LMFDB - Embedded newform 1170.2.w.a.343.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(307,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [2,0,0,-2,-4] 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:	$0$
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.a.307.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -2.00000 q^{7} +1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} +(2.00000 + 3.00000i) q^{13} +2.00000i q^{14} +1.00000 q^{16} +(1.00000 + 1.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(2.00000 + 1.00000i) q^{20} +(1.00000 - 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(3.00000 - 2.00000i) q^{26} +2.00000 q^{28} +8.00000i q^{29} +(1.00000 - 1.00000i) q^{31} -1.00000i q^{32} +(1.00000 - 1.00000i) q^{34} +(4.00000 + 2.00000i) q^{35} +8.00000 q^{37} +(-3.00000 + 3.00000i) q^{38} +(1.00000 - 2.00000i) q^{40} +(7.00000 - 7.00000i) q^{41} +(1.00000 - 1.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(1.00000 + 1.00000i) q^{46} +10.0000 q^{47} -3.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +(-2.00000 - 3.00000i) q^{52} +(-1.00000 - 1.00000i) q^{53} +(-1.00000 - 3.00000i) q^{55} -2.00000i q^{56} +8.00000 q^{58} +(9.00000 - 9.00000i) q^{59} +2.00000 q^{61} +(-1.00000 - 1.00000i) q^{62} -1.00000 q^{64} +(-1.00000 - 8.00000i) q^{65} +12.0000i q^{67} +(-1.00000 - 1.00000i) q^{68} +(2.00000 - 4.00000i) q^{70} +(-5.00000 + 5.00000i) q^{71} +6.00000i q^{73} -8.00000i q^{74} +(3.00000 + 3.00000i) q^{76} +(-2.00000 - 2.00000i) q^{77} +10.0000i q^{79} +(-2.00000 - 1.00000i) q^{80} +(-7.00000 - 7.00000i) q^{82} +18.0000 q^{83} +(-1.00000 - 3.00000i) q^{85} +(-1.00000 - 1.00000i) q^{86} +(-1.00000 + 1.00000i) q^{88} +(-11.0000 + 11.0000i) q^{89} +(-4.00000 - 6.00000i) q^{91} +(1.00000 - 1.00000i) q^{92} -10.0000i q^{94} +(3.00000 + 9.00000i) q^{95} +14.0000i q^{97} +3.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 4 q^{5} - 4 q^{7} - 2 q^{10} + 2 q^{11} + 4 q^{13} + 2 q^{16} + 2 q^{17} - 6 q^{19} + 4 q^{20} + 2 q^{22} - 2 q^{23} + 6 q^{25} + 6 q^{26} + 4 q^{28} + 2 q^{31} + 2 q^{34} + 8 q^{35} + 16 q^{37}+ \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 + 2 * q^17 - 6 * q^19 + 4 * q^20 + 2 * q^22 - 2 * q^23 + 6 * q^25 + 6 * q^26 + 4 * q^28 + 2 * q^31 + 2 * q^34 + 8 * q^35 + 16 * q^37 - 6 * q^38 + 2 * q^40 + 14 * q^41 + 2 * q^43 - 2 * q^44 + 2 * q^46 + 20 * q^47 - 6 * q^49 + 8 * q^50 - 4 * q^52 - 2 * q^53 - 2 * q^55 + 16 * q^58 + 18 * q^59 + 4 * q^61 - 2 * q^62 - 2 * q^64 - 2 * q^65 - 2 * q^68 + 4 * q^70 - 10 * q^71 + 6 * q^76 - 4 * q^77 - 4 * q^80 - 14 * q^82 + 36 * q^83 - 2 * q^85 - 2 * q^86 - 2 * q^88 - 22 * q^89 - 8 * q^91 + 2 * 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	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$		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
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	0.817898	−	0.575363i	$-0.195139\pi$
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	−0.575363	+	0.817898i	$0.695139\pi$
$18$		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	$0.911786\pi$
$20$	2.00000	+	1.00000i	0.447214	+	0.223607i
$21$		0			0
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$		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
$29$			8.00000i			1.48556i	0.669534	+	0.742781i	$0.266494\pi$
$29$			8.00000i			1.48556i	−0.669534	+	0.742781i	$0.733506\pi$
$30$		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
$34$	1.00000	−	1.00000i	0.171499	−	0.171499i
$35$	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
$41$	7.00000	−	7.00000i	1.09322	−	1.09322i	0.0980332	−	0.995183i	$-0.468745\pi$
$41$	7.00000	−	7.00000i	1.09322	−	1.09322i	0.995183	−	0.0980332i	$-0.0312551\pi$
$42$		0			0
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	−0.626734	−	0.779233i	$-0.715609\pi$
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	0.779233	+	0.626734i	$0.215609\pi$
$44$	−1.00000	−	1.00000i	−0.150756	−	0.150756i
$45$		0			0
$46$	1.00000	+	1.00000i	0.147442	+	0.147442i
$47$	10.0000			1.45865			0.729325	−	0.684167i	$-0.239834\pi$
$47$	10.0000			1.45865			0.729325	+	0.684167i	$0.239834\pi$
$48$		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	0.635083	−	0.772444i	$-0.280966\pi$
$53$	−1.00000	−	1.00000i	−0.137361	−	0.137361i	−0.772444	+	0.635083i	$0.780966\pi$
$54$		0			0
$55$	−1.00000	−	3.00000i	−0.134840	−	0.404520i
$56$		−	2.00000i		−	0.267261i
$57$		0			0
$58$	8.00000			1.05045
$59$	9.00000	−	9.00000i	1.17170	−	1.17170i	0.189896	−	0.981804i	$-0.439185\pi$
$59$	9.00000	−	9.00000i	1.17170	−	1.17170i	0.981804	−	0.189896i	$-0.0608151\pi$
$60$		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
$67$			12.0000i			1.46603i	0.680211	+	0.733017i	$0.261888\pi$
$67$			12.0000i			1.46603i	−0.680211	+	0.733017i	$0.738112\pi$
$68$	−1.00000	−	1.00000i	−0.121268	−	0.121268i
$69$		0			0
$70$	2.00000	−	4.00000i	0.239046	−	0.478091i
$71$	−5.00000	+	5.00000i	−0.593391	+	0.593391i	−0.938546	−	0.345155i	$-0.887826\pi$
$71$	−5.00000	+	5.00000i	−0.593391	+	0.593391i	0.345155	+	0.938546i	$0.387826\pi$
$72$		0			0
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$		−	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
$79$			10.0000i			1.12509i	0.826767	+	0.562544i	$0.190177\pi$
$79$			10.0000i			1.12509i	−0.826767	+	0.562544i	$0.809823\pi$
$80$	−2.00000	−	1.00000i	−0.223607	−	0.111803i
$81$		0			0
$82$	−7.00000	−	7.00000i	−0.773021	−	0.773021i
$83$	18.0000			1.97576			0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000			1.97576			0.987878	+	0.155230i	$0.0496119\pi$
$84$		0			0
$85$	−1.00000	−	3.00000i	−0.108465	−	0.325396i
$86$	−1.00000	−	1.00000i	−0.107833	−	0.107833i
$87$		0			0
$88$	−1.00000	+	1.00000i	−0.106600	+	0.106600i
$89$	−11.0000	+	11.0000i	−1.16600	+	1.16600i	−0.182858	+	0.983139i	$0.558535\pi$
$89$	−11.0000	+	11.0000i	−1.16600	+	1.16600i	−0.983139	+	0.182858i	$0.941465\pi$
$90$		0			0
$91$	−4.00000	−	6.00000i	−0.419314	−	0.628971i
$92$	1.00000	−	1.00000i	0.104257	−	0.104257i
$93$		0			0
$94$		−	10.0000i		−	1.03142i
$95$	3.00000	+	9.00000i	0.307794	+	0.923381i
$96$		0			0
$97$			14.0000i			1.42148i	0.703452	+	0.710742i	$0.251641\pi$
$97$			14.0000i			1.42148i	−0.703452	+	0.710742i	$0.748359\pi$
