LMFDB - Embedded newform 847.2.f.h.729.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, 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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	847.729
Dual form			847.2.f.h.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.927051 - 2.85317i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-4.85410 + 3.52671i) q^{9} +O(q^{10})$	\(q+(-0.927051 - 2.85317i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-4.85410 + 3.52671i) q^{9} +6.00000 q^{12} +(-3.23607 + 2.35114i) q^{13} +(0.927051 - 2.85317i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(1.61803 + 1.17557i) q^{17} +(1.85410 + 5.70634i) q^{19} +(-1.61803 + 1.17557i) q^{20} -3.00000 q^{21} -5.00000 q^{23} +(-1.23607 - 3.80423i) q^{25} +(7.28115 + 5.29007i) q^{27} +(1.61803 + 1.17557i) q^{28} +(-3.09017 + 9.51057i) q^{29} +(-0.809017 + 0.587785i) q^{31} +(0.809017 - 0.587785i) q^{35} +(-3.70820 - 11.4127i) q^{36} +(-1.54508 + 4.75528i) q^{37} +(9.70820 + 7.05342i) q^{39} +(0.618034 + 1.90211i) q^{41} +8.00000 q^{43} -6.00000 q^{45} +(2.47214 + 7.60845i) q^{47} +(-3.70820 + 11.4127i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.85410 - 5.70634i) q^{51} +(-2.47214 - 7.60845i) q^{52} +(4.85410 - 3.52671i) q^{53} +(14.5623 - 10.5801i) q^{57} +(0.927051 - 2.85317i) q^{59} +(4.85410 + 3.52671i) q^{60} +(-1.61803 - 1.17557i) q^{61} +(1.85410 + 5.70634i) q^{63} +(6.47214 - 4.70228i) q^{64} -4.00000 q^{65} -3.00000 q^{67} +(-3.23607 + 2.35114i) q^{68} +(4.63525 + 14.2658i) q^{69} +(-0.809017 - 0.587785i) q^{71} +(-3.09017 + 9.51057i) q^{73} +(-9.70820 + 7.05342i) q^{75} -12.0000 q^{76} +(4.85410 - 3.52671i) q^{79} +(-1.23607 - 3.80423i) q^{80} +(2.78115 - 8.55951i) q^{81} +(9.70820 + 7.05342i) q^{83} +(1.85410 - 5.70634i) q^{84} +(0.618034 + 1.90211i) q^{85} +30.0000 q^{87} -15.0000 q^{89} +(1.23607 + 3.80423i) q^{91} +(3.09017 - 9.51057i) q^{92} +(2.42705 + 1.76336i) q^{93} +(-1.85410 + 5.70634i) q^{95} +(4.04508 - 2.93893i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} + 2 q^{4} + q^{5} - q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 3 * q^3 + 2 * q^4 + q^5 - q^7 - 6 * q^9	$ 4 q + 3 q^{3} + 2 q^{4} + q^{5} - q^{7} - 6 q^{9} + 24 q^{12} - 4 q^{13} - 3 q^{15} - 4 q^{16} + 2 q^{17} - 6 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{23} + 4 q^{25} + 9 q^{27} + 2 q^{28} + 10 q^{29} - q^{31} + q^{35} + 12 q^{36} + 5 q^{37} + 12 q^{39} - 2 q^{41} + 32 q^{43} - 24 q^{45} - 8 q^{47} + 12 q^{48} - q^{49} - 6 q^{51} + 8 q^{52} + 6 q^{53} + 18 q^{57} - 3 q^{59} + 6 q^{60} - 2 q^{61} - 6 q^{63} + 8 q^{64} - 16 q^{65} - 12 q^{67} - 4 q^{68} - 15 q^{69} - q^{71} + 10 q^{73} - 12 q^{75} - 48 q^{76} + 6 q^{79} + 4 q^{80} - 9 q^{81} + 12 q^{83} - 6 q^{84} - 2 q^{85} + 120 q^{87} - 60 q^{89} - 4 q^{91} - 10 q^{92} + 3 q^{93} + 6 q^{95} + 5 q^{97}+O(q^{100}) $ 4 * q + 3 * q^3 + 2 * q^4 + q^5 - q^7 - 6 * q^9 + 24 * q^12 - 4 * q^13 - 3 * q^15 - 4 * q^16 + 2 * q^17 - 6 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^23 + 4 * q^25 + 9 * q^27 + 2 * q^28 + 10 * q^29 - q^31 + q^35 + 12 * q^36 + 5 * q^37 + 12 * q^39 - 2 * q^41 + 32 * q^43 - 24 * q^45 - 8 * q^47 + 12 * q^48 - q^49 - 6 * q^51 + 8 * q^52 + 6 * q^53 + 18 * q^57 - 3 * q^59 + 6 * q^60 - 2 * q^61 - 6 * q^63 + 8 * q^64 - 16 * q^65 - 12 * q^67 - 4 * q^68 - 15 * q^69 - q^71 + 10 * q^73 - 12 * q^75 - 48 * q^76 + 6 * q^79 + 4 * q^80 - 9 * q^81 + 12 * q^83 - 6 * q^84 - 2 * q^85 + 120 * q^87 - 60 * q^89 - 4 * q^91 - 10 * q^92 + 3 * q^93 + 6 * q^95 + 5 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$2$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$3$	−0.927051	−	2.85317i	−0.535233	−	1.64728i	−0.743145	−	0.669131i	$-0.766667\pi$
$3$	−0.927051	−	2.85317i	−0.535233	−	1.64728i	0.207912	−	0.978148i	$-0.433333\pi$
$4$	−0.618034	+	1.90211i	−0.309017	+	0.951057i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i	0.753804	−	0.657099i	$-0.228217\pi$
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i	−0.392000	+	0.919965i	$0.628217\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$		0			0
$9$	−4.85410	+	3.52671i	−1.61803	+	1.17557i
$10$		0			0
$11$		0			0
$11$		0			0
$12$	6.00000			1.73205
$13$	−3.23607	+	2.35114i	−0.897524	+	0.652089i	−0.937829	−	0.347098i	$-0.887167\pi$
$13$	−3.23607	+	2.35114i	−0.897524	+	0.652089i	0.0403050	+	0.999187i	$0.487167\pi$
$14$		0			0
$15$	0.927051	−	2.85317i	0.239364	−	0.736685i
$16$	−3.23607	−	2.35114i	−0.809017	−	0.587785i
$17$	1.61803	+	1.17557i	0.392431	+	0.285118i	0.766451	−	0.642303i	$-0.222021\pi$
$17$	1.61803	+	1.17557i	0.392431	+	0.285118i	−0.374020	+	0.927421i	$0.622021\pi$
$18$		0			0
$19$	1.85410	+	5.70634i	0.425360	+	1.30912i	0.902649	+	0.430377i	$0.141620\pi$
$19$	1.85410	+	5.70634i	0.425360	+	1.30912i	−0.477289	+	0.878746i	$0.658380\pi$
$20$	−1.61803	+	1.17557i	−0.361803	+	0.262866i
$21$	−3.00000			−0.654654
$22$		0			0
$23$	−5.00000			−1.04257			−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−5.00000			−1.04257			−0.521286	+	0.853382i	$0.674548\pi$
$24$		0			0
$25$	−1.23607	−	3.80423i	−0.247214	−	0.760845i
$26$		0			0
$27$	7.28115	+	5.29007i	1.40126	+	1.01807i
$28$	1.61803	+	1.17557i	0.305780	+	0.222162i
$29$	−3.09017	+	9.51057i	−0.573830	+	1.76607i	0.0662984	+	0.997800i	$0.478881\pi$
$29$	−3.09017	+	9.51057i	−0.573830	+	1.76607i	−0.640129	+	0.768268i	$0.721119\pi$
$30$		0			0
$31$	−0.809017	+	0.587785i	−0.145304	+	0.105569i	−0.658062	−	0.752964i	$-0.728624\pi$
$31$	−0.809017	+	0.587785i	−0.145304	+	0.105569i	0.512758	+	0.858533i	$0.328624\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	−3.70820	−	11.4127i	−0.618034	−	1.90211i
$37$	−1.54508	+	4.75528i	−0.254010	+	0.781764i	0.740013	+	0.672593i	$0.234819\pi$
$37$	−1.54508	+	4.75528i	−0.254010	+	0.781764i	−0.994023	+	0.109171i	$0.965181\pi$
$38$		0			0
$39$	9.70820	+	7.05342i	1.55456	+	1.12945i
$40$		0			0
$41$	0.618034	+	1.90211i	0.0965207	+	0.297060i	0.987647	−	0.156695i	$-0.0500840\pi$
$41$	0.618034	+	1.90211i	0.0965207	+	0.297060i	−0.891126	+	0.453755i	$0.850084\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	−6.00000			−0.894427
$46$		0			0
$47$	2.47214	+	7.60845i	0.360598	+	1.10981i	0.952692	+	0.303938i	$0.0983015\pi$
$47$	2.47214	+	7.60845i	0.360598	+	1.10981i	−0.592094	+	0.805869i	$0.701699\pi$
$48$	−3.70820	+	11.4127i	−0.535233	+	1.64728i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	1.85410	−	5.70634i	0.259626	−	0.799047i
$52$	−2.47214	−	7.60845i	−0.342824	−	1.05510i
$53$	4.85410	−	3.52671i	0.666762	−	0.484431i	−0.202178	−	0.979349i	$-0.564802\pi$
$53$	4.85410	−	3.52671i	0.666762	−	0.484431i	0.868940	+	0.494918i	$0.164802\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	14.5623	−	10.5801i	1.92882	−	1.40137i
$58$		0			0
$59$	0.927051	−	2.85317i	0.120692	−	0.371451i	−0.872400	−	0.488793i	$-0.837437\pi$
$59$	0.927051	−	2.85317i	0.120692	−	0.371451i	0.993092	+	0.117342i	$0.0374373\pi$
$60$	4.85410	+	3.52671i	0.626662	+	0.455296i
$61$	−1.61803	−	1.17557i	−0.207168	−	0.150516i	0.479363	−	0.877616i	$-0.340868\pi$
$61$	−1.61803	−	1.17557i	−0.207168	−	0.150516i	−0.686531	+	0.727100i	$0.740868\pi$
$62$		0			0
$63$	1.85410	+	5.70634i	0.233595	+	0.718931i
$64$	6.47214	−	4.70228i	0.809017	−	0.587785i
$65$	−4.00000			−0.496139
