LMFDB - Embedded newform 847.2.n.e.807.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			807.3
Character	$\chi$	$=$	847.807
Dual form			847.2.n.e.487.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67566 - 0.746054i) q^{2} +(2.15064 - 0.457134i) q^{3} +(0.912994 - 1.01398i) q^{4} +(0.0664333 + 0.632070i) q^{5} +(3.26271 - 2.37050i) q^{6} +(2.59624 - 0.509441i) q^{7} +(-0.360239 + 1.10870i) q^{8} +(1.67566 - 0.746054i) q^{9} +O(q^{10})$	\(q+(1.67566 - 0.746054i) q^{2} +(2.15064 - 0.457134i) q^{3} +(0.912994 - 1.01398i) q^{4} +(0.0664333 + 0.632070i) q^{5} +(3.26271 - 2.37050i) q^{6} +(2.59624 - 0.509441i) q^{7} +(-0.360239 + 1.10870i) q^{8} +(1.67566 - 0.746054i) q^{9} +(0.582878 + 1.00958i) q^{10} +(1.50000 - 2.59808i) q^{12} +(1.45729 + 1.05878i) q^{13} +(3.97036 - 2.79059i) q^{14} +(0.431815 + 1.32899i) q^{15} +(0.508759 + 4.84051i) q^{16} +(-2.58921 - 1.15279i) q^{17} +(2.25126 - 2.50027i) q^{18} +(-3.72247 - 4.13422i) q^{19} +(0.701561 + 0.509714i) q^{20} +(5.35071 - 2.28245i) q^{21} +(-1.08288 + 1.87560i) q^{23} +(-0.267921 + 2.54910i) q^{24} +(4.49564 - 0.955577i) q^{25} +(3.23184 + 0.686948i) q^{26} +(-2.07362 + 1.50658i) q^{27} +(1.85379 - 3.09766i) q^{28} +(-3.22315 - 9.91982i) q^{29} +(1.71507 + 1.90478i) q^{30} +(-0.672151 + 6.39509i) q^{31} +(3.29804 + 5.71237i) q^{32} -5.19869 q^{34} +(0.494479 + 1.60716i) q^{35} +(0.773386 - 2.38024i) q^{36} +(-5.93332 - 1.26117i) q^{37} +(-9.32196 - 4.15040i) q^{38} +(3.61812 + 1.61089i) q^{39} +(-0.724709 - 0.154042i) q^{40} +(2.32865 - 7.16684i) q^{41} +(7.26316 - 7.81655i) q^{42} -4.86718 q^{43} +(0.582878 + 1.00958i) q^{45} +(-0.415242 + 3.95076i) q^{46} +(-1.89648 - 2.10625i) q^{47} +(3.30692 + 10.1777i) q^{48} +(6.48094 - 2.64526i) q^{49} +(6.82027 - 4.95522i) q^{50} +(-6.09545 - 1.29563i) q^{51} +(2.40408 - 0.511004i) q^{52} +(-0.780806 + 7.42887i) q^{53} +(-2.35071 + 4.07155i) q^{54} +(-0.370450 + 3.06197i) q^{56} +(-9.89559 - 7.18957i) q^{57} +(-12.8016 - 14.2177i) q^{58} +(7.90027 - 8.77414i) q^{59} +(1.74182 + 0.775507i) q^{60} +(0.452766 + 4.30779i) q^{61} +(3.64478 + 11.2175i) q^{62} +(3.97036 - 2.79059i) q^{63} +(1.91288 + 1.38979i) q^{64} +(-0.572413 + 0.991448i) q^{65} +(0.801309 + 1.38791i) q^{67} +(-3.53284 + 1.57292i) q^{68} +(-1.47149 + 4.52877i) q^{69} +(2.02761 + 2.32416i) q^{70} +(-3.47233 + 2.52280i) q^{71} +(0.223511 + 2.12657i) q^{72} +(-10.7017 + 11.8855i) q^{73} +(-10.8831 + 2.31328i) q^{74} +(9.23169 - 4.11021i) q^{75} -7.59061 q^{76} +7.26456 q^{78} +(4.35015 - 1.93681i) q^{79} +(-3.02575 + 0.643142i) q^{80} +(-7.45297 + 8.27736i) q^{81} +(-1.44482 - 13.7465i) q^{82} +(7.46854 - 5.42621i) q^{83} +(2.57080 - 7.50939i) q^{84} +(0.556635 - 1.71315i) q^{85} +(-8.15576 + 3.63118i) q^{86} +(-11.4665 - 19.8606i) q^{87} +(-0.182224 + 0.315621i) q^{89} +(1.72991 + 1.25685i) q^{90} +(4.32286 + 2.00645i) q^{91} +(0.913165 + 2.81043i) q^{92} +(1.47785 + 14.0608i) q^{93} +(-4.74924 - 2.11450i) q^{94} +(2.36582 - 2.62751i) q^{95} +(9.70422 + 10.7776i) q^{96} +(2.10027 + 1.52593i) q^{97} +(8.88637 - 9.26770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8}+O(q^{10}) $ 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} + 36 q^{10} + 36 q^{12} + 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} - 3 q^{17} + 10 q^{18} - 11 q^{19} - 28 q^{20} + 40 q^{21} - 48 q^{23} + 2 q^{24} + 3 q^{25} + q^{26} - 4 q^{27} - 13 q^{28} + 18 q^{29} + 2 q^{30} - 3 q^{31} + 12 q^{32} - 80 q^{34} - 9 q^{35} + 18 q^{36} - 4 q^{37} + 8 q^{38} - 5 q^{39} - 3 q^{40} + 10 q^{41} + 2 q^{42} + 16 q^{43} + 36 q^{45} - 10 q^{46} - 3 q^{47} - 20 q^{48} + 24 q^{49} + 6 q^{50} + 2 q^{51} - 7 q^{52} + 17 q^{53} + 32 q^{54} + 12 q^{56} - 40 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} - 24 q^{61} - 26 q^{62} - 12 q^{63} + 14 q^{64} - 60 q^{65} + 64 q^{67} + 5 q^{68} + 6 q^{69} + 27 q^{70} - 14 q^{71} + 10 q^{72} - 20 q^{73} + 22 q^{74} + 25 q^{75} - 312 q^{76} - 48 q^{78} + 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} + 22 q^{83} - 12 q^{84} - 22 q^{85} - 21 q^{86} - 120 q^{87} - 4 q^{89} - 20 q^{90} + 15 q^{91} - 50 q^{92} - 26 q^{93} - 10 q^{94} - 17 q^{95} + 27 q^{96} - 18 q^{97} - 96 q^{98}+O(q^{100}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 + 36 * q^10 + 36 * q^12 + 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 - 3 * q^17 + 10 * q^18 - 11 * q^19 - 28 * q^20 + 40 * q^21 - 48 * q^23 + 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 - 13 * q^28 + 18 * q^29 + 2 * q^30 - 3 * q^31 + 12 * q^32 - 80 * q^34 - 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 - 5 * q^39 - 3 * q^40 + 10 * q^41 + 2 * q^42 + 16 * q^43 + 36 * q^45 - 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 + 6 * q^50 + 2 * q^51 - 7 * q^52 + 17 * q^53 + 32 * q^54 + 12 * q^56 - 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 - 24 * q^61 - 26 * q^62 - 12 * q^63 + 14 * q^64 - 60 * q^65 + 64 * q^67 + 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 + 10 * q^72 - 20 * q^73 + 22 * q^74 + 25 * q^75 - 312 * q^76 - 48 * q^78 + 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 + 22 * q^83 - 12 * q^84 - 22 * q^85 - 21 * q^86 - 120 * q^87 - 4 * q^89 - 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 - 10 * q^94 - 17 * q^95 + 27 * q^96 - 18 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.67566	−	0.746054i	1.18487	−	0.527540i	0.282824	−	0.959172i	$-0.408729\pi$
$2$	1.67566	−	0.746054i	1.18487	−	0.527540i	0.902050	+	0.431632i	$0.142062\pi$
$3$	2.15064	−	0.457134i	1.24168	−	0.263926i	0.460173	−	0.887829i	$-0.347787\pi$
$3$	2.15064	−	0.457134i	1.24168	−	0.263926i	0.781502	+	0.623903i	$0.214454\pi$
$4$	0.912994	−	1.01398i	0.456497	−	0.506991i
$5$	0.0664333	+	0.632070i	0.0297099	+	0.282670i	0.999283	+	0.0378677i	$0.0120565\pi$
$5$	0.0664333	+	0.632070i	0.0297099	+	0.282670i	−0.969573	+	0.244803i	$0.921277\pi$
$6$	3.26271	−	2.37050i	1.33200	−	0.967752i
$7$	2.59624	−	0.509441i	0.981287	−	0.192550i
$7$	2.59624	−	0.509441i	0.981287	−	0.192550i
$8$	−0.360239	+	1.10870i	−0.127364	+	0.391985i
$9$	1.67566	−	0.746054i	0.558555	−	0.248685i
$10$	0.582878	+	1.00958i	0.184322	+	0.319256i
$11$		0			0
$11$		0			0
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	1.45729	+	1.05878i	0.404179	+	0.293653i	0.771241	−	0.636543i	$-0.219636\pi$
$13$	1.45729	+	1.05878i	0.404179	+	0.293653i	−0.367062	+	0.930197i	$0.619636\pi$
$14$	3.97036	−	2.79059i	1.06112	−	0.745816i
$15$	0.431815	+	1.32899i	0.111494	+	0.343144i
$16$	0.508759	+	4.84051i	0.127190	+	1.21013i
$17$	−2.58921	−	1.15279i	−0.627976	−	0.279593i	0.0679698	−	0.997687i	$-0.478348\pi$
$17$	−2.58921	−	1.15279i	−0.627976	−	0.279593i	−0.695946	+	0.718095i	$0.745014\pi$
$18$	2.25126	−	2.50027i	0.530626	−	0.589320i
$19$	−3.72247	−	4.13422i	−0.853992	−	0.948455i	0.145169	−	0.989407i	$-0.453628\pi$
$19$	−3.72247	−	4.13422i	−0.853992	−	0.948455i	−0.999161	+	0.0409522i	$0.986961\pi$
$20$	0.701561	+	0.509714i	0.156874	+	0.113976i
$21$	5.35071	−	2.28245i	1.16762	−	0.498073i
$22$		0			0
$23$	−1.08288	+	1.87560i	−0.225796	+	0.391090i	−0.956558	−	0.291542i	$-0.905832\pi$
$23$	−1.08288	+	1.87560i	−0.225796	+	0.391090i	0.730762	+	0.682632i	$0.239165\pi$
$24$	−0.267921	+	2.54910i	−0.0546891	+	0.520332i
$25$	4.49564	−	0.955577i	0.899128	−	0.191115i
$26$	3.23184	+	0.686948i	0.633815	+	0.134722i
$27$	−2.07362	+	1.50658i	−0.399069	+	0.289941i
$28$	1.85379	−	3.09766i	0.350333	−	0.585403i
$29$	−3.22315	−	9.91982i	−0.598523	−	1.84206i	−0.536344	−	0.843999i	$-0.680195\pi$
$29$	−3.22315	−	9.91982i	−0.598523	−	1.84206i	−0.0621790	−	0.998065i	$-0.519805\pi$
$30$	1.71507	+	1.90478i	0.313128	+	0.347764i
$31$	−0.672151	+	6.39509i	−0.120722	+	1.14859i	0.751586	+	0.659635i	$0.229289\pi$
$31$	−0.672151	+	6.39509i	−0.120722	+	1.14859i	−0.872308	+	0.488957i	$0.837377\pi$
$32$	3.29804	+	5.71237i	0.583016	+	1.00981i
$33$		0			0
$34$	−5.19869			−0.891568
$35$	0.494479	+	1.60716i	0.0835822	+	0.271660i
$36$	0.773386	−	2.38024i	0.128898	−	0.396706i
$37$	−5.93332	−	1.26117i	−0.975431	−	0.207334i	−0.307492	−	0.951551i	$-0.599490\pi$
$37$	−5.93332	−	1.26117i	−0.975431	−	0.207334i	−0.667939	+	0.744216i	$0.732823\pi$
$38$	−9.32196	−	4.15040i	−1.51222	−	0.673284i
$39$	3.61812	+	1.61089i	0.579362	+	0.257949i
$40$	−0.724709	−	0.154042i	−0.114586	−	0.0243561i
$41$	2.32865	−	7.16684i	0.363674	−	1.11927i	−0.587134	−	0.809490i	$-0.699744\pi$
$41$	2.32865	−	7.16684i	0.363674	−	1.11927i	0.950807	−	0.309783i	$-0.100256\pi$
$42$	7.26316	−	7.81655i	1.12073	−	1.20612i
$43$	−4.86718			−0.742238			−0.371119	−	0.928585i	$-0.621026\pi$
$43$	−4.86718			−0.742238			−0.371119	+	0.928585i	$0.621026\pi$
$44$		0			0
$45$	0.582878	+	1.00958i	0.0868904	+	0.150499i
$46$	−0.415242	+	3.95076i	−0.0612241	+	0.582508i
$47$	−1.89648	−	2.10625i	−0.276630	−	0.307229i	0.588780	−	0.808293i	$-0.299608\pi$
$47$	−1.89648	−	2.10625i	−0.276630	−	0.307229i	−0.865410	+	0.501065i	$0.832942\pi$
$48$	3.30692	+	10.1777i	0.477313	+	1.46902i
$49$	6.48094	−	2.64526i	0.925849	−	0.377895i
$50$	6.82027	−	4.95522i	0.964532	−	0.700773i
$51$	−6.09545	−	1.29563i	−0.853534	−	0.181424i
$52$	2.40408	−	0.511004i	0.333386	−	0.0708635i
$53$	−0.780806	+	7.42887i	−0.107252	+	1.02043i	0.800044	+	0.599942i	$0.204810\pi$
$53$	−0.780806	+	7.42887i	−0.107252	+	1.02043i	−0.907296	+	0.420493i	$0.861857\pi$
$54$	−2.35071	+	4.07155i	−0.319891	+	0.554068i
$55$		0			0
$56$	−0.370450	+	3.06197i	−0.0495034	+	0.409174i
$57$	−9.89559	−	7.18957i	−1.31070	−	0.952282i
$58$	−12.8016	−	14.2177i	−1.68094	−	1.86687i
$59$	7.90027	−	8.77414i	1.02853	−	1.14230i	0.0388119	−	0.999247i	$-0.487643\pi$
