LMFDB - Embedded newform 42.12.f.a.5.6

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			5.6
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.6

$q$-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} +(-131.210 + 399.914i) q^{3} +(512.000 + 886.810i) q^{4} +(6258.52 - 10840.1i) q^{5} +(10034.8 - 8983.37i) q^{6} +(-41292.3 + 16500.6i) q^{7} -32768.0i q^{8} +(-142715. - 104945. i) q^{9} +(-346882. + 200273. i) q^{10} +(435052. - 251177. i) q^{11} +(-421827. + 88397.5i) q^{12} +563130. i q^{13} +(1.40834e6 + 203398. i) q^{14} +(3.51391e6 + 3.92519e6i) q^{15} +(-524288. + 908093. i) q^{16} +(-329541. - 570781. i) q^{17} +(2.27591e6 + 5.19177e6i) q^{18} +(6.21252e6 + 3.58680e6i) q^{19} +1.28174e7 q^{20} +(-1.18087e6 - 1.86784e7i) q^{21} -1.60754e7 q^{22} +(-8.20976e6 - 4.73991e6i) q^{23} +(1.31044e7 + 4.29949e6i) q^{24} +(-5.39240e7 - 9.33991e7i) q^{25} +(9.01008e6 - 1.56059e7i) q^{26} +(6.06947e7 - 4.33038e7i) q^{27} +(-3.57746e7 - 2.81701e7i) q^{28} +1.28782e8i q^{29} +(-3.45773e7 - 1.65001e8i) q^{30} +(-1.63510e8 + 9.44024e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(4.33661e7 + 2.06940e8i) q^{33} +2.10906e7i q^{34} +(-7.95606e7 + 5.50881e8i) q^{35} +(1.99965e7 - 1.80293e8i) q^{36} +(7.10853e7 - 1.23123e8i) q^{37} +(-1.14778e8 - 1.98801e8i) q^{38} +(-2.25203e8 - 7.38882e7i) q^{39} +(-3.55207e8 - 2.05079e8i) q^{40} -1.33125e9 q^{41} +(-2.66129e8 + 5.36525e8i) q^{42} -8.00252e8 q^{43} +(4.45493e8 + 2.57206e8i) q^{44} +(-2.03080e9 + 8.90237e8i) q^{45} +(1.51677e8 + 2.62712e8i) q^{46} +(8.34818e8 - 1.44595e9i) q^{47} +(-2.94367e8 - 3.28821e8i) q^{48} +(1.43278e9 - 1.36270e9i) q^{49} +3.45113e9i q^{50} +(2.71502e8 - 5.68957e7i) q^{51} +(-4.99389e8 + 2.88323e8i) q^{52} +(-5.10052e9 + 2.94479e9i) q^{53} +(-2.37488e9 + 2.28954e8i) q^{54} -6.28799e9i q^{55} +(5.40693e8 + 1.35307e9i) q^{56} +(-2.24956e9 + 2.01385e9i) q^{57} +(2.06051e9 - 3.56890e9i) q^{58} +(-3.40089e9 - 5.89051e9i) q^{59} +(-1.68178e9 + 5.12587e9i) q^{60} +(-7.55358e9 - 4.36106e9i) q^{61} +6.04176e9 q^{62} +(7.62469e9 + 1.97855e9i) q^{63} -1.07374e9 q^{64} +(6.10437e9 + 3.52436e9i) q^{65} +(2.10925e9 - 6.42875e9i) q^{66} +(3.88865e9 + 6.73534e9i) q^{67} +(3.37450e8 - 5.84480e8i) q^{68} +(2.97276e9 - 2.66127e9i) q^{69} +(1.10189e10 - 1.39935e10i) q^{70} -1.50248e10i q^{71} +(-3.43885e9 + 4.67648e9i) q^{72} +(-2.86914e10 + 1.65650e10i) q^{73} +(-3.93995e9 + 2.27473e9i) q^{74} +(4.44269e10 - 9.31005e9i) q^{75} +7.34577e9i q^{76} +(-1.38197e10 + 1.75503e10i) q^{77} +(5.05881e9 + 5.65090e9i) q^{78} +(4.77500e8 - 8.27054e8i) q^{79} +(6.56253e9 + 1.13666e10i) q^{80} +(9.35402e9 + 2.99545e10i) q^{81} +(3.68927e10 + 2.13000e10i) q^{82} -1.04978e10 q^{83} +(1.59596e10 - 1.06106e10i) q^{84} -8.24975e9 q^{85} +(2.21772e10 + 1.28040e10i) q^{86} +(-5.15016e10 - 1.68974e10i) q^{87} +(-8.23058e9 - 1.42558e10i) q^{88} +(1.87137e10 - 3.24132e10i) q^{89} +(7.05229e10 + 7.82178e9i) q^{90} +(-9.29200e9 - 2.32529e10i) q^{91} -9.70733e9i q^{92} +(-1.62987e10 - 7.77764e10i) q^{93} +(-4.62703e10 + 2.67142e10i) q^{94} +(7.77623e10 - 4.48961e10i) q^{95} +(2.89661e9 + 1.38224e10i) q^{96} +2.70123e10i q^{97} +(-6.15097e10 + 1.48397e10i) q^{98} +(-8.84483e10 - 9.80991e9i) 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
$3$	−131.210	+	399.914i	−0.311745	+	0.950166i
$3$	−131.210	+	399.914i	−0.311745	+	0.950166i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	6258.52	−	10840.1i	0.895646	−	1.55130i	0.0626426	−	0.998036i	$-0.480047\pi$
$5$	6258.52	−	10840.1i	0.895646	−	1.55130i	0.833003	−	0.553268i	$-0.186620\pi$
$6$	10034.8	−	8983.37i	0.526839	−	0.471637i
$7$	−41292.3	+	16500.6i	−0.928603	+	0.371075i
$7$	−41292.3	+	16500.6i	−0.928603	+	0.371075i
$8$		−	32768.0i		−	0.353553i
$9$	−142715.	−	104945.i	−0.805630	−	0.592419i
$10$	−346882.	+	200273.i	−1.09694	+	0.633317i
$11$	435052.	−	251177.i	0.814482	−	0.470241i	−0.0340281	−	0.999421i	$-0.510834\pi$
$11$	435052.	−	251177.i	0.814482	−	0.470241i	0.848510	+	0.529180i	$0.177500\pi$
$12$	−421827.	+	88397.5i	−0.489370	+	0.102552i
$13$			563130.i			0.420649i	0.977632	+	0.210325i	$0.0674521\pi$
$13$			563130.i			0.420649i	−0.977632	+	0.210325i	$0.932548\pi$
$14$	1.40834e6	+	203398.i	0.699846	+	0.101075i
$15$	3.51391e6	+	3.92519e6i	1.19478	+	1.33462i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−329541.	−	570781.i	−0.0562912	−	0.0974991i	0.836507	−	0.547957i	$-0.184594\pi$
$17$	−329541.	−	570781.i	−0.0562912	−	0.0974991i	−0.892798	+	0.450458i	$0.851261\pi$
$18$	2.27591e6	+	5.19177e6i	0.283894	+	0.647614i
$19$	6.21252e6	+	3.58680e6i	0.575603	+	0.332325i	0.759384	−	0.650643i	$-0.225500\pi$
$19$	6.21252e6	+	3.58680e6i	0.575603	+	0.332325i	−0.183781	+	0.982967i	$0.558834\pi$
$20$	1.28174e7			0.895646
$21$	−1.18087e6	−	1.86784e7i	−0.0630950	−	0.998008i
$22$	−1.60754e7			−0.665022
$23$	−8.20976e6	−	4.73991e6i	−0.265967	−	0.153556i	0.361087	−	0.932532i	$-0.382406\pi$
$23$	−8.20976e6	−	4.73991e6i	−0.265967	−	0.153556i	−0.627053	+	0.778976i	$0.715739\pi$
$24$	1.31044e7	+	4.29949e6i	0.335934	+	0.110219i
$25$	−5.39240e7	−	9.33991e7i	−1.10436	−	1.91281i
$26$	9.01008e6	−	1.56059e7i	0.148722	−	0.257594i
$27$	6.06947e7	−	4.33038e7i	0.814048	−	0.580798i
$28$	−3.57746e7	−	2.81701e7i	−0.392831	−	0.309328i
$29$			1.28782e8i			1.16591i	0.812504	+	0.582955i	$0.198104\pi$
$29$			1.28782e8i			1.16591i	−0.812504	+	0.582955i	$0.801896\pi$
$30$	−3.45773e7	−	1.65001e8i	−0.259791	−	1.23971i
$31$	−1.63510e8	+	9.44024e7i	−1.02578	+	0.592235i	−0.915773	−	0.401696i	$-0.868421\pi$
$31$	−1.63510e8	+	9.44024e7i	−1.02578	+	0.592235i	−0.110008	+	0.993931i	$0.535088\pi$
$32$	2.90590e7	−	1.67772e7i	0.153093	−	0.0883883i
$33$	4.33661e7	+	2.06940e8i	0.192896	+	0.920488i
$34$			2.10906e7i			0.0796077i
$35$	−7.95606e7	+	5.50881e8i	−0.256049	+	1.77290i
$36$	1.99965e7	−	1.80293e8i	0.0551177	−	0.496953i
$37$	7.10853e7	−	1.23123e8i	0.168527	−	0.291898i	−0.769375	−	0.638797i	$-0.779432\pi$
$37$	7.10853e7	−	1.23123e8i	0.168527	−	0.291898i	0.937902	+	0.346899i	$0.112765\pi$
$38$	−1.14778e8	−	1.98801e8i	−0.234989	−	0.407013i
$39$	−2.25203e8	−	7.38882e7i	−0.399687	−	0.131135i
$40$	−3.55207e8	−	2.05079e8i	−0.548469	−	0.316659i
$41$	−1.33125e9			−1.79452			−0.897261	−	0.441500i	$-0.854447\pi$
$41$	−1.33125e9			−1.79452			−0.897261	+	0.441500i	$0.854447\pi$
$42$	−2.66129e8	+	5.36525e8i	−0.314211	+	0.633460i
$43$	−8.00252e8			−0.830138			−0.415069	−	0.909790i	$-0.636243\pi$
$43$	−8.00252e8			−0.830138			−0.415069	+	0.909790i	$0.636243\pi$
$44$	4.45493e8	+	2.57206e8i	0.407241	+	0.235121i
$45$	−2.03080e9	+	8.90237e8i	−1.64058	+	0.719179i
$46$	1.51677e8	+	2.62712e8i	0.108580	+	0.188067i
$47$	8.34818e8	−	1.44595e9i	0.530950	−	0.919633i	−0.468397	−	0.883518i	$-0.655168\pi$
$47$	8.34818e8	−	1.44595e9i	0.530950	−	0.919633i	0.999348	−	0.0361148i	$-0.0114982\pi$
$48$	−2.94367e8	−	3.28821e8i	−0.166749	−	0.186266i
$49$	1.43278e9	−	1.36270e9i	0.724607	−	0.689162i
$50$			3.45113e9i			1.56181i
$51$	2.71502e8	−	5.68957e7i	0.110189	−	0.0230910i
$52$	−4.99389e8	+	2.88323e8i	−0.182146	+	0.105162i
$53$	−5.10052e9	+	2.94479e9i	−1.67532	+	0.967246i	−0.710739	+	0.703456i	$0.751639\pi$
$53$	−5.10052e9	+	2.94479e9i	−1.67532	+	0.967246i	−0.964580	+	0.263790i	$0.915028\pi$
$54$	−2.37488e9	+	2.28954e8i	−0.703843	+	0.0678552i
$55$		−	6.28799e9i		−	1.68468i
$56$	5.40693e8	+	1.35307e9i	0.131195	+	0.328311i
$57$	−2.24956e9	+	2.01385e9i	−0.495205	+	0.443318i
$58$	2.06051e9	−	3.56890e9i	0.412212	−	0.713972i
$59$	−3.40089e9	−	5.89051e9i	−0.619307	−	1.07267i	−0.989612	−	0.143762i	$-0.954080\pi$
$59$	−3.40089e9	−	5.89051e9i	−0.619307	−	1.07267i	0.370305	−	0.928910i	$-0.379253\pi$
$60$	−1.68178e9	+	5.12587e9i	−0.279213	+	0.851012i
$61$	−7.55358e9	−	4.36106e9i	−1.14509	−	0.661117i	−0.197402	−	0.980323i	$-0.563250\pi$
$61$	−7.55358e9	−	4.36106e9i	−1.14509	−	0.661117i	−0.947685	+	0.319206i	$0.896584\pi$
$62$	6.04176e9			0.837546
$63$	7.62469e9	+	1.97855e9i	0.967942	+	0.251173i
$64$	−1.07374e9			−0.125000
$65$	6.10437e9	+	3.52436e9i	0.652555	+	0.376753i
$66$	2.10925e9	−	6.42875e9i	0.207317	−	0.631881i
$67$	3.88865e9	+	6.73534e9i	0.351874	+	0.609464i	0.986578	−	0.163291i	$-0.0522111\pi$
$67$	3.88865e9	+	6.73534e9i	0.351874	+	0.609464i	−0.634703	+	0.772756i	$0.718878\pi$
$68$	3.37450e8	−	5.84480e8i	0.0281456	−	0.0487496i
$69$	2.97276e9	−	2.66127e9i	0.228818	−	0.204842i
$70$	1.10189e10	−	1.39935e10i	0.783611	−	0.995146i
$71$		−	1.50248e10i		−	0.988299i	−0.869377	−	0.494149i	$-0.835480\pi$
$71$		−	1.50248e10i		−	0.988299i	0.869377	−	0.494149i	$-0.164520\pi$
$72$	−3.43885e9	+	4.67648e9i	−0.209452	+	0.284833i
$73$	−2.86914e10	+	1.65650e10i	−1.61985	+	0.935222i	−0.632895	+	0.774238i	$0.718133\pi$
$73$	−2.86914e10	+	1.65650e10i	−1.61985	+	0.935222i	−0.986957	+	0.160984i	$0.948533\pi$
$74$	−3.93995e9	+	2.27473e9i	−0.206403	+	0.119167i
$75$	4.44269e10	−	9.31005e9i	2.16177	−	0.453018i
$76$			7.34577e9i			0.332325i
$77$	−1.38197e10	+	1.75503e10i	−0.581835	+	0.738901i
$78$	5.05881e9	+	5.65090e9i	0.198394	+	0.221614i
$79$	4.77500e8	−	8.27054e8i	0.0174592	−	0.0302402i	−0.857164	−	0.515044i	$-0.827776\pi$
$79$	4.77500e8	−	8.27054e8i	0.0174592	−	0.0302402i	0.874623	+	0.484804i	$0.161109\pi$
$80$	6.56253e9	+	1.13666e10i	0.223911	+	0.387826i
$81$	9.35402e9	+	2.99545e10i	0.298079	+	0.954541i
$82$	3.68927e10	+	2.13000e10i	1.09892	+	0.634460i
$83$	−1.04978e10			−0.292528			−0.146264	−	0.989246i	$-0.546725\pi$
$83$	−1.04978e10			−0.292528			−0.146264	+	0.989246i	$0.546725\pi$
