LMFDB - Embedded newform 315.2.p.c.307.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(118,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 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("315.118"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.p (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.51528766367$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Root			$-1.58114 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	315.307
Dual form			315.2.p.c.118.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.58114 - 1.58114i) q^{5} +(2.58114 - 0.581139i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.16228i q^{10} +1.00000 q^{11} +(1.58114 + 1.58114i) q^{13} +(3.16228 + 2.00000i) q^{14} +4.00000 q^{16} +(1.58114 - 1.58114i) q^{17} -3.16228 q^{19} +(1.00000 + 1.00000i) q^{22} +(-2.00000 + 2.00000i) q^{23} +5.00000i q^{25} +3.16228i q^{26} -3.00000i q^{29} +3.16228i q^{31} +3.16228 q^{34} +(-5.00000 - 3.16228i) q^{35} +(-6.00000 - 6.00000i) q^{37} +(-3.16228 - 3.16228i) q^{38} -6.32456 q^{40} +9.48683i q^{41} +(-3.00000 + 3.00000i) q^{43} -4.00000 q^{46} +(-4.74342 + 4.74342i) q^{47} +(6.32456 - 3.00000i) q^{49} +(-5.00000 + 5.00000i) q^{50} +(-1.00000 + 1.00000i) q^{53} +(-1.58114 - 1.58114i) q^{55} +(4.00000 - 6.32456i) q^{56} +(3.00000 - 3.00000i) q^{58} +9.48683 q^{59} +6.32456i q^{61} +(-3.16228 + 3.16228i) q^{62} -8.00000i q^{64} -5.00000i q^{65} +(-1.00000 - 1.00000i) q^{67} +(-1.83772 - 8.16228i) q^{70} +6.00000 q^{71} -12.0000i q^{74} +(2.58114 - 0.581139i) q^{77} +13.0000i q^{79} +(-6.32456 - 6.32456i) q^{80} +(-9.48683 + 9.48683i) q^{82} +(-3.16228 - 3.16228i) q^{83} -5.00000 q^{85} -6.00000 q^{86} +(2.00000 - 2.00000i) q^{88} -6.32456 q^{89} +(5.00000 + 3.16228i) q^{91} -9.48683 q^{94} +(5.00000 + 5.00000i) q^{95} +(1.58114 - 1.58114i) q^{97} +(9.32456 + 3.32456i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{7} + 8 q^{8} + 4 q^{11} + 16 q^{16} + 4 q^{22} - 8 q^{23} - 20 q^{35} - 24 q^{37} - 12 q^{43} - 16 q^{46} - 20 q^{50} - 4 q^{53} + 16 q^{56} + 12 q^{58} - 4 q^{67} - 20 q^{70} + 24 q^{71}+ \cdots + 12 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^7 + 8 * q^8 + 4 * q^11 + 16 * q^16 + 4 * q^22 - 8 * q^23 - 20 * q^35 - 24 * q^37 - 12 * q^43 - 16 * q^46 - 20 * q^50 - 4 * q^53 + 16 * q^56 + 12 * q^58 - 4 * q^67 - 20 * q^70 + 24 * q^71 + 4 * q^77 - 20 * q^85 - 24 * q^86 + 8 * q^88 + 20 * q^91 + 20 * q^95 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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	0.965926	−	0.258819i	$-0.0833333\pi$
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.58114	−	1.58114i	−0.707107	−	0.707107i
$5$	−1.58114	−	1.58114i	−0.707107	−	0.707107i
$6$		0			0
$7$	2.58114	−	0.581139i	0.975579	−	0.219650i
$7$	2.58114	−	0.581139i	0.975579	−	0.219650i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$		−	3.16228i		−	1.00000i
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$		0			0
$13$	1.58114	+	1.58114i	0.438529	+	0.438529i	0.891517	−	0.452988i	$-0.149642\pi$
$13$	1.58114	+	1.58114i	0.438529	+	0.438529i	−0.452988	+	0.891517i	$0.649642\pi$
$14$	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	$-0.662592\pi$
$17$	1.58114	−	1.58114i	0.383482	−	0.383482i	0.872355	+	0.488873i	$0.162592\pi$
$18$		0			0
$19$	−3.16228			−0.725476			−0.362738	−	0.931891i	$-0.618158\pi$
$19$	−3.16228			−0.725476			−0.362738	+	0.931891i	$0.618158\pi$
$20$		0			0
$21$		0			0
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	−2.00000	+	2.00000i	−0.417029	+	0.417029i	−0.884178	−	0.467150i	$-0.845281\pi$
$23$	−2.00000	+	2.00000i	−0.417029	+	0.417029i	0.467150	+	0.884178i	$0.345281\pi$
$24$		0			0
$25$			5.00000i			1.00000i
$26$			3.16228i			0.620174i
$27$		0			0
$28$		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
$33$		0			0
$34$	3.16228			0.542326
$35$	−5.00000	−	3.16228i	−0.845154	−	0.534522i
$36$		0			0
$37$	−6.00000	−	6.00000i	−0.986394	−	0.986394i	0.0135147	−	0.999909i	$-0.495698\pi$
$37$	−6.00000	−	6.00000i	−0.986394	−	0.986394i	−0.999909	+	0.0135147i	$0.995698\pi$
$38$	−3.16228	−	3.16228i	−0.512989	−	0.512989i
$39$		0			0
$40$	−6.32456			−1.00000
$41$			9.48683i			1.48159i	0.671729	+	0.740797i	$0.265552\pi$
$41$			9.48683i			1.48159i	−0.671729	+	0.740797i	$0.734448\pi$
$42$		0			0
$43$	−3.00000	+	3.00000i	−0.457496	+	0.457496i	−0.897833	−	0.440337i	$-0.854859\pi$
$43$	−3.00000	+	3.00000i	−0.457496	+	0.457496i	0.440337	+	0.897833i	$0.354859\pi$
$44$		0			0
$45$		0			0
$46$	−4.00000			−0.589768
$47$	−4.74342	+	4.74342i	−0.691898	+	0.691898i	−0.962649	−	0.270751i	$-0.912728\pi$
$47$	−4.74342	+	4.74342i	−0.691898	+	0.691898i	0.270751	+	0.962649i	$0.412728\pi$
$48$		0			0
$49$	6.32456	−	3.00000i	0.903508	−	0.428571i
$50$	−5.00000	+	5.00000i	−0.707107	+	0.707107i
$51$		0			0
$52$		0			0
$53$	−1.00000	+	1.00000i	−0.137361	+	0.137361i	−0.772444	−	0.635083i	$-0.780966\pi$
$53$	−1.00000	+	1.00000i	−0.137361	+	0.137361i	0.635083	+	0.772444i	$0.280966\pi$
$54$		0			0
$55$	−1.58114	−	1.58114i	−0.213201	−	0.213201i
$56$	4.00000	−	6.32456i	0.534522	−	0.845154i
$57$		0			0
$58$	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
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$		−	5.00000i		−	0.620174i
$66$		0			0
$67$	−1.00000	−	1.00000i	−0.122169	−	0.122169i	0.643379	−	0.765548i	$-0.277532\pi$
$67$	−1.00000	−	1.00000i	−0.122169	−	0.122169i	−0.765548	+	0.643379i	$0.777532\pi$
$68$		0			0
$69$		0			0
$70$	−1.83772	−	8.16228i	−0.219650	−	0.975579i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$73$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$74$		−	12.0000i		−	1.39497i
