LMFDB - Embedded newform 1170.2.w.c.343.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(307,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("1170.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.w (of order $4$, degree $2$, 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:	$9.34249703649$
Analytic rank:	$0$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1170.343
Dual form			1170.2.w.c.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$		0			0
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$		−	1.00000i		−	0.353553i
$9$		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
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$14$		−	2.00000i		−	0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$	5.00000	+	5.00000i	1.21268	+	1.21268i	0.970143	+	0.242536i	$0.0779791\pi$
$17$	5.00000	+	5.00000i	1.21268	+	1.21268i	0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$	3.00000	+	3.00000i	0.688247	+	0.688247i	0.961844	−	0.273597i	$-0.0882135\pi$
$19$	3.00000	+	3.00000i	0.688247	+	0.688247i	−0.273597	+	0.961844i	$0.588214\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$		0			0
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	−5.00000	+	5.00000i	−1.04257	+	1.04257i	−0.0435195	+	0.999053i	$0.513857\pi$
$23$	−5.00000	+	5.00000i	−1.04257	+	1.04257i	−0.999053	+	0.0435195i	$0.986143\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	3.00000	+	2.00000i	0.588348	+	0.392232i
$27$		0			0
$28$	2.00000			0.377964
$29$			4.00000i			0.742781i	0.928477	+	0.371391i	$0.121119\pi$
$29$			4.00000i			0.742781i	−0.928477	+	0.371391i	$0.878881\pi$
$30$		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	$0.209465\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−5.00000	+	5.00000i	−0.857493	+	0.857493i
$35$	−4.00000	−	2.00000i	−0.676123	−	0.338062i
$36$		0			0
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	−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	$-0.931260\pi$
$43$	−5.00000	+	5.00000i	−0.762493	+	0.762493i	0.214280	+	0.976772i	$0.431260\pi$
$44$	1.00000	+	1.00000i	0.150756	+	0.150756i
$45$		0			0
$46$	−5.00000	−	5.00000i	−0.737210	−	0.737210i
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$		0			0
$49$	−3.00000			−0.428571
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$		0			0
$52$	−2.00000	+	3.00000i	−0.277350	+	0.416025i
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	0.772444	−	0.635083i	$-0.219034\pi$
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	−0.635083	+	0.772444i	$0.719034\pi$
$54$		0			0
$55$	−1.00000	−	3.00000i	−0.134840	−	0.404520i
$56$			2.00000i			0.267261i
$57$		0			0
$58$	−4.00000			−0.525226
$59$	3.00000	−	3.00000i	0.390567	−	0.390567i	−0.484323	−	0.874889i	$-0.660934\pi$
$59$	3.00000	−	3.00000i	0.390567	−	0.390567i	0.874889	+	0.484323i	$0.160934\pi$
$60$		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
$65$	7.00000	−	4.00000i	0.868243	−	0.496139i
$66$		0			0
$67$			12.0000i			1.46603i	0.680211	+	0.733017i	$0.261888\pi$
$67$			12.0000i			1.46603i	−0.680211	+	0.733017i	$0.738112\pi$
$68$	−5.00000	−	5.00000i	−0.606339	−	0.606339i
$69$		0			0
$70$	2.00000	−	4.00000i	0.239046	−	0.478091i
$71$	−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
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$			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	$-0.711343\pi$
$79$		−	14.0000i		−	1.57512i	0.616236	−	0.787562i	$-0.288657\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$		0			0
$82$	−1.00000	−	1.00000i	−0.110432	−	0.110432i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$	5.00000	+	15.0000i	0.542326	+	1.62698i
$86$	−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	−0.972962	−	0.230964i	$-0.925812\pi$
$89$	−7.00000	+	7.00000i	−0.741999	+	0.741999i	0.230964	+	0.972962i	$0.425812\pi$
$90$		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
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$		−	3.00000i		−	0.303046i
$99$		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	$-0.636736\pi$
$103$	5.00000	−	5.00000i	0.492665	−	0.492665i	0.909145	+	0.416480i	$0.136736\pi$
$104$	−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	−0.304125	+	0.952632i	$0.598364\pi$
$107$	−13.0000	+	13.0000i	−1.25676	+	1.25676i	−0.952632	+	0.304125i	$0.901636\pi$
$108$		0			0
$109$	13.0000	+	13.0000i	1.24517	+	1.24517i	0.957826	+	0.287348i	$0.0927736\pi$
$109$	13.0000	+	13.0000i	1.24517	+	1.24517i	0.287348	+	0.957826i	$0.407226\pi$
$110$	3.00000	−	1.00000i	0.286039	−	0.0953463i