$59$	7.90027	−	8.77414i	1.02853	−	1.14230i	0.989716	−	0.143049i	$-0.0456907\pi$
$60$	1.74182	+	0.775507i	0.224868	+	0.100117i
$61$	0.452766	+	4.30779i	0.0579708	+	0.551555i	0.984506	+	0.175348i	$0.0561052\pi$
$61$	0.452766	+	4.30779i	0.0579708	+	0.551555i	−0.926536	+	0.376207i	$0.877228\pi$
$62$	3.64478	+	11.2175i	0.462888	+	1.42462i
$63$	3.97036	−	2.79059i	0.500218	−	0.351581i
$64$	1.91288	+	1.38979i	0.239110	+	0.173723i
$65$	−0.572413	+	0.991448i	−0.0709990	+	0.122974i
$66$		0			0
$67$	0.801309	+	1.38791i	0.0978954	+	0.169560i	0.910813	−	0.412818i	$-0.135456\pi$
$67$	0.801309	+	1.38791i	0.0978954	+	0.169560i	−0.812918	+	0.582378i	$0.802122\pi$
$68$	−3.53284	+	1.57292i	−0.428420	+	0.190745i
$69$	−1.47149	+	4.52877i	−0.177146	+	0.545200i
$70$	2.02761	+	2.32416i	0.242346	+	0.277790i
$71$	−3.47233	+	2.52280i	−0.412090	+	0.299401i	−0.774447	−	0.632638i	$-0.781972\pi$
$71$	−3.47233	+	2.52280i	−0.412090	+	0.299401i	0.362358	+	0.932039i	$0.381972\pi$
$72$	0.223511	+	2.12657i	0.0263411	+	0.250618i
$73$	−10.7017	+	11.8855i	−1.25254	+	1.39109i	−0.364577	+	0.931173i	$0.618786\pi$
$73$	−10.7017	+	11.8855i	−1.25254	+	1.39109i	−0.887963	+	0.459914i	$0.847880\pi$
$74$	−10.8831	+	2.31328i	−1.26514	+	0.268914i
$75$	9.23169	−	4.11021i	1.06598	−	0.474607i
$76$	−7.59061			−0.870703
$77$		0			0
$78$	7.26456			0.822549
$79$	4.35015	−	1.93681i	0.489430	−	0.217908i	−0.147157	−	0.989113i	$-0.547012\pi$
$79$	4.35015	−	1.93681i	0.489430	−	0.217908i	0.636587	+	0.771205i	$0.280346\pi$
$80$	−3.02575	+	0.643142i	−0.338289	+	0.0719055i
$81$	−7.45297	+	8.27736i	−0.828107	+	0.919706i
$82$	−1.44482	−	13.7465i	−0.159553	−	1.51805i
$83$	7.46854	−	5.42621i	0.819779	−	0.595604i	−0.0968702	−	0.995297i	$-0.530883\pi$
$83$	7.46854	−	5.42621i	0.819779	−	0.595604i	0.916649	+	0.399693i	$0.130883\pi$
$84$	2.57080	−	7.50939i	0.280497	−	0.819342i
$85$	0.556635	−	1.71315i	0.0603755	−	0.185817i
$86$	−8.15576	+	3.63118i	−0.879458	+	0.391560i
$87$	−11.4665	−	19.8606i	−1.22934	−	2.12928i
$88$		0			0
$89$	−0.182224	+	0.315621i	−0.0193157	+	0.0334558i	−0.875522	−	0.483179i	$-0.839482\pi$
$89$	−0.182224	+	0.315621i	−0.0193157	+	0.0334558i	0.856206	+	0.516635i	$0.172815\pi$
$90$	1.72991	+	1.25685i	0.182348	+	0.132484i
$91$	4.32286	+	2.00645i	0.453159	+	0.210333i
$92$	0.913165	+	2.81043i	0.0952040	+	0.293008i
$93$	1.47785	+	14.0608i	0.153246	+	1.45804i
$94$	−4.74924	−	2.11450i	−0.489847	−	0.218094i
$95$	2.36582	−	2.62751i	0.242728	−	0.269577i
$96$	9.70422	+	10.7776i	0.990433	+	1.09999i
$97$	2.10027	+	1.52593i	0.213250	+	0.154935i	0.689283	−	0.724492i	$-0.257926\pi$
$97$	2.10027	+	1.52593i	0.213250	+	0.154935i	−0.476033	+	0.879427i	$0.657926\pi$
$98$	8.88637	−	9.26770i	0.897659	−	0.936179i
$99$		0			0
$100$	3.13555	−	5.43094i	0.313555	−	0.543094i
$101$	1.03484	−	9.84588i	0.102971	−	0.979701i	−0.814032	−	0.580820i	$-0.802732\pi$
$101$	1.03484	−	9.84588i	0.102971	−	0.979701i	0.917003	−	0.398881i	$-0.130601\pi$
$102$	−11.1805	+	2.37650i	−1.10704	+	0.235308i
$103$	−6.09545	−	1.29563i	−0.600603	−	0.127662i	−0.102430	−	0.994740i	$-0.532662\pi$
$103$	−6.09545	−	1.29563i	−0.600603	−	0.127662i	−0.498172	+	0.867078i	$0.665995\pi$
$104$	−1.69885	+	1.23428i	−0.166585	+	0.121031i
$105$	1.79814	+	3.23039i	0.175480	+	0.315254i
$106$	4.23397	+	13.0308i	0.411240	+	1.26567i
$107$	7.42655	+	8.24802i	0.717952	+	0.797366i	0.986125	−	0.166005i	$-0.0530867\pi$
$107$	7.42655	+	8.24802i	0.717952	+	0.797366i	−0.268173	+	0.963371i	$0.586420\pi$
$108$	−0.365564	+	3.47811i	−0.0351764	+	0.334681i
$109$	7.15202	+	12.3877i	0.685039	+	1.18652i	0.973424	+	0.229008i	$0.0735483\pi$
$109$	7.15202	+	12.3877i	0.685039	+	1.18652i	−0.288385	+	0.957514i	$0.593118\pi$
$110$		0			0
$111$	−13.3370			−1.26589
$112$	3.78681	+	12.3080i	0.357820	+	1.16299i
$113$	−2.68518	+	8.26413i	−0.252600	+	0.777424i	0.741693	+	0.670740i	$0.234023\pi$
$113$	−2.68518	+	8.26413i	−0.252600	+	0.777424i	−0.994293	+	0.106684i	$0.965977\pi$
$114$	−21.9455	−	4.66466i	−2.05538	−	0.436885i
$115$	−1.25745	−	0.559853i	−0.117258	−	0.0522066i
$116$	−13.0012	−	5.78852i	−1.20713	−	0.537451i
$117$	3.23184	+	0.686948i	0.298783	+	0.0635084i
$118$	6.69222	−	20.5965i	0.616069	−	1.89607i
$119$	−7.30949	−	1.67387i	−0.670060	−	0.153444i
$120$	−1.62901			−0.148707
$121$		0			0
$122$	3.97252	+	6.88061i	0.359655	+	0.622942i
$123$	1.73189	−	16.4778i	0.156159	−	1.48576i
$124$	5.87084	+	6.52023i	0.527217	+	0.585534i
$125$	1.88463	+	5.80031i	0.168567	+	0.518795i
$126$	4.57106	−	7.63819i	0.407223	−	0.680464i
$127$	−16.9885	+	12.3429i	−1.50748	+	1.09525i	−0.540206	+	0.841533i	$0.681654\pi$
$127$	−16.9885	+	12.3429i	−1.50748	+	1.09525i	−0.967278	+	0.253718i	$0.918346\pi$
$128$	−8.66167	−	1.84109i	−0.765591	−	0.162731i
$129$	−10.4676	+	2.22495i	−0.921618	+	0.195896i
$130$	−0.219498	+	2.08838i	−0.0192513	+	0.183163i
$131$	6.85071	−	11.8658i	0.598549	−	1.03672i	−0.394486	−	0.918902i	$-0.629077\pi$
$131$	6.85071	−	11.8658i	0.598549	−	1.03672i	0.993035	−	0.117816i	$-0.0375893\pi$
$132$		0			0
$133$	−11.7706	−	8.83705i	−1.02064	−	0.766270i
$134$	2.37818	+	1.72785i	0.205443	+	0.149263i
$135$	−1.09002	−	1.21059i	−0.0938139	−	0.104191i
$136$	2.21083	−	2.45538i	0.189577	−	0.210547i
$137$	6.63651	+	2.95476i	0.566995	+	0.252442i	0.670154	−	0.742223i	$-0.266228\pi$
$137$	6.63651	+	2.95476i	0.566995	+	0.252442i	−0.103159	+	0.994665i	$0.532895\pi$
$138$	0.912989	+	8.68651i	0.0777188	+	0.739445i
$139$	−0.804253	−	2.47524i	−0.0682159	−	0.209947i	0.911138	−	0.412102i	$-0.135205\pi$
$139$	−0.804253	−	2.47524i	−0.0682159	−	0.209947i	−0.979353	+	0.202155i	$0.935205\pi$
$140$	2.08109	+	0.965937i	0.175884	+	0.0816366i
$141$	−5.04149	−	3.66286i	−0.424570	−	0.308468i
$142$	−3.93632	+	6.81790i	−0.330328	+	0.572146i
$143$		0			0
$144$	4.46379	+	7.73152i	0.371983	+	0.644293i
$145$	6.05590	−	2.69626i	0.502915	−	0.223912i
$146$	−9.06529	+	27.9001i	−0.750249	+	2.30903i
$147$	12.7290	−	8.65167i	1.04987	−	0.713578i
$148$	−6.69588	+	4.86484i	−0.550398	+	0.399888i
$149$	0.104528	+	0.994522i	0.00856331	+	0.0814744i	0.997969	−	0.0637035i	$-0.0202912\pi$
$149$	0.104528	+	0.994522i	0.00856331	+	0.0814744i	−0.989406	+	0.145178i	$0.953625\pi$
$150$	12.4028	−	13.7747i	1.01268	−	1.12470i
$151$	−1.69752	+	0.360818i	−0.138142	+	0.0293630i	−0.276464	−	0.961024i	$-0.589163\pi$
$151$	−1.69752	+	0.360818i	−0.138142	+	0.0293630i	0.138322	+	0.990387i	$0.455829\pi$
$152$	5.92459	−	2.63780i	0.480547	−	0.213954i
$153$	−5.19869			−0.420289
$154$		0			0
$155$	−4.08680			−0.328260
$156$	4.93673	−	2.19797i	0.395255	−	0.175979i
$157$	7.76609	−	1.65073i	0.619802	−	0.131743i	0.112700	−	0.993629i	$-0.464050\pi$
$157$	7.76609	−	1.65073i	0.619802	−	0.131743i	0.507102	+	0.861886i	$0.330717\pi$
$158$	5.84442	−	6.49089i	0.464957	−	0.516388i
$159$	1.71675	+	16.3338i	0.136147	+	1.29535i
$160$	−3.39152	+	2.46408i	−0.268123	+	0.194803i
$161$	−1.85591	+	5.42117i	−0.146266	+	0.427248i
$162$	−6.31332	+	19.4304i	−0.496021	+	1.52660i
$163$	−14.6217	+	6.51001i	−1.14526	+	0.509903i	−0.889544	−	0.456849i	$-0.848978\pi$
$163$	−14.6217	+	6.51001i	−1.14526	+	0.509903i	−0.255717	+	0.966752i	$0.582311\pi$
$164$	−5.14101	−	8.90449i	−0.401446	−	0.695324i
$165$		0			0
$166$	8.46652	−	14.6644i	0.657130	−	1.13818i
$167$	−0.937823	−	0.681368i	−0.0725709	−	0.0527259i	0.550908	−	0.834566i	$-0.314281\pi$
$167$	−0.937823	−	0.681368i	−0.0725709	−	0.0527259i	−0.623479	+	0.781840i	$0.714281\pi$
$168$	0.603026	+	6.75456i	0.0465245	+	0.521126i
$169$	−3.01455	−	9.27783i	−0.231888	−	0.713679i
$170$	−0.345366	−	3.28594i	−0.0264884	−	0.252020i
$171$	−9.32196	−	4.15040i	−0.712868	−	0.317389i
$172$	−4.44370	+	4.93523i	−0.338829	+	0.376308i
$173$	−0.664752	−	0.738282i	−0.0505402	−	0.0561305i	0.717345	−	0.696719i	$-0.245357\pi$
$173$	−0.664752	−	0.738282i	−0.0505402	−	0.0561305i	−0.767885	+	0.640588i	$0.778691\pi$
$174$	−34.0311	−	24.7251i	−2.57989	−	1.87440i
$175$	11.1850	−	4.77117i	0.845503	−	0.360667i
$176$		0			0
$177$	12.9797	−	22.4815i	0.975615	−	1.68982i
$178$	−0.0698759	+	0.664824i	−0.00523742	+	0.0498307i
$179$	19.2323	−	4.08795i	1.43749	−	0.305548i	0.577721	−	0.816234i	$-0.303942\pi$
$179$	19.2323	−	4.08795i	1.43749	−	0.305548i	0.859767	+	0.510687i	$0.170609\pi$
$180$	1.55586	+	0.330707i	0.115967	+	0.0246495i
$181$	19.3134	−	14.0320i	1.43555	−	1.04299i	0.446602	−	0.894732i	$-0.352634\pi$
$181$	19.3134	−	14.0320i	1.43555	−	1.04299i	0.988949	−	0.148257i	$-0.0473662\pi$
$182$	8.74059	+	0.137054i	0.647896	+	0.0101591i
$183$	2.94297	+	9.05754i	0.217551	+	0.669553i
$184$	−1.68938	−	1.87625i	−0.124543	−	0.138319i
$185$	0.402975	−	3.83406i	0.0296273	−	0.281885i
$186$	12.9665	+	22.4587i	0.950752	+	1.64675i
$187$		0			0
$188$	−3.86718			−0.282043
$189$	−4.61612	+	4.96782i	−0.335773	+	0.361356i
$190$	2.00406	−	6.16786i	0.145390	−	0.447463i
$191$	10.8885	+	2.31442i	0.787863	+	0.167465i	0.584237	−	0.811583i	$-0.301394\pi$
$191$	10.8885	+	2.31442i	0.787863	+	0.167465i	0.203626	+	0.979049i	$0.434727\pi$
$192$	4.74924	+	2.11450i	0.342747	+	0.152601i
$193$	3.30212	+	1.47020i	0.237692	+	0.105827i	0.522126	−	0.852868i	$-0.325139\pi$
$193$	3.30212	+	1.47020i	0.237692	+	0.105827i	−0.284434	+	0.958696i	$0.591806\pi$
$194$	4.65777	+	0.990040i	0.334409	+	0.0710807i
$195$	−0.777832	+	2.39392i	−0.0557017	+	0.171432i
$196$	3.23481	−	8.98667i	0.231058	−	0.641905i
$197$	2.41831			0.172298			0.0861489	−	0.996282i	$-0.472544\pi$
$197$	2.41831			0.172298			0.0861489	+	0.996282i	$0.472544\pi$
$198$		0			0
$199$	9.24809	+	16.0182i	0.655580	+	1.13550i	0.981748	+	0.190186i	$0.0609091\pi$
