LMFDB - Embedded newform 1170.2.m.a.577.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(73,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.73"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,0,2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1170.577
Dual form			1170.2.m.a.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -2.00000i q^{7} -1.00000 q^{8} +(1.00000 + 2.00000i) q^{10} +(-1.00000 - 1.00000i) q^{11} +(-3.00000 - 2.00000i) q^{13} +2.00000i q^{14} +1.00000 q^{16} +(-5.00000 + 5.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(-1.00000 - 2.00000i) q^{20} +(1.00000 + 1.00000i) q^{22} +(5.00000 + 5.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(3.00000 + 2.00000i) q^{26} -2.00000i q^{28} -4.00000i q^{29} +(1.00000 - 1.00000i) q^{31} -1.00000 q^{32} +(5.00000 - 5.00000i) q^{34} +(-4.00000 + 2.00000i) q^{35} +8.00000i q^{37} +(3.00000 + 3.00000i) q^{38} +(1.00000 + 2.00000i) q^{40} +(-1.00000 + 1.00000i) q^{41} +(5.00000 + 5.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(-5.00000 - 5.00000i) q^{46} +2.00000i q^{47} +3.00000 q^{49} +(3.00000 - 4.00000i) q^{50} +(-3.00000 - 2.00000i) q^{52} +(1.00000 - 1.00000i) q^{53} +(-1.00000 + 3.00000i) q^{55} +2.00000i q^{56} +4.00000i q^{58} +(-3.00000 + 3.00000i) q^{59} +2.00000 q^{61} +(-1.00000 + 1.00000i) q^{62} +1.00000 q^{64} +(-1.00000 + 8.00000i) q^{65} -12.0000 q^{67} +(-5.00000 + 5.00000i) q^{68} +(4.00000 - 2.00000i) q^{70} +(-1.00000 + 1.00000i) q^{71} -6.00000 q^{73} -8.00000i q^{74} +(-3.00000 - 3.00000i) q^{76} +(-2.00000 + 2.00000i) q^{77} +14.0000i q^{79} +(-1.00000 - 2.00000i) q^{80} +(1.00000 - 1.00000i) q^{82} -6.00000i q^{83} +(15.0000 + 5.00000i) q^{85} +(-5.00000 - 5.00000i) q^{86} +(1.00000 + 1.00000i) q^{88} +(7.00000 - 7.00000i) q^{89} +(-4.00000 + 6.00000i) q^{91} +(5.00000 + 5.00000i) q^{92} -2.00000i q^{94} +(-3.00000 + 9.00000i) q^{95} -2.00000 q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 2 q^{8} + 2 q^{10} - 2 q^{11} - 6 q^{13} + 2 q^{16} - 10 q^{17} - 6 q^{19} - 2 q^{20} + 2 q^{22} + 10 q^{23} - 6 q^{25} + 6 q^{26} + 2 q^{31} - 2 q^{32} + 10 q^{34} - 8 q^{35}+ \cdots - 6 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 2 * q^8 + 2 * q^10 - 2 * q^11 - 6 * q^13 + 2 * q^16 - 10 * q^17 - 6 * q^19 - 2 * q^20 + 2 * q^22 + 10 * q^23 - 6 * q^25 + 6 * q^26 + 2 * q^31 - 2 * q^32 + 10 * q^34 - 8 * q^35 + 6 * q^38 + 2 * q^40 - 2 * q^41 + 10 * q^43 - 2 * q^44 - 10 * q^46 + 6 * q^49 + 6 * q^50 - 6 * q^52 + 2 * q^53 - 2 * q^55 - 6 * q^59 + 4 * q^61 - 2 * q^62 + 2 * q^64 - 2 * q^65 - 24 * q^67 - 10 * q^68 + 8 * q^70 - 2 * q^71 - 12 * q^73 - 6 * q^76 - 4 * q^77 - 2 * q^80 + 2 * q^82 + 30 * q^85 - 10 * q^86 + 2 * q^88 + 14 * q^89 - 8 * q^91 + 10 * q^92 - 6 * q^95 - 4 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$		0			0
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	0.540094	−	0.841605i	$-0.318389\pi$
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	−0.841605	+	0.540094i	$0.818389\pi$
$12$		0			0
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$14$			2.00000i			0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$	−5.00000	+	5.00000i	−1.21268	+	1.21268i	−0.242536	+	0.970143i	$0.577979\pi$
$17$	−5.00000	+	5.00000i	−1.21268	+	1.21268i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		0			0
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	0.273597	−	0.961844i	$-0.411786\pi$
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	−0.961844	+	0.273597i	$0.911786\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$		0			0
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	5.00000	+	5.00000i	1.04257	+	1.04257i	0.999053	+	0.0435195i	$0.0138571\pi$
$23$	5.00000	+	5.00000i	1.04257	+	1.04257i	0.0435195	+	0.999053i	$0.486143\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	3.00000	+	2.00000i	0.588348	+	0.392232i
$27$		0			0
$28$		−	2.00000i		−	0.377964i
$29$		−	4.00000i		−	0.742781i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$		−	4.00000i		−	0.742781i	0.928477	−	0.371391i	$-0.121119\pi$
$30$		0			0
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	−0.611578	−	0.791184i	$-0.709465\pi$
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	0.791184	+	0.611578i	$0.209465\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	5.00000	−	5.00000i	0.857493	−	0.857493i
$35$	−4.00000	+	2.00000i	−0.676123	+	0.338062i
$36$		0			0
$37$			8.00000i			1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$	3.00000	+	3.00000i	0.486664	+	0.486664i
$39$		0			0
$40$	1.00000	+	2.00000i	0.158114	+	0.316228i
$41$	−1.00000	+	1.00000i	−0.156174	+	0.156174i	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−1.00000	+	1.00000i	−0.156174	+	0.156174i	0.624695	+	0.780869i	$0.285223\pi$
$42$		0			0
$43$	5.00000	+	5.00000i	0.762493	+	0.762493i	0.976772	−	0.214280i	$-0.0687403\pi$
$43$	5.00000	+	5.00000i	0.762493	+	0.762493i	−0.214280	+	0.976772i	$0.568740\pi$
$44$	−1.00000	−	1.00000i	−0.150756	−	0.150756i
$45$		0			0
$46$	−5.00000	−	5.00000i	−0.737210	−	0.737210i
$47$			2.00000i			0.291730i	0.989305	+	0.145865i	$0.0465965\pi$
$47$			2.00000i			0.291730i	−0.989305	+	0.145865i	$0.953403\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$	3.00000	−	4.00000i	0.424264	−	0.565685i
$51$		0			0
$52$	−3.00000	−	2.00000i	−0.416025	−	0.277350i
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$		0			0
$55$	−1.00000	+	3.00000i	−0.134840	+	0.404520i
$56$			2.00000i			0.267261i
$57$		0			0
$58$			4.00000i			0.525226i
$59$	−3.00000	+	3.00000i	−0.390567	+	0.390567i	−0.874889	−	0.484323i	$-0.839066\pi$
$59$	−3.00000	+	3.00000i	−0.390567	+	0.390567i	0.484323	+	0.874889i	$0.339066\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	−1.00000	+	1.00000i	−0.127000	+	0.127000i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.00000	+	8.00000i	−0.124035	+	0.992278i
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	−5.00000	+	5.00000i	−0.606339	+	0.606339i
$69$		0			0
$70$	4.00000	−	2.00000i	0.478091	−	0.239046i
$71$	−1.00000	+	1.00000i	−0.118678	+	0.118678i	−0.763952	−	0.645273i	$-0.776743\pi$
$71$	−1.00000	+	1.00000i	−0.118678	+	0.118678i	0.645273	+	0.763952i	$0.276743\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$		−	8.00000i		−	0.929981i
$75$		0			0
$76$	−3.00000	−	3.00000i	−0.344124	−	0.344124i
$77$	−2.00000	+	2.00000i	−0.227921	+	0.227921i
$78$		0			0
$79$			14.0000i			1.57512i	0.616236	+	0.787562i	$0.288657\pi$
$79$			14.0000i			1.57512i	−0.616236	+	0.787562i	$0.711343\pi$
$80$	−1.00000	−	2.00000i	−0.111803	−	0.223607i
$81$		0			0
