LMFDB - Embedded newform 630.2.k.a.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(361,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.361
Dual form			630.2.k.a.541.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{11} +5.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{19} +1.00000 q^{20} -3.00000 q^{22} +(-4.50000 - 7.79423i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.50000 - 4.33013i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(5.00000 - 8.66025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.50000 + 0.866025i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(-0.500000 - 0.866025i) q^{40} -9.00000 q^{41} +8.00000 q^{43} +(1.50000 + 2.59808i) q^{44} +(-4.50000 + 7.79423i) q^{46} +(1.50000 + 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} +1.00000 q^{50} +(-2.50000 + 4.33013i) q^{52} +(-1.50000 + 2.59808i) q^{53} -3.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +(6.00000 - 10.3923i) q^{59} +(-4.00000 - 6.92820i) q^{61} -10.0000 q^{62} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(-0.500000 - 2.59808i) q^{70} +6.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(0.500000 - 0.866025i) q^{74} +5.00000 q^{76} +(1.50000 + 7.79423i) q^{77} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(4.50000 + 7.79423i) q^{82} +(-4.00000 - 6.92820i) q^{86} +(1.50000 - 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-10.0000 + 8.66025i) q^{91} +9.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(-2.50000 + 4.33013i) q^{95} +8.00000 q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - q^{5} - 4 q^{7} + 2 q^{8} - q^{10} + 3 q^{11} + 10 q^{13} + 5 q^{14} - q^{16} - 5 q^{19} + 2 q^{20} - 6 q^{22} - 9 q^{23} - q^{25} - 5 q^{26} - q^{28} + 10 q^{31} - q^{32}+ \cdots - 13 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - q^5 - 4 * q^7 + 2 * q^8 - q^10 + 3 * q^11 + 10 * q^13 + 5 * q^14 - q^16 - 5 * q^19 + 2 * q^20 - 6 * q^22 - 9 * q^23 - q^25 - 5 * q^26 - q^28 + 10 * q^31 - q^32 + 5 * q^35 + q^37 - 5 * q^38 - q^40 - 18 * q^41 + 16 * q^43 + 3 * q^44 - 9 * q^46 + 3 * q^47 + 2 * q^49 + 2 * q^50 - 5 * q^52 - 3 * q^53 - 6 * q^55 - 4 * q^56 + 12 * q^59 - 8 * q^61 - 20 * q^62 + 2 * q^64 - 5 * q^65 - 8 * q^67 - q^70 + 12 * q^71 - 2 * q^73 + q^74 + 10 * q^76 + 3 * q^77 - 8 * q^79 - q^80 + 9 * q^82 - 8 * q^86 + 3 * q^88 + 6 * q^89 - 20 * q^91 + 18 * q^92 + 3 * q^94 - 5 * q^95 + 16 * q^97 - 13 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$	2.50000	+	0.866025i	0.668153	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	−3.00000			−0.639602
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.768613	−	0.639713i	$-0.779053\pi$
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.169701	−	0.985496i	$-0.554280\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.50000	−	4.33013i	−0.490290	−	0.849208i
$27$		0			0
$28$	−0.500000	−	2.59808i	−0.0944911	−	0.490990i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.0680129	−	0.997684i	$-0.478334\pi$
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.830014	−	0.557743i	$-0.188333\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$	2.50000	+	0.866025i	0.422577	+	0.146385i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−2.50000	+	4.33013i	−0.405554	+	0.702439i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$		0			0
$46$	−4.50000	+	7.79423i	−0.663489	+	1.14920i
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	1.00000			0.141421
$51$		0			0
$52$	−2.50000	+	4.33013i	−0.346688	+	0.600481i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$	−2.00000	+	1.73205i	−0.267261	+	0.231455i
$57$		0			0
$58$		0			0
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	−10.0000			−1.27000
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.50000	−	4.33013i	−0.310087	−	0.537086i
$66$		0			0
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$		0			0
$69$		0			0
$70$	−0.500000	−	2.59808i	−0.0597614	−	0.310530i
$71$	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
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$		0			0
$76$	5.00000			0.573539
$77$	1.50000	+	7.79423i	0.170941	+	0.888235i
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$		0			0
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	−10.0000	+	8.66025i	−1.04828	+	0.907841i
$92$	9.00000			0.938315
$93$		0			0
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	−2.50000	+	4.33013i	−0.256495	+	0.444262i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$	−6.50000	+	2.59808i	−0.656599	+	0.262445i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	5.00000			0.490290
$105$		0			0
$106$	3.00000			0.291386
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$		0			0
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$		0			0
$112$	2.50000	+	0.866025i	0.236228	+	0.0818317i
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$		0			0
$115$	−4.50000	+	7.79423i	−0.419627	+	0.726816i
$116$		0			0
$117$		0			0
$118$	−12.0000			−1.10469
$119$		0			0
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−4.00000	+	6.92820i	−0.362143	+	0.627250i
$123$		0			0
$124$	5.00000	+	8.66025i	0.449013	+	0.777714i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.50000	+	4.33013i	−0.219265	+	0.379777i
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	0.599699	−	0.800226i	$-0.295287\pi$