$199$	9.24809	+	16.0182i	0.655580	+	1.13550i	−0.326168	+	0.945312i	$0.605758\pi$
$200$	−0.560054	+	5.32855i	−0.0396018	+	0.376786i
$201$	2.35779	+	2.61859i	0.166306	+	0.184701i
$202$	−5.61151	−	17.2704i	−0.394824	−	1.21514i
$203$	−13.4216	−	24.1123i	−0.942013	−	1.69235i
$204$	−6.87885	+	4.99778i	−0.481616	+	0.349915i
$205$	4.68465	+	0.995753i	0.327190	+	0.0695464i
$206$	−11.1805	+	2.37650i	−0.778985	+	0.165578i
$207$	−0.415242	+	3.95076i	−0.0288613	+	0.274597i
$208$	−4.38364	+	7.59270i	−0.303951	+	0.526459i
$209$		0			0
$210$	5.42312	+	4.07155i	0.374231	+	0.280964i
$211$	6.35497	+	4.61716i	0.437494	+	0.317858i	0.784638	−	0.619954i	$-0.212849\pi$
$211$	6.35497	+	4.61716i	0.437494	+	0.317858i	−0.347144	+	0.937812i	$0.612849\pi$
$212$	6.81988	+	7.57424i	0.468391	+	0.520201i
$213$	−6.31449	+	7.01295i	−0.432662	+	0.480520i
$214$	18.5979	+	8.28031i	1.27132	+	0.566030i
$215$	−0.323343	−	3.07640i	−0.0220518	−	0.209809i
$216$	−0.923342	−	2.84175i	−0.0628255	−	0.193357i
$217$	1.51285	+	16.9456i	0.102699	+	1.15034i
$218$	21.2262	+	15.4218i	1.43762	+	1.04449i
$219$	−17.5823	+	30.4535i	−1.18810	+	2.05786i
$220$		0			0
$221$	−2.55267	−	4.42136i	−0.171711	−	0.297413i
$222$	−22.3483	+	9.95010i	−1.49992	+	0.667807i
$223$	6.28447	−	19.3416i	0.420839	−	1.29521i	−0.486083	−	0.873913i	$-0.661575\pi$
$223$	6.28447	−	19.3416i	0.420839	−	1.29521i	0.906922	−	0.421298i	$-0.138425\pi$
$224$	11.4726	+	13.1505i	0.766546	+	0.878657i
$225$	6.82027	−	4.95522i	0.454685	−	0.330348i
$226$	1.66603	+	15.8512i	0.110823	+	1.05441i
$227$	4.83087	−	5.36523i	0.320636	−	0.356103i	−0.561182	−	0.827693i	$-0.689653\pi$
$227$	4.83087	−	5.36523i	0.320636	−	0.356103i	0.881818	+	0.471590i	$0.156320\pi$
$228$	−16.3247	+	3.46993i	−1.08113	+	0.229801i
$229$	11.0277	−	4.90985i	0.728731	−	0.324452i	−0.00861876	−	0.999963i	$-0.502743\pi$
$229$	11.0277	−	4.90985i	0.728731	−	0.324452i	0.737350	+	0.675511i	$0.236077\pi$
$230$	−2.52475			−0.166477
$231$		0			0
$232$	12.1592			0.798291
$233$	−6.89015	+	3.06769i	−0.451389	+	0.200971i	−0.619823	−	0.784742i	$-0.712796\pi$
$233$	−6.89015	+	3.06769i	−0.451389	+	0.200971i	0.168434	+	0.985713i	$0.446129\pi$
$234$	5.92798	−	1.26003i	0.387524	−	0.0823707i
$235$	1.20531	−	1.33863i	0.0786258	−	0.0873228i
$236$	−1.68392	−	16.0215i	−0.109614	−	1.04291i
$237$	8.47024	−	6.15399i	0.550201	−	0.399745i
$238$	−13.4971	+	2.64842i	−0.874884	+	0.171672i
$239$	−3.04266	+	9.36434i	−0.196813	+	0.605729i	0.803138	+	0.595794i	$0.203162\pi$
$239$	−3.04266	+	9.36434i	−0.196813	+	0.605729i	−0.999951	+	0.00993486i	$0.996838\pi$
$240$	−6.21330	+	2.76634i	−0.401067	+	0.178567i
$241$	0.837515	+	1.45062i	0.0539491	+	0.0934426i	0.891739	−	0.452551i	$-0.149486\pi$
$241$	0.837515	+	1.45062i	0.0539491	+	0.0934426i	−0.837790	+	0.545993i	$0.816152\pi$
$242$		0			0
$243$	−8.40011	+	14.5494i	−0.538867	+	0.933346i
$244$	4.78139	+	3.47388i	0.306097	+	0.222393i
$245$	2.10254	+	3.92068i	0.134326	+	0.250483i
$246$	−9.39129	−	28.9034i	−0.598767	−	1.84281i
$247$	−1.04747	−	9.96604i	−0.0666491	−	0.634124i
$248$	−6.84811	−	3.04897i	−0.434855	−	0.193610i
$249$	13.5817	−	15.0840i	0.860704	−	0.955908i
$250$	7.48536	+	8.31333i	0.473415	+	0.525781i
$251$	−15.9974	−	11.6228i	−1.00974	−	0.733623i	−0.0455893	−	0.998960i	$-0.514517\pi$
$251$	−15.9974	−	11.6228i	−1.00974	−	0.733623i	−0.964156	+	0.265338i	$0.914517\pi$
$252$	0.795307	−	6.57367i	0.0500997	−	0.414102i
$253$		0			0
$254$	−19.2586	+	33.3568i	−1.20839	+	2.09299i
$255$	0.413987	−	3.93883i	0.0259249	−	0.246659i
$256$	−20.5132	+	4.36021i	−1.28207	+	0.272513i
$257$	−2.66053	−	0.565513i	−0.165959	−	0.0352757i	0.124183	−	0.992259i	$-0.460369\pi$
$257$	−2.66053	−	0.565513i	−0.165959	−	0.0352757i	−0.290142	+	0.956984i	$0.593702\pi$
$258$	−15.8802	+	11.5376i	−0.988658	+	0.718302i
$259$	−16.0468	−	0.251618i	−0.997100	−	0.0156348i
$260$	0.482701	+	1.48560i	0.0299359	+	0.0921331i
$261$	−12.8016	−	14.2177i	−0.792401	−	0.880051i
$262$	2.62698	−	24.9941i	0.162295	−	1.54414i
$263$	−6.34744	−	10.9941i	−0.391400	−	0.677924i	0.601235	−	0.799073i	$-0.294676\pi$
$263$	−6.34744	−	10.9941i	−0.391400	−	0.677924i	−0.992634	+	0.121148i	$0.961342\pi$
$264$		0			0
$265$	−4.74744			−0.291633
$266$	−26.3164	−	6.02646i	−1.61356	−	0.369506i
$267$	−0.247618	+	0.762090i	−0.0151540	+	0.0466391i
$268$	2.13890	+	0.454638i	0.130654	+	0.0277714i
$269$	−6.48009	−	2.88512i	−0.395098	−	0.175909i	0.199564	−	0.979885i	$-0.436047\pi$
$269$	−6.48009	−	2.88512i	−0.395098	−	0.175909i	−0.594662	+	0.803976i	$0.702714\pi$
$270$	−2.72967	−	1.21533i	−0.166122	−	0.0739625i
$271$	17.8181	+	3.78735i	1.08237	+	0.230065i	0.714376	−	0.699762i	$-0.246711\pi$
$271$	17.8181	+	3.78735i	1.08237	+	0.230065i	0.367996	+	0.929827i	$0.380044\pi$
$272$	4.26282	−	13.1196i	0.258471	−	0.795493i
$273$	10.2142	+	2.33904i	0.618189	+	0.141565i
$274$	13.3250			0.804991
$275$		0			0
$276$	3.24864	+	5.62680i	0.195545	+	0.338694i
$277$	−1.44758	+	13.7728i	−0.0869764	+	0.827525i	0.860876	+	0.508815i	$0.169916\pi$
$277$	−1.44758	+	13.7728i	−0.0869764	+	0.827525i	−0.947852	+	0.318710i	$0.896750\pi$
$278$	−3.19432	−	3.54765i	−0.191582	−	0.212774i
$279$	3.64478	+	11.2175i	0.218207	+	0.671573i
$280$	−1.95999	−	0.0307331i	−0.117132	−	0.00183666i
$281$	−17.0160	+	12.3628i	−1.01509	+	0.737506i	−0.965270	−	0.261253i	$-0.915864\pi$
$281$	−17.0160	+	12.3628i	−1.01509	+	0.737506i	−0.0498191	+	0.998758i	$0.515864\pi$
$282$	−11.1805	−	2.37650i	−0.665791	−	0.141518i
$283$	−0.344743	+	0.0732775i	−0.0204929	+	0.00435589i	−0.218147	−	0.975916i	$-0.570001\pi$
$283$	−0.344743	+	0.0732775i	−0.0204929	+	0.00435589i	0.197654	+	0.980272i	$0.436668\pi$
$284$	−0.612146	+	5.82418i	−0.0363242	+	0.345601i
$285$	3.88692	−	6.73234i	0.230241	−	0.398789i
$286$		0			0
$287$	2.39465	−	19.7932i	0.141352	−	1.16835i
$288$	9.78814	+	7.11150i	0.576772	+	0.419049i
$289$	−6.00014	−	6.66383i	−0.352949	−	0.391990i
$290$	8.13610	−	9.03606i	0.477768	−	0.530615i
$291$	5.21449	+	2.32164i	0.305679	+	0.136097i
$292$	2.28105	+	21.7027i	0.133488	+	1.27005i
$293$	−1.07020	−	3.29375i	−0.0625220	−	0.192423i	0.914917	−	0.403643i	$-0.132256\pi$
$293$	−1.07020	−	3.29375i	−0.0625220	−	0.192423i	−0.977438	+	0.211220i	$0.932256\pi$
$294$	14.8749	−	23.9938i	0.867519	−	1.39935i
$295$	6.07071	+	4.41063i	0.353451	+	0.256797i
$296$	3.53566	−	6.12395i	0.205506	−	0.355947i
$297$		0			0
$298$	0.917122	+	1.58850i	0.0531274	+	0.0920194i
$299$	−3.56392	+	1.58676i	−0.206107	+	0.0917647i
$300$	4.26079	−	13.1134i	0.245997	−	0.757101i
$301$	−12.6364	+	2.47954i	−0.728348	+	0.142918i
$302$	−2.57528	+	1.87105i	−0.148191	+	0.107667i
$303$	−2.27530	−	21.6480i	−0.130713	−	1.24365i
$304$	18.1179	−	20.1220i	1.03913	−	1.15407i
$305$	−2.69274	+	0.572360i	−0.154186	+	0.0327733i
$306$	−8.71126	+	3.87850i	−0.497990	+	0.221719i
$307$	−6.51473			−0.371815			−0.185908	−	0.982567i	$-0.559523\pi$
$307$	−6.51473			−0.371815			−0.185908	+	0.982567i	$0.559523\pi$
$308$		0			0
$309$	−13.7014			−0.779447
$310$	−6.84811	+	3.04897i	−0.388946	+	0.173170i
$311$	−11.3759	+	2.41803i	−0.645071	+	0.137114i	−0.518819	−	0.854884i	$-0.673628\pi$
$311$	−11.3759	+	2.41803i	−0.645071	+	0.137114i	−0.126252	+	0.991998i	$0.540295\pi$
$312$	−3.08938	+	3.43110i	−0.174902	+	0.194248i
$313$	2.83248	+	26.9493i	0.160101	+	1.52326i	0.719575	+	0.694415i	$0.244337\pi$
$313$	2.83248	+	26.9493i	0.160101	+	1.52326i	−0.559474	+	0.828848i	$0.688997\pi$
$314$	11.7818	−	8.56000i	0.664887	−	0.483069i
$315$	2.02761	+	2.32416i	0.114243	+	0.130952i
$316$	2.00777	−	6.17927i	0.112946	−	0.347611i
$317$	3.52786	−	1.57070i	0.198144	−	0.0882194i	−0.305266	−	0.952267i	$-0.598745\pi$
$317$	3.52786	−	1.57070i	0.198144	−	0.0882194i	0.503410	+	0.864048i	$0.332079\pi$
$318$	15.0626	+	26.0892i	0.844668	+	1.46301i
$319$		0			0
$320$	−0.751365	+	1.30140i	−0.0420026	+	0.0727506i
$321$	19.7423	+	14.3436i	1.10191	+	0.800583i
$322$	0.934611	+	10.4687i	0.0520838	+	0.583396i
$323$	4.87236	+	14.9956i	0.271105	+	0.834377i
$324$	1.58858	+	15.1144i	0.0882546	+	0.839686i
$325$	7.56320	+	3.36735i	0.419531	+	0.186787i
$326$	−19.6443	+	21.8172i	−1.08800	+	1.20834i
$327$	21.0443	+	23.3720i	1.16375	+	1.29248i
$328$	7.10701	+	5.16355i	0.392419	+	0.285109i
$329$	−5.99673	−	4.50220i	−0.330610	−	0.248214i
$330$		0			0
$331$	−3.07514	+	5.32630i	−0.169025	+	0.292760i	−0.938077	−	0.346426i	$-0.887395\pi$
$331$	−3.07514	+	5.32630i	−0.169025	+	0.292760i	0.769052	+	0.639186i	$0.220729\pi$
$332$	1.31665	−	12.5271i	0.0722605	−	0.687512i
$333$	−10.8831	+	2.31328i	−0.596393	+	0.126767i
$334$	−2.07981	−	0.442078i	−0.113802	−	0.0241894i
$335$	−0.824022	+	0.598687i	−0.0450211	+	0.0327097i
$336$	13.7705	+	24.7390i	0.751241	+	1.34962i
$337$	−3.63427	−	11.1851i	−0.197971	−	0.609293i	−0.999929	−	0.0119123i	$-0.996208\pi$
$337$	−3.63427	−	11.1851i	−0.197971	−	0.609293i	0.801958	−	0.597381i	$-0.203792\pi$
$338$	−11.9731	−	13.2975i	−0.651253	−	0.723289i
$339$	−1.99705	+	19.0007i	−0.108465	+	1.03198i
$340$	−1.22890	−	2.12851i	−0.0666462	−	0.115435i
$341$		0			0
$342$	−18.7169			−1.01209
$343$	15.4785	−	10.1694i	0.835760	−	0.549096i
$344$	1.75335	−	5.39624i	0.0945341	−	0.290946i
$345$	−2.96026	−	0.629222i	−0.159375	−	0.0338762i
$346$	−1.66470	−	0.741172i	−0.0894948	−	0.0398456i
$347$	−0.768097	−	0.341979i	−0.0412336	−	0.0183584i	0.386016	−	0.922492i	$-0.373851\pi$
$347$	−0.768097	−	0.341979i	−0.0412336	−	0.0183584i	−0.427250	+	0.904134i	$0.640518\pi$
$348$	−30.6072	−	6.50575i	−1.64072	−	0.348745i
$349$	2.82186	−	8.68480i	0.151051	−	0.464887i	−0.846689	−	0.532089i	$-0.821407\pi$
$349$	2.82186	−	8.68480i	0.151051	−	0.464887i	0.997739	+	0.0672022i	$0.0214073\pi$