$66$		0			0
$67$	−3.00000			−0.366508			−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000			−0.366508			−0.183254	+	0.983066i	$0.558663\pi$
$68$	−3.23607	+	2.35114i	−0.392431	+	0.285118i
$69$	4.63525	+	14.2658i	0.558019	+	1.71741i
$70$		0			0
$71$	−0.809017	−	0.587785i	−0.0960127	−	0.0697573i	0.538743	−	0.842470i	$-0.318899\pi$
$71$	−0.809017	−	0.587785i	−0.0960127	−	0.0697573i	−0.634756	+	0.772713i	$0.718899\pi$
$72$		0			0
$73$	−3.09017	+	9.51057i	−0.361677	+	1.11313i	0.590359	+	0.807141i	$0.298986\pi$
$73$	−3.09017	+	9.51057i	−0.361677	+	1.11313i	−0.952036	+	0.305987i	$0.901014\pi$
$74$		0			0
$75$	−9.70820	+	7.05342i	−1.12101	+	0.814459i
$76$	−12.0000			−1.37649
$77$		0			0
$78$		0			0
$79$	4.85410	−	3.52671i	0.546129	−	0.396786i	−0.280227	−	0.959934i	$-0.590410\pi$
$79$	4.85410	−	3.52671i	0.546129	−	0.396786i	0.826356	+	0.563148i	$0.190410\pi$
$80$	−1.23607	−	3.80423i	−0.138197	−	0.425325i
$81$	2.78115	−	8.55951i	0.309017	−	0.951057i
$82$		0			0
$83$	9.70820	+	7.05342i	1.06561	+	0.774214i	0.975119	−	0.221683i	$-0.0711551\pi$
$83$	9.70820	+	7.05342i	1.06561	+	0.774214i	0.0904951	+	0.995897i	$0.471155\pi$
$84$	1.85410	−	5.70634i	0.202299	−	0.622613i
$85$	0.618034	+	1.90211i	0.0670352	+	0.206313i
$86$		0			0
$87$	30.0000			3.21634
$88$		0			0
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$		0			0
$91$	1.23607	+	3.80423i	0.129575	+	0.398791i
$92$	3.09017	−	9.51057i	0.322172	−	0.991545i
$93$	2.42705	+	1.76336i	0.251673	+	0.182851i
$94$		0			0
$95$	−1.85410	+	5.70634i	−0.190227	+	0.585458i
$96$		0			0
$97$	4.04508	−	2.93893i	0.410716	−	0.298403i	−0.363176	−	0.931721i	$-0.618307\pi$
$97$	4.04508	−	2.93893i	0.410716	−	0.298403i	0.773892	+	0.633318i	$0.218307\pi$
$98$		0			0
$99$		0			0
$100$	8.00000			0.800000
$101$	−9.70820	+	7.05342i	−0.966002	+	0.701842i	−0.954537	−	0.298092i	$-0.903650\pi$
$101$	−9.70820	+	7.05342i	−0.966002	+	0.701842i	−0.0114654	+	0.999934i	$0.503650\pi$
$102$		0			0
$103$	−3.70820	+	11.4127i	−0.365380	+	1.12452i	0.584362	+	0.811493i	$0.301345\pi$
$103$	−3.70820	+	11.4127i	−0.365380	+	1.12452i	−0.949743	+	0.313032i	$0.898655\pi$
$104$		0			0
$105$	−2.42705	−	1.76336i	−0.236856	−	0.172086i
$106$		0			0
$107$	3.09017	+	9.51057i	0.298738	+	0.919421i	0.981940	+	0.189192i	$0.0605868\pi$
$107$	3.09017	+	9.51057i	0.298738	+	0.919421i	−0.683202	+	0.730229i	$0.739413\pi$
$108$	−14.5623	+	10.5801i	−1.40126	+	1.01807i
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$		0			0
$111$	15.0000			1.42374
$112$	−3.23607	+	2.35114i	−0.305780	+	0.222162i
$113$	−5.87132	−	18.0701i	−0.552328	−	1.69989i	−0.702898	−	0.711290i	$-0.748111\pi$
$113$	−5.87132	−	18.0701i	−0.552328	−	1.69989i	0.150571	−	0.988599i	$-0.451889\pi$
$114$		0			0
$115$	−4.04508	−	2.93893i	−0.377206	−	0.274056i
$116$	−16.1803	−	11.7557i	−1.50231	−	1.09149i
$117$	7.41641	−	22.8254i	0.685647	−	2.11020i
$118$		0			0
$119$	1.61803	−	1.17557i	0.148325	−	0.107764i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	4.85410	−	3.52671i	0.437680	−	0.317993i
$124$	−0.618034	−	1.90211i	−0.0555011	−	0.170815i
$125$	2.78115	−	8.55951i	0.248754	−	0.765586i
$126$		0			0
$127$	1.61803	+	1.17557i	0.143577	+	0.104315i	0.657255	−	0.753668i	$-0.271717\pi$
$127$	1.61803	+	1.17557i	0.143577	+	0.104315i	−0.513678	+	0.857983i	$0.671717\pi$
$128$		0			0
$129$	−7.41641	−	22.8254i	−0.652978	−	2.00966i
$130$		0			0
$131$	−18.0000			−1.57267			−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000			−1.57267			−0.786334	+	0.617802i	$0.788023\pi$
$132$		0			0
$133$	6.00000			0.520266
$134$		0			0
$135$	2.78115	+	8.55951i	0.239364	+	0.736685i
$136$		0			0
$137$	2.42705	+	1.76336i	0.207357	+	0.150654i	0.686617	−	0.727019i	$-0.259095\pi$
$137$	2.42705	+	1.76336i	0.207357	+	0.150654i	−0.479260	+	0.877673i	$0.659095\pi$
$138$		0			0
$139$	3.09017	−	9.51057i	0.262105	−	0.806676i	−0.730241	−	0.683189i	$-0.760592\pi$
$139$	3.09017	−	9.51057i	0.262105	−	0.806676i	0.992346	−	0.123486i	$-0.0394076\pi$
$140$	0.618034	+	1.90211i	0.0522334	+	0.160758i
$141$	19.4164	−	14.1068i	1.63516	−	1.18801i
$142$		0			0
$143$		0			0
$144$	24.0000			2.00000
$145$	−8.09017	+	5.87785i	−0.671852	+	0.488129i
$146$		0			0
$147$	−0.927051	+	2.85317i	−0.0764619	+	0.235325i
$148$	−8.09017	−	5.87785i	−0.665008	−	0.483157i
$149$	−17.7984	−	12.9313i	−1.45810	−	1.05937i	−0.983853	−	0.178979i	$-0.942720\pi$
$149$	−17.7984	−	12.9313i	−1.45810	−	1.05937i	−0.474247	−	0.880392i	$-0.657280\pi$
$150$		0			0
$151$	−1.85410	−	5.70634i	−0.150885	−	0.464375i	0.846836	−	0.531854i	$-0.178505\pi$
$151$	−1.85410	−	5.70634i	−0.150885	−	0.464375i	−0.997721	+	0.0674788i	$0.978505\pi$
$152$		0			0
$153$	−12.0000			−0.970143
$154$		0			0
$155$	−1.00000			−0.0803219
$156$	−19.4164	+	14.1068i	−1.55456	+	1.12945i
$157$	2.16312	+	6.65740i	0.172636	+	0.531318i	0.999518	−	0.0310576i	$-0.00988752\pi$
$157$	2.16312	+	6.65740i	0.172636	+	0.531318i	−0.826882	+	0.562376i	$0.809888\pi$
$158$		0			0
$159$	−14.5623	−	10.5801i	−1.15487	−	0.839059i
$160$		0			0
$161$	−1.54508	+	4.75528i	−0.121770	+	0.374769i
$162$		0			0
$163$	−3.23607	+	2.35114i	−0.253468	+	0.184156i	−0.707263	−	0.706951i	$-0.750070\pi$
$163$	−3.23607	+	2.35114i	−0.253468	+	0.184156i	0.453794	+	0.891107i	$0.350070\pi$
$164$	−4.00000			−0.312348
$165$		0			0
$166$		0			0
$167$	−1.61803	+	1.17557i	−0.125207	+	0.0909684i	−0.648626	−	0.761107i	$-0.724656\pi$
$167$	−1.61803	+	1.17557i	−0.125207	+	0.0909684i	0.523419	+	0.852075i	$0.324656\pi$
$168$		0			0
$169$	0.927051	−	2.85317i	0.0713116	−	0.219475i
$170$		0			0
$171$	−29.1246	−	21.1603i	−2.22721	−	1.61817i
$172$	−4.94427	+	15.2169i	−0.376997	+	1.16028i
$173$	−4.94427	−	15.2169i	−0.375906	−	1.15692i	−0.942865	−	0.333174i	$-0.891880\pi$
$173$	−4.94427	−	15.2169i	−0.375906	−	1.15692i	0.566959	−	0.823746i	$-0.308120\pi$
$174$		0			0
$175$	−4.00000			−0.302372
$176$		0			0
$177$	−9.00000			−0.676481
$178$		0			0
$179$	0.309017	+	0.951057i	0.0230970	+	0.0710853i	0.961941	−	0.273258i	$-0.0881014\pi$
$179$	0.309017	+	0.951057i	0.0230970	+	0.0710853i	−0.938844	+	0.344344i	$0.888101\pi$
$180$	3.70820	−	11.4127i	0.276393	−	0.850651i
$181$	−4.04508	−	2.93893i	−0.300669	−	0.218449i	0.427213	−	0.904151i	$-0.359495\pi$
$181$	−4.04508	−	2.93893i	−0.300669	−	0.218449i	−0.727882	+	0.685702i	$0.759495\pi$
$182$		0			0
$183$	−1.85410	+	5.70634i	−0.137059	+	0.421825i
$184$		0			0
$185$	−4.04508	+	2.93893i	−0.297401	+	0.216074i
$186$		0			0
$187$		0			0
$188$	−16.0000			−1.16692
$189$	7.28115	−	5.29007i	0.529626	−	0.384796i
$190$		0			0
$191$	1.54508	−	4.75528i	0.111798	−	0.344080i	−0.879467	−	0.475959i	$-0.842101\pi$
$191$	1.54508	−	4.75528i	0.111798	−	0.344080i	0.991266	+	0.131879i	$0.0421010\pi$
$192$	−19.4164	−	14.1068i	−1.40126	−	1.01807i
$193$	11.3262	+	8.22899i	0.815280	+	0.592336i	0.915357	−	0.402644i	$-0.131909\pi$
$193$	11.3262	+	8.22899i	0.815280	+	0.592336i	−0.100076	+	0.994980i	$0.531909\pi$
$194$		0			0
$195$	3.70820	+	11.4127i	0.265550	+	0.817279i
$196$	1.61803	−	1.17557i	0.115574	−	0.0839693i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$		0			0
$201$	2.78115	+	8.55951i	0.196167	+	0.603741i
$202$		0			0
$203$	8.09017	+	5.87785i	0.567819	+	0.412544i
$204$	9.70820	+	7.05342i	0.679710	+	0.493838i