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	−0.992865	+	0.119241i	$0.961954\pi$
$132$		0			0
$133$	12.5000	+	4.33013i	1.08389	+	0.375470i
$134$	8.00000			0.691095
$135$		0			0
$136$		0			0
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$		0			0
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$	−2.00000	+	1.73205i	−0.169031	+	0.146385i
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	7.50000	−	12.9904i	0.627182	−	1.08631i
$144$		0			0
$145$		0			0
$146$	2.00000			0.165521
$147$		0			0
$148$	−1.00000			−0.0821995
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$		0			0
$154$	6.00000	−	5.19615i	0.483494	−	0.418718i
$155$	−10.0000			−0.803219
$156$		0			0
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	−0.948373	−	0.317156i	$-0.897272\pi$
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	0.748852	+	0.662738i	$0.230606\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$		0			0
$160$	1.00000			0.0790569
$161$	22.5000	+	7.79423i	1.77325	+	0.614271i
$162$		0			0
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$		0			0
$167$	3.00000			0.232147			0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000			0.232147			0.116073	+	0.993241i	$0.462969\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$		0			0
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$		0			0
$175$	−0.500000	−	2.59808i	−0.0377964	−	0.196396i
$176$	−3.00000			−0.226134
$177$		0			0
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	0.436870	+	0.899525i	$0.356087\pi$
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	−0.997446	+	0.0714220i	$0.977246\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	12.5000	+	4.33013i	0.926562	+	0.320970i
$183$		0			0
$184$	−4.50000	−	7.79423i	−0.331744	−	0.574598i
$185$	0.500000	−	0.866025i	0.0367607	−	0.0636715i
$186$		0			0
$187$		0			0
$188$	−3.00000			−0.218797
$189$		0			0
$190$	5.00000			0.362738
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$		0			0
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	−4.00000	−	6.92820i	−0.287183	−	0.497416i
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$	−15.0000			−1.06871			−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000			−1.06871			−0.534353	+	0.845262i	$0.679445\pi$
$198$		0			0
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	−0.429745	−	0.902950i	$-0.641397\pi$
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	0.996850	−	0.0793045i	$-0.0252700\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$		0			0
$208$	−2.50000	−	4.33013i	−0.173344	−	0.300240i
$209$	−15.0000			−1.03757
$210$		0			0
$211$	5.00000			0.344214			0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000			0.344214			0.172107	+	0.985078i	$0.444942\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$		0			0
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$	−4.00000	−	6.92820i	−0.272798	−	0.472500i
$216$		0			0
$217$	5.00000	+	25.9808i	0.339422	+	1.76369i
$218$	14.0000			0.948200
$219$		0			0
$220$	1.50000	−	2.59808i	0.101130	−	0.175162i
$221$		0			0
$222$		0			0
$223$	−28.0000			−1.87502			−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000			−1.87502			−0.937509	+	0.347960i	$0.886874\pi$
$224$	−0.500000	−	2.59808i	−0.0334077	−	0.173591i
$225$		0			0
$226$	−9.00000	−	15.5885i	−0.598671	−	1.03693i
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$	9.00000			0.593442
$231$		0			0
$232$		0			0
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$		0			0
$235$	1.50000	−	2.59808i	0.0978492	−	0.169480i
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$		0			0
$238$		0			0
$239$	−30.0000			−1.94054			−0.970269	−	0.242028i	$-0.922188\pi$
$239$	−30.0000			−1.94054			−0.970269	+	0.242028i	$0.922188\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$		0			0
$244$	8.00000			0.512148
$245$	−6.50000	+	2.59808i	−0.415270	+	0.165985i
$246$		0			0
$247$	−12.5000	−	21.6506i	−0.795356	−	1.37760i
$248$	5.00000	−	8.66025i	0.317500	−	0.549927i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−9.00000			−0.568075			−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000			−0.568075			−0.284037	+	0.958813i	$0.591674\pi$
$252$		0			0
$253$	−27.0000			−1.69748
$254$	6.50000	+	11.2583i	0.407846	+	0.706410i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	0.615948	−	0.787787i	$-0.288773\pi$
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	−0.990217	+	0.139533i	$0.955440\pi$
$258$		0			0
$259$	−2.50000	−	0.866025i	−0.155342	−	0.0538122i
$260$	5.00000			0.310087
$261$		0			0
$262$	−4.50000	+	7.79423i	−0.278011	+	0.481529i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$		0			0
$265$	3.00000			0.184289
$266$	−2.50000	−	12.9904i	−0.153285	−	0.796491i
$267$		0			0
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	−0.623082	−	0.782157i	$-0.714120\pi$
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	0.988908	+	0.148527i	$0.0474530\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$		0			0
$273$		0			0
$274$	18.0000			1.08742
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$		0			0
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	−10.0000	−	17.3205i	−0.599760	−	1.03882i
$279$		0			0
$280$	2.50000	+	0.866025i	0.149404	+	0.0517549i
$281$	21.0000			1.25275			0.626377	−	0.779520i	$-0.284537\pi$
$281$	21.0000			1.25275			0.626377	+	0.779520i	$0.284537\pi$
$282$		0			0