$350$	15.1827	−	16.3395i	0.811548	−	0.873381i
$351$	−4.61701			−0.246438
$352$		0			0
$353$	−11.3639	−	19.6829i	−0.604840	−	1.04761i	−0.992077	−	0.125633i	$-0.959904\pi$
$353$	−11.3639	−	19.6829i	−0.604840	−	1.04761i	0.387237	−	0.921980i	$-0.373429\pi$
$354$	4.97722	−	47.3551i	0.264536	−	2.51689i
$355$	−1.82526	−	2.02716i	−0.0968749	−	0.107590i
$356$	0.153665	+	0.472932i	0.00814423	+	0.0250654i
$357$	−16.4853	−	0.258493i	−0.872495	−	0.0136809i
$358$	29.1770	−	21.1983i	1.54205	−	1.12037i
$359$	25.6456	+	5.45114i	1.35352	+	0.287700i	0.826876	−	0.562384i	$-0.190116\pi$
$359$	25.6456	+	5.45114i	1.35352	+	0.287700i	0.526647	+	0.850084i	$0.323449\pi$
$360$	−1.32929	+	0.282550i	−0.0700598	+	0.0148917i
$361$	−1.24896	+	11.8831i	−0.0657348	+	0.625424i
$362$	21.8941	−	37.9217i	1.15073	−	1.99312i
$363$		0			0
$364$	5.98126	−	2.55143i	0.313503	−	0.133731i
$365$	−8.22339	−	5.97464i	−0.430432	−	0.312727i
$366$	11.6888	+	12.9818i	0.610986	+	0.678569i
$367$	−2.55758	+	2.84048i	−0.133504	+	0.148272i	−0.806190	−	0.591657i	$-0.798474\pi$
$367$	−2.55758	+	2.84048i	−0.133504	+	0.148272i	0.672685	+	0.739929i	$0.265141\pi$
$368$	−9.62980	−	4.28746i	−0.501988	−	0.223499i
$369$	−1.44482	−	13.7465i	−0.0752142	−	0.715615i
$370$	−2.18516	−	6.72523i	−0.113601	−	0.349628i
$371$	1.75741	+	19.6849i	0.0912401	+	1.02199i
$372$	15.6067	+	11.3389i	0.809170	+	0.587896i
$373$	−7.55387	+	13.0837i	−0.391124	+	0.677447i	−0.992598	−	0.121445i	$-0.961247\pi$
$373$	−7.55387	+	13.0837i	−0.391124	+	0.677447i	0.601474	+	0.798893i	$0.294580\pi$
$374$		0			0
$375$	6.70469	+	11.6129i	0.346229	+	0.599686i
$376$	3.01839	−	1.34387i	0.155662	−	0.0693050i
$377$	5.80588	−	17.8687i	0.299018	−	0.920283i
$378$	−4.02880	+	11.7683i	−0.207219	+	0.605295i
$379$	9.20374	−	6.68691i	0.472764	−	0.343483i	−0.325753	−	0.945455i	$-0.605618\pi$
$379$	9.20374	−	6.68691i	0.472764	−	0.343483i	0.798518	+	0.601971i	$0.205618\pi$
$380$	−0.504269	−	4.79780i	−0.0258685	−	0.246122i
$381$	−30.8938	+	34.3111i	−1.58274	+	1.75781i
$382$	19.9721	−	4.24521i	1.02186	−	0.217204i
$383$	8.11751	−	3.61415i	0.414786	−	0.184674i	−0.188724	−	0.982030i	$-0.560435\pi$
$383$	8.11751	−	3.61415i	0.414786	−	0.184674i	0.603510	+	0.797356i	$0.293769\pi$
$384$	−19.4698			−0.993564
$385$		0			0
$386$	6.63009			0.337463
$387$	−8.15576	+	3.63118i	−0.414580	+	0.184583i
$388$	3.46480	−	0.736466i	0.175899	−	0.0373884i
$389$	−13.3150	+	14.7879i	−0.675100	+	0.749774i	−0.979207	−	0.202864i	$-0.934975\pi$
$389$	−13.3150	+	14.7879i	−0.675100	+	0.749774i	0.304107	+	0.952638i	$0.401642\pi$
$390$	0.482608	+	4.59171i	0.0244378	+	0.232510i
$391$	4.96597	−	3.60799i	0.251140	−	0.182464i
$392$	0.598118	+	8.13835i	0.0302095	+	0.411049i
$393$	9.30920	−	28.6508i	0.469587	−	1.44524i
$394$	4.05228	−	1.80419i	0.204151	−	0.0908939i
$395$	1.51320	+	2.62093i	0.0761371	+	0.131873i
$396$		0			0
$397$	17.4303	−	30.1902i	0.874803	−	1.51520i	0.0178296	−	0.999841i	$-0.494324\pi$
$397$	17.4303	−	30.1902i	0.874803	−	1.51520i	0.856973	−	0.515361i	$-0.172342\pi$
$398$	27.4471	+	19.9415i	1.37580	+	0.999577i
$399$	−29.3540	−	13.6246i	−1.46954	−	0.682085i
$400$	6.91268	+	21.2750i	0.345634	+	1.06375i
$401$	−1.19124	−	11.3339i	−0.0594876	−	0.565986i	−0.983153	−	0.182786i	$-0.941489\pi$
$401$	−1.19124	−	11.3339i	−0.0594876	−	0.565986i	0.923665	−	0.383200i	$-0.125178\pi$
$402$	5.90447	+	2.62884i	0.294488	+	0.131115i
$403$	−7.75053	+	8.60784i	−0.386081	+	0.428787i
$404$	−9.03874	−	10.0385i	−0.449694	−	0.499436i
$405$	−5.72700	−	4.16091i	−0.284577	−	0.206757i
$406$	−40.4792	−	30.3908i	−2.00895	−	1.50827i
$407$		0			0
$408$	3.63228	−	6.29129i	0.179825	−	0.311465i
$409$	0.427300	−	4.06549i	0.0211286	−	0.201026i	−0.978865	−	0.204506i	$-0.934441\pi$
$409$	0.427300	−	4.06549i	0.0211286	−	0.201026i	0.999994	+	0.00348044i	$0.00110786\pi$
$410$	8.59278	−	1.82645i	0.424367	−	0.0902021i
$411$	15.6235	+	3.32087i	0.770650	+	0.163807i
$412$	−6.87885	+	4.99778i	−0.338897	+	0.246223i
$413$	16.0411	−	26.8045i	0.789331	−	1.31896i
$414$	2.25168	+	6.92995i	0.110664	+	0.340588i
$415$	3.92591	+	4.36016i	0.192715	+	0.214032i
$416$	−1.24196	+	11.8165i	−0.0608922	+	0.579350i
$417$	−2.86118	−	4.95570i	−0.140112	−	0.242682i
$418$		0			0
$419$	32.8002			1.60240			0.801198	−	0.598399i	$-0.204196\pi$
$419$	32.8002			1.60240			0.801198	+	0.598399i	$0.204196\pi$
$420$	4.91725	+	1.12605i	0.239937	+	0.0549457i
$421$	−2.63322	+	8.10422i	−0.128335	+	0.394975i	−0.994494	−	0.104794i	$-0.966582\pi$
$421$	−2.63322	+	8.10422i	−0.128335	+	0.394975i	0.866159	+	0.499769i	$0.166582\pi$
$422$	14.0934	+	2.99565i	0.686058	+	0.145826i
$423$	−4.74924	−	2.11450i	−0.230916	−	0.102810i
$424$	−7.95512	−	3.54185i	−0.386335	−	0.172007i
$425$	−12.7417	−	2.70834i	−0.618065	−	0.131374i
$426$	−5.34893	+	16.4623i	−0.259156	+	0.797602i
$427$	3.37005	+	10.9534i	0.163088	+	0.530072i
$428$	15.1437			0.732000
$429$		0			0
$430$	−2.83697	−	4.91378i	−0.136811	−	0.236964i
$431$	1.74922	−	16.6427i	0.0842568	−	0.801650i	−0.868044	−	0.496488i	$-0.834623\pi$
$431$	1.74922	−	16.6427i	0.0842568	−	0.801650i	0.952300	−	0.305162i	$-0.0987106\pi$
$432$	−8.34757	−	9.27092i	−0.401623	−	0.446047i
$433$	−7.99306	−	24.6001i	−0.384122	−	1.18221i	−0.937115	−	0.349020i	$-0.886514\pi$
$433$	−7.99306	−	24.6001i	−0.384122	−	1.18221i	0.552993	−	0.833186i	$-0.313486\pi$
$434$	15.1774	+	27.2665i	0.728538	+	1.30883i
$435$	11.7915	−	8.56705i	0.565361	−	0.410759i
$436$	19.0906	+	4.05784i	0.914275	+	0.194335i
$437$	11.7851	−	2.50500i	0.563759	−	0.119831i
$438$	−6.74214	+	64.1472i	−0.322152	+	3.06507i
$439$	4.78430	−	8.28665i	0.228342	−	0.395500i	−0.728975	−	0.684541i	$-0.760003\pi$
$439$	4.78430	−	8.28665i	0.228342	−	0.395500i	0.957317	+	0.289040i	$0.0933362\pi$
$440$		0			0
$441$	8.88637	−	9.26770i	0.423161	−	0.441319i
$442$	−7.57600	−	5.50428i	−0.360353	−	0.261812i
$443$	12.7355	+	14.1442i	0.605083	+	0.672012i	0.965387	−	0.260822i	$-0.0839937\pi$
$443$	12.7355	+	14.1442i	0.605083	+	0.672012i	−0.360304	+	0.932835i	$0.617327\pi$
$444$	−12.1766	+	13.5235i	−0.577875	+	0.641795i
$445$	−0.211601	−	0.0942106i	−0.0100308	−	0.00446601i
$446$	−3.89922	−	37.0986i	−0.184633	−	1.75667i
$447$	0.679433	+	2.09108i	0.0321361	+	0.0989047i
$448$	5.67431	+	2.63373i	0.268086	+	0.124432i
$449$	−26.9746	−	19.5982i	−1.27301	−	0.924896i	−0.273692	−	0.961817i	$-0.588245\pi$
$449$	−26.9746	−	19.5982i	−1.27301	−	0.924896i	−0.999318	+	0.0369217i	$0.988245\pi$
$450$	7.73163	−	13.3916i	0.364472	−	0.631285i
$451$		0			0
$452$	5.92813	+	10.2678i	0.278836	+	0.482958i
$453$	−3.48581	+	1.55198i	−0.163778	+	0.0729186i
$454$	4.09217	−	12.5944i	0.192055	−	0.591085i
$455$	−0.981038	+	2.86565i	−0.0459918	+	0.134344i
$456$	11.5359	−	8.38129i	0.540216	−	0.392490i
$457$	−1.25021	−	11.8950i	−0.0584826	−	0.556425i	−0.984056	−	0.177857i	$-0.943083\pi$
$457$	−1.25021	−	11.8950i	−0.0584826	−	0.556425i	0.925574	−	0.378567i	$-0.123583\pi$
$458$	14.8157	−	16.4545i	0.692293	−	0.768870i
$459$	7.10581	−	1.51039i	0.331671	−	0.0704988i
$460$	−1.71573	+	0.763890i	−0.0799961	+	0.0356166i
$461$	12.4896			0.581701			0.290850	−	0.956769i	$-0.406062\pi$
$461$	12.4896			0.581701			0.290850	+	0.956769i	$0.406062\pi$
$462$		0			0
$463$	12.3095			0.572071			0.286035	−	0.958219i	$-0.407662\pi$
$463$	12.3095			0.572071			0.286035	+	0.958219i	$0.407662\pi$
$464$	46.3772	−	20.6485i	2.15301	−	0.958581i
$465$	−8.78926	+	1.86821i	−0.407592	+	0.0866363i
$466$	−9.25692	+	10.2808i	−0.428818	+	0.476251i
$467$	−3.42443	−	32.5813i	−0.158464	−	1.50768i	−0.727921	−	0.685661i	$-0.759513\pi$
$467$	−3.42443	−	32.5813i	−0.158464	−	1.50768i	0.569457	−	0.822021i	$-0.307153\pi$
$468$	3.64720	−	2.64985i	0.168592	−	0.122489i
$469$	2.78745	+	3.19512i	0.128712	+	0.147537i
$470$	1.02100	−	3.14233i	0.0470954	−	0.144945i
$471$	15.9475	−	7.10028i	0.734822	−	0.327164i
$472$	6.88191	+	11.9198i	0.316766	+	0.548654i
$473$		0			0
$474$	9.60208	−	16.6313i	0.441038	−	0.763900i
$475$	−20.6854	−	15.0288i	−0.949113	−	0.689571i
$476$	−8.37080	+	5.88346i	−0.383675	+	0.269668i
$477$	4.23397	+	13.0308i	0.193860	+	0.596641i
$478$	1.88783	+	17.9615i	0.0863472	+	0.821539i
$479$	23.7321	+	10.5662i	1.08435	+	0.482782i	0.869534	−	0.493873i	$-0.164419\pi$
$479$	23.7321	+	10.5662i	1.08435	+	0.482782i	0.214812	+	0.976655i	$0.431086\pi$
$480$	−6.16754	+	6.84974i	−0.281508	+	0.312647i
$481$	−7.31126	−	8.11997i	−0.333365	−	0.370239i
$482$	2.48563	+	1.80592i	0.113218	+	0.0822573i
$483$	−1.51320	+	12.5074i	−0.0688528	+	0.569107i
$484$		0			0
$485$	−0.824970	+	1.42889i	−0.0374600	+	0.0648825i
$486$	−3.22112	+	30.6469i	−0.146113	+	1.39017i
$487$	−14.2180	+	3.02213i	−0.644280	+	0.136946i	−0.518453	−	0.855106i	$-0.673492\pi$
$487$	−14.2180	+	3.02213i	−0.644280	+	0.136946i	−0.125827	+	0.992052i	$0.540159\pi$
$488$	−4.93915	−	1.04985i	−0.223585	−	0.0475244i
$489$	−28.4702	+	20.6848i	−1.28747	+	0.935398i
$490$	6.44819	+	5.00113i	0.291300	+	0.225928i
$491$	−12.1738	−	37.4671i	−0.549395	−	1.69087i	−0.710303	−	0.703896i	$-0.751442\pi$
$491$	−12.1738	−	37.4671i	−0.549395	−	1.69087i	0.160908	−	0.986969i	$-0.448558\pi$
$492$	−15.1270	−	16.8003i	−0.681979	−	0.757415i
$493$	−3.09008	+	29.4001i	−0.139170	+	1.32411i
$494$	−9.19041	−	15.9183i	−0.413496	−	0.716196i
$495$		0			0
$496$	−31.2975			−1.40530
$497$	−7.72979	+	8.31873i	−0.346729	+	0.373146i
$498$	11.5049	−	35.4083i	0.515546	−	1.58669i
$499$	25.6573	+	5.45364i	1.14858	+	0.244138i	0.742595	−	0.669741i	$-0.233595\pi$
$499$	25.6573	+	5.45364i	1.14858	+	0.244138i	0.405986	+	0.913879i	$0.366928\pi$
$500$	7.60207	+	3.38466i	0.339975	+	0.151367i
