LMFDB - Embedded newform 650.2.j.d.307.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(307,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,2,-2,0,-2,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
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			307.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	650.307
Dual form			650.2.j.d.343.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(1.00000 - 1.00000i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{6} +2.00000 q^{7} +1.00000i q^{8} +1.00000i q^{9} +(1.00000 - 1.00000i) q^{11} +(-1.00000 + 1.00000i) q^{12} +(-2.00000 - 3.00000i) q^{13} -2.00000i q^{14} +1.00000 q^{16} +(5.00000 - 5.00000i) q^{17} +1.00000 q^{18} +(3.00000 - 3.00000i) q^{19} +(2.00000 - 2.00000i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-5.00000 - 5.00000i) q^{23} +(1.00000 + 1.00000i) q^{24} +(-3.00000 + 2.00000i) q^{26} +(4.00000 + 4.00000i) q^{27} -2.00000 q^{28} +4.00000i q^{29} +(1.00000 + 1.00000i) q^{31} -1.00000i q^{32} -2.00000i q^{33} +(-5.00000 - 5.00000i) q^{34} -1.00000i q^{36} -8.00000 q^{37} +(-3.00000 - 3.00000i) q^{38} +(-5.00000 - 1.00000i) q^{39} +(1.00000 + 1.00000i) q^{41} +(-2.00000 - 2.00000i) q^{42} +(5.00000 + 5.00000i) q^{43} +(-1.00000 + 1.00000i) q^{44} +(-5.00000 + 5.00000i) q^{46} +2.00000 q^{47} +(1.00000 - 1.00000i) q^{48} -3.00000 q^{49} -10.0000i q^{51} +(2.00000 + 3.00000i) q^{52} +(1.00000 - 1.00000i) q^{53} +(4.00000 - 4.00000i) q^{54} +2.00000i q^{56} -6.00000i q^{57} +4.00000 q^{58} +(-3.00000 - 3.00000i) q^{59} +2.00000 q^{61} +(1.00000 - 1.00000i) q^{62} +2.00000i q^{63} -1.00000 q^{64} -2.00000 q^{66} +12.0000i q^{67} +(-5.00000 + 5.00000i) q^{68} -10.0000 q^{69} +(1.00000 + 1.00000i) q^{71} -1.00000 q^{72} -6.00000i q^{73} +8.00000i q^{74} +(-3.00000 + 3.00000i) q^{76} +(2.00000 - 2.00000i) q^{77} +(-1.00000 + 5.00000i) q^{78} +14.0000i q^{79} +5.00000 q^{81} +(1.00000 - 1.00000i) q^{82} +6.00000 q^{83} +(-2.00000 + 2.00000i) q^{84} +(5.00000 - 5.00000i) q^{86} +(4.00000 + 4.00000i) q^{87} +(1.00000 + 1.00000i) q^{88} +(7.00000 + 7.00000i) q^{89} +(-4.00000 - 6.00000i) q^{91} +(5.00000 + 5.00000i) q^{92} +2.00000 q^{93} -2.00000i q^{94} +(-1.00000 - 1.00000i) q^{96} +2.00000i q^{97} +3.00000i q^{98} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{16} + 10 q^{17} + 2 q^{18} + 6 q^{19} + 4 q^{21} - 2 q^{22} - 10 q^{23} + 2 q^{24} - 6 q^{26} + 8 q^{27} - 4 q^{28} + 2 q^{31}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 2 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^16 + 10 * q^17 + 2 * q^18 + 6 * q^19 + 4 * q^21 - 2 * q^22 - 10 * q^23 + 2 * q^24 - 6 * q^26 + 8 * q^27 - 4 * q^28 + 2 * q^31 - 10 * q^34 - 16 * q^37 - 6 * q^38 - 10 * q^39 + 2 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 10 * q^46 + 4 * q^47 + 2 * q^48 - 6 * q^49 + 4 * q^52 + 2 * q^53 + 8 * q^54 + 8 * q^58 - 6 * q^59 + 4 * q^61 + 2 * q^62 - 2 * q^64 - 4 * q^66 - 10 * q^68 - 20 * q^69 + 2 * q^71 - 2 * q^72 - 6 * q^76 + 4 * q^77 - 2 * q^78 + 10 * q^81 + 2 * q^82 + 12 * q^83 - 4 * q^84 + 10 * q^86 + 8 * q^87 + 2 * q^88 + 14 * q^89 - 8 * q^91 + 10 * q^92 + 4 * q^93 - 2 * q^96 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	−0.356822	−	0.934172i	$-0.616140\pi$
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	0.934172	+	0.356822i	$0.116140\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−1.00000	−	1.00000i	−0.408248	−	0.408248i
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$		0			0
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	−0.540094	−	0.841605i	$-0.681611\pi$
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	0.841605	+	0.540094i	$0.181611\pi$
$12$	−1.00000	+	1.00000i	−0.288675	+	0.288675i
$13$	−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	0.242536	−	0.970143i	$-0.422021\pi$
$17$	5.00000	−	5.00000i	1.21268	−	1.21268i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$	1.00000			0.235702
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	−0.273597	−	0.961844i	$-0.588214\pi$
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	0.961844	+	0.273597i	$0.0882135\pi$
$20$		0			0
$21$	2.00000	−	2.00000i	0.436436	−	0.436436i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	−5.00000	−	5.00000i	−1.04257	−	1.04257i	−0.999053	−	0.0435195i	$-0.986143\pi$
$23$	−5.00000	−	5.00000i	−1.04257	−	1.04257i	−0.0435195	−	0.999053i	$-0.513857\pi$
$24$	1.00000	+	1.00000i	0.204124	+	0.204124i
$25$		0			0
$26$	−3.00000	+	2.00000i	−0.588348	+	0.392232i
$27$	4.00000	+	4.00000i	0.769800	+	0.769800i
$28$	−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	0.791184	−	0.611578i	$-0.209465\pi$
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	−0.611578	+	0.791184i	$0.709465\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	2.00000i		−	0.348155i
$34$	−5.00000	−	5.00000i	−0.857493	−	0.857493i
$35$		0			0
$36$		−	1.00000i		−	0.166667i
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$	−3.00000	−	3.00000i	−0.486664	−	0.486664i
$39$	−5.00000	−	1.00000i	−0.800641	−	0.160128i
$40$		0			0
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	0.780869	−	0.624695i	$-0.214777\pi$
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$	−2.00000	−	2.00000i	−0.308607	−	0.308607i
$43$	5.00000	+	5.00000i	0.762493	+	0.762493i	0.976772	−	0.214280i	$-0.0687403\pi$
$43$	5.00000	+	5.00000i	0.762493	+	0.762493i	−0.214280	+	0.976772i	$0.568740\pi$
$44$	−1.00000	+	1.00000i	−0.150756	+	0.150756i
$45$		0			0
$46$	−5.00000	+	5.00000i	−0.737210	+	0.737210i
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$	1.00000	−	1.00000i	0.144338	−	0.144338i
$49$	−3.00000			−0.428571
$50$		0			0
$51$		−	10.0000i		−	1.40028i
$52$	2.00000	+	3.00000i	0.277350	+	0.416025i
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$	4.00000	−	4.00000i	0.544331	−	0.544331i
$55$		0			0
$56$			2.00000i			0.267261i
$57$		−	6.00000i		−	0.794719i
$58$	4.00000			0.525226
$59$	−3.00000	−	3.00000i	−0.390567	−	0.390567i	0.484323	−	0.874889i	$-0.339066\pi$
$59$	−3.00000	−	3.00000i	−0.390567	−	0.390567i	−0.874889	+	0.484323i	$0.839066\pi$
$60$		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
$63$			2.00000i			0.251976i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−2.00000			−0.246183
$67$			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