$205$	−0.618034	+	1.90211i	−0.0431654	+	0.132849i
$206$		0			0
$207$	24.2705	−	17.6336i	1.68692	−	1.22562i
$208$	16.0000			1.10940
$209$		0			0
$210$		0			0
$211$	−1.61803	+	1.17557i	−0.111390	+	0.0809296i	−0.642086	−	0.766633i	$-0.721931\pi$
$211$	−1.61803	+	1.17557i	−0.111390	+	0.0809296i	0.530696	+	0.847562i	$0.321931\pi$
$212$	3.70820	+	11.4127i	0.254680	+	0.783826i
$213$	−0.927051	+	2.85317i	−0.0635205	+	0.195496i
$214$		0			0
$215$	6.47214	+	4.70228i	0.441396	+	0.320693i
$216$		0			0
$217$	0.309017	+	0.951057i	0.0209774	+	0.0645619i
$218$		0			0
$219$	30.0000			2.02721
$220$		0			0
$221$	−8.00000			−0.538138
$222$		0			0
$223$	0.309017	+	0.951057i	0.0206933	+	0.0636875i	0.960870	−	0.277000i	$-0.0893402\pi$
$223$	0.309017	+	0.951057i	0.0206933	+	0.0636875i	−0.940177	+	0.340687i	$0.889340\pi$
$224$		0			0
$225$	19.4164	+	14.1068i	1.29443	+	0.940456i
$226$		0			0
$227$	−1.23607	+	3.80423i	−0.0820407	+	0.252495i	−0.983660	−	0.180035i	$-0.942379\pi$
$227$	−1.23607	+	3.80423i	−0.0820407	+	0.252495i	0.901620	+	0.432530i	$0.142379\pi$
$228$	11.1246	+	34.2380i	0.736745	+	2.26747i
$229$	5.66312	−	4.11450i	0.374229	−	0.271894i	−0.384733	−	0.923028i	$-0.625707\pi$
$229$	5.66312	−	4.11450i	0.374229	−	0.271894i	0.758963	+	0.651134i	$0.225707\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.85410	−	3.52671i	0.318003	−	0.231043i	−0.417320	−	0.908760i	$-0.637031\pi$
$233$	4.85410	−	3.52671i	0.318003	−	0.231043i	0.735323	+	0.677717i	$0.237031\pi$
$234$		0			0
$235$	−2.47214	+	7.60845i	−0.161264	+	0.496321i
$236$	4.85410	+	3.52671i	0.315975	+	0.229569i
$237$	−14.5623	−	10.5801i	−0.945923	−	0.687254i
$238$		0			0
$239$	−1.23607	−	3.80423i	−0.0799546	−	0.246075i	0.903087	−	0.429458i	$-0.141295\pi$
$239$	−1.23607	−	3.80423i	−0.0799546	−	0.246075i	−0.983042	+	0.183383i	$0.941295\pi$
$240$	−9.70820	+	7.05342i	−0.626662	+	0.455296i
$241$	12.0000			0.772988			0.386494	−	0.922292i	$-0.373686\pi$
$241$	12.0000			0.772988			0.386494	+	0.922292i	$0.373686\pi$
$242$		0			0
$243$		0			0
$244$	3.23607	−	2.35114i	0.207168	−	0.150516i
$245$	−0.309017	−	0.951057i	−0.0197424	−	0.0607608i
$246$		0			0
$247$	−19.4164	−	14.1068i	−1.23544	−	0.897597i
$248$		0			0
$249$	11.1246	−	34.2380i	0.704994	−	2.16975i
$250$		0			0
$251$	16.9894	−	12.3435i	1.07236	−	0.779114i	0.0960240	−	0.995379i	$-0.469387\pi$
$251$	16.9894	−	12.3435i	1.07236	−	0.779114i	0.976335	+	0.216265i	$0.0693875\pi$
$252$	−12.0000			−0.755929
$253$		0			0
$254$		0			0
$255$	4.85410	−	3.52671i	0.303976	−	0.220851i
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	−1.85410	+	5.70634i	−0.115656	+	0.355952i	−0.992083	−	0.125582i	$-0.959920\pi$
$257$	−1.85410	+	5.70634i	−0.115656	+	0.355952i	0.876428	+	0.481534i	$0.159920\pi$
$258$		0			0
$259$	4.04508	+	2.93893i	0.251349	+	0.182616i
$260$	2.47214	−	7.60845i	0.153315	−	0.471856i
$261$	−18.5410	−	57.0634i	−1.14766	−	3.53214i
$262$		0			0
$263$	−18.0000			−1.10993			−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000			−1.10993			−0.554964	+	0.831875i	$0.687268\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$	13.9058	+	42.7975i	0.851019	+	2.61917i
$268$	1.85410	−	5.70634i	0.113257	−	0.348570i
$269$	14.5623	+	10.5801i	0.887879	+	0.645082i	0.935324	−	0.353792i	$-0.115108\pi$
$269$	14.5623	+	10.5801i	0.887879	+	0.645082i	−0.0474448	+	0.998874i	$0.515108\pi$
$270$		0			0
$271$	−4.94427	+	15.2169i	−0.300343	+	0.924361i	0.681031	+	0.732255i	$0.261532\pi$
$271$	−4.94427	+	15.2169i	−0.300343	+	0.924361i	−0.981374	+	0.192106i	$0.938468\pi$
$272$	−2.47214	−	7.60845i	−0.149895	−	0.461330i
$273$	9.70820	−	7.05342i	0.587567	−	0.426893i
$274$		0			0
$275$		0			0
$276$	−30.0000			−1.80579
$277$	19.4164	−	14.1068i	1.16662	−	0.847598i	0.176019	−	0.984387i	$-0.443678\pi$
$277$	19.4164	−	14.1068i	1.16662	−	0.847598i	0.990600	+	0.136789i	$0.0436781\pi$
$278$		0			0
$279$	1.85410	−	5.70634i	0.111002	−	0.341630i
$280$		0			0
$281$	−3.23607	−	2.35114i	−0.193048	−	0.140257i	0.487063	−	0.873367i	$-0.338068\pi$
$281$	−3.23607	−	2.35114i	−0.193048	−	0.140257i	−0.680111	+	0.733110i	$0.738068\pi$
$282$		0			0
$283$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$283$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$284$	1.61803	−	1.17557i	0.0960127	−	0.0697573i
$285$	18.0000			1.06623
$286$		0			0
$287$	2.00000			0.118056
$288$		0			0
$289$	−4.01722	−	12.3637i	−0.236307	−	0.727279i
$290$		0			0
$291$	−12.1353	−	8.81678i	−0.711381	−	0.516849i
$292$	−16.1803	−	11.7557i	−0.946883	−	0.687951i
$293$	1.85410	−	5.70634i	0.108318	−	0.333368i	−0.882177	−	0.470918i	$-0.843923\pi$
$293$	1.85410	−	5.70634i	0.108318	−	0.333368i	0.990495	+	0.137550i	$0.0439228\pi$
$294$		0			0
$295$	2.42705	−	1.76336i	0.141308	−	0.102667i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	16.1803	−	11.7557i	0.935733	−	0.679850i
$300$	−7.41641	−	22.8254i	−0.428187	−	1.31782i
$301$	2.47214	−	7.60845i	0.142492	−	0.438544i
$302$		0			0
$303$	29.1246	+	21.1603i	1.67317	+	1.21563i
$304$	7.41641	−	22.8254i	0.425360	−	1.30912i
$305$	−0.618034	−	1.90211i	−0.0353885	−	0.108915i
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$	36.0000			2.04797
$310$		0			0
$311$	2.47214	+	7.60845i	0.140182	+	0.431436i	0.996360	−	0.0852452i	$-0.0271674\pi$
$311$	2.47214	+	7.60845i	0.140182	+	0.431436i	−0.856178	+	0.516681i	$0.827167\pi$
$312$		0			0
$313$	18.6074	+	13.5191i	1.05175	+	0.764142i	0.972545	−	0.232716i	$-0.0747612\pi$
$313$	18.6074	+	13.5191i	1.05175	+	0.764142i	0.0792071	+	0.996858i	$0.474761\pi$
$314$		0			0
$315$	−1.85410	+	5.70634i	−0.104467	+	0.321516i
$316$	3.70820	+	11.4127i	0.208603	+	0.642013i
$317$	−7.28115	+	5.29007i	−0.408950	+	0.297120i	−0.773177	−	0.634191i	$-0.781333\pi$
$317$	−7.28115	+	5.29007i	−0.408950	+	0.297120i	0.364226	+	0.931310i	$0.381333\pi$
$318$		0			0
$319$		0			0
$320$	8.00000			0.447214
$321$	24.2705	−	17.6336i	1.35465	−	0.984209i
$322$		0			0
$323$	−3.70820	+	11.4127i	−0.206330	+	0.635018i
$324$	14.5623	+	10.5801i	0.809017	+	0.587785i
$325$	12.9443	+	9.40456i	0.718019	+	0.521671i
$326$		0			0
$327$	3.70820	+	11.4127i	0.205064	+	0.631123i
$328$		0			0
$329$	8.00000			0.441054
$330$		0			0
$331$	−17.0000			−0.934405			−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000			−0.934405			−0.467202	+	0.884150i	$0.654738\pi$
$332$	−19.4164	+	14.1068i	−1.06561	+	0.774214i
$333$	−9.27051	−	28.5317i	−0.508021	−	1.56353i
$334$		0			0
$335$	−2.42705	−	1.76336i	−0.132604	−	0.0963424i
$336$	9.70820	+	7.05342i	0.529626	+	0.384796i
$337$	5.56231	−	17.1190i	0.302998	−	0.932532i	−0.677419	−	0.735598i	$-0.736901\pi$
$337$	5.56231	−	17.1190i	0.302998	−	0.932532i	0.980417	−	0.196934i	$-0.0630986\pi$
$338$		0			0
$339$	−46.1140	+	33.5038i	−2.50457	+	1.81967i
$340$	−4.00000			−0.216930
$341$		0			0
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$		0			0
$345$	−4.63525	+	14.2658i	−0.249554	+	0.768047i
$346$		0			0
$347$	11.3262	+	8.22899i	0.608024	+	0.441756i	0.848718	−	0.528846i	$-0.177375\pi$
$347$	11.3262	+	8.22899i	0.608024	+	0.441756i	−0.240694	+	0.970601i	$0.577375\pi$
$348$	−18.5410	+	57.0634i	−0.993903	+	3.05892i
$349$	10.5066	+	32.3359i	0.562404	+	1.73090i	0.675541	+	0.737323i	$0.263910\pi$
$349$	10.5066	+	32.3359i	0.562404	+	1.73090i	−0.113136	+	0.993579i	$0.536090\pi$
$350$		0			0
