$857$	3.17413e15	+	5.49776e15i	0.234547	+	0.406248i	0.959141	−	0.282928i	$-0.0913059\pi$
$857$	3.17413e15	+	5.49776e15i	0.234547	+	0.406248i	−0.724594	+	0.689176i	$0.757973\pi$
$858$	5.88960e13	−	5.83741e13i	0.00432420	−	0.00428588i
$859$	−6.45134e15	−	3.72468e15i	−0.470638	−	0.271723i	0.245869	−	0.969303i	$-0.420927\pi$
$859$	−6.45134e15	−	3.72468e15i	−0.470638	−	0.271723i	−0.716507	+	0.697580i	$0.754260\pi$
$860$	8.23083e15			0.596626
$861$	4.93669e14	−	2.66151e15i	0.0355565	−	0.191695i
$862$	1.30491e16			0.933882
$863$	−2.11534e16	−	1.22129e16i	−1.50425	−	0.868479i	−0.999988	−	0.00492813i	$-0.998431\pi$
$863$	−2.11534e16	−	1.22129e16i	−1.50425	−	0.868479i	−0.504262	−	0.863551i	$-0.668235\pi$
$864$	6.79717e14	−	2.40768e15i	0.0480289	−	0.170127i
$865$	6.53847e15	+	1.13250e16i	0.459079	+	0.795148i
$866$	7.74594e15	−	1.34164e16i	0.540413	−	0.936022i
$867$	1.95430e16	−	5.14341e15i	1.35483	−	0.356571i
$868$	−9.96625e14	−	1.20018e16i	−0.0686552	−	0.826777i
$869$		−	2.56958e15i		−	0.175895i
$870$	1.56888e14	−	5.75262e14i	0.0106717	−	0.0391300i
$871$	3.79785e14	−	2.19269e14i	0.0256707	−	0.0148210i
$872$	1.79883e15	−	1.03856e15i	0.120823	−	0.0697573i
$873$	1.64066e16	+	1.46044e14i	1.09507	+	0.00974780i
$874$		−	7.81180e15i		−	0.518129i
$875$	−9.16829e15	−	1.32176e16i	−0.604288	−	0.871178i
$876$	−3.25930e15	−	1.23841e16i	−0.213478	−	0.811132i
$877$	1.30164e16	−	2.25451e16i	0.847215	−	1.46742i	−0.0364695	−	0.999335i	$-0.511611\pi$
$877$	1.30164e16	−	2.25451e16i	0.847215	−	1.46742i	0.883684	−	0.468084i	$-0.155055\pi$
$878$	2.92539e15	+	5.06693e15i	0.189219	+	0.327736i
$879$	−2.00297e16	−	2.02088e16i	−1.28747	−	1.29898i
$880$	−7.07542e14	−	4.08500e14i	−0.0451957	−	0.0260938i
$881$	−1.18729e15			−0.0753684			−0.0376842	−	0.999290i	$-0.511998\pi$
$881$	−1.18729e15			−0.0753684			−0.0376842	+	0.999290i	$0.511998\pi$
$882$	7.05152e15	+	8.71292e15i	0.444842	+	0.549651i
$883$	2.34944e16			1.47293			0.736463	−	0.676477i	$-0.236494\pi$
$883$	2.34944e16			1.47293			0.736463	+	0.676477i	$0.236494\pi$
$884$	−4.09524e14	−	2.36439e14i	−0.0255148	−	0.0147310i
$885$	−8.36332e15	−	8.43810e15i	−0.517834	−	0.522464i
$886$	3.73761e15	+	6.47372e15i	0.229989	+	0.398353i
$887$	1.19962e16	−	2.07780e16i	0.733606	−	1.27064i	−0.221726	−	0.975109i	$-0.571169\pi$
$887$	1.19962e16	−	2.07780e16i	0.733606	−	1.27064i	0.955332	−	0.295534i	$-0.0954976\pi$
$888$	7.33771e14	+	2.78804e15i	0.0445953	+	0.169445i
$889$	−1.50717e16	−	2.17283e16i	−0.910338	−	1.31240i
$890$			1.80331e16i			1.08250i
$891$	−3.32005e15	+	1.83882e15i	−0.198069	+	0.109701i
$892$	5.89681e15	−	3.40452e15i	0.349631	−	0.201860i
$893$	1.13221e15	−	6.53683e14i	0.0667182	−	0.0385198i