$84$	1.59596e10	−	1.06106e10i	0.416376	−	0.276823i
$85$	−8.24975e9			−0.201668
$86$	2.21772e10	+	1.28040e10i	0.508354	+	0.293498i
$87$	−5.15016e10	−	1.68974e10i	−1.10781	−	0.363467i
$88$	−8.23058e9	−	1.42558e10i	−0.166255	−	0.287963i
$89$	1.87137e10	−	3.24132e10i	0.355235	−	0.615285i	−0.631923	−	0.775031i	$-0.717734\pi$
$89$	1.87137e10	−	3.24132e10i	0.355235	−	0.615285i	0.987158	+	0.159746i	$0.0510675\pi$
$90$	7.05229e10	+	7.82178e9i	1.25892	+	0.139628i
$91$	−9.29200e9	−	2.32529e10i	−0.156092	−	0.390616i
$92$		−	9.70733e9i		−	0.153556i
$93$	−1.62987e10	−	7.77764e10i	−0.242939	−	1.15929i
$94$	−4.62703e10	+	2.67142e10i	−0.650278	+	0.375438i
$95$	7.77623e10	−	4.48961e10i	1.03107	−	0.595290i
$96$	2.89661e9	+	1.38224e10i	0.0362575	+	0.173018i
$97$			2.70123e10i			0.319386i	0.987167	+	0.159693i	$0.0510505\pi$
$97$			2.70123e10i			0.319386i	−0.987167	+	0.159693i	$0.948950\pi$
$98$	−6.15097e10	+	1.48397e10i	−0.687385	+	0.165837i
$99$	−8.84483e10	−	9.80991e9i	−0.934751	−	0.103674i
$100$	5.52182e10	−	9.56406e10i	0.552182	−	0.956406i
$101$	8.86810e9	+	1.53600e10i	0.0839582	+	0.145420i	0.904947	−	0.425525i	$-0.139910\pi$
$101$	8.86810e9	+	1.53600e10i	0.0839582	+	0.145420i	−0.820989	+	0.570945i	$0.806577\pi$
$102$	−8.43443e9	−	2.76730e9i	−0.0756405	−	0.0248173i
$103$	1.74172e11	+	1.00558e11i	1.48038	+	0.854699i	0.999753	−	0.0222250i	$-0.00707502\pi$
$103$	1.74172e11	+	1.00558e11i	1.48038	+	0.854699i	0.480629	+	0.876924i	$0.340408\pi$
$104$	1.84526e10			0.148722
$105$	−2.09866e11	−	1.04098e11i	−1.60472	−	0.795982i
$106$	1.88466e11			1.36789
$107$	7.11129e10	+	4.10571e10i	0.490160	+	0.282994i	0.724641	−	0.689127i	$-0.242006\pi$
$107$	7.11129e10	+	4.10571e10i	0.490160	+	0.282994i	−0.234481	+	0.972121i	$0.575339\pi$
$108$	6.94779e10	+	3.16531e10i	0.455005	+	0.207294i
$109$	−8.08839e10	−	1.40095e11i	−0.503519	−	0.872121i	−0.999992	−	0.00406864i	$-0.998705\pi$
$109$	−8.08839e10	−	1.40095e11i	−0.503519	−	0.872121i	0.496472	−	0.868053i	$-0.334628\pi$
$110$	−1.00608e11	+	1.74258e11i	−0.595624	+	1.03165i
$111$	3.99116e10	+	4.45830e10i	0.224814	+	0.251127i
$112$	6.66495e9	−	4.61484e10i	0.0357353	−	0.247433i
$113$			2.76208e11i			1.41028i	0.709069	+	0.705139i	$0.249116\pi$
$113$			2.76208e11i			1.41028i	−0.709069	+	0.705139i	$0.750884\pi$
$114$	9.45631e10	−	1.98165e10i	0.459986	−	0.0963942i
$115$	−1.02762e11	+	5.93296e10i	−0.476424	+	0.275064i
$116$	−1.14205e11	+	6.59362e10i	−0.504854	+	0.291478i
$117$	5.90978e10	−	8.03670e10i	0.249201	−	0.338888i
$118$			2.17657e11i			0.875833i
$119$	2.30258e10	+	1.81313e10i	0.0884516	+	0.0696498i
$120$	1.28621e11	−	1.15144e11i	0.471861	−	0.422419i
$121$	−1.64757e10	+	2.85368e10i	−0.0577463	+	0.100020i
$122$	1.39554e11	+	2.41714e11i	0.467480	+	0.809699i
$123$	1.74673e11	−	5.32386e11i	0.559434	−	1.70509i
$124$	−1.67434e11	−	9.66681e10i	−0.512890	−	0.296117i
$125$	−7.38753e11			−2.16518
$126$	−1.79645e11	−	1.76826e11i	−0.503938	−	0.496031i
$127$	−6.44469e11			−1.73094			−0.865469	−	0.500963i	$-0.832979\pi$
$127$	−6.44469e11			−1.73094			−0.865469	+	0.500963i	$0.832979\pi$
$128$	2.97564e10	+	1.71799e10i	0.0765466	+	0.0441942i
$129$	1.05001e11	−	3.20032e11i	0.258792	−	0.788769i
$130$	−1.12779e11	−	1.95340e11i	−0.266404	−	0.461426i
$131$	−3.25683e11	+	5.64100e11i	−0.737570	+	1.27751i	0.216017	+	0.976390i	$0.430693\pi$
$131$	−3.25683e11	+	5.64100e11i	−0.737570	+	1.27751i	−0.953587	+	0.301118i	$0.902640\pi$
$132$	−1.61313e11	+	1.44411e11i	−0.350359	+	0.313649i
$133$	−3.15714e11	−	4.55968e10i	−0.657824	−	0.0950058i
$134$		−	2.48874e11i		−	0.497626i
$135$	−8.95572e10	−	9.28952e11i	−0.171896	−	1.78302i
$136$	−1.87034e10	+	1.07984e10i	−0.0344712	+	0.0199019i
$137$	1.30107e9	−	7.51175e8i	0.00230324	−	0.00132977i	−0.498848	−	0.866690i	$-0.666243\pi$
$137$	1.30107e9	−	7.51175e8i	0.00230324	−	0.00132977i	0.501151	+	0.865360i	$0.332910\pi$
$138$	−1.24964e11	+	2.61873e10i	−0.212544	+	0.0445405i
$139$		−	7.47761e10i		−	0.122231i	−0.998131	−	0.0611155i	$-0.980534\pi$
$139$		−	7.47761e10i		−	0.122231i	0.998131	−	0.0611155i	$-0.0194658\pi$
$140$	−5.29262e11	+	2.11496e11i	−0.831699	+	0.332352i
$141$	4.68718e11	+	5.23578e11i	0.708282	+	0.791182i
$142$	−2.40397e11	+	4.16380e11i	−0.349416	+	0.605207i
$143$	1.41445e11	+	2.44991e11i	0.197807	+	0.342611i
$144$	1.70124e11	−	7.45769e10i	0.228966	−	0.100372i
$145$	1.39600e12	+	8.05982e11i	1.80868	+	1.04424i
$146$	1.06016e12			1.32260
$147$	3.56966e11	+	7.51790e11i	0.428926	+	0.903340i
$148$	1.45583e11			0.168527
$149$	−4.48317e11	−	2.58836e11i	−0.500105	−	0.288735i	0.228652	−	0.973508i	$-0.426568\pi$
$149$	−4.48317e11	−	2.58836e11i	−0.500105	−	0.288735i	−0.728757	+	0.684773i	$0.759901\pi$
$150$	−1.38016e12	−	4.52823e11i	−1.48397	−	0.486885i
$151$	−3.31782e10	−	5.74662e10i	−0.0343937	−	0.0595716i	0.848316	−	0.529490i	$-0.177617\pi$
$151$	−3.31782e10	−	5.74662e10i	−0.0343937	−	0.0595716i	−0.882710	+	0.469918i	$0.844283\pi$
$152$	1.17532e11	−	2.03572e11i	0.117495	−	0.203506i
$153$	−1.28705e10	+	1.16043e11i	−0.0124105	+	0.111896i
$154$	6.63789e11	−	2.65254e11i	0.617541	−	0.246773i
$155$			2.36328e12i			2.12173i
$156$	−4.97793e10	−	2.37543e11i	−0.0431383	−	0.205853i
$157$	−1.08687e12	+	6.27508e11i	−0.909351	+	0.525014i	−0.880222	−	0.474562i	$-0.842607\pi$
$157$	−1.08687e12	+	6.27508e11i	−0.909351	+	0.525014i	−0.0291286	+	0.999576i	$0.509273\pi$
$158$	−2.64657e10	+	1.52800e10i	−0.0213831	+	0.0123455i
$159$	−5.08422e11	−	2.42615e12i	−0.396771	−	1.89336i
$160$		−	4.20002e11i		−	0.316659i
$161$	4.17212e11	+	6.02555e10i	0.303958	+	0.0438990i
$162$	2.20046e11	−	9.79788e11i	0.154946	−	0.689922i
$163$	5.75602e11	−	9.96973e11i	0.391824	−	0.678659i	−0.600866	−	0.799349i	$-0.705178\pi$
$163$	5.75602e11	−	9.96973e11i	0.391824	−	0.678659i	0.992690	+	0.120691i	$0.0385110\pi$
$164$	−6.81601e11	−	1.18057e12i	−0.448631	−	0.777051i
$165$	2.51465e12	+	8.25047e11i	1.60072	+	0.525191i
$166$	2.90922e11	+	1.67964e11i	0.179136	+	0.103424i
$167$	1.96526e12			1.17079			0.585395	−	0.810748i	$-0.300939\pi$
$167$	1.96526e12			1.17079			0.585395	+	0.810748i	$0.300939\pi$
$168$	−6.12054e11	+	3.86947e10i	−0.352849	+	0.0223075i
$169$	1.47505e12			0.823054
$170$	2.28624e11	+	1.31996e11i	0.123496	+	0.0713003i
$171$	−5.10202e11	−	1.16387e12i	−0.266848	−	0.608729i
$172$	−4.09729e11	−	7.09672e11i	−0.207534	−	0.359460i
$173$	−6.93882e11	+	1.20184e12i	−0.340433	+	0.589647i	−0.984513	−	0.175311i	$-0.943907\pi$
$173$	−6.93882e11	+	1.20184e12i	−0.340433	+	0.589647i	0.644080	+	0.764958i	$0.277240\pi$
$174$	1.15689e12	+	1.29230e12i	0.549886	+	0.614247i
$175$	3.76779e12	+	2.96688e12i	1.73531	+	1.36644i
$176$			5.26757e11i			0.235121i
$177$	2.80193e12	−	5.87168e11i	1.21228	−	0.254044i
$178$	−1.03722e12	+	5.98840e11i	−0.435072	+	0.251189i
$179$	1.98766e11	−	1.14757e11i	0.0808443	−	0.0466755i	−0.459033	−	0.888419i	$-0.651804\pi$
$179$	1.98766e11	−	1.14757e11i	0.0808443	−	0.0466755i	0.539877	+	0.841744i	$0.318471\pi$
$180$	−1.82924e12	−	1.34513e12i	−0.721559	−	0.530598i
$181$		−	3.99811e12i		−	1.52976i	−0.644175	−	0.764878i	$-0.722799\pi$
$181$		−	3.99811e12i		−	1.52976i	0.644175	−	0.764878i	$-0.277201\pi$
$182$	−1.14539e11	+	7.93076e11i	−0.0425170	+	0.294390i
$183$	2.73515e12	−	2.44856e12i	0.985146	−	0.881923i
$184$	−1.55317e11	+	2.69017e11i	−0.0542902	+	0.0940335i
$185$	−8.89777e11	−	1.54114e12i	−0.301882	−	0.522875i
$186$	−7.92739e11	+	2.41618e12i	−0.261101	+	0.795808i
$187$	−2.86735e11	−	1.65546e11i	−0.0916962	−	0.0529408i
$188$	1.70971e12			0.530950
$189$	−1.79168e12	+	2.78961e12i	−0.540408	+	0.841403i
$190$	−2.87335e12			−0.841868
$191$	2.03265e12	+	1.17355e12i	0.578601	+	0.334056i	0.760577	−	0.649247i	$-0.224916\pi$
$191$	2.03265e12	+	1.17355e12i	0.578601	+	0.334056i	−0.181976	+	0.983303i	$0.558249\pi$
$192$	1.40886e11	−	4.29404e11i	0.0389682	−	0.118771i
$193$	−3.21534e12	−	5.56913e12i	−0.864294	−	1.49700i	−0.867747	−	0.497007i	$-0.834432\pi$
$193$	−3.21534e12	−	5.56913e12i	−0.864294	−	1.49700i	0.00345278	−	0.999994i	$-0.498901\pi$
$194$	4.32196e11	−	7.48586e11i	0.112920	−	0.195583i
$195$	−2.21039e12	+	1.97879e12i	−0.561409	+	0.502584i
$196$	1.94204e12	+	5.72906e11i	0.479568	+	0.141473i
$197$		−	2.83497e11i		−	0.0680745i	−0.999421	−	0.0340372i	$-0.989164\pi$
$197$		−	2.83497e11i		−	0.0680745i	0.999421	−	0.0340372i	$-0.0108365\pi$
$198$	2.29419e12	+	1.68703e12i	0.535761	+	0.393972i
$199$	1.05318e12	−	6.08055e11i	0.239228	−	0.138118i	−0.375594	−	0.926784i	$-0.622561\pi$
$199$	1.05318e12	−	6.08055e11i	0.239228	−	0.138118i	0.614822	+	0.788666i	$0.289228\pi$
$200$	−3.06050e12	+	1.76698e12i	−0.676281	+	0.390451i
$201$	−3.20379e12	+	6.71381e11i	−0.688787	+	0.144341i
$202$		−	5.67559e11i		−	0.118735i
$203$	−2.12498e12	−	5.31770e12i	−0.432640	−	1.08267i
$204$	1.89465e11	+	2.11640e11i	0.0375459	+	0.0419404i
$205$	−8.33166e12	+	1.44309e13i	−1.60726	+	2.78385i
$206$	−3.21787e12	−	5.57351e12i	−0.604363	−	1.04679i
$207$	6.74224e11	+	1.53803e12i	0.123301	+	0.281273i
$208$	−5.11375e11	−	2.95242e11i	−0.0910732	−	0.0525812i
$209$	3.60369e12			0.625091
$210$	4.15039e12	+	6.24271e12i	0.701267	+	1.05479i
$211$	−6.89868e12			−1.13557			−0.567783	−	0.823178i	$-0.692199\pi$
$211$	−6.89868e12			−1.13557			−0.567783	+	0.823178i	$0.692199\pi$
$212$	−5.22294e12	−	3.01546e12i	−0.837659	−	0.483623i
$213$	6.00863e12	+	1.97141e12i	0.939047	+	0.308097i
$214$	−1.31383e12	−	2.27561e12i	−0.200107	−	0.346595i
$215$	−5.00839e12	+	8.67479e12i	−0.743510	+	1.28780i
$216$	−1.41898e12	−	1.98884e12i	−0.205343	−	0.287809i
$217$	5.19400e12	−	6.59611e12i	0.732780	−	0.930592i