$98$			3.00000i			0.303046i
$99$		0			0
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$			12.0000i			1.19404i	0.802225	+	0.597022i	$0.203650\pi$
$101$			12.0000i			1.19404i	−0.802225	+	0.597022i	$0.796350\pi$
$102$		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
$107$	1.00000	−	1.00000i	0.0966736	−	0.0966736i	−0.657116	−	0.753790i	$-0.728224\pi$
$107$	1.00000	−	1.00000i	0.0966736	−	0.0966736i	0.753790	+	0.657116i	$0.228224\pi$
$108$		0			0
$109$	−5.00000	−	5.00000i	−0.478913	−	0.478913i	0.425871	−	0.904784i	$-0.359968\pi$
$109$	−5.00000	−	5.00000i	−0.478913	−	0.478913i	−0.904784	+	0.425871i	$0.859968\pi$
$110$	−3.00000	+	1.00000i	−0.286039	+	0.0953463i
$111$		0			0
$112$	−2.00000			−0.188982
$113$	3.00000	+	3.00000i	0.282216	+	0.282216i	0.833992	−	0.551776i	$-0.186050\pi$
$113$	3.00000	+	3.00000i	0.282216	+	0.282216i	−0.551776	+	0.833992i	$0.686050\pi$
$114$		0			0
$115$	3.00000	−	1.00000i	0.279751	−	0.0932505i
$116$		−	8.00000i		−	0.742781i
$117$		0			0
$118$	−9.00000	−	9.00000i	−0.828517	−	0.828517i
$119$	−2.00000	−	2.00000i	−0.183340	−	0.183340i
$120$		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
$127$	3.00000	+	3.00000i	0.266207	+	0.266207i	0.827570	−	0.561363i	$-0.189723\pi$
$127$	3.00000	+	3.00000i	0.266207	+	0.266207i	−0.561363	+	0.827570i	$0.689723\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−8.00000	+	1.00000i	−0.701646	+	0.0877058i
$131$	−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
$136$	−1.00000	+	1.00000i	−0.0857493	+	0.0857493i
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$		0			0
$139$		−	2.00000i		−	0.169638i	−0.996396	−	0.0848189i	$-0.972969\pi$
$139$		−	2.00000i		−	0.169638i	0.996396	−	0.0848189i	$-0.0270312\pi$
$140$	−4.00000	−	2.00000i	−0.338062	−	0.169031i
$141$		0			0
$142$	5.00000	+	5.00000i	0.419591	+	0.419591i
$143$	−1.00000	+	5.00000i	−0.0836242	+	0.418121i
$144$		0			0
$145$	8.00000	−	16.0000i	0.664364	−	1.32873i
$146$	6.00000			0.496564
$147$		0			0
$148$	−8.00000			−0.657596
$149$	1.00000	+	1.00000i	0.0819232	+	0.0819232i	0.746881	−	0.664958i	$-0.231550\pi$
$149$	1.00000	+	1.00000i	0.0819232	+	0.0819232i	−0.664958	+	0.746881i	$0.731550\pi$
$150$		0			0
$151$	3.00000	+	3.00000i	0.244137	+	0.244137i	0.818559	−	0.574422i	$-0.194773\pi$
$151$	3.00000	+	3.00000i	0.244137	+	0.244137i	−0.574422	+	0.818559i	$0.694773\pi$
$152$	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
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.222108	+	0.975022i	$0.571294\pi$
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.975022	+	0.222108i	$0.928706\pi$
$158$	10.0000			0.795557
$159$		0			0
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$	2.00000	−	2.00000i	0.157622	−	0.157622i
$162$		0			0
$163$		−	20.0000i		−	1.56652i	−0.621694	−	0.783260i	$-0.713555\pi$
$163$		−	20.0000i		−	1.56652i	0.621694	−	0.783260i	$-0.286445\pi$
$164$	−7.00000	+	7.00000i	−0.546608	+	0.546608i
$165$		0			0
$166$		−	18.0000i		−	1.39707i
$167$	−14.0000			−1.08335			−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000			−1.08335			−0.541676	+	0.840587i	$0.682210\pi$
$168$		0			0
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	−3.00000	+	1.00000i	−0.230089	+	0.0766965i
$171$		0			0
$172$	−1.00000	+	1.00000i	−0.0762493	+	0.0762493i
$173$	9.00000	−	9.00000i	0.684257	−	0.684257i	−0.276699	−	0.960957i	$-0.589241\pi$
$173$	9.00000	−	9.00000i	0.684257	−	0.684257i	0.960957	+	0.276699i	$0.0892406\pi$
$174$		0			0
$175$	−6.00000	−	8.00000i	−0.453557	−	0.604743i
$176$	1.00000	+	1.00000i	0.0753778	+	0.0753778i
$177$		0			0
$178$	11.0000	+	11.0000i	0.824485	+	0.824485i
$179$	−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
$181$			16.0000i			1.18927i	0.803996	+	0.594635i	$0.202704\pi$
$181$			16.0000i			1.18927i	−0.803996	+	0.594635i	$0.797296\pi$
$182$	−6.00000	+	4.00000i	−0.444750	+	0.296500i
$183$		0			0
$184$	−1.00000	−	1.00000i	−0.0737210	−	0.0737210i
$185$	−16.0000	−	8.00000i	−1.17634	−	0.588172i
$186$		0			0
$187$			2.00000i			0.146254i
$188$	−10.0000			−0.729325
$189$		0			0
$190$	9.00000	−	3.00000i	0.652929	−	0.217643i
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$		0			0
$193$			2.00000i			0.143963i	0.997406	+	0.0719816i	$0.0229323\pi$
$193$			2.00000i			0.143963i	−0.997406	+	0.0719816i	$0.977068\pi$
$194$	14.0000			1.00514
$195$		0			0
$196$	3.00000			0.214286
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		0			0
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$	−4.00000	+	3.00000i	−0.282843	+	0.212132i
$201$		0			0
$202$	12.0000			0.844317
$203$		−	16.0000i		−	1.12298i
$204$		0			0
$205$	−21.0000	+	7.00000i	−1.46670	+	0.488901i
$206$	−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	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$	1.00000	+	1.00000i	0.0686803	+	0.0686803i
$213$		0			0
$214$	−1.00000	−	1.00000i	−0.0683586	−	0.0683586i
$215$	−3.00000	+	1.00000i	−0.204598	+	0.0681994i
$216$		0			0
$217$	−2.00000	+	2.00000i	−0.135769	+	0.135769i
$218$	−5.00000	+	5.00000i	−0.338643	+	0.338643i
$219$		0			0
$220$	1.00000	+	3.00000i	0.0674200	+	0.202260i
$221$	−1.00000	+	5.00000i	−0.0672673	+	0.336336i
$222$		0			0
$223$	18.0000			1.20537			0.602685	−	0.797980i	$-0.294098\pi$
$223$	18.0000			1.20537			0.602685	+	0.797980i	$0.294098\pi$
$224$			2.00000i			0.133631i
$225$		0			0
$226$	3.00000	−	3.00000i	0.199557	−	0.199557i
$227$			12.0000i			0.796468i	0.917284	+	0.398234i	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$		0			0
$229$	15.0000	−	15.0000i	0.991228	−	0.991228i	−0.00873396	−	0.999962i	$-0.502780\pi$
$229$	15.0000	−	15.0000i	0.991228	−	0.991228i	0.999962	+	0.00873396i	$0.00278014\pi$
$230$	−1.00000	−	3.00000i	−0.0659380	−	0.197814i
$231$		0			0
$232$	−8.00000			−0.525226
$233$	1.00000	−	1.00000i	0.0655122	−	0.0655122i	−0.673592	−	0.739104i	$-0.735249\pi$
$233$	1.00000	−	1.00000i	0.0655122	−	0.0655122i	0.739104	+	0.673592i	$0.235249\pi$
$234$		0			0
$235$	−20.0000	−	10.0000i	−1.30466	−	0.652328i
$236$	−9.00000	+	9.00000i	−0.585850	+	0.585850i
$237$		0			0
$238$	−2.00000	+	2.00000i	−0.129641	+	0.129641i
$239$	−1.00000	−	1.00000i	−0.0646846	−	0.0646846i	0.674024	−	0.738709i	$-0.264564\pi$
$239$	−1.00000	−	1.00000i	−0.0646846	−	0.0646846i	−0.738709	+	0.674024i	$0.764564\pi$