$283$	11.0000	−	19.0526i	0.653882	−	1.13256i	−0.328291	−	0.944577i	$-0.606473\pi$
$283$	11.0000	−	19.0526i	0.653882	−	1.13256i	0.982173	−	0.187980i	$-0.0601941\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−15.0000			−0.886969
$287$	18.0000	−	15.5885i	1.06251	−	0.920158i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$		0			0
$295$	−12.0000			−0.698667
$296$	0.500000	+	0.866025i	0.0290619	+	0.0503367i
$297$		0			0
$298$		0			0
$299$	−22.5000	−	38.9711i	−1.30121	−	2.25376i
$300$		0			0
$301$	−16.0000	+	13.8564i	−0.922225	+	0.798670i
$302$	−10.0000			−0.575435
$303$		0			0
$304$	−2.50000	+	4.33013i	−0.143385	+	0.248350i
$305$	−4.00000	+	6.92820i	−0.229039	+	0.396708i
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−7.50000	−	2.59808i	−0.427352	−	0.148039i
$309$		0			0
$310$	5.00000	+	8.66025i	0.283981	+	0.491869i
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	−0.984475	−	0.175525i	$-0.943838\pi$
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	0.644246	+	0.764818i	$0.277171\pi$
$312$		0			0
$313$	2.00000	+	3.46410i	0.113047	+	0.195803i	0.916997	−	0.398894i	$-0.130606\pi$
$313$	2.00000	+	3.46410i	0.113047	+	0.195803i	−0.803951	+	0.594696i	$0.797272\pi$
$314$	5.00000			0.282166
$315$		0			0
$316$	8.00000			0.450035
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$		0			0
$319$		0			0
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	−4.50000	−	23.3827i	−0.250775	−	1.30307i
$323$		0			0
$324$		0			0
$325$	−2.50000	+	4.33013i	−0.138675	+	0.240192i
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$		0			0
$328$	−9.00000			−0.496942
$329$	−7.50000	−	2.59808i	−0.413488	−	0.143237i
$330$		0			0
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	0.674351	−	0.738411i	$-0.264424\pi$
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	−0.976658	+	0.214799i	$0.931090\pi$
$332$		0			0
$333$		0			0
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$	8.00000			0.437087
$336$		0			0
$337$	20.0000			1.08947			0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000			1.08947			0.544735	+	0.838608i	$0.316630\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$		0			0
$340$		0			0
$341$	−15.0000	−	25.9808i	−0.812296	−	1.40694i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	8.00000			0.431331
$345$		0			0
$346$	4.50000	−	7.79423i	0.241921	−	0.419020i
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	−0.110885	−	0.993833i	$-0.535369\pi$
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	0.916127	−	0.400887i	$-0.131298\pi$
$348$		0			0
$349$	−28.0000			−1.49881			−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000			−1.49881			−0.749403	+	0.662114i	$0.769659\pi$
$350$	−2.00000	+	1.73205i	−0.106904	+	0.0925820i
$351$		0			0
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	15.0000			0.792775
$359$	6.00000	+	10.3923i	0.316668	+	0.548485i	0.979791	−	0.200026i	$-0.0641026\pi$
$359$	6.00000	+	10.3923i	0.316668	+	0.548485i	−0.663123	+	0.748511i	$0.730769\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−4.00000	−	6.92820i	−0.210235	−	0.364138i
$363$		0			0
$364$	−2.50000	−	12.9904i	−0.131036	−	0.680881i
$365$	2.00000			0.104685
$366$		0			0
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	−0.504093	−	0.863649i	$-0.668173\pi$
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	0.999989	+	0.00473247i	$0.00150640\pi$
$368$	−4.50000	+	7.79423i	−0.234579	+	0.406302i
$369$		0			0
$370$	−1.00000			−0.0519875
$371$	−1.50000	−	7.79423i	−0.0778761	−	0.404656i
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$		0			0
$375$		0			0
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$		0			0
$378$		0			0
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$	−2.50000	−	4.33013i	−0.128247	−	0.222131i
$381$		0			0
$382$	9.00000	−	15.5885i	0.460480	−	0.797575i
$383$	13.5000	+	23.3827i	0.689818	+	1.19480i	0.971897	+	0.235408i	$0.0756427\pi$
$383$	13.5000	+	23.3827i	0.689818	+	1.19480i	−0.282079	+	0.959391i	$0.591024\pi$
$384$		0			0
$385$	6.00000	−	5.19615i	0.305788	−	0.264820i
$386$	−10.0000			−0.508987
$387$		0			0
$388$	−4.00000	+	6.92820i	−0.203069	+	0.351726i
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$		0			0
$392$	1.00000	−	6.92820i	0.0505076	−	0.349927i
$393$		0			0
$394$	7.50000	+	12.9904i	0.377845	+	0.654446i
$395$	−4.00000	+	6.92820i	−0.201262	+	0.348596i
$396$		0			0
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$	−16.0000			−0.802008
$399$		0			0
$400$	1.00000			0.0500000
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		0			0
$403$	25.0000	−	43.3013i	1.24534	−	2.15699i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.00000			0.148704
$408$		0			0
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	−0.889689	−	0.456566i	$-0.849079\pi$
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	0.840243	+	0.542211i	$0.182412\pi$
$410$	4.50000	−	7.79423i	0.222239	−	0.384930i
$411$		0			0
$412$	8.00000			0.394132
$413$	6.00000	+	31.1769i	0.295241	+	1.53412i
$414$		0			0
$415$		0			0
$416$	−2.50000	+	4.33013i	−0.122573	+	0.212302i
$417$		0			0
$418$	7.50000	+	12.9904i	0.366837	+	0.635380i
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$		0			0
$421$	14.0000			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$422$	−2.50000	−	4.33013i	−0.121698	−	0.210787i
$423$		0			0