$218$			5.17657e12i			0.712084i
$219$	−2.85996e12	−	1.36476e13i	−0.383635	−	1.83068i
$220$	5.57625e12	−	3.21945e12i	0.729487	−	0.421170i
$221$	3.21424e11	−	1.85574e11i	0.0410129	−	0.0236788i
$222$	−3.92735e11	−	1.87411e12i	−0.0488831	−	0.233267i
$223$			8.88493e12i			1.07889i	0.842021	+	0.539445i	$0.181366\pi$
$223$			8.88493e12i			1.07889i	−0.842021	+	0.539445i	$0.818634\pi$
$224$	−9.23078e11	+	1.17226e12i	−0.109364	+	0.138887i
$225$	−2.10604e12	+	1.89885e13i	−0.243480	+	2.19527i
$226$	4.41933e12	−	7.65450e12i	0.498609	−	0.863616i
$227$	6.23327e12	+	1.07963e13i	0.686395	+	1.18887i	0.972996	+	0.230821i	$0.0741410\pi$
$227$	6.23327e12	+	1.07963e13i	0.686395	+	1.18887i	−0.286602	+	0.958050i	$0.592526\pi$
$228$	−2.93767e12	−	9.63838e11i	−0.315763	−	0.103601i
$229$	−1.51422e11	−	8.74238e10i	−0.0158889	−	0.00917349i	0.492034	−	0.870576i	$-0.336253\pi$
$229$	−1.51422e11	−	8.74238e10i	−0.0158889	−	0.00917349i	−0.507923	+	0.861402i	$0.669587\pi$
$230$	3.79709e12			0.388999
$231$	−5.20533e12	−	7.82947e12i	−0.520694	−	0.783189i
$232$	4.21992e12			0.412212
$233$	−4.78942e12	−	2.76518e12i	−0.456905	−	0.263794i	0.253837	−	0.967247i	$-0.418307\pi$
$233$	−4.78942e12	−	2.76518e12i	−0.456905	−	0.263794i	−0.710742	+	0.703453i	$0.751641\pi$
$234$	−2.92364e12	+	1.28163e12i	−0.272419	+	0.119420i
$235$	−1.04494e13	−	1.80990e13i	−0.951087	−	1.64733i
$236$	3.48251e12	−	6.03188e12i	0.309654	−	0.536336i
$237$	2.68098e11	+	2.99476e11i	0.0232904	+	0.0260164i
$238$	−3.48009e11	−	8.70880e11i	−0.0295404	−	0.0739240i
$239$		−	1.16852e13i		−	0.969280i	−0.874714	−	0.484640i	$-0.838951\pi$
$239$		−	1.16852e13i		−	0.969280i	0.874714	−	0.484640i	$-0.161049\pi$
$240$	−5.40674e12	+	1.13303e12i	−0.438302	+	0.0918501i
$241$	1.73798e12	−	1.00342e12i	0.137706	−	0.0795043i	−0.429564	−	0.903036i	$-0.641333\pi$
$241$	1.73798e12	−	1.00342e12i	0.137706	−	0.0795043i	0.567270	+	0.823532i	$0.308000\pi$
$242$	9.13176e11	−	5.27223e11i	0.0707245	−	0.0408328i
$243$	−1.32066e13	−	1.89529e11i	−0.999897	−	0.0143496i
$244$		−	8.93145e12i		−	0.661117i
$245$	−5.80465e12	−	2.40600e13i	−0.420109	−	1.74133i
$246$	−1.33589e13	+	1.19591e13i	−0.945424	+	0.846363i
$247$	−2.01984e12	+	3.49846e12i	−0.139792	+	0.242127i
$248$	3.09338e12	+	5.35789e12i	0.209387	+	0.362668i
$249$	1.37741e12	−	4.19820e12i	0.0911941	−	0.277950i
$250$	2.04729e13	+	1.18200e13i	1.32590	+	0.765507i
$251$	−2.35605e12			−0.149273			−0.0746363	−	0.997211i	$-0.523780\pi$
$251$	−2.35605e12			−0.149273			−0.0746363	+	0.997211i	$0.523780\pi$
$252$	2.14925e12	+	7.77467e12i	0.133224	+	0.481925i
$253$	−4.76223e12			−0.288833
$254$	1.78600e13	+	1.03115e13i	1.05998	+	0.611979i
$255$	1.08245e12	−	3.29919e12i	0.0628690	−	0.191618i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	9.60767e12	−	1.66410e13i	0.534547	−	0.925862i	−0.464638	−	0.885501i	$-0.653816\pi$
$257$	9.60767e12	−	1.66410e13i	0.534547	−	0.925862i	0.999185	−	0.0403618i	$-0.0128511\pi$
$258$	−8.03038e12	+	7.18896e12i	−0.437349	+	0.391524i
$259$	−9.03663e11	+	6.25700e12i	−0.0481790	+	0.333594i
$260$			7.21788e12i			0.376753i
$261$	1.35150e13	−	1.83791e13i	0.690708	−	0.939292i
$262$	1.80512e13	−	1.04219e13i	0.903335	−	0.521540i
$263$	1.43021e13	−	8.25730e12i	0.700878	−	0.404652i	−0.106796	−	0.994281i	$-0.534059\pi$
$263$	1.43021e13	−	8.25730e12i	0.700878	−	0.404652i	0.807674	+	0.589629i	$0.200726\pi$
$264$	6.78102e12	−	1.42102e12i	0.325442	−	0.0681991i
$265$			7.37200e13i			3.46524i
$266$	8.01977e12	+	6.31504e12i	0.369244	+	0.290755i
$267$	1.05070e13	+	1.17368e13i	0.473880	+	0.529344i
$268$	−3.98198e12	+	6.89699e12i	−0.175937	+	0.304732i
$269$	−6.01234e12	−	1.04137e13i	−0.260259	−	0.450782i	0.706051	−	0.708161i	$-0.250475\pi$
$269$	−6.01234e12	−	1.04137e13i	−0.260259	−	0.450782i	−0.966311	+	0.257378i	$0.917141\pi$
$270$	−1.23813e13	+	2.71768e13i	−0.525130	+	1.15265i
$271$	−4.32589e12	−	2.49755e12i	−0.179781	−	0.103797i	0.407409	−	0.913246i	$-0.366432\pi$
$271$	−4.32589e12	−	2.49755e12i	−0.179781	−	0.103797i	−0.587190	+	0.809449i	$0.699766\pi$
$272$	6.91097e11			0.0281456
$273$	1.05184e13	−	6.64982e11i	0.419811	−	0.0265409i
$274$	−4.80752e10			−0.00188058
$275$	−4.69195e13	−	2.70890e13i	−1.79897	−	1.03863i
$276$	3.88209e12	+	1.27370e12i	0.145904	+	0.0478704i
$277$	1.59776e13	+	2.76741e13i	0.588673	+	1.01961i	0.994407	+	0.105620i	$0.0336827\pi$
$277$	1.59776e13	+	2.76741e13i	0.588673	+	1.01961i	−0.405734	+	0.913991i	$0.632984\pi$
$278$	−1.19642e12	+	2.07226e12i	−0.0432152	+	0.0748509i
$279$	3.32424e13	+	3.68695e12i	1.17725	+	0.130570i
$280$	1.80513e13	+	2.60704e12i	0.626814	+	0.0905271i
$281$		−	1.81369e13i		−	0.617560i	−0.951133	−	0.308780i	$-0.900079\pi$
$281$		−	1.81369e13i		−	0.617560i	0.951133	−	0.308780i	$-0.0999207\pi$
$282$	−4.61224e12	−	2.20093e13i	−0.154008	−	0.734913i
$283$	−2.74714e13	+	1.58606e13i	−0.899613	+	0.519392i	−0.877075	−	0.480354i	$-0.840508\pi$
$283$	−2.74714e13	+	1.58606e13i	−0.899613	+	0.519392i	−0.0225382	+	0.999746i	$0.507175\pi$
$284$	1.33242e13	−	7.69270e12i	0.427946	−	0.247075i
$285$	7.75138e12	+	3.69890e13i	0.244192	+	1.16527i
$286$		−	9.05251e12i		−	0.279741i
$287$	5.49705e13	−	2.19665e13i	1.66640	−	0.665902i
$288$	−5.90784e12	−	6.55246e11i	−0.175699	−	0.0194870i
$289$	1.69188e13	−	2.93041e13i	0.493663	−	0.855049i
$290$	−2.57914e13	−	4.46721e13i	−0.738391	−	1.27893i
$291$	−1.08026e13	−	3.54428e12i	−0.303470	−	0.0995672i
$292$	−2.93799e13	−	1.69625e13i	−0.809926	−	0.467611i
$293$	5.90556e13			1.59768			0.798839	−	0.601545i	$-0.205448\pi$
$293$	5.90556e13			1.59768			0.798839	+	0.601545i	$0.205448\pi$
$294$	2.13609e12	−	2.65457e13i	0.0567165	−	0.704829i
$295$	−8.51380e13			−2.21872
$296$	−4.03451e12	−	2.32932e12i	−0.103202	−	0.0595834i
$297$	1.55284e13	−	3.40845e13i	0.389912	−	0.855848i
$298$	8.28275e12	+	1.43461e13i	0.204167	+	0.353627i
$299$	2.66918e12	−	4.62316e12i	0.0645932	−	0.111879i
$300$	3.10028e13	+	3.46315e13i	0.736605	+	0.822819i
$301$	3.30443e13	−	1.32047e13i	0.770869	−	0.308043i
$302$			2.12340e12i			0.0486400i
$303$	−7.30626e12	+	1.53109e12i	−0.164347	+	0.0344403i
$304$	−6.51430e12	+	3.76103e12i	−0.143901	+	0.0830812i
$305$	−9.45484e13	+	5.45875e13i	−2.05119	+	1.18425i
$306$	2.21336e12	−	3.00994e12i	0.0471612	−	0.0641343i
$307$		−	5.78462e13i		−	1.21064i	−0.795983	−	0.605319i	$-0.793046\pi$
$307$		−	5.78462e13i		−	1.21064i	0.795983	−	0.605319i	$-0.206954\pi$
$308$	−2.26395e13	−	3.26969e12i	−0.465412	−	0.0672169i
$309$	−6.30678e13	+	5.64595e13i	−1.27361	+	1.14016i
$310$	3.78124e13	−	6.54930e13i	0.750145	−	1.29929i
$311$	3.81509e13	+	6.60793e13i	0.743571	+	1.28790i	0.950859	+	0.309623i	$0.100203\pi$
$311$	3.81509e13	+	6.60793e13i	0.743571	+	1.28790i	−0.207288	+	0.978280i	$0.566464\pi$
$312$	−2.42117e12	+	7.37946e12i	−0.0463634	+	0.141311i
$313$	−3.77329e12	−	2.17851e12i	−0.0709947	−	0.0409888i	0.464082	−	0.885792i	$-0.346384\pi$
$313$	−3.77329e12	−	2.17851e12i	−0.0709947	−	0.0409888i	−0.535077	+	0.844803i	$0.679717\pi$
$314$	4.01605e13			0.742482
$315$	6.91669e13	−	7.02694e13i	1.25658	−	1.27661i
$316$	9.77920e11			0.0174592
$317$	−3.35580e13	−	1.93747e13i	−0.588804	−	0.339946i	0.175821	−	0.984422i	$-0.443742\pi$
$317$	−3.35580e13	−	1.93747e13i	−0.588804	−	0.339946i	−0.764624	+	0.644476i	$0.777075\pi$
$318$	−2.47287e13	+	7.53703e13i	−0.426434	+	1.29972i
$319$	3.23471e13	+	5.60267e13i	0.548259	+	0.949613i
$320$	−6.72003e12	+	1.16394e13i	−0.111956	+	0.193913i
$321$	−2.57500e13	+	2.30519e13i	−0.421696	+	0.377511i
$322$	−1.05980e13	−	8.34523e12i	−0.170615	−	0.134348i
$323$		−	4.72799e12i		−	0.0748278i
$324$	−2.17747e13	+	2.36320e13i	−0.338809	+	0.367707i
$325$	5.25958e13	−	3.03662e13i	0.804623	−	0.464550i
$326$	−3.19031e13	+	1.84193e13i	−0.479884	+	0.277061i
$327$	6.66387e13	−	1.39647e13i	0.985629	−	0.206547i
$328$			4.36225e13i			0.634460i
$329$	−1.06125e13	+	7.34816e13i	−0.151789	+	1.05100i
$330$	−5.64874e13	−	6.30988e13i	−0.794556	−	0.887554i
$331$	5.95979e13	−	1.03227e14i	0.824474	−	1.42803i	−0.0778461	−	0.996965i	$-0.524804\pi$
$331$	5.95979e13	−	1.03227e14i	0.824474	−	1.42803i	0.902320	−	0.431066i	$-0.141862\pi$
$332$	−5.37485e12	−	9.30952e12i	−0.0731319	−	0.126668i
$333$	−2.30662e13	+	1.01115e13i	−0.308697	+	0.135323i
$334$	−5.44629e13	−	3.14442e13i	−0.716960	−	0.413937i
$335$	9.73488e13			1.26062
$336$	1.75809e13	+	8.72053e12i	0.223962	+	0.111090i
$337$	−6.70814e13			−0.840694			−0.420347	−	0.907364i	$-0.638092\pi$
$337$	−6.70814e13			−0.840694			−0.420347	+	0.907364i	$0.638092\pi$
$338$	−4.08776e13	−	2.36007e13i	−0.504016	−	0.290994i
$339$	−1.10459e14	−	3.62412e13i	−1.34000	−	0.439648i
$340$	−4.22387e12	−	7.31596e12i	−0.0504169	−	0.0873247i
$341$	−4.74235e13	+	8.21399e13i	−0.556986	+	0.964729i
$342$	−4.48272e12	+	4.04172e13i	−0.0518082	+	0.467114i
$343$	−3.66776e13	+	7.99109e13i	−0.417141	+	0.908842i
$344$			2.62227e13i			0.293498i
$345$	−1.02433e13	−	4.88805e13i	−0.112833	−	0.538432i
$346$	3.84588e13	−	2.22042e13i	0.416944	−	0.240723i
$347$	−4.15394e13	+	2.39828e13i	−0.443249	+	0.255910i	−0.704975	−	0.709232i	$-0.749042\pi$
$347$	−4.15394e13	+	2.39828e13i	−0.443249	+	0.255910i	0.261726	+	0.965142i	$0.415708\pi$
$348$	−1.13840e13	−	5.43236e13i	−0.119566	−	0.570562i
$349$			7.88994e13i			0.815707i	0.913047	+	0.407853i	$0.133723\pi$
$349$			7.88994e13i			0.815707i	−0.913047	+	0.407853i	$0.866277\pi$
$350$	−5.69459e13	−	1.42505e14i	−0.579547	−	1.45030i
$351$	2.43856e13	+	3.41790e13i	0.244312	+	0.342429i
$352$	8.42811e12	−	1.45979e13i	0.0831277	−	0.143981i