$111$		0			0
$112$	−2.00000			−0.188982
$113$	−9.00000	−	9.00000i	−0.846649	−	0.846649i	0.143065	−	0.989713i	$-0.454304\pi$
$113$	−9.00000	−	9.00000i	−0.846649	−	0.846649i	−0.989713	+	0.143065i	$0.954304\pi$
$114$		0			0
$115$	−15.0000	+	5.00000i	−1.39876	+	0.466252i
$116$		−	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
$122$			2.00000i			0.181071i
$123$		0			0
$124$	−1.00000	+	1.00000i	−0.0898027	+	0.0898027i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$	15.0000	+	15.0000i	1.33103	+	1.33103i	0.904445	+	0.426589i	$0.140285\pi$
$127$	15.0000	+	15.0000i	1.33103	+	1.33103i	0.426589	+	0.904445i	$0.359715\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	4.00000	+	7.00000i	0.350823	+	0.613941i
$131$	−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
$137$	12.0000			1.02523			0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000			1.02523			0.512615	+	0.858619i	$0.328677\pi$
$138$		0			0
$139$		−	14.0000i		−	1.18746i	−0.804663	−	0.593732i	$-0.797654\pi$
$139$		−	14.0000i		−	1.18746i	0.804663	−	0.593732i	$-0.202346\pi$
$140$	4.00000	+	2.00000i	0.338062	+	0.169031i
$141$		0			0
$142$	−1.00000	−	1.00000i	−0.0839181	−	0.0839181i
$143$	−5.00000	+	1.00000i	−0.418121	+	0.0836242i
$144$		0			0
$145$	−4.00000	+	8.00000i	−0.332182	+	0.664364i
$146$	6.00000			0.496564
$147$		0			0
$148$	−8.00000			−0.657596
$149$	−13.0000	−	13.0000i	−1.06500	−	1.06500i	−0.997735	−	0.0672664i	$-0.978572\pi$
$149$	−13.0000	−	13.0000i	−1.06500	−	1.06500i	−0.0672664	−	0.997735i	$-0.521428\pi$
$150$		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	−0.577186	−	0.816612i	$-0.695849\pi$
$157$	3.00000	−	3.00000i	0.239426	−	0.239426i	0.816612	+	0.577186i	$0.195849\pi$
$158$	14.0000			1.11378
$159$		0			0
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$	10.0000	−	10.0000i	0.788110	−	0.788110i
$162$		0			0
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	1.00000	−	1.00000i	0.0780869	−	0.0780869i
$165$		0			0
$166$			6.00000i			0.465690i
$167$	2.00000			0.154765			0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000			0.154765			0.0773823	+	0.997001i	$0.475344\pi$
$168$		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	0.152057	−	0.988372i	$-0.451410\pi$
$173$	15.0000	−	15.0000i	1.14043	−	1.14043i	0.988372	−	0.152057i	$-0.0485898\pi$
$174$		0			0
$175$	−6.00000	−	8.00000i	−0.453557	−	0.604743i
$176$	−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	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$		0			0
$181$		−	20.0000i		−	1.48659i	−0.668965	−	0.743294i	$-0.733262\pi$
$181$		−	20.0000i		−	1.48659i	0.668965	−	0.743294i	$-0.266738\pi$
$182$	−6.00000	−	4.00000i	−0.444750	−	0.296500i
$183$		0			0
$184$	5.00000	+	5.00000i	0.368605	+	0.368605i
$185$	16.0000	+	8.00000i	1.17634	+	0.588172i
$186$		0			0
$187$		−	10.0000i		−	0.731272i
$188$	−2.00000			−0.145865
$189$		0			0
$190$	−9.00000	+	3.00000i	−0.652929	+	0.217643i
$191$	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
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$		0			0
$202$		0			0
$203$		−	8.00000i		−	0.561490i
$204$		0			0
$205$	−3.00000	+	1.00000i	−0.209529	+	0.0698430i
$206$	5.00000	+	5.00000i	0.348367	+	0.348367i
$207$		0			0
$208$	2.00000	−	3.00000i	0.138675	−	0.208013i
$209$		−	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
$215$	−15.0000	+	5.00000i	−1.02299	+	0.340997i
$216$		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
$223$	−6.00000			−0.401790			−0.200895	−	0.979613i	$-0.564385\pi$
$223$	−6.00000			−0.401790			−0.200895	+	0.979613i	$0.564385\pi$
$224$		−	2.00000i		−	0.133631i
$225$		0			0
$226$	9.00000	−	9.00000i	0.598671	−	0.598671i
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		0			0
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	−0.799248	−	0.601002i	$-0.794768\pi$
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	0.601002	+	0.799248i	$0.294768\pi$
$230$	−5.00000	−	15.0000i	−0.329690	−	0.989071i
$231$		0			0
$232$	4.00000			0.262613
$233$	5.00000	−	5.00000i	0.327561	−	0.327561i	−0.524097	−	0.851658i	$-0.675597\pi$
$233$	5.00000	−	5.00000i	0.327561	−	0.327561i	0.851658	+	0.524097i	$0.175597\pi$
$234$		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	0.896280	−	0.443488i	$-0.146259\pi$
$239$	7.00000	+	7.00000i	0.452792	+	0.452792i	−0.443488	+	0.896280i	$0.646259\pi$
$240$		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	$0.735496\pi$
$242$	9.00000			0.578542
$243$		0			0
$244$	−2.00000			−0.128037