$75$		0			0
$76$		0			0
$77$	2.58114	−	0.581139i	0.294148	−	0.0662269i
$78$		0			0
$79$			13.0000i			1.46261i	0.682048	+	0.731307i	$0.261089\pi$
$79$			13.0000i			1.46261i	−0.682048	+	0.731307i	$0.738911\pi$
$80$	−6.32456	−	6.32456i	−0.707107	−	0.707107i
$81$		0			0
$82$	−9.48683	+	9.48683i	−1.04765	+	1.04765i
$83$	−3.16228	−	3.16228i	−0.347105	−	0.347105i	0.511925	−	0.859030i	$-0.328933\pi$
$83$	−3.16228	−	3.16228i	−0.347105	−	0.347105i	−0.859030	+	0.511925i	$0.828933\pi$
$84$		0			0
$85$	−5.00000			−0.542326
$86$	−6.00000			−0.646997
$87$		0			0
$88$	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
$93$		0			0
$94$	−9.48683			−0.978492
$95$	5.00000	+	5.00000i	0.512989	+	0.512989i
$96$		0			0
$97$	1.58114	−	1.58114i	0.160540	−	0.160540i	−0.622266	−	0.782806i	$-0.713788\pi$
$97$	1.58114	−	1.58114i	0.160540	−	0.160540i	0.782806	+	0.622266i	$0.213788\pi$
$98$	9.32456	+	3.32456i	0.941922	+	0.335831i
$99$		0			0
$100$		0			0
$101$			3.16228i			0.314658i	0.987546	+	0.157329i	$0.0502884\pi$
$101$			3.16228i			0.314658i	−0.987546	+	0.157329i	$0.949712\pi$
$102$		0			0
$103$	−11.0680	−	11.0680i	−1.09056	−	1.09056i	−0.995469	−	0.0950911i	$-0.969686\pi$
$103$	−11.0680	−	11.0680i	−1.09056	−	1.09056i	−0.0950911	−	0.995469i	$-0.530314\pi$
$104$	6.32456			0.620174
$105$		0			0
$106$	−2.00000			−0.194257
$107$	3.00000	+	3.00000i	0.290021	+	0.290021i	0.837088	−	0.547068i	$-0.184256\pi$
$107$	3.00000	+	3.00000i	0.290021	+	0.290021i	−0.547068	+	0.837088i	$0.684256\pi$
$108$		0			0
$109$		−	7.00000i		−	0.670478i	−0.942133	−	0.335239i	$-0.891183\pi$
$109$		−	7.00000i		−	0.670478i	0.942133	−	0.335239i	$-0.108817\pi$
$110$		−	3.16228i		−	0.301511i
$111$		0			0
$112$	10.3246	−	2.32456i	0.975579	−	0.219650i
$113$	−12.0000	+	12.0000i	−1.12887	+	1.12887i	−0.138503	+	0.990362i	$0.544229\pi$
$113$	−12.0000	+	12.0000i	−1.12887	+	1.12887i	−0.990362	+	0.138503i	$0.955771\pi$
$114$		0			0
$115$	6.32456			0.589768
$116$		0			0
$117$		0			0
$118$	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
$123$		0			0
$124$		0			0
$125$	7.90569	−	7.90569i	0.707107	−	0.707107i
$126$		0			0
$127$	9.00000	+	9.00000i	0.798621	+	0.798621i	0.982878	−	0.184257i	$-0.0589879\pi$
$127$	9.00000	+	9.00000i	0.798621	+	0.798621i	−0.184257	+	0.982878i	$0.558988\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$		0			0
$130$	5.00000	−	5.00000i	0.438529	−	0.438529i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$	−8.16228	+	1.83772i	−0.707759	+	0.159351i
$134$		−	2.00000i		−	0.172774i
$135$		0			0
$136$		−	6.32456i		−	0.542326i
$137$	−2.00000	−	2.00000i	−0.170872	−	0.170872i	0.616491	−	0.787362i	$-0.288554\pi$
$137$	−2.00000	−	2.00000i	−0.170872	−	0.170872i	−0.787362	+	0.616491i	$0.788554\pi$
$138$		0			0
$139$	18.9737			1.60933			0.804663	−	0.593732i	$-0.202346\pi$
$139$	18.9737			1.60933			0.804663	+	0.593732i	$0.202346\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	+	6.00000i	0.503509	+	0.503509i
$143$	1.58114	+	1.58114i	0.132221	+	0.132221i
$144$		0			0
$145$	−4.74342	+	4.74342i	−0.393919	+	0.393919i
$146$		0			0
$147$		0			0
$148$		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
$153$		0			0
$154$	3.16228	+	2.00000i	0.254824	+	0.161165i
$155$	5.00000	−	5.00000i	0.401610	−	0.401610i
$156$		0			0
$157$	−6.32456	+	6.32456i	−0.504754	+	0.504754i	−0.912912	−	0.408157i	$-0.866172\pi$
$157$	−6.32456	+	6.32456i	−0.504754	+	0.504754i	0.408157	+	0.912912i	$0.366172\pi$
$158$	−13.0000	+	13.0000i	−1.03422	+	1.03422i
$159$		0			0
$160$		0			0
$161$	−4.00000	+	6.32456i	−0.315244	+	0.498445i
$162$		0			0
$163$	6.00000	−	6.00000i	0.469956	−	0.469956i	−0.431944	−	0.901900i	$-0.642172\pi$
$163$	6.00000	−	6.00000i	0.469956	−	0.469956i	0.901900	+	0.431944i	$0.142172\pi$
$164$		0			0
$165$		0			0
$166$		−	6.32456i		−	0.490881i
$167$	11.0680	−	11.0680i	0.856465	−	0.856465i	−0.134454	−	0.990920i	$-0.542928\pi$
$167$	11.0680	−	11.0680i	0.856465	−	0.856465i	0.990920	+	0.134454i	$0.0429282\pi$
$168$		0			0
$169$		−	8.00000i		−	0.615385i
$170$	−5.00000	−	5.00000i	−0.383482	−	0.383482i
$171$		0			0
$172$		0			0
$173$	−11.0680	−	11.0680i	−0.841482	−	0.841482i	0.147569	−	0.989052i	$-0.452855\pi$
$173$	−11.0680	−	11.0680i	−0.841482	−	0.841482i	−0.989052	+	0.147569i	$0.952855\pi$
$174$		0			0
$175$	2.90569	+	12.9057i	0.219650	+	0.975579i
$176$	4.00000			0.301511
$177$		0			0
$178$	−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	$-0.307520\pi$
$182$	1.83772	+	8.16228i	0.136221	+	0.605028i
$183$		0			0
$184$			8.00000i			0.589768i
$185$			18.9737i			1.39497i
$186$		0			0
$187$	1.58114	−	1.58114i	0.115624	−	0.115624i
$188$		0			0
$189$		0			0
$190$			10.0000i			0.725476i
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$		0			0
$193$	−8.00000	+	8.00000i	−0.575853	+	0.575853i	−0.933758	−	0.357905i	$-0.883491\pi$
$193$	−8.00000	+	8.00000i	−0.575853	+	0.575853i	0.357905	+	0.933758i	$0.383491\pi$
$194$	3.16228			0.227038
$195$		0			0
$196$		0			0
$197$	1.00000	+	1.00000i	0.0712470	+	0.0712470i	0.741832	−	0.670585i	$-0.233957\pi$
$197$	1.00000	+	1.00000i	0.0712470	+	0.0712470i	−0.670585	+	0.741832i	$0.733957\pi$
$198$		0			0
$199$	9.48683			0.672504			0.336252	−	0.941772i	$-0.390841\pi$
$199$	9.48683			0.672504			0.336252	+	0.941772i	$0.390841\pi$
$200$	10.0000	+	10.0000i	0.707107	+	0.707107i
$201$		0			0
$202$	−3.16228	+	3.16228i	−0.222497	+	0.222497i
$203$	−1.74342	−	7.74342i	−0.122364	−	0.543481i
$204$		0			0
$205$	15.0000	−	15.0000i	1.04765	−	1.04765i