$240$		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
$247$	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
$251$		−	18.0000i		−	1.13615i	−0.822977	−	0.568075i	$-0.807688\pi$
$251$		−	18.0000i		−	1.13615i	0.822977	−	0.568075i	$-0.192312\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$	3.00000	−	3.00000i	0.188237	−	0.188237i
$255$		0			0
$256$	1.00000			0.0625000
$257$	21.0000	+	21.0000i	1.30994	+	1.30994i	0.921452	+	0.388492i	$0.127004\pi$
$257$	21.0000	+	21.0000i	1.30994	+	1.30994i	0.388492	+	0.921452i	$0.372996\pi$
$258$		0			0
$259$	−16.0000			−0.994192
$260$	1.00000	+	8.00000i	0.0620174	+	0.496139i
$261$		0			0
$262$			12.0000i			0.741362i
$263$	3.00000	+	3.00000i	0.184988	+	0.184988i	0.793525	−	0.608537i	$-0.208243\pi$
$263$	3.00000	+	3.00000i	0.184988	+	0.184988i	−0.608537	+	0.793525i	$0.708243\pi$
$264$		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
$269$			4.00000i			0.243884i	0.992537	+	0.121942i	$0.0389122\pi$
$269$			4.00000i			0.243884i	−0.992537	+	0.121942i	$0.961088\pi$
$270$		0			0
$271$	3.00000	+	3.00000i	0.182237	+	0.182237i	0.792330	−	0.610093i	$-0.208868\pi$
$271$	3.00000	+	3.00000i	0.182237	+	0.182237i	−0.610093	+	0.792330i	$0.708868\pi$
$272$	1.00000	+	1.00000i	0.0606339	+	0.0606339i
$273$		0			0
$274$		0			0
$275$	−1.00000	+	7.00000i	−0.0603023	+	0.422116i
$276$		0			0
$277$	11.0000	+	11.0000i	0.660926	+	0.660926i	0.955598	−	0.294672i	$-0.0952105\pi$
$277$	11.0000	+	11.0000i	0.660926	+	0.660926i	−0.294672	+	0.955598i	$0.595211\pi$
$278$	−2.00000			−0.119952
$279$		0			0
$280$	−2.00000	+	4.00000i	−0.119523	+	0.239046i
$281$	−9.00000	−	9.00000i	−0.536895	−	0.536895i	0.385721	−	0.922616i	$-0.373953\pi$
$281$	−9.00000	−	9.00000i	−0.536895	−	0.536895i	−0.922616	+	0.385721i	$0.873953\pi$
$282$		0			0
$283$	−15.0000	+	15.0000i	−0.891657	+	0.891657i	−0.994679	−	0.103022i	$-0.967149\pi$
$283$	−15.0000	+	15.0000i	−0.891657	+	0.891657i	0.103022	+	0.994679i	$0.467149\pi$
$284$	5.00000	−	5.00000i	0.296695	−	0.296695i
$285$		0			0
$286$	5.00000	+	1.00000i	0.295656	+	0.0591312i
$287$	−14.0000	+	14.0000i	−0.826394	+	0.826394i
$288$		0			0
$289$		−	15.0000i		−	0.882353i
$290$	−16.0000	−	8.00000i	−0.939552	−	0.469776i
$291$		0			0
$292$		−	6.00000i		−	0.351123i
$293$			22.0000i			1.28525i	0.766179	+	0.642627i	$0.222155\pi$
$293$			22.0000i			1.28525i	−0.766179	+	0.642627i	$0.777845\pi$
$294$		0			0
$295$	−27.0000	+	9.00000i	−1.57200	+	0.524000i
$296$			8.00000i			0.464991i
$297$		0			0
$298$	1.00000	−	1.00000i	0.0579284	−	0.0579284i
$299$	−5.00000	−	1.00000i	−0.289157	−	0.0578315i
$300$		0			0
$301$	−2.00000	+	2.00000i	−0.115278	+	0.115278i
$302$	3.00000	−	3.00000i	0.172631	−	0.172631i
$303$		0			0
$304$	−3.00000	−	3.00000i	−0.172062	−	0.172062i
$305$	−4.00000	−	2.00000i	−0.229039	−	0.114520i
$306$		0			0
$307$	10.0000			0.570730			0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000			0.570730			0.285365	+	0.958419i	$0.407885\pi$
$308$	2.00000	+	2.00000i	0.113961	+	0.113961i
$309$		0			0
$310$	1.00000	+	3.00000i	0.0567962	+	0.170389i
$311$			2.00000i			0.113410i	0.998391	+	0.0567048i	$0.0180594\pi$
$311$			2.00000i			0.113410i	−0.998391	+	0.0567048i	$0.981941\pi$
$312$		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	$0.632875\pi$
$314$	15.0000	+	15.0000i	0.846499	+	0.846499i
$315$		0			0
$316$		−	10.0000i		−	0.562544i
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$		0			0
$319$	−8.00000	+	8.00000i	−0.447914	+	0.447914i
$320$	2.00000	+	1.00000i	0.111803	+	0.0559017i
$321$		0			0
$322$	−2.00000	−	2.00000i	−0.111456	−	0.111456i
$323$		−	6.00000i		−	0.333849i
$324$		0			0
$325$	−6.00000	+	17.0000i	−0.332820	+	0.942990i
$326$	−20.0000			−1.10770
$327$		0			0
$328$	7.00000	+	7.00000i	0.386510	+	0.386510i
$329$	−20.0000			−1.10264
$330$		0			0
$331$	21.0000	−	21.0000i	1.15426	−	1.15426i	0.168576	−	0.985689i	$-0.446083\pi$
$331$	21.0000	−	21.0000i	1.15426	−	1.15426i	0.985689	−	0.168576i	$-0.0539168\pi$
$332$	−18.0000			−0.987878
$333$		0			0
$334$			14.0000i			0.766046i
$335$	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
$340$	1.00000	+	3.00000i	0.0542326	+	0.162698i
$341$	2.00000			0.108306
$342$		0			0
$343$	20.0000			1.07990
$344$	1.00000	+	1.00000i	0.0539164	+	0.0539164i
$345$		0			0
$346$	−9.00000	−	9.00000i	−0.483843	−	0.483843i
$347$	5.00000	−	5.00000i	0.268414	−	0.268414i	−0.560047	−	0.828461i	$-0.689217\pi$
$347$	5.00000	−	5.00000i	0.268414	−	0.268414i	0.828461	+	0.560047i	$0.189217\pi$
$348$		0			0
$349$	−21.0000	+	21.0000i	−1.12410	+	1.12410i	−0.132986	+	0.991118i	$0.542457\pi$
$349$	−21.0000	+	21.0000i	−1.12410	+	1.12410i	−0.991118	+	0.132986i	$0.957543\pi$
$350$	−8.00000	+	6.00000i	−0.427618	+	0.320713i
$351$		0			0
$352$	1.00000	−	1.00000i	0.0533002	−	0.0533002i
$353$	−4.00000			−0.212899			−0.106449	−	0.994318i	$-0.533948\pi$
$353$	−4.00000			−0.212899			−0.106449	+	0.994318i	$0.533948\pi$
$354$		0			0
$355$	15.0000	−	5.00000i	0.796117	−	0.265372i
$356$	11.0000	−	11.0000i	0.582999	−	0.582999i
$357$		0			0
$358$			20.0000i			1.05703i
$359$	5.00000	−	5.00000i	0.263890	−	0.263890i	−0.562742	−	0.826632i	$-0.690254\pi$
$359$	5.00000	−	5.00000i	0.263890	−	0.263890i	0.826632	+	0.562742i	$0.190254\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$	16.0000			0.840941
$363$		0			0
$364$	4.00000	+	6.00000i	0.209657	+	0.314485i
$365$	6.00000	−	12.0000i	0.314054	−	0.628109i
$366$		0			0
$367$	−21.0000	+	21.0000i	−1.09619	+	1.09619i	−0.101339	+	0.994852i	$0.532313\pi$
$367$	−21.0000	+	21.0000i	−1.09619	+	1.09619i	−0.994852	+	0.101339i	$0.967687\pi$
$368$	−1.00000	+	1.00000i	−0.0521286	+	0.0521286i
$369$		0			0
$370$	−8.00000	+	16.0000i	−0.415900	+	0.831800i
$371$	2.00000	+	2.00000i	0.103835	+	0.103835i
$372$		0			0
$373$	5.00000	+	5.00000i	0.258890	+	0.258890i	0.824603	−	0.565712i	$-0.191399\pi$
$373$	5.00000	+	5.00000i	0.258890	+	0.258890i	−0.565712	+	0.824603i	$0.691399\pi$
$374$	2.00000			0.103418
$375$		0			0
$376$			10.0000i			0.515711i
$377$	−24.0000	+	16.0000i	−1.23606	+	0.824042i
$378$		0			0
$379$	−23.0000	−	23.0000i	−1.18143	−	1.18143i	−0.979374	−	0.202057i	$-0.935237\pi$
$379$	−23.0000	−	23.0000i	−1.18143	−	1.18143i	−0.202057	−	0.979374i	$-0.564763\pi$