$894$	1.38392e15	−	5.07440e15i	0.0810501	−	0.297186i
$895$		−	1.52883e16i		−	0.889885i
$896$	1.26439e14	+	1.52264e15i	0.00731456	+	0.0880852i
$897$	−5.43450e14	+	1.43028e14i	−0.0312465	+	0.00822360i
$898$	5.91284e15	−	1.02413e16i	0.337891	−	0.585244i
$899$	−9.08759e14	−	1.57402e15i	−0.0516144	−	0.0893987i
$900$	−1.14453e15	−	6.74448e14i	−0.0646089	−	0.0380728i
$901$	4.08245e16	+	2.35700e16i	2.29052	+	1.32243i
$902$	−5.59745e14			−0.0312143
$903$	−4.25858e15	+	2.29592e16i	−0.236038	+	1.27255i
$904$	−5.04274e15			−0.277805
$905$	1.00918e16	+	5.82653e15i	0.552590	+	0.319038i
$906$	−2.18090e15	+	2.16157e15i	−0.118695	+	0.117643i
$907$	9.48785e15	+	1.64334e16i	0.513249	+	0.888973i	0.999882	+	0.0153664i	$0.00489149\pi$
$907$	9.48785e15	+	1.64334e16i	0.513249	+	0.888973i	−0.486633	+	0.873606i	$0.661775\pi$
$908$	−3.40411e15	+	5.89609e15i	−0.183034	+	0.317024i
$909$	1.96088e16	−	1.10896e16i	1.04797	−	0.592674i
$910$	1.99096e14	−	4.22085e14i	0.0105763	−	0.0224219i
$911$			3.72765e16i			1.96827i	0.177427	+	0.984134i	$0.443223\pi$
$911$			3.72765e16i			1.96827i	−0.177427	+	0.984134i	$0.556777\pi$
$912$	3.96315e15	+	1.08085e15i	0.208002	+	0.0567275i
$913$	−4.08546e15	+	2.35874e15i	−0.213133	+	0.123053i
$914$	2.15158e16	−	1.24221e16i	1.11571	−	0.644158i
$915$	−7.93944e15	−	2.16528e15i	−0.409236	−	0.111609i
$916$		−	1.05015e16i		−	0.538054i
$917$	−1.94840e16	+	1.61794e15i	−0.992307	+	0.0824008i
$918$	1.50981e16	+	1.55067e16i	0.764340	+	0.785028i
$919$	−1.21826e16	+	2.11010e16i	−0.613064	+	1.06186i	0.377656	+	0.925946i	$0.376730\pi$
$919$	−1.21826e16	+	2.11010e16i	−0.613064	+	1.06186i	−0.990721	+	0.135913i	$0.956603\pi$
$920$	2.76833e15	+	4.79488e15i	0.138479	+	0.239853i
$921$	−2.24898e16	+	2.22905e16i	−1.11830	+	1.10839i
$922$	−2.08109e15	−	1.20152e15i	−0.102866	−	0.0593894i
$923$	−5.21848e14			−0.0256410
$924$	1.50555e15	−	1.76227e15i	0.0735359	−	0.0860749i
$925$	1.53089e15			0.0743298
$926$	−1.24428e16	−	7.18386e15i	−0.600563	−	0.346735i
$927$	1.03530e16	−	1.75688e16i	0.496737	−	0.842955i
$928$	1.15292e14	+	1.99692e14i	0.00549902	+	0.00952458i
$929$	−1.53945e16	+	2.66641e16i	−0.729927	+	1.26427i	0.226987	+	0.973898i	$0.427113\pi$
$929$	−1.53945e16	+	2.66641e16i	−0.729927	+	1.26427i	−0.956914	+	0.290373i	$0.906221\pi$
$930$	2.21933e16	−	5.84094e15i	1.04608	−	0.275313i
$931$	−1.42028e16	+	1.17054e16i	−0.665506	+	0.548481i
$932$			5.88535e15i			0.274148i
$933$	−9.35681e15	+	3.43086e16i	−0.433290	+	1.58874i
$934$	−8.38307e15	+	4.83997e15i	−0.385918	+	0.222810i
$935$	6.12089e15	−	3.53390e15i	0.280124	−	0.161730i
$936$	2.63038e12	−	2.95497e14i	0.000119674	−	0.0134442i
$937$		−	3.06873e16i		−	1.38801i	−0.719972	−	0.694003i	$-0.755846\pi$