$353$	−6.52510e12	−	1.13018e13i	−0.0633616	−	0.109745i	0.832604	−	0.553868i	$-0.186849\pi$
$353$	−6.52510e12	−	1.13018e13i	−0.0633616	−	0.109745i	−0.895966	+	0.444123i	$0.853515\pi$
$354$	−8.70439e13	−	2.85587e13i	−0.832186	−	0.273037i
$355$	−1.62870e14	−	9.40330e13i	−1.53315	−	0.885166i
$356$	3.83258e13			0.355235
$357$	−1.02721e13	+	6.82932e12i	−0.0937532	+	0.0623307i
$358$	−7.34447e12			−0.0660091
$359$	−3.91784e13	−	2.26196e13i	−0.346758	−	0.200201i	0.316498	−	0.948593i	$-0.397493\pi$
$359$	−3.91784e13	−	2.26196e13i	−0.346758	−	0.200201i	−0.663257	+	0.748392i	$0.730826\pi$
$360$	2.91713e13	+	6.65452e13i	0.254268	+	0.580033i
$361$	−3.25148e13	−	5.63173e13i	−0.279121	−	0.483451i
$362$	−6.39697e13	+	1.10799e14i	−0.540851	+	0.936781i
$363$	−9.25046e12	−	1.03332e13i	−0.0770330	−	0.0860492i
$364$	1.58634e13	−	2.01457e13i	0.130119	−	0.165244i
$365$			4.14688e14i			3.35051i
$366$	−1.14976e14	+	2.40942e13i	−0.915083	+	0.191764i
$367$	1.30726e14	−	7.54749e13i	1.02494	−	0.591751i	0.109411	−	0.993997i	$-0.465103\pi$
$367$	1.30726e14	−	7.54749e13i	1.02494	−	0.591751i	0.915532	+	0.402245i	$0.131770\pi$
$368$	8.60856e12	−	4.97015e12i	0.0664917	−	0.0383890i
$369$	1.89989e14	+	1.39709e14i	1.44572	+	1.06311i
$370$			5.69458e13i			0.426925i
$371$	1.62022e14	−	2.05759e14i	1.19679	−	1.51986i
$372$	6.06279e13	−	5.42754e13i	0.441252	−	0.395018i
$373$	−8.29658e13	+	1.43701e14i	−0.594978	+	1.03053i	0.398573	+	0.917137i	$0.369506\pi$
$373$	−8.29658e13	+	1.43701e14i	−0.594978	+	1.03053i	−0.993550	+	0.113394i	$0.963828\pi$
$374$	5.29748e12	+	9.17551e12i	0.0374348	+	0.0648390i
$375$	9.69318e13	−	2.95437e14i	0.674985	−	2.05728i
$376$	−4.73808e13	−	2.73553e13i	−0.325139	−	0.187719i
$377$	−7.25208e13			−0.490439
$378$	9.42864e13	−	4.86411e13i	0.628412	−	0.324189i
$379$	−4.45474e12			−0.0292622			−0.0146311	−	0.999893i	$-0.504657\pi$
$379$	−4.45474e12			−0.0292622			−0.0146311	+	0.999893i	$0.504657\pi$
$380$	7.96286e13	+	4.59736e13i	0.515537	+	0.297645i
$381$	8.45607e13	−	2.57732e14i	0.539612	−	1.64468i
$382$	−3.75537e13	−	6.50449e13i	−0.236213	−	0.409133i
$383$	7.12045e13	−	1.23330e14i	0.441483	−	0.764671i	−0.556317	−	0.830970i	$-0.687786\pi$
$383$	7.12045e13	−	1.23330e14i	0.441483	−	0.764671i	0.997800	+	0.0662994i	$0.0211192\pi$
$384$	−1.07748e13	+	9.64582e12i	−0.0658548	+	0.0589546i
$385$	1.03756e14	+	2.59646e14i	0.625142	+	1.56440i
$386$			2.05782e14i			1.22230i
$387$	1.14208e14	+	8.39827e13i	0.668784	+	0.491790i
$388$	−2.39547e13	+	1.38303e13i	−0.138298	+	0.0798466i
$389$	−1.04221e14	+	6.01722e13i	−0.593244	+	0.342510i	−0.766379	−	0.642388i	$-0.777944\pi$
$389$	−1.04221e14	+	6.01722e13i	−0.593244	+	0.342510i	0.173135	+	0.984898i	$0.444610\pi$
$390$	9.29168e13	−	1.94715e13i	0.521482	−	0.109281i
$391$			6.24797e12i			0.0345754i
$392$	−4.46529e13	−	4.69495e13i	−0.243656	−	0.256187i
$393$	−1.82858e14	−	2.04261e14i	−0.983910	−	1.09907i
$394$	−4.53595e12	+	7.85650e12i	−0.0240680	+	0.0416869i
$395$	−5.97688e12	−	1.03523e13i	−0.0312745	−	0.0541691i
$396$	−3.65860e13	−	8.34595e13i	−0.188795	−	0.430678i
$397$	5.22418e12	+	3.01618e12i	0.0265871	+	0.0153501i	0.513235	−	0.858248i	$-0.328447\pi$
$397$	5.22418e12	+	3.01618e12i	0.0265871	+	0.0153501i	−0.486648	+	0.873598i	$0.661780\pi$
$398$	−3.89155e13			−0.195329
$399$	5.96596e13	−	1.20276e14i	0.295345	−	0.595424i
$400$	1.13087e14			0.552182
$401$	−2.14159e14	−	1.23645e14i	−1.03143	−	0.595499i	−0.114039	−	0.993476i	$-0.536379\pi$
$401$	−2.14159e14	−	1.23645e14i	−1.03143	−	0.595499i	−0.917395	+	0.397977i	$0.869712\pi$
$402$	9.95280e13	+	3.26547e13i	0.472827	+	0.155132i
$403$	−5.31608e13	−	9.20773e13i	−0.249123	−	0.431494i
$404$	−9.08094e12	+	1.57286e13i	−0.0419791	+	0.0727099i
$405$	3.83251e14	+	8.60726e13i	1.74776	+	0.392520i
$406$	−2.61939e13	+	1.81368e14i	−0.117844	+	0.815957i
$407$		−	7.14201e13i		−	0.316994i
$408$	−1.86436e12	−	8.89659e12i	−0.00816391	−	0.0389576i
$409$	1.76829e14	−	1.02092e14i	0.763970	−	0.441078i	−0.0667495	−	0.997770i	$-0.521263\pi$
$409$	1.76829e14	−	1.02092e14i	0.763970	−	0.441078i	0.830719	+	0.556692i	$0.187929\pi$
$410$	4.61787e14	−	2.66613e14i	1.96848	−	1.13650i
$411$	1.29691e11	+	6.18878e11i	0.000545483	+	0.00260301i
$412$			2.05943e14i			0.854699i
$413$	2.37628e14	+	1.87116e14i	0.973132	+	0.766277i
$414$	5.92385e12	−	5.34108e13i	0.0239388	−	0.215837i
$415$	−6.57004e13	+	1.13796e14i	−0.262001	+	0.453799i
$416$	9.44775e12	+	1.63640e13i	0.0371805	+	0.0643985i
$417$	2.99040e13	+	9.81137e12i	0.116140	+	0.0381049i
$418$	−9.98685e13	−	5.76591e13i	−0.382789	−	0.221003i
$419$	−8.37838e13			−0.316944			−0.158472	−	0.987363i	$-0.550657\pi$
$419$	−8.37838e13			−0.316944			−0.158472	+	0.987363i	$0.550657\pi$
$420$	−1.51357e13	−	2.39409e14i	−0.0565108	−	0.893861i
$421$	3.96767e14			1.46212			0.731061	−	0.682312i	$-0.239025\pi$
$421$	3.96767e14			1.46212			0.731061	+	0.682312i	$0.239025\pi$
$422$	1.91182e14	+	1.10379e14i	0.695390	+	0.401484i
$423$	−2.70886e14	+	1.18748e14i	−0.972557	+	0.426338i
$424$	9.64948e13	+	1.67134e14i	0.341973	+	0.592315i
$425$	−3.55403e13	+	6.15576e13i	−0.124332	+	0.215349i
$426$	−1.34974e14	−	1.50771e14i	−0.466118	−	0.520674i
$427$	3.83865e14	+	5.54394e13i	1.30866	+	0.189002i
$428$			8.40849e13i			0.282994i
$429$	−1.16534e14	+	2.44208e13i	−0.387203	+	0.0811417i
$430$	2.77593e14	−	1.60268e14i	0.910610	−	0.525741i
$431$	−7.34302e13	+	4.23950e13i	−0.237821	+	0.137306i	−0.614175	−	0.789170i	$-0.710511\pi$
$431$	−7.34302e13	+	4.23950e13i	−0.237821	+	0.137306i	0.376354	+	0.926476i	$0.377178\pi$
$432$	7.50238e12	+	7.78201e13i	0.0239904	+	0.248846i
$433$			3.07354e14i			0.970412i	0.874400	+	0.485206i	$0.161255\pi$
$433$			3.07354e14i			0.970412i	−0.874400	+	0.485206i	$0.838745\pi$
$434$	−2.49478e14	+	9.96928e13i	−0.777748	+	0.310792i
$435$	−5.05493e14	+	4.52528e14i	−1.55605	+	1.39301i
$436$	8.28251e13	−	1.43457e14i	0.251760	−	0.436061i
$437$	−3.40022e13	−	5.88936e13i	−0.102061	−	0.176775i
$438$	−1.39103e14	+	4.23971e14i	−0.412315	+	1.25669i
$439$	−2.27200e14	−	1.31174e14i	−0.665049	−	0.383966i	0.129149	−	0.991625i	$-0.458775\pi$
$439$	−2.27200e14	−	1.31174e14i	−0.665049	−	0.383966i	−0.794198	+	0.607659i	$0.792109\pi$
$440$	−2.06045e14			−0.595624
$441$	−3.47489e14	+	4.41135e13i	−0.992038	+	0.125939i
$442$	−1.18768e13			−0.0334869
$443$	−6.78562e13	−	3.91768e13i	−0.188960	−	0.109096i	0.402536	−	0.915404i	$-0.368129\pi$
$443$	−6.78562e13	−	3.91768e13i	−0.188960	−	0.109096i	−0.591495	+	0.806308i	$0.701462\pi$
$444$	−1.91019e13	+	5.82205e13i	−0.0525376	+	0.160129i
$445$	−2.34241e14	−	4.05717e14i	−0.636329	−	1.10215i
$446$	1.42159e14	−	2.46226e14i	0.381445	−	0.660683i
$447$	1.62336e14	−	1.45326e14i	0.430252	−	0.385170i
$448$	4.43373e13	−	1.77174e13i	0.116075	−	0.0463844i
$449$		−	5.21675e14i		−	1.34910i	−0.738227	−	0.674552i	$-0.764337\pi$
$449$		−	5.21675e14i		−	1.34910i	0.738227	−	0.674552i	$-0.235663\pi$
$450$	3.62180e14	−	4.92528e14i	0.925244	−	1.25824i
$451$	−5.79164e14	+	3.34380e14i	−1.46161	+	0.843859i
$452$	−2.44944e14	+	1.41419e14i	−0.610669	+	0.352570i
$453$	2.73348e13	−	5.72825e12i	0.0673250	−	0.0141085i
$454$		−	3.98929e14i		−	0.970709i
$455$	−3.10218e14	−	4.48030e13i	−0.745768	−	0.107707i
$456$	6.59898e13	+	7.37134e13i	0.156737	+	0.175081i
$457$	−6.82177e12	+	1.18157e13i	−0.0160088	+	0.0277280i	−0.873919	−	0.486072i	$-0.838429\pi$
$457$	−6.82177e12	+	1.18157e13i	−0.0160088	+	0.0277280i	0.857910	+	0.513800i	$0.171763\pi$
$458$	2.79756e12	+	4.84552e12i	0.00648664	+	0.0112352i
$459$	−4.47184e13	−	2.03730e13i	−0.102451	−	0.0466752i
$460$	−1.05228e14	−	6.07535e13i	−0.238212	−	0.137532i
$461$	7.83162e14			1.75185			0.875924	−	0.482449i	$-0.160253\pi$
$461$	7.83162e14			1.75185			0.875924	+	0.482449i	$0.160253\pi$
$462$	1.89829e13	+	3.00262e14i	0.0419596	+	0.663697i
$463$	−4.16047e14			−0.908756			−0.454378	−	0.890809i	$-0.650138\pi$
$463$	−4.16047e14			−0.908756			−0.454378	+	0.890809i	$0.650138\pi$
$464$	−1.16946e14	−	6.75187e13i	−0.252427	−	0.145739i
$465$	−9.45107e14	−	3.10085e14i	−2.01600	−	0.661439i
$466$	8.84856e13	+	1.53262e14i	0.186531	+	0.323081i
$467$	−2.06714e14	+	3.58039e14i	−0.430653	+	0.745912i	−0.996930	−	0.0783027i	$-0.975050\pi$
$467$	−2.06714e14	+	3.58039e14i	−0.430653	+	0.745912i	0.566277	+	0.824215i	$0.308383\pi$
$468$	1.01528e14	+	1.12606e13i	0.209043	+	0.0231852i
$469$	−2.71709e14	−	2.13953e14i	−0.552909	−	0.435379i
$470$			6.68765e14i			1.34504i
$471$	−1.08340e14	−	5.16991e14i	−0.215364	−	1.02770i
$472$	−1.93020e14	+	1.11440e14i	−0.379247	+	0.218958i
$473$	−3.48151e14	+	2.01005e14i	−0.676132	+	0.390365i
$474$	−2.63811e12	−	1.25889e13i	−0.00506422	−	0.0241661i
$475$		−	7.73658e14i		−	1.46803i
$476$	−4.28979e12	+	2.97027e13i	−0.00804633	+	0.0557131i
$477$	1.03696e15	+	1.15011e14i	1.92270	+	0.213249i
$478$	−1.86964e14	+	3.23831e14i	−0.342692	+	0.593560i
$479$	−1.26739e14	−	2.19518e14i	−0.229649	−	0.397763i	0.728055	−	0.685518i	$-0.240424\pi$
$479$	−1.26739e14	−	2.19518e14i	−0.229649	−	0.397763i	−0.957704	+	0.287755i	$0.907091\pi$
$480$	1.67964e14	+	5.51084e13i	0.300878	+	0.0987168i
$481$	6.93345e13	+	4.00303e13i	0.122787	+	0.0708909i
$482$	−6.42191e13			−0.112436
$483$	−7.88393e13	+	1.58943e14i	−0.136469	+	0.275125i
$484$	−3.37422e13			−0.0577463
$485$	2.92815e14	+	1.69057e14i	0.495465	+	0.286057i
$486$	3.62959e14	+	2.16557e14i	0.607236	+	0.362304i
$487$	4.24273e13	+	7.34862e13i	0.0701837	+	0.121562i	0.898982	−	0.437986i	$-0.144308\pi$
$487$	4.24273e13	+	7.34862e13i	0.0701837	+	0.121562i	−0.828798	+	0.559548i	$0.810975\pi$