$424$	−1.50000	+	2.59808i	−0.0728464	+	0.126174i
$425$		0			0
$426$		0			0
$427$	20.0000	+	6.92820i	0.967868	+	0.335279i
$428$	−6.00000			−0.290021
$429$		0			0
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$		0			0
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$	20.0000	−	17.3205i	0.960031	−	0.831411i
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	−22.5000	+	38.9711i	−1.07632	+	1.86424i
$438$		0			0
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$	−3.00000			−0.143019
$441$		0			0
$442$		0			0
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$		0			0
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$	14.0000	+	24.2487i	0.662919	+	1.14821i
$447$		0			0
$448$	−2.00000	+	1.73205i	−0.0944911	+	0.0818317i
$449$	33.0000			1.55737			0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000			1.55737			0.778683	+	0.627417i	$0.215888\pi$
$450$		0			0
$451$	−13.5000	+	23.3827i	−0.635690	+	1.10105i
$452$	−9.00000	+	15.5885i	−0.423324	+	0.733219i
$453$		0			0
$454$		0			0
$455$	12.5000	+	4.33013i	0.586009	+	0.202999i
$456$		0			0
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	−7.00000	+	12.1244i	−0.327089	+	0.566534i
$459$		0			0
$460$	−4.50000	−	7.79423i	−0.209814	−	0.363408i
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$		0			0
$463$	−1.00000			−0.0464739			−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000			−0.0464739			−0.0232370	+	0.999730i	$0.507397\pi$
$464$		0			0
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$		0			0
$469$	−4.00000	−	20.7846i	−0.184703	−	0.959744i
$470$	−3.00000			−0.138380
$471$		0			0
$472$	6.00000	−	10.3923i	0.276172	−	0.478345i
$473$	12.0000	−	20.7846i	0.551761	−	0.955677i
$474$		0			0
$475$	5.00000			0.229416
$476$		0			0
$477$		0			0
$478$	15.0000	+	25.9808i	0.686084	+	1.18833i
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$	2.50000	+	4.33013i	0.113990	+	0.197437i
$482$	−1.00000			−0.0455488
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−4.00000	−	6.92820i	−0.181631	−	0.314594i
$486$		0			0
$487$	20.0000	−	34.6410i	0.906287	−	1.56973i	0.0871056	−	0.996199i	$-0.472238\pi$
$487$	20.0000	−	34.6410i	0.906287	−	1.56973i	0.819181	−	0.573535i	$-0.194428\pi$
$488$	−4.00000	−	6.92820i	−0.181071	−	0.313625i
$489$		0			0
$490$	5.50000	+	4.33013i	0.248465	+	0.195615i
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$		0			0
$494$	−12.5000	+	21.6506i	−0.562402	+	0.974108i
$495$		0			0
$496$	−10.0000			−0.449013
$497$	−12.0000	+	10.3923i	−0.538274	+	0.466159i
$498$		0			0
$499$	8.00000	+	13.8564i	0.358129	+	0.620298i	0.987648	−	0.156687i	$-0.0500814\pi$
$499$	8.00000	+	13.8564i	0.358129	+	0.620298i	−0.629519	+	0.776985i	$0.716748\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	4.50000	+	7.79423i	0.200845	+	0.347873i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$		0			0
$506$	13.5000	+	23.3827i	0.600148	+	1.03949i
$507$		0			0
$508$	6.50000	−	11.2583i	0.288391	−	0.499508i
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$	−1.00000	−	5.19615i	−0.0442374	−	0.229864i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−6.00000	+	10.3923i	−0.264649	+	0.458385i
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$		0			0
$517$	9.00000			0.395820
$518$	0.500000	+	2.59808i	0.0219687	+	0.114153i
$519$		0			0
$520$	−2.50000	−	4.33013i	−0.109632	−	0.189889i
$521$	13.5000	−	23.3827i	0.591446	−	1.02441i	−0.402592	−	0.915379i	$-0.631891\pi$
$521$	13.5000	−	23.3827i	0.591446	−	1.02441i	0.994038	−	0.109035i	$-0.0347759\pi$
$522$		0			0
$523$	11.0000	+	19.0526i	0.480996	+	0.833110i	0.999762	−	0.0218062i	$-0.00694167\pi$
$523$	11.0000	+	19.0526i	0.480996	+	0.833110i	−0.518766	+	0.854916i	$0.673608\pi$
$524$	9.00000			0.393167
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$		0			0
$529$	−29.0000	+	50.2295i	−1.26087	+	2.18389i
$530$	−1.50000	−	2.59808i	−0.0651558	−	0.112853i
$531$		0			0
$532$	−10.0000	+	8.66025i	−0.433555	+	0.375470i
$533$	−45.0000			−1.94917
$534$		0			0
$535$	3.00000	−	5.19615i	0.129701	−	0.224649i
$536$	−4.00000	+	6.92820i	−0.172774	+	0.299253i
$537$		0			0
$538$	−12.0000			−0.517357
$539$	−16.5000	−	12.9904i	−0.710705	−	0.559535i
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$		0			0
$544$		0			0
$545$	14.0000			0.599694
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	−9.00000	−	15.5885i	−0.384461	−	0.665906i
$549$		0			0
$550$	1.50000	−	2.59808i	0.0639602	−	0.110782i
$551$		0			0
$552$		0			0
$553$	20.0000	+	6.92820i	0.850487	+	0.294617i
$554$	26.0000			1.10463
$555$		0			0
$556$	−10.0000	+	17.3205i	−0.424094	+	0.734553i
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	−0.0747252	−	0.997204i	$-0.523808\pi$
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	0.900967	−	0.433888i	$-0.142859\pi$
$558$		0			0
$559$	40.0000			1.69182
$560$	−0.500000	−	2.59808i	−0.0211289	−	0.109789i
$561$		0			0
$562$	−10.5000	−	18.1865i	−0.442916	−	0.767153i
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	−0.922293	−	0.386492i	$-0.873687\pi$
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	0.795858	+	0.605483i	$0.207020\pi$
$564$		0			0
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	−22.0000			−0.924729
$567$		0			0
$568$	6.00000			0.251754
$569$	13.5000	+	23.3827i	0.565949	+	0.980253i	0.996961	+	0.0779066i	$0.0248236\pi$
$569$	13.5000	+	23.3827i	0.565949	+	0.980253i	−0.431011	+	0.902347i	$0.641843\pi$
