LMFDB - Embedded newform 1386.2.bu.b.827.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			827.5
Character	$\chi$	$=$	1386.827
Dual form			1386.2.bu.b.1205.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.678594 + 0.220489i) q^{5} +(0.587785 - 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.678594 + 0.220489i) q^{5} +(0.587785 - 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} -0.713516i q^{10} +(2.13750 - 2.53596i) q^{11} +(-2.85938 - 0.929069i) q^{13} +(0.587785 + 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(1.78526 + 5.49448i) q^{17} +(-3.17850 - 4.37483i) q^{19} +(0.678594 + 0.220489i) q^{20} +(1.75132 + 2.81654i) q^{22} -1.21867i q^{23} +(-3.63321 + 2.63968i) q^{25} +(1.76719 - 2.43233i) q^{26} +(-0.951057 + 0.309017i) q^{28} +(-3.65547 - 2.65585i) q^{29} +(0.763965 - 2.35124i) q^{31} -1.00000 q^{32} -5.77723 q^{34} +(-0.220489 + 0.678594i) q^{35} +(-8.85087 - 6.43054i) q^{37} +(5.14292 - 1.67104i) q^{38} +(-0.419394 + 0.577247i) q^{40} +(1.05885 - 0.769297i) q^{41} -11.1814i q^{43} +(-3.21987 + 0.795244i) q^{44} +(1.15903 + 0.376590i) q^{46} +(5.21375 + 7.17611i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-1.38776 - 4.27109i) q^{50} +(1.76719 + 2.43233i) q^{52} +(-7.54739 - 2.45230i) q^{53} +(-0.891344 + 2.19218i) q^{55} -1.00000i q^{56} +(3.65547 - 2.65585i) q^{58} +(2.51610 - 3.46311i) q^{59} +(11.8885 - 3.86282i) q^{61} +(2.00009 + 1.45315i) q^{62} +(0.309017 - 0.951057i) q^{64} +2.14521 q^{65} -14.4081 q^{67} +(1.78526 - 5.49448i) q^{68} +(-0.577247 - 0.419394i) q^{70} +(8.42572 - 2.73768i) q^{71} +(-4.32183 + 5.94849i) q^{73} +(8.85087 - 6.43054i) q^{74} +5.40759i q^{76} +(-0.795244 - 3.21987i) q^{77} +(7.16894 + 2.32933i) q^{79} +(-0.419394 - 0.577247i) q^{80} +(0.404444 + 1.24475i) q^{82} +(-4.54956 - 14.0021i) q^{83} +(-2.42294 - 3.33489i) q^{85} +(10.6341 + 3.45524i) q^{86} +(0.238674 - 3.30803i) q^{88} -11.3121i q^{89} +(-2.43233 + 1.76719i) q^{91} +(-0.716317 + 0.985926i) q^{92} +(-8.43602 + 2.74103i) q^{94} +(3.12151 + 2.26791i) q^{95} +(5.26368 - 16.2000i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.678594	+	0.220489i	−0.303476	+	0.0986055i	−0.456797	−	0.889571i	$-0.651003\pi$
$5$	−0.678594	+	0.220489i	−0.303476	+	0.0986055i	0.153320	+	0.988177i	$0.451003\pi$
$6$		0			0
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$		0			0
$10$		−	0.713516i		−	0.225634i
$11$	2.13750	−	2.53596i	0.644480	−	0.764621i
$11$	2.13750	−	2.53596i	0.644480	−	0.764621i
$12$		0			0
$13$	−2.85938	−	0.929069i	−0.793049	−	0.257677i	−0.115647	−	0.993290i	$-0.536894\pi$
$13$	−2.85938	−	0.929069i	−0.793049	−	0.257677i	−0.677402	+	0.735613i	$0.736894\pi$
$14$	0.587785	+	0.809017i	0.157092	+	0.216219i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.78526	+	5.49448i	0.432990	+	1.33261i	0.895132	+	0.445800i	$0.147081\pi$
$17$	1.78526	+	5.49448i	0.432990	+	1.33261i	−0.462142	+	0.886806i	$0.652919\pi$
$18$		0			0
$19$	−3.17850	−	4.37483i	−0.729198	−	1.00366i	−0.999168	−	0.0407865i	$-0.987014\pi$
$19$	−3.17850	−	4.37483i	−0.729198	−	1.00366i	0.269970	−	0.962869i	$-0.412986\pi$
$20$	0.678594	+	0.220489i	0.151738	+	0.0493027i
$21$		0			0
$22$	1.75132	+	2.81654i	0.373382	+	0.600488i
$23$		−	1.21867i		−	0.254111i	−0.991896	−	0.127055i	$-0.959447\pi$
$23$		−	1.21867i		−	0.254111i	0.991896	−	0.127055i	$-0.0405526\pi$
$24$		0			0
$25$	−3.63321	+	2.63968i	−0.726642	+	0.527936i
$26$	1.76719	−	2.43233i	0.346575	−	0.477020i
$27$		0			0
$28$	−0.951057	+	0.309017i	−0.179733	+	0.0583987i
$29$	−3.65547	−	2.65585i	−0.678803	−	0.493179i	0.194157	−	0.980970i	$-0.437803\pi$
$29$	−3.65547	−	2.65585i	−0.678803	−	0.493179i	−0.872960	+	0.487791i	$0.837803\pi$
$30$		0			0
$31$	0.763965	−	2.35124i	0.137212	−	0.422296i	−0.858715	−	0.512453i	$-0.828737\pi$
$31$	0.763965	−	2.35124i	0.137212	−	0.422296i	0.995928	+	0.0901572i	$0.0287369\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−5.77723			−0.990787
$35$	−0.220489	+	0.678594i	−0.0372694	+	0.114703i
$36$		0			0
$37$	−8.85087	−	6.43054i	−1.45507	−	1.05717i	−0.984612	−	0.174753i	$-0.944087\pi$
$37$	−8.85087	−	6.43054i	−1.45507	−	1.05717i	−0.470462	−	0.882420i	$-0.655913\pi$
$38$	5.14292	−	1.67104i	0.834292	−	0.271078i
$39$		0			0
$40$	−0.419394	+	0.577247i	−0.0663120	+	0.0912707i
$41$	1.05885	−	0.769297i	0.165364	−	0.120144i	−0.502025	−	0.864853i	$-0.667412\pi$
$41$	1.05885	−	0.769297i	0.165364	−	0.120144i	0.667390	+	0.744709i	$0.267412\pi$
$42$		0			0
$43$		−	11.1814i		−	1.70514i	−0.522610	−	0.852572i	$-0.675041\pi$
$43$		−	11.1814i		−	1.70514i	0.522610	−	0.852572i	$-0.324959\pi$
$44$	−3.21987	+	0.795244i	−0.485414	+	0.119888i
$45$		0			0
$46$	1.15903	+	0.376590i	0.170889	+	0.0555252i
$47$	5.21375	+	7.17611i	0.760503	+	1.04674i	0.997172	+	0.0751527i	$0.0239444\pi$
$47$	5.21375	+	7.17611i	0.760503	+	1.04674i	−0.236669	+	0.971590i	$0.576056\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$	−1.38776	−	4.27109i	−0.196259	−	0.604024i
$51$		0			0
$52$	1.76719	+	2.43233i	0.245066	+	0.337304i
$53$	−7.54739	−	2.45230i	−1.03671	−	0.336849i	−0.259273	−	0.965804i	$-0.583483\pi$
$53$	−7.54739	−	2.45230i	−1.03671	−	0.336849i	−0.777442	+	0.628955i	$0.783483\pi$
$54$		0			0
$55$	−0.891344	+	2.19218i	−0.120189	+	0.295594i
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	3.65547	−	2.65585i	0.479986	−	0.348731i
$59$	2.51610	−	3.46311i	0.327568	−	0.450859i	−0.613191	−	0.789935i	$-0.710114\pi$
$59$	2.51610	−	3.46311i	0.327568	−	0.450859i	0.940759	+	0.339076i	$0.110114\pi$
$60$		0			0
$61$	11.8885	−	3.86282i	1.52217	−	0.494584i	0.575781	−	0.817604i	$-0.304698\pi$
$61$	11.8885	−	3.86282i	1.52217	−	0.494584i	0.946392	+	0.323020i	$0.104698\pi$
$62$	2.00009	+	1.45315i	0.254011	+	0.184550i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	2.14521			0.266080
$66$		0			0
$67$	−14.4081			−1.76022			−0.880112	−	0.474766i	$-0.842533\pi$
$67$	−14.4081			−1.76022			−0.880112	+	0.474766i	$0.842533\pi$
$68$	1.78526	−	5.49448i	0.216495	−	0.666303i
$69$		0			0
$70$	−0.577247	−	0.419394i	−0.0689942	−	0.0501272i
$71$	8.42572	−	2.73768i	0.999949	−	0.324903i	0.237104	−	0.971484i	$-0.423802\pi$
$71$	8.42572	−	2.73768i	0.999949	−	0.324903i	0.762845	+	0.646581i	$0.223802\pi$
$72$		0			0
$73$	−4.32183	+	5.94849i	−0.505832	+	0.696219i	−0.983210	−	0.182480i	$-0.941588\pi$
$73$	−4.32183	+	5.94849i	−0.505832	+	0.696219i	0.477377	+	0.878698i	$0.341588\pi$
$74$	8.85087	−	6.43054i	1.02889	−	0.747535i
$75$		0			0
$76$			5.40759i			0.620293i
$77$	−0.795244	−	3.21987i	−0.0906265	−	0.366939i
$78$		0			0
$79$	7.16894	+	2.32933i	0.806569	+	0.262070i	0.683144	−	0.730284i	$-0.260612\pi$
$79$	7.16894	+	2.32933i	0.806569	+	0.262070i	0.123425	+	0.992354i	$0.460612\pi$
$80$	−0.419394	−	0.577247i	−0.0468897	−	0.0645381i
$81$		0			0
$82$	0.404444	+	1.24475i	0.0446633	+	0.137460i
$83$	−4.54956	−	14.0021i	−0.499379	−	1.53693i	−0.810019	−	0.586404i	$-0.800543\pi$
$83$	−4.54956	−	14.0021i	−0.499379	−	1.53693i	0.310640	−	0.950528i	$-0.399457\pi$
$84$		0			0
$85$	−2.42294	−	3.33489i	−0.262805	−	0.361719i
$86$	10.6341	+	3.45524i	1.14671	+	0.372588i
$87$		0			0
$88$	0.238674	−	3.30803i	0.0254427	−	0.352637i
$89$		−	11.3121i		−	1.19908i	−0.800343	−	0.599542i	$-0.795349\pi$
