LMFDB - Embedded newform 175.2.f.c.118.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(118,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.118"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,0,0,0,0,-4,8,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.1
Root			$-1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	175.118
Dual form			175.2.f.c.132.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.00000i) q^{2} +(-1.58114 + 1.58114i) q^{3} +3.16228i q^{6} +(0.581139 + 2.58114i) q^{7} +(2.00000 + 2.00000i) q^{8} -2.00000i q^{9} -1.00000 q^{11} +(1.58114 - 1.58114i) q^{13} +(3.16228 + 2.00000i) q^{14} +4.00000 q^{16} +(-1.58114 - 1.58114i) q^{17} +(-2.00000 - 2.00000i) q^{18} +3.16228 q^{19} +(-5.00000 - 3.16228i) q^{21} +(-1.00000 + 1.00000i) q^{22} +(-2.00000 - 2.00000i) q^{23} -6.32456 q^{24} -3.16228i q^{26} +(-1.58114 - 1.58114i) q^{27} -3.00000i q^{29} +3.16228i q^{31} +(1.58114 - 1.58114i) q^{33} -3.16228 q^{34} +(6.00000 - 6.00000i) q^{37} +(3.16228 - 3.16228i) q^{38} +5.00000i q^{39} -9.48683i q^{41} +(-8.16228 + 1.83772i) q^{42} +(3.00000 + 3.00000i) q^{43} -4.00000 q^{46} +(4.74342 + 4.74342i) q^{47} +(-6.32456 + 6.32456i) q^{48} +(-6.32456 + 3.00000i) q^{49} +5.00000 q^{51} +(-1.00000 - 1.00000i) q^{53} -3.16228 q^{54} +(-4.00000 + 6.32456i) q^{56} +(-5.00000 + 5.00000i) q^{57} +(-3.00000 - 3.00000i) q^{58} +9.48683 q^{59} +6.32456i q^{61} +(3.16228 + 3.16228i) q^{62} +(5.16228 - 1.16228i) q^{63} +8.00000i q^{64} -3.16228i q^{66} +(1.00000 - 1.00000i) q^{67} +6.32456 q^{69} -6.00000 q^{71} +(4.00000 - 4.00000i) q^{72} -12.0000i q^{74} +(-0.581139 - 2.58114i) q^{77} +(5.00000 + 5.00000i) q^{78} -13.0000i q^{79} +11.0000 q^{81} +(-9.48683 - 9.48683i) q^{82} +(3.16228 - 3.16228i) q^{83} +6.00000 q^{86} +(4.74342 + 4.74342i) q^{87} +(-2.00000 - 2.00000i) q^{88} -6.32456 q^{89} +(5.00000 + 3.16228i) q^{91} +(-5.00000 - 5.00000i) q^{93} +9.48683 q^{94} +(1.58114 + 1.58114i) q^{97} +(-3.32456 + 9.32456i) q^{98} +2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{7} + 8 q^{8} - 4 q^{11} + 16 q^{16} - 8 q^{18} - 20 q^{21} - 4 q^{22} - 8 q^{23} + 24 q^{37} - 20 q^{42} + 12 q^{43} - 16 q^{46} + 20 q^{51} - 4 q^{53} - 16 q^{56} - 20 q^{57} - 12 q^{58}+ \cdots + 12 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^7 + 8 * q^8 - 4 * q^11 + 16 * q^16 - 8 * q^18 - 20 * q^21 - 4 * q^22 - 8 * q^23 + 24 * q^37 - 20 * q^42 + 12 * q^43 - 16 * q^46 + 20 * q^51 - 4 * q^53 - 16 * q^56 - 20 * q^57 - 12 * q^58 + 8 * q^63 + 4 * q^67 - 24 * q^71 + 16 * q^72 + 4 * q^77 + 20 * q^78 + 44 * q^81 + 24 * q^86 - 8 * q^88 + 20 * q^91 - 20 * q^93 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	1.00000	−	1.00000i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$3$	−1.58114	+	1.58114i	−0.912871	+	0.912871i	−0.996497	−	0.0836263i	$-0.973350\pi$
$3$	−1.58114	+	1.58114i	−0.912871	+	0.912871i	0.0836263	+	0.996497i	$0.473350\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$			3.16228i			1.29099i
$7$	0.581139	+	2.58114i	0.219650	+	0.975579i
$7$	0.581139	+	2.58114i	0.219650	+	0.975579i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$		−	2.00000i		−	0.666667i
$10$		0			0
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$		0			0
$13$	1.58114	−	1.58114i	0.438529	−	0.438529i	−0.452988	−	0.891517i	$-0.649642\pi$
$13$	1.58114	−	1.58114i	0.438529	−	0.438529i	0.891517	+	0.452988i	$0.149642\pi$
$14$	3.16228	+	2.00000i	0.845154	+	0.534522i
$15$		0			0
$16$	4.00000			1.00000
$17$	−1.58114	−	1.58114i	−0.383482	−	0.383482i	0.488873	−	0.872355i	$-0.337408\pi$
$17$	−1.58114	−	1.58114i	−0.383482	−	0.383482i	−0.872355	+	0.488873i	$0.837408\pi$
$18$	−2.00000	−	2.00000i	−0.471405	−	0.471405i
$19$	3.16228			0.725476			0.362738	−	0.931891i	$-0.381842\pi$
$19$	3.16228			0.725476			0.362738	+	0.931891i	$0.381842\pi$
$20$		0			0
$21$	−5.00000	−	3.16228i	−1.09109	−	0.690066i
$22$	−1.00000	+	1.00000i	−0.213201	+	0.213201i
$23$	−2.00000	−	2.00000i	−0.417029	−	0.417029i	0.467150	−	0.884178i	$-0.345281\pi$
$23$	−2.00000	−	2.00000i	−0.417029	−	0.417029i	−0.884178	+	0.467150i	$0.845281\pi$
$24$	−6.32456			−1.29099
$25$		0			0
$26$		−	3.16228i		−	0.620174i
$27$	−1.58114	−	1.58114i	−0.304290	−	0.304290i
$28$		0			0
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$		0			0
$31$			3.16228i			0.567962i	0.958830	+	0.283981i	$0.0916552\pi$
$31$			3.16228i			0.567962i	−0.958830	+	0.283981i	$0.908345\pi$
$32$		0			0
$33$	1.58114	−	1.58114i	0.275241	−	0.275241i
$34$	−3.16228			−0.542326
$35$		0			0
$36$		0			0
$37$	6.00000	−	6.00000i	0.986394	−	0.986394i	−0.0135147	−	0.999909i	$-0.504302\pi$
$37$	6.00000	−	6.00000i	0.986394	−	0.986394i	0.999909	+	0.0135147i	$0.00430201\pi$
$38$	3.16228	−	3.16228i	0.512989	−	0.512989i
$39$			5.00000i			0.800641i
$40$		0			0
$41$		−	9.48683i		−	1.48159i	−0.671729	−	0.740797i	$-0.734448\pi$
$41$		−	9.48683i		−	1.48159i	0.671729	−	0.740797i	$-0.265552\pi$
$42$	−8.16228	+	1.83772i	−1.25947	+	0.283567i
$43$	3.00000	+	3.00000i	0.457496	+	0.457496i	0.897833	−	0.440337i	$-0.145141\pi$
$43$	3.00000	+	3.00000i	0.457496	+	0.457496i	−0.440337	+	0.897833i	$0.645141\pi$
$44$		0			0
$45$		0			0
$46$	−4.00000			−0.589768
$47$	4.74342	+	4.74342i	0.691898	+	0.691898i	0.962649	−	0.270751i	$-0.0872720\pi$
$47$	4.74342	+	4.74342i	0.691898	+	0.691898i	−0.270751	+	0.962649i	$0.587272\pi$
$48$	−6.32456	+	6.32456i	−0.912871	+	0.912871i
$49$	−6.32456	+	3.00000i	−0.903508	+	0.428571i
$50$		0			0
$51$	5.00000			0.700140
$52$		0			0
$53$	−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	$0.780966\pi$
$54$	−3.16228			−0.430331
$55$		0			0
$56$	−4.00000	+	6.32456i	−0.534522	+	0.845154i
$57$	−5.00000	+	5.00000i	−0.662266	+	0.662266i
$58$	−3.00000	−	3.00000i	−0.393919	−	0.393919i
$59$	9.48683			1.23508			0.617540	−	0.786539i	$-0.288129\pi$
$59$	9.48683			1.23508			0.617540	+	0.786539i	$0.288129\pi$
$60$		0			0
$61$			6.32456i			0.809776i	0.914366	+	0.404888i	$0.132690\pi$
$61$			6.32456i			0.809776i	−0.914366	+	0.404888i	$0.867310\pi$
$62$	3.16228	+	3.16228i	0.401610	+	0.401610i
$63$	5.16228	−	1.16228i	0.650386	−	0.146433i
$64$			8.00000i			1.00000i
$65$		0			0
$66$		−	3.16228i		−	0.389249i
$67$	1.00000	−	1.00000i	0.122169	−	0.122169i	−0.643379	−	0.765548i	$-0.722468\pi$
$67$	1.00000	−	1.00000i	0.122169	−	0.122169i	0.765548	+	0.643379i	$0.222468\pi$
$68$		0			0
$69$	6.32456			0.761387
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	4.00000	−	4.00000i	0.471405	−	0.471405i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		−	12.0000i		−	1.39497i
$75$		0			0
$76$		0			0
$77$	−0.581139	−	2.58114i	−0.0662269	−	0.294148i
$78$	5.00000	+	5.00000i	0.566139	+	0.566139i
$79$		−	13.0000i		−	1.46261i	−0.682048	−	0.731307i	$-0.738911\pi$
$79$		−	13.0000i		−	1.46261i	0.682048	−	0.731307i	$-0.261089\pi$
$80$		0			0
$81$	11.0000			1.22222
$82$	−9.48683	−	9.48683i	−1.04765	−	1.04765i