$937$		−	3.06873e16i		−	1.38801i	0.719972	−	0.694003i	$-0.244154\pi$
$938$	1.00719e16	−	6.98633e15i	0.452893	−	0.314147i
$939$	−3.24451e15	−	1.23279e16i	−0.145040	−	0.551096i
$940$	−4.63301e14	+	8.02461e14i	−0.0205902	+	0.0356632i
$941$	1.88681e15	+	3.26805e15i	0.0833651	+	0.144393i	0.904693	−	0.426063i	$-0.140100\pi$
$941$	1.88681e15	+	3.26805e15i	0.0833651	+	0.144393i	−0.821328	+	0.570456i	$0.806767\pi$
$942$	2.42987e15	+	2.45159e15i	0.106734	+	0.107688i
$943$	3.28508e15	+	1.89664e15i	0.143460	+	0.0828269i
$944$	4.59431e15			0.199468
$945$	−1.40181e16	+	1.61157e16i	−0.605082	+	0.695623i
$946$	4.82857e15			0.207213
$947$	−2.35239e16	−	1.35815e16i	−1.00365	−	0.579460i	−0.0943272	−	0.995541i	$-0.530070\pi$
$947$	−2.35239e16	−	1.35815e16i	−1.00365	−	0.579460i	−0.909328	+	0.416081i	$0.863403\pi$
$948$	−6.44613e15	−	6.50376e15i	−0.273434	−	0.275879i
$949$	−7.56305e14	−	1.30996e15i	−0.0318958	−	0.0552451i
$950$	1.09066e15	−	1.88908e15i	0.0457308	−	0.0792081i
$951$	−8.17684e15	−	3.10688e16i	−0.340873	−	1.29519i
$952$	−1.19544e16	−	5.63884e15i	−0.495478	−	0.233715i
$953$			1.96766e16i			0.810846i	0.914129	+	0.405423i	$0.132876\pi$
$953$			1.96766e16i			0.810846i	−0.914129	+	0.405423i	$0.867124\pi$
$954$	−2.62217e14	+	2.94574e16i	−0.0107435	+	1.20692i
$955$	5.92961e15	−	3.42346e15i	0.241550	−	0.139459i
$956$	−4.10210e15	+	2.36835e15i	−0.166145	+	0.0959239i
$957$	9.20377e13	−	3.37474e14i	0.00370638	−	0.0135902i
$958$			2.51113e16i			1.00545i
$959$	−2.83629e16	−	1.33787e16i	−1.12914	−	0.532611i
$960$	−2.81561e15	+	7.41025e14i	−0.111450	+	0.0293320i
$961$	2.22717e16	−	3.85757e16i	0.876546	−	1.51822i
$962$	1.70268e14	+	2.94912e14i	0.00666300	+	0.0115406i
$963$	1.69019e16	−	2.86823e16i	0.657644	−	1.11601i
$964$	−7.32769e15	−	4.23064e15i	−0.283494	−	0.163675i
$965$	−2.56525e16			−0.986800
$966$	−1.48072e16	+	5.24116e15i	−0.566368	+	0.200472i
$967$	1.37805e16			0.524108			0.262054	−	0.965053i	$-0.415600\pi$
$967$	1.37805e16			0.524108			0.262054	+	0.965053i	$0.415600\pi$
$968$	7.68148e15	+	4.43490e15i	0.290489	+	0.167714i
$969$	−2.52401e16	+	2.50164e16i	−0.949095	+	0.940684i
$970$	−9.54709e15	−	1.65361e16i	−0.356966	−	0.618283i
$971$	−3.05209e15	+	5.28637e15i	−0.113473	+	0.196541i	−0.917168	−	0.398500i	$-0.869531\pi$
$971$	−3.05209e15	+	5.28637e15i	−0.113473	+	0.196541i	0.803695	+	0.595041i	$0.202864\pi$
$972$	−3.79033e15	+	1.29829e16i	−0.140124	+	0.479964i
$973$	1.83812e16	−	1.27500e16i	0.675700	−	0.468696i
$974$		−	2.38514e16i		−	0.871847i
$975$	−1.51388e14	−	4.12873e13i	−0.00550258	−	0.00150069i
$976$	2.75603e15	−	1.59119e15i	0.0996116	−	0.0575108i