$89$		−	11.3121i		−	1.19908i	0.800343	−	0.599542i	$-0.204651\pi$
$90$		0			0
$91$	−2.43233	+	1.76719i	−0.254978	+	0.185252i
$92$	−0.716317	+	0.985926i	−0.0746813	+	0.102790i
$93$		0			0
$94$	−8.43602	+	2.74103i	−0.870109	+	0.282716i
$95$	3.12151	+	2.26791i	0.320260	+	0.232683i
$96$		0			0
$97$	5.26368	−	16.2000i	0.534446	−	1.64486i	−0.210397	−	0.977616i	$-0.567476\pi$
$97$	5.26368	−	16.2000i	0.534446	−	1.64486i	0.744843	−	0.667240i	$-0.232524\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	4.49089			0.449089
$101$	−2.74449	+	8.44667i	−0.273087	+	0.840475i	0.716632	+	0.697451i	$0.245683\pi$
$101$	−2.74449	+	8.44667i	−0.273087	+	0.840475i	−0.989719	+	0.143024i	$0.954317\pi$
$102$		0			0
$103$	0.542167	+	0.393907i	0.0534213	+	0.0388128i	0.614175	−	0.789170i	$-0.289489\pi$
$103$	0.542167	+	0.393907i	0.0534213	+	0.0388128i	−0.560754	+	0.827982i	$0.689489\pi$
$104$	−2.85938	+	0.929069i	−0.280385	+	0.0911027i
$105$		0			0
$106$	4.66455	−	6.42020i	0.453061	−	0.623585i
$107$	3.26469	−	2.37194i	0.315609	−	0.229304i	−0.418690	−	0.908129i	$-0.637511\pi$
$107$	3.26469	−	2.37194i	0.315609	−	0.229304i	0.734300	+	0.678825i	$0.237511\pi$
$108$		0			0
$109$			0.474569i			0.0454555i	0.999742	+	0.0227278i	$0.00723509\pi$
$109$			0.474569i			0.0454555i	−0.999742	+	0.0227278i	$0.992765\pi$
$110$	−1.80945	−	1.52514i	−0.172524	−	0.145416i
$111$		0			0
$112$	0.951057	+	0.309017i	0.0898664	+	0.0291994i
$113$	1.02516	+	1.41101i	0.0964386	+	0.132736i	0.854509	−	0.519436i	$-0.173858\pi$
$113$	1.02516	+	1.41101i	0.0964386	+	0.132736i	−0.758071	+	0.652172i	$0.773858\pi$
$114$		0			0
$115$	0.268703	+	0.826984i	0.0250567	+	0.0771166i
$116$	1.39626	+	4.29726i	0.129640	+	0.398991i
$117$		0			0
$118$	2.51610	+	3.46311i	0.231626	+	0.318806i
$119$	5.49448	+	1.78526i	0.503678	+	0.163655i
$120$		0			0
$121$	−1.86219	−	10.8412i	−0.169290	−	0.985566i
$122$			12.5004i			1.13173i
$123$		0			0
$124$	−2.00009	+	1.45315i	−0.179613	+	0.130497i
$125$	3.98043	−	5.47859i	0.356020	−	0.490020i
$126$		0			0
$127$	−18.6358	+	6.05515i	−1.65366	+	0.537308i	−0.979529	−	0.201302i	$-0.935483\pi$
$127$	−18.6358	+	6.05515i	−1.65366	+	0.537308i	−0.674134	+	0.738609i	$0.735483\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$		0			0
$130$	−0.662906	+	2.04021i	−0.0581407	+	0.178939i
$131$	−12.3704			−1.08081			−0.540403	−	0.841406i	$-0.681728\pi$
$131$	−12.3704			−1.08081			−0.540403	+	0.841406i	$0.681728\pi$
$132$		0			0
$133$	−5.40759			−0.468898
$134$	4.45233	−	13.7029i	0.384623	−	1.18375i
$135$		0			0
$136$	4.67388	+	3.39577i	0.400782	+	0.291185i
$137$	5.80408	−	1.88586i	0.495876	−	0.161120i	−0.0503935	−	0.998729i	$-0.516048\pi$
$137$	5.80408	−	1.88586i	0.495876	−	0.161120i	0.546269	+	0.837610i	$0.316048\pi$
$138$		0			0
$139$	1.94882	−	2.68232i	0.165296	−	0.227511i	−0.718331	−	0.695701i	$-0.755094\pi$
$139$	1.94882	−	2.68232i	0.165296	−	0.227511i	0.883628	+	0.468190i	$0.155094\pi$
$140$	0.577247	−	0.419394i	0.0487862	−	0.0354453i
$141$		0			0
$142$			8.85932i			0.743458i
$143$	−8.46801	+	5.26539i	−0.708130	+	0.440314i
$144$		0			0
$145$	3.06616	+	0.996257i	0.254631	+	0.0827346i
$146$	−4.32183	−	5.94849i	−0.357678	−	0.492301i
$147$		0			0
$148$	3.38073	+	10.4048i	0.277895	+	0.855271i
$149$	5.64833	+	17.3838i	0.462729	+	1.42413i	0.861816	+	0.507221i	$0.169327\pi$
$149$	5.64833	+	17.3838i	0.462729	+	1.42413i	−0.399086	+	0.916913i	$0.630673\pi$
$150$		0			0
$151$	−0.258688	−	0.356054i	−0.0210518	−	0.0289753i	0.798361	−	0.602179i	$-0.205700\pi$
$151$	−0.258688	−	0.356054i	−0.0210518	−	0.0289753i	−0.819413	+	0.573203i	$0.805700\pi$
$152$	−5.14292	−	1.67104i	−0.417146	−	0.135539i
$153$		0			0
$154$	3.30803	+	0.238674i	0.266568	+	0.0192329i
$155$			1.76399i			0.141687i
$156$		0			0
$157$	10.5340	−	7.65339i	0.840704	−	0.610807i	−0.0818631	−	0.996644i	$-0.526087\pi$
$157$	10.5340	−	7.65339i	0.840704	−	0.610807i	0.922567	+	0.385836i	$0.126087\pi$
$158$	−4.43065	+	6.09827i	−0.352484	+	0.485152i
$159$		0			0
$160$	0.678594	−	0.220489i	0.0536476	−	0.0174312i
$161$	−0.985926	−	0.716317i	−0.0777019	−	0.0564537i
$162$		0			0
$163$	−0.558339	+	1.71839i	−0.0437325	+	0.134595i	−0.970539	−	0.240945i	$-0.922543\pi$
$163$	−0.558339	+	1.71839i	−0.0437325	+	0.134595i	0.926806	+	0.375540i	$0.122543\pi$
$164$	−1.30881			−0.102201
$165$		0			0
$166$	14.7227			1.14270
$167$	3.12223	−	9.60924i	0.241606	−	0.743586i	−0.754571	−	0.656219i	$-0.772155\pi$
$167$	3.12223	−	9.60924i	0.241606	−	0.743586i	0.996176	−	0.0873668i	$-0.0278452\pi$
$168$		0			0
$169$	−3.20434	−	2.32809i	−0.246487	−	0.179084i
$170$	3.92040	−	1.27381i	0.300681	−	0.0976971i
$171$		0			0
$172$	−6.57225	+	9.04593i	−0.501129	+	0.689745i
$173$	5.53806	−	4.02363i	0.421051	−	0.305911i	−0.357010	−	0.934101i	$-0.616204\pi$
$173$	5.53806	−	4.02363i	0.421051	−	0.305911i	0.778060	+	0.628189i	$0.216204\pi$
$174$		0			0
$175$			4.49089i			0.339480i
$176$	3.07237	+	1.24923i	0.231588	+	0.0941641i
$177$		0			0
$178$	10.7585	+	3.49564i	0.806383	+	0.262010i
$179$	−7.55337	−	10.3963i	−0.564566	−	0.777058i	0.427332	−	0.904095i	$-0.359453\pi$
$179$	−7.55337	−	10.3963i	−0.564566	−	0.777058i	−0.991898	+	0.127037i	$0.959453\pi$
$180$		0			0
$181$	5.90723	+	18.1806i	0.439081	+	1.35135i	0.888846	+	0.458206i	$0.151508\pi$
$181$	5.90723	+	18.1806i	0.439081	+	1.35135i	−0.449765	+	0.893147i	$0.648492\pi$
$182$	−0.929069	−	2.85938i	−0.0688672	−	0.211951i
$183$		0			0
$184$	−0.716317	−	0.985926i	−0.0528076	−	0.0726835i
$185$	7.42401	+	2.41221i	0.545824	+	0.177349i
$186$		0			0
$187$	17.7498	+	7.21708i	1.29799	+	0.527765i
$188$		−	8.87016i		−	0.646923i
$189$		0			0
$190$	−3.12151	+	2.26791i	−0.226458	+	0.164532i
$191$	−13.1512	+	18.1011i	−0.951588	+	1.30975i	−0.000769242		1.00000i	$0.500245\pi$
$191$	−13.1512	+	18.1011i	−0.951588	+	1.30975i	−0.950819	+	0.309748i	$0.899755\pi$
$192$		0			0
$193$	2.98670	−	0.970439i	0.214988	−	0.0698537i	−0.199543	−	0.979889i	$-0.563946\pi$
$193$	2.98670	−	0.970439i	0.214988	−	0.0698537i	0.414531	+	0.910035i	$0.363946\pi$
$194$	13.7805	+	10.0121i	0.989382	+	0.718828i
$195$		0			0
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	−22.4027			−1.59613			−0.798064	−	0.602573i	$-0.794142\pi$
$197$	−22.4027			−1.59613			−0.798064	+	0.602573i	$0.794142\pi$
$198$		0			0
$199$	2.99700			0.212451			0.106226	−	0.994342i	$-0.466123\pi$
$199$	2.99700			0.212451			0.106226	+	0.994342i	$0.466123\pi$
$200$	−1.38776	+	4.27109i	−0.0981297	+	0.302012i
$201$		0			0
$202$	−7.18517	−	5.22033i	−0.505547	−	0.367301i
$203$	−4.29726	+	1.39626i	−0.301609	+	0.0979985i
$204$		0			0
$205$	−0.548906	+	0.755504i	−0.0383373	+	0.0527667i
$206$	−0.542167	+	0.393907i	−0.0377746	+	0.0274448i
$207$		0			0
$208$		−	3.00653i		−	0.208465i
$209$	−17.8884	−	1.29065i	−1.23737	−	0.0892761i
$210$		0			0
$211$	20.3398	+	6.60879i	1.40025	+	0.454968i	0.909271	−	0.416205i	$-0.136640\pi$
$211$	20.3398	+	6.60879i	1.40025	+	0.454968i	0.490977	+	0.871173i	$0.336640\pi$
$212$	4.66455	+	6.42020i	0.320362	+	0.440941i
$213$		0			0
$214$	1.24700	+	3.83787i	0.0852432	+	0.262352i
$215$	2.46537	+	7.58762i	0.168137	+	0.517471i
$216$		0			0
$217$	−1.45315	−	2.00009i	−0.0986461	−	0.135775i
$218$	−0.451342	−	0.146650i	−0.0305688	−	0.00993239i