$69$	−10.0000			−1.20386
$70$		0			0
$71$	1.00000	+	1.00000i	0.118678	+	0.118678i	0.763952	−	0.645273i	$-0.223257\pi$
$71$	1.00000	+	1.00000i	0.118678	+	0.118678i	−0.645273	+	0.763952i	$0.723257\pi$
$72$	−1.00000			−0.117851
$73$		−	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
$78$	−1.00000	+	5.00000i	−0.113228	+	0.566139i
$79$			14.0000i			1.57512i	0.616236	+	0.787562i	$0.288657\pi$
$79$			14.0000i			1.57512i	−0.616236	+	0.787562i	$0.711343\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$	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	$0.393190\pi$
$84$	−2.00000	+	2.00000i	−0.218218	+	0.218218i
$85$		0			0
$86$	5.00000	−	5.00000i	0.539164	−	0.539164i
$87$	4.00000	+	4.00000i	0.428845	+	0.428845i
$88$	1.00000	+	1.00000i	0.106600	+	0.106600i
$89$	7.00000	+	7.00000i	0.741999	+	0.741999i	0.972962	−	0.230964i	$-0.0741879\pi$
$89$	7.00000	+	7.00000i	0.741999	+	0.741999i	−0.230964	+	0.972962i	$0.574188\pi$
$90$		0			0
$91$	−4.00000	−	6.00000i	−0.419314	−	0.628971i
$92$	5.00000	+	5.00000i	0.521286	+	0.521286i
$93$	2.00000			0.207390
$94$		−	2.00000i		−	0.206284i
$95$		0			0
$96$	−1.00000	−	1.00000i	−0.102062	−	0.102062i
$97$			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
$99$	1.00000	+	1.00000i	0.100504	+	0.100504i
$100$		0			0
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	−10.0000			−0.990148
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	0.416480	−	0.909145i	$-0.363264\pi$
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	−0.909145	+	0.416480i	$0.863264\pi$
$104$	3.00000	−	2.00000i	0.294174	−	0.196116i
$105$		0			0
$106$	−1.00000	−	1.00000i	−0.0971286	−	0.0971286i
$107$	−13.0000	−	13.0000i	−1.25676	−	1.25676i	−0.952632	−	0.304125i	$-0.901636\pi$
$107$	−13.0000	−	13.0000i	−1.25676	−	1.25676i	−0.304125	−	0.952632i	$-0.598364\pi$
$108$	−4.00000	−	4.00000i	−0.384900	−	0.384900i
$109$	13.0000	−	13.0000i	1.24517	−	1.24517i	0.287348	−	0.957826i	$-0.407226\pi$
$109$	13.0000	−	13.0000i	1.24517	−	1.24517i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$		0			0
$111$	−8.00000	+	8.00000i	−0.759326	+	0.759326i
$112$	2.00000			0.188982
$113$	−9.00000	+	9.00000i	−0.846649	+	0.846649i	−0.989713	−	0.143065i	$-0.954304\pi$
$113$	−9.00000	+	9.00000i	−0.846649	+	0.846649i	0.143065	+	0.989713i	$0.454304\pi$
$114$	−6.00000			−0.561951
$115$		0			0
$116$		−	4.00000i		−	0.371391i
$117$	3.00000	−	2.00000i	0.277350	−	0.184900i
$118$	−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
$123$	2.00000			0.180334
$124$	−1.00000	−	1.00000i	−0.0898027	−	0.0898027i
$125$		0			0
$126$	2.00000			0.178174
$127$	−15.0000	+	15.0000i	−1.33103	+	1.33103i	−0.426589	+	0.904445i	$0.640285\pi$
$127$	−15.0000	+	15.0000i	−1.33103	+	1.33103i	−0.904445	+	0.426589i	$0.859715\pi$
$128$			1.00000i			0.0883883i
$129$	10.0000			0.880451
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$			2.00000i			0.174078i
$133$	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	$0.328677\pi$
$138$			10.0000i			0.851257i
$139$			14.0000i			1.18746i	0.804663	+	0.593732i	$0.202346\pi$
$139$			14.0000i			1.18746i	−0.804663	+	0.593732i	$0.797654\pi$
$140$		0			0
$141$	2.00000	−	2.00000i	0.168430	−	0.168430i
$142$	1.00000	−	1.00000i	0.0839181	−	0.0839181i
$143$	−5.00000	−	1.00000i	−0.418121	−	0.0836242i
$144$			1.00000i			0.0833333i
$145$		0			0
$146$	−6.00000			−0.496564
$147$	−3.00000	+	3.00000i	−0.247436	+	0.247436i
$148$	8.00000			0.657596
$149$	13.0000	−	13.0000i	1.06500	−	1.06500i	0.0672664	−	0.997735i	$-0.478572\pi$
$149$	13.0000	−	13.0000i	1.06500	−	1.06500i	0.997735	−	0.0672664i	$-0.0214278\pi$
$150$		0			0
$151$	−9.00000	+	9.00000i	−0.732410	+	0.732410i	−0.971097	−	0.238687i	$-0.923283\pi$
$151$	−9.00000	+	9.00000i	−0.732410	+	0.732410i	0.238687	+	0.971097i	$0.423283\pi$
$152$	3.00000	+	3.00000i	0.243332	+	0.243332i
$153$	5.00000	+	5.00000i	0.404226	+	0.404226i
$154$	−2.00000	−	2.00000i	−0.161165	−	0.161165i
$155$		0			0
$156$	5.00000	+	1.00000i	0.400320	+	0.0800641i
$157$	−3.00000	−	3.00000i	−0.239426	−	0.239426i	0.577186	−	0.816612i	$-0.304151\pi$
$157$	−3.00000	−	3.00000i	−0.239426	−	0.239426i	−0.816612	+	0.577186i	$0.804151\pi$
$158$	14.0000			1.11378
$159$		−	2.00000i		−	0.158610i
$160$		0			0
$161$	−10.0000	−	10.0000i	−0.788110	−	0.788110i
$162$		−	5.00000i		−	0.392837i
$163$			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	$0.475344\pi$
$168$	2.00000	+	2.00000i	0.154303	+	0.154303i
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$		0			0
$171$	3.00000	+	3.00000i	0.229416	+	0.229416i
$172$	−5.00000	−	5.00000i	−0.381246	−	0.381246i
$173$	15.0000	+	15.0000i	1.14043	+	1.14043i	0.988372	+	0.152057i	$0.0485898\pi$
$173$	15.0000	+	15.0000i	1.14043	+	1.14043i	0.152057	+	0.988372i	$0.451410\pi$
$174$	4.00000	−	4.00000i	0.303239	−	0.303239i
$175$		0			0
$176$	1.00000	−	1.00000i	0.0753778	−	0.0753778i
$177$	−6.00000			−0.450988
$178$	7.00000	−	7.00000i	0.524672	−	0.524672i
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$		0			0
$181$			20.0000i			1.48659i	0.668965	+	0.743294i	$0.266738\pi$
$181$			20.0000i			1.48659i	−0.668965	+	0.743294i	$0.733262\pi$
$182$	−6.00000	+	4.00000i	−0.444750	+	0.296500i
$183$	2.00000	−	2.00000i	0.147844	−	0.147844i
$184$	5.00000	−	5.00000i	0.368605	−	0.368605i
$185$		0			0
$186$		−	2.00000i		−	0.146647i
$187$		−	10.0000i		−	0.731272i
$188$	−2.00000			−0.145865
$189$	8.00000	+	8.00000i	0.581914	+	0.581914i
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$	−1.00000	+	1.00000i	−0.0721688	+	0.0721688i
$193$			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	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$	1.00000	−	1.00000i	0.0710669	−	0.0710669i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$	12.0000	+	12.0000i	0.846415	+	0.846415i
$202$		0			0
$203$			8.00000i			0.561490i
$204$			10.0000i			0.700140i
$205$		0			0
$206$	−5.00000	+	5.00000i	−0.348367	+	0.348367i
$207$	5.00000	−	5.00000i	0.347524	−	0.347524i
$208$	−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
$213$	2.00000			0.137038
$214$	−13.0000	+	13.0000i	−0.888662	+	0.888662i
$215$		0			0
$216$	−4.00000	+	4.00000i	−0.272166	+	0.272166i
$217$	2.00000	+	2.00000i	0.135769	+	0.135769i
$218$	−13.0000	−	13.0000i	−0.880471	−	0.880471i
$219$	−6.00000	−	6.00000i	−0.405442	−	0.405442i