$82$	1.00000	−	1.00000i	0.110432	−	0.110432i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$		0			0
$85$	15.0000	+	5.00000i	1.62698	+	0.542326i
$86$	−5.00000	−	5.00000i	−0.539164	−	0.539164i
$87$		0			0
$88$	1.00000	+	1.00000i	0.106600	+	0.106600i
$89$	7.00000	−	7.00000i	0.741999	−	0.741999i	−0.230964	−	0.972962i	$-0.574188\pi$
$89$	7.00000	−	7.00000i	0.741999	−	0.741999i	0.972962	+	0.230964i	$0.0741879\pi$
$90$		0			0
$91$	−4.00000	+	6.00000i	−0.419314	+	0.628971i
$92$	5.00000	+	5.00000i	0.521286	+	0.521286i
$93$		0			0
$94$		−	2.00000i		−	0.206284i
$95$	−3.00000	+	9.00000i	−0.307794	+	0.923381i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		0			0
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	0.416480	−	0.909145i	$-0.363264\pi$
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	−0.909145	+	0.416480i	$0.863264\pi$
$104$	3.00000	+	2.00000i	0.294174	+	0.196116i
$105$		0			0
$106$	−1.00000	+	1.00000i	−0.0971286	+	0.0971286i
$107$	−13.0000	−	13.0000i	−1.25676	−	1.25676i	−0.952632	−	0.304125i	$-0.901636\pi$
$107$	−13.0000	−	13.0000i	−1.25676	−	1.25676i	−0.304125	−	0.952632i	$-0.598364\pi$
$108$		0			0
$109$	−13.0000	−	13.0000i	−1.24517	−	1.24517i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$	−13.0000	−	13.0000i	−1.24517	−	1.24517i	−0.287348	−	0.957826i	$-0.592774\pi$
$110$	1.00000	−	3.00000i	0.0953463	−	0.286039i
$111$		0			0
$112$		−	2.00000i		−	0.188982i
$113$	−9.00000	+	9.00000i	−0.846649	+	0.846649i	−0.989713	−	0.143065i	$-0.954304\pi$
$113$	−9.00000	+	9.00000i	−0.846649	+	0.846649i	0.143065	+	0.989713i	$0.454304\pi$
$114$		0			0
$115$	5.00000	−	15.0000i	0.466252	−	1.39876i
$116$		−	4.00000i		−	0.371391i
$117$		0			0
$118$	3.00000	−	3.00000i	0.276172	−	0.276172i
$119$	10.0000	+	10.0000i	0.916698	+	0.916698i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$	−2.00000			−0.181071
$123$		0			0
$124$	1.00000	−	1.00000i	0.0898027	−	0.0898027i
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$	−15.0000	+	15.0000i	−1.33103	+	1.33103i	−0.426589	+	0.904445i	$0.640285\pi$
$127$	−15.0000	+	15.0000i	−1.33103	+	1.33103i	−0.904445	+	0.426589i	$0.859715\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	1.00000	−	8.00000i	0.0877058	−	0.701646i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$	−6.00000	+	6.00000i	−0.520266	+	0.520266i
$134$	12.0000			1.03664
$135$		0			0
$136$	5.00000	−	5.00000i	0.428746	−	0.428746i
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$		0			0
$139$			14.0000i			1.18746i	0.804663	+	0.593732i	$0.202346\pi$
$139$			14.0000i			1.18746i	−0.804663	+	0.593732i	$0.797654\pi$
$140$	−4.00000	+	2.00000i	−0.338062	+	0.169031i
$141$		0			0
$142$	1.00000	−	1.00000i	0.0839181	−	0.0839181i
$143$	1.00000	+	5.00000i	0.0836242	+	0.418121i
$144$		0			0
$145$	−8.00000	+	4.00000i	−0.664364	+	0.332182i
$146$	6.00000			0.496564
$147$		0			0
$148$			8.00000i			0.657596i
$149$	13.0000	+	13.0000i	1.06500	+	1.06500i	0.997735	+	0.0672664i	$0.0214278\pi$
$149$	13.0000	+	13.0000i	1.06500	+	1.06500i	0.0672664	+	0.997735i	$0.478572\pi$
$150$		0			0
$151$	−9.00000	−	9.00000i	−0.732410	−	0.732410i	0.238687	−	0.971097i	$-0.423283\pi$
$151$	−9.00000	−	9.00000i	−0.732410	−	0.732410i	−0.971097	+	0.238687i	$0.923283\pi$
$152$	3.00000	+	3.00000i	0.243332	+	0.243332i
$153$		0			0
$154$	2.00000	−	2.00000i	0.161165	−	0.161165i
$155$	−3.00000	−	1.00000i	−0.240966	−	0.0803219i
$156$		0			0
$157$	3.00000	+	3.00000i	0.239426	+	0.239426i	0.816612	−	0.577186i	$-0.195849\pi$
$157$	3.00000	+	3.00000i	0.239426	+	0.239426i	−0.577186	+	0.816612i	$0.695849\pi$
$158$		−	14.0000i		−	1.11378i
$159$		0			0
$160$	1.00000	+	2.00000i	0.0790569	+	0.158114i
$161$	10.0000	−	10.0000i	0.788110	−	0.788110i
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	−1.00000	+	1.00000i	−0.0780869	+	0.0780869i
$165$		0			0
$166$			6.00000i			0.465690i
$167$			2.00000i			0.154765i	0.997001	+	0.0773823i	$0.0246562\pi$
$167$			2.00000i			0.154765i	−0.997001	+	0.0773823i	$0.975344\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$	−15.0000	−	5.00000i	−1.15045	−	0.383482i
$171$		0			0
$172$	5.00000	+	5.00000i	0.381246	+	0.381246i
$173$	−15.0000	−	15.0000i	−1.14043	−	1.14043i	−0.988372	−	0.152057i	$-0.951410\pi$
$173$	−15.0000	−	15.0000i	−1.14043	−	1.14043i	−0.152057	−	0.988372i	$-0.548590\pi$
$174$		0			0
$175$	8.00000	+	6.00000i	0.604743	+	0.453557i
$176$	−1.00000	−	1.00000i	−0.0753778	−	0.0753778i
$177$		0			0
$178$	−7.00000	+	7.00000i	−0.524672	+	0.524672i
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$		0			0
$181$		−	20.0000i		−	1.48659i	−0.668965	−	0.743294i	$-0.733262\pi$
$181$		−	20.0000i		−	1.48659i	0.668965	−	0.743294i	$-0.266738\pi$
$182$	4.00000	−	6.00000i	0.296500	−	0.444750i
$183$		0			0
$184$	−5.00000	−	5.00000i	−0.368605	−	0.368605i
$185$	16.0000	−	8.00000i	1.17634	−	0.588172i
$186$		0			0
$187$	10.0000			0.731272
$188$			2.00000i			0.145865i
$189$		0			0
$190$	3.00000	−	9.00000i	0.217643	−	0.652929i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$	−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
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	3.00000	−	4.00000i	0.212132	−	0.282843i
$201$		0			0
$202$		0			0
$203$	−8.00000			−0.561490
$204$		0			0
$205$	3.00000	+	1.00000i	0.209529	+	0.0698430i
$206$	5.00000	+	5.00000i	0.348367	+	0.348367i
$207$		0			0
$208$	−3.00000	−	2.00000i	−0.208013	−	0.138675i
$209$			6.00000i			0.415029i
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	1.00000	−	1.00000i	0.0686803	−	0.0686803i
$213$		0			0
$214$	13.0000	+	13.0000i	0.888662	+	0.888662i
$215$	5.00000	−	15.0000i	0.340997	−	1.02299i
$216$		0			0
$217$	−2.00000	−	2.00000i	−0.135769	−	0.135769i
$218$	13.0000	+	13.0000i	0.880471	+	0.880471i
$219$		0			0
$220$	−1.00000	+	3.00000i	−0.0674200	+	0.202260i
$221$	25.0000	−	5.00000i	1.68168	−	0.336336i
$222$		0			0
$223$			6.00000i			0.401790i	0.979613	+	0.200895i	$0.0643850\pi$
$223$			6.00000i			0.401790i	−0.979613	+	0.200895i	$0.935615\pi$
$224$			2.00000i			0.133631i
$225$		0			0
$226$	9.00000	−	9.00000i	0.598671	−	0.598671i
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$		0			0
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	−0.601002	−	0.799248i	$-0.705232\pi$
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	0.799248	+	0.601002i	$0.205232\pi$
$230$	−5.00000	+	15.0000i	−0.329690	+	0.989071i
$231$		0			0
$232$			4.00000i			0.262613i
$233$	−5.00000	−	5.00000i	−0.327561	−	0.327561i	0.524097	−	0.851658i	$-0.324403\pi$
$233$	−5.00000	−	5.00000i	−0.327561	−	0.327561i	−0.851658	+	0.524097i	$0.824403\pi$
$234$		0			0