$219$		0			0
$220$	2.00964	−	1.24959i	0.135490	−	0.0842476i
$221$		−	17.3694i		−	1.16839i
$222$		0			0
$223$	−4.52226	+	3.28561i	−0.302833	+	0.220021i	−0.728815	−	0.684711i	$-0.759929\pi$
$223$	−4.52226	+	3.28561i	−0.302833	+	0.220021i	0.425982	+	0.904732i	$0.359929\pi$
$224$	−0.587785	+	0.809017i	−0.0392731	+	0.0540547i
$225$		0			0
$226$	−1.65874	+	0.538957i	−0.110338	+	0.0358509i
$227$	23.2800	+	16.9139i	1.54515	+	1.12261i	0.947003	+	0.321225i	$0.104094\pi$
$227$	23.2800	+	16.9139i	1.54515	+	1.12261i	0.598143	+	0.801390i	$0.295906\pi$
$228$		0			0
$229$	6.96337	−	21.4311i	0.460153	−	1.41620i	−0.404825	−	0.914394i	$-0.632668\pi$
$229$	6.96337	−	21.4311i	0.460153	−	1.41620i	0.864978	−	0.501810i	$-0.167332\pi$
$230$	−0.869542			−0.0573359
$231$		0			0
$232$	−4.51841			−0.296648
$233$	−5.35127	+	16.4695i	−0.350573	+	1.07895i	0.607959	+	0.793969i	$0.291989\pi$
$233$	−5.35127	+	16.4695i	−0.350573	+	1.07895i	−0.958532	+	0.284985i	$0.908011\pi$
$234$		0			0
$235$	−5.12027	−	3.72009i	−0.334010	−	0.242672i
$236$	−4.07114	+	1.32279i	−0.265008	+	0.0861064i
$237$		0			0
$238$	−3.39577	+	4.67388i	−0.220115	+	0.302963i
$239$	5.78293	−	4.20155i	0.374067	−	0.271775i	−0.384829	−	0.922988i	$-0.625739\pi$
$239$	5.78293	−	4.20155i	0.374067	−	0.271775i	0.758895	+	0.651213i	$0.225739\pi$
$240$		0			0
$241$		−	21.8082i		−	1.40479i	−0.711787	−	0.702395i	$-0.752114\pi$
$241$		−	21.8082i		−	1.40479i	0.711787	−	0.702395i	$-0.247886\pi$
$242$	10.8861	+	1.57908i	0.699783	+	0.101507i
$243$		0			0
$244$	−11.8885	−	3.86282i	−0.761086	−	0.247292i
$245$	0.419394	+	0.577247i	0.0267941	+	0.0368789i
$246$		0			0
$247$	5.02402	+	15.4624i	0.319671	+	0.983846i
$248$	−0.763965	−	2.35124i	−0.0485118	−	0.149304i
$249$		0			0
$250$	3.98043	+	5.47859i	0.251744	+	0.346496i
$251$	−11.3553	−	3.68955i	−0.716738	−	0.232882i	−0.0721298	−	0.997395i	$-0.522980\pi$
$251$	−11.3553	−	3.68955i	−0.716738	−	0.232882i	−0.644608	+	0.764513i	$0.722980\pi$
$252$		0			0
$253$	−3.09050	−	2.60491i	−0.194298	−	0.163769i
$254$		−	19.5949i		−	1.22949i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−10.4858	+	14.4324i	−0.654085	+	0.900271i	−0.999268	−	0.0382646i	$-0.987817\pi$
$257$	−10.4858	+	14.4324i	−0.654085	+	0.900271i	0.345183	+	0.938536i	$0.387817\pi$
$258$		0			0
$259$	−10.4048	+	3.38073i	−0.646524	+	0.210069i
$260$	−1.73551	−	1.26092i	−0.107632	−	0.0781990i
$261$		0			0
$262$	3.82266	−	11.7650i	0.236165	−	0.726841i
$263$	−9.67113			−0.596347			−0.298174	−	0.954512i	$-0.596377\pi$
$263$	−9.67113			−0.596347			−0.298174	+	0.954512i	$0.596377\pi$
$264$		0			0
$265$	5.66232			0.347834
$266$	1.67104	−	5.14292i	0.102458	−	0.315333i
$267$		0			0
$268$	11.6564	+	8.46884i	0.712026	+	0.517317i
$269$	−30.3733	+	9.86888i	−1.85189	+	0.601716i	−0.855405	+	0.517960i	$0.826692\pi$
$269$	−30.3733	+	9.86888i	−1.85189	+	0.601716i	−0.996486	+	0.0837564i	$0.973308\pi$
$270$		0			0
$271$	−6.55002	+	9.01533i	−0.397885	+	0.547642i	−0.960212	−	0.279273i	$-0.909906\pi$
$271$	−6.55002	+	9.01533i	−0.397885	+	0.547642i	0.562326	+	0.826915i	$0.309906\pi$
$272$	−4.67388	+	3.39577i	−0.283396	+	0.205899i
$273$		0			0
$274$			6.10277i			0.368682i
$275$	−1.07186	+	14.8560i	−0.0646355	+	0.895850i
$276$		0			0
$277$	11.4169	+	3.70958i	0.685975	+	0.222887i	0.631209	−	0.775612i	$-0.282559\pi$
$277$	11.4169	+	3.70958i	0.685975	+	0.222887i	0.0547655	+	0.998499i	$0.482559\pi$
$278$	1.94882	+	2.68232i	0.116882	+	0.160875i
$279$		0			0
$280$	0.220489	+	0.678594i	0.0131767	+	0.0405538i
$281$	−5.04700	−	15.5331i	−0.301079	−	0.926625i	−0.981111	−	0.193443i	$-0.938034\pi$
$281$	−5.04700	−	15.5331i	−0.301079	−	0.926625i	0.680033	−	0.733182i	$-0.261966\pi$
$282$		0			0
$283$	16.7925	+	23.1128i	0.998208	+	1.37392i	0.926419	+	0.376495i	$0.122871\pi$
$283$	16.7925	+	23.1128i	0.998208	+	1.37392i	0.0717891	+	0.997420i	$0.477129\pi$
$284$	−8.42572	−	2.73768i	−0.499974	−	0.162452i
$285$		0			0
$286$	−2.39093	−	9.68065i	−0.141378	−	0.572429i
$287$		−	1.30881i		−	0.0772564i
$288$		0			0
$289$	−13.2488	+	9.62582i	−0.779342	+	0.566225i
$290$	−1.89499	+	2.60823i	−0.111278	+	0.153161i
$291$		0			0
$292$	6.99287	−	2.27212i	0.409227	−	0.132966i
$293$	1.62651	+	1.18173i	0.0950217	+	0.0690373i	0.634282	−	0.773102i	$-0.281296\pi$
$293$	1.62651	+	1.18173i	0.0950217	+	0.0690373i	−0.539260	+	0.842139i	$0.681296\pi$
$294$		0			0
$295$	−0.943833	+	2.90482i	−0.0549521	+	0.169125i
$296$	−10.9403			−0.635891
$297$		0			0
$298$	−18.2784			−1.05884
$299$	−1.13223	+	3.48465i	−0.0654786	+	0.201522i
$300$		0			0
$301$	−9.04593	−	6.57225i	−0.521398	−	0.378818i
$302$	0.418566	−	0.136000i	0.0240858	−	0.00782595i
$303$		0			0
$304$	3.17850	−	4.37483i	0.182300	−	0.250914i
$305$	−7.21579	+	5.24258i	−0.413175	+	0.300189i
$306$		0			0
$307$			1.61585i			0.0922212i	0.998936	+	0.0461106i	$0.0146827\pi$
$307$			1.61585i			0.0922212i	−0.998936	+	0.0461106i	$0.985317\pi$
$308$	−1.24923	+	3.07237i	−0.0711814	+	0.175064i
$309$		0			0
$310$	−1.67765	−	0.545101i	−0.0952841	−	0.0309597i
$311$	16.4986	+	22.7084i	0.935552	+	1.28768i	0.957654	+	0.287922i	$0.0929643\pi$
$311$	16.4986	+	22.7084i	0.935552	+	1.28768i	−0.0221015	+	0.999756i	$0.507036\pi$
$312$		0			0
$313$	−6.49388	−	19.9861i	−0.367056	−	1.12968i	−0.948684	−	0.316227i	$-0.897584\pi$
$313$	−6.49388	−	19.9861i	−0.367056	−	1.12968i	0.581628	−	0.813455i	$-0.302416\pi$
$314$	4.02363	+	12.3835i	0.227066	+	0.698839i
$315$		0			0
$316$	−4.43065	−	6.09827i	−0.249244	−	0.343054i
$317$	−16.2376	−	5.27590i	−0.911992	−	0.296324i	−0.184814	−	0.982773i	$-0.559168\pi$
$317$	−16.2376	−	5.27590i	−0.911992	−	0.296324i	−0.727178	+	0.686449i	$0.759168\pi$
$318$		0			0
$319$	−14.5487	+	3.59324i	−0.814571	+	0.201183i
$320$			0.713516i			0.0398868i
$321$		0			0
$322$	0.985926	−	0.716317i	0.0549435	−	0.0399188i
$323$	18.3629	−	25.2744i	1.02174	−	1.40631i
$324$		0			0
$325$	12.8412	−	4.17235i	0.712300	−	0.231440i
$326$	−1.46175	−	1.06202i	−0.0809589	−	0.0588201i
$327$		0			0
$328$	0.404444	−	1.24475i	0.0223317	−	0.0687298i
$329$	8.87016			0.489028
$330$		0			0
$331$	−6.13700			−0.337320			−0.168660	−	0.985674i	$-0.553944\pi$
$331$	−6.13700			−0.337320			−0.168660	+	0.985674i	$0.553944\pi$
$332$	−4.54956	+	14.0021i	−0.249690	+	0.768466i
$333$		0			0
$334$	8.17411	+	5.93884i	0.447268	+	0.324959i
$335$	9.77722	−	3.17681i	0.534187	−	0.173568i
$336$		0			0
$337$	−0.280897	+	0.386621i	−0.0153014	+	0.0210606i	−0.816599	−	0.577205i	$-0.804143\pi$
$337$	−0.280897	+	0.386621i	−0.0153014	+	0.0210606i	0.801298	+	0.598266i	$0.204143\pi$
$338$	3.20434	−	2.32809i	0.174293	−	0.126631i
$339$		0			0
$340$			4.12215i			0.223555i
$341$	−4.32968	−	6.96317i	−0.234465	−	0.377077i
$342$		0			0
$343$	−0.951057	−	0.309017i	−0.0513522	−	0.0166853i
$344$	−6.57225	−	9.04593i	−0.354352	−	0.487724i
$345$		0			0
$346$	2.11535	+	6.51037i	0.113722	+	0.350000i
$347$	8.19002	+	25.2063i	0.439663	+	1.35314i	0.888231	+	0.459396i	$0.151934\pi$
$347$	8.19002	+	25.2063i	0.439663	+	1.35314i	−0.448568	+	0.893749i	$0.648066\pi$
$348$		0			0
$349$	10.8861	+	14.9834i	0.582718	+	0.802042i	0.993990	−	0.109470i	$-0.0349155\pi$
$349$	10.8861	+	14.9834i	0.582718	+	0.802042i	−0.411272	+	0.911513i	$0.634915\pi$