$570$		0			0
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	0.983444	+	0.181210i	$0.0580014\pi$
$572$	7.50000	+	12.9904i	0.313591	+	0.543155i
$573$		0			0
$574$	−22.5000	−	7.79423i	−0.939132	−	0.325325i
$575$	9.00000			0.375326
$576$		0			0
$577$	11.0000	−	19.0526i	0.457936	−	0.793168i	−0.540916	−	0.841077i	$-0.681922\pi$
$577$	11.0000	−	19.0526i	0.457936	−	0.793168i	0.998852	+	0.0479084i	$0.0152556\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	−10.5000	−	18.1865i	−0.433751	−	0.751279i
$587$	42.0000			1.73353			0.866763	−	0.498721i	$-0.166197\pi$
$587$	42.0000			1.73353			0.866763	+	0.498721i	$0.166197\pi$
$588$		0			0
$589$	−50.0000			−2.06021
$590$	6.00000	+	10.3923i	0.247016	+	0.427844i
$591$		0			0
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	0.999965	−	0.00831589i	$-0.00264706\pi$
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	−0.507184	+	0.861838i	$0.669314\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−22.5000	+	38.9711i	−0.920093	+	1.59365i
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	−0.621480	−	0.783430i	$-0.713468\pi$
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	0.989210	+	0.146503i	$0.0468017\pi$
$600$		0			0
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$	20.0000	+	6.92820i	0.815139	+	0.282372i
$603$		0			0
$604$	5.00000	+	8.66025i	0.203447	+	0.352381i
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	12.5000	+	21.6506i	0.507359	+	0.878772i	0.999964	+	0.00851879i	$0.00271165\pi$
$607$	12.5000	+	21.6506i	0.507359	+	0.878772i	−0.492604	+	0.870253i	$0.663955\pi$
$608$	5.00000			0.202777
$609$		0			0
$610$	8.00000			0.323911
$611$	7.50000	+	12.9904i	0.303418	+	0.525535i
$612$		0			0
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	−0.955458	−	0.295126i	$-0.904638\pi$
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	0.733316	+	0.679888i	$0.237972\pi$
$614$	14.0000	+	24.2487i	0.564994	+	0.978598i
$615$		0			0
$616$	1.50000	+	7.79423i	0.0604367	+	0.314038i
$617$	−12.0000			−0.483102			−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000			−0.483102			−0.241551	+	0.970388i	$0.577656\pi$
$618$		0			0
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	0.412341	+	0.911030i	$0.364711\pi$
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	−0.995145	+	0.0984169i	$0.968622\pi$
$620$	5.00000	−	8.66025i	0.200805	−	0.347804i
$621$		0			0
$622$	12.0000			0.481156
$623$	−15.0000	−	5.19615i	−0.600962	−	0.208179i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.00000	−	3.46410i	0.0799361	−	0.138453i
$627$		0			0
$628$	−2.50000	−	4.33013i	−0.0997609	−	0.172791i
$629$		0			0
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	−4.00000	−	6.92820i	−0.159111	−	0.275589i
$633$		0			0
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$	6.50000	+	11.2583i	0.257945	+	0.446773i
$636$		0			0
$637$	5.00000	−	34.6410i	0.198107	−	1.37253i
$638$		0			0
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	−0.330997	−	0.943632i	$-0.607385\pi$
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	0.982708	−	0.185164i	$-0.0592817\pi$
$642$		0			0
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$	−18.0000	+	15.5885i	−0.709299	+	0.614271i
$645$		0			0
$646$		0			0
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	−0.940822	−	0.338902i	$-0.889945\pi$
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	0.763908	+	0.645325i	$0.223278\pi$
$648$		0			0
$649$	−18.0000	−	31.1769i	−0.706562	−	1.22380i
$650$	5.00000			0.196116
$651$		0			0
$652$	−16.0000			−0.626608
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	0.941248	+	0.337715i	$0.109654\pi$
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	−0.178154	+	0.984003i	$0.557013\pi$
$654$		0			0
$655$	−4.50000	+	7.79423i	−0.175830	+	0.304546i
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$		0			0
$658$	1.50000	+	7.79423i	0.0584761	+	0.303851i
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	−0.155235	−	0.987878i	$-0.549613\pi$
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	0.933144	−	0.359502i	$-0.117053\pi$
$662$	−5.50000	+	9.52628i	−0.213764	+	0.370249i
$663$		0			0
$664$		0			0
$665$	−2.50000	−	12.9904i	−0.0969458	−	0.503745i
$666$		0			0
$667$		0			0
$668$	−1.50000	+	2.59808i	−0.0580367	+	0.100523i
$669$		0			0
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$	−24.0000			−0.926510
$672$		0			0
$673$	20.0000			0.770943			0.385472	−	0.922720i	$-0.374039\pi$
$673$	20.0000			0.770943			0.385472	+	0.922720i	$0.374039\pi$
$674$	−10.0000	−	17.3205i	−0.385186	−	0.667161i
$675$		0			0
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	1.50000	+	2.59808i	0.0576497	+	0.0998522i	0.893410	−	0.449242i	$-0.148306\pi$
$677$	1.50000	+	2.59808i	0.0576497	+	0.0998522i	−0.835760	+	0.549095i	$0.814973\pi$
$678$		0			0
$679$	−16.0000	+	13.8564i	−0.614024	+	0.531760i
$680$		0			0
$681$		0			0
$682$	−15.0000	+	25.9808i	−0.574380	+	0.994855i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$		0			0
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	−7.50000	+	12.9904i	−0.285727	+	0.494894i
$690$		0			0
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	0.999276	+	0.0380440i	$0.0121127\pi$
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	−0.466691	+	0.884420i	$0.654554\pi$
$692$	−9.00000			−0.342129