$351$	−36.0000			−1.92154
$352$		0			0
$353$	9.00000			0.479022			0.239511	−	0.970894i	$-0.423013\pi$
$353$	9.00000			0.479022			0.239511	+	0.970894i	$0.423013\pi$
$354$		0			0
$355$	−0.309017	−	0.951057i	−0.0164009	−	0.0504768i
$356$	9.27051	−	28.5317i	0.491336	−	1.51218i
$357$	−4.85410	−	3.52671i	−0.256906	−	0.186653i
$358$		0			0
$359$	−2.47214	+	7.60845i	−0.130474	+	0.401559i	−0.994859	−	0.101273i	$-0.967708\pi$
$359$	−2.47214	+	7.60845i	−0.130474	+	0.401559i	0.864384	+	0.502832i	$0.167708\pi$
$360$		0			0
$361$	−13.7533	+	9.99235i	−0.723857	+	0.525913i
$362$		0			0
$363$		0			0
$364$	−8.00000			−0.419314
$365$	−8.09017	+	5.87785i	−0.423459	+	0.307661i
$366$		0			0
$367$	−3.39919	+	10.4616i	−0.177436	+	0.546092i	−0.999736	−	0.0229617i	$-0.992690\pi$
$367$	−3.39919	+	10.4616i	−0.177436	+	0.546092i	0.822300	+	0.569054i	$0.192690\pi$
$368$	16.1803	+	11.7557i	0.843459	+	0.612808i
$369$	−9.70820	−	7.05342i	−0.505389	−	0.367187i
$370$		0			0
$371$	−1.85410	−	5.70634i	−0.0962602	−	0.296258i
$372$	−4.85410	+	3.52671i	−0.251673	+	0.182851i
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$		0			0
$375$	−27.0000			−1.39427
$376$		0			0
$377$	−12.3607	−	38.0423i	−0.636607	−	1.95928i
$378$		0			0
$379$	23.4615	+	17.0458i	1.20514	+	0.875583i	0.994780	−	0.102042i	$-0.0325377\pi$
$379$	23.4615	+	17.0458i	1.20514	+	0.875583i	0.210356	+	0.977625i	$0.432538\pi$
$380$	−9.70820	−	7.05342i	−0.498020	−	0.361833i
$381$	1.85410	−	5.70634i	0.0949885	−	0.292345i
$382$		0			0
$383$	−13.7533	+	9.99235i	−0.702760	+	0.510585i	−0.880830	−	0.473433i	$-0.843015\pi$
$383$	−13.7533	+	9.99235i	−0.702760	+	0.510585i	0.178070	+	0.984018i	$0.443015\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−38.8328	+	28.2137i	−1.97398	+	1.43418i
$388$	3.09017	+	9.51057i	0.156880	+	0.482826i
$389$	2.78115	−	8.55951i	0.141010	−	0.433984i	−0.855466	−	0.517858i	$-0.826729\pi$
$389$	2.78115	−	8.55951i	0.141010	−	0.433984i	0.996476	+	0.0838742i	$0.0267294\pi$
$390$		0			0
$391$	−8.09017	−	5.87785i	−0.409137	−	0.297256i
$392$		0			0
$393$	16.6869	+	51.3571i	0.841744	+	2.59062i
$394$		0			0
$395$	6.00000			0.301893
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$		0			0
$399$	−5.56231	−	17.1190i	−0.278464	−	0.857023i
$400$	−4.94427	+	15.2169i	−0.247214	+	0.760845i
$401$	4.85410	+	3.52671i	0.242402	+	0.176116i	0.702353	−	0.711829i	$-0.252133\pi$
$401$	4.85410	+	3.52671i	0.242402	+	0.176116i	−0.459951	+	0.887945i	$0.652133\pi$
$402$		0			0
$403$	1.23607	−	3.80423i	0.0615729	−	0.189502i
$404$	−7.41641	−	22.8254i	−0.368980	−	1.13560i
$405$	7.28115	−	5.29007i	0.361803	−	0.262866i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−21.0344	+	15.2824i	−1.04009	+	0.755667i	−0.970302	−	0.241895i	$-0.922231\pi$
$409$	−21.0344	+	15.2824i	−1.04009	+	0.755667i	−0.0697838	+	0.997562i	$0.522231\pi$
$410$		0			0
$411$	2.78115	−	8.55951i	0.137184	−	0.422209i
$412$	−19.4164	−	14.1068i	−0.956578	−	0.694994i
$413$	−2.42705	−	1.76336i	−0.119427	−	0.0867691i
$414$		0			0
$415$	3.70820	+	11.4127i	0.182029	+	0.560226i
$416$		0			0
$417$	−30.0000			−1.46911
$418$		0			0
$419$	16.0000			0.781651			0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000			0.781651			0.390826	+	0.920465i	$0.372190\pi$
$420$	4.85410	−	3.52671i	0.236856	−	0.172086i
$421$	6.79837	+	20.9232i	0.331332	+	1.01974i	0.968501	+	0.249012i	$0.0801057\pi$
$421$	6.79837	+	20.9232i	0.331332	+	1.01974i	−0.637168	+	0.770725i	$0.719894\pi$
$422$		0			0
$423$	−38.8328	−	28.2137i	−1.88812	−	1.37180i
$424$		0			0
$425$	2.47214	−	7.60845i	0.119916	−	0.369064i
$426$		0			0
$427$	−1.61803	+	1.17557i	−0.0783022	+	0.0568898i
$428$	−20.0000			−0.966736
$429$		0			0
$430$		0			0
$431$	−16.1803	+	11.7557i	−0.779380	+	0.566252i	−0.904793	−	0.425852i	$-0.859974\pi$
$431$	−16.1803	+	11.7557i	−0.779380	+	0.566252i	0.125413	+	0.992105i	$0.459974\pi$
$432$	−11.1246	−	34.2380i	−0.535233	−	1.64728i
$433$	−7.72542	+	23.7764i	−0.371260	+	1.14262i	0.574707	+	0.818359i	$0.305116\pi$
$433$	−7.72542	+	23.7764i	−0.371260	+	1.14262i	−0.945967	+	0.324262i	$0.894884\pi$
$434$		0			0
$435$	24.2705	+	17.6336i	1.16368	+	0.845464i
$436$	2.47214	−	7.60845i	0.118394	−	0.364379i
$437$	−9.27051	−	28.5317i	−0.443469	−	1.36486i
$438$		0			0
$439$	14.0000			0.668184			0.334092	−	0.942541i	$-0.391570\pi$
$439$	14.0000			0.668184			0.334092	+	0.942541i	$0.391570\pi$
$440$		0			0
$441$	6.00000			0.285714
$442$		0			0
$443$	−12.0517	−	37.0912i	−0.572592	−	1.76226i	−0.644237	−	0.764826i	$-0.722825\pi$
$443$	−12.0517	−	37.0912i	−0.572592	−	1.76226i	0.0716450	−	0.997430i	$-0.477175\pi$
$444$	−9.27051	+	28.5317i	−0.439959	+	1.35405i
$445$	−12.1353	−	8.81678i	−0.575266	−	0.417955i
$446$		0			0
$447$	−20.3951	+	62.7697i	−0.964656	+	2.96891i
$448$	−2.47214	−	7.60845i	−0.116797	−	0.359466i
$449$	−12.1353	+	8.81678i	−0.572698	+	0.416090i	−0.836084	−	0.548601i	$-0.815161\pi$
$449$	−12.1353	+	8.81678i	−0.572698	+	0.416090i	0.263386	+	0.964690i	$0.415161\pi$
$450$		0			0
$451$		0			0
$452$	38.0000			1.78737
$453$	−14.5623	+	10.5801i	−0.684197	+	0.497098i
$454$		0			0
$455$	−1.23607	+	3.80423i	−0.0579478	+	0.178345i
$456$		0			0
$457$	6.47214	+	4.70228i	0.302754	+	0.219963i	0.728781	−	0.684747i	$-0.240087\pi$
$457$	6.47214	+	4.70228i	0.302754	+	0.219963i	−0.426027	+	0.904710i	$0.640087\pi$
$458$		0			0
$459$	5.56231	+	17.1190i	0.259626	+	0.799047i
$460$	8.09017	−	5.87785i	0.377206	−	0.274056i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	13.0000			0.604161			0.302081	−	0.953282i	$-0.402319\pi$
$463$	13.0000			0.604161			0.302081	+	0.953282i	$0.402319\pi$
$464$	32.3607	−	23.5114i	1.50231	−	1.09149i
$465$	0.927051	+	2.85317i	0.0429910	+	0.132313i
$466$		0			0
$467$	−2.42705	−	1.76336i	−0.112311	−	0.0815984i	0.530212	−	0.847865i	$-0.322112\pi$
$467$	−2.42705	−	1.76336i	−0.112311	−	0.0815984i	−0.642523	+	0.766267i	$0.722112\pi$
$468$	38.8328	+	28.2137i	1.79505	+	1.30418i
$469$	−0.927051	+	2.85317i	−0.0428072	+	0.131747i
$470$		0			0
$471$	16.9894	−	12.3435i	0.782828	−	0.568758i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	19.4164	−	14.1068i	0.890886	−	0.647266i
$476$	1.23607	+	3.80423i	0.0566551	+	0.174366i
$477$	−11.1246	+	34.2380i	−0.509361	+	1.56765i
$478$		0			0
$479$	−22.6525	−	16.4580i	−1.03502	−	0.751985i	−0.0657112	−	0.997839i	$-0.520932\pi$
$479$	−22.6525	−	16.4580i	−1.03502	−	0.751985i	−0.969307	+	0.245854i	$0.920932\pi$
$480$		0			0
$481$	−6.18034	−	19.0211i	−0.281799	−	0.867289i
$482$		0			0
$483$	15.0000			0.682524
$484$		0			0
$485$	5.00000			0.227038
$486$		0			0
$487$	−4.01722	−	12.3637i	−0.182038	−	0.560254i	0.817847	−	0.575436i	$-0.195167\pi$
$487$	−4.01722	−	12.3637i	−0.182038	−	0.560254i	−0.999885	+	0.0151813i	$0.995167\pi$
$488$		0			0
$489$	9.70820	+	7.05342i	0.439020	+	0.318967i
$490$		0			0
$491$	9.27051	−	28.5317i	0.418372	−	1.28762i	−0.490827	−	0.871257i	$-0.663305\pi$
$491$	9.27051	−	28.5317i	0.418372	−	1.28762i	0.909200	−	0.416361i	$-0.136695\pi$
$492$	3.70820	+	11.4127i	0.167179	+	0.514523i
$493$	−16.1803	+	11.7557i	−0.728726	+	0.529450i
$494$		0			0
$495$		0			0
$496$	4.00000			0.179605
$497$	−0.809017	+	0.587785i	−0.0362894	+	0.0263658i
$498$		0			0
$499$	13.5967	−	41.8465i	0.608674	−	1.87331i	0.139444	−	0.990230i	$-0.455468\pi$
