LMFDB - Embedded newform 630.2.k.b.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(361,630)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$1$
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 70)
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.b.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-3.00000 + 5.19615i) q^{11} -4.00000 q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{19} +1.00000 q^{20} +6.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.00000 + 3.46410i) q^{26} +(2.50000 + 0.866025i) q^{28} +3.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.00000 + 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{40} -9.00000 q^{41} -7.00000 q^{43} +(-3.00000 - 5.19615i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-6.50000 + 2.59808i) q^{49} +1.00000 q^{50} +(2.00000 - 3.46410i) q^{52} +(-3.00000 + 5.19615i) q^{53} +6.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-2.50000 - 4.33013i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(-2.50000 + 4.33013i) q^{67} +(2.50000 + 0.866025i) q^{70} +6.00000 q^{71} +(8.00000 - 13.8564i) q^{73} +(2.00000 - 3.46410i) q^{74} +2.00000 q^{76} +(15.0000 + 5.19615i) q^{77} +(-1.00000 - 1.73205i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(4.50000 + 7.79423i) q^{82} -3.00000 q^{83} +(3.50000 + 6.06218i) q^{86} +(-3.00000 + 5.19615i) q^{88} +(-7.50000 - 12.9904i) q^{89} +(2.00000 + 10.3923i) q^{91} +3.00000 q^{92} +(-1.00000 + 1.73205i) q^{95} +14.0000 q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - q^{5} - q^{7} + 2 q^{8} - q^{10} - 6 q^{11} - 8 q^{13} - 4 q^{14} - q^{16} - 2 q^{19} + 2 q^{20} + 12 q^{22} - 3 q^{23} - q^{25} + 4 q^{26} + 5 q^{28} + 6 q^{29} - 8 q^{31}+ \cdots + 11 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - q^5 - q^7 + 2 * q^8 - q^10 - 6 * q^11 - 8 * q^13 - 4 * q^14 - q^16 - 2 * q^19 + 2 * q^20 + 12 * q^22 - 3 * q^23 - q^25 + 4 * q^26 + 5 * q^28 + 6 * q^29 - 8 * q^31 - q^32 - 4 * q^35 + 4 * q^37 - 2 * q^38 - q^40 - 18 * q^41 - 14 * q^43 - 6 * q^44 - 3 * q^46 - 13 * q^49 + 2 * q^50 + 4 * q^52 - 6 * q^53 + 12 * q^55 - q^56 - 3 * q^58 - 6 * q^59 - 5 * q^61 + 16 * q^62 + 2 * q^64 + 4 * q^65 - 5 * q^67 + 5 * q^70 + 12 * q^71 + 16 * q^73 + 4 * q^74 + 4 * q^76 + 30 * q^77 - 2 * q^79 - q^80 + 9 * q^82 - 6 * q^83 + 7 * q^86 - 6 * q^88 - 15 * q^89 + 4 * q^91 + 6 * q^92 - 2 * q^95 + 28 * q^97 + 11 * 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
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$		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
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	6.00000			1.27920
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$		0			0
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$	−2.00000	+	1.73205i	−0.338062	+	0.292770i
$36$		0			0
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$		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
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$		0			0
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	1.00000			0.141421
$51$		0			0
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$		0			0
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$	8.00000			1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000	+	3.46410i	0.248069	+	0.429669i
$66$		0			0
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$		0			0
$69$		0			0
$70$	2.50000	+	0.866025i	0.298807	+	0.103510i
$71$	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
$73$	8.00000	−	13.8564i	0.936329	−	1.62177i	0.164083	−	0.986447i	$-0.447534\pi$
$73$	8.00000	−	13.8564i	0.936329	−	1.62177i	0.772246	−	0.635323i	$-0.219133\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$		0			0
$76$	2.00000			0.229416
$77$	15.0000	+	5.19615i	1.70941	+	0.592157i
$78$		0			0
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	0.804272	−	0.594261i	$-0.202555\pi$
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	−0.916781	+	0.399390i	$0.869222\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$	−3.00000			−0.329293			−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000			−0.329293			−0.164646	+	0.986353i	$0.552648\pi$
$84$		0			0
$85$		0			0
$86$	3.50000	+	6.06218i	0.377415	+	0.653701i
$87$		0			0
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$		0			0
$91$	2.00000	+	10.3923i	0.209657	+	1.08941i
$92$	3.00000			0.312772
$93$		0			0
$94$		0			0
$95$	−1.00000	+	1.73205i	−0.102598	+	0.177705i
$96$		0			0
$97$	14.0000			1.42148			0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000			1.42148			0.710742	+	0.703452i	$0.248359\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	−0.203317	−	0.979113i	$-0.565172\pi$
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	0.949595	−	0.313478i	$-0.101494\pi$
$102$		0			0
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	0.889607	−	0.456727i	$-0.150978\pi$
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	−0.840341	+	0.542059i	$0.817645\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	6.00000			0.582772
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	−0.958952	−	0.283567i	$-0.908482\pi$
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	0.233900	−	0.972261i	$-0.424851\pi$
$108$		0			0
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$	−3.00000	−	5.19615i	−0.286039	−	0.495434i
$111$		0			0
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$		0			0
$118$	6.00000			0.552345
$119$		0			0