$245$	−6.00000	−	3.00000i	−0.383326	−	0.191663i
$246$		0			0
$247$	15.0000	−	3.00000i	0.954427	−	0.190885i
$248$	−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
$253$	10.0000			0.628695
$254$	−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	$-0.480131\pi$
$257$	−15.0000	−	15.0000i	−0.935674	−	0.935674i	−0.998053	+	0.0623783i	$0.980131\pi$
$258$		0			0
$259$	−16.0000			−0.994192
$260$	−7.00000	+	4.00000i	−0.434122	+	0.248069i
$261$		0			0
$262$		−	12.0000i		−	0.741362i
$263$	−9.00000	−	9.00000i	−0.554964	−	0.554964i	0.372906	−	0.927869i	$-0.378362\pi$
$263$	−9.00000	−	9.00000i	−0.554964	−	0.554964i	−0.927869	+	0.372906i	$0.878362\pi$
$264$		0			0
$265$	1.00000	+	3.00000i	0.0614295	+	0.184289i
$266$	6.00000	−	6.00000i	0.367884	−	0.367884i
$267$		0			0
$268$		−	12.0000i		−	0.733017i
$269$		−	16.0000i		−	0.975537i	−0.872973	−	0.487769i	$-0.837811\pi$
$269$		−	16.0000i		−	0.975537i	0.872973	−	0.487769i	$-0.162189\pi$
$270$		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
$275$	1.00000	−	7.00000i	0.0603023	−	0.422116i
$276$		0			0
$277$	5.00000	+	5.00000i	0.300421	+	0.300421i	0.841178	−	0.540758i	$-0.181862\pi$
$277$	5.00000	+	5.00000i	0.300421	+	0.300421i	−0.540758	+	0.841178i	$0.681862\pi$
$278$	14.0000			0.839664
$279$		0			0
$280$	−2.00000	+	4.00000i	−0.119523	+	0.239046i
$281$	−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	$-0.532851\pi$
$283$	15.0000	−	15.0000i	0.891657	−	0.891657i	0.994679	+	0.103022i	$0.0328511\pi$
$284$	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
$292$			6.00000i			0.351123i
$293$			26.0000i			1.51894i	0.650545	+	0.759468i	$0.274541\pi$
$293$			26.0000i			1.51894i	−0.650545	+	0.759468i	$0.725459\pi$
$294$		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
$305$	4.00000	+	2.00000i	0.229039	+	0.114520i
$306$		0			0
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	−2.00000	−	2.00000i	−0.113961	−	0.113961i
$309$		0			0
$310$	1.00000	+	3.00000i	0.0567962	+	0.170389i
$311$			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	0.914130	−	0.405420i	$-0.132875\pi$
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	−0.405420	+	0.914130i	$0.632875\pi$
$314$	3.00000	+	3.00000i	0.169300	+	0.169300i
$315$		0			0
$316$			14.0000i			0.787562i
$317$		−	2.00000i		−	0.112331i	−0.998421	−	0.0561656i	$-0.982113\pi$
$317$		−	2.00000i		−	0.112331i	0.998421	−	0.0561656i	$-0.0178875\pi$
$318$		0			0
$319$	4.00000	−	4.00000i	0.223957	−	0.223957i
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$		0			0
$322$	10.0000	+	10.0000i	0.557278	+	0.557278i
$323$			30.0000i			1.66924i
$324$		0			0
$325$	18.0000	−	1.00000i	0.998460	−	0.0554700i
$326$	−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	$0.363749\pi$
$332$	−6.00000			−0.329293
$333$		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	$-0.311690\pi$
$337$	−5.00000	−	5.00000i	−0.272367	−	0.272367i	−0.830053	+	0.557685i	$0.811690\pi$
$338$	12.0000	−	5.00000i	0.652714	−	0.271964i
$339$		0			0
$340$	−5.00000	−	15.0000i	−0.271163	−	0.813489i
$341$	−2.00000			−0.108306
$342$		0			0
$343$	20.0000			1.07990
$344$	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	−0.493797	−	0.869577i	$-0.664392\pi$
$347$	7.00000	−	7.00000i	0.375780	−	0.375780i	0.869577	+	0.493797i	$0.164392\pi$
$348$		0			0
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	−0.782826	−	0.622240i	$-0.786223\pi$
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	0.622240	+	0.782826i	$0.286223\pi$
$350$	8.00000	−	6.00000i	0.427618	−	0.320713i
$351$		0			0
$352$	1.00000	−	1.00000i	0.0533002	−	0.0533002i
$353$	16.0000			0.851594			0.425797	−	0.904819i	$-0.359994\pi$
$353$	16.0000			0.851594			0.425797	+	0.904819i	$0.359994\pi$
$354$		0			0
$355$	−3.00000	+	1.00000i	−0.159223	+	0.0530745i
$356$	7.00000	−	7.00000i	0.370999	−	0.370999i
$357$		0			0
$358$			20.0000i			1.05703i
$359$	13.0000	−	13.0000i	0.686114	−	0.686114i	−0.275257	−	0.961371i	$-0.588763\pi$
$359$	13.0000	−	13.0000i	0.686114	−	0.686114i	0.961371	+	0.275257i	$0.0887629\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$	20.0000			1.05118
$363$		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	−0.624459	−	0.781058i	$-0.714680\pi$
$367$	3.00000	−	3.00000i	0.156599	−	0.156599i	0.781058	+	0.624459i	$0.214680\pi$
$368$	−5.00000	+	5.00000i	−0.260643	+	0.260643i
$369$		0			0
$370$	−8.00000	+	16.0000i	−0.415900	+	0.831800i
$371$	−2.00000	−	2.00000i	−0.103835	−	0.103835i
$372$		0			0
$373$	−1.00000	−	1.00000i	−0.0517780	−	0.0517780i	0.680744	−	0.732522i	$-0.261657\pi$