$499$	13.5967	−	41.8465i	0.608674	−	1.87331i	0.469230	−	0.883076i	$-0.344532\pi$
$500$	14.5623	+	10.5801i	0.651246	+	0.473158i
$501$	4.85410	+	3.52671i	0.216865	+	0.157562i
$502$		0			0
$503$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$503$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$504$		0			0
$505$	−12.0000			−0.533993
$506$		0			0
$507$	−9.00000			−0.399704
$508$	−3.23607	+	2.35114i	−0.143577	+	0.104315i
$509$	−9.57953	−	29.4828i	−0.424605	−	1.30680i	−0.903372	−	0.428858i	$-0.858916\pi$
$509$	−9.57953	−	29.4828i	−0.424605	−	1.30680i	0.478767	−	0.877942i	$-0.341084\pi$
$510$		0			0
$511$	8.09017	+	5.87785i	0.357888	+	0.260021i
$512$		0			0
$513$	−16.6869	+	51.3571i	−0.736745	+	2.26747i
$514$		0			0
$515$	−9.70820	+	7.05342i	−0.427795	+	0.310811i
$516$	48.0000			2.11308
$517$		0			0
$518$		0			0
$519$	−38.8328	+	28.2137i	−1.70457	+	1.23844i
$520$		0			0
$521$	2.16312	−	6.65740i	0.0947680	−	0.291666i	−0.892425	−	0.451195i	$-0.850998\pi$
$521$	2.16312	−	6.65740i	0.0947680	−	0.291666i	0.987193	+	0.159530i	$0.0509977\pi$
$522$		0			0
$523$	25.8885	+	18.8091i	1.13203	+	0.822466i	0.985989	−	0.166813i	$-0.0533477\pi$
$523$	25.8885	+	18.8091i	1.13203	+	0.822466i	0.146038	+	0.989279i	$0.453348\pi$
$524$	11.1246	−	34.2380i	0.485981	−	1.49570i
$525$	3.70820	+	11.4127i	0.161839	+	0.498090i
$526$		0			0
$527$	−2.00000			−0.0871214
$528$		0			0
$529$	2.00000			0.0869565
$530$		0			0
$531$	5.56231	+	17.1190i	0.241384	+	0.742902i
$532$	−3.70820	+	11.4127i	−0.160771	+	0.494802i
$533$	−6.47214	−	4.70228i	−0.280339	−	0.203678i
$534$		0			0
$535$	−3.09017	+	9.51057i	−0.133600	+	0.411178i
$536$		0			0
$537$	2.42705	−	1.76336i	0.104735	−	0.0760944i
$538$		0			0
$539$		0			0
$540$	−18.0000			−0.774597
$541$	25.8885	−	18.8091i	1.11304	−	0.808668i	0.129896	−	0.991528i	$-0.458536\pi$
$541$	25.8885	−	18.8091i	1.11304	−	0.808668i	0.983139	+	0.182860i	$0.0585355\pi$
$542$		0			0
$543$	−4.63525	+	14.2658i	−0.198918	+	0.612206i
$544$		0			0
$545$	−3.23607	−	2.35114i	−0.138618	−	0.100712i
$546$		0			0
$547$	7.41641	+	22.8254i	0.317103	+	0.975942i	0.974880	+	0.222730i	$0.0714967\pi$
$547$	7.41641	+	22.8254i	0.317103	+	0.975942i	−0.657778	+	0.753212i	$0.728503\pi$
$548$	−4.85410	+	3.52671i	−0.207357	+	0.150654i
$549$	12.0000			0.512148
$550$		0			0
$551$	−60.0000			−2.55609
$552$		0			0
$553$	−1.85410	−	5.70634i	−0.0788444	−	0.242658i
$554$		0			0
$555$	12.1353	+	8.81678i	0.515113	+	0.374251i
$556$	16.1803	+	11.7557i	0.686199	+	0.498553i
$557$	−4.32624	+	13.3148i	−0.183309	+	0.564166i	−0.999915	−	0.0130289i	$-0.995853\pi$
$557$	−4.32624	+	13.3148i	−0.183309	+	0.564166i	0.816607	+	0.577195i	$0.195853\pi$
$558$		0			0
$559$	−25.8885	+	18.8091i	−1.09497	+	0.795541i
$560$	−4.00000			−0.169031
$561$		0			0
$562$		0			0
$563$	16.1803	−	11.7557i	0.681920	−	0.495444i	−0.192074	−	0.981380i	$-0.561521\pi$
$563$	16.1803	−	11.7557i	0.681920	−	0.495444i	0.873994	+	0.485937i	$0.161521\pi$
$564$	14.8328	+	45.6507i	0.624574	+	1.92224i
$565$	5.87132	−	18.0701i	0.247008	−	0.760214i
$566$		0			0
$567$	−7.28115	−	5.29007i	−0.305780	−	0.222162i
$568$		0			0
$569$	5.56231	+	17.1190i	0.233184	+	0.717667i	0.997357	+	0.0726553i	$0.0231473\pi$
$569$	5.56231	+	17.1190i	0.233184	+	0.717667i	−0.764173	+	0.645011i	$0.776853\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$		0			0
$573$	−15.0000			−0.626634
$574$		0			0
$575$	6.18034	+	19.0211i	0.257738	+	0.793236i
$576$	−14.8328	+	45.6507i	−0.618034	+	1.90211i
$577$	20.2254	+	14.6946i	0.841995	+	0.611746i	0.922927	−	0.384974i	$-0.125790\pi$
$577$	20.2254	+	14.6946i	0.841995	+	0.611746i	−0.0809319	+	0.996720i	$0.525790\pi$
$578$		0			0
$579$	12.9787	−	39.9444i	0.539377	−	1.66003i
$580$	−6.18034	−	19.0211i	−0.256625	−	0.789809i
$581$	9.70820	−	7.05342i	0.402764	−	0.292625i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	19.4164	−	14.1068i	0.802770	−	0.583246i
$586$		0			0
$587$	11.1246	−	34.2380i	0.459162	−	1.41315i	−0.407017	−	0.913421i	$-0.633431\pi$
$587$	11.1246	−	34.2380i	0.459162	−	1.41315i	0.866179	−	0.499734i	$-0.166569\pi$
$588$	−4.85410	−	3.52671i	−0.200180	−	0.145439i
$589$	−4.85410	−	3.52671i	−0.200010	−	0.145316i
$590$		0			0
$591$	16.6869	+	51.3571i	0.686408	+	2.11255i
$592$	16.1803	−	11.7557i	0.665008	−	0.483157i
$593$	−30.0000			−1.23195			−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000			−1.23195			−0.615976	+	0.787765i	$0.711238\pi$
$594$		0			0
$595$	2.00000			0.0819920
$596$	35.5967	−	25.8626i	1.45810	−	1.05937i
$597$	7.41641	+	22.8254i	0.303533	+	0.934180i
$598$		0			0
$599$	38.8328	+	28.2137i	1.58667	+	1.15278i	0.908511	+	0.417861i	$0.137220\pi$
$599$	38.8328	+	28.2137i	1.58667	+	1.15278i	0.678155	+	0.734919i	$0.262780\pi$
$600$		0			0
$601$	−2.47214	+	7.60845i	−0.100841	+	0.310355i	−0.988732	−	0.149698i	$-0.952170\pi$
$601$	−2.47214	+	7.60845i	−0.100841	+	0.310355i	0.887891	+	0.460053i	$0.152170\pi$
$602$		0			0
$603$	14.5623	−	10.5801i	0.593023	−	0.430856i
$604$	12.0000			0.488273
$605$		0			0
$606$		0			0
$607$	−8.09017	+	5.87785i	−0.328370	+	0.238575i	−0.739739	−	0.672894i	$-0.765051\pi$
$607$	−8.09017	+	5.87785i	−0.328370	+	0.238575i	0.411369	+	0.911469i	$0.365051\pi$
$608$		0			0
$609$	9.27051	−	28.5317i	0.375660	−	1.15616i
$610$		0			0
$611$	−25.8885	−	18.8091i	−1.04734	−	0.760936i
$612$	7.41641	−	22.8254i	0.299791	−	0.922660i
$613$	−4.94427	−	15.2169i	−0.199697	−	0.614605i	−0.999890	−	0.0148615i	$-0.995269\pi$
$613$	−4.94427	−	15.2169i	−0.199697	−	0.614605i	0.800192	−	0.599744i	$-0.204731\pi$
$614$		0			0
$615$	6.00000			0.241943
$616$		0			0
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$		0			0
$619$	5.25329	+	16.1680i	0.211148	+	0.649845i	0.999405	+	0.0344993i	$0.0109837\pi$
$619$	5.25329	+	16.1680i	0.211148	+	0.649845i	−0.788257	+	0.615346i	$0.789016\pi$
$620$	0.618034	−	1.90211i	0.0248208	−	0.0763907i
$621$	−36.4058	−	26.4503i	−1.46091	−	1.06142i
$622$		0			0
$623$	−4.63525	+	14.2658i	−0.185708	+	0.571549i
$624$	−14.8328	−	45.6507i	−0.593788	−	1.82749i
$625$	−8.89919	+	6.46564i	−0.355967	+	0.258626i
$626$		0			0
$627$		0			0
$628$	−14.0000			−0.558661
$629$	−8.09017	+	5.87785i	−0.322576	+	0.234365i
$630$		0			0
$631$	8.34346	−	25.6785i	0.332148	−	1.02225i	−0.635962	−	0.771720i	$-0.719397\pi$
$631$	8.34346	−	25.6785i	0.332148	−	1.02225i	0.968110	−	0.250526i	$-0.0806035\pi$
$632$		0			0
$633$	4.85410	+	3.52671i	0.192933	+	0.140174i
$634$		0			0
$635$	0.618034	+	1.90211i	0.0245259	+	0.0754831i
$636$	29.1246	−	21.1603i	1.15487	−	0.839059i
$637$	4.00000			0.158486
$638$		0			0
$639$	6.00000			0.237356
$640$		0			0
$641$	4.63525	+	14.2658i	0.183082	+	0.563467i	0.999910	−	0.0134135i	$-0.00426978\pi$
$641$	4.63525	+	14.2658i	0.183082	+	0.563467i	−0.816828	+	0.576881i	$0.804270\pi$
$642$		0			0
$643$	23.4615	+	17.0458i	0.925231	+	0.672220i	0.944821	−	0.327588i	$-0.106236\pi$
$643$	23.4615	+	17.0458i	0.925231	+	0.672220i	−0.0195896	+	0.999808i	$0.506236\pi$
$644$	−8.09017	−	5.87785i	−0.318797	−	0.231620i
$645$	7.41641	−	22.8254i	0.292021	−	0.898748i
$646$		0			0
$647$	16.9894	−	12.3435i	0.667921	−	0.485273i	−0.201408	−	0.979507i	$-0.564552\pi$
$647$	16.9894	−	12.3435i	0.667921	−	0.485273i	0.869328	+	0.494235i	$0.164552\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	2.42705	−	1.76336i	0.0951236	−	0.0691114i