$220$		0			0
$221$	−25.0000	−	5.00000i	−1.68168	−	0.336336i
$222$	8.00000	+	8.00000i	0.536925	+	0.536925i
$223$	6.00000			0.401790			0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000			0.401790			0.200895	+	0.979613i	$0.435615\pi$
$224$		−	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	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$			6.00000i			0.397360i
$229$	−3.00000	−	3.00000i	−0.198246	−	0.198246i	0.601002	−	0.799248i	$-0.294768\pi$
$229$	−3.00000	−	3.00000i	−0.198246	−	0.198246i	−0.799248	+	0.601002i	$0.794768\pi$
$230$		0			0
$231$		−	4.00000i		−	0.263181i
$232$	−4.00000			−0.262613
$233$	5.00000	+	5.00000i	0.327561	+	0.327561i	0.851658	−	0.524097i	$-0.175597\pi$
$233$	5.00000	+	5.00000i	0.327561	+	0.327561i	−0.524097	+	0.851658i	$0.675597\pi$
$234$	−2.00000	−	3.00000i	−0.130744	−	0.196116i
$235$		0			0
$236$	3.00000	+	3.00000i	0.195283	+	0.195283i
$237$	14.0000	+	14.0000i	0.909398	+	0.909398i
$238$	−10.0000	−	10.0000i	−0.648204	−	0.648204i
$239$	−7.00000	+	7.00000i	−0.452792	+	0.452792i	−0.896280	−	0.443488i	$-0.853741\pi$
$239$	−7.00000	+	7.00000i	−0.452792	+	0.452792i	0.443488	+	0.896280i	$0.353741\pi$
$240$		0			0
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	−0.674165	−	0.738581i	$-0.735496\pi$
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	0.738581	+	0.674165i	$0.235496\pi$
$242$	9.00000			0.578542
$243$	−7.00000	+	7.00000i	−0.449050	+	0.449050i
$244$	−2.00000			−0.128037
$245$		0			0
$246$		−	2.00000i		−	0.127515i
$247$	−15.0000	−	3.00000i	−0.954427	−	0.190885i
$248$	−1.00000	+	1.00000i	−0.0635001	+	0.0635001i
$249$	6.00000	−	6.00000i	0.380235	−	0.380235i
$250$		0			0
$251$		−	30.0000i		−	1.89358i	−0.321847	−	0.946792i	$-0.604304\pi$
$251$		−	30.0000i		−	1.89358i	0.321847	−	0.946792i	$-0.395696\pi$
$252$		−	2.00000i		−	0.125988i
$253$	−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	−0.998053	−	0.0623783i	$-0.980131\pi$
$257$	−15.0000	+	15.0000i	−0.935674	+	0.935674i	0.0623783	+	0.998053i	$0.480131\pi$
$258$		−	10.0000i		−	0.622573i
$259$	−16.0000			−0.994192
$260$		0			0
$261$	−4.00000			−0.247594
$262$		−	12.0000i		−	0.741362i
$263$	−9.00000	+	9.00000i	−0.554964	+	0.554964i	−0.927869	−	0.372906i	$-0.878362\pi$
$263$	−9.00000	+	9.00000i	−0.554964	+	0.554964i	0.372906	+	0.927869i	$0.378362\pi$
$264$	2.00000			0.123091
$265$		0			0
$266$	−6.00000	−	6.00000i	−0.367884	−	0.367884i
$267$	14.0000			0.856786
$268$		−	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	−0.925488	−	0.378777i	$-0.876345\pi$
$271$	−9.00000	+	9.00000i	−0.546711	+	0.546711i	0.378777	+	0.925488i	$0.376345\pi$
$272$	5.00000	−	5.00000i	0.303170	−	0.303170i
$273$	−10.0000	−	2.00000i	−0.605228	−	0.121046i
$274$		−	12.0000i		−	0.724947i
$275$		0			0
$276$	10.0000			0.601929
$277$	−5.00000	+	5.00000i	−0.300421	+	0.300421i	−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−5.00000	+	5.00000i	−0.300421	+	0.300421i	0.540758	+	0.841178i	$0.318138\pi$
$278$	14.0000			0.839664
$279$	−1.00000	+	1.00000i	−0.0598684	+	0.0598684i
$280$		0			0
$281$	21.0000	−	21.0000i	1.25275	−	1.25275i	0.298275	−	0.954480i	$-0.403589\pi$
$281$	21.0000	−	21.0000i	1.25275	−	1.25275i	0.954480	−	0.298275i	$-0.0964112\pi$
$282$	−2.00000	−	2.00000i	−0.119098	−	0.119098i
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	0.103022	−	0.994679i	$-0.467149\pi$
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	−0.994679	+	0.103022i	$0.967149\pi$
$284$	−1.00000	−	1.00000i	−0.0593391	−	0.0593391i
$285$		0			0
$286$	−1.00000	+	5.00000i	−0.0591312	+	0.295656i
$287$	2.00000	+	2.00000i	0.118056	+	0.118056i
$288$	1.00000			0.0589256
$289$		−	33.0000i		−	1.94118i
$290$		0			0
$291$	2.00000	+	2.00000i	0.117242	+	0.117242i
$292$			6.00000i			0.351123i
$293$		−	26.0000i		−	1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$		−	26.0000i		−	1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$	3.00000	+	3.00000i	0.174964	+	0.174964i
$295$		0			0
$296$		−	8.00000i		−	0.464991i
$297$	8.00000			0.464207
$298$	−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
$305$		0			0
$306$	5.00000	−	5.00000i	0.285831	−	0.285831i
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	−2.00000	+	2.00000i	−0.113961	+	0.113961i
$309$	−10.0000			−0.568880
$310$		0			0
$311$			10.0000i			0.567048i	0.958965	+	0.283524i	$0.0915036\pi$
$311$			10.0000i			0.567048i	−0.958965	+	0.283524i	$0.908496\pi$
$312$	1.00000	−	5.00000i	0.0566139	−	0.283069i
$313$	−9.00000	+	9.00000i	−0.508710	+	0.508710i	−0.914130	−	0.405420i	$-0.867125\pi$
$313$	−9.00000	+	9.00000i	−0.508710	+	0.508710i	0.405420	+	0.914130i	$0.367125\pi$
$314$	−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	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$	−2.00000			−0.112154
$319$	4.00000	+	4.00000i	0.223957	+	0.223957i
$320$		0			0
$321$	−26.0000			−1.45118
$322$	−10.0000	+	10.0000i	−0.557278	+	0.557278i
$323$		−	30.0000i		−	1.66924i
$324$	−5.00000			−0.277778
$325$		0			0
$326$	4.00000			0.221540
$327$		−	26.0000i		−	1.43780i
$328$	−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	0.415094	−	0.909779i	$-0.363749\pi$
$331$	−9.00000	−	9.00000i	−0.494685	−	0.494685i	−0.909779	+	0.415094i	$0.863749\pi$
$332$	−6.00000			−0.329293
$333$		−	8.00000i		−	0.438397i
$334$		−	2.00000i		−	0.109435i
$335$		0			0
$336$	2.00000	−	2.00000i	0.109109	−	0.109109i
$337$	5.00000	−	5.00000i	0.272367	−	0.272367i	−0.557685	−	0.830053i	$-0.688310\pi$
$337$	5.00000	−	5.00000i	0.272367	−	0.272367i	0.830053	+	0.557685i	$0.188310\pi$
$338$	12.0000	+	5.00000i	0.652714	+	0.271964i
$339$			18.0000i			0.977626i
$340$		0			0
$341$	2.00000			0.108306
$342$	3.00000	−	3.00000i	0.162221	−	0.162221i
$343$	−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	0.869577	−	0.493797i	$-0.164392\pi$
$347$	7.00000	+	7.00000i	0.375780	+	0.375780i	−0.493797	+	0.869577i	$0.664392\pi$
$348$	−4.00000	−	4.00000i	−0.214423	−	0.214423i
$349$	−3.00000	−	3.00000i	−0.160586	−	0.160586i	0.622240	−	0.782826i	$-0.286223\pi$
$349$	−3.00000	−	3.00000i	−0.160586	−	0.160586i	−0.782826	+	0.622240i	$0.786223\pi$
$350$		0			0
$351$	4.00000	−	20.0000i	0.213504	−	1.06752i
$352$	−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	$0.359994\pi$
$354$			6.00000i			0.318896i
$355$		0			0