$83$	3.16228	−	3.16228i	0.347105	−	0.347105i	−0.511925	−	0.859030i	$-0.671067\pi$
$83$	3.16228	−	3.16228i	0.347105	−	0.347105i	0.859030	+	0.511925i	$0.171067\pi$
$84$		0			0
$85$		0			0
$86$	6.00000			0.646997
$87$	4.74342	+	4.74342i	0.508548	+	0.508548i
$88$	−2.00000	−	2.00000i	−0.213201	−	0.213201i
$89$	−6.32456			−0.670402			−0.335201	−	0.942147i	$-0.608804\pi$
$89$	−6.32456			−0.670402			−0.335201	+	0.942147i	$0.608804\pi$
$90$		0			0
$91$	5.00000	+	3.16228i	0.524142	+	0.331497i
$92$		0			0
$93$	−5.00000	−	5.00000i	−0.518476	−	0.518476i
$94$	9.48683			0.978492
$95$		0			0
$96$		0			0
$97$	1.58114	+	1.58114i	0.160540	+	0.160540i	0.782806	−	0.622266i	$-0.213788\pi$
$97$	1.58114	+	1.58114i	0.160540	+	0.160540i	−0.622266	+	0.782806i	$0.713788\pi$
$98$	−3.32456	+	9.32456i	−0.335831	+	0.941922i
$99$			2.00000i			0.201008i
$100$		0			0
$101$		−	3.16228i		−	0.314658i	−0.987546	−	0.157329i	$-0.949712\pi$
$101$		−	3.16228i		−	0.314658i	0.987546	−	0.157329i	$-0.0502884\pi$
$102$	5.00000	−	5.00000i	0.495074	−	0.495074i
$103$	−11.0680	+	11.0680i	−1.09056	+	1.09056i	−0.0950911	+	0.995469i	$0.530314\pi$
$103$	−11.0680	+	11.0680i	−1.09056	+	1.09056i	−0.995469	+	0.0950911i	$0.969686\pi$
$104$	6.32456			0.620174
$105$		0			0
$106$	−2.00000			−0.194257
$107$	3.00000	−	3.00000i	0.290021	−	0.290021i	−0.547068	−	0.837088i	$-0.684256\pi$
$107$	3.00000	−	3.00000i	0.290021	−	0.290021i	0.837088	+	0.547068i	$0.184256\pi$
$108$		0			0
$109$			7.00000i			0.670478i	0.942133	+	0.335239i	$0.108817\pi$
$109$			7.00000i			0.670478i	−0.942133	+	0.335239i	$0.891183\pi$
$110$		0			0
$111$			18.9737i			1.80090i
$112$	2.32456	+	10.3246i	0.219650	+	0.975579i
$113$	−12.0000	−	12.0000i	−1.12887	−	1.12887i	−0.990362	−	0.138503i	$-0.955771\pi$
$113$	−12.0000	−	12.0000i	−1.12887	−	1.12887i	−0.138503	−	0.990362i	$-0.544229\pi$
$114$			10.0000i			0.936586i
$115$		0			0
$116$		0			0
$117$	−3.16228	−	3.16228i	−0.292353	−	0.292353i
$118$	9.48683	−	9.48683i	0.873334	−	0.873334i
$119$	3.16228	−	5.00000i	0.289886	−	0.458349i
$120$		0			0
$121$	−10.0000			−0.909091
$122$	6.32456	+	6.32456i	0.572598	+	0.572598i
$123$	15.0000	+	15.0000i	1.35250	+	1.35250i
$124$		0			0
$125$		0			0
$126$	4.00000	−	6.32456i	0.356348	−	0.563436i
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	−0.982878	−	0.184257i	$-0.941012\pi$
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	0.184257	+	0.982878i	$0.441012\pi$
$128$	8.00000	+	8.00000i	0.707107	+	0.707107i
$129$	−9.48683			−0.835269
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$	1.83772	+	8.16228i	0.159351	+	0.707759i
$134$		−	2.00000i		−	0.172774i
$135$		0			0
$136$		−	6.32456i		−	0.542326i
$137$	−2.00000	+	2.00000i	−0.170872	+	0.170872i	−0.787362	−	0.616491i	$-0.788554\pi$
$137$	−2.00000	+	2.00000i	−0.170872	+	0.170872i	0.616491	+	0.787362i	$0.288554\pi$
$138$	6.32456	−	6.32456i	0.538382	−	0.538382i
$139$	−18.9737			−1.60933			−0.804663	−	0.593732i	$-0.797654\pi$
$139$	−18.9737			−1.60933			−0.804663	+	0.593732i	$0.797654\pi$
$140$		0			0
$141$	−15.0000			−1.26323
$142$	−6.00000	+	6.00000i	−0.503509	+	0.503509i
$143$	−1.58114	+	1.58114i	−0.132221	+	0.132221i
$144$		−	8.00000i		−	0.666667i
$145$		0			0
$146$		0			0
$147$	5.25658	−	14.7434i	0.433556	−	1.21602i
$148$		0			0
$149$			12.0000i			0.983078i	0.870855	+	0.491539i	$0.163566\pi$
$149$			12.0000i			0.983078i	−0.870855	+	0.491539i	$0.836434\pi$
$150$		0			0
$151$	9.00000			0.732410			0.366205	−	0.930534i	$-0.380657\pi$
$151$	9.00000			0.732410			0.366205	+	0.930534i	$0.380657\pi$
$152$	6.32456	+	6.32456i	0.512989	+	0.512989i
$153$	−3.16228	+	3.16228i	−0.255655	+	0.255655i
$154$	−3.16228	−	2.00000i	−0.254824	−	0.161165i
$155$		0			0
$156$		0			0
$157$	−6.32456	−	6.32456i	−0.504754	−	0.504754i	0.408157	−	0.912912i	$-0.366172\pi$
$157$	−6.32456	−	6.32456i	−0.504754	−	0.504754i	−0.912912	+	0.408157i	$0.866172\pi$
$158$	−13.0000	−	13.0000i	−1.03422	−	1.03422i
$159$	3.16228			0.250785
$160$		0			0
$161$	4.00000	−	6.32456i	0.315244	−	0.498445i
$162$	11.0000	−	11.0000i	0.864242	−	0.864242i
$163$	−6.00000	−	6.00000i	−0.469956	−	0.469956i	0.431944	−	0.901900i	$-0.357828\pi$
$163$	−6.00000	−	6.00000i	−0.469956	−	0.469956i	−0.901900	+	0.431944i	$0.857828\pi$
$164$		0			0
$165$		0			0
$166$		−	6.32456i		−	0.490881i
$167$	−11.0680	−	11.0680i	−0.856465	−	0.856465i	0.134454	−	0.990920i	$-0.457072\pi$
$167$	−11.0680	−	11.0680i	−0.856465	−	0.856465i	−0.990920	+	0.134454i	$0.957072\pi$
$168$	−3.67544	−	16.3246i	−0.283567	−	1.25947i
$169$			8.00000i			0.615385i
$170$		0			0
$171$		−	6.32456i		−	0.483651i
$172$		0			0
$173$	11.0680	−	11.0680i	0.841482	−	0.841482i	−0.147569	−	0.989052i	$-0.547145\pi$
$173$	11.0680	−	11.0680i	0.841482	−	0.841482i	0.989052	+	0.147569i	$0.0471450\pi$
$174$	9.48683			0.719195
$175$		0			0
$176$	−4.00000			−0.301511
$177$	−15.0000	+	15.0000i	−1.12747	+	1.12747i
$178$	−6.32456	+	6.32456i	−0.474045	+	0.474045i
$179$			6.00000i			0.448461i	0.974536	+	0.224231i	$0.0719869\pi$
$179$			6.00000i			0.448461i	−0.974536	+	0.224231i	$0.928013\pi$
$180$		0			0
$181$		−	22.1359i		−	1.64535i	−0.568511	−	0.822676i	$-0.692480\pi$
$181$		−	22.1359i		−	1.64535i	0.568511	−	0.822676i	$-0.307520\pi$
$182$	8.16228	−	1.83772i	0.605028	−	0.136221i
$183$	−10.0000	−	10.0000i	−0.739221	−	0.739221i
$184$		−	8.00000i		−	0.589768i
$185$		0			0
$186$	−10.0000			−0.733236
$187$	1.58114	+	1.58114i	0.115624	+	0.115624i
$188$		0			0
$189$	3.16228	−	5.00000i	0.230022	−	0.363696i
$190$		0			0
$191$	−3.00000			−0.217072			−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000			−0.217072			−0.108536	+	0.994092i	$0.534616\pi$
$192$	−12.6491	−	12.6491i	−0.912871	−	0.912871i
$193$	8.00000	+	8.00000i	0.575853	+	0.575853i	0.933758	−	0.357905i	$-0.116509\pi$
$193$	8.00000	+	8.00000i	0.575853	+	0.575853i	−0.357905	+	0.933758i	$0.616509\pi$
$194$	3.16228			0.227038
$195$		0			0
$196$		0			0
$197$	1.00000	−	1.00000i	0.0712470	−	0.0712470i	−0.670585	−	0.741832i	$-0.733957\pi$
$197$	1.00000	−	1.00000i	0.0712470	−	0.0712470i	0.741832	+	0.670585i	$0.233957\pi$
$198$	2.00000	+	2.00000i	0.142134	+	0.142134i
$199$	−9.48683			−0.672504			−0.336252	−	0.941772i	$-0.609159\pi$
$199$	−9.48683			−0.672504			−0.336252	+	0.941772i	$0.609159\pi$
$200$		0			0
$201$			3.16228i			0.223050i
$202$	−3.16228	−	3.16228i	−0.222497	−	0.222497i
$203$	7.74342	−	1.74342i	0.543481	−	0.122364i
$204$		0			0
$205$		0			0
$206$			22.1359i			1.54228i
$207$	−4.00000	+	4.00000i	−0.278019	+	0.278019i
$208$	6.32456	−	6.32456i	0.438529	−	0.438529i
$209$	−3.16228			−0.218739
$210$		0			0
$211$	17.0000			1.17033			0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000			1.17033			0.585164	+	0.810915i	$0.301030\pi$
$212$		0			0
$213$	9.48683	−	9.48683i	0.650027	−	0.650027i
$214$		−	6.00000i		−	0.410152i
$215$		0			0
$216$		−	6.32456i		−	0.430331i