$501$	−2.32840	−	1.03667i	−0.104025	−	0.0463150i
$502$	−35.4774	−	7.54096i	−1.58344	−	0.336570i
$503$	1.21942	−	3.75300i	0.0543714	−	0.167338i	−0.920183	−	0.391488i	$-0.871961\pi$
$503$	1.21942	−	3.75300i	0.0543714	−	0.167338i	0.974555	+	0.224150i	$0.0719605\pi$
$504$	1.66365	+	5.40722i	0.0741048	+	0.240857i
$505$	6.29204			0.279992
$506$		0			0
$507$	−10.7244	−	18.5753i	−0.476289	−	0.824956i
$508$	−2.99494	+	28.4950i	−0.132879	+	1.26426i
$509$	11.3120	+	12.5633i	0.501397	+	0.556858i	0.939713	−	0.341963i	$-0.111092\pi$
$509$	11.3120	+	12.5633i	0.501397	+	0.556858i	−0.438316	+	0.898821i	$0.644425\pi$
$510$	−2.24487	−	6.90901i	−0.0994046	−	0.305936i
$511$	−21.7293	+	36.3094i	−0.961247	+	1.60623i
$512$	−16.7923	+	12.2003i	−0.742120	+	0.539182i
$513$	13.9475	+	2.96463i	0.615797	+	0.130892i
$514$	−4.88006	+	1.03729i	−0.215250	+	0.0457528i
$515$	0.413987	−	3.93883i	0.0182425	−	0.173565i
$516$	−7.30077	+	12.6453i	−0.321398	+	0.556678i
$517$		0			0
$518$	−27.0768	+	11.5502i	−1.18969	+	0.507485i
$519$	−1.76714	−	1.28390i	−0.0775688	−	0.0563570i
$520$	−0.893014	−	0.991792i	−0.0391612	−	0.0434930i
$521$	1.04229	−	1.15758i	0.0456636	−	0.0507146i	−0.719880	−	0.694098i	$-0.755803\pi$
$521$	1.04229	−	1.15758i	0.0456636	−	0.0507146i	0.765544	+	0.643384i	$0.222470\pi$
$522$	−32.0584	−	14.2733i	−1.40316	−	0.624726i
$523$	1.30689	+	12.4342i	0.0571464	+	0.543711i	0.985217	+	0.171308i	$0.0547994\pi$
$523$	1.30689	+	12.4342i	0.0571464	+	0.543711i	−0.928071	+	0.372403i	$0.878534\pi$
$524$	−5.77703	−	17.7799i	−0.252371	−	0.776718i
$525$	21.8738	−	15.3741i	0.954651	−	0.670981i
$526$	−18.8384	−	13.6869i	−0.821391	−	0.596776i
$527$	9.11254	−	15.7834i	0.396949	−	0.687535i
$528$		0			0
$529$	9.15475	+	15.8565i	0.398033	+	0.689413i
$530$	−7.95512	+	3.54185i	−0.345548	+	0.153848i
$531$	6.69222	−	20.5965i	0.290418	−	0.893814i
$532$	−19.7071	+	3.86697i	−0.854410	+	0.167654i
$533$	10.9816	−	7.97863i	0.475668	−	0.345593i
$534$	0.153635	+	1.46174i	0.00664846	+	0.0632558i
$535$	−4.71996	+	5.24204i	−0.204062	+	0.226633i
$536$	−1.82744	+	0.388434i	−0.0789332	+	0.0167778i
$537$	39.4931	−	17.5834i	1.70425	−	0.758782i
$538$	−13.0109			−0.560941
$539$		0			0
$540$	−2.22270			−0.0956497
$541$	−15.1302	+	6.73639i	−0.650498	+	0.289620i	−0.705334	−	0.708875i	$-0.749203\pi$
$541$	−15.1302	+	6.73639i	−0.650498	+	0.289620i	0.0548363	+	0.998495i	$0.482536\pi$
$542$	32.6827	−	6.94692i	1.40384	−	0.298396i
$543$	35.1217	−	39.0066i	1.50722	−	1.67393i
$544$	−1.95415	−	18.5925i	−0.0837834	−	0.797145i
$545$	−7.35474	+	5.34353i	−0.315042	+	0.228892i
$546$	18.8606	−	3.70086i	0.807157	−	0.158382i
$547$	−2.05326	+	6.31928i	−0.0877909	+	0.270193i	−0.985308	−	0.170787i	$-0.945369\pi$
$547$	−2.05326	+	6.31928i	−0.0877909	+	0.270193i	0.897517	+	0.440980i	$0.145369\pi$
$548$	9.05517	−	4.03162i	0.386818	−	0.172222i
$549$	3.97252	+	6.88061i	0.169543	+	0.293657i
$550$		0			0
$551$	−29.0127	+	50.2514i	−1.23598	+	2.14078i
$552$	−4.49096	−	3.26288i	−0.191148	−	0.138877i
$553$	10.3073	−	7.24457i	0.438313	−	0.308071i
$554$	7.84957	+	24.1585i	0.333496	+	1.02640i
$555$	−0.886019	−	8.42990i	−0.0376094	−	0.357830i
$556$	−3.24412	−	1.44438i	−0.137582	−	0.0612552i
$557$	8.77357	−	9.74403i	0.371748	−	0.412868i	−0.528023	−	0.849230i	$-0.677067\pi$
$557$	8.77357	−	9.74403i	0.371748	−	0.412868i	0.899771	+	0.436362i	$0.143733\pi$
$558$	14.4763	+	16.0775i	0.612830	+	0.680617i
$559$	−7.09289	−	5.15328i	−0.299997	−	0.217961i
$560$	−7.52793	+	3.21119i	−0.318113	+	0.135698i
$561$		0			0
$562$	−19.2898	+	33.4108i	−0.813689	+	1.40935i
$563$	−3.18692	+	30.3215i	−0.134313	+	1.27790i	0.694957	+	0.719052i	$0.255423\pi$
$563$	−3.18692	+	30.3215i	−0.134313	+	1.27790i	−0.829269	+	0.558849i	$0.811243\pi$
$564$	−8.31692	+	1.76782i	−0.350206	+	0.0744385i
$565$	−5.40189	−	1.14821i	−0.227259	−	0.0483055i
$566$	−0.523005	+	0.379986i	−0.0219836	+	0.0159720i
$567$	−15.1329	+	25.2869i	−0.635521	+	1.06195i
$568$	−1.54616	−	4.75858i	−0.0648753	−	0.199666i
$569$	−23.6591	−	26.2760i	−0.991839	−	1.10155i	−0.994830	−	0.101554i	$-0.967619\pi$
$569$	−23.6591	−	26.2760i	−0.991839	−	1.10155i	0.00299086	−	0.999996i	$-0.499048\pi$
$570$	1.49048	−	14.1810i	0.0624294	−	0.593976i
$571$	20.6422	+	35.7533i	0.863849	+	1.49623i	0.868185	+	0.496240i	$0.165287\pi$
$571$	20.6422	+	35.7533i	0.863849	+	1.49623i	−0.00433587	+	0.999991i	$0.501380\pi$
$572$		0			0
$573$	24.4753			1.02247
$574$	−10.7541	−	34.9532i	−0.448869	−	1.45892i
$575$	−3.07595	+	9.46680i	−0.128276	+	0.394793i
$576$	4.24220	+	0.901707i	0.176758	+	0.0375711i
$577$	7.95013	+	3.53963i	0.330968	+	0.147357i	0.565492	−	0.824754i	$-0.308686\pi$
$577$	7.95013	+	3.53963i	0.330968	+	0.147357i	−0.234524	+	0.972110i	$0.575353\pi$
$578$	−15.0258	−	6.68991i	−0.624991	−	0.278264i
$579$	7.77376	+	1.65236i	0.323067	+	0.0686699i
$580$	2.79504	−	8.60225i	0.116058	−	0.357189i
$581$	16.6258	−	17.8925i	0.689755	−	0.742308i
$582$	10.4698			0.433987
$583$		0			0
$584$	−9.32224	−	16.1466i	−0.385757	−	0.668151i
$585$	−0.219498	+	2.08838i	−0.00907513	+	0.0863441i
$586$	−4.25062	−	4.72079i	−0.175591	−	0.195014i
$587$	−7.12404	−	21.9255i	−0.294040	−	0.904963i	−0.983542	−	0.180679i	$-0.942170\pi$
$587$	−7.12404	−	21.9255i	−0.294040	−	0.904963i	0.689502	−	0.724284i	$-0.257830\pi$
$588$	2.84882	−	20.8059i	0.117483	−	0.858020i
$589$	28.9408	−	21.0267i	1.19248	−	0.866390i
$590$	13.4630	+	2.86166i	0.554265	+	0.117813i
$591$	5.20093	−	1.10549i	0.213938	−	0.0454739i
$592$	3.08606	−	29.3619i	0.126836	−	1.20677i
$593$	−15.0494	+	26.0663i	−0.618005	+	1.07042i	0.371844	+	0.928295i	$0.378725\pi$
$593$	−15.0494	+	26.0663i	−0.618005	+	1.07042i	−0.989849	+	0.142121i	$0.954608\pi$
$594$		0			0
$595$	0.572413	−	4.73131i	0.0234666	−	0.193965i
$596$	1.10386	+	0.802002i	0.0452159	+	0.0328513i
$597$	27.2118	+	30.2218i	1.11370	+	1.23689i
$598$	−4.78813	+	5.31775i	−0.195801	+	0.217459i
$599$	26.7225	+	11.8976i	1.09185	+	0.486125i	0.872049	−	0.489419i	$-0.162791\pi$
$599$	26.7225	+	11.8976i	1.09185	+	0.486125i	0.219805	+	0.975544i	$0.429458\pi$
$600$	1.23138	+	11.7158i	0.0502711	+	0.478297i
$601$	−8.28853	−	25.5095i	−0.338096	−	1.04055i	−0.965177	−	0.261599i	$-0.915750\pi$
$601$	−8.28853	−	25.5095i	−0.338096	−	1.04055i	0.627081	−	0.778954i	$-0.284250\pi$
$602$	−19.3244	+	13.5823i	−0.787606	+	0.553573i
$603$	2.37818	+	1.72785i	0.0968469	+	0.0703634i
$604$	−1.18396	+	2.05068i	−0.0481746	+	0.0834409i
$605$		0			0
$606$	−19.9633	−	34.5774i	−0.810952	−	1.40461i
$607$	29.4249	−	13.1008i	1.19432	−	0.531746i	0.289352	−	0.957223i	$-0.406560\pi$
$607$	29.4249	−	13.1008i	1.19432	−	0.531746i	0.904969	+	0.425477i	$0.139893\pi$
$608$	11.3393	−	34.8989i	0.459871	−	1.41534i
$609$	−39.8877	−	45.7214i	−1.61633	−	1.85272i
$610$	−4.08512	+	2.96802i	−0.165402	+	0.120171i
$611$	−0.533654	−	5.07738i	−0.0215893	−	0.205409i
$612$	−4.74637	+	5.27138i	−0.191861	+	0.213083i
$613$	−43.6205	+	9.27182i	−1.76181	+	0.374485i	−0.971281	−	0.237934i	$-0.923530\pi$
$613$	−43.6205	+	9.27182i	−1.76181	+	0.374485i	−0.790533	+	0.612419i	$0.790197\pi$
$614$	−10.9165	+	4.86034i	−0.440554	+	0.196147i
$615$	10.5302			0.424619
$616$		0			0
$617$	−0.531290			−0.0213889			−0.0106945	−	0.999943i	$-0.503404\pi$
$617$	−0.531290			−0.0213889			−0.0106945	+	0.999943i	$0.503404\pi$
$618$	−22.9590	+	10.2220i	−0.923546	+	0.411189i
$619$	−40.8330	+	8.67933i	−1.64122	+	0.348852i	−0.933759	−	0.357902i	$-0.883492\pi$
$619$	−40.8330	+	8.67933i	−1.64122	+	0.348852i	−0.707459	+	0.706754i	$0.750159\pi$
$620$	−3.73122	+	4.14394i	−0.149850	+	0.166425i
$621$	−0.580252	−	5.52073i	−0.0232847	−	0.221539i
$622$	−17.2583	+	12.5389i	−0.691994	+	0.502763i
$623$	−0.312307	+	0.912261i	−0.0125123	+	0.0365490i
$624$	−5.95679	+	18.3331i	−0.238462	+	0.733911i
$625$	17.4526	−	7.77040i	0.698104	−	0.310816i
$626$	24.8519	+	43.0448i	0.993282	+	1.72041i
$627$		0			0
$628$	5.41658	−	9.38179i	0.216145	−	0.374374i
$629$	13.9087	+	10.1053i	0.554578	+	0.402924i
$630$	5.13154	+	2.38180i	0.204446	+	0.0948933i
$631$	−0.0671302	−	0.206606i	−0.00267241	−	0.00822484i	0.949711	−	0.313127i	$-0.101376\pi$
$631$	−0.0671302	−	0.206606i	−0.00267241	−	0.00822484i	−0.952384	+	0.304902i	$0.901376\pi$
$632$	0.580252	+	5.52073i	0.0230812	+	0.219603i
$633$	15.7779	+	7.02479i	0.627117	+	0.279210i
$634$	4.73967	−	5.26394i	0.188236	−	0.209058i
$635$	−8.93015	−	9.91794i	−0.354382	−	0.393581i
$636$	18.1296	+	13.1719i	0.718884	+	0.522300i
$637$	12.2454	+	3.00700i	0.485179	+	0.119142i
$638$		0			0
$639$	−3.93632	+	6.81790i	−0.155718	+	0.269712i
$640$	0.588278	−	5.59709i	0.0232537	−	0.221245i
$641$	9.47874	−	2.01477i	0.374388	−	0.0795786i	−0.0168749	−	0.999858i	$-0.505372\pi$
$641$	9.47874	−	2.01477i	0.374388	−	0.0795786i	0.391263	+	0.920279i	$0.372038\pi$
$642$	43.7826	+	9.30628i	1.72796	+	0.367290i
$643$	−13.3191	+	9.67686i	−0.525252	+	0.381618i	−0.818579	−	0.574394i	$-0.805238\pi$
$643$	−13.3191	+	9.67686i	−0.525252	+	0.381618i	0.293327	+	0.956012i	$0.405238\pi$
$644$	3.80254	+	6.83136i	0.149841	+	0.269193i
$645$	−2.10172	−	6.46843i	−0.0827551	−	0.254694i
$646$	19.3520	+	21.4925i	0.761393	+	0.845612i
$647$	−0.0913288	+	0.868935i	−0.00359050	+	0.0341614i	−0.996170	−	0.0874324i	$-0.972134\pi$
$647$	−0.0913288	+	0.868935i	−0.00359050	+	0.0341614i	0.992580	+	0.121594i	$0.0388005\pi$
$648$	−6.49226	−	11.2449i	−0.255040	−	0.441743i
$649$		0			0
$650$	15.1856			0.595628
$651$	11.0000	+	35.7524i	0.431125	+	1.40125i
$652$	−6.74850	+	20.7698i	−0.264292	+	0.813407i
$653$	39.0604	+	8.30255i	1.52855	+	0.324904i	0.894032	−	0.448003i	$-0.147865\pi$