$356$	−7.00000	−	7.00000i	−0.370999	−	0.370999i
$357$		−	20.0000i		−	1.05851i
$358$			20.0000i			1.05703i
$359$	−13.0000	−	13.0000i	−0.686114	−	0.686114i	0.275257	−	0.961371i	$-0.411237\pi$
$359$	−13.0000	−	13.0000i	−0.686114	−	0.686114i	−0.961371	+	0.275257i	$0.911237\pi$
$360$		0			0
$361$			1.00000i			0.0526316i
$362$	20.0000			1.05118
$363$	9.00000	+	9.00000i	0.472377	+	0.472377i
$364$	4.00000	+	6.00000i	0.209657	+	0.314485i
$365$		0			0
$366$	−2.00000	−	2.00000i	−0.104542	−	0.104542i
$367$	−3.00000	−	3.00000i	−0.156599	−	0.156599i	0.624459	−	0.781058i	$-0.285320\pi$
$367$	−3.00000	−	3.00000i	−0.156599	−	0.156599i	−0.781058	+	0.624459i	$0.785320\pi$
$368$	−5.00000	−	5.00000i	−0.260643	−	0.260643i
$369$	−1.00000	+	1.00000i	−0.0520579	+	0.0520579i
$370$		0			0
$371$	2.00000	−	2.00000i	0.103835	−	0.103835i
$372$	−2.00000			−0.103695
$373$	1.00000	−	1.00000i	0.0517780	−	0.0517780i	−0.680744	−	0.732522i	$-0.738343\pi$
$373$	1.00000	−	1.00000i	0.0517780	−	0.0517780i	0.732522	+	0.680744i	$0.238343\pi$
$374$	−10.0000			−0.517088
$375$		0			0
$376$			2.00000i			0.103142i
$377$	12.0000	−	8.00000i	0.618031	−	0.412021i
$378$	8.00000	−	8.00000i	0.411476	−	0.411476i
$379$	−17.0000	+	17.0000i	−0.873231	+	0.873231i	−0.992823	−	0.119592i	$-0.961841\pi$
$379$	−17.0000	+	17.0000i	−0.873231	+	0.873231i	0.119592	+	0.992823i	$0.461841\pi$
$380$		0			0
$381$			30.0000i			1.53695i
$382$			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	$0.451012\pi$
$384$	1.00000	+	1.00000i	0.0510310	+	0.0510310i
$385$		0			0
$386$	14.0000			0.712581
$387$	−5.00000	+	5.00000i	−0.254164	+	0.254164i
$388$		−	2.00000i		−	0.101535i
$389$	10.0000			0.507020			0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000			0.507020			0.253510	+	0.967333i	$0.418415\pi$
$390$		0			0
$391$	−50.0000			−2.52861
$392$		−	3.00000i		−	0.151523i
$393$	12.0000	−	12.0000i	0.605320	−	0.605320i
$394$	−18.0000			−0.906827
$395$		0			0
$396$	−1.00000	−	1.00000i	−0.0502519	−	0.0502519i
$397$	−8.00000			−0.401508			−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000			−0.401508			−0.200754	+	0.979642i	$0.564339\pi$
$398$		0			0
$399$		−	12.0000i		−	0.600751i
$400$		0			0
$401$	1.00000	−	1.00000i	0.0499376	−	0.0499376i	−0.681697	−	0.731635i	$-0.738758\pi$
$401$	1.00000	−	1.00000i	0.0499376	−	0.0499376i	0.731635	+	0.681697i	$0.238758\pi$
$402$	12.0000	−	12.0000i	0.598506	−	0.598506i
$403$	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
$408$	10.0000			0.495074
$409$	3.00000	−	3.00000i	0.148340	−	0.148340i	−0.629036	−	0.777376i	$-0.716550\pi$
$409$	3.00000	−	3.00000i	0.148340	−	0.148340i	0.777376	+	0.629036i	$0.216550\pi$
$410$		0			0
$411$	12.0000	−	12.0000i	0.591916	−	0.591916i
$412$	5.00000	+	5.00000i	0.246332	+	0.246332i
$413$	−6.00000	−	6.00000i	−0.295241	−	0.295241i
$414$	−5.00000	−	5.00000i	−0.245737	−	0.245737i
$415$		0			0
$416$	−3.00000	+	2.00000i	−0.147087	+	0.0980581i
$417$	14.0000	+	14.0000i	0.685583	+	0.685583i
$418$	−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	0.452919	−	0.891552i	$-0.350383\pi$
$421$	−9.00000	−	9.00000i	−0.438633	−	0.438633i	−0.891552	+	0.452919i	$0.850383\pi$
$422$		−	12.0000i		−	0.584151i
$423$			2.00000i			0.0972433i
$424$	1.00000	+	1.00000i	0.0485643	+	0.0485643i
$425$		0			0
$426$		−	2.00000i		−	0.0969003i
$427$	4.00000			0.193574
$428$	13.0000	+	13.0000i	0.628379	+	0.628379i
$429$	−6.00000	+	4.00000i	−0.289683	+	0.193122i
$430$		0			0
$431$	21.0000	+	21.0000i	1.01153	+	1.01153i	0.999933	+	0.0116017i	$0.00369302\pi$
$431$	21.0000	+	21.0000i	1.01153	+	1.01153i	0.0116017	+	0.999933i	$0.496307\pi$
$432$	4.00000	+	4.00000i	0.192450	+	0.192450i
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	0.247925	−	0.968779i	$-0.420251\pi$
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	−0.968779	+	0.247925i	$0.920251\pi$
$434$	2.00000	−	2.00000i	0.0960031	−	0.0960031i
$435$		0			0
$436$	−13.0000	+	13.0000i	−0.622587	+	0.622587i
$437$	−30.0000			−1.43509
$438$	−6.00000	+	6.00000i	−0.286691	+	0.286691i
$439$	−40.0000			−1.90910			−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000			−1.90910			−0.954548	+	0.298057i	$0.903661\pi$
$440$		0			0
$441$		−	3.00000i		−	0.142857i
$442$	−5.00000	+	25.0000i	−0.237826	+	1.18913i
$443$	−19.0000	+	19.0000i	−0.902717	+	0.902717i	−0.995670	−	0.0929532i	$-0.970369\pi$
$443$	−19.0000	+	19.0000i	−0.902717	+	0.902717i	0.0929532	+	0.995670i	$0.470369\pi$
$444$	8.00000	−	8.00000i	0.379663	−	0.379663i
$445$		0			0
$446$		−	6.00000i		−	0.284108i
$447$		−	26.0000i		−	1.22976i
$448$	−2.00000			−0.0944911
$449$	7.00000	+	7.00000i	0.330350	+	0.330350i	0.852720	−	0.522369i	$-0.174952\pi$
$449$	7.00000	+	7.00000i	0.330350	+	0.330350i	−0.522369	+	0.852720i	$0.674952\pi$
$450$		0			0
$451$	2.00000			0.0941763
$452$	9.00000	−	9.00000i	0.423324	−	0.423324i
$453$			18.0000i			0.845714i
$454$	12.0000			0.563188
$455$		0			0
$456$	6.00000			0.280976
$457$		−	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
$459$	40.0000			1.86704
$460$		0			0
$461$	11.0000	+	11.0000i	0.512321	+	0.512321i	0.915237	−	0.402916i	$-0.132003\pi$
$461$	11.0000	+	11.0000i	0.512321	+	0.512321i	−0.402916	+	0.915237i	$0.632003\pi$
$462$	−4.00000			−0.186097
$463$		−	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	−0.813265	−	0.581893i	$-0.802312\pi$
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	0.581893	+	0.813265i	$0.302312\pi$
$468$	−3.00000	+	2.00000i	−0.138675	+	0.0924500i
$469$			24.0000i			1.10822i
$470$		0			0
$471$	−6.00000			−0.276465
$472$	3.00000	−	3.00000i	0.138086	−	0.138086i
$473$	10.0000			0.459800
$474$	14.0000	−	14.0000i	0.643041	−	0.643041i
$475$		0			0
$476$	−10.0000	+	10.0000i	−0.458349	+	0.458349i
$477$	1.00000	+	1.00000i	0.0457869	+	0.0457869i
$478$	7.00000	+	7.00000i	0.320173	+	0.320173i
$479$	−13.0000	−	13.0000i	−0.593985	−	0.593985i	0.344720	−	0.938705i	$-0.387974\pi$
$479$	−13.0000	−	13.0000i	−0.593985	−	0.593985i	−0.938705	+	0.344720i	$0.887974\pi$
$480$		0			0
$481$	16.0000	+	24.0000i	0.729537	+	1.09431i
$482$	−1.00000	−	1.00000i	−0.0455488	−	0.0455488i
$483$	−20.0000			−0.910032
$484$		−	9.00000i		−	0.409091i
$485$		0			0
$486$	7.00000	+	7.00000i	0.317526	+	0.317526i
$487$			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
$489$	4.00000	+	4.00000i	0.180886	+	0.180886i