$217$	−8.16228	+	1.83772i	−0.554092	+	0.124753i
$218$	7.00000	+	7.00000i	0.474100	+	0.474100i
$219$		0			0
$220$		0			0
$221$	−5.00000			−0.336336
$222$	18.9737	+	18.9737i	1.27343	+	1.27343i
$223$	−14.2302	+	14.2302i	−0.952928	+	0.952928i	−0.998941	−	0.0460129i	$-0.985348\pi$
$223$	−14.2302	+	14.2302i	−0.952928	+	0.952928i	0.0460129	+	0.998941i	$0.485348\pi$
$224$		0			0
$225$		0			0
$226$	−24.0000			−1.59646
$227$	1.58114	+	1.58114i	0.104944	+	0.104944i	0.757629	−	0.652685i	$-0.226358\pi$
$227$	1.58114	+	1.58114i	0.104944	+	0.104944i	−0.652685	+	0.757629i	$0.726358\pi$
$228$		0			0
$229$	15.8114			1.04485			0.522423	−	0.852686i	$-0.325028\pi$
$229$	15.8114			1.04485			0.522423	+	0.852686i	$0.325028\pi$
$230$		0			0
$231$	5.00000	+	3.16228i	0.328976	+	0.208063i
$232$	6.00000	−	6.00000i	0.393919	−	0.393919i
$233$	18.0000	+	18.0000i	1.17922	+	1.17922i	0.979943	+	0.199276i	$0.0638589\pi$
$233$	18.0000	+	18.0000i	1.17922	+	1.17922i	0.199276	+	0.979943i	$0.436141\pi$
$234$	−6.32456			−0.413449
$235$		0			0
$236$		0			0
$237$	20.5548	+	20.5548i	1.33518	+	1.33518i
$238$	−1.83772	−	8.16228i	−0.119122	−	0.529082i
$239$		−	19.0000i		−	1.22901i	−0.788914	−	0.614504i	$-0.789356\pi$
$239$		−	19.0000i		−	1.22901i	0.788914	−	0.614504i	$-0.210644\pi$
$240$		0			0
$241$			25.2982i			1.62960i	0.579741	+	0.814801i	$0.303154\pi$
$241$			25.2982i			1.62960i	−0.579741	+	0.814801i	$0.696846\pi$
$242$	−10.0000	+	10.0000i	−0.642824	+	0.642824i
$243$	−12.6491	+	12.6491i	−0.811441	+	0.811441i
$244$		0			0
$245$		0			0
$246$	30.0000			1.91273
$247$	5.00000	−	5.00000i	0.318142	−	0.318142i
$248$	−6.32456	+	6.32456i	−0.401610	+	0.401610i
$249$			10.0000i			0.633724i
$250$		0			0
$251$			12.6491i			0.798405i	0.916863	+	0.399202i	$0.130713\pi$
$251$			12.6491i			0.798405i	−0.916863	+	0.399202i	$0.869287\pi$
$252$		0			0
$253$	2.00000	+	2.00000i	0.125739	+	0.125739i
$254$			18.0000i			1.12942i
$255$		0			0
$256$		0			0
$257$	−12.6491	−	12.6491i	−0.789030	−	0.789030i	0.192305	−	0.981335i	$-0.438404\pi$
$257$	−12.6491	−	12.6491i	−0.789030	−	0.789030i	−0.981335	+	0.192305i	$0.938404\pi$
$258$	−9.48683	+	9.48683i	−0.590624	+	0.590624i
$259$	18.9737	+	12.0000i	1.17897	+	0.745644i
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	−7.00000	−	7.00000i	−0.431638	−	0.431638i	0.457547	−	0.889185i	$-0.348728\pi$
$263$	−7.00000	−	7.00000i	−0.431638	−	0.431638i	−0.889185	+	0.457547i	$0.848728\pi$
$264$	6.32456			0.389249
$265$		0			0
$266$	10.0000	+	6.32456i	0.613139	+	0.387783i
$267$	10.0000	−	10.0000i	0.611990	−	0.611990i
$268$		0			0
$269$	−18.9737			−1.15684			−0.578422	−	0.815737i	$-0.696331\pi$
$269$	−18.9737			−1.15684			−0.578422	+	0.815737i	$0.696331\pi$
$270$		0			0
$271$		−	12.6491i		−	0.768379i	−0.923254	−	0.384189i	$-0.874481\pi$
$271$		−	12.6491i		−	0.768379i	0.923254	−	0.384189i	$-0.125519\pi$
$272$	−6.32456	−	6.32456i	−0.383482	−	0.383482i
$273$	−12.9057	+	2.90569i	−0.781088	+	0.175861i
$274$			4.00000i			0.241649i
$275$		0			0
$276$		0			0
$277$	18.0000	−	18.0000i	1.08152	−	1.08152i	0.0851468	−	0.996368i	$-0.472864\pi$
$277$	18.0000	−	18.0000i	1.08152	−	1.08152i	0.996368	−	0.0851468i	$-0.0271359\pi$
$278$	−18.9737	+	18.9737i	−1.13796	+	1.13796i
$279$	6.32456			0.378641
$280$		0			0
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$	−15.0000	+	15.0000i	−0.893237	+	0.893237i
$283$	4.74342	−	4.74342i	0.281967	−	0.281967i	−0.551926	−	0.833893i	$-0.686107\pi$
$283$	4.74342	−	4.74342i	0.281967	−	0.281967i	0.833893	+	0.551926i	$0.186107\pi$
$284$		0			0
$285$		0			0
$286$			3.16228i			0.186989i
$287$	24.4868	−	5.51317i	1.44541	−	0.325432i
$288$		0			0
$289$		−	12.0000i		−	0.705882i
$290$		0			0
$291$	−5.00000			−0.293105
$292$		0			0
$293$	7.90569	−	7.90569i	0.461856	−	0.461856i	−0.437408	−	0.899263i	$-0.644103\pi$
$293$	7.90569	−	7.90569i	0.461856	−	0.461856i	0.899263	+	0.437408i	$0.144103\pi$
$294$	−9.48683	−	20.0000i	−0.553283	−	1.16642i
$295$		0			0
$296$	24.0000			1.39497
$297$	1.58114	+	1.58114i	0.0917470	+	0.0917470i
$298$	12.0000	+	12.0000i	0.695141	+	0.695141i
$299$	−6.32456			−0.365758
$300$		0			0
$301$	−6.00000	+	9.48683i	−0.345834	+	0.546812i
$302$	9.00000	−	9.00000i	0.517892	−	0.517892i
$303$	5.00000	+	5.00000i	0.287242	+	0.287242i
$304$	12.6491			0.725476
$305$		0			0
$306$			6.32456i			0.361551i
$307$	4.74342	+	4.74342i	0.270721	+	0.270721i	0.829390	−	0.558669i	$-0.188688\pi$
$307$	4.74342	+	4.74342i	0.270721	+	0.270721i	−0.558669	+	0.829390i	$0.688688\pi$
$308$		0			0
$309$		−	35.0000i		−	1.99108i
$310$		0			0
$311$		−	22.1359i		−	1.25521i	−0.778530	−	0.627607i	$-0.784034\pi$
$311$		−	22.1359i		−	1.25521i	0.778530	−	0.627607i	$-0.215966\pi$
$312$	−10.0000	+	10.0000i	−0.566139	+	0.566139i
$313$	14.2302	−	14.2302i	0.804341	−	0.804341i	−0.179430	−	0.983771i	$-0.557425\pi$
$313$	14.2302	−	14.2302i	0.804341	−	0.804341i	0.983771	+	0.179430i	$0.0574252\pi$
$314$	−12.6491			−0.713831
$315$		0			0
$316$		0			0
$317$	−19.0000	+	19.0000i	−1.06715	+	1.06715i	−0.0695692	+	0.997577i	$0.522162\pi$
$317$	−19.0000	+	19.0000i	−1.06715	+	1.06715i	−0.997577	+	0.0695692i	$0.977838\pi$
$318$	3.16228	−	3.16228i	0.177332	−	0.177332i
$319$			3.00000i			0.167968i
$320$		0			0
$321$			9.48683i			0.529503i
$322$	−2.32456	−	10.3246i	−0.129542	−	0.575365i
$323$	−5.00000	−	5.00000i	−0.278207	−	0.278207i
$324$		0			0
$325$		0			0
$326$	−12.0000			−0.664619
$327$	−11.0680	−	11.0680i	−0.612060	−	0.612060i
$328$	18.9737	−	18.9737i	1.04765	−	1.04765i
$329$	−9.48683	+	15.0000i	−0.523026	+	0.826977i
$330$		0			0
$331$	−6.00000			−0.329790			−0.164895	−	0.986311i	$-0.552728\pi$
$331$	−6.00000			−0.329790			−0.164895	+	0.986311i	$0.552728\pi$
$332$		0			0
$333$	−12.0000	−	12.0000i	−0.657596	−	0.657596i
$334$	−22.1359			−1.21122
$335$		0			0
$336$	−20.0000	−	12.6491i	−1.09109	−	0.690066i
$337$	8.00000	−	8.00000i	0.435788	−	0.435788i	−0.454804	−	0.890592i	$-0.650291\pi$
$337$	8.00000	−	8.00000i	0.435788	−	0.435788i	0.890592	+	0.454804i	$0.150291\pi$
$338$	8.00000	+	8.00000i	0.435143	+	0.435143i
$339$	37.9473			2.06102
$340$		0			0
$341$		−	3.16228i		−	0.171247i
$342$	−6.32456	−	6.32456i	−0.341993	−	0.341993i
$343$	−11.4189	−	14.5811i	−0.616561	−	0.787307i
$344$			12.0000i			0.646997i
$345$		0			0
$346$		−	22.1359i		−	1.19004i
$347$	−24.0000	+	24.0000i	−1.28839	+	1.28839i	−0.352621	+	0.935766i	$0.614710\pi$
$347$	−24.0000	+	24.0000i	−1.28839	+	1.28839i	−0.935766	+	0.352621i	$0.885290\pi$
$348$		0			0
$349$	34.7851			1.86200			0.931001	−	0.365018i	$-0.118937\pi$
$349$	34.7851			1.86200			0.931001	+	0.365018i	$0.118937\pi$
$350$		0			0
$351$	−5.00000			−0.266880
$352$		0			0
$353$	−14.2302	+	14.2302i	−0.757400	+	0.757400i	−0.975848	−	0.218449i	$-0.929900\pi$
$353$	−14.2302	+	14.2302i	−0.757400	+	0.757400i	0.218449	+	0.975848i	$0.429900\pi$
$354$			30.0000i			1.59448i
$355$		0			0
$356$		0			0