$488$	−1.42903e14	+	2.47516e14i	−0.233740	+	0.404850i
$489$	3.23178e14	+	3.61004e14i	0.522689	+	0.583866i
$490$	−2.24096e14	+	7.59643e14i	−0.358390	+	1.21487i
$491$		−	7.84932e14i		−	1.24132i	−0.784080	−	0.620660i	$-0.786865\pi$
$491$		−	7.84932e14i		−	1.24132i	0.784080	−	0.620660i	$-0.213135\pi$
$492$	5.61558e14	−	1.17679e14i	0.878186	−	0.184031i
$493$	7.35062e13	−	4.24388e13i	0.113675	−	0.0656305i
$494$	1.11951e14	−	6.46347e13i	0.171210	−	0.0988480i
$495$	−6.59895e14	+	8.97390e14i	−0.998036	+	1.35723i
$496$		−	1.97976e14i		−	0.296117i
$497$	2.47919e14	+	6.20409e14i	0.366733	+	0.917737i
$498$	−1.05343e14	+	9.43053e13i	−0.154115	+	0.137967i
$499$	−1.03883e14	+	1.79930e14i	−0.150311	+	0.260345i	−0.931342	−	0.364147i	$-0.881361\pi$
$499$	−1.03883e14	+	1.79930e14i	−0.150311	+	0.260345i	0.781031	+	0.624492i	$0.214694\pi$
$500$	−3.78242e14	−	6.55134e14i	−0.541295	−	0.937551i
$501$	−2.57862e14	+	7.85934e14i	−0.364989	+	1.11245i
$502$	6.52929e13	+	3.76969e13i	0.0914104	+	0.0527758i
$503$	−7.31678e14			−1.01320			−0.506601	−	0.862180i	$-0.669098\pi$
$503$	−7.31678e14			−1.01320			−0.506601	+	0.862180i	$0.669098\pi$
$504$	6.48331e13	−	2.49846e14i	0.0888032	−	0.342219i
$505$	2.22005e14			0.300787
$506$	1.31975e14	+	7.61957e13i	0.176874	+	0.102118i
$507$	−1.93541e14	+	5.89891e14i	−0.256583	+	0.782038i
$508$	−3.29968e14	−	5.71521e14i	−0.432734	−	0.749518i
$509$	1.66437e14	−	2.88277e14i	0.215925	−	0.373992i	−0.737634	−	0.675201i	$-0.764057\pi$
$509$	1.66437e14	−	2.88277e14i	0.215925	−	0.373992i	0.953558	+	0.301209i	$0.0973901\pi$
$510$	−8.27847e13	+	7.41106e13i	−0.106246	+	0.0951139i
$511$	9.11400e14	−	1.15743e15i	1.15716	−	1.46954i
$512$			3.51844e13i			0.0441942i
$513$	5.32389e14	−	5.13259e13i	0.661582	−	0.0637809i
$514$	−5.32511e14	+	3.07445e14i	−0.654684	+	0.377982i
$515$	2.18012e15	−	1.25869e15i	2.65180	−	1.53102i
$516$	3.37568e14	−	7.07403e13i	0.406245	−	0.0851321i
$517$		−	8.38750e14i		−	0.998699i
$518$	1.25155e14	−	1.58941e14i	0.147447	−	0.187250i
$519$	−3.89587e14	−	4.35186e14i	−0.454134	−	0.507288i
$520$	1.15486e14	−	2.00028e14i	0.133202	−	0.230713i
$521$	2.20669e14	+	3.82210e14i	0.251845	+	0.436209i	0.964034	−	0.265779i	$-0.0856293\pi$
$521$	2.20669e14	+	3.82210e14i	0.251845	+	0.436209i	−0.712189	+	0.701988i	$0.752296\pi$
$522$	−6.68605e14	+	2.93095e14i	−0.755061	+	0.330995i
$523$	1.01024e15	+	5.83260e14i	1.12892	+	0.651783i	0.943663	−	0.330907i	$-0.107355\pi$
$523$	1.01024e15	+	5.83260e14i	1.12892	+	0.651783i	0.185257	+	0.982690i	$0.440688\pi$
$524$	−6.66999e14			−0.737570
$525$	−1.68087e15	+	1.11751e15i	−1.83932	+	1.22285i
$526$	−5.28467e14			−0.572264
$527$	1.07766e14	+	6.22189e13i	0.115485	+	0.0666752i
$528$	−2.10657e14	−	6.91158e13i	−0.223404	−	0.0732977i
$529$	−4.31471e14	−	7.47330e14i	−0.452841	−	0.784344i
$530$	1.17952e15	−	2.04299e15i	1.22515	−	2.12202i
$531$	−1.32824e14	+	1.19757e15i	−0.136539	+	1.23107i
$532$	−1.21210e14	−	3.03324e14i	−0.123317	−	0.308598i
$533$		−	7.49668e14i		−	0.754865i
$534$	−1.03391e14	−	4.93373e14i	−0.103040	−	0.491698i
$535$	8.90123e14	−	5.13913e14i	0.878019	−	0.506925i
$536$	2.20704e14	−	1.27423e14i	0.215478	−	0.124406i
$537$	1.98130e13	+	9.45464e13i	0.0191466	+	0.0913663i
$538$			3.84790e14i			0.368062i
$539$	2.81057e14	−	9.52728e14i	0.266106	−	0.902050i
$540$	7.77950e14	−	5.55043e14i	0.729099	−	0.520189i
$541$	−7.85100e14	+	1.35983e15i	−0.728349	+	1.26154i	0.229231	+	0.973372i	$0.426379\pi$
$541$	−7.85100e14	+	1.35983e15i	−0.728349	+	1.26154i	−0.957580	+	0.288166i	$0.906954\pi$
$542$	7.99217e13	+	1.38429e14i	0.0733954	+	0.127125i
$543$	1.59890e15	+	5.24591e14i	1.45352	+	0.476894i
$544$	−1.91522e13	−	1.10576e13i	−0.0172356	−	0.00995096i
$545$	−2.02485e15			−1.80390
$546$	−3.02133e14	−	1.49865e14i	−0.266464	−	0.132173i
$547$	1.36524e15			1.19201			0.596004	−	0.802982i	$-0.296754\pi$
$547$	1.36524e15			1.19201			0.596004	+	0.802982i	$0.296754\pi$
$548$	1.33230e12	+	7.69203e11i	0.00115162	+	0.000664887i
$549$	6.20335e14	+	1.41510e15i	0.530858	+	1.21099i
$550$	8.66847e14	+	1.50142e15i	0.734425	+	1.27206i
$551$	−4.61915e14	+	8.00059e14i	−0.387461	+	0.671102i
$552$	−8.72046e13	−	9.74113e13i	−0.0724226	−	0.0808992i
$553$	−6.07016e12	+	4.20300e13i	−0.00499128	+	0.0345598i
$554$		−	1.02257e15i		−	0.832509i
$555$	7.33070e14	−	1.53621e14i	0.590928	−	0.123834i
$556$	6.63122e13	−	3.82854e13i	0.0529276	−	0.0305577i
$557$	1.91258e14	−	1.10423e14i	0.151152	−	0.0872679i	−0.422516	−	0.906355i	$-0.638853\pi$
$557$	1.91258e14	−	1.10423e14i	0.151152	−	0.0872679i	0.573669	+	0.819087i	$0.305520\pi$
$558$	−8.62249e14	−	6.34054e14i	−0.674752	−	0.496179i
$559$		−	4.50646e14i		−	0.349197i
$560$	−4.58539e14	−	3.61069e14i	−0.351837	−	0.277048i
$561$	1.03827e14	−	9.29478e13i	0.0788884	−	0.0706226i
$562$	−2.90191e14	+	5.02625e14i	−0.218340	+	0.378177i
$563$	1.03336e15	+	1.78983e15i	0.769938	+	1.33357i	0.937596	+	0.347726i	$0.113046\pi$
$563$	1.03336e15	+	1.78983e15i	0.769938	+	1.33357i	−0.167658	+	0.985845i	$0.553621\pi$
$564$	−2.24331e14	+	6.83736e14i	−0.165521	+	0.504491i
$565$	2.99411e15	+	1.72865e15i	2.18777	+	1.26311i
$566$	1.01508e15			0.734531
$567$	−8.80518e14	−	1.08254e15i	−0.631003	−	0.775780i
$568$	−4.92333e14			−0.349416
$569$	−1.87412e15	−	1.08202e15i	−1.31728	−	0.760533i	−0.333992	−	0.942576i	$-0.608396\pi$
$569$	−1.87412e15	−	1.08202e15i	−1.31728	−	0.760533i	−0.983291	+	0.182043i	$0.941729\pi$
$570$	3.77012e14	−	1.14909e15i	0.262448	−	0.799914i
$571$	1.31105e14	+	2.27081e14i	0.0903901	+	0.156560i	0.907675	−	0.419673i	$-0.137855\pi$
$571$	1.31105e14	+	2.27081e14i	0.0903901	+	0.156560i	−0.817285	+	0.576233i	$0.804522\pi$
$572$	−1.44840e14	+	2.50871e14i	−0.0989033	+	0.171306i
$573$	−7.36024e14	+	6.58904e14i	−0.497785	+	0.445627i
$574$	−1.87485e15	−	2.70774e14i	−1.25589	−	0.181381i
$575$			1.02238e15i			0.678326i
$576$	1.53239e14	+	1.12684e14i	0.100704	+	0.0740524i
$577$	1.72763e15	−	9.97446e14i	1.12456	−	0.649265i	0.181999	−	0.983299i	$-0.441743\pi$
$577$	1.72763e15	−	9.97446e14i	1.12456	−	0.649265i	0.942561	+	0.334033i	$0.108410\pi$
$578$	−9.37733e14	+	5.41400e14i	−0.604611	+	0.349072i
$579$	2.64906e15	−	5.55133e14i	1.69184	−	0.354539i
$580$			1.65065e15i			1.04424i
$581$	4.33477e14	−	1.73220e14i	0.271642	−	0.108550i
$582$	2.42661e14	+	2.71063e14i	0.150634	+	0.168265i
$583$	−1.47933e15	+	2.56227e15i	−0.909678	+	1.57561i
$584$	5.42801e14	+	9.40158e14i	0.330651	+	0.572704i
$585$	−5.01319e14	−	1.14360e15i	−0.302522	−	0.690109i
$586$	−1.63660e15	−	9.44890e14i	−0.978374	−	0.564864i
$587$	−8.14518e14			−0.482382			−0.241191	−	0.970478i	$-0.577538\pi$
$587$	−8.14518e14			−0.482382			−0.241191	+	0.970478i	$0.577538\pi$
$588$	−4.83928e14	+	7.01478e14i	−0.283926	+	0.411565i
$589$	−1.35441e15			−0.787257
$590$	2.35941e15	+	1.36221e15i	1.35868	+	0.784436i
$591$	1.13374e14	+	3.71976e13i	0.0646820	+	0.0212219i
$592$	7.45384e13	+	1.29104e14i	0.0421319	+	0.0729745i
$593$	9.34195e14	−	1.61807e15i	0.523162	−	0.906144i	−0.476474	−	0.879188i	$-0.658085\pi$
$593$	9.34195e14	−	1.61807e15i	0.523162	−	0.906144i	0.999637	−	0.0269554i	$-0.00858122\pi$
$594$	−9.75688e14	+	6.96123e14i	−0.541359	+	0.386243i
$595$	3.40651e14	−	1.36126e14i	0.187269	−	0.0748338i
$596$		−	5.30096e14i		−	0.288735i
$597$	1.04981e14	+	5.00965e14i	0.0566570	+	0.270364i
$598$	−1.47941e14	+	8.54139e13i	−0.0791102	+	0.0456743i
$599$	9.88456e14	−	5.70685e14i	0.523733	−	0.302377i	−0.214728	−	0.976674i	$-0.568886\pi$
$599$	9.88456e14	−	5.70685e14i	0.523733	−	0.302377i	0.738461	+	0.674297i	$0.235553\pi$
$600$	−3.05072e14	−	1.45578e15i	−0.160166	−	0.764301i
$601$		−	2.12879e15i		−	1.10745i	−0.832701	−	0.553723i	$-0.813206\pi$
$601$		−	2.12879e15i		−	1.10745i	0.832701	−	0.553723i	$-0.186794\pi$
$602$	−1.12702e15	−	1.62770e14i	−0.580968	−	0.0839060i
$603$	1.51874e14	−	1.36933e15i	0.0775780	−	0.699460i
$604$	3.39744e13	−	5.88454e13i	0.0171969	−	0.0297858i
$605$	2.06227e14	+	3.57196e14i	0.103441	+	0.179164i
$606$	2.26974e14	+	7.44693e13i	0.112818	+	0.0370150i
$607$	−2.18703e15	−	1.26268e15i	−1.07725	−	0.621951i	−0.147098	−	0.989122i	$-0.546993\pi$
$607$	−2.18703e15	−	1.26268e15i	−1.07725	−	0.621951i	−0.930154	+	0.367171i	$0.880326\pi$
$608$	2.40706e14			0.117495
$609$	2.40544e15	−	1.52074e14i	1.16359	−	0.0735632i
$610$	3.49360e15			1.67479
$611$	8.14256e14	+	4.70111e14i	0.386843	+	0.223344i
$612$	−1.09498e14	+	4.80003e13i	−0.0515551	+	0.0226001i
$613$	−1.91486e15	−	3.31664e15i	−0.893521	−	1.54762i	−0.835624	−	0.549301i	$-0.814894\pi$
$613$	−1.91486e15	−	3.31664e15i	−0.893521	−	1.54762i	−0.0578966	−	0.998323i	$-0.518439\pi$
$614$	−9.25540e14	+	1.60308e15i	−0.428025	+	0.741361i
$615$	−4.67790e15	−	5.22542e15i	−2.14406	−	2.39501i
$616$	5.75089e14	+	4.52844e14i	0.261241	+	0.205710i
$617$		−	1.14687e15i		−	0.516354i	−0.966098	−	0.258177i	$-0.916878\pi$
$617$		−	1.14687e15i		−	0.516354i	0.966098	−	0.258177i	$-0.0831217\pi$
$618$	2.65114e15	−	5.55569e14i	1.18303	−	0.247914i
$619$	−1.41022e15	+	8.14191e14i	−0.623718	+	0.360104i	−0.778315	−	0.627874i	$-0.783925\pi$
$619$	−1.41022e15	+	8.14191e14i	−0.623718	+	0.360104i	0.154597	+	0.987978i	$0.450592\pi$
$620$	−2.09578e15	+	1.21000e15i	−0.918736	+	0.530433i
$621$	−7.03545e14	+	6.78264e13i	−0.305695	+	0.0294710i
$622$		−	2.44166e15i		−	1.05157i
$623$	−2.37896e14	+	1.64720e15i	−0.101555	+	0.703174i
$624$	1.85169e14	−	1.65767e14i	0.0783525	−	0.0701427i
$625$	−1.99049e15	+	3.44763e15i	−0.834872	+	1.44604i
$626$	6.97123e13	+	1.20745e14i	0.0289835	+	0.0502008i