$490$		0			0
$491$			10.0000i			0.451294i	0.974209	+	0.225647i	$0.0724495\pi$
$491$			10.0000i			0.451294i	−0.974209	+	0.225647i	$0.927550\pi$
$492$	−2.00000			−0.0901670
$493$	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
$498$	−6.00000	−	6.00000i	−0.268866	−	0.268866i
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.0300737	−	0.999548i	$-0.490426\pi$
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.999548	−	0.0300737i	$-0.00957421\pi$
$500$		0			0
$501$	2.00000	−	2.00000i	0.0893534	−	0.0893534i
$502$	−30.0000			−1.33897
$503$	−9.00000	+	9.00000i	−0.401290	+	0.401290i	−0.878688	−	0.477397i	$-0.841580\pi$
$503$	−9.00000	+	9.00000i	−0.401290	+	0.401290i	0.477397	+	0.878688i	$0.341580\pi$
$504$	−2.00000			−0.0890871
$505$		0			0
$506$			10.0000i			0.444554i
$507$	7.00000	+	17.0000i	0.310881	+	0.754997i
$508$	15.0000	−	15.0000i	0.665517	−	0.665517i
$509$	13.0000	−	13.0000i	0.576215	−	0.576215i	−0.357643	−	0.933858i	$-0.616420\pi$
$509$	13.0000	−	13.0000i	0.576215	−	0.576215i	0.933858	+	0.357643i	$0.116420\pi$
$510$		0			0
$511$		−	12.0000i		−	0.530849i
$512$		−	1.00000i		−	0.0441942i
$513$	24.0000			1.05963
$514$	15.0000	+	15.0000i	0.661622	+	0.661622i
$515$		0			0
$516$	−10.0000			−0.440225
$517$	2.00000	−	2.00000i	0.0879599	−	0.0879599i
$518$			16.0000i			0.703000i
$519$	30.0000			1.31685
$520$		0			0
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$			4.00000i			0.175075i
$523$	21.0000	−	21.0000i	0.918266	−	0.918266i	−0.0786374	−	0.996903i	$-0.525057\pi$
$523$	21.0000	−	21.0000i	0.918266	−	0.918266i	0.996903	+	0.0786374i	$0.0250569\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	9.00000	+	9.00000i	0.392419	+	0.392419i
$527$	10.0000			0.435607
$528$		−	2.00000i		−	0.0870388i
$529$			27.0000i			1.17391i
$530$		0			0
$531$	3.00000	−	3.00000i	0.130189	−	0.130189i
$532$	−6.00000	+	6.00000i	−0.260133	+	0.260133i
$533$	1.00000	−	5.00000i	0.0433148	−	0.216574i
$534$		−	14.0000i		−	0.605839i
$535$		0			0
$536$	−12.0000			−0.518321
$537$	−20.0000	+	20.0000i	−0.863064	+	0.863064i
$538$	−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	−0.873595	−	0.486654i	$-0.838217\pi$
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	0.486654	+	0.873595i	$0.338217\pi$
$542$	9.00000	+	9.00000i	0.386583	+	0.386583i
$543$	20.0000	+	20.0000i	0.858282	+	0.858282i
$544$	−5.00000	−	5.00000i	−0.214373	−	0.214373i
$545$		0			0
$546$	−2.00000	+	10.0000i	−0.0855921	+	0.427960i
$547$	7.00000	+	7.00000i	0.299298	+	0.299298i	0.840739	−	0.541441i	$-0.182121\pi$
$547$	7.00000	+	7.00000i	0.299298	+	0.299298i	−0.541441	+	0.840739i	$0.682121\pi$
$548$	−12.0000			−0.512615
$549$			2.00000i			0.0853579i
$550$		0			0
$551$	12.0000	+	12.0000i	0.511217	+	0.511217i
$552$		−	10.0000i		−	0.425628i
$553$			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	$0.554211\pi$
$558$	1.00000	+	1.00000i	0.0423334	+	0.0423334i
$559$	5.00000	−	25.0000i	0.211477	−	1.05739i
$560$		0			0
$561$	−10.0000	−	10.0000i	−0.422200	−	0.422200i
$562$	−21.0000	−	21.0000i	−0.885832	−	0.885832i
$563$	5.00000	+	5.00000i	0.210725	+	0.210725i	0.804575	−	0.593851i	$-0.202393\pi$
$563$	5.00000	+	5.00000i	0.210725	+	0.210725i	−0.593851	+	0.804575i	$0.702393\pi$
$564$	−2.00000	+	2.00000i	−0.0842152	+	0.0842152i
$565$		0			0
$566$	−15.0000	+	15.0000i	−0.630497	+	0.630497i
$567$	10.0000			0.419961
$568$	−1.00000	+	1.00000i	−0.0419591	+	0.0419591i
$569$	10.0000			0.419222			0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000			0.419222			0.209611	+	0.977785i	$0.432780\pi$
$570$		0			0
$571$			10.0000i			0.418487i	0.977864	+	0.209243i	$0.0671001\pi$
$571$			10.0000i			0.418487i	−0.977864	+	0.209243i	$0.932900\pi$
$572$	5.00000	+	1.00000i	0.209061	+	0.0418121i
$573$	−8.00000	+	8.00000i	−0.334205	+	0.334205i
$574$	2.00000	−	2.00000i	0.0834784	−	0.0834784i
$575$		0			0
$576$		−	1.00000i		−	0.0416667i
$577$			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
$579$	14.0000	+	14.0000i	0.581820	+	0.581820i
$580$		0			0
$581$	12.0000			0.497844
$582$	2.00000	−	2.00000i	0.0829027	−	0.0829027i
$583$		−	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	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$	3.00000	−	3.00000i	0.123718	−	0.123718i
$589$	6.00000			0.247226
$590$		0			0
$591$	−18.0000	−	18.0000i	−0.740421	−	0.740421i
$592$	−8.00000			−0.328798
$593$			14.0000i			0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$			14.0000i			0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$		−	8.00000i		−	0.328244i
$595$		0			0
$596$	−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
$603$	−12.0000			−0.488678
$604$	9.00000	−	9.00000i	0.366205	−	0.366205i
$605$		0			0
$606$		0			0
$607$	−3.00000	−	3.00000i	−0.121766	−	0.121766i	0.643598	−	0.765364i	$-0.277441\pi$
$607$	−3.00000	−	3.00000i	−0.121766	−	0.121766i	−0.765364	+	0.643598i	$0.777441\pi$
$608$	−3.00000	−	3.00000i	−0.121666	−	0.121666i
$609$	8.00000	+	8.00000i	0.324176	+	0.324176i
$610$		0			0
$611$	−4.00000	−	6.00000i	−0.161823	−	0.242734i
$612$	−5.00000	−	5.00000i	−0.202113	−	0.202113i
$613$	−4.00000			−0.161558			−0.0807792	−	0.996732i	$-0.525741\pi$
$613$	−4.00000			−0.161558			−0.0807792	+	0.996732i	$0.525741\pi$
$614$		−	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	$-0.722783\pi$
$617$		−	38.0000i		−	1.52982i	0.644136	−	0.764911i	$-0.277217\pi$
$618$			10.0000i			0.402259i
$619$	−3.00000	−	3.00000i	−0.120580	−	0.120580i	0.644242	−	0.764822i	$-0.277173\pi$
$619$	−3.00000	−	3.00000i	−0.120580	−	0.120580i	−0.764822	+	0.644242i	$0.777173\pi$
$620$		0			0
$621$		−	40.0000i		−	1.60514i
$622$	10.0000			0.400963
$623$	14.0000	+	14.0000i	0.560898	+	0.560898i
$624$	−5.00000	−	1.00000i	−0.200160	−	0.0400320i
$625$		0			0
$626$	9.00000	+	9.00000i	0.359712	+	0.359712i
$627$	−6.00000	−	6.00000i	−0.239617	−	0.239617i
$628$	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	−0.453403	−	0.891306i	$-0.649790\pi$
$631$	11.0000	−	11.0000i	0.437903	−	0.437903i	0.891306	+	0.453403i	$0.149790\pi$
$632$	−14.0000			−0.556890
$633$	12.0000	−	12.0000i	0.476957	−	0.476957i
$634$	2.00000			0.0794301
$635$		0			0
$636$			2.00000i			0.0793052i
$637$	6.00000	+	9.00000i	0.237729	+	0.356593i
$638$	4.00000	−	4.00000i	0.158362	−	0.158362i
$639$	−1.00000	+	1.00000i	−0.0395594	+	0.0395594i