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	−2.50000	+	4.33013i	−0.226339	+	0.392031i
$123$		0			0
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	−4.00000	+	3.46410i	−0.346844	+	0.300376i
$134$	5.00000			0.431934
$135$		0			0
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$	−0.500000	−	2.59808i	−0.0422577	−	0.219578i
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	12.0000	−	20.7846i	1.00349	−	1.73810i
$144$		0			0
$145$	−1.50000	−	2.59808i	−0.124568	−	0.215758i
$146$	−16.0000			−1.32417
$147$		0			0
$148$	−4.00000			−0.328798
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	0.990485	+	0.137619i	$0.0439449\pi$
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	−0.376061	+	0.926595i	$0.622722\pi$
$150$		0			0
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	0.935857	+	0.352381i	$0.114628\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$		0			0
$154$	−3.00000	−	15.5885i	−0.241747	−	1.25615i
$155$	8.00000			0.642575
$156$		0			0
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.0242497	−	0.999706i	$-0.492280\pi$
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.853646	−	0.520854i	$-0.174386\pi$
$158$	−1.00000	+	1.73205i	−0.0795557	+	0.137795i
$159$		0			0
$160$	1.00000			0.0790569
$161$	−6.00000	+	5.19615i	−0.472866	+	0.409514i
$162$		0			0
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	1.50000	+	2.59808i	0.116423	+	0.201650i
$167$	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
$169$	3.00000			0.230769
$170$		0			0
$171$		0			0
$172$	3.50000	−	6.06218i	0.266872	−	0.462237i
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$	2.50000	+	0.866025i	0.188982	+	0.0654654i
$176$	6.00000			0.452267
$177$		0			0
$178$	−7.50000	+	12.9904i	−0.562149	+	0.973670i
$179$	−12.0000	+	20.7846i	−0.896922	+	1.55351i	−0.0655145	+	0.997852i	$0.520869\pi$
$179$	−12.0000	+	20.7846i	−0.896922	+	1.55351i	−0.831408	+	0.555663i	$0.812464\pi$
$180$		0			0
$181$	11.0000			0.817624			0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000			0.817624			0.408812	+	0.912619i	$0.365943\pi$
$182$	8.00000	−	6.92820i	0.592999	−	0.513553i
$183$		0			0
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	2.00000			0.145095
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$		0			0
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	−15.0000			−1.05540
$203$	−1.50000	−	7.79423i	−0.105279	−	0.547048i
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	0.500000	−	0.866025i	0.0348367	−	0.0603388i
$207$		0			0
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	12.0000			0.830057
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	−7.50000	+	12.9904i	−0.512689	+	0.888004i
$215$	3.50000	+	6.06218i	0.238698	+	0.413437i
$216$		0			0
$217$	20.0000	+	6.92820i	1.35769	+	0.470317i
$218$	11.0000			0.745014
$219$		0			0
$220$	−3.00000	+	5.19615i	−0.202260	+	0.350325i
$221$		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	$0.886874\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$		0			0
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$		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	$0.986407\pi$
$230$	3.00000			0.197814
$231$		0			0
$232$	3.00000			0.196960
$233$	−6.00000	−	10.3923i	−0.393073	−	0.680823i	0.599780	−	0.800165i	$-0.295255\pi$
$233$	−6.00000	−	10.3923i	−0.393073	−	0.680823i	−0.992853	+	0.119342i	$0.961921\pi$
$234$		0			0
$235$		0			0
$236$	−3.00000	−	5.19615i	−0.195283	−	0.338241i
$237$		0			0
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$	−12.5000	+	21.6506i	−0.803530	+	1.39176i
$243$		0			0
$244$	5.00000			0.320092
$245$	5.50000	+	4.33013i	0.351382	+	0.276642i
$246$		0			0
$247$	4.00000	+	6.92820i	0.254514	+	0.440831i
$248$	−4.00000	+	6.92820i	−0.254000	+	0.439941i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$	8.00000	−	6.92820i	0.497096	−	0.430498i
$260$	−4.00000			−0.248069
$261$		0			0
$262$		0			0
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	0.336270	+	0.941766i	$0.390834\pi$
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	−0.983728	+	0.179664i	$0.942499\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$	5.00000	+	1.73205i	0.306570	+	0.106199i
$267$		0			0
$268$	−2.50000	−	4.33013i	−0.152712	−	0.264505i
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	−0.541533	−	0.840679i	$-0.682156\pi$
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	0.998816	+	0.0486418i	$0.0154893\pi$
$270$		0			0
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$		0			0
$273$		0			0
$274$	−12.0000			−0.724947
$275$	−3.00000	−	5.19615i	−0.180907	−	0.313340i
$276$		0			0
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	5.00000	+	8.66025i	0.299880	+	0.519408i
$279$		0			0
$280$	−2.00000	+	1.73205i	−0.119523	+	0.103510i
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−24.0000			−1.41915
$287$	4.50000	+	23.3827i	0.265627	+	1.38024i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−1.50000	+	2.59808i	−0.0880830	+	0.152564i
$291$		0			0
$292$	8.00000	+	13.8564i	0.468165	+	0.810885i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$		0			0
$295$	6.00000			0.349334
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$		0			0
$298$	7.50000	−	12.9904i	0.434463	−	0.752513i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	3.50000	+	18.1865i	0.201737	+	1.04825i
$302$	−4.00000			−0.230174
$303$		0			0
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	−2.50000	+	4.33013i	−0.143150	+	0.247942i
$306$		0			0