$373$	−1.00000	−	1.00000i	−0.0517780	−	0.0517780i	−0.732522	+	0.680744i	$0.761657\pi$
$374$	10.0000			0.517088
$375$		0			0
$376$		−	2.00000i		−	0.103142i
$377$	12.0000	+	8.00000i	0.618031	+	0.412021i
$378$		0			0
$379$	−17.0000	−	17.0000i	−0.873231	−	0.873231i	0.119592	−	0.992823i	$-0.461841\pi$
$379$	−17.0000	−	17.0000i	−0.873231	−	0.873231i	−0.992823	+	0.119592i	$0.961841\pi$
$380$	−3.00000	−	9.00000i	−0.153897	−	0.461690i
$381$		0			0
$382$			8.00000i			0.409316i
$383$	6.00000			0.306586			0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000			0.306586			0.153293	+	0.988181i	$0.451012\pi$
$384$		0			0
$385$	2.00000	+	6.00000i	0.101929	+	0.305788i
$386$	−14.0000			−0.712581
$387$		0			0
$388$		−	2.00000i		−	0.101535i
$389$	−10.0000			−0.507020			−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000			−0.507020			−0.253510	+	0.967333i	$0.581585\pi$
$390$		0			0
$391$	−50.0000			−2.52861
$392$			3.00000i			0.151523i
$393$		0			0
$394$	−18.0000			−0.906827
$395$	14.0000	−	28.0000i	0.704416	−	1.40883i
$396$		0			0
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$		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
$403$	−1.00000	−	5.00000i	−0.0498135	−	0.249068i
$404$		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	0.777376	−	0.629036i	$-0.216550\pi$
$409$	3.00000	+	3.00000i	0.148340	+	0.148340i	−0.629036	+	0.777376i	$0.716550\pi$
$410$	−1.00000	−	3.00000i	−0.0493865	−	0.148159i
$411$		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
$418$	6.00000			0.293470
$419$		−	26.0000i		−	1.27018i	−0.772437	−	0.635092i	$-0.780962\pi$
$419$		−	26.0000i		−	1.27018i	0.772437	−	0.635092i	$-0.219038\pi$
$420$		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	$0.350383\pi$
$422$			12.0000i			0.584151i
$423$		0			0
$424$	1.00000	−	1.00000i	0.0485643	−	0.0485643i
$425$	−5.00000	+	35.0000i	−0.242536	+	1.69775i
$426$		0			0
$427$	−4.00000			−0.193574
$428$	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	$-0.579749\pi$
$433$	15.0000	−	15.0000i	0.720854	−	0.720854i	0.968779	+	0.247925i	$0.0797487\pi$
$434$	−2.00000	−	2.00000i	−0.0960031	−	0.0960031i
$435$		0			0
$436$	−13.0000	−	13.0000i	−0.622587	−	0.622587i
$437$	−30.0000			−1.43509
$438$		0			0
$439$	−40.0000			−1.90910			−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000			−1.90910			−0.954548	+	0.298057i	$0.903661\pi$
$440$	−3.00000	+	1.00000i	−0.143019	+	0.0476731i
$441$		0			0
$442$	5.00000	+	25.0000i	0.237826	+	1.18913i
$443$	−19.0000	−	19.0000i	−0.902717	−	0.902717i	0.0929532	−	0.995670i	$-0.470369\pi$
$443$	−19.0000	−	19.0000i	−0.902717	−	0.902717i	−0.995670	+	0.0929532i	$0.970369\pi$
$444$		0			0
$445$	−21.0000	+	7.00000i	−0.995495	+	0.331832i
$446$		−	6.00000i		−	0.284108i
$447$		0			0
$448$	2.00000			0.0944911
$449$	−7.00000	+	7.00000i	−0.330350	+	0.330350i	−0.852720	−	0.522369i	$-0.825048\pi$
$449$	−7.00000	+	7.00000i	−0.330350	+	0.330350i	0.522369	+	0.852720i	$0.325048\pi$
$450$		0			0
$451$	2.00000			0.0941763
$452$	9.00000	+	9.00000i	0.423324	+	0.423324i
$453$		0			0
$454$	12.0000			0.563188
$455$	−14.0000	+	8.00000i	−0.656330	+	0.375046i
$456$		0			0
$457$		−	38.0000i		−	1.77757i	−0.458329	−	0.888783i	$-0.651552\pi$
$457$		−	38.0000i		−	1.77757i	0.458329	−	0.888783i	$-0.348448\pi$
$458$	−3.00000	−	3.00000i	−0.140181	−	0.140181i
$459$		0			0
$460$	15.0000	−	5.00000i	0.699379	−	0.233126i
$461$	−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
$463$		−	16.0000i		−	0.743583i	−0.928316	−	0.371792i	$-0.878744\pi$
$463$		−	16.0000i		−	0.743583i	0.928316	−	0.371792i	$-0.121256\pi$
$464$			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	$-0.302312\pi$
$467$	−5.00000	−	5.00000i	−0.231372	−	0.231372i	−0.813265	+	0.581893i	$0.802312\pi$
$468$		0			0
$469$		−	24.0000i		−	1.10822i
$470$	−2.00000	+	4.00000i	−0.0922531	+	0.184506i
$471$		0			0
$472$	−3.00000	−	3.00000i	−0.138086	−	0.138086i
$473$	10.0000			0.459800
$474$		0			0
$475$	−3.00000	+	21.0000i	−0.137649	+	0.963546i
$476$	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	−0.344720	−	0.938705i	$-0.612026\pi$
$479$	13.0000	−	13.0000i	0.593985	−	0.593985i	0.938705	+	0.344720i	$0.112026\pi$
$480$		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
$487$			32.0000i			1.45006i	0.688718	+	0.725029i	$0.258174\pi$
$487$			32.0000i			1.45006i	−0.688718	+	0.725029i	$0.741826\pi$
$488$		−	2.00000i		−	0.0905357i
$489$		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	$0.00957421\pi$