$235$	4.00000	−	2.00000i	0.260931	−	0.130466i
$236$	−3.00000	+	3.00000i	−0.195283	+	0.195283i
$237$		0			0
$238$	−10.0000	−	10.0000i	−0.648204	−	0.648204i
$239$	−7.00000	−	7.00000i	−0.452792	−	0.452792i	0.443488	−	0.896280i	$-0.353741\pi$
$239$	−7.00000	−	7.00000i	−0.452792	−	0.452792i	−0.896280	+	0.443488i	$0.853741\pi$
$240$		0			0
$241$	1.00000	+	1.00000i	0.0644157	+	0.0644157i	0.738581	−	0.674165i	$-0.235496\pi$
$241$	1.00000	+	1.00000i	0.0644157	+	0.0644157i	−0.674165	+	0.738581i	$0.735496\pi$
$242$			9.00000i			0.578542i
$243$		0			0
$244$	2.00000			0.128037
$245$	−3.00000	−	6.00000i	−0.191663	−	0.383326i
$246$		0			0
$247$	3.00000	+	15.0000i	0.190885	+	0.954427i
$248$	−1.00000	+	1.00000i	−0.0635001	+	0.0635001i
$249$		0			0
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$		−	30.0000i		−	1.89358i	−0.321847	−	0.946792i	$-0.604304\pi$
$251$		−	30.0000i		−	1.89358i	0.321847	−	0.946792i	$-0.395696\pi$
$252$		0			0
$253$		−	10.0000i		−	0.628695i
$254$	15.0000	−	15.0000i	0.941184	−	0.941184i
$255$		0			0
$256$	1.00000			0.0625000
$257$	15.0000	−	15.0000i	0.935674	−	0.935674i	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	15.0000	−	15.0000i	0.935674	−	0.935674i	0.998053	+	0.0623783i	$0.0198685\pi$
$258$		0			0
$259$	16.0000			0.994192
$260$	−1.00000	+	8.00000i	−0.0620174	+	0.496139i
$261$		0			0
$262$	12.0000			0.741362
$263$	−9.00000	+	9.00000i	−0.554964	+	0.554964i	−0.927869	−	0.372906i	$-0.878362\pi$
$263$	−9.00000	+	9.00000i	−0.554964	+	0.554964i	0.372906	+	0.927869i	$0.378362\pi$
$264$		0			0
$265$	−3.00000	−	1.00000i	−0.184289	−	0.0614295i
$266$	6.00000	−	6.00000i	0.367884	−	0.367884i
$267$		0			0
$268$	−12.0000			−0.733017
$269$			16.0000i			0.975537i	0.872973	+	0.487769i	$0.162189\pi$
$269$			16.0000i			0.975537i	−0.872973	+	0.487769i	$0.837811\pi$
$270$		0			0
$271$	−9.00000	−	9.00000i	−0.546711	−	0.546711i	0.378777	−	0.925488i	$-0.376345\pi$
$271$	−9.00000	−	9.00000i	−0.546711	−	0.546711i	−0.925488	+	0.378777i	$0.876345\pi$
$272$	−5.00000	+	5.00000i	−0.303170	+	0.303170i
$273$		0			0
$274$		−	12.0000i		−	0.724947i
$275$	7.00000	−	1.00000i	0.422116	−	0.0603023i
$276$		0			0
$277$	−5.00000	+	5.00000i	−0.300421	+	0.300421i	−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−5.00000	+	5.00000i	−0.300421	+	0.300421i	0.540758	+	0.841178i	$0.318138\pi$
$278$		−	14.0000i		−	0.839664i
$279$		0			0
$280$	4.00000	−	2.00000i	0.239046	−	0.119523i
$281$	−21.0000	−	21.0000i	−1.25275	−	1.25275i	−0.954480	−	0.298275i	$-0.903589\pi$
$281$	−21.0000	−	21.0000i	−1.25275	−	1.25275i	−0.298275	−	0.954480i	$-0.596411\pi$
$282$		0			0
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	0.103022	−	0.994679i	$-0.467149\pi$
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	−0.994679	+	0.103022i	$0.967149\pi$
$284$	−1.00000	+	1.00000i	−0.0593391	+	0.0593391i
$285$		0			0
$286$	−1.00000	−	5.00000i	−0.0591312	−	0.295656i
$287$	2.00000	+	2.00000i	0.118056	+	0.118056i
$288$		0			0
$289$		−	33.0000i		−	1.94118i
$290$	8.00000	−	4.00000i	0.469776	−	0.234888i
$291$		0			0
$292$	−6.00000			−0.351123
$293$	26.0000			1.51894			0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000			1.51894			0.759468	+	0.650545i	$0.225459\pi$
$294$		0			0
$295$	9.00000	+	3.00000i	0.524000	+	0.174667i
$296$		−	8.00000i		−	0.464991i
$297$		0			0
$298$	−13.0000	−	13.0000i	−0.753070	−	0.753070i
$299$	−5.00000	−	25.0000i	−0.289157	−	1.44579i
$300$		0			0
$301$	10.0000	−	10.0000i	0.576390	−	0.576390i
$302$	9.00000	+	9.00000i	0.517892	+	0.517892i
$303$		0			0
$304$	−3.00000	−	3.00000i	−0.172062	−	0.172062i
$305$	−2.00000	−	4.00000i	−0.114520	−	0.229039i
$306$		0			0
$307$		−	2.00000i		−	0.114146i	−0.998370	−	0.0570730i	$-0.981823\pi$
$307$		−	2.00000i		−	0.114146i	0.998370	−	0.0570730i	$-0.0181768\pi$
$308$	−2.00000	+	2.00000i	−0.113961	+	0.113961i
$309$		0			0
$310$	3.00000	+	1.00000i	0.170389	+	0.0567962i
$311$			10.0000i			0.567048i	0.958965	+	0.283524i	$0.0915036\pi$
$311$			10.0000i			0.567048i	−0.958965	+	0.283524i	$0.908496\pi$
$312$		0			0
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$	−3.00000	−	3.00000i	−0.169300	−	0.169300i
$315$		0			0
$316$			14.0000i			0.787562i
$317$	2.00000			0.112331			0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000			0.112331			0.0561656	+	0.998421i	$0.482113\pi$
$318$		0			0
$319$	−4.00000	+	4.00000i	−0.223957	+	0.223957i
$320$	−1.00000	−	2.00000i	−0.0559017	−	0.111803i
$321$		0			0
$322$	−10.0000	+	10.0000i	−0.557278	+	0.557278i
$323$	30.0000			1.66924
$324$		0			0
$325$	17.0000	−	6.00000i	0.942990	−	0.332820i
$326$	−4.00000			−0.221540
$327$		0			0
$328$	1.00000	−	1.00000i	0.0552158	−	0.0552158i
$329$	4.00000			0.220527
$330$		0			0
$331$	−9.00000	+	9.00000i	−0.494685	+	0.494685i	−0.909779	−	0.415094i	$-0.863749\pi$
$331$	−9.00000	+	9.00000i	−0.494685	+	0.494685i	0.415094	+	0.909779i	$0.363749\pi$
$332$		−	6.00000i		−	0.329293i
$333$		0			0
$334$		−	2.00000i		−	0.109435i
$335$	12.0000	+	24.0000i	0.655630	+	1.31126i
$336$		0			0
$337$	5.00000	−	5.00000i	0.272367	−	0.272367i	−0.557685	−	0.830053i	$-0.688310\pi$
$337$	5.00000	−	5.00000i	0.272367	−	0.272367i	0.830053	+	0.557685i	$0.188310\pi$
$338$	−5.00000	−	12.0000i	−0.271964	−	0.652714i
$339$		0			0
$340$	15.0000	+	5.00000i	0.813489	+	0.271163i
$341$	−2.00000			−0.108306
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$	−5.00000	−	5.00000i	−0.269582	−	0.269582i
$345$		0			0
$346$	15.0000	+	15.0000i	0.806405	+	0.806405i
$347$	7.00000	+	7.00000i	0.375780	+	0.375780i	0.869577	−	0.493797i	$-0.164392\pi$
$347$	7.00000	+	7.00000i	0.375780	+	0.375780i	−0.493797	+	0.869577i	$0.664392\pi$
$348$		0			0
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	−0.622240	−	0.782826i	$-0.713777\pi$
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	0.782826	+	0.622240i	$0.213777\pi$
$350$	−8.00000	−	6.00000i	−0.427618	−	0.320713i
$351$		0			0
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$		−	16.0000i		−	0.851594i	−0.904819	−	0.425797i	$-0.859994\pi$
$353$		−	16.0000i		−	0.851594i	0.904819	−	0.425797i	$-0.140006\pi$
$354$		0			0
$355$	3.00000	+	1.00000i	0.159223	+	0.0530745i
$356$	7.00000	−	7.00000i	0.370999	−	0.370999i
$357$		0			0
$358$	20.0000			1.05703
$359$	−13.0000	+	13.0000i	−0.686114	+	0.686114i	−0.961371	−	0.275257i	$-0.911237\pi$
$359$	−13.0000	+	13.0000i	−0.686114	+	0.686114i	0.275257	+	0.961371i	$0.411237\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$			20.0000i			1.05118i
$363$		0			0
$364$	−4.00000	+	6.00000i	−0.209657	+	0.314485i
$365$	6.00000	+	12.0000i	0.314054	+	0.628109i
$366$		0			0