$307$	5.00000			0.285365			0.142683	−	0.989769i	$-0.454427\pi$
$307$	5.00000			0.285365			0.142683	+	0.989769i	$0.454427\pi$
$308$	−12.0000	+	10.3923i	−0.683763	+	0.592157i
$309$		0			0
$310$	−4.00000	−	6.92820i	−0.227185	−	0.393496i
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$		0			0
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	0.730554	−	0.682855i	$-0.239262\pi$
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	−0.956647	+	0.291250i	$0.905929\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	2.00000			0.112509
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	0.983866	−	0.178908i	$-0.0572566\pi$
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	−0.646872	+	0.762598i	$0.723923\pi$
$318$		0			0
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	7.50000	+	2.59808i	0.417959	+	0.144785i
$323$		0			0
$324$		0			0
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$		0			0
$328$	−9.00000			−0.496942
$329$		0			0
$330$		0			0
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	1.50000	−	2.59808i	0.0823232	−	0.142588i
$333$		0			0
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$	5.00000			0.273179
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$		0			0
$340$		0			0
$341$	−24.0000	−	41.5692i	−1.29967	−	2.25110i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−7.00000			−0.377415
$345$		0			0
$346$		0			0
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	−0.719590	−	0.694399i	$-0.755670\pi$
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	0.961162	+	0.275983i	$0.0890035\pi$
$348$		0			0
$349$	17.0000			0.909989			0.454995	−	0.890494i	$-0.349641\pi$
$349$	17.0000			0.909989			0.454995	+	0.890494i	$0.349641\pi$
$350$	−0.500000	−	2.59808i	−0.0267261	−	0.138873i
$351$		0			0
$352$	−3.00000	−	5.19615i	−0.159901	−	0.276956i
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$		0			0
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	15.0000			0.794998
$357$		0			0
$358$	24.0000			1.26844
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	0.986865	+	0.161546i	$0.0516481\pi$
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	−0.353529	+	0.935423i	$0.615019\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−5.50000	−	9.52628i	−0.289074	−	0.500690i
$363$		0			0
$364$	−10.0000	−	3.46410i	−0.524142	−	0.181568i
$365$	−16.0000			−0.837478
$366$		0			0
$367$	−17.5000	+	30.3109i	−0.913493	+	1.58222i	−0.104399	+	0.994535i	$0.533292\pi$
$367$	−17.5000	+	30.3109i	−0.913493	+	1.58222i	−0.809093	+	0.587680i	$0.800041\pi$
$368$	−1.50000	+	2.59808i	−0.0781929	+	0.135434i
$369$		0			0
$370$	−4.00000			−0.207950
$371$	15.0000	+	5.19615i	0.778761	+	0.269771i
$372$		0			0
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−34.0000			−1.74646			−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000			−1.74646			−0.873231	+	0.487306i	$0.837980\pi$
$380$	−1.00000	−	1.73205i	−0.0512989	−	0.0888523i
$381$		0			0
$382$	−3.00000	+	5.19615i	−0.153493	+	0.265858i
$383$	−7.50000	−	12.9904i	−0.383232	−	0.663777i	0.608290	−	0.793715i	$-0.291856\pi$
$383$	−7.50000	−	12.9904i	−0.383232	−	0.663777i	−0.991522	+	0.129937i	$0.958522\pi$
$384$		0			0
$385$	−3.00000	−	15.5885i	−0.152894	−	0.794461i
$386$	2.00000			0.101797
$387$		0			0
$388$	−7.00000	+	12.1244i	−0.355371	+	0.615521i
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$		0			0
$392$	−6.50000	+	2.59808i	−0.328300	+	0.131223i
$393$		0			0
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	−1.00000	+	1.73205i	−0.0503155	+	0.0871489i
$396$		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	$0.947600\pi$
$398$	−4.00000			−0.200502
$399$		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
$403$	16.0000	−	27.7128i	0.797017	−	1.38047i
$404$	7.50000	+	12.9904i	0.373139	+	0.646296i
$405$		0			0
$406$	−6.00000	+	5.19615i	−0.297775	+	0.257881i
$407$	−24.0000			−1.18964
$408$		0			0
$409$	6.50000	−	11.2583i	0.321404	−	0.556689i	−0.659374	−	0.751815i	$-0.729178\pi$
$409$	6.50000	−	11.2583i	0.321404	−	0.556689i	0.980778	+	0.195127i	$0.0625118\pi$
$410$	4.50000	−	7.79423i	0.222239	−	0.384930i
$411$		0			0
$412$	−1.00000			−0.0492665
$413$	15.0000	+	5.19615i	0.738102	+	0.255686i
$414$		0			0
$415$	1.50000	+	2.59808i	0.0736321	+	0.127535i
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$		0			0
$418$	−6.00000	−	10.3923i	−0.293470	−	0.508304i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$	5.00000	+	8.66025i	0.243396	+	0.421575i
$423$		0			0
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$		0			0
$426$		0			0
$427$	−10.0000	+	8.66025i	−0.483934	+	0.419099i
$428$	15.0000			0.725052
$429$		0			0
$430$	3.50000	−	6.06218i	0.168785	−	0.292344i
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$		0			0
$433$	−22.0000			−1.05725			−0.528626	−	0.848855i	$-0.677293\pi$
$433$	−22.0000			−1.05725			−0.528626	+	0.848855i	$0.677293\pi$
$434$	−4.00000	−	20.7846i	−0.192006	−	0.997693i
$435$		0			0
$436$	−5.50000	−	9.52628i	−0.263402	−	0.456226i
$437$	−3.00000	+	5.19615i	−0.143509	+	0.248566i
$438$		0			0
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$		0			0
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	0.999999	−	0.00130426i	$-0.000415158\pi$
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	−0.501129	+	0.865373i	$0.667082\pi$
$444$		0			0
$445$	−7.50000	+	12.9904i	−0.355534	+	0.615803i
$446$	14.0000	+	24.2487i	0.662919	+	1.14821i
$447$		0			0
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	27.0000	−	46.7654i	1.27138	−	2.20210i