$499$	23.0000	+	23.0000i	1.02962	+	1.02962i	0.0300737	+	0.999548i	$0.490426\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$		0			0
$502$	30.0000			1.33897
$503$	−9.00000	−	9.00000i	−0.401290	−	0.401290i	0.477397	−	0.878688i	$-0.341580\pi$
$503$	−9.00000	−	9.00000i	−0.401290	−	0.401290i	−0.878688	+	0.477397i	$0.841580\pi$
$504$		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	0.357643	−	0.933858i	$-0.383580\pi$
$509$	−13.0000	−	13.0000i	−0.576215	−	0.576215i	−0.933858	+	0.357643i	$0.883580\pi$
$510$		0			0
$511$			12.0000i			0.530849i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	15.0000	−	15.0000i	0.661622	−	0.661622i
$515$	15.0000	−	5.00000i	0.660979	−	0.220326i
$516$		0			0
$517$	−2.00000	−	2.00000i	−0.0879599	−	0.0879599i
$518$		−	16.0000i		−	0.703000i
$519$		0			0
$520$	−4.00000	−	7.00000i	−0.175412	−	0.306970i
$521$	−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	0.0786374	−	0.996903i	$-0.474943\pi$
$523$	−21.0000	−	21.0000i	−0.918266	−	0.918266i	−0.996903	+	0.0786374i	$0.974943\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$	9.00000	−	9.00000i	0.392419	−	0.392419i
$527$	10.0000			0.435607
$528$		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
$533$	1.00000	+	5.00000i	0.0433148	+	0.216574i
$534$		0			0
$535$	−39.0000	+	13.0000i	−1.68612	+	0.562039i
$536$	12.0000			0.518321
$537$		0			0
$538$	16.0000			0.689809
$539$	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	−0.840739	−	0.541441i	$-0.817879\pi$
$547$	−7.00000	+	7.00000i	−0.299298	+	0.299298i	0.541441	+	0.840739i	$0.317879\pi$
$548$	−12.0000			−0.512615
$549$		0			0
$550$	7.00000	+	1.00000i	0.298481	+	0.0426401i
$551$	−12.0000	+	12.0000i	−0.511217	+	0.511217i
$552$		0			0
$553$			28.0000i			1.19068i
$554$	−5.00000	+	5.00000i	−0.212430	+	0.212430i
$555$		0			0
$556$			14.0000i			0.593732i
$557$	−8.00000			−0.338971			−0.169485	−	0.985533i	$-0.554211\pi$
$557$	−8.00000			−0.338971			−0.169485	+	0.985533i	$0.554211\pi$
$558$		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	$-0.702393\pi$
$563$	5.00000	−	5.00000i	0.210725	−	0.210725i	0.804575	+	0.593851i	$0.202393\pi$
$564$		0			0
$565$	−9.00000	−	27.0000i	−0.378633	−	1.13590i
$566$	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	$-0.567220\pi$
$569$	−10.0000			−0.419222			−0.209611	+	0.977785i	$0.567220\pi$
$570$		0			0
$571$		−	10.0000i		−	0.418487i	−0.977864	−	0.209243i	$-0.932900\pi$
$571$		−	10.0000i		−	0.418487i	0.977864	−	0.209243i	$-0.0671001\pi$
$572$	5.00000	−	1.00000i	0.209061	−	0.0418121i
$573$		0			0
$574$	2.00000	+	2.00000i	0.0834784	+	0.0834784i
$575$	−35.0000	−	5.00000i	−1.45960	−	0.208514i
$576$		0			0
$577$			22.0000i			0.915872i	0.888985	+	0.457936i	$0.151411\pi$
$577$			22.0000i			0.915872i	−0.888985	+	0.457936i	$0.848589\pi$
$578$	−33.0000			−1.37262
$579$		0			0
$580$	4.00000	−	8.00000i	0.166091	−	0.332182i
$581$	−12.0000			−0.497844
$582$		0			0
$583$		−	2.00000i		−	0.0828315i
$584$	−6.00000			−0.248282
$585$		0			0
$586$	−26.0000			−1.07405
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$	3.00000	+	9.00000i	0.123508	+	0.370524i
$591$		0			0
$592$	8.00000			0.328798
$593$		−	14.0000i		−	0.574911i	−0.957794	−	0.287456i	$-0.907191\pi$
$593$		−	14.0000i		−	0.574911i	0.957794	−	0.287456i	$-0.0928094\pi$
$594$		0			0
$595$	−10.0000	−	30.0000i	−0.409960	−	1.22988i
$596$	13.0000	+	13.0000i	0.532501	+	0.532501i
$597$		0			0
$598$	−25.0000	+	5.00000i	−1.02233	+	0.204465i
$599$			14.0000i			0.572024i	0.958226	+	0.286012i	$0.0923298\pi$
$599$			14.0000i			0.572024i	−0.958226	+	0.286012i	$0.907670\pi$
$600$		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
$605$	9.00000	−	18.0000i	0.365902	−	0.731804i
$606$		0			0
$607$	3.00000	−	3.00000i	0.121766	−	0.121766i	−0.643598	−	0.765364i	$-0.722559\pi$
$607$	3.00000	−	3.00000i	0.121766	−	0.121766i	0.765364	+	0.643598i	$0.222559\pi$
$608$	−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
$613$	4.00000			0.161558			0.0807792	−	0.996732i	$-0.474259\pi$
$613$	4.00000			0.161558			0.0807792	+	0.996732i	$0.474259\pi$
$614$		−	2.00000i		−	0.0807134i
$615$		0			0
$616$	2.00000	−	2.00000i	0.0805823	−	0.0805823i
$617$			38.0000i			1.52982i	0.644136	+	0.764911i	$0.277217\pi$
$617$			38.0000i			1.52982i	−0.644136	+	0.764911i	$0.722783\pi$
$618$		0			0
$619$	−3.00000	+	3.00000i	−0.120580	+	0.120580i	−0.764822	−	0.644242i	$-0.777173\pi$
$619$	−3.00000	+	3.00000i	−0.120580	+	0.120580i	0.644242	+	0.764822i	$0.277173\pi$
$620$	−3.00000	+	1.00000i	−0.120483	+	0.0401610i