$380$	−3.00000	−	9.00000i	−0.153897	−	0.461690i
$381$		0			0
$382$			8.00000i			0.409316i
$383$	−18.0000			−0.919757			−0.459879	−	0.887982i	$-0.652107\pi$
$383$	−18.0000			−0.919757			−0.459879	+	0.887982i	$0.652107\pi$
$384$		0			0
$385$	2.00000	+	6.00000i	0.101929	+	0.305788i
$386$	2.00000			0.101797
$387$		0			0
$388$		−	14.0000i		−	0.710742i
$389$	−2.00000			−0.101404			−0.0507020	−	0.998714i	$-0.516146\pi$
$389$	−2.00000			−0.101404			−0.0507020	+	0.998714i	$0.516146\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$		−	3.00000i		−	0.151523i
$393$		0			0
$394$	6.00000			0.302276
$395$	10.0000	−	20.0000i	0.503155	−	1.00631i
$396$		0			0
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$		−	24.0000i		−	1.20301i
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	19.0000	+	19.0000i	0.948815	+	0.948815i	0.998752	−	0.0499376i	$-0.0159023\pi$
$401$	19.0000	+	19.0000i	0.948815	+	0.948815i	−0.0499376	+	0.998752i	$0.515902\pi$
$402$		0			0
$403$	5.00000	+	1.00000i	0.249068	+	0.0498135i
$404$		−	12.0000i		−	0.597022i
$405$		0			0
$406$	−16.0000			−0.794067
$407$	8.00000	+	8.00000i	0.396545	+	0.396545i
$408$		0			0
$409$	−9.00000	−	9.00000i	−0.445021	−	0.445021i	0.448674	−	0.893695i	$-0.351896\pi$
$409$	−9.00000	−	9.00000i	−0.445021	−	0.445021i	−0.893695	+	0.448674i	$0.851896\pi$
$410$	7.00000	+	21.0000i	0.345705	+	1.03712i
$411$		0			0
$412$	−5.00000	+	5.00000i	−0.246332	+	0.246332i
$413$	−18.0000	+	18.0000i	−0.885722	+	0.885722i
$414$		0			0
$415$	−36.0000	−	18.0000i	−1.76717	−	0.883585i
$416$	3.00000	−	2.00000i	0.147087	−	0.0980581i
$417$		0			0
$418$	−6.00000			−0.293470
$419$		−	22.0000i		−	1.07477i	−0.843337	−	0.537385i	$-0.819412\pi$
$419$		−	22.0000i		−	1.07477i	0.843337	−	0.537385i	$-0.180588\pi$
$420$		0			0
$421$	9.00000	−	9.00000i	0.438633	−	0.438633i	−0.452919	−	0.891552i	$-0.649617\pi$
$421$	9.00000	−	9.00000i	0.438633	−	0.438633i	0.891552	+	0.452919i	$0.149617\pi$
$422$			12.0000i			0.584151i
$423$		0			0
$424$	1.00000	−	1.00000i	0.0485643	−	0.0485643i
$425$	−1.00000	+	7.00000i	−0.0485071	+	0.339550i
$426$		0			0
$427$	−4.00000			−0.193574
$428$	−1.00000	+	1.00000i	−0.0483368	+	0.0483368i
$429$		0			0
$430$	1.00000	+	3.00000i	0.0482243	+	0.144673i
$431$	15.0000	−	15.0000i	0.722525	−	0.722525i	−0.246594	−	0.969119i	$-0.579311\pi$
$431$	15.0000	−	15.0000i	0.722525	−	0.722525i	0.969119	+	0.246594i	$0.0793115\pi$
$432$		0			0
$433$	−9.00000	+	9.00000i	−0.432512	+	0.432512i	−0.889482	−	0.456970i	$-0.848935\pi$
$433$	−9.00000	+	9.00000i	−0.432512	+	0.432512i	0.456970	+	0.889482i	$0.348935\pi$
$434$	2.00000	+	2.00000i	0.0960031	+	0.0960031i
$435$		0			0
$436$	5.00000	+	5.00000i	0.239457	+	0.239457i
$437$	6.00000			0.287019
$438$		0			0
$439$	32.0000			1.52728			0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000			1.52728			0.763638	+	0.645644i	$0.223411\pi$
$440$	3.00000	−	1.00000i	0.143019	−	0.0476731i
$441$		0			0
$442$	5.00000	+	1.00000i	0.237826	+	0.0475651i
$443$	−17.0000	−	17.0000i	−0.807694	−	0.807694i	0.176590	−	0.984284i	$-0.443493\pi$
$443$	−17.0000	−	17.0000i	−0.807694	−	0.807694i	−0.984284	+	0.176590i	$0.943493\pi$
$444$		0			0
$445$	33.0000	−	11.0000i	1.56435	−	0.521450i
$446$		−	18.0000i		−	0.852325i
$447$		0			0
$448$	2.00000			0.0944911
$449$	13.0000	−	13.0000i	0.613508	−	0.613508i	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	13.0000	−	13.0000i	0.613508	−	0.613508i	0.943858	+	0.330350i	$0.107167\pi$
$450$		0			0
$451$	14.0000			0.659234
$452$	−3.00000	−	3.00000i	−0.141108	−	0.141108i
$453$		0			0
$454$	12.0000			0.563188
$455$	2.00000	+	16.0000i	0.0937614	+	0.750092i
$456$		0			0
$457$		−	2.00000i		−	0.0935561i	−0.998905	−	0.0467780i	$-0.985105\pi$
$457$		−	2.00000i		−	0.0935561i	0.998905	−	0.0467780i	$-0.0148953\pi$
$458$	−15.0000	−	15.0000i	−0.700904	−	0.700904i
$459$		0			0
$460$	−3.00000	+	1.00000i	−0.139876	+	0.0466252i
$461$	11.0000	−	11.0000i	0.512321	−	0.512321i	−0.402916	−	0.915237i	$-0.632003\pi$
$461$	11.0000	−	11.0000i	0.512321	−	0.512321i	0.915237	+	0.402916i	$0.132003\pi$
$462$		0			0
$463$		−	16.0000i		−	0.743583i	−0.928316	−	0.371792i	$-0.878744\pi$
$463$		−	16.0000i		−	0.743583i	0.928316	−	0.371792i	$-0.121256\pi$
$464$			8.00000i			0.371391i
$465$		0			0
$466$	−1.00000	−	1.00000i	−0.0463241	−	0.0463241i
$467$	−7.00000	−	7.00000i	−0.323921	−	0.323921i	0.526348	−	0.850269i	$-0.323561\pi$
$467$	−7.00000	−	7.00000i	−0.323921	−	0.323921i	−0.850269	+	0.526348i	$0.823561\pi$
$468$		0			0
$469$		−	24.0000i		−	1.10822i
$470$	−10.0000	+	20.0000i	−0.461266	+	0.922531i
$471$		0			0
$472$	9.00000	+	9.00000i	0.414259	+	0.414259i
$473$	2.00000			0.0919601
$474$		0			0
$475$	3.00000	−	21.0000i	0.137649	−	0.963546i
$476$	2.00000	+	2.00000i	0.0916698	+	0.0916698i
$477$		0			0
$478$	−1.00000	+	1.00000i	−0.0457389	+	0.0457389i
$479$	−19.0000	+	19.0000i	−0.868132	+	0.868132i	−0.992266	−	0.124133i	$-0.960385\pi$
$479$	−19.0000	+	19.0000i	−0.868132	+	0.868132i	0.124133	+	0.992266i	$0.460385\pi$
$480$		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
$485$	14.0000	−	28.0000i	0.635707	−	1.27141i
$486$		0			0
$487$			8.00000i			0.362515i	0.983436	+	0.181257i	$0.0580167\pi$
$487$			8.00000i			0.362515i	−0.983436	+	0.181257i	$0.941983\pi$
$488$			2.00000i			0.0905357i
$489$		0			0
$490$	3.00000	−	6.00000i	0.135526	−	0.271052i
$491$			38.0000i			1.71492i	0.514554	+	0.857458i	$0.327958\pi$
$491$			38.0000i			1.71492i	−0.514554	+	0.857458i	$0.672042\pi$
$492$		0			0
$493$	−8.00000	+	8.00000i	−0.360302	+	0.360302i
$494$	−15.0000	−	3.00000i	−0.674882	−	0.134976i
$495$		0			0
$496$	1.00000	−	1.00000i	0.0449013	−	0.0449013i
$497$	10.0000	−	10.0000i	0.448561	−	0.448561i
$498$		0			0
$499$	−19.0000	−	19.0000i	−0.850557	−	0.850557i	0.139645	−	0.990202i	$-0.455404\pi$
$499$	−19.0000	−	19.0000i	−0.850557	−	0.850557i	−0.990202	+	0.139645i	$0.955404\pi$
$500$	2.00000	+	11.0000i	0.0894427	+	0.491935i
$501$		0			0
$502$	−18.0000			−0.803379
$503$	15.0000	+	15.0000i	0.668817	+	0.668817i	0.957442	−	0.288625i	$-0.0931982\pi$
$503$	15.0000	+	15.0000i	0.668817	+	0.668817i	−0.288625	+	0.957442i	$0.593198\pi$
$504$		0			0
$505$	12.0000	−	24.0000i	0.533993	−	1.06799i
$506$			2.00000i			0.0889108i
$507$		0			0