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$		0			0
$454$	12.0000			0.563188
$455$	8.00000	−	6.92820i	0.375046	−	0.324799i
$456$		0			0
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	−0.948566	−	0.316579i	$-0.897466\pi$
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	0.200118	−	0.979772i	$-0.435868\pi$
$458$	−7.00000	+	12.1244i	−0.327089	+	0.566534i
$459$		0			0
$460$	−1.50000	−	2.59808i	−0.0699379	−	0.121136i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	−13.0000			−0.604161			−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000			−0.604161			−0.302081	+	0.953282i	$0.597681\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$		0			0
$466$	−6.00000	+	10.3923i	−0.277945	+	0.481414i
$467$	−7.50000	−	12.9904i	−0.347059	−	0.601123i	0.638667	−	0.769483i	$-0.279486\pi$
$467$	−7.50000	−	12.9904i	−0.347059	−	0.601123i	−0.985726	+	0.168360i	$0.946153\pi$
$468$		0			0
$469$	12.5000	+	4.33013i	0.577196	+	0.199947i
$470$		0			0
$471$		0			0
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$	21.0000	−	36.3731i	0.965581	−	1.67244i
$474$		0			0
$475$	2.00000			0.0917663
$476$		0			0
$477$		0			0
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	−0.695773	−	0.718262i	$-0.744938\pi$
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	0.969920	+	0.243426i	$0.0782712\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$	2.00000			0.0910975
$483$		0			0
$484$	25.0000			1.13636
$485$	−7.00000	−	12.1244i	−0.317854	−	0.550539i
$486$		0			0
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	−2.50000	−	4.33013i	−0.113170	−	0.196016i
$489$		0			0
$490$	1.00000	−	6.92820i	0.0451754	−	0.312984i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		0			0
$493$		0			0
$494$	4.00000	−	6.92820i	0.179969	−	0.311715i
$495$		0			0
$496$	8.00000			0.359211
$497$	−3.00000	−	15.5885i	−0.134568	−	0.699238i
$498$		0			0
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	0.999962	−	0.00872186i	$-0.00277629\pi$
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	−0.507534	+	0.861632i	$0.669443\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	−6.00000	−	10.3923i	−0.267793	−	0.463831i
$503$	−21.0000			−0.936344			−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000			−0.936344			−0.468172	+	0.883637i	$0.655087\pi$
$504$		0			0
$505$	−15.0000			−0.667491
$506$	−9.00000	−	15.5885i	−0.400099	−	0.692991i
$507$		0			0
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	10.5000	+	18.1865i	0.465404	+	0.806104i	0.999220	−	0.0394971i	$-0.0125756\pi$
$509$	10.5000	+	18.1865i	0.465404	+	0.806104i	−0.533815	+	0.845601i	$0.679242\pi$
$510$		0			0
$511$	−40.0000	−	13.8564i	−1.76950	−	0.612971i
$512$	1.00000			0.0441942
$513$		0			0
$514$		0			0
$515$	0.500000	−	0.866025i	0.0220326	−	0.0381616i
$516$		0			0
$517$		0			0
$518$	−10.0000	−	3.46410i	−0.439375	−	0.152204i
$519$		0			0
$520$	2.00000	+	3.46410i	0.0877058	+	0.151911i
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	−0.993011	−	0.118020i	$-0.962345\pi$
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	0.598714	+	0.800963i	$0.295679\pi$
$522$		0			0
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	0.990873	+	0.134801i	$0.0430394\pi$
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	−0.378695	+	0.925521i	$0.623627\pi$
$524$		0			0
$525$		0			0
$526$	21.0000			0.915644
$527$		0			0
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−3.00000	−	5.19615i	−0.130312	−	0.225706i
$531$		0			0
$532$	−1.00000	−	5.19615i	−0.0433555	−	0.225282i
$533$	36.0000			1.55933
$534$		0			0
$535$	−7.50000	+	12.9904i	−0.324253	+	0.561623i
$536$	−2.50000	+	4.33013i	−0.107984	+	0.187033i
$537$		0			0
$538$	−15.0000			−0.646696
$539$	6.00000	−	41.5692i	0.258438	−	1.79051i
$540$		0			0
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$	−1.00000	+	1.73205i	−0.0429537	+	0.0743980i
$543$		0			0
$544$		0			0
$545$	11.0000			0.471188
$546$		0			0
$547$	−19.0000			−0.812381			−0.406191	−	0.913788i	$-0.633143\pi$
$547$	−19.0000			−0.812381			−0.406191	+	0.913788i	$0.633143\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$		0			0
$550$	−3.00000	+	5.19615i	−0.127920	+	0.221565i
$551$	−3.00000	−	5.19615i	−0.127804	−	0.221364i
$552$		0			0
$553$	−4.00000	+	3.46410i	−0.170097	+	0.147309i
$554$	8.00000			0.339887
$555$		0			0
$556$	5.00000	−	8.66025i	0.212047	−	0.367277i
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	−0.991254	−	0.131965i	$-0.957871\pi$
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	0.609912	+	0.792469i	$0.291205\pi$
$558$		0			0
$559$	28.0000			1.18427
$560$	2.50000	+	0.866025i	0.105644	+	0.0365963i
$561$		0			0
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	13.5000	−	23.3827i	0.568957	−	0.985463i	−0.427712	−	0.903915i	$-0.640680\pi$
$563$	13.5000	−	23.3827i	0.568957	−	0.985463i	0.996669	−	0.0815478i	$-0.0259863\pi$
$564$		0			0
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	6.00000			0.251754
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	11.0000	−	19.0526i	0.460336	−	0.797325i	−0.538642	−	0.842535i	$-0.681062\pi$
$571$	11.0000	−	19.0526i	0.460336	−	0.797325i	0.998978	+	0.0452101i	$0.0143957\pi$
$572$	12.0000	+	20.7846i	0.501745	+	0.869048i
$573$		0			0
$574$	18.0000	−	15.5885i	0.751305	−	0.650650i
$575$	3.00000			0.125109
$576$		0			0
$577$	−13.0000	+	22.5167i	−0.541197	+	0.937381i	0.457639	+	0.889138i	$0.348695\pi$