$206$		−	22.1359i		−	1.54228i
$207$		0			0
$208$	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
$213$		0			0
$214$			6.00000i			0.410152i
$215$	9.48683			0.646997
$216$		0			0
$217$	1.83772	+	8.16228i	0.124753	+	0.554092i
$218$	7.00000	−	7.00000i	0.474100	−	0.474100i
$219$		0			0
$220$		0			0
$221$	5.00000			0.336336
$222$		0			0
$223$	−14.2302	−	14.2302i	−0.952928	−	0.952928i	0.0460129	−	0.998941i	$-0.485348\pi$
$223$	−14.2302	−	14.2302i	−0.952928	−	0.952928i	−0.998941	+	0.0460129i	$0.985348\pi$
$224$		0			0
$225$		0			0
$226$	−24.0000			−1.59646
$227$	−1.58114	+	1.58114i	−0.104944	+	0.104944i	−0.757629	−	0.652685i	$-0.773642\pi$
$227$	−1.58114	+	1.58114i	−0.104944	+	0.104944i	0.652685	+	0.757629i	$0.273642\pi$
$228$		0			0
$229$	−15.8114			−1.04485			−0.522423	−	0.852686i	$-0.674972\pi$
$229$	−15.8114			−1.04485			−0.522423	+	0.852686i	$0.674972\pi$
$230$	6.32456	+	6.32456i	0.417029	+	0.417029i
$231$		0			0
$232$	−6.00000	−	6.00000i	−0.393919	−	0.393919i
$233$	18.0000	−	18.0000i	1.17922	−	1.17922i	0.199276	−	0.979943i	$-0.436141\pi$
$233$	18.0000	−	18.0000i	1.17922	−	1.17922i	0.979943	−	0.199276i	$-0.0638589\pi$
$234$		0			0
$235$	15.0000			0.978492
$236$		0			0
$237$		0			0
$238$	8.16228	−	1.83772i	0.529082	−	0.119122i
$239$		−	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
$243$		0			0
$244$		0			0
$245$	−14.7434	−	5.25658i	−0.941922	−	0.335831i
$246$		0			0
$247$	−5.00000	−	5.00000i	−0.318142	−	0.318142i
$248$	6.32456	+	6.32456i	0.401610	+	0.401610i
$249$		0			0
$250$	15.8114			1.00000
$251$		−	12.6491i		−	0.798405i	−0.916863	−	0.399202i	$-0.869287\pi$
$251$		−	12.6491i		−	0.798405i	0.916863	−	0.399202i	$-0.130713\pi$
$252$		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	$-0.561596\pi$
$257$	12.6491	−	12.6491i	0.789030	−	0.789030i	0.981335	+	0.192305i	$0.0615964\pi$
$258$		0			0
$259$	−18.9737	−	12.0000i	−1.17897	−	0.745644i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−7.00000	+	7.00000i	−0.431638	+	0.431638i	−0.889185	−	0.457547i	$-0.848728\pi$
$263$	−7.00000	+	7.00000i	−0.431638	+	0.431638i	0.457547	+	0.889185i	$0.348728\pi$
$264$		0			0
$265$	3.16228			0.194257
$266$	−10.0000	−	6.32456i	−0.613139	−	0.387783i
$267$		0			0
$268$		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
$273$		0			0
$274$		−	4.00000i		−	0.241649i
$275$			5.00000i			0.301511i
$276$		0			0
$277$	−18.0000	−	18.0000i	−1.08152	−	1.08152i	−0.996368	−	0.0851468i	$-0.972864\pi$
$277$	−18.0000	−	18.0000i	−1.08152	−	1.08152i	−0.0851468	−	0.996368i	$-0.527136\pi$
$278$	18.9737	+	18.9737i	1.13796	+	1.13796i
$279$		0			0
$280$	−16.3246	+	3.67544i	−0.975579	+	0.219650i
$281$	−9.00000			−0.536895			−0.268447	−	0.963294i	$-0.586511\pi$
$281$	−9.00000			−0.536895			−0.268447	+	0.963294i	$0.586511\pi$
$282$		0			0
$283$	4.74342	+	4.74342i	0.281967	+	0.281967i	0.833893	−	0.551926i	$-0.186107\pi$
$283$	4.74342	+	4.74342i	0.281967	+	0.281967i	−0.551926	+	0.833893i	$0.686107\pi$
$284$		0			0
$285$		0			0
$286$			3.16228i			0.186989i
$287$	5.51317	+	24.4868i	0.325432	+	1.44541i
$288$		0			0
$289$			12.0000i			0.705882i
$290$	−9.48683			−0.557086
$291$		0			0
$292$		0			0
$293$	−7.90569	−	7.90569i	−0.461856	−	0.461856i	0.437408	−	0.899263i	$-0.355897\pi$
$293$	−7.90569	−	7.90569i	−0.461856	−	0.461856i	−0.899263	+	0.437408i	$0.855897\pi$
$294$		0			0
$295$	−15.0000	−	15.0000i	−0.873334	−	0.873334i
$296$	−24.0000			−1.39497
$297$		0			0
$298$	−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
$303$		0			0
$304$	−12.6491			−0.725476
$305$	10.0000	−	10.0000i	0.572598	−	0.572598i
$306$		0			0
$307$	4.74342	−	4.74342i	0.270721	−	0.270721i	−0.558669	−	0.829390i	$-0.688688\pi$
$307$	4.74342	−	4.74342i	0.270721	−	0.270721i	0.829390	+	0.558669i	$0.188688\pi$
$308$		0			0
$309$		0			0
$310$	10.0000			0.567962
$311$			22.1359i			1.25521i	0.778530	+	0.627607i	$0.215966\pi$
$311$			22.1359i			1.25521i	−0.778530	+	0.627607i	$0.784034\pi$
$312$		0			0
$313$	14.2302	+	14.2302i	0.804341	+	0.804341i	0.983771	−	0.179430i	$-0.0574252\pi$
$313$	14.2302	+	14.2302i	0.804341	+	0.804341i	−0.179430	+	0.983771i	$0.557425\pi$
$314$	−12.6491			−0.713831
$315$		0			0
$316$		0			0
$317$	−19.0000	−	19.0000i	−1.06715	−	1.06715i	−0.997577	−	0.0695692i	$-0.977838\pi$
$317$	−19.0000	−	19.0000i	−1.06715	−	1.06715i	−0.0695692	−	0.997577i	$-0.522162\pi$
$318$		0			0
$319$		−	3.00000i		−	0.167968i
$320$	−12.6491	+	12.6491i	−0.707107	+	0.707107i
$321$		0			0
$322$	−10.3246	+	2.32456i	−0.575365	+	0.129542i
$323$	−5.00000	+	5.00000i	−0.278207	+	0.278207i
$324$		0			0
$325$	−7.90569	+	7.90569i	−0.438529	+	0.438529i
$326$	12.0000			0.664619
$327$		0			0
$328$	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
$333$		0			0
$334$	22.1359			1.21122
$335$			3.16228i			0.172774i
$336$		0			0
$337$	−8.00000	−	8.00000i	−0.435788	−	0.435788i	0.454804	−	0.890592i	$-0.349709\pi$
$337$	−8.00000	−	8.00000i	−0.435788	−	0.435788i	−0.890592	+	0.454804i	$0.849709\pi$
$338$	8.00000	−	8.00000i	0.435143	−	0.435143i
$339$		0			0
$340$		0			0
$341$			3.16228i			0.171247i
$342$		0			0
$343$	14.5811	−	11.4189i	0.787307	−	0.616561i
$344$			12.0000i			0.646997i
$345$		0			0
$346$		−	22.1359i		−	1.19004i
$347$	−24.0000	−	24.0000i	−1.28839	−	1.28839i	−0.935766	−	0.352621i	$-0.885290\pi$
$347$	−24.0000	−	24.0000i	−1.28839	−	1.28839i	−0.352621	−	0.935766i	$-0.614710\pi$
$348$		0			0
$349$	−34.7851			−1.86200			−0.931001	−	0.365018i	$-0.881063\pi$
$349$	−34.7851			−1.86200			−0.931001	+	0.365018i	$0.881063\pi$
$350$	−10.0000	+	15.8114i	−0.534522	+	0.845154i
$351$		0			0