$508$	−3.00000	−	3.00000i	−0.133103	−	0.133103i
$509$	1.00000	+	1.00000i	0.0443242	+	0.0443242i	0.728922	−	0.684597i	$-0.240022\pi$
$509$	1.00000	+	1.00000i	0.0443242	+	0.0443242i	−0.684597	+	0.728922i	$0.740022\pi$
$510$		0			0
$511$		−	12.0000i		−	0.530849i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	21.0000	−	21.0000i	0.926270	−	0.926270i
$515$	−15.0000	+	5.00000i	−0.660979	+	0.220326i
$516$		0			0
$517$	10.0000	+	10.0000i	0.439799	+	0.439799i
$518$			16.0000i			0.703000i
$519$		0			0
$520$	8.00000	−	1.00000i	0.350823	−	0.0438529i
$521$	10.0000			0.438108			0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000			0.438108			0.219054	+	0.975713i	$0.429703\pi$
$522$		0			0
$523$	−15.0000	−	15.0000i	−0.655904	−	0.655904i	0.298504	−	0.954408i	$-0.403512\pi$
$523$	−15.0000	−	15.0000i	−0.655904	−	0.655904i	−0.954408	+	0.298504i	$0.903512\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$	3.00000	−	3.00000i	0.130806	−	0.130806i
$527$	2.00000			0.0871214
$528$		0			0
$529$			21.0000i			0.913043i
$530$	3.00000	−	1.00000i	0.130312	−	0.0434372i
$531$		0			0
$532$	−6.00000	−	6.00000i	−0.260133	−	0.260133i
$533$	35.0000	+	7.00000i	1.51602	+	0.303204i
$534$		0			0
$535$	−3.00000	+	1.00000i	−0.129701	+	0.0432338i
$536$	−12.0000			−0.518321
$537$		0			0
$538$	4.00000			0.172452
$539$	−3.00000	−	3.00000i	−0.129219	−	0.129219i
$540$		0			0
$541$	−27.0000	−	27.0000i	−1.16082	−	1.16082i	−0.984296	−	0.176524i	$-0.943515\pi$
$541$	−27.0000	−	27.0000i	−1.16082	−	1.16082i	−0.176524	−	0.984296i	$-0.556485\pi$
$542$	3.00000	−	3.00000i	0.128861	−	0.128861i
$543$		0			0
$544$	1.00000	−	1.00000i	0.0428746	−	0.0428746i
$545$	5.00000	+	15.0000i	0.214176	+	0.642529i
$546$		0			0
$547$	23.0000	−	23.0000i	0.983409	−	0.983409i	−0.0164556	−	0.999865i	$-0.505238\pi$
$547$	23.0000	−	23.0000i	0.983409	−	0.983409i	0.999865	+	0.0164556i	$0.00523822\pi$
$548$		0			0
$549$		0			0
$550$	7.00000	+	1.00000i	0.298481	+	0.0426401i
$551$	24.0000	−	24.0000i	1.02243	−	1.02243i
$552$		0			0
$553$		−	20.0000i		−	0.850487i
$554$	11.0000	−	11.0000i	0.467345	−	0.467345i
$555$		0			0
$556$			2.00000i			0.0848189i
$557$	32.0000			1.35588			0.677942	−	0.735116i	$-0.262872\pi$
$557$	32.0000			1.35588			0.677942	+	0.735116i	$0.262872\pi$
$558$		0			0
$559$	5.00000	+	1.00000i	0.211477	+	0.0422955i
$560$	4.00000	+	2.00000i	0.169031	+	0.0845154i
$561$		0			0
$562$	−9.00000	+	9.00000i	−0.379642	+	0.379642i
$563$	31.0000	−	31.0000i	1.30649	−	1.30649i	0.382566	−	0.923928i	$-0.375040\pi$
$563$	31.0000	−	31.0000i	1.30649	−	1.30649i	0.923928	−	0.382566i	$-0.124960\pi$
$564$		0			0
$565$	−3.00000	−	9.00000i	−0.126211	−	0.378633i
$566$	15.0000	+	15.0000i	0.630497	+	0.630497i
$567$		0			0
$568$	−5.00000	−	5.00000i	−0.209795	−	0.209795i
$569$	−26.0000			−1.08998			−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000			−1.08998			−0.544988	+	0.838444i	$0.683466\pi$
$570$		0			0
$571$		−	22.0000i		−	0.920671i	−0.887745	−	0.460336i	$-0.847729\pi$
$571$		−	22.0000i		−	0.920671i	0.887745	−	0.460336i	$-0.152271\pi$
$572$	1.00000	−	5.00000i	0.0418121	−	0.209061i
$573$		0			0
$574$	14.0000	+	14.0000i	0.584349	+	0.584349i
$575$	−7.00000	−	1.00000i	−0.291920	−	0.0417029i
$576$		0			0
$577$		−	14.0000i		−	0.582828i	−0.956597	−	0.291414i	$-0.905874\pi$
$577$		−	14.0000i		−	0.582828i	0.956597	−	0.291414i	$-0.0941257\pi$
$578$	−15.0000			−0.623918
$579$		0			0
$580$	−8.00000	+	16.0000i	−0.332182	+	0.664364i
$581$	−36.0000			−1.49353
$582$		0			0
$583$		−	2.00000i		−	0.0828315i
$584$	−6.00000			−0.248282
$585$		0			0
$586$	22.0000			0.908812
$587$		−	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
$590$	9.00000	+	27.0000i	0.370524	+	1.11157i
$591$		0			0
$592$	8.00000			0.328798
$593$		−	10.0000i		−	0.410651i	−0.978694	−	0.205325i	$-0.934175\pi$
$593$		−	10.0000i		−	0.410651i	0.978694	−	0.205325i	$-0.0658253\pi$
$594$		0			0
$595$	2.00000	+	6.00000i	0.0819920	+	0.245976i
$596$	−1.00000	−	1.00000i	−0.0409616	−	0.0409616i
$597$		0			0
$598$	−1.00000	+	5.00000i	−0.0408930	+	0.204465i
$599$		−	26.0000i		−	1.06233i	−0.847268	−	0.531166i	$-0.821754\pi$
$599$		−	26.0000i		−	1.06233i	0.847268	−	0.531166i	$-0.178246\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	2.00000	+	2.00000i	0.0815139	+	0.0815139i
$603$		0			0
$604$	−3.00000	−	3.00000i	−0.122068	−	0.122068i
$605$	−9.00000	+	18.0000i	−0.365902	+	0.731804i
$606$		0			0
$607$	−9.00000	+	9.00000i	−0.365299	+	0.365299i	−0.865759	−	0.500461i	$-0.833164\pi$
$607$	−9.00000	+	9.00000i	−0.365299	+	0.365299i	0.500461	+	0.865759i	$0.333164\pi$
$608$	−3.00000	+	3.00000i	−0.121666	+	0.121666i
$609$		0			0
$610$	−2.00000	+	4.00000i	−0.0809776	+	0.161955i
$611$	20.0000	+	30.0000i	0.809113	+	1.21367i
$612$		0			0
$613$	4.00000			0.161558			0.0807792	−	0.996732i	$-0.474259\pi$
$613$	4.00000			0.161558			0.0807792	+	0.996732i	$0.474259\pi$
$614$		−	10.0000i		−	0.403567i
$615$		0			0
$616$	2.00000	−	2.00000i	0.0805823	−	0.0805823i
$617$		−	38.0000i		−	1.52982i	−0.644136	−	0.764911i	$-0.722783\pi$
$617$		−	38.0000i		−	1.52982i	0.644136	−	0.764911i	$-0.277217\pi$
$618$		0			0
$619$	−9.00000	+	9.00000i	−0.361741	+	0.361741i	−0.864453	−	0.502713i	$-0.832335\pi$
$619$	−9.00000	+	9.00000i	−0.361741	+	0.361741i	0.502713	+	0.864453i	$0.332335\pi$
$620$	3.00000	−	1.00000i	0.120483	−	0.0401610i
$621$		0			0
$622$	2.00000			0.0801927
$623$	22.0000	−	22.0000i	0.881411	−	0.881411i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	9.00000	−	9.00000i	0.359712	−	0.359712i
$627$		0			0
$628$	15.0000	−	15.0000i	0.598565	−	0.598565i
$629$	8.00000	+	8.00000i	0.318981	+	0.318981i
$630$		0			0
$631$	23.0000	+	23.0000i	0.915616	+	0.915616i	0.996707	−	0.0810911i	$-0.0258405\pi$
$631$	23.0000	+	23.0000i	0.915616	+	0.915616i	−0.0810911	+	0.996707i	$0.525840\pi$
$632$	−10.0000			−0.397779
$633$		0			0
$634$	2.00000			0.0794301
$635$	−3.00000	−	9.00000i	−0.119051	−	0.357154i
$636$		0			0
$637$	−6.00000	−	9.00000i	−0.237729	−	0.356593i
$638$	8.00000	+	8.00000i	0.316723	+	0.316723i
$639$		0			0
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$			24.0000i			0.947943i	0.880540	+	0.473972i	$0.157180\pi$
$641$			24.0000i			0.947943i	−0.880540	+	0.473972i	$0.842820\pi$
$642$		0			0