$357$	2.90569	+	12.9057i	0.153786	+	0.683042i
$358$	6.00000	+	6.00000i	0.317110	+	0.317110i
$359$			22.0000i			1.16112i	0.814219	+	0.580558i	$0.197165\pi$
$359$			22.0000i			1.16112i	−0.814219	+	0.580558i	$0.802835\pi$
$360$		0			0
$361$	−9.00000			−0.473684
$362$	−22.1359	−	22.1359i	−1.16344	−	1.16344i
$363$	15.8114	−	15.8114i	0.829883	−	0.829883i
$364$		0			0
$365$		0			0
$366$	−20.0000			−1.04542
$367$	17.3925	+	17.3925i	0.907883	+	0.907883i	0.996101	−	0.0882186i	$-0.0281174\pi$
$367$	17.3925	+	17.3925i	0.907883	+	0.907883i	−0.0882186	+	0.996101i	$0.528117\pi$
$368$	−8.00000	−	8.00000i	−0.417029	−	0.417029i
$369$	−18.9737			−0.987730
$370$		0			0
$371$	2.00000	−	3.16228i	0.103835	−	0.164177i
$372$		0			0
$373$	−12.0000	−	12.0000i	−0.621336	−	0.621336i	0.324537	−	0.945873i	$-0.394792\pi$
$373$	−12.0000	−	12.0000i	−0.621336	−	0.621336i	−0.945873	+	0.324537i	$0.894792\pi$
$374$	3.16228			0.163517
$375$		0			0
$376$			18.9737i			0.978492i
$377$	−4.74342	−	4.74342i	−0.244298	−	0.244298i
$378$	−1.83772	−	8.16228i	−0.0945222	−	0.419822i
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$		0			0
$381$		−	28.4605i		−	1.45808i
$382$	−3.00000	+	3.00000i	−0.153493	+	0.153493i
$383$	15.8114	−	15.8114i	0.807924	−	0.807924i	−0.176395	−	0.984319i	$-0.556444\pi$
$383$	15.8114	−	15.8114i	0.807924	−	0.807924i	0.984319	+	0.176395i	$0.0564437\pi$
$384$	−25.2982			−1.29099
$385$		0			0
$386$	16.0000			0.814379
$387$	6.00000	−	6.00000i	0.304997	−	0.304997i
$388$		0			0
$389$		−	23.0000i		−	1.16615i	−0.812420	−	0.583073i	$-0.801850\pi$
$389$		−	23.0000i		−	1.16615i	0.812420	−	0.583073i	$-0.198150\pi$
$390$		0			0
$391$			6.32456i			0.319847i
$392$	−18.6491	−	6.64911i	−0.941922	−	0.335831i
$393$		0			0
$394$		−	2.00000i		−	0.100759i
$395$		0			0
$396$		0			0
$397$	23.7171	+	23.7171i	1.19033	+	1.19033i	0.976976	+	0.213351i	$0.0684376\pi$
$397$	23.7171	+	23.7171i	1.19033	+	1.19033i	0.213351	+	0.976976i	$0.431562\pi$
$398$	−9.48683	+	9.48683i	−0.475532	+	0.475532i
$399$	−15.8114	−	10.0000i	−0.791559	−	0.500626i
$400$		0			0
$401$	−1.00000			−0.0499376			−0.0249688	−	0.999688i	$-0.507949\pi$
$401$	−1.00000			−0.0499376			−0.0249688	+	0.999688i	$0.507949\pi$
$402$	3.16228	+	3.16228i	0.157720	+	0.157720i
$403$	5.00000	+	5.00000i	0.249068	+	0.249068i
$404$		0			0
$405$		0			0
$406$	6.00000	−	9.48683i	0.297775	−	0.470824i
$407$	−6.00000	+	6.00000i	−0.297409	+	0.297409i
$408$	10.0000	+	10.0000i	0.495074	+	0.495074i
$409$	3.16228			0.156365			0.0781823	−	0.996939i	$-0.475088\pi$
$409$	3.16228			0.156365			0.0781823	+	0.996939i	$0.475088\pi$
$410$		0			0
$411$		−	6.32456i		−	0.311967i
$412$		0			0
$413$	5.51317	+	24.4868i	0.271285	+	1.20492i
$414$			8.00000i			0.393179i
$415$		0			0
$416$		0			0
$417$	30.0000	−	30.0000i	1.46911	−	1.46911i
$418$	−3.16228	+	3.16228i	−0.154672	+	0.154672i
$419$	−15.8114			−0.772437			−0.386218	−	0.922407i	$-0.626219\pi$
$419$	−15.8114			−0.772437			−0.386218	+	0.922407i	$0.626219\pi$
$420$		0			0
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	17.0000	−	17.0000i	0.827547	−	0.827547i
$423$	9.48683	−	9.48683i	0.461266	−	0.461266i
$424$		−	4.00000i		−	0.194257i
$425$		0			0
$426$		−	18.9737i		−	0.919277i
$427$	−16.3246	+	3.67544i	−0.790001	+	0.177867i
$428$		0			0
$429$		−	5.00000i		−	0.241402i
$430$		0			0
$431$	−23.0000			−1.10787			−0.553936	−	0.832560i	$-0.686875\pi$
$431$	−23.0000			−1.10787			−0.553936	+	0.832560i	$0.686875\pi$
$432$	−6.32456	−	6.32456i	−0.304290	−	0.304290i
$433$	−9.48683	+	9.48683i	−0.455908	+	0.455908i	−0.897310	−	0.441402i	$-0.854481\pi$
$433$	−9.48683	+	9.48683i	−0.455908	+	0.455908i	0.441402	+	0.897310i	$0.354481\pi$
$434$	−6.32456	+	10.0000i	−0.303588	+	0.480015i
$435$		0			0
$436$		0			0
$437$	−6.32456	−	6.32456i	−0.302545	−	0.302545i
$438$		0			0
$439$	−12.6491			−0.603709			−0.301855	−	0.953354i	$-0.597606\pi$
$439$	−12.6491			−0.603709			−0.301855	+	0.953354i	$0.597606\pi$
$440$		0			0
$441$	6.00000	+	12.6491i	0.285714	+	0.602339i
$442$	−5.00000	+	5.00000i	−0.237826	+	0.237826i
$443$	−1.00000	−	1.00000i	−0.0475114	−	0.0475114i	0.682952	−	0.730463i	$-0.260696\pi$
$443$	−1.00000	−	1.00000i	−0.0475114	−	0.0475114i	−0.730463	+	0.682952i	$0.760696\pi$
$444$		0			0
$445$		0			0
$446$			28.4605i			1.34764i
$447$	−18.9737	−	18.9737i	−0.897424	−	0.897424i
$448$	−20.6491	+	4.64911i	−0.975579	+	0.219650i
$449$			17.0000i			0.802280i	0.916017	+	0.401140i	$0.131386\pi$
$449$			17.0000i			0.802280i	−0.916017	+	0.401140i	$0.868614\pi$
$450$		0			0
$451$			9.48683i			0.446718i
$452$		0			0
$453$	−14.2302	+	14.2302i	−0.668595	+	0.668595i
$454$	3.16228			0.148413
$455$		0			0
$456$	−20.0000			−0.936586
$457$	1.00000	−	1.00000i	0.0467780	−	0.0467780i	−0.683331	−	0.730109i	$-0.739469\pi$
$457$	1.00000	−	1.00000i	0.0467780	−	0.0467780i	0.730109	+	0.683331i	$0.239469\pi$
$458$	15.8114	−	15.8114i	0.738818	−	0.738818i
$459$			5.00000i			0.233380i
$460$		0			0
$461$		−	6.32456i		−	0.294564i	−0.989095	−	0.147282i	$-0.952948\pi$
$461$		−	6.32456i		−	0.294564i	0.989095	−	0.147282i	$-0.0470525\pi$
$462$	8.16228	−	1.83772i	0.379744	−	0.0854986i
$463$	4.00000	+	4.00000i	0.185896	+	0.185896i	0.793919	−	0.608023i	$-0.208037\pi$
$463$	4.00000	+	4.00000i	0.185896	+	0.185896i	−0.608023	+	0.793919i	$0.708037\pi$
$464$		−	12.0000i		−	0.557086i
$465$		0			0
$466$	36.0000			1.66767
$467$	11.0680	+	11.0680i	0.512165	+	0.512165i	0.915189	−	0.403025i	$-0.132041\pi$
$467$	11.0680	+	11.0680i	0.512165	+	0.512165i	−0.403025	+	0.915189i	$0.632041\pi$
$468$		0			0
$469$	3.16228	+	2.00000i	0.146020	+	0.0923514i
$470$		0			0
$471$	20.0000			0.921551
$472$	18.9737	+	18.9737i	0.873334	+	0.873334i
$473$	−3.00000	−	3.00000i	−0.137940	−	0.137940i
$474$	41.1096			1.88823
$475$		0			0
$476$		0			0
$477$	−2.00000	+	2.00000i	−0.0915737	+	0.0915737i
$478$	−19.0000	−	19.0000i	−0.869040	−	0.869040i
$479$	−6.32456			−0.288976			−0.144488	−	0.989507i	$-0.546154\pi$
$479$	−6.32456			−0.288976			−0.144488	+	0.989507i	$0.546154\pi$
$480$		0			0
$481$		−	18.9737i		−	0.865125i
$482$	25.2982	+	25.2982i	1.15230	+	1.15230i
$483$	3.67544	+	16.3246i	0.167239	+	0.742793i
$484$		0			0
$485$		0			0
$486$			25.2982i			1.14755i
$487$	−4.00000	+	4.00000i	−0.181257	+	0.181257i	−0.791904	−	0.610646i	$-0.790910\pi$
$487$	−4.00000	+	4.00000i	−0.181257	+	0.181257i	0.610646	+	0.791904i	$0.290910\pi$
$488$	−12.6491	+	12.6491i	−0.572598	+	0.572598i
$489$	18.9737			0.858019
$490$		0			0
$491$	−41.0000			−1.85030			−0.925152	−	0.379597i	$-0.876063\pi$
$491$	−41.0000			−1.85030			−0.925152	+	0.379597i	$0.876063\pi$
$492$		0			0
$493$	−4.74342	+	4.74342i	−0.213633	+	0.213633i
$494$		−	10.0000i		−	0.449921i
$495$		0			0
$496$			12.6491i			0.567962i
$497$	−3.48683	−	15.4868i	−0.156406	−	0.694679i
$498$	10.0000	+	10.0000i	0.448111	+	0.448111i
$499$		−	19.0000i		−	0.850557i	−0.905063	−	0.425278i	$-0.860176\pi$