$350$	−4.27109	−	1.38776i	−0.228300	−	0.0741790i
$351$		0			0
$352$	−2.13750	+	2.53596i	−0.113929	+	0.135167i
$353$			15.7076i			0.836031i	0.908440	+	0.418015i	$0.137274\pi$
$353$			15.7076i			0.836031i	−0.908440	+	0.418015i	$0.862726\pi$
$354$		0			0
$355$	−5.11401	+	3.71555i	−0.271424	+	0.197201i
$356$	−6.64911	+	9.15172i	−0.352402	+	0.485040i
$357$		0			0
$358$	12.2216	−	3.97104i	0.645932	−	0.209876i
$359$	9.33172	+	6.77989i	0.492509	+	0.357829i	0.806148	−	0.591713i	$-0.201548\pi$
$359$	9.33172	+	6.77989i	0.492509	+	0.357829i	−0.313639	+	0.949542i	$0.601548\pi$
$360$		0			0
$361$	−3.16496	+	9.74075i	−0.166577	+	0.512671i
$362$	−19.1162			−1.00473
$363$		0			0
$364$	3.00653			0.157585
$365$	1.62120	−	4.98953i	0.0848573	−	0.261164i
$366$		0			0
$367$	14.8105	+	10.7605i	0.773104	+	0.561693i	0.902902	−	0.429847i	$-0.141433\pi$
$367$	14.8105	+	10.7605i	0.773104	+	0.561693i	−0.129797	+	0.991541i	$0.541433\pi$
$368$	1.15903	−	0.376590i	0.0604184	−	0.0196311i
$369$		0			0
$370$	−4.58829	+	6.31524i	−0.238534	+	0.328314i
$371$	−6.42020	+	4.66455i	−0.333320	+	0.242171i
$372$		0			0
$373$		−	8.25765i		−	0.427565i	−0.976881	−	0.213783i	$-0.931422\pi$
$373$		−	8.25765i		−	0.427565i	0.976881	−	0.213783i	$-0.0685784\pi$
$374$	−12.3488	+	14.6508i	−0.638543	+	0.757577i
$375$		0			0
$376$	8.43602	+	2.74103i	0.435055	+	0.141358i
$377$	7.98490	+	10.9903i	0.411243	+	0.566028i
$378$		0			0
$379$	−3.68900	−	11.3536i	−0.189491	−	0.583194i	0.810506	−	0.585731i	$-0.199192\pi$
$379$	−3.68900	−	11.3536i	−0.189491	−	0.583194i	−0.999997	+	0.00253702i	$0.999192\pi$
$380$	−1.19231	−	3.66956i	−0.0611643	−	0.188244i
$381$		0			0
$382$	−13.1512	−	18.1011i	−0.672874	−	0.926132i
$383$	−11.3301	−	3.68138i	−0.578942	−	0.188110i	0.00488446	−	0.999988i	$-0.498445\pi$
$383$	−11.3301	−	3.68138i	−0.578942	−	0.188110i	−0.583827	+	0.811878i	$0.698445\pi$
$384$		0			0
$385$	1.24959	+	2.00964i	0.0636852	+	0.102421i
$386$			3.14041i			0.159842i
$387$		0			0
$388$	−13.7805	+	10.0121i	−0.699599	+	0.508288i
$389$	9.28357	−	12.7777i	0.470696	−	0.647857i	−0.505988	−	0.862541i	$-0.668872\pi$
$389$	9.28357	−	12.7777i	0.470696	−	0.647857i	0.976684	+	0.214683i	$0.0688720\pi$
$390$		0			0
$391$	6.69596	−	2.17565i	0.338629	−	0.110027i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$		0			0
$394$	6.92282	−	21.3063i	0.348767	−	1.07339i
$395$	−5.37839			−0.270616
$396$		0			0
$397$	−23.3075			−1.16977			−0.584886	−	0.811116i	$-0.698861\pi$
$397$	−23.3075			−1.16977			−0.584886	+	0.811116i	$0.698861\pi$
$398$	−0.926123	+	2.85031i	−0.0464223	+	0.142873i
$399$		0			0
$400$	−3.63321	−	2.63968i	−0.181661	−	0.131984i
$401$	2.26999	−	0.737563i	0.113358	−	0.0368321i	−0.251789	−	0.967782i	$-0.581019\pi$
$401$	2.26999	−	0.737563i	0.113358	−	0.0368321i	0.365147	+	0.930950i	$0.381019\pi$
$402$		0			0
$403$	−4.36893	+	6.01332i	−0.217632	+	0.299545i
$404$	7.18517	−	5.22033i	0.357475	−	0.259721i
$405$		0			0
$406$		−	4.51841i		−	0.224245i
$407$	−35.2263	+	8.70019i	−1.74610	+	0.431253i
$408$		0			0
$409$	22.9285	+	7.44993i	1.13374	+	0.368375i	0.814997	−	0.579465i	$-0.196738\pi$
$409$	22.9285	+	7.44993i	1.13374	+	0.368375i	0.318746	+	0.947840i	$0.396738\pi$
$410$	−0.548906	−	0.755504i	−0.0271085	−	0.0373117i
$411$		0			0
$412$	−0.207089	−	0.637356i	−0.0102026	−	0.0314003i
$413$	−1.32279	−	4.07114i	−0.0650903	−	0.200327i
$414$		0			0
$415$	6.17461	+	8.49862i	0.303100	+	0.417181i
$416$	2.85938	+	0.929069i	0.140193	+	0.0455514i
$417$		0			0
$418$	6.75531	−	16.6141i	0.330413	−	0.812622i
$419$		−	0.111301i		−	0.00543741i	−0.999996	−	0.00271870i	$-0.999135\pi$
$419$		−	0.111301i		−	0.00543741i	0.999996	−	0.00271870i	$-0.000865391\pi$
$420$		0			0
$421$	−17.8734	+	12.9858i	−0.871097	+	0.632889i	−0.930881	−	0.365323i	$-0.880959\pi$
$421$	−17.8734	+	12.9858i	−0.871097	+	0.632889i	0.0597843	+	0.998211i	$0.480959\pi$
$422$	−12.5707	+	17.3020i	−0.611931	+	0.842250i
$423$		0			0
$424$	−7.54739	+	2.45230i	−0.366534	+	0.119094i
$425$	−20.9899	−	15.2501i	−1.01816	−	0.739736i
$426$		0			0
$427$	3.86282	−	11.8885i	0.186935	−	0.575327i
$428$	−4.03538			−0.195057
$429$		0			0
$430$	−7.97809			−0.384738
$431$	8.34102	−	25.6710i	0.401773	−	1.23653i	−0.521787	−	0.853076i	$-0.674735\pi$
$431$	8.34102	−	25.6710i	0.401773	−	1.23653i	0.923560	−	0.383454i	$-0.125265\pi$
$432$		0			0
$433$	−29.3100	−	21.2949i	−1.40855	−	1.02337i	−0.993532	−	0.113556i	$-0.963776\pi$
$433$	−29.3100	−	21.2949i	−1.40855	−	1.02337i	−0.415016	−	0.909814i	$-0.636224\pi$
$434$	2.35124	−	0.763965i	0.112863	−	0.0366715i
$435$		0			0
$436$	0.278945	−	0.383935i	0.0133590	−	0.0183871i
$437$	−5.33149	+	3.87355i	−0.255040	+	0.185297i
$438$		0			0
$439$			6.89662i			0.329158i	0.986364	+	0.164579i	$0.0526265\pi$
$439$			6.89662i			0.329158i	−0.986364	+	0.164579i	$0.947373\pi$
$440$	0.567419	+	2.29743i	0.0270507	+	0.109526i
$441$		0			0
$442$	16.5193	+	5.36745i	0.785743	+	0.255303i
$443$	16.8040	+	23.1288i	0.798384	+	1.09888i	0.993013	+	0.118005i	$0.0376498\pi$
$443$	16.8040	+	23.1288i	0.798384	+	1.09888i	−0.194629	+	0.980877i	$0.562350\pi$
$444$		0			0
$445$	2.49420	+	7.67635i	0.118236	+	0.363894i
$446$	−1.72735	−	5.31623i	−0.0817924	−	0.251731i
$447$		0			0
$448$	−0.587785	−	0.809017i	−0.0277702	−	0.0382225i
$449$	10.8020	+	3.50978i	0.509778	+	0.165637i	0.552601	−	0.833446i	$-0.313635\pi$
$449$	10.8020	+	3.50978i	0.509778	+	0.165637i	−0.0428233	+	0.999083i	$0.513635\pi$
$450$		0			0
$451$	0.312378	−	4.32957i	0.0147093	−	0.203871i
$452$		−	1.74410i		−	0.0820356i
$453$		0			0
$454$	−23.2800	+	16.9139i	−1.09258	+	0.793808i
$455$	1.26092	−	1.73551i	0.0591129	−	0.0813619i
$456$		0			0
$457$	16.9004	−	5.49127i	0.790567	−	0.256871i	0.114221	−	0.993455i	$-0.463563\pi$
$457$	16.9004	−	5.49127i	0.790567	−	0.256871i	0.676345	+	0.736585i	$0.263563\pi$
$458$	18.2303	+	13.2451i	0.851848	+	0.618904i
$459$		0			0
$460$	0.268703	−	0.826984i	0.0125284	−	0.0385583i
$461$	6.69027			0.311597			0.155798	−	0.987789i	$-0.450205\pi$
$461$	6.69027			0.311597			0.155798	+	0.987789i	$0.450205\pi$
$462$		0			0
$463$	−34.9758			−1.62547			−0.812733	−	0.582637i	$-0.802021\pi$
$463$	−34.9758			−1.62547			−0.812733	+	0.582637i	$0.802021\pi$
$464$	1.39626	−	4.29726i	0.0648199	−	0.199495i
$465$		0			0
$466$	−14.0098	−	10.1787i	−0.648991	−	0.471520i
$467$	10.7388	−	3.48924i	0.496932	−	0.161463i	−0.0498192	−	0.998758i	$-0.515865\pi$
$467$	10.7388	−	3.48924i	0.496932	−	0.161463i	0.546751	+	0.837295i	$0.315865\pi$
$468$		0			0
$469$	−8.46884	+	11.6564i	−0.391055	+	0.538241i
$470$	5.12027	−	3.72009i	0.236180	−	0.171595i
$471$		0			0
$472$		−	4.28064i		−	0.197033i
$473$	−28.3555	−	23.9002i	−1.30379	−	1.09893i
$474$		0			0
$475$	23.0963	+	7.50445i	1.05973	+	0.344328i
$476$	−3.39577	−	4.67388i	−0.155645	−	0.214227i
$477$		0			0
$478$	2.20888	+	6.79824i	0.101032	+	0.310944i
$479$	8.09490	+	24.9135i	0.369865	+	1.13833i	0.946878	+	0.321593i	$0.104218\pi$
$479$	8.09490	+	24.9135i	0.369865	+	1.13833i	−0.577012	+	0.816735i	$0.695782\pi$
$480$		0			0
$481$	19.3336	+	26.6104i	0.881536	+	1.21333i
$482$	20.7408	+	6.73911i	0.944720	+	0.306958i
$483$		0			0
$484$	−4.86577	+	9.86531i	−0.221171	+	0.448423i
$485$			12.1538i			0.551874i
$486$		0			0