$653$	39.0604	+	8.30255i	1.52855	+	0.324904i	0.634520	+	0.772907i	$0.281198\pi$
$654$	52.6999	+	23.4635i	2.06073	+	0.917496i
$655$	7.95512	+	3.54185i	0.310832	+	0.138391i
$656$	35.8759	+	7.62566i	1.40072	+	0.297732i
$657$	−9.06529	+	27.9001i	−0.353671	+	1.08849i
$658$	−13.4074	−	3.07029i	−0.522674	−	0.119692i
$659$	−6.89465			−0.268578			−0.134289	−	0.990942i	$-0.542875\pi$
$659$	−6.89465			−0.268578			−0.134289	+	0.990942i	$0.542875\pi$
$660$		0			0
$661$	20.0072	+	34.6535i	0.778190	+	1.34786i	0.932984	+	0.359917i	$0.117195\pi$
$661$	20.0072	+	34.6535i	0.778190	+	1.34786i	−0.154795	+	0.987947i	$0.549472\pi$
$662$	−1.17920	+	11.2193i	−0.0458308	+	0.436051i
$663$	−7.51105	−	8.34186i	−0.291705	−	0.323971i
$664$	3.32559	+	10.2351i	0.129058	+	0.397199i
$665$	4.80368	−	8.02690i	0.186279	−	0.311270i
$666$	−16.5107	+	11.9957i	−0.639775	+	0.464824i
$667$	22.0959	+	4.69663i	0.855556	+	0.181854i
$668$	−1.54712	+	0.328851i	−0.0598600	+	0.0127236i
$669$	4.67396	−	44.4698i	0.180706	−	1.71930i
$670$	−0.934131	+	1.61796i	−0.0360886	+	0.0625073i
$671$		0			0
$672$	30.6851	+	23.0376i	1.18370	+	0.888695i
$673$	−25.3860	−	18.4440i	−0.978559	−	0.710965i	−0.0211728	−	0.999776i	$-0.506740\pi$
$673$	−25.3860	−	18.4440i	−0.978559	−	0.710965i	−0.957386	+	0.288811i	$0.906740\pi$
$674$	−14.4345	−	16.0312i	−0.555997	−	0.617498i
$675$	−7.88261	+	8.75453i	−0.303402	+	0.336962i
$676$	−12.1598	−	5.41390i	−0.467685	−	0.208227i
$677$	3.81858	+	36.3314i	0.146760	+	1.39633i	0.781646	+	0.623722i	$0.214380\pi$
$677$	3.81858	+	36.3314i	0.146760	+	1.39633i	−0.634886	+	0.772606i	$0.718953\pi$
$678$	10.8291	+	33.3287i	0.415891	+	1.27998i
$679$	6.23018	+	2.89173i	0.239092	+	0.110974i
$680$	1.69885	+	1.23428i	0.0651477	+	0.0473326i
$681$	7.93686	−	13.7470i	0.304141	−	0.526788i
$682$		0			0
$683$	7.63501	+	13.2242i	0.292146	+	0.506011i	0.974317	−	0.225181i	$-0.0722975\pi$
$683$	7.63501	+	13.2242i	0.292146	+	0.506011i	−0.682171	+	0.731192i	$0.738964\pi$
$684$	−12.7193	+	5.66301i	−0.486335	+	0.216531i
$685$	−1.42673	+	4.39103i	−0.0545127	+	0.167773i
$686$	18.3498	−	28.5883i	0.700600	−	1.09151i
$687$	21.4722	−	15.6005i	0.819216	−	0.595195i
$688$	−2.47622	−	23.5596i	−0.0944049	−	0.898203i
$689$	−9.00342	+	9.99932i	−0.343003	+	0.380944i
$690$	−5.42983	+	1.15415i	−0.206710	+	0.0439376i
$691$	−35.0658	+	15.6123i	−1.33397	+	0.593920i	−0.944921	−	0.327299i	$-0.893862\pi$
$691$	−35.0658	+	15.6123i	−1.33397	+	0.593920i	−0.389045	+	0.921219i	$0.627195\pi$
$692$	−1.35552			−0.0515291
$693$		0			0
$694$	−1.54221			−0.0585414
$695$	1.51109	−	0.672783i	0.0573191	−	0.0255201i
$696$	26.1501	−	5.55838i	0.991219	−	0.210690i
$697$	−14.2912	+	15.8720i	−0.541319	+	0.601195i
$698$	−1.75083	−	16.6581i	−0.0662700	−	0.630517i
$699$	−13.4159	+	9.74723i	−0.507437	+	0.368674i
$700$	5.37391	−	15.6974i	0.203115	−	0.593306i
$701$	5.53313	−	17.0292i	0.208983	−	0.643184i	−0.790543	−	0.612407i	$-0.790202\pi$
$701$	5.53313	−	17.0292i	0.208983	−	0.643184i	0.999526	−	0.0307778i	$-0.00979843\pi$
$702$	−7.73655	+	3.44453i	−0.291997	+	0.130006i
$703$	16.8726	+	29.2243i	0.636364	+	1.10221i
$704$		0			0
$705$	1.98026	−	3.42991i	0.0745809	−	0.129178i
$706$	−33.7266	−	24.5038i	−1.26932	−	0.922212i
$707$	−2.32919	−	26.0895i	−0.0875981	−	0.981195i
$708$	−10.9455	−	33.6867i	−0.411356	−	1.26602i
$709$	−3.59571	−	34.2109i	−0.135040	−	1.28482i	−0.826720	−	0.562614i	$-0.809796\pi$
$709$	−3.59571	−	34.2109i	−0.135040	−	1.28482i	0.691680	−	0.722204i	$-0.256871\pi$
$710$	−4.57090	−	2.03509i	−0.171543	−	0.0763757i
$711$	5.84442	−	6.49089i	0.219183	−	0.243427i
$712$	−0.284285	−	0.315731i	−0.0106540	−	0.0118325i
$713$	−11.2668	−	8.18579i	−0.421944	−	0.306560i
$714$	−27.8167	+	11.8658i	−1.04101	+	0.444066i
$715$		0			0
$716$	13.4138	−	23.2335i	0.501299	−	0.868276i
$717$	−2.26292	+	21.5303i	−0.0845104	+	0.804062i
$718$	47.0403	−	9.99872i	1.75553	−	0.373149i
$719$	−48.3373	−	10.2744i	−1.80268	−	0.383171i	−0.820579	−	0.571533i	$-0.806349\pi$
$719$	−48.3373	−	10.2744i	−1.80268	−	0.383171i	−0.982100	+	0.188362i	$0.939682\pi$
$720$	−4.59032	+	3.33506i	−0.171071	+	0.124290i
$721$	−16.4853	−	0.258493i	−0.613945	−	0.00962679i
$722$	6.77257	+	20.8438i	0.252049	+	0.775727i
$723$	2.46432	+	2.73691i	0.0916492	+	0.101787i
$724$	3.40480	−	32.3945i	0.126538	−	1.20393i
$725$	−23.9693	−	41.5160i	−0.890196	−	1.54186i
$726$		0			0
$727$	−19.8201			−0.735086			−0.367543	−	0.930007i	$-0.619801\pi$
$727$	−19.8201			−0.735086			−0.367543	+	0.930007i	$0.619801\pi$
$728$	−3.78182	+	4.06996i	−0.140164	+	0.150843i
$729$	−1.08887	+	3.35120i	−0.0403286	+	0.124119i
$730$	−18.2371	−	3.87641i	−0.674984	−	0.143472i
$731$	12.6021	+	5.61084i	0.466107	+	0.207524i
$732$	11.8711	+	5.28536i	0.438769	+	0.195352i
$733$	29.9778	+	6.37198i	1.10726	+	0.235355i	0.725032	−	0.688715i	$-0.241825\pi$
$733$	29.9778	+	6.37198i	1.10726	+	0.235355i	0.382224	+	0.924070i	$0.375158\pi$
$734$	−2.16649	+	6.66778i	−0.0799667	+	0.246112i
$735$	6.31409	+	7.47084i	0.232899	+	0.275566i
$736$	−14.2855			−0.526570
$737$		0			0
$738$	−12.6767	−	21.9566i	−0.466635	−	0.808235i
$739$	−1.78763	+	17.0082i	−0.0657591	+	0.625656i	0.911161	+	0.412051i	$0.135187\pi$
$739$	−1.78763	+	17.0082i	−0.0657591	+	0.625656i	−0.976920	+	0.213606i	$0.931479\pi$
$740$	−3.51975	−	3.90908i	−0.129389	−	0.143701i
$741$	−6.80855	−	20.9546i	−0.250118	−	0.769785i
$742$	17.6308	+	31.6742i	0.647249	+	1.16280i
$743$	5.64089	−	4.09835i	0.206944	−	0.150354i	−0.479486	−	0.877550i	$-0.659177\pi$
$743$	5.64089	−	4.09835i	0.206944	−	0.150354i	0.686430	+	0.727196i	$0.259177\pi$
$744$	−16.1216	−	3.42676i	−0.591048	−	0.125631i
$745$	−0.621664	+	0.132139i	−0.0227760	+	0.00484119i
$746$	−2.89661	+	27.5594i	−0.106053	+	1.00902i
$747$	8.46652	−	14.6644i	0.309774	−	0.536544i
$748$		0			0
$749$	23.4830	+	17.6305i	0.858050	+	0.644203i
$750$	19.8986	+	14.4572i	0.726596	+	0.527903i
$751$	10.1927	+	11.3201i	0.371936	+	0.413077i	0.899835	−	0.436230i	$-0.143687\pi$
$751$	10.1927	+	11.3201i	0.371936	+	0.413077i	−0.527899	+	0.849307i	$0.677020\pi$
$752$	9.23050	−	10.2515i	0.336602	−	0.373834i
$753$	−39.7178	−	17.6835i	−1.44740	−	0.644423i
$754$	−3.60228	−	34.2734i	−0.131187	−	1.24816i
$755$	−0.340834	−	1.04898i	−0.0124042	−	0.0381763i
$756$	0.822798	+	9.21625i	0.0299249	+	0.335192i
$757$	11.7571	+	8.54204i	0.427320	+	0.310466i	0.780576	−	0.625061i	$-0.214926\pi$
$757$	11.7571	+	8.54204i	0.427320	+	0.310466i	−0.353257	+	0.935526i	$0.614926\pi$
$758$	10.4336	−	18.0715i	0.378965	−	0.656387i
$759$		0			0
$760$	2.06086	+	3.56952i	0.0747553	+	0.129480i
$761$	−1.56529	+	0.696912i	−0.0567417	+	0.0252630i	−0.434911	−	0.900473i	$-0.643220\pi$
$761$	−1.56529	+	0.696912i	−0.0567417	+	0.0252630i	0.378170	+	0.925736i	$0.376554\pi$
$762$	−26.1698	+	80.5424i	−0.948032	+	2.91774i
$763$	24.8791	+	28.5178i	0.900686	+	1.03241i
$764$	12.2879	−	8.92768i	0.444561	−	0.322992i
$765$	−0.345366	−	3.28594i	−0.0124867	−	0.118803i
$766$	10.9059	−	12.1122i	0.394045	−	0.437632i
$767$	20.8029	−	4.42179i	0.751149	−	0.159662i
$768$	−42.1233	+	18.7545i	−1.51999	+	0.676745i
$769$	−36.5874			−1.31937			−0.659687	−	0.751540i	$-0.729311\pi$
$769$	−36.5874			−1.31937			−0.659687	+	0.751540i	$0.729311\pi$
$770$		0			0
$771$	−5.98037			−0.215378
$772$	4.50557	−	2.00601i	0.162159	−	0.0721979i
$773$	−26.2350	+	5.57643i	−0.943609	+	0.200570i	−0.653931	−	0.756554i	$-0.726881\pi$
$773$	−26.2350	+	5.57643i	−0.943609	+	0.200570i	−0.289678	+	0.957124i	$0.593548\pi$
$774$	−10.9573	+	12.1693i	−0.393851	+	0.437415i
$775$	3.08926	+	29.3923i	0.110969	+	1.05580i
$776$	−2.44840	+	1.77887i	−0.0878925	+	0.0638576i
$777$	−34.6260	+	6.79440i	−1.24220	+	0.243748i
$778$	−11.2790	+	34.7132i	−0.404372	+	1.24453i
$779$	−38.2976	+	17.0512i	−1.37215	+	0.610922i
$780$	1.71724	+	2.97434i	0.0614870	+	0.106499i
$781$		0			0
$782$	5.62955	−	9.75067i	0.201312	−	0.348683i
$783$	21.6285	+	15.7141i	0.772941	+	0.561575i
$784$	16.1017	+	30.0253i	0.575059	+	1.07233i
$785$	1.55931	+	4.79905i	0.0556540	+	0.171286i
$786$	−5.77592	−	54.9542i	−0.206020	−	1.96015i
$787$	4.52351	+	2.01399i	0.161246	+	0.0717911i	0.485772	−	0.874085i	$-0.338538\pi$
$787$	4.52351	+	2.01399i	0.161246	+	0.0717911i	−0.324527	+	0.945876i	$0.605205\pi$
$788$	2.20791	−	2.45213i	0.0786534	−	0.0873534i
$789$	−18.6769	−	20.7427i	−0.664913	−	0.738461i
$790$	4.49096	+	3.26288i	0.159781	+	0.116088i
$791$	−2.76129	+	22.8236i	−0.0981801	+	0.811514i
$792$		0			0
$793$	−3.90120	+	6.75707i	−0.138536	+	0.239951i
$794$	6.68385	−	63.5926i	0.237201	−	2.25682i
$795$	−10.2101	+	2.17022i	−0.362114	+	0.0769696i
$796$	24.6856	+	5.24708i	0.874958	+	0.185978i
$797$	21.5860	−	15.6832i	0.764616	−	0.555526i	−0.135707	−	0.990749i	$-0.543330\pi$
$797$	21.5860	−	15.6832i	0.764616	−	0.555526i	0.900323	+	0.435223i	$0.143330\pi$
$798$	−59.3522	−	0.930656i	−2.10104	−	0.0329449i
$799$	2.48231	+	7.63977i	0.0878179	+	0.270276i
$800$	20.2854	+	22.5292i	0.717197	+	0.796528i
$801$	−0.0698759	+	0.664824i	−0.00246894	+	0.0234904i
$802$	−10.4518	−	18.1030i	−0.369066	−	0.639240i
$803$		0			0
$804$	4.80785			0.169560
$805$	−3.54986	−	0.812917i	−0.125116	−	0.0286516i
$806$	−6.56538	+	20.2062i	−0.231256	+	0.711732i
$807$	−15.2553	−	3.24261i	−0.537011	−	0.114145i
$808$	10.5433	+	4.69420i	0.370913	+	0.165141i
$809$	−36.1216	−	16.0824i	−1.26997	−	0.565426i	−0.342567	−	0.939493i	$-0.611296\pi$
$809$	−36.1216	−	16.0824i	−1.26997	−	0.565426i	−0.927402	+	0.374067i	$0.877963\pi$
$810$	−12.7008	−	2.69964i	−0.446260	−	0.0948555i
$811$	−10.3380	+	31.8170i	−0.363015	+	1.11724i	0.588200	+	0.808715i	$0.299837\pi$
$811$	−10.3380	+	31.8170i	−0.363015	+	1.11724i	−0.951215	+	0.308529i	$0.900163\pi$