$367$	3.00000	+	3.00000i	0.156599	+	0.156599i	0.781058	−	0.624459i	$-0.214680\pi$
$367$	3.00000	+	3.00000i	0.156599	+	0.156599i	−0.624459	+	0.781058i	$0.714680\pi$
$368$	5.00000	+	5.00000i	0.260643	+	0.260643i
$369$		0			0
$370$	−16.0000	+	8.00000i	−0.831800	+	0.415900i
$371$	−2.00000	−	2.00000i	−0.103835	−	0.103835i
$372$		0			0
$373$	−1.00000	+	1.00000i	−0.0517780	+	0.0517780i	−0.732522	−	0.680744i	$-0.761657\pi$
$373$	−1.00000	+	1.00000i	−0.0517780	+	0.0517780i	0.680744	+	0.732522i	$0.261657\pi$
$374$	−10.0000			−0.517088
$375$		0			0
$376$		−	2.00000i		−	0.103142i
$377$	−8.00000	+	12.0000i	−0.412021	+	0.618031i
$378$		0			0
$379$	17.0000	+	17.0000i	0.873231	+	0.873231i	0.992823	−	0.119592i	$-0.0381586\pi$
$379$	17.0000	+	17.0000i	0.873231	+	0.873231i	−0.119592	+	0.992823i	$0.538159\pi$
$380$	−3.00000	+	9.00000i	−0.153897	+	0.461690i
$381$		0			0
$382$	−8.00000			−0.409316
$383$		−	6.00000i		−	0.306586i	−0.988181	−	0.153293i	$-0.951012\pi$
$383$		−	6.00000i		−	0.306586i	0.988181	−	0.153293i	$-0.0489878\pi$
$384$		0			0
$385$	6.00000	+	2.00000i	0.305788	+	0.101929i
$386$	−14.0000			−0.712581
$387$		0			0
$388$	−2.00000			−0.101535
$389$	10.0000			0.507020			0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000			0.507020			0.253510	+	0.967333i	$0.418415\pi$
$390$		0			0
$391$	−50.0000			−2.52861
$392$	−3.00000			−0.151523
$393$		0			0
$394$	18.0000			0.906827
$395$	28.0000	−	14.0000i	1.40883	−	0.704416i
$396$		0			0
$397$			8.00000i			0.401508i	0.979642	+	0.200754i	$0.0643393\pi$
$397$			8.00000i			0.401508i	−0.979642	+	0.200754i	$0.935661\pi$
$398$		0			0
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	−1.00000	−	1.00000i	−0.0499376	−	0.0499376i	0.681697	−	0.731635i	$-0.261242\pi$
$401$	−1.00000	−	1.00000i	−0.0499376	−	0.0499376i	−0.731635	+	0.681697i	$0.761242\pi$
$402$		0			0
$403$	−5.00000	+	1.00000i	−0.249068	+	0.0498135i
$404$		0			0
$405$		0			0
$406$	8.00000			0.397033
$407$	8.00000	−	8.00000i	0.396545	−	0.396545i
$408$		0			0
$409$	−3.00000	−	3.00000i	−0.148340	−	0.148340i	0.629036	−	0.777376i	$-0.283450\pi$
$409$	−3.00000	−	3.00000i	−0.148340	−	0.148340i	−0.777376	+	0.629036i	$0.783450\pi$
$410$	−3.00000	−	1.00000i	−0.148159	−	0.0493865i
$411$		0			0
$412$	−5.00000	−	5.00000i	−0.246332	−	0.246332i
$413$	6.00000	+	6.00000i	0.295241	+	0.295241i
$414$		0			0
$415$	−12.0000	+	6.00000i	−0.589057	+	0.294528i
$416$	3.00000	+	2.00000i	0.147087	+	0.0980581i
$417$		0			0
$418$		−	6.00000i		−	0.293470i
$419$			26.0000i			1.27018i	0.772437	+	0.635092i	$0.219038\pi$
$419$			26.0000i			1.27018i	−0.772437	+	0.635092i	$0.780962\pi$
$420$		0			0
$421$	−9.00000	+	9.00000i	−0.438633	+	0.438633i	−0.891552	−	0.452919i	$-0.850383\pi$
$421$	−9.00000	+	9.00000i	−0.438633	+	0.438633i	0.452919	+	0.891552i	$0.350383\pi$
$422$	−12.0000			−0.584151
$423$		0			0
$424$	−1.00000	+	1.00000i	−0.0485643	+	0.0485643i
$425$	−5.00000	−	35.0000i	−0.242536	−	1.69775i
$426$		0			0
$427$		−	4.00000i		−	0.193574i
$428$	−13.0000	−	13.0000i	−0.628379	−	0.628379i
$429$		0			0
$430$	−5.00000	+	15.0000i	−0.241121	+	0.723364i
$431$	−21.0000	+	21.0000i	−1.01153	+	1.01153i	−0.0116017	+	0.999933i	$0.503693\pi$
$431$	−21.0000	+	21.0000i	−1.01153	+	1.01153i	−0.999933	+	0.0116017i	$0.996307\pi$
$432$		0			0
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	0.247925	−	0.968779i	$-0.420251\pi$
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	−0.968779	+	0.247925i	$0.920251\pi$
$434$	2.00000	+	2.00000i	0.0960031	+	0.0960031i
$435$		0			0
$436$	−13.0000	−	13.0000i	−0.622587	−	0.622587i
$437$		−	30.0000i		−	1.43509i
$438$		0			0
$439$	40.0000			1.90910			0.954548	−	0.298057i	$-0.0963387\pi$
$439$	40.0000			1.90910			0.954548	+	0.298057i	$0.0963387\pi$
$440$	1.00000	−	3.00000i	0.0476731	−	0.143019i
$441$		0			0
$442$	−25.0000	+	5.00000i	−1.18913	+	0.237826i
$443$	−19.0000	+	19.0000i	−0.902717	+	0.902717i	−0.995670	−	0.0929532i	$-0.970369\pi$
$443$	−19.0000	+	19.0000i	−0.902717	+	0.902717i	0.0929532	+	0.995670i	$0.470369\pi$
$444$		0			0
$445$	−21.0000	−	7.00000i	−0.995495	−	0.331832i
$446$		−	6.00000i		−	0.284108i
$447$		0			0
$448$		−	2.00000i		−	0.0944911i
$449$	7.00000	−	7.00000i	0.330350	−	0.330350i	−0.522369	−	0.852720i	$-0.674952\pi$
$449$	7.00000	−	7.00000i	0.330350	−	0.330350i	0.852720	+	0.522369i	$0.174952\pi$
$450$		0			0
$451$	2.00000			0.0941763
$452$	−9.00000	+	9.00000i	−0.423324	+	0.423324i
$453$		0			0
$454$	−12.0000			−0.563188
$455$	16.0000	+	2.00000i	0.750092	+	0.0937614i
$456$		0			0
$457$	38.0000			1.77757			0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000			1.77757			0.888783	+	0.458329i	$0.151552\pi$
$458$	−3.00000	+	3.00000i	−0.140181	+	0.140181i
$459$		0			0
$460$	5.00000	−	15.0000i	0.233126	−	0.699379i
$461$	−11.0000	+	11.0000i	−0.512321	+	0.512321i	−0.915237	−	0.402916i	$-0.867997\pi$
$461$	−11.0000	+	11.0000i	−0.512321	+	0.512321i	0.402916	+	0.915237i	$0.367997\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		−	4.00000i		−	0.185695i
$465$		0			0
$466$	5.00000	+	5.00000i	0.231621	+	0.231621i
$467$	5.00000	−	5.00000i	0.231372	−	0.231372i	−0.581893	−	0.813265i	$-0.697688\pi$
$467$	5.00000	−	5.00000i	0.231372	−	0.231372i	0.813265	+	0.581893i	$0.197688\pi$
$468$		0			0
$469$			24.0000i			1.10822i
$470$	−4.00000	+	2.00000i	−0.184506	+	0.0922531i
$471$		0			0
$472$	3.00000	−	3.00000i	0.138086	−	0.138086i
$473$		−	10.0000i		−	0.459800i
$474$		0			0
$475$	21.0000	−	3.00000i	0.963546	−	0.137649i
$476$	10.0000	+	10.0000i	0.458349	+	0.458349i
$477$		0			0
$478$	7.00000	+	7.00000i	0.320173	+	0.320173i
$479$	−13.0000	+	13.0000i	−0.593985	+	0.593985i	−0.938705	−	0.344720i	$-0.887974\pi$
$479$	−13.0000	+	13.0000i	−0.593985	+	0.593985i	0.344720	+	0.938705i	$0.387974\pi$
$480$		0			0
$481$	16.0000	−	24.0000i	0.729537	−	1.09431i
$482$	−1.00000	−	1.00000i	−0.0455488	−	0.0455488i
$483$		0			0
$484$		−	9.00000i		−	0.409091i
$485$	2.00000	+	4.00000i	0.0908153	+	0.181631i
$486$		0			0
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$	−2.00000			−0.0905357
$489$		0			0
$490$	3.00000	+	6.00000i	0.135526	+	0.271052i
$491$			10.0000i			0.451294i	0.974209	+	0.225647i	$0.0724495\pi$
$491$			10.0000i			0.451294i	−0.974209	+	0.225647i	$0.927550\pi$
$492$		0			0
$493$	20.0000	+	20.0000i	0.900755	+	0.900755i
$494$	−3.00000	−	15.0000i	−0.134976	−	0.674882i
$495$		0			0
$496$	1.00000	−	1.00000i	0.0449013	−	0.0449013i
$497$	2.00000	+	2.00000i	0.0897123	+	0.0897123i
$498$		0			0
$499$	−23.0000	−	23.0000i	−1.02962	−	1.02962i	−0.999548	−	0.0300737i	$-0.990426\pi$
$499$	−23.0000	−	23.0000i	−1.02962	−	1.02962i	−0.0300737	−	0.999548i	$-0.509574\pi$