$352$		0			0
$353$	14.2302	+	14.2302i	0.757400	+	0.757400i	0.975848	−	0.218449i	$-0.0700996\pi$
$353$	14.2302	+	14.2302i	0.757400	+	0.757400i	−0.218449	+	0.975848i	$0.570100\pi$
$354$		0			0
$355$	−9.48683	−	9.48683i	−0.503509	−	0.503509i
$356$		0			0
$357$		0			0
$358$	−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
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	17.3925	−	17.3925i	0.907883	−	0.907883i	−0.0882186	−	0.996101i	$-0.528117\pi$
$367$	17.3925	−	17.3925i	0.907883	−	0.907883i	0.996101	+	0.0882186i	$0.0281174\pi$
$368$	−8.00000	+	8.00000i	−0.417029	+	0.417029i
$369$		0			0
$370$	−18.9737	+	18.9737i	−0.986394	+	0.986394i
$371$	−2.00000	+	3.16228i	−0.103835	+	0.164177i
$372$		0			0
$373$	12.0000	−	12.0000i	0.621336	−	0.621336i	−0.324537	−	0.945873i	$-0.605208\pi$
$373$	12.0000	−	12.0000i	0.621336	−	0.621336i	0.945873	+	0.324537i	$0.105208\pi$
$374$	3.16228			0.163517
$375$		0			0
$376$			18.9737i			0.978492i
$377$	4.74342	−	4.74342i	0.244298	−	0.244298i
$378$		0			0
$379$			8.00000i			0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$			8.00000i			0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$		0			0
$381$		0			0
$382$	3.00000	+	3.00000i	0.153493	+	0.153493i
$383$	−15.8114	−	15.8114i	−0.807924	−	0.807924i	0.176395	−	0.984319i	$-0.443556\pi$
$383$	−15.8114	−	15.8114i	−0.807924	−	0.807924i	−0.984319	+	0.176395i	$0.943556\pi$
$384$		0			0
$385$	−5.00000	−	3.16228i	−0.254824	−	0.161165i
$386$	−16.0000			−0.814379
$387$		0			0
$388$		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
$392$	6.64911	−	18.6491i	0.335831	−	0.941922i
$393$		0			0
$394$			2.00000i			0.100759i
$395$	20.5548	−	20.5548i	1.03422	−	1.03422i
$396$		0			0
$397$	23.7171	−	23.7171i	1.19033	−	1.19033i	0.213351	−	0.976976i	$-0.431562\pi$
$397$	23.7171	−	23.7171i	1.19033	−	1.19033i	0.976976	−	0.213351i	$-0.0684376\pi$
$398$	9.48683	+	9.48683i	0.475532	+	0.475532i
$399$		0			0
$400$			20.0000i			1.00000i
$401$	1.00000			0.0499376			0.0249688	−	0.999688i	$-0.492051\pi$
$401$	1.00000			0.0499376			0.0249688	+	0.999688i	$0.492051\pi$
$402$		0			0
$403$	−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
$408$		0			0
$409$	−3.16228			−0.156365			−0.0781823	−	0.996939i	$-0.524912\pi$
$409$	−3.16228			−0.156365			−0.0781823	+	0.996939i	$0.524912\pi$
$410$	30.0000			1.48159
$411$		0			0
$412$		0			0
$413$	24.4868	−	5.51317i	1.20492	−	0.271285i
$414$		0			0
$415$			10.0000i			0.490881i
$416$		0			0
$417$		0			0
$418$	−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
$423$		0			0
$424$			4.00000i			0.194257i
$425$	7.90569	+	7.90569i	0.383482	+	0.383482i
$426$		0			0
$427$	3.67544	+	16.3246i	0.177867	+	0.790001i
$428$		0			0
$429$		0			0
$430$	9.48683	+	9.48683i	0.457496	+	0.457496i
$431$	23.0000			1.10787			0.553936	−	0.832560i	$-0.313125\pi$
$431$	23.0000			1.10787			0.553936	+	0.832560i	$0.313125\pi$
$432$		0			0
$433$	−9.48683	−	9.48683i	−0.455908	−	0.455908i	0.441402	−	0.897310i	$-0.354481\pi$
$433$	−9.48683	−	9.48683i	−0.455908	−	0.455908i	−0.897310	+	0.441402i	$0.854481\pi$
$434$	−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	$-0.402394\pi$
$439$	12.6491			0.603709			0.301855	+	0.953354i	$0.402394\pi$
$440$	−6.32456			−0.301511
$441$		0			0
$442$	5.00000	+	5.00000i	0.237826	+	0.237826i
$443$	−1.00000	+	1.00000i	−0.0475114	+	0.0475114i	−0.730463	−	0.682952i	$-0.760696\pi$
$443$	−1.00000	+	1.00000i	−0.0475114	+	0.0475114i	0.682952	+	0.730463i	$0.260696\pi$
$444$		0			0
$445$	10.0000	+	10.0000i	0.474045	+	0.474045i
$446$		−	28.4605i		−	1.34764i
$447$		0			0
$448$	−4.64911	−	20.6491i	−0.219650	−	0.975579i
$449$			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
$453$		0			0
$454$	−3.16228			−0.148413
$455$	−2.90569	−	12.9057i	−0.136221	−	0.605028i
$456$		0			0
$457$	−1.00000	−	1.00000i	−0.0467780	−	0.0467780i	0.683331	−	0.730109i	$-0.260531\pi$
$457$	−1.00000	−	1.00000i	−0.0467780	−	0.0467780i	−0.730109	+	0.683331i	$0.760531\pi$
$458$	−15.8114	−	15.8114i	−0.738818	−	0.738818i
$459$		0			0
$460$		0			0
$461$			6.32456i			0.294564i	0.989095	+	0.147282i	$0.0470525\pi$
$461$			6.32456i			0.294564i	−0.989095	+	0.147282i	$0.952948\pi$
$462$		0			0
$463$	−4.00000	+	4.00000i	−0.185896	+	0.185896i	−0.793919	−	0.608023i	$-0.791963\pi$
$463$	−4.00000	+	4.00000i	−0.185896	+	0.185896i	0.608023	+	0.793919i	$0.291963\pi$
$464$		−	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	$-0.867959\pi$
$467$	−11.0680	+	11.0680i	−0.512165	+	0.512165i	0.403025	+	0.915189i	$0.367959\pi$
$468$		0			0
$469$	−3.16228	−	2.00000i	−0.146020	−	0.0923514i
$470$	15.0000	+	15.0000i	0.691898	+	0.691898i
$471$		0			0
$472$	18.9737	−	18.9737i	0.873334	−	0.873334i
$473$	−3.00000	+	3.00000i	−0.137940	+	0.137940i
$474$		0			0
$475$		−	15.8114i		−	0.725476i
$476$		0			0
$477$		0			0
$478$	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
$483$		0			0
$484$		0			0
$485$	−5.00000			−0.227038
$486$		0			0
$487$	4.00000	+	4.00000i	0.181257	+	0.181257i	0.791904	−	0.610646i	$-0.209090\pi$
$487$	4.00000	+	4.00000i	0.181257	+	0.181257i	−0.610646	+	0.791904i	$0.709090\pi$
$488$	12.6491	+	12.6491i	0.572598	+	0.572598i
$489$		0			0
$490$	−9.48683	−	20.0000i	−0.428571	−	0.903508i
$491$	41.0000			1.85030			0.925152	−	0.379597i	$-0.123937\pi$
$491$	41.0000			1.85030			0.925152	+	0.379597i	$0.123937\pi$
$492$		0			0
$493$	−4.74342	−	4.74342i	−0.213633	−	0.213633i
$494$		−	10.0000i		−	0.449921i
$495$		0			0
$496$			12.6491i			0.567962i
$497$	15.4868	−	3.48683i	0.694679	−	0.156406i
$498$		0			0