$643$	−10.0000			−0.394362			−0.197181	−	0.980367i	$-0.563179\pi$
$643$	−10.0000			−0.394362			−0.197181	+	0.980367i	$0.563179\pi$
$644$	−2.00000	+	2.00000i	−0.0788110	+	0.0788110i
$645$		0			0
$646$	−6.00000			−0.236067
$647$	13.0000	+	13.0000i	0.511083	+	0.511083i	0.914858	−	0.403775i	$-0.132302\pi$
$647$	13.0000	+	13.0000i	0.511083	+	0.511083i	−0.403775	+	0.914858i	$0.632302\pi$
$648$		0			0
$649$	18.0000			0.706562
$650$	17.0000	+	6.00000i	0.666795	+	0.235339i
$651$		0			0
$652$			20.0000i			0.783260i
$653$	15.0000	+	15.0000i	0.586995	+	0.586995i	0.936817	−	0.349821i	$-0.113758\pi$
$653$	15.0000	+	15.0000i	0.586995	+	0.586995i	−0.349821	+	0.936817i	$0.613758\pi$
$654$		0			0
$655$	24.0000	+	12.0000i	0.937758	+	0.468879i
$656$	7.00000	−	7.00000i	0.273304	−	0.273304i
$657$		0			0
$658$			20.0000i			0.779681i
$659$		−	38.0000i		−	1.48027i	−0.672458	−	0.740135i	$-0.734762\pi$
$659$		−	38.0000i		−	1.48027i	0.672458	−	0.740135i	$-0.265238\pi$
$660$		0			0
$661$	13.0000	+	13.0000i	0.505641	+	0.505641i	0.913186	−	0.407544i	$-0.133615\pi$
$661$	13.0000	+	13.0000i	0.505641	+	0.505641i	−0.407544	+	0.913186i	$0.633615\pi$
$662$	−21.0000	−	21.0000i	−0.816188	−	0.816188i
$663$		0			0
$664$			18.0000i			0.698535i
$665$	−6.00000	−	18.0000i	−0.232670	−	0.698010i
$666$		0			0
$667$	−8.00000	−	8.00000i	−0.309761	−	0.309761i
$668$	14.0000			0.541676
$669$		0			0
$670$	−24.0000	−	12.0000i	−0.927201	−	0.463600i
$671$	2.00000	+	2.00000i	0.0772091	+	0.0772091i
$672$		0			0
$673$	−17.0000	+	17.0000i	−0.655302	+	0.655302i	−0.954265	−	0.298963i	$-0.903359\pi$
$673$	−17.0000	+	17.0000i	−0.655302	+	0.655302i	0.298963	+	0.954265i	$0.403359\pi$
$674$	−5.00000	+	5.00000i	−0.192593	+	0.192593i
$675$		0			0
$676$	5.00000	−	12.0000i	0.192308	−	0.461538i
$677$	−13.0000	+	13.0000i	−0.499631	+	0.499631i	−0.911323	−	0.411692i	$-0.864938\pi$
$677$	−13.0000	+	13.0000i	−0.499631	+	0.499631i	0.411692	+	0.911323i	$0.364938\pi$
$678$		0			0
$679$		−	28.0000i		−	1.07454i
$680$	3.00000	−	1.00000i	0.115045	−	0.0383482i
$681$		0			0
$682$		−	2.00000i		−	0.0765840i
$683$		−	12.0000i		−	0.459167i	−0.973289	−	0.229584i	$-0.926264\pi$
$683$		−	12.0000i		−	0.459167i	0.973289	−	0.229584i	$-0.0737364\pi$
$684$		0			0
$685$		0			0
$686$		−	20.0000i		−	0.763604i
$687$		0			0
$688$	1.00000	−	1.00000i	0.0381246	−	0.0381246i
$689$	1.00000	−	5.00000i	0.0380970	−	0.190485i
$690$		0			0
$691$	21.0000	−	21.0000i	0.798878	−	0.798878i	−0.184041	−	0.982919i	$-0.558918\pi$
$691$	21.0000	−	21.0000i	0.798878	−	0.798878i	0.982919	+	0.184041i	$0.0589179\pi$
$692$	−9.00000	+	9.00000i	−0.342129	+	0.342129i
$693$		0			0
$694$	−5.00000	−	5.00000i	−0.189797	−	0.189797i
$695$	−2.00000	+	4.00000i	−0.0758643	+	0.151729i
$696$		0			0
$697$	14.0000			0.530288
$698$	21.0000	+	21.0000i	0.794862	+	0.794862i
$699$		0			0
$700$	6.00000	+	8.00000i	0.226779	+	0.302372i
$701$			12.0000i			0.453234i	0.973984	+	0.226617i	$0.0727665\pi$
$701$			12.0000i			0.453234i	−0.973984	+	0.226617i	$0.927233\pi$
$702$		0			0
$703$	−24.0000	−	24.0000i	−0.905177	−	0.905177i
$704$	−1.00000	−	1.00000i	−0.0376889	−	0.0376889i
$705$		0			0
$706$			4.00000i			0.150542i
$707$		−	24.0000i		−	0.902613i
$708$		0			0
$709$	−33.0000	+	33.0000i	−1.23934	+	1.23934i	−0.279070	+	0.960271i	$0.590026\pi$
$709$	−33.0000	+	33.0000i	−1.23934	+	1.23934i	−0.960271	+	0.279070i	$0.909974\pi$
$710$	−5.00000	−	15.0000i	−0.187647	−	0.562940i
$711$		0			0
$712$	−11.0000	−	11.0000i	−0.412242	−	0.412242i
$713$			2.00000i			0.0749006i
$714$		0			0
$715$	7.00000	−	9.00000i	0.261785	−	0.336581i
$716$	20.0000			0.747435
$717$		0			0
$718$	−5.00000	−	5.00000i	−0.186598	−	0.186598i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$		0			0
$721$	−10.0000	+	10.0000i	−0.372419	+	0.372419i
$722$	−1.00000			−0.0372161
$723$		0			0
$724$		−	16.0000i		−	0.594635i
$725$	−32.0000	+	24.0000i	−1.18845	+	0.891338i
$726$		0			0
$727$	−1.00000	−	1.00000i	−0.0370879	−	0.0370879i	0.688320	−	0.725408i	$-0.258349\pi$
$727$	−1.00000	−	1.00000i	−0.0370879	−	0.0370879i	−0.725408	+	0.688320i	$0.758349\pi$
$728$	6.00000	−	4.00000i	0.222375	−	0.148250i
$729$		0			0
$730$	−12.0000	−	6.00000i	−0.444140	−	0.222070i
$731$	2.00000			0.0739727
$732$		0			0
$733$	20.0000			0.738717			0.369358	−	0.929287i	$-0.379577\pi$
$733$	20.0000			0.738717			0.369358	+	0.929287i	$0.379577\pi$
$734$	21.0000	+	21.0000i	0.775124	+	0.775124i
$735$		0			0
$736$	1.00000	+	1.00000i	0.0368605	+	0.0368605i
$737$	−12.0000	+	12.0000i	−0.442026	+	0.442026i
$738$		0			0
$739$	−5.00000	+	5.00000i	−0.183928	+	0.183928i	−0.793065	−	0.609137i	$-0.791516\pi$
$739$	−5.00000	+	5.00000i	−0.183928	+	0.183928i	0.609137	+	0.793065i	$0.291516\pi$
$740$	16.0000	+	8.00000i	0.588172	+	0.294086i
$741$		0			0
$742$	2.00000	−	2.00000i	0.0734223	−	0.0734223i
$743$	−18.0000			−0.660356			−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000			−0.660356			−0.330178	+	0.943919i	$0.607109\pi$
$744$		0			0
$745$	−1.00000	−	3.00000i	−0.0366372	−	0.109911i
$746$	5.00000	−	5.00000i	0.183063	−	0.183063i
$747$		0			0
$748$		−	2.00000i		−	0.0731272i
$749$	−2.00000	+	2.00000i	−0.0730784	+	0.0730784i
$750$		0			0
$751$			38.0000i			1.38664i	0.720630	+	0.693320i	$0.243853\pi$
$751$			38.0000i			1.38664i	−0.720630	+	0.693320i	$0.756147\pi$
$752$	10.0000			0.364662
$753$		0			0
$754$	16.0000	+	24.0000i	0.582686	+	0.874028i
$755$	−3.00000	−	9.00000i	−0.109181	−	0.327544i
$756$		0			0
$757$	25.0000	−	25.0000i	0.908640	−	0.908640i	−0.0875221	−	0.996163i	$-0.527895\pi$
$757$	25.0000	−	25.0000i	0.908640	−	0.908640i	0.996163	+	0.0875221i	$0.0278948\pi$
$758$	−23.0000	+	23.0000i	−0.835398	+	0.835398i
$759$		0			0
$760$	−9.00000	+	3.00000i	−0.326464	+	0.108821i
$761$	−1.00000	−	1.00000i	−0.0362500	−	0.0362500i	0.688749	−	0.724999i	$-0.258160\pi$
$761$	−1.00000	−	1.00000i	−0.0362500	−	0.0362500i	−0.724999	+	0.688749i	$0.758160\pi$
$762$		0			0
$763$	10.0000	+	10.0000i	0.362024	+	0.362024i
$764$	8.00000			0.289430
$765$		0			0
$766$			18.0000i			0.650366i
$767$	45.0000	+	9.00000i	1.62486	+	0.324971i
$768$		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
$772$		−	2.00000i		−	0.0719816i
$773$	−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
$776$	−14.0000			−0.502571