$977$	2.74613e16	−	1.58548e16i	0.986962	−	0.569823i	0.0825975	−	0.996583i	$-0.473678\pi$
$977$	2.74613e16	−	1.58548e16i	0.986962	−	0.569823i	0.904365	+	0.426760i	$0.140345\pi$
$978$	2.98378e16	+	8.13751e15i	1.06636	+	0.290822i
$979$			1.05790e16i			0.375960i
$980$	4.56958e15	−	1.22179e16i	0.161485	−	0.431771i
$981$	−9.77426e15	+	5.52776e15i	−0.343482	+	0.194254i
$982$	6.96802e14	−	1.20690e15i	0.0243499	−	0.0421752i
$983$	−3.61149e15	−	6.25528e15i	−0.125499	−	0.217371i	0.796429	−	0.604733i	$-0.206720\pi$
$983$	−3.61149e15	−	6.25528e15i	−0.125499	−	0.217371i	−0.921928	+	0.387361i	$0.873387\pi$
$984$	−1.41675e15	+	1.40419e15i	−0.0489576	+	0.0485237i
$985$	2.48050e15	+	1.43212e15i	0.0852393	+	0.0492130i
$986$	−1.99476e15			−0.0681661
$987$	−1.99868e15	−	1.70753e15i	−0.0679204	−	0.0580260i
$988$	4.85220e14			0.0163974
$989$	−2.83384e16	−	1.63612e16i	−0.952347	−	0.549838i
$990$	3.80523e15	+	2.24235e15i	0.127171	+	0.0749393i
$991$	1.35586e16	+	2.34841e16i	0.450618	+	0.780494i	0.998425	−	0.0561115i	$-0.0178702\pi$
$991$	1.35586e16	+	2.34841e16i	0.450618	+	0.780494i	−0.547806	+	0.836605i	$0.684537\pi$
$992$	−4.43731e15	+	7.68564e15i	−0.146658	+	0.254019i
$993$	5.41405e16	−	1.42489e16i	1.77951	−	0.468340i
$994$	−1.45363e16	+	1.20709e15i	−0.475148	+	0.0394561i
$995$		−	3.86460e16i		−	1.25625i
$996$	−4.42334e15	+	1.62190e16i	−0.142996	+	0.524323i
$997$	−2.99627e16	+	1.72990e16i	−0.963290	+	0.556156i	−0.897184	−	0.441657i	$-0.854391\pi$
$997$	−2.99627e16	+	1.72990e16i	−0.963290	+	0.556156i	−0.0661060	+	0.997813i	$0.521058\pi$
$998$	2.37340e16	−	1.37029e16i	0.758846	−	0.438120i
$999$	−3.83252e15	−	1.51072e16i	−0.121864	−	0.480366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.4	✓	60
3.2	odd	2	inner	42.12.f.a.5.24	yes	60
7.3	odd	6	inner	42.12.f.a.17.24	yes	60
21.17	even	6	inner	42.12.f.a.17.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.4	✓	60	1.1	even	1	trivial
42.12.f.a.5.24	yes	60	3.2	odd	2	inner
42.12.f.a.17.4	yes	60	21.17	even	6	inner
42.12.f.a.17.24	yes	60	7.3	odd	6	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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	42.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-27.7128 - 16.0000i) q^{2} +(-296.285 - 298.935i) q^{3} +(512.000 + 886.810i) q^{4} +(-3221.21 + 5579.29i) q^{5} +(3427.95 + 13024.9i) q^{6} +(25344.2 + 36537.6i) q^{7} -32768.0i q^{8} +(-1576.82 + 177140. i) q^{9} +(178537. - 103079. i) q^{10} +(104738. - 60470.5i) q^{11} +(113400. - 415803. i) q^{12} -50908.1i q^{13} +(-117756. - 1.41807e6i) q^{14} +(2.62224e6 - 690133. i) q^{15} +(-524288. + 908093. i) q^{16} +(-4.53557e6 - 7.85584e6i) q^{17} +(2.87794e6 - 4.88382e6i) q^{18} +(8.06088e6 + 