$693$		0			0
$694$	−30.0000			−1.13878
$695$	−10.0000	−	17.3205i	−0.379322	−	0.657004i
$696$		0			0
$697$		0			0
$698$	14.0000	+	24.2487i	0.529908	+	0.917827i
$699$		0			0
$700$	2.50000	+	0.866025i	0.0944911	+	0.0327327i
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$	2.50000	−	4.33013i	0.0942893	−	0.163314i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	−24.0000			−0.903252
$707$		0			0
$708$		0			0
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	0.999549	+	0.0300298i	$0.00956021\pi$
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	−0.473768	+	0.880650i	$0.657106\pi$
$710$	−3.00000	+	5.19615i	−0.112588	+	0.195008i
$711$		0			0
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	−90.0000			−3.37053
$714$		0			0
$715$	−15.0000			−0.560968
$716$	−7.50000	−	12.9904i	−0.280288	−	0.485473i
$717$		0			0
$718$	6.00000	−	10.3923i	0.223918	−	0.387837i
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	0.983608	−	0.180319i	$-0.0577130\pi$
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	−0.647965	+	0.761670i	$0.724380\pi$
$720$		0			0
$721$	20.0000	+	6.92820i	0.744839	+	0.258020i
$722$	6.00000			0.223297
$723$		0			0
$724$	−4.00000	+	6.92820i	−0.148659	+	0.257485i
$725$		0			0
$726$		0			0
$727$	23.0000			0.853023			0.426511	−	0.904482i	$-0.359742\pi$
$727$	23.0000			0.853023			0.426511	+	0.904482i	$0.359742\pi$
$728$	−10.0000	+	8.66025i	−0.370625	+	0.320970i
$729$		0			0
$730$	−1.00000	−	1.73205i	−0.0370117	−	0.0641061i
$731$		0			0
$732$		0			0
$733$	0.500000	+	0.866025i	0.0184679	+	0.0319874i	0.875112	−	0.483921i	$-0.160788\pi$
$733$	0.500000	+	0.866025i	0.0184679	+	0.0319874i	−0.856644	+	0.515908i	$0.827454\pi$
$734$	−19.0000			−0.701303
$735$		0			0
$736$	9.00000			0.331744
$737$	12.0000	+	20.7846i	0.442026	+	0.765611i
$738$		0			0
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	−0.908337	−	0.418238i	$-0.862648\pi$
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	0.816373	+	0.577524i	$0.195981\pi$
$740$	0.500000	+	0.866025i	0.0183804	+	0.0318357i
$741$		0			0
$742$	−6.00000	+	5.19615i	−0.220267	+	0.190757i
$743$	39.0000			1.43077			0.715386	−	0.698730i	$-0.246251\pi$
$743$	39.0000			1.43077			0.715386	+	0.698730i	$0.246251\pi$
$744$		0			0
$745$		0			0
$746$	5.00000	−	8.66025i	0.183063	−	0.317074i
$747$		0			0
$748$		0			0
$749$	−15.0000	−	5.19615i	−0.548088	−	0.189863i
$750$		0			0
$751$	−1.00000	−	1.73205i	−0.0364905	−	0.0632034i	0.847203	−	0.531269i	$-0.178285\pi$
$751$	−1.00000	−	1.73205i	−0.0364905	−	0.0632034i	−0.883694	+	0.468065i	$0.844951\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$		0			0
$754$		0			0
$755$	−10.0000			−0.363937
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	9.50000	+	16.4545i	0.345056	+	0.597654i
$759$		0			0
$760$	−2.50000	+	4.33013i	−0.0906845	+	0.157070i
$761$	−16.5000	−	28.5788i	−0.598125	−	1.03598i	−0.993098	−	0.117289i	$-0.962579\pi$
$761$	−16.5000	−	28.5788i	−0.598125	−	1.03598i	0.394973	−	0.918693i	$-0.370754\pi$
$762$		0			0
$763$	−7.00000	−	36.3731i	−0.253417	−	1.31679i
$764$	−18.0000			−0.651217
$765$		0			0
$766$	13.5000	−	23.3827i	0.487775	−	0.844851i
$767$	30.0000	−	51.9615i	1.08324	−	1.87622i
$768$		0			0
$769$	35.0000			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$770$	−7.50000	−	2.59808i	−0.270281	−	0.0936282i
$771$		0			0
$772$	5.00000	+	8.66025i	0.179954	+	0.311689i
$773$	16.5000	−	28.5788i	0.593464	−	1.02791i	−0.400298	−	0.916385i	$-0.631093\pi$
$773$	16.5000	−	28.5788i	0.593464	−	1.02791i	0.993762	−	0.111524i	$-0.0355733\pi$
$774$		0			0
$775$	5.00000	+	8.66025i	0.179605	+	0.311086i
$776$	8.00000			0.287183
$777$		0			0
$778$	6.00000			0.215110
$779$	22.5000	+	38.9711i	0.806146	+	1.39629i
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		0			0
$783$		0			0
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$	5.00000			0.178458
$786$		0			0
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	−0.963394	−	0.268091i	$-0.913607\pi$
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	0.713871	+	0.700278i	$0.246941\pi$
$788$	7.50000	−	12.9904i	0.267176	−	0.462763i
$789$		0			0
$790$	8.00000			0.284627
$791$	−36.0000	+	31.1769i	−1.28001	+	1.10852i
$792$		0			0
$793$	−20.0000	−	34.6410i	−0.710221	−	1.23014i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		0			0
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	7.50000	−	12.9904i	0.264834	−	0.458706i
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$		0			0
$805$	−4.50000	−	23.3827i	−0.158604	−	0.824131i
$806$	−50.0000			−1.76117
$807$		0			0
$808$		0			0
$809$	−13.5000	+	23.3827i	−0.474635	+	0.822091i	−0.999578	−	0.0290457i	$-0.990753\pi$
$809$	−13.5000	+	23.3827i	−0.474635	+	0.822091i	0.524943	+	0.851137i	$0.324086\pi$
$810$		0			0
$811$	−7.00000			−0.245803			−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000			−0.245803			−0.122902	+	0.992419i	$0.539220\pi$
$812$		0			0
$813$		0			0
$814$	−1.50000	−	2.59808i	−0.0525750	−	0.0910625i
$815$	8.00000	−	13.8564i	0.280228	−	0.485369i
$816$		0			0
$817$	−20.0000	−	34.6410i	−0.699711	−	1.21194i
$818$	2.00000			0.0699284
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$		0			0
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$	−4.00000	−	6.92820i	−0.139347	−	0.241355i
$825$		0			0
$826$	24.0000	−	20.7846i	0.835067	−	0.723189i