$777$		0			0
$778$			2.00000i			0.0717035i
$779$	−42.0000			−1.50481
$780$		0			0
$781$	−10.0000			−0.357828
$782$			2.00000i			0.0715199i
$783$		0			0
$784$	−3.00000			−0.107143
$785$	45.0000	−	15.0000i	1.60612	−	0.535373i
$786$		0			0
$787$	−30.0000			−1.06938			−0.534692	−	0.845047i	$-0.679572\pi$
$787$	−30.0000			−1.06938			−0.534692	+	0.845047i	$0.679572\pi$
$788$		−	6.00000i		−	0.213741i
$789$		0			0
$790$	−20.0000	−	10.0000i	−0.711568	−	0.355784i
$791$	−6.00000	−	6.00000i	−0.213335	−	0.213335i
$792$		0			0
$793$	4.00000	+	6.00000i	0.142044	+	0.213066i
$794$		−	8.00000i		−	0.283909i
$795$		0			0
$796$	−24.0000			−0.850657
$797$	5.00000	+	5.00000i	0.177109	+	0.177109i	0.790094	−	0.612985i	$-0.210032\pi$
$797$	5.00000	+	5.00000i	0.177109	+	0.177109i	−0.612985	+	0.790094i	$0.710032\pi$
$798$		0			0
$799$	10.0000	+	10.0000i	0.353775	+	0.353775i
$800$	4.00000	−	3.00000i	0.141421	−	0.106066i
$801$		0			0
$802$	19.0000	−	19.0000i	0.670913	−	0.670913i
$803$	−6.00000	+	6.00000i	−0.211735	+	0.211735i
$804$		0			0
$805$	−6.00000	+	2.00000i	−0.211472	+	0.0704907i
$806$	1.00000	−	5.00000i	0.0352235	−	0.176117i
$807$		0			0
$808$	−12.0000			−0.422159
$809$			12.0000i			0.421898i	0.977497	+	0.210949i	$0.0676553\pi$
$809$			12.0000i			0.421898i	−0.977497	+	0.210949i	$0.932345\pi$
$810$		0			0
$811$	5.00000	−	5.00000i	0.175574	−	0.175574i	−0.613849	−	0.789423i	$-0.710380\pi$
$811$	5.00000	−	5.00000i	0.175574	−	0.175574i	0.789423	+	0.613849i	$0.210380\pi$
$812$			16.0000i			0.561490i
$813$		0			0
$814$	8.00000	−	8.00000i	0.280400	−	0.280400i
$815$	−20.0000	+	40.0000i	−0.700569	+	1.40114i
$816$		0			0
$817$	−6.00000			−0.209913
$818$	−9.00000	+	9.00000i	−0.314678	+	0.314678i
$819$		0			0
$820$	21.0000	−	7.00000i	0.733352	−	0.244451i
$821$	19.0000	−	19.0000i	0.663105	−	0.663105i	−0.293006	−	0.956111i	$-0.594656\pi$
$821$	19.0000	−	19.0000i	0.663105	−	0.663105i	0.956111	+	0.293006i	$0.0946556\pi$
$822$		0			0
$823$	−3.00000	+	3.00000i	−0.104573	+	0.104573i	−0.757458	−	0.652884i	$-0.773559\pi$
$823$	−3.00000	+	3.00000i	−0.104573	+	0.104573i	0.652884	+	0.757458i	$0.273559\pi$
$824$	5.00000	+	5.00000i	0.174183	+	0.174183i
$825$		0			0
$826$	18.0000	+	18.0000i	0.626300	+	0.626300i
$827$	−26.0000			−0.904109			−0.452054	−	0.891990i	$-0.649309\pi$
$827$	−26.0000			−0.904109			−0.452054	+	0.891990i	$0.649309\pi$
$828$		0			0
$829$	−18.0000			−0.625166			−0.312583	−	0.949890i	$-0.601194\pi$
$829$	−18.0000			−0.625166			−0.312583	+	0.949890i	$0.601194\pi$
$830$	−18.0000	+	36.0000i	−0.624789	+	1.24958i
$831$		0			0
$832$	−2.00000	−	3.00000i	−0.0693375	−	0.104006i
$833$	−3.00000	−	3.00000i	−0.103944	−	0.103944i
$834$		0			0
$835$	28.0000	+	14.0000i	0.968980	+	0.484490i
$836$			6.00000i			0.207514i
$837$		0			0
$838$	−22.0000			−0.759977
$839$	−7.00000	+	7.00000i	−0.241667	+	0.241667i	−0.817539	−	0.575873i	$-0.804662\pi$
$839$	−7.00000	+	7.00000i	−0.241667	+	0.241667i	0.575873	+	0.817539i	$0.304662\pi$
$840$		0			0
$841$	−35.0000			−1.20690
$842$	−9.00000	−	9.00000i	−0.310160	−	0.310160i
$843$		0			0
$844$	12.0000			0.413057
$845$	22.0000	−	19.0000i	0.756823	−	0.653620i
$846$		0			0
$847$			18.0000i			0.618487i
$848$	−1.00000	−	1.00000i	−0.0343401	−	0.0343401i
$849$		0			0
$850$	7.00000	+	1.00000i	0.240098	+	0.0342997i
$851$	−8.00000	+	8.00000i	−0.274236	+	0.274236i
$852$		0			0
$853$		−	38.0000i		−	1.30110i	−0.759465	−	0.650548i	$-0.774539\pi$
$853$		−	38.0000i		−	1.30110i	0.759465	−	0.650548i	$-0.225461\pi$
$854$			4.00000i			0.136877i
$855$		0			0
$856$	1.00000	+	1.00000i	0.0341793	+	0.0341793i
$857$	−11.0000	−	11.0000i	−0.375753	−	0.375753i	0.493814	−	0.869567i	$-0.335602\pi$
$857$	−11.0000	−	11.0000i	−0.375753	−	0.375753i	−0.869567	+	0.493814i	$0.835602\pi$
$858$		0			0
$859$		−	34.0000i		−	1.16007i	−0.814593	−	0.580033i	$-0.803040\pi$
$859$		−	34.0000i		−	1.16007i	0.814593	−	0.580033i	$-0.196960\pi$
$860$	3.00000	−	1.00000i	0.102299	−	0.0340997i
$861$		0			0
$862$	−15.0000	−	15.0000i	−0.510902	−	0.510902i
$863$	−34.0000			−1.15737			−0.578687	−	0.815550i	$-0.696435\pi$
$863$	−34.0000			−1.15737			−0.578687	+	0.815550i	$0.696435\pi$
$864$		0			0
$865$	−27.0000	+	9.00000i	−0.918028	+	0.306009i
$866$	9.00000	+	9.00000i	0.305832	+	0.305832i
$867$		0			0
$868$	2.00000	−	2.00000i	0.0678844	−	0.0678844i
$869$	−10.0000	+	10.0000i	−0.339227	+	0.339227i
$870$		0			0
$871$	−36.0000	+	24.0000i	−1.21981	+	0.813209i
$872$	5.00000	−	5.00000i	0.169321	−	0.169321i
$873$		0			0
$874$		−	6.00000i		−	0.202953i
$875$	4.00000	+	22.0000i	0.135225	+	0.743736i
$876$		0			0
$877$		−	6.00000i		−	0.202606i	−0.994856	−	0.101303i	$-0.967699\pi$
$877$		−	6.00000i		−	0.202606i	0.994856	−	0.101303i	$-0.0323011\pi$
$878$		−	32.0000i		−	1.07995i
$879$		0			0
$880$	−1.00000	−	3.00000i	−0.0337100	−	0.101130i
$881$			20.0000i			0.673817i	0.941537	+	0.336909i	$0.109381\pi$
$881$			20.0000i			0.673817i	−0.941537	+	0.336909i	$0.890619\pi$
$882$		0			0
$883$	25.0000	−	25.0000i	0.841317	−	0.841317i	−0.147713	−	0.989030i	$-0.547191\pi$
$883$	25.0000	−	25.0000i	0.841317	−	0.841317i	0.989030	+	0.147713i	$0.0471913\pi$
$884$	1.00000	−	5.00000i	0.0336336	−	0.168168i
$885$		0			0
$886$	−17.0000	+	17.0000i	−0.571126	+	0.571126i
$887$	−19.0000	+	19.0000i	−0.637958	+	0.637958i	−0.950051	−	0.312094i	$-0.898970\pi$
$887$	−19.0000	+	19.0000i	−0.637958	+	0.637958i	0.312094	+	0.950051i	$0.398970\pi$
$888$		0			0
$889$	−6.00000	−	6.00000i	−0.201234	−	0.201234i
$890$	−11.0000	−	33.0000i	−0.368721	−	1.10616i
$891$		0			0
$892$	−18.0000			−0.602685
$893$	−30.0000	−	30.0000i	−1.00391	−	1.00391i
$894$		0			0
$895$	40.0000	+	20.0000i	1.33705	+	0.668526i
$896$		−	2.00000i		−	0.0668153i
$897$		0			0
$898$	−13.0000	−	13.0000i	−0.433816	−	0.433816i
$899$	8.00000	+	8.00000i	0.266815	+	0.266815i
$900$		0			0
$901$		−	2.00000i		−	0.0666297i
$902$		−	14.0000i		−	0.466149i
$903$		0			0
$904$	−3.00000	+	3.00000i	−0.0997785	+	0.0997785i
$905$	16.0000	−	32.0000i	0.531858	−	1.06372i
$906$		0			0
$907$	7.00000	+	7.00000i	0.232431	+	0.232431i	0.813707	−	0.581276i	$-0.197446\pi$
$907$	7.00000	+	7.00000i	0.232431	+	0.232431i	−0.581276	+	0.813707i	$0.697446\pi$
$908$		−	12.0000i		−	0.398234i
$909$		0			0
$910$	16.0000	−	2.00000i	0.530395	−	0.0662994i