$621$		0			0
$622$	−10.0000			−0.400963
$623$	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	$0.649790\pi$
$632$	−14.0000			−0.556890
$633$		0			0
$634$	2.00000			0.0794301
$635$	15.0000	+	45.0000i	0.595257	+	1.78577i
$636$		0			0
$637$	−6.00000	+	9.00000i	−0.237729	+	0.356593i
$638$	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
$643$	−46.0000			−1.81406			−0.907031	−	0.421063i	$-0.861657\pi$
$643$	−46.0000			−1.81406			−0.907031	+	0.421063i	$0.861657\pi$
$644$	−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	$-0.205612\pi$
$647$	5.00000	+	5.00000i	0.196570	+	0.196570i	−0.601958	+	0.798528i	$0.705612\pi$
$648$		0			0
$649$	−6.00000			−0.235521
$650$	1.00000	+	18.0000i	0.0392232	+	0.706018i
$651$		0			0
$652$		−	4.00000i		−	0.156652i
$653$	21.0000	+	21.0000i	0.821794	+	0.821794i	0.986365	−	0.164572i	$-0.0526242\pi$
$653$	21.0000	+	21.0000i	0.821794	+	0.821794i	−0.164572	+	0.986365i	$0.552624\pi$
$654$		0			0
$655$	−24.0000	−	12.0000i	−0.937758	−	0.468879i
$656$	−1.00000	+	1.00000i	−0.0390434	+	0.0390434i
$657$		0			0
$658$		−	4.00000i		−	0.155936i
$659$			14.0000i			0.545363i	0.962104	+	0.272681i	$0.0879105\pi$
$659$			14.0000i			0.545363i	−0.962104	+	0.272681i	$0.912090\pi$
$660$		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
$665$	−6.00000	−	18.0000i	−0.232670	−	0.698010i
$666$		0			0
$667$	−20.0000	−	20.0000i	−0.774403	−	0.774403i
$668$	−2.00000			−0.0773823
$669$		0			0
$670$	−24.0000	−	12.0000i	−0.927201	−	0.463600i
$671$	−2.00000	−	2.00000i	−0.0772091	−	0.0772091i
$672$		0			0
$673$	−5.00000	+	5.00000i	−0.192736	+	0.192736i	−0.796877	−	0.604141i	$-0.793516\pi$
$673$	−5.00000	+	5.00000i	−0.192736	+	0.192736i	0.604141	+	0.796877i	$0.293516\pi$
$674$	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	−0.993935	−	0.109973i	$-0.964924\pi$
$677$	−23.0000	+	23.0000i	−0.883962	+	0.883962i	0.109973	+	0.993935i	$0.464924\pi$
$678$		0			0
$679$		−	4.00000i		−	0.153506i
$680$	15.0000	−	5.00000i	0.575224	−	0.191741i
$681$		0			0
$682$		−	2.00000i		−	0.0765840i
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$		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
$695$	14.0000	−	28.0000i	0.531050	−	1.06210i
$696$		0			0
$697$	−10.0000			−0.378777
$698$	−3.00000	−	3.00000i	−0.113552	−	0.113552i
$699$		0			0
$700$	6.00000	+	8.00000i	0.226779	+	0.302372i
$701$		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	−0.761193	−	0.648526i	$-0.775386\pi$
$709$	−3.00000	+	3.00000i	−0.112667	+	0.112667i	0.648526	+	0.761193i	$0.275386\pi$
$710$	−1.00000	−	3.00000i	−0.0375293	−	0.112588i
$711$		0			0
$712$	7.00000	+	7.00000i	0.262336	+	0.262336i
$713$			10.0000i			0.374503i
$714$		0			0
$715$	−11.0000	−	3.00000i	−0.411377	−	0.112194i
$716$	−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
$722$	1.00000			0.0372161
$723$		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	0.929660	+	0.368418i	$0.120100\pi$
$727$	35.0000	+	35.0000i	1.29808	+	1.29808i	0.368418	+	0.929660i	$0.379900\pi$
$728$	6.00000	+	4.00000i	0.222375	+	0.148250i
$729$		0			0
$730$	12.0000	+	6.00000i	0.444140	+	0.222070i
$731$	−50.0000			−1.84932
$732$		0			0
$733$	44.0000			1.62518			0.812589	−	0.582838i	$-0.198058\pi$
$733$	44.0000			1.62518			0.812589	+	0.582838i	$0.198058\pi$
$734$	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	$-0.337542\pi$
$739$	37.0000	−	37.0000i	1.36107	−	1.36107i	0.872560	−	0.488507i	$-0.162458\pi$
$740$	−16.0000	−	8.00000i	−0.588172	−	0.294086i
$741$		0			0
$742$	2.00000	−	2.00000i	0.0734223	−	0.0734223i
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$		0			0
$745$	−13.0000	−	39.0000i	−0.476283	−	1.42885i
$746$	1.00000	−	1.00000i	0.0366126	−	0.0366126i
$747$		0			0
$748$			10.0000i			0.365636i
$749$	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	$-0.0584036\pi$
$752$	2.00000			0.0729325
$753$		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	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−17.0000	+	17.0000i	−0.617876	+	0.617876i	0.327111	+	0.944986i	$0.393925\pi$
$758$	17.0000	−	17.0000i	0.617468	−	0.617468i
$759$		0			0
$760$	9.00000	−	3.00000i	0.326464	−	0.108821i
$761$	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
$767$	−3.00000	−	15.0000i	−0.108324	−	0.541619i
$768$		0			0
$769$	23.0000	+	23.0000i	0.829401	+	0.829401i	0.987434	−	0.158033i	$-0.0505151\pi$
$769$	23.0000	+	23.0000i	0.829401	+	0.829401i	−0.158033	+	0.987434i	$0.550515\pi$
$770$	−6.00000	+	2.00000i	−0.216225	+	0.0720750i