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$		0			0
$829$	20.0000	−	34.6410i	0.694629	−	1.20313i	−0.275677	−	0.961250i	$-0.588902\pi$
$829$	20.0000	−	34.6410i	0.694629	−	1.20313i	0.970306	−	0.241882i	$-0.0777647\pi$
$830$		0			0
$831$		0			0
$832$	5.00000			0.173344
$833$		0			0
$834$		0			0
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$	7.50000	−	12.9904i	0.259393	−	0.449282i
$837$		0			0
$838$	−4.50000	−	7.79423i	−0.155450	−	0.269247i
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	−7.00000	−	12.1244i	−0.241236	−	0.417833i
$843$		0			0
$844$	−2.50000	+	4.33013i	−0.0860535	+	0.149049i
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$	−5.00000	−	1.73205i	−0.171802	−	0.0595140i
$848$	3.00000			0.103020
$849$		0			0
$850$		0			0
$851$	4.50000	−	7.79423i	0.154258	−	0.267183i
$852$		0			0
$853$	−37.0000			−1.26686			−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000			−1.26686			−0.633428	+	0.773802i	$0.718353\pi$
$854$	−4.00000	−	20.7846i	−0.136877	−	0.711235i
$855$		0			0
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	−0.912705	−	0.408619i	$-0.866010\pi$
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	0.810227	+	0.586116i	$0.199344\pi$
$858$		0			0
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	0.898126	−	0.439738i	$-0.144929\pi$
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	−0.829887	+	0.557931i	$0.811595\pi$
$860$	8.00000			0.272798
$861$		0			0
$862$	24.0000			0.817443
$863$	−10.5000	−	18.1865i	−0.357424	−	0.619077i	0.630106	−	0.776509i	$-0.283012\pi$
$863$	−10.5000	−	18.1865i	−0.357424	−	0.619077i	−0.987530	+	0.157433i	$0.949678\pi$
$864$		0			0
$865$	4.50000	−	7.79423i	0.153005	−	0.265012i
$866$	8.00000	+	13.8564i	0.271851	+	0.470860i
$867$		0			0
$868$	−25.0000	−	8.66025i	−0.848555	−	0.293948i
$869$	−24.0000			−0.814144
$870$		0			0
$871$	−20.0000	+	34.6410i	−0.677674	+	1.17377i
$872$	−7.00000	+	12.1244i	−0.237050	+	0.410582i
$873$		0			0
$874$	45.0000			1.52215
$875$	−2.00000	+	1.73205i	−0.0676123	+	0.0585540i
$876$		0			0
$877$	−2.50000	−	4.33013i	−0.0844190	−	0.146218i	0.820724	−	0.571324i	$-0.193570\pi$
$877$	−2.50000	−	4.33013i	−0.0844190	−	0.146218i	−0.905143	+	0.425106i	$0.860237\pi$
$878$	−4.00000	+	6.92820i	−0.134993	+	0.233816i
$879$		0			0
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$		0			0
$883$	14.0000			0.471138			0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000			0.471138			0.235569	+	0.971858i	$0.424305\pi$
$884$		0			0
$885$		0			0
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$		0			0
$889$	26.0000	−	22.5167i	0.872012	−	0.755185i
$890$	−6.00000			−0.201120
$891$		0			0
$892$	14.0000	−	24.2487i	0.468755	−	0.811907i
$893$	7.50000	−	12.9904i	0.250978	−	0.434707i
$894$		0			0
$895$	15.0000			0.501395
$896$	2.50000	+	0.866025i	0.0835191	+	0.0289319i
$897$		0			0
$898$	−16.5000	−	28.5788i	−0.550612	−	0.953688i
$899$		0			0
$900$		0			0
$901$		0			0
$902$	27.0000			0.899002
$903$		0			0
$904$	18.0000			0.598671
$905$	−4.00000	−	6.92820i	−0.132964	−	0.230301i
$906$		0			0
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	−0.770996	−	0.636841i	$-0.780241\pi$
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	0.937018	+	0.349281i	$0.113574\pi$
$908$		0			0
$909$		0			0
$910$	−2.50000	−	12.9904i	−0.0828742	−	0.430627i
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		0			0
$913$		0			0
$914$	5.00000	−	8.66025i	0.165385	−	0.286456i
$915$		0			0
$916$	14.0000			0.462573
$917$	22.5000	+	7.79423i	0.743015	+	0.257388i
$918$		0			0
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	0.999052	−	0.0435419i	$-0.0138642\pi$
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	−0.537234	+	0.843433i	$0.680531\pi$
$920$	−4.50000	+	7.79423i	−0.148361	+	0.256968i
$921$		0			0
$922$	6.00000	+	10.3923i	0.197599	+	0.342252i
$923$	30.0000			0.987462
$924$		0			0
$925$	−1.00000			−0.0328798
$926$	0.500000	+	0.866025i	0.0164310	+	0.0284594i
$927$		0			0
$928$		0			0
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	0.985482	+	0.169779i	$0.0543055\pi$
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	−0.345708	+	0.938342i	$0.612361\pi$
$930$		0			0
$931$	−32.5000	+	12.9904i	−1.06514	+	0.425743i
$932$	6.00000			0.196537
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	44.0000			1.43742			0.718709	−	0.695311i	$-0.244734\pi$
$937$	44.0000			1.43742			0.718709	+	0.695311i	$0.244734\pi$
$938$	−16.0000	+	13.8564i	−0.522419	+	0.452428i
$939$		0			0
$940$	1.50000	+	2.59808i	0.0489246	+	0.0847399i
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	−0.974609	−	0.223912i	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$		0			0
$943$	40.5000	+	70.1481i	1.31886	+	2.28434i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	−24.0000			−0.780307
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$		0			0
$949$	−5.00000	+	8.66025i	−0.162307	+	0.281124i
$950$	−2.50000	−	4.33013i	−0.0811107	−	0.140488i
$951$		0			0
$952$		0			0
$953$	−12.0000			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$954$		0			0
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$	15.0000	−	25.9808i	0.485135	−	0.840278i
$957$		0			0
$958$	18.0000			0.581554
$959$	−9.00000	−	46.7654i	−0.290625	−	1.51013i
$960$		0			0
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	2.50000	−	4.33013i	0.0806032	−	0.139609i