$640$		0			0
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$			26.0000i			1.02614i
$643$	46.0000			1.81406			0.907031	−	0.421063i	$-0.138343\pi$
$643$	46.0000			1.81406			0.907031	+	0.421063i	$0.138343\pi$
$644$	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	−0.601958	−	0.798528i	$-0.705612\pi$
$647$	5.00000	−	5.00000i	0.196570	−	0.196570i	0.798528	+	0.601958i	$0.205612\pi$
$648$			5.00000i			0.196419i
$649$	−6.00000			−0.235521
$650$		0			0
$651$	4.00000			0.156772
$652$		−	4.00000i		−	0.156652i
$653$	21.0000	−	21.0000i	0.821794	−	0.821794i	−0.164572	−	0.986365i	$-0.552624\pi$
$653$	21.0000	−	21.0000i	0.821794	−	0.821794i	0.986365	+	0.164572i	$0.0526242\pi$
$654$	−26.0000			−1.01668
$655$		0			0
$656$	1.00000	+	1.00000i	0.0390434	+	0.0390434i
$657$	6.00000			0.234082
$658$		−	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	0.233373	−	0.972387i	$-0.425024\pi$
$661$	31.0000	−	31.0000i	1.20576	−	1.20576i	0.972387	−	0.233373i	$-0.0749763\pi$
$662$	−9.00000	+	9.00000i	−0.349795	+	0.349795i
$663$	−30.0000	+	20.0000i	−1.16510	+	0.776736i
$664$			6.00000i			0.232845i
$665$		0			0
$666$	−8.00000			−0.309994
$667$	20.0000	−	20.0000i	0.774403	−	0.774403i
$668$	−2.00000			−0.0773823
$669$	6.00000	−	6.00000i	0.231973	−	0.231973i
$670$		0			0
$671$	2.00000	−	2.00000i	0.0772091	−	0.0772091i
$672$	−2.00000	−	2.00000i	−0.0771517	−	0.0771517i
$673$	5.00000	+	5.00000i	0.192736	+	0.192736i	0.796877	−	0.604141i	$-0.206484\pi$
$673$	5.00000	+	5.00000i	0.192736	+	0.192736i	−0.604141	+	0.796877i	$0.706484\pi$
$674$	−5.00000	−	5.00000i	−0.192593	−	0.192593i
$675$		0			0
$676$	5.00000	−	12.0000i	0.192308	−	0.461538i
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	0.109973	−	0.993935i	$-0.464924\pi$
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	−0.993935	+	0.109973i	$0.964924\pi$
$678$	18.0000			0.691286
$679$			4.00000i			0.153506i
$680$		0			0
$681$	12.0000	+	12.0000i	0.459841	+	0.459841i
$682$		−	2.00000i		−	0.0765840i
$683$		−	36.0000i		−	1.37750i	−0.724998	−	0.688751i	$-0.758159\pi$
$683$		−	36.0000i		−	1.37750i	0.724998	−	0.688751i	$-0.241841\pi$
$684$	−3.00000	−	3.00000i	−0.114708	−	0.114708i
$685$		0			0
$686$			20.0000i			0.763604i
$687$	−6.00000			−0.228914
$688$	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	0.514884	−	0.857260i	$-0.327835\pi$
$691$	−9.00000	−	9.00000i	−0.342376	−	0.342376i	−0.857260	+	0.514884i	$0.827835\pi$
$692$	−15.0000	−	15.0000i	−0.570214	−	0.570214i
$693$	2.00000	+	2.00000i	0.0759737	+	0.0759737i
$694$	7.00000	−	7.00000i	0.265716	−	0.265716i
$695$		0			0
$696$	−4.00000	+	4.00000i	−0.151620	+	0.151620i
$697$	10.0000			0.378777
$698$	−3.00000	+	3.00000i	−0.113552	+	0.113552i
$699$	10.0000			0.378235
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−20.0000	−	4.00000i	−0.754851	−	0.150970i
$703$	−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
$708$	6.00000			0.225494
$709$	−3.00000	−	3.00000i	−0.112667	−	0.112667i	0.648526	−	0.761193i	$-0.275386\pi$
$709$	−3.00000	−	3.00000i	−0.112667	−	0.112667i	−0.761193	+	0.648526i	$0.775386\pi$
$710$		0			0
$711$	−14.0000			−0.525041
$712$	−7.00000	+	7.00000i	−0.262336	+	0.262336i
$713$		−	10.0000i		−	0.374503i
$714$	−20.0000			−0.748481
$715$		0			0
$716$	20.0000			0.747435
$717$			14.0000i			0.522840i
$718$	−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
$723$		−	2.00000i		−	0.0743808i
$724$		−	20.0000i		−	0.743294i
$725$		0			0
$726$	9.00000	−	9.00000i	0.334021	−	0.334021i
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.368418	+	0.929660i	$0.620100\pi$
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.929660	+	0.368418i	$0.879900\pi$
$728$	6.00000	−	4.00000i	0.222375	−	0.148250i
$729$			29.0000i			1.07407i
$730$		0			0
$731$	50.0000			1.84932
$732$	−2.00000	+	2.00000i	−0.0739221	+	0.0739221i
$733$	−44.0000			−1.62518			−0.812589	−	0.582838i	$-0.801942\pi$
$733$	−44.0000			−1.62518			−0.812589	+	0.582838i	$0.801942\pi$
$734$	−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
$738$	1.00000	+	1.00000i	0.0368105	+	0.0368105i
$739$	37.0000	+	37.0000i	1.36107	+	1.36107i	0.872560	+	0.488507i	$0.162458\pi$
$739$	37.0000	+	37.0000i	1.36107	+	1.36107i	0.488507	+	0.872560i	$0.337542\pi$
$740$		0			0
$741$	−18.0000	+	12.0000i	−0.661247	+	0.440831i
$742$	−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	$0.464896\pi$
$744$			2.00000i			0.0733236i
$745$		0			0
$746$	−1.00000	−	1.00000i	−0.0366126	−	0.0366126i
$747$			6.00000i			0.219529i
$748$			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	$0.0584036\pi$
$751$			10.0000i			0.364905i	−0.983215	+	0.182453i	$0.941596\pi$
$752$	2.00000			0.0729325
$753$	−30.0000	−	30.0000i	−1.09326	−	1.09326i
$754$	−8.00000	−	12.0000i	−0.291343	−	0.437014i
$755$		0			0
$756$	−8.00000	−	8.00000i	−0.290957	−	0.290957i
$757$	17.0000	+	17.0000i	0.617876	+	0.617876i	0.944986	−	0.327111i	$-0.106075\pi$
$757$	17.0000	+	17.0000i	0.617876	+	0.617876i	−0.327111	+	0.944986i	$0.606075\pi$
$758$	17.0000	+	17.0000i	0.617468	+	0.617468i
$759$	−10.0000	+	10.0000i	−0.362977	+	0.362977i
$760$		0			0
$761$	−19.0000	+	19.0000i	−0.688749	+	0.688749i	−0.961956	−	0.273206i	$-0.911916\pi$
$761$	−19.0000	+	19.0000i	−0.688749	+	0.688749i	0.273206	+	0.961956i	$0.411916\pi$
$762$	30.0000			1.08679
$763$	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
$768$	1.00000	−	1.00000i	0.0360844	−	0.0360844i
$769$	23.0000	−	23.0000i	0.829401	−	0.829401i	−0.158033	−	0.987434i	$-0.550515\pi$
$769$	23.0000	−	23.0000i	0.829401	−	0.829401i	0.987434	+	0.158033i	$0.0505151\pi$
$770$		0			0
$771$			30.0000i			1.08042i
$772$		−	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	$0.642054\pi$
$774$	5.00000	+	5.00000i	0.179721	+	0.179721i
$775$		0			0
$776$	−2.00000			−0.0717958
$777$	−16.0000	+	16.0000i	−0.573997	+	0.573997i
$778$		−	10.0000i		−	0.358517i
$779$	6.00000			0.214972
$780$		0			0
$781$	2.00000			0.0715656
$782$			50.0000i			1.78800i
$783$	−16.0000	+	16.0000i	−0.571793	+	0.571793i
$784$	−3.00000			−0.107143
$785$		0			0
$786$	−12.0000	−	12.0000i	−0.428026	−	0.428026i
$787$	42.0000			1.49714			0.748569	−	0.663057i	$-0.230741\pi$
$787$	42.0000			1.49714			0.748569	+	0.663057i	$0.230741\pi$
$788$			18.0000i			0.641223i
$789$			18.0000i			0.640817i
$790$		0			0