$812$	−36.7033	−	8.40505i	−1.28803	−	0.294959i
$813$	40.0517			1.40467
$814$		0			0
$815$	−5.08615	−	8.80947i	−0.178160	−	0.308582i
$816$	3.17039	−	30.1643i	0.110986	−	1.05596i
$817$	18.1179	+	20.1220i	0.633865	+	0.703979i
$818$	−2.31706	−	7.13119i	−0.0810142	−	0.249336i
$819$	8.74059	+	0.137054i	0.305421	+	0.00478907i
$820$	5.28673	−	3.84104i	0.184621	−	0.134135i
$821$	−55.6194	−	11.8223i	−1.94113	−	0.412600i	−0.996403	−	0.0847388i	$-0.972994\pi$
$821$	−55.6194	−	11.8223i	−1.94113	−	0.412600i	−0.944726	−	0.327861i	$-0.893672\pi$
$822$	28.6573	−	6.09129i	0.999537	−	0.212458i
$823$	4.19949	−	39.9555i	0.146385	−	1.39276i	−0.636827	−	0.771007i	$-0.719753\pi$
$823$	4.19949	−	39.9555i	0.146385	−	1.39276i	0.783212	−	0.621755i	$-0.213580\pi$
$824$	3.63228	−	6.29129i	0.126536	−	0.219168i
$825$		0			0
$826$	6.88191	−	56.8829i	0.239452	−	1.97921i
$827$	4.64007	+	3.37121i	0.161351	+	0.117228i	0.665531	−	0.746370i	$-0.268205\pi$
$827$	4.64007	+	3.37121i	0.161351	+	0.117228i	−0.504180	+	0.863599i	$0.668205\pi$
$828$	3.62689	+	4.02807i	0.126043	+	0.139985i
$829$	−23.8184	+	26.4530i	−0.827248	+	0.918752i	−0.997780	−	0.0666002i	$-0.978785\pi$
$829$	−23.8184	+	26.4530i	−0.827248	+	0.918752i	0.170532	+	0.985352i	$0.445451\pi$
$830$	9.83142	+	4.37723i	0.341254	+	0.151936i
$831$	3.18277	+	30.2821i	0.110409	+	1.05047i
$832$	1.31613	+	4.05065i	0.0456288	+	0.140431i
$833$	−19.8299	−	0.622029i	−0.687067	−	0.0215520i
$834$	−8.49159	−	6.16950i	−0.294040	−	0.213632i
$835$	0.368370	−	0.638036i	0.0127480	−	0.0220801i
$836$		0			0
$837$	−8.24090	−	14.2737i	−0.284847	−	0.493370i
$838$	54.9622	−	24.4707i	1.89864	−	0.845328i
$839$	−12.9085	+	39.7282i	−0.445651	+	1.37157i	0.436118	+	0.899889i	$0.356353\pi$
$839$	−12.9085	+	39.7282i	−0.445651	+	1.37157i	−0.881769	+	0.471682i	$0.843647\pi$
$840$	−4.22930	+	0.829883i	−0.145925	+	0.0286337i
$841$	−64.5527	+	46.9003i	−2.22595	+	1.61725i
$842$	1.63379	+	15.5445i	0.0563041	+	0.535698i
$843$	−30.9439	+	34.3667i	−1.06576	+	1.18365i
$844$	10.4838	−	2.22839i	0.360866	−	0.0767044i
$845$	5.66397	−	2.52176i	0.194847	−	0.0867513i
$846$	−9.53566			−0.327843
$847$		0			0
$848$	−36.3568			−1.24850
$849$	−0.707923	+	0.315188i	−0.0242959	+	0.0108172i
$850$	−23.3714	+	4.96775i	−0.801634	+	0.170392i
$851$	8.79050	−	9.76284i	0.301334	−	0.334666i
$852$	1.34592	+	12.8056i	0.0461104	+	0.438712i
$853$	−40.2786	+	29.2641i	−1.37911	+	1.00199i	−0.382152	+	0.924099i	$0.624817\pi$
$853$	−40.2786	+	29.2641i	−1.37911	+	1.00199i	−0.996962	+	0.0778858i	$0.975183\pi$
$854$	13.8189	+	15.8400i	0.472873	+	0.542033i
$855$	2.00406	−	6.16786i	0.0685373	−	0.210936i
$856$	−11.8199	+	5.26256i	−0.403996	+	0.179871i
$857$	−12.7394	−	22.0652i	−0.435168	−	0.753734i	0.562141	−	0.827041i	$-0.309978\pi$
$857$	−12.7394	−	22.0652i	−0.435168	−	0.753734i	−0.997309	+	0.0733077i	$0.976644\pi$
$858$		0			0
$859$	−8.08080	+	13.9964i	−0.275713	+	0.477549i	−0.970315	−	0.241845i	$-0.922247\pi$
$859$	−8.08080	+	13.9964i	−0.275713	+	0.477549i	0.694602	+	0.719395i	$0.255581\pi$
$860$	−3.41462	−	2.48087i	−0.116438	−	0.0845970i
$861$	−3.89807	−	43.6627i	−0.132846	−	1.48802i
$862$	−9.48524	−	29.1926i	−0.323069	−	0.994303i
$863$	−0.303031	−	2.88315i	−0.0103153	−	0.0981434i	0.988153	−	0.153473i	$-0.0490458\pi$
$863$	−0.303031	−	2.88315i	−0.0103153	−	0.0981434i	−0.998468	+	0.0553294i	$0.982379\pi$
$864$	−15.4450	−	6.87656i	−0.525450	−	0.233945i
$865$	0.422484	−	0.469216i	0.0143649	−	0.0159538i
$866$	−31.7467	−	35.2583i	−1.07880	−	1.19813i
$867$	−15.9504	−	11.5887i	−0.541705	−	0.393572i
$868$	18.5638	+	13.9372i	0.630096	+	0.473061i
$869$		0			0
$870$	13.3672	−	23.1526i	0.453190	−	0.784948i
$871$	−0.301754	+	2.87099i	−0.0102245	+	0.0972799i
$872$	−16.3106	+	3.46693i	−0.552348	+	0.117405i
$873$	4.65777	+	0.990040i	0.157642	+	0.0335078i
$874$	17.8790	−	12.9899i	0.604768	−	0.439389i
$875$	7.84788	+	14.0989i	0.265307	+	0.476629i
$876$	14.8267	+	45.6320i	0.500949	+	1.54176i
$877$	−5.63063	−	6.25345i	−0.190133	−	0.211164i	0.640540	−	0.767925i	$-0.278711\pi$
$877$	−5.63063	−	6.25345i	−0.190133	−	0.211164i	−0.830673	+	0.556761i	$0.812044\pi$
$878$	1.83459	−	17.4550i	0.0619145	−	0.589077i
$879$	−3.80731	−	6.59445i	−0.128417	−	0.222425i
$880$		0			0
$881$	41.5335			1.39930			0.699649	−	0.714486i	$-0.253340\pi$
$881$	41.5335			1.39930			0.699649	+	0.714486i	$0.253340\pi$
$882$	7.97638	−	22.1593i	0.268579	−	0.746142i
$883$	−17.4518	+	53.7112i	−0.587300	+	1.80752i	0.00252951	+	0.999997i	$0.499195\pi$
$883$	−17.4518	+	53.7112i	−0.587300	+	1.80752i	−0.589830	+	0.807528i	$0.700805\pi$
$884$	−6.81376	−	1.44831i	−0.229171	−	0.0487119i
$885$	15.0722	+	6.71057i	0.506646	+	0.225573i
$886$	31.8928	+	14.1996i	1.07146	+	0.477045i
$887$	33.8239	+	7.18949i	1.13569	+	0.241399i	0.737137	−	0.675744i	$-0.236177\pi$
$887$	33.8239	+	7.18949i	1.13569	+	0.241399i	0.398558	+	0.917143i	$0.369511\pi$
$888$	4.80449	−	14.7867i	0.161228	−	0.496209i
$889$	−37.8182	+	40.6996i	−1.26838	+	1.36502i
$890$	−0.424858			−0.0142413
$891$		0			0
$892$	−13.8744	−	24.0311i	−0.464548	−	0.804621i
$893$	−1.64813	+	15.6809i	−0.0551526	+	0.524742i
$894$	2.69856	+	2.99705i	0.0902533	+	0.100236i
$895$	3.86153	+	11.8846i	0.129077	+	0.397258i
$896$	−23.4257	−	0.367320i	−0.782598	−	0.0122713i
$897$	−6.93937	+	5.04174i	−0.231699	+	0.168339i
$898$	−59.8217	−	12.7155i	−1.99628	−	0.424321i
$899$	65.6046	−	13.9447i	2.18804	−	0.465081i
$900$	1.20236	−	11.4397i	0.0400788	−	0.381324i
$901$	10.5856	−	18.3348i	0.352658	−	0.610821i
$902$		0			0
$903$	−26.0429	+	11.1091i	−0.866652	+	0.369688i
$904$	−8.19514	−	5.95412i	−0.272566	−	0.198031i
$905$	10.1523	+	11.2752i	0.337472	+	0.374801i
$906$	−4.68319	+	5.20121i	−0.155589	+	0.172799i
$907$	7.67638	+	3.41774i	0.254890	+	0.113484i	0.530204	−	0.847870i	$-0.322115\pi$
$907$	7.67638	+	3.41774i	0.254890	+	0.113484i	−0.275314	+	0.961354i	$0.588782\pi$
$908$	−1.02969	−	9.79684i	−0.0341714	−	0.325119i
$909$	−5.61151	−	17.2704i	−0.186122	−	0.572824i
$910$	0.494038	+	5.53377i	0.0163772	+	0.183443i
$911$	0.480304	+	0.348962i	0.0159132	+	0.0115616i	0.595713	−	0.803197i	$-0.296869\pi$
$911$	0.480304	+	0.348962i	0.0159132	+	0.0115616i	−0.579800	+	0.814759i	$0.696869\pi$
$912$	29.7667	−	51.5575i	0.985675	−	1.70724i
$913$		0			0
$914$	−10.9693	−	18.9993i	−0.362831	−	0.628441i
$915$	−5.52949	+	2.46189i	−0.182799	+	0.0813875i
$916$	5.08973	−	15.6646i	0.168169	−	0.517572i
$917$	11.7412	−	34.2965i	0.387728	−	1.13257i
$918$	10.7801	−	7.83222i	0.355797	−	0.258502i
$919$	1.70768	+	16.2475i	0.0563311	+	0.535955i	0.985903	+	0.167315i	$0.0535097\pi$
$919$	1.70768	+	16.2475i	0.0563311	+	0.535955i	−0.929572	+	0.368640i	$0.879824\pi$
$920$	1.07369	−	1.19246i	0.0353986	−	0.0393141i
$921$	−14.0109	+	2.97810i	−0.461674	+	0.0981318i
$922$	20.9285	−	9.31795i	0.689242	−	0.306870i
$923$	−7.73128			−0.254478
$924$		0			0
$925$	−27.8792			−0.916662
$926$	20.6266	−	9.18355i	0.677832	−	0.301790i
$927$	−11.1805	+	2.37650i	−0.367217	+	0.0780544i
$928$	46.0356	−	51.1277i	1.51119	−	1.67835i
$929$	−0.930428	−	8.85244i	−0.0305264	−	0.290439i	−0.999126	−	0.0418114i	$-0.986687\pi$
$929$	−0.930428	−	8.85244i	−0.0305264	−	0.290439i	0.968599	−	0.248628i	$-0.0799795\pi$
$930$	−13.3341	+	9.68776i	−0.437241	+	0.317674i
$931$	−35.0612	−	16.9467i	−1.14908	−	0.555406i
$932$	−3.18008	+	9.78728i	−0.104167	+	0.320593i
$933$	−23.3603	+	10.4007i	−0.764780	+	0.340502i
$934$	−30.0456	−	52.0405i	−0.983122	−	1.70282i
$935$		0			0
$936$	−1.92585	+	3.33567i	−0.0629485	+	0.109030i
$937$	−36.5967	−	26.5891i	−1.19556	−	0.868627i	−0.201721	−	0.979443i	$-0.564653\pi$
$937$	−36.5967	−	26.5891i	−1.19556	−	0.868627i	−0.993841	+	0.110817i	$0.964653\pi$
$938$	7.05456	+	3.27437i	0.230340	+	0.106912i
$939$	18.4111	+	56.6635i	0.600823	+	1.84914i
$940$	−0.256909	−	2.44433i	−0.00837946	−	0.0797252i
$941$	−6.33365	−	2.81992i	−0.206471	−	0.0919269i	0.300896	−	0.953657i	$-0.402714\pi$
$941$	−6.33365	−	2.81992i	−0.206471	−	0.0919269i	−0.507367	+	0.861730i	$0.669381\pi$
$942$	21.4255	−	23.7954i	0.698079	−	0.775295i
$943$	10.9205	+	12.1284i	0.355620	+	0.394956i
$944$	46.4907	+	33.7775i	1.51314	+	1.09936i
$945$	−3.44668	−	2.58768i	−0.112120	−	0.0841773i
$946$		0			0
$947$	−10.3716	+	17.9642i	−0.337033	+	0.583758i	−0.983873	−	0.178867i	$-0.942757\pi$
$947$	−10.3716	+	17.9642i	−0.337033	+	0.583758i	0.646840	+	0.762626i	$0.276090\pi$
$948$	1.49324	−	14.2072i	0.0484982	−	0.461430i
$949$	−28.1796	+	5.98976i	−0.914749	+	0.194436i
$950$	−45.8742	−	9.75086i	−1.48835	−	0.316360i
$951$	6.86914	−	4.99072i	0.222747	−	0.161835i
$952$	4.48899	−	7.50105i	0.145489	−	0.243110i
$953$	6.24450	+	19.2186i	0.202279	+	0.622551i	0.999814	+	0.0192785i	$0.00613692\pi$
$953$	6.24450	+	19.2186i	0.202279	+	0.622551i	−0.797535	+	0.603273i	$0.793863\pi$
$954$	16.8164	+	18.6765i	0.544452	+	0.604675i
$955$	−0.739518	+	7.03604i	−0.0239302	+	0.227681i
$956$	6.71735	+	11.6348i	0.217254	+	0.376296i
$957$		0			0
$958$	47.6499			1.53950
$959$	18.7352	+	4.29037i	0.604993	+	0.138543i
$960$	−1.02100	+	3.14233i	−0.0329528	+	0.101418i
$961$	−10.1228	−	2.15167i	−0.326543	−	0.0694088i
$962$	−18.3092	−	8.15176i	−0.590311	−	0.262823i
$963$	18.5979	+	8.28031i	0.599308	+	0.266829i
$964$	2.23555	+	0.475180i	0.0720022	+	0.0153045i
$965$	−0.709898	+	2.18484i	−0.0228524	+	0.0703326i
$966$	6.79560	+	22.0872i	0.218645	+	0.710643i
$967$	−7.98254			−0.256701			−0.128351	−	0.991729i	$-0.540968\pi$
$967$	−7.98254			−0.256701			−0.128351	+	0.991729i	$0.540968\pi$
$968$		0			0
$969$	17.3337	+	30.0229i	0.556839	+	0.964473i