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$		0			0
$913$	18.0000	+	18.0000i	0.595713	+	0.595713i
$914$	−2.00000			−0.0661541
$915$		0			0
$916$	−15.0000	+	15.0000i	−0.495614	+	0.495614i
$917$	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	$-0.0741699\pi$
$920$	1.00000	+	3.00000i	0.0329690	+	0.0989071i
$921$		0			0
$922$	−11.0000	−	11.0000i	−0.362266	−	0.362266i
$923$	−25.0000	−	5.00000i	−0.822885	−	0.164577i
$924$		0			0
$925$	24.0000	+	32.0000i	0.789115	+	1.05215i
$926$	−16.0000			−0.525793
$927$		0			0
$928$	8.00000			0.262613
$929$	13.0000	+	13.0000i	0.426516	+	0.426516i	0.887440	−	0.460924i	$-0.152482\pi$
$929$	13.0000	+	13.0000i	0.426516	+	0.426516i	−0.460924	+	0.887440i	$0.652482\pi$
$930$		0			0
$931$	9.00000	+	9.00000i	0.294963	+	0.294963i
$932$	−1.00000	+	1.00000i	−0.0327561	+	0.0327561i
$933$		0			0
$934$	−7.00000	+	7.00000i	−0.229047	+	0.229047i
$935$	2.00000	−	4.00000i	0.0654070	−	0.130814i
$936$		0			0
$937$	9.00000	−	9.00000i	0.294017	−	0.294017i	−0.544648	−	0.838665i	$-0.683337\pi$
$937$	9.00000	−	9.00000i	0.294017	−	0.294017i	0.838665	+	0.544648i	$0.183337\pi$
$938$	−24.0000			−0.783628
$939$		0			0
$940$	20.0000	+	10.0000i	0.652328	+	0.326164i
$941$	−17.0000	+	17.0000i	−0.554184	+	0.554184i	−0.927646	−	0.373462i	$-0.878171\pi$
$941$	−17.0000	+	17.0000i	−0.554184	+	0.554184i	0.373462	+	0.927646i	$0.378171\pi$
$942$		0			0
$943$			14.0000i			0.455903i
$944$	9.00000	−	9.00000i	0.292925	−	0.292925i
$945$		0			0
$946$		−	2.00000i		−	0.0650256i
$947$	−10.0000			−0.324956			−0.162478	−	0.986712i	$-0.551949\pi$
$947$	−10.0000			−0.324956			−0.162478	+	0.986712i	$0.551949\pi$
$948$		0			0
$949$	−18.0000	+	12.0000i	−0.584305	+	0.389536i
$950$	−21.0000	−	3.00000i	−0.681330	−	0.0973329i
$951$		0			0
$952$	2.00000	−	2.00000i	0.0648204	−	0.0648204i
$953$	5.00000	−	5.00000i	0.161966	−	0.161966i	−0.621471	−	0.783437i	$-0.713465\pi$
$953$	5.00000	−	5.00000i	0.161966	−	0.161966i	0.783437	+	0.621471i	$0.213465\pi$
$954$		0			0
$955$	16.0000	+	8.00000i	0.517748	+	0.258874i
$956$	1.00000	+	1.00000i	0.0323423	+	0.0323423i
$957$		0			0
$958$	19.0000	+	19.0000i	0.613862	+	0.613862i
$959$		0			0
$960$		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
$965$	2.00000	−	4.00000i	0.0643823	−	0.128765i
$966$		0			0
$967$			24.0000i			0.771788i	0.922543	+	0.385894i	$0.126107\pi$
$967$			24.0000i			0.771788i	−0.922543	+	0.385894i	$0.873893\pi$
$968$	9.00000			0.289271
$969$		0			0
$970$	−28.0000	−	14.0000i	−0.899026	−	0.449513i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$		0			0
$973$			4.00000i			0.128234i
$974$	8.00000			0.256337
$975$		0			0
$976$	2.00000			0.0640184
$977$		−	2.00000i		−	0.0639857i	−0.999488	−	0.0319928i	$-0.989815\pi$
$977$		−	2.00000i		−	0.0639857i	0.999488	−	0.0319928i	$-0.0101854\pi$
$978$		0			0
$979$	−22.0000			−0.703123
$980$	−6.00000	−	3.00000i	−0.191663	−	0.0958315i
$981$		0			0
$982$	38.0000			1.21263
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$		0			0
$985$	6.00000	−	12.0000i	0.191176	−	0.382352i
$986$	8.00000	+	8.00000i	0.254772	+	0.254772i
$987$		0			0
$988$	−3.00000	+	15.0000i	−0.0954427	+	0.477214i
$989$			2.00000i			0.0635963i
$990$		0			0
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$	−1.00000	−	1.00000i	−0.0317500	−	0.0317500i
$993$		0			0
$994$	−10.0000	−	10.0000i	−0.317181	−	0.317181i
$995$	−48.0000	−	24.0000i	−1.52170	−	0.760851i
$996$		0			0
$997$	13.0000	−	13.0000i	0.411714	−	0.411714i	−0.470621	−	0.882335i	$-0.655970\pi$
$997$	13.0000	−	13.0000i	0.411714	−	0.411714i	0.882335	+	0.470621i	$0.155970\pi$
$998$	−19.0000	+	19.0000i	−0.601434	+	0.601434i
$999$		0			0

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -2.00000 q^{7} +1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} +(2.00000 + 3.00000i) q^{13} +2.00000i q^{14} +1.00000 q^{16} +(1.00000 + 1.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(2.00000 + 1.00000i) q^{20} +(1.00000 - 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(3.00000 - 2.00000i) q^{26} +2.00000 q^{28} +8.00000i q^{29} +(1.00000 - 1.00000i) q^{31} -1.00000i q^{32} +(1.00000 - 1.00000i) q^{34} +(4.00000 + 2.00000i) q^{35} +8.00000 q^{37} +(-3.00000 + 3.00000i) q^{38} +(1.00000 - 2.00000i) q^{40} +(7.00000 - 7.00000i) q^{41} +(1.00000 - 1.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(1.00000 + 1.00000i) q^{46} +10.0000 q^{47} -3.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +(-2.00000 - 3.00000i) q^{52} +(-1.00000 - 1.00000i) q^{53} +(-1.00000 - 3.00000i) q^{55} -2.00000i q^{56} +8.00000 q^{58} +(9.00000 - 9.00000i) q^{59} +2.00000 q^{61} +(-1.00000 - 1.00000i) q^{62} -1.00000 q^{64} +(-1.00000 - 8.00000i) q^{65} +12.0000i q^{67} +(-1.00000 - 1.00000i) q^{68} +(2.00000 - 4.00000i) q^{70} +(-5.00000 + 5.00000i) q^{71} +6.00000i q^{73} -8.00000i q^{74} +(3.00000 + 3.00000i) q^{76} +(-2.00000 - 2.00000i) q^{77} +10.0000i q^{79} +(-2.00000 - 1.00000i) q^{80} +(-7.00000 - 7.00000i) q^{82} +18.0000 q^{83} +(-1.00000 - 3.00000i) q^{85} +(-1.00000 - 1.00000i) q^{86} +(-1.00000 + 1.00000i) q^{88} +(-11.0000 + 11.0000i) q^{89} +(-4.00000 - 6.00000i) q^{91} +(1.00000 - 1.00000i) q^{92} -10.0000i q^{94} +(3.00000 + 9.00000i) q^{95} +14.0000i q^{97} +3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 4 q^{5} - 4 q^{7} - 2 q^{10} + 2 q^{11} + 4 q^{13} + 2 q^{16} + 2 q^{17} - 6 q^{19} + 4 q^{20} + 2 q^{22} - 2 q^{23} + 6 q^{25} + 6 q^{26} + 4 q^{28} + 2 q^{31} + 2 q^{34} + 8 q^{35} + 16 q^{37}+ \cdots + 6 q^{95}+O(q^{100}) \) 2 * q - 2 * q^4 - 4 * q^5 - 4 * q^7 - 2 * q^10 + 2 * q^11 + 4 * q^13 + 2 * q^16 + 2 * q^17 - 6 * q^19 + 4 * q^20 + 2 * q^22 - 2 * q^23 + 6 * q^25 + 6 * q^26 + 4 * q^28 + 2 * q^31 + 2 * q^34 + 8 * q^35 + 16 * q^37 - 6 * q^38 + 2 * q^40 + 14 * q^41 + 2 * q^43 - 2 * q^44 + 2 * q^46 + 20 * q^47 - 6 * q^49 + 8 * q^50 - 4 * q^52 - 2 * q^53 - 2 * q^55 + 16 * q^58 + 18 * q^59 + 4 * q^61 - 2 * q^62 - 2 * q^64 - 2 * q^65 - 2 * q^68 + 4 * q^70 - 10 * q^71 + 6 * q^76 - 4 * q^77 - 4 * q^80 - 14 * q^82 + 36 * q^83 - 2 * q^85 - 2 * q^86 - 2 * q^88 - 22 * q^89 - 8 * q^91 + 2 * q^92 + 6 * q^95

Introduction

L-functions

Modular forms

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