$487$	−19.0151	+	13.8153i	−0.861655	+	0.626029i	−0.928335	−	0.371746i	$-0.878759\pi$
$487$	−19.0151	+	13.8153i	−0.861655	+	0.626029i	0.0666799	+	0.997774i	$0.478759\pi$
$488$	7.34753	−	10.1130i	0.332607	−	0.457794i
$489$		0			0
$490$	−0.678594	+	0.220489i	−0.0306558	+	0.00996066i
$491$	−8.14729	−	5.91935i	−0.367682	−	0.267137i	0.388567	−	0.921420i	$-0.372970\pi$
$491$	−8.14729	−	5.91935i	−0.367682	−	0.267137i	−0.756249	+	0.654284i	$0.772970\pi$
$492$		0			0
$493$	8.06655	−	24.8263i	0.363299	−	1.11812i
$494$	−16.2581			−0.731486
$495$		0			0
$496$	2.47224			0.111007
$497$	2.73768	−	8.42572i	0.122802	−	0.377945i
$498$		0			0
$499$	−14.8105	−	10.7605i	−0.663011	−	0.481706i	0.204667	−	0.978832i	$-0.434389\pi$
$499$	−14.8105	−	10.7605i	−0.663011	−	0.481706i	−0.867678	+	0.497126i	$0.834389\pi$
$500$	−6.44046	+	2.09263i	−0.288026	+	0.0935854i
$501$		0			0
$502$	7.01794	−	9.65937i	0.313226	−	0.431119i
$503$	16.9278	−	12.2988i	0.754772	−	0.548374i	−0.142530	−	0.989790i	$-0.545524\pi$
$503$	16.9278	−	12.2988i	0.754772	−	0.548374i	0.897302	+	0.441416i	$0.145524\pi$
$504$		0			0
$505$		−	6.33699i		−	0.281992i
$506$	3.43244	−	2.13428i	0.152590	−	0.0948804i
$507$		0			0
$508$	18.6358	+	6.05515i	0.826831	+	0.268654i
$509$	3.22095	+	4.43326i	0.142766	+	0.196501i	0.874412	−	0.485184i	$-0.161247\pi$
$509$	3.22095	+	4.43326i	0.142766	+	0.196501i	−0.731646	+	0.681685i	$0.761247\pi$
$510$		0			0
$511$	2.27212	+	6.99287i	0.100513	+	0.309347i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	−10.4858	−	14.4324i	−0.462508	−	0.636588i
$515$	−0.454763	−	0.147762i	−0.0200393	−	0.00651115i
$516$		0			0
$517$	29.3427	+	2.11707i	1.29049	+	0.0931088i
$518$		−	10.9403i		−	0.480688i
$519$		0			0
$520$	1.73551	−	1.26092i	0.0761071	−	0.0552951i
$521$	−7.75656	+	10.6760i	−0.339821	+	0.467724i	−0.944389	−	0.328830i	$-0.893346\pi$
$521$	−7.75656	+	10.6760i	−0.339821	+	0.467724i	0.604568	+	0.796554i	$0.293346\pi$
$522$		0			0
$523$	12.4708	−	4.05200i	0.545308	−	0.177181i	−0.0233917	−	0.999726i	$-0.507446\pi$
$523$	12.4708	−	4.05200i	0.545308	−	0.177181i	0.568700	+	0.822545i	$0.307446\pi$
$524$	10.0079	+	7.27114i	0.437196	+	0.317641i
$525$		0			0
$526$	2.98854	−	9.19779i	0.130307	−	0.401043i
$527$	14.2827			0.622165
$528$		0			0
$529$	21.5148			0.935428
$530$	−1.74975	+	5.38519i	−0.0760044	+	0.233918i
$531$		0			0
$532$	4.37483	+	3.17850i	0.189673	+	0.137806i
$533$	−3.74238	+	1.21597i	−0.162100	+	0.0526696i
$534$		0			0
$535$	−1.69241	+	2.32941i	−0.0731694	+	0.100709i
$536$	−11.6564	+	8.46884i	−0.503478	+	0.365798i
$537$		0			0
$538$		−	31.9364i		−	1.37687i
$539$	−3.07237	−	1.24923i	−0.132336	−	0.0538081i
$540$		0			0
$541$	20.0051	+	6.50007i	0.860088	+	0.279460i	0.705665	−	0.708545i	$-0.250648\pi$
$541$	20.0051	+	6.50007i	0.860088	+	0.279460i	0.154423	+	0.988005i	$0.450648\pi$
$542$	−6.55002	−	9.01533i	−0.281347	−	0.387241i
$543$		0			0
$544$	−1.78526	−	5.49448i	−0.0765425	−	0.235574i
$545$	−0.104637	−	0.322040i	−0.00448216	−	0.0137947i
$546$		0			0
$547$	15.0960	+	20.7778i	0.645457	+	0.888396i	0.998892	−	0.0470634i	$-0.0149863\pi$
$547$	15.0960	+	20.7778i	0.645457	+	0.888396i	−0.353435	+	0.935459i	$0.614986\pi$
$548$	−5.80408	−	1.88586i	−0.247938	−	0.0805599i
$549$		0			0
$550$	−13.7977	−	5.61015i	−0.588335	−	0.239218i
$551$			24.4337i			1.04091i
$552$		0			0
$553$	6.09827	−	4.43065i	0.259325	−	0.188410i
$554$	−7.05603	+	9.71179i	−0.299782	+	0.412615i
$555$		0			0
$556$	−3.15325	+	1.02455i	−0.133728	+	0.0434507i
$557$	30.0879	+	21.8602i	1.27487	+	0.926245i	0.999385	−	0.0350620i	$-0.0111629\pi$
$557$	30.0879	+	21.8602i	1.27487	+	0.926245i	0.275481	+	0.961306i	$0.411163\pi$
$558$		0			0
$559$	−10.3883	+	31.9718i	−0.439377	+	1.35226i
$560$	−0.713516			−0.0301516
$561$		0			0
$562$	16.3324			0.688942
$563$	3.25853	−	10.0287i	0.137330	−	0.422660i	−0.858615	−	0.512621i	$-0.828674\pi$
$563$	3.25853	−	10.0287i	0.137330	−	0.422660i	0.995945	+	0.0899617i	$0.0286745\pi$
$564$		0			0
$565$	−1.00678	−	0.731466i	−0.0423554	−	0.0307730i
$566$	−27.1708	+	8.82831i	−1.14207	+	0.371082i
$567$		0			0
$568$	5.20738	−	7.16734i	0.218497	−	0.300735i
$569$	14.7103	−	10.6877i	0.616690	−	0.448051i	−0.235074	−	0.971977i	$-0.575533\pi$
$569$	14.7103	−	10.6877i	0.616690	−	0.448051i	0.851764	+	0.523926i	$0.175533\pi$
$570$		0			0
$571$		−	8.91710i		−	0.373169i	−0.982439	−	0.186585i	$-0.940258\pi$
$571$		−	8.91710i		−	0.373169i	0.982439	−	0.186585i	$-0.0597418\pi$
$572$	9.94568	+	0.717580i	0.415850	+	0.0300035i
$573$		0			0
$574$	1.24475	+	0.404444i	0.0519548	+	0.0168811i
$575$	3.21691	+	4.42769i	0.134154	+	0.184648i
$576$		0			0
$577$	5.54179	+	17.0559i	0.230708	+	0.710045i	0.997662	+	0.0683432i	$0.0217713\pi$
$577$	5.54179	+	17.0559i	0.230708	+	0.710045i	−0.766954	+	0.641702i	$0.778229\pi$
$578$	−5.06059	−	15.5749i	−0.210493	−	0.647831i
$579$		0			0
$580$	−1.89499	−	2.60823i	−0.0786853	−	0.108301i
$581$	−14.0021	−	4.54956i	−0.580905	−	0.188748i
$582$		0			0
$583$	−22.3515	+	13.8981i	−0.925704	+	0.575601i
$584$			7.35274i			0.304259i
$585$		0			0
$586$	−1.62651	+	1.18173i	−0.0671905	+	0.0488168i
$587$	15.9112	−	21.8999i	0.656726	−	0.903906i	−0.342642	−	0.939466i	$-0.611322\pi$
$587$	15.9112	−	21.8999i	0.656726	−	0.903906i	0.999368	+	0.0355605i	$0.0113216\pi$
$588$		0			0
$589$	−12.7146	+	4.13121i	−0.523894	+	0.170224i
$590$	−2.47099	−	1.79528i	−0.101729	−	0.0739104i
$591$		0			0
$592$	3.38073	−	10.4048i	0.138947	−	0.427636i
$593$	7.88072			0.323622			0.161811	−	0.986822i	$-0.448266\pi$
$593$	7.88072			0.323622			0.161811	+	0.986822i	$0.448266\pi$
$594$		0			0
$595$	−4.12215			−0.168992
$596$	5.64833	−	17.3838i	0.231365	−	0.712067i
$597$		0			0
$598$	−2.96422	−	2.15363i	−0.121216	−	0.0880685i
$599$	30.0130	−	9.75182i	1.22630	−	0.398449i	0.376927	−	0.926243i	$-0.376981\pi$
$599$	30.0130	−	9.75182i	1.22630	−	0.398449i	0.849372	+	0.527794i	$0.176981\pi$
$600$		0			0
$601$	17.7649	−	24.4513i	0.724645	−	0.997389i	−0.274711	−	0.961527i	$-0.588582\pi$
$601$	17.7649	−	24.4513i	0.724645	−	0.997389i	0.999357	−	0.0358620i	$-0.0114177\pi$
$602$	9.04593	−	6.57225i	0.368684	−	0.267865i
$603$		0			0
$604$			0.440107i			0.0179077i
$605$	3.65404	+	6.94620i	0.148558	+	0.282403i
$606$		0			0
$607$	12.4550	+	4.04689i	0.505535	+	0.164258i	0.550671	−	0.834723i	$-0.314372\pi$
$607$	12.4550	+	4.04689i	0.505535	+	0.164258i	−0.0451358	+	0.998981i	$0.514372\pi$
$608$	3.17850	+	4.37483i	0.128905	+	0.177423i
$609$		0			0
$610$	−2.75619	−	8.48267i	−0.111595	−	0.343453i
$611$	−8.24099	−	25.3632i	−0.333395	−	1.02608i
$612$		0			0
$613$	−13.0547	−	17.9682i	−0.527274	−	0.725730i	0.459438	−	0.888210i	$-0.348051\pi$
$613$	−13.0547	−	17.9682i	−0.527274	−	0.725730i	−0.986712	+	0.162480i	$0.948051\pi$
$614$	−1.53676	−	0.499324i	−0.0620186	−	0.0201511i
$615$		0			0
$616$	−2.53596	−	2.13750i	−0.102177	−	0.0861223i
$617$		−	37.7924i		−	1.52146i	−0.649066	−	0.760732i	$-0.724840\pi$
$617$		−	37.7924i		−	1.52146i	0.649066	−	0.760732i	$-0.275160\pi$
$618$		0			0
$619$	23.9490	−	17.4000i	0.962593	−	0.699365i	0.00884136	−	0.999961i	$-0.497186\pi$
$619$	23.9490	−	17.4000i	0.962593	−	0.699365i	0.953751	+	0.300596i	$0.0971857\pi$
$620$	1.03684	−	1.42709i	0.0416407	−	0.0573135i
$621$		0			0