$500$	11.0000	+	2.00000i	0.491935	+	0.0894427i
$501$		0			0
$502$			30.0000i			1.33897i
$503$	−9.00000	+	9.00000i	−0.401290	+	0.401290i	−0.878688	−	0.477397i	$-0.841580\pi$
$503$	−9.00000	+	9.00000i	−0.401290	+	0.401290i	0.477397	+	0.878688i	$0.341580\pi$
$504$		0			0
$505$		0			0
$506$			10.0000i			0.444554i
$507$		0			0
$508$	−15.0000	+	15.0000i	−0.665517	+	0.665517i
$509$	13.0000	+	13.0000i	0.576215	+	0.576215i	0.933858	−	0.357643i	$-0.116420\pi$
$509$	13.0000	+	13.0000i	0.576215	+	0.576215i	−0.357643	+	0.933858i	$0.616420\pi$
$510$		0			0
$511$			12.0000i			0.530849i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−15.0000	+	15.0000i	−0.661622	+	0.661622i
$515$	−5.00000	+	15.0000i	−0.220326	+	0.660979i
$516$		0			0
$517$	2.00000	−	2.00000i	0.0879599	−	0.0879599i
$518$	−16.0000			−0.703000
$519$		0			0
$520$	1.00000	−	8.00000i	0.0438529	−	0.350823i
$521$	−22.0000			−0.963837			−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000			−0.963837			−0.481919	+	0.876216i	$0.660060\pi$
$522$		0			0
$523$	−21.0000	+	21.0000i	−0.918266	+	0.918266i	−0.996903	−	0.0786374i	$-0.974943\pi$
$523$	−21.0000	+	21.0000i	−0.918266	+	0.918266i	0.0786374	+	0.996903i	$0.474943\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	9.00000	−	9.00000i	0.392419	−	0.392419i
$527$			10.0000i			0.435607i
$528$		0			0
$529$			27.0000i			1.17391i
$530$	3.00000	+	1.00000i	0.130312	+	0.0434372i
$531$		0			0
$532$	−6.00000	+	6.00000i	−0.260133	+	0.260133i
$533$	5.00000	−	1.00000i	0.216574	−	0.0433148i
$534$		0			0
$535$	−13.0000	+	39.0000i	−0.562039	+	1.68612i
$536$	12.0000			0.518321
$537$		0			0
$538$		−	16.0000i		−	0.689809i
$539$	−3.00000	−	3.00000i	−0.129219	−	0.129219i
$540$		0			0
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$	9.00000	+	9.00000i	0.386583	+	0.386583i
$543$		0			0
$544$	5.00000	−	5.00000i	0.214373	−	0.214373i
$545$	−13.0000	+	39.0000i	−0.556859	+	1.67058i
$546$		0			0
$547$	−7.00000	−	7.00000i	−0.299298	−	0.299298i	0.541441	−	0.840739i	$-0.317879\pi$
$547$	−7.00000	−	7.00000i	−0.299298	−	0.299298i	−0.840739	+	0.541441i	$0.817879\pi$
$548$			12.0000i			0.512615i
$549$		0			0
$550$	−7.00000	+	1.00000i	−0.298481	+	0.0426401i
$551$	−12.0000	+	12.0000i	−0.511217	+	0.511217i
$552$		0			0
$553$	28.0000			1.19068
$554$	5.00000	−	5.00000i	0.212430	−	0.212430i
$555$		0			0
$556$			14.0000i			0.593732i
$557$		−	8.00000i		−	0.338971i	−0.985533	−	0.169485i	$-0.945789\pi$
$557$		−	8.00000i		−	0.338971i	0.985533	−	0.169485i	$-0.0542106\pi$
$558$		0			0
$559$	−5.00000	−	25.0000i	−0.211477	−	1.05739i
$560$	−4.00000	+	2.00000i	−0.169031	+	0.0845154i
$561$		0			0
$562$	21.0000	+	21.0000i	0.885832	+	0.885832i
$563$	−5.00000	−	5.00000i	−0.210725	−	0.210725i	0.593851	−	0.804575i	$-0.297607\pi$
$563$	−5.00000	−	5.00000i	−0.210725	−	0.210725i	−0.804575	+	0.593851i	$0.797607\pi$
$564$		0			0
$565$	27.0000	+	9.00000i	1.13590	+	0.378633i
$566$	15.0000	+	15.0000i	0.630497	+	0.630497i
$567$		0			0
$568$	1.00000	−	1.00000i	0.0419591	−	0.0419591i
$569$	10.0000			0.419222			0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000			0.419222			0.209611	+	0.977785i	$0.432780\pi$
$570$		0			0
$571$		−	10.0000i		−	0.418487i	−0.977864	−	0.209243i	$-0.932900\pi$
$571$		−	10.0000i		−	0.418487i	0.977864	−	0.209243i	$-0.0671001\pi$
$572$	1.00000	+	5.00000i	0.0418121	+	0.209061i
$573$		0			0
$574$	−2.00000	−	2.00000i	−0.0834784	−	0.0834784i
$575$	−35.0000	+	5.00000i	−1.45960	+	0.208514i
$576$		0			0
$577$	−22.0000			−0.915872			−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000			−0.915872			−0.457936	+	0.888985i	$0.651411\pi$
$578$			33.0000i			1.37262i
$579$		0			0
$580$	−8.00000	+	4.00000i	−0.332182	+	0.166091i
$581$	−12.0000			−0.497844
$582$		0			0
$583$	−2.00000			−0.0828315
$584$	6.00000			0.248282
$585$		0			0
$586$	−26.0000			−1.07405
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		0			0
$589$	−6.00000			−0.247226
$590$	−9.00000	−	3.00000i	−0.370524	−	0.123508i
$591$		0			0
$592$			8.00000i			0.328798i
$593$	−14.0000			−0.574911			−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000			−0.574911			−0.287456	+	0.957794i	$0.592809\pi$
$594$		0			0
$595$	10.0000	−	30.0000i	0.409960	−	1.22988i
$596$	13.0000	+	13.0000i	0.532501	+	0.532501i
$597$		0			0
$598$	5.00000	+	25.0000i	0.204465	+	1.02233i
$599$		−	14.0000i		−	0.572024i	−0.958226	−	0.286012i	$-0.907670\pi$
$599$		−	14.0000i		−	0.572024i	0.958226	−	0.286012i	$-0.0923298\pi$
$600$		0			0
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$	−10.0000	+	10.0000i	−0.407570	+	0.407570i
$603$		0			0
$604$	−9.00000	−	9.00000i	−0.366205	−	0.366205i
$605$	−18.0000	+	9.00000i	−0.731804	+	0.365902i
$606$		0			0
$607$	3.00000	+	3.00000i	0.121766	+	0.121766i	0.765364	−	0.643598i	$-0.222559\pi$
$607$	3.00000	+	3.00000i	0.121766	+	0.121766i	−0.643598	+	0.765364i	$0.722559\pi$
$608$	3.00000	+	3.00000i	0.121666	+	0.121666i
$609$		0			0
$610$	2.00000	+	4.00000i	0.0809776	+	0.161955i
$611$	4.00000	−	6.00000i	0.161823	−	0.242734i
$612$		0			0
$613$		−	4.00000i		−	0.161558i	−0.996732	−	0.0807792i	$-0.974259\pi$
$613$		−	4.00000i		−	0.161558i	0.996732	−	0.0807792i	$-0.0257409\pi$
$614$			2.00000i			0.0807134i
$615$		0			0
$616$	2.00000	−	2.00000i	0.0805823	−	0.0805823i
$617$	−38.0000			−1.52982			−0.764911	−	0.644136i	$-0.777217\pi$
$617$	−38.0000			−1.52982			−0.764911	+	0.644136i	$0.777217\pi$
$618$		0			0
$619$	3.00000	−	3.00000i	0.120580	−	0.120580i	−0.644242	−	0.764822i	$-0.722827\pi$
$619$	3.00000	−	3.00000i	0.120580	−	0.120580i	0.764822	+	0.644242i	$0.222827\pi$
$620$	−3.00000	−	1.00000i	−0.120483	−	0.0401610i
$621$		0			0
$622$		−	10.0000i		−	0.400963i
$623$	−14.0000	−	14.0000i	−0.560898	−	0.560898i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−9.00000	+	9.00000i	−0.359712	+	0.359712i
$627$		0			0
$628$	3.00000	+	3.00000i	0.119713	+	0.119713i
$629$	−40.0000	−	40.0000i	−1.59490	−	1.59490i
$630$		0			0
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	0.891306	−	0.453403i	$-0.149790\pi$
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	−0.453403	+	0.891306i	$0.649790\pi$
$632$		−	14.0000i		−	0.556890i
$633$		0			0
$634$	−2.00000			−0.0794301
$635$	45.0000	+	15.0000i	1.78577	+	0.595257i
$636$		0			0
$637$	−9.00000	−	6.00000i	−0.356593	−	0.237729i
$638$	4.00000	−	4.00000i	0.158362	−	0.158362i
$639$		0			0
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$		0			0
$643$			46.0000i			1.81406i	0.421063	+	0.907031i	$0.361657\pi$
$643$			46.0000i			1.81406i	−0.421063	+	0.907031i	$0.638343\pi$
$644$	10.0000	−	10.0000i	0.394055	−	0.394055i