$627$	−4.72840e14	+	1.44117e15i	−0.194869	+	0.593940i
$628$	−1.11296e15	−	6.42568e14i	−0.454675	−	0.262507i
$629$	−9.37021e13			−0.0379464
$630$	−3.04112e15	+	8.40693e14i	−1.22084	+	0.337493i
$631$	7.71425e14			0.306996			0.153498	−	0.988149i	$-0.450946\pi$
$631$	7.71425e14			0.306996			0.153498	+	0.988149i	$0.450946\pi$
$632$	−2.71009e13	−	1.56467e13i	−0.0106915	−	0.00617276i
$633$	9.05176e14	−	2.75888e15i	0.354008	−	1.07898i
$634$	6.19992e14	+	1.07386e15i	0.240378	+	0.416347i
$635$	−4.03342e15	+	6.98609e15i	−1.55031	+	2.68521i
$636$	1.89123e15	−	1.69306e15i	0.720658	−	0.645148i
$637$	7.67377e14	+	8.06844e14i	0.289896	+	0.304805i
$638$		−	2.07021e15i		−	0.775356i
$639$	−1.57678e15	+	2.14426e15i	−0.585487	+	0.796203i
$640$	3.72462e14	−	2.15041e14i	0.137117	−	0.0791647i
$641$	1.56856e15	−	9.05610e14i	0.572510	−	0.330539i	−0.185641	−	0.982618i	$-0.559436\pi$
$641$	1.56856e15	−	9.05610e14i	0.572510	−	0.330539i	0.758151	+	0.652079i	$0.226103\pi$
$642$	1.08244e15	−	2.26834e14i	0.391705	−	0.0820853i
$643$		−	3.36872e15i		−	1.20866i	−0.796734	−	0.604331i	$-0.793441\pi$
$643$		−	3.36872e15i		−	1.20866i	0.796734	−	0.604331i	$-0.206559\pi$
$644$	1.60177e14	+	4.00838e14i	0.0569808	+	0.142593i
$645$	−2.81201e15	−	3.14114e15i	−0.991834	−	1.10792i
$646$	−7.56479e13	+	1.31026e14i	−0.0264556	+	0.0458225i
$647$	1.62584e15	+	2.81604e15i	0.563773	+	0.976484i	0.997163	+	0.0752770i	$0.0239841\pi$
$647$	1.62584e15	+	2.81604e15i	0.563773	+	0.976484i	−0.433390	+	0.901207i	$0.642683\pi$
$648$	9.81550e14	−	3.06513e14i	0.337481	−	0.105387i
$649$	−2.95913e15	−	1.70845e15i	−1.00883	−	0.582448i
$650$	−1.94344e15			−0.656972
$651$	1.95637e15	+	2.94263e15i	0.655776	+	0.986370i
$652$	1.17883e15			0.391824
$653$	1.35242e14	+	7.80819e13i	0.0445747	+	0.0257352i	0.522122	−	0.852871i	$-0.325141\pi$
$653$	1.35242e14	+	7.80819e13i	0.0445747	+	0.0257352i	−0.477547	+	0.878606i	$0.658474\pi$
$654$	−2.07018e15	−	6.79217e14i	−0.676598	−	0.221989i
$655$	4.07658e15	+	7.06085e15i	1.32120	+	2.28839i
$656$	6.97959e14	−	1.20890e15i	0.224315	−	0.388526i
$657$	5.83310e15	+	6.46956e14i	1.85904	+	0.206189i
$658$	1.46981e15	−	1.86658e15i	0.464535	−	0.589935i
$659$		−	1.22672e15i		−	0.384483i	−0.981348	−	0.192241i	$-0.938424\pi$
$659$		−	1.22672e15i		−	0.384483i	0.981348	−	0.192241i	$-0.0615757\pi$
$660$	5.55843e14	+	2.65244e15i	0.172767	+	0.824431i
$661$	−1.23609e15	+	7.13655e14i	−0.381014	+	0.219979i	−0.678259	−	0.734823i	$-0.737265\pi$
$661$	−1.23609e15	+	7.13655e14i	−0.381014	+	0.219979i	0.297245	+	0.954801i	$0.403932\pi$
$662$	−3.30325e15	+	1.90713e15i	−1.00977	+	0.582991i
$663$	3.20397e13	+	1.52891e14i	0.00971323	+	0.0463509i
$664$			3.43991e14i			0.103424i
$665$	−2.47017e15	+	3.13699e15i	−0.736560	+	0.935394i
$666$	8.01012e14	+	8.88412e13i	0.236881	+	0.0262728i
$667$	6.10414e14	−	1.05727e15i	0.179033	−	0.310094i
$668$	1.00621e15	+	1.74281e15i	0.292698	+	0.506967i
$669$	−3.55321e15	−	1.16579e15i	−1.02512	−	0.336339i
$670$	−2.69781e15	−	1.55758e15i	−0.771969	−	0.445696i
$671$	−4.38160e15			−1.24354
$672$	−3.47687e14	−	5.22964e14i	−0.0978717	−	0.147211i
$673$	−3.73740e14			−0.104349			−0.0521743	−	0.998638i	$-0.516615\pi$
$673$	−3.73740e14			−0.104349			−0.0521743	+	0.998638i	$0.516615\pi$
$674$	1.85901e15	+	1.07330e15i	0.514818	+	0.297230i
$675$	−7.31743e15	−	3.33371e15i	−2.00996	−	0.915709i
$676$	7.55223e14	+	1.30808e15i	0.205764	+	0.356393i
$677$	2.02924e15	−	3.51474e15i	0.548397	−	0.949851i	−0.449988	−	0.893035i	$-0.648572\pi$
$677$	2.02924e15	−	3.51474e15i	0.548397	−	0.949851i	0.998385	−	0.0568162i	$-0.0180949\pi$
$678$	2.48128e15	+	2.77170e15i	0.665139	+	0.742989i
$679$	−4.45720e14	−	1.11540e15i	−0.118516	−	0.296583i
$680$			2.70328e14i			0.0713003i
$681$	−5.13547e15	+	1.07618e15i	−1.34360	+	0.281564i
$682$	2.62848e15	−	1.51755e15i	0.682166	−	0.393849i
$683$	1.38633e15	−	8.00399e14i	0.356906	−	0.206060i	−0.310817	−	0.950470i	$-0.600603\pi$
$683$	1.38633e15	−	8.00399e14i	0.356906	−	0.206060i	0.667723	+	0.744410i	$0.267269\pi$
$684$	7.70904e14	−	1.04835e15i	0.196876	−	0.267731i
$685$		−	1.88050e13i		−	0.00476403i
$686$	2.29501e15	−	1.62771e15i	0.576770	−	0.409068i
$687$	5.48301e13	−	4.90850e13i	0.0136696	−	0.0122373i
$688$	4.19563e14	−	7.26704e14i	0.103767	−	0.179730i
$689$	−1.65830e15	−	2.87226e15i	−0.406871	−	0.704722i
$690$	−4.98216e14	+	1.51851e15i	−0.121268	+	0.369613i
$691$	2.03451e15	+	1.17463e15i	0.491282	+	0.283642i	0.725106	−	0.688637i	$-0.241791\pi$
$691$	2.03451e15	+	1.17463e15i	0.491282	+	0.283642i	−0.233824	+	0.972279i	$0.575124\pi$
$692$	−1.42107e15			−0.340433
$693$	3.81410e15	−	1.05438e15i	0.906483	−	0.250590i
$694$	1.53490e15			0.361912
$695$	−8.10578e14	−	4.67987e14i	−0.189617	−	0.109476i
$696$	−5.53695e14	+	1.68760e15i	−0.128505	+	0.391669i
$697$	4.38702e14	+	7.59854e14i	0.101016	+	0.174964i
$698$	1.26239e15	−	2.18653e15i	0.288396	−	0.499516i
$699$	1.73425e15	−	1.55254e15i	0.393086	−	0.351899i
$700$	−7.01954e14	+	4.86036e15i	−0.157859	+	1.09302i
$701$			1.68670e15i			0.376348i	0.982136	+	0.188174i	$0.0602568\pi$
$701$			1.68670e15i			0.376348i	−0.982136	+	0.188174i	$0.939743\pi$
$702$	−1.28931e14	−	1.33737e15i	−0.0285433	−	0.296071i
$703$	8.83239e14	−	5.09938e14i	0.194010	−	0.112012i
$704$	−4.67133e14	+	2.69700e14i	−0.101810	+	0.0587802i
$705$	8.60910e15	−	1.80411e15i	1.86173	−	0.390142i
$706$			4.17606e14i			0.0896068i
$707$	−6.19634e14	−	4.87921e14i	−0.131926	−	0.103883i
$708$	1.95529e15	+	2.18415e15i	0.413075	+	0.461423i
$709$	1.73718e15	−	3.00889e15i	0.364159	−	0.630742i	−0.624482	−	0.781039i	$-0.714690\pi$
$709$	1.73718e15	−	3.00889e15i	0.364159	−	0.630742i	0.988641	+	0.150298i	$0.0480232\pi$
$710$	3.00906e15	+	5.21184e15i	0.625907	+	1.08410i
$711$	−1.54942e14	+	6.79216e13i	−0.0319805	+	0.0140193i
$712$	−1.06211e15	−	6.13212e14i	−0.217536	−	0.125595i
$713$	1.78984e15			0.363765
$714$	3.93939e14	−	2.49052e13i	0.0794491	−	0.00502285i
$715$	3.54096e15			0.708659
$716$	2.03536e14	+	1.17512e14i	0.0404221	+	0.0233377i
$717$	4.67309e15	+	1.53322e15i	0.920977	+	0.302168i
$718$	7.23829e14	+	1.25371e15i	0.141564	+	0.245195i
$719$	−2.28021e15	+	3.94944e15i	−0.442554	+	0.766526i	−0.997878	−	0.0651081i	$-0.979261\pi$
$719$	−2.28021e15	+	3.94944e15i	−0.442554	+	0.766526i	0.555324	+	0.831634i	$0.312594\pi$
$720$	2.56304e14	−	2.31089e15i	0.0493659	−	0.445094i
$721$	−8.85125e15	−	1.27833e15i	−1.69184	−	0.244343i
$722$			2.08095e15i			0.394736i
$723$	1.73243e14	+	8.26702e14i	0.0326132	+	0.155628i
$724$	3.54556e15	−	2.04703e15i	0.662404	−	0.382439i
$725$	1.20281e16	−	6.94442e15i	2.23017	−	1.28759i
$726$	9.10257e13	+	4.34369e14i	0.0167499	+	0.0799295i
$727$			8.66288e15i			1.58206i	0.611777	+	0.791030i	$0.290455\pi$
$727$			8.66288e15i			1.58206i	−0.611777	+	0.791030i	$0.709545\pi$
$728$	−7.61952e14	+	3.04480e14i	−0.138104	+	0.0551870i
$729$	1.80863e15	−	5.25662e15i	0.325348	−	0.945594i
$730$	6.63501e15	−	1.14922e16i	1.18458	−	2.05176i
$731$	2.63716e14	+	4.56769e14i	0.0467294	+	0.0809377i
$732$	3.57181e15	+	1.17190e15i	0.628170	+	0.206100i
$733$	−5.10594e15	−	2.94791e15i	−0.891258	−	0.514568i	−0.0169043	−	0.999857i	$-0.505381\pi$
$733$	−5.10594e15	−	2.94791e15i	−0.891258	−	0.514568i	−0.874354	+	0.485289i	$0.838714\pi$
$734$	−4.83039e15			−0.836863
$735$	1.03835e16	+	8.35548e14i	1.78552	+	0.143678i
$736$	−3.18090e14			−0.0542902
$737$	3.38353e15	+	1.95348e15i	0.573191	+	0.330932i
$738$	−3.02980e15	−	6.91155e15i	−0.509454	−	1.16216i
$739$	−4.01666e15	−	6.95706e15i	−0.670379	−	1.16113i	−0.977797	−	0.209556i	$-0.932798\pi$
$739$	−4.01666e15	−	6.95706e15i	−0.670379	−	1.16113i	0.307418	−	0.951575i	$-0.400535\pi$
$740$	9.11132e14	−	1.57813e15i	0.150941	−	0.261437i
$741$	−1.13406e15	−	1.26679e15i	−0.186481	−	0.208308i
$742$	−7.78222e15	+	3.10982e15i	−1.27023	+	0.507590i
$743$		−	8.49682e15i		−	1.37663i	−0.725411	−	0.688316i	$-0.758350\pi$
$743$		−	8.49682e15i		−	1.37663i	0.725411	−	0.688316i	$-0.241650\pi$
$744$	−2.54858e15	+	5.34076e14i	−0.409870	+	0.0858919i
$745$	−5.61160e15	+	3.23986e15i	−0.895833	+	0.517209i
$746$	4.59843e15	−	2.65491e15i	0.728696	−	0.420713i
$747$	1.49819e15	+	1.10169e15i	0.235669	+	0.173299i
$748$		−	3.39039e14i		−	0.0529408i
$749$	−3.61389e15	−	5.21933e14i	−0.560176	−	0.0809030i
$750$	−7.41325e15	+	6.63649e15i	−1.14070	+	1.02118i
$751$	−3.42821e15	+	5.93784e15i	−0.523658	+	0.907003i	0.475962	+	0.879466i	$0.342100\pi$
$751$	−3.42821e15	+	5.93784e15i	−0.523658	+	0.907003i	−0.999621	+	0.0275373i	$0.991234\pi$
$752$	8.75370e14	+	1.51619e15i	0.132738	+	0.229908i
$753$	3.09138e14	−	9.42218e14i	0.0465350	−	0.141834i
$754$	2.00976e15	+	1.16033e15i	0.300332	+	0.173397i
$755$	−8.30584e14			−0.123218
$756$	−3.39120e15	−	1.60601e14i	−0.499440	−	0.0236526i
$757$	−2.23307e15			−0.326495			−0.163247	−	0.986585i	$-0.552197\pi$
$757$	−2.23307e15			−0.326495			−0.163247	+	0.986585i	$0.552197\pi$
$758$	1.23453e14	+	7.12758e13i	0.0179194	+	0.0103457i
$759$	6.24852e14	−	1.90448e15i	0.0900425	−	0.274440i
$760$	−1.47116e15	−	2.54812e15i	−0.210467	−	0.364539i
$761$	−3.83893e15	+	6.64922e15i	−0.545249	+	0.944399i	0.453342	+	0.891336i	$0.350231\pi$
$761$	−3.83893e15	+	6.64922e15i	−0.545249	+	0.944399i	−0.998591	+	0.0530621i	$0.983102\pi$
$762$	−6.46713e15	+	5.78950e15i	−0.911925	+	0.816374i
$763$	5.65154e15	+	4.45021e15i	0.791192	+	0.623011i
$764$			2.40344e15i			0.334056i
$765$	1.17736e15	+	8.65772e14i	0.162470	+	0.119472i
$766$	−3.94655e15	+	2.27854e15i	−0.540704	+	0.312176i
$767$	3.31712e15	−	1.91514e15i	0.451219	−	0.260511i