$652$	−2.47214	−	7.60845i	−0.0968163	−	0.297970i
$653$	−5.25329	+	16.1680i	−0.205577	+	0.632701i	0.794112	+	0.607771i	$0.207936\pi$
$653$	−5.25329	+	16.1680i	−0.205577	+	0.632701i	−0.999689	+	0.0249299i	$0.992064\pi$
$654$		0			0
$655$	−14.5623	−	10.5801i	−0.568996	−	0.413400i
$656$	2.47214	−	7.60845i	0.0965207	−	0.297060i
$657$	−18.5410	−	57.0634i	−0.723354	−	2.22625i
$658$		0			0
$659$	2.00000			0.0779089			0.0389545	−	0.999241i	$-0.487597\pi$
$659$	2.00000			0.0779089			0.0389545	+	0.999241i	$0.487597\pi$
$660$		0			0
$661$	35.0000			1.36134			0.680671	−	0.732589i	$-0.261688\pi$
$661$	35.0000			1.36134			0.680671	+	0.732589i	$0.261688\pi$
$662$		0			0
$663$	7.41641	+	22.8254i	0.288029	+	0.886463i
$664$		0			0
$665$	4.85410	+	3.52671i	0.188234	+	0.136760i
$666$		0			0
$667$	15.4508	−	47.5528i	0.598259	−	1.84125i
$668$	−1.23607	−	3.80423i	−0.0478249	−	0.147190i
$669$	2.42705	−	1.76336i	0.0938352	−	0.0681753i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	3.23607	−	2.35114i	0.124741	−	0.0906298i	−0.523665	−	0.851924i	$-0.675436\pi$
$673$	3.23607	−	2.35114i	0.124741	−	0.0906298i	0.648407	+	0.761294i	$0.275436\pi$
$674$		0			0
$675$	11.1246	−	34.2380i	0.428187	−	1.31782i
$676$	4.85410	+	3.52671i	0.186696	+	0.135643i
$677$	30.7426	+	22.3358i	1.18154	+	0.858436i	0.992344	−	0.123504i	$-0.0394132\pi$
$677$	30.7426	+	22.3358i	1.18154	+	0.858436i	0.189192	+	0.981940i	$0.439413\pi$
$678$		0			0
$679$	−1.54508	−	4.75528i	−0.0592949	−	0.182491i
$680$		0			0
$681$	12.0000			0.459841
$682$		0			0
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	58.2492	−	42.3205i	2.22721	−	1.61817i
$685$	0.927051	+	2.85317i	0.0354208	+	0.109014i
$686$		0			0
$687$	−16.9894	−	12.3435i	−0.648184	−	0.470934i
$688$	−25.8885	−	18.8091i	−0.986991	−	0.717091i
$689$	−7.41641	+	22.8254i	−0.282543	+	0.869577i
$690$		0			0
$691$	−12.1353	+	8.81678i	−0.461647	+	0.335406i	−0.794177	−	0.607687i	$-0.792098\pi$
$691$	−12.1353	+	8.81678i	−0.461647	+	0.335406i	0.332530	+	0.943093i	$0.392098\pi$
$692$	32.0000			1.21646
$693$		0			0
$694$		0			0
$695$	8.09017	−	5.87785i	0.306878	−	0.222960i
$696$		0			0
$697$	−1.23607	+	3.80423i	−0.0468194	+	0.144095i
$698$		0			0
$699$	−14.5623	−	10.5801i	−0.550797	−	0.400177i
$700$	2.47214	−	7.60845i	0.0934380	−	0.287572i
$701$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$701$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$702$		0			0
$703$	−30.0000			−1.13147
$704$		0			0
$705$	24.0000			0.903892
$706$		0			0
$707$	3.70820	+	11.4127i	0.139461	+	0.429218i
$708$	5.56231	−	17.1190i	0.209044	−	0.643372i
$709$	−31.5517	−	22.9236i	−1.18495	−	0.860915i	−0.192226	−	0.981351i	$-0.561571\pi$
$709$	−31.5517	−	22.9236i	−1.18495	−	0.860915i	−0.992721	+	0.120436i	$0.961571\pi$
$710$		0			0
$711$	−11.1246	+	34.2380i	−0.417206	+	1.28403i
$712$		0			0
$713$	4.04508	−	2.93893i	0.151490	−	0.110064i
$714$		0			0
$715$		0			0
$716$	−2.00000			−0.0747435
$717$	−9.70820	+	7.05342i	−0.362560	+	0.263415i
$718$		0			0
$719$	−3.39919	+	10.4616i	−0.126768	+	0.390153i	−0.994219	−	0.107370i	$-0.965757\pi$
$719$	−3.39919	+	10.4616i	−0.126768	+	0.390153i	0.867451	+	0.497523i	$0.165757\pi$
$720$	19.4164	+	14.1068i	0.723607	+	0.525731i
$721$	9.70820	+	7.05342i	0.361552	+	0.262683i
$722$		0			0
$723$	−11.1246	−	34.2380i	−0.413729	−	1.27333i
$724$	8.09017	−	5.87785i	0.300669	−	0.218449i
$725$	40.0000			1.48556
$726$		0			0
$727$	−19.0000			−0.704671			−0.352335	−	0.935874i	$-0.614612\pi$
$727$	−19.0000			−0.704671			−0.352335	+	0.935874i	$0.614612\pi$
$728$		0			0
$729$	−8.34346	−	25.6785i	−0.309017	−	0.951057i
$730$		0			0
$731$	12.9443	+	9.40456i	0.478761	+	0.347840i
$732$	−9.70820	−	7.05342i	−0.358826	−	0.260702i
$733$	1.23607	−	3.80423i	0.0456552	−	0.140512i	−0.925630	−	0.378429i	$-0.876464\pi$
$733$	1.23607	−	3.80423i	0.0456552	−	0.140512i	0.971286	+	0.237917i	$0.0764645\pi$
$734$		0			0
$735$	−2.42705	+	1.76336i	−0.0895231	+	0.0650424i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−14.5623	+	10.5801i	−0.535683	+	0.389197i	−0.822479	−	0.568795i	$-0.807410\pi$
$739$	−14.5623	+	10.5801i	−0.535683	+	0.389197i	0.286796	+	0.957992i	$0.407410\pi$
$740$	−3.09017	−	9.51057i	−0.113597	−	0.349615i
$741$	−22.2492	+	68.4761i	−0.817346	+	2.51553i
$742$		0			0
$743$	−19.4164	−	14.1068i	−0.712319	−	0.517530i	0.171602	−	0.985166i	$-0.445106\pi$
$743$	−19.4164	−	14.1068i	−0.712319	−	0.517530i	−0.883921	+	0.467636i	$0.845106\pi$
$744$		0			0
$745$	−6.79837	−	20.9232i	−0.249073	−	0.766568i
$746$		0			0
$747$	−72.0000			−2.63434
$748$		0			0
$749$	10.0000			0.365392
$750$		0			0
$751$	−7.10739	−	21.8743i	−0.259352	−	0.798205i	−0.992941	−	0.118611i	$-0.962156\pi$
$751$	−7.10739	−	21.8743i	−0.259352	−	0.798205i	0.733588	−	0.679594i	$-0.237844\pi$
$752$	9.88854	−	30.4338i	0.360598	−	1.10981i
$753$	−50.9681	−	37.0305i	−1.85738	−	1.34947i
$754$		0			0
$755$	1.85410	−	5.70634i	0.0674777	−	0.207675i
$756$	5.56231	+	17.1190i	0.202299	+	0.622613i
$757$	−30.7426	+	22.3358i	−1.11736	+	0.811810i	−0.983807	−	0.179232i	$-0.942639\pi$
$757$	−30.7426	+	22.3358i	−1.11736	+	0.811810i	−0.133554	+	0.991042i	$0.542639\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−38.8328	+	28.2137i	−1.40769	+	1.02275i	−0.414035	+	0.910261i	$0.635881\pi$
$761$	−38.8328	+	28.2137i	−1.40769	+	1.02275i	−0.993653	+	0.112485i	$0.964119\pi$
$762$		0			0
$763$	−1.23607	+	3.80423i	−0.0447487	+	0.137722i
$764$	8.09017	+	5.87785i	0.292692	+	0.212653i
$765$	−9.70820	−	7.05342i	−0.351001	−	0.255017i
$766$		0			0
$767$	3.70820	+	11.4127i	0.133895	+	0.412088i
$768$	38.8328	−	28.2137i	1.40126	−	1.01807i
$769$	−40.0000			−1.44244			−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000			−1.44244			−0.721218	+	0.692708i	$0.756418\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	−22.6525	+	16.4580i	−0.815280	+	0.592336i
$773$	−1.85410	−	5.70634i	−0.0666874	−	0.205243i	0.912160	−	0.409834i	$-0.134413\pi$
$773$	−1.85410	−	5.70634i	−0.0666874	−	0.205243i	−0.978847	+	0.204591i	$0.934413\pi$
$774$		0			0
$775$	3.23607	+	2.35114i	0.116243	+	0.0844555i
$776$		0			0
$777$	4.63525	−	14.2658i	0.166289	−	0.511784i
$778$		0			0
$779$	−9.70820	+	7.05342i	−0.347833	+	0.252715i
$780$	−24.0000			−0.859338
$781$		0			0
$782$		0			0
$783$	−72.8115	+	52.9007i	−2.60207	+	1.89052i
$784$	1.23607	+	3.80423i	0.0441453	+	0.135865i
$785$	−2.16312	+	6.65740i	−0.0772050	+	0.237613i
$786$		0			0
$787$	−17.7984	−	12.9313i	−0.634444	−	0.460950i	0.223493	−	0.974705i	$-0.428254\pi$
$787$	−17.7984	−	12.9313i	−0.634444	−	0.460950i	−0.857937	+	0.513755i	$0.828254\pi$
$788$	11.1246	−	34.2380i	0.396298	−	1.21968i
$789$	16.6869	+	51.3571i	0.594070	+	1.82836i
$790$		0			0
$791$	−19.0000			−0.675562
$792$		0			0
$793$	8.00000			0.284088
$794$		0			0
$795$	−5.56231	−	17.1190i	−0.197275	−	0.607149i
$796$	4.94427	−	15.2169i	0.175245	−	0.539349i
$797$	−18.6074	−	13.5191i	−0.659108	−	0.478870i	0.207254	−	0.978287i	$-0.433547\pi$
$797$	−18.6074	−	13.5191i	−0.659108	−	0.478870i	−0.866361	+	0.499417i	$0.833547\pi$
$798$		0			0
$799$	−4.94427	+	15.2169i	−0.174916	+	0.538335i
$800$		0			0
$801$	72.8115	−	52.9007i	2.57267	−	1.86915i
$802$		0			0
$803$		0			0
$804$	−18.0000			−0.634811
$805$	−4.04508	+	2.93893i	−0.142571	+	0.103584i