$499$			19.0000i			0.850557i	0.905063	+	0.425278i	$0.139824\pi$
$499$			19.0000i			0.850557i	−0.905063	+	0.425278i	$0.860176\pi$
$500$		0			0
$501$		0			0
$502$	12.6491	−	12.6491i	0.564557	−	0.564557i
$503$	7.90569	+	7.90569i	0.352497	+	0.352497i	0.861038	−	0.508541i	$-0.169815\pi$
$503$	7.90569	+	7.90569i	0.352497	+	0.352497i	−0.508541	+	0.861038i	$0.669815\pi$
$504$		0			0
$505$	5.00000	−	5.00000i	0.222497	−	0.222497i
$506$	−4.00000			−0.177822
$507$		0			0
$508$		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
$513$		0			0
$514$	25.2982			1.11586
$515$			35.0000i			1.54228i
$516$		0			0
$517$	−4.74342	+	4.74342i	−0.208615	+	0.208615i
$518$	−6.97367	−	30.9737i	−0.306405	−	1.36090i
$519$		0			0
$520$	−10.0000	−	10.0000i	−0.438529	−	0.438529i
$521$		−	41.1096i		−	1.80104i	−0.434810	−	0.900522i	$-0.643184\pi$
$521$		−	41.1096i		−	1.80104i	0.434810	−	0.900522i	$-0.356816\pi$
$522$		0			0
$523$	18.9737	+	18.9737i	0.829660	+	0.829660i	0.987470	−	0.157809i	$-0.0504431\pi$
$523$	18.9737	+	18.9737i	0.829660	+	0.829660i	−0.157809	+	0.987470i	$0.550443\pi$
$524$		0			0
$525$		0			0
$526$	−14.0000			−0.610429
$527$	5.00000	+	5.00000i	0.217803	+	0.217803i
$528$		0			0
$529$			15.0000i			0.652174i
$530$	3.16228	+	3.16228i	0.137361	+	0.137361i
$531$		0			0
$532$		0			0
$533$	−15.0000	+	15.0000i	−0.649722	+	0.649722i
$534$		0			0
$535$		−	9.48683i		−	0.410152i
$536$	−4.00000			−0.172774
$537$		0			0
$538$	−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
$543$		0			0
$544$		0			0
$545$	−11.0680	+	11.0680i	−0.474100	+	0.474100i
$546$		0			0
$547$	14.0000	+	14.0000i	0.598597	+	0.598597i	0.939939	−	0.341342i	$-0.110882\pi$
$547$	14.0000	+	14.0000i	0.598597	+	0.598597i	−0.341342	+	0.939939i	$0.610882\pi$
$548$		0			0
$549$		0			0
$550$	−5.00000	+	5.00000i	−0.213201	+	0.213201i
$551$			9.48683i			0.404153i
$552$		0			0
$553$	7.55480	+	33.5548i	0.321263	+	1.42690i
$554$		−	36.0000i		−	1.52949i
$555$		0			0
$556$		0			0
$557$	6.00000	+	6.00000i	0.254228	+	0.254228i	0.822702	−	0.568473i	$-0.192466\pi$
$557$	6.00000	+	6.00000i	0.254228	+	0.254228i	−0.568473	+	0.822702i	$0.692466\pi$
$558$		0			0
$559$	−9.48683			−0.401250
$560$	−20.0000	−	12.6491i	−0.845154	−	0.534522i
$561$		0			0
$562$	−9.00000	−	9.00000i	−0.379642	−	0.379642i
$563$	9.48683	+	9.48683i	0.399822	+	0.399822i	0.878170	−	0.478348i	$-0.158764\pi$
$563$	9.48683	+	9.48683i	0.399822	+	0.399822i	−0.478348	+	0.878170i	$0.658764\pi$
$564$		0			0
$565$	37.9473			1.59646
$566$			9.48683i			0.398761i
$567$		0			0
$568$	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
$573$		0			0
$574$	−18.9737	+	30.0000i	−0.791946	+	1.25218i
$575$	−10.0000	−	10.0000i	−0.417029	−	0.417029i
$576$		0			0
$577$	−20.5548	+	20.5548i	−0.855708	+	0.855708i	−0.990829	−	0.135121i	$-0.956858\pi$
$577$	−20.5548	+	20.5548i	−0.855708	+	0.855708i	0.135121	+	0.990829i	$0.456858\pi$
$578$	−12.0000	+	12.0000i	−0.499134	+	0.499134i
$579$		0			0
$580$		0			0
$581$	−10.0000	−	6.32456i	−0.414870	−	0.262387i
$582$		0			0
$583$	−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	$-0.902675\pi$
$587$	−15.8114	+	15.8114i	−0.652606	+	0.652606i	0.301014	+	0.953620i	$0.402675\pi$
$588$		0			0
$589$		−	10.0000i		−	0.412043i
$590$		−	30.0000i		−	1.23508i
$591$		0			0
$592$	−24.0000	−	24.0000i	−0.986394	−	0.986394i
$593$	20.5548	+	20.5548i	0.844085	+	0.844085i	0.989387	−	0.145303i	$-0.0464156\pi$
$593$	20.5548	+	20.5548i	0.844085	+	0.844085i	−0.145303	+	0.989387i	$0.546416\pi$
$594$		0			0
$595$	−12.9057	+	2.90569i	−0.529082	+	0.119122i
$596$		0			0
$597$		0			0
$598$	−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	$0.850899\pi$
$602$	−15.4868	+	3.48683i	−0.631196	+	0.142113i
$603$		0			0
$604$		0			0
$605$	15.8114	+	15.8114i	0.642824	+	0.642824i
$606$		0			0
$607$	−14.2302	+	14.2302i	−0.577588	+	0.577588i	−0.934238	−	0.356650i	$-0.883919\pi$
$607$	−14.2302	+	14.2302i	−0.577588	+	0.577588i	0.356650	+	0.934238i	$0.383919\pi$
$608$		0			0
$609$		0			0
$610$	20.0000			0.809776
$611$	−15.0000			−0.606835
$612$		0			0
$613$	17.0000	−	17.0000i	0.686624	−	0.686624i	−0.274861	−	0.961484i	$-0.588632\pi$
$613$	17.0000	−	17.0000i	0.686624	−	0.686624i	0.961484	+	0.274861i	$0.0886317\pi$
$614$	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	0.621991	−	0.783025i	$-0.286324\pi$
$617$	−4.00000	−	4.00000i	−0.161034	−	0.161034i	−0.783025	+	0.621991i	$0.786324\pi$
$618$		0			0
$619$	25.2982			1.01682			0.508411	−	0.861115i	$-0.330233\pi$
$619$	25.2982			1.01682			0.508411	+	0.861115i	$0.330233\pi$
$620$		0			0
$621$		0			0
$622$	−22.1359	+	22.1359i	−0.887570	+	0.887570i
$623$	−16.3246	+	3.67544i	−0.654029	+	0.147254i
$624$		0			0
$625$	−25.0000			−1.00000
$626$			28.4605i			1.13751i
$627$		0			0
$628$		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
$633$		0			0
$634$		−	38.0000i		−	1.50917i
$635$		−	28.4605i		−	1.12942i
$636$		0			0
$637$	14.7434	+	5.25658i	0.584155	+	0.208273i
$638$	3.00000	−	3.00000i	0.118771	−	0.118771i
$639$		0			0
$640$	−25.2982			−1.00000
$641$	−44.0000			−1.73790			−0.868948	−	0.494904i	$-0.835203\pi$
$641$	−44.0000			−1.73790			−0.868948	+	0.494904i	$0.835203\pi$
$642$		0			0
$643$	−4.74342	−	4.74342i	−0.187062	−	0.187062i	0.607363	−	0.794425i	$-0.292228\pi$
$643$	−4.74342	−	4.74342i	−0.187062	−	0.187062i	−0.794425	+	0.607363i	$0.792228\pi$
$644$		0			0
$645$		0			0
$646$	−10.0000			−0.393445
$647$	12.6491	−	12.6491i	0.497288	−	0.497288i	−0.413305	−	0.910593i	$-0.635626\pi$
$647$	12.6491	−	12.6491i	0.497288	−	0.497288i	0.910593	+	0.413305i	$0.135626\pi$
$648$		0			0
$649$	9.48683			0.372391