$771$		0			0
$772$		−	14.0000i		−	0.503871i
$773$	−24.0000			−0.863220			−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000			−0.863220			−0.431610	+	0.902060i	$0.642054\pi$
$774$		0			0
$775$	7.00000	+	1.00000i	0.251447	+	0.0359211i
$776$	2.00000			0.0717958
$777$		0			0
$778$		−	10.0000i		−	0.358517i
$779$	−6.00000			−0.214972
$780$		0			0
$781$	2.00000			0.0715656
$782$		−	50.0000i		−	1.78800i
$783$		0			0
$784$	−3.00000			−0.107143
$785$	9.00000	−	3.00000i	0.321224	−	0.107075i
$786$		0			0
$787$	−42.0000			−1.49714			−0.748569	−	0.663057i	$-0.769259\pi$
$787$	−42.0000			−1.49714			−0.748569	+	0.663057i	$0.769259\pi$
$788$		−	18.0000i		−	0.641223i
$789$		0			0
$790$	28.0000	+	14.0000i	0.996195	+	0.498098i
$791$	18.0000	+	18.0000i	0.640006	+	0.640006i
$792$		0			0
$793$	4.00000	−	6.00000i	0.142044	−	0.213066i
$794$			8.00000i			0.283909i
$795$		0			0
$796$		0			0
$797$	−5.00000	−	5.00000i	−0.177109	−	0.177109i	0.612985	−	0.790094i	$-0.289968\pi$
$797$	−5.00000	−	5.00000i	−0.177109	−	0.177109i	−0.790094	+	0.612985i	$0.789968\pi$
$798$		0			0
$799$	10.0000	+	10.0000i	0.353775	+	0.353775i
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$		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	$-0.781886\pi$
$809$		−	36.0000i		−	1.26569i	0.774277	−	0.632846i	$-0.218114\pi$
$810$		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	$0.161942\pi$
$812$			8.00000i			0.280745i
$813$		0			0
$814$	8.00000	−	8.00000i	0.280400	−	0.280400i
$815$	−4.00000	+	8.00000i	−0.140114	+	0.280228i
$816$		0			0
$817$	−30.0000			−1.04957
$818$	−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	$-0.870547\pi$
$823$	−15.0000	+	15.0000i	−0.522867	+	0.522867i	0.395569	+	0.918436i	$0.370547\pi$
$824$	−5.00000	−	5.00000i	−0.174183	−	0.174183i
$825$		0			0
$826$	−6.00000	−	6.00000i	−0.208767	−	0.208767i
$827$	2.00000			0.0695468			0.0347734	−	0.999395i	$-0.488929\pi$
$827$	2.00000			0.0695468			0.0347734	+	0.999395i	$0.488929\pi$
$828$		0			0
$829$	30.0000			1.04194			0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000			1.04194			0.520972	+	0.853574i	$0.325570\pi$
$830$	−6.00000	+	12.0000i	−0.208263	+	0.416526i
$831$		0			0
$832$	−2.00000	+	3.00000i	−0.0693375	+	0.104006i
$833$	−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
$838$	26.0000			0.898155
$839$	13.0000	−	13.0000i	0.448810	−	0.448810i	−0.446149	−	0.894959i	$-0.647205\pi$
$839$	13.0000	−	13.0000i	0.448810	−	0.448810i	0.894959	+	0.446149i	$0.147205\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$	−9.00000	−	9.00000i	−0.310160	−	0.310160i
$843$		0			0
$844$	−12.0000			−0.413057
$845$	2.00000	−	29.0000i	0.0688021	−	0.997630i
$846$		0			0
$847$			18.0000i			0.618487i
$848$	1.00000	+	1.00000i	0.0343401	+	0.0343401i
$849$		0			0
$850$	−35.0000	−	5.00000i	−1.20049	−	0.171499i
$851$	−40.0000	+	40.0000i	−1.37118	+	1.37118i
$852$		0			0
$853$		−	26.0000i		−	0.890223i	−0.895475	−	0.445112i	$-0.853164\pi$
$853$		−	26.0000i		−	0.890223i	0.895475	−	0.445112i	$-0.146836\pi$
$854$		−	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	$-0.211463\pi$
$857$	5.00000	+	5.00000i	0.170797	+	0.170797i	−0.616533	+	0.787329i	$0.711463\pi$
$858$		0			0
$859$			26.0000i			0.887109i	0.896248	+	0.443554i	$0.146283\pi$
$859$			26.0000i			0.887109i	−0.896248	+	0.443554i	$0.853717\pi$
$860$	15.0000	−	5.00000i	0.511496	−	0.170499i
$861$		0			0
$862$	−21.0000	−	21.0000i	−0.715263	−	0.715263i
$863$	46.0000			1.56586			0.782929	−	0.622111i	$-0.213725\pi$
$863$	46.0000			1.56586			0.782929	+	0.622111i	$0.213725\pi$
$864$		0			0
$865$	45.0000	−	15.0000i	1.53005	−	0.510015i
$866$	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
$877$		−	18.0000i		−	0.607817i	−0.952701	−	0.303908i	$-0.901708\pi$
$877$		−	18.0000i		−	0.607817i	0.952701	−	0.303908i	$-0.0982917\pi$
$878$		−	40.0000i		−	1.34993i
$879$		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	$-0.787963\pi$
$883$	−5.00000	+	5.00000i	−0.168263	+	0.168263i	0.617952	+	0.786216i	$0.287963\pi$
$884$	−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	−0.978502	−	0.206238i	$-0.933878\pi$
$887$	−23.0000	+	23.0000i	−0.772264	+	0.772264i	0.206238	+	0.978502i	$0.433878\pi$
$888$		0			0
$889$	−30.0000	−	30.0000i	−1.00617	−	1.00617i
$890$	−7.00000	−	21.0000i	−0.234641	−	0.703922i
$891$		0			0
$892$	6.00000			0.200895
$893$	6.00000	+	6.00000i	0.200782	+	0.200782i
$894$		0			0
$895$	40.0000	+	20.0000i	1.33705	+	0.668526i
$896$			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