$970$	−0.316344	+	3.00981i	−0.0101572	+	0.0966392i
$971$	−9.22015	−	10.2400i	−0.295889	−	0.328618i	0.576809	−	0.816879i	$-0.304298\pi$
$971$	−9.22015	−	10.2400i	−0.295889	−	0.328618i	−0.872697	+	0.488262i	$0.837631\pi$
$972$	7.08361	+	21.8011i	0.227207	+	0.699271i
$973$	−3.34902	−	6.01659i	−0.107365	−	0.192883i
$974$	−21.5700	+	15.6715i	−0.691146	+	0.502147i
$975$	17.8051	+	3.78459i	0.570219	+	0.121204i
$976$	−20.6215	+	4.38325i	−0.660080	+	0.140304i
$977$	−1.25653	+	11.9551i	−0.0401999	+	0.382477i	0.955862	+	0.293816i	$0.0949254\pi$
$977$	−1.25653	+	11.9551i	−0.0401999	+	0.382477i	−0.996062	+	0.0886607i	$0.971741\pi$
$978$	−32.2745	+	55.9010i	−1.03202	+	1.78752i
$979$		0			0
$980$	5.89511	+	1.44761i	0.188312	+	0.0462423i
$981$	21.2262	+	15.4218i	0.677702	+	0.492379i
$982$	−48.3516	−	53.6999i	−1.54296	−	1.71363i
$983$	−29.8796	+	33.1846i	−0.953010	+	1.05843i	0.0452212	+	0.998977i	$0.485601\pi$
$983$	−29.8796	+	33.1846i	−0.953010	+	1.05843i	−0.998231	+	0.0594481i	$0.981066\pi$
$984$	17.6451	+	7.85610i	0.562505	+	0.250443i
$985$	0.160657	+	1.52854i	0.00511894	+	0.0487035i
$986$	16.7561	+	51.5701i	0.533624	+	1.64233i
$987$	−14.9549	−	6.94132i	−0.476021	−	0.220945i
$988$	−11.0617	−	8.03681i	−0.351920	−	0.255685i
$989$	5.27056	−	9.12888i	0.167594	−	0.290282i
$990$		0			0
$991$	11.4830	+	19.8891i	0.364769	+	0.631799i	0.988739	−	0.149650i	$-0.0478146\pi$
$991$	11.4830	+	19.8891i	0.364769	+	0.631799i	−0.623970	+	0.781448i	$0.714481\pi$
$992$	−38.7479	+	17.2517i	−1.23025	+	0.547741i
$993$	−4.17871	+	12.8607i	−0.132607	+	0.408123i
$994$	−6.74632	+	19.7062i	−0.213980	+	0.625044i
$995$	−9.51023	+	6.90958i	−0.301494	+	0.219049i
$996$	−2.89490	−	27.5432i	−0.0917285	−	0.872738i
$997$	0.902641	−	1.00248i	0.0285869	−	0.0317490i	−0.728682	−	0.684852i	$-0.759867\pi$
$997$	0.902641	−	1.00248i	0.0285869	−	0.0317490i	0.757269	+	0.653103i	$0.226533\pi$
$998$	47.0618	−	10.0033i	1.48972	−	0.316649i
$999$	14.2035	−	6.32381i	0.449379	−	0.200076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.e.807.3		24
7.4	even	3	inner	847.2.n.e.81.1		24
11.2	odd	10		847.2.n.d.632.3		24
11.3	even	5	inner	847.2.n.e.366.1		24
11.4	even	5	inner	847.2.n.e.9.3		24
11.5	even	5		77.2.e.b.23.1	✓	6
11.6	odd	10		847.2.e.d.485.3		6
11.7	odd	10		847.2.n.d.9.1		24
11.8	odd	10		847.2.n.d.366.3		24
11.9	even	5	inner	847.2.n.e.632.1		24
11.10	odd	2		847.2.n.d.807.1		24
33.5	odd	10		693.2.i.g.100.3		6
44.27	odd	10		1232.2.q.k.177.1		6
77.4	even	15	inner	847.2.n.e.130.1		24
77.5	odd	30		539.2.a.i.1.3		3
77.16	even	15		539.2.a.h.1.3		3
77.18	odd	30		847.2.n.d.130.3		24
77.25	even	15	inner	847.2.n.e.487.3		24
77.27	odd	10		539.2.e.l.177.1		6
77.32	odd	6		847.2.n.d.81.3		24
77.38	odd	30		539.2.e.l.67.1		6
77.39	odd	30		847.2.e.d.606.3		6
77.46	odd	30		847.2.n.d.753.1		24
77.53	even	15	inner	847.2.n.e.753.3		24
77.60	even	15		77.2.e.b.67.1	yes	6
77.61	even	30		5929.2.a.w.1.1		3
77.72	odd	30		5929.2.a.v.1.1		3
77.74	odd	30		847.2.n.d.487.1		24
231.5	even	30		4851.2.a.bn.1.1		3
231.137	odd	30		693.2.i.g.298.3		6
231.170	odd	30		4851.2.a.bo.1.1		3
308.159	even	30		8624.2.a.ck.1.1		3
308.247	odd	30		8624.2.a.cl.1.3		3
308.291	odd	30		1232.2.q.k.529.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.1	✓	6	11.5	even	5
77.2.e.b.67.1	yes	6	77.60	even	15
539.2.a.h.1.3		3	77.16	even	15
539.2.a.i.1.3		3	77.5	odd	30
539.2.e.l.67.1		6	77.38	odd	30
539.2.e.l.177.1		6	77.27	odd	10
693.2.i.g.100.3		6	33.5	odd	10
693.2.i.g.298.3		6	231.137	odd	30
847.2.e.d.485.3		6	11.6	odd	10
847.2.e.d.606.3		6	77.39	odd	30
847.2.n.d.9.1		24	11.7	odd	10
847.2.n.d.81.3		24	77.32	odd	6
847.2.n.d.130.3		24	77.18	odd	30
847.2.n.d.366.3		24	11.8	odd	10
847.2.n.d.487.1		24	77.74	odd	30
847.2.n.d.632.3		24	11.2	odd	10
847.2.n.d.753.1		24	77.46	odd	30
847.2.n.d.807.1		24	11.10	odd	2
847.2.n.e.9.3		24	11.4	even	5	inner
847.2.n.e.81.1		24	7.4	even	3	inner
847.2.n.e.130.1		24	77.4	even	15	inner
847.2.n.e.366.1		24	11.3	even	5	inner
847.2.n.e.487.3		24	77.25	even	15	inner
847.2.n.e.632.1		24	11.9	even	5	inner
847.2.n.e.753.3		24	77.53	even	15	inner
847.2.n.e.807.3		24	1.1	even	1	trivial
1232.2.q.k.177.1		6	44.27	odd	10
1232.2.q.k.529.1		6	308.291	odd	30
4851.2.a.bn.1.1		3	231.5	even	30
4851.2.a.bo.1.1		3	231.170	odd	30
5929.2.a.v.1.1		3	77.72	odd	30
5929.2.a.w.1.1		3	77.61	even	30
8624.2.a.ck.1.1		3	308.159	even	30
8624.2.a.cl.1.3		3	308.247	odd	30

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.67566 - 0.746054i) q^{2} +(2.15064 - 0.457134i) q^{3} +(0.912994 - 1.01398i) q^{4} +(0.0664333 + 0.632070i) q^{5} +(3.26271 - 2.37050i) q^{6} +(2.59624 - 0.509441i) q^{7} +(-0.360239 + 1.10870i) q^{8} +(1.67566 - 0.746054i) q^{9} +O(q^{10})\)	\(q+(1.67566 - 0.746054i) q^{2} +(2.15064 - 0.457134i) q^{3} +(0.912994 - 1.01398i) q^{4} +(0.0664333 + 0.632070i) q^{5} +(3.26271 - 2.37050i) q^{6} +(2.59624 - 0.509441i) q^{7} +(-0.360239 + 1.10870i) q^{8} +(1.67566 - 0.746054i) q^{9} +(0.582878 + 1.00958i) q^{10} +(1.50000 - 2.59808i) q^{12} +(1.45729 + 1.05878i) q^{13} +(3.97036 - 2.79059i) q^{14} +(0.431815 + 1.32899i) q^{15} +(0.508759 + 4.84051i) q^{16} +(-2.58921 - 1.15279i) q^{17} +(2.25126 - 2.50027i) q^{18} +(-3.72247 - 4.13422i) q^{19} +(0.701561 + 0.509714i) q^{20} +(5.35071 - 2.28245i) q^{21} +(-1.08288 + 1.87560i) q^{23} +(-0.267921 + 2.54910i) q^{24} +(4.49564 - 0.955577i) q^{25} +(3.23184 + 0.686948i) q^{26} +(-2.07362 + 1.50658i) q^{27} +(1.85379 - 3.09766i) q^{28} +(-3.22315 - 9.91982i) q^{29} +(1.71507 + 1.90478i) q^{30} +(-0.672151 + 6.39509i) q^{31} +(3.29804 + 5.71237i) q^{32} -5.19869 q^{34} +(0.494479 + 1.60716i) q^{35} +(0.773386 - 2.38024i) q^{36} +(-5.93332 - 1.26117i) q^{37} +(-9.32196 - 4.15040i) q^{38} +(3.61812 + 1.61089i) q^{39} +(-0.724709 - 0.154042i) q^{40} +(2.32865 - 7.16684i) q^{41} +(7.26316 - 7.81655i) q^{42} -4.86718 q^{43} +(0.582878 + 1.00958i) q^{45} +(-0.415242 + 3.95076i) q^{46} +(-1.89648 - 2.10625i) q^{47} +(3.30692 + 10.1777i) q^{48} +(6.48094 - 2.64526i) q^{49} +(6.82027 - 4.95522i) q^{50} +(-6.09545 - 1.29563i) q^{51} +(2.40408 - 0.511004i) q^{52} +(-0.780806 + 7.42887i) q^{53} +(-2.35071 + 4.07155i) q^{54} +(-0.370450 + 3.06197i) q^{56} +(-9.89559 - 7.18957i) q^{57} +(-12.8016 - 14.2177i) q^{58} +(7.90027 - 8.77414i) q^{59} +(1.74182 + 0.775507i) q^{60} +(0.452766 + 4.30779i) q^{61} +(3.64478 + 11.2175i) q^{62} +(3.97036 - 2.79059i) q^{63} +(1.91288 + 1.38979i) q^{64} +(-0.572413 + 0.991448i) q^{65} +(0.801309 + 1.38791i) q^{67} +(-3.53284 + 1.57292i) q^{68} +(-1.47149 + 4.52877i) q^{69} +(2.02761 + 2.32416i) q^{70} +(-3.47233 + 2.52280i) q^{71} +(0.223511 + 2.12657i) q^{72} +(-10.7017 + 11.8855i) q^{73} +(-10.8831 + 2.31328i) q^{74} +(9.23169 - 4.11021i) q^{75} -7.59061 q^{76} +7.26456 q^{78} +(4.35015 - 1.93681i) q^{79} +(-3.02575 + 0.643142i) q^{80} +(-7.45297 + 8.27736i) q^{81} +(-1.44482 - 13.7465i) q^{82} +(7.46854 - 5.42621i) q^{83} +(2.57080 - 7.50939i) q^{84} +(0.556635 - 1.71315i) q^{85} +(-8.15576 + 3.63118i) q^{86} +(-11.4665 - 19.8606i) q^{87} +(-0.182224 + 0.315621i) q^{89} +(1.72991 + 1.25685i) q^{90} +(4.32286 + 2.00645i) q^{91} +(0.913165 + 2.81043i) q^{92} +(1.47785 + 14.0608i) q^{93} +(-4.74924 - 2.11450i) q^{94} +(2.36582 - 2.62751i) q^{95} +(9.70422 + 10.7776i) q^{96} +(2.10027 + 1.52593i) q^{97} +(8.88637 - 9.26770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8}+O(q^{10}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} + 36 q^{10} + 36 q^{12} + 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} - 3 q^{17} + 10 q^{18} - 11 q^{19} - 28 q^{20} + 40 q^{21} - 48 q^{23} + 2 q^{24} + 3 q^{25} + q^{26} - 4 q^{27} - 13 q^{28} + 18 q^{29} + 2 q^{30} - 3 q^{31} + 12 q^{32} - 80 q^{34} - 9 q^{35} + 18 q^{36} - 4 q^{37} + 8 q^{38} - 5 q^{39} - 3 q^{40} + 10 q^{41} + 2 q^{42} + 16 q^{43} + 36 q^{45} - 10 q^{46} - 3 q^{47} - 20 q^{48} + 24 q^{49} + 6 q^{50} + 2 q^{51} - 7 q^{52} + 17 q^{53} + 32 q^{54} + 12 q^{56} - 40 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} - 24 q^{61} - 26 q^{62} - 12 q^{63} + 14 q^{64} - 60 q^{65} + 64 q^{67} + 5 q^{68} + 6 q^{69} + 27 q^{70} - 14 q^{71} + 10 q^{72} - 20 q^{73} + 22 q^{74} + 25 q^{75} - 312 q^{76} - 48 q^{78} + 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} + 22 q^{83} - 12 q^{84} - 22 q^{85} - 21 q^{86} - 120 q^{87} - 4 q^{89} - 20 q^{90} + 15 q^{91} - 50 q^{92} - 26 q^{93} - 10 q^{94} - 17 q^{95} + 27 q^{96} - 18 q^{97} - 96 q^{98}+O(q^{100}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 + 36 * q^10 + 36 * q^12 + 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 - 3 * q^17 + 10 * q^18 - 11 * q^19 - 28 * q^20 + 40 * q^21 - 48 * q^23 + 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 - 13 * q^28 + 18 * q^29 + 2 * q^30 - 3 * q^31 + 12 * q^32 - 80 * q^34 - 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 - 5 * q^39 - 3 * q^40 + 10 * q^41 + 2 * q^42 + 16 * q^43 + 36 * q^45 - 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 + 6 * q^50 + 2 * q^51 - 7 * q^52 + 17 * q^53 + 32 * q^54 + 12 * q^56 - 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 - 24 * q^61 - 26 * q^62 - 12 * q^63 + 14 * q^64 - 60 * q^65 + 64 * q^67 + 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 + 10 * q^72 - 20 * q^73 + 22 * q^74 + 25 * q^75 - 312 * q^76 - 48 * q^78 + 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 + 22 * q^83 - 12 * q^84 - 22 * q^85 - 21 * q^86 - 120 * q^87 - 4 * q^89 - 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 - 10 * q^94 - 17 * q^95 + 27 * q^96 - 18 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more