$622$	−26.6954	+	8.67385i	−1.07039	+	0.347790i
$623$	−9.15172	−	6.64911i	−0.366656	−	0.266391i
$624$		0			0
$625$	5.44569	−	16.7601i	0.217827	−	0.670404i
$626$	21.0146			0.839914
$627$		0			0
$628$	−13.0207			−0.519584
$629$	19.5313	−	60.1111i	0.778763	−	2.39679i
$630$		0			0
$631$	−23.0098	−	16.7176i	−0.916005	−	0.665516i	0.0265218	−	0.999648i	$-0.491557\pi$
$631$	−23.0098	−	16.7176i	−0.916005	−	0.665516i	−0.942526	+	0.334132i	$0.891557\pi$
$632$	7.16894	−	2.32933i	0.285165	−	0.0926558i
$633$		0			0
$634$	10.0354	−	13.8125i	0.398555	−	0.548564i
$635$	11.3111	−	8.21798i	0.448866	−	0.326120i
$636$		0			0
$637$			3.00653i			0.119123i
$638$	1.07842	−	14.9470i	0.0426952	−	0.591758i
$639$		0			0
$640$	−0.678594	−	0.220489i	−0.0268238	−	0.00871558i
$641$	1.84023	+	2.53286i	0.0726849	+	0.100042i	0.843812	−	0.536640i	$-0.180307\pi$
$641$	1.84023	+	2.53286i	0.0726849	+	0.100042i	−0.771127	+	0.636682i	$0.780307\pi$
$642$		0			0
$643$	5.51981	+	16.9882i	0.217680	+	0.669950i	0.998952	+	0.0457601i	$0.0145710\pi$
$643$	5.51981	+	16.9882i	0.217680	+	0.669950i	−0.781272	+	0.624190i	$0.785429\pi$
$644$	0.376590	+	1.15903i	0.0148397	+	0.0456720i
$645$		0			0
$646$	18.3629	+	25.2744i	0.722480	+	0.994409i
$647$	−8.41472	−	2.73411i	−0.330817	−	0.107489i	0.138899	−	0.990307i	$-0.455644\pi$
$647$	−8.41472	−	2.73411i	−0.330817	−	0.107489i	−0.469716	+	0.882818i	$0.655644\pi$
$648$		0			0
$649$	−3.40416	−	13.7831i	−0.133625	−	0.541035i
$650$			13.5020i			0.529592i
$651$		0			0
$652$	1.46175	−	1.06202i	0.0572466	−	0.0415921i
$653$	13.2980	−	18.3031i	0.520389	−	0.716255i	−0.465238	−	0.885185i	$-0.654031\pi$
$653$	13.2980	−	18.3031i	0.520389	−	0.716255i	0.985628	+	0.168931i	$0.0540314\pi$
$654$		0			0
$655$	8.39448	−	2.72753i	0.327999	−	0.106573i
$656$	1.05885	+	0.769297i	0.0413410	+	0.0300360i
$657$		0			0
$658$	−2.74103	+	8.43602i	−0.106856	+	0.328870i
$659$	−2.96235			−0.115397			−0.0576983	−	0.998334i	$-0.518376\pi$
$659$	−2.96235			−0.115397			−0.0576983	+	0.998334i	$0.518376\pi$
$660$		0			0
$661$	4.98281			0.193809			0.0969044	−	0.995294i	$-0.469106\pi$
$661$	4.98281			0.193809			0.0969044	+	0.995294i	$0.469106\pi$
$662$	1.89644	−	5.83664i	0.0737072	−	0.226847i
$663$		0			0
$664$	−11.9109	−	8.65378i	−0.462233	−	0.335832i
$665$	3.66956	−	1.19231i	0.142299	−	0.0462359i
$666$		0			0
$667$	−3.23661	+	4.45482i	−0.125322	+	0.172491i
$668$	−8.17411	+	5.93884i	−0.316266	+	0.229781i
$669$		0			0
$670$			10.2804i			0.397166i
$671$	15.6158	−	38.4057i	0.602841	−	1.48263i
$672$		0			0
$673$	−21.7754	−	7.07526i	−0.839381	−	0.272731i	−0.142389	−	0.989811i	$-0.545478\pi$
$673$	−21.7754	−	7.07526i	−0.839381	−	0.272731i	−0.696991	+	0.717079i	$0.745478\pi$
$674$	−0.280897	−	0.386621i	−0.0108197	−	0.0148921i
$675$		0			0
$676$	1.22395	+	3.76692i	0.0470749	+	0.144882i
$677$	14.4690	+	44.5311i	0.556090	+	1.71147i	0.693047	+	0.720893i	$0.256268\pi$
$677$	14.4690	+	44.5311i	0.556090	+	1.71147i	−0.136957	+	0.990577i	$0.543732\pi$
$678$		0			0
$679$	−10.0121	−	13.7805i	−0.384230	−	0.528847i
$680$	−3.92040	−	1.27381i	−0.150340	−	0.0488485i
$681$		0			0
$682$	7.96031	−	1.96604i	0.304816	−	0.0752834i
$683$		−	29.8739i		−	1.14309i	−0.820570	−	0.571546i	$-0.806344\pi$
$683$		−	29.8739i		−	1.14309i	0.820570	−	0.571546i	$-0.193656\pi$
$684$		0			0
$685$	−3.52280	+	2.55947i	−0.134599	+	0.0977922i
$686$	0.587785	−	0.809017i	0.0224417	−	0.0308884i
$687$		0			0
$688$	10.6341	−	3.45524i	0.405422	−	0.131730i
$689$	19.3025	+	14.0241i	0.735367	+	0.534276i
$690$		0			0
$691$	4.96372	−	15.2767i	0.188829	−	0.581155i	−0.811165	−	0.584818i	$-0.801166\pi$
$691$	4.96372	−	15.2767i	0.188829	−	0.581155i	0.999993	+	0.00366302i	$0.00116598\pi$
$692$	−6.84541			−0.260224
$693$		0			0
$694$	−26.5035			−1.00606
$695$	−0.731035	+	2.24990i	−0.0277297	+	0.0853434i
$696$		0			0
$697$	6.11721	+	4.44441i	0.231706	+	0.168344i
$698$	−17.6140	+	5.72314i	−0.666701	+	0.216624i
$699$		0			0
$700$	2.63968	−	3.63321i	0.0997706	−	0.137322i
$701$	23.5689	−	17.1238i	0.890185	−	0.646757i	−0.0457412	−	0.998953i	$-0.514565\pi$
$701$	23.5689	−	17.1238i	0.890185	−	0.646757i	0.935926	+	0.352196i	$0.114565\pi$
$702$		0			0
$703$			59.1606i			2.23128i
$704$	−1.75132	−	2.81654i	−0.0660053	−	0.106152i
$705$		0			0
$706$	−14.9388	−	4.85391i	−0.562229	−	0.182679i
$707$	5.22033	+	7.18517i	0.196331	+	0.270226i
$708$		0			0
$709$	0.760460	+	2.34046i	0.0285597	+	0.0878977i	0.964320	−	0.264738i	$-0.0852855\pi$
$709$	0.760460	+	2.34046i	0.0285597	+	0.0878977i	−0.935761	+	0.352636i	$0.885285\pi$
$710$	−1.95338	−	6.01188i	−0.0733090	−	0.225622i
$711$		0			0
$712$	−6.64911	−	9.15172i	−0.249186	−	0.342975i
$713$	−2.86539	−	0.931023i	−0.107310	−	0.0348671i
$714$		0			0
$715$	4.58538	−	5.44016i	0.171484	−	0.203450i
$716$			12.8506i			0.480248i
$717$		0			0
$718$	−9.33172	+	6.77989i	−0.348257	+	0.253023i
$719$	18.2530	−	25.1231i	0.680723	−	0.936935i	−0.319219	−	0.947681i	$-0.603421\pi$
$719$	18.2530	−	25.1231i	0.680723	−	0.936935i	0.999942	+	0.0107460i	$0.00342063\pi$
$720$		0			0
$721$	0.637356	−	0.207089i	0.0237364	−	0.00771241i
$722$	−8.28598	−	6.02011i	−0.308372	−	0.224045i
$723$		0			0
$724$	5.90723	−	18.1806i	0.219541	−	0.675677i
$725$	20.2917			0.753614
$726$		0			0
$727$	−4.18453			−0.155196			−0.0775978	−	0.996985i	$-0.524725\pi$
$727$	−4.18453			−0.155196			−0.0775978	+	0.996985i	$0.524725\pi$
$728$	−0.929069	+	2.85938i	−0.0344336	+	0.105976i
$729$		0			0
$730$	4.24435	+	3.08370i	0.157090	+	0.114133i
$731$	61.4358	−	19.9617i	2.27229	−	0.738310i
$732$		0			0
$733$	−15.3808	+	21.1699i	−0.568104	+	0.781929i	−0.992329	−	0.123629i	$-0.960547\pi$
$733$	−15.3808	+	21.1699i	−0.568104	+	0.781929i	0.424224	+	0.905557i	$0.360547\pi$
$734$	−14.8105	+	10.7605i	−0.546667	+	0.397177i
$735$		0			0
$736$			1.21867i			0.0449208i
$737$	−30.7972	+	36.5383i	−1.13443	+	1.34590i
$738$		0			0
$739$	32.7610	+	10.6447i	1.20513	+	0.391571i	0.841646	−	0.540029i	$-0.181587\pi$
$739$	32.7610	+	10.6447i	1.20513	+	0.391571i	0.363485	+	0.931600i	$0.381587\pi$
$740$	−4.58829	−	6.31524i	−0.168669	−	0.232153i
$741$		0			0
$742$	−2.45230	−	7.54739i	−0.0900267	−	0.277074i
$743$	−0.330418	−	1.01692i	−0.0121219	−	0.0373072i	0.944813	−	0.327611i	$-0.106244\pi$
$743$	−0.330418	−	1.01692i	−0.0121219	−	0.0373072i	−0.956934	+	0.290304i	$0.906244\pi$
$744$		0			0
$745$	−7.66585	−	10.5511i	−0.280855	−	0.386564i
$746$	7.85349	+	2.55176i	0.287537	+	0.0934264i
$747$		0			0
$748$	−10.1178	−	16.2718i	−0.369942	−	0.594956i
$749$		−	4.03538i		−	0.147449i
$750$		0			0
$751$	6.59960	−	4.79489i	0.240823	−	0.174968i	−0.460827	−	0.887490i	$-0.652447\pi$
$751$	6.59960	−	4.79489i	0.240823	−	0.174968i	0.701650	+	0.712522i	$0.252447\pi$
$752$	−5.21375	+	7.17611i	−0.190126	+	0.261686i
$753$		0			0
$754$	−12.9198	+	4.19791i	−0.470513	+	0.152879i
$755$	0.254050	+	0.184578i	0.00924583	+	0.00671749i
$756$		0			0
$757$	1.67328	−	5.14982i	0.0608164	−	0.187174i	−0.916033	−	0.401104i	$-0.868627\pi$
$757$	1.67328	−	5.14982i	0.0608164	−	0.187174i	0.976849	+	0.213930i	$0.0686266\pi$
$758$	11.9379			0.433602
$759$		0			0
$760$	3.85840			0.139959
$761$	4.64530	−	14.2968i	0.168392	−	0.518257i	−0.830878	−	0.556454i	$-0.812161\pi$