$577$	−13.0000	+	22.5167i	−0.541197	+	0.937381i	−0.998836	+	0.0482425i	$0.984638\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$		0			0
$580$	3.00000			0.124568
$581$	1.50000	+	7.79423i	0.0622305	+	0.323359i
$582$		0			0
$583$	−18.0000	−	31.1769i	−0.745484	−	1.29122i
$584$	8.00000	−	13.8564i	0.331042	−	0.573382i
$585$		0			0
$586$	6.00000	+	10.3923i	0.247858	+	0.429302i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	16.0000			0.659269
$590$	−3.00000	−	5.19615i	−0.123508	−	0.213922i
$591$		0			0
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	0.921026	−	0.389501i	$-0.127353\pi$
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	−0.797831	+	0.602881i	$0.794019\pi$
$594$		0			0
$595$		0			0
$596$	−15.0000			−0.614424
$597$		0			0
$598$	6.00000	−	10.3923i	0.245358	−	0.424973i
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	−46.0000			−1.87638			−0.938190	−	0.346122i	$-0.887498\pi$
$601$	−46.0000			−1.87638			−0.938190	+	0.346122i	$0.887498\pi$
$602$	14.0000	−	12.1244i	0.570597	−	0.494152i
$603$		0			0
$604$	2.00000	+	3.46410i	0.0813788	+	0.140952i
$605$	−12.5000	+	21.6506i	−0.508197	+	0.880223i
$606$		0			0
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$	5.00000			0.202444
$611$		0			0
$612$		0			0
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	−0.658012	−	0.753007i	$-0.728603\pi$
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	0.981129	+	0.193352i	$0.0619359\pi$
$614$	−2.50000	−	4.33013i	−0.100892	−	0.174750i
$615$		0			0
$616$	15.0000	+	5.19615i	0.604367	+	0.209359i
$617$	12.0000			0.483102			0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000			0.483102			0.241551	+	0.970388i	$0.422344\pi$
$618$		0			0
$619$	−7.00000	+	12.1244i	−0.281354	+	0.487319i	−0.971718	−	0.236143i	$-0.924117\pi$
$619$	−7.00000	+	12.1244i	−0.281354	+	0.487319i	0.690365	+	0.723462i	$0.257450\pi$
$620$	−4.00000	+	6.92820i	−0.160644	+	0.278243i
$621$		0			0
$622$	18.0000			0.721734
$623$	−30.0000	+	25.9808i	−1.20192	+	1.04090i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.00000	+	6.92820i	−0.159872	+	0.276907i
$627$		0			0
$628$	11.0000	+	19.0526i	0.438948	+	0.760280i
$629$		0			0
$630$		0			0
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$	−1.00000	−	1.73205i	−0.0397779	−	0.0688973i
$633$		0			0
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$		0			0
$637$	26.0000	−	10.3923i	1.03016	−	0.411758i
$638$	18.0000			0.712627
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−1.50000	+	2.59808i	−0.0592464	+	0.102618i	−0.894127	−	0.447813i	$-0.852203\pi$
$641$	−1.50000	+	2.59808i	−0.0592464	+	0.102618i	0.834881	+	0.550431i	$0.185536\pi$
$642$		0			0
$643$	20.0000			0.788723			0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000			0.788723			0.394362	+	0.918955i	$0.370966\pi$
$644$	−1.50000	−	7.79423i	−0.0591083	−	0.307136i
$645$		0			0
$646$		0			0
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	−0.835033	−	0.550200i	$-0.814551\pi$
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	0.894004	+	0.448059i	$0.147885\pi$
$648$		0			0
$649$	−18.0000	−	31.1769i	−0.706562	−	1.22380i
$650$	−4.00000			−0.156893
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−24.0000	−	41.5692i	−0.939193	−	1.62673i	−0.766982	−	0.641669i	$-0.778242\pi$
$653$	−24.0000	−	41.5692i	−0.939193	−	1.62673i	−0.172211	−	0.985060i	$-0.555091\pi$
$654$		0			0
$655$		0			0
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$		0			0
$658$		0			0
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$		0			0
$661$	−20.5000	+	35.5070i	−0.797358	+	1.38106i	0.123974	+	0.992286i	$0.460436\pi$
$661$	−20.5000	+	35.5070i	−0.797358	+	1.38106i	−0.921331	+	0.388778i	$0.872897\pi$
$662$	14.0000	−	24.2487i	0.544125	−	0.942453i
$663$		0			0
$664$	−3.00000			−0.116423
$665$	5.00000	+	1.73205i	0.193892	+	0.0671660i
$666$		0			0
$667$	−4.50000	−	7.79423i	−0.174241	−	0.301794i
$668$	−1.50000	+	2.59808i	−0.0580367	+	0.100523i
$669$		0			0
$670$	−2.50000	−	4.33013i	−0.0965834	−	0.167287i
$671$	30.0000			1.15814
$672$		0			0
$673$	8.00000			0.308377			0.154189	−	0.988041i	$-0.450724\pi$
$673$	8.00000			0.308377			0.154189	+	0.988041i	$0.450724\pi$
$674$	11.0000	+	19.0526i	0.423704	+	0.733877i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	0.957984	−	0.286820i	$-0.0925982\pi$
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	−0.727386	+	0.686229i	$0.759265\pi$
$678$		0			0
$679$	−7.00000	−	36.3731i	−0.268635	−	1.39587i
$680$		0			0
$681$		0			0
$682$	−24.0000	+	41.5692i	−0.919007	+	1.59177i
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	−0.766997	−	0.641651i	$-0.778250\pi$
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	0.939184	+	0.343413i	$0.111583\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$		0			0
$688$	3.50000	+	6.06218i	0.133436	+	0.231118i
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	0.995785	−	0.0917209i	$-0.0292368\pi$
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	−0.577325	+	0.816514i	$0.695903\pi$
$692$		0			0
$693$		0			0
$694$	−9.00000			−0.341635
$695$	5.00000	+	8.66025i	0.189661	+	0.328502i
$696$		0			0
$697$		0			0
$698$	−8.50000	−	14.7224i	−0.321730	−	0.557252i
$699$		0			0
$700$	−2.00000	+	1.73205i	−0.0755929	+	0.0654654i
$701$	3.00000			0.113308			0.0566542	−	0.998394i	$-0.481957\pi$
$701$	3.00000			0.113308			0.0566542	+	0.998394i	$0.481957\pi$
$702$		0			0
$703$	4.00000	−	6.92820i	0.150863	−	0.261302i
$704$	−3.00000	+	5.19615i	−0.113067	+	0.195837i
$705$		0			0
$706$	6.00000			0.225813