$650$	−15.8114			−0.620174
$651$		0			0
$652$		0			0
$653$	19.0000	−	19.0000i	0.743527	−	0.743527i	−0.229728	−	0.973255i	$-0.573784\pi$
$653$	19.0000	−	19.0000i	0.743527	−	0.743527i	0.973255	+	0.229728i	$0.0737835\pi$
$654$		0			0
$655$		0			0
$656$			37.9473i			1.48159i
$657$		0			0
$658$	−24.4868	+	5.51317i	−0.954596	+	0.214926i
$659$			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
$663$		0			0
$664$	−12.6491			−0.490881
$665$	15.8114	+	10.0000i	0.613139	+	0.387783i
$666$		0			0
$667$	6.00000	+	6.00000i	0.232321	+	0.232321i
$668$		0			0
$669$		0			0
$670$	−3.16228	+	3.16228i	−0.122169	+	0.122169i
$671$			6.32456i			0.244157i
$672$		0			0
$673$	−24.0000	+	24.0000i	−0.925132	+	0.925132i	−0.997386	−	0.0722542i	$-0.976981\pi$
$673$	−24.0000	+	24.0000i	−0.925132	+	0.925132i	0.0722542	+	0.997386i	$0.476981\pi$
$674$		−	16.0000i		−	0.616297i
$675$		0			0
$676$		0			0
$677$	−14.2302	+	14.2302i	−0.546913	+	0.546913i	−0.925547	−	0.378634i	$-0.876394\pi$
$677$	−14.2302	+	14.2302i	−0.546913	+	0.546913i	0.378634	+	0.925547i	$0.376394\pi$
$678$		0			0
$679$	3.16228	−	5.00000i	0.121357	−	0.191882i
$680$	−10.0000	+	10.0000i	−0.383482	+	0.383482i
$681$		0			0
$682$	−3.16228	+	3.16228i	−0.121090	+	0.121090i
$683$	−32.0000	+	32.0000i	−1.22445	+	1.22445i	−0.258411	+	0.966035i	$0.583199\pi$
$683$	−32.0000	+	32.0000i	−1.22445	+	1.22445i	−0.966035	+	0.258411i	$0.916801\pi$
$684$		0			0
$685$			6.32456i			0.241649i
$686$	26.0000	+	3.16228i	0.992685	+	0.120736i
$687$		0			0
$688$	−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
$693$		0			0
$694$		−	48.0000i		−	1.82206i
$695$	−30.0000	−	30.0000i	−1.13796	−	1.13796i
$696$		0			0
$697$	15.0000	+	15.0000i	0.568166	+	0.568166i
$698$	−34.7851	−	34.7851i	−1.31663	−	1.31663i
$699$		0			0
$700$		0			0
$701$	13.0000			0.491003			0.245502	−	0.969396i	$-0.421047\pi$
$701$	13.0000			0.491003			0.245502	+	0.969396i	$0.421047\pi$
$702$		0			0
$703$	18.9737	+	18.9737i	0.715605	+	0.715605i
$704$		−	8.00000i		−	0.301511i
$705$		0			0
$706$			28.4605i			1.07113i
$707$	1.83772	+	8.16228i	0.0691147	+	0.306974i
$708$		0			0
$709$			9.00000i			0.338002i	0.985616	+	0.169001i	$0.0540541\pi$
$709$			9.00000i			0.338002i	−0.985616	+	0.169001i	$0.945946\pi$
$710$		−	18.9737i		−	0.712069i
$711$		0			0
$712$	−12.6491	+	12.6491i	−0.474045	+	0.474045i
$713$	−6.32456	−	6.32456i	−0.236856	−	0.236856i
$714$		0			0
$715$		−	5.00000i		−	0.186989i
$716$		0			0
$717$		0			0
$718$	−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
$723$		0			0
$724$		0			0
$725$	15.0000			0.557086
$726$		0			0
$727$	−9.48683	+	9.48683i	−0.351847	+	0.351847i	−0.860796	−	0.508949i	$-0.830034\pi$
$727$	−9.48683	+	9.48683i	−0.351847	+	0.351847i	0.508949	+	0.860796i	$0.330034\pi$
$728$	16.3246	−	3.67544i	0.605028	−	0.136221i
$729$		0			0
$730$		0			0
$731$			9.48683i			0.350883i
$732$		0			0
$733$	−17.3925	−	17.3925i	−0.642408	−	0.642408i	0.308739	−	0.951147i	$-0.400093\pi$
$733$	−17.3925	−	17.3925i	−0.642408	−	0.642408i	−0.951147	+	0.308739i	$0.900093\pi$
$734$	34.7851			1.28394
$735$		0			0
$736$		0			0
$737$	−1.00000	−	1.00000i	−0.0368355	−	0.0368355i
$738$		0			0
$739$		−	37.0000i		−	1.36107i	−0.732717	−	0.680534i	$-0.761748\pi$
$739$		−	37.0000i		−	1.36107i	0.732717	−	0.680534i	$-0.238252\pi$
$740$		0			0
$741$		0			0
$742$	−5.16228	+	1.16228i	−0.189513	+	0.0426686i
$743$	9.00000	−	9.00000i	0.330178	−	0.330178i	−0.522476	−	0.852654i	$-0.674992\pi$
$743$	9.00000	−	9.00000i	0.330178	−	0.330178i	0.852654	+	0.522476i	$0.174992\pi$
$744$		0			0
$745$	18.9737	−	18.9737i	0.695141	−	0.695141i
$746$	24.0000			0.878702
$747$		0			0
$748$		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
$753$		0			0
$754$	9.48683			0.345490
$755$	−14.2302	−	14.2302i	−0.517892	−	0.517892i
$756$		0			0
$757$	−16.0000	−	16.0000i	−0.581530	−	0.581530i	0.353794	−	0.935324i	$-0.384892\pi$
$757$	−16.0000	−	16.0000i	−0.581530	−	0.581530i	−0.935324	+	0.353794i	$0.884892\pi$
$758$	−8.00000	+	8.00000i	−0.290573	+	0.290573i
$759$		0			0
$760$	20.0000			0.725476
$761$		−	25.2982i		−	0.917060i	−0.888679	−	0.458530i	$-0.848376\pi$
$761$		−	25.2982i		−	0.917060i	0.888679	−	0.458530i	$-0.151624\pi$
$762$		0			0
$763$	−4.06797	−	18.0680i	−0.147270	−	0.654104i
$764$		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	$-0.369315\pi$
$769$	22.1359			0.798243			0.399121	+	0.916898i	$0.369315\pi$
$770$	−1.83772	−	8.16228i	−0.0662269	−	0.294148i
$771$		0			0
$772$		0			0
$773$	−36.3662	−	36.3662i	−1.30800	−	1.30800i	−0.922856	−	0.385145i	$-0.874151\pi$
$773$	−36.3662	−	36.3662i	−1.30800	−	1.30800i	−0.385145	−	0.922856i	$-0.625849\pi$
$774$		0			0
$775$	−15.8114			−0.567962
$776$		−	6.32456i		−	0.227038i
$777$		0			0
$778$	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
$783$		0			0
$784$	25.2982	−	12.0000i	0.903508	−	0.428571i
$785$	20.0000			0.713831
$786$		0			0
$787$	−17.3925	+	17.3925i	−0.619977	+	0.619977i	−0.945525	−	0.325549i	$-0.894451\pi$
$787$	−17.3925	+	17.3925i	−0.619977	+	0.619977i	0.325549	+	0.945525i	$0.394451\pi$
$788$		0			0
$789$		0			0
$790$	41.1096			1.46261
$791$	−24.0000	+	37.9473i	−0.853342	+	1.34925i
$792$		0			0
$793$	−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	$-0.737391\pi$
$797$	1.58114	−	1.58114i	0.0560068	−	0.0560068i	0.734555	+	0.678549i	$0.237391\pi$
$798$		0			0
$799$			15.0000i			0.530662i
$800$		0			0
$801$		0			0
$802$	1.00000	+	1.00000i	0.0353112	+	0.0353112i
$803$		0			0
$804$		0			0
$805$	16.3246	−	3.67544i	0.575365	−	0.129542i
$806$	−10.0000			−0.352235
$807$		0			0