$761$	4.64530	−	14.2968i	0.168392	−	0.518257i	0.999270	+	0.0381970i	$0.0121614\pi$
$762$		0			0
$763$	0.383935	+	0.278945i	0.0138994	+	0.0100985i
$764$	21.2791	−	6.91400i	0.769851	−	0.250140i
$765$		0			0
$766$	7.00240	−	9.63798i	0.253007	−	0.348234i
$767$	−10.4120	+	7.56473i	−0.375954	+	0.273147i
$768$		0			0
$769$		−	9.70737i		−	0.350057i	−0.984563	−	0.175028i	$-0.943998\pi$
$769$		−	9.70737i		−	0.350057i	0.984563	−	0.175028i	$-0.0560017\pi$
$770$	−2.29743	+	0.567419i	−0.0827937	+	0.0204484i
$771$		0			0
$772$	−2.98670	−	0.970439i	−0.107494	−	0.0349269i
$773$	−6.14965	−	8.46427i	−0.221188	−	0.304439i	0.683974	−	0.729507i	$-0.260250\pi$
$773$	−6.14965	−	8.46427i	−0.221188	−	0.304439i	−0.905161	+	0.425068i	$0.860250\pi$
$774$		0			0
$775$	3.43089	+	10.5592i	0.123241	+	0.379297i
$776$	−5.26368	−	16.2000i	−0.188955	−	0.581544i
$777$		0			0
$778$	9.28357	+	12.7777i	0.332832	+	0.458104i
$779$	−6.73109	−	2.18706i	−0.241166	−	0.0783597i
$780$		0			0
$781$	11.0673	−	27.2191i	0.396020	−	0.973975i
$782$			7.04055i			0.251770i
$783$		0			0
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	−5.46082	+	7.51617i	−0.194905	+	0.268264i
$786$		0			0
$787$	31.2355	−	10.1490i	1.11342	−	0.361773i	0.306169	−	0.951977i	$-0.400953\pi$
$787$	31.2355	−	10.1490i	1.11342	−	0.361773i	0.807254	+	0.590204i	$0.200953\pi$
$788$	18.1242	+	13.1680i	0.645647	+	0.469090i
$789$		0			0
$790$	1.66202	−	5.11516i	0.0591318	−	0.181989i
$791$	1.74410			0.0620131
$792$		0			0
$793$	−37.5827			−1.33460
$794$	7.20242	−	22.1668i	0.255604	−	0.786670i
$795$		0			0
$796$	−2.42462	−	1.76159i	−0.0859384	−	0.0624379i
$797$	−44.8409	+	14.5697i	−1.58835	+	0.516085i	−0.964190	−	0.265214i	$-0.914557\pi$
$797$	−44.8409	+	14.5697i	−1.58835	+	0.516085i	−0.624157	+	0.781299i	$0.714557\pi$
$798$		0			0
$799$	−30.1210	+	41.4581i	−1.06561	+	1.46668i
$800$	3.63321	−	2.63968i	0.128453	−	0.0933268i
$801$		0			0
$802$			2.38680i			0.0842810i
$803$	5.84722	+	23.6749i	0.206344	+	0.835469i
$804$		0			0
$805$	0.826984	+	0.268703i	0.0291473	+	0.00947055i
$806$	−4.36893	−	6.01332i	−0.153889	−	0.211810i
$807$		0			0
$808$	2.74449	+	8.44667i	0.0965508	+	0.297153i
$809$	−11.0245	−	33.9300i	−0.387602	−	1.19292i	−0.934575	−	0.355765i	$-0.884220\pi$
$809$	−11.0245	−	33.9300i	−0.387602	−	1.19292i	0.546974	−	0.837150i	$-0.315780\pi$
$810$		0			0
$811$	−7.11726	−	9.79606i	−0.249921	−	0.343986i	0.665563	−	0.746342i	$-0.268192\pi$
$811$	−7.11726	−	9.79606i	−0.249921	−	0.343986i	−0.915483	+	0.402356i	$0.868192\pi$
$812$	4.29726	+	1.39626i	0.150804	+	0.0489993i
$813$		0			0
$814$	2.61116	−	36.1907i	0.0915210	−	1.26848i
$815$		−	1.28920i		−	0.0451586i
$816$		0			0
$817$	−48.9167	+	35.5400i	−1.71138	+	1.24339i
$818$	−14.1706	+	19.5042i	−0.495464	+	0.681947i
$819$		0			0
$820$	0.888148	−	0.288577i	0.0310155	−	0.0100775i
$821$	−6.01965	−	4.37353i	−0.210087	−	0.152637i	0.477766	−	0.878487i	$-0.341447\pi$
$821$	−6.01965	−	4.37353i	−0.210087	−	0.152637i	−0.687853	+	0.725850i	$0.741447\pi$
$822$		0			0
$823$	2.33384	−	7.18282i	0.0813526	−	0.250377i	−0.902105	−	0.431517i	$-0.857979\pi$
$823$	2.33384	−	7.18282i	0.0813526	−	0.250377i	0.983457	+	0.181139i	$0.0579785\pi$
$824$	0.670155			0.0233460
$825$		0			0
$826$	4.28064			0.148943
$827$	−7.12889	+	21.9405i	−0.247896	+	0.762945i	0.747251	+	0.664542i	$0.231373\pi$
$827$	−7.12889	+	21.9405i	−0.247896	+	0.762945i	−0.995147	+	0.0984028i	$0.968627\pi$
$828$		0			0
$829$	−27.2871	−	19.8253i	−0.947721	−	0.688560i	0.00254576	−	0.999997i	$-0.499190\pi$
$829$	−27.2871	−	19.8253i	−0.947721	−	0.688560i	−0.950267	+	0.311437i	$0.899190\pi$
$830$	−9.99073	+	3.24619i	−0.346783	+	0.112677i
$831$		0			0
$832$	−1.76719	+	2.43233i	−0.0612664	+	0.0843260i
$833$	4.67388	−	3.39577i	0.161940	−	0.117657i
$834$		0			0
$835$			7.20919i			0.249484i
$836$	13.7134	+	11.5587i	0.474289	+	0.399767i
$837$		0			0
$838$	0.105854	+	0.0343939i	0.00365665	+	0.00118812i
$839$	2.86475	+	3.94299i	0.0989022	+	0.136127i	0.855600	−	0.517638i	$-0.173188\pi$
$839$	2.86475	+	3.94299i	0.0989022	+	0.136127i	−0.756698	+	0.653765i	$0.773188\pi$
$840$		0			0
$841$	−2.65260	−	8.16387i	−0.0914691	−	0.281513i
$842$	−6.82703	−	21.0115i	−0.235275	−	0.724102i
$843$		0			0
$844$	−12.5707	−	17.3020i	−0.432700	−	0.595561i
$845$	2.68776	+	0.873306i	0.0924617	+	0.0300426i
$846$		0			0
$847$	−9.86531	−	4.86577i	−0.338976	−	0.167190i
$848$		−	7.93580i		−	0.272516i
$849$		0			0
$850$	20.9899	−	15.2501i	0.719948	−	0.523073i
$851$	−7.83671	+	10.7863i	−0.268639	+	0.369750i
$852$		0			0
$853$	38.4909	−	12.5064i	1.31790	−	0.428213i	0.436128	−	0.899884i	$-0.356349\pi$
$853$	38.4909	−	12.5064i	1.31790	−	0.428213i	0.881774	+	0.471672i	$0.156349\pi$
$854$	10.1130	+	7.34753i	0.346060	+	0.251427i
$855$		0			0
$856$	1.24700	−	3.83787i	0.0426216	−	0.131176i
$857$	−12.9271			−0.441580			−0.220790	−	0.975321i	$-0.570864\pi$
$857$	−12.9271			−0.441580			−0.220790	+	0.975321i	$0.570864\pi$
$858$		0			0
$859$	−34.2974			−1.17021			−0.585106	−	0.810957i	$-0.698947\pi$
$859$	−34.2974			−1.17021			−0.585106	+	0.810957i	$0.698947\pi$
$860$	2.46537	−	7.58762i	0.0840683	−	0.258736i
$861$		0			0
$862$	21.8371	+	15.8656i	0.743774	+	0.540383i
$863$	29.8822	−	9.70931i	1.01720	−	0.330509i	0.247483	−	0.968892i	$-0.420397\pi$
$863$	29.8822	−	9.70931i	1.01720	−	0.330509i	0.769719	+	0.638383i	$0.220397\pi$
$864$		0			0
$865$	−2.87093	+	3.95149i	−0.0976144	+	0.134355i
$866$	29.3100	−	21.2949i	0.995994	−	0.723632i
$867$		0			0
$868$			2.47224i			0.0839134i
$869$	21.2307	−	13.2012i	0.720202	−	0.447820i
$870$		0			0
$871$	41.1981	+	13.3861i	1.39594	+	0.453570i
$872$	0.278945	+	0.383935i	0.00944627	+	0.0130017i
$873$		0			0
$874$	−2.03645	−	6.26754i	−0.0688838	−	0.212003i
$875$	−2.09263	−	6.44046i	−0.0707439	−	0.217727i
$876$		0			0
$877$	−25.4470	−	35.0248i	−0.859285	−	1.18270i	−0.981739	−	0.190230i	$-0.939077\pi$
$877$	−25.4470	−	35.0248i	−0.859285	−	1.18270i	0.122454	−	0.992474i	$-0.460923\pi$
$878$	−6.55908	−	2.13117i	−0.221358	−	0.0719236i
$879$		0			0
$880$	−2.36033	−	0.170298i	−0.0795667	−	0.00574073i
$881$		−	2.60856i		−	0.0878845i	−0.999034	−	0.0439422i	$-0.986008\pi$
$881$		−	2.60856i		−	0.0878845i	0.999034	−	0.0439422i	$-0.0139918\pi$
$882$		0			0
$883$	−43.5779	+	31.6612i	−1.46651	+	1.06548i	−0.484906	+	0.874566i	$0.661146\pi$
$883$	−43.5779	+	31.6612i	−1.46651	+	1.06548i	−0.981606	+	0.190917i	$0.938854\pi$
$884$	−10.2095	+	14.0522i	−0.343382	+	0.472625i
$885$		0			0
$886$	−27.1895	+	8.83441i	−0.913450	+	0.296798i
$887$	30.6438	+	22.2640i	1.02892	+	0.747553i	0.968092	−	0.250595i	$-0.0806263\pi$
$887$	30.6438	+	22.2640i	1.02892	+	0.747553i	0.0608266	+	0.998148i	$0.480626\pi$
$888$		0			0
$889$	−6.05515	+	18.6358i	−0.203083	+	0.625026i
$890$	−8.07139			−0.270554
$891$		0			0
$892$	5.58982			0.187161
$893$	14.8224	−	45.6186i	0.496012	−	1.52657i
$894$		0			0
$895$	7.41795	+	5.38945i	0.247955	+	0.180150i
$896$	0.951057	−	0.309017i	0.0317726	−	0.0103235i
$897$		0			0
$898$	−6.67600	+	9.18873i	−0.222781	+	0.306632i
$899$	−9.03720	+	6.56591i	−0.301408	+	0.218985i
$900$		0			0
$901$		−	45.8470i		−	1.52738i
$902$	4.02113	+	1.63500i	0.133889	+	0.0544395i
$903$		0			0
$904$	1.65874	+	0.538957i	0.0551688	+	0.0179254i
$905$	−8.01723	−	11.0348i	−0.266502	−	0.366808i