$791$	−18.0000	+	18.0000i	−0.640006	+	0.640006i
$792$	−1.00000	+	1.00000i	−0.0355335	+	0.0355335i
$793$	−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	−0.790094	−	0.612985i	$-0.789968\pi$
$797$	−5.00000	+	5.00000i	−0.177109	+	0.177109i	0.612985	+	0.790094i	$0.289968\pi$
$798$	−12.0000			−0.424795
$799$	10.0000	−	10.0000i	0.353775	−	0.353775i
$800$		0			0
$801$	−7.00000	+	7.00000i	−0.247333	+	0.247333i
$802$	−1.00000	−	1.00000i	−0.0353112	−	0.0353112i
$803$	−6.00000	−	6.00000i	−0.211735	−	0.211735i
$804$	−12.0000	−	12.0000i	−0.423207	−	0.423207i
$805$		0			0
$806$	−5.00000	−	1.00000i	−0.176117	−	0.0352235i
$807$	−16.0000	−	16.0000i	−0.563227	−	0.563227i
$808$		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	0.873352	−	0.487090i	$-0.161942\pi$
$811$	11.0000	+	11.0000i	0.386262	+	0.386262i	−0.487090	+	0.873352i	$0.661942\pi$
$812$		−	8.00000i		−	0.280745i
$813$			18.0000i			0.631288i
$814$	8.00000	+	8.00000i	0.280400	+	0.280400i
$815$		0			0
$816$		−	10.0000i		−	0.350070i
$817$	30.0000			1.04957
$818$	−3.00000	−	3.00000i	−0.104893	−	0.104893i
$819$	6.00000	−	4.00000i	0.209657	−	0.139771i
$820$		0			0
$821$	−29.0000	−	29.0000i	−1.01211	−	1.01211i	−0.999926	−	0.0121812i	$-0.996123\pi$
$821$	−29.0000	−	29.0000i	−1.01211	−	1.01211i	−0.0121812	−	0.999926i	$-0.503877\pi$
$822$	−12.0000	−	12.0000i	−0.418548	−	0.418548i
$823$	15.0000	+	15.0000i	0.522867	+	0.522867i	0.918436	−	0.395569i	$-0.129453\pi$
$823$	15.0000	+	15.0000i	0.522867	+	0.522867i	−0.395569	+	0.918436i	$0.629453\pi$
$824$	5.00000	−	5.00000i	0.174183	−	0.174183i
$825$		0			0
$826$	−6.00000	+	6.00000i	−0.208767	+	0.208767i
$827$	2.00000			0.0695468			0.0347734	−	0.999395i	$-0.488929\pi$
$827$	2.00000			0.0695468			0.0347734	+	0.999395i	$0.488929\pi$
$828$	−5.00000	+	5.00000i	−0.173762	+	0.173762i
$829$	30.0000			1.04194			0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000			1.04194			0.520972	+	0.853574i	$0.325570\pi$
$830$		0			0
$831$			10.0000i			0.346896i
$832$	2.00000	+	3.00000i	0.0693375	+	0.104006i
$833$	−15.0000	+	15.0000i	−0.519719	+	0.519719i
$834$	14.0000	−	14.0000i	0.484780	−	0.484780i
$835$		0			0
$836$			6.00000i			0.207514i
$837$			8.00000i			0.276520i
$838$	−26.0000			−0.898155
$839$	−13.0000	−	13.0000i	−0.448810	−	0.448810i	0.446149	−	0.894959i	$-0.352795\pi$
$839$	−13.0000	−	13.0000i	−0.448810	−	0.448810i	−0.894959	+	0.446149i	$0.852795\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$	−9.00000	+	9.00000i	−0.310160	+	0.310160i
$843$		−	42.0000i		−	1.44656i
$844$	−12.0000			−0.413057
$845$		0			0
$846$	2.00000			0.0687614
$847$			18.0000i			0.618487i
$848$	1.00000	−	1.00000i	0.0343401	−	0.0343401i
$849$	−30.0000			−1.02960
$850$		0			0
$851$	40.0000	+	40.0000i	1.37118	+	1.37118i
$852$	−2.00000			−0.0685189
$853$		−	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	−0.616533	−	0.787329i	$-0.711463\pi$
$857$	5.00000	−	5.00000i	0.170797	−	0.170797i	0.787329	+	0.616533i	$0.211463\pi$
$858$	4.00000	+	6.00000i	0.136558	+	0.204837i
$859$		−	26.0000i		−	0.887109i	−0.896248	−	0.443554i	$-0.853717\pi$
$859$		−	26.0000i		−	0.887109i	0.896248	−	0.443554i	$-0.146283\pi$
$860$		0			0
$861$	4.00000			0.136320
$862$	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	$0.213725\pi$
$864$	4.00000	−	4.00000i	0.136083	−	0.136083i
$865$		0			0
$866$	−15.0000	+	15.0000i	−0.509721	+	0.509721i
$867$	−33.0000	−	33.0000i	−1.12074	−	1.12074i
$868$	−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
$873$	−2.00000			−0.0676897
$874$			30.0000i			1.01477i
$875$		0			0
$876$	6.00000	+	6.00000i	0.202721	+	0.202721i
$877$		−	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
$879$	−26.0000	−	26.0000i	−0.876958	−	0.876958i
$880$		0			0
$881$		−	20.0000i		−	0.673817i	−0.941537	−	0.336909i	$-0.890619\pi$
$881$		−	20.0000i		−	0.673817i	0.941537	−	0.336909i	$-0.109381\pi$
$882$	−3.00000			−0.101015
$883$	5.00000	+	5.00000i	0.168263	+	0.168263i	0.786216	−	0.617952i	$-0.212037\pi$
$883$	5.00000	+	5.00000i	0.168263	+	0.168263i	−0.617952	+	0.786216i	$0.712037\pi$
$884$	25.0000	+	5.00000i	0.840841	+	0.168168i
$885$		0			0
$886$	19.0000	+	19.0000i	0.638317	+	0.638317i
$887$	−23.0000	−	23.0000i	−0.772264	−	0.772264i	0.206238	−	0.978502i	$-0.433878\pi$
$887$	−23.0000	−	23.0000i	−0.772264	−	0.772264i	−0.978502	+	0.206238i	$0.933878\pi$
$888$	−8.00000	−	8.00000i	−0.268462	−	0.268462i
$889$	−30.0000	+	30.0000i	−1.00617	+	1.00617i
$890$		0			0
$891$	5.00000	−	5.00000i	0.167506	−	0.167506i
$892$	−6.00000			−0.200895
$893$	6.00000	−	6.00000i	0.200782	−	0.200782i
$894$	−26.0000			−0.869570
$895$		0			0
$896$			2.00000i			0.0668153i
$897$	20.0000	+	30.0000i	0.667781	+	1.00167i
$898$	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
$903$	20.0000			0.665558
$904$	−9.00000	−	9.00000i	−0.299336	−	0.299336i
$905$		0			0
$906$	18.0000			0.598010
$907$	35.0000	−	35.0000i	1.16216	−	1.16216i	0.178153	−	0.984003i	$-0.442988\pi$
$907$	35.0000	−	35.0000i	1.16216	−	1.16216i	0.984003	−	0.178153i	$-0.0570122\pi$
$908$		−	12.0000i		−	0.398234i
$909$		0			0
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		−	6.00000i		−	0.198680i
$913$	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
$918$		−	40.0000i		−	1.32020i
$919$			14.0000i			0.461817i	0.972975	+	0.230909i	$0.0741699\pi$
$919$			14.0000i			0.461817i	−0.972975	+	0.230909i	$0.925830\pi$
$920$		0			0
$921$	2.00000	−	2.00000i	0.0659022	−	0.0659022i
$922$	11.0000	−	11.0000i	0.362266	−	0.362266i
$923$	1.00000	−	5.00000i	0.0329154	−	0.164577i
$924$			4.00000i			0.131590i
$925$		0			0
$926$	−16.0000			−0.525793
$927$	5.00000	−	5.00000i	0.164222	−	0.164222i
$928$	4.00000			0.131306
$929$	−17.0000	+	17.0000i	−0.557752	+	0.557752i	−0.928667	−	0.370915i	$-0.879044\pi$
$929$	−17.0000	+	17.0000i	−0.557752	+	0.557752i	0.370915	+	0.928667i	$0.379044\pi$
$930$		0			0
$931$	−9.00000	+	9.00000i	−0.294963	+	0.294963i
$932$	−5.00000	−	5.00000i	−0.163780	−	0.163780i
$933$	10.0000	+	10.0000i	0.327385	+	0.327385i
$934$	5.00000	+	5.00000i	0.163605	+	0.163605i
$935$		0			0
$936$	2.00000	+	3.00000i	0.0653720	+	0.0980581i
$937$	−33.0000	−	33.0000i	−1.07806	−	1.07806i	−0.996683	−	0.0813798i	$-0.974067\pi$
$937$	−33.0000	−	33.0000i	−1.07806	−	1.07806i	−0.0813798	−	0.996683i	$-0.525933\pi$
$938$	24.0000			0.783628
$939$			18.0000i			0.587408i