$808$	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
$813$		0			0
$814$		−	12.0000i		−	0.420600i
$815$	−18.9737			−0.664619
$816$		0			0
$817$	9.48683	−	9.48683i	0.331902	−	0.331902i
$818$	−3.16228	−	3.16228i	−0.110566	−	0.110566i
$819$		0			0
$820$		0			0
$821$	23.0000			0.802706			0.401353	−	0.915924i	$-0.368540\pi$
$821$	23.0000			0.802706			0.401353	+	0.915924i	$0.368540\pi$
$822$		0			0
$823$	−3.00000	+	3.00000i	−0.104573	+	0.104573i	−0.757458	−	0.652884i	$-0.773559\pi$
$823$	−3.00000	+	3.00000i	−0.104573	+	0.104573i	0.652884	+	0.757458i	$0.273559\pi$
$824$	−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	0.995789	−	0.0916799i	$-0.0292237\pi$
$827$	26.0000	+	26.0000i	0.904109	+	0.904109i	−0.0916799	+	0.995789i	$0.529224\pi$
$828$		0			0
$829$	−28.4605			−0.988474			−0.494237	−	0.869327i	$-0.664552\pi$
$829$	−28.4605			−0.988474			−0.494237	+	0.869327i	$0.664552\pi$
$830$	−10.0000	+	10.0000i	−0.347105	+	0.347105i
$831$		0			0
$832$	12.6491	−	12.6491i	0.438529	−	0.438529i
$833$	5.25658	−	14.7434i	0.182130	−	0.510829i
$834$		0			0
$835$	−35.0000			−1.21122
$836$		0			0
$837$		0			0
$838$	−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
$843$		0			0
$844$		0			0
$845$	−12.6491	+	12.6491i	−0.435143	+	0.435143i
$846$		0			0
$847$	−25.8114	+	5.81139i	−0.886890	+	0.199682i
$848$	−4.00000	+	4.00000i	−0.137361	+	0.137361i
$849$		0			0
$850$			15.8114i			0.542326i
$851$	24.0000			0.822709
$852$		0			0
$853$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$853$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$854$	−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	−0.0837245	+	0.996489i	$0.526682\pi$
$857$	−31.6228	+	31.6228i	−1.08021	+	1.08021i	−0.996489	+	0.0837245i	$0.973318\pi$
$858$		0			0
$859$	−12.6491			−0.431582			−0.215791	−	0.976440i	$-0.569233\pi$
$859$	−12.6491			−0.431582			−0.215791	+	0.976440i	$0.569233\pi$
$860$		0			0
$861$		0			0
$862$	23.0000	+	23.0000i	0.783383	+	0.783383i
$863$	13.0000	−	13.0000i	0.442525	−	0.442525i	−0.450335	−	0.892860i	$-0.648695\pi$
$863$	13.0000	−	13.0000i	0.442525	−	0.442525i	0.892860	+	0.450335i	$0.148695\pi$
$864$		0			0
$865$			35.0000i			1.19004i
$866$		−	18.9737i		−	0.644751i
$867$		0			0
$868$		0			0
$869$			13.0000i			0.440995i
$870$		0			0
$871$		−	3.16228i		−	0.107150i
$872$	−14.0000	−	14.0000i	−0.474100	−	0.474100i
$873$		0			0
$874$	12.6491			0.427863
$875$	15.8114	−	25.0000i	0.534522	−	0.845154i
$876$		0			0
$877$	17.0000	+	17.0000i	0.574049	+	0.574049i	0.933257	−	0.359208i	$-0.116953\pi$
$877$	17.0000	+	17.0000i	0.574049	+	0.574049i	−0.359208	+	0.933257i	$0.616953\pi$
$878$	12.6491	+	12.6491i	0.426887	+	0.426887i
$879$		0			0
$880$	−6.32456	−	6.32456i	−0.213201	−	0.213201i
$881$		−	37.9473i		−	1.27848i	−0.769008	−	0.639239i	$-0.779249\pi$
$881$		−	37.9473i		−	1.27848i	0.769008	−	0.639239i	$-0.220751\pi$
$882$		0			0
$883$	−18.0000	+	18.0000i	−0.605748	+	0.605748i	−0.941832	−	0.336084i	$-0.890897\pi$
$883$	−18.0000	+	18.0000i	−0.605748	+	0.605748i	0.336084	+	0.941832i	$0.390897\pi$
$884$		0			0
$885$		0			0
$886$	−2.00000			−0.0671913
$887$	3.16228	−	3.16228i	0.106179	−	0.106179i	−0.652022	−	0.758200i	$-0.726079\pi$
$887$	3.16228	−	3.16228i	0.106179	−	0.106179i	0.758200	+	0.652022i	$0.226079\pi$
$888$		0			0
$889$	28.4605	+	18.0000i	0.954534	+	0.603701i
$890$			20.0000i			0.670402i
$891$		0			0
$892$		0			0
$893$	15.0000	−	15.0000i	0.501956	−	0.501956i
$894$		0			0
$895$	9.48683	−	9.48683i	0.317110	−	0.317110i
$896$	16.0000	−	25.2982i	0.534522	−	0.845154i
$897$		0			0
$898$	−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
$903$		0			0
$904$			48.0000i			1.59646i
$905$	−35.0000	+	35.0000i	−1.16344	+	1.16344i
$906$		0			0
$907$	22.0000	+	22.0000i	0.730498	+	0.730498i	0.970718	−	0.240220i	$-0.0772197\pi$
$907$	22.0000	+	22.0000i	0.730498	+	0.730498i	−0.240220	+	0.970718i	$0.577220\pi$
$908$		0			0
$909$		0			0
$910$	10.0000	−	15.8114i	0.331497	−	0.524142i
$911$	−54.0000			−1.78910			−0.894550	−	0.446968i	$-0.852504\pi$
$911$	−54.0000			−1.78910			−0.894550	+	0.446968i	$0.852504\pi$
$912$		0			0
$913$	−3.16228	−	3.16228i	−0.104656	−	0.104656i
$914$		−	2.00000i		−	0.0661541i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		−	27.0000i		−	0.890648i	−0.895370	−	0.445324i	$-0.853089\pi$
$919$		−	27.0000i		−	0.890648i	0.895370	−	0.445324i	$-0.146911\pi$
$920$	12.6491	−	12.6491i	0.417029	−	0.417029i
$921$		0			0
$922$	−6.32456	+	6.32456i	−0.208288	+	0.208288i
$923$	9.48683	+	9.48683i	0.312263	+	0.312263i
$924$		0			0
$925$	30.0000	−	30.0000i	0.986394	−	0.986394i
$926$	−8.00000			−0.262896
$927$		0			0
$928$		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
$933$		0			0
$934$	−22.1359			−0.724310
$935$	−5.00000			−0.163517
$936$		0			0
$937$	14.2302	−	14.2302i	0.464882	−	0.464882i	−0.435370	−	0.900252i	$-0.643382\pi$
$937$	14.2302	−	14.2302i	0.464882	−	0.464882i	0.900252	+	0.435370i	$0.143382\pi$
$938$	−1.16228	−	5.16228i	−0.0379497	−	0.168554i
$939$		0			0
$940$		0			0
$941$			37.9473i			1.23705i	0.785766	+	0.618524i	$0.212269\pi$
$941$			37.9473i			1.23705i	−0.785766	+	0.618524i	$0.787731\pi$
$942$		0			0
$943$	−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	0.584165	−	0.811635i	$-0.301422\pi$
$947$	−7.00000	−	7.00000i	−0.227469	−	0.227469i	−0.811635	+	0.584165i	$0.801422\pi$
$948$		0			0
$949$		0			0
$950$	15.8114	−	15.8114i	0.512989	−	0.512989i
$951$		0			0
$952$	−3.67544	−	16.3246i	−0.119122	−	0.529082i
$953$	3.00000	−	3.00000i	0.0971795	−	0.0971795i	−0.656846	−	0.754025i	$-0.728110\pi$