4.65395e6i) q^{19} -6.59703e6 q^{20} +(3.41326e6 - 1.84018e7i) q^{21} -3.87011e6 q^{22} +(2.27133e7 + 1.31135e7i) q^{23} +(-9.79549e6 + 9.70868e6i) q^{24} +(3.66173e6 + 6.34231e6i) q^{25} +(-814529. + 1.41081e6i) q^{26} +(5.34205e7 - 5.20126e7i) q^{27} +(-1.94257e7 + 4.11827e7i) q^{28} +6.87194e6i q^{29} +(-8.37118e7 - 2.28303e7i) q^{30} +(-2.29050e8 + 1.32242e8i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(-4.91090e7 - 1.33933e7i) q^{33} +2.90277e8i q^{34} +(-2.85493e8 + 2.37072e7i) q^{35} +(-1.57897e8 + 8.92973e7i) q^{36} +(1.04519e8 - 1.81032e8i) q^{37} +(-1.48927e8 - 2.57948e8i) q^{38} +(-1.52182e7 + 1.50833e7i) q^{39} +(1.82822e8 + 1.05552e8i) q^{40} +1.44633e8 q^{41} +(-3.89020e8 + 4.55354e8i) q^{42} -1.24766e9 q^{43} +(1.07252e8 + 6.19217e7i) q^{44} +(-9.83236e8 - 5.79402e8i) q^{45} +(-4.19632e8 - 7.26824e8i) q^{46} +(7.02288e7 - 1.21640e8i) q^{47} +(4.26800e8 - 1.12327e8i) q^{48} +(-6.92673e8 + 1.85203e9i) q^{49} -2.34351e8i q^{50} +(-1.00456e9 + 3.68341e9i) q^{51} +(4.51458e7 - 2.60649e7i) q^{52} +(-4.50048e9 + 2.59835e9i) q^{53} +(-2.31263e9 + 5.86689e8i) q^{54} +7.79151e8i q^{55} +(1.19727e9 - 8.30478e8i) q^{56} +(-9.97095e8 - 3.78858e9i) q^{57} +(1.09951e8 - 1.90441e8i) q^{58} +(-2.19074e9 - 3.79447e9i) q^{59} +(1.95460e9 + 1.97208e9i) q^{60} +(-2.62835e9 - 1.51748e9i) q^{61} +8.46349e9 q^{62} +(-6.51224e9 + 4.43185e9i) q^{63} -1.07374e9 q^{64} +(2.84031e8 + 1.63985e8i) q^{65} +(1.14666e9 + 1.15691e9i) q^{66} +(4.30716e9 + 7.46022e9i) q^{67} +(4.64443e9 - 8.04439e9i) q^{68} +(-2.80953e9 - 1.06751e10i) q^{69} +(8.29113e9 + 3.91089e9i) q^{70} -1.02508e10i q^{71} +(5.80452e9 + 5.16692e7i) q^{72} +(2.57319e10 - 1.48563e10i) q^{73} +(-5.79304e9 + 3.34461e9i) q^{74} +(8.11017e8 - 2.97375e9i) q^{75} +9.53130e9i q^{76} +(4.86394e9 + 2.29430e9i) q^{77} +(6.63072e8 - 1.74510e8i) q^{78} +(1.06233e10 - 1.84001e10i) q^{79} +(-3.37768e9 - 5.85031e9i) q^{80} +(-3.13761e10 - 5.58636e8i) q^{81} +(-4.00818e9 - 2.31412e9i) q^{82} -3.90065e10 q^{83} +(1.80665e10 - 6.39482e9i) q^{84} +5.84401e10 q^{85} +(3.45761e10 + 1.99625e10i) q^{86} +(2.05426e9 - 2.03606e9i) q^{87} +(-1.98150e9 - 3.43205e9i) q^{88} +(-4.37364e10 + 7.57537e10i) q^{89} +(1.79778e10 + 3.17886e10i) q^{90} +(1.86006e9 - 1.29022e9i) q^{91} +2.68565e10i q^{92} +(1.07396e11 + 2.92896e10i) q^{93} +(-3.89247e9 + 2.24732e9i) q^{94} +(-5.19315e10 + 2.99827e10i) q^{95} +(-1.36250e10 - 3.71589e9i) q^{96} -9.26196e10i q^{97} +(4.88284e10 - 4.02423e10i) q^{98} +(1.05466e10 + 1.86486e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) \) 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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