$707$	−37.5000	−	12.9904i	−1.41033	−	0.488554i
$708$		0			0
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	0.995228	+	0.0975728i	$0.0311079\pi$
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	−0.413114	+	0.910679i	$0.635559\pi$
$710$	−3.00000	+	5.19615i	−0.112588	+	0.195008i
$711$		0			0
$712$	−7.50000	−	12.9904i	−0.281074	−	0.486835i
$713$	24.0000			0.898807
$714$		0			0
$715$	−24.0000			−0.897549
$716$	−12.0000	−	20.7846i	−0.448461	−	0.776757i
$717$		0			0
$718$	12.0000	−	20.7846i	0.447836	−	0.775675i
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$		0			0
$721$	2.00000	−	1.73205i	0.0744839	−	0.0645049i
$722$	−15.0000			−0.558242
$723$		0			0
$724$	−5.50000	+	9.52628i	−0.204406	+	0.354041i
$725$	−1.50000	+	2.59808i	−0.0557086	+	0.0964901i
$726$		0			0
$727$	−19.0000			−0.704671			−0.352335	−	0.935874i	$-0.614612\pi$
$727$	−19.0000			−0.704671			−0.352335	+	0.935874i	$0.614612\pi$
$728$	2.00000	+	10.3923i	0.0741249	+	0.385164i
$729$		0			0
$730$	8.00000	+	13.8564i	0.296093	+	0.512849i
$731$		0			0
$732$		0			0
$733$	17.0000	+	29.4449i	0.627909	+	1.08757i	0.987971	+	0.154642i	$0.0494225\pi$
$733$	17.0000	+	29.4449i	0.627909	+	1.08757i	−0.360061	+	0.932929i	$0.617244\pi$
$734$	35.0000			1.29187
$735$		0			0
$736$	3.00000			0.110581
$737$	−15.0000	−	25.9808i	−0.552532	−	0.957014i
$738$		0			0
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	−0.999688	−	0.0249776i	$-0.992049\pi$
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	0.521475	+	0.853266i	$0.325382\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$		0			0
$742$	−3.00000	−	15.5885i	−0.110133	−	0.572270i
$743$	−39.0000			−1.43077			−0.715386	−	0.698730i	$-0.753749\pi$
$743$	−39.0000			−1.43077			−0.715386	+	0.698730i	$0.753749\pi$
$744$		0			0
$745$	7.50000	−	12.9904i	0.274779	−	0.475931i
$746$	2.00000	−	3.46410i	0.0732252	−	0.126830i
$747$		0			0
$748$		0			0
$749$	−30.0000	+	25.9808i	−1.09618	+	0.949316i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$		0			0
$753$		0			0
$754$	6.00000	+	10.3923i	0.218507	+	0.378465i
$755$	−4.00000			−0.145575
$756$		0			0
$757$	−28.0000			−1.01768			−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000			−1.01768			−0.508839	+	0.860862i	$0.669925\pi$
$758$	17.0000	+	29.4449i	0.617468	+	1.06949i
$759$		0			0
$760$	−1.00000	+	1.73205i	−0.0362738	+	0.0628281i
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	0.942207	+	0.335032i	$0.108747\pi$
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	−0.180957	+	0.983491i	$0.557920\pi$
$762$		0			0
$763$	27.5000	+	9.52628i	0.995567	+	0.344874i
$764$	6.00000			0.217072
$765$		0			0
$766$	−7.50000	+	12.9904i	−0.270986	+	0.469362i
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$		0			0
$769$	50.0000			1.80305			0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000			1.80305			0.901523	+	0.432731i	$0.142450\pi$
$770$	−12.0000	+	10.3923i	−0.432450	+	0.374513i
$771$		0			0
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	−6.00000	+	10.3923i	−0.215805	+	0.373785i	−0.953521	−	0.301326i	$-0.902571\pi$
$773$	−6.00000	+	10.3923i	−0.215805	+	0.373785i	0.737716	+	0.675111i	$0.235904\pi$
$774$		0			0
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$	14.0000			0.502571
$777$		0			0
$778$	30.0000			1.07555
$779$	9.00000	+	15.5885i	0.322458	+	0.558514i
$780$		0			0
$781$	−18.0000	+	31.1769i	−0.644091	+	1.11560i
$782$		0			0
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	−22.0000			−0.785214
$786$		0			0
$787$	21.5000	−	37.2391i	0.766392	−	1.32743i	−0.173115	−	0.984902i	$-0.555383\pi$
$787$	21.5000	−	37.2391i	0.766392	−	1.32743i	0.939507	−	0.342529i	$-0.111283\pi$
$788$	−3.00000	+	5.19615i	−0.106871	+	0.185105i
$789$		0			0
$790$	2.00000			0.0711568
$791$	3.00000	+	15.5885i	0.106668	+	0.554262i
$792$		0			0
$793$	10.0000	+	17.3205i	0.355110	+	0.615069i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	48.0000			1.70025			0.850124	−	0.526583i	$-0.176527\pi$
$797$	48.0000			1.70025			0.850124	+	0.526583i	$0.176527\pi$
$798$		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
$803$	48.0000	+	83.1384i	1.69388	+	2.93389i
$804$		0			0
$805$	7.50000	+	2.59808i	0.264340	+	0.0915702i
$806$	−32.0000			−1.12715
$807$		0			0
$808$	7.50000	−	12.9904i	0.263849	−	0.457000i
$809$	10.5000	−	18.1865i	0.369160	−	0.639404i	−0.620274	−	0.784385i	$-0.712979\pi$
$809$	10.5000	−	18.1865i	0.369160	−	0.639404i	0.989434	+	0.144981i	$0.0463120\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	7.50000	+	2.59808i	0.263198	+	0.0911746i
$813$		0			0
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$	7.00000	+	12.1244i	0.244899	+	0.424178i
$818$	−13.0000			−0.454534
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$		0			0
$823$	9.50000	−	16.4545i	0.331149	−	0.573567i	−0.651588	−	0.758573i	$-0.725897\pi$
$823$	9.50000	−	16.4545i	0.331149	−	0.573567i	0.982737	+	0.185006i	$0.0592303\pi$
$824$	0.500000	+	0.866025i	0.0174183	+	0.0301694i
$825$		0			0
$826$	−3.00000	−	15.5885i	−0.104383	−	0.542392i
$827$	−15.0000			−0.521601			−0.260801	−	0.965393i	$-0.583986\pi$
$827$	−15.0000			−0.521601			−0.260801	+	0.965393i	$0.583986\pi$
$828$		0			0
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	0.848137	+	0.529777i	$0.177724\pi$
$830$	1.50000	−	2.59808i	0.0520658	−	0.0901805i
$831$		0			0
$832$	−4.00000			−0.138675
$833$		0			0
$834$		0			0
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$		0			0
$838$		0			0