$906$		0			0
$907$	−0.427602	−	1.31602i	−0.0141983	−	0.0436979i	0.943706	−	0.330784i	$-0.107313\pi$
$907$	−0.427602	−	1.31602i	−0.0141983	−	0.0436979i	−0.957905	+	0.287086i	$0.907313\pi$
$908$	−8.89216	−	27.3672i	−0.295097	−	0.908214i
$909$		0			0
$910$	1.26092	+	1.73551i	0.0417991	+	0.0575316i
$911$	24.1827	+	7.85743i	0.801208	+	0.260328i	0.680870	−	0.732405i	$-0.261602\pi$
$911$	24.1827	+	7.85743i	0.801208	+	0.260328i	0.120339	+	0.992733i	$0.461602\pi$
$912$		0			0
$913$	−45.2335	−	18.3920i	−1.49701	−	0.608686i
$914$			17.7701i			0.587783i
$915$		0			0
$916$	−18.2303	+	13.2451i	−0.602348	+	0.437631i
$917$	−7.27114	+	10.0079i	−0.240114	+	0.330489i
$918$		0			0
$919$	−4.54093	+	1.47544i	−0.149792	+	0.0486702i	−0.382953	−	0.923768i	$-0.625093\pi$
$919$	−4.54093	+	1.47544i	−0.149792	+	0.0486702i	0.233162	+	0.972438i	$0.425093\pi$
$920$	0.703474	+	0.511104i	0.0231929	+	0.0168506i
$921$		0			0
$922$	−2.06741	+	6.36282i	−0.0680864	+	0.209548i
$923$	−26.6358			−0.876729
$924$		0			0
$925$	49.1317			1.61544
$926$	10.8081	−	33.2640i	0.355177	−	1.09312i
$927$		0			0
$928$	3.65547	+	2.65585i	0.119997	+	0.0871826i
$929$	−10.7285	+	3.48591i	−0.351991	+	0.114369i	−0.479676	−	0.877446i	$-0.659246\pi$
$929$	−10.7285	+	3.48591i	−0.351991	+	0.114369i	0.127684	+	0.991815i	$0.459246\pi$
$930$		0			0
$931$	−3.17850	+	4.37483i	−0.104171	+	0.143379i
$932$	14.0098	−	10.1787i	0.458906	−	0.333415i
$933$		0			0
$934$			11.2914i			0.369467i
$935$	−13.6362	−	0.983848i	−0.445951	−	0.0321753i
$936$		0			0
$937$	41.3693	+	13.4417i	1.35148	+	0.439122i	0.893189	−	0.449682i	$-0.148463\pi$
$937$	41.3693	+	13.4417i	1.35148	+	0.439122i	0.458288	+	0.888804i	$0.348463\pi$
$938$	−8.46884	−	11.6564i	−0.276517	−	0.380594i
$939$		0			0
$940$	1.95577	+	6.01924i	0.0637901	+	0.196326i
$941$	1.42812	+	4.39530i	0.0465554	+	0.143283i	0.971632	−	0.236498i	$-0.0759996\pi$
$941$	1.42812	+	4.39530i	0.0465554	+	0.143283i	−0.925077	+	0.379780i	$0.876000\pi$
$942$		0			0
$943$	−0.937521	−	1.29039i	−0.0305299	−	0.0420208i
$944$	4.07114	+	1.32279i	0.132504	+	0.0430532i
$945$		0			0
$946$	31.4928	−	19.5821i	1.02392	−	0.636671i
$947$			0.699545i			0.0227322i	0.999935	+	0.0113661i	$0.00361801\pi$
$947$			0.699545i			0.0227322i	−0.999935	+	0.0113661i	$0.996382\pi$
$948$		0			0
$949$	17.8843	−	12.9937i	0.580550	−	0.421794i
$950$	−14.2743	+	19.6469i	−0.463120	+	0.637430i
$951$		0			0
$952$	5.49448	−	1.78526i	0.178077	−	0.0578607i
$953$	0.494636	+	0.359374i	0.0160228	+	0.0116413i	0.595768	−	0.803157i	$-0.296848\pi$
$953$	0.494636	+	0.359374i	0.0160228	+	0.0116413i	−0.579745	+	0.814798i	$0.696848\pi$
$954$		0			0
$955$	4.93325	−	15.1830i	0.159636	−	0.491310i
$956$	−7.14810			−0.231186
$957$		0			0
$958$	−26.1956			−0.846343
$959$	1.88586	−	5.80408i	0.0608976	−	0.187423i
$960$		0			0
$961$	20.1348	+	14.6288i	0.649511	+	0.471897i
$962$	−31.2824	+	10.1643i	−1.00859	+	0.327709i
$963$		0			0
$964$	−12.8185	+	17.6432i	−0.412858	+	0.568250i
$965$	−1.81279	+	1.31707i	−0.0583557	+	0.0423979i
$966$		0			0
$967$		−	46.0966i		−	1.48237i	−0.671303	−	0.741183i	$-0.734265\pi$
$967$		−	46.0966i		−	1.48237i	0.671303	−	0.741183i	$-0.265735\pi$
$968$	−7.87886	−	7.67617i	−0.253236	−	0.246722i
$969$		0			0
$970$	−11.5589	−	3.75572i	−0.371135	−	0.120589i
$971$	29.1156	+	40.0741i	0.934363	+	1.28604i	0.958133	+	0.286322i	$0.0924328\pi$
$971$	29.1156	+	40.0741i	0.934363	+	1.28604i	−0.0237707	+	0.999717i	$0.507567\pi$
$972$		0			0
$973$	−1.02455	−	3.15325i	−0.0328457	−	0.101089i
$974$	−7.26311	−	22.3535i	−0.232725	−	0.716254i
$975$		0			0
$976$	7.34753	+	10.1130i	0.235189	+	0.323709i
$977$	−20.0279	−	6.50746i	−0.640749	−	0.208192i	−0.0294182	−	0.999567i	$-0.509365\pi$
$977$	−20.0279	−	6.50746i	−0.640749	−	0.208192i	−0.611331	+	0.791375i	$0.709365\pi$
$978$		0			0
$979$	−28.6871	−	24.1797i	−0.916845	−	0.772787i
$980$		−	0.713516i		−	0.0227924i
$981$		0			0
$982$	8.14729	−	5.91935i	0.259991	−	0.188894i
$983$	−0.416195	+	0.572843i	−0.0132746	+	0.0182709i	−0.815603	−	0.578612i	$-0.803594\pi$
$983$	−0.416195	+	0.572843i	−0.0132746	+	0.0182709i	0.802328	+	0.596883i	$0.203594\pi$
$984$		0			0
$985$	15.2024	−	4.93954i	0.484387	−	0.157387i
$986$	21.1185	+	15.3435i	0.672550	+	0.488636i
$987$		0			0
$988$	5.02402	−	15.4624i	0.159835	−	0.491923i
$989$	−13.6264			−0.433295
$990$		0			0
$991$	36.2714			1.15220			0.576099	−	0.817380i	$-0.304574\pi$
$991$	36.2714			1.15220			0.576099	+	0.817380i	$0.304574\pi$
$992$	−0.763965	+	2.35124i	−0.0242559	+	0.0746520i
$993$		0			0
$994$	7.16734	+	5.20738i	0.227334	+	0.165168i
$995$	−2.03374	+	0.660803i	−0.0644740	+	0.0209489i
$996$		0			0
$997$	−20.2371	+	27.8540i	−0.640916	+	0.882145i	−0.998664	−	0.0516732i	$-0.983545\pi$
$997$	−20.2371	+	27.8540i	−0.640916	+	0.882145i	0.357748	+	0.933818i	$0.383545\pi$
$998$	14.8105	−	10.7605i	0.468820	−	0.340617i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.b.827.5	yes	48
3.2	odd	2		1386.2.bu.a.827.8	✓	48
11.6	odd	10		1386.2.bu.a.1205.8	yes	48
33.17	even	10	inner	1386.2.bu.b.1205.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.827.8	✓	48	3.2	odd	2
1386.2.bu.a.1205.8	yes	48	11.6	odd	10
1386.2.bu.b.827.5	yes	48	1.1	even	1	trivial
1386.2.bu.b.1205.5	yes	48	33.17	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.678594 + 0.220489i) q^{5} +(0.587785 - 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.678594 + 0.220489i) q^{5} +(0.587785 - 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} -0.713516i q^{10} +(2.13750 - 2.53596i) q^{11} +(-2.85938 - 0.929069i) q^{13} +(0.587785 + 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(1.78526 + 5.49448i) q^{17} +(-3.17850 - 4.37483i) q^{19} +(0.678594 + 0.220489i) q^{20} +(1.75132 + 2.81654i) q^{22} -1.21867i q^{23} +(-3.63321 + 2.63968i) q^{25} +(1.76719 - 2.43233i) q^{26} +(-0.951057 + 0.309017i) q^{28} +(-3.65547 - 2.65585i) q^{29} +(0.763965 - 2.35124i) q^{31} -1.00000 q^{32} -5.77723 q^{34} +(-0.220489 + 0.678594i) q^{35} +(-8.85087 - 6.43054i) q^{37} +(5.14292 - 1.67104i) q^{38} +(-0.419394 + 0.577247i) q^{40} +(1.05885 - 0.769297i) q^{41} -11.1814i q^{43} +(-3.21987 + 0.795244i) q^{44} +(1.15903 + 0.376590i) q^{46} +(5.21375 + 7.17611i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-1.38776 - 4.27109i) q^{50} +(1.76719 + 2.43233i) q^{52} +(-7.54739 - 2.45230i) q^{53} +(-0.891344 + 2.19218i) q^{55} -1.00000i q^{56} +(3.65547 - 2.65585i) q^{58} +(2.51610 - 3.46311i) q^{59} +(11.8885 - 3.86282i) q^{61} +(2.00009 + 1.45315i) q^{62} +(0.309017 - 0.951057i) q^{64} +2.14521 q^{65} -14.4081 q^{67} +(1.78526 - 5.49448i) q^{68} +(-0.577247 - 0.419394i) q^{70} +(8.42572 - 2.73768i) q^{71} +(-4.32183 + 5.94849i) q^{73} +(8.85087 - 6.43054i) q^{74} +5.40759i q^{76} +(-0.795244 - 3.21987i) q^{77} +(7.16894 + 2.32933i) q^{79} +(-0.419394 - 0.577247i) q^{80} +(0.404444 + 1.24475i) q^{82} +(-4.54956 - 14.0021i) q^{83} +(-2.42294 - 3.33489i) q^{85} +(10.6341 + 3.45524i) q^{86} +(0.238674 - 3.30803i) q^{88} -11.3121i q^{89} +(-2.43233 + 1.76719i) q^{91} +(-0.716317 + 0.985926i) q^{92} +(-8.43602 + 2.74103i) q^{94} +(3.12151 + 2.26791i) q^{95} +(5.26368 - 16.2000i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more