$499$		−	19.0000i		−	0.850557i	0.905063	−	0.425278i	$-0.139824\pi$
$500$		0			0
$501$	35.0000			1.56368
$502$	12.6491	+	12.6491i	0.564557	+	0.564557i
$503$	−7.90569	+	7.90569i	−0.352497	+	0.352497i	−0.861038	−	0.508541i	$-0.830185\pi$
$503$	−7.90569	+	7.90569i	−0.352497	+	0.352497i	0.508541	+	0.861038i	$0.330185\pi$
$504$	12.6491	+	8.00000i	0.563436	+	0.356348i
$505$		0			0
$506$	4.00000			0.177822
$507$	−12.6491	−	12.6491i	−0.561767	−	0.561767i
$508$		0			0
$509$	18.9737			0.840993			0.420496	−	0.907294i	$-0.361856\pi$
$509$	18.9737			0.840993			0.420496	+	0.907294i	$0.361856\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−5.00000	−	5.00000i	−0.220755	−	0.220755i
$514$	−25.2982			−1.11586
$515$		0			0
$516$		0			0
$517$	−4.74342	−	4.74342i	−0.208615	−	0.208615i
$518$	30.9737	−	6.97367i	1.36090	−	0.306405i
$519$			35.0000i			1.53633i
$520$		0			0
$521$			41.1096i			1.80104i	0.434810	+	0.900522i	$0.356816\pi$
$521$			41.1096i			1.80104i	−0.434810	+	0.900522i	$0.643184\pi$
$522$	−6.00000	+	6.00000i	−0.262613	+	0.262613i
$523$	18.9737	−	18.9737i	0.829660	−	0.829660i	−0.157809	−	0.987470i	$-0.550443\pi$
$523$	18.9737	−	18.9737i	0.829660	−	0.829660i	0.987470	+	0.157809i	$0.0504431\pi$
$524$		0			0
$525$		0			0
$526$	−14.0000			−0.610429
$527$	5.00000	−	5.00000i	0.217803	−	0.217803i
$528$	6.32456	−	6.32456i	0.275241	−	0.275241i
$529$		−	15.0000i		−	0.652174i
$530$		0			0
$531$		−	18.9737i		−	0.823387i
$532$		0			0
$533$	−15.0000	−	15.0000i	−0.649722	−	0.649722i
$534$		−	20.0000i		−	0.865485i
$535$		0			0
$536$	4.00000			0.172774
$537$	−9.48683	−	9.48683i	−0.409387	−	0.409387i
$538$	−18.9737	+	18.9737i	−0.818013	+	0.818013i
$539$	6.32456	−	3.00000i	0.272418	−	0.129219i
$540$		0			0
$541$	9.00000			0.386940			0.193470	−	0.981106i	$-0.438026\pi$
$541$	9.00000			0.386940			0.193470	+	0.981106i	$0.438026\pi$
$542$	−12.6491	−	12.6491i	−0.543326	−	0.543326i
$543$	35.0000	+	35.0000i	1.50199	+	1.50199i
$544$		0			0
$545$		0			0
$546$	−10.0000	+	15.8114i	−0.427960	+	0.676665i
$547$	−14.0000	+	14.0000i	−0.598597	+	0.598597i	−0.939939	−	0.341342i	$-0.889118\pi$
$547$	−14.0000	+	14.0000i	−0.598597	+	0.598597i	0.341342	+	0.939939i	$0.389118\pi$
$548$		0			0
$549$	12.6491			0.539851
$550$		0			0
$551$		−	9.48683i		−	0.404153i
$552$	12.6491	+	12.6491i	0.538382	+	0.538382i
$553$	33.5548	−	7.55480i	1.42690	−	0.321263i
$554$		−	36.0000i		−	1.52949i
$555$		0			0
$556$		0			0
$557$	6.00000	−	6.00000i	0.254228	−	0.254228i	−0.568473	−	0.822702i	$-0.692466\pi$
$557$	6.00000	−	6.00000i	0.254228	−	0.254228i	0.822702	+	0.568473i	$0.192466\pi$
$558$	6.32456	−	6.32456i	0.267740	−	0.267740i
$559$	9.48683			0.401250
$560$		0			0
$561$	−5.00000			−0.211100
$562$	9.00000	−	9.00000i	0.379642	−	0.379642i
$563$	−9.48683	+	9.48683i	−0.399822	+	0.399822i	−0.878170	−	0.478348i	$-0.841236\pi$
$563$	−9.48683	+	9.48683i	−0.399822	+	0.399822i	0.478348	+	0.878170i	$0.341236\pi$
$564$		0			0
$565$		0			0
$566$		−	9.48683i		−	0.398761i
$567$	6.39253	+	28.3925i	0.268461	+	1.19237i
$568$	−12.0000	−	12.0000i	−0.503509	−	0.503509i
$569$			32.0000i			1.34151i	0.741679	+	0.670755i	$0.234030\pi$
$569$			32.0000i			1.34151i	−0.741679	+	0.670755i	$0.765970\pi$
$570$		0			0
$571$	−26.0000			−1.08807			−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000			−1.08807			−0.544033	+	0.839064i	$0.683103\pi$
$572$		0			0
$573$	4.74342	−	4.74342i	0.198159	−	0.198159i
$574$	18.9737	−	30.0000i	0.791946	−	1.25218i
$575$		0			0
$576$	16.0000			0.666667
$577$	−20.5548	−	20.5548i	−0.855708	−	0.855708i	0.135121	−	0.990829i	$-0.456858\pi$
$577$	−20.5548	−	20.5548i	−0.855708	−	0.855708i	−0.990829	+	0.135121i	$0.956858\pi$
$578$	−12.0000	−	12.0000i	−0.499134	−	0.499134i
$579$	−25.2982			−1.05136
$580$		0			0
$581$	10.0000	+	6.32456i	0.414870	+	0.262387i
$582$	−5.00000	+	5.00000i	−0.207257	+	0.207257i
$583$	1.00000	+	1.00000i	0.0414158	+	0.0414158i
$584$		0			0
$585$		0			0
$586$		−	15.8114i		−	0.653162i
$587$	15.8114	+	15.8114i	0.652606	+	0.652606i	0.953620	−	0.301014i	$-0.0973251\pi$
$587$	15.8114	+	15.8114i	0.652606	+	0.652606i	−0.301014	+	0.953620i	$0.597325\pi$
$588$		0			0
$589$			10.0000i			0.412043i
$590$		0			0
$591$			3.16228i			0.130079i
$592$	24.0000	−	24.0000i	0.986394	−	0.986394i
$593$	−20.5548	+	20.5548i	−0.844085	+	0.844085i	−0.989387	−	0.145303i	$-0.953584\pi$
$593$	−20.5548	+	20.5548i	−0.844085	+	0.844085i	0.145303	+	0.989387i	$0.453584\pi$
$594$	3.16228			0.129750
$595$		0			0
$596$		0			0
$597$	15.0000	−	15.0000i	0.613909	−	0.613909i
$598$	−6.32456	+	6.32456i	−0.258630	+	0.258630i
$599$		−	13.0000i		−	0.531166i	−0.964088	−	0.265583i	$-0.914436\pi$
$599$		−	13.0000i		−	0.531166i	0.964088	−	0.265583i	$-0.0855644\pi$
$600$		0			0
$601$			22.1359i			0.902944i	0.892285	+	0.451472i	$0.149101\pi$
$601$			22.1359i			0.902944i	−0.892285	+	0.451472i	$0.850899\pi$
$602$	3.48683	+	15.4868i	0.142113	+	0.631196i
$603$	−2.00000	−	2.00000i	−0.0814463	−	0.0814463i
$604$		0			0
$605$		0			0
$606$	10.0000			0.406222
$607$	−14.2302	−	14.2302i	−0.577588	−	0.577588i	0.356650	−	0.934238i	$-0.383919\pi$
$607$	−14.2302	−	14.2302i	−0.577588	−	0.577588i	−0.934238	+	0.356650i	$0.883919\pi$
$608$		0			0
$609$	−9.48683	+	15.0000i	−0.384426	+	0.607831i
$610$		0			0
$611$	15.0000			0.606835
$612$		0			0
$613$	−17.0000	−	17.0000i	−0.686624	−	0.686624i	0.274861	−	0.961484i	$-0.411368\pi$
$613$	−17.0000	−	17.0000i	−0.686624	−	0.686624i	−0.961484	+	0.274861i	$0.911368\pi$
$614$	9.48683			0.382857
$615$		0			0
$616$	4.00000	−	6.32456i	0.161165	−	0.254824i
$617$	−4.00000	+	4.00000i	−0.161034	+	0.161034i	−0.783025	−	0.621991i	$-0.786324\pi$
$617$	−4.00000	+	4.00000i	−0.161034	+	0.161034i	0.621991	+	0.783025i	$0.286324\pi$
$618$	−35.0000	−	35.0000i	−1.40791	−	1.40791i
$619$	−25.2982			−1.01682			−0.508411	−	0.861115i	$-0.669767\pi$
$619$	−25.2982			−1.01682			−0.508411	+	0.861115i	$0.669767\pi$
$620$		0			0
$621$			6.32456i			0.253796i
$622$	−22.1359	−	22.1359i	−0.887570	−	0.887570i
$623$	−3.67544	−	16.3246i	−0.147254	−	0.654029i
$624$			20.0000i			0.800641i
$625$		0			0
$626$		−	28.4605i		−	1.13751i
$627$	5.00000	−	5.00000i	0.199681	−	0.199681i
$628$		0			0
$629$	−18.9737			−0.756530
$630$		0			0
$631$	−31.0000			−1.23409			−0.617045	−	0.786928i	$-0.711670\pi$
$631$	−31.0000			−1.23409			−0.617045	+	0.786928i	$0.711670\pi$
$632$	26.0000	−	26.0000i	1.03422	−	1.03422i
$633$	−26.8794	+	26.8794i	−1.06836	+	1.06836i
$634$			38.0000i			1.50917i
$635$		0			0
$636$		0			0
$637$	−5.25658	+	14.7434i	−0.208273	+	0.584155i
$638$	3.00000	+	3.00000i	0.118771	+	0.118771i
$639$			12.0000i			0.474713i
$640$		0			0
$641$	44.0000			1.73790			0.868948	−	0.494904i	$-0.164797\pi$
$641$	44.0000			1.73790			0.868948	+	0.494904i	$0.164797\pi$
$642$	9.48683	+	9.48683i	0.374415	+	0.374415i
$643$	−4.74342	+	4.74342i	−0.187062	+	0.187062i	−0.794425	−	0.607363i	$-0.792228\pi$