$645$		0			0
$646$	−30.0000			−1.18033
$647$	−5.00000	+	5.00000i	−0.196570	+	0.196570i	−0.798528	−	0.601958i	$-0.794388\pi$
$647$	−5.00000	+	5.00000i	−0.196570	+	0.196570i	0.601958	+	0.798528i	$0.294388\pi$
$648$		0			0
$649$	6.00000			0.235521
$650$	−17.0000	+	6.00000i	−0.666795	+	0.235339i
$651$		0			0
$652$	4.00000			0.156652
$653$	21.0000	−	21.0000i	0.821794	−	0.821794i	−0.164572	−	0.986365i	$-0.552624\pi$
$653$	21.0000	−	21.0000i	0.821794	−	0.821794i	0.986365	+	0.164572i	$0.0526242\pi$
$654$		0			0
$655$	12.0000	+	24.0000i	0.468879	+	0.937758i
$656$	−1.00000	+	1.00000i	−0.0390434	+	0.0390434i
$657$		0			0
$658$	−4.00000			−0.155936
$659$		−	14.0000i		−	0.545363i	−0.962104	−	0.272681i	$-0.912090\pi$
$659$		−	14.0000i		−	0.545363i	0.962104	−	0.272681i	$-0.0879105\pi$
$660$		0			0
$661$	31.0000	+	31.0000i	1.20576	+	1.20576i	0.972387	+	0.233373i	$0.0749763\pi$
$661$	31.0000	+	31.0000i	1.20576	+	1.20576i	0.233373	+	0.972387i	$0.425024\pi$
$662$	9.00000	−	9.00000i	0.349795	−	0.349795i
$663$		0			0
$664$			6.00000i			0.232845i
$665$	18.0000	+	6.00000i	0.698010	+	0.232670i
$666$		0			0
$667$	20.0000	−	20.0000i	0.774403	−	0.774403i
$668$			2.00000i			0.0773823i
$669$		0			0
$670$	−12.0000	−	24.0000i	−0.463600	−	0.927201i
$671$	−2.00000	−	2.00000i	−0.0772091	−	0.0772091i
$672$		0			0
$673$	5.00000	+	5.00000i	0.192736	+	0.192736i	0.796877	−	0.604141i	$-0.206484\pi$
$673$	5.00000	+	5.00000i	0.192736	+	0.192736i	−0.604141	+	0.796877i	$0.706484\pi$
$674$	−5.00000	+	5.00000i	−0.192593	+	0.192593i
$675$		0			0
$676$	5.00000	+	12.0000i	0.192308	+	0.461538i
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	0.109973	−	0.993935i	$-0.464924\pi$
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	−0.993935	+	0.109973i	$0.964924\pi$
$678$		0			0
$679$			4.00000i			0.153506i
$680$	−15.0000	−	5.00000i	−0.575224	−	0.191741i
$681$		0			0
$682$	2.00000			0.0765840
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$	24.0000	−	12.0000i	0.916993	−	0.458496i
$686$			20.0000i			0.763604i
$687$		0			0
$688$	5.00000	+	5.00000i	0.190623	+	0.190623i
$689$	−5.00000	+	1.00000i	−0.190485	+	0.0380970i
$690$		0			0
$691$	−9.00000	+	9.00000i	−0.342376	+	0.342376i	−0.857260	−	0.514884i	$-0.827835\pi$
$691$	−9.00000	+	9.00000i	−0.342376	+	0.342376i	0.514884	+	0.857260i	$0.327835\pi$
$692$	−15.0000	−	15.0000i	−0.570214	−	0.570214i
$693$		0			0
$694$	−7.00000	−	7.00000i	−0.265716	−	0.265716i
$695$	28.0000	−	14.0000i	1.06210	−	0.531050i
$696$		0			0
$697$		−	10.0000i		−	0.378777i
$698$	−3.00000	+	3.00000i	−0.113552	+	0.113552i
$699$		0			0
$700$	8.00000	+	6.00000i	0.302372	+	0.226779i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	24.0000	−	24.0000i	0.905177	−	0.905177i
$704$	−1.00000	−	1.00000i	−0.0376889	−	0.0376889i
$705$		0			0
$706$			16.0000i			0.602168i
$707$		0			0
$708$		0			0
$709$	3.00000	−	3.00000i	0.112667	−	0.112667i	−0.648526	−	0.761193i	$-0.724614\pi$
$709$	3.00000	−	3.00000i	0.112667	−	0.112667i	0.761193	+	0.648526i	$0.224614\pi$
$710$	−3.00000	−	1.00000i	−0.112588	−	0.0375293i
$711$		0			0
$712$	−7.00000	+	7.00000i	−0.262336	+	0.262336i
$713$	10.0000			0.374503
$714$		0			0
$715$	9.00000	−	7.00000i	0.336581	−	0.261785i
$716$	−20.0000			−0.747435
$717$		0			0
$718$	13.0000	−	13.0000i	0.485156	−	0.485156i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	−10.0000	+	10.0000i	−0.372419	+	0.372419i
$722$			1.00000i			0.0372161i
$723$		0			0
$724$		−	20.0000i		−	0.743294i
$725$	16.0000	+	12.0000i	0.594225	+	0.445669i
$726$		0			0
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.368418	+	0.929660i	$0.620100\pi$
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.929660	+	0.368418i	$0.879900\pi$
$728$	4.00000	−	6.00000i	0.148250	−	0.222375i
$729$		0			0
$730$	−6.00000	−	12.0000i	−0.222070	−	0.444140i
$731$	−50.0000			−1.84932
$732$		0			0
$733$		−	44.0000i		−	1.62518i	−0.582838	−	0.812589i	$-0.698058\pi$
$733$		−	44.0000i		−	1.62518i	0.582838	−	0.812589i	$-0.301942\pi$
$734$	−3.00000	−	3.00000i	−0.110732	−	0.110732i
$735$		0			0
$736$	−5.00000	−	5.00000i	−0.184302	−	0.184302i
$737$	12.0000	+	12.0000i	0.442026	+	0.442026i
$738$		0			0
$739$	−37.0000	+	37.0000i	−1.36107	+	1.36107i	−0.488507	+	0.872560i	$0.662458\pi$
$739$	−37.0000	+	37.0000i	−1.36107	+	1.36107i	−0.872560	+	0.488507i	$0.837542\pi$
$740$	16.0000	−	8.00000i	0.588172	−	0.294086i
$741$		0			0
$742$	2.00000	+	2.00000i	0.0734223	+	0.0734223i
$743$		−	6.00000i		−	0.220119i	−0.993925	−	0.110059i	$-0.964896\pi$
$743$		−	6.00000i		−	0.220119i	0.993925	−	0.110059i	$-0.0351041\pi$
$744$		0			0
$745$	13.0000	−	39.0000i	0.476283	−	1.42885i
$746$	1.00000	−	1.00000i	0.0366126	−	0.0366126i
$747$		0			0
$748$	10.0000			0.365636
$749$	−26.0000	+	26.0000i	−0.950019	+	0.950019i
$750$		0			0
$751$		−	10.0000i		−	0.364905i	−0.983215	−	0.182453i	$-0.941596\pi$
$751$		−	10.0000i		−	0.364905i	0.983215	−	0.182453i	$-0.0584036\pi$
$752$			2.00000i			0.0729325i
$753$		0			0
$754$	8.00000	−	12.0000i	0.291343	−	0.437014i
$755$	−9.00000	+	27.0000i	−0.327544	+	0.982631i
$756$		0			0
$757$	−17.0000	−	17.0000i	−0.617876	−	0.617876i	0.327111	−	0.944986i	$-0.393925\pi$
$757$	−17.0000	−	17.0000i	−0.617876	−	0.617876i	−0.944986	+	0.327111i	$0.893925\pi$
$758$	−17.0000	−	17.0000i	−0.617468	−	0.617468i
$759$		0			0
$760$	3.00000	−	9.00000i	0.108821	−	0.326464i
$761$	19.0000	+	19.0000i	0.688749	+	0.688749i	0.961956	−	0.273206i	$-0.0880841\pi$
$761$	19.0000	+	19.0000i	0.688749	+	0.688749i	−0.273206	+	0.961956i	$0.588084\pi$
$762$		0			0
$763$	−26.0000	+	26.0000i	−0.941263	+	0.941263i
$764$	8.00000			0.289430
$765$		0			0
$766$			6.00000i			0.216789i
$767$	15.0000	−	3.00000i	0.541619	−	0.108324i
$768$		0			0
$769$	−23.0000	−	23.0000i	−0.829401	−	0.829401i	0.158033	−	0.987434i	$-0.449485\pi$
$769$	−23.0000	−	23.0000i	−0.829401	−	0.829401i	−0.987434	+	0.158033i	$0.949485\pi$
$770$	−6.00000	−	2.00000i	−0.216225	−	0.0720750i
$771$		0			0
$772$	14.0000			0.503871
$773$			24.0000i			0.863220i	0.902060	+	0.431610i	$0.142054\pi$
$773$			24.0000i			0.863220i	−0.902060	+	0.431610i	$0.857946\pi$
$774$		0			0
$775$	1.00000	+	7.00000i	0.0359211	+	0.251447i
$776$	2.00000			0.0717958
$777$		0			0
$778$	−10.0000			−0.358517
$779$	6.00000			0.214972
$780$		0			0
$781$	2.00000			0.0715656
$782$	50.0000			1.78800
$783$		0			0
$784$	3.00000			0.107143
$785$	3.00000	−	9.00000i	0.107075	−	0.321224i
$786$		0			0
$787$		−	42.0000i		−	1.49714i	−0.663057	−	0.748569i	$-0.730741\pi$
$787$		−	42.0000i		−	1.49714i	0.663057	−	0.748569i	$-0.269259\pi$
$788$	−18.0000			−0.641223
$789$		0			0