$806$		0			0
$807$	16.6869	−	51.3571i	0.587407	−	1.80785i
$808$		0			0
$809$	24.2705	+	17.6336i	0.853306	+	0.619963i	0.926055	−	0.377387i	$-0.123177\pi$
$809$	24.2705	+	17.6336i	0.853306	+	0.619963i	−0.0727498	+	0.997350i	$0.523177\pi$
$810$		0			0
$811$	6.79837	+	20.9232i	0.238723	+	0.734714i	0.996606	+	0.0823233i	$0.0262340\pi$
$811$	6.79837	+	20.9232i	0.238723	+	0.734714i	−0.757882	+	0.652391i	$0.773766\pi$
$812$	−16.1803	+	11.7557i	−0.567819	+	0.412544i
$813$	48.0000			1.68343
$814$		0			0
$815$	−4.00000			−0.140114
$816$	−19.4164	+	14.1068i	−0.679710	+	0.493838i
$817$	14.8328	+	45.6507i	0.518935	+	1.59712i
$818$		0			0
$819$	−19.4164	−	14.1068i	−0.678464	−	0.492933i
$820$	−3.23607	−	2.35114i	−0.113008	−	0.0821054i
$821$	−5.56231	+	17.1190i	−0.194126	+	0.597458i	0.805860	+	0.592106i	$0.201703\pi$
$821$	−5.56231	+	17.1190i	−0.194126	+	0.597458i	−0.999986	+	0.00535152i	$0.998297\pi$
$822$		0			0
$823$	20.2254	−	14.6946i	0.705014	−	0.512223i	−0.176547	−	0.984292i	$-0.556493\pi$
$823$	20.2254	−	14.6946i	0.705014	−	0.512223i	0.881561	+	0.472070i	$0.156493\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.1803	−	11.7557i	0.562646	−	0.408786i	−0.269781	−	0.962922i	$-0.586951\pi$
$827$	16.1803	−	11.7557i	0.562646	−	0.408786i	0.832426	+	0.554136i	$0.186951\pi$
$828$	18.5410	+	57.0634i	0.644345	+	1.98309i
$829$	−8.96149	+	27.5806i	−0.311246	+	0.957915i	0.666027	+	0.745928i	$0.267994\pi$
$829$	−8.96149	+	27.5806i	−0.311246	+	0.957915i	−0.977272	+	0.211987i	$0.932006\pi$
$830$		0			0
$831$	−58.2492	−	42.3205i	−2.02064	−	1.46808i
$832$	−9.88854	+	30.4338i	−0.342824	+	1.05510i
$833$	−0.618034	−	1.90211i	−0.0214136	−	0.0659043i
$834$		0			0
$835$	−2.00000			−0.0692129
$836$		0			0
$837$	−9.00000			−0.311086
$838$		0			0
$839$	13.9058	+	42.7975i	0.480080	+	1.47754i	0.838982	+	0.544160i	$0.183151\pi$
$839$	13.9058	+	42.7975i	0.480080	+	1.47754i	−0.358901	+	0.933376i	$0.616849\pi$
$840$		0			0
$841$	−57.4402	−	41.7328i	−1.98070	−	1.43906i
$842$		0			0
$843$	−3.70820	+	11.4127i	−0.127717	+	0.393074i
$844$	−1.23607	−	3.80423i	−0.0425472	−	0.130947i
$845$	2.42705	−	1.76336i	0.0834931	−	0.0606613i
$846$		0			0
$847$		0			0
$848$	−24.0000			−0.824163
$849$		0			0
$850$		0			0
$851$	7.72542	−	23.7764i	0.264824	−	0.815045i
$852$	−4.85410	−	3.52671i	−0.166299	−	0.120823i
$853$	−27.5066	−	19.9847i	−0.941807	−	0.684263i	0.00704774	−	0.999975i	$-0.497757\pi$
$853$	−27.5066	−	19.9847i	−0.941807	−	0.684263i	−0.948855	+	0.315712i	$0.897757\pi$
$854$		0			0
$855$	−11.1246	−	34.2380i	−0.380454	−	1.17092i
$856$		0			0
$857$	28.0000			0.956462			0.478231	−	0.878234i	$-0.341278\pi$
$857$	28.0000			0.956462			0.478231	+	0.878234i	$0.341278\pi$
$858$		0			0
$859$	55.0000			1.87658			0.938288	−	0.345855i	$-0.112411\pi$
$859$	55.0000			1.87658			0.938288	+	0.345855i	$0.112411\pi$
$860$	−12.9443	+	9.40456i	−0.441396	+	0.320693i
$861$	−1.85410	−	5.70634i	−0.0631876	−	0.194472i
$862$		0			0
$863$	−42.0689	−	30.5648i	−1.43204	−	1.04044i	−0.989632	−	0.143626i	$-0.954124\pi$
$863$	−42.0689	−	30.5648i	−1.43204	−	1.04044i	−0.442409	−	0.896813i	$-0.645876\pi$
$864$		0			0
$865$	4.94427	−	15.2169i	0.168110	−	0.517390i
$866$		0			0
$867$	−31.5517	+	22.9236i	−1.07155	+	0.778527i
$868$	−2.00000			−0.0678844
$869$		0			0
$870$		0			0
$871$	9.70820	−	7.05342i	0.328950	−	0.238996i
$872$		0			0
$873$	−9.27051	+	28.5317i	−0.313759	+	0.965652i
$874$		0			0
$875$	−7.28115	−	5.29007i	−0.246148	−	0.178837i
$876$	−18.5410	+	57.0634i	−0.626443	+	1.92799i
$877$	11.7426	+	36.1401i	0.396521	+	1.22037i	0.927771	+	0.373151i	$0.121723\pi$
$877$	11.7426	+	36.1401i	0.396521	+	1.22037i	−0.531250	+	0.847215i	$0.678277\pi$
$878$		0			0
$879$	−18.0000			−0.607125
$880$		0			0
$881$	27.0000			0.909653			0.454827	−	0.890580i	$-0.349701\pi$
$881$	27.0000			0.909653			0.454827	+	0.890580i	$0.349701\pi$
$882$		0			0
$883$	−13.5967	−	41.8465i	−0.457567	−	1.40825i	−0.868095	−	0.496398i	$-0.834656\pi$
$883$	−13.5967	−	41.8465i	−0.457567	−	1.40825i	0.410528	−	0.911848i	$-0.365344\pi$
$884$	4.94427	−	15.2169i	0.166294	−	0.511800i
$885$	−7.28115	−	5.29007i	−0.244753	−	0.177824i
$886$		0			0
$887$	0.618034	−	1.90211i	0.0207516	−	0.0638667i	−0.940144	−	0.340776i	$-0.889310\pi$
$887$	0.618034	−	1.90211i	0.0207516	−	0.0638667i	0.960896	+	0.276909i	$0.0893102\pi$
$888$		0			0
$889$	1.61803	−	1.17557i	0.0542671	−	0.0394274i
$890$		0			0
$891$		0			0
$892$	−2.00000			−0.0669650
$893$	−38.8328	+	28.2137i	−1.29949	+	0.944135i
$894$		0			0
$895$	−0.309017	+	0.951057i	−0.0103293	+	0.0317903i
$896$		0			0
$897$	−48.5410	−	35.2671i	−1.62074	−	1.17753i
$898$		0			0
$899$	−3.09017	−	9.51057i	−0.103063	−	0.317195i
$900$	−38.8328	+	28.2137i	−1.29443	+	0.940456i
$901$	12.0000			0.399778
$902$		0			0
$903$	−24.0000			−0.798670
$904$		0			0
$905$	−1.54508	−	4.75528i	−0.0513604	−	0.158071i
$906$		0			0
$907$	32.3607	+	23.5114i	1.07452	+	0.780684i	0.976719	−	0.214523i	$-0.0688195\pi$
$907$	32.3607	+	23.5114i	1.07452	+	0.780684i	0.0977997	+	0.995206i	$0.468820\pi$
$908$	−6.47214	−	4.70228i	−0.214785	−	0.156051i
$909$	22.2492	−	68.4761i	0.737960	−	2.27121i
$910$		0			0
$911$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$911$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$912$	−72.0000			−2.38416
$913$		0			0
$914$		0			0
$915$	−4.85410	+	3.52671i	−0.160472	+	0.116589i
$916$	4.32624	+	13.3148i	0.142943	+	0.439933i
$917$	−5.56231	+	17.1190i	−0.183684	+	0.565320i
$918$		0			0
$919$	38.8328	+	28.2137i	1.28098	+	0.930684i	0.999582	−	0.0289084i	$-0.00920311\pi$
$919$	38.8328	+	28.2137i	1.28098	+	0.930684i	0.281394	+	0.959592i	$0.409203\pi$
$920$		0			0
$921$	−25.9574	−	79.8887i	−0.855326	−	2.63242i
$922$		0			0
$923$	4.00000			0.131662
$924$		0			0
$925$	20.0000			0.657596
$926$		0			0
$927$	−22.2492	−	68.4761i	−0.730760	−	2.24905i
$928$		0			0
$929$	24.2705	+	17.6336i	0.796290	+	0.578538i	0.909823	−	0.414996i	$-0.136217\pi$
$929$	24.2705	+	17.6336i	0.796290	+	0.578538i	−0.113534	+	0.993534i	$0.536217\pi$
$930$		0			0
$931$	1.85410	−	5.70634i	0.0607657	−	0.187018i
$932$	3.70820	+	11.4127i	0.121466	+	0.373835i
$933$	19.4164	−	14.1068i	0.635665	−	0.461837i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	29.1246	−	21.1603i	0.951460	−	0.691276i	0.000307959	−	1.00000i	$-0.499902\pi$
$937$	29.1246	−	21.1603i	0.951460	−	0.691276i	0.951152	+	0.308724i	$0.0999020\pi$
$938$		0			0
$939$	21.3222	−	65.6229i	0.695823	−	2.14152i
$940$	−12.9443	−	9.40456i	−0.422196	−	0.306743i
$941$	46.9230	+	34.0915i	1.52965	+	1.11135i	0.956435	+	0.291944i	$0.0943022\pi$
$941$	46.9230	+	34.0915i	1.52965	+	1.11135i	0.573210	+	0.819408i	$0.305698\pi$
$942$		0			0
$943$	−3.09017	−	9.51057i	−0.100630	−	0.309707i
$944$	−9.70820	+	7.05342i	−0.315975	+	0.229569i
$945$	9.00000			0.292770
$946$		0			0
$947$	5.00000			0.162478			0.0812391	−	0.996695i	$-0.474112\pi$
$947$	5.00000			0.162478			0.0812391	+	0.996695i	$0.474112\pi$
$948$	29.1246	−	21.1603i	0.945923	−	0.687254i
$949$	−12.3607	−	38.0423i	−0.401245	−	1.23490i
$950$		0			0
$951$	21.8435	+	15.8702i	0.708323	+	0.514627i
$952$		0			0
$953$	−13.5967	+	41.8465i	−0.440442	+	1.35554i	0.446964	+	0.894552i	$0.352505\pi$
$953$	−13.5967	+	41.8465i	−0.440442	+	1.35554i	−0.887406	+	0.460989i	$0.847495\pi$