$643$	−4.74342	+	4.74342i	−0.187062	+	0.187062i	0.607363	+	0.794425i	$0.292228\pi$
$644$		0			0
$645$		0			0
$646$	−10.0000			−0.393445
$647$	−12.6491	−	12.6491i	−0.497288	−	0.497288i	0.413305	−	0.910593i	$-0.364374\pi$
$647$	−12.6491	−	12.6491i	−0.497288	−	0.497288i	−0.910593	+	0.413305i	$0.864374\pi$
$648$	22.0000	+	22.0000i	0.864242	+	0.864242i
$649$	−9.48683			−0.372391
$650$		0			0
$651$	10.0000	−	15.8114i	0.391931	−	0.619697i
$652$		0			0
$653$	19.0000	+	19.0000i	0.743527	+	0.743527i	0.973255	−	0.229728i	$-0.0737835\pi$
$653$	19.0000	+	19.0000i	0.743527	+	0.743527i	−0.229728	+	0.973255i	$0.573784\pi$
$654$	−22.1359			−0.865584
$655$		0			0
$656$		−	37.9473i		−	1.48159i
$657$		0			0
$658$	5.51317	+	24.4868i	0.214926	+	0.954596i
$659$			1.00000i			0.0389545i	0.999810	+	0.0194772i	$0.00620019\pi$
$659$			1.00000i			0.0389545i	−0.999810	+	0.0194772i	$0.993800\pi$
$660$		0			0
$661$		−	12.6491i		−	0.491993i	−0.969271	−	0.245997i	$-0.920885\pi$
$661$		−	12.6491i		−	0.491993i	0.969271	−	0.245997i	$-0.0791152\pi$
$662$	−6.00000	+	6.00000i	−0.233197	+	0.233197i
$663$	7.90569	−	7.90569i	0.307032	−	0.307032i
$664$	12.6491			0.490881
$665$		0			0
$666$	−24.0000			−0.929981
$667$	−6.00000	+	6.00000i	−0.232321	+	0.232321i
$668$		0			0
$669$		−	45.0000i		−	1.73980i
$670$		0			0
$671$		−	6.32456i		−	0.244157i
$672$		0			0
$673$	24.0000	+	24.0000i	0.925132	+	0.925132i	0.997386	−	0.0722542i	$-0.0230193\pi$
$673$	24.0000	+	24.0000i	0.925132	+	0.925132i	−0.0722542	+	0.997386i	$0.523019\pi$
$674$		−	16.0000i		−	0.616297i
$675$		0			0
$676$		0			0
$677$	14.2302	+	14.2302i	0.546913	+	0.546913i	0.925547	−	0.378634i	$-0.123606\pi$
$677$	14.2302	+	14.2302i	0.546913	+	0.546913i	−0.378634	+	0.925547i	$0.623606\pi$
$678$	37.9473	−	37.9473i	1.45736	−	1.45736i
$679$	−3.16228	+	5.00000i	−0.121357	+	0.191882i
$680$		0			0
$681$	−5.00000			−0.191600
$682$	−3.16228	−	3.16228i	−0.121090	−	0.121090i
$683$	−32.0000	−	32.0000i	−1.22445	−	1.22445i	−0.966035	−	0.258411i	$-0.916801\pi$
$683$	−32.0000	−	32.0000i	−1.22445	−	1.22445i	−0.258411	−	0.966035i	$-0.583199\pi$
$684$		0			0
$685$		0			0
$686$	−26.0000	−	3.16228i	−0.992685	−	0.120736i
$687$	−25.0000	+	25.0000i	−0.953809	+	0.953809i
$688$	12.0000	+	12.0000i	0.457496	+	0.457496i
$689$	−3.16228			−0.120473
$690$		0			0
$691$			31.6228i			1.20299i	0.798878	+	0.601494i	$0.205427\pi$
$691$			31.6228i			1.20299i	−0.798878	+	0.601494i	$0.794573\pi$
$692$		0			0
$693$	−5.16228	+	1.16228i	−0.196099	+	0.0441513i
$694$			48.0000i			1.82206i
$695$		0			0
$696$			18.9737i			0.719195i
$697$	−15.0000	+	15.0000i	−0.568166	+	0.568166i
$698$	34.7851	−	34.7851i	1.31663	−	1.31663i
$699$	−56.9210			−2.15295
$700$		0			0
$701$	−13.0000			−0.491003			−0.245502	−	0.969396i	$-0.578953\pi$
$701$	−13.0000			−0.491003			−0.245502	+	0.969396i	$0.578953\pi$
$702$	−5.00000	+	5.00000i	−0.188713	+	0.188713i
$703$	18.9737	−	18.9737i	0.715605	−	0.715605i
$704$		−	8.00000i		−	0.301511i
$705$		0			0
$706$			28.4605i			1.07113i
$707$	8.16228	−	1.83772i	0.306974	−	0.0691147i
$708$		0			0
$709$		−	9.00000i		−	0.338002i	−0.985616	−	0.169001i	$-0.945946\pi$
$709$		−	9.00000i		−	0.338002i	0.985616	−	0.169001i	$-0.0540541\pi$
$710$		0			0
$711$	−26.0000			−0.975076
$712$	−12.6491	−	12.6491i	−0.474045	−	0.474045i
$713$	6.32456	−	6.32456i	0.236856	−	0.236856i
$714$	15.8114	+	10.0000i	0.591726	+	0.374241i
$715$		0			0
$716$		0			0
$717$	30.0416	+	30.0416i	1.12193	+	1.12193i
$718$	22.0000	+	22.0000i	0.821033	+	0.821033i
$719$	31.6228			1.17933			0.589665	−	0.807648i	$-0.299260\pi$
$719$	31.6228			1.17933			0.589665	+	0.807648i	$0.299260\pi$
$720$		0			0
$721$	−35.0000	−	22.1359i	−1.30347	−	0.824386i
$722$	−9.00000	+	9.00000i	−0.334945	+	0.334945i
$723$	−40.0000	−	40.0000i	−1.48762	−	1.48762i
$724$		0			0
$725$		0			0
$726$		−	31.6228i		−	1.17363i
$727$	−9.48683	−	9.48683i	−0.351847	−	0.351847i	0.508949	−	0.860796i	$-0.330034\pi$
$727$	−9.48683	−	9.48683i	−0.351847	−	0.351847i	−0.860796	+	0.508949i	$0.830034\pi$
$728$	3.67544	+	16.3246i	0.136221	+	0.605028i
$729$		−	7.00000i		−	0.259259i
$730$		0			0
$731$		−	9.48683i		−	0.350883i
$732$		0			0
$733$	−17.3925	+	17.3925i	−0.642408	+	0.642408i	−0.951147	−	0.308739i	$-0.900093\pi$
$733$	−17.3925	+	17.3925i	−0.642408	+	0.642408i	0.308739	+	0.951147i	$0.400093\pi$
$734$	34.7851			1.28394
$735$		0			0
$736$		0			0
$737$	−1.00000	+	1.00000i	−0.0368355	+	0.0368355i
$738$	−18.9737	+	18.9737i	−0.698430	+	0.698430i
$739$			37.0000i			1.36107i	0.732717	+	0.680534i	$0.238252\pi$
$739$			37.0000i			1.36107i	−0.732717	+	0.680534i	$0.761748\pi$
$740$		0			0
$741$			15.8114i			0.580846i
$742$	−1.16228	−	5.16228i	−0.0426686	−	0.189513i
$743$	9.00000	+	9.00000i	0.330178	+	0.330178i	0.852654	−	0.522476i	$-0.174992\pi$
$743$	9.00000	+	9.00000i	0.330178	+	0.330178i	−0.522476	+	0.852654i	$0.674992\pi$
$744$		−	20.0000i		−	0.733236i
$745$		0			0
$746$	−24.0000			−0.878702
$747$	−6.32456	−	6.32456i	−0.231403	−	0.231403i
$748$		0			0
$749$	9.48683	+	6.00000i	0.346641	+	0.219235i
$750$		0			0
$751$	37.0000			1.35015			0.675075	−	0.737749i	$-0.264111\pi$
$751$	37.0000			1.35015			0.675075	+	0.737749i	$0.264111\pi$
$752$	18.9737	+	18.9737i	0.691898	+	0.691898i
$753$	−20.0000	−	20.0000i	−0.728841	−	0.728841i
$754$	−9.48683			−0.345490
$755$		0			0
$756$		0			0
$757$	16.0000	−	16.0000i	0.581530	−	0.581530i	−0.353794	−	0.935324i	$-0.615108\pi$
$757$	16.0000	−	16.0000i	0.581530	−	0.581530i	0.935324	+	0.353794i	$0.115108\pi$
$758$	−8.00000	−	8.00000i	−0.290573	−	0.290573i
$759$	−6.32456			−0.229567
$760$		0			0
$761$			25.2982i			0.917060i	0.888679	+	0.458530i	$0.151624\pi$
$761$			25.2982i			0.917060i	−0.888679	+	0.458530i	$0.848376\pi$
$762$	−28.4605	−	28.4605i	−1.03102	−	1.03102i
$763$	−18.0680	+	4.06797i	−0.654104	+	0.147270i
$764$		0			0
$765$		0			0
$766$		−	31.6228i		−	1.14258i
$767$	15.0000	−	15.0000i	0.541619	−	0.541619i
$768$		0			0
$769$	−22.1359			−0.798243			−0.399121	−	0.916898i	$-0.630685\pi$
$769$	−22.1359			−0.798243			−0.399121	+	0.916898i	$0.630685\pi$
$770$		0			0
$771$	40.0000			1.44056
$772$		0			0
$773$	36.3662	−	36.3662i	1.30800	−	1.30800i	0.385145	−	0.922856i	$-0.374151\pi$
$773$	36.3662	−	36.3662i	1.30800	−	1.30800i	0.922856	−	0.385145i	$-0.125849\pi$
$774$		−	12.0000i		−	0.431331i
$775$		0			0
$776$			6.32456i			0.227038i
$777$	−48.9737	+	11.0263i	−1.75692	+	0.395568i
$778$	−23.0000	−	23.0000i	−0.824590	−	0.824590i
$779$		−	30.0000i		−	1.07486i
$780$		0			0
$781$	6.00000			0.214697
$782$	6.32456	+	6.32456i	0.226166	+	0.226166i
$783$	−4.74342	+	4.74342i	−0.169516	+	0.169516i
$784$	−25.2982	+	12.0000i	−0.903508	+	0.428571i
$785$		0			0
$786$		0			0
$787$	−17.3925	−	17.3925i	−0.619977	−	0.619977i	0.325549	−	0.945525i	$-0.394451\pi$
$787$	−17.3925	−	17.3925i	−0.619977	−	0.619977i	−0.945525	+	0.325549i	$0.894451\pi$
$788$		0			0
$789$	22.1359			0.788060