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	−8.50000	−	14.7224i	−0.292929	−	0.507369i
$843$		0			0
$844$	5.00000	−	8.66025i	0.172107	−	0.298098i
$845$	−1.50000	−	2.59808i	−0.0516016	−	0.0893765i
$846$		0			0
$847$	−50.0000	+	43.3013i	−1.71802	+	1.48785i
$848$	6.00000			0.206041
$849$		0			0
$850$		0			0
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$		0			0
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$	12.5000	+	4.33013i	0.427741	+	0.148174i
$855$		0			0
$856$	−7.50000	−	12.9904i	−0.256345	−	0.444002i
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	−0.810227	−	0.586116i	$-0.800656\pi$
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	0.912705	+	0.408619i	$0.133990\pi$
$858$		0			0
$859$	−16.0000	−	27.7128i	−0.545913	−	0.945549i	−0.998549	−	0.0538535i	$-0.982850\pi$
$859$	−16.0000	−	27.7128i	−0.545913	−	0.945549i	0.452636	−	0.891695i	$-0.350484\pi$
$860$	−7.00000			−0.238698
$861$		0			0
$862$	−30.0000			−1.02180
$863$	13.5000	+	23.3827i	0.459545	+	0.795956i	0.998937	−	0.0460992i	$-0.0146790\pi$
$863$	13.5000	+	23.3827i	0.459545	+	0.795956i	−0.539392	+	0.842055i	$0.681346\pi$
$864$		0			0
$865$		0			0
$866$	11.0000	+	19.0526i	0.373795	+	0.647432i
$867$		0			0
$868$	−16.0000	+	13.8564i	−0.543075	+	0.470317i
$869$	12.0000			0.407072
$870$		0			0
$871$	10.0000	−	17.3205i	0.338837	−	0.586883i
$872$	−5.50000	+	9.52628i	−0.186254	+	0.322601i
$873$		0			0
$874$	6.00000			0.202953
$875$	−0.500000	−	2.59808i	−0.0169031	−	0.0878310i
$876$		0			0
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$	14.0000	−	24.2487i	0.472477	−	0.818354i
$879$		0			0
$880$	−3.00000	−	5.19615i	−0.101130	−	0.175162i
$881$	−57.0000			−1.92038			−0.960189	−	0.279350i	$-0.909881\pi$
$881$	−57.0000			−1.92038			−0.960189	+	0.279350i	$0.909881\pi$
$882$		0			0
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$		0			0
$885$		0			0
$886$	10.5000	−	18.1865i	0.352754	−	0.610989i
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	0.634141	−	0.773217i	$-0.281354\pi$
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	−0.986696	+	0.162573i	$0.948021\pi$
$888$		0			0
$889$	−4.00000	−	20.7846i	−0.134156	−	0.697093i
$890$	15.0000			0.502801
$891$		0			0
$892$	14.0000	−	24.2487i	0.468755	−	0.811907i
$893$		0			0
$894$		0			0
$895$	24.0000			0.802232
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$		0			0
$898$	−4.50000	−	7.79423i	−0.150167	−	0.260097i
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$		0			0
$901$		0			0
$902$	−54.0000			−1.79800
$903$		0			0
$904$	−6.00000			−0.199557
$905$	−5.50000	−	9.52628i	−0.182826	−	0.316664i
$906$		0			0
$907$	12.5000	−	21.6506i	0.415056	−	0.718898i	−0.580379	−	0.814347i	$-0.697095\pi$
$907$	12.5000	−	21.6506i	0.415056	−	0.718898i	0.995434	+	0.0954492i	$0.0304288\pi$
$908$	−6.00000	−	10.3923i	−0.199117	−	0.344881i
$909$		0			0
$910$	−10.0000	−	3.46410i	−0.331497	−	0.114834i
$911$	−18.0000			−0.596367			−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000			−0.596367			−0.298183	+	0.954509i	$0.596381\pi$
$912$		0			0
$913$	9.00000	−	15.5885i	0.297857	−	0.515903i
$914$	−16.0000	+	27.7128i	−0.529233	+	0.916658i
$915$		0			0
$916$	14.0000			0.462573
$917$		0			0
$918$		0			0
$919$	−7.00000	−	12.1244i	−0.230909	−	0.399946i	0.727167	−	0.686461i	$-0.240837\pi$
$919$	−7.00000	−	12.1244i	−0.230909	−	0.399946i	−0.958076	+	0.286515i	$0.907503\pi$
$920$	−1.50000	+	2.59808i	−0.0494535	+	0.0856560i
$921$		0			0
$922$	9.00000	+	15.5885i	0.296399	+	0.513378i
$923$	−24.0000			−0.789970
$924$		0			0
$925$	−4.00000			−0.131519
$926$	6.50000	+	11.2583i	0.213603	+	0.369972i
$927$		0			0
$928$	−1.50000	+	2.59808i	−0.0492399	+	0.0852860i
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	0.640768	−	0.767735i	$-0.278616\pi$
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	−0.985262	+	0.171054i	$0.945283\pi$
$930$		0			0
$931$	11.0000	+	8.66025i	0.360510	+	0.283828i
$932$	12.0000			0.393073
$933$		0			0
$934$	−7.50000	+	12.9904i	−0.245407	+	0.425058i
$935$		0			0
$936$		0			0
$937$	−28.0000			−0.914720			−0.457360	−	0.889282i	$-0.651205\pi$
$937$	−28.0000			−0.914720			−0.457360	+	0.889282i	$0.651205\pi$
$938$	−2.50000	−	12.9904i	−0.0816279	−	0.424151i
$939$		0			0
$940$		0			0
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	−0.910773	−	0.412908i	$-0.864513\pi$
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	0.812975	+	0.582298i	$0.197846\pi$
$942$		0			0
$943$	13.5000	+	23.3827i	0.439620	+	0.761445i
$944$	6.00000			0.195283
$945$		0			0
$946$	−42.0000			−1.36554
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	0.840624	−	0.541619i	$-0.182188\pi$
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	−0.889368	+	0.457193i	$0.848855\pi$
$948$		0			0
$949$	−32.0000	+	55.4256i	−1.03876	+	1.79919i
$950$	−1.00000	−	1.73205i	−0.0324443	−	0.0561951i
$951$		0			0
$952$		0			0
$953$	−60.0000			−1.94359			−0.971795	−	0.235826i	$-0.924220\pi$
$953$	−60.0000			−1.94359			−0.971795	+	0.235826i	$0.924220\pi$
$954$		0			0
$955$	−3.00000	+	5.19615i	−0.0970777	+	0.168144i
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$		0			0
$958$	−12.0000			−0.387702
$959$	−30.0000	−	10.3923i	−0.968751	−	0.335585i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−8.00000	+	13.8564i	−0.257930	+	0.446748i
$963$		0			0
$964$	−1.00000	−	1.73205i	−0.0322078	−	0.0557856i
$965$	2.00000			0.0643823
$966$		0			0
$967$	35.0000			1.12552			0.562762	−	0.826619i	$-0.309739\pi$