$768$	4.52933e14	−	9.49161e13i	0.0611713	−	0.0128190i
$769$		−	1.28901e15i		−	0.172846i	−0.996259	−	0.0864232i	$-0.972456\pi$
$769$		−	1.28901e15i		−	0.172846i	0.996259	−	0.0864232i	$-0.0275437\pi$
$770$	1.27896e15	−	8.85561e15i	0.170278	−	1.17901i
$771$	5.39433e15	+	6.02570e15i	0.713080	+	0.796541i
$772$	3.29251e15	−	5.70279e15i	0.432147	−	0.748500i
$773$	1.18145e15	+	2.04632e15i	0.153967	+	0.266678i	0.932682	−	0.360699i	$-0.117462\pi$
$773$	1.18145e15	+	2.04632e15i	0.153967	+	0.266678i	−0.778716	+	0.627377i	$0.784128\pi$
$774$	−1.82130e15	−	4.15472e15i	−0.235671	−	0.537609i
$775$	1.76342e16	+	1.01811e16i	2.26567	+	1.30808i
$776$	8.85138e14			0.112920
$777$	−2.38369e15	−	1.18237e15i	−0.301950	−	0.149774i
$778$	3.85102e15			0.484382
$779$	−8.27043e15	−	4.77494e15i	−1.03293	−	0.596364i
$780$	−2.88653e15	−	9.47058e14i	−0.357978	−	0.117451i
$781$	−3.77389e15	−	6.53657e15i	−0.464739	−	0.804951i
$782$	9.99676e13	−	1.73149e14i	0.0122242	−	0.0211730i
$783$	5.57673e15	+	7.81637e15i	0.677158	+	0.949107i
$784$	4.86267e14	+	2.01555e15i	0.0586322	+	0.243027i
$785$			1.57091e16i			1.88091i
$786$	1.79935e15	+	8.58637e15i	0.213940	+	1.02091i
$787$	−1.27557e15	+	7.36452e14i	−0.150607	+	0.0869527i	−0.573409	−	0.819269i	$-0.694380\pi$
$787$	−1.27557e15	+	7.36452e14i	−0.150607	+	0.0869527i	0.422803	+	0.906222i	$0.361046\pi$
$788$	2.51408e14	−	1.45150e14i	0.0294771	−	0.0170186i
$789$	1.42563e15	+	6.80303e15i	0.165991	+	0.792098i
$790$			3.82520e14i			0.0442288i
$791$	−4.55761e15	−	1.14053e16i	−0.523319	−	1.30959i
$792$	−3.21451e14	+	2.89827e15i	−0.0366544	+	0.330484i
$793$	2.45584e15	−	4.25365e15i	0.278098	−	0.481680i
$794$	−9.65179e13	−	1.67174e14i	−0.0108541	−	0.0187999i
$795$	−2.94816e16	−	9.67280e15i	−3.29255	−	1.08027i
$796$	1.07846e15	+	6.22648e14i	0.119614	+	0.0690591i
$797$	6.99029e15			0.769971			0.384985	−	0.922923i	$-0.374206\pi$
$797$	6.99029e15			0.769971			0.384985	+	0.922923i	$0.374206\pi$
$798$	−3.57774e15	+	2.37862e15i	−0.391375	+	0.260201i
$799$	−1.10043e15			−0.119551
$800$	−3.13395e15	−	1.80939e15i	−0.338141	−	0.195226i
$801$	−6.07234e15	+	2.66192e15i	−0.650695	+	0.285244i
$802$	3.95663e15	+	6.85308e15i	0.421081	+	0.729334i
$803$	−8.32149e15	+	1.44132e16i	−0.879560	+	1.52344i
$804$	−2.23573e15	−	2.49740e15i	−0.234698	−	0.262168i
$805$	3.26430e15	−	4.14549e15i	0.340340	−	0.432214i
$806$			3.40229e15i			0.352313i
$807$	4.95346e15	−	1.03804e15i	0.509453	−	0.106760i
$808$	5.03317e14	−	2.90590e14i	0.0514137	−	0.0296837i
$809$	1.20713e15	−	6.96935e14i	0.122472	−	0.0707092i	−0.437513	−	0.899212i	$-0.644140\pi$
$809$	1.20713e15	−	6.96935e14i	0.122472	−	0.0707092i	0.559984	+	0.828503i	$0.310807\pi$
$810$	−9.24381e15	−	8.51733e15i	−0.931501	−	0.858294i
$811$			8.96106e15i			0.896901i	0.893808	+	0.448451i	$0.148024\pi$
$811$			8.96106e15i			0.896901i	−0.893808	+	0.448451i	$0.851976\pi$
$812$	3.62780e15	−	4.60711e15i	0.360649	−	0.458006i
$813$	1.56641e15	−	1.40228e15i	0.154670	−	0.138464i
$814$	−1.14272e15	+	1.97925e15i	−0.112074	+	0.194118i
$815$	−7.20483e15	−	1.24791e16i	−0.701871	−	1.21568i
$816$	−9.06788e13	+	2.76379e14i	−0.00877425	+	0.0267430i
$817$	−4.97158e15	−	2.87035e15i	−0.477830	−	0.275875i
$818$	−6.53392e15			−0.623779
$819$	−1.11418e15	+	4.29369e15i	−0.105656	+	0.407164i
$820$	−1.70632e16			−1.60726
$821$	−1.11603e16	−	6.44339e15i	−1.04421	−	0.602875i	−0.123187	−	0.992383i	$-0.539311\pi$
$821$	−1.11603e16	−	6.44339e15i	−1.04421	−	0.602875i	−0.921023	+	0.389509i	$0.872645\pi$
$822$	6.30794e12	−	1.92259e13i	0.000586263	−	0.00178687i
$823$	−7.49448e14	−	1.29808e15i	−0.0691899	−	0.119840i	0.829355	−	0.558722i	$-0.188708\pi$
$823$	−7.49448e14	−	1.29808e15i	−0.0691899	−	0.119840i	−0.898545	+	0.438882i	$0.855375\pi$
$824$	3.29509e15	−	5.70727e15i	0.302182	−	0.523394i
$825$	1.69895e16	−	1.52094e16i	1.54769	−	1.38553i
$826$	−3.59148e15	−	8.98756e15i	−0.325000	−	0.813301i
$827$			9.78197e15i			0.879318i	0.898165	+	0.439659i	$0.144901\pi$
$827$			9.78197e15i			0.879318i	−0.898165	+	0.439659i	$0.855099\pi$
$828$	−1.01874e15	+	1.38538e15i	−0.0909695	+	0.123709i
$829$	−7.48383e15	+	4.32079e15i	−0.663856	+	0.383277i	−0.793745	−	0.608251i	$-0.791871\pi$
$829$	−7.48383e15	+	4.32079e15i	−0.663856	+	0.383277i	0.129889	+	0.991529i	$0.458538\pi$
$830$	3.64148e15	−	2.10241e15i	0.320885	−	0.185263i
$831$	−1.31637e16	+	2.75856e15i	−1.15232	+	0.241478i
$832$		−	6.04656e14i		−	0.0525812i
$833$	−1.24996e15	−	3.68742e14i	−0.107982	−	0.0318548i
$834$	−6.71741e14	−	7.50364e14i	−0.0576486	−	0.0643960i
$835$	1.22996e16	−	2.13035e16i	1.04861	−	1.81625i
$836$	1.84509e15	+	3.19579e15i	0.156273	+	0.270672i
$837$	−5.83619e15	+	1.28103e16i	−0.491066	+	1.07788i
$838$	2.32188e15	+	1.34054e15i	0.194088	+	0.112057i
$839$	1.01251e16			0.840831			0.420416	−	0.907332i	$-0.361884\pi$
$839$	1.01251e16			0.840831			0.420416	+	0.907332i	$0.361884\pi$
$840$	−3.41110e15	+	6.87688e15i	−0.281422	+	0.567356i
$841$	−4.38422e15			−0.359348
$842$	−1.09955e16	−	6.34827e15i	−0.895364	−	0.516938i
$843$	7.25321e15	+	2.37975e15i	0.586784	+	0.192521i
$844$	−3.53213e15	−	6.11782e15i	−0.283892	−	0.491715i
$845$	9.23159e15	−	1.59896e16i	0.737165	−	1.27681i
$846$	9.40699e15	+	1.04334e15i	0.746301	+	0.0827731i
$847$	2.09445e14	−	1.45021e15i	0.0165087	−	0.114307i
$848$		−	6.17567e15i		−	0.483623i
$849$	−2.73836e15	−	1.30673e16i	−0.213058	−	1.01670i
$850$	1.96984e15	−	1.13729e15i	0.152275	−	0.0879158i
$851$	−1.16719e15	+	6.73876e14i	−0.0896454	+	0.0517568i
$852$	1.32816e15	+	6.33787e15i	0.101352	+	0.483644i
$853$			1.24721e16i			0.945627i	0.881163	+	0.472813i	$0.156762\pi$
$853$			1.24721e16i			0.945627i	−0.881163	+	0.472813i	$0.843238\pi$
$854$	−9.75095e15	−	7.67822e15i	−0.734562	−	0.578419i
$855$	−1.58095e16	−	1.75345e15i	−1.18332	−	0.131244i
$856$	1.34536e15	−	2.33023e15i	0.100053	−	0.173298i
$857$	7.85377e15	+	1.36031e16i	0.580342	+	1.00518i	0.995439	+	0.0954043i	$0.0304144\pi$
$857$	7.85377e15	+	1.36031e16i	0.580342	+	1.00518i	−0.415097	+	0.909777i	$0.636252\pi$
$858$	3.62022e15	+	1.18778e15i	0.265800	+	0.0872079i
$859$	5.05801e15	+	2.92024e15i	0.368992	+	0.213038i	0.673018	−	0.739626i	$-0.264998\pi$
$859$	5.05801e15	+	2.92024e15i	0.368992	+	0.213038i	−0.304026	+	0.952664i	$0.598331\pi$
$860$	−1.02572e16			−0.743510
$861$	1.57203e15	+	2.48657e16i	0.113225	+	1.79095i
$862$	2.71328e15			0.194180
$863$	1.99363e16	+	1.15102e16i	1.41770	+	0.818510i	0.996097	−	0.0882703i	$-0.0281339\pi$
$863$	1.99363e16	+	1.15102e16i	1.41770	+	0.818510i	0.421604	+	0.906780i	$0.361467\pi$
$864$	1.03721e15	−	2.27665e15i	0.0732893	−	0.160868i
$865$	8.68534e15	+	1.50434e16i	0.609815	+	1.05623i
$866$	4.91767e15	−	8.51765e15i	0.343092	−	0.594253i
$867$	9.49922e15	+	1.06110e16i	0.658541	+	0.735619i
$868$	8.50883e15	+	1.22888e15i	0.586153	+	0.0846548i
$869$		−	4.79749e14i		−	0.0328401i
$870$	2.12491e16	−	4.45293e15i	1.44539	−	0.302893i
$871$	−3.79287e15	+	2.18982e15i	−0.256371	+	0.148016i
$872$	−4.59063e15	+	2.65040e15i	−0.308341	+	0.178021i
$873$	2.83481e15	−	3.85505e15i	0.189211	−	0.257307i
$874$			2.17614e15i			0.144336i
$875$	3.05048e16	−	1.21899e16i	2.01059	−	0.803444i
$876$	1.06385e16	−	9.52379e15i	0.696798	−	0.623788i
$877$	−6.81149e15	+	1.17978e16i	−0.443347	+	0.767900i	−0.997935	−	0.0642247i	$-0.979543\pi$
$877$	−6.81149e15	+	1.17978e16i	−0.443347	+	0.767900i	0.554588	+	0.832125i	$0.312876\pi$
$878$	4.19757e15	+	7.27040e15i	0.271505	+	0.470260i
$879$	−7.74868e15	+	2.36171e16i	−0.498069	+	1.51806i
$880$	5.71008e15	+	3.29672e15i	0.364744	+	0.210585i
$881$	1.84948e15			0.117404			0.0587018	−	0.998276i	$-0.481304\pi$
$881$	1.84948e15			0.117404			0.0587018	+	0.998276i	$0.481304\pi$
$882$	1.03357e16	+	4.33731e15i	0.652023	+	0.273617i
$883$	−2.58256e16			−1.61908			−0.809538	−	0.587068i	$-0.800282\pi$
$883$	−2.58256e16			−1.61908			−0.809538	+	0.587068i	$0.800282\pi$
$884$	3.29138e14	+	1.90028e14i	0.0205065	+	0.0118394i
$885$	1.11710e16	−	3.40479e16i	0.691676	−	2.10815i
$886$	1.25366e15	+	2.17140e15i	0.0771424	+	0.133615i
$887$	8.12393e15	−	1.40711e16i	0.496806	−	0.860492i	−0.503188	−	0.864177i	$-0.667840\pi$
$887$	8.12393e15	−	1.40711e16i	0.496806	−	0.860492i	0.999993	+	0.00368469i	$0.00117287\pi$
$888$	1.46090e15	−	1.30782e15i	0.0887867	−	0.0794837i
$889$	2.66116e16	−	1.06341e16i	1.60735	−	0.642308i
$890$			1.49914e16i			0.899906i
$891$	1.15934e16	+	1.06823e16i	0.691644	+	0.637288i
$892$	−7.87925e15	+	4.54908e15i	−0.467173	+	0.269723i
$893$	1.03727e16	−	5.98866e15i	0.611233	−	0.352896i
$894$	−6.82400e15	+	1.43003e15i	−0.399653	+	0.0837507i
$895$		−	2.87284e15i		−	0.167219i
$896$	−1.51219e15	−	2.18397e14i	−0.0874807	−	0.0126343i
$897$	1.49864e15	+	1.67405e15i	0.0861667	+	0.0962519i
$898$	−8.34680e15	+	1.44571e16i	−0.476980	+	0.826154i
$899$	−1.21573e16	−	2.10571e16i	−0.690493	−	1.19597i
$900$	−1.79175e16	+	7.85446e15i	−1.01145	+	0.443387i
$901$	3.36166e15	+	1.94086e15i	0.188611	+	0.108895i
$902$	2.14003e16			1.19340
$903$	9.44992e14	+	1.49474e16i	0.0523776	+	0.828484i
$904$	9.05079e15			0.498609
$905$	−4.33397e16	−	2.50222e16i	−2.37312	−	1.37012i
$906$	−8.49177e14	−	2.78611e14i	−0.0462161	−	0.0151633i
$907$	−8.41397e15	−	1.45734e16i	−0.455157	−	0.788355i	0.543540	−	0.839383i	$-0.317083\pi$
$907$	−8.41397e15	−	1.45734e16i	−0.455157	−	0.788355i	−0.998697	+	0.0510283i	$0.983750\pi$
$908$	−6.38287e15	+	1.10555e16i	−0.343197	+	0.594435i
$909$	3.46350e14	−	3.12277e15i	0.0185103	−	0.166893i
$910$	7.88015e15	+	6.20510e15i	0.418608	+	0.329626i