$940$		0			0
$941$	−29.0000	−	29.0000i	−0.945373	−	0.945373i	0.0532103	−	0.998583i	$-0.483055\pi$
$941$	−29.0000	−	29.0000i	−0.945373	−	0.945373i	−0.998583	+	0.0532103i	$0.983055\pi$
$942$			6.00000i			0.195491i
$943$		−	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	$0.711821\pi$
$948$	−14.0000	−	14.0000i	−0.454699	−	0.454699i
$949$	−18.0000	+	12.0000i	−0.584305	+	0.389536i
$950$		0			0
$951$	2.00000	+	2.00000i	0.0648544	+	0.0648544i
$952$	10.0000	+	10.0000i	0.324102	+	0.324102i
$953$	−35.0000	−	35.0000i	−1.13376	−	1.13376i	−0.989546	−	0.144215i	$-0.953934\pi$
$953$	−35.0000	−	35.0000i	−1.13376	−	1.13376i	−0.144215	−	0.989546i	$-0.546066\pi$
$954$	1.00000	−	1.00000i	0.0323762	−	0.0323762i
$955$		0			0
$956$	7.00000	−	7.00000i	0.226396	−	0.226396i
$957$	8.00000			0.258603
$958$	−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
$963$	13.0000	−	13.0000i	0.418919	−	0.418919i
$964$	−1.00000	+	1.00000i	−0.0322078	+	0.0322078i
$965$		0			0
$966$			20.0000i			0.643489i
$967$		−	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
$969$	−30.0000	−	30.0000i	−0.963739	−	0.963739i
$970$		0			0
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$	7.00000	−	7.00000i	0.224525	−	0.224525i
$973$			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	$0.114471\pi$
$977$			22.0000i			0.703842i	−0.936030	+	0.351921i	$0.885529\pi$
$978$	4.00000	−	4.00000i	0.127906	−	0.127906i
$979$	14.0000			0.447442
$980$		0			0
$981$	13.0000	+	13.0000i	0.415058	+	0.415058i
$982$	10.0000			0.319113
$983$			24.0000i			0.765481i	0.923856	+	0.382741i	$0.125020\pi$
$983$			24.0000i			0.765481i	−0.923856	+	0.382741i	$0.874980\pi$
$984$			2.00000i			0.0637577i
$985$		0			0
$986$	20.0000	−	20.0000i	0.636930	−	0.636930i
$987$	4.00000	−	4.00000i	0.127321	−	0.127321i
$988$	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
$993$	−18.0000			−0.571213
$994$	2.00000	−	2.00000i	0.0634361	−	0.0634361i
$995$		0			0
$996$	−6.00000	+	6.00000i	−0.190117	+	0.190117i
$997$	17.0000	+	17.0000i	0.538395	+	0.538395i	0.923057	−	0.384662i	$-0.125682\pi$
$997$	17.0000	+	17.0000i	0.538395	+	0.538395i	−0.384662	+	0.923057i	$0.625682\pi$
$998$	−23.0000	−	23.0000i	−0.728052	−	0.728052i
$999$	−32.0000	−	32.0000i	−1.01244	−	1.01244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.j.d.307.1		2
5.2	odd	4		130.2.g.c.73.1	yes	2
5.3	odd	4		650.2.g.b.593.1		2
5.4	even	2		130.2.j.b.47.1	yes	2
13.5	odd	4		650.2.g.b.57.1		2
15.2	even	4		1170.2.m.a.73.1		2
15.14	odd	2		1170.2.w.c.307.1		2
20.7	even	4		1040.2.bg.f.593.1		2
20.19	odd	2		1040.2.cd.e.177.1		2
65.18	even	4	inner	650.2.j.d.343.1		2
65.44	odd	4		130.2.g.c.57.1	✓	2
65.57	even	4		130.2.j.b.83.1	yes	2
195.44	even	4		1170.2.m.a.577.1		2
195.122	odd	4		1170.2.w.c.343.1		2
260.187	odd	4		1040.2.cd.e.993.1		2
260.239	even	4		1040.2.bg.f.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.c.57.1	✓	2	65.44	odd	4
130.2.g.c.73.1	yes	2	5.2	odd	4
130.2.j.b.47.1	yes	2	5.4	even	2
130.2.j.b.83.1	yes	2	65.57	even	4
650.2.g.b.57.1		2	13.5	odd	4
650.2.g.b.593.1		2	5.3	odd	4
650.2.j.d.307.1		2	1.1	even	1	trivial
650.2.j.d.343.1		2	65.18	even	4	inner
1040.2.bg.f.577.1		2	260.239	even	4
1040.2.bg.f.593.1		2	20.7	even	4
1040.2.cd.e.177.1		2	20.19	odd	2
1040.2.cd.e.993.1		2	260.187	odd	4
1170.2.m.a.73.1		2	15.2	even	4
1170.2.m.a.577.1		2	195.44	even	4
1170.2.w.c.307.1		2	15.14	odd	2
1170.2.w.c.343.1		2	195.122	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.00000 - 1.00000i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{6} +2.00000 q^{7} +1.00000i q^{8} +1.00000i q^{9} +(1.00000 - 1.00000i) q^{11} +(-1.00000 + 1.00000i) q^{12} +(-2.00000 - 3.00000i) q^{13} -2.00000i q^{14} +1.00000 q^{16} +(5.00000 - 5.00000i) q^{17} +1.00000 q^{18} +(3.00000 - 3.00000i) q^{19} +(2.00000 - 2.00000i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-5.00000 - 5.00000i) q^{23} +(1.00000 + 1.00000i) q^{24} +(-3.00000 + 2.00000i) q^{26} +(4.00000 + 4.00000i) q^{27} -2.00000 q^{28} +4.00000i q^{29} +(1.00000 + 1.00000i) q^{31} -1.00000i q^{32} -2.00000i q^{33} +(-5.00000 - 5.00000i) q^{34} -1.00000i q^{36} -8.00000 q^{37} +(-3.00000 - 3.00000i) q^{38} +(-5.00000 - 1.00000i) q^{39} +(1.00000 + 1.00000i) q^{41} +(-2.00000 - 2.00000i) q^{42} +(5.00000 + 5.00000i) q^{43} +(-1.00000 + 1.00000i) q^{44} +(-5.00000 + 5.00000i) q^{46} +2.00000 q^{47} +(1.00000 - 1.00000i) q^{48} -3.00000 q^{49} -10.0000i q^{51} +(2.00000 + 3.00000i) q^{52} +(1.00000 - 1.00000i) q^{53} +(4.00000 - 4.00000i) q^{54} +2.00000i q^{56} -6.00000i q^{57} +4.00000 q^{58} +(-3.00000 - 3.00000i) q^{59} +2.00000 q^{61} +(1.00000 - 1.00000i) q^{62} +2.00000i q^{63} -1.00000 q^{64} -2.00000 q^{66} +12.0000i q^{67} +(-5.00000 + 5.00000i) q^{68} -10.0000 q^{69} +(1.00000 + 1.00000i) q^{71} -1.00000 q^{72} -6.00000i q^{73} +8.00000i q^{74} +(-3.00000 + 3.00000i) q^{76} +(2.00000 - 2.00000i) q^{77} +(-1.00000 + 5.00000i) q^{78} +14.0000i q^{79} +5.00000 q^{81} +(1.00000 - 1.00000i) q^{82} +6.00000 q^{83} +(-2.00000 + 2.00000i) q^{84} +(5.00000 - 5.00000i) q^{86} +(4.00000 + 4.00000i) q^{87} +(1.00000 + 1.00000i) q^{88} +(7.00000 + 7.00000i) q^{89} +(-4.00000 - 6.00000i) q^{91} +(5.00000 + 5.00000i) q^{92} +2.00000 q^{93} -2.00000i q^{94} +(-1.00000 - 1.00000i) q^{96} +2.00000i q^{97} +3.00000i q^{98} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{16} + 10 q^{17} + 2 q^{18} + 6 q^{19} + 4 q^{21} - 2 q^{22} - 10 q^{23} + 2 q^{24} - 6 q^{26} + 8 q^{27} - 4 q^{28} + 2 q^{31}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 2 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^16 + 10 * q^17 + 2 * q^18 + 6 * q^19 + 4 * q^21 - 2 * q^22 - 10 * q^23 + 2 * q^24 - 6 * q^26 + 8 * q^27 - 4 * q^28 + 2 * q^31 - 10 * q^34 - 16 * q^37 - 6 * q^38 - 10 * q^39 + 2 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 10 * q^46 + 4 * q^47 + 2 * q^48 - 6 * q^49 + 4 * q^52 + 2 * q^53 + 8 * q^54 + 8 * q^58 - 6 * q^59 + 4 * q^61 + 2 * q^62 - 2 * q^64 - 4 * q^66 - 10 * q^68 - 20 * q^69 + 2 * q^71 - 2 * q^72 - 6 * q^76 + 4 * q^77 - 2 * q^78 + 10 * q^81 + 2 * q^82 + 12 * q^83 - 4 * q^84 + 10 * q^86 + 8 * q^87 + 2 * q^88 + 14 * q^89 - 8 * q^91 + 10 * q^92 + 4 * q^93 - 2 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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