$790$	−28.0000	+	14.0000i	−0.996195	+	0.498098i
$791$	18.0000	+	18.0000i	0.640006	+	0.640006i
$792$		0			0
$793$	−6.00000	−	4.00000i	−0.213066	−	0.142044i
$794$		−	8.00000i		−	0.283909i
$795$		0			0
$796$		0			0
$797$	5.00000	−	5.00000i	0.177109	−	0.177109i	−0.612985	−	0.790094i	$-0.710032\pi$
$797$	5.00000	−	5.00000i	0.177109	−	0.177109i	0.790094	+	0.612985i	$0.210032\pi$
$798$		0			0
$799$	−10.0000	−	10.0000i	−0.353775	−	0.353775i
$800$	3.00000	−	4.00000i	0.106066	−	0.141421i
$801$		0			0
$802$	1.00000	+	1.00000i	0.0353112	+	0.0353112i
$803$	6.00000	+	6.00000i	0.211735	+	0.211735i
$804$		0			0
$805$	−30.0000	−	10.0000i	−1.05736	−	0.352454i
$806$	5.00000	−	1.00000i	0.176117	−	0.0352235i
$807$		0			0
$808$		0			0
$809$			36.0000i			1.26569i	0.774277	+	0.632846i	$0.218114\pi$
$809$			36.0000i			1.26569i	−0.774277	+	0.632846i	$0.781886\pi$
$810$		0			0
$811$	11.0000	−	11.0000i	0.386262	−	0.386262i	−0.487090	−	0.873352i	$-0.661942\pi$
$811$	11.0000	−	11.0000i	0.386262	−	0.386262i	0.873352	+	0.487090i	$0.161942\pi$
$812$	−8.00000			−0.280745
$813$		0			0
$814$	−8.00000	+	8.00000i	−0.280400	+	0.280400i
$815$	−4.00000	−	8.00000i	−0.140114	−	0.280228i
$816$		0			0
$817$		−	30.0000i		−	1.04957i
$818$	3.00000	+	3.00000i	0.104893	+	0.104893i
$819$		0			0
$820$	3.00000	+	1.00000i	0.104765	+	0.0349215i
$821$	29.0000	−	29.0000i	1.01211	−	1.01211i	0.0121812	−	0.999926i	$-0.496123\pi$
$821$	29.0000	−	29.0000i	1.01211	−	1.01211i	0.999926	−	0.0121812i	$-0.00387748\pi$
$822$		0			0
$823$	15.0000	+	15.0000i	0.522867	+	0.522867i	0.918436	−	0.395569i	$-0.129453\pi$
$823$	15.0000	+	15.0000i	0.522867	+	0.522867i	−0.395569	+	0.918436i	$0.629453\pi$
$824$	5.00000	+	5.00000i	0.174183	+	0.174183i
$825$		0			0
$826$	−6.00000	−	6.00000i	−0.208767	−	0.208767i
$827$			2.00000i			0.0695468i	0.999395	+	0.0347734i	$0.0110710\pi$
$827$			2.00000i			0.0695468i	−0.999395	+	0.0347734i	$0.988929\pi$
$828$		0			0
$829$	−30.0000			−1.04194			−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000			−1.04194			−0.520972	+	0.853574i	$0.674430\pi$
$830$	12.0000	−	6.00000i	0.416526	−	0.208263i
$831$		0			0
$832$	−3.00000	−	2.00000i	−0.104006	−	0.0693375i
$833$	−15.0000	+	15.0000i	−0.519719	+	0.519719i
$834$		0			0
$835$	4.00000	−	2.00000i	0.138426	−	0.0692129i
$836$			6.00000i			0.207514i
$837$		0			0
$838$		−	26.0000i		−	0.898155i
$839$	−13.0000	+	13.0000i	−0.448810	+	0.448810i	−0.894959	−	0.446149i	$-0.852795\pi$
$839$	−13.0000	+	13.0000i	−0.448810	+	0.448810i	0.446149	+	0.894959i	$0.352795\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$	9.00000	−	9.00000i	0.310160	−	0.310160i
$843$		0			0
$844$	12.0000			0.413057
$845$	19.0000	−	22.0000i	0.653620	−	0.756823i
$846$		0			0
$847$	−18.0000			−0.618487
$848$	1.00000	−	1.00000i	0.0343401	−	0.0343401i
$849$		0			0
$850$	5.00000	+	35.0000i	0.171499	+	1.20049i
$851$	−40.0000	+	40.0000i	−1.37118	+	1.37118i
$852$		0			0
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$			4.00000i			0.136877i
$855$		0			0
$856$	13.0000	+	13.0000i	0.444331	+	0.444331i
$857$	−5.00000	+	5.00000i	−0.170797	+	0.170797i	−0.787329	−	0.616533i	$-0.788537\pi$
$857$	−5.00000	+	5.00000i	−0.170797	+	0.170797i	0.616533	+	0.787329i	$0.288537\pi$
$858$		0			0
$859$		−	26.0000i		−	0.887109i	−0.896248	−	0.443554i	$-0.853717\pi$
$859$		−	26.0000i		−	0.887109i	0.896248	−	0.443554i	$-0.146283\pi$
$860$	5.00000	−	15.0000i	0.170499	−	0.511496i
$861$		0			0
$862$	21.0000	−	21.0000i	0.715263	−	0.715263i
$863$		−	46.0000i		−	1.56586i	−0.622111	−	0.782929i	$-0.713725\pi$
$863$		−	46.0000i		−	1.56586i	0.622111	−	0.782929i	$-0.286275\pi$
$864$		0			0
$865$	−15.0000	+	45.0000i	−0.510015	+	1.53005i
$866$	15.0000	+	15.0000i	0.509721	+	0.509721i
$867$		0			0
$868$	−2.00000	−	2.00000i	−0.0678844	−	0.0678844i
$869$	14.0000	−	14.0000i	0.474917	−	0.474917i
$870$		0			0
$871$	36.0000	+	24.0000i	1.21981	+	0.813209i
$872$	13.0000	+	13.0000i	0.440236	+	0.440236i
$873$		0			0
$874$			30.0000i			1.01477i
$875$	4.00000	−	22.0000i	0.135225	−	0.743736i
$876$		0			0
$877$	18.0000			0.607817			0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000			0.607817			0.303908	+	0.952701i	$0.401708\pi$
$878$	−40.0000			−1.34993
$879$		0			0
$880$	−1.00000	+	3.00000i	−0.0337100	+	0.101130i
$881$		−	20.0000i		−	0.673817i	−0.941537	−	0.336909i	$-0.890619\pi$
$881$		−	20.0000i		−	0.673817i	0.941537	−	0.336909i	$-0.109381\pi$
$882$		0			0
$883$	5.00000	+	5.00000i	0.168263	+	0.168263i	0.786216	−	0.617952i	$-0.212037\pi$
$883$	5.00000	+	5.00000i	0.168263	+	0.168263i	−0.617952	+	0.786216i	$0.712037\pi$
$884$	25.0000	−	5.00000i	0.840841	−	0.168168i
$885$		0			0
$886$	19.0000	−	19.0000i	0.638317	−	0.638317i
$887$	−23.0000	−	23.0000i	−0.772264	−	0.772264i	0.206238	−	0.978502i	$-0.433878\pi$
$887$	−23.0000	−	23.0000i	−0.772264	−	0.772264i	−0.978502	+	0.206238i	$0.933878\pi$
$888$		0			0
$889$	30.0000	+	30.0000i	1.00617	+	1.00617i
$890$	21.0000	+	7.00000i	0.703922	+	0.234641i
$891$		0			0
$892$			6.00000i			0.200895i
$893$	6.00000	−	6.00000i	0.200782	−	0.200782i
$894$		0			0
$895$	20.0000	+	40.0000i	0.668526	+	1.33705i
$896$			2.00000i			0.0668153i
$897$		0			0
$898$	−7.00000	+	7.00000i	−0.233593	+	0.233593i
$899$	−4.00000	−	4.00000i	−0.133407	−	0.133407i
$900$		0			0
$901$			10.0000i			0.333148i
$902$	−2.00000			−0.0665927
$903$		0			0
$904$	9.00000	−	9.00000i	0.299336	−	0.299336i
$905$	−40.0000	+	20.0000i	−1.32964	+	0.664822i
$906$		0			0
$907$	35.0000	−	35.0000i	1.16216	−	1.16216i	0.178153	−	0.984003i	$-0.442988\pi$
$907$	35.0000	−	35.0000i	1.16216	−	1.16216i	0.984003	−	0.178153i	$-0.0570122\pi$
$908$	12.0000			0.398234
$909$		0			0
$910$	−16.0000	−	2.00000i	−0.530395	−	0.0662994i
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$	−6.00000	+	6.00000i	−0.198571	+	0.198571i
$914$	−38.0000			−1.25693
$915$		0			0
$916$	3.00000	−	3.00000i	0.0991228	−	0.0991228i
$917$			24.0000i			0.792550i
$918$		0			0
$919$			14.0000i			0.461817i	0.972975	+	0.230909i	$0.0741699\pi$
$919$			14.0000i			0.461817i	−0.972975	+	0.230909i	$0.925830\pi$
$920$	−5.00000	+	15.0000i	−0.164845	+	0.494535i
$921$		0			0
$922$	11.0000	−	11.0000i	0.362266	−	0.362266i
$923$	5.00000	−	1.00000i	0.164577	−	0.0329154i
$924$		0			0
$925$	−32.0000	−	24.0000i	−1.05215	−	0.789115i
$926$	16.0000			0.525793
$927$		0			0
$928$			4.00000i			0.131306i
$929$	−17.0000	−	17.0000i	−0.557752	−	0.557752i	0.370915	−	0.928667i	$-0.379044\pi$
$929$	−17.0000	−	17.0000i	−0.557752	−	0.557752i	−0.928667	+	0.370915i	$0.879044\pi$
$930$		0			0
$931$	−9.00000	−	9.00000i	−0.294963	−	0.294963i