$790$		0			0
$791$	24.0000	−	37.9473i	0.853342	−	1.34925i
$792$	−4.00000	+	4.00000i	−0.142134	+	0.142134i
$793$	10.0000	+	10.0000i	0.355110	+	0.355110i
$794$	47.4342			1.68338
$795$		0			0
$796$		0			0
$797$	−1.58114	−	1.58114i	−0.0560068	−	0.0560068i	0.678549	−	0.734555i	$-0.262609\pi$
$797$	−1.58114	−	1.58114i	−0.0560068	−	0.0560068i	−0.734555	+	0.678549i	$0.762609\pi$
$798$	−25.8114	+	5.81139i	−0.913713	+	0.205721i
$799$		−	15.0000i		−	0.530662i
$800$		0			0
$801$			12.6491i			0.446934i
$802$	−1.00000	+	1.00000i	−0.0353112	+	0.0353112i
$803$		0			0
$804$		0			0
$805$		0			0
$806$	10.0000			0.352235
$807$	30.0000	−	30.0000i	1.05605	−	1.05605i
$808$	6.32456	−	6.32456i	0.222497	−	0.222497i
$809$		−	3.00000i		−	0.105474i	−0.998608	−	0.0527372i	$-0.983205\pi$
$809$		−	3.00000i		−	0.105474i	0.998608	−	0.0527372i	$-0.0167946\pi$
$810$		0			0
$811$		−	37.9473i		−	1.33251i	−0.745724	−	0.666256i	$-0.767896\pi$
$811$		−	37.9473i		−	1.33251i	0.745724	−	0.666256i	$-0.232104\pi$
$812$		0			0
$813$	20.0000	+	20.0000i	0.701431	+	0.701431i
$814$			12.0000i			0.420600i
$815$		0			0
$816$	20.0000			0.700140
$817$	9.48683	+	9.48683i	0.331902	+	0.331902i
$818$	3.16228	−	3.16228i	0.110566	−	0.110566i
$819$	6.32456	−	10.0000i	0.220998	−	0.349428i
$820$		0			0
$821$	−23.0000			−0.802706			−0.401353	−	0.915924i	$-0.631460\pi$
$821$	−23.0000			−0.802706			−0.401353	+	0.915924i	$0.631460\pi$
$822$	−6.32456	−	6.32456i	−0.220594	−	0.220594i
$823$	3.00000	+	3.00000i	0.104573	+	0.104573i	0.757458	−	0.652884i	$-0.226441\pi$
$823$	3.00000	+	3.00000i	0.104573	+	0.104573i	−0.652884	+	0.757458i	$0.726441\pi$
$824$	−44.2719			−1.54228
$825$		0			0
$826$	30.0000	+	18.9737i	1.04383	+	0.660178i
$827$	26.0000	−	26.0000i	0.904109	−	0.904109i	−0.0916799	−	0.995789i	$-0.529224\pi$
$827$	26.0000	−	26.0000i	0.904109	−	0.904109i	0.995789	+	0.0916799i	$0.0292237\pi$
$828$		0			0
$829$	28.4605			0.988474			0.494237	−	0.869327i	$-0.335448\pi$
$829$	28.4605			0.988474			0.494237	+	0.869327i	$0.335448\pi$
$830$		0			0
$831$			56.9210i			1.97457i
$832$	12.6491	+	12.6491i	0.438529	+	0.438529i
$833$	14.7434	+	5.25658i	0.510829	+	0.182130i
$834$		−	60.0000i		−	2.07763i
$835$		0			0
$836$		0			0
$837$	5.00000	−	5.00000i	0.172825	−	0.172825i
$838$	−15.8114	+	15.8114i	−0.546195	+	0.546195i
$839$	50.5964			1.74678			0.873392	−	0.487019i	$-0.161916\pi$
$839$	50.5964			1.74678			0.873392	+	0.487019i	$0.161916\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	19.0000	−	19.0000i	0.654783	−	0.654783i
$843$	−14.2302	+	14.2302i	−0.490116	+	0.490116i
$844$		0			0
$845$		0			0
$846$		−	18.9737i		−	0.652328i
$847$	−5.81139	−	25.8114i	−0.199682	−	0.886890i
$848$	−4.00000	−	4.00000i	−0.137361	−	0.137361i
$849$			15.0000i			0.514799i
$850$		0			0
$851$	−24.0000			−0.822709
$852$		0			0
$853$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$853$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$854$	−12.6491	+	20.0000i	−0.432844	+	0.684386i
$855$		0			0
$856$	12.0000			0.410152
$857$	31.6228	+	31.6228i	1.08021	+	1.08021i	0.996489	+	0.0837245i	$0.0266816\pi$
$857$	31.6228	+	31.6228i	1.08021	+	1.08021i	0.0837245	+	0.996489i	$0.473318\pi$
$858$	−5.00000	−	5.00000i	−0.170697	−	0.170697i
$859$	12.6491			0.431582			0.215791	−	0.976440i	$-0.430767\pi$
$859$	12.6491			0.431582			0.215791	+	0.976440i	$0.430767\pi$
$860$		0			0
$861$	−30.0000	+	47.4342i	−1.02240	+	1.61655i
$862$	−23.0000	+	23.0000i	−0.783383	+	0.783383i
$863$	13.0000	+	13.0000i	0.442525	+	0.442525i	0.892860	−	0.450335i	$-0.148695\pi$
$863$	13.0000	+	13.0000i	0.442525	+	0.442525i	−0.450335	+	0.892860i	$0.648695\pi$
$864$		0			0
$865$		0			0
$866$			18.9737i			0.644751i
$867$	18.9737	+	18.9737i	0.644379	+	0.644379i
$868$		0			0
$869$			13.0000i			0.440995i
$870$		0			0
$871$		−	3.16228i		−	0.107150i
$872$	−14.0000	+	14.0000i	−0.474100	+	0.474100i
$873$	3.16228	−	3.16228i	0.107027	−	0.107027i
$874$	−12.6491			−0.427863
$875$		0			0
$876$		0			0
$877$	−17.0000	+	17.0000i	−0.574049	+	0.574049i	−0.933257	−	0.359208i	$-0.883047\pi$
$877$	−17.0000	+	17.0000i	−0.574049	+	0.574049i	0.359208	+	0.933257i	$0.383047\pi$
$878$	−12.6491	+	12.6491i	−0.426887	+	0.426887i
$879$			25.0000i			0.843229i
$880$		0			0
$881$			37.9473i			1.27848i	0.769008	+	0.639239i	$0.220751\pi$
$881$			37.9473i			1.27848i	−0.769008	+	0.639239i	$0.779249\pi$
$882$	18.6491	+	6.64911i	0.627948	+	0.223887i
$883$	18.0000	+	18.0000i	0.605748	+	0.605748i	0.941832	−	0.336084i	$-0.109103\pi$
$883$	18.0000	+	18.0000i	0.605748	+	0.605748i	−0.336084	+	0.941832i	$0.609103\pi$
$884$		0			0
$885$		0			0
$886$	−2.00000			−0.0671913
$887$	−3.16228	−	3.16228i	−0.106179	−	0.106179i	0.652022	−	0.758200i	$-0.273921\pi$
$887$	−3.16228	−	3.16228i	−0.106179	−	0.106179i	−0.758200	+	0.652022i	$0.773921\pi$
$888$	−37.9473	+	37.9473i	−1.27343	+	1.27343i
$889$	−28.4605	−	18.0000i	−0.954534	−	0.603701i
$890$		0			0
$891$	−11.0000			−0.368514
$892$		0			0
$893$	15.0000	+	15.0000i	0.501956	+	0.501956i
$894$	−37.9473			−1.26915
$895$		0			0
$896$	−16.0000	+	25.2982i	−0.534522	+	0.845154i
$897$	10.0000	−	10.0000i	0.333890	−	0.333890i
$898$	17.0000	+	17.0000i	0.567297	+	0.567297i
$899$	9.48683			0.316404
$900$		0			0
$901$			3.16228i			0.105351i
$902$	9.48683	+	9.48683i	0.315877	+	0.315877i
$903$	−5.51317	−	24.4868i	−0.183467	−	0.814871i
$904$		−	48.0000i		−	1.59646i
$905$		0			0
$906$			28.4605i			0.945537i
$907$	−22.0000	+	22.0000i	−0.730498	+	0.730498i	−0.970718	−	0.240220i	$-0.922780\pi$
$907$	−22.0000	+	22.0000i	−0.730498	+	0.730498i	0.240220	+	0.970718i	$0.422780\pi$
$908$		0			0
$909$	−6.32456			−0.209772
$910$		0			0
$911$	54.0000			1.78910			0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000			1.78910			0.894550	+	0.446968i	$0.147496\pi$
$912$	−20.0000	+	20.0000i	−0.662266	+	0.662266i
$913$	−3.16228	+	3.16228i	−0.104656	+	0.104656i
$914$		−	2.00000i		−	0.0661541i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	5.00000	+	5.00000i	0.165025	+	0.165025i
$919$			27.0000i			0.890648i	0.895370	+	0.445324i	$0.146911\pi$
$919$			27.0000i			0.890648i	−0.895370	+	0.445324i	$0.853089\pi$
$920$		0			0
$921$	−15.0000			−0.494267
$922$	−6.32456	−	6.32456i	−0.208288	−	0.208288i
$923$	−9.48683	+	9.48683i	−0.312263	+	0.312263i
$924$		0			0
$925$		0			0
$926$	8.00000			0.262896
$927$	22.1359	+	22.1359i	0.727040	+	0.727040i
$928$		0			0
$929$	3.16228			0.103751			0.0518755	−	0.998654i	$-0.483480\pi$
$929$	3.16228			0.103751			0.0518755	+	0.998654i	$0.483480\pi$
$930$		0			0
$931$	−20.0000	+	9.48683i	−0.655474	+	0.310918i
$932$		0			0
$933$	35.0000	+	35.0000i	1.14585	+	1.14585i
$934$	22.1359			0.724310
$935$		0			0
$936$		−	12.6491i		−	0.413449i
$937$	14.2302	+	14.2302i	0.464882	+	0.464882i	0.900252	−	0.435370i	$-0.143382\pi$
$937$	14.2302	+	14.2302i	0.464882	+	0.464882i	−0.435370	+	0.900252i	$0.643382\pi$