$967$	35.0000			1.12552			0.562762	+	0.826619i	$0.309739\pi$
$968$	−12.5000	−	21.6506i	−0.401765	−	0.695878i
$969$		0			0
$970$	−7.00000	+	12.1244i	−0.224756	+	0.389290i
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$		0			0
$973$	5.00000	+	25.9808i	0.160293	+	0.832905i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	−2.50000	+	4.33013i	−0.0800230	+	0.138604i
$977$	−3.00000	+	5.19615i	−0.0959785	+	0.166240i	−0.910017	−	0.414572i	$-0.863931\pi$
$977$	−3.00000	+	5.19615i	−0.0959785	+	0.166240i	0.814038	+	0.580812i	$0.197265\pi$
$978$		0			0
$979$	90.0000			2.87641
$980$	−6.50000	+	2.59808i	−0.207635	+	0.0829925i
$981$		0			0
$982$		0			0
$983$	19.5000	−	33.7750i	0.621953	−	1.07725i	−0.367168	−	0.930155i	$-0.619673\pi$
$983$	19.5000	−	33.7750i	0.621953	−	1.07725i	0.989122	−	0.147100i	$-0.0469940\pi$
$984$		0			0
$985$	−3.00000	−	5.19615i	−0.0955879	−	0.165563i
$986$		0			0
$987$		0			0
$988$	−8.00000			−0.254514
$989$	10.5000	+	18.1865i	0.333881	+	0.578298i
$990$		0			0
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	−0.553308	−	0.832977i	$-0.686635\pi$
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	0.998033	+	0.0626908i	$0.0199682\pi$
$992$	−4.00000	−	6.92820i	−0.127000	−	0.219971i
$993$		0			0
$994$	−12.0000	+	10.3923i	−0.380617	+	0.329624i
$995$	−4.00000			−0.126809
$996$		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	$0.237825\pi$
$998$	11.0000	−	19.0526i	0.348199	−	0.603098i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.k.b.361.1		2
3.2	odd	2		70.2.e.c.11.1	✓	2
7.2	even	3	inner	630.2.k.b.541.1		2
7.3	odd	6		4410.2.a.bd.1.1		1
7.4	even	3		4410.2.a.bm.1.1		1
12.11	even	2		560.2.q.g.81.1		2
15.2	even	4		350.2.j.b.249.1		4
15.8	even	4		350.2.j.b.249.2		4
15.14	odd	2		350.2.e.e.151.1		2
21.2	odd	6		70.2.e.c.51.1	yes	2
21.5	even	6		490.2.e.h.471.1		2
21.11	odd	6		490.2.a.c.1.1		1
21.17	even	6		490.2.a.b.1.1		1
21.20	even	2		490.2.e.h.361.1		2
84.11	even	6		3920.2.a.p.1.1		1
84.23	even	6		560.2.q.g.401.1		2
84.59	odd	6		3920.2.a.bc.1.1		1
105.2	even	12		350.2.j.b.149.2		4
105.17	odd	12		2450.2.c.l.99.1		2
105.23	even	12		350.2.j.b.149.1		4
105.32	even	12		2450.2.c.g.99.1		2
105.38	odd	12		2450.2.c.l.99.2		2
105.44	odd	6		350.2.e.e.51.1		2
105.53	even	12		2450.2.c.g.99.2		2
105.59	even	6		2450.2.a.bc.1.1		1
105.74	odd	6		2450.2.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.c.11.1	✓	2	3.2	odd	2
70.2.e.c.51.1	yes	2	21.2	odd	6
350.2.e.e.51.1		2	105.44	odd	6
350.2.e.e.151.1		2	15.14	odd	2
350.2.j.b.149.1		4	105.23	even	12
350.2.j.b.149.2		4	105.2	even	12
350.2.j.b.249.1		4	15.2	even	4
350.2.j.b.249.2		4	15.8	even	4
490.2.a.b.1.1		1	21.17	even	6
490.2.a.c.1.1		1	21.11	odd	6
490.2.e.h.361.1		2	21.20	even	2
490.2.e.h.471.1		2	21.5	even	6
560.2.q.g.81.1		2	12.11	even	2
560.2.q.g.401.1		2	84.23	even	6
630.2.k.b.361.1		2	1.1	even	1	trivial
630.2.k.b.541.1		2	7.2	even	3	inner
2450.2.a.w.1.1		1	105.74	odd	6
2450.2.a.bc.1.1		1	105.59	even	6
2450.2.c.g.99.1		2	105.32	even	12
2450.2.c.g.99.2		2	105.53	even	12
2450.2.c.l.99.1		2	105.17	odd	12
2450.2.c.l.99.2		2	105.38	odd	12
3920.2.a.p.1.1		1	84.11	even	6
3920.2.a.bc.1.1		1	84.59	odd	6
4410.2.a.bd.1.1		1	7.3	odd	6
4410.2.a.bm.1.1		1	7.4	even	3

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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-3.00000 + 5.19615i) q^{11} -4.00000 q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{19} +1.00000 q^{20} +6.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.00000 + 3.46410i) q^{26} +(2.50000 + 0.866025i) q^{28} +3.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.00000 + 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{40} -9.00000 q^{41} -7.00000 q^{43} +(-3.00000 - 5.19615i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-6.50000 + 2.59808i) q^{49} +1.00000 q^{50} +(2.00000 - 3.46410i) q^{52} +(-3.00000 + 5.19615i) q^{53} +6.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-2.50000 - 4.33013i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(-2.50000 + 4.33013i) q^{67} +(2.50000 + 0.866025i) q^{70} +6.00000 q^{71} +(8.00000 - 13.8564i) q^{73} +(2.00000 - 3.46410i) q^{74} +2.00000 q^{76} +(15.0000 + 5.19615i) q^{77} +(-1.00000 - 1.73205i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(4.50000 + 7.79423i) q^{82} -3.00000 q^{83} +(3.50000 + 6.06218i) q^{86} +(-3.00000 + 5.19615i) q^{88} +(-7.50000 - 12.9904i) q^{89} +(2.00000 + 10.3923i) q^{91} +3.00000 q^{92} +(-1.00000 + 1.73205i) q^{95} +14.0000 q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - q^{5} - q^{7} + 2 q^{8} - q^{10} - 6 q^{11} - 8 q^{13} - 4 q^{14} - q^{16} - 2 q^{19} + 2 q^{20} + 12 q^{22} - 3 q^{23} - q^{25} + 4 q^{26} + 5 q^{28} + 6 q^{29} - 8 q^{31}+ \cdots + 11 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - q^5 - q^7 + 2 * q^8 - q^10 - 6 * q^11 - 8 * q^13 - 4 * q^14 - q^16 - 2 * q^19 + 2 * q^20 + 12 * q^22 - 3 * q^23 - q^25 + 4 * q^26 + 5 * q^28 + 6 * q^29 - 8 * q^31 - q^32 - 4 * q^35 + 4 * q^37 - 2 * q^38 - q^40 - 18 * q^41 - 14 * q^43 - 6 * q^44 - 3 * q^46 - 13 * q^49 + 2 * q^50 + 4 * q^52 - 6 * q^53 + 12 * q^55 - q^56 - 3 * q^58 - 6 * q^59 - 5 * q^61 + 16 * q^62 + 2 * q^64 + 4 * q^65 - 5 * q^67 + 5 * q^70 + 12 * q^71 + 16 * q^73 + 4 * q^74 + 4 * q^76 + 30 * q^77 - 2 * q^79 - q^80 + 9 * q^82 - 6 * q^83 + 7 * q^86 - 6 * q^88 - 15 * q^89 + 4 * q^91 + 6 * q^92 - 2 * q^95 + 28 * q^97 + 11 * q^98

Introduction

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