$954$		0			0
$955$	4.04508	−	2.93893i	0.130896	−	0.0951014i
$956$	8.00000			0.258738
$957$		0			0
$958$		0			0
$959$	2.42705	−	1.76336i	0.0783736	−	0.0569417i
$960$	−7.41641	−	22.8254i	−0.239364	−	0.736685i
$961$	−9.27051	+	28.5317i	−0.299049	+	0.920377i
$962$		0			0
$963$	−48.5410	−	35.2671i	−1.56421	−	1.13647i
$964$	−7.41641	+	22.8254i	−0.238866	+	0.735155i
$965$	4.32624	+	13.3148i	0.139267	+	0.428618i
$966$		0			0
$967$	34.0000			1.09337			0.546683	−	0.837340i	$-0.315890\pi$
$967$	34.0000			1.09337			0.546683	+	0.837340i	$0.315890\pi$
$968$		0			0
$969$	36.0000			1.15649
$970$		0			0
$971$	8.96149	+	27.5806i	0.287588	+	0.885105i	0.985611	+	0.169029i	$0.0540633\pi$
$971$	8.96149	+	27.5806i	0.287588	+	0.885105i	−0.698023	+	0.716075i	$0.745937\pi$
$972$		0			0
$973$	−8.09017	−	5.87785i	−0.259359	−	0.188435i
$974$		0			0
$975$	14.8328	−	45.6507i	0.475030	−	1.46199i
$976$	2.47214	+	7.60845i	0.0791311	+	0.243541i
$977$	25.0795	−	18.2213i	0.802365	−	0.582952i	−0.109242	−	0.994015i	$-0.534842\pi$
$977$	25.0795	−	18.2213i	0.802365	−	0.582952i	0.911607	+	0.411063i	$0.134842\pi$
$978$		0			0
$979$		0			0
$980$	2.00000			0.0638877
$981$	19.4164	−	14.1068i	0.619918	−	0.450397i
$982$		0			0
$983$	−8.34346	+	25.6785i	−0.266115	+	0.819018i	0.725319	+	0.688412i	$0.241692\pi$
$983$	−8.34346	+	25.6785i	−0.266115	+	0.819018i	−0.991434	+	0.130605i	$0.958308\pi$
$984$		0			0
$985$	−14.5623	−	10.5801i	−0.463994	−	0.337111i
$986$		0			0
$987$	−7.41641	−	22.8254i	−0.236067	−	0.726539i
$988$	38.8328	−	28.2137i	1.23544	−	0.897597i
$989$	−40.0000			−1.27193
$990$		0			0
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$		0			0
$993$	15.7599	+	48.5039i	0.500124	+	1.53922i
$994$		0			0
$995$	−6.47214	−	4.70228i	−0.205181	−	0.149072i
$996$	58.2492	+	42.3205i	1.84570	+	1.34098i
$997$	3.70820	−	11.4127i	0.117440	−	0.361443i	−0.875008	−	0.484108i	$-0.839144\pi$
$997$	3.70820	−	11.4127i	0.117440	−	0.361443i	0.992448	+	0.122665i	$0.0391441\pi$
$998$		0			0
$999$	−36.4058	+	26.4503i	−1.15183	+	0.836852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.h.729.1		4
11.2	odd	10		77.2.a.a.1.1	✓	1
11.3	even	5	inner	847.2.f.h.148.1		4
11.4	even	5	inner	847.2.f.h.323.1		4
11.5	even	5	inner	847.2.f.h.372.1		4
11.6	odd	10		847.2.f.i.372.1		4
11.7	odd	10		847.2.f.i.323.1		4
11.8	odd	10		847.2.f.i.148.1		4
11.9	even	5		847.2.a.b.1.1		1
11.10	odd	2		847.2.f.i.729.1		4
33.2	even	10		693.2.a.c.1.1		1
33.20	odd	10		7623.2.a.j.1.1		1
44.35	even	10		1232.2.a.l.1.1		1
55.2	even	20		1925.2.b.e.1849.2		2
55.13	even	20		1925.2.b.e.1849.1		2
55.24	odd	10		1925.2.a.h.1.1		1
77.2	odd	30		539.2.e.f.67.1		2
77.13	even	10		539.2.a.c.1.1		1
77.20	odd	10		5929.2.a.f.1.1		1
77.24	even	30		539.2.e.c.177.1		2
77.46	odd	30		539.2.e.f.177.1		2
77.68	even	30		539.2.e.c.67.1		2
88.13	odd	10		4928.2.a.bj.1.1		1
88.35	even	10		4928.2.a.a.1.1		1
231.167	odd	10		4851.2.a.j.1.1		1
308.167	odd	10		8624.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.a.1.1	✓	1	11.2	odd	10
539.2.a.c.1.1		1	77.13	even	10
539.2.e.c.67.1		2	77.68	even	30
539.2.e.c.177.1		2	77.24	even	30
539.2.e.f.67.1		2	77.2	odd	30
539.2.e.f.177.1		2	77.46	odd	30
693.2.a.c.1.1		1	33.2	even	10
847.2.a.b.1.1		1	11.9	even	5
847.2.f.h.148.1		4	11.3	even	5	inner
847.2.f.h.323.1		4	11.4	even	5	inner
847.2.f.h.372.1		4	11.5	even	5	inner
847.2.f.h.729.1		4	1.1	even	1	trivial
847.2.f.i.148.1		4	11.8	odd	10
847.2.f.i.323.1		4	11.7	odd	10
847.2.f.i.372.1		4	11.6	odd	10
847.2.f.i.729.1		4	11.10	odd	2
1232.2.a.l.1.1		1	44.35	even	10
1925.2.a.h.1.1		1	55.24	odd	10
1925.2.b.e.1849.1		2	55.13	even	20
1925.2.b.e.1849.2		2	55.2	even	20
4851.2.a.j.1.1		1	231.167	odd	10
4928.2.a.a.1.1		1	88.35	even	10
4928.2.a.bj.1.1		1	88.13	odd	10
5929.2.a.f.1.1		1	77.20	odd	10
7623.2.a.j.1.1		1	33.20	odd	10
8624.2.a.a.1.1		1	308.167	odd	10

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.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.927051 - 2.85317i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-4.85410 + 3.52671i) q^{9} +O(q^{10})\)	\(q+(-0.927051 - 2.85317i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-4.85410 + 3.52671i) q^{9} +6.00000 q^{12} +(-3.23607 + 2.35114i) q^{13} +(0.927051 - 2.85317i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(1.61803 + 1.17557i) q^{17} +(1.85410 + 5.70634i) q^{19} +(-1.61803 + 1.17557i) q^{20} -3.00000 q^{21} -5.00000 q^{23} +(-1.23607 - 3.80423i) q^{25} +(7.28115 + 5.29007i) q^{27} +(1.61803 + 1.17557i) q^{28} +(-3.09017 + 9.51057i) q^{29} +(-0.809017 + 0.587785i) q^{31} +(0.809017 - 0.587785i) q^{35} +(-3.70820 - 11.4127i) q^{36} +(-1.54508 + 4.75528i) q^{37} +(9.70820 + 7.05342i) q^{39} +(0.618034 + 1.90211i) q^{41} +8.00000 q^{43} -6.00000 q^{45} +(2.47214 + 7.60845i) q^{47} +(-3.70820 + 11.4127i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.85410 - 5.70634i) q^{51} +(-2.47214 - 7.60845i) q^{52} +(4.85410 - 3.52671i) q^{53} +(14.5623 - 10.5801i) q^{57} +(0.927051 - 2.85317i) q^{59} +(4.85410 + 3.52671i) q^{60} +(-1.61803 - 1.17557i) q^{61} +(1.85410 + 5.70634i) q^{63} +(6.47214 - 4.70228i) q^{64} -4.00000 q^{65} -3.00000 q^{67} +(-3.23607 + 2.35114i) q^{68} +(4.63525 + 14.2658i) q^{69} +(-0.809017 - 0.587785i) q^{71} +(-3.09017 + 9.51057i) q^{73} +(-9.70820 + 7.05342i) q^{75} -12.0000 q^{76} +(4.85410 - 3.52671i) q^{79} +(-1.23607 - 3.80423i) q^{80} +(2.78115 - 8.55951i) q^{81} +(9.70820 + 7.05342i) q^{83} +(1.85410 - 5.70634i) q^{84} +(0.618034 + 1.90211i) q^{85} +30.0000 q^{87} -15.0000 q^{89} +(1.23607 + 3.80423i) q^{91} +(3.09017 - 9.51057i) q^{92} +(2.42705 + 1.76336i) q^{93} +(-1.85410 + 5.70634i) q^{95} +(4.04508 - 2.93893i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} + 2 q^{4} + q^{5} - q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 3 * q^3 + 2 * q^4 + q^5 - q^7 - 6 * q^9	\( 4 q + 3 q^{3} + 2 q^{4} + q^{5} - q^{7} - 6 q^{9} + 24 q^{12} - 4 q^{13} - 3 q^{15} - 4 q^{16} + 2 q^{17} - 6 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{23} + 4 q^{25} + 9 q^{27} + 2 q^{28} + 10 q^{29} - q^{31} + q^{35} + 12 q^{36} + 5 q^{37} + 12 q^{39} - 2 q^{41} + 32 q^{43} - 24 q^{45} - 8 q^{47} + 12 q^{48} - q^{49} - 6 q^{51} + 8 q^{52} + 6 q^{53} + 18 q^{57} - 3 q^{59} + 6 q^{60} - 2 q^{61} - 6 q^{63} + 8 q^{64} - 16 q^{65} - 12 q^{67} - 4 q^{68} - 15 q^{69} - q^{71} + 10 q^{73} - 12 q^{75} - 48 q^{76} + 6 q^{79} + 4 q^{80} - 9 q^{81} + 12 q^{83} - 6 q^{84} - 2 q^{85} + 120 q^{87} - 60 q^{89} - 4 q^{91} - 10 q^{92} + 3 q^{93} + 6 q^{95} + 5 q^{97}+O(q^{100}) \) 4 * q + 3 * q^3 + 2 * q^4 + q^5 - q^7 - 6 * q^9 + 24 * q^12 - 4 * q^13 - 3 * q^15 - 4 * q^16 + 2 * q^17 - 6 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^23 + 4 * q^25 + 9 * q^27 + 2 * q^28 + 10 * q^29 - q^31 + q^35 + 12 * q^36 + 5 * q^37 + 12 * q^39 - 2 * q^41 + 32 * q^43 - 24 * q^45 - 8 * q^47 + 12 * q^48 - q^49 - 6 * q^51 + 8 * q^52 + 6 * q^53 + 18 * q^57 - 3 * q^59 + 6 * q^60 - 2 * q^61 - 6 * q^63 + 8 * q^64 - 16 * q^65 - 12 * q^67 - 4 * q^68 - 15 * q^69 - q^71 + 10 * q^73 - 12 * q^75 - 48 * q^76 + 6 * q^79 + 4 * q^80 - 9 * q^81 + 12 * q^83 - 6 * q^84 - 2 * q^85 + 120 * q^87 - 60 * q^89 - 4 * q^91 - 10 * q^92 + 3 * q^93 + 6 * q^95 + 5 * q^97

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