$963$		0			0
$964$	0.500000	+	0.866025i	0.0161039	+	0.0278928i
$965$	−10.0000			−0.321911
$966$		0			0
$967$	−28.0000			−0.900419			−0.450210	−	0.892923i	$-0.648651\pi$
$967$	−28.0000			−0.900419			−0.450210	+	0.892923i	$0.648651\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		0			0
$970$	−4.00000	+	6.92820i	−0.128432	+	0.222451i
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$		0			0
$973$	−40.0000	+	34.6410i	−1.28234	+	1.11054i
$974$	−40.0000			−1.28168
$975$		0			0
$976$	−4.00000	+	6.92820i	−0.128037	+	0.221766i
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	−0.814038	−	0.580812i	$-0.802735\pi$
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	0.910017	+	0.414572i	$0.136069\pi$
$978$		0			0
$979$	18.0000			0.575282
$980$	1.00000	−	6.92820i	0.0319438	−	0.221313i
$981$		0			0
$982$	6.00000	+	10.3923i	0.191468	+	0.331632i
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	−0.785295	−	0.619122i	$-0.787489\pi$
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	0.928823	+	0.370525i	$0.120822\pi$
$984$		0			0
$985$	7.50000	+	12.9904i	0.238970	+	0.413908i
$986$		0			0
$987$		0			0
$988$	25.0000			0.795356
$989$	−36.0000	−	62.3538i	−1.14473	−	1.98274i
$990$		0			0
$991$	29.0000	−	50.2295i	0.921215	−	1.59559i	0.123678	−	0.992322i	$-0.460531\pi$
$991$	29.0000	−	50.2295i	0.921215	−	1.59559i	0.797537	−	0.603269i	$-0.206136\pi$
$992$	5.00000	+	8.66025i	0.158750	+	0.274963i
$993$		0			0
$994$	15.0000	+	5.19615i	0.475771	+	0.164812i
$995$	−16.0000			−0.507234
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$	8.00000	−	13.8564i	0.253236	−	0.438617i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.k.a.361.1		2
3.2	odd	2		210.2.i.c.151.1	yes	2
7.2	even	3	inner	630.2.k.a.541.1		2
7.3	odd	6		4410.2.a.w.1.1		1
7.4	even	3		4410.2.a.bh.1.1		1
12.11	even	2		1680.2.bg.n.1201.1		2
15.2	even	4		1050.2.o.c.949.1		4
15.8	even	4		1050.2.o.c.949.2		4
15.14	odd	2		1050.2.i.i.151.1		2
21.2	odd	6		210.2.i.c.121.1	✓	2
21.5	even	6		1470.2.i.p.961.1		2
21.11	odd	6		1470.2.a.f.1.1		1
21.17	even	6		1470.2.a.e.1.1		1
21.20	even	2		1470.2.i.p.361.1		2
84.23	even	6		1680.2.bg.n.961.1		2
105.2	even	12		1050.2.o.c.499.2		4
105.23	even	12		1050.2.o.c.499.1		4
105.44	odd	6		1050.2.i.i.751.1		2
105.59	even	6		7350.2.a.cx.1.1		1
105.74	odd	6		7350.2.a.cd.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.c.121.1	✓	2	21.2	odd	6
210.2.i.c.151.1	yes	2	3.2	odd	2
630.2.k.a.361.1		2	1.1	even	1	trivial
630.2.k.a.541.1		2	7.2	even	3	inner
1050.2.i.i.151.1		2	15.14	odd	2
1050.2.i.i.751.1		2	105.44	odd	6
1050.2.o.c.499.1		4	105.23	even	12
1050.2.o.c.499.2		4	105.2	even	12
1050.2.o.c.949.1		4	15.2	even	4
1050.2.o.c.949.2		4	15.8	even	4
1470.2.a.e.1.1		1	21.17	even	6
1470.2.a.f.1.1		1	21.11	odd	6
1470.2.i.p.361.1		2	21.20	even	2
1470.2.i.p.961.1		2	21.5	even	6
1680.2.bg.n.961.1		2	84.23	even	6
1680.2.bg.n.1201.1		2	12.11	even	2
4410.2.a.w.1.1		1	7.3	odd	6
4410.2.a.bh.1.1		1	7.4	even	3
7350.2.a.cd.1.1		1	105.74	odd	6
7350.2.a.cx.1.1		1	105.59	even	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{11} +5.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{19} +1.00000 q^{20} -3.00000 q^{22} +(-4.50000 - 7.79423i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.50000 - 4.33013i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(5.00000 - 8.66025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.50000 + 0.866025i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(-0.500000 - 0.866025i) q^{40} -9.00000 q^{41} +8.00000 q^{43} +(1.50000 + 2.59808i) q^{44} +(-4.50000 + 7.79423i) q^{46} +(1.50000 + 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} +1.00000 q^{50} +(-2.50000 + 4.33013i) q^{52} +(-1.50000 + 2.59808i) q^{53} -3.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +(6.00000 - 10.3923i) q^{59} +(-4.00000 - 6.92820i) q^{61} -10.0000 q^{62} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(-0.500000 - 2.59808i) q^{70} +6.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(0.500000 - 0.866025i) q^{74} +5.00000 q^{76} +(1.50000 + 7.79423i) q^{77} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(4.50000 + 7.79423i) q^{82} +(-4.00000 - 6.92820i) q^{86} +(1.50000 - 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-10.0000 + 8.66025i) q^{91} +9.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(-2.50000 + 4.33013i) q^{95} +8.00000 q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - q^{5} - 4 q^{7} + 2 q^{8} - q^{10} + 3 q^{11} + 10 q^{13} + 5 q^{14} - q^{16} - 5 q^{19} + 2 q^{20} - 6 q^{22} - 9 q^{23} - q^{25} - 5 q^{26} - q^{28} + 10 q^{31} - q^{32}+ \cdots - 13 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - q^5 - 4 * q^7 + 2 * q^8 - q^10 + 3 * q^11 + 10 * q^13 + 5 * q^14 - q^16 - 5 * q^19 + 2 * q^20 - 6 * q^22 - 9 * q^23 - q^25 - 5 * q^26 - q^28 + 10 * q^31 - q^32 + 5 * q^35 + q^37 - 5 * q^38 - q^40 - 18 * q^41 + 16 * q^43 + 3 * q^44 - 9 * q^46 + 3 * q^47 + 2 * q^49 + 2 * q^50 - 5 * q^52 - 3 * q^53 - 6 * q^55 - 4 * q^56 + 12 * q^59 - 8 * q^61 - 20 * q^62 + 2 * q^64 - 5 * q^65 - 8 * q^67 - q^70 + 12 * q^71 - 2 * q^73 + q^74 + 10 * q^76 + 3 * q^77 - 8 * q^79 - q^80 + 9 * q^82 - 8 * q^86 + 3 * q^88 + 6 * q^89 - 20 * q^91 + 18 * q^92 + 3 * q^94 - 5 * q^95 + 16 * q^97 - 13 * q^98

Introduction

L-functions

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