$953$	3.00000	−	3.00000i	0.0971795	−	0.0971795i	0.754025	+	0.656846i	$0.228110\pi$
$954$		0			0
$955$	−4.74342	−	4.74342i	−0.153493	−	0.153493i
$956$		0			0
$957$		0			0
$958$	−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
$963$		0			0
$964$		0			0
$965$	25.2982			0.814379
$966$		0			0
$967$	−33.0000	−	33.0000i	−1.06121	−	1.06121i	−0.998000	−	0.0632081i	$-0.979867\pi$
$967$	−33.0000	−	33.0000i	−1.06121	−	1.06121i	−0.0632081	−	0.998000i	$-0.520133\pi$
$968$	−20.0000	+	20.0000i	−0.642824	+	0.642824i
$969$		0			0
$970$	−5.00000	−	5.00000i	−0.160540	−	0.160540i
$971$			34.7851i			1.11631i	0.829738	+	0.558153i	$0.188490\pi$
$971$			34.7851i			1.11631i	−0.829738	+	0.558153i	$0.811510\pi$
$972$		0			0
$973$	48.9737	−	11.0263i	1.57002	−	0.353488i
$974$			8.00000i			0.256337i
$975$		0			0
$976$			25.2982i			0.809776i
$977$	1.00000	+	1.00000i	0.0319928	+	0.0319928i	0.722922	−	0.690929i	$-0.242798\pi$
$977$	1.00000	+	1.00000i	0.0319928	+	0.0319928i	−0.690929	+	0.722922i	$0.742798\pi$
$978$		0			0
$979$	−6.32456			−0.202134
$980$		0			0
$981$		0			0
$982$	41.0000	+	41.0000i	1.30836	+	1.30836i
$983$	−20.5548	−	20.5548i	−0.655596	−	0.655596i	0.298739	−	0.954335i	$-0.403434\pi$
$983$	−20.5548	−	20.5548i	−0.655596	−	0.655596i	−0.954335	+	0.298739i	$0.903434\pi$
$984$		0			0
$985$		−	3.16228i		−	0.100759i
$986$		−	9.48683i		−	0.302122i
$987$		0			0
$988$		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
$993$		0			0
$994$	18.9737	+	12.0000i	0.601808	+	0.380617i
$995$	−15.0000	−	15.0000i	−0.475532	−	0.475532i
$996$		0			0
$997$	−14.2302	+	14.2302i	−0.450677	+	0.450677i	−0.895579	−	0.444902i	$-0.853238\pi$
$997$	−14.2302	+	14.2302i	−0.450677	+	0.450677i	0.444902	+	0.895579i	$0.353238\pi$
$998$	−19.0000	+	19.0000i	−0.601434	+	0.601434i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.p.c.307.1		4
3.2	odd	2		35.2.f.a.27.1	yes	4
5.3	odd	4	inner	315.2.p.c.118.2		4
7.6	odd	2	inner	315.2.p.c.307.2		4
12.11	even	2		560.2.bj.a.97.2		4
15.2	even	4		175.2.f.c.118.1		4
15.8	even	4		35.2.f.a.13.2	yes	4
15.14	odd	2		175.2.f.c.132.2		4
21.2	odd	6		245.2.l.c.227.2		8
21.5	even	6		245.2.l.c.227.1		8
21.11	odd	6		245.2.l.c.117.1		8
21.17	even	6		245.2.l.c.117.2		8
21.20	even	2		35.2.f.a.27.2	yes	4
35.13	even	4	inner	315.2.p.c.118.1		4
60.23	odd	4		560.2.bj.a.433.1		4
84.83	odd	2		560.2.bj.a.97.1		4
105.23	even	12		245.2.l.c.178.2		8
105.38	odd	12		245.2.l.c.68.2		8
105.53	even	12		245.2.l.c.68.1		8
105.62	odd	4		175.2.f.c.118.2		4
105.68	odd	12		245.2.l.c.178.1		8
105.83	odd	4		35.2.f.a.13.1	✓	4
105.104	even	2		175.2.f.c.132.1		4
420.83	even	4		560.2.bj.a.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.f.a.13.1	✓	4	105.83	odd	4
35.2.f.a.13.2	yes	4	15.8	even	4
35.2.f.a.27.1	yes	4	3.2	odd	2
35.2.f.a.27.2	yes	4	21.20	even	2
175.2.f.c.118.1		4	15.2	even	4
175.2.f.c.118.2		4	105.62	odd	4
175.2.f.c.132.1		4	105.104	even	2
175.2.f.c.132.2		4	15.14	odd	2
245.2.l.c.68.1		8	105.53	even	12
245.2.l.c.68.2		8	105.38	odd	12
245.2.l.c.117.1		8	21.11	odd	6
245.2.l.c.117.2		8	21.17	even	6
245.2.l.c.178.1		8	105.68	odd	12
245.2.l.c.178.2		8	105.23	even	12
245.2.l.c.227.1		8	21.5	even	6
245.2.l.c.227.2		8	21.2	odd	6
315.2.p.c.118.1		4	35.13	even	4	inner
315.2.p.c.118.2		4	5.3	odd	4	inner
315.2.p.c.307.1		4	1.1	even	1	trivial
315.2.p.c.307.2		4	7.6	odd	2	inner
560.2.bj.a.97.1		4	84.83	odd	2
560.2.bj.a.97.2		4	12.11	even	2
560.2.bj.a.433.1		4	60.23	odd	4
560.2.bj.a.433.2		4	420.83	even	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.58114 - 1.58114i) q^{5} +(2.58114 - 0.581139i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.16228i q^{10} +1.00000 q^{11} +(1.58114 + 1.58114i) q^{13} +(3.16228 + 2.00000i) q^{14} +4.00000 q^{16} +(1.58114 - 1.58114i) q^{17} -3.16228 q^{19} +(1.00000 + 1.00000i) q^{22} +(-2.00000 + 2.00000i) q^{23} +5.00000i q^{25} +3.16228i q^{26} -3.00000i q^{29} +3.16228i q^{31} +3.16228 q^{34} +(-5.00000 - 3.16228i) q^{35} +(-6.00000 - 6.00000i) q^{37} +(-3.16228 - 3.16228i) q^{38} -6.32456 q^{40} +9.48683i q^{41} +(-3.00000 + 3.00000i) q^{43} -4.00000 q^{46} +(-4.74342 + 4.74342i) q^{47} +(6.32456 - 3.00000i) q^{49} +(-5.00000 + 5.00000i) q^{50} +(-1.00000 + 1.00000i) q^{53} +(-1.58114 - 1.58114i) q^{55} +(4.00000 - 6.32456i) q^{56} +(3.00000 - 3.00000i) q^{58} +9.48683 q^{59} +6.32456i q^{61} +(-3.16228 + 3.16228i) q^{62} -8.00000i q^{64} -5.00000i q^{65} +(-1.00000 - 1.00000i) q^{67} +(-1.83772 - 8.16228i) q^{70} +6.00000 q^{71} -12.0000i q^{74} +(2.58114 - 0.581139i) q^{77} +13.0000i q^{79} +(-6.32456 - 6.32456i) q^{80} +(-9.48683 + 9.48683i) q^{82} +(-3.16228 - 3.16228i) q^{83} -5.00000 q^{85} -6.00000 q^{86} +(2.00000 - 2.00000i) q^{88} -6.32456 q^{89} +(5.00000 + 3.16228i) q^{91} -9.48683 q^{94} +(5.00000 + 5.00000i) q^{95} +(1.58114 - 1.58114i) q^{97} +(9.32456 + 3.32456i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{7} + 8 q^{8} + 4 q^{11} + 16 q^{16} + 4 q^{22} - 8 q^{23} - 20 q^{35} - 24 q^{37} - 12 q^{43} - 16 q^{46} - 20 q^{50} - 4 q^{53} + 16 q^{56} + 12 q^{58} - 4 q^{67} - 20 q^{70} + 24 q^{71}+ \cdots + 12 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^7 + 8 * q^8 + 4 * q^11 + 16 * q^16 + 4 * q^22 - 8 * q^23 - 20 * q^35 - 24 * q^37 - 12 * q^43 - 16 * q^46 - 20 * q^50 - 4 * q^53 + 16 * q^56 + 12 * q^58 - 4 * q^67 - 20 * q^70 + 24 * q^71 + 4 * q^77 - 20 * q^85 - 24 * q^86 + 8 * q^88 + 20 * q^91 + 20 * q^95 + 12 * q^98

Introduction

L-functions

Modular forms

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Database

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