$911$		−	5.35338e14i		−	0.0282668i	−0.999900	−	0.0141334i	$-0.995501\pi$
$911$		−	5.35338e14i		−	0.0282668i	0.999900	−	0.0141334i	$-0.00449895\pi$
$912$	−6.49348e14	−	3.09864e15i	−0.0340805	−	0.162630i
$913$	−4.56707e15	+	2.63680e15i	−0.238258	+	0.137559i
$914$	3.78101e14	−	2.18297e14i	0.0196067	−	0.0113199i
$915$	−9.42461e15	−	4.49736e16i	−0.485789	−	2.31815i
$916$		−	1.79044e14i		−	0.00917349i
$917$	4.14020e15	−	2.86670e16i	0.210858	−	1.45999i
$918$	9.13303e14	+	1.28009e15i	0.0462360	+	0.0648045i
$919$	−6.52935e15	+	1.13092e16i	−0.328575	+	0.569109i	−0.982229	−	0.187685i	$-0.939902\pi$
$919$	−6.52935e15	+	1.13092e16i	−0.328575	+	0.569109i	0.653654	+	0.756793i	$0.273235\pi$
$920$	1.94411e15	+	3.36730e15i	0.0972497	+	0.168441i
$921$	2.31335e16	+	7.59000e15i	1.15031	+	0.377410i
$922$	−2.17036e16	−	1.25306e16i	−1.07278	−	0.619372i
$923$	8.46092e15			0.415727
$924$	4.27812e15	−	8.62483e15i	0.208957	−	0.421264i
$925$	−1.53328e16			−0.744462
$926$	1.15298e16	+	6.65676e15i	0.556497	+	0.321294i
$927$	−1.43038e16	−	3.26297e16i	−0.686300	−	1.56558i
$928$	2.16060e15	+	3.74227e15i	0.103053	+	0.178493i
$929$	−1.64315e16	+	2.84602e16i	−0.779096	+	1.34943i	0.153367	+	0.988169i	$0.450988\pi$
$929$	−1.64315e16	+	2.84602e16i	−0.779096	+	1.34943i	−0.932463	+	0.361265i	$0.882345\pi$
$930$	2.12302e16	+	2.37150e16i	1.00069	+	1.11781i
$931$	1.37889e16	−	3.32669e15i	0.646112	−	0.155879i
$932$		−	5.66308e15i		−	0.263794i
$933$	−3.14318e16	+	6.58680e15i	−1.45553	+	0.305018i
$934$	1.14573e16	−	6.61485e15i	0.527440	−	0.304517i
$935$	−3.58907e15	+	2.07215e15i	−0.164255	+	0.0948325i
$936$	−2.63347e15	−	1.93652e15i	−0.119815	−	0.0881058i
$937$			2.54407e15i			0.115070i	0.998344	+	0.0575348i	$0.0183240\pi$
$937$			2.54407e15i			0.115070i	−0.998344	+	0.0575348i	$0.981676\pi$
$938$	4.10658e15	+	1.02766e16i	0.184656	+	0.462097i
$939$	1.36631e15	−	1.22315e15i	0.0610784	−	0.0546787i
$940$	1.07002e16	−	1.85333e16i	0.475543	−	0.823665i
$941$	1.55904e16	+	2.70034e16i	0.688835	+	1.19310i	0.972215	+	0.234090i	$0.0752109\pi$
$941$	1.55904e16	+	2.70034e16i	0.688835	+	1.19310i	−0.283380	+	0.959008i	$0.591456\pi$
$942$	−5.26945e15	+	1.60607e16i	−0.231465	+	0.705481i
$943$	1.09293e16	+	6.31001e15i	0.477283	+	0.275560i
$944$	7.13218e15			0.309654
$945$	1.90263e16	+	3.68808e16i	0.821258	+	1.59194i
$946$	1.28643e16			0.552060
$947$	−4.54360e15	−	2.62325e15i	−0.193854	−	0.111922i	0.399932	−	0.916545i	$-0.369034\pi$
$947$	−4.54360e15	−	2.62325e15i	−0.193854	−	0.111922i	−0.593786	+	0.804623i	$0.702367\pi$
$948$	−1.28313e14	+	3.91084e14i	−0.00544282	+	0.0165891i
$949$	−9.32822e15	−	1.61570e16i	−0.393400	−	0.681390i
$950$	−1.23785e16	+	2.14403e16i	−0.519026	+	0.898980i
$951$	1.21514e16	−	1.08782e16i	0.506562	−	0.453485i
$952$	5.94125e14	−	7.54508e14i	0.0246249	−	0.0312724i
$953$			3.80591e16i			1.56837i	0.620529	+	0.784184i	$0.286918\pi$
$953$			3.80591e16i			1.56837i	−0.620529	+	0.784184i	$0.713082\pi$
$954$	−2.68970e16	−	1.97787e16i	−1.10201	−	0.810366i
$955$	2.54428e16	−	1.46894e16i	1.03644	−	0.598391i
$956$	1.03626e16	−	5.98284e15i	0.419711	−	0.242320i
$957$	−2.66501e16	+	5.58476e15i	−1.07321	+	0.224900i
$958$			8.11127e15i			0.324772i
$959$	−4.13294e13	+	5.24863e13i	−0.00164535	+	0.00208951i
$960$	−3.77303e15	−	4.21464e15i	−0.149348	−	0.166828i
$961$	5.11940e15	−	8.86706e15i	0.201484	−	0.348981i
$962$	−1.28097e15	−	2.21870e15i	−0.0501275	−	0.0868233i
$963$	−5.84013e15	−	1.33224e16i	−0.227236	−	0.518369i
$964$	1.77969e15	+	1.02751e15i	0.0688528	+	0.0397522i
$965$	−8.04930e16			−3.09640
$966$	4.72794e15	−	3.14331e15i	0.180841	−	0.120230i
$967$	5.13204e15			0.195184			0.0975920	−	0.995227i	$-0.468886\pi$
$967$	5.13204e15			0.195184			0.0975920	+	0.995227i	$0.468886\pi$
$968$	9.35093e14	+	5.39876e14i	0.0353623	+	0.0204164i
$969$	1.89079e15	+	6.20359e14i	0.0710988	+	0.0233272i
$970$	−5.40981e15	−	9.37007e15i	−0.202273	−	0.350347i
$971$	−6.71621e15	+	1.16328e16i	−0.249700	+	0.432493i	−0.963443	−	0.267915i	$-0.913665\pi$
$971$	−6.71621e15	+	1.16328e16i	−0.249700	+	0.432493i	0.713743	+	0.700408i	$0.246999\pi$
$972$	−6.59368e15	−	1.18088e16i	−0.243761	−	0.436556i
$973$	1.23385e15	+	3.08768e15i	0.0453568	+	0.113504i
$974$		−	2.71535e15i		−	0.0992547i
$975$	5.24277e15	+	2.50181e16i	0.190561	+	0.909347i
$976$	7.92050e15	−	4.57290e15i	0.286272	−	0.165279i
$977$	1.42630e16	−	8.23477e15i	0.512616	−	0.295959i	−0.221293	−	0.975207i	$-0.571028\pi$
$977$	1.42630e16	−	8.23477e15i	0.512616	−	0.295959i	0.733908	+	0.679249i	$0.237694\pi$
$978$	−3.18011e15	−	1.51753e16i	−0.113652	−	0.542342i
$979$		−	1.88019e16i		−	0.668185i
$980$	1.83646e16	−	1.74663e16i	0.648991	−	0.617245i
$981$	−3.15898e15	+	2.84820e16i	−0.111011	+	1.00090i
$982$	−1.25589e16	+	2.17527e16i	−0.438873	+	0.760150i
$983$	1.53597e16	+	2.66038e16i	0.533751	+	0.924483i	0.999223	+	0.0394205i	$0.0125512\pi$
$983$	1.53597e16	+	2.66038e16i	0.533751	+	0.924483i	−0.465472	+	0.885063i	$0.654115\pi$
$984$	−1.74452e16	−	5.72370e15i	−0.602842	−	0.197790i
$985$	−3.07313e15	−	1.77427e15i	−0.105604	−	0.0609706i
$986$	−2.71609e15			−0.0928155
$987$	−2.79938e16	−	1.38856e16i	−0.951301	−	0.471868i
$988$	−4.13662e15			−0.139792
$989$	6.56988e15	+	3.79312e15i	0.220789	+	0.127473i
$990$	3.26458e16	−	1.43109e16i	1.09102	−	0.478269i
$991$	−8.93500e15	−	1.54759e16i	−0.296954	−	0.514340i	0.678483	−	0.734616i	$-0.262638\pi$
$991$	−8.93500e15	−	1.54759e16i	−0.296954	−	0.514340i	−0.975438	+	0.220276i	$0.929304\pi$
$992$	−3.16762e15	+	5.48648e15i	−0.104693	+	0.181334i
$993$	3.34619e16	+	3.73784e16i	1.09984	+	1.22857i
$994$	3.05602e15	−	2.11600e16i	0.0998920	−	0.691656i
$995$		−	1.52221e16i		−	0.494820i
$996$	4.42824e15	−	9.27976e14i	0.143154	−	0.0299992i
$997$	−5.16492e15	+	2.98197e15i	−0.166050	+	0.0958692i	−0.580722	−	0.814102i	$-0.697230\pi$
$997$	−5.16492e15	+	2.98197e15i	−0.166050	+	0.0958692i	0.414672	+	0.909971i	$0.363896\pi$
$998$	5.75775e15	−	3.32424e15i	0.184092	−	0.106286i
$999$	−1.01721e15	−	1.05512e16i	−0.0323444	−	0.335499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.6	✓	60
3.2	odd	2	inner	42.12.f.a.5.16	yes	60
7.3	odd	6	inner	42.12.f.a.17.16	yes	60
21.17	even	6	inner	42.12.f.a.17.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.6	✓	60	1.1	even	1	trivial
42.12.f.a.5.16	yes	60	3.2	odd	2	inner
42.12.f.a.17.6	yes	60	21.17	even	6	inner
42.12.f.a.17.16	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} +(-131.210 + 399.914i) q^{3} +(512.000 + 886.810i) q^{4} +(6258.52 - 10840.1i) q^{5} +(10034.8 - 8983.37i) q^{6} +(-41292.3 + 16500.6i) q^{7} -32768.0i q^{8} +(-142715. - 104945. i) q^{9} +(-346882. + 200273. i) q^{10} +(435052. - 251177. i) q^{11} +(-421827. + 88397.5i) q^{12} +563130. i q^{13} +(1.40834e6 + 203398. i) q^{14} +(3.51391e6 + 3.92519e6i) q^{15} +(-524288. + 908093. i) q^{16} +(-329541. - 570781. i) q^{17} +(2.27591e6 + 5.19177e6i) q^{18} +(6.21252e6 + 3.58680e6i) q^{19} +1.28174e7 q^{20} +(-1.18087e6 - 1.86784e7i) q^{21} -1.60754e7 q^{22} +(-8.20976e6 - 4.73991e6i) q^{23} +(1.31044e7 + 4.29949e6i) q^{24} +(-5.39240e7 - 9.33991e7i) q^{25} +(9.01008e6 - 1.56059e7i) q^{26} +(6.06947e7 - 4.33038e7i) q^{27} +(-3.57746e7 - 2.81701e7i) q^{28} +1.28782e8i q^{29} +(-3.45773e7 - 1.65001e8i) q^{30} +(-1.63510e8 + 9.44024e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(4.33661e7 + 2.06940e8i) q^{33} +2.10906e7i q^{34} +(-7.95606e7 + 5.50881e8i) q^{35} +(1.99965e7 - 1.80293e8i) q^{36} +(7.10853e7 - 1.23123e8i) q^{37} +(-1.14778e8 - 1.98801e8i) q^{38} +(-2.25203e8 - 7.38882e7i) q^{39} +(-3.55207e8 - 2.05079e8i) q^{40} -1.33125e9 q^{41} +(-2.66129e8 + 5.36525e8i) q^{42} -8.00252e8 q^{43} +(4.45493e8 + 2.57206e8i) q^{44} +(-2.03080e9 + 8.90237e8i) q^{45} +(1.51677e8 + 2.62712e8i) q^{46} +(8.34818e8 - 1.44595e9i) q^{47} +(-2.94367e8 - 3.28821e8i) q^{48} +(1.43278e9 - 1.36270e9i) q^{49} +3.45113e9i q^{50} +(2.71502e8 - 5.68957e7i) q^{51} +(-4.99389e8 + 2.88323e8i) q^{52} +(-5.10052e9 + 2.94479e9i) q^{53} +(-2.37488e9 + 2.28954e8i) q^{54} -6.28799e9i q^{55} +(5.40693e8 + 1.35307e9i) q^{56} +(-2.24956e9 + 2.01385e9i) q^{57} +(2.06051e9 - 3.56890e9i) q^{58} +(-3.40089e9 - 5.89051e9i) q^{59} +(-1.68178e9 + 5.12587e9i) q^{60} +(-7.55358e9 - 4.36106e9i) q^{61} +6.04176e9 q^{62} +(7.62469e9 + 1.97855e9i) q^{63} -1.07374e9 q^{64} +(6.10437e9 + 3.52436e9i) q^{65} +(2.10925e9 - 6.42875e9i) q^{66} +(3.88865e9 + 6.73534e9i) q^{67} +(3.37450e8 - 5.84480e8i) q^{68} +(2.97276e9 - 2.66127e9i) q^{69} +(1.10189e10 - 1.39935e10i) q^{70} -1.50248e10i q^{71} +(-3.43885e9 + 4.67648e9i) q^{72} +(-2.86914e10 + 1.65650e10i) q^{73} +(-3.93995e9 + 2.27473e9i) q^{74} +(4.44269e10 - 9.31005e9i) q^{75} +7.34577e9i q^{76} +(-1.38197e10 + 1.75503e10i) q^{77} +(5.05881e9 + 5.65090e9i) q^{78} +(4.77500e8 - 8.27054e8i) q^{79} +(6.56253e9 + 1.13666e10i) q^{80} +(9.35402e9 + 2.99545e10i) q^{81} +(3.68927e10 + 2.13000e10i) q^{82} -1.04978e10 q^{83} +(1.59596e10 - 1.06106e10i) q^{84} -8.24975e9 q^{85} +(2.21772e10 + 1.28040e10i) q^{86} +(-5.15016e10 - 1.68974e10i) q^{87} +(-8.23058e9 - 1.42558e10i) q^{88} +(1.87137e10 - 3.24132e10i) q^{89} +(7.05229e10 + 7.82178e9i) q^{90} +(-9.29200e9 - 2.32529e10i) q^{91} -9.70733e9i q^{92} +(-1.62987e10 - 7.77764e10i) q^{93} +(-4.62703e10 + 2.67142e10i) q^{94} +(7.77623e10 - 4.48961e10i) q^{95} +(2.89661e9 + 1.38224e10i) q^{96} +2.70123e10i q^{97} +(-6.15097e10 + 1.48397e10i) q^{98} +(-8.84483e10 - 9.80991e9i) 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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