$932$	−5.00000	−	5.00000i	−0.163780	−	0.163780i
$933$		0			0
$934$	−5.00000	+	5.00000i	−0.163605	+	0.163605i
$935$	−10.0000	−	20.0000i	−0.327035	−	0.654070i
$936$		0			0
$937$	33.0000	+	33.0000i	1.07806	+	1.07806i	0.996683	+	0.0813798i	$0.0259327\pi$
$937$	33.0000	+	33.0000i	1.07806	+	1.07806i	0.0813798	+	0.996683i	$0.474067\pi$
$938$		−	24.0000i		−	0.783628i
$939$		0			0
$940$	4.00000	−	2.00000i	0.130466	−	0.0652328i
$941$	29.0000	−	29.0000i	0.945373	−	0.945373i	−0.0532103	−	0.998583i	$-0.516945\pi$
$941$	29.0000	−	29.0000i	0.945373	−	0.945373i	0.998583	+	0.0532103i	$0.0169454\pi$
$942$		0			0
$943$	−10.0000			−0.325645
$944$	−3.00000	+	3.00000i	−0.0976417	+	0.0976417i
$945$		0			0
$946$			10.0000i			0.325128i
$947$		−	38.0000i		−	1.23483i	−0.786636	−	0.617417i	$-0.788179\pi$
$947$		−	38.0000i		−	1.23483i	0.786636	−	0.617417i	$-0.211821\pi$
$948$		0			0
$949$	18.0000	+	12.0000i	0.584305	+	0.389536i
$950$	−21.0000	+	3.00000i	−0.681330	+	0.0973329i
$951$		0			0
$952$	−10.0000	−	10.0000i	−0.324102	−	0.324102i
$953$	35.0000	+	35.0000i	1.13376	+	1.13376i	0.989546	+	0.144215i	$0.0460656\pi$
$953$	35.0000	+	35.0000i	1.13376	+	1.13376i	0.144215	+	0.989546i	$0.453934\pi$
$954$		0			0
$955$	−8.00000	−	16.0000i	−0.258874	−	0.517748i
$956$	−7.00000	−	7.00000i	−0.226396	−	0.226396i
$957$		0			0
$958$	13.0000	−	13.0000i	0.420011	−	0.420011i
$959$	24.0000			0.775000
$960$		0			0
$961$			29.0000i			0.935484i
$962$	−16.0000	+	24.0000i	−0.515861	+	0.773791i
$963$		0			0
$964$	1.00000	+	1.00000i	0.0322078	+	0.0322078i
$965$	−14.0000	−	28.0000i	−0.450676	−	0.901352i
$966$		0			0
$967$	48.0000			1.54358			0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000			1.54358			0.771788	+	0.635880i	$0.219363\pi$
$968$			9.00000i			0.289271i
$969$		0			0
$970$	−2.00000	−	4.00000i	−0.0642161	−	0.128432i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$		0			0
$973$	28.0000			0.897639
$974$	32.0000			1.02535
$975$		0			0
$976$	2.00000			0.0640184
$977$	22.0000			0.703842			0.351921	−	0.936030i	$-0.385529\pi$
$977$	22.0000			0.703842			0.351921	+	0.936030i	$0.385529\pi$
$978$		0			0
$979$	−14.0000			−0.447442
$980$	−3.00000	−	6.00000i	−0.0958315	−	0.191663i
$981$		0			0
$982$		−	10.0000i		−	0.319113i
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$		0			0
$985$	18.0000	+	36.0000i	0.573528	+	1.14706i
$986$	−20.0000	−	20.0000i	−0.636930	−	0.636930i
$987$		0			0
$988$	3.00000	+	15.0000i	0.0954427	+	0.477214i
$989$			50.0000i			1.58991i
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	−1.00000	+	1.00000i	−0.0317500	+	0.0317500i
$993$		0			0
$994$	−2.00000	−	2.00000i	−0.0634361	−	0.0634361i
$995$		0			0
$996$		0			0
$997$	−17.0000	−	17.0000i	−0.538395	−	0.538395i	0.384662	−	0.923057i	$-0.374318\pi$
$997$	−17.0000	−	17.0000i	−0.538395	−	0.538395i	−0.923057	+	0.384662i	$0.874318\pi$
$998$	23.0000	+	23.0000i	0.728052	+	0.728052i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.m.a.577.1		2
3.2	odd	2		130.2.g.c.57.1	✓	2
5.3	odd	4		1170.2.w.c.343.1		2
12.11	even	2		1040.2.bg.f.577.1		2
13.8	odd	4		1170.2.w.c.307.1		2
15.2	even	4		650.2.j.d.343.1		2
15.8	even	4		130.2.j.b.83.1	yes	2
15.14	odd	2		650.2.g.b.57.1		2
39.8	even	4		130.2.j.b.47.1	yes	2
60.23	odd	4		1040.2.cd.e.993.1		2
65.8	even	4	inner	1170.2.m.a.73.1		2
156.47	odd	4		1040.2.cd.e.177.1		2
195.8	odd	4		130.2.g.c.73.1	yes	2
195.47	odd	4		650.2.g.b.593.1		2
195.164	even	4		650.2.j.d.307.1		2
780.203	even	4		1040.2.bg.f.593.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.c.57.1	✓	2	3.2	odd	2
130.2.g.c.73.1	yes	2	195.8	odd	4
130.2.j.b.47.1	yes	2	39.8	even	4
130.2.j.b.83.1	yes	2	15.8	even	4
650.2.g.b.57.1		2	15.14	odd	2
650.2.g.b.593.1		2	195.47	odd	4
650.2.j.d.307.1		2	195.164	even	4
650.2.j.d.343.1		2	15.2	even	4
1040.2.bg.f.577.1		2	12.11	even	2
1040.2.bg.f.593.1		2	780.203	even	4
1040.2.cd.e.177.1		2	156.47	odd	4
1040.2.cd.e.993.1		2	60.23	odd	4
1170.2.m.a.73.1		2	65.8	even	4	inner
1170.2.m.a.577.1		2	1.1	even	1	trivial
1170.2.w.c.307.1		2	13.8	odd	4
1170.2.w.c.343.1		2	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -2.00000i q^{7} -1.00000 q^{8} +(1.00000 + 2.00000i) q^{10} +(-1.00000 - 1.00000i) q^{11} +(-3.00000 - 2.00000i) q^{13} +2.00000i q^{14} +1.00000 q^{16} +(-5.00000 + 5.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(-1.00000 - 2.00000i) q^{20} +(1.00000 + 1.00000i) q^{22} +(5.00000 + 5.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(3.00000 + 2.00000i) q^{26} -2.00000i q^{28} -4.00000i q^{29} +(1.00000 - 1.00000i) q^{31} -1.00000 q^{32} +(5.00000 - 5.00000i) q^{34} +(-4.00000 + 2.00000i) q^{35} +8.00000i q^{37} +(3.00000 + 3.00000i) q^{38} +(1.00000 + 2.00000i) q^{40} +(-1.00000 + 1.00000i) q^{41} +(5.00000 + 5.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(-5.00000 - 5.00000i) q^{46} +2.00000i q^{47} +3.00000 q^{49} +(3.00000 - 4.00000i) q^{50} +(-3.00000 - 2.00000i) q^{52} +(1.00000 - 1.00000i) q^{53} +(-1.00000 + 3.00000i) q^{55} +2.00000i q^{56} +4.00000i q^{58} +(-3.00000 + 3.00000i) q^{59} +2.00000 q^{61} +(-1.00000 + 1.00000i) q^{62} +1.00000 q^{64} +(-1.00000 + 8.00000i) q^{65} -12.0000 q^{67} +(-5.00000 + 5.00000i) q^{68} +(4.00000 - 2.00000i) q^{70} +(-1.00000 + 1.00000i) q^{71} -6.00000 q^{73} -8.00000i q^{74} +(-3.00000 - 3.00000i) q^{76} +(-2.00000 + 2.00000i) q^{77} +14.0000i q^{79} +(-1.00000 - 2.00000i) q^{80} +(1.00000 - 1.00000i) q^{82} -6.00000i q^{83} +(15.0000 + 5.00000i) q^{85} +(-5.00000 - 5.00000i) q^{86} +(1.00000 + 1.00000i) q^{88} +(7.00000 - 7.00000i) q^{89} +(-4.00000 + 6.00000i) q^{91} +(5.00000 + 5.00000i) q^{92} -2.00000i q^{94} +(-3.00000 + 9.00000i) q^{95} -2.00000 q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 2 q^{8} + 2 q^{10} - 2 q^{11} - 6 q^{13} + 2 q^{16} - 10 q^{17} - 6 q^{19} - 2 q^{20} + 2 q^{22} + 10 q^{23} - 6 q^{25} + 6 q^{26} + 2 q^{31} - 2 q^{32} + 10 q^{34} - 8 q^{35}+ \cdots - 6 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 2 * q^8 + 2 * q^10 - 2 * q^11 - 6 * q^13 + 2 * q^16 - 10 * q^17 - 6 * q^19 - 2 * q^20 + 2 * q^22 + 10 * q^23 - 6 * q^25 + 6 * q^26 + 2 * q^31 - 2 * q^32 + 10 * q^34 - 8 * q^35 + 6 * q^38 + 2 * q^40 - 2 * q^41 + 10 * q^43 - 2 * q^44 - 10 * q^46 + 6 * q^49 + 6 * q^50 - 6 * q^52 + 2 * q^53 - 2 * q^55 - 6 * q^59 + 4 * q^61 - 2 * q^62 + 2 * q^64 - 2 * q^65 - 24 * q^67 - 10 * q^68 + 8 * q^70 - 2 * q^71 - 12 * q^73 - 6 * q^76 - 4 * q^77 - 2 * q^80 + 2 * q^82 + 30 * q^85 - 10 * q^86 + 2 * q^88 + 14 * q^89 - 8 * q^91 + 10 * q^92 - 6 * q^95 - 4 * q^97 - 6 * q^98

Introduction

L-functions

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