$938$	5.16228	−	1.16228i	0.168554	−	0.0379497i
$939$			45.0000i			1.46852i
$940$		0			0
$941$		−	37.9473i		−	1.23705i	−0.785766	−	0.618524i	$-0.787731\pi$
$941$		−	37.9473i		−	1.23705i	0.785766	−	0.618524i	$-0.212269\pi$
$942$	20.0000	−	20.0000i	0.651635	−	0.651635i
$943$	−18.9737	+	18.9737i	−0.617868	+	0.617868i
$944$	37.9473			1.23508
$945$		0			0
$946$	−6.00000			−0.195077
$947$	−7.00000	+	7.00000i	−0.227469	+	0.227469i	−0.811635	−	0.584165i	$-0.801422\pi$
$947$	−7.00000	+	7.00000i	−0.227469	+	0.227469i	0.584165	+	0.811635i	$0.301422\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		−	60.0833i		−	1.94833i
$952$	16.3246	−	3.67544i	0.529082	−	0.119122i
$953$	3.00000	+	3.00000i	0.0971795	+	0.0971795i	0.754025	−	0.656846i	$-0.228110\pi$
$953$	3.00000	+	3.00000i	0.0971795	+	0.0971795i	−0.656846	+	0.754025i	$0.728110\pi$
$954$			4.00000i			0.129505i
$955$		0			0
$956$		0			0
$957$	−4.74342	−	4.74342i	−0.153333	−	0.153333i
$958$	−6.32456	+	6.32456i	−0.204337	+	0.204337i
$959$	−6.32456	−	4.00000i	−0.204231	−	0.129167i
$960$		0			0
$961$	21.0000			0.677419
$962$	−18.9737	−	18.9737i	−0.611736	−	0.611736i
$963$	−6.00000	−	6.00000i	−0.193347	−	0.193347i
$964$		0			0
$965$		0			0
$966$	20.0000	+	12.6491i	0.643489	+	0.406978i
$967$	33.0000	−	33.0000i	1.06121	−	1.06121i	0.0632081	−	0.998000i	$-0.479867\pi$
$967$	33.0000	−	33.0000i	1.06121	−	1.06121i	0.998000	−	0.0632081i	$-0.0201332\pi$
$968$	−20.0000	−	20.0000i	−0.642824	−	0.642824i
$969$	15.8114			0.507935
$970$		0			0
$971$		−	34.7851i		−	1.11631i	−0.829738	−	0.558153i	$-0.811510\pi$
$971$		−	34.7851i		−	1.11631i	0.829738	−	0.558153i	$-0.188490\pi$
$972$		0			0
$973$	−11.0263	−	48.9737i	−0.353488	−	1.57002i
$974$			8.00000i			0.256337i
$975$		0			0
$976$			25.2982i			0.809776i
$977$	1.00000	−	1.00000i	0.0319928	−	0.0319928i	−0.690929	−	0.722922i	$-0.742798\pi$
$977$	1.00000	−	1.00000i	0.0319928	−	0.0319928i	0.722922	+	0.690929i	$0.242798\pi$
$978$	18.9737	−	18.9737i	0.606711	−	0.606711i
$979$	6.32456			0.202134
$980$		0			0
$981$	14.0000			0.446986
$982$	−41.0000	+	41.0000i	−1.30836	+	1.30836i
$983$	20.5548	−	20.5548i	0.655596	−	0.655596i	−0.298739	−	0.954335i	$-0.596566\pi$
$983$	20.5548	−	20.5548i	0.655596	−	0.655596i	0.954335	+	0.298739i	$0.0965658\pi$
$984$			60.0000i			1.91273i
$985$		0			0
$986$			9.48683i			0.302122i
$987$	−8.71708	−	38.7171i	−0.277468	−	1.23238i
$988$		0			0
$989$		−	12.0000i		−	0.381578i
$990$		0			0
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$		0			0
$993$	9.48683	−	9.48683i	0.301056	−	0.301056i
$994$	−18.9737	−	12.0000i	−0.601808	−	0.380617i
$995$		0			0
$996$		0			0
$997$	−14.2302	−	14.2302i	−0.450677	−	0.450677i	0.444902	−	0.895579i	$-0.353238\pi$
$997$	−14.2302	−	14.2302i	−0.450677	−	0.450677i	−0.895579	+	0.444902i	$0.853238\pi$
$998$	−19.0000	−	19.0000i	−0.601434	−	0.601434i
$999$	−18.9737			−0.600300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.f.c.118.1		4
5.2	odd	4	inner	175.2.f.c.132.2		4
5.3	odd	4		35.2.f.a.27.1	yes	4
5.4	even	2		35.2.f.a.13.2	yes	4
7.6	odd	2	inner	175.2.f.c.118.2		4
15.8	even	4		315.2.p.c.307.1		4
15.14	odd	2		315.2.p.c.118.2		4
20.3	even	4		560.2.bj.a.97.2		4
20.19	odd	2		560.2.bj.a.433.1		4
35.3	even	12		245.2.l.c.117.2		8
35.4	even	6		245.2.l.c.68.1		8
35.9	even	6		245.2.l.c.178.2		8
35.13	even	4		35.2.f.a.27.2	yes	4
35.18	odd	12		245.2.l.c.117.1		8
35.19	odd	6		245.2.l.c.178.1		8
35.23	odd	12		245.2.l.c.227.2		8
35.24	odd	6		245.2.l.c.68.2		8
35.27	even	4	inner	175.2.f.c.132.1		4
35.33	even	12		245.2.l.c.227.1		8
35.34	odd	2		35.2.f.a.13.1	✓	4
105.83	odd	4		315.2.p.c.307.2		4
105.104	even	2		315.2.p.c.118.1		4
140.83	odd	4		560.2.bj.a.97.1		4
140.139	even	2		560.2.bj.a.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.f.a.13.1	✓	4	35.34	odd	2
35.2.f.a.13.2	yes	4	5.4	even	2
35.2.f.a.27.1	yes	4	5.3	odd	4
35.2.f.a.27.2	yes	4	35.13	even	4
175.2.f.c.118.1		4	1.1	even	1	trivial
175.2.f.c.118.2		4	7.6	odd	2	inner
175.2.f.c.132.1		4	35.27	even	4	inner
175.2.f.c.132.2		4	5.2	odd	4	inner
245.2.l.c.68.1		8	35.4	even	6
245.2.l.c.68.2		8	35.24	odd	6
245.2.l.c.117.1		8	35.18	odd	12
245.2.l.c.117.2		8	35.3	even	12
245.2.l.c.178.1		8	35.19	odd	6
245.2.l.c.178.2		8	35.9	even	6
245.2.l.c.227.1		8	35.33	even	12
245.2.l.c.227.2		8	35.23	odd	12
315.2.p.c.118.1		4	105.104	even	2
315.2.p.c.118.2		4	15.14	odd	2
315.2.p.c.307.1		4	15.8	even	4
315.2.p.c.307.2		4	105.83	odd	4
560.2.bj.a.97.1		4	140.83	odd	4
560.2.bj.a.97.2		4	20.3	even	4
560.2.bj.a.433.1		4	20.19	odd	2
560.2.bj.a.433.2		4	140.139	even	2

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.58114 + 1.58114i) q^{3} +3.16228i q^{6} +(0.581139 + 2.58114i) q^{7} +(2.00000 + 2.00000i) q^{8} -2.00000i q^{9} -1.00000 q^{11} +(1.58114 - 1.58114i) q^{13} +(3.16228 + 2.00000i) q^{14} +4.00000 q^{16} +(-1.58114 - 1.58114i) q^{17} +(-2.00000 - 2.00000i) q^{18} +3.16228 q^{19} +(-5.00000 - 3.16228i) q^{21} +(-1.00000 + 1.00000i) q^{22} +(-2.00000 - 2.00000i) q^{23} -6.32456 q^{24} -3.16228i q^{26} +(-1.58114 - 1.58114i) q^{27} -3.00000i q^{29} +3.16228i q^{31} +(1.58114 - 1.58114i) q^{33} -3.16228 q^{34} +(6.00000 - 6.00000i) q^{37} +(3.16228 - 3.16228i) q^{38} +5.00000i q^{39} -9.48683i q^{41} +(-8.16228 + 1.83772i) q^{42} +(3.00000 + 3.00000i) q^{43} -4.00000 q^{46} +(4.74342 + 4.74342i) q^{47} +(-6.32456 + 6.32456i) q^{48} +(-6.32456 + 3.00000i) q^{49} +5.00000 q^{51} +(-1.00000 - 1.00000i) q^{53} -3.16228 q^{54} +(-4.00000 + 6.32456i) q^{56} +(-5.00000 + 5.00000i) q^{57} +(-3.00000 - 3.00000i) q^{58} +9.48683 q^{59} +6.32456i q^{61} +(3.16228 + 3.16228i) q^{62} +(5.16228 - 1.16228i) q^{63} +8.00000i q^{64} -3.16228i q^{66} +(1.00000 - 1.00000i) q^{67} +6.32456 q^{69} -6.00000 q^{71} +(4.00000 - 4.00000i) q^{72} -12.0000i q^{74} +(-0.581139 - 2.58114i) q^{77} +(5.00000 + 5.00000i) q^{78} -13.0000i q^{79} +11.0000 q^{81} +(-9.48683 - 9.48683i) q^{82} +(3.16228 - 3.16228i) q^{83} +6.00000 q^{86} +(4.74342 + 4.74342i) q^{87} +(-2.00000 - 2.00000i) q^{88} -6.32456 q^{89} +(5.00000 + 3.16228i) q^{91} +(-5.00000 - 5.00000i) q^{93} +9.48683 q^{94} +(1.58114 + 1.58114i) q^{97} +(-3.32456 + 9.32456i) q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{7} + 8 q^{8} - 4 q^{11} + 16 q^{16} - 8 q^{18} - 20 q^{21} - 4 q^{22} - 8 q^{23} + 24 q^{37} - 20 q^{42} + 12 q^{43} - 16 q^{46} + 20 q^{51} - 4 q^{53} - 16 q^{56} - 20 q^{57} - 12 q^{58}+ \cdots + 12 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^7 + 8 * q^8 - 4 * q^11 + 16 * q^16 - 8 * q^18 - 20 * q^21 - 4 * q^22 - 8 * q^23 + 24 * q^37 - 20 * q^42 + 12 * q^43 - 16 * q^46 + 20 * q^51 - 4 * q^53 - 16 * q^56 - 20 * q^57 - 12 * q^58 + 8 * q^63 + 4 * q^67 - 24 * q^71 + 16 * q^72 + 4 * q^77 + 20 * q^78 + 44 * q^81 + 24 * q^86 - 8 * q^88 + 20 * q^91 - 20 * q^93 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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