$902$			2.00000i			0.0665927i
$903$		0			0
$904$	−9.00000	+	9.00000i	−0.299336	+	0.299336i
$905$	20.0000	−	40.0000i	0.664822	−	1.32964i
$906$		0			0
$907$	−35.0000	−	35.0000i	−1.16216	−	1.16216i	−0.984003	−	0.178153i	$-0.942988\pi$
$907$	−35.0000	−	35.0000i	−1.16216	−	1.16216i	−0.178153	−	0.984003i	$-0.557012\pi$
$908$			12.0000i			0.398234i
$909$		0			0
$910$	−8.00000	−	14.0000i	−0.265197	−	0.464095i
$911$	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
$917$	24.0000			0.792550
$918$		0			0
$919$		−	14.0000i		−	0.461817i	−0.972975	−	0.230909i	$-0.925830\pi$
$919$		−	14.0000i		−	0.461817i	0.972975	−	0.230909i	$-0.0741699\pi$
$920$	5.00000	+	15.0000i	0.164845	+	0.494535i
$921$		0			0
$922$	−11.0000	−	11.0000i	−0.362266	−	0.362266i
$923$	1.00000	+	5.00000i	0.0329154	+	0.164577i
$924$		0			0
$925$	24.0000	+	32.0000i	0.789115	+	1.05215i
$926$	16.0000			0.525793
$927$		0			0
$928$	−4.00000			−0.131306
$929$	17.0000	+	17.0000i	0.557752	+	0.557752i	0.928667	−	0.370915i	$-0.120956\pi$
$929$	17.0000	+	17.0000i	0.557752	+	0.557752i	−0.370915	+	0.928667i	$0.620956\pi$
$930$		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	0.0813798	−	0.996683i	$-0.474067\pi$
$937$	33.0000	−	33.0000i	1.07806	−	1.07806i	0.996683	−	0.0813798i	$-0.0259327\pi$
$938$	24.0000			0.783628
$939$		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
$943$		−	10.0000i		−	0.325645i
$944$	3.00000	−	3.00000i	0.0976417	−	0.0976417i
$945$		0			0
$946$			10.0000i			0.325128i
$947$	−38.0000			−1.23483			−0.617417	−	0.786636i	$-0.711821\pi$
$947$	−38.0000			−1.23483			−0.617417	+	0.786636i	$0.711821\pi$
$948$		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	−0.144215	+	0.989546i	$0.546066\pi$
$953$	−35.0000	+	35.0000i	−1.13376	+	1.13376i	−0.989546	+	0.144215i	$0.953934\pi$
$954$		0			0
$955$	16.0000	+	8.00000i	0.517748	+	0.258874i
$956$	−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
$962$	24.0000	+	16.0000i	0.773791	+	0.515861i
$963$		0			0
$964$	−1.00000	−	1.00000i	−0.0322078	−	0.0322078i
$965$	−14.0000	+	28.0000i	−0.450676	+	0.901352i
$966$		0			0
$967$		−	48.0000i		−	1.54358i	−0.635880	−	0.771788i	$-0.719363\pi$
$967$		−	48.0000i		−	1.54358i	0.635880	−	0.771788i	$-0.280637\pi$
$968$	−9.00000			−0.289271
$969$		0			0
$970$	−4.00000	−	2.00000i	−0.128432	−	0.0642161i
$971$	−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
$973$			28.0000i			0.897639i
$974$	−32.0000			−1.02535
$975$		0			0
$976$	2.00000			0.0640184
$977$		−	22.0000i		−	0.703842i	−0.936030	−	0.351921i	$-0.885529\pi$
$977$		−	22.0000i		−	0.703842i	0.936030	−	0.351921i	$-0.114471\pi$
$978$		0			0
$979$	14.0000			0.447442
$980$	6.00000	+	3.00000i	0.191663	+	0.0958315i
$981$		0			0
$982$	−10.0000			−0.319113
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$		0			0
$985$	−18.0000	+	36.0000i	−0.573528	+	1.14706i
$986$	−20.0000	−	20.0000i	−0.636930	−	0.636930i
$987$		0			0
$988$	−15.0000	+	3.00000i	−0.477214	+	0.0954427i
$989$		−	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	−0.923057	−	0.384662i	$-0.874318\pi$
$997$	−17.0000	+	17.0000i	−0.538395	+	0.538395i	0.384662	+	0.923057i	$0.374318\pi$
$998$	−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.w.c.343.1		2
3.2	odd	2		130.2.j.b.83.1	yes	2
5.2	odd	4		1170.2.m.a.577.1		2
12.11	even	2		1040.2.cd.e.993.1		2
13.8	odd	4		1170.2.m.a.73.1		2
15.2	even	4		130.2.g.c.57.1	✓	2
15.8	even	4		650.2.g.b.57.1		2
15.14	odd	2		650.2.j.d.343.1		2
39.8	even	4		130.2.g.c.73.1	yes	2
60.47	odd	4		1040.2.bg.f.577.1		2
65.47	even	4	inner	1170.2.w.c.307.1		2
156.47	odd	4		1040.2.bg.f.593.1		2
195.8	odd	4		650.2.j.d.307.1		2
195.47	odd	4		130.2.j.b.47.1	yes	2
195.164	even	4		650.2.g.b.593.1		2
780.47	even	4		1040.2.cd.e.177.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.c.57.1	✓	2	15.2	even	4
130.2.g.c.73.1	yes	2	39.8	even	4
130.2.j.b.47.1	yes	2	195.47	odd	4
130.2.j.b.83.1	yes	2	3.2	odd	2
650.2.g.b.57.1		2	15.8	even	4
650.2.g.b.593.1		2	195.164	even	4
650.2.j.d.307.1		2	195.8	odd	4
650.2.j.d.343.1		2	15.14	odd	2
1040.2.bg.f.577.1		2	60.47	odd	4
1040.2.bg.f.593.1		2	156.47	odd	4
1040.2.cd.e.177.1		2	780.47	even	4
1040.2.cd.e.993.1		2	12.11	even	2
1170.2.m.a.73.1		2	13.8	odd	4
1170.2.m.a.577.1		2	5.2	odd	4
1170.2.w.c.307.1		2	65.47	even	4	inner
1170.2.w.c.343.1		2	1.1	even	1	trivial

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

